UC-NRLF 
 
 *B E&Q M7S 
 
 WIS SLOWS 
 
 
 RCIA1 CALCULATOR. 
 
/ 
 
Digitized by the Internet Archive 
 
 in 2007 with funding from 
 
 Microsoft Corporation 
 
 http://www.archive.org/details/foreigndomesticcOOwinsrich 
 
THE 
 
 FOREIGN AND DOMESTIC 
 
 COMMERCIAL CALCULATOR ; 
 
 OR, 
 
 A COMPLETE LIBRARY OF NUMERICAL, ARITHMETICAL, AND 
 
 MATHEMATICAL FACTS, TABLES, DATA, FORMULAS, AND 
 
 PRACTICAL RULES FOR THE MERCHANT AND 
 
 MERCANTILE ACCOUNTANT. 
 
 BY 
 
 E. S. WINSLOW. 
 
 Author of "Comprehensive Mathematics," " Computists' Manual," 
 
 " Machinists' and Mechanics' Practical Calculator and Guide," 
 
 " Tin-plate and Sheet-iron Workers' Monitor." 
 
 Fourth Edition. JEnlarped. 
 
 BOSTON: 
 PUBLISHED BY THE AUTHOE. 
 
 186 7. 
 
HFS 
 
 GEO. W. LINDSEY, Local Agent for the sale of Winslow's Mathematical 
 Works, No. 897 Washington Street, Boston. 
 
 Entered, according to Act of Congress, in the year 1867, by 
 
 E. S. WIN SLOW, 
 
 In the Clerk's Office of the District Court of the District of Massachusetts. 
 
 Stkekottpkd bt C. J. Pktkbs & So*. 
 
 Printed by Wm. A. 11*11, No. 40, CongreM Street, Bo»ton. 
 
PREFACE 
 
 TO THE COMPEEHENSIVE, MATHEMATICS. 
 
 On presenting this work to the public, it may be proper to state 
 that it has been designed and written mainly for the practical 
 man. It contains a vast array of Numerical, Arithmetical, and 
 Mathematical facts, tables, data, formulas, and rules, pertaining 
 to a great variety of subjects, and applicable to a diversity of ends, 
 as well as much information of a more general nature, valuable to 
 the artisan, and commercial classes ; thus meeting the wants, in an 
 eminent degree, of the lovers of the exact sciences, and the prac- 
 tical wants of students in the mathematics. 
 
 The facts and data alluded to have been gathered, with much 
 care and patience, from a great variety of sources, or derived, often 
 by toilsome investigations, from known and accredited truths. 
 The care that has been taken in respect to these, it is thought, 
 should secure for this particular department reliance and trust. 
 
 The tables, which are numerous, have, with few exceptions, been 
 composed and arranged expressly for the work, and a confidence 
 is felt that they may be relied on for accuracy. 
 
 From the valuable works of Dr. Ure, Adcock, Gregory, Grier, 
 Brunton ; from the publications of the transactions of London, 
 Edinburgh, and Dublin Philosophical Societies ; and from the pub- 
 lications by the Smithsonian Institute, much valuable information 
 lias been gained, relating mainly to machinery and the arts ; and 
 to these sources the author feels indebted. 
 
 The conciseness with which the work has been generally written 
 would, perhaps, be found an objection, were it not that all the pro- 
 positions and problems of intricacy are accompanied with exam- 
 ples and illustrations, and, in the matters of Geometry, additionally 
 accompanied with diagrams. The whole, it is thought, will appear 
 clear to him who consults it. A prominent feature in the design 
 has been to produce a useful work, and one which in the way of 
 price«hall be readily accessible to all. 
 
 284302 
 
PREFACE. 
 
 PREFA CE 
 
 TO THE FOREIGN AND DOMESTIC COMMERCIAL 
 CALCULATOR. 
 
 This work is composed of the first four sections of the author's 
 " Comprehensive Mathematics." It was thought advisable 
 to publish this portion of that work in a separate form on account 
 of price ; more especially as it contains all of a commercial nature 
 treated of in that work. Indeed, the contents of that work were 
 arranged expressly to this end. The Table of Contents in both 
 works is the same. The work being stereotyped, this could not well 
 be avoided. The Table of Contents, therefore, in either work, is 
 that of the " Comprehensive Mathematics," and the first 
 four sections thereof; that is, Section I., Section II., Section III., 
 and Section A., is that of the " Foreign and Domestic Commer- 
 cial Calculator." 
 
 PREFA CE 
 TO THE TIN-PLATE AND SHEET-IRON WORKERS 5 MONITOR. 
 
 This work is composed of Section VI. of the author's " Com- 
 prehensive Mathematics," with portions of other sections of 
 that work. It embraces all that is contained in the last-mentioned 
 work of special interest to the Tinsmith, as such. It may be re- 
 lied on for accuracy in all particulars, and is believed to bo tlu* 
 first and only reliable work of the kind ever published. It is pub- 
 lished in separate form on account of price, and with the view of 
 affording apprentices and students every possible facility of obtain- 
 ing it. It contains over 100 pages, nearly 50 diagrams, and step- 
 by-step directions for constructing, mechanically, not less than BO 
 unlike and diiK rent patterns, embracing all of the more difficult 
 and complicated in use, and several of new and beautiful designs. 
 
CONTENTS. 
 
 SECTION A. 
 
 PAGE 
 
 Foreign Moneys of Account ... a 1 
 Foreign Linear and Surface Meas- 
 ures a 14 
 
 Foreign Weights • «8 
 
 Foreign Liquid Measures .... a 35 
 
 Foreign Dry Measures a 44 
 
 Custom House Allowances on Du- 
 tiable Goods, &c a 51 
 
 Table of Established Tares . . .a 52 
 
 SECTION I. 
 
 MONEYS OF ACCOUNT, COINS, 
 WEIGHTS, AND MEASURES OF 
 THE UNITED STATES; FOREIGN 
 GOLD COINS, &C. 
 
 Explanations of Signs 
 
 12 
 
 Moneys of Account of the United 
 States 13 
 
 Comparative Value of Gold and 
 Silver ■ . . . 13 
 
 Gold, pure ; value of, by weight . . 15 
 Mint Gold, Standard of, &c. . . . 15 
 Gold Coins, their weights and val- 
 ues 15 
 
 Silver, pure; value of, by weight . 10 
 Mint Silver, Standard of, &c. . . . 16 
 Silver Coins, their weights and 
 
 values 10 
 
 Copper Coins, &c 10 
 
 Present Far Value of Silver Coins 
 
 issued prior to June, 1853 .... 17 
 Currencies of the different States 
 
 of the Union 17 
 
 The Metrical System of Weights 
 
 and Measures 18 
 
 Foreign Gold Coins, Tables of, &c. 19 
 Foreign Silver Coins, Values of, 25 
 
 1* 
 
 WEIGHTS AND MEASURES. 
 
 PACK 
 
 Long or Linear Measure ... 25 
 
 Cloth Measure 25 
 
 Land Measure 25 
 
 Engineer's Chain 25 
 
 Shoemaker's Measure 26 
 
 Miscellaneous Measures 26 
 
 Square or Superficial Meas- 
 
 uhe 26 
 
 Measure for Land 26 
 
 Circular Measure 27 
 
 Cubic or Solid Measure ... 27 
 General Measure of Weight, 28 
 
 Gross Weight 28 
 
 Troy Weight 28 
 
 Apothecaries 1 Weight, 28 
 
 Diamonds, Measure of Value, &c, 28 
 
 Liquid Measure 28 
 
 Imperial Liquid Measure 29 
 
 Ale 3Ieasure 29 
 
 Dry Measure 29 
 
 Imperial Dry Measure 30 
 
 SECTION II. 
 
 MISCELLANEOUS facts, calcu- 
 lations, AND MATHEMATICAL 
 DATA. 
 
 Specific Gravities, Tables of, 31 
 
 Weight per Bushel of Articles . . 35 
 Weight per Barrel of Articles ... 35 
 Weights of different Measures of 
 
 various Articles 35 
 
 Weight of Coals, &c, Tables . 35, 55 
 Practical Approximate Weight in 
 
 Pounds of Various Articles ... 36 
 
 Ropes and Cables . 
 v 
 
CONTENTS. 
 
 PAOB 
 
 Weight and Strength of Iron 
 Chains 37 
 
 Comparative Weight of Metals, 
 Table 38 
 
 Weight of Rolled Iron, Square Bar, 
 Tables 38 
 
 Weight of Various Metals, differ- 
 ent Forms of Bar 39 
 
 Weight of Bound-rolled Iron, Ta- 
 bus 40 
 
 Weight of Cast-iron Prisms of dif- 
 ferent forms, &c 40 
 
 Weight of Flat-rolled Iron, Table, 42 
 
 Weight of Different Metals, in Plate, 44 
 
 The American Wire Gauge . 45 
 
 The Values of the Nos. American 
 Wire Gauge and Birmingham 
 Wire Gauge, in the United States, 
 
 inch, Tables of 45 
 
 The Number of Linear Feet in a 
 Found of different kinds of Wire 
 of different Sizes, Table of, &c, 46 
 Characteristics. &c, of Alloys of 
 
 Copper und Zinc,— Brass. ... 47 
 The Weight per Square Foot of dif- 
 ferent Boiled Metals of different 
 thicknesses by the Wire Gauge, 
 
 Table 48 
 
 Tin Plates, Sizes, &c, Table, vj 
 .Sheet Iron, Sheet Zinc, Copper 
 Sheathing, Yellow Metal, Weight 
 
 of, &c 49 
 
 Capacity in Gallons of Cylindrical 
 
 Cans, &c, Table 50 
 
 Weight of Pipes 52 
 
 Weight of Pipes, Table 53 
 
 Weight of Cast-iron and Lead 
 
 Balls 54 
 
 Weight of Hollow Balls or Shells, 54 
 
 Analysis of Coals 55 
 
 Weight, Heating Power, Ac, of 
 Is and other kinds of Fuel, 
 
 Tabu 55 
 
 iiArioN of Lumber . . . 5G 
 
 Hoard Measure 5f, 
 
 T6 Measure Square Timber . ... 5(5 
 -me Round Timber .... 50 
 Tab lb relative to the Measurement 
 
 of Round Timber 57 
 
 To flind the Solidity of the gr< 
 
 ingular stick that can be cut 
 
 from a Log of Given Dimensions, 58 
 
 To Bud the solidity of the greatest 
 
 ire St irk that can be oat from 
 
 a Hound Stick of Given Dimen- 
 
 
 
 To find the Contenti oi ■ Login 
 
 Hoard Measure 69 
 
 o GO 
 
 paos 
 
 To find the Dimensions of Vessels 
 of different Forms, for holding 
 Given Quantities 62 
 
 Cask Gauging, all Forms of 
 Casks 63 
 
 To find the Contents of a Cask, the 
 same as would be given by the 
 Gauging Bod 66 
 
 To find the Diagonal and Length 
 of a Cask 66 
 
 Ullage 07 
 
 To find the Ullage of a Standing 
 Cask 67 
 
 To find the Ullage when the Cask is 
 upon its Bilge 67 
 
 To find the Quantity of Liquor in a 
 Cask by its Weight 68 
 
 Customary Bide by Freighting Mer- 
 chants for finding the Cubic 
 Measurement of Casks 68 
 
 Tonnage ok Vessels, to Calcu- 
 late 69 
 
 Of Conduits, or Pipes 70 
 
 To find the requisite thickness of a 
 Pipe to support a Given Head of 
 Water 70 
 
 To find the Velocity of Water pass- 
 ing through a Pipe 71 
 
 To find the Head of Water requi- 
 site to a Bequired Velocity 
 through a Pipe 71 
 
 To find the Quantity of Water Dis- 
 charged by a Pipe in a Given 
 Time , 71 
 
 To find the Specific Gravity of a 
 Hodv heavier than Water .... 72 
 
 To find the Specific Gravity of a 
 Body lighter than Water .... 72 
 
 To find tne Specific Gravity of a 
 Thud 72 
 
 To find the Quantity of each of the 
 several Metals composing an AI- 
 lov 72 
 
 To find the Lifting-power of a Bal- 
 loon 73 
 
 To find the Diameter of a Halloon 
 equal to the Raising of :• Given 
 Weight 73 
 
 To find the Thickness of ■ iMlow 
 Metallic Globe that shall bai 
 Given Buoyancy in a (liven 
 Liquid 73 
 
 To Cut a Square Sheet of Metal bo 
 as to form a Vessel of the Great- 
 est Capacity the Sheet admits of. 73 
 
 Comparative cohesive Forces of 
 Substances, Table 74 
 
 Alloys having a Tenacity greater 
 than the Sum of their Con- 
 stituents 71 
 
CONTENTS. 
 
 Vll 
 
 PAOB 
 
 Alloys having a Density greater 
 than the Mean of their Con- 
 stituents 75 
 
 Alloys having a Density less than 
 the Mean Of their Constituents . 75 
 
 Relative Powers of different Metals 
 to Conduct Electricity 75 
 
 Dilations of Solids Imf Seat, Table 7S 
 
 Melting Points of Metals and other 
 Substances, TABLE 7G 
 
 Relative Powers 'of Substances to 
 Radiate Heat, Table 76 
 
 Dolling Points of Fluids 76 
 
 Freezing Points of Fluids .... 77 
 Expansion of Fluids by Heat . . . 77 
 Relative Powers of Substances to 
 
 Conduct Heat 77 
 
 Ductility and .Ualeability of Metals, 77 
 Quantity per cent, of Nutritious 
 Matter contained in different Ar- 
 ticles of Food 78 
 
 Standard, &*., of Alcohol 78 
 
 Quantity per cent, of Absolute Al- 
 cohol contained in different Pure 
 Liquors, Wines, &C., TABLE . . 7S 
 Proof of Spirituous Liquors ... 78 
 Comparative Weight ot Timber in 
 a Green and Seasoned State, TA- 
 BLE, &c 79 
 
 Relative Power of different kinds of 
 
 Fuel to Produce Heat, TABLE, . 79 
 Relative illuminating Power of dif- 
 ferent Materials, Table and Re- 
 marks, 80 
 
 Thermometers, different kinds, 
 to Reduce one to another, &c, . 82 
 
 Horse-Power 83 
 
 Animal Power 83 
 
 Steam, Tables in relation to, 
 
 &c, &}, 308 
 
 Velocity and Force of Wind, Ta- 
 
 BLE 84 
 
 Curvature of the Earth . . . . 84, 213 
 Degrees of Longitude, Lengths of, 
 
 &c 84 
 
 Time, with respect to Longitude, 84 
 
 Velocity of Sound 84 
 
 Velocity of Light 85 
 
 Gravitation 85,302 
 
 Area of the Earth, its Density, &c, 85 
 
 Chemical Elements 80 
 
 Elementary Constituents of Bodies, 
 
 Table . . . . - 87 
 
 Combinations by Weight of the 
 Gases in forming Compounds, 
 
 Table 87 
 
 Combinations by Volume of the 
 Gases, their Condensation, &c, 
 
 in forming Compounds 88 
 
 Atomic Weight «9 
 
 PAOB 
 
 CImmical and other Properties of 
 Various Substances 90 
 
 SECTION III. 
 
 practical arithmetic. 
 
 Vulgar Fractions 95 
 
 Reduction of Vulgar Fractions . . 95 
 Addition of Vulgar Fractions . . . 09 
 Subtraction of Vulgar Fractions . 99 
 Division of Vulgar Fractions . . . 100 
 Multiplication of Vulgar Fractions 100 
 Multiplication and Division of 
 
 Fractions Combined 101 
 
 Cancellation 90, 97, 102 
 
 To Reduce a Fraction in a higber, 
 to an equivalent in a given low- 
 er denomination 102 
 
 To Reduce a Fraction in a lower, 
 to an equivalent in a given high- 
 er denomination 102 
 
 To Reduce a Fraction to Whole 
 Numbers in lower given denom- 
 inations 103 
 
 To Reduce Fractions in lower de- 
 nominations to given higher de- 
 nominations 103 
 
 To work Vulgar Fractions by the 
 Rule of Three, or Proportion . . 104 
 
 Decimal Fractions 104 
 
 Addition of Decimals 105 
 
 Subtraction of Decimals 105 
 
 Multiplication of Decimals .... 106 
 
 Division of Decimals 106 
 
 Reduction of Decimals 107 
 
 To work Decimals by the Rule of 
 
 Three 108 
 
 Proportion, or Rule of Three ... 109 
 
 Compound Proportion 110 
 
 Conjoined Proportion, or Chain 
 
 Rule 112 
 
 Percentage 114 
 
 interest 120 
 
 Compound Interest 122 
 
 Bank Interest, or Bank Discount . 127 
 
 Discount 129 
 
 Compound Discount 129 
 
 Profit and Loss 130 
 
 Equation of Payments 132 
 
 General Average 134 
 
 Assessment of Taxes 136 
 
 Insurance 136 
 
 Life Insurance • 136 
 
 Fellowship 138 
 
Vlll 
 
 CONTENTS. 
 
 TkOX 
 
 Alligation 139 
 
 Involution 141 
 
 Evolution 141 
 
 To Extract the Square Root ... 142 
 To Extract the Cube Root .... 143 
 
 To Extract any Root 145 
 
 Arithmetical Progression 146 
 
 Geometrical Progression 150 
 
 Annuities 154 
 
 Of Installments generally . . . . 1G4 
 
 Permutation 1GG 
 
 combination 167 
 
 Problems 169 
 
 SECTION IV. 
 
 GEOMETR*. 
 
 Definitions, Construction of 
 Figures, &c 172 
 
 To Bisect a Line 176 
 
 To Erect a Perpendicular 176 
 
 To Let Fall a Perpendicular . . . 176 
 
 To Erect a Perpendicular on the 
 end of a Line 177 
 
 To draw a Circle through any three 
 points not in a straight line, and 
 to find the Centre of a Circle, or 
 Arc 177 
 
 To find the Length of an Arc of a 
 a Circle approximately by Me- 
 chanics 177 
 
 From a given Point to draw a 
 Tangent to a Circle 177 
 
 To draw from or to the Circumfer- 
 ence of a Circle, lines tending 
 to the Centre, when the latter is 
 inaccessible 177 
 
 To describe an Oval Arch on a 
 given Conjugate Diameter ... 178 
 
 To describe an Oval of a given 
 Length and Breadth 178 
 
 To describe an Arc or Segment of 
 a Circle of Large Radius . . . .179 
 
 To describe an Oval Arch, the 
 Span and Ki.»e being given . . .17!) 
 
 Gothic Arches, to draw 180 
 
 Polygons, to oonstruot 181 
 
 Polygons, to inscribe in a given 
 
 Circle 181 
 
 Polygons, to circumscribe about a 
 
 given Circle 181 
 
 To produce a Square of the mom 
 
 Area m a given Triangle . . . - 181 
 Mini ;l Parabola ... 
 • a Hyperbola . , 
 To biBect auy given Triangle . . . 1S2 
 
 MM 
 
 To draw a Triangle equal in Area 
 to two given Triangles 183 
 
 To describe a Circle equal in Area 
 to two given Circles 183 
 
 To construct a Tothed, or Cog- 
 wheel 183 
 
 Of the Conic Sections . . . . 1S4 
 
 Mensuration of Lines and Super- 
 ficies. 
 
 Triangles 185 
 
 Of Right- Angled Triangles . . • 186 
 Of Oblique- Angled Triangles . . 187 
 To find the Area of a Triangle . 188 
 To find the Hypotenuse of a Tri- 
 angle 189 
 
 To find the Base, or Perpendicu- 
 lar, of a Triangle 188, 189 
 
 To find the Height of an inacces- 
 sible Object 189 
 
 To find the Distance of au inac- 
 cessible Object 190 
 
 To find the Area of a Square, 
 Rectangle, Rhombus, or Rhom- 
 boid 190 
 
 To find the Area of a Trapezoid . 191 
 To find the Area of a Trapezium . 191 
 Of Polygons, Table, &c. ... 194 
 To find the Perpendieular of a 
 Rhombus, Rhomboid, or Trape- 
 zoid • 192 
 
 To find the Diagonal of a Rhom- 
 bus. Ithoniboid, or Trapezoid . 192 
 To find the Area of a regular or 
 
 irregular Polygon 195 
 
 Circle 196 
 
 The Circle and its Sections . . . .197 
 To find the Diameter, Circumfer- 
 ence, and Area of a Circle . . . 198 
 To find the Length of an Arc of a 
 
 Circle 199 
 
 To find the Area of a Sector of a 
 
 Circle 201 
 
 To find the Area of a Segment of 
 
 I I irele 201 
 
 To find the Area of a Zone ... 202 
 TO And the Diameter of a Circle of 
 
 Which a given Zone is a part . . 202 
 To And the Area ofs Crescent . . 202 
 To find the side of a Square that 
 ■hall contain an Area equal to 
 thai Of a given Circle 202 
 
 To And the Diameter of b Circle 
 that shall have an Ana equal to 
 that of a given Square 202 
 
 To And the Diameters of three 
 equal circles th< that 
 
 can be inscribed in a given ♦ir- 
 ele 
 
CONTENTS. 
 
 PAGE 
 
 To find the Diameters of four equal 
 circles the greatest that can be 
 inscribed in a given Circle . . . 202 
 To find the Side of a Square in- 
 scribed in a given Circle .... 203 
 To find the Diameter of a Circle 
 that will circumscribe a given 
 
 Triangle 203 
 
 To find the Diameter of the great- 
 est Circle that can be inscribed 
 
 in a given Triangle 203 
 
 To divide a Circle into any num- 
 ber of Concentric Circles of 
 
 equal Areas 204 
 
 To find the Area of the space con- 
 tained between two Concentric 
 
 Circles . . . 205 
 
 Ellipse 205 
 
 To find the Area of an Ellipse . . 20? 
 To find the Length of the Circum- 
 ference of an Ellipse . ..... 207 
 
 To find the Area of an Elliptic Seg- 
 ment 207 
 
 Parabola 209 
 
 To find the Area of a Parabola . . 210 
 To find the Area of a Zone of a 
 
 Parabola 210 
 
 To find the Altitude of a Parabola, 210 
 To find the Length of a Semi-para- 
 bola 210 
 
 Hyperbola 211 
 
 To find the Length of a Semi- 
 hyperbola 212 
 
 To find the Area of a Hyperbola . 212 
 
 Cycloid, and Epicycloid ... 212 
 
 To find the Length of the Curve of 
 
 a Cycloid 213 
 
 To find the Area of a Cycloid. . . 213 
 To find the Distance of Objects at 
 
 Sea, &c 213 
 
 Stereometry, or Mensuration 
 of Solids. 
 
 Of Prisms 214 
 
 Of Right Prisms or Cubes .... 215 
 Of Parallelopipedons .... 215 
 
 Of Pyramids 215 
 
 Of Frustums of Pyramids . . 216 
 
 Of Prismoids 216 
 
 Of the Wedge 217 
 
 Of Cylinders 217 
 
 To find the Length of a Helix . . 217 
 
 Of Cones 218 
 
 Of Frustums of Cones. . . .65,218 
 Of Spheres or Globes .... 219 
 
 PAGE 
 
 Of Spherical Segments 219 
 
 Of Spherical Zones 220 
 
 To find the greatest Cube that can 
 be cut from a given Sphere . . . 220 
 
 Of Spheroids . 221 
 
 Of Segments of Spheroids . . . .221 
 Of the Middle Frustum of a Spher- 
 oid 65,221 
 
 Of Spindles 222 
 
 Of the Middle Frustum of a Para- 
 bolic Spindle 65, 222 
 
 Of Parabolic Conoids ... 65, 223 
 
 Of Hyperboloids 223 
 
 To find the Surface of a Cylindri- 
 cal Ring 224 
 
 To find the Solidity of a Cylindri- 
 cal Ring ' 224 
 
 Of the regular bodies .... 225 
 Promiscuous Examples in 
 
 Geometry 226 
 
 Trigonometry 231 
 
 Tables of Sines, Cosines, Tan- 
 gents, &c 241 
 
 Tables of Squares, Cubes, 
 Square and Cube Roots, &c. 245 
 
 SECTION V. 
 
 mechanical powers, mechani- 
 cal centres, circular mo- 
 tion, strength of materi- 
 als; STEAM, THE STEAM EN- 
 GINE, ETC. 
 
 The Lever 271 
 
 The Wheel and Axle .... 272 
 
 The Pulley 273 
 
 The Inclined Plane 274 
 
 The Wedge 275 
 
 TnE Screw 275 
 
 Transverse Strength of Bodies . 279 
 
 Deflections of Shafts, &c 286 
 
 Resistance of Bodies to Tortion . 287 
 Resistance of Bodies to Compres- 
 sion 289 
 
 Centres of Surfaces 291 
 
 Centres of Solids 293 
 
 Centres of Oscillation and 
 
 Percussion 294 
 
 Centre of Gyration 298 
 
 Central Forces 300 
 
CONTENTS. 
 
 MM 
 
 FltWheels 301 
 
 The Governor 301 
 
 Force of Gravity 302 
 
 To find the Height of a Stream 
 
 projected vertically from a Pipe, 303 
 To find the Tower requisite to 
 
 E reject a Stream to aiiy given 
 
 bight 303 
 
 Of Pendulums 304 
 
 Screw-Cutting in a Lathe . . 305 
 Table of Change Wheels for 
 
 Screw-Cutting in a Lathe . . . 30S 
 Of Steam and the Steam Ex* 
 
 gine 308 
 
 Velocity of Projectiles, &c . ... 313 
 Steam, "acting expansively . . . . 313 
 Of the Eccentric in a Steam En- 
 gine 314 
 
 Of Continuous Circular Mo- 
 tion 314 
 
 To find the number of Revolu- 
 tions made by the last, to one 
 revolution of the first, in a train 
 of Wheels and Pinions .... 315 
 The distance from Centre to Cen- 
 tre of two Wheels to work in 
 contact given, and the ratio of 
 Velocity between them, to find 
 their Requisite Diameters . . . 317 
 To find the Velocity of a Belt . . 317 
 To find the Draft on a Machine . 317 
 To find the devolutions of the 
 
 Throstle Spindle 318 
 
 To find the Twist given to the 
 
 Yarn by the Throstle 318 
 
 Tkktii OF Wheels, &c 318 
 
 To construct a Tooth, &c 319 
 
 To find the Horse-Power of a 
 
 Tooth 319 
 
 Journals of Shafts 880 
 
 Hydrostatics 820 
 
 hydraulics 322 
 
 Water- Win. i:i. I 888 
 
 To find UM Tower of a Stream . . 881 
 To c.n-tni.-i .i Water-Wheel to a 
 
 D Power and Pall 325 
 
 Dynamics 320 
 
 Hydrostatic Press 320 
 
 SECTION VI. 
 
 IUO0, (MB l'ROB- 
 
 • < I II IN... 
 
 Remarksanp Di.i iNMiuNs . . ,887 
 
 To construct a Pattern for the 
 Lateral Portion of a vessel In the 
 form of a Frustum of a Cone of 
 given diameters and depth . . . 329 
 
 To (.instinct a Pattern for the 
 Body of a vessel In the form of a 
 Frustum of • Cone of given di- 
 mensions, without plotting the 
 dimensions 332 
 
 To construct a Pattern for the 
 Lateral Portion Of a Flaring Ves- 
 sel of given symmetry of outline 
 and given capacity ." 333 
 
 TABLE OF Relative Propor- 
 tions, Chords, &e 333 
 
 The special tabular figure, the di- 
 ameter of one end, and the Cubic 
 
 Capacity of the vessel being 
 given, to find the diameter of 
 the other end 330 
 
 To construct a Pat tern for the body 
 of a Haring Vessel of gives 
 tabular outline, and given dimen- 
 sions, without plotting the di- 
 mensions . 338 
 
 The Capacity in gallons of a vessel 
 
 . In the form of a Frustum of a 
 
 Cone being given, and any two 
 
 of its dimensions, to find the 
 
 other dimension 340 
 
 To construct Patterns for flaring 
 oval vessels of different eccentri- 
 cities and given dimensions, Nos. 
 1,2,3 S|8 
 
 To describe the bases for Nos. 1,2, 8, 843 
 
 OF CYLINDRICAL Ei.nows . . . .348 
 
 To construct a Pattern for a Right- 
 angled Cylindrical Elbow . . . ,810 
 
 To construct Oblique-angled El- 
 bows 352 
 
 To construct Right-angled Elliptic 
 Elbows 353 
 
 To construct Oblique-angled Ellip- 
 tic Elbows 353 
 
 To construct Right Semi-liyperho- 
 las by intersecting lines '. ,840,863 
 
 To construct the Quadranl of a Cir- 
 cle by intersecting lines . . . 
 
 To construe! the Quadrant of a 
 
 J riven Ellipse by intersecting 
 (net 354 
 
 To construct the Quadrant of a Qy- 
 
 cloidal Ellipse bv intersecting 
 lines ". 
 
 TO describe an Ellipse of given di- 
 mension- b\ means of t w u I',. 
 a Pencil, au ■ String 
 
 To find the length of the circum- 
 ference of a given Ellipse . . 
 
 To construct a Semi-parabola by 
 Interaafltlng Hnti 355 
 
CONTENTS. 
 
 PAOK 
 
 Ovals, to describe . 178, 343, MS, :t47 
 
 Of Circular Kmiows 355 
 
 TABUS applicable to Circular El- 
 bows 350 
 
 To construct a Right-angled Circu- 
 lar BlbOW of 3, 4, 5, 6, 7, or 8 
 
 pieces, &c 355 
 
 To construct a Collar for a Cylin- 
 drical I'ipc of the same- diameter 
 
 as the receiving pipe 359 
 
 To construct a Cylindrical Collar 
 of a given Diameter to lit a Ue- 
 ecivinu-pipe of a greater given 
 
 Diameter 300 
 
 To construct a Cylindrical Collar 
 to lit an Elliptic-cylinder at ei- 
 ther right section of the El- 
 lipse 301 
 
 To construct a Cylindrical Collar 
 of a given Diameter, to fit a Cyl- 
 inder of the same Diameter, at 
 any given Angle to the side of 
 
 the Cylinder 301 
 
 To construct a Cylindrical Collar, 
 or Spout, of a given Diameter, 
 to fit a Cylinder of a greater giv- 
 en Diameter, at a given Angle 
 to the side of the Cylinder . . .302 
 Of Spouts for Vessels .... 303 
 Of Pitched or Bevelled Covers . . 304 
 To construct a Bevelled Circular 
 Cover of a given Rise and giv- 
 en Diameter 304 
 
 PAGE 
 
 To construct a Pattern for a Bev- 
 elled Elliptical Cover of a given 
 Rise to fit an Elliptic Boiler of 
 given Diameters 305 
 
 To construct a Bevelled Cover of a 
 given Rise, to fit a False-Oval 
 Boiler of given length and width 305 
 
 Of Can-tops 306 
 
 To construct a Can-top of a given 
 Depth and given Diameters . . 306 
 
 To construct a Can-top of a given 
 Pitch, and given Diameters . . 867 
 
 OF Lips for Mkasures . . . . 308 
 
 To construct a Lip for a Measure, 
 the Diameter of the Top of the 
 Measure being given 309 
 
 OfShBBTPAJTI 309 
 
 To cut the Corners for a Perpen- 
 dicular-sided Sheet Pan .... 370 
 
 To cut the Corners for an Oblique- 
 sided Sheet Pan 370 
 
 To construct a Heart, or Heart- 
 shaped Cake-Cutter 370 
 
 To construct a Mouth-piece for a 
 Speaking-Tube 370 
 
 To construct a Pattern for the 
 Body of a Circular - bottomed 
 Flaring Coal-Hod, all the curves 
 -to be arcs of circles 371 
 
 Solders, Alloys, and Compo- 
 sitions 373 
 
DEFINITIONS 
 
 OF THE SIGNS USED IN THE FOLLOWING WORK. 
 
 es Equal to. The sign of equality ; as 16 oz. = 1 lb. 
 
 -f- Plus, or More. The sign of addition ; as 8 -}- 12 = 20. 
 
 — Minus, or Less. The sign of subtraction ; as 12 — 8 = 4. 
 
 X Multiplied by. The sign of multiplication ; as 12 X 8 = 96. 
 
 -J- Divided by. The sign of division ; as 12 -r- 4 = 3. 
 
 *r Difference between the given numbers or quantities; thus, 12 s> 8, or 
 8 is* 12, shows that the less number is to be subtracted from the 
 greater, and the difference, or remainder, only, .is to be used ; so, 
 too, height j- breadth, shows that the difference between the height 
 and breadth is to be taken; 
 
 : :: : Proportion; as 2 : 4 :: 3 : 6 ; that is, as 2 is to 4, so is 3 to 6. 
 
 V Sign of the square root ; prefixed to any number indicates that the 
 square root of that number is to be taken, or employed ; as 
 V64 = 8. 
 
 ^/ Sign of the cube root ; and indicates that the cube root of the num- 
 ber to which it is prefixed is to be employed, instead of the num- 
 ber itself; as ^64 = 4. 
 
 8 To be squared, or the square of; shows that the square of the number 
 to which it is affixed is the quantity to be employed ; as 12 2 -r- 
 6 = 24 ; that is, that the square of 12, or 144 -r- 6 = 24. 
 
 8 Indicates that the cube of the number to which it is subjoined is to 
 to be used ; as 4 3 = 64. 
 
 • Decimal point, or separatrix. See Decimal Fractions. 
 
 Vinculum. Signifies that the two or more quantities over 
 
 which it is drawn, are to be taken collectively, or as forming 
 one quantity ; thus, 4 + 6 X 4 = 40 ; whereas, without the 
 vinculum, 4 -f 6 X 4 = 28 ; also, 12 — 2X3+4 = 2 ; and 
 V52ZZ3 2=S 4. So, also, V(5 2 — 3 2 )=-4,and(44-6)X4 
 = 40. 
 
 4_2 ( half of 4 2 or ) 
 
 2 ( half of the square of 4 ) ~ 
 
 (42 \2 
 - J (the square of half the square of 4) = 64. 
 
 i^ 2 or 4 (6) 2 (half the square of b.) 
 (hh)- (the square of half b ) 
 (2b) 2 (the square of twice b.) 
 
SECTION I. 
 MONEYS, WEIGHTS AND MEASURES, 
 
 OP THE UNITED STATES ;— THEIR DENOMINATIONS, VALUES, 
 COMPARATIVE VALUES, MAGNITUDES, Ac. 
 
 MONEYS OF ACCOUNT OF THE UNITED STATES. 
 
 These are the mill, the cent, the dime, and the dollar. 
 10 mills =ss 1 cent, 10 cents = 1 dime, 10 dimes =» 1 dollar. 
 
 The dollar is the unit or ultimate money of account of the United 
 States, or of what is sometimes called Federal money. 
 
 In practice, the dime, as a denomination of value, is rejected. 
 Thus, 
 
 10 mills = 1 cent, and 100 cents = 1 dollar. 
 
 This mark, $, is equivalent to the word dollar, or dollars, in this 
 money. 
 
 COINS OF THE UNITED STATES. 
 
 Until June, 1834, the government of the United States estimated 
 gold in comparison with silver as 15 to 1, and in comparison with 
 copper as 850 to 1. 
 
 From June, 1834, until February, 1853, the same government 
 estimated gold in comparison with silver as 16 to 1, and in com- 
 parison with copper as 720 to 1. 
 
 For all time since February, 1853, this government has estimated 
 gold in comparison with silver as 14 £ to 1, and in comparison with 
 copper as 720 to 1. 
 
 The standard for mint gold with this government until 1834, 
 was 11 parts pure gold and 1 part alloy, the alloy to consist of 
 silver and copper mixed, not exceeding one half copper. 
 
 The gold coins, therefore, struck at the United States mint prior 
 to 1834, are 22 carats fine. 
 2 
 
14 CURRENCY OP THE UNITED STATES. 
 
 In what, until 1834, constituted a dollar of gold coin of United 
 States mintage, there were put 24.75 grains of pure gold ; and 27 
 grains of the standard mint gold of that day were at that time worth 
 $1. Twenty-seven grains of that gold, or gold of that standard, 
 are now, by the present government standard of valuation, worth 
 $1.0652. 
 
 The standard for mint silver with this government until 1834, 
 was 1485 parts pure silver and 179 parts pure copper, = 8^fe 
 parts pure silver and 1 part pure copper. 
 
 The silver coins, therefore, struck at the United States mint prior 
 to 1834, are lOf f f ounces fine. 
 
 In that which, until 1834, constituted a dollar of silver coin of 
 this government's mintage, there were put 37l£ grains of pure 
 silver ; and 416 grains of the standard mint silver of that day were 
 at that time of the value of $1. Four hundred and sixteen grains 
 of that silver, or silver of that standard, are now, by the present 
 government standard of valuation, worth $1.0744. 
 
 The cent, until 1834, was of pure copper, and weighed 208 
 grains; since 1834, pure copper, weight 168 grains. 
 
 The standard for mint gold with this government is now, and for 
 all time since June, 1834, has been, 9 parts pure gold and one part 
 alloy, the alloy to consist of silver and copper mixed, not exceeding 
 one half silver. 
 
 The gold coins, therefore, struck at the United States mint and 
 dated subsequent to 1834, are 21f carats fine. 
 
 The standard weight for these coins is 25* grains to the dollar ; and 
 in every 25f grains of these coins there are 23-j^ny grains of pure 
 gold. 
 
 The standard for mint silver with this government is now, and 
 for all time since June, 1834, has been, 9 parts pure silver and 1 
 part pure copper. 
 
 The silver coins, therefore, struck at the United States mint and 
 dated subsequent to 1834, are lOf ounces fine. 
 
 In what, from June, 1834, until February, 1853, constituted a 
 dollar of silver coin of this government's mintage, there were put 
 371$ grains of pure silver ; and 412£ grains of the standard mint 
 silver of that day (the present standard) were worth, from June, 
 1834, until February, 1853, $1. Four hundred twelve and one 
 half grains of thin standard of silver are now worth, by the present 
 standard of valuation, $1.0742. 
 
 The standard weight for silver coins with this government at 
 present is 384 grains to the dollar. 
 
 The new cent, established by the Congress of 1856, is 7 parts 
 copper and 1 part nickel, and its legal weight is 72 grain*. 
 
 The foregoing is not applicable to the three-cent pieces of United 
 
CURRENCY OF THE UNITED STATES. 
 
 15 
 
 States mintage. These pieces were ordered by the Congress of 1850- 
 1851, and an especial standard of purity was assigned them, 
 viz., three parts silver and one part copper ; their weigiit was fixed 
 at 12§ grains each, and their current value at three cents each. 
 The law of 1853, regulating the currency, does not apply to these. 
 They are now, as in 1851, legally the same. These pieces are worth, 
 even now, less than their nominal values, compared with the present 
 standard of purity and weight for other United States coins. They 
 are worth, by this comparison, 2.863 cents each. 
 
 In the preceding calculations, the alloy for gold, in each instance, 
 was taken to consist of equal parts of silver and copper. The law, 
 until 1834, provided that it should consist of ' silver and copper 
 mixed, not exceeding one half copper;' and the present law pro- 
 vides that it shall consist of ' silver and copper mixed, not exceed- 
 ing one half silver.' 
 
 The metals used as alloys were taken at their values as money. 
 Federal money was established by the Congress of the United 
 States, in 1786. 
 Boston, June, 1866. 
 
 GOLD, — PURE. 
 
 24 carats fine = Pure Gold. 
 
 1 grain = $0.0429. 
 
 23.30859 « — $1.00. 
 
 1 dwt. = $1.02966. 
 
 1 ounce =$20.5932. 
 
 MINT GOLD. — U. S. 
 Alloy half each, silver and cojrper. 
 Nine parts pure gold and one part alloy ; or, 
 
 21| carats fine = Standard Coin. 
 1 grain =$0 03876. 
 
 254 " =$1.00. 
 
 1 dwt. =$0.93023. 
 
 1 ounce =$18.60465. 
 
 GOLD COINS. — U. S. 
 
 Double Eagle, 
 
 Eagle, - - - - 
 
 Half Eagle, - 
 
 Quarter Eagle, 
 
 Gold Dollar, - 
 
 Triple Gold Dollar, 
 
 Eagle, prior to 1834, ($10£,) 
 
 Half do., " " » ($5*,) 
 
 Weight In 
 
 Standard 
 
 Grains. 
 
 Value. 
 
 516 
 
 $20.00 
 
 258 
 
 10.00 
 
 129 
 
 5.00 
 
 64£ 
 
 2.50 
 
 25| 
 
 1.00 
 
 77| 
 
 3.00 
 
 270 
 
 10.64 
 
 135 
 
 5.32 
 
16 
 
 CURRENCY OF THE UNITED STATES. 
 
 Private and Uncurrent. 
 
 
 
 Wedffal iu 
 
 Grains. 
 
 Sales. 
 
 A. Bechtler, N. 0., $5 piece, 
 
 
 $4.75 
 
 m M 2£ " - 
 
 - 
 
 - 
 
 
 2.37 
 
 (< <( 1 '* - 
 
 . 
 
 . 
 
 
 .93 
 
 T. Reed, Georgia, 5 " - 
 
 - 
 
 - 
 
 
 4.75 
 
 K (4 2^ " - 
 
 - 
 
 . 
 
 
 2.37 
 
 M (( J (( 
 
 . 
 
 . 
 
 
 .93 
 
 Moffat, California, 5 " - 
 
 - 
 
 - 
 
 129 
 
 5.00 
 
 SILVER, — PURE. 
 
 12 ounces fine = Pure Silver. 
 1 dwt. = $0.06928. 
 
 3463| grains = $i. 
 1 ounce = $1.3857. 
 
 MINT SILVER. — U. S. 
 
 Alloy, all copper. 
 
 Nine parts pure silver and one part alloy ; or, 
 10 oz. 16 dwts. fine = Standard Coin. 
 
 1 dwt. — $0,062. 
 
 384 grains — $1.00. 
 
 1 ounce = $1.23958. 
 
 SILVER COINS. — U. S. 
 
 Dollar, 
 
 Half Dollar, 
 
 Quarter Dollar, - 
 
 Dime, .--..- 
 
 Half Dime, 
 
 Three-Cent Piece, £ silver and £ copper, 
 
 Weight in 
 
 Cniins. 
 
 384 
 192 
 
 96 
 
 38f 
 
 19* 
 12f 
 
 Standard 
 Value. 
 
 $1.00 
 .50 
 .25 
 .10 
 .05 
 .03 
 
 The copper coins of the United States are the cent and half cent ; 
 thev are of pure copper. The weight of the former is 168 grains, 
 and that of the latter, 84 grains. 
 
 Notk. — The silver coins of the United States, issued Bince February, 1863, are not 
 legal tender in the United States in sums exceeding./?i;e dollars. 
 
CURRENCY OF TIIE UNITED STATES. 
 
 17 
 
 TABLE, 
 
 Exhibiting the standard weight and present par value of the silver coins 
 of the United States, of dales subsequent to 1834, and prior to 1853. 
 
 
 Weight In 
 
 Present 
 
 
 Grains. 
 
 par value. 
 
 Dollar, - 
 
 4124 
 
 $1.0742 
 
 Half Dollar, - . 
 
 206j 
 
 .5371 
 
 Quarter Dollar, - 
 
 103* 
 
 .2685 
 
 Dime, - - - - - 
 
 41* 
 
 .1074 
 
 Half Dime, - 
 
 m 
 
 .0537 
 
 Three-Cent Piece, - 
 
 12| 
 
 .03 
 
 CURRENCIES OF THE DIFFERENT STATES OF THE UNION. 
 
 4 Farthings = 1 Penny, 12 Pence = 1 Shilling, 20 Shillings =» 
 1 Pound. 
 
 In Massachusetts, Connecticut, Rhode Island, New Hampshire, 
 Vermont, Maine, Kentucky, Indiana, Illinois, Missouri, Virginia, 
 Tennessee, Mississippi, Texas and Florida, 6 shillings = 1 dollar ; 
 $! = •&£• 
 
 In New York, Ohio and Michigan, 8 shillings = 1 dollar ; $1 =a 
 
 In New Jersey, Pennsylvania, Delaware and Maryland, 7 shil- 
 lings and 6 pence =* 1 dollar ; 1 dollar = % £. 
 
 In North Carolina, 10 shillings =* 1 dollar ; $1 = £ £. 
 
 In South Carolina and Georgia, 4 shillings and 8 pence »■ 1 dol- 
 lar ; $1 = ,& £. 
 
 Note. — These currencies, so called, are nominal at present in a great measure. The 
 denominations serve in the different States a3 verbal expressions of value. But they are 
 neither the names of the moneys of account in any of the States, nor are they the national 
 names of any of the real moneys in circulation. All values in money in the United States 
 are legally expressed in dollars, cents, and mills. 
 
 2* 
 
18 METRICAL SYSTEM OF WEIGHTS AND MEASURES. 
 
 THE METRICAL SYSTEM OF WEIGHTS AND MEAS- 
 URES. 
 
 In this system, the Metre is the basis, and is one forty-millionth 
 of the polar circumference of the earth. 
 
 The Metre is the •principal unit measure of length; the Are 
 of surface; the Stere of solidity; the Litre of capacity; and the 
 Gram of weight. 
 
 The gram is the weight, in a vacuum, of one cubic centimetre 
 of pure water at its maximum density. 
 
 The Metre, almost exactly . == 39.3685 U. S. inches. 
 
 The Are (100 square metres) z= 3.95337 " square rods. 
 
 The Stere (a cubic metre) . =z 35.31042 " cubic feet. 
 
 t\ tu s .. . . . v (61.0164 " " inches. 
 The Litre (a cubic de C1 metre)=:j lMm u wine quarts . 
 
 The Gram . = 15.44242 " grains. 
 
 The divisions by 10, 100, 1,000, of each of these units, are ex- 
 pressed by the same prefixes, viz., deci, centi, milli; and the multi- 
 ples by 10, 100, 1,000, 10,000, of each, by deca, hecto, kilo, na/ria. 
 The former series were derived from the Latin language, the latter 
 from the Greek. 
 
 To illustrate with the metre : — 
 
 10 millimetres =i 1 centimetre, 10 centimetres =: 1 decimetre, 10 
 decimetres =1 Metre, 10 Metres = 1 decametre, 10 decame- 
 tres = 1 /hectometre, 10 hectometres = 1 Mometre, 10 kilometres 
 =. 1 m^nametre. 
 
 In commerce, the ordinary weight is the kilogram, and 100 kilo- 
 grams (usually called kilos) r=z 1 quintal; 10 quintals = 1 millier, 
 or tonneau. The kilogram = 15,442.42 -f- 7000 = 2.20606 avoir- 
 dupois pounds. 
 
 In practice, the terms milliare, declare, decare, kiloare, and myri- 
 are are usually dropped, and 
 
 100 centare =z 1 are; 100 ares = 1 hectare. 
 
 Also the terms millistere, hectostere, kilostere, and myriastere, are 
 usually rejected, and 100 centisteres z= 1 decistere; 10 decisteres 
 ■=. 1 stere ; 10 stores =. 1 decastere zr: 353.1042 cubic feet. 
 1 centiare (square metre) = 1.19589413 square yards. 
 1 kilometre . . . = 0.62135 statute miles. 
 1 hectare . . . E= 2.471 = U. S. acres. 
 1 kilolitre . . . = 1 stere = 61,016.403233 cubic in. 
 A hectolitre = 26.41403 wine gallons =l 2.83741 Winchester bush. 
 
 Notk. — The system is the one recommended by tbf Statistical OO Bf W 
 1865 aa a general system of weights ami measure* to be adopted by all nations. 
 
fOREIGN GOLD COINS. 
 
 19 
 
 FOREIGN GOLD COINS. 
 
 Note. — The coins of any country, both gold and silver, circulating as for- 
 eign in any other, particularly those of the smaller denominations, are usually 
 keld at an estimate below their standard par value, compared with the money 
 standard of the country in which they circulate as foreign. Many of them, 
 more particularly the silver, having circulation in the United States, are much 
 worn and otherwise depreciated. In some instances, owing to frequent changes 
 made both with regard to weight and purity, certain of them, having the same 
 name and general appearance, boar a premium at home; others, a discount. 
 Others, again, can hardly be said to have a definable value anywhere. The par 
 value of the old pistole of Geneva, for instance, weighing 103i grains, is $3,985, 
 while that of the new, weighing 873 grains, would, at the same degree of 
 purity, be worth but $3,386 ; whereas, owing to its higher standard of fine- 
 ness, its par value is $3,443. The ducat of Austria, coined in 1831, weighs 
 53A grains, — its purity is 23.64, and its par value $2,269; while the half 
 sovereign, closely resembling the ducat, coined in 1835, and weighing 87 grains, 
 has a purity only of 21.64, and a par value, consequently, of but $3,378. The 
 circulating value of the ducat in the United States, in general, is $2.20, and 
 that of, the haif sovereign of Austria, $3.25. 
 
 
 Standard 
 
 Standard 
 
 Par value 
 
 Circulating 
 
 Par val- 
 
 ARGENTINE REPUBLIC. 
 
 of 
 parity in 
 
 weight 
 
 in 
 Federal 
 
 value in 
 Federal 
 
 ue per 
 grain. 
 
 Doubloon to 1832, 
 
 carats. 
 
 grains. 
 
 money. 
 
 ■money. 
 
 ct*. 
 
 19.56 
 
 418 
 
 $14,671 
 
 $ 
 
 3.50 
 
 to " 
 
 20.83 
 
 415 
 
 15.512 
 
 
 3.73 
 
 AUSTRIA. 
 
 
 
 
 
 
 Sovereign, half in propor- 
 
 
 
 
 
 
 tion, to 1785, 
 
 22.00 
 
 170 
 
 6.711 
 
 6.50 
 
 3.94 
 
 Sovereign, half in propor- 
 
 
 
 
 
 
 tion, since 1785, 
 
 21.64 
 
 174 
 
 6.756 
 
 6.50 
 
 3.88 
 
 Ducat, double in propor- 
 
 
 
 
 
 
 tion, 
 
 23.64 
 
 53* 
 
 2.269 
 
 2.20 
 
 4.24 
 
 BELGIUM. 
 
 
 
 
 
 
 Sovereign, half in pro., 
 
 22.00 
 
 170 
 
 6.711 
 
 
 3.94 
 — - — 1 
 
20 
 
 FOBE1GK GOLD COINS, 
 
 
 Standard 
 of 
 
 Standard 
 weight 
 
 Par rsltw 
 in 
 
 Circulating 
 rahie in 
 
 Par »aT| 
 ue per j 
 
 parity in 
 
 in 
 
 Federal 
 
 Federal 
 
 grain. 
 
 Twenty Franc, more in pro. 
 
 carats. 
 
 gTaini. 
 
 money. 
 
 money. 
 
 eta. 
 
 21.50 
 
 99£ 
 
 $3,840 
 
 $3.83 
 
 3.85 
 
 Ducat, 
 
 
 
 
 2.20 
 
 
 Bolivia, Colombia, Chili, 
 
 
 
 
 
 
 Ecuador, Peru, New 
 
 
 
 
 
 
 Grenada, and Mexico. 
 
 
 
 
 
 
 Received by U. S. Gov- 
 
 
 
 
 
 
 ernment, — those of not 
 
 
 
 
 
 
 less than 20.86 carats 
 
 
 
 
 
 
 fine, at 89-j^ cts. per dwt. 
 
 
 
 
 
 
 Doubloon, (8 E) 
 
 20.86 
 
 417 
 
 15.620 
 
 15.60 
 
 3.74 
 
 Half do. 
 
 t< 
 
 208£ 
 
 7.810 
 
 7.50 
 
 M 
 
 Quarter do. 
 
 II 
 
 1044 
 
 3.905 
 
 3.75 
 
 M 
 
 Eighth do. 
 
 M 
 
 52 
 
 1.952 
 
 1.75 
 
 II 
 
 Sixteenth do. 
 
 M 
 
 26 
 
 .976 
 
 .90 
 
 (( 
 
 Pistole, half in pro., 
 
 
 
 
 3.75 
 
 
 BRAZIL. 
 
 
 
 
 
 
 Received by the U. S. 
 
 
 
 
 
 
 Government, — those of 
 
 
 
 
 
 
 not less than 22 carats 
 
 
 
 
 
 
 fine, at 94^ cts. per dwt. 
 
 
 
 
 
 
 Dobraon, 
 
 22.00 
 
 828 
 
 32.719 
 
 32.00 
 
 3.95 
 
 Dobra, 
 
 M 
 
 438 
 
 17.306 
 
 17.00 
 
 M 
 
 Joannes, {standard variable) 
 
 M 
 
 432 
 
 17.064 
 
 Sl3to$17 
 
 II 
 
 Half do. do. do. 
 
 It 
 
 216 
 
 8.532 
 
 $6 to 8.50 
 
 (( 
 
 Moidore, (BBBB) half in 
 
 
 
 
 
 
 pro., {standard variable) 
 
 21.79 
 
 165 
 
 6.451 
 
 6.00 
 
 3.90 
 
 Crusado, do. do. 
 
 M 
 
 16* 
 
 .635 
 
 
 N 
 
 DENMiP*. 
 
 
 
 
 
 
 Christian d'or 
 
 21.74 
 
 103 
 
 4.018 
 
 
 3.90 
 
 Ducat, species, 
 
 23.48 
 
 53£ 
 
 2.254 
 
 2.20 
 
 4.21 
 
 11 current, 
 
 21.03 
 
 48 
 
 1.811 
 
 
 3.77 
 
 FRANCE. 
 
 
 
 
 
 
 {Alloy mostly silver.) 
 
 
 
 
 
 
 Rec'd by U. S. Govern- 
 
 
 
 
 
 
 ment, — those the purity 
 
 
 
 
 
 
 of which is not less than 
 
 
 
 
 
 
 21^ carats fine, at 93^ 
 
 
 
 
 
 
 cts. per dwt. 
 
 
 
 
 
 
 Chr. d'or, double in pro., 
 
 21.60 
 
 101 
 
 3.914 
 
 3.90 
 
 3.87 
 
FOREIGN GOLD COINS. 
 
 21 
 
 
 Standard 
 
 Btaad utJ 
 
 Var value 
 
 Circulating 
 
 Par val- 
 
 
 of 
 
 weight 
 
 in 
 
 value in 
 
 ue per 
 
 
 purity in 
 
 in 
 
 Federal 
 
 federal 
 
 grain. 
 
 Franc d'or, double in pro., 
 
 emus. 
 
 grains. 
 
 money. 
 
 money. 
 
 ct». 
 
 21.60 
 
 101 
 
 $3,914 
 
 $3.90 
 
 3.87 
 
 Louis d'or, " " " 
 
 
 
 
 
 
 to 1786, 
 
 21.49 
 
 125£ 
 
 4.840 
 
 
 3.85 
 
 Louis d'or, double in pro., 
 
 
 
 
 
 
 since 1786, 
 
 21.68 
 
 118 
 
 4.573 
 
 4.50 
 
 3.87 
 
 Napoleon (20 F.) double &c. 
 
 21.60 
 
 994 
 
 3.856 
 
 3.83 
 
 (4 
 
 GERMANY. 
 
 
 
 
 
 
 BADEN. 
 
 
 
 
 
 
 Zehn Gulden, 5 in pro.. 
 
 21.60 
 
 1054 
 
 4.088 
 
 4.00 
 
 3.87 
 
 BAVARIA. 
 
 
 
 
 
 
 Carolin, 
 
 18.49 
 
 149£ 
 
 4.952 
 
 
 3.32 
 
 Ducat, double in pro., 
 
 23.58 
 
 53| 
 
 2.275 
 
 2.20 
 
 4.23 
 
 Maximilian, 
 
 18.49 
 
 100 
 
 3.317 
 
 
 3.31 
 
 BRUNSWICK. 
 
 
 
 
 
 
 Ducat, 
 
 23.22 
 
 534 
 
 2.220 
 
 
 4.16 
 
 Pistole, double in pro., 
 
 21.60 
 
 117^ 
 
 4.548 
 
 
 3.87 
 
 Ten Thaler, 5 in pro., to 
 
 
 
 
 
 
 1813, 
 
 21.55 
 
 202 
 
 7.811 
 
 7.80 
 
 3.86 
 
 Ten Thaler, less in pro., 
 
 
 
 
 
 
 since 1813, 
 
 21.50 
 
 204 
 
 7.873 
 
 7.80 
 
 3.85 
 
 HANOVER. 
 
 
 
 
 
 
 Ducat, double in pro., 
 
 23.83 
 
 534 
 
 2.287 
 
 2.20 
 
 4.27 
 
 George d'or, " " " 
 
 21.67 
 
 1024 
 
 3.987 
 
 
 3.88 
 
 Zehn Thaler, 5 " " 
 
 21.36 
 
 2044 
 
 7.838 
 
 7.80 
 
 3.83 
 
 HESSE. 
 
 
 
 
 
 
 Ten Thaler, 5 in pro., to 
 
 
 
 
 
 
 1785, 
 
 21.36 
 
 202 
 
 7.742 
 
 
 u 
 
 Ten Thaler, 5 in pro., since 
 
 
 
 
 
 
 1785, 
 
 21.41 
 
 203 
 
 7.799 
 
 
 3.84 
 
 SAXONY. 
 
 
 
 
 
 
 Ducat, 
 
 23.49 
 
 534 
 
 2.256 
 
 2.20 
 
 4.21 
 
 Augus 
 
 tus d'or, double in 
 
 
 
 
 
 
 pro. 
 
 , since 1784. 
 
 WURTEMBURG. 
 
 21.55 
 
 1024 
 
 3.964 
 
 
 3.86 
 
 Carolii 
 
 k. 
 
 18.51 
 
 1474 
 
 4.899 
 
 
 3.32 
 
 Ducat, 
 
 23.28 
 
 534 
 
 2.235 
 
 4.17 
 
22 
 
 FOREIGN GOLD COINS. 
 
 
 Standard 
 
 Standard 
 
 Par ralue 
 
 Circulating 
 
 Par ral- 
 
 
 of 
 
 weight 
 
 in 
 
 Talue in 
 
 ue per 
 
 
 purity in 
 
 in 
 
 Federal 
 
 Federal 
 
 grain. 
 
 GREAT BRITAIN. 
 
 carats. 
 
 grain*. 
 
 money. 
 
 money. 
 
 CtM. 
 
 
 
 
 
 (Alloy, since 1826, all copper.) 
 
 
 
 
 
 
 Rec'd by U. S. Govem- 
 
 
 
 
 
 
 ment, — those of 22 ca- 
 
 
 
 
 
 
 rats fine, set 94y^y cts. 
 
 
 
 
 
 
 per dwt. 
 
 
 
 
 
 
 Guinea, half h* pro., to 
 
 
 
 
 
 
 ; 1785, 
 
 22.00 
 
 127 
 
 $5,016 
 
 
 3.95 
 
 Guinea, half in pro., since 
 
 
 
 
 
 
 1785, 
 
 « 
 
 1294 
 
 5.111 
 
 $5.00 
 
 <( 
 
 Sovereign, half in pro., 
 
 M 
 
 123£ 
 
 4.866 
 
 4.83 
 
 <( 
 
 iFive do. 
 
 U 
 
 616| 
 
 24.332 
 
 24.20 
 
 tt 
 
 Sovereign, (dragon) half 
 
 
 
 
 
 
 in pro., 
 
 It 
 
 1224 
 
 4.838 
 
 4.80 
 
 a 
 
 Double Sovereign (dragon} 
 
 u 
 
 246 
 
 9.717 
 
 9.67 
 
 u 
 
 GREECE. 
 
 
 
 
 
 
 Twenty Drachm, more hi 
 
 
 
 
 
 
 pro., 
 
 21.60 
 
 89 
 
 3.449 
 
 3.30 
 
 3.87 
 
 HOLLAND. 
 
 • 
 
 
 
 
 
 Ducat, 
 
 23.58 
 
 53£ 
 
 2.263 
 
 2.20 
 
 4.23 
 
 Ryder, 
 
 22.00 
 
 153 
 
 6.043 
 
 
 3.95 
 
 Double do. 
 
 M 
 
 309 
 
 12.205 
 
 
 (i 
 
 Ten Gulden, 5 in pro., 
 
 21.60 
 
 104 
 
 4.025 
 
 4.00 
 
 3.87 
 
 INDIA. 
 
 
 
 
 
 \ 
 
 Pagoda, star, 
 
 19.00 
 
 52| 
 
 1.798 
 
 
 3.40 
 
 Mohur, (E. I. Co.) 1835. 
 
 22.00 
 
 180 
 
 7.106 
 
 6.75 
 
 3.95 
 
 Half Sovereign, do. 
 
 
 
 
 2.41 
 
 
 BOMBAY. 
 
 
 
 
 
 
 Rupee, 
 
 22.09 
 
 179 
 
 7.095 
 
 
 3.96 
 
 MADRAS. 
 
 
 
 
 
 
 Rupee, 
 
 22.00 
 
 180 
 
 7.106 
 
 
 3.95 
 
 ITALY. 
 
 
 
 
 
 
 Eturia, Ruspone, 
 
 23.97 
 
 1611 
 
 6.935 
 
 
 4.30 
 
 Genoa, Sequin, 
 
 23.86 
 
 53£ 
 
 2.291 
 
 
 4.28 
 
 Milan, Pistole, 
 
 21.76 
 
 974 
 
 3.807 
 
 
 3.90 
 
 " Sequin, 
 
 23.76 
 
 534 
 
 2.281 
 
 
 4.26 
 
FOREIGN GOLD COINS. 
 
 28 
 
 
 Standard 
 
 Stnndnrd 
 
 Par value 
 
 Circulating 
 
 Par val- 
 
 
 of 
 
 weight 
 
 in 
 
 value in 
 
 ue per 
 
 
 purity in 
 
 in 
 
 Federal 
 
 Federal 
 
 grain. 
 
 Milan, Twenty Lire, more 
 
 carats. 
 
 ."r.iinv 
 
 money. 
 
 money. 
 
 ett. 
 
 
 
 
 
 
 in proportion, 
 
 21.58 
 
 99£ 
 
 $3,853 
 
 $3.83 
 
 3.86 
 
 Naples, Ducat, multiples 
 
 
 
 
 
 
 in pro., 
 
 21.43 
 
 22£ 
 
 .865 
 
 
 3.84 
 
 Naples, Oncetta, 
 
 23.88 
 
 58 
 
 2.485 
 
 
 4.28 
 
 Pauma, Doppia, to 1786, 
 
 21.24 
 
 110 
 
 4.192 
 
 
 3.81 
 
 " Pistole, since 1796, 
 
 20.95 
 
 no 
 
 4.135 
 
 
 3.75 
 
 " Twenty Lire, 
 
 21.62 
 
 994 
 
 3.860 
 
 3.83 
 
 3.87 
 
 Piedmont, Carlino, half in 
 
 
 
 
 
 
 pro., since 1785, 
 
 21.69 
 
 702 
 
 27.321 
 
 
 3.89 
 
 Piedmont, Pistole, half in 
 
 
 
 
 
 
 pro., since 1785, 
 
 21.54 
 
 140 
 
 5.411 
 
 
 3.86 
 
 Piedmont, Sequin, half in 
 
 
 
 
 
 • 
 
 pro., since 1785, 
 
 23.64 
 
 53i 
 
 2.280 
 
 
 4.23 
 
 Piedmont, Twenty Lire, 
 
 
 
 
 
 
 more in pro. , 
 
 20.00 
 
 991 
 
 3.563 
 
 3,50 
 
 3.59 
 
 Rome, Ten Scudi, 5 in pro. 
 
 21.60 
 
 2674 
 
 10.368 
 
 
 3.87 
 
 " Sequin, since 1760, 
 
 23.90 
 
 52i 
 
 2.251 
 
 
 4.28 
 
 Sardinia, Carlino, £ in 
 
 
 
 
 
 
 pro., 
 
 21.31 
 
 2474 
 
 9.465 
 
 
 3.82 
 
 Tuscany, Zeehino, double 
 
 
 
 
 
 
 in pro., 
 
 23.86 
 
 531 
 
 2.302 
 
 
 4.30 
 
 Venice, Zeehino, double 
 
 
 
 
 
 
 in pro., 
 
 23.84 
 
 54 
 
 2.310 
 
 
 
 MALTA. 
 
 
 
 
 
 
 Sequin, 
 
 23.70 
 
 53£ 
 
 2.275 
 
 
 4.25 
 
 Louis d'or, double and 
 
 
 
 
 
 
 demi in pro., 
 
 20.25 
 
 128 
 
 4.651 
 
 
 3.63 
 
 NETHERLANDS. 
 
 
 
 
 
 
 Dueat, 
 
 23.52 
 
 534 
 
 2.257 
 
 
 4.21 
 
 Zehn Gulden, 5 in pro., 
 
 21.55 
 
 1031 
 
 4.013 
 
 4.00 
 
 3.86 
 
 POLAND. 
 
 
 
 
 
 
 Ducat, 
 
 23.58 
 
 534 
 
 2.264 
 
 
 4.23 
 
 PORTUGAL. 
 
 
 
 
 
 
 Rec'd by the U. S. Gov- 
 
 
 
 
 
 
 ernment, — those the pu- 
 
 
 
 
 
 
 rity of which is not less 
 
 
 
 
 
 
 than 22 carats fine, at 
 
 
 
 
 
 
 94-j^ cts. per dwt. 
 
 
 
 
 
24 
 
 FOREIGN GOLD COINS. 
 
 
 Standard 
 
 Standard 
 
 Par value 
 
 Circulating 
 
 Par val- 
 
 
 of 
 
 weight 
 
 in 
 
 value in 
 
 ue per 
 
 
 purity in 
 
 in 
 
 Federal 
 
 Federal 
 
 grain. 
 
 Dobraon, 24,000 reis, 
 
 carats. 
 
 grains. 
 
 money. 
 
 money. 
 
 ctt. 
 
 22.00 
 
 828 
 
 $32,706 
 
 $32.00 
 
 3.95 
 
 Dobra, 
 
 <( 
 
 438 
 
 17.301 
 
 17.00 
 
 u 
 
 Joannes, {standard variable) 
 
 a 
 
 432 
 
 17.064 
 
 813 to 31 7 
 
 a 
 
 Half " " " 
 
 (< 
 
 216 
 
 8.532 
 
 86 to 8.50 
 
 <i 
 
 Moidore, 4000 reis, M 
 
 
 
 
 m to $4} 
 
 
 Coroa, 5000 " 
 
 " 
 
 147£ 
 
 5.83 
 
 5.75 
 
 «< 
 
 Milrea, 
 
 22.00 
 
 191 
 
 .780 
 
 
 3.95 
 
 PRUSSIA. 
 
 
 
 
 
 
 Ducat, 
 
 23.49 
 
 53£ 
 
 2.255 
 
 2.20 
 
 4.21 
 
 Frederick d'or, double in 
 
 
 
 
 
 
 pro., 
 
 21.60 
 
 102£ 
 
 3.973 
 
 
 3.87 
 
 RUSSIA. 
 
 
 
 
 
 
 Ducat, 
 
 23.64 
 
 54 
 
 2.291 
 
 
 4.24 
 
 Imperial, (10 R.) half in 
 
 
 
 
 
 
 pro., 1801, 
 
 23.55 
 
 185$ 
 
 7.828 
 
 
 4.22 
 
 Imperial, (10 R.) half in 
 
 
 
 
 
 
 pro., since 1818, 
 
 22.00 
 
 199 
 
 7.856 
 
 7.80 
 
 3.95 
 
 SICILY. 
 
 
 
 
 
 
 Oncia, double in pro., 
 
 20.39 
 
 68£ 
 
 2.495 
 
 
 3.64 
 
 Twenty Lire, more in pro., 
 
 21.60 
 
 99* 
 
 3.856 
 
 3.83 
 
 3.87 
 
 SPAIN. 
 
 
 
 
 
 
 Rec'd by U. S. Govern- 
 
 
 
 
 
 
 ment, — those the stand- 
 
 
 
 
 
 
 ard purity of which is 
 
 
 
 
 
 
 not less than 20.86 ca- 
 
 
 
 
 
 
 rats fine, at 89 ^ cts. 
 
 
 
 
 
 
 per dwt. 
 
 
 
 
 
 
 Doubloon (8 S) parts in pro. 
 " (8 E) parts as 
 
 21.45 
 
 416* 
 
 16.031 
 
 16.00 
 
 3.84 
 
 
 
 
 
 
 Bolivian, &c. 
 
 20.86 
 
 417 
 
 15.620 
 
 15.00 
 
 3.74 
 
 Pistole, to 1782, 
 
 21.48 
 
 103 
 
 3.970 
 
 
 3.85 
 
 " since " 
 
 20.93 
 
 101 
 
 3.906 
 
 
 3.75 
 
 Escudo, to 1788, 
 
 20.98 
 
 52 
 
 1.957 
 
 
 1.76 
 
 " since " 
 
 20.42 
 
 52 
 
 1.905 
 
 
 3.W. 
 
 Coronilla " 1800, 
 
 20.29 
 
 27 
 
 .983 
 
 
 B.64 
 
 SWEDEN. 
 
 
 
 
 
 
 Ducat, 
 
 23.45 
 
 53 
 
 2.230 
 
 
 4.20 
 
LONG OR LINEAR MEASURE. 
 
 25 
 
 SWITZERLAND. 
 
 Berne, Ducat, double in 
 
 pro., 
 Berne, Pistole, 
 Geneva, Pistole, 
 
 " {old) 
 Zurich, Ducat, double in 
 
 pro., 
 
 TURKEY. 
 Misseir, half in pro. 1820, 
 Sequin fonducli, 
 Yeermeeblekblek, 
 
 J Standard 
 
 Standard 
 
 Par value 
 
 Circulating 
 
 of 
 
 weight 
 
 in 
 
 value in 
 
 purity in 
 
 in 
 
 Federal 
 
 Federal 
 
 carats. 
 
 grams. 
 
 ■money. 
 
 money. 
 
 23.53 
 
 47 
 
 $1,984 
 
 
 21.62 
 
 117£ 
 
 4.558 
 
 
 21.87 
 
 87$ 
 
 3.443 
 
 
 21.51 
 
 1034 
 
 3.985 
 
 
 23.50 
 
 53* 
 
 2.256 
 
 
 15.88 
 
 36£ 
 
 1.040 
 
 
 19.25 
 
 53 
 
 1.830 
 
 
 22.88 
 
 73| 
 
 3.027 
 
 
 Par<ral 
 
 ue per 
 
 4.22 
 3.88 
 3.92 
 3.85 
 
 4.21 
 
 2.84 
 3.45 
 4.10 
 
 Note. — The Milled Dollars, or Pesos (silver) of Spain, Mexico, Peru, Chili, and Cen- 
 tral America, and the re stamped of Brazil, weighing not less than 415 grains, and of 10 
 oz. 15 dwts. fu*e, are received by the United States Government at $1.00 each. 
 
 The Five Franc silver pieces of France, of 10 oz. 16 dwts. fine, and weighing 384 
 grains, are received at i)3 cents each. 
 
 The standard silver coins of Great Britain are 11 oz. 2 dwts. fine. 
 
 LONG OR LINEAR MEASURE. — U. S. 
 
 Standard. — A brass rod, the length of which, at 62° Fahrenheit, 
 is f f ;^§jf§ that of a pendulum beating seconds in vacuo, at the level 
 of the sea, at the latitude of London, = $f; T ^# at 32° Fah., at the 
 gravitation at New York, — the Yard. 
 
 6 points = 1 line. 
 
 12 lines (72 points) = 1 inch. 
 
 12 inches = 1 foot. 
 
 3 feet (36 inches) = 1 yard. 
 
 5£ yards (16£ft.) = l rod. 
 40 rods (220 yds.) = 1 furlong. 
 8 fur. (5280 feet) = 1 stat. mile. 
 
 2| inches = 1 nail. 
 
 4 nails (9 inches) = 1 quarter 
 
 SPECIAL, FOR CLOTH. 
 
 4 quarters (36 inches) = 1 yard. 
 
 7-j- 9 ^ inches 
 25 links 
 
 SPECIAL, FOR LAND. 
 
 = 1 link. I 100 links (66 feet) = 1 chain. 
 
 = 1 rod. | 80 chains (320 rods) = 1 s. mile. 
 
 engineer's chain. 
 
 10 inches = 1 link. 
 
 120 links (100 feet) = 1 chain. 
 
SQUARE OR SUPERFICIAL MEASURE. 
 
 SHOEMAKER'S MEASURE. 
 
 No. 1 is 4 J inches in length, and each succeeding number is an 
 addition of J of an. inch. No. 1 man's size = 8£| inches. 
 
 MISCELLANEOUS. 
 
 Fathom == 6 feet. 
 
 Knot = 471 feet. 
 
 Hair's breadth 
 Digit 
 
 Cable's length = 120 fathom*. 
 Geometrical pace= 4.4 feet. 
 
 = 5^ inch. 
 = 10 lines. 
 Palm = 3 inches. 
 
 Hand = 4 " 
 
 SpaD == 9 «* 
 
 12 particular things = 1 dozen. 
 
 12 dozen (144) = 1 gross. 
 
 12 gross (1728) = 1 great gross. 
 
 20 particular things = 1 score. 
 
 24 sheets of paper = I quire. 
 
 20 quires = 1 ream. 
 
 SQUARE OR SUPERFICIAL MEASURE. 
 (Length X breadth.) 
 144 square inches = 1 square foot, 
 yard. 
 
 9 
 
 304 
 
 40 
 
 4 
 
 feet = 1 
 
 yards = 1 
 
 rods = 1 
 
 roods = 1 
 
 rod. 
 
 rood. 
 
 acre. 
 
 SPECIAL, FOR LAND. 
 
 srisuiAL, run l,as\u. 
 
 62|^4 square inches = 1 square link. 
 " links = 1 " 
 
 10000 
 10 
 Square rod 
 
 Rood 
 
 chains = 1 
 
 chain, 
 acre. 
 272$ square feet, 
 yards 
 
 Acre ( 160 square rods) == 
 
 Square mile 
 
 220 X 198 square feet 
 
 The square of 12.649 " rods 
 
 " " of 69.5701 " yards 
 " " of 208.710321 " feet 
 
 1210 
 
 10890 
 
 4840 
 
 43560 
 
 640 
 
 102400 
 
 feet. 
 
 yards. 
 
 feet. 
 
 acres. 
 
 rods. 
 
 sq. rods. 
 > =1 acre. 
 
CUBIC OR SOLID MEASURE. 
 
 27 
 
 CIRCULAR MEASURE. 
 
 Minute, or 
 Geogra- 
 phical m. 
 (60") 
 
 League 
 
 Degree 
 
 1.152 s. miles. 
 -^ 6086 feet. 
 
 -f 
 
 = 360 degiees. 
 
 = < 24897 s. ra. 
 
 Great Circle 
 Equatorial cir- 
 cumference 
 of the earth 
 Equatorial diam.= 7925 
 Polar diam. = 7899 
 Mean radius = 3955.92 
 
 hi 
 
 viz., 
 
 = 3 miles. 
 
 60 geo. miles. 
 69.158 s. ms. 
 Sign(-j^ zod.)=30 degrees. 
 
 Note. — In the expressions, square feet and feet square, there is this difference ; 
 the former expresses an area in which there are as many square feet as the number 
 named, and the latter an area in which there are as many square feet as the square of tha 
 number named. The former particularizes no form of area, the latter asserts a squam 
 
 CUBIC OR SOLID MEASURE. — U. S. 
 (Length X breadth X depth.) 
 
 f 1.273 cylindrical feet. 
 > __ J 2200 " inches. 
 
 $ ) 3300 spherical " 
 
 (_6600 conical " 
 
 f 0.785398 cubic feet. 
 J 1357.2 " inches. 
 ) 2592 spherical " 
 1 5 184 conical " 
 
 27 cubic feet = 1 cubic yard. 
 
 40 " of round timber = 1 ton. 
 42 " of shipping " = 1 ton. 
 
 50 " of hewn " = 1 ton. 
 
 128 " = 1 cord. 
 
 Cubic foot of pure water,"! 
 
 at the maximum density J , cn . . . . 
 
 at the level of the sea, I = \ 62^ avoirdupois pounds. 
 (39°.83, barometer 30 < 1UUU 
 
 inches ) . . J 49.1 
 
 = } 785.4 
 
 Cubic foot, 
 1728 cu. inches 
 
 Cylindrical foot 
 1728 " inches 
 
 h 
 
 ounces. 
 
 Cylindrical foot 
 
 Cubic inch 
 
 = Jo. 
 
 (25 
 
 Cylindrical inch = 
 
 Pound = 
 
 " distilled = 
 
 Cubic inch u = 
 
 Pound at 62°, distilled = 
 
 Cubic inch at 62°, " = 
 " " 39°.83, in vacuo = 
 
 036 169" 
 
 5787 " 
 253.1829 
 0.028415 avd. 
 0.4546 " 
 27.648 cubic inches. 
 27.7015 " 
 252.6839 grains. 
 27.7274 cub. inches. 
 252.458 grains. 
 253.0864 " 
 
 pounds. 
 
 ounces. 
 
 pounds. 
 
 ounces. 
 
 grains. 
 
 pounds. 
 
 ounces. 
 
 Cubic foot of salt water (sea) weighs 64.3 pounds. 
 
28 
 
 GENERAL MEASURE OP WEIGHT. 
 
 GENERAL MEASURE OF WE 
 
 AVOIRDUPOIS. 
 
 a 
 
 Standard. — The pound is the 
 weight, taken in air, of 27.7015 
 cubic inches of distilled water at 
 its maximum density, (39°.83 F., 
 the barometer being at 30 inches) 
 = 27.7274 cubic inches of distilled 
 water at 62° = 7000 Troy grains. 
 
 27^£ grains = 1 dram. 
 
 16 drams (437£ grs.) = 1 ounce. 
 16 ounces (7000 grs.)= 1 pound. 
 
 SPECIAL GROSS. 
 
 28 pounds 
 
 4 quartere > 
 112 pounds 5 
 20cwt. 
 
 SPECIAL DIAMOND. 
 
 16 parts = 1 grain = 0.8 troy gr. 
 4 grs. =1 carat = 3,2 " " 
 
 Note. 
 
 = 1 quarter. 
 5 1 quintal. 
 
 cwt. 
 1 ton. 
 
 SPECIAL TROT. 
 
 (Exclusively for gold and sil- 
 ver bullion, precious stones, and 
 gold, silver and copper coins, and 
 with reference to their monetary 
 value only.) 
 
 24 grain& = 1 penny w't. 
 
 20dwts. (480 grs.)= 1 ounce. 
 12 oz. (5760 grs.) =» 1 pound. 
 
 SPECIAL APOTHECARIES'. 
 
 (Exclusively for compounding 
 medicines, for recipes and pre- 
 scriptions.) 
 20 grains = 1 scruple, B>. 
 
 3 scruples = 1 dram, 5. 
 
 8 drams(480 g.)= 1 ounce, 5. 
 12 oz. (5760 g.) = 1 pound, lb. 
 
 1 lb. avoir. = lj 3 ^ lbs. troy. 
 
 1 lb. troy = IH lbs. avoir. 
 
 1 oz. avoir. = \^§ oz. troy. 
 
 1 oz. troy = ly^ oz. avpir. 
 
 The comparative vaTuc of diamonds of the same quality is as the square of 
 Iheir respective weights. A diamond of fair quality, weighing 1 carat in the rough state^ 
 ib estimated worth about 89-j-^j. ; and it will require one-of twice that weight to make 
 one when worked down equal to 1 carat in weight. Hence, to determine the value of a 
 wrought diamond of any given numt>er of carats : — Rule. — Double the weight in carata 
 and multiply the square by 9.50. Thus, the value of a wrought diamond," weighing 2 
 carats, is 2-f2=4 X 4 = 16 X 9^0=8152l 
 
 LIQUID MEASURE. — U. S. 
 
 The " Wine" or " Winchester" Gallon, of 231 cubic inches 
 capacity, is the Government or Customs gallon of the Unitqd States 
 for all liquids, and the legal gallon of each state in which no law 
 exists fixing a state or statute gallon of its own. It contains 58372| 
 grains of distilled water at 39°. 83, the barometer being at 30 inches. 
 
 4 gills = 1 pint, 2 pints = 1 quart. 
 
 4 quarts, or 231 cubic in. ) $ I gallon. 
 
 t. J-J8.2 
 
 0.13368 cub. ft., 294.1176 cyl. in. 
 
 .355 av'd. lbs. pure water. 
 
DRY MEASURE. 29 
 
 0.128 cubic foot, 
 in. 
 
 w -j u c *u x fO.128 cubn 
 Liquid gallon of the ) 001104 « 
 
 iTrf 1 : 7 York *r 8-01' lbs. pure water 
 281.62 cylindnc in. ) ^ ^^ b ^ {a 
 
 Barrel «= 31£ gallons. I Puncheon a* 84 galloi 
 Tierce *■ 42 M Pipe or Butt «= 126 " 
 
 Hogshead = 63 " | Tun = 252 " 
 
 Imperial gallon, > { 
 
 277.274 cub. in. { ~ \ 
 
 10 av'd lbs. distilled water 
 at62°F.,b. 36 in. 
 
 Ale gallon, £ _ J 10£ av'd lbs. pure water 
 282 cub. in. J | at 39°.83, b. 30 in. 
 
 0.8331 Imperial gallon, 
 1 Wine gallons { 0.8191 Ale " 
 
 16742 W. bushel. 
 
 (0.1 
 1 Imperial gallon = 1.2 Wine gallons. 
 
 DRY MEASURE. — U. S. 
 
 The " Winchester Bushel," so called, of 21503^ cubic inches 
 capacity, is the Government bushel of the United States, and the legal 
 bushel of each state having no special or statute bushel of its own. 
 The standard Winchester bushel measure is a cylindrical vessel hav- 
 ing an outside diameter of 19^ inches, an inside diameter of 18£ 
 inches, and an inside depth of 8 inches. The standard " heaped " or 
 " coal " bushel of England was this measure heaped to a true cone 6 
 inches high, the base being 19£ inches, or equal to the outside diam- 
 eter of the measure. Its ratio to the even bushel was, therefore, as 
 1.28, nearly, to 1. The present " Imperial " measure of England has 
 the same outside diameter and the same depth as the Winchester, and 
 an internal diameter of 18.8 inches, and the same height of cone is 
 retained for forming the heaped bushel. Its ratio, therefore, to the 
 even bushel is a trifle less than was that of the Winchester. In the 
 United States the " heaped bushel " is usually estimated at 5 even, 
 pecks, or as 1.25 to 1 of the standard even bushel, which, if taken as 
 
 * By enactment of the Legislature of the State of New York, this gallon ceased to be the 
 legal gallon of that State, April 11, 1852 ; and the United States Government gallon, of 231 
 cubic inches capacity, was adopted in its stead. 
 
 3* 
 
30 DRY MEASURE. 
 
 the rule, requires a cone on the Winchester measure of 5.4 inches to 
 equal the heaped Winchester bushel. 
 
 4 gills sm 1 pint. 
 
 2 pints =» 1 quart. 
 
 4 quarts . . - ^ a 
 
 or half peck. 
 8 quarts . . = " 1 peck. 
 
 4 pecks "] fl bushel. 
 
 2150.42 cubic in. ( J 2738 cyl. in. 
 
 1.244456 " ft. r — S 77.7785 av'd lbs. 
 1.5844 cyl. " J (.pure water. 
 
 Bush»l of the ) (1.28 cubic feet. 
 
 State of New York*} = I 2211.84 " in. 
 2816.1955 cyl. in. ) ( 80 av'd lbs. pure water. 
 
 ! 1.272 cubic feet. 
 2198 " in. 
 79.50 av'd lbs. pure water. 
 Heaped Win. bushel > { 2747.7 cubic in. 
 
 1.28— even" " J** \l. 59 cubic ft. 
 Imperial bushel = 2218.192 " in. 
 
 Chaldron = 36 Winch, heaped bushels. 
 
 1 Winchester bushel - i g'^ ^P erial „ bu8hel - 
 
 } 9.3092 Wine gallons. 
 
 1 Imperial bushel = 1.0315 Winchester bushels. 
 
 Note. — The Imperial bushel, mentioned above, is the present legal bushel of Great 
 Britain ; and the Imperial gallon, mentioned on the preceding page, is the present legal 
 gallon of Great Britain, for all liquids. The gallon for liquids is the same as the gallon 
 for dry measure. Eight Imperial gallons make one bushel. The subdivisions of the gal- 
 lon and the bushel, and their denominations, are the same as in the Winchester measures. 
 In Great Britain, in addition, to the denominations of dry measure used in the United 
 States, the 
 
 Strike, = 2 bushels. 
 
 Coomb, = 4 " 
 
 Quarter, = 8 " 
 
 Wey or load, = 40 " 
 
 Last, =80 bushels. 
 
 Sack of corn, = 3 " 
 
 Bole of corn, = 6 " 
 
 Last of gunpowder, . . = 42 barrels. 
 
 * This bushel ceased to be the legal bushel of this State April 11, 1852, and the United 
 States Government bushel, of 2160^^ cubic inches capacity, was adopted as the legal 
 bushel in its stead. 
 
 t This bushel is now, January, 1852, no longer the legal bushel of this State, and the 
 " Winchester bushel is adopted In its stead. 
 
SECTION II. 
 
 MISCELLANEOUS FACTS, CALCULATIONS, AND PRACTICAL 
 MATHEMATICAL DATA. 
 
 SPECIFIC GRAVITIES. 
 The specific gravity of a body is its weight relative to the weight 
 of an equal bulk of pure water at the maximum density, (39°. 83, b. 
 30 in.) the water being taken as 1., a cubic foot of which weighs 
 1000 avoirdupois ounces, or 62£ lbs. The specific gravity, therefore, 
 of any body multiplied by 1000, or, which is the same thing, the dec- 
 imal being carried to three places of figures, or thousands, as in the 
 following tables, the whole taken as an integer equals the number 
 of ounces in a cubic foot of the material : multiplied by 62.5, or con- 
 sidered an integer and divided by 16, it equals the number of pounds 
 in a cubic foot ; and multiplied by .036169, or taken as an integer 
 and divided by 27648, it equals the decimal fraction of a pound per 
 cubic inch ; by which, it is readily seen, the specific gravity of a 
 commodity being known, its weight per any given bulk is easily and 
 accurately ascertained ; as, also, its specific gravity, the weight and 
 bulk being known. The weight of any one article relative to that of 
 any other, is as its respective specific gravity to the specific gravity 
 of the other. 
 
 METALS. 
 
 Specific 
 gravity. 
 
 
 Specific 
 gravity. 
 
 Antimony, . 
 
 6.712 
 
 Gold, pure, hammerec 
 
 19.546 
 
 Arsenic, 
 
 5.810 
 
 Iridium, 
 
 15.363 
 
 Bismuth, 
 
 9.823 
 
 Iron, cast, 
 
 7.209 
 
 Bronze, 
 
 8.700 
 
 " wrought, . 
 
 7.787 
 
 Brass, best, . ■ . 
 
 8.504 
 
 Lead, 
 
 11.352 
 
 Copper, cast, 
 
 8.788 
 
 Mercury, 32°, . 
 
 13.598 
 
 " wire-drawn, 
 
 8.878 
 
 " ' 60°, . 
 
 13.580 
 
 Cadmium, . 
 
 8.604 
 
 « —39°, . 
 
 15.000 
 
 Cobalt, 
 
 7.700 
 
 Manganese, 
 
 8.013 
 
 Chromium, 
 
 5.900 
 
 Molybdenum, 
 
 8.611 
 
 Glucinium, 
 
 3.000 
 
 Nickel, 
 
 8.280 
 
 Gold, pure, cast, . 
 
 19.258 
 
 Osmium, . 
 
 10.000 
 
32 
 
 SPECIFIC GRAVITIES. 
 
 
 Speeific 
 
 
 Specific 
 
 
 parity. 
 
 
 gravity. 
 
 Platinum, cast, . 
 
 19.500 
 
 Granite, red, 
 
 2.625 
 
 " hammered, 
 
 20.337 
 
 " Lockport, 
 
 2.655 
 
 " rolled, 
 
 22.069 
 
 " Quincy, 
 
 2.652 
 
 Potassium, 60°, . 
 
 0.865 
 
 " Susquehanna, 
 
 2.704 
 
 Palladium, 
 
 11.870 
 
 Grindstone, . 
 
 2.143 
 
 Rhodium, 
 
 11.000 
 
 Gypsum, opaque, 
 Hone, white, 
 
 2.168 
 
 Silver, pure, cast, 
 
 10.474 
 
 2.876 
 
 " hammered, 
 
 10.511 
 
 Hornblende, 
 
 3.600 
 
 Sodium, 
 
 0.970 
 
 Ivory, 
 
 1.822 
 
 Steel, soft, 
 
 7.836 
 
 Jasper, 
 
 2.690 
 
 " tempered, 
 
 7.818 
 
 Limestone, green, 
 
 3.180 
 
 Tin, cast, 
 
 7.291 
 
 " white, 
 
 3.156 
 
 Tellurium, 
 
 6.115 
 
 Lime, compact, . 
 
 2.720 
 
 Tungsten, 
 
 17.600 
 
 " foliated, . 
 
 2.837 
 
 Titanium, 
 
 4.200 
 
 11 quick, 
 
 0.804 
 
 Uranium, 
 
 9.000 
 
 Loadstone, . 
 
 4.930 
 
 Zinc, cast, 
 
 6.861 
 
 Magnesia, hyd., . 
 
 2.333 
 
 
 
 Marble, common, 
 
 2.686 
 
 STONES AND EA 
 
 UTIIS. 
 
 " white Ital. 
 
 2.708 
 
 Alabaster, white, 
 
 2.730 
 
 " Rutland, Vt., 
 
 2.708 
 
 " yellow, 
 
 2.699 
 
 " Parian, . 
 
 2.838 
 
 Amber, 
 
 1.078 
 
 Nitre, crude, 
 
 1.900 
 
 Asbestos, starry, 
 
 3.073 
 
 Pearl, oriental, . 
 
 2.650 
 
 Borax, 
 
 1.714 
 
 Peat, hard, 
 
 1.329 
 
 Bone, ox, . 
 
 1.656 
 
 Porcelain, China, 
 
 2.385 
 
 Brick, 
 
 1.900 
 
 Porphyra, red, 
 
 2.766 
 
 Chalk, white, . 
 
 2.782 
 
 " green, 
 
 2.675 
 
 Charcoal, . 
 
 .441 
 
 Quartz, 
 
 2.647 
 
 " triturated, 
 
 1.380 
 
 Rock Crystal, 
 
 2.654 
 
 Cinnabar, . 
 
 7.786 
 
 Ruby, 
 
 4.283 
 
 Clay, . . 
 
 1.934 
 
 Stone, common, . 
 
 2.520 
 
 Coal, bitum. avg., 
 
 1.270 
 
 " paving, 
 
 2.416 
 
 " anth. " 
 
 1.520 
 
 " pumice, 
 
 0.915 
 
 Coral, red, 
 
 2.700 
 
 " rotten, 
 
 1.981 
 
 Earth, loose, 
 
 1.500 
 
 Salt, common, solid, 
 
 2.130 
 
 Emery, 
 
 4.000 
 
 Saltpetre, refined, 
 
 2.090 
 
 Feldspar, 
 
 2.500 
 
 Sand, dry, . 
 
 1.800 
 
 Flint, white, 
 
 2.594 
 
 Serpentine, 
 
 2.430 
 
 " black, 
 
 2.582 
 
 Shale, 
 
 2.600 
 
 Garnet, 
 
 4.085 
 
 Slate, 
 
 2.672 
 
 Glass, flint, 
 
 2.933 
 
 Spar, fluor, 
 
 3.156 
 
 " white, 
 
 2.892 
 
 Stalactite, . 
 
 2.321 
 
 " plate, 
 
 2.710 
 
 Tale, black, 
 
 2.900 
 
 " green, 
 
 2.642 
 
 Topaz, 
 
 4.011 
 
SPECIFIC GRAVITIES. 
 
 33 
 
 
 Specific 
 
 
 Specifio 
 
 
 trr*Tity. 
 
 
 gnmiy. 
 
 SIMPLE SUBSTANCE 
 
 Pine, yellow, 
 
 .568 
 
 neither metallic 
 
 ; nor gaseous. 
 
 Poplar, white, 
 
 .383 
 
 Boron, 
 
 1.968 
 
 Plum, . 
 
 .785 
 
 Biomine, 
 
 2.970 
 
 Quince, 
 
 .705 
 
 Carbon, 
 
 3.521 
 
 Spruce, white, 
 
 .551 
 
 Iodine, 
 
 4.943 
 
 Sassafras, 
 
 .482 
 
 Phosphorus, 
 
 1.770 
 
 Sycamore, 
 
 .604 
 
 Selenium, . 
 
 . * . 4.320 
 
 Walnut, 
 
 .671 
 
 Silicon, 
 
 1.184 
 
 Willow, 
 
 .585 
 
 Sulphur, 
 
 1.990 
 
 Yew, Spanish, 
 
 .807 
 
 
 
 " Dutch, 
 
 .788 
 
 WOODS, 
 
 (dry.) 
 
 
 
 Apple, 
 
 0.793 
 
 Highly seasoned Am. 
 
 Alder, 
 
 .800 
 
 Ash, white, . 
 
 .722 
 
 Ash, . 
 
 .760 
 
 Beech, 
 
 .624 
 
 Beech, 
 
 .696 
 
 Birch, 
 
 .526 
 
 Birch, 
 
 .720 
 
 Cedar, . 
 
 .452 
 
 Box, French, 
 
 1.328 
 
 Cherry, 
 
 .606 
 
 " Dutch, 
 
 .912 
 
 Cypress, 
 Elm, . 
 
 .441 
 
 Cedar, 
 
 .561 
 
 .600 
 
 Cherry, 
 
 .715 
 
 Fir, . . 
 
 .491 
 
 Chestnut, . 
 
 .610 
 
 Hickory, red, 
 
 .838 
 
 Cocoa, 
 
 1.040 
 
 Maple, hard, 
 
 .560 
 
 Cork, 
 
 .240 
 
 Oak, white, uplanc 
 
 1, . .687 
 
 Cypress, 
 
 .644 
 
 " James River, 
 
 .759 
 
 Ebony, American 
 
 1.331 
 
 Pine, yellow, 
 
 .541 
 
 " foreign, 
 
 1.290 
 
 " pitch, . 
 
 .536 
 
 Elm, . 
 
 .671 
 
 " white, 
 
 .473 
 
 Fir, yellow, 
 
 .657 
 
 Poplar, (tulip,) 
 
 .587 
 
 " white, 
 
 .569 
 
 Spruce, white, 
 
 .465 
 
 Hacmetac, . 
 
 .592 
 
 
 
 Hickory, red, 
 
 .900 
 
 GUMS, FAT 
 
 3, &C. 
 
 Lignum vitse, 
 Larch, 
 
 1.333 
 .544 
 
 Asphaltum, . 
 
 5 .905 
 ' \ 1.650 
 
 Logwood, . 
 
 .913 
 
 Beeswax, 
 
 .965 
 
 Mahogany, Spanis 
 
 h, best, 1.065 
 
 Butter, 
 
 .942 
 
 <( tt 
 
 com., .800 
 
 Camphor, 
 
 .988 
 
 " St. Dc 
 
 mingo, .720 
 
 Gamboge, 
 
 . 1.222 
 
 Maple, red, 
 
 .750 
 
 Gunpowder, . 
 
 .900 
 
 Mulberry, . 
 
 .897 
 
 " shakei 
 
 l, . 1.000 
 
 Oak, live, . 
 
 1.120 
 
 solid, 
 
 5 1.550 
 * \ 1.800 
 
 " white, 
 
 .785 
 
 Orange, 
 
 .705 
 
 Gum, Arabic, 
 
 . 1.454 
 
 Pear, 
 
 .661 
 
 " Caoutchouc, . 
 
 .933 
 
 Pine, white, 
 
 .554 
 
 " Mastic, 
 
 . 1.074 
 
34 
 
 SPECIFIC OrHAVITlES. 
 
 Honey, 
 
 Ice, . 
 
 Indigo, 
 
 Lard, 
 
 Pitch, 
 
 Rosin, 
 
 Spermaceti, 
 
 Starch, 
 
 Sugar, dry, 
 
 Tallow, 
 
 Tar, . 
 
 LIQUIDS. 
 
 Acid, acetic, 
 
 " citric, 
 
 " fluoric, 
 
 n nitric, 
 
 " nitrous, 
 
 M sulphuric, 
 
 ' ' muriatic, 
 
 u silicic, 
 Alcohol, anhyd. 
 " 90 °/ 
 Beer, 
 
 Blood, human, 
 Camphene, pure, 
 Cider, whole, 
 Ether, sulph., 
 
 " nitric, 
 Milk, cow's, 
 Molasses, 75 % 
 Oils, linseed, 
 
 " olive, 
 
 " sassafras, 
 " turpentine, com. 
 " sperm, pure, 
 " whale, pTd, 
 Proof spirits, 
 Vinegar, 
 Water, pure, 
 " sea, 
 ** Dead sea, 
 
 Specific 
 gravity. 
 
 1.450 
 
 .930 
 1.009 
 
 .941 
 1.150 
 1.100 
 
 .943 
 1.530 
 1.606 
 
 .938 
 1.015 
 
 1.062 
 
 1.034 
 
 1.060 
 
 1.485 
 
 1.420 
 
 1.846 
 
 1.200 
 
 2.660 
 
 .794 
 
 .834 
 
 1.034 
 
 1.054 
 
 .863 
 
 1.018 
 
 .715 
 
 .908 
 
 1.032 
 
 1.400 
 
 .934 
 
 .917 
 
 .927 
 
 1.090 
 
 .875 
 
 .874 
 
 .923 
 
 .925 
 
 1.025 
 
 1.000 
 
 1.026 
 
 1.240 
 
 Win 
 it 
 
 3, champagne, 
 claret, 
 
 Specific 
 gravity. 
 
 .997 
 .994 
 
 << 
 
 port, 
 sherry, 
 
 .997 
 .992 
 
 ELASTIC FLUIDS! 
 
 The measure of which is atmospheric air, 
 at 60°, b. 30 in., its assumed gravity 1 ; one 
 cubic foot of which weighs 527.04 grains, = 
 .305 of a grain per cubic inch. It is, at 
 this temperature and density, to pure water 
 at the maximum density, as .0012046 to 1, 
 or as 1 to 830.1. 
 
 SIMPLE OR ELEMENTARY GASES. 
 
 Hydrogen, 
 
 .0689 
 
 Oxygen, . 
 
 1.1025 
 
 Nitrogen, . 
 
 .9760 
 
 Fluorine, . 
 
 
 Chlorine, 
 
 2.470 
 
 Carbon, vapor of, 
 
 I .422 
 
 (tJteoretically,) 
 
 COMPOUND GASES. 
 
 Ammoniacal, . . .591 
 
 Carbonic acid, . . 1.525 
 
 " oxide, . . .763 
 
 Carbureted hydrogen, . .559 
 
 Chloro-carbonic, . 3.389 
 
 Cyanogen, . . . 1.818 
 
 I Muriatic acid gas, . 1.247 
 
 | Nitrous acid gas, . 3.176 
 
 Nitrous oxide gas, . 1.040 
 
 Olefiant, . . . .982 
 
 Phosphureted hydrogen, 1.185 
 
 Sulphureted " . 1.177 
 
 Sfam, 212° . . .484 
 
 Smoke, of wood, . .900 
 
 " of coal, . .102 
 
 Vapor, of water, . .623 
 
 " of alcohol, . 1.613 
 
 " of spirits turpentine, 5.013 
 
WEIGHT PER BUSHEL — 
 
 BARREL GALLON, < 
 
 fee. 
 
 35 
 
 Weight per Bushel (even 
 
 Winchester) of different Grains, Seeds, $c. 
 
 Articles. 
 
 
 it*. 
 
 Articles. 
 
 It.*. 
 
 Barley, (N. E. 47 lbs.) 
 
 
 48 
 
 Hemp seed, 
 
 40 
 
 Beans, 
 
 
 64 
 
 Oats, 
 
 
 32 
 
 Buckwheat, 
 
 
 46 
 
 Peas, 
 
 
 64 
 
 Blue-grass seed 
 
 
 14 
 
 Rye, . . 
 
 
 56 
 
 Corn, 
 
 
 56 
 
 Salt, T. I., 
 
 
 80 
 
 Cranberries, . 
 
 
 
 " boiled, . 
 
 
 56 
 
 Clover seed, 
 
 
 60 
 
 Timothy seed, 
 
 
 46 
 
 Dried Apples, 
 
 
 22 
 
 Wheat, . 
 
 
 60 
 
 " Peaches, 
 
 
 33 
 
 Potatoes, h'p'd, 
 
 
 60 
 
 Flaxseed, (N. E. 52 lbs.) 
 
 
 56 
 
 
 
 Weight per Barrel (L 
 
 ega 
 
 I or by Usage) of different 
 
 Articles. 
 
 Flour, . % . 
 
 196 lbs. 
 
 Cider, in Mass., 
 
 32 gals. 
 
 Boiled Salt, . . 5 
 
 180 
 
 <« 
 
 Soap, 
 
 256 lbs. 
 
 Beef, I 
 
 SOO 
 
 it 
 
 Raisins, . 
 
 112 " 
 
 Pork, 5 
 
 !00 
 
 H 
 
 Anchovies, 
 
 30 " 
 
 Pickled Fish, . . fi 
 
 !00 
 
 (( 
 
 Lime, 
 
 
 " " in > 
 
 Massachusetts, } 
 
 30 
 
 gls. 
 
 Ground Plaster, 
 
 
 Hydraulic Cement, . 
 
 300 " 
 
 A Gallon of Train Oil weighs . . . 7f lbs. 
 A " " Molasses, standard, (75 per cent.,) 11| " 
 
 A Puncheon of Prunes, 
 
 A Firkin of Butter, (legal,) 
 
 A Keg of powder, .... 
 
 A Hogshead of Salt is 
 
 A Perch of Stone = 24i| cubic feet. 
 
 A Gallon of Alcohol, 90 per cent., weighs 
 
 8 bush. 
 
 6.965 lbs. 
 
 7.732 
 
 8.3 
 
 7.33 
 
 7.71 
 
 7.66 
 
 7.31 
 
 7.21 
 
 Weight of Coals, djrc, broken to the medium size, per Measure of 
 Capacity. 
 
 The average weight of Bituminous Coals, broken as above, is about 
 62 per cent, that of a bulk of equal dimensions in the solid mass, or 
 
 A 
 A 
 A 
 A 
 
 
 " Proof Spirits, 
 " Wine, (average,) 
 " Sperm Oil, 
 " Whale " p'f 'd, 
 
 A 
 
 <( 
 
 " Olive " 
 
 A 
 A 
 
 
 11 Spirits Turpentine, 
 " Camphene, pure, 
 
 1120 
 56 
 25 
 
ROPES AND CABLES. 
 
 of the specific gravity of the article ; that of Anthracite is about 
 5 7 per cent 
 
 Arerage weight t 
 peroubio foot. ) lbf. 
 
 Average weight per J 
 W. Coal buabel. J 
 
 lb*. 
 
 Anthracite, ... 54 
 
 Anthracite, 
 
 86 
 
 Bituminous, ... 50 
 
 Bituminous, 
 
 80 
 
 Charcoal, of pine, . . 18.6 
 
 Charcoal, hard wood, 
 
 " of hardwood,. 19.02 
 
 Coke, best, 
 
 . . . 32 
 
 Practical Approximate Weight in Pounds of Various Articles. 
 
 Sand, dry, per cubic foot, 
 
 95 
 
 Clay, compact, per cubic foot, 
 
 135 
 
 Granite, " " " . 
 
 165 
 
 Lime, quick, " " " . 
 
 50 
 
 Marble, " " " 
 
 . - 169 
 
 Slate, " " " 
 
 167 
 
 Peat, hard, " « " . 
 
 83 
 
 Seasoned Beech Wood, per cord, . 
 " Yellow Birch Wood, per cord, 
 
 5616 
 
 4736 
 
 " Red Maple Wood, " " . 
 
 5040 
 
 « " Oak Wood, " " 
 
 6200 
 
 " White Pine Wood, " " 
 
 4264 
 
 " Hickory Wood, " " 
 
 6960 
 
 " Chestnut Wood, 
 
 U ii 
 
 4880 
 
 '? 
 
 Meadow Hay, well settled, per cubic foot, 8J lbs., or 
 240 cubic feet = 2000 lbs., or 268 T ^ cubic feet 
 =. 1 long ton 
 
 Meadow Hay, in large old stacks, per cubic foot, 
 
 Clover Hay, in settled bulk, " " " 
 
 Corn on Cob, in crib, 
 " shelled, in bin, 
 
 Wheat, in bin, 
 
 Oats, in bin, 
 
 Potatoes, in bin, 
 
 Common Brick, 7| X 3f X 2£ in. 
 
 Front " 8XHX2| in. 
 
 ROPES AND CABLES. 
 
 The strength of cords depends somewhat upon the fineness of 
 the strands ; — damp cordage is stronger than dry, and untarred 
 stonier than tarred ; but the latter is impervious to water and less 
 elastic. 
 
 Silk cords have three times the strength of those of flax of 
 equal circumference, and Manilla has about half that of hemp. 
 
 it (( 
 
 U 
 
 22 
 
 u u 
 
 M 
 
 45 
 
 (« u 
 
 tt 
 
 48 
 
 ({ it 
 
 u 
 
 25 
 
 (( (t 
 
 u 
 
 38, 
 
 » M, . 
 
 . 
 
 4500 
 
 U If 
 
 . 
 
 6185 
 
WEIGHT AND STRENGTH OF IKON CHAINS. 
 
 87 
 
 Ropes made of iron wire are full three times stronger than those 
 of hemp of equal circumference. 
 
 White ropes are found to be most durable. The best qualities of 
 hemp are — 1. pearl gray; 2. greenish; 3. yellow. A brown color 
 has less strength. 
 
 The breaking weight of a good hemp rope is 6400 lbs. per square 
 inch, but no cordage may be counted on with safety as capable of sus- 
 taining a weight or strain above half that required to break it, and 
 the weight of the rope itself should be included in the estimate. 
 
 The reliable strength of a good hemp cable, in pounds, is usually 
 estimated as equal to the square of its circumference in inches X by 
 120. That of rope X 200. Thus, a cable of 9 inches in circumfer- 
 ence may be relied on as having a sustaining power = 9 X 9 X l20 
 = 9720 lbs. 
 
 The weight, in pounds, of a cable laid rope, per linear foot = the 
 square of its circumference in inehes X -036, very nearly. 
 
 The weight, in pounds, of a linear foot of manilht, rope— the 
 square of its circumference in inches X -03, very nearly. Thus, a 
 man ilia rope of three inches circumference weighs per linear foot 
 3 X 3 X 03 = -fJv lbs., = 3^ feet per lb. 
 
 A good hemp rope stretches about £, and its diameter is diminished 
 about £ before breaking. 
 
 WEIGHT AND STRENGTH OF IRON CHAINS. 
 
 Diameter of 
 
 Wire 
 in Inches. 
 
 Weight of 
 
 lFoot 
 
 of Chain. 
 
 Breaking 
 Weight 
 of Chain. 
 
 Diameter of 
 
 Wire 
 in Inehes. 
 
 Weight of 
 lFoot 
 of Chain. 
 
 Breaking 
 Weight 
 of Chain. 
 
 
 lbs. 
 
 lbs. 
 
 
 lbs. 
 
 lbs. 
 
 A 
 
 0.325 
 
 2240 
 
 1 
 
 4.217 
 
 26880 
 
 i 
 
 0.65 
 
 4256 
 
 « 
 
 4.833 
 
 32704 
 
 A 
 
 0.967 
 
 6720 
 
 f 
 
 5.75 
 
 38752 
 
 1 
 
 1.383 
 
 9634 
 
 if 
 
 6.667 
 
 45696 
 
 7 
 TS 
 
 1.767 
 
 13216 
 
 i 
 
 7.5 
 
 51744 
 
 i 
 
 2.633 
 
 17248 
 
 « 
 
 9.333 
 
 58464 
 
 * 
 
 3.333 
 
 21728 
 
 1 
 
 10.817 
 
 65632 
 
38 
 
 COMPARATIVE WEIGHT OF METALS. 
 
 Comparative Weight of Metals, Weight per Measure of Solidity, $c 
 
 
 Specific 
 
 Ratio of 
 
 Pounris 
 
 n a Cubic 
 
 Iron, wrought or rolled, 
 
 Gravity. 
 
 Comparison 
 
 Foot. 
 
 Inch. 
 
 7.787 
 
 1. 
 
 486.65 
 
 .28163 
 
 Cast Iron, 
 
 7.209 
 
 .9258 
 
 450.55 
 
 .26073 
 
 Steel, soft, rolled, . 
 
 7.836 
 
 1.0064 
 
 489.75 
 
 .28342 
 
 Copper, pure, " 
 
 8.878 
 
 1.1401 
 
 554.83 
 
 .32110 
 
 Brass, best, " 
 
 8.604 
 
 1.1050 
 
 537.75 
 
 .3112 
 
 Bronze, gun metal, . 
 
 8.700 
 
 1.1173 
 
 543.75 
 
 .31464 
 
 Lead, .... 
 
 11.352 
 
 1.4579 
 
 709.50 
 
 .4106 
 
 TABLE, 
 
 Exhibiting the Weight in pounds of One Foot in Length of Wrought 
 or Rolled Iron of any size, {cross section,) from ft inch to 12 inches. 
 
 SQUARE BAR. 
 
 Size 
 
 Weight 
 
 Size 
 
 Weight 
 
 Size 
 
 Weight 
 
 Size 
 
 Weight 
 
 Inches. 
 1 
 
 in 
 
 Pounds. 
 
 Inches. 
 
 2& 
 
 in 
 Pound*. 
 
 in 
 
 Inches. 
 
 in 
 Pounds. 
 
 Inch**. 
 
 Pounds. 
 
 .053 
 
 19.066; 
 
 41 
 
 72.305 
 
 71 
 
 203.024 
 
 1 
 
 .211 
 
 24 
 
 21.120 
 
 4| 
 
 76.264 
 
 8 
 
 216.336 
 
 1 
 
 .475 
 
 81 
 
 23.292 
 
 4ft 
 
 80.333 
 
 H 
 
 230.068 
 
 1 
 
 .8-15 
 
 2| 
 
 25.560; 
 
 5 
 
 84.480 
 
 84 
 
 214.220 
 
 1 
 
 1.320 
 
 2* 
 
 27.939, 
 
 5ft 
 
 88.784 
 
 81 
 
 258.800 
 
 1 
 
 1.901 
 
 3 
 
 30.416, 
 
 H 
 
 93.168 
 
 9 
 
 273.792 
 
 I 
 
 2.588 
 
 3ft 
 
 33.010. 
 
 58 
 
 97.657 
 
 9* 
 
 289.220 
 
 
 3.380 
 
 H 
 
 35.704 1 
 
 ' 54 
 
 102.240 
 
 94 
 
 305.056 
 
 11 
 
 4.278 
 
 3S 
 
 38.503, 
 
 5& 
 
 106.953 
 
 0| 
 
 321.332 
 
 n 
 
 5.280 
 
 34 
 
 41.408 
 
 5| 
 
 111.756 
 
 10 
 
 337.920 
 
 it 
 
 6.390 
 
 3& 
 
 44.418 
 
 5* 
 
 116.671 
 
 10.1 
 
 355.136 
 
 u 
 
 7.604 
 
 31 
 
 47.534 
 
 6 
 
 121.664 
 
 104 
 
 373.679 
 
 it 
 
 8.926 
 
 3* 
 
 50.756 
 
 6i 
 
 132.040 
 
 10| 
 
 390.628 
 
 ii 
 
 10.352 
 
 4 
 
 54.084 
 
 64 
 
 142.816 
 
 n 
 
 408.960 
 
 ii 
 
 11.883 
 
 4ft 
 
 57.517 
 
 63 
 
 151.012 
 
 Hi 
 
 427.812 
 
 2 
 
 13.520 
 
 H 
 
 61.055 
 
 7 
 
 165.632 
 
 ii4 
 
 117.024 
 
 24 
 
 15.263 
 
 4& 
 
 64.700 
 
 7| 
 
 177.672 
 
 ill 
 
 166. 084 
 
 n 
 
 17.112 
 
 44 
 
 68.448 
 
 U 
 
 190.136 
 
 12 
 
 486.656 
 
COMPARATIVE WEIGHT OF METALS. 39 
 
 To determine the weight, in pounds, of one foot in length, or of any 
 length, of a bar of any of the following metals of form prescribed, of 
 any size, multiply the weight in pounds, of an equal length of square 
 rolled iron of the same size, (see table of square rolled iron,) if the 
 weight be sought of 
 
 Iron, Round rolled, by 7854 
 
 Steel, Square " " 1.0064 
 
 Round " " 7904 
 
 Cast Iron, Square bar, " 9258 
 
 " " Round " " 7271 
 
 Copper, Square rolled, " 1.1401 
 
 " Round " " 8954 
 
 Brass, Square " " 1.105 
 
 " Round " " 8679 
 
 Bronze, Square bar, " 1.1173 
 
 " Round " " 8775 
 
 Lead, Square " " 1.4579 
 
 Round " " 1.145 
 
 The weight of a bar of any metal, or other substance, of any given 
 length, of a flat form, (and any other form maybe included in the 
 rule,) is readily obtained by multiplying its cubic contents (feet or 
 inches) by the weight (pounds, ounces, or grains) of a cubic foot or 
 inch of the article sought to be weighed ; that is — 
 
 Length X breadth X thickness X weight per unit of measure. 
 
 For the weight in pounds of a cubic foot or inch of different metals, 
 see " Table of weights of metals per measure of solidity, &c„" 
 
 • OR, FOR FLAT OR SQUARE BARS, 
 
 Multiply the sectional area in inches by the length in feet, and that 
 product, if the metal be 
 
 Wrought Iron, by 3.3795 
 
 Cast " " 3.1287 
 
 Steel, " . ' 3.4 
 
 Example. — Required the weight of a bar of #teel, whose length is 
 7 feet, breadth 2£ inches, and thickness £ of an inch. 
 
 2.5 X .75 X 7 X 3.4 = 44.625 lbs. Ans. 
 
 Example. — Required the weight of a cast iron beam, whose length 
 is 14 leet, breadth 9 inches, and thickness 14 inch. 
 
 14 X 9 X 1-5 X 3.1287 = 591.32 lbs. Ans. 
 
40 
 
 WEIGHT OF ROUND ROLLED IRON, 
 
 TABLE, 
 
 Exhibiting the weight in pounds of One Foot in Length of Round Rolled 
 Iron of any diameter , from J inch to 12 inches. 
 
 Diameter 
 
 Weight 
 
 Diana, in 
 
 Weight 
 
 Diam. in 
 
 Weight 
 
 Diam. in 
 
 Weight 
 
 in inches. 
 
 in lbs. 
 
 inches. 
 
 in lbs. 
 
 inches. 
 
 in lbs. 
 
 inches. 
 
 i in lbs. 
 
 1 
 
 ^041 
 
 2| 
 
 14.975 
 
 4| 
 
 56,788 
 
 71 
 
 159.456 
 
 1 
 
 ,165 
 
 24 
 
 16.688 
 
 41 
 
 59.900 
 
 8 
 
 169.S56 
 
 1 
 
 ,373 
 
 2| 
 
 18.293 
 
 ±1 
 
 63.094 
 
 H 
 
 180.696 
 
 4 
 
 .663 
 
 23 
 
 20.076 
 
 5 
 
 66.752 
 
 4 
 
 191.808 
 
 I 
 
 1.043 
 
 2& 
 
 21.944 
 
 51 
 
 69,731 
 
 H 
 
 208.260 
 
 i 
 
 1.493 
 
 3 
 
 23.888 
 
 H 
 
 73,172 
 
 9 
 
 215.040 
 
 I 
 
 2.032 
 
 H 
 
 25,926 
 
 51 
 
 76.700 
 
 n 
 
 227.152 
 
 i •! 
 
 2,654 
 
 n 
 
 28.040 
 
 54 
 
 80.304 
 
 % 
 
 239.600 
 
 I| 
 
 3,360 
 
 H 
 
 30.240 
 
 H 
 
 84.001 
 
 91 
 
 252.376 
 
 11 
 
 4.172 
 
 4 
 
 32.512 
 
 51 
 
 87.776 
 
 10 
 
 266.288 
 
 If 
 
 5.019 
 
 3| 
 
 34.886 
 
 &l 
 
 91.634 
 
 101 
 
 278.924 
 
 4 
 
 5.972 
 
 3| 
 
 37.332 
 
 6 
 
 95,552 
 
 m 
 
 292.688 
 
 it 
 
 7.010 
 
 *1 
 
 39.864 
 
 H 
 
 103,704 
 
 101 
 
 306.800 
 
 ii 
 
 8.128 
 
 4 
 
 42.464 
 
 64 
 
 112.160 
 
 11 
 
 321.216 
 
 U 
 
 9.333 
 
 4| 
 
 45.174 
 
 61 
 
 120.960 
 
 III 
 
 336.004 
 
 2 
 
 10.616 
 
 U 
 
 47.952 
 
 7 
 
 130.048 
 
 Hi 
 
 351.104 
 
 2* 
 
 11.988 
 
 M 
 
 50.815 
 
 7i 
 
 139.544 
 
 ill 
 
 366.536 
 
 1 2| 
 
 13.440 
 
 *h 
 
 53.760 
 
 74 
 
 149.328 
 
 12 
 
 382.208 
 
 To find the weight of an equilateral three-sided cast iron prism. 
 width of side m inches X !• 354 X length in feet = weight in lbs. 
 
 Example. — A three-&ided cast iron prism is 14 feet m length, and 
 the width of each Bide is 6 inches ; required the weight of the prism. 
 
 6 2 X 1.354 X 14 = 682.4 lbs. Ans. 
 To find the weight of an equilateral rectangular cast iron prism. 
 
 width of side in inches" X 3.128 X length in feet = weight in lbs. 
 To find the weight of an equilateral five-sided cast iron prism. 
 
 width of side in inches 2 X 5.381 X length in feet = weight in lbs. 
 To find the weight of an equilateral six-sided cast iron prism. 
 
 width of side in inches 2 X 8.128 X length in feet = weight in lbs. 
 To find the weight of an equilateral eight-sided cast iron prism. 
 
 width of side in inches 2 X 15-1 X length in feet = weight in lbs. 
 
 To find the weight of a cast iron cylinder. 
 
 diameter in inches 2 X 2.457 X length in feet = weight in lbs. 
 
 In a quantity of cast iron weighing 125 lbs., how many cubic 
 inches ? 
 
 By tabular weight per cubic inch — 
 
 125 -j- .26073 =* 479.4 cubic inches. An*. 
 
RELATING TO CAST IRON. 41 
 
 Or, by tabular weight per cubic foot — 
 
 450.55 : 1728 : : 125 : 479.4 cubic inches. Ans. 
 How many cubic inches of copper will weigh as much as 479.4 
 cubic inches of cast iron ? 
 
 By tabular weight per cubic inch — 
 
 .3211 : .2G073 : : 479.4 : 389.27 cubic inches. Ans. 
 Or, by specific gravities — 
 
 8.878 : 7.209 : : 479.4 : 389.27 cubic inches. Ans. 
 Or, by tabular ratio of weight — 
 .9258 
 479.4 x 1J401 - 389.28. 
 
 A cast ircn rectangular weight is to be constructed having a 
 breadth of 4 inches and a thickness of 2 inches, and its weight is 
 to be 18 lbs. ; what must be its length ? 
 18 
 4X2X.20073 =as8 - 63inches - Ans ' 
 A cast iron cylinder is to be 2 inches in diameter, and is to weigh 
 
 6 lbs. ; what must be its length ? 
 
 .26073 X .7854 =.2047 lb. — weight of 1 cyl. inch, then 
 /» 
 
 2^X.2047 =7 - 327iDCheS - AnS - 
 A cast iron cylinder is to weigh 6 lbs., and its length is to bo 
 7.327 inches ; what must be its diameter? 
 
 **( 7.327 X .2047 ) = 2 inches. Ans. ' 
 
 A cast iron weight, in the form of a prismoid, or the frustrum of 
 a pyramid, or the frustrum of a cone, is to be constructed that will 
 weigh 14 lbs., and the area of one of the bases is to be 16 inches, 
 and that of the other 4 inches ; what must be the length of tho 
 weight ? 
 
 14 
 
 ^/IG X4 = 8and8-fl6-f-4-h3 = 9.33, and 9 33 x 26073 
 ■be 5.75 inches. Ans. ' 
 
 Note. — For Rules in detail pertaining to the foregoing, see Geometrt, Mensuration 
 of superficies — of solids. 
 
 A model for a piece of casting, made of dry white pine, weighs 
 
 7 lbs. ; what will the casting weigh, if made of common brass ? 
 By specific gravities — 
 
 .554 : 8.604 : : 7 : 108.71 lbs. Ans. 
 
 Note. — As the specific gravity of the substance of which the model is composed must 
 generally remain to some extent uncertain, calculations of this kind can only be relied on 
 as approximate. 
 
 4* 
 
TABLE 
 
 Exhibiting the Weight of One Foot in Length of Flat, Rolled Iron; 
 Breadth and Thickness in Inches, Weight in Pounds. 
 
 Br. and Th. 
 
 Wei't. 
 
 Br. and Th. 
 
 Wei't. 
 
 Br. and Th. 
 
 Wei't. 
 
 Br. and Th. 
 
 WeFt. 
 
 inch. 
 
 
 lbs. 
 
 inch. 
 
 lbs. 
 
 inch. 
 
 lbs. 
 
 inch. 
 
 lbs. 
 
 h by 
 
 1 
 
 .211 
 
 H by | 
 
 3.696 
 
 11 by h 
 
 2.957 
 
 2J by & 
 
 3.591 
 
 
 | 
 
 .422 
 
 1 
 
 4.224 
 
 1 
 
 3.696 
 
 | 
 
 4.488 
 
 
 i 
 
 .634 
 
 n 
 
 4.752 
 
 i 
 
 4.435 
 
 % 
 
 5.386 
 
 t by 
 
 \ 
 
 .264 
 
 n by | 
 
 .581 
 
 1 
 
 6.175 
 
 i 
 
 6.284 
 
 
 I 
 
 .528 
 
 i 
 
 1.161 
 
 1 
 
 5.914 
 
 1 
 
 7.181 
 
 
 I 
 
 .792 
 
 § 
 
 1.742 
 
 n 
 
 6.653 
 
 1| 
 
 8.079 
 
 
 I 
 
 1.056 
 
 I 
 
 2.323 
 
 n 
 
 7.393 
 
 14 
 
 8.977 
 
 1 by 
 
 1 
 
 .316 
 
 1 
 
 2.904 
 
 n 
 
 8.132 
 
 l| 
 
 9.874 
 
 
 i 
 
 .633 
 
 1 
 
 3.485 
 
 n 
 
 8.871 
 
 1| 
 
 10.772 
 
 
 1 
 
 .950 
 
 I 
 
 4.066 
 
 n 
 
 9.610 
 
 H by I 
 
 .960 
 
 
 I 
 
 1.267 
 
 1 
 
 4.647 
 
 n by 4 
 
 .792 
 
 i 
 
 1.901 
 
 
 | 
 
 1.584 
 
 n 
 
 5.228 
 
 1 
 
 1.584 
 
 1 
 
 2.851 
 
 i by 
 
 i 
 
 .369 
 
 n 
 
 5.808 
 
 1 
 
 2.376 
 
 | 
 
 3.802 
 
 
 i 
 
 .739 
 
 U by J 
 
 .634 
 
 i 
 
 3.168 
 
 
 4.752 
 
 
 i 
 
 1.108 
 
 i 
 
 1.267 
 
 § 
 
 3.960 
 
 | 
 
 5.703 
 
 
 i 
 
 1.478 
 
 i 
 
 1.901 
 
 \ 
 
 4.752 
 
 | 
 
 6.653 
 
 
 i 
 
 1.848 
 
 1 
 
 2.534 
 
 i 
 
 5.544 
 
 1 
 
 7.604 
 
 
 i 
 
 2.218 
 
 1 
 
 3.168 
 
 i 
 
 6.336 
 
 n 
 
 8.554 
 
 1 by 
 
 i 
 
 .422 
 
 1 
 
 3.802 
 
 n 
 
 7-129 
 
 H 
 
 9.505 
 
 
 i 
 
 .845 
 
 I 
 
 4.435 
 
 n 
 
 7.921 
 
 n 
 
 10.455 
 
 
 l 
 
 1.267 
 
 1 
 
 5.069 
 
 n 
 
 8.713 
 
 n 
 
 11.406 
 
 
 i 
 
 1.690 
 
 11 
 
 5.703 
 
 H 
 
 9.505 
 
 n 
 
 12.356 
 
 
 i 
 
 2.112 
 
 H 
 
 6.337 
 
 If 
 
 10.297 
 
 n 
 
 13.307 
 
 
 1 
 
 2.534 
 
 11 
 
 6.970 
 
 11 
 
 11.089 
 
 21 by J 
 
 1.003 
 
 
 i 
 
 2.957 
 
 H by i 
 
 .686 
 
 2 by * 
 
 .845 
 
 i 
 
 2.006 
 
 H by 
 
 i 
 
 .475 
 
 i 
 
 1.373 
 
 l 
 
 1.690 
 
 
 3.010 
 
 
 I 
 
 .950 
 
 i 
 
 2.069 
 
 1 
 
 2.534 
 
 i 
 
 4.013 
 
 
 I 
 
 1.425 
 
 I 
 
 2.746 
 
 i 
 
 3.379 
 
 1 
 
 6.016 
 
 
 i 
 
 1.901 
 
 i 
 
 3.432 
 
 
 4.224 
 
 i 
 
 6.019 
 
 
 i 
 
 2.376 
 
 i 
 
 4.119 
 
 I 
 
 5.069 
 
 i 
 
 7.023 
 
 
 : i 
 
 2.851 
 
 1 
 
 4.805 
 
 i 
 
 5.914 
 
 i 
 
 8.026 
 
 
 I 
 
 3.326 
 
 l 
 
 5.492 
 
 1 
 
 6.759 
 
 n 
 
 9.029 
 
 
 i 
 
 8.802 
 
 U 
 
 6.178 
 
 IS 
 
 7.604 
 
 n 
 
 10.032 
 
 U by 
 
 j 
 
 .528 
 
 n 
 
 6.864 
 
 H 
 
 8.449 
 
 ii 
 
 11.036 
 
 
 i 
 
 1.056 
 
 IS 
 
 7.551 
 
 l| 
 
 9.294 
 
 n 
 
 12.089 
 
 
 .2 
 
 1.684 
 
 n 
 
 8.237 
 
 U 
 
 10.138 
 
 n 
 
 13.042 
 
 
 1 
 
 2.112 
 
 H by J 
 
 .739 
 
 2» by J 
 
 .898 
 
 n 
 
 14.046 
 
 
 1 
 
 2.640 
 
 i 
 
 1.478 
 
 \ 
 
 1.796 
 
 2 
 
 16.052 
 
 
 1 
 
 8.168 
 
 i 
 
 2.218 
 
 I 
 
 2.698 
 
 2* by i 
 
 1.056 
 
WEIGHT OF FLAT, ROLLED IRON. 
 
 TABLE. — Continued. 
 
 43 
 
 Br. andTh 
 
 Weight. 
 
 Br. and Th 
 
 Weight. 
 
 Br. and Th. 
 
 Weight. 
 
 Br. and Th. 
 
 Weight. 
 
 inch. 
 
 lbs. 
 
 inch. 
 
 I*. 
 
 inch. 
 
 lbs. 
 
 inch. 
 
 lbs. 
 
 24 by i 
 
 2.112 
 
 21 by 1| 
 
 16.264 
 
 34 by | 
 
 6.865 
 
 8| by 1| 
 
 20.694 
 
 I 
 
 3.168 
 
 n 
 
 17.426 
 
 1 
 
 8.238 
 
 U 
 
 22.178 
 
 h 
 
 4.224 
 
 2 
 
 18.587 
 
 I 
 
 9.610 
 
 n 
 
 23.762 
 
 1 
 
 5.280 
 
 at 
 
 19.749 
 
 1 
 
 10.983 
 
 2 
 
 25.347 
 
 1 
 
 6.336 
 
 24 
 
 20.911 
 
 « 
 
 12.356 
 
 24 
 
 28.515 
 
 i 
 
 7.393 
 
 2} by i 
 
 1.214 
 
 li 
 
 13.729 
 
 2i 
 
 81.683 
 
 1 
 
 8.449 
 
 i 
 
 2.429 
 
 18 
 
 15.102 
 
 21 
 
 34.851 
 
 n 
 
 9.505 
 
 s 
 
 3.644 
 
 li 
 
 16.475 
 
 4 by J 
 
 1.690 
 
 14 
 
 10.561 
 
 i 
 
 4.858 
 
 U 
 
 17.848 
 
 4 
 
 3.379 
 
 18 
 
 11.617 
 
 § 
 
 6.073 
 
 11 
 
 19.221 
 
 i 
 
 6.759 
 
 li 
 
 12.673 
 
 1 
 
 7.287 
 
 11 
 
 20.594 
 
 1 
 
 10.139 
 
 1| 
 
 13.729 
 
 I 
 
 8.502 
 
 2 
 
 21.967 
 
 l 
 
 13.518 
 
 11 
 
 14.785 
 
 1 
 
 9.716 
 
 21 
 
 24.713 
 
 14 
 
 16.898 
 
 H 
 
 15.841 
 
 1* 
 
 10.931 
 
 2i 
 
 27.459 
 
 li 
 
 20.277 
 
 2 
 
 16.898 
 
 14 
 
 12.145 
 
 3i by J 
 
 1.478 
 
 it 
 
 23.657 
 
 2| by k 
 
 1.109 
 
 11 
 
 13.360 
 
 i 
 
 2.957 
 
 2 
 
 27.036 
 
 4 
 
 2.218 
 
 11 
 
 14.574 
 
 § 
 
 4.436 
 
 24 
 
 30.416 
 
 1 
 
 8.327 
 
 if 
 
 15.789 
 
 i 
 
 5.914 
 
 2i 
 
 33.795 
 
 4 
 
 4.436 
 
 11 
 
 17.003 
 
 & 
 
 7.393 
 
 21 
 
 37.175 
 
 I 
 
 5.545 
 
 n 
 
 18.218 
 
 1 
 
 8.871 
 
 3 
 
 40.555 
 
 i 
 
 6.653 
 
 2 
 
 19.432 
 
 $ 
 
 10.350 
 
 34 
 
 43.934 
 
 I 
 
 7.762 
 
 2J 
 
 20.647 
 
 1 
 
 11.828 
 
 41 by ft 
 
 1.795 
 
 1 
 
 8.871 
 
 2* 
 
 21.861 
 
 H 
 
 13.307 
 
 k 
 
 8.591 
 
 U 
 
 9.980 
 
 3 by i 
 
 1.267 
 
 ii 
 
 14.785 
 
 i 
 
 7.181 
 
 u 
 
 11.089 
 
 4 
 
 2.535 
 
 ii 
 
 16.264 
 
 1 
 
 10.772 
 
 If 
 
 12.198 
 
 & 
 
 3.802 
 
 ii 
 
 17.748 
 
 1 
 
 14.363 
 
 1J 
 
 13.307 
 
 i 
 
 5.069 
 
 it 
 
 19.221 
 
 14 
 
 17.954 
 
 it 
 
 14.416 
 
 | 
 
 6.337 
 
 li 
 
 20.700 
 
 li 
 
 21.544 
 
 15 
 
 15.525 
 
 | 
 
 7.604 
 
 li 
 
 22.178 
 
 H 
 
 25.135 
 
 li 
 
 16.034 
 
 J 
 
 8.871 
 
 2 
 
 23.657 
 
 2 
 
 28.726 
 
 2 
 
 17.742 
 
 1 
 
 10.139 
 
 21 
 
 26.614 
 
 24 
 
 32.317 
 
 2J 
 
 18.851 
 
 li 
 
 11.406 
 
 2i 
 
 29.571 
 
 2i 
 
 35.908 
 
 2| by J 
 
 1.162 
 
 H 
 
 12.673 
 
 2% 
 
 32.528 
 
 21 
 
 39.498 
 
 4 
 
 2.323 
 
 11 
 
 13.941 
 
 3| by | 
 
 1.584 
 
 3 
 
 43.089 
 
 1 
 
 3.485 
 
 ii 
 
 15.208 
 
 1 
 
 3.168 
 
 34 
 
 46.680 
 
 4 
 
 4.647 
 
 it 
 
 16.475 
 
 i 
 
 4.752 
 
 3i 
 
 50.271 
 
 s 
 
 5.808 
 
 11 
 
 17.743 
 
 i 
 
 6.337 
 
 4i by i 
 
 3.802 
 
 I 
 
 6.970 
 
 ii 
 
 19.010 
 
 I 
 
 7.921 
 
 i 
 
 7.604 
 
 I 
 
 8.132 
 
 21 
 
 20.277 
 
 1 
 
 9.505 
 
 1 
 
 11.406 
 
 1 
 
 9.294 
 
 2 
 
 22.812 
 
 £ 
 
 11.089 
 
 1 
 
 15.208 
 
 11 
 
 10.455 
 
 24 
 
 25.345 
 
 1 
 
 12.673 
 
 14 
 
 19.010 
 
 li 
 
 11.617 
 
 31 by a 
 
 1.373 
 
 li 
 
 14.257 
 
 li 
 
 22.812 
 
 11 
 
 12.779 
 
 4 
 
 2.746 
 
 U 
 
 15.842 
 
 11 
 
 26.614 
 
 li 
 
 13.940 
 
 1 
 
 4.119 
 
 If 
 
 17.426 
 
 2 
 
 30.416 
 
 It 
 
 15.102 
 
 i 
 
 5.492 
 
 li 
 
 19.010 
 
 24 
 
 34.218 
 
44 
 
 WEIGHT OF FLAT, ROLLED IRON. 
 TABLE. — Continued. 
 
 Br. and Th. 
 
 Weight. 
 
 Br. and Th.j Weight. 
 
 Br. and Th. 
 
 Weight. 
 
 Br. and Th. 
 
 Weight. 
 
 inch. 
 
 lbs. 
 
 inch. lbs. 
 
 inch. 
 
 lbs. 
 
 inch. 
 
 lbs. 
 
 44 by 24 
 
 38.020 
 
 4| by 3 ,48.158 
 
 51 by | 
 
 13.307 
 
 54 by 2 
 
 37.175 
 
 2| 
 
 U.822 
 
 3i;52.172 
 
 1 
 
 17'. 743 
 
 24 
 
 46.469 
 
 3 
 
 46.624 
 
 3^ 56.185 
 
 li 
 
 22.178 
 
 3 
 
 55.762 
 
 H 
 
 49.426 
 
 5 by i 4.224 
 
 u 
 
 26.614 
 
 51 by i 
 
 4.858 
 
 H 
 
 53.228 
 
 4 8.449 
 
 11 
 
 31.049 
 
 4 
 
 9.716 
 
 4| by i 
 
 4.013 
 
 112.673 
 
 2 
 
 35.485 
 
 I 
 
 14.674 
 
 4 
 
 8.026 
 
 1 16.898 
 
 • 21 
 
 39.921 
 
 1 
 
 19.482 
 
 \ 
 
 12.040 
 
 14 '21. 122 
 
 2* 
 
 44.856 
 
 Vi 
 
 24.290 
 
 1 
 
 16.053 
 
 14 25.347 
 
 3 
 
 53.228 
 
 14 29.146 
 
 14 
 
 20.006 
 
 11 29.571 
 
 54 by 1 
 
 4.647 
 
 11 
 
 34.007 
 
 1| 
 
 24.079 
 
 2 33.795 
 
 4 
 
 9.294 
 
 2 
 
 38.865 
 
 1| 
 
 28.092 
 
 2\ 38.020 
 2| 42.244 
 
 1 
 
 13.941 
 
 24 
 
 43.723 
 
 2 
 
 32.106 
 
 1 
 
 18.587 
 
 24 
 
 48.581 
 
 H 
 
 36.119 
 
 3 46.469 
 
 li 
 
 23.234 
 
 3 
 
 58.297 
 
 24 
 
 40.132 
 
 64. by 4 4.436 
 
 Id 
 
 27.881 
 
 6 by 4 
 
 5.069 
 
 n 
 
 44.145 
 
 4! 8.871 
 
 13 
 
 32.528 
 
 
 
 WEIGHT OF METALS IN PLATE. 
 The weight of a square foot one inch thick of 
 
 Malleable Iron 
 
 = 40.554 lbs. 
 
 Com. plate " 
 Cast Iron 
 
 = 37.761 " 
 
 = 37.546 " 
 
 Copper, wrought . 
 
 = 46.240 " 
 
 " com. plate . 
 
 = 45.312 " 
 
 Brass, plate, com. . 
 
 = 42.812 " 
 
 Zinc, cast, pure 
 
 = 35.734 " 
 
 " sheet . 
 
 = 37.448 " 
 
 Lead, cast 
 
 = 59.125 " 
 
 And for any other thickness, greater or less, it is the same in pro- 
 portion ; thus, a square foot of sheet copper ^ of an inch thick 
 = 46.24-^16 = 2.89 lbs. And 5 square feet at that thickness 
 = 2.89 X 5= 14.45 lbs., &c. So, too, 5 square feet at 2J inches 
 thickness = 46.24 X 2.5 X 5 = 578 lbs. 
 
AMERICAN WIRE GAUGE. 
 
 45 
 
 THE AMERICAN WIRE GAUGE. 
 
 The American Wire Gauge was prepared by Messrs. Brown and 
 Sharp, manufacturers of machinists' tools, Providence, R. I. It is 
 graded upon geometrical principles, is rapidly becoming the stand- 
 ard gauge with manufacturers of wire and plate in the United 
 States, and cannot fail to supersede the use of the Birmingham 
 Gauge in this country. 
 
 TABLE 
 
 Showing the Linear Measures represented by Nos. American Wire 
 
 Gauge and Birmingham Wire Gauge, or the values of 
 
 the Nos. in the United-States Standard Inch. 
 
 
 American 
 
 Birm. 
 
 
 American 
 
 Birm. 
 
 
 American 
 
 Birm. 
 
 American 
 
 Birm. 
 
 No. 
 
 Gauge. 
 
 Gauge. 
 
 No. 
 
 Gauge. 
 
 Gauge 
 
 No. 
 
 Gauge. 
 
 Gauge. 
 
 No. 
 
 Gauge. 
 
 Gauge. 
 
 
 'inch. 
 
 Inch. 
 
 
 Inch. 
 
 Inch. 
 
 
 Inch. 
 
 Inch. 
 
 
 Inch. 
 
 Inch. 
 
 0000 
 
 .46000 
 
 .454 
 
 8 
 
 .12849 
 
 .165 
 
 19 
 
 .03589 
 
 .042 
 
 30 
 
 .01003 
 
 .012 
 
 000 
 
 .40964 
 
 .425 
 
 9 
 
 .11443 
 
 .148 
 
 20 
 
 .03196 
 
 .035 
 
 31 
 
 .0089^3 
 
 .010 
 
 00 
 
 .36480.380 
 
 10 
 
 .10189 
 
 .134 
 
 21 
 
 .02846 
 
 .032; 
 
 32 
 
 .00795 
 
 .009 
 
 
 
 .32486.340 
 
 11 
 
 .09074 
 
 .120 
 
 22 
 
 .02535 
 
 .028 
 
 33 
 
 .00708 
 
 .008 
 
 1 
 
 .28930.300 
 
 12 
 
 .08081 
 
 .109 
 
 23 
 
 .02257 
 
 .025 
 
 34 
 
 .00630 
 
 .007 
 
 2 
 
 .25763.284 
 
 13 
 
 .07196 
 
 .095 
 
 24 
 
 .02010 
 
 .022 
 
 35 
 
 .00561 
 
 .005 
 
 3 
 
 .22942 
 
 .259 
 
 14 
 
 .06408 
 
 .083 
 
 25 
 
 .01790 
 
 .020 
 
 36 
 
 .00500 
 
 .004 
 
 4 
 
 .20431 
 
 .238 
 
 15 
 
 .05707 
 
 .072 
 
 26 
 
 .01594 
 
 .018! 
 
 37 
 
 .00445 
 
 
 5 
 
 .18194 
 
 .220 
 
 16 
 
 .05082 
 
 .065 
 
 27 
 
 .01419 
 
 .016 
 
 38 
 
 .00396 
 
 
 6 
 
 .16202 
 
 .203 
 
 17 
 
 .04526 
 
 .058 
 
 28 
 
 .01264 
 
 .014 
 
 39 
 
 .00353 
 
 
 7 
 
 .14428 
 
 .180 
 
 18 
 
 .04030 
 
 .049 
 
 29 
 
 .01126 
 
 .013 
 
 40 
 
 .00314 
 
 
 Thus the diameter or size of No. 4 wire, American gauge, is 
 0.20431 of an inch; Birmingham gauge, 0.238 of an inch: so the 
 thickness of No. 4 plate, American gauge, is 0.20431 of an 
 inch ; Birmingham gauge, 0.238 of an inch ; and so for the other 
 Nos. on the gauges respectively. 
 
TABLE 
 
 Showing the Number of Linear Feet in One Pound, Avoirdupois, of 
 Different Kinds of Wire : Sizes or Diameters corre- 
 sponding to Nos. American Wire-gauge. 
 
 No. 
 
 Iron. 
 
 Copper. 
 
 Brass. 
 
 No. 
 19 
 
 Iron. 
 
 Copper. 
 
 Brass. 
 
 
 Feet. 
 
 Feet. 
 
 Feet. 
 
 Feet. 
 
 Feet. 
 
 Feet. 
 
 0000 
 
 1.7834 
 
 1.5616 
 
 1.6552 
 
 293.00 
 
 256.57 
 
 271.94 
 
 000 
 
 2.2488 
 
 1.9692 
 
 2.0872 
 
 20 
 
 396.41 
 
 347.12 
 
 367.92 
 
 00 
 
 2.8356 
 
 2.4830 
 
 2.6318 
 
 21 
 
 465.83 
 
 407.91 
 
 432.35 
 
 
 
 3.5757 
 
 3.1311 
 
 3.3187 
 
 22 
 
 587.35 
 
 514.32 
 
 545.13 
 
 1 
 
 4.5088 
 
 3.9482 
 
 4.1847 
 
 23 
 
 . 740.74 
 
 648.63 
 
 687.50 
 
 2 
 
 5.6854 
 
 4.9785 
 
 5.2768 
 
 '24 
 
 934.03 
 
 817.89 
 
 866.90 
 
 3 
 
 7.1695 
 
 6.2780 
 
 6.6542 
 
 25 
 
 1177.7 
 
 1031.3 
 
 1093.0 
 
 4 
 
 9.0403 
 
 7.9162 
 
 8.3906 
 
 26 
 
 1485.0 
 
 1300.4 
 
 1378.3 
 
 5 
 
 11.400 
 
 9.9825 
 
 10.581 
 
 27 
 
 1872.7 
 
 1639.8 
 
 1738.1 
 
 6 
 
 14.375 
 
 12.588 
 
 13.342 
 
 28 
 
 2361.4 
 
 2067.8 
 
 2191.7 
 
 7 
 
 18.127 
 
 15.873 
 
 16.824 
 
 29 
 
 2977.9 
 
 2607.6 
 
 2763.8 
 
 8 
 
 22.857 
 
 20.015 
 
 21.214 
 
 30 
 
 3754.8 
 
 3287.9 
 
 3484.9 
 
 9 
 
 28.819 
 
 25.235 
 
 26.748 
 
 31 
 
 4734.2 
 
 4145.5 
 
 4394.0 
 
 10 
 
 36.348 
 
 31.828 
 
 33.735 
 
 32 
 
 5970.6 
 
 5221.2 
 
 5541.4 
 
 11 45.829 
 
 40.131 
 
 42.535 
 
 33 
 
 7528.1 
 
 6592.0 
 
 6987.0 
 
 12 
 
 57.790 
 
 50.604 
 
 53.636 
 
 34 
 
 9495.6 
 
 8314.9 
 
 8813.1 
 
 13 
 
 72.949 
 
 63.878 
 
 67.706 
 
 35 
 
 11972 
 
 10483 
 
 11111 
 
 14 
 
 91.861 
 
 80.439 
 
 85.258 
 
 36 
 
 15094 
 
 13217 
 
 14009 
 
 15 
 
 115.86 
 
 100.75 
 
 107.53 
 
 37 
 
 19030 
 
 16664 
 
 17662 
 
 it; U6.10 
 
 127.94 
 
 135.60 
 
 38 
 
 24003 
 
 21018 
 
 22278 
 
 17184.26 
 
 168.35 
 
 171.02 
 
 39 
 
 30266 
 
 26503 
 
 28091 
 
 181232.34 
 
 203.45 
 
 215.64 
 
 40 
 
 38176 
 
 33342 
 
 35432 
 
 Notk. — In tliis TABLE the iron and copper employed are supposed to be 
 nearly pure. The ipedJta ff&rlty of the former was taken at 7.774 j that of the 
 latter, at &.S78. The specihe gravity ol the brass wus taken at S.37G. 
 
WIRE AND WIRE GAUGES. 
 
 47 
 
 To find the number of feel in a pound of wire of any material not 
 given in the table, of any size, American gauge, its specific 
 gravity being known. 
 
 Rule. — Multiply the number of i'eet in a pound of iron wire of 
 the same size by 7.774, and divide the product by the specific grav- 
 ity of the wire whose length is sought; or ordinarily, for steel wire, 
 multiply the number of feet in a pound of iron wire of the same 
 size by 0.991. 
 
 To find the number of feet in a pound of wire of any given No., 
 Birmingham gauge. 
 Rule. — Multiply the number of feet in a pound of the same 
 kind of wire, same No., American gauge, by the size, American 
 gauge, and divide the product by the size, Birmingham gauge. 
 
 Example. — In a pound of copper wire No. 16, American 
 gauge, there are 127.94 feet : how many feet are there of the same 
 kind of wire, same No., Birmingham gauge ? 
 
 (127.94 X -05082) -^ .065 = 100.03. Ans. 
 
 To find the weight of any given length of wire of any given No. or 
 size, American gauge, or the length in any given weight, by help 
 of the foregoing table. 
 Example. — Required the weight of 600 feet of No. 18 iron 
 
 wire. 
 
 600 -f- 232.34 = 2.5822 lbs. = 2 lbs. 9± oz., nearly. Ans. 
 
 Example. — Required the length in feet of 2^ lbs. of No. 31 
 brass wire. 
 
 4394 X 2.5 = 10985. Ans. 
 
 Characteristics of Alloys of Copper and Zinc — Brass. 
 
 Parts by Weight. 
 
 Specific 
 Gravity. 
 
 Color. 
 
 Denomination. 
 
 Copper. 
 
 Zinc. 
 
 83 
 80 
 741 
 
 491 
 33 
 
 17 
 
 20 
 
 25£ 
 34 
 501 
 67 
 
 8.415 
 8.448 
 8.397 
 8.299 
 8.230 
 8.284 
 
 Yellowish Red. 
 
 u a 
 
 Pale yellow. 
 Full 
 
 M (4 
 
 Deep " 
 
 Bath Metal. 
 Dutch Brass. 
 Rolled Sheet Brass. 
 English Sheet Brass. 
 German Sheet Brass. 
 Watchmaker's Brass. 
 
 Note. — To alloys of copper and zinc, generally, there is added a small 
 quantity of lead, which renders them the better adapted for turning 2 planing, 
 or riling ; and, for the same reason, to alloys of copper and tin, there is usually 
 added a small quantity of zinc (see Alloys and Compositions), 
 
TABLE 
 
 Showing the Weight of One Square Foot of Rolled Metals, thickness 
 corresponding to Nos., American Wire-gauge. 
 
 Thickness. 
 
 Iron. 
 
 Steel. 
 
 Copper. 
 
 Brass. 
 
 Lead. 
 
 Zinc. 
 
 No. 
 
 Pounds. 
 
 Pounds. 
 
 Pounds. 
 
 Pounds. 
 
 Pounds. 
 
 Pounds. 
 
 1 
 
 10.849 
 
 10.999 
 
 13.109 
 
 12.401 
 
 17.102 
 
 10.833 
 
 2 
 
 9.6611 
 
 9.7953 
 
 11.674 
 
 11.043 
 
 15.228 
 
 9.6466 
 
 3 
 
 8.6032 
 
 8.7227 
 
 10.396 
 
 9.8340 
 
 13.562 
 
 8.5903 
 
 4 
 
 7.6616 
 
 7.7680 
 
 9.2578 
 
 8.7576 
 
 12.078 
 
 7.6501 
 
 5 
 
 6.8228 
 
 6.9175 
 
 8.2442 
 
 7.7988 
 
 10.755 
 
 6.8126 
 
 6 
 
 6.0758 
 
 6.1601 
 
 7.3416 
 
 6.9450 
 
 9.5779 
 
 6.0667 
 
 7 
 
 5.4105 
 
 5.4856 
 
 6.5377 
 
 6.1845 
 
 8.5291 
 
 5.4024 
 
 8 
 
 4.8184 
 
 4.8853 
 
 5.8222 
 
 5.5077 
 
 7.5957 
 
 4.8112 
 
 9 
 
 4.2911 
 
 4.3507 
 
 5.1851 
 
 4.9050 
 
 6.7645 
 
 4.2847 
 
 10 
 
 3.8209 
 
 3.8740 
 
 4.6169 
 
 4.3675 
 
 6.0233 
 
 3.8151 
 
 11 
 
 3.4028 
 
 3.4501 
 
 4.1117 
 
 3.8896 
 
 5.3642 
 
 3.3977 
 
 12 
 
 3.0303 
 
 3.0720 
 
 3.6616 
 
 3.4638 
 
 4.7770 
 
 3.0257 
 
 13 
 
 2.6985 
 
 2.7360 
 
 3.2607 
 
 3.0845 
 
 4.2539 
 
 2.6934 
 
 14 
 
 2.4035 
 
 2.4365 
 
 2.9042 
 
 2.7473 
 
 3.7889 
 
 2.3999 
 
 15 
 
 2.1401 
 
 2.1698 
 
 2.5829 
 
 2.4463 
 
 3.3737 
 
 2.1369 
 
 16 
 
 1.9058 
 
 1.9322 
 
 2.3028 
 
 2.1784 
 
 3.0043 
 
 1.9029 
 
 17 
 
 1.6971 
 
 1.7207 
 
 2.0506 
 
 1.9399 
 
 * 2.6753 
 
 1.6945 
 
 18 
 
 1.5114 
 
 1.5324 
 
 1.8263 
 
 1.7276 
 
 2.3826 
 
 1.5091 
 
 19 
 
 1.3459 
 
 1.3646 
 
 1.6263 
 
 1.5384 
 
 2.1217 
 
 1.3439 
 
 20 
 
 1.1985 
 
 1.2152 
 
 1.4482 
 
 1.3700 
 
 1.8893 
 
 1.1967 
 
 21 
 
 1.0673 
 
 1.0821 
 
 1.2897 
 
 1.2300 
 
 1.6768 
 
 1.0657 
 
 22 
 
 .95051 
 
 .96371 
 
 1.1485 
 
 1.0865 
 
 1.4984 
 
 .94908 
 
 23 
 
 .84641 
 
 .85815 
 
 1.0227 
 
 .96749 
 
 1.3343 
 
 .84514 
 
 24 
 
 .75375 
 
 .76422 
 
 .91078 
 
 .86158 
 
 1.1882 
 
 .75262 
 
 25 
 
 .67125 
 
 .68057 
 
 .81109 
 
 .76728 
 
 1.0582 
 
 .67024 
 
 2G 
 
 .59775 
 
 .60605 
 
 .72228 
 
 .68326 
 
 .94229 
 
 .59685 
 
 27 
 
 .53231 
 
 .53970 
 
 .64345 
 
 .60846 
 
 .83913 
 
 .53151 
 
 28 
 
 .47404 
 
 .48062 
 
 .57280 
 
 .54185 
 
 .74728 
 
 .47333 
 
 29 
 
 .42214 
 
 .42800 
 
 .51009 
 
 .48242 
 
 .66546 
 
 .42151 
 
 80 
 
 .37594 
 
 ..'{si 16 
 
 .4 5426 
 
 .42972 
 
 .59263 
 
 .37538 
 
 Notk. — In calculating the foregoing tablk, tho specific gravities were 
 
 taken as follows: viz., iron, 
 lead, 11.350; Zinc, 7.189. 
 
 7.200} steel, 7.300; copper, 8,700 j brass, 8.ii30j 
 
TIN PLATES. 
 
 49 
 
 TIN PLATES. 
 
 Brand 
 
 Marks. 
 
 Size of 
 
 No. of 
 
 Sheets in 
 
 Sheets 
 
 Inches. 
 
 in Box. 
 
 IC 
 
 14X14 
 
 200 
 
 IC 
 
 14 X 10 
 
 225 
 
 HC 
 
 14X10 
 
 225 
 
 HX 
 
 14 X 10 
 
 225 
 
 IX 
 
 14 X 10 
 
 225 
 
 IXX 
 
 14 X 10 
 
 225 
 
 IXXX 
 
 14 X 10 
 
 225 
 
 IXXXX 
 
 14 X 10 
 
 225 
 
 IX 
 
 14 X 14 
 
 200 
 
 IXX 
 
 14X14 
 
 200 
 
 DC 
 
 17X12£ 
 
 100 
 
 DX 
 
 17X12* 
 
 100 
 
 DXX 
 
 17X12* 
 
 100 
 
 DXXX 
 
 17X12* 
 
 100 
 
 DXXXX 
 
 17X12* 
 
 100 
 
 SDC 
 
 15XH 
 
 200 
 
 SDX 
 
 loXH 
 
 200 
 
 140 
 112 
 119 
 147 
 140 
 161 
 182 
 203 
 174 
 200 
 105 
 12G 
 147 
 168 
 189 
 168 
 189 
 
 Brand Marks. 
 
 Size of 
 Sheets in 
 Inches. 
 
 No. of 
 Sheets 
 in Box. 
 
 15 X 
 
 15 X 
 15 X 
 14 X 
 
 SDXX 
 SDXXX 
 SDXXXX 
 TT 
 
 IC12X 
 " 1X12 X 
 
 IXXI12X 
 
 " IXXX! 12 X 
 
 «IXXXXll2X 
 
 ICJ20 X 
 
 " IX|20 X 
 
 IXX 20 X 
 
 « IXXX 20 X 
 
 " IXXXX 20 x 
 
 Ternes IC 20 X 
 
 " IX;20 X 
 
 200 
 200 
 200 
 225 
 225 
 225 
 225 
 225 
 225 
 112 
 112 
 112 
 112 
 112 
 112 
 112 
 
 Net 
 Weight 
 in lbs. 
 
 210 
 231 
 252 
 112 
 119 
 147 
 168 
 189 
 210 
 112 
 140 
 161 
 182 
 203 
 112 
 140 
 
 Note. — The above table includes all the regular sizes and qualities of 
 tin plates, except " wasters." Other sizes, such as 10 X 10, 11 X H» 13 X 13, 
 &c, of the different brands, are often imported into the United States to 
 order. 
 
 Common English Sheet Iron, Nos. 10 to 28, Birmingham gauge, 
 widths from 24 to 36 inches. 
 
 R. G. Sheet Iron, Nos. 10 to 30, Birmingham gauge, widths from 
 24 to 36 inches. 
 
 American Puddled Sheet Iron, Nos. 22 to 28, Birmingham 
 gauge, widths from 24 to 36 inches. 
 
 Russia Sheet Iron, Nos. 16 to 8 inclusive, Russia gauge, sheets 
 28 X 56 inches. 
 
 Sheet Zinc, Nos. 16 to 8, Liege gauge, widths from 24 to 40 
 inches ; length 84 inches. 
 
 Copper Sheathing, 14 X 48 inches, 14 to 32 oz. (even numbers), 
 per square foot. 
 
 Yellow Metal, in sheets, 48 X 14 inches, 14 to 32 oz. (even num- 
 bers), per square foot. 
 5 
 
TABLE 
 
 Showing the Capacity, in Wine Gallons, of Cylindrical Cans, of 
 different diameters, at One Inch depth. Diameter in Inches. 
 
 Diam'r. 
 
 Gallons. 
 
 Diam'r. 
 
 Gallons. 
 
 Diam'r. 
 
 Gallons. 
 
 Diam'r. 
 
 Gallons. 
 
 inches. 
 
 
 inches. 
 
 
 inches. 
 
 
 inches. 
 
 
 6 
 
 .1224 
 
 124 
 
 .5102 
 
 184 
 
 1.104 
 
 24| 
 
 2.083 
 
 64 
 
 .1328 
 
 124 
 
 .5313 
 
 l8i 
 
 1.195 
 
 2.-> 
 
 2.125 
 
 64 
 
 .1437 
 
 12| 
 
 .5527 
 
 i'.>- 
 
 1.227 
 
 254 
 
 2.107 
 
 61 
 
 .1549 
 
 13 
 
 .5746 
 
 104 
 
 1.260 
 
 254 
 
 2.211 ! 
 
 7 
 
 .1666 
 
 134 
 
 .5969 
 
 194 
 
 1.293 
 
 251 
 
 2.254 1 
 
 74 
 
 .1787 
 
 134 
 
 .011)7 
 
 195 
 
 L.326 
 
 26 
 
 2.298 
 
 74 
 
 .1913 
 
 13| 
 
 .6428 
 
 20 
 
 1.360 
 
 204 
 
 2.343 
 
 71 
 
 .2042 
 
 14 
 
 .6604 
 
 204 
 
 1.394 
 
 204 
 
 2.388 
 
 8 
 
 .2176 
 
 Hi 
 
 .6904 
 
 204 
 
 1.429 
 
 261 
 
 2.433 
 
 84 
 
 .2314 
 
 144 
 
 .7149 
 
 201 
 
 1.404 
 
 27 
 
 2.479 
 
 84 
 
 .2467 
 
 141 
 
 .7397 
 
 21 
 
 1.499 
 
 274 
 
 2.524 
 
 81 
 
 .2603 
 
 15 
 
 .7650 
 
 214 
 
 1.535 
 
 274 
 
 2.571 
 
 9 
 
 .2754 
 
 154 
 
 .7907 
 
 214 
 
 1.572 
 
 271 
 
 2.518 
 
 94 
 
 .2909 
 
 154 
 
 .8169 
 
 21| 
 
 1.608 
 
 28 
 
 2.000 
 
 94 
 
 .3069 
 
 151 
 
 .8434 
 
 22 
 
 1.646 
 
 284 
 
 2.713 
 
 91 
 
 .3233 
 
 16 
 
 .8704 
 
 224 
 
 1.683 
 
 284 
 
 2.702 
 
 10 
 
 .3400 
 
 164 
 
 .8978 
 
 224 
 
 1.721 
 
 281 
 
 2.810 
 
 104 
 
 .3572 
 
 164 
 
 .9257 
 
 221 
 
 1.760 
 
 29 
 
 2.859 
 
 104 
 
 .3749 
 
 161 
 
 .9539 
 
 23 
 
 1.799 
 
 294 
 
 2.909 
 
 101 
 
 .3929 
 
 17 
 
 .9826 
 
 234 
 
 1.837 
 
 291 
 
 3.009 
 
 11 
 
 .4114 
 
 174 
 
 1.0120 
 
 234 
 
 1.877 
 
 30 
 
 3.060 
 
 11*. 
 
 .4303 
 
 174 
 
 1.0410 
 
 231 
 
 1.918 
 
 304 
 
 3.163 
 
 114 
 
 .4497 
 
 171 
 
 1.0710 
 
 24 
 
 1.958 
 
 31 
 
 3.264 
 
 111 
 
 .4694 
 
 18 
 
 1.1020 
 
 244 
 
 1.999 
 
 314 
 
 3.374 
 
 12 
 
 .4896 
 
 184 
 
 1.1320 
 
 244 
 
 2.041 
 
 32 
 
 3.482 
 
 Applications of the foregoing table. 
 
 Example. — A cylindrical can is 114 inches in diameter, and its 
 depth is 18f inches ; required its capacity. 
 
 .4303 X 18f = 8 gallons. Ans. 
 
 Example. — The diameter of a can containing oil is 264 inches, and 
 the oil is 144 inches in depth. How many gallons are there of the oil ? 
 
 2.388 X 144 = 34.6 gallons. Ans. 
 
 Example. — A can is to be constructed that will hold just 36 gal- 
 lons, and its diameter is to be 18 inches ; what must be its depth 7 
 
 36 4- 1 . 102 = 32| inches. Ans. 
 
CAPACITY OF CYLINDRICAL CANS. 51 
 
 » 
 
 Example. — A cylindrical can is to be constructed that shall have 
 a depth of 15 inches and a capacity of just 5 gallons ; what must be 
 its diameter? 
 
 5 -T- 15 = .3333 = capacity of can in gallons for each inch of depth ; 
 and against .3333 gallon in the table, or the quantity in gallons 
 nearest thereto, is 10 inches, the required, or nearest tabular diam- 
 eter. Ans. 
 
 Note. — The table is not intended to meet demands of the nature of the one contained in 
 the last example, with accuracy, unless the fractional part of the diameter, if there be a 
 fractional part, is i, i or % inch. As, however, the diameter opposite the tabular gallon 
 nearest the one sought, even at its greatest possible remove, can be but about i inch from 
 the diameter required, we can, by inspection, determine the diameter to be taken, or true 
 answer to the Inquiry, sufficiently near for practical purposes, be the fraction what it may. 
 Or, to throw the demand into a mathematical formula : As the tabular gallon nearest the 
 one sought is to the diameter opposite, so is the tabular gallon required to the required 
 diameter, nearly. Thus, in answer to the last query, 
 
 .3400 : 10 : : 3333 : 9.8 inches, the required or true diameter, nearly. 
 
 For a mathematical formula strictly applicable to this question, see Gauging 
 
 Or, for a formula more strictly geometrical, we have 
 
 .Capacity X 231 .. 
 
 aY — —^ = diameter. 
 
 W Depth X -7864 
 
 The true diameter, therefore, for the supposed can, i3 
 
52 WEIGHT OF PIPES. 
 
 WEIGHT OF PIPES. 
 
 The weight of one foot in length of a pipe, of any diametei 
 and thickness, may be ascertained by multiplying the square of its 
 exterior diameter, in inches, by the weight of 12 cylindrical inches of 
 the material of which the pipe is composed, and by multiplying the 
 square of its interior diameter, in inches, by the same factor and sub- 
 tracting the product of the latter from that of the former, — the 
 remainder or difference will be the weight. This is evident from the 
 fact that the process obtains the weight of two solid cylinders of equal 
 length, (one foot,) the diameter of one being that of the pipe, and the 
 other that of the vacancy, or bore. For very large pipes, the dimen- 
 sions may be taken in feet, and the weight of a cylindrical foot of the 
 material used as the factor, or multiplier, if desired. 
 
 The weight of 12 cylindrical inches (length 1 foot, diameter 1 inch) 
 of 
 
 Malleable Iron = 2.6543 lbs. 
 
 Cast Iron =2.4573 " 
 
 Copper, wrought, = 3.0317 " 
 
 Lead " =3.8697 " 
 
 Cast Iron— 1 cyl. foot— = 353.86 " 
 
 Therefore — Example. — Required the weight of a copper pipe 
 whose length is 5 feet, exterior diameter 3^ inches, and interior 
 diameter 3 inches. 
 
 3i = Jj£ X -V- = 10.5625 X 3.0317 = 32.022 + 
 3 X 3 = 9 X 3.0317 = 27.285 -f- 
 
 Ans. 4.737 X 5 = 23.685 lbs. 
 
 Example. — Required the weight of a cast iron pipe, whose length 
 is 10 feet, exterior diameter 38 i#ches, and interior diameter 3 feet. 
 38 2 X 2.4573 — 36 2 X 2.4573 = 363.68 X 10 = 3636.8 lbs. Ans. 
 
 Or, 38* — 36* = 148 X 2.4573 = 363.68 X 10 = 3636.8 lbs. Ans. 
 
 Example. — Required the weight of a lead pipe, whose length is 
 1200 feet, exterior diameter £ of an inch, and interior diameter A 
 of an inch. 
 
 I X I =• *| = .765625, and A X A = AV = -316406, and 
 .765625 — .316406 = .449219 X 3.8697 X 1200 = 2086 lbs. Ans. 
 
 Example. — The length of a cast-iron cylinder is 1 foot, its 
 exterior diameter is 12 inches, and its interior diameter 10 inches ; 
 required its weight. 
 
 12* — 10" = 44 X 2.4573 = 108.12 lbs. Ans. 
 Or, 144 : 353.86 : : 44 : 108.12 lbs. Ans. 
 
WEIGHT OF HPES. 
 
 53 
 
 The following Table exhibits the coefficients of weight, in pounds, of 
 one foot in length, of various thicknesses, of different kinds of pipe, of 
 any diameter whatever. 
 
 
 Thickness 
 in Inches. 
 
 Wrought 
 Iron. 
 
 Copper. 
 
 Lead. 
 
 
 
 Jz 
 
 .332 
 
 .379 
 
 .484 
 
 
 
 1 
 TF 
 
 .664 
 
 .758 
 
 .9675 
 
 
 
 A 
 
 .995 
 
 1.137 
 
 1.451 
 
 
 
 i 
 
 1.327 
 
 1.516 
 
 1.935 
 
 
 
 A 
 
 1.658 
 
 1.894 
 
 2.417 
 
 
 
 3 
 TF 
 
 1.99 
 
 2.274 
 
 2.901 
 
 
 
 A 
 
 2.323 
 
 2.653 
 
 3.386 
 
 
 
 J 
 
 2.654 
 
 3.032 
 
 3.87 
 
 
 
 A 
 
 3.318 
 
 3.79 
 
 4.837 
 
 
 
 1 
 
 3.981 
 
 CAST 
 
 4.548 
 
 IRON. 
 
 5.805 
 
 
 
 
 Thickness. 
 
 Factor. 
 
 Thickness. 
 
 Factor. 
 
 Thickness. 
 
 Factor. 
 
 A 
 
 1.842 
 
 I 
 
 6.143 
 
 »1 
 
 12.287 
 
 i 
 
 2.457 
 
 7.372 
 
 11 
 
 . 14.744 
 
 f 
 
 3.68G 
 
 i 
 
 8.C 
 
 l! 
 
 17.201 
 
 J 
 
 4.901 
 
 i 
 
 9.829 
 
 2 
 
 19.659 
 
 To obtain the weight of pipes by means of the above Table — 
 Rule. — Multiply the diameter of the pipe, taken from the interior 
 surface of the metal on the one side to the exterior surface on the 
 opposite, (interior diameter -f- thickness,) in inches, by the number 
 in the table under the respective, metal's name, and opposite the 
 thickness corresponding to that of the pipe — the product will be the 
 weight, in pounds, of one foot in length of the pipe, and that product 
 multiplied by the length of the pipe, in feet, will give the weight for 
 any length required. 
 
 Example. — Required the weight of a copper pipe whose length is 
 5 feet, interior diameter and thickness 3 J inches, and thickness J of an 
 inch. 
 
 31 = fy = 3.125 X 1-516 X5 = 23.687 lbs. Ans. 
 
 Example. — Required the weight of a cast iron pipe, 10 feet in 
 length, whose interior diameter is 3 feet, and whose thickness is 1 inch. 
 36 -4- 1 = 37 X 9.829 X 10 = 3636.73 lbs. Ans. 
 5* 
 
54 WEIGHT OF BALLS AND SHELLS. 
 
 WEIGHT OF CAST IRON AND LEAD BALLS. 
 
 To find the weight of a sphere or globe of any material — 
 Rule. — Multiply the cube of the diameter, in inches, or feet, by 
 the weight of a spherical inch or foot of the material. 
 The weight of a spherical inch of 
 
 Cast Iron . = .1365 lbs. 
 Lead . . = .215 " 
 Therefore — Example. — r Required the weight of a leaden ball 
 whose diameter is £ of an inch. 
 
 JX JX} = Vt= .015625 X -215 = .00336 lb. Ans. 
 
 Example. — Required the weight of a cast iron ball whose diameter 
 is 8 inches. 
 
 8 3 X • 1365 = 69.888 lbs. Ans. 
 
 Example. — How many leaden balls, having a diameter \ of an inch 
 each, are there in a pound ? 
 
 1 -7- .00336 =^U$$m = 298. Ans. 
 
 Example. — What must be the diameter of a cast iron ball, to 
 weigh 69.888 lbs? 
 
 69.888 -*• .1365 = ^/512 = 8 inches. Ans. 
 
 Example. — What must be the diameter of a leaden ball to equal 
 in weight that of a cast iron ball, whose diameter is 8 inches? 
 [Lead is to cast iron as .215 to .1365, as 1.575 to 1.] 
 8 3 = 512 -j- 1.575 = ^325 = 6.875 inches. Ans. 
 
 WEIGHT OF HOLLOW BALLS OR SHELLS. 
 
 The weight of a hollow ball is the weight of a solid ball of the 
 same diameter, less the weight of a solid ball whose diameter is that 
 of the interior diameter of the shell. 
 
 Example. — Required the weight of a cast iron shell whose ex- 
 terior diameter is 6| inches, and interior diameter 4J inches. 
 
 6\ =2£ X V- X V = 24414 X .1365 = 33.33 
 
 4| =4.25 3 X -1365 = 10.48 
 
 22.85 lbs. Ans. 
 
 Or, If we multiply the difference of the cubes, in inches, of the two 
 diameters — the exterior and interior — by the weight of a spherical 
 inch, we shall obtain the same result. 
 
 \mple. — Required the weight of I cast iron shell whose ex- 
 terior diameter is 10 inches and interior diameter 8 incht .->. 
 lo ZZ& x .1305 =» 66.612 lbs. Ans. 
 
ANALYSIS OF COALS. 
 
 55 
 
 ANALYSIS OF COALS. 
 
 Description. 
 
 Breckinridge, Ky., 
 "Albert," N. B., 
 Chippenville, Pa. , 
 Kanawha, " 
 Pittsburg, " 
 Cannel, 
 Newcastle, 
 Cumberland, 
 Anthracite, a'v'g. 
 
 Volatile Matter. 
 
 Carbon. 
 
 62.25 
 
 29.10 
 
 61.74 
 
 32.14 
 
 49.80 
 
 
 41.85 
 
 
 32.95 
 
 
 35.28 
 
 64.72 
 
 24.72 
 
 75.28 
 
 18.40 
 
 80. 
 
 3.43 
 
 89.46 
 
 Ash. 
 
 8.65 
 6.12 
 
 1.60 
 7.11 
 
 Woods of most descriptions vary little from 80 per cent, volatile 
 matter, and 20 per cent, charcoal. 
 
 Table — Exhibiting the Weights, Evaporative Powers, SfC, of Fuels, 
 .from Report of Professor Walter R. Johnson. 
 
 
 
 Weisht 
 
 Lbs. of Water 
 
 *t iM9 degree* 
 
 Lbs. of Water 
 
 Weight of 
 
 Designation of Fuel. 
 
 Specific 
 Grtv- 
 
 DM 
 
 Cubic 
 
 converted mio 
 Steam by I 
 
 at 212 degrees 
 converted into 
 
 Clinkers 
 from 100 lbs. 
 
 
 ity. 
 
 Foot. 
 
 Cubic Foot of 
 
 Fuel. 
 
 Steam by 1 lb. 
 of Fuel. 
 
 of Coal. 
 
 Anthracite Coals. 
 
 
 
 
 
 Beaver Meadow, No. 3 
 
 1.610 
 
 54.93 
 
 526.5 
 
 9.21 
 
 1.01 
 
 Beaver Meadow, No. 5 
 
 1.554 
 
 56.19 
 
 572.9 
 
 9.88 
 
 .60 
 
 Forest Improvement 
 
 1.477 
 
 53.66 
 
 577.3 
 
 10.06 
 
 .81 
 
 Lackawanna 
 
 1.421 
 
 48.89 
 
 493.0 
 
 9.79 
 
 1.24 
 
 Lehigh 
 
 1.590 
 
 55.32 
 
 515.4 
 
 8.93 
 
 1.08 
 
 Peach Mountain 
 
 1.464 
 
 53.79 
 
 581.3 
 
 10.11 
 
 3.03 
 
 Bituminous Coals. 
 
 
 
 
 
 
 Blossburgh 
 
 1.324 
 
 53.05 
 
 522.6 
 
 9.72 
 
 3.40 
 
 Cannclton, la. 
 
 1.273 
 
 47.65 
 
 360.0 
 
 7.34 
 
 1.64 
 
 Clover Hill 
 
 1.285 
 
 45.49 
 
 359.3 
 
 7.67 
 
 3.86 
 
 Cumberland, average, 
 
 1.325 
 
 53.60 
 
 552.8 
 
 10.07 
 
 3.33 
 
 Liverpool 
 
 1.262 
 
 47.88 
 
 411.2 
 
 7.84 
 
 1.86 
 
 Midlothian 
 
 1.294 
 
 54.04 
 
 461.6 
 
 8.29 
 
 8.82 
 
 Newcastle 
 
 1.257 
 
 50.82 
 
 453.9 
 
 8.66 
 
 3.14 
 
 Pictou 
 
 1.318 
 
 49.25 
 
 478.7 
 
 8.41 
 
 6.13 
 
 Pittsburgh 
 
 1.252 
 
 46.81 
 
 384.1 
 
 8.20 
 
 .94 
 
 Scotch 
 
 1.519 
 
 51.09 
 
 369.1 
 
 6.95 
 
 6.63 
 
 Sydney 
 
 1.338 
 
 47.44 
 
 386.1 
 
 7.99 
 
 2.25 
 
 Coke. 
 
 
 
 
 
 
 Cumberland 
 
 
 31.57 
 
 284.0 
 
 8.99 
 
 3.55 
 
 Midlothian 
 
 
 32.70 
 
 282.5 
 
 8.63 
 
 10.51 
 
 Natural Virginia 
 
 1.323 
 
 46.64 
 
 407.9 
 
 8.47 
 
 5.31 
 
 Wood. 
 
 
 
 
 
 
 Dry Pine Wood 
 
 
 21.01 
 
 98.6 
 
 4.69 
 
 
66 MENSURATION OP LUMBER. 
 
 MENSURATION OF LUMBER. 
 
 To find the contents of a board. 
 
 Rule. — Multiply the length in feet by the width in inches, and 
 divide the product by 12 ; the quotient will be the contents in square 
 feet. 
 
 Example. — A board is 16 feet long and 10 inches wide; how 
 many square feet does it contain ? 
 
 16 X 10 = 160 -S- 12 — 13^. Ans. 
 
 To find the contents of a plank, joist, or stick of square timber. 
 
 Rule. — Multiply the product of the depth and width in inches by 
 the length in feet, and divide the last product by 12 ; the quotient is 
 the contents in feet, board measure. 
 
 Example. — A joist is 16 feet long, 5 inches wide, and 2£ inches 
 thick ; how many feet does it contain, board measure ? 
 
 5 X 2.5 X 16 -M2 = 16^. Ans. 
 
 To find the solidity of a plank, joist, or stick of square timber. 
 
 Rule. — Multiply the product of the depth and width in inches 
 by the length in feet, and divide the last product by 144 ; the quo- 
 tient will be the contents in cubic feet. 
 
 Example. — A stick of timber is 10 by 6 inches, and 14 feet in 
 length ; what is its solidity 1 
 
 10 X 6 = 60 X 14 =* 840 -*■ 144 - 5f feet. Ans. 
 
 Note. — If aboard, plank, or joist is narrower at one end than the other, 
 add the two ends together and divide the Slim toy 2j the quotient will be the 
 mean width. And if a stick of squared timber, who se solidity is required, is 
 narrower at one end than the other (A -+- a + S Aa) ■+■ 3 = mean area. A and 
 a being the areas of the ends. 
 
 To measure round timber. 
 
 Kile (in general practice.^ — Multiply the length, in feet, by 
 rfie square of \ the girt, in incnes, taken about \ the distance from 
 the larger end, and divide the product by 144 ; the quotient is con- 
 sidered the contents in cubic feet. For a strictly correct rule fix 
 measuring round timber, see Mensuration of Solids — Frustum of a 
 Cone. 
 
 Example. — A stick of round timber is 40 feet in length, and 
 girts 88 inches ; what is its solidity 1 
 
 88 -i- 4 = 22X22 = 484X40 = 19360 ^-144 -134.44 cub. ft. Ans. 
 
MENSURATION OF LUMBER. 
 
 57 
 
 The following TABLE is intended to facilitate the measuring of Round 
 Timber, and is predicated upon the foregoing Rule. 
 
 i Girt in 
 
 Area in 
 
 i Girt in 
 
 Area in 
 
 i Girt in 
 
 Area in 
 
 i Girt in 
 
 Area in 
 
 Inches. 
 
 Feet. 
 
 Inches. 
 
 Feet. 
 
 Inches. 
 
 Feet. 
 
 Inches. 
 
 Feet. 
 
 6 
 
 .25 
 
 12 
 
 1. 
 
 18 
 
 2.25 
 
 24 
 
 4. 
 
 H 
 
 .272 
 
 12* 
 
 1.042 
 
 184 
 
 2.313 
 
 24* 
 
 4.084 
 
 62 
 
 .294 
 
 124 
 
 1.085 
 
 184 
 
 2.376 
 
 244 
 
 4.168 
 
 61 
 
 .317 
 
 12| 
 
 1.129 
 
 181 
 
 2.442 
 
 241 
 
 4.254 
 
 7 
 
 .34 
 
 13 
 
 1.174 
 
 19 
 
 2.506 
 
 25 
 
 4.34 
 
 n 
 
 .364 
 
 13* 
 
 1.219 
 
 l'.M 
 
 2.574 
 
 25* 
 
 4.428 
 
 n 
 
 .39 
 
 134 
 
 1.265 
 
 194 
 
 2.64 
 
 254 
 
 4.516 
 
 n 
 
 .417 
 
 133 
 
 1.313 
 
 191 
 
 2.709 
 
 251 
 
 4.605 
 
 8 
 
 .444 
 
 14 
 
 1.361 
 
 20 
 
 2.777 
 
 26 
 
 4.694 
 
 H 
 
 .472 
 
 1*4 
 
 1.41 
 
 20* 
 
 2.898 
 
 26* 
 
 4.785 
 
 H 
 
 .501 
 
 144 
 
 1.46 
 
 204 
 
 2.917 
 
 264 
 
 4.876 
 
 8| 
 
 .531 
 
 141 
 
 1.511 
 
 201 
 
 2.99 
 
 261 
 
 4.969 
 
 9 
 
 .562 
 
 15 
 
 1.562 
 
 21 
 
 3.062 
 
 27 
 
 5.062 
 
 H 
 
 .594 
 
 161 
 
 1.615 
 
 21* 
 
 3.136 
 
 27* 
 
 5.158 
 
 H 
 
 .626 
 
 154 
 
 1.668 
 
 214 
 
 3.209 
 
 274 
 
 5.252 
 
 91 
 
 659 
 
 151 
 
 1.722 
 
 211 
 
 3.285 
 
 271 
 
 5.348 
 
 10 
 
 .694 
 
 16 
 
 1.777 
 
 22 
 
 3.362 
 
 28 
 
 5.444 
 
 10* 
 
 .73 
 
 16* 
 
 1.833 
 
 22* 
 
 3.438 
 
 28* 
 
 5.542 
 
 m 
 
 .766 
 
 164 
 
 1.89 
 
 224 
 
 3.516 
 
 284 
 
 5.64 
 
 103 
 
 .803 
 
 161 
 
 1.948 
 
 221 
 
 3.598 
 
 281 
 
 5.74 
 
 11 
 
 .84 
 
 17 
 
 2.006 
 
 23 
 
 3.673 
 
 29 
 
 5.84 
 
 H* 
 
 .878 
 
 17* 
 
 2.066 
 
 23* 
 
 3.754 
 
 29* 
 
 5.941 
 
 114 
 
 .918 
 
 174 
 
 2.126 
 
 234 
 
 3.835 
 
 294 
 
 6.044 
 
 ill 
 
 .959 
 
 171 
 
 2.187 
 
 231 
 
 3.917 
 
 30 
 
 6.25 
 
 To find the solidity of a log by help of the preceding table. 
 
 Rule. — Multiply the tabular area opposite the corresponding 
 * girt, by the length of the log in feet, and the product will be the 
 solidity in feet. 
 
 Example. — The * girt of a log is 22 inches, and the length of the 
 log is 40 feet ; required the solidity of the log. 
 
 3.362 X 40 = 134.48 cubic feet. Ans. 
 
 Note. — Though custom has established, in a very general way, the preceding method 
 as that whereby to measure round timber, and holds, in most instances, the solidity to be 
 that which the method will give, there seems, if the object sought be the real solidity 
 of the stick, neither accuracy, justice, nor certainty, in the practice. 
 
 Thus, in the preceding example, the stick was supposed to be 40 feet in length, and 88 
 inches in circumference at £ the distance from the larger end, and was found, by the 
 method, to contain 134.44 cubic feet : now 88 -j- 3.1416 = 28 inches, = the diameter at i 
 the distance from the greater base, and retaining this diameter and the length, we may 
 
58 MENSURATION OF LUMBER. 
 
 suppose, with sufficient liberality, and without being far from the general run of such 
 sticks, the diameter at the greater base to be 30 inches, and that of the less to be 24 
 Inches, and — 
 By a correct rule the stick contains — 
 
 30 X 24 = 720 -4- 12 = 732 X- 7854X40 =22996-^144 = 159.7 cubic feet, or 19 per 
 cent, more than given by the method under consideration ; and we need hardly add that 
 the nearer the stick approaches to the figure of a cylinder, the wider will be the difference 
 between the truth and the result obtained by the method referred to. Thus, suppose tho 
 Btick a cylinder, 28 inches in diameter, and 40 feet in length ; and we have, by the falla- 
 cious rule, as above, 134.44 cubic feet ; and — 
 
 By a correct method, we have — 
 
 28 2 X .7854X40 = 24630 -J- 144 =171 cubic feet, or over 27 per cent, more than fur- 
 nished by the erroneous mode of practice. 
 
 Again : suppose the stick in the form of a cone, 30 inches at the base, and tapering to a 
 point at 150 feet in length ; and we have, by a correct rule — 
 
 30 2 -r- 3= 300 X -7854X150 = 35343 4-144 = 245.44 cubic feet; and by the ordinary 
 method of gauging, or the aforementioned practice, we have — 
 
 20 X 3.1416 = 62.832 -7- 4 = 15.708 2 X 150 = 37011.19 -7- 144= 257 cubic feet, or nearly 
 4} per cent, more than the stick actually contains. 
 
 In short, without taking into account anything for the thickness of the bark, that may 
 be supposed to be on the stick, the method is correct only when the stick tapers at the 
 rate of 5i inches diameter per each 10 feet in length, or over i inch diameter to each foot 
 in length of the stick. 
 
 If, however, we suppose the stick as before, (30 inches at the greater base, 24 inches at 
 the smaller, and 40 feet in length,) and suppose the bark upon it to be 1 inch thick, we 
 shall have, by the usual method, 134.44 cubic feet, as before. And, exclusive of the bark, 
 b y a corr ect metho d, we shall have. 
 
 30 — 2X24 — 2 = 616 -4- 12 =628 X-T854X 40 = 19729 -r 144 =137 cubic feet, or 
 only about 2 per cent, more than that furnished us by the usual practice. 
 
 The following simple rule for measuring round timber is suffi- 
 ciently correct for most practical purposes : — 
 
 Rule. — Multiply the square of one-fifth of the mean girt, (exclu- 
 sive of bark,) in inches, by twice the length of the stick in feet, and 
 divide the product by 144 ; the quotient will be the solidity in feet. 
 
 To find the solidity of the greatest rectangular stick that may be cut 
 from a given log, or from a stick of round timber of given dimen- 
 sions. 
 
 Rule. — Multiply the square of the mean diameter of the log, in 
 inches, by half the length of the log, in feet, and divide the product 
 by 144. 
 
 Example. — The diameter (exclusive of bark) of the greater base 
 of a stick of round timber is 30 inches, and that of the less base is 
 24 inches, and the stick is 40 feet in length ; required the solidity 
 of the greatest rectangular stick that may be cut from it. 
 
 30 X 24 -\- \ (30 — 24) 2 = 732 = square of mean diameter,* and 
 
 732 X 20 = 14640 -J- 144 = 101 § cubic feet. Ans. . 
 
 * Kxc.ept in the case of a cylinder, then is | difference betwixt the mr/iti diameter of a 
 
 wing drcoUr bnei, and ibtmiddU dtametar <>f thai Mild. Dm ne*n dtaaaatar 
 
 reduces the solid to a cylinder ; the middle diameter is the diameter midway between tho 
 two 
 
MENSURATION Otf LUMBER. s 59 
 
 Note. — The foregoing stick will make — 
 
 14640 — 16 = 915 feet of square-edged boards 1 inch thick ; 
 Or, 101$ >< 9= 91&- 
 
 To find the solidity of the greatest square stick that may be cut from a 
 given log, or from a stick of round timber of given dimensions. 
 
 Rule. — Multiply the square of the diameter of the less end of the 
 log, in inches, by half the length of the log, in feet, and divide 
 the product by l44. 
 
 Example. — The preceding supposed log will make a square stick 
 containing — 
 
 24 2 X - 4 2 a — 1152 -a- 144— 80 cubic feet. 
 
 Diameter multiplied by .7071 = side of inscribed square. 
 
 To find the contents, in Board Measure, of a log, no allowance being 
 made for wane or saw-chip. 
 
 Rule. — Multiply the square of the mean diameter, in inches, by 
 the length in feet, and divide the product by 15.28. 
 
 Or, Multiply the square of the mean diameter in inches, by the 
 length in feet, and that product by .7854, and divide the last prod- 
 uct by 12. 
 
 The cubic contents of a log multiplied by 12, equal the contents 
 of the log, board measure. 
 
 The convex surface of a Frustum of a Cone = (C + c) X h slant 
 length ; C being the circumference of the greater base, and c the 
 circumference of the less. 
 
60 GAUGING. 
 
 GAUGING. 
 
 Rules for finding the capacity in gallons or bushels of different 
 shaped Cisterns, Bins, Casks, <5fc, and also, by way of examples, for 
 constructing them to given capacities. 
 
 Rule — 1. When the vessel is rectangular. Multiply the interior 
 length, breadth, and depth, in feet together, and the product by the 
 capacity of a cubic foot, in gallons or bushels, as desired for its 
 capacity. 
 
 Rule — 2. When the vessel is cylindrical. Multiply the square of 
 its interior diameter in feet, by its interior depth in feet, and the prod- 
 uct by the capacity of a cylindrical foot in gallons or bushels, as 
 desired for its capacity. 
 
 Rule — 3. When the vessel is a rhombus or rhomboid. Multiply 
 its interior length, in feet, its right-angular breath in feet, and its 
 depth in feet together, and the product by the capacity of a cubic foot 
 in the special measure desired for its capacity. 
 
 Rule — 4. When the vessel is a frustum of a cone — a round vessel 
 larger at one end than the other, whose bases are planes. Multiply 
 the interior diameter of the two ends together, in feet, add J the 
 square of their difference in feet to the product, multiply the sum by 
 the perpendicular depth of the vessel in feet, and that product by the 
 capacity of a cylindrical foot in the unit of measure desired for its 
 capacity. 
 
 Rule — 5. When the vessel is a prismoid or the frustum of any 
 regular pyramid. To the square root of the product of the areas of its 
 ends in feet, add the areas of its ends in feet, multiply the sum by 
 £ its perpendicular depth in feet, and that product by the capacity of 
 a cubic foot in gallons or bushels, as desired for its capacity. 
 
 If it is found more convenient to take the dimensions in inches, do 
 so ; proceed as directed for feet, divide the product by 1728, and mul- 
 tiply the quotient by the capacity of the respective foot as directed. 
 Or, multiply the capacity in inches by the capacity of the respective 
 inch in gallons or bushels ; — by the quotient obtained by dividing the 
 capacity of the respective foot in gallons or bushels by 1728 — for 
 the contents. 
 
 Rule — 6. When the vessel is a barrel, hogshead, pipe, <5fc. Mul- 
 tiply the difference in inches between the bung diameter and head 
 diameter, (interior,) if the staves be 
 
 much curved, . by .7 "1 
 
 medium curved, . by .85 l^g^jwro go 
 
 straighter than medium, by .6 [ P ° 
 nearly straight, . by .55 J 
 
 and add the product to the head diameter, taken in inches ; then mul 
 tiply the square of the sum by the length of the cask in inches, and 
 divide the product by the capacity in cylindrical inches of a gallon o* 
 
GAUGING. 61 
 
 bushel as desired for the contents. Or, divide the contents in cylin- 
 drical inches, as above found, by 1728, and multiply the quotient by 
 the capacity of a cylindrical foot in gallons or bushelt as desired for 
 its contents. Or, multiply the capacity in cylindrical inches by the 
 capacity of a cylindrical inch, in gallons or bushels, as desired, — 
 that is, by the quotient obtained by dividing the capacity of a cylin- 
 drical foot in gallons or bushels, by 1728, for the contents. 
 The capacity of a 
 
 CUBIC FOOT =3 
 
 7.4805 Winchester wine gallons. 
 
 6.1276 Ale 
 
 6.2321 Imperial " 
 
 .80356 Winchester bushel. 
 
 .62888 " heaped " 
 
 .64285 " \\ even " 
 
 .779 Imperial " " 
 
 CYLINDRICAL FOOT = 
 
 5.8751 Winchester wine gallons. 
 
 4.8126 Ale 
 
 4.8947 Impend 
 .63111 Winchester bushel. 
 
 .49391 " heaped " 
 
 .50489 " \\ even « 
 
 .61183 Imperial " 
 
 Example. — Required the capacity in Winchester bushels of a 
 rectangular bin, whose interior length is 12 feet, breadth 6 feet, and 
 depth 5 feet. 
 
 12 X 6 X 5 X -8035 — 289.26 bushels. Ans. 
 Example. — Required the capacity in Winchester wine gallons of 
 a cylindrical can, whose interior diameter is 18 inches, and depth 3 
 feet. 
 
 18 X 18 X 36X 5.875 -f- 1728 = 39.66 gallons. Ans. 
 Or, 1.5 X 1.5 X 3 X 5.875 =* 39.66 gallons. Ans. 
 
 Or, 18 X 18 X 36 X .0034 — 39.66 gallons. Ans. 
 
 Example. — How many Winchester bushels in 39.66 wine gal- 
 lons? 
 
 39.66 X .10742 = 4.26 bushels. Ans. 
 
 Example. — How many wine gallons in 4.26 Winchester bushels ? 
 4.26 X 9.3092 = 39.66 gallons. Ans. 
 
 Example. — How many wine gallons will a cistern in the form of 
 a frustum of a cone hold, having the interior diameter of one of its 
 ends 6 feet, and that at the other 8 feet, and its perpendicular depth 
 9 feet? 
 
 8 — 6 = 2, and 2- -f- 3 = 1.333 = £ square of dif. of diameters, and 
 6X8 + 1.333 = 49.333 X 9 X 5.8751 = 2608.55 gals. Ans. 
 
 Or, 6 X 8 -f 8' 2 4-6 2 = 148 X § X 5.8751 = 2608.55 gals. Ans. 
 Or, (8 3 — & ) -^ (8 — 6) = 148 X # X 5.8751 = 2008.55 gals. Ans. 
 Or, 96 — 72 = 24 and (24 s -r- 3) = 192, and 
 
 96 X 72 + 192 = 7104 X108 X -0034 = 2608.55 gals. Ans. 
 6 
 
62 GAUGING. 
 
 Example. — What is the capacity in "Winchester bushels of a cis- 
 tern whose form is prismoid, the dimensions (interior) of one end 
 being 8 by 6 feet, of the other '4 by 3 feet, and its perpendicular 
 depth 12 feet? 
 
 8 X 6 = 48 = area of one end, and 4 X 3 = 12 = area of the other 
 end ; then — 
 
 48 X 12 = V576 = 24 + 48 + 12 = 84 X J # X .80356= 270 bush- 
 els. Ans. 
 
 Or, (8 -|- 4) -+- 2 = 6, and (6 -f- 3) -J- 2 = 4.5 = mean sectional areas 
 of ends, and 
 
 6X4. 5X4 = 4 area of mean perimeter, then 
 8 X 6 + 4 X 3 + 6 X 4.5 X 4 = 168 X "V 2 - X .80356 = 270 bus. Ans. 
 
 Example. — What must be the depth of a rectangular bin whose 
 length is 12 feet, and breadth 6 feet, to hold 289.26 bushels? 
 289.26 -T- (12 X 6 X .80356) = 5 feet. Ans. 
 
 Example. — A cylindrical can, whose depth is to be 36 inches, is 
 required to be made that will hold 40 gallons ; what must be the 
 diameter of the can ? 
 
 40 -4- (3 X 5.8751) = V2.27 = 1.506 feet. Ans. 
 Or, 40 ~- (36 X .0034) = V326.8 = 18.07 inches. Ans. 
 
 Example. — A cylindrical can, whose interior diameter is to be 18 
 inches, is required that will hold 40 gallons ; what must be the 
 interior depth of the can 1 
 
 40 -r- (18 2 X .0034) = 36.31 inches. Ans. 
 Or, 40 -r- (1.6* X 5.8751) = 3.026 feet. Ans. 
 
 Example. — A cistern is to be built in the form of a frustum of a 
 cone, that will hold 1800 gallons, and the diameter of one of its 
 ends is to be 5 feet, and that of the other 7£ feet ; what must be the 
 depth ! 
 
 7.5 — 5 — 2.5, and>2.5 2 -f- 3 = 2.0833 = J square of difference of 
 diameter, and 
 
 1800 -T- (7.5 X 5 + 2.0833) X 5.8751 = 7.74 feet. Ans. 
 /7.5X 5 + 7.52 + 52 \ 
 
 Or, 1800 -i-( -J X 5.8751 )= 7.74 feet. Ans. 
 
 Example. — The form, capacity, depth, and diameter of one end 
 being determined on, and being as above, what must be the diameter 
 of the other end ? 
 
 c 
 Yj- — \d 2 = y,c being the solidity in cylindrical measurement, h 
 
GAUGING. 63 
 
 the depth, d the diameter of the given end or base, and y a quantity 
 the square root of which is the sum of the required base and half the 
 given base ; then 
 
 1800 -T- 5.8751 = 306.378 = solidity in cylindrical feet, and 
 
 306.378 -j- fcf* = 118.75 — (5 2 -± % ) =» V100 - 10 — £ = 7.5 
 feet. Ans. 
 
 Example. — A measure is to be built in the form of a frustum of a 
 cone, that will hold exactly 1 wine gallon, and the diameter of 
 one of its ends is to be 4 inches, and that of the other 6 inches ; 
 what must be its depth 1 
 
 1 -T- (6 X 4 + U) X -0034 = 11.61 inches. Ans. 
 
 231 6 X 4 -f 6 2 -f 42 
 Or, nQZA -5- 3 = 11.61 inches. Ans. 
 
 Example. — A measure in the form of a frustum of a cone holds 1 
 wine gallon ; the diameter of one of its ends is 6 inches, and its 
 depth is 11.61 inches ; what is the diameter of the other end ? 
 
 Jilt = 294.1176 h- Ll ir 6 - 1 - = 76 - (6* -J- | ) = V49 - 7 — } 
 = 4 inches. Ans. 
 
 CASK GAUGING. 
 
 Cask-gauging, in a general sense, is a practical art, rather 
 than a scientific achievement or problem, and makes no pretensions 
 to strict accuracy with regard to the conclusions arrived at. The 
 aim is, by means of a few satisfactory measurements taken of the 
 outside, and an estimate of the probable mean thickness of the ma- 
 terial of which the cask is composed (of which there must always 
 remain some doubt), or by means of a few measurements taken of , 
 the inside, to determine, 1st, the capacity of the cask, and, 2d, the 
 ullage, or capacity of the occupied or unoccupied space in a cask 
 but partly full. And the Ruie (Rule 6, page 60^), which re- 
 duces the supposed cask, or cask of supposed curvature, to a cylin- 
 der, is as practically correct for the capacity of ordinary casks, as 
 any rule, or set of rules, that can be offered for general purposes. 
 
 Casks have no fixed form of their own, to which they severally 
 and collectively correspond, nor are they in any considerable degree 
 in conformity with any regular geometrical figure. 
 
 Some casks — a few — those having their staves much curved 
 throughout their entire length, are nearest in keeping with the 
 middle frustum of a spheroid ; others, slightly less curved than 
 the preceding, correspond in a considerable degree to the middle 
 
64 GAUGING. 
 
 frustum of a parabolic spindle; others, again — thoso having very 
 little longitudinal curvature of stave to their semi-lengths — are 
 nearly in keeping with the equal frustums of a paraboloid ; and others 
 — a very few — those whose staves are straight from the bung diam- 
 eter to the heads, or equal to that form, are in accordance with the 
 equal frustums of a cone. 
 
 The gauging rod, which is intended to be correct for casks of the 
 most common form, gives for all casks, as may be seen in one of the 
 following Examples, a solidity slightly greater (about 2£ per cent.) 
 than would be obtained by supposing the cask in conformity with 
 the third figure above alluded to. 
 
 The Rule for finding the contents of a cask, by four dimensions, 
 hereafter to be given, is intended as a general Rule for all casks, 
 and, when the diameter midway between the bung and head can be 
 accurately ascertained, will lead to a very close approach to the 
 truth. 
 
 From the length of a cask, taken from outside to outside of the 
 heads, with callipers, it is usual to deduct from 1 to 2 inches, to cor- 
 respond with the thickness of the heads, according to the size of the 
 cask, and the remainder is taken as the length of the interior. 
 
 To the diameter of each head, taken externally, from \ inch to 
 y'V inch should be added for common-sized barrels, -£$ inch for 40 gal- 
 lon casks, and from £ inch to ^ inch for larger casks, to correspond 
 with the interior diameters of the heads. 
 
 If the staves are of uniform thickness, any sectional diameter of a 
 cask may be nearly or quite ascertained, by dividing the circumfer- 
 ence at that place by 3.141G, and subtracting twice the thickness of 
 the stave from the quotient. 
 
 For obtaining the diagonal of a cask by mathematical process,— 
 the interior length, &c. &c. — see Rules, below. 
 
 In the following formulas D denotes the bung diameter, d the 
 head diameter, and / the length of the cask. 
 
 The solidity of any cask is equal to its length multiplied by the 
 square of its mean diameter multiplied by .7854. 
 
 To calculate the contents of a cask from four dimensions. 
 
 Rule. — To the square of the bung diameter add the square of 
 the head diameter, and the square of double the diameter midway 
 between the bung and head, and multiply the sum by £ the length 
 of the cask, for its cylindrical contents; the product multiplied by 
 .Oil ; I expresses the contents in wine gallons. 
 
 Bl ami'LK. — The length of the cask is 40 inchos, its bung diameter 
 28 inches, head diameter 20 inches, and the diameter midway be- 
 
QAUGINQ. 65 
 
 tween the bung and head is 25. G inches ; how many gallons' capacity 
 has the cask 1 ' 
 
 20 2 -f 28-' + 25.6 X 2* = 3805.44 X V" X .0034 = 86.26 gals. Am. 
 
 (D 2 -f- <F -f 2m )X^X -7854 = cubic contents. 
 
 - = square of mean diameter. 
 
 By Rule 6, p. 68, this cask will hold — 
 
 28 — 20 = 8 X .65 = 5.2 -|- 20 = 25.2 X 25.2 X 40 X .0034 — 86.36 
 gallons. 
 
 When the cask is in the form of the middle frustum of a spheroid. 
 
 | D 2 -{- J d 2 = square of mean diameter. 
 
 And a cask of this form, having the same head diameter, bung 
 diameter, and length as the preceding, will hold — 
 
 2X282 + 2Q2 X40 X .0034 =* 89.216 gallons, 
 o 
 
 When the cask is in the form of the middle frustum of a parabolic 
 spindle. 
 
 f D 2 -]- J d' 2 — j 2 5 (D^ dy as square of mean diameter. 
 And a cask of this form, having the same head diameter, bung 
 diameter, and length as the preceding, will hold — 
 
 522§ + 133|= 656 — 8.533 = 647.467 X 40 X .0034 s 88.055 gals. 
 
 When the cask is in the form of two equal frustums of a paraboloid, 
 h D 2 -j- h d 2 = square of mean diameter. 
 
 And a cask of this form, having the same head diameter, bung 
 diameter, and length as the preceding, will hold — 
 
 28« + 20 2 
 
 f- X 40 X -W34 =s 80.51 gallons. 
 
 When the cask is in the form of the equal frustums of a cone. 
 £D2_j_£ d~ — i (D ^r d) 2 == square of mean diameter. 
 Or, ^D 2 +^+JDrf== " " " 
 Or, DX^-H(I>^ rf ) 2 = " " " 
 And a cask of this form, having the same head diameter, bung 
 diameter, and length as the preceding, will hold — 
 
 28 X 20 + 21J X40X-0034 = 79.06 gals. 
 6* 
 
66 GAUGING. 
 
 To find the contents of a cask the same as would be given by the 
 gauging rod. 
 
 The gauging rod is constructed upon the principle that the oabe 
 of the diagonal of a cask, in inches, multiplied by ^j^jrj> equals the 
 contents of the cask, in Imperial gallons. 
 
 The contents in wine gallons of either of the aforementioned 
 casks, therefore, by the gauging rod, would be — 
 
 3T24F X .0027 « 82J gals. 
 
 The decimal coefficient to take the place of .0027, for finding the 
 contents of a cask in the form of the middle frustum of a spheroid 
 = .002926 ; and for finding the contents of a cask in the form of the 
 equal frustums of a cone = .002593. And between these extremes 
 lies the decimal for other casks, or casks of intervening figures. 
 
 To find the diagonal of a cask, when the interior is inaccessible. 
 
 Rule. — From the bung diameter subtract half the difference of 
 the bung and head diameters, and to the square of the remainder 
 add the square of half the length of the cask, and the square root 
 of the sum will be the diagonal. 
 
 Example. — What is the diagonal of a cask whose bung diameter 
 is 28 inches, head diameter 20 inches, and length 40 inches? 
 
 28-20 = 8-h2 = 4,and28 — 4 = 24, then 
 
 V (242 _j_ 20-') =* 31.241 inches. Ans. 
 
 To find the length of a cash, the head diameter, bung diameter and 
 diagonal being given. 
 
 V I diagonal 2 — D — — ^ — ) = £ /. 
 
 And the interior length of a cask, whose interior head diameter, 
 bung diameter and diagonal, are as the preceding, will be 
 V (31.2412 — 242) = 20 X 2 = 40 i ncne8 . 
 
 To find the solidity of a sphere. 
 D 2 X I D X .7854 = cubic contents, D being the diameter. 
 
 To find the solidity of a spherical frustum. 
 
 I 3 A 2 + — ^ — )XhX .7854 » cubic contents, b and d being tho 
 
 bases, and h the height. 
 
 None. — Hr Kul' s in di-uil iK.TUiiiiing to the foregoing figures, and for ether figures, 
 •ee Mensuration or Souns. 
 
ULLAGE. 67 
 
 ULLAGE. 
 
 The ullage or wantage of a cask is the quantity the cask lacks of 
 being full. 
 
 To find the ullage of a standing cask, when the cask is half f nil or more. 
 
 Rule. — To the square of the head diameter, add the square of 
 the diameter at the surface of the liquor, and the square of twice 
 the diameter midway between the surface of the liquor and the upper 
 head, and divide the sum by 6 ; the quotient, multiplied by the 
 distance from the surface of the liquor to the upper head, multiplied 
 by .0034, will give the ullage in wine gallons. 
 
 Example. — The diameters are as follows — at the upper head, 20 
 inches ; at the surface of the liquor, 22 inches ; and at a point midway 
 between these, 21^ inches ; and the distance from the upper head 
 to the surface of the liquor is 5 inches ; required the ullage. 
 
 (20* -f 22*+ 21.25 X 2 2 ) -j- 6 = 448.37 X 5 X .0034 = 7.62 gal- 
 Ions. Ans, 
 
 When the cask is standing, and less than half full, to find the ullage. 
 
 Rule. — Make use of the bung diameter in place of the head 
 diameter, and proceed in all respects as directed in the last Rule, 
 and add the quantity found to half the capacity of the cask ; the 
 sum will be the ullage. j 
 
 Example. — The bung diameter is 28 inches ; the diameter at the 
 surface of the liquor, below the bung, is 26 inches ; the diameter 
 midway between the bung and the surface of the liquor is 27.3 
 inches ; and the distance from the surface of the liquor to the bung 
 diameter is 5 inches ; required the quantity the cask lacks of being 
 half full ; and also the ullage of the cask, its capacity being 86.26 
 gallons. 
 
 (282 -f-26* -t- 27.3X2*) H- 6 = 740.2 X 5 X -0034 = 12.58 gal-' 
 
 Ions less than £ full. Ans, 
 And, 86.2G -j- 2 = 43.13 -f- 12.58 = 55.73 gallons ullage. Ans. 
 
 When the cask is upon its bilge, and half full or more, to find the ullage. 
 
 Rule. — Divide the distance from the bung to the surface of the 
 liquor — (the height of the empty segment) — by the whole bung 
 diameter, and take the quotient as the height of the segment of a 
 circle whose diameter is 1, and find the area of the segment; mul- 
 tiply the area by the capacity of the cask, in gallons, and that 
 product by 1.25 ; the last product will be the ullage, in gallons, as 
 
68 ULLAGE. 
 
 found by the aid of the wantage-rod ; and will be correct for casks 
 of the most common form. 
 
 Note. — The area of the segment of a circle = 
 
 (ch'd i arc -j- 4 ch'd i arc -|- ch'd seg.) X height seg. X y 4 o"*» yer * nearl y> 
 And, having the diameter of the circle and the height of the segment given, the chord 
 of half the arc, and the chord of the segment may be found, thus — 
 radius — height = cosine ; radius 2 — cosine 2 = sine 2 ; */ {sine ) X 2 = ch'd of seg. 
 sine 2 + heigkt seg. 2 = ch'd i arc 2 , and +/ (ch'd i arc2) = ch'd * arc. 
 
 Example. — The bung diameter is 28 inches, the height of the 
 empty segment 5.6 inches, and the capacity of the cask 86.26 gal- 
 lons ; required the ullage of the cask, in gallons. 
 
 5.6 -r 28 = .2 = height of seg., diameter as 1. 
 1 -r- 2 = .5 = radius. 
 .5 — .2 — .3 = cosine. 
 
 .5 2 — .3 2 = .16 = sine 2 , or square of half the base of the segment. 
 V-16" = .4 X 2 = .8 = chord of segment, or base of segment. 
 .4? -{- .2 2 = .2 = square of chord of half the arc. 
 V-2 = .4472 = chord of half the arc, then — 
 .4472 -j- 3 = .1491, and .1491 + .4472 -f- .8 X -2 X A = -1H7, 
 area of segment, and 
 
 .1117 X 86.26 X 1.25 = 12 gallons. Ans. 
 
 When the cask is upon its bilge, and less than half full, to find the 
 
 ullage. 
 Rule. — Divide the depth of the liquor by the bung diameter, and 
 proceed in all respects as directed in the last Rule ; then subtract 
 the quantity found from the capacity of the cask, and the difference 
 will be the ullage of the cask. 
 
 To find the quantity of liquor in a cask by its weight. 
 
 Example. — The weight of a cask of proof spirits is 300 lbs., and 
 the weight of the empty cask {tare) is 32 lbs. How many gallons 
 are there of the liquor ? 
 
 300 — 32 = 268 ~ 7.732 = 345 gallons. Ans. 
 
 Customary Rule by Freighting Merchants, for finding the cubic meas- 
 urement of casks. 
 
 Bung diameter 2 X £ length of cask = cubic measurement. 
 
 Note. — One cubic foot contains 7.4805 wine gallons. 
 
 * For several Rules in detail, for finding the area of the segment of a circle, sec Geom- 
 *m— Mensuration of Superficies. 
 
TONNAGE. 
 
 TONNAGE. 
 
 GOVERNMENT MEASUREMENT. 
 
 length — f breadth X breadth X depth 
 ^ = tonnage. 
 
 In a double-decked vessel, the length is reckoned from the fore 
 part of the main stem to the after side of the sternpost above the 
 upper deck ; the breadth is taken at the broadest part above the 
 main wales, and half this breadth is taken for the depth. 
 
 In a single-decked vessel the length and breadth are taken as for 
 a double-decked vessel, and the distance between the ceiling of the 
 hold and the under side of the deck plank is taken as the depth. 
 
 Example. — The length of a double-decked vessel is 260 feet, and 
 the breadth is 60 feet ; required the tonnage. 
 
 260 — -MP- = 224 X 60 X - 6 #- = 403200 -7- 95 = 4244.2 tons. Ans. 
 
 Example. — The length of a single-decked vessel is 180 feet, the 
 breadth 34 feet, and depth 18 feet ; required the tonnage. 
 
 180 — f of 34 = 159.6 X 34 X 18 -*• 95 — 1028.16 tons. Ans. 
 
 CARPENTER'S MEASUREMENT. 
 
 For a double-decked — 
 
 length of keel X breadth main beam X h breadth 
 95 = tonnage. 
 
 For a single-decked — 
 length of keel X breadth main beam X depth of hold 
 
 95 
 
 ■= tonnage, 
 
70 CONDUITS OK PIPES, 
 
 OF CONDUITS OR PIPES. 
 Pressure of Water in Vertical Pipes, <5fC. 
 
 h = height of column in inches ; o = circumference of column in inches-; 
 t = thickness of pipe in inches equal in strength to lateral pressure at bas« 
 of column ; w am weight of a cubic inch of water in pounds ; C = cohesive 
 strength in pounds per inch area of transverse section of the material of 
 which the pipe is composed — table, p. 72. 
 
 h o = area of interior of pipe in inches ; h w = pressure in pounds per 
 square inch at the base of the column, or maximum lateral pressure in 
 pounds per square inch on the pipe tending to burst it ; how = maximum 
 lateral pressure in pounds on the pipej tending to burst it at the bottom - r 
 and how ■—• 2 = mean lateral pressure in pounds on the pipe, or pressure 
 in pounds on the pipe tending to burst it at half the height of the column. 
 
 how-r-C = t; how-i-t=C; Ct-r-ow = h; Qt -— hw = o. 
 
 Notb. —The reliable cohesion of a material is not above 4 its ultimate force, as given 
 in the Table of Cohesive Forces. By experiment, it has been found that a cast iron pipe 
 15 inches in diameter and $ of an inch thick, will support a head of water of 600 feet ; and 
 that one of the same diameter made of oak, and two inches thick, will support a head of 
 ISO feet : 12000 lbs. per square inch for cast rron, 1200 for oak, 750 for lead, are counted 
 safe estimates. The ultimate cohesion of an alloy, composed of lead 8 parts and zinc I 
 part, is 3000 pounds per square inch. 
 
 Concerning the Discharge of Pipes, <3{C. 
 
 Small pipes, whether vertical, horizontal, or inclined, under equal 
 heads, discharge proportionally less water than large ones. That 
 form of pipe, therefore, which presents the least perimeter to its area, 
 other things being equal, will give the greatest discharge. A round 
 pipe, consequently, will discharge more water in a given time than a 
 pipe of any other form, of equal area. 
 
 The greater the length of a pipe discharging vertically, the greater 
 the discharge. Because the friction of the particles against its sides, 
 and consequent retardation, is more than overcome by the gravity of 
 the fluid. 
 
 The greater the length of & pipe discharging horizontally, the less 
 proportionally will be the discharge. The proportion compared with 
 a less length is in the inverse ratio of the square root of the two 
 lengths, nearly. 
 
 Other things being equal, rectilinear pipes give a greater discharge 
 than curvilinear, and curvilinear greater than angular. The head, 
 the diameters and the lengths being the same, the time occupied in 
 passing an equal quantity of water through a straight pipe is 9, 
 through one curved to a semicircle 10, and through one having one 
 right aiiijle, otherwise straight, 11. All interior inequalities ;in<l 
 roughness should be avoided. 
 
 It has been ascertained that a velocity of 60 feet a minute (1 foot 
 a second) through a horizontal pipe, 4 inches in diameter and' 100 feet 
 
CONDUITS OR PIPES. 71 
 
 in length, is produced by a head 2} inches, only f of an inch above 
 the upper surface of the orifice ; and that, to maintain an equal 
 velocity through a pipe similarly situated, of equal length, having a 
 diameter of \ inch only, a head of 1 fa f eet * s required. To increase 
 the velocity through the last mentioned pipe to 2 feet a second, 
 requires a head 4|£ feet ; to 3 feet, a head of 10 T ^- ; to 4 feet, a 
 head of 17|^, &c. 
 
 From the foregoing, the following, it is believed, reliable rules, are 
 deduced. 
 
 To find the velocity of water passing through a straiglit horizontal pipe 
 of any length and diameter, the head, or height of the fluid above the 
 centre of the orifice, being known. 
 
 Rule. — Multiply the head, in feet, by 2500, and divide the product 
 by the length of the pipe, in feet, multiplied by 13.9, divided by the 
 interior diameter of the pipe in inches ; the square root of the quotient 
 will be the velocity in feet per second. 
 
 Example. — The head is 6 feet, the length of the pipe 1340 feet, 
 and its diameter 5 inches ; required the velocity of the water passing 
 through it. 
 
 2500 X 6 == 15000 -7- ( IfliOff 1 3-9 ) -*- ^4.03 — = 2 feet per 
 second. Ans. 
 
 To find the head necessary to produce a required velocity through a pipe 
 of given length and diameter. 
 Rule. — Multiply the square of the required velocity, in feet, per 
 second, by the length of the pipe multiplied by the quotient obtained 
 by dividing 13.9 by the diameter of the pipe in inches, and divide the 
 product thus obtained by 2500 ; the quotient will be the head in feet. 
 
 Example. — The length of a pipe lying horizontal and straight is 
 1340 feet, and its diameter is 5 inches ; what head is necessary to 
 cause the water to flow through it at the rate of 2 feet a second ? 
 2' 2 X 1340 X H~ -T- 2500 = 6 feet. Ans. 
 
 To find the quantity of water flowing through a pipe of any length and 
 diameter. 
 Rule. — Multiply the velocity in feet per second by the area of the 
 discharging orifice, in feet, and the product is the quantity in cubic 
 feet discharged per second. 
 
 Example. — The velocity is 2 feet a second, and the diameter of 
 the pipe 5 inches; what quantity of water is discharged in each 
 second of time ? 
 5 -f- 12*= .4166, and .4166 2 X -7854 X 2 = .273 cubic foot. Ans. 
 
72 MISCELLANEOUS FHOBLEMS. 
 
 i 
 
 MISCELLANEOUS PROBLEMS. 
 To find the specific gravity of a body heavier than water. 
 
 Rule. — Weigh the body in water and out of water, and divide the 
 weight out of water by the difference of the two weights. 
 
 Example. — A piece of metal weighs 10 lbs. in atmosphere, and 
 but 8i in water ; required its specific gravity. 
 
 10 — 8.25 — 1.75, and 10 -f- 1.75 = 5.714. Ans. 
 
 To find the specific gravity of a body lighter than water. 
 Rule. — Weigh the body in air ; then connect it with a piece of 
 metal whose weight, both in and out of water, is known, and of suf- 
 ficient weight that the two will sink in water ; and find their combined 
 weight in water ; then divide the weight of the body in air by the 
 weight of the two substances in air, less the sum of the difference of 
 the weight of the metal in air and water and the combined weight of 
 the two substances in water, and the quotient will be the specific 
 gravity sought. 
 
 Example. — The combined weight, in water, of a piece of wood, 
 and piece of metal, is 4 lbs. ; the wood weighs in atmosphere 10 lbs. ; 
 and the metal in atmosphere 12, and in water 11 lbs. ; required the 
 specific gravity of the wood. 
 
 10 -r- (10 -{- 12 — 12 ^ 11 -f 4) = .588. Ans. 
 To find the specific gravity of a fluid. 
 Rule. — Multiply the known specific gravity of a body by the dif- 
 ference of its weight in and out of the fluid, and divide the product by 
 its weight out of the fluid ; the quotient will be the specific gravity of 
 the fluid in which the body is weighed. 
 
 Example. — The specific gravity of a brass ball is 8.6 ; its weight 
 in atmosphere is 8 oz., and in a certain fluid 7{ oz. ; required the 
 specific gravity of the fluid. 
 8 _ 7.25 = .75, and 8.6 X -75 = 6.45, and 6.45 -H 8 = .806. Ans. 
 
 To find the proportion of one to the other of two simples forming a 
 compound, or the extent to which a metal is debased, (the metal and the 
 alloy used being knoun.) 
 
 The Rule strictly bears upon that of Alligation Alternate, which 
 see. 
 
 Example. — The specific gravity of gold is 19.258, and that of 
 copper, 8.788; an article composed of the two metals, has a specific 
 gravity of 18 ; in what proportion are the metals mixed] 
 18^ 19.258 X 8.788=11.055 
 18 ^ 8.788 X 19-258 = 177.4, then 
 
MISCELLANEOUS PROBLEMS. 73 
 
 11.055 + 177.4 : 11.055 : : 18 — 1.056 oopper, ) An$ 
 11.055 4-177.4 : 177.4 : : 18 « 16.944 gold. S 
 Or, 18 — 1.056 = 16.914 gold. Copper to gold as 1 to 16.04 + 
 
 To find the lifting fower of* balloon. 
 Rule. — Multiply the capacity of the balloon, in feet, by the dif- 
 ference of weight between a cubic foot of atmosphere and a cubic foot 
 of the gas used to inflate the balloon, and the product is the weight 
 the balloon will raise. 
 
 Example. — A balloon, whose diameter is 24 feet, is inflated with 
 hydrogen ; what weight will it raise 1 
 
 Specific gravity of air is 1, weight of a cubic foot 527.04 grains; 
 specific gravity of hydrogen is .0689. 
 
 527.04 X '0689 = 8(5,31 grains = weight of 1 cubic foot of hydrogen. 
 527.04 — 36.31 = 490.73 grs. = dif. of weight of air and hydrogen. 
 24 3 X .5236 = 7238.24 = capacity in cubic feet of balloon. 
 Then, 7238.24 X 490.73 = 35,52021 grs. = i^$>£-L = 507 T V lbs. 
 
 Ans. 
 
 To find the diameter of « balloon that shall be equal to the raising of a 
 
 given weight. 
 
 The weight to be raised is 507^ lbs. 
 
 507T4X 7000-7-490.73 = 7238.24, and 7238.24 -f- .5236 = fy 13824 
 
 = 24 feet. Ans. 
 
 To find the thickness of a concave or Jiollow metallic ball or globe, tfiat shall 
 have a given buoyancy in a given liquid. 
 
 Example. — A concave globe is to be made of brass, specific grav- 
 ity 8.6, and its diameter is to be 12 inches; what must be its thick- 
 ness that it may sink exactly to its centre in pure water T 
 
 Weight of a cubic inch of water .036169 lb. ; of the brass .3112 lb. 
 Then, 12 3 X -5236 X .036169 -r- 2 = 16.3625 cubic inches of water 
 to be displaced. , 
 
 16.3625 -=- .3 112 = 52.5787 cubic inches of metal in the ball. 
 
 12 2 X 3.1416 = 452.39 square inches of surface of the ball. 
 And, 52.5787 -f- 452.39 = .1162 + = £ inch thick, full. Ans. 
 
 To cut a square sheet of copper, tin, etc., so as to form a vessel of the 
 greatest cubical capacity the sheet admits of. 
 
 Rule. — From each corner of the sheet, at right angles to the side, 
 cut £ part of the length of the side, and turn up the sides till the 
 corners meet. 
 
 7 
 
74 
 
 COMPARATIVE COHESIVE FORCE. 
 
 Comparative Cohesive Force of Metals, Woods, and other substances, 
 Wrought Iron (medium quality) being the unit of comparison, or 1 ; 
 the cohesive force of which is 60000 lbs. per inch, transverse area. 
 
 Wrought iron, . 
 
 . 1.00 
 
 Ash, white, 
 
 .23 
 
 " " wire, . 
 
 1.71 
 
 " red, 
 
 .30 
 
 Copper, cast, . 
 
 , .40 
 
 Beech, . 
 
 .19 
 
 " wire, . 
 
 .76 
 
 Birch, 
 
 .25 
 
 Gold, cast, 
 
 .34 
 
 Box, . 
 
 .33 
 
 " wire, 
 
 .51 
 
 Cedar, . 
 
 .19 
 
 Iron, cast, (average). 
 
 . .38 
 
 Chestnut, sweet, 
 
 .17 
 
 Lead, " 
 
 .015 
 
 Cypress, . 
 
 .10 
 
 " milled, . 
 
 . .055 
 
 Elm, . . ' . 
 
 .22 
 
 Platinum, wire, 
 
 .88 
 
 Locust, . 
 
 -34 
 
 Silver, cast, 
 
 .66 
 
 Mahogany, best, 
 
 36 
 
 " wire, . 
 
 .68 
 
 Maple, 
 
 .18 
 
 Steel, soft, * . 
 
 2.00 
 
 Oak, Amer., white, . 
 
 .19 
 
 " fine, 
 
 2.25 
 
 Pine, pitch, 
 
 .20 
 
 Tin, cast block, 
 
 .083 
 
 Sycamore, 
 
 .22 
 
 Zinc, " . 
 
 .043 
 
 Walnut, . 
 
 .30 
 
 " sheet, 
 
 .27 
 
 Willow, . 
 
 .22 
 
 Brass, cast, 
 
 .75 
 
 Ivory, 
 
 .27 
 
 Gun metal, 
 
 .50 
 
 Whalebone, . . 
 
 .13 
 
 Gold 5, copper 1, 
 
 . .83 
 
 Marble, . 
 
 .15 
 
 Silver 5, " 1, . 
 
 .80 
 
 Glass, plate, 
 
 .16 
 
 Brick, 
 
 .05 
 
 Hemp fibres, glued, . 
 
 . 1.53 
 
 Slate, 
 
 .20 
 
 
 
 The strength of white oak to cast iron, is as 2 to 9. 
 The stiffness of " " " " is as 1 to 13. 
 
 To determine the vmght, or force, in pounds, necessary to tear asun- 
 der a bar, rod, or piece of any of the above named substances, of any 
 given transverse area : 
 
 Rule. — Multiply the comparative cohesive force of the substance, 
 as given in the table, by the cohesive force per square inch, area of 
 cross section (60000 lbs.) of wrought iron, which gives the cohesive 
 force of 1 square inch area of cross section of the substance whose 
 power is sought to be ascertained, and the product of 1 square inch 
 thus found, multiplied by area of cross section, in inches, of the rod, 
 piece, or bar itself, gives the cohesive force thereof. 
 
 Alloys having a tenacity greater than the sum of their constituents, 
 Swedish copper 6 pts., Malacca tin 1 ; tenacity per sq. inch, 64000 lbs. 
 Chili copper 6 pts., Malacca tin 1 ; " " " 60000 " 
 
 Japan copper 5 pts., Banca tin 1 ; " " M 57000 " 
 
 Anglesea copper 6 pts., Cornish tin I ; •• " M 41000 M 
 
LINEAR DILATION OF SOLIDS BY HEAT. 
 
 75 
 
 Common block-tin 4 pts., lead 1, zinc 1 ; tenacity per sq. in., 13000 lbs. 
 Malacca tin 4 pt8.,tegulu8 of antimony 1; " " " 12000" 
 
 Block-tin 3 pts., lead l part; " " «' 10000 " 
 
 Block-tin 8 pts. , zinc 1 part; " " " 10200" 
 
 Zinc 1 part, lead 1 purl; « " M 4500 " 
 
 A Hoys having a density greater than the mean of their constituents. 
 
 Cold with antimony, bismuth, cobalt, tin, or zinc. 
 
 Silver with antimony, bismuth, lead, tin, or zinc. 
 
 Copper with bismuth, palladium, tin, or zinc. 
 
 Lead with antimony. 
 
 Platinum with molybdinum. 
 
 Palladium with bismuth. 
 
 Alloys having a density less than the mean of their constituents. 
 Gold with copper, iron, iridium, lead, nickel, or silver. 
 Silver with copper or lead. 
 Iron with antimony, bismuth, or lead. 
 Tin with antimony, load, or palladium. 
 Nickel with arsenic. 
 Zinc with antimony. 
 
 RELATIVE POWER OF DIFFERENT METALS TO CONDUCT ELEC-. 
 
 TRICITY, 
 
 {the mass of each being equal.) 
 
 Copper, .... 1000 1 Platinum, . . .188 
 
 Gold, .... 936 1 Iron, . . . .158 
 
 Silver, .... 736 1 Tin, . . . .155 
 
 Zinc, .... 285 (Lead, .... 83 
 
 LINEAR DILATION OF SOLIDS BY HEAT. 
 
 Length which a bar heated to 212° has greater than when at the tem- 
 perature of 32°. 
 
 Brass, cast, 
 
 . .0018671 
 
 Iron, wrought, . 
 
 .0012575 
 
 Copper, 
 
 . .0017674 
 
 Lead, 
 
 .0028568 
 
 Fire brick, 
 
 . .0004928 
 
 Marble, . 
 
 .0011016 
 
 Glass, 
 
 . .0008545 
 
 Platinum, . 
 
 .0009342 
 
 Gold, 
 
 . .0014880 
 
 Silver, 
 
 .0020205 
 
 Granite, . 
 
 . .0007894 
 
 Steel, 
 
 .0011898 
 
 Iron, cast, 
 
 . .0011111 
 
 Zinc, 
 
 .0029420 
 
 Note. — To find the surface dilation of any particular article, double its linear dilation, 
 and to find the di ation in volume, triple it. To find the elongation in linear inches per 
 linear foot, of an) particular article, multiply its respective linear dilation, as given in tlie 
 by 12. 
 
76 
 
 EFFECTS OF HEAT. 
 
 MELTING POINT OF METALS AND OTHER BODIES. 
 Lime, palladium, platinum, porcelain, rhodium, silex, may be melted 
 by means of strong lenses, or by the hydro-oxygen blowpipe. Co- 
 balt, manganese, plaster of Paris, pottery \ iron, nickel, &c, at from 
 2700° to 3250° Fahrenheit; others as follows : — 
 
 
 Degree* Pah. 
 
 
 Degrees Fab. 
 
 Antimony, 
 
 . 809 
 
 Nitre, 
 
 . 660 
 
 Beeswax, bleached, . 
 
 . 155 
 
 Silver, 
 
 . 1873 
 
 Bismuth, . 
 
 . 506 
 
 Solder, common, 
 
 . 475 
 
 Brass, 
 
 , . 
 
 . 1900 
 
 " plumbers', 
 
 . 360 
 
 Copper, 
 
 „ 
 
 . 1996 
 
 Sugar, 
 
 . 400 
 
 Glass, flint, 
 
 „ 
 
 . 1178 
 
 Sulphur, . 
 
 . 226 
 
 Gold, 
 
 t . 
 
 . 2016 
 
 Tallow, . 
 
 . 127 
 
 Lead, 
 
 1 
 
 . 612 
 
 Tin,. 
 
 . 442 
 
 Mercury, . 
 
 . 
 
 . —39 
 
 Zinc, 
 
 . 680 
 
 Cast iron thoroughly melts at 
 
 2786 
 
 Greatest heat of a smith's i 
 
 brge, (com.) . 
 
 2346 
 
 Welding heat of iron, 
 
 . . . 
 
 1892 
 
 Iron red hot in twilight, 
 
 
 884 
 
 Lead 1, tin I, bismuth 4, melts at 
 
 . 201 
 
 Lead 2, ti» 3, bismuth 5, 
 
 <i it. 
 
 . 212 
 
 RELATIVE POWER OF DIFFERENT BODIES TO RADI/ 
 
 kTE HEAT. 
 
 Water, . 
 
 100 
 
 Lead, bright, . 
 
 19 
 
 Copper, .... 
 
 12 
 
 Mercury, 
 
 20 
 
 Glass, .... 
 
 90 
 
 Paper, white, . 
 Silver, . 
 
 100 
 
 Ice, 
 
 85 
 
 12 
 
 India ink, 
 
 88 
 
 Tin, blackened, 
 
 . 100 
 
 Iron, polished, 
 
 15 
 
 " clean, 
 
 12 
 
 Lampblack, 
 
 
 100 
 
 " scraped, . 
 
 16 
 
 Nora. — The power of a body to rejlect heat is inverse to its power of radiation. 
 
 BOILING POINT OF LIQUIDS. 
 Barometer at 30 in. 
 
 Acid, nitric, 
 
 253° 
 
 Oils, essential, avg 
 
 ., . 318° 
 
 " sulphuric, . 
 
 600° 
 
 " turpentine, 
 
 316? 
 
 Alcohol, anhyd., . 
 
 168.5c 
 
 11 linseed, 
 
 640° 
 
 " 90 per cent., . 
 
 174o 
 
 Phosphorus, 
 
 554^ 
 
 Ether, sulph., 
 
 97° 
 
 Sulphur, 
 
 560° 
 
 Mercury, 
 
 656° 
 
 Water, 
 
 212° 
 
 Nora — Barometer at 31 inches, water boils al213°57; at 20, it boil* at210°.3S; at 
 88, it boils at 2080.69 ; at 27, it boils at 206°. 85, and in vacuo ii tx>ils at 88°. No liquid, 
 ■nder pressure of the atmosphere alone, can be heated above its boiling point. At that 
 point the steam emitted sustains the weight of the atmosphere. 
 
EFFECTS OF HEAT, ETC. 
 
 77 
 
 FREEZING POINT OF LIQUIDS. 
 
 Acid, nitric, 
 
 . —55° 
 
 Oil, linseed, avg., 
 
 —11° 
 
 " sulphuric, 
 
 1° 
 
 Proof spirits, 
 
 —7° 
 
 Ether, . 
 
 . —47° 
 
 Spirits turpentine, 
 
 16° 
 
 Mercury, 
 
 . —39° 
 
 Vinegar, 
 
 28° 
 
 Milk, . 
 
 30° 
 
 Water, 
 
 32° 
 
 Oil, cinnamon, 
 
 30° 
 
 Wine, strong, . 
 
 20° 
 
 " fennel, . 
 
 14° 
 
 Rapeseed Oil, 
 
 25* 
 
 ** olive, 
 
 36° 
 
 
 
 Note. — Water expands in freezing .11, or i its bulk. 
 
 EXPANSION OF FLUIDS BY BEING HEATED FROM 32° TO 212?, P. 
 
 Atmospheric air, 3-^ per each degree, = .375 
 
 Gases, all kinds, T fo " " " 
 
 Mercury, exposed, ...... .018 
 
 Muriatic acid, (sp. gr. 1.137,) 060 
 
 Nitric acid, (sp. gr. 1.40,) 110 
 
 Sulphuric acid, (sp. gr. 1.85,) 060 
 
 " ether, — to its boiling point, . . .070 
 
 Alcohol, (90 per cent.,) " " . . .110 
 
 Oils, fixed, 080 
 
 " turpentine, 070 
 
 Water, . • 046 
 
 RELATIVE POWER OF SUBSTANCES TO CONDUCT HEAT. 
 
 363 
 
 304 
 
 180 
 
 12 
 
 11 
 
 Note. — Different woods have a conducting power in ratio to each other, as is Iheic 
 respective specific gravities, the more dense having the greater. 
 
 Gold, 
 
 . 1000 
 
 Zinc, 
 
 Silver, . 
 
 973 
 
 Tin, 
 
 Copper, . 
 
 898 
 
 Lead, 
 
 Platinum, 
 
 381 
 
 Porcelain, 
 
 Iron, 
 
 374 
 
 Fire brick, 
 
 METALS IN ORDER OF DUCTILITY AND MALLEABILITY. 
 
 Ductility. 
 
 1. Platinum. 
 
 2. Gold. 
 
 3. Silver. 
 
 4. Iron. 
 
 5. Copper. 
 
 6. Zinc. 
 
 7. Tin. 
 
 8. Lead. 
 
 Malleability. 
 
 1. Gold. 
 
 2. Silver. 
 
 3. Copper. 
 
 4. Tin. 
 
 5. Platinum. 
 
 6. Lead. 
 
 7. Zinc. 
 
 8. Iron. 
 
 7* 
 
78 
 
 MUTKITI'VK AND ALCOHOLIC PROPERTIES OF BODIES. 
 
 Quantity per cent, by weight of Nutritious Matter contained in different 
 articles of Food. 
 
 Articles. 
 
 
 
 per ct. 
 
 Article*. 
 
 perct. 
 
 Lentils, .... 
 
 Oats, 
 
 74 
 
 Peas, 
 
 
 
 93 
 
 Meats, avg., . 
 
 35 
 
 Beans, 
 
 
 
 92 
 
 Potatoes, . 
 
 25 
 
 Corn, (maize,) 
 
 
 
 89 
 
 Beets, 
 
 14 
 
 Wheat, . 
 
 
 
 85 
 
 Carrots, . 
 
 10 
 
 Barley, . 
 
 
 
 83 
 
 Cabbage, . 
 
 7 
 
 Rice, 
 
 
 
 88 
 
 Greens, . 
 
 6 
 
 Rye, 
 
 i 
 
 
 79 
 
 Turnips, white, 
 
 4 
 
 Specific gravity, and quantity per cent., by volume, of Absolute Alcohol 
 contained, necessary to constitute the following named unadulterated 
 articles. 
 
 - — - J - Sp. e-rar. Per cent. 
 
 Art,cles - 60*. 6. 30. ofAloohoF. 
 
 Absolute Alcohol, (anhydrous,) . . . .7939 100 
 
 Alcohol, highest by distillation, . . . .825 92.6 
 
 •■ commercial standard, . . . .8335 90 
 
 Proof Spirits, — standard, . . . .9254 54 
 
 Quantity per cent., by volume, (general average) of Absolute Alcohol 
 contained in different pure or unadulterated Liquors, Wines, $c. 
 
 per cent. 
 
 22 
 20 
 18 
 17 
 10 
 16 
 14 
 12 
 17 
 19 
 
 Proof of Spirituous Liquors. 
 
 The weight, in air, of a cubic inch of Proof Spirits, at 60° F., is 
 233 grains ; therefore, an inch cube of any heavy body, at that tempera- 
 ture, weighing 233 grains less in spirits than in air, shows the spirits 
 in which it is weighed to be proof. If the body lose less of its weight, 
 the spirit is above proof, — if more, it is below. 
 
 Liquor*, 4c. 
 
 peT cent. 
 
 Wine*. 
 
 Rum, 
 
 50 
 
 Port, 
 
 Brandy, . 
 
 50 
 
 Madeira, 
 
 Gin, Holland, . 
 
 48 
 
 Sherry, 
 
 Whiskey, Scotch, 
 
 50 
 
 Lisbon, . 
 
 " Irish, 
 
 50 
 
 Claret, . 
 
 Cider, whole, 
 
 9 
 
 Malaga, . 
 
 Ale, 
 
 8 
 
 Champagne, 
 
 Porter, 
 
 7 
 
 Burgundy, 
 
 Brown Stout, . 
 
 6 
 
 Muscat, 
 
 Perry, . 
 
 9 
 
 Currant, 
 
COMPARATIVE WEIGHT OF TIMBER. 
 
 79 
 
 Comparative Weight of different kinds of Timber in a green and per' 
 feclly seasoned state. 
 Assuming the weight of each kind destitute of water to be 100, that 
 of the same kind green is as follows : — 
 
 Ash, 
 
 Beech, 
 
 Birch, 
 
 153 
 174 
 
 169 
 
 Cedar, . 
 Elm, swamp, 
 Fir, Amer., 
 
 148 I Maple, red, . 149 
 198 I Oak, Am., . 151 
 171 I Pine, white, . 152 
 
 Notb. — Woods which have been felled, cleft and housed for 12 months, still retain 
 from 90 to 25 per cent, of water. They therefore contain but from 75 to 80 per cent, of 
 healing matter ; and it will require from 23 to 29 per cent, the weight of such woods to 
 dispel the water they contain. They are, therefore, less valuable hy weight, as fuel, by 
 this per cent., than woods perfectly free from moisture. They never, however, contain, 
 exposed to an ordinary atmosphere, less than 10 per cent, of water, however long kept; 
 and even though rendered anhydrous by a strong heat, they again imbibe, on exposure to 
 the atmosphere, from 10 to 12 per cent, of dampness. 
 
 Relative power of different seasoned Woods, Coals, ^-c, as fuel, to pro- 
 duce heat, — the Woods supposed to be seasoned to mean dryness, 
 (77£ per cent.,) and the other articles to contain but their usual quan- 
 tity of moisture. 
 
 Hickory, shell-bark, 
 1 ' red-heart, 
 
 Walnut, com. 
 
 Beech, red, 
 
 Chestnut, 
 
 Elm, white, 
 
 Maple, hard, 
 
 Oak, white, 
 " red, . 
 
 Pine, white, 
 " yellow, 
 
 Birch, black, 
 " white, 
 
 Coal, Cumberland, (bit.) 
 " Lackawanna (anth.) 
 " Lehigh, " 
 
 " Newcastle, (bit.) 
 11 Pictou, (bit.) 
 " Pittsburgh, (bit.) 
 " Peach Mountain, (anth.) 
 
 Charcoal, 
 
 Coke, Virginia, natural, 
 " Cumberland, 
 
 Peat, ordinary, . 
 
 Alcohol, common, 
 
 Beeswax, yellow, 
 
 Tallow, . 
 
 Ratio of Heatin* 
 Power per equal 
 
 Bulk. 
 
 Weight. 
 
 1.00 
 
 1.00 
 
 .81 
 
 .99 
 
 .95 
 
 .98 
 
 .74 
 
 .99 
 
 .49 
 
 .98 
 
 .58 
 
 .98 
 
 .66 
 
 .98 
 
 .81 
 
 .99 
 
 .69 
 
 .99 
 
 .42 
 
 1.01 
 
 .48 
 
 1.03 
 
 .63 
 
 .99 
 
 .48 
 
 .99 
 
 2.56 
 
 2.28 
 
 2.28 
 
 2.22 
 
 2.39 
 
 2.03 
 
 2.10 
 
 1.96 
 
 2.21 
 
 1.91 
 
 1.78 
 
 1.82 
 
 2.69 
 
 2.29 
 
 1.14 
 
 2.53 
 
 1.89 
 
 2.12 
 
 1.31 
 
 2.25 
 
 
 .62 
 
 
 2.02 
 
 
 2.90 
 
 
 3.10 
 
80 
 
 ILLUMINATION. 
 
 Notb. — By help of the preceding table, the price of either one article being known, 
 the relative or par value of either other, as fuel, may be readily ascertained : — Example : 
 
 Maple (66) : $5.00 : : Pine (42) : $3.18. 
 
 ILLUMINATION— ARTIFICIAL. 
 The following Table shows : — 
 
 1. The materials and methods of using — column Materials. 
 
 2. The comparative maximum intensity of light afforded by each 
 material, used or consumed as indicated, — column Intensities. 
 
 3. The weight, in grains, of material consumed per hour, by each 
 method respectively, in producing its respective light, or light of in- 
 tensity ascribed — column Weight. 
 
 4. The ratio of weight required of each material, under each spe- 
 cial method of consumption, for the production of equal lights in 
 equal times — column Ratios. 
 
 Materials. Intens. Weisrht. Ratios. 
 
 Camphene * Paragon Lamp, ... 16. 853 1. 
 
 Sperm Oil. Parker's heating Lamp, . . 11. 696 1.19 
 
 " Mech. orCarcel " . . 10. 815 1.53 
 
 " " French annular " 5. 543 2.04 
 
 " Common hand " 1. 112 2.10 
 
 Whale " pTd., P's heating" . . 9. 780 1.63 
 
 Woo: Candles, 3's or 4's, 15 in. or 12 in., . 1. 125 2.35 
 
 " " 6's, 9 in., .... .92 122 2.50 
 
 4's, 13£ in.', .... 1. 142 2.66 
 
 4's, 13£ in., .... 1. 168 3.15 
 
 dipped, 10's, .... .70 150 4.02 
 
 mould, 10's, .... .66 132 3.75 
 
 8's, .... .57 132 4.35 
 
 " " " 6's, ... .79 163 3.87 
 
 4's, 131 in., . . 1. 186 3.49 
 
 " Coal Gas," intensity being ... 1. 740 
 
 Note. — The consumption of 1.43 cubic feet of gas per hour, gives a light equal to one 
 wax candle, — the consumption of 1.% cubic feet per hour, a light equal to four wax can- 
 dles, and the consumption of 3 cubic feet per hour, a light equal to tea wax candles. A 
 cubic foot of gas weL'hs 518 grains. 
 
 The average yield of hi carbureted hydrogen — Olefiant gas — Coal Gas, obtained from 
 the following articles, is as annexed. 
 
 1 lb. Bituminous Coal, 4£ cubic feet. 
 
 1 lb. Oil, or Oleine, 15 " " 
 
 1 II). Tar, 12 " 
 
 1 lb. Rosin, or Pitch, 10 " 
 
 A pipe whose interior diameter is i inch, will supply gas equal in illuminating power to 
 20 wax candles. 
 
 Sperm " 
 Stearine" 
 Tallow," 
 
 1 lb. Camphene, 
 1 lb. Sperm Oil, 
 1 lb. Whale " p'Pd. 
 
 lyV pinU 
 1*- 
 
ILLUMINATION. 81 
 
 By the foregoing table, it is readily seen in what ratio the several 
 intensities, furnished by the different methods, stand one to another, 
 — that the French annular lamp, for instance, has a maximum power 
 = half that of the mechanical, or T ^ that of the camphene, or 5 
 wax candles, 3 to the lb., — that the camphene, at its maximum 
 power, yields an intensity equal to that afforded by 16 -j- .57, » 28 
 tallow candles, moulds, 8 to the lb., — that as the intensity of a six 
 wax candle, 13 in., is .92, and that of an eight mould tallow .57, 57 
 candles of the former yield an intensity equal to that afforded by 92 
 of the latter, &c, &c. 
 
 The quantity of material consumed in any given time by either 
 of the foregoing methods, in the production of any given intensity of 
 light, is readily ascertained by help of the preceding table. Suppose, 
 for example, an intensity equal to that afforded by 1 camphene para- 
 gon lamp at its greatest power, is required, and for three hours, and 
 that it is proposed to produce the same by tallow candles, moulds, 10 
 to the lb. ; the quantity by weight of candles consumed in the produc- 
 tion is required, and, consequently, the number of lights that must 
 be used. 
 
 ILLUSTRATION. 
 Intens. of camph., (16) ■— intensity of candles, (.66) = 24 candles, and grs. in 1 h. by 
 1 candle, (132) X 24 X 3 hours = 1 lb. 5f oz. Ana. 
 
 The economy of use, as between any two materials, under either 
 their respective forms, or methods of consumption, for the production 
 of equal lights in equal times, and therefore for the production of any 
 intensity, is also, by help of the given table, easily learned, the 
 market price of both being known ; and, thereby, the per cent., if any 
 difference exist, in favor of the more economical, or less expensive 
 of the two, may be found. To illustrate : — 
 
 1. The price of camphene is 10 cents a pound, and that of sperm 
 oil, 15 ; the economy of use as between the two for the production of 
 equal lights — equal intensities in equal times, greater or less — the 
 former consumed in the paragon lamp, and the latter in Parker's heat- 
 ing, is desired, and the per cent, in favor of the less expensive. 
 
 10X1= 10, and 15 X 1.19= 17.85; showing the economy to 
 be in favor of the camphene — showing it so to an extent 17.85 — 10 
 = tW^* or to an extent 7 cts. 8j mills per 17 cts. 8 J mills — to 
 an extent, therefore, 
 
 17.85 : 7.85 : : 100 = 44 per cent. Ans. 
 
 2. The price of sperm candles, 4's, is 40 cts. a pound, and the price 
 of tallow, mould 10's, is 11 cts. It is desired to know which of the 
 two, for the production of an intensity nearest obtainable to that af- 
 forded by one of the wax, but not less than that of 1 wax, is the less 
 expensive, and to what extent per cent. 
 
 By casting the eye to the table, it is readily seen that two tallow 
 candles must be employed, the comparative intensity of which 
 
82 THERMOMETERS. 
 
 is .66 each ; therefore, .66 X 2 = 1.32, and 3.75 X 1.32 = 4.95, 
 equivalent weight ; consequently — 
 
 40 X 2.66 = 106.4, and 11 X 4.95 = 54.45, and 106.4 — 54.45 == 
 51.95. Therefore, 
 
 106.4 : 51.95 : : lOO = 48-^ per cent. Arts. 
 
 Showing that an intensity nearly J greater is afforded by the tallow 
 than the wax, and at an expense 49 per cent. less. The same rule 
 of practice is applicable, as between any two methods, for equal or 
 greater or less intensities, as desired. 
 
 THERMOMETERS. 
 
 Boiling point. 
 
 212° 
 
 80° 
 
 100° 
 
 Freezing point. 
 
 32 s 
 0° 
 0° 
 
 Fahrenheit's, . 
 
 Reaumur's, .... 
 
 Centigrade, .... 
 
 To reduce Reaumur to Fahrenheit. 
 When it is desired to reduce the -\-°, (degrees above the zero) : — 
 
 Rule. — Multiply the degrees Reaumur, by 2.25, and add 32° to 
 the product ; the sum will be the degrees Fahrenheit. 
 
 When it is desired to reduce the — °, (degrees below the zero) : — 
 
 Rule. — Multiply the — ° Reaumur by 2.25, and subtract the 
 product from 32° ; the difference will be the degrees Fahrenheit. 
 
 Example. — The degrees R. are 40 ; required the equivalent 
 degrees F. 
 
 40 X 2.25 = 90 + 32 = 122°. Ans. 
 
 Example. — The degrees below 0, R., are 10 ; what are the cor- 
 responding degrees F. 1 
 
 10 X 2.25 = 22.5, and 32 — 22.5 — 9£°. Ans. 
 
 ' Example. — Tbfl degrees below 0, R., are 16 ; what point on the 
 scale F. corresponds thereto? 
 
 16 X 2.25 = 36, and 32 — 36 = — 4 ; 4° below 0. Ans. 
 
 1\> reduce the Cmtigrade to Fahrenheit. 
 Rule. — Multiply the degrees C. by 1.8, and in all other respects 
 proceed as directed for Reaumur, above. 
 
 Note. — The zero of Wodgowood't pyrometer is And tt the tamNMtamof banitd*hoC 
 
 in daylight, = 1077O f. f ;m ,i ,.,„•], degree W. equals 13U° F. The instrument is not con- 
 sidered reliable, and is but litUe used 
 
HORSE POWER — ANIMAL POWER — STEAM. 88 
 
 HORSE POWER. 
 
 A house-power, in machinery, as a measure of force, is estimated 
 equal to the raising of 33000 lbs. over a single pulley one foot a 
 minute, = 550 lbs. raised one foot a second, = 1000 lbs. raised 33 feet 
 a minute. 
 
 ANIMAL POWER. 
 
 A man of ordinary strength is supposed capable of exerting a force 
 of 30 lbs. for 10 hours in a day, at a velocity of 2£ feet a second, = 
 75 lbs. raised 1 foot a second. 
 
 The ordinary working power of a horse is calculated at 750 lbs. for 
 8 hours in a day, at a velocity of 2 feet a second, = 375 lbs. raised 
 1 foot a second, = 5 times the effective power of a man during asso- 
 ciated labor, and 4 times his power per day ; and as machinery may 
 be supposed to work continually, = a trifle less than 23 per cent, per 
 day of a machine horse-power. 
 
 STEAM. 
 
 Table exhibiting the expansive force and various conditions of steam 
 under different degrees of temperature. 
 
 Decrees of 
 heat. 
 
 Pressure in 
 atmospheres. 
 
 Density. 
 Water m 1. 
 
 Volume. 
 Water as 1. 
 
 Spec, gravity. 
 Air as 1. 
 
 Weight of a 
 
 cubic loot in 
 
 grains. 
 
 212 
 
 1 
 
 .00059 
 
 1694 
 
 .484 
 
 254 
 
 250.5 
 
 2 
 
 .00110 
 
 909 
 
 .915 
 
 483 
 
 270 
 
 3 
 
 .00160 
 
 625 
 
 1.330 
 
 700 
 
 293.8 
 
 4 
 
 .00210 
 
 476 
 
 1.728 
 
 910 
 
 308 
 
 5 
 
 .00258 
 
 387 
 
 2.120 
 
 1110 
 
 359 
 
 10 
 
 .00492 
 
 203 
 
 3.970 
 
 2100 
 
 418.5 
 
 20 
 
 .00973 
 
 106 
 
 7.440 
 
 3940 
 
 [An atmosphere is 14^ lbs. to the square inch.] 
 
 Note. — By the above table it is seen that any given quantity of steam having a tem- 
 perature of 212° F., occupies a space, under the ordinary pressure of the atmosphere, 
 1694 times greater than it occupied when as water in a natural state. It exerts a mechan- 
 ical force, consequently, = 1694 times the weight or force of the atmosphere resting on 
 the bulk from which it was generated, or resting on l-1694th of the space it occupies. 
 A force, if we consider the volume as so many cubic inches, equal to the raising of 2087 
 lbs. 12 inches high, by a quantity of steam less than a cubic foot, heated only to the tem- 
 perature of boiling water, and weighing but 248 grains, and that, too, the product of a 
 single cubic inch of water. 
 
 The mean. pressure of the atmosphere at the earth's surface is equal 
 to the weight of a column of mercury 29.9 inches in height, or to a 
 column of water 33.87 feet in height, = 2110.8 lbs. per square foot, or 
 
84 
 
 VELOCITY AND FORCE OF WIND. 
 
 14.7 lbs. per square inch. Its density above the earth is uniformly 
 less as its altitude is greater, and its extent is not above 50 miles — 
 its mean altitude is about 45 miles ; at 44 miles it ceases to reflect 
 light. Were it of uniform density throughout, and of that at the sur- 
 face, its altitude would be but 54 miles. Its weight is to pure water 
 of equal temperature and volume, as 1 to 829. It revolves with the 
 earth, and its average humidity, at 40° of latitude, is 4 grains per cubic 
 foot. Its weight at 60°, b. 30, compared with an equal bulk of pure 
 water at 40°, b. 30, is as 1 to 830.1. 
 
 VELOCITY AND FORCE OF WIND. 
 
 
 Mean ve 
 
 locity in 
 
 1 
 
 
 Miles per 
 
 Feet per 
 
 Force in lb». per 
 
 Appellations. 
 
 hour. 
 
 second. 
 
 square foot. 
 
 Just perceptible, 
 
 2£ 
 
 3| 
 
 .032 
 
 Gentle, pleasant wind, . 
 
 4£ 
 
 H 
 
 .101 
 
 Pleasant, brisk gale, . 
 
 m 
 
 18} 
 
 .80 
 
 Very brisk, " 
 
 22£ 
 
 33 
 
 2.52 
 
 High wind, 
 
 32£ 
 
 47| 
 
 5.23 
 
 Very high wind, . 
 
 42£ 
 
 62J 
 
 8.92 
 
 Storm, or tempest, 
 
 50 
 
 73J 
 
 12.30 
 
 Great storm, 
 
 60 
 
 88 
 
 17.71 
 
 Hurricane, 
 
 80 
 
 in* 
 
 31.49 
 
 Tornado, moving buildings, &c, 
 
 100 
 
 146.7 
 
 49.20 
 
 The curvature of the earth is 6.99 inches (.5825 foot) in a single 
 
 statute mile, or 8.05 inches in a geographical mile, and is as the 
 
 square of the distance for any distance greater or less, or space 
 
 between two levels ; thus, for three statute miles it is 
 
 1 : 3 2 : : 6.99 : 54 feet, nearly. 
 
 The horizontal refraction is T (r. 
 
 Degrees of longitude are to each other in length, as the cosines of 
 their latitudes. At the equator a degree of longitude is 60 geographical 
 miles in length, at 90° of latitude it is ; consequently, a degree of 
 
 longitude at 
 
 
 
 
 5° 
 
 = 59.77 miles. 
 
 40° 
 
 = 45.96 miles 
 
 10° 
 
 = 59.09 " 
 
 50° 
 
 = 38.57 " 
 
 20° 
 
 = 56.38 " 
 
 70° 
 
 = 20.52 " 
 
 30° 
 
 = 51.96 " 
 
 85° . 
 
 = 5.23 " 
 
 Time is to longitude 4 minutes to a degree, — faster, east of any 
 given point ; slower, west. 
 
 The mean velocity of sound at the temperature of 33° is 1100 feet 
 a second. Its velocity is increased £ a foot a second for overy degree 
 
GRAVITATION. 85 
 
 above 33°, and decreased £ a foot a second for every degree below 
 33 . 
 
 In water, sound passes at the rate of 4,708 feet a second. 
 
 Light travels at the rate of 192,000 miles per second. 
 
 GRAVITATION. 
 
 Gravity, or Gravitation, is a property of all bodies, by which 
 they mutually attract each other proportionally to their masses, 
 and inversely as the square of the distance of their centres apart. 
 Practically, therefore, with reference to our Earth and the bodies 
 upon or near its surface, gravity is a constant force centred at the 
 Earth's centre, and is there continually operating to draw all bodies 
 with a uniformly accelerating velocity to that point, and through 
 very nearly equal spaces, in equal intervals of time from rest, at all 
 localities. 
 
 Putting R 1 to represent the Equatorial radius of the earth, and r 
 to represent the Polar, and making IV = 3962.5 statute miles, and 
 r= 3949.5, which is nearly in accordance with the mean of the 
 most reliable measurements of the arcs of a degree of latitude at 
 different locailties, we have e a = (R 12 — r 2 ) -7- R> 2 = .006550751 , the 
 square of the ellipticity of the earth, and R = 2R' -7- (2 -f- e 2 sinH), 
 the radius at any given latitude I. 
 
 And since the initial velocity due to gravity at the level of the 
 sea at the Equator is G = 32.0741 feet per second, or, in other 
 words, since a body falling in vacuo at the equator, at the level of 
 the sea, describes a space of 16.03705 feet in the first second of 
 time from rest, we have g = [R t ^G)-^-RJ i , the initial velocity at 
 the level of the sea at any given radius R ; or g = (22441.2 — R)\ 
 
 a i a 11 / 22441.2 V / 2h \ 
 
 And finally g= {——) x (l -g^) at any given ra- 
 
 dius R, at any given altitude, Ji, in feet, above the level of the sea. 
 
 Note. — When I, reckoned from the equator, is higher than 45°, sin 2 I =s 
 cos a ('JO — I). 
 
 The momentum, or force, with which a falling body strikes, is the 
 product of its weight and velocity (the weight multiplied by the 
 square root of the product of the .space fallen through and 64.33, 
 or 4 times 16 T ^) ; thus, 100 lbs., falling 50 feet, will strike with a 
 
 50 X 64.333=^3216.66 = 56.71 X 100 = 5671 lbs. 
 An entire revolution of the earth, from west to east, is performed 
 in 23 hours, 56 minutes, and 4 seconds. A solar year = 365 days, 
 5 hours, 48 minutes, 57 seconds. 
 
 The area of the earth is nearly 1 9 7,000,000 square miles. Its crust 
 
 is supposed to be about 30 miles in thickness, and its mean density 5 
 
 times that of water. About f of its area, or 150,000,000 square 
 
 miles, is covered by water. The portions of land in the several 
 
 8 
 
80 CHEMICAL ELEMENTS. 
 
 divisions, in square miles, are, in round numbers, as follows, 
 viz: — 
 
 Asia, . . 16,300,000 1 Europe, . . 3,700,000 
 
 Africa, . . 11,000,000 Australia, . . 3,000,000 
 
 America, . . 14,500,000 1 
 
 America is 9000 miles long, or T ^y the circumference of the 
 earth. 
 
 The population of the globe is about 1,000,000,000, of which there 
 are, in 
 
 Asia, . . 456,000,000 I Africa, . . 62,000,000 
 
 Europe, . . 258,000,000 | America, . . 55,000,000 
 
 CHEMICAL ELEMENTS. 
 
 The chemical elements — simple substances in nature — as far as 
 has been determined, are 58 in number : 13 non-metallic and 45 
 metallic. 
 
 Of the non-metallic, 5 — bromine, chlorine, fluorine, iodine, and oxy- 
 gen, (formerly termed "supporters of combustion,") have an intense 
 affinity for all the others, which they penetrate, corrode, and appar- 
 ently consume, always with the production, to some extent, of light 
 and heat. They are all non-conductors of electricity and negative 
 electrics. 
 
 The remaining 8 — hydrogen, nitrogen or azote, carbon, boron, sili- 
 con, phosphorus, selenium, and sulphur, are eminently susceptible of 
 the impressions of the preceding five ; when acted upon by either of 
 them to a certain extent, light and heat are manifestly evolved, and 
 they are thereby converted into incombustible compounds. 
 
 Of the metals, 7 — potassium, sodium, calcium, barytium, lithium, 
 strontium, and magnesia, by the action of oxygen, are converted into 
 bodies possessed of alkaline properties. 
 
 Seven of them — glucinum, irhium, terbium, yttrium, allumiuni, zir- 
 conium, and thorium, — by the action of oxygen, are converted into 
 tin- earths proper. 
 
 In short, all the metals are acted upon by oxygen, as also by most 
 or all of the non-metallic family. The compounds thus formed are 
 alkaline, saline, or acidulous, or an alkali, ■ salt, or BO arid, according 
 to the nature of the materials and the extent of combination. 
 
 Metals combine with each other, forming alloy*. W one of the 
 
 metaU in combination is mercury, the compound is called an amalgam. 
 
 Silicon is the base of the mineral World, and carbon of the organ- 
 oid. 
 
 For a very general list of the metals, see Table of Specific (Jrav- 
 ities. 
 
CONSTITUENTS OF BODIES. 
 
 87 
 
 TABLE 
 
 Exhibiting the Elementary Constituents and per cent, by weight of each, 
 in 100 parts of different compounds. 
 
 Com pound*. 
 
 Constituents nn>j per cent. 
 
 Atmospheric air, ... a 
 
 Hydrogen. 
 
 Oxysren. 
 
 Azote. 
 
 ( 'in DOB, 
 
 
 20.8 
 
 79.2 
 
 
 AV;iter, pure, 
 
 11.1 
 
 88.9 
 
 
 
 Alcohol, anhydrous, 
 
 12.9 
 
 34.44 
 
 
 52.66 
 
 Olive oil, .... 
 
 13.4 
 
 9.4 
 
 
 77.2 
 
 Sperm " . ... 
 
 10.97 
 
 10.13 
 
 
 78.9 
 
 Castor " 
 
 10.3 
 
 15.7 
 
 
 74.00 
 
 Stearine, (solid of fats,) 
 
 11.23 
 
 6.3 
 
 0.30 
 
 82.17 
 
 Oleine, (liquid of fats,) 
 
 11.54 
 
 12.07 
 
 0.35 
 
 76.03 
 
 Linseed oil, . 
 
 11.35 
 
 12.64 
 
 
 76.01 
 
 Oil of turpentine, 
 
 11.74 
 
 3.66 
 
 
 84.6 
 
 " Camphene," (pure spts. turp.) 
 
 11.5 
 
 
 
 88.5 
 
 Caoutchouc, (gum elastic,) . 
 
 10. 
 
 
 
 90. 
 
 Camphor, .... 
 
 11.14 
 
 11.48 
 
 
 77.38 
 
 Copal, resin, 
 
 9. 
 
 11.1 
 
 
 79.9 
 
 Guaiac, resin, 
 
 7.05 
 
 25.07 
 
 
 67.88 
 
 Wax, yellow, 
 
 11.37 
 
 7.94 
 
 
 80.69 
 
 Coals, cannel, 
 
 3.93 
 
 21.05 
 
 2.80 
 
 72.22 
 
 " Cumberland, 
 
 3.02 
 
 14.42 
 
 2.56 
 
 80. 
 
 " Anthracite, . . b 
 
 
 
 
 93. 
 
 Charcoal, .... 
 
 
 
 
 97. 
 
 Diamond, .... 
 
 
 
 
 100. 
 
 Oak wood, dry, c 
 
 5.69 
 
 41.78 
 
 
 52.53 
 
 Beech " " 
 
 5.82 
 
 42.73 
 
 
 51.45 
 
 Acetic acid, dry, 
 
 5.82 
 
 46.64 
 
 
 47.54 
 
 Citric " crystals, . 
 
 4.5 
 
 59.7' 
 
 
 35.8 
 
 Oxalic " -dry, 
 
 
 79.67 
 
 
 20.33 
 
 Malic, " crystals, . 
 
 3.51 
 
 55.02 
 
 
 41.47 
 
 Tartaric " dry, 
 
 3. 
 
 60.2 
 
 
 36.80 
 
 Formic " 
 
 2.68 
 
 64.78 
 
 
 32.54 
 
 Tannin, tannic acid, solid, 
 
 4.20 
 
 44.24 
 
 
 51.56 
 
 Nitric acid, dry, . . 
 
 
 73.85 
 
 26.15 
 
 
 Nitrous " anhydrous, liquid, 
 
 
 61 32 
 
 30.68 
 
 
 Ammoniacal gas, 
 
 17.47 
 
 
 82.53 
 
 
 Carbonic acid " . 
 
 
 72.32 
 
 
 27.68 
 
 Carb. hydrogen gas, 
 
 24.51 
 
 
 
 75.49 
 
 Bi-carb. hyd., okfient gas, . 
 
 14.05 
 
 
 
 85.95 
 
 Cyanogen " 
 
 
 
 53.8 
 
 46.2 
 
 Nitric oxyde " 
 
 
 53. 
 
 47.00 
 
 
 Nitrous " " 
 
 
 36.36 
 
 63.64 
 
 
 Ether, sulphuric, . 
 
 13.85 
 
 21.24 
 
 
 65.05 
 
 Creosote, .... 
 
 7.8 
 
 16. 
 
 
 76.2 
 
88 
 
 CONSTITUENTS OF BODIES. 
 
 Compound!. 
 
 
 
 L 
 Hydro g-en. 
 
 onstituenti 
 Oxygen. 
 
 and per cen 
 Azote. 
 
 Carbon. 
 
 Morphia, .... 
 
 6.37 
 
 16.29 
 
 5. 
 
 72.34 
 
 Quina, — quinine, 
 
 
 7.52 
 
 8.61 
 
 8.11 
 
 75.76 
 
 Veratrine, .... 
 
 
 8.55 
 
 19.61 
 
 5.05 
 
 66.79 
 
 Indigo, 
 
 
 
 4.38 
 
 14.25 
 
 10. 
 
 71.37 
 
 Silk, pure white, 
 
 
 
 3.94 
 
 34.04 
 
 11.33 
 
 50.69 
 
 Starch, — farina, < 
 
 lextrine, 
 
 
 6.8 
 
 49.7 
 
 
 43.5 
 
 Sugar, 
 
 . 
 
 
 6.29 
 
 50.33 
 
 
 43.38 
 
 Gluten, 
 
 , . 
 
 
 7.8 
 
 22. 
 
 14.5 
 
 55.7 
 
 Wheat, 
 
 , 
 
 c 
 
 6. 
 
 44.4 
 
 2.4 
 
 47.02 
 
 Rye, . 
 
 . 
 
 
 5.7 
 
 45.3 
 
 1.7 
 
 47.03 
 
 Oats, . 
 
 , # 
 
 
 6.6 
 
 38.2 
 
 2.3 
 
 52.9 
 
 Potatoes, 
 
 # 
 
 
 6.1 
 
 46.4 
 
 1.06 
 
 45.9 
 
 Peas, . 
 
 g 
 
 
 6.4 
 
 41.3 
 
 4.3 
 
 48. 
 
 Beet root, . 
 
 § 
 
 
 6.2 
 
 46.3 
 
 1.8 
 
 45.7 
 
 Turnips, 
 
 . 
 
 
 6. 
 
 45.9 
 
 1.8 
 
 46.3 
 
 Fibrin, 
 
 . 
 
 '. d 
 
 7.03 
 
 20.30 
 
 19.31 
 
 53.36 
 
 Gelatin, 
 
 , 
 
 . d 
 
 7.91 
 
 27.21 
 
 17. 
 
 47.88 
 
 Albumen, 
 
 • 
 
 . d 
 
 7.54 
 
 23.88 
 
 15.70 
 
 52.88 
 
 Muriatic acid gas, — Hydrogen 5.53 -|- 94.47 chlorine. 
 Sulphuric acid, dry, — Oxygen 79.67 -\- 20.33 sulphur. 
 Silicic acid — Silica, dry, — Oxygen 51.96 -J- 48.04 silicon. 
 Boracic acid — Borax, dry,— " 68.81 -f- 31.19 boron. 
 
 a. The atmosphere, in addition to its constituents as given in the 
 table, contains, besides a small quantity of vapor, from 1 to 3 parts in 
 a thousand of carbonic acid gas, and a trace merely of ammoniacal gas. 
 
 b. Anthracite coal, charcoal, plumbago, coke, &c, have no other 
 constituent than carbon ; they are combined, to a small extent, with 
 foreign matters, such as iron, silica, sulphur, alumina, '&c. 
 
 c. The constituents of woods, grains, &c, are given per cent., with- 
 out regard to the foreign matters (metallic) which they contain. In 
 oak, chestnut, and Norway pine, the ashes amount to about -fa of 1 per 
 cent., and in ash and maple to -^ of 1. In anthracite coals, at an 
 average, they are about 7 per cent. 
 
 d. Fibrin, Gelatin, Albumen — Proximate animal constituents — 
 Nutritious properties of animal matter. 
 
 Fibrin is the basis of the muscle (lean meat) of all animals, and is 
 also a large constituent of the blood. 
 
 Gelatin exists largely in the skin, cartilages, ligaments, tendons and 
 bones of animals. It also exists in the muscles and the membram s. 
 
 Albumen exists in the skin, glands and vessels, and in the serum of 
 the blood. It constitutes nearly the whole of the white of an egg. 
 
CONSTITUENTS OP BODIES. 89 
 
 The relative quantities by volume of the several gases going to 
 constitute any particular compound, are readily ascertained by help 
 of their respective specific gravities, compared with their relative 
 weights, as given per cent, in the preceding table:— thus, the sp. 
 gr. of hydrogen is .0689, and that of oxygen 1.1025, and 1.1025 -J- 
 .0689 = 16 ; showing the weight of the latter to be 16 times that of 
 the former per equal volumes, or, relatively, as 16 to 1. The per 
 cent, by weight, as shown by the table, in which these two gases 
 combine to form water, for instance, is 11.1 and 88.9 ; or 11.1 of 
 hydrogen and 88.9 of oxygen in 100 of the compound ; or as 88.9 -j- 
 11.1, — as 8 to 1: 16 -j- 8 = 2 : two volumes, therefore, of the 
 lighter gas (hydrogen) combine with one of oxygen to form water. 
 Water, consequently, ts a Protoxide of Hydrogen. 
 
 Upon the principle of atomic weights — primal quantities, by 
 weight, in which bodies combine, based upon some fixed radix, usually 
 hydrogen as it forms with water, and as 1, — we have, for water, — 
 II 1 -\- O* = Aq. 9. An atom of hydrogen, therefore, is 1, an atom 
 of oxygen 8, and an atom of water 9. 
 
 By the same rule as the preceding, the constituents of atmospheric 
 air are found to be to each other in volume as 4 to 1, — 4 volumes of 
 nitrogen and 1 volume of oxygen =» atmospheric air. The weight 
 of nitrogen to hydrogen per equal volumes, is as 14.14 to 1. Atomic- 
 ally, therefore, oxygen being 8, it is as 7.07 to 1 ; hence we have 
 N 4 -j- O = 36.28, the atomic weight of atmosphere. 
 
 The vast condensation of the gases which takes place, in some in- 
 stances, in forming compounds, may be conceived of, and the process 
 for determining the same exhibited by a single illustration. We will 
 take, for example, water. A single cubic inch of distilled water, at 
 60°, weighs 252.48 grains. Its weight is to that of dry atmosphere, 
 at the same temperature, as 827.8 to 1. A cubic inch of dry atmos- 
 phere, therefore, at that density, weighs .305 of a grain. Hydrogen, 
 we find by the table of Specific Gravities, weighs .0689 as much 
 as atmosphere, and oxygen 1.1025 as much. A cubic inch of hydro- 
 gen, therefore, weighs .0689 X .305 = .0210145 of a grain, and 
 a cubic inch of oxygen 1.1025 X .305,= .3362625 of a grain. 
 The constituents of water by volume are 2 of the first mentioned gas 
 to 1 of the hitter; and .0210145 X 2 -f .3362625 = .3782915 of a 
 grain, = weight of three cubic inches of the uncondensed compound, 
 ] of which, .1260972 of a grain, is the weight of a volume 1 cubic 
 inch. 
 
 As the weight of a given volume of the uncondensed compound, is 
 to the weight of an equal volume of the condensed compound, so are 
 their respective volumes, inversely : then — 
 
 .1260972 : 252.18 :: 1 : 2002.26, the number of cubic inches of the 
 two gases condensed into 1 inch to form water ; a condensation of 
 2001 times. Of this volume of gases, §, or 1334.84 cubic inches, is 
 hydrogen ; the remaining third, 667.42 cubic inches, is oxygen. 
 
 8* 
 
90 PROPERTIES, ETC., OF BODIES. 
 
 The foregoing method, though strictly correct, does not exhibit in a 
 general way the most expeditious for solving questions of that nature, 
 the condensation which takes place in the gases on being converted 
 into solids, or* dense compounds. It was resorted to, in part, as a 
 means through which to exhibit principles and proportions pertaining 
 thereto. 
 
 As before ; one cubic inch of water weighs 252.48 grains, .*. of 
 which, or 28.05-}- grains, is hydrogen, and |^ or 224. 43 — grains, is 
 oxygen. The volume of 1 grain of oxygen is 2.97-j- cubic inches, and 
 the volume of hydrogen is 16 times as much, or47.58-|- cubic inches. 
 Therefore, 28.05 X 47.58 = 1334.62, and 224.43 X 2.97 = 665.56, 
 *= 2001.18, condensation, as before. 
 
 Properties of tlie simple substances, and some of their compounds, not 
 given in the foregoing. 
 Bromine, — at common temperatures, a deep reddish-brown vola- 
 tile liquid ; taste caustic ; odor rank ; boils at 116° ; congeals at 4° ; 
 exists in sea-water, in many salt and mineral springs, and in most 
 marine plants ; action upon the animal system very energetic and 
 poisonous — a single drop placed upon the beak of a bird destroys the 
 bird almost instantly. A lighted taper, enveloped in its fumes, burns 
 with a flame green at the base and red at the top ; powdered tin or 
 antimony brought in contact is instantly inflamed ; potash is exploded 
 with violence. 
 
 Chlorine, — a greenish-yellow, dense gas ; taste astringent; odor 
 pungent and disagreeable ; by a pressure of 60 lbs. to the square inch 
 is reduced to a liquid, and thence, by a reduction of the temperature 
 below 32°, into a solid. It exists largely in sea-water — is a constit- 
 uent of common salt, and forms compounds with many minerals ; is 
 deleterious, irritating to the lungs, and corrosive ; has eminent 
 bleaching properties, and is the greatest disinfecting agent known ; 
 a lighted taper immersed in it burns with a red flame ; pulverized 
 antimony is inflamed on coming in contact, so is linen saturated with 
 oil of turpentine ; phosphorus is ignited by it, and burns, while im- 
 mersed, with a pale-green flame ; with hydrogen, mixed measure for 
 measure, it is highly explosive and dangerous. 
 
 Fluorine, — a gas, similar to chlorine, — exists abundantly in 
 fluor-spar. 
 
 Oxygen, — a transparent, colorless, tasteless, inodorous, innoxious 
 gas ; supports respiration and combustion, but will not sustain life for 
 any length of time, if breathed in a pure state. It is by far the most 
 abundant substance in existence ; constitutes ^ of the atmosphere ; 
 
PROPERTIES, ETC., OF BODIES. 01 
 
 g of water ; and nearly the whole crust of the earth is oxidized sub- 
 stances. For further combinations and properties, see tables of Ele- 
 mentary Constituents and Chemical Elements. 
 
 Iodine, — at common temperatures, a soft, pliable, opaque, bluish- 
 black solid ; taste acrid ; odor pungent and unpleasant ; fuses at 225° ; 
 boils at 317° ; its vapor is of a beautiful violet color ; it inflames 
 phosphorus, and is an energetic poison ; exists mainly in sea-weeds 
 and sponges. 
 
 Hydrogen, — a transparent, colorless, tasteless, inodorous, innox- 
 ious gas ; if pure, will not support respiration ; if mixed with oxy- 
 gen, produces a profound sleep ; exists largely in water ; is the basis 
 of most liquids, and is by far the lightest substance known ; burns in 
 the atmosphere with a pale, bluish light ; mixed with common air, 1 
 measure to 3, it is explosive ; mixed with oxygen, 2 measures to 1, 
 it is violently so. 
 
 Nitrogen, or Azote, — a transparent, colorless, tasteless, inodorous 
 gas ; will not support respiration or combustion, if pure ; exists 
 largely as a constituent of the atmosphere — in animals, and in fun- 
 gous plants ; is evolved from some hot springs ; in connection with 
 some bodies, appears combustible. 
 
 Carbon, — the diamond is the only pure carbon in existence ; pure 
 carbon cannot be formed by art ; charcoal is 97 per cent, carbon ; plum- 
 bago, 95 ; anthracite, 93. Carbon is supposed by some to be the hard- 
 est substance in nature. A piece of charcoal will scratch glass; but 
 it is doubtful if this is not due to the form of its crystals, rather than 
 to the first mentioned quality. It is doubtless the most durable. For 
 combinations, &c, see table. 
 
 Boron, — a tasteless, inodorous, dark olive-colored solid. 
 
 Silicon, — a tasteless, inodorous solid, of a dark-brown color; 
 exists largely in soils, quartz, flint, rock-crystal, &c. ; burns readily 
 in air — vividly in oxygen gas ; explodes with soda, potassa, barryta. 
 
 Phosphorus, — a transparent, nearly colorless solid, of a wax- 
 like texture ; fuses at 108°, and at 550° is converted into a vapor; 
 exists mainly in bones — most abundant in those of man — is poison- 
 ous ; at common temperatures it is luminous in the dark, and by fric- 
 tion is instantly ignited, burning with an intense, hot, white flame ; 
 must be kept immersed in water. 
 
 Selenium, — a tasteless, inodorous, opaque, brittle, lead-colored 
 
92 PROPERTIES, ETC., OF BODIES. 
 
 solid, in the mass ; in powder, a deep-red color ; becomes fluid at 
 216°, boils at 050°; vapor, a deep yellow; exists but sparingly, 
 mainly in combination with volcanic matter ; is found in small quan- 
 tities combined with the ores of lead, silver, copper, mercury. 
 
 Ammoniacal gas, — N -f- H 3 ; transparent, colorless, highly pun- 
 gent and stimulating ; alkaline ; is converted into a transparent liquid 
 by a pressure of 6.5 atmospheres, at 50° ; does not support respira- 
 tion ; is inflammable. 
 
 Carbonic acid gas, — C -f- O' 2 ; transparent, colorless, inodorous, 
 dense ; is converted into a liquid by a pressure of 36 atmospheres ; 
 exists extensively in nature, in mines, deep wells, pits ; is evolved 
 from the earth, from ordinary combustion, especially from the combus- 
 tion of charcoal, and from many mineral springs ; is expired by man 
 and animals ; forms 44 per cent, of the carbonate of lime called mar- 
 ble ; the brisk, sparkling appearance of soda-water, and most mineral 
 waters, is due to its presence. It is neither a combustible nor a sup- 
 porter of combustion ; and, when mixed with the atmosphere to an 
 extent in which a candle will not burn, is destructive of life. Being 
 heavier than atmosphere, it maybe drawn up from wells in large open 
 buckets ; or it may be expelled by exploding gunpowder near the bot- 
 tom. Large quantities of water thrown in will absorb it. 
 
 The above gas is expired by man to the extent of 1632 cubic inches 
 per hour ; it is generated by the burning of a wax candle to the ex- 
 tent of 800 cubic inches per hour : and, by the burning of "Cam- 
 phenc," (in the production of light equal to that afforded by 1 \v;ix 
 candle,) to the extent of 875 cubic inches per hour. Two burning 
 candles, therefore, vitiate the air to about the same extent as 1 per- 
 son. 
 
 Carbonic oxide gas, — C -\- O ; transparent, colorless, insipid ; 
 odor offensive ; does not support combustion; an animal confined in 
 it soon dies ; is highly inflammable, burning with a pale blue flame ; 
 mixed with oxygen, 1 to 2, is explosive — with atmosphere, even in 
 small quantity, is productive of giddiness and fainting. 
 
 Carburrtul hydrogen gas, — C -j- H a ; transparent, colorless, taste- 
 less, nearly inodorous; exists in marshes and stagnant pools — is 
 there formed by the decomposition of vegetable matter ; extinguishes 
 all burning bodies, but at the same time is itself highly eombustible, 
 burning with a bright but yellowish flame ; it is destructive to life, it 
 respired. 
 
 : no gen — Bkarburct of Nitrogen — a gas, — N -f- C ; trans 
 :, colorless, highly pungent and irritating ; under a pressure of 
 
TROrERTIES, ETC., OF BODIES. \)d 
 
 3.6 atmosphen s, becomes a limpid liquid ; burns with a beautiful 
 purple flame. 
 
 Hydrochloric acid gas — Muriatic acid gas, — II -j- CI. (chlorine) ; 
 transparent, colorless, pungent, acrid, suffocating ; strong acid taste. 
 
 Nitrous oxide gas — Protoxide of Nitrogen, " laughing gas," — 
 N -j- O ; transparent, colorless, inodorous ; taste sweetish ; powerful 
 stimulant, when breathed, exciting both to mental and muscular ac- 
 tion ; can support respiration but from 3 to 4 minutes ; is often per- 
 nicious in its effects. 
 
 Nitric oxide gas — Binoxide of Nitrogen, — N -f- O 2 ; transparent, 
 colorless ; wholly irrespirable ; lighted charcoal and phosphorus burn 
 in it with increased brilliancy. 
 
 Olcfiant gas — Bicarburctcd hydrogen gas — " coal gas," — C 2 -j- 
 H 2 ; transparent, colorless, tasteless, nearly inodorous, when pure ; 
 does not support respiration or combustion ; a lighted taper immersed 
 in it is immediately extinguished. It burns with a strong, clear, 
 white light ; mixed with oxygen, in the proportion of 1 volume to 3, 
 it is highly explosive and dangerous. 
 
 Phosphureted hydrogen gas, — P -\- H 3 ; colorless ; odor highly 
 offensive ; taste bitter ; exists in the vicinity of swamps, marshes, 
 and grave -yards ; is formed by the decomposition of bones, mainly ; 
 is highly inflammable ; takes fire spontaneously on coming in contact 
 with the atmosphere ; mixed with pure oxygen, it explodes. It is 
 the veritable " Will o' the wisp." 
 
 Sulphureted hydrogen gas — Hydrosulphuric acid gas, — S -j- H ; 
 transparent, colorless.; taste exceedingly nauseous ; odor offensive 
 and disgusting ; is furnished by the sulphurets of the metals in gen- 
 eral — also by filthy sewers and putrescent eggs. It is very destruc- 
 tive to life ; placed on the skin of animals, it proves fatal. It burns 
 with a pale blue flame, and, mixed with pure oxygen, it is explosive. 
 
 Hydrocyanic acid — Prussic acid, — N -j- C 2 -j- H ; a colorless, 
 limpid, highly volatile liquid; odor strong, but agreeable — similar 
 to that of peach-blossoms ; it boils at 79° and congeals at ; exists 
 in laurel, the bitter almond, peach and peach kernel. It is a most 
 virulent poison, — a drop placed upon a man's arm caused death in a 
 few minutes. A cat, or dog, punctured in the tongue with a needle 
 fresh dipped in it, is almost instantly deprived of life.- 
 
 Hydrofluoric acid, — F -j- H ; a colorless liquid, in well stopped 
 lead or silver bottles, at any temperature between 32° and 59°. It is 
 
9i PROPERTIES, ETC., OP BQDIES. 
 
 obtained by tbe action of sulphuric acid on fluor-spar. It readily 
 acts upon and is used for etching on glass. It is the most destructive 
 to animal matter of any known substance. 
 
 Nitrohydrochhric acid — " aqua regia," — (1 part nitric acid and 4 
 parts muriatic acid, by measure ;) — a solvent for gold. The best sol- 
 vent for gold is a solution of sal ammoniac in nitric acid. 
 
 Nitrosulphuric acid, — (1 part nitric acid and 10 parts sulphuric 
 acid, by measure) — a solvent for silver; scarcely acts upon gold, 
 iron, copper, or lead, unless diluted with water ; is used for separat- 
 ing the silver from old plated ware, &c. The best solvent for silver, 
 and one which will not act in the least upon gold, copper, iron, or 
 lead, is a solution of 1 part of nitre in 10 parts of concentrated sul- 
 phuric acid, by weight, heated to 160°. This mixture will dissolve 
 about £ its weight of silver. The silver may be recovered by adding 
 common salt to the solution, and the chloride decomposed by the car- 
 bonate of soda. 
 
 Selenic acid, — Se -j~ O 3 ; obtained by fusing nitrate of potassa with 
 selenium — a solvent for gold, iron, copper, and zinc. 
 
 Silicic acid, — (Silica — silex ; base Silicon) — Si -j- O 3 ; exists 
 largely in sand. Common glass is fused sand and protoxide of potas- 
 sium (carbonate of potassa — potash) in the proportion of 1 part by 
 weight of the former to 3 of the latter. 
 
 Manganese, compounded with oxygen, in different proportions, im- 
 parts the various colors and tints given to fancy glass ware, now se 
 generally in vogue. 
 
SECTION III. 
 PRACTICAL ARITHMETIC. 
 
 VULGAR FRACTIONS. 
 
 A fraction is one or more parts of a Unit. 
 
 A vulgar fraction consists of two terms, one written above the 
 other, with a line drawn between them. 
 
 The term below the line is called the denominator, as showing the 
 denomination of the fraction, or number of parts into which the unit 
 is broken. 
 
 The term above the line is called the numerator, as numbering the 
 parts employed. These together constitute the fraction and its 
 value. 
 
 A vulgar fraction always denotes division, of which the denomina- 
 tor is the divisor and the numerator the dividend. Its value as a unit 
 is the quotient arising therefrom. 
 
 A simple fraction is either a proper or improper fraction. 
 
 A proper fraction is one whose numerator is less than its denomina- 
 tor, as £, f , |L, &c. 
 
 An improper fraction has its numerator equal to or greater than its 
 denominator, as f , £, f f , &c. 
 
 A mixed fraction is a compound of a whole number and a fraction, 
 as lj, 6Ji, 12ft, &c. 
 
 A compound fraction is a fraction of a fraction, as £ of | ; | of 
 4 of if, &c. 
 
 A complex fraction has a fraction for its numerator or denom- 
 inator, or both, as |, -, |, — , &c, and is read J -J- 3 ; 4 -5- g ; 
 
 £-H; si-i-V&c. 
 
 REDUCTION OF VULGAR FRACTIONS. 
 To reduce a fraction to its lowest terms. 
 
 This consists in concentrating the expression without changing the 
 value of the fraction or the relation of its parts. 
 
 It supposes division, and, consequently, by a measure or measures 
 common to both terms. 
 
 It is said to be accomplished when no number greater than 1 will 
 divide both terms without a remainder: — therefore, 
 
96 VULGAR FRACTIONS. 
 
 Rule. — Divide both terms by any number that will divide them 
 without a remainder, and the quotient again as before ; continue so to 
 do until no number greater than 1 will divide them, — or divioe by 
 the greatest common measure at once. 
 
 Example. — Reduce jW? l0 * ts lowest terms. 
 *)-Afe-Wi^2-i|f + 9-if-5-3-f Ant. 
 
 To reduce an improper fraction to a mixed or whole number. 
 
 Rule. — Divide the numerator by the denominator and to the 
 whole number in the quotient annex the remainder, if any, in form of 
 a fraction , making the divisor the denominator as before ; then reduce 
 the fraction to its lowest terms. 
 
 Example. £«. 1± ; |J- 1 T ^ = i£ ; ff - 2. 
 
 To reduce a mixed fraction to an equivalent improper fraction. 
 
 Rule. — Multiply the whole number by the denominator of the 
 fractional part, and to the product add the numerator, and place their 
 sum over the said denominator. 
 
 Example. — Reduce 3£ and 12§ to improper fractions. 
 
 3X4 = 12 4-1 = ^-. Ans. 12 X 9 + 8 — ■!£&. Ans. 
 
 To reduce a whole number to an equivalent fraction having a given 
 denominator . 
 
 Rule. — Multiply the whole number by the given denominator, 
 and place the said denominator under the product. 
 
 Example. — How may 8 be converted into a fraction whose de- 
 nominator is 12 ? 
 
 8 X 12 — f f • Ans. 
 
 To reduce a compound fraction to a simple one. 
 Rule. — Multiply all the numerators together for a numerator, and 
 all the denominators together for a denominator ; the fraction thus 
 formed will be an equivalent, but often not in its lowest terms. Or, 
 concentrate the expression, when practicable, by reciprocally expung- 
 ing, or writing out, such factors as exist or are attainable common to 
 both terms, and then multiply the remaining terms as directed above. 
 
 Note. —This last practice is called cancellation, or canoeUloa the tafBI 
 an has been stated, in reciprocally annulling, or casting out, aqua! value- from both terms, 
 whereby tho expression is concentrated, and the relation of the parts kept umDaturbsd ; 
 
 ami it may always be carried to tin: extent of reducing the fraction to its lowest tonus, 
 my multiplication, as final, is resorted to; and ofte.i. therefore, to the extent that 
 ruch multiplication is inadmissible, the terms having been cancelled by cueh other until 
 but a single numlier is left in each. 
 
VULGAR FRACTIONS. 
 
 97 
 
 Example. — Reduce § of $ of A to a simple fraction. 
 
 Operation by multiplication, |Xf Xi 53 ^ 33 !- Ans. 
 
 23 1 
 Operation by cancellation, a . = \. Ans. 
 
 Example. — Reduce § of £ of *g- of £ of £ of 2 to a simple 
 fraction. 
 
 By multiplication, § X £ X -V X f X $ X \ - Iff 2 - f. ^>». 
 The last example stated ) 2 3 12 6 5 2 
 for cancellation, ) 3 4 8 8 9 
 
 PROCESS OF CANCELLING THE ABOVE. 
 
 1. The 3 in num. equals the 3 in denom., therefore erase both. 
 
 2. The first 2 in num. equals or measures the 4 in denom. twice, therefore place a 2 
 under the 4, and erase the 4 and 2 which measured it — (as 4 : 2 : : 2:1.) 
 
 3. The 2 (remaining factor of 4 and 2 erased) in denom., and the remaining 2 in num., 
 will cancel each other, — erase them. 
 
 4. The 12 and 6 in num. == 72, and the 9 and 8 in denom. =72; these, therefore, in 
 their relations as factors equal each other, and may be erased. 
 
 The remaining factors represent the true value of the compound fraction, and will be 
 found = |, as by multiplication. 
 
 Example. — Reduce T f of fa to a simple fraction. 
 
 3 
 
 3 
 
 ** X 1. Or X$ X ~ (= 18 + 6, and 12 + 6) =§ X fa 
 
 To reduce fractions of different denominations to an equivalent simple 
 one, — to a fraction having a common denominator. 
 Rule. — . Multiply each numerator by all the denominators except 
 its own and add the products together for the numerator, and multiply 
 all the denominators together for a denominator. 
 
 Note. — Whole numbers and fractions other than simple, must first be reduced to sim- 
 ple fractions before they can be reduced to a fraction having a common denominator. 
 
 Example. — Reduce f and | to an equivalent simple fraction. 
 
 2 X 3 = 8 + 9 = J.£. AnSt 
 
 Example. — Reduce £, f, £, and *£ to an equivalent. 
 ^ + f = T^ + i = W + J / = Wir 4 -==6 T y TT . An* L 
 
 9 
 
98 VULGAR FRACTIONS. 
 
 To reduce a complex fraction to a simple one. 
 Rule — Multiply the numerator of the upper fraction by the 
 denominator of the lower, for the new numerator ; and the denomi- 
 nator of the upper by the numerator of the lower for the new denom- 
 inator. 
 
 1 4 1 51 
 
 Examples. — Reduce — , — , ^, and — each to a simple fraction. 
 
 l + l-i; t+trVi l + i-ixfc-fc-ii si = 
 
 V, and V X J = V. = If- **>■ 
 
 To reduce Vulgar Fractions to equivalent Decimals. 
 
 Rule. — Divide the numerator by the denominator ; the quotient is 
 the decimal, or the whole number and decimal, as the case may be. 
 
 Example. — Reduce £, 4f , \ #, to decimals. 
 7 4-8 = 0.875; 4|=-2£,= 4.6; 14 -J- 12 = 1.166 +. Ans. 
 
 To find the greatest common measure or divisor of both terms of a simple 
 fraction, or of two numbers. 
 
 Rule. — Divide the greater number by the less ; then divide the 
 divisor by the remainder ; and so on, continuing to divide the last 
 divisor by the last remainder until nothing remains ; the last divisor 
 is the greatest common measure of the two terms. 
 
 Example. — What is the greatest common measure of ££§ or of 
 132 and 256 1 
 
 132 ) 256 ( 1 
 132 
 
 124 ) 132 ( 1 
 124 
 
 8 ) 124 ( 15 
 120 
 
 4)8(2 
 8 
 
 4. Ans. 
 
 To find the least common denominator of two or more fractions of dif- 
 ferent denominators, or the least common multiple of two or more 
 numbers. 
 
 Rule. — Divide the given denominators, or numbers, by any num- 
 ber greater than 1, that will divide at least two of them without a 
 remainder, which quotient together with the undivided numbers set 
 in a line beneath. Divide the second line as before, and so on, until 
 
VULGAR FRACTIONS. 99 
 
 there are no two numbers in the line that can be thus divided ; the 
 product of all the divisors and remaining numbers in the last (undi- 
 vided) dividend is the ieast common denominator, or multiple sought. 
 
 Example. — What is the least common denominator of 2V 2^, 
 and •&, or of 20, 25, and 50 ? 
 
 5 ) 20.25.50 
 
 2) 4.5.10 
 
 5 ) 2.5. 5 
 
 2.1.1 
 
 5X2X5X2= 100. Arts. 
 
 ADDITION OF VULGAR FRACTIONS. 
 
 Sum of the products of each numerator with all the denominators except that of th« 
 numerator involved, forms numerator of sum. 
 Product of all the denominators forms denominator of sum. 
 
 Rule. — Arrange the several fractions to be added, one after 
 another, in a line from left to right ; then multiply the numerator of 
 the first by the denominator of the second, and the denominator of the 
 first by the numerator of the second, and add the two products 
 together for the numerator of the sum ; then multiply the two denom- 
 inators together for its denominator ; bringdown the next fraction, and 
 proceed in like manner as before, continuing so to do until all the 
 fractions have been brought down and added. Or, reduce all to a 
 common denominator, then add the numerators together for the 
 numerator of the sum, and write the common denominator beneath. 
 
 Examples. — Add together |, §, f, and ^. 
 
 4X| = |X| = MX§ = W- = -^= s 3j. Arts. 
 
 i-* + i = * = tt.««i ! + ♦ = *=», "dtf + tt-B 
 
 = -^ = 34. Ans. 
 
 SUBTRACTION OF VULGAR FRACTIONS. 
 
 Product of numerator of minuend and denominator of subtrahend, forms numerator of 
 minuend, for common denominator. 
 
 Product of numerator of subtrahend and denominator of minuend, forms numerator of 
 subtrahend, for common denominator. 
 
 Product of denominators forms common denominator. 
 
 Difference of new found numerators forms the numerator, and common denominator the 
 denominator, of the difference, or remainder sought. 
 
 Rule. — Write the subtrahend to the right of the minuend, with 
 the sign ( — ) between them ; then multiply the numerator of the 
 minuend by the denominator of the subtrahend, and the denominator of 
 the minuend by the numerator of the subtrahend ; subtract the latter 
 product from the former, and to the remainder or difference affix tho 
 
100 VULGAR FRACTIONS. 
 
 product of the two denominators for a denominator ', the sum thus 
 formed is the answer, or true difference. 
 
 Examples. — Subtract J from |, also f from \±. 
 
 1-1 = ^^ = 1 = 4- -*«. 
 
 if-i= 55 ~ 51 ° 8 V A**- 
 
 DIVISION OF VULGAR FRACTIONS. 
 
 Product of numerators of dividend and denominators of divisor, forms numerator of 
 quotient. 
 
 Product of denominators of dividend and numerators of divisor, forms denominator of 
 quotient; llierefore, 
 
 Rule. — Write the divisor to the right of the dividend with the 
 sign (-T-) between them ; then multiply the numerator of the dividend 
 by the denominator of the divisor, for the numerator of the quotient, 
 and the denominator of the dividend by the numerator of the divisor, 
 for the denominator of the quotient. Or, invert the divisor, and mul- 
 tiply as in multiplication of fractions. Or, proceed by cancellation, 
 when practicable. 
 
 Examples. — Divide \ by j ; j by \ ; ^ by \\ ; and \ of } of 
 | of ^ by J of J of } of J. 
 
 \*\w%\ l+i^ts **4*-H5 *I5*HH- Ans - 
 1X1x1x1=^=^ and jxixix§= F 6 ff -A. 
 
 and T V + -A = f| - ¥ = 6|. Aw. 
 
 FORM FOR CANCELLATION. EXAMPLE LAST GIVEN. 
 
 1354 4243 20 
 
 - — : — - — — - = — . A?is., as above. 
 
 2 4 6 3 113 2 3 ' 
 
 Note. — The foregoing example can be cancelled to the extent of leaving but a A and a 
 5 (=20) numerators, and a 3 denominator. Units, or l's, in the expressions, are value- 
 less, as a sum multiplied by 1 is not increased. 
 
 MULTIPLICATION OF VULGAR FRACTIONS. 
 
 Product of numerators of multiplier and multiplicand, forms numerator of product. 
 Product of denominators of multiplier and multiplicand, forms denominator of product. 
 
 Rule. — Multiply the numerators together for a numerator, and the 
 denominators together for the denominator. 
 
 I x amples. — Multiply \ by \ ; J by 7 ; JJ by ^ ; \ of \ of } 
 
 Of I Off. 
 
 I'XfHh 3xi = v ; px-p-WV-f *x§xf 
 
 -A-i.an«llX|Xi = A = i,andiXi=»TV Ans 
 
VTTLGATt tRACTiGNS. 1Q1 
 
 It has been seen that a compound fraction is converted into an 
 equivalent simple one, by multiplying the numerators together for a 
 numerator, and the denominators together for a denominator; and 
 it has also been seen that a series of simple fractions are con- 
 verted into a product, by the same process. It is therefore evident 
 that compound fractions and simple, or a series of compound and a 
 series of simple, may be multiplied into each other, for a product, by 
 multiplying all the numerators of both together for a numerator, and 
 all the denominators of both together for a denominator; and that the 
 product will be the same as would be obtained, if the compound were 
 first converted into an equivalent simple fraction, and the simple frac- 
 tions into a product or factor, and these multiplied together for a 
 product. 
 
 It has also been seen that a fraction is divided by a fraction by mul- 
 tiplying the numerator of the dividend by the denominator of the 
 divisor, for the numerator of the quotient, and the denominator of the 
 dividend by the numerator of the divisor, for the denominator of the 
 quotient ; and that this multiplication becomes direct as in multiply- 
 ing for a product, if the divisor is inverted. And it is clear that a 
 compound divisor, or a series of simple divisors, or both, may be used 
 instead of their simple equivalent, and with the same result, if all are 
 inverted. 
 
 It is therefore evident that any proposition, or problem, in fractions, 
 consisting of multiplications and divisions both, and these only, no 
 matter how extensive and numerous, or whether in compound frac- 
 tions, or simple, or both, may be solved, and the true result obtained, 
 as a product, by simply multiplying all the numerators in the state- 
 ment together for a numerator, and all the denominators in the state- 
 ment for a denominator, all the divisors in the statement being 
 inverted ; that is, all the numerators of the divisors being made denom- 
 inators in the statement, and all the denominators of the divisor being 
 made numerators in the statement. And it is further evident that a 
 proposition stated in this way, admits of easy cancellation as far as 
 cancellation is practicable, which is often to great extent. 
 
 Example. — It is required to divide 12 by | of | ; to multiply the 
 quotient by the product of 4 and 8 ; to divide that product by £ of | 
 of 8 ; to multiply the quotient by £ of ■§ of T 9 ^ ; and to divide that 
 product by the product of 5 and 9. 
 
 9* 
 
102 VULGAR FRACTIONS. 
 
 8TATEMENT. 
 (Dividends read from right to left, divisors from left to right) 
 
 Numerators of dividends and denominators of divisors. 
 
 i & § i i i 
 
 3 O 3 <0 3 O 
 
 Numerator of? 7^£^£~£^£^£ S Dividend of 
 
 statement. S •-< ( statement. 
 
 Denominator ) «« l^rtaooocorjjiOda < Divisor of 
 
 of statement. \ ^^-^ ^ — ^..^ ^_, i statement. 
 
 jo jo t^f n 
 
 •aioeiAipjo BjotBaauinu pus spuaptAtp jo r-JoiBUtujouaa 
 
 The answer to the above proposition is 1£|, and the proposition 
 as stated may be readily cancelled to its lowest terms. It. may be 
 cancelled to the extent of leaving but 4, 4, 2 in the numerator, and 7, 
 3, in the denominator, ^J^- 2 - = §f — l^f- 
 
 To reduce a fraction in a higher denomination to an equivalent fraction 
 in a given lower denomination. 
 Rule. — Multiply the fraction to be reduced — numerators into 
 numerator and denominators into denominator — by a fraction whose 
 numerator represents the number of parts of the lower denomination, 
 required to make one of the denomination to be reduced. 
 
 Example. — Reduce I of a foot to an equivalent fraction in inches. 
 
 Example. — Reduce | of a pound to an equivalent fraction in § 
 ounces. 
 
 $ X Jf - - 8 5°- + I = W " ¥• Ans ' 
 Or ) fX J r 6 -Xf = ^ - == - 2 f Arts. 
 
 To reduce a fraction in a lower denomination to an equivalent fraction 
 in a gwen higher it nrnni nation. 
 Rule. — Multiply the fraction to be reduced — numerator into 
 denominator and denominator into numerator — by a fraction whose 
 numerator represents the number of parts required of the lower 
 denomination to make 1 of the higher. 
 
 •mple. — Reduce Q inches to an equivalent fraction in feet. 
 %l .*- J£ «. jj «■ J. Ans. Or, V X T V -= §* ~ £• Ans. 
 
* VULGAR FRACTIONS. 103 
 
 Example. — Reduce *g- two third ounces to an equivalent frac- 
 tion iir pounds. 
 
 ¥X§ = - 8 ^-7- J T 6 - = fS-t. Ans. 
 Or, VX§XtV -*»-"*■ Ans. 
 
 To reduce a fraction in a higher to whole numbers in lower denomi- 
 nations,. 
 Rule. — Multiply the numerator of the given fraction by the num- 
 ber of parts of the next lower denomination that make one of the 
 given fraction, and divide the product by the denominator. Multiply 
 the numerator of the fractional part of the quotient thus obtained by 
 the number of parts in the next lower denomination that make 1 of 
 the denomination of the quotient, and divide by its denominator for 
 whole numbers as before ; so proceed until the whole numbers in each 
 denomination desired are obtained. 
 
 Example. — How many hours, minutes, and seconds, in y 9 ^ of a 
 day? 
 
 ^24 = 2^6 = ^^ |X60= ±^Q_ = 25 , $X 6 - 3 OQ. „ 42 ^ . 
 
 15 h., 25 m., 42f- sec. Ans. 
 Example. — How many minutes in T 9 ¥ of a day ? 
 
 _S. X 2 4 X 6 =±2_9_60 = 925 ^ Ans , 
 
 To reduce fractions, or ichole numbers and fractions, in loioer denomi- 
 nations, to their value in a higher denomination. 
 Rule. — Reduce the mixed numbers to improper fractions, find 
 their common denominator, and change each whole number and 
 numerator to correspond therewith. Then reduce the higher numbers 
 to their values in the lowest denomination, add the value in the lowest 
 denomination thereto, and take their sum for a numerator. Multiply 
 the common denominator by the number required of the lowest denom- 
 ination to make one of the next higher, that product by the number 
 required of that denomination to make 1 of the next higher, and so 
 on, until the highest denomination desired is reached, and take the 
 product for a denominator, and reduce to lowest terms. 
 
 Example. — Reduce 5\ oz., 3^ dwts., 2^ grs., troy, to lbs. 
 Y- • ¥" • J*- 1 **^" ; therefore, 
 160 X 20 = 3200 
 96 
 
 3296 X 24 = 79104 
 
 75 
 
 79179 
 
 30 X 24 X 20 X 12 = 172800 
 
 = .458 -fibs. Ans. 
 
104 DECIMAL FRACTIONS. 
 
 Example. — Reduce 11 hours, 59 minutes, 60 seconds, to the frac- 
 tion of a day. 
 
 11 X 60 = 660 
 59 
 
 719 X 60 = 43140 
 60 
 
 43200 . 
 
 Ans. 
 
 60 X 60 X 24 = 86400 
 
 !-'■ 
 
 Example. — Reduce 15 h., 25 m., 42f sec, to the fraction o\ a 
 day. 
 
 15 X 60 X 60 = 54000 
 25 X 60 = 1500 
 42f 
 
 55542f 
 
 7 
 
 388800 
 
 7 X 00 X 60 X 24 = 604800 
 
 To work fractions, or whole numbers and fractions, by the Rule of 
 Three, or Proportion. 
 
 Rule. — Reduce the mixed terms to simple fractions, state the 
 question as in whole numbers, invert the divisor, and multiply and 
 divide as in whole numbers. 
 
 Example. — If 2£ yards of cassimere cost $4J, what will | of a 
 "ard cost? 2 J = £ ; 4 J = Y" » then > 
 
 *:■¥■••-• I^^Y-SfSf-W-Si^. Ans. 
 
 DECIMAL FRACTIONS. 
 
 A decimal fraction is written with its numerator only. Its denomi- 
 nator is understood. It occupies one or more places of figures, and 
 has a point or dot (.) prefixed or placed before it. The dot (.) alone 
 distinguishes it from an integer or whole number. It supposes a 
 denominator whose value is a unit broken into parts, having a ten- 
 fold relation to the number of places the numerator occupies. The 
 denominator, therefore, of any decimal is always a unit (1) with as 
 many ciphers annexed as the numerator has places of figures. Thus, 
 the denominator of .1, .2, .3, &c, is 10, and the fractions are read, 
 one tenth, two tenths, three tenths, &c. The denominator of .01, .11, 
 .12, &c, is 100, and these are read, one hundredth, eleven hundredths, 
 
DECIMAL FRACTIONS. 105 
 
 twelve hundredths, &c. The denominator of .001, .101, .125, &c, is 
 1000, and these are read one thousandth, one hundred and one thousandths, 
 one hundred and twenty-Jive thousandths, &c. The denominator of a 
 decimal occupying four places of figures as .7525 is 10000, and so on 
 continually. 
 
 The first figure on the right of the decimal point is in the place of 
 tenths, the second in the place of tenths of tenths, or hundredths, the 
 third in the place of tenths of tenths of tenths, or thousandths, &c. 
 Thus the value of a decimal occupying four places of figures, as 
 
 »«** , , • 7525 752* 75.* l h ± 
 
 •7525, for example, is , « , = , = — ± -4 — «= 
 
 __l__ r 10000 1000 100 10 ~ 100 
 
 £ i 
 
 1 . A decimal is converted into a vulgar fraction of 
 
 1 ' 100 ^ 
 
 equal value, by affixing its denominator. 
 
 Ciphers placed on the right of decimals do not change their value. 
 Thus, .1850 = .185, plainly for the reason that the denominator of 
 the latter bears the same relation to that of the former that 185 bears 
 to 1850 ; from both terms of the fraction a ten fold has been dropped. 
 
 Ciphers placed on the left of decimals decrease their value ten fold 
 for every cipher so placed. Thus, .1 = -jVj, «01 = T £ T , .001 = 
 
 A mixed number is a whole number and a decimal. Thus, 4.25 is 
 a mixed number. Its value is 4 units, or ones, and -^Jfr of 1, = 
 ^-^ = 4£. The number on the left of the separatrix is always a 
 whole number — that on its right, always a decimal. 
 
 ADDITION OF DECIMALS. 
 
 Rule. — Set the numbers directly under each other according to 
 their values, whole numbers under whole numbers, and decimals un- 
 der decimals ; add as in whole numbers, and point off as many places 
 for decimals in the sum as there are figures in that decimal occupying" 
 the greatest number of places. 
 
 Examples. — Add together .125, .34, .1, .8672. Also, 125, 34.11, 
 .235. 1.4322. 
 
 .125 
 
 .34 
 
 .1 
 
 .8072 
 1.4322 Ans. 
 
 125. 
 34.11 
 .235 
 1.4322 
 i1«l7772 Ans. 
 
 SUBTRACTION OF DECIMALS. 
 
 Rule. — Set the numbers, the less under the greater, and in other 
 icsoects as directed for addition ; subtract as in whole numbers, and 
 
106 
 
 DECIMAL FRACTIONS. 
 
 point off as many places for decimals in the remainder as the decimal 
 having the greatest number of figures occupies places. 
 
 Examples. — 
 
 .8 
 .2653 
 
 Subtract .2653 from .8. 
 
 .5347 Arts. 
 
 Also, 11.5 from 238.134. 
 
 238.134 
 
 11.5 
 226.634 Ans. 
 
 MULTIPLICATION OF DECIMALS. 
 Rule. — Multiply as in whole numbers, and point off as many 
 places for decimals in the product as there aTe decimal places in the 
 multiplicand and multiplier both. If the product has not so many 
 places, prefix ciphers to supply the deficiency. 
 
 Examples. — Multiply 14.125 by 3.4. Also, 5.14 by .007. 
 
 14.125 
 3.4 
 56500 
 42375 
 48.0250 = 48.025. Ans. 
 
 5.14 
 .007 
 
 .03598 Arts. 
 
 Notb. — Multiplying by a decimal is equivalent to dividing by a whole number that 
 hears the same relation to a unit that a unit bears to a decimal. Multiplying by a deci- 
 mal, therefore, is equivalent to dividing by the denominator of a fraction of equal value; 
 whose numerator is 1, or of dividing by the denominator of a fraction of equal value whose 
 numerator is more than 1, and multiplying the quotient by the numerator. Thus, the 
 decimal .23 == ^j = {, and the decimal .875 = yV^ = J. And 14.23 X - 2 "' — 
 8.6676. and 14.23 -j- 4 =a 3.5575. So, also, 1 1.23 X -875 = 12.45125, and 14.23 -f- 8 = 
 X 7 = 12 1.") 125. It is sometimes a saving of labor and matter of convenience to 
 achieve multiplication by this process. 
 
 DIVISION OF DECIMALS. 
 Rule. — Write the numbers as for division of whole numbers, then 
 remove the separatrix in the dividend as many places of figures to the 
 right, (supplying the places with ciphers if they are not occupied,) as 
 there are decimal figures in the divisor ; consider the divisor a whole 
 number and divide as in division of whole numbers. 
 
 Example. — Divide .5 by .17. Also, .129 by 4. 
 
 .17). 50(2.94+. Ans. 
 34 
 
 160 
 153 
 70 
 
 4).129(.032-f-. 
 12 
 
 9 
 
 I 
 
 Ans. 
 
DECIMAL FRACTIONS. 
 
 107 
 
 Examples. — Divide 16.5 by 1.232. Also, 1.2145 by 12.231. 
 
 12.231,) l.214,50(.099294- > A 
 
 1 100 79 .0993— f Ans ' 
 
 .232,} 16.500, (13.3928-L-. Ans 
 1232 
 
 4180 
 
 3696 
 4840 
 3696 
 11440 
 11088 
 
 113 710 
 110 079 
 3 6310 
 2 4462 
 
 1 18480 
 1 10079 
 8401 
 
 3520 
 2464 
 10560 
 ,9856 
 704 
 
 Notk. — Dividing by a decimal is equivalent to multiplying by a whole number that 
 bears the same proportion to a unit that a unit bears to the decimal. Dividing by a deci- 
 mal, therefore, is equivalent to multiplying by the denominator of a fraction of equal 
 value whose numerator is 1, or multiplying by the denominator of a fraction of equal 
 value whose numerator is more than 1, and dividing the product by the numerator. Di- 
 viding by a fraction is equivalent to multiplying by its denominator and dividing the 
 product by its numerator, or dividing by its numerator and multiplying the quotient by 
 its denominator. Thus, .5 = T 5 as \, and .75 = ^fo = J. And 12.24 -f- .5 = 24.43, 
 and 12.24 V 2 = 24. 13. So, also. 12.24 -i- .75 = 16. 32, and 12.24 X 4 = 4S - 96 + 3 =* 
 16.32. This method of accomplishing division may often be resorted to with convenience. 
 
 REDUCTION OF DECIMALS. 
 
 To reduce a decimal in a higher to whole members in successive lower 
 denominations. 
 Rule. — Multiply the decimal by that number in the next lower 
 denomination that equals one of the denomination of the decimal, and 
 point off as many places for a remainder as the decimal so multiplied 
 has places. Multiply the remainder by the number in the next lower 
 denomination that equals 1 of the denomination of the remainder, and 
 point off as before ; so continue, until the reduction is carried to the 
 lowest denomination required. 
 
 Example. — What is the value of .62525 of a dollar? 
 . .62525 
 
 100 
 
 Cents, 62.52500 
 10 
 
 Mills, 
 
 5.25000 An.. 62 cents 5| mills. 
 
108 DECIMAL FE ACTIONS. 
 
 Example. — What is the value of .46325 of a barrel? 
 
 .46325 
 32 
 
 Gallons, 14.82400 
 4 
 
 Quarts. 3.296 
 
 Pints, .592 
 
 4 
 
 Gills, 2.368. Ans. 14 gals. 3 qts. 2^6^ gilfc. 
 
 Example. — How many pence in .875 of a pound ? 
 ' .875 X 240 -» 210. Ans. 
 
 To reduce decimals, or whole numbers and decimals, in lower denomin- 
 ations, to their value in a higher denomination. 
 Rule. — Reduce all the given denominations to their value in the 
 lowest denomination, then divide their sum by the number required of 
 the lowest denomination to make one of the denomination to which 
 the whole is to be reduced. 
 
 Example. — Reduce 14 gallons, 3 quarts, 2.368 gills, to the deci- 
 mal of a barrel. 
 
 14 X 4 = 56 -f- 3 = 59 X 8 = 472 -f 2.368 = 474.368. 
 8 X 4 X 32 = 1024 ) 474.368 ( .46325. Ans. 
 
 To work decimals, or whole numbers and decimals, by the Rule of 
 Three, or Proportion. 
 Rule. — State the question and work it as in whole numbers, 
 taking care to point off as many places for decimals in the product to 
 be used as the dividend, as there are decimals in the two terms which 
 form it, and to remove the decimal point therein as many places to the 
 right as there are decimals in the term to be used as a divisor, before 
 the division is had. 
 
 Example. — If .75 of a pound of copper is worth .31 of a dollar 
 how much is 3.75 lbs. worth ? 
 
 .75 : .31 :: 3.75 
 .31 
 375 
 1125 
 
 .75) 1.16,25 ($1.55. Ans. 
 
PROPORTION. X09 
 
 PROPORTION, OR RULE OF THREE. 
 
 The Rule of Proportion involves the employment of three terms 
 — a divisor and two factors for forming a dividend — and seeks a 
 quotient, which, when the proposition is written in ratio, bears the 
 same relation to the third term that the second term bears to the first 
 Two of the terms given are of like name or nature, and the other is 
 of the name or nature of the quotient or answer s«ught. That of 
 the nature of the answer is always one of the factors for forming the 
 dividend, and, if the answer is to be greater than that term, the larger 
 of the remaining two is the other ; but if the answer is to be less 
 than that term, the less of the remaining two is the other — the 
 remaining term is the divisor. 
 
 Example. — If $12 buy 4 yards of cloth, how many yards will 
 $108 buy? 
 
 £ X 108 108 
 
 jg— = — m 36 yards. Ans. 
 
 3 
 
 Example. — If 4 yards of cloth cost $12, how many dollars will 
 36 yards cost? 
 
 1 1^l.— = 108 dollars. Ans. 
 4 
 
 Example. — If 30 men can finish a piece of work in 12 days, how 
 many men will be required to finish it in 8 days ? 
 
 30 X 12 , 
 
 — = 45 men. Ans. 
 
 8 
 
 Example. — If 45 men require 8 days to finish a piece of work, 
 how many men will finish the same work in 12 days? 
 
 — — — = 30rnen. Ans. 
 IS 
 
 Example. — If 8 days are required by 45 men to finish a piece 
 of work, how many days will be required by 30 men to finish the 
 same work? 
 
 8 X 45 
 
 30 = 12 days. Ans. 
 
 Example. — If 12 days are required by 30 men to perform a piece 
 of work, how many days will be required by 45 men to do the same 
 work? 
 
 12 X 30 
 
 — — — = 8 days. Ans. 
 45 
 
 Example. — I borrowed of my friend $150, which I kept 3 months, 
 and, on returning it, lent him $200 ; how long may he keep the sum 
 10 
 
110 COMPOUND PROPORTION. 
 
 that the interest, at the same rate peT cent., may amount to that which 
 his own would have drawn ! 
 
 150 X 3 -J- 200 = 2£ months. Ans. 
 
 Example. — A garrison of 250 men is provided with provisions for 
 30 days, how many men must be sent out that the provisions may last 
 those remaining 42 days? 
 
 250 X 30 -j- 42 = 179, and 250 — 179 = 71. Ans. 
 
 Example. — If to the short arm of a lever 2 inches from the ful- 
 crum there be suspended a weight of 100 lbs., what power on the 
 long arm of the lever 20 inches from the fulcrum will be required to 
 raise it 1 
 
 20 : 2 :: 100= 10 lbs. Ans. 
 
 Example. — At what distance from the fnlcrum on the long arm of 
 a lever must I place a pound weight, to equipoise or weigh 20 lbs., 
 suspended 2 inches from the fulcrum at the other end 1 
 1 : 2 :: 20 : 40 inches. Ans. 
 
 Note. — If we examine the foregoing with reference to the fact, we shall see that every 
 proposition in simple proportion consists of &4erm and a half! or, in other words, of a 
 compound term consisting of two factors, and a factor for which another factor is sought 
 that together shall equal the compound. We have only to multiply the factors of the 
 compound together — and a little observation will enable us to distinguish it — and divide 
 by the remaining factor, and the work is accomplished. See Compound Proportion. 
 
 COMPOUND PROPORTION, OR DOUBLE RULE OF THREE. 
 
 Compound Proportion, like single proportion, consists of three 
 terms given by which to find a fourth — a divisor and two factors for 
 forming a dividend — but unlike single proportion, one or more of the 
 terms is a compound, or consists of two or more factors ; #nd some- 
 times a portion of the fourth term is given, which, however, is always 
 a part of the divisor. 
 
 Of the given terms, two are suppositive, dissimilar in their natures, 
 and relate to each other, and to each other only ; and upon their rela- 
 tion 'the whole is made to depend ; the remaining term is of the nature 
 of one of the former, and relates to the fourth term, which is of tho 
 nature of the other. 
 
 The object sought is a number, which, multiplied into the factor or 
 factors of the fourth term given, if any, and if not, which of itself, 
 beam the same proportion to the dissimilar term to which it relates, 
 as the suppositive term of like nature hears to the term to which it 
 relates. 
 
 Rule. — Observe the denomination in which the demand is mad. 1 , 
 and of the suppositive terms make that of like nature the second, and 
 the other the first ; maVe the remaining term the third term ; and, if 
 
COMPOTTND PROPORTION. Ill 
 
 there are any factors pertaining to the fourth term, ufllx. them to the 
 first ; multiply the second and third terms together and divide hy the 
 first, and the quotient is the answer, term, or portion of a term, 
 sought. 
 
 Example. — If 12 horses in 6 days consume 36 bushels of oats, 
 how many bushels will suffice 21 horses 7 days* 
 12 x 6 : 36 ::2l x 7 : *• 
 3 
 
 30 X 21 X 7 147 
 
 7~i ^ — = — — = 73£ bushels. Ans. 
 
 &% X v 2 
 
 2 
 
 Example. — If 12 horses in 6 days consume 36 bushels of oata, 
 how many horses will consume 73£ bushels in 7 days ? 
 36 : 12 x 6 :: 73£ : 7 x *• 
 12 X 6 X 73£ 147 
 36 X 7 == T = 21 h0TSeS - AnS ' 
 
 Example. — If the interest on $1 is 1.4 cts. for 73 days, (exact 
 interest at 7 per cent.,) what will be the interest on $150.42 for 146 
 days? 
 
 73 : 1.4 :: 150.42 X 146 : x. 
 1.4 X 180.48 X 146 ^ ^ ^ 
 
 Example. — If the interest on $1 is 1.2 cts. for 73 days, (exact 
 interest at 6 per cent.,) what will be the interest on $125 for 90 
 days? 
 
 73 : 1.2 :: 125 X 90 : x — $1.85. Ans. 
 
 Example. — If $100 at 7 per cent, gain $1.75 in 3 months, how 
 much at 6 per cent, will $170 gain in 11£ months? 
 
 100 x 7 X 3 : 1.75 :: 170 x 6 x 11.5 ' *. 
 1.75 X 170 X 6 X 11-5 -j- 100 X 7 X 3 = $9.77,5. Ans. 
 
 Example. — By working 10 hours a day 6 men laid 22 rods of wall 
 in 3 days ; how many men at that rate, who work but 9 hours a day, 
 will lay 40 rods of wall in 8 days ? 
 
 22 : 6 x 3 X 10 :: 40 : 9 x 8 X -r- 
 
 6 X 3 X 10 X 40 -r 22 X 9 X 8 = 4 T 6 T . Ans. 
 
 Example. — If it costs $112 to keep 16 horses 30 days, and it 
 costs as much to keep 2 horses as it costs to keep 5 oxen, how much 
 will it cost to keep 28 oxen 36 days ? 
 
112 CONJOINED PROPORTION, OK CHAIN RTTLE, 
 
 • 16 x 30 : 112 : : f x 28 x 26 : x. 
 
 Or,— 16 X 30 X 5 : 112 :: 28 X 36 X 2 : ar. 
 
 Ill 28 ff* ^ 88X18 XT 
 U 30 5 5X5 
 
 5 
 
 Example. — If 24 men, in 8 days of 10 hours each, ean dig a 
 trench 250 feet long, 8 feet wide, and 4 feet deep, how many men, in 
 12 days of eight hours each, will be required to dig a trench 80 feet 
 long, 6 feet wide, and 4 feet deep ? 
 250X8X4:24X8X10 - 80X6X4 : 12X8X^=5— . Ans. 
 
 Example. — If 120 men in six months perform a given task, work- 
 ing 10 hours a day, how many men will be required to accomplish a 
 like task in 5 months, working 9 hours a day? 
 
 120 X 6 X 10 = 5 X 9 X x. 
 Or, — I : 120 X 6 x 10 :: 1 : 5 X 9 X ^. == 160. Ans. 
 
 Example. — The weight of a bar of wrought iron, 1 foot in length, 
 1 inch in breadth, and 1 inch thick, being 3.38 lbs., (and it is so,) 
 what will be the weight of that bar whose length is 12£ feet, breadth 
 3| inches, and thickness | of an inch ? 
 
 l :3.38 :: 12.5 X 3.25 x .75 : x. 
 Or, — 1 : 3.38 :: 3£ X *& X f : », and 
 3.38X25 X 13X3 = 1 lbg 
 
 2X4X4 ^ 
 
 Example. — The weight of a bar of wrought iron, one foot in length 
 and 1 inch square, being 3.38 lbs., what length shall I cut from a bar 
 whose breadth is 2f inches, and thickness £ inch, in order to obtain 
 
 10 lbs.? 3.38 : l " 10 : -y. x £ X *• 
 
 1 X 10 X 4 X 2 
 
 = 2 feet l^P n inches. Ans. 
 
 3.38 X 11 X 1 
 
 CONJOINED PROPORTION, OR CHAIN RULE. 
 
 The Chain Rule is a process for determining the value of a given 
 quantity in one denomination of value, in some other given denomi- 
 nation of value ; or the immediate relationship which exists between 
 two denominations of value, by means of a chain of approximate steps, 
 
CONJOINED PROPORTION, OR CHAIN RULE. 113 
 
 circumstances, or equivalent values, known to exist, which connect 
 them. In every instance at least five terms or values are employed 
 in the process, and in all instances the number employed will be un- 
 even. A proposition involving but three terms, of this nature, is a 
 question in single proportion. The equivalent values employed are 
 divided into antecedents and consequents, or causes and effects ; and the 
 value or quantity for which an equivalent is sought, is called the odd 
 term. 
 
 Rule. — 1. When the value in the denomination of the first antece- 
 dent is sought of a given quantity in the denomination of the last conse- 
 quei\t. — Multiply all the antecedents and the odd term together for a 
 dividend, and all the consequents together for a divisor; the quotient 
 will be the answer or equivalent sought. 
 
 Rule. — 2. When the value in the denomination of the last consequent 
 is sought of a given quantity in the denomination of the first antecedent, 
 — Multiply all the consequents and the odd term together for a divi- 
 dend, and all the antecedents together for a divisor ; the quotient will 
 be the answer required. 
 
 Example. — I am required to give the value, in Federal money, of 
 5 Canada shillings, and know no immediate connection or relationship 
 between the two currencies — that of Canada and that of the United 
 States. The nearest that I do know is that 20 Canada shillings have 
 a value equal to 32 New York shillings, and that 12 New York shil- 
 lings equal in value 9 New England shillings, and that 15 New Eng- 
 land shillings equal $2.50 ; and with this knowledge will seek the 
 value, in Federal money, of the 5 Canada shillings. 
 2^0X^X32X5 Am _ 
 
 15 X 12 X 20 
 
 Example. — If $2£ equal 15 New England shillings, and nine shil- 
 lings in New England equal 12 shillings in New York, and 32 shil- 
 lings in New York equal 20 shillings in Canada, how many shillings 
 in Canada will equal $1 1 
 
 *4£U^ » « 
 
 3 * 
 Example. — If 14 bushels of wheat weigh as much as 15 bushels 
 of fine salt, and 10 bushels of fine salt as much as 7 bushels of coarse, 
 and 7 bushels of coarse salt as much as 4 bushels of sand, how many 
 bushels of sand will weigh as much as 40 bushels of wheat ? 
 15X7 X4X40 s ushek AM 
 
 14 X 10 X 7 T 
 
 10* 
 
114 PERCENTAGE, 
 
 PERCENTAGE. 
 
 Pure percentage, or percentage, is a rate by the hundred of a 
 part of a quantity or number denominated the principal, or basis. 
 But percentage, considered as a means, and as commonly applied, 
 is mixed and related in an eminent degree ; and in this light may 
 be regarded as divided into orders bearing different names. 
 
 Thus Interest is percentage related to intervals of time in the 
 past. 
 
 Discount is percentage related to interest, and intervals of time 
 in the future. 
 
 Profit and Loss is comparative percentage, or percentage related 
 to the positive and negative interests in business, etc., etc. 
 
 Pure percentage is commonly called brokerage when paid to 
 a broker for services in his line. 
 
 It is called commission when paid to or received by a factor 
 or commission merchant for buying or selling goods. 
 
 It is called premium by an insurance company, when taken for 
 insuring against loss. 
 
 It is called primage when it is a charge in addition to the 
 freight of a vessel, etc. 
 
 Comparative percentage relates to the differences of quantities, 
 and is confined always to the idea of more or less. It implies ratio. 
 This description of percentage, though much in practice, seems not 
 to be well understood ; and often a quantity is indirectly stated to 
 be many times less than nothing, or many times greater than it is. 
 The difference of two quantities cannot be as great as a hundred 
 per cent, of the greater, however widely unequal the quantities 
 may be, nor as small as no per cent, of the greater or lesser, how- 
 ever nearly equal they may be. No quantity or number can be as 
 small as 1 time less than another quantity or number ; and there- 
 fore cannot be as small as 100 per cent. less. But, since one quan- 
 tity may be many by 1 time, or many times greater than another 
 with which it is compared, it may be said to be many by 100 times, 
 or many hundred per cent, greater. 
 
 When one of two quantities in comparison is stated to be three 
 times less, or three hnndred per cent, less, for instance, than the 
 other, the expression is incorrect and absurd. The meaning evi- 
 dently is, that it is two-thirds less, or only one-third as large as the 
 other, — that it is 66$ per cent less, or only 33£ per cent, as large 
 as the other. In common comparison, 1 is the measuring unit. In 
 percentage, 100 is the measuring unit. 
 
PERCENTAGE. 115 
 
 Let a = principal. 
 b = percentage. 
 
 s = amount (sum of the principal and percentage). 
 d = difference of the principal and percentage. 
 r = rate of the percentage. 
 p = rate per cent, of the percentage. 
 
 a = s— - b = b -r- r=z 100b ^-pz=z 100s -^- (100 -j-jp), 
 
 6 =s — a—arzzzap-±- 100, 
 
 p = 1 OOr =1006 -f- a = 100(s — a) -^ a, 
 
 r =;? -f- 100 = 6 -J- a = (.* — a) -7- a, 
 
 s = a -|- 6 = a(l + r) = a(\ 00 -+- p) ~ 100, 
 
 d = o — 6 = 2a — 5 := s — 2b = a(l — r). 
 
 To find the Percentage. 
 
 EXAMPLES. 
 
 What is I of 1 per cent, of $200 ? 
 
 6 =ar = op -^-100 = $0.50. ^ras. 
 ^ of 2 per cent, of 50 is what part of 50 ? 
 50X8X2 
 7X100 =**• ^ 
 What is I of I of \ of 24 per cent, of 150 lbs. ? 
 150 X 12 ~ 100 = 18 lbs. Ans. 
 What is 2| percent, of 19 bushels ? 
 
 ■¥ X ^ = 0.45125 bushels. ^Ins. 
 
 Bought a job lot of merchandise for $850, and sold it the same 
 day, brokerage, 2\ per cent., for $975 ; what was the net gain? 
 s — sr — a = s — (sr -f- a) = s(l — r) — a = 975 — 975 X -025 
 
 — 850 = $100,625. Jns. 
 
 To find the Rate or Bate Per Cent. 
 
 EXAMPLES. 
 
 What per cent, of $20 is $2 ? 
 
 r = b-^-a,p=zl00b—-az=. 10* per cent. Ans. 
 12 dozen is equal to what per cent, of 2 dozen ? 
 12 — 2 = 6, 600 per cent. Ans. 
 
116 PERCENTAGE. 
 
 What part of 5£ lbs. is f of 2 lbs. ? 
 
 r=J X A = «=0.27A- iin«. 
 
 24£ per cent, is what per cent, of 36f per cent. ? 
 
 66 f per cent. Ans. 
 
 For an article that cost $4, $5 were received ; what per cent, 
 of $4 was received ? 
 
 p = 5 X 100 -J- 4 = 125 per cent. Ans. 
 
 A farmer sowed 4 bushels of wheat, which produced 48 bushels ; 
 what per cent, was the increase ? 48 is more than 4 by what per 
 cent, of 4 ? The difference of 48 and 4 is what per cent, of 4 r 
 
 a — b a 100(a — b) 48 — 4 AQ . . . 
 
 100(48 — 4) -f- 4 = 1100 percent. .4 ns. 
 
 What per cent, would have been the decrease, if he had sowed 
 48 bushels, and harvested only 4 bushels ? 4 is less than 48 by 
 what rate of 48 V The difference of 48 and 4 is what per cent, of 
 48? 
 
 r=z(a — b)-r-a = l = 0.91§, or 91§ per cent. Ans. 
 
 Since water is composed of 8 atoms of oxygen and 1 atom of 
 hydrogen, what per cent, of it is oxygen ? 8 is what per cent, 
 of the sum of 8 and 1 ? 
 
 = 1- * ,p = -^ = At = -8889-, 
 
 '— a+&~~ a-f&'^a-j-ft - 8 + 1 
 
 or 88.89 - per cent. Ans. 
 
 What per cent, of it is hydrogen ? 1 is what pe^r cent, of the 
 sum of 8 and 1 ? 
 
 a b 100b 1 
 
 a-\-b a-\-b r a-\-b 8 -f- 1 
 
 11.11 -f- per cent. Ans. 
 
 How many volumes of water must be added to 100 volumes of 
 90 per cent, alcohol to reduce it to 50 per cent, alcohol or common 
 proof? 90 is more than 50 by what per cent, of 50 ? The differ- 
 ence of 90 and 50 is what per cent, of 50 ? 
 
 (a — 6)100 (90 — 50)100 OA . 
 P= b = 50 =8 °' An8 ' 
 
PERCENTAGE. 117 
 
 How many volumes of 50 per cent, akohol must be added to 
 100 volumes of 90 per cent, alcohol to produce 80 per cent, alcohol ? 
 90 is more than 80 by what per cent, of the difference of 80 and 
 50 ? The difference of 90 and 80 is what per cent, of the differ- 
 ence of 80 and 50 ? 
 
 (a-i)100 = (90-80)100 = 3 
 * b — V 80— -50 * 
 
 How many volumes of 90 per cent, alcohol must be added to 100 
 volumes of 50 per cent, alcohol to raise it to 80 per cent, alcohol ? 
 50 is less than 80 by what per cent, of the difference of 90 and 80 ? 
 The difference of 80 and 50 is what per cent, of the difference of 
 90 and 80 ? 
 
 0- y) ioo = go^o)ioo = 300 , Am . 
 
 a — o 90 — 80 
 
 If to 2 volumes of 95 per cent, alcohol, 1 volume of 50 per cent, 
 alcohol be added, what per cent, alcohol will be the mixture ? The 
 sum of 50 and twice 95 is what per cent, of the sum of 2 and 1 ? 
 
 2a + b 2X95 + 50 D/% 
 
 y^y = 2 + l =80 per cent. Ans. 
 
 In a barrel of apples, the number of sound ones was 60 per 
 cent, greater than the number that were damaged. What per 
 cent, less was the number that were damaged than the number 
 that were sound ? 60 per cent, is what per cent, of the sum of 
 100 per cent, and 60 per cent. ? .6 is what rate of 1 + .6 ? 
 
 a . 100 O.a m 1 60 
 
 = .375, or 
 
 l-{-a 1-}- a l+.a l.a 1 + 60 
 
 37^ per cent. Ans. 
 
 Since the number of damaged apples was 37£ per cent, less than 
 the number that were sound, what per cent, greater was the num- 
 ber that were sound than the number that were damaged ? 
 
 r = a + (1 — a) = 1 + (1 — a) — 1 = 60 per cent. Ans. 
 
 Since the number of sound ones was 60 per cent, greater than 
 
 the number that were damaged, what per cent, of the whole were 
 
 sound ? 
 
 a + a* l + .a 100 + 60 OA . 
 
 r = — -L— =— L_ , p r=z J =80 per cent. Ans. 
 
 What per cent, of the whole were damaged ? 
 
 (100 — 60) + 2 = 20 per cent. Ans. 
 
118 PERCENTAGE. 
 
 Since 20 per cent, of fhe apples were damaged, what per cent, 
 less was the number that were damaged than the number that were 
 sound ? 
 
 1 — 2. a 1 100 — 2a _„ 100 
 r=z = 1 , v= = 100 - = 
 
 2 — 2. a 2 — 2. a 9F 200 — 2a 200 — 40 
 
 37^ per cent. Ans. 
 
 What per cent, greater was the number that were sound than 
 the number that were damaged ? 
 
 r = 2 — (1 -}-2.a) = 2 — 2. a — 1 = 60 percent. Ans. 
 
 Since 80 per cent, of the whole were sound, what per cent, less 
 was the number that were damaged than the number that were 
 i sound? 
 
 2. a— 1 , 1 2X-80 — 1 M1 . 
 
 = 1 = -^ = 37£ per cent. Ans. 
 
 2. a 2. a 2X-80 
 
 Since the number of damaged ones was 3 7£ per cent, less than 
 the number that were sound, what per cent, of the whole were 
 sound? 
 
 1 100 100 
 
 80 per cent. *Ans. 
 
 2 — 2.a ir 2 — 2a 2 — 2X37.5 
 
 Since 80 per cent, of the whole were sound, what per cent 
 greater was the number that were sound than the number that 
 were damaged ? 
 
 r sa ~" ,a = 2.a — 1 = 2 X .80 — 1 = 60 per cent. Ans. 
 2 
 
 Lost 20 per cent, of a cargo of coal by jettison, and 5 per cent, 
 of the remainder by screening, what per cent, of the coal was 
 saved ? 
 
 a — b'=d' I r = (l — r') (1 — r") = (l— .20)— (1 — .20) 
 d'—b" = d"$ X .05 =(1— .20)(1 — .05) = 76 per cent. Ans. 
 d" — b'" = d"',8ic. 
 
 Yesterday drew 12 per cent, of my balance of $1,2 73 in the 
 bank, and deposited $1,000; and to-day have drawn 31| per cent, 
 of the balance left over, or as it stood last night. What per cent of 
 the sum of the first-mentioned balance and deposit of yesterday 
 have I drawn ? 
 
 b'-\-b" 512 + 1487.575 Q7 OQr , . . A 
 
 r =z — L = • — . = 37.9354 4- per cent Ans. 
 
 a-\-m 4273 + 1000 ' * 
 
PERCENTAGE. 119 
 
 Wli.it per cent, of the said sum is remaining in the bank ? 
 
 fr'.|-6"_ a-J- m — V — b" _ u + m — (7/ -f h") 
 7+£~ a4-i» ~^fm =62.0646- 
 
 1 ' l per cent. Ans. 
 
 What per cent, predicating it upon the first-mentioned balance, 
 have I drawn ? 
 
 b'4-b" 512.76 -f- 1487.576 , CQ104 . . 
 
 r= — X — ss !— — = 46.81 34 - per cent. Ans. 
 
 a 4273 ■ 
 
 What per cent, have I drawn, predicating it upon what I now 
 have in the bank ? 
 
 b'+w h !_ztl" — 
 
 r — ^-ZF+^=-T''-~ o+»— £&l+&")~~ 61.1225 -f 
 
 percent. vlns. 
 What amount of money must I deposit to makfe good 62^ per 
 cent, of the aforementioned sum V 
 
 d=zr (a -\- m) +V -\-b" — (a + m) =r (a + w)— d" = 
 
 $22.96. Ans. 
 
 To Jind the Principal or Basis. 
 
 EXAMPLES. 
 
 The percentage being 250, and the rate .06, what is the 
 principal ? 
 a = b^-r= 100b -^-p = 250-^.06 = 25,000-^-6 =4,1 66f. Ans. 
 
 A tax at the rate of £ of 1 per cent, on the valuation was $27.50. 
 What was the valuation ? 
 
 n = tX6X100 => Anfi 
 
 5 
 
 Sold 120 barrels of flour, which amounted to 12 per cent, of a 
 certain consignment. The consignment consisted of how many 
 barrels ? 
 
 120-^0.12 = 1,000. An*. 
 
 216 bushels is more by 8 per cent., or 8 percent, more, than what 
 number of bushels ? 8 per cent, more than what number is equal 
 to 216 ? What number, plus 8 per cent, of it, will make 216 ? 
 
 a = s-r(l~L-r) = 216-7-1.08 = 200. Ans. 
 
 200 lbs. is less by 8 per cent., or 8 per cent, less, than what num- 
 
120 INTEREST. 
 
 ber of lbs. ? 8 per cent, less than what number is 200 ? What 
 number, minus 8 per cent, of it, is equal to 200 ? 
 
 a = d -±- (1 — r) = 200 ~ (1— .08) = 21 7fa Ans. 
 
 .-. 217^— 217^X.08 = 200=a — b = d=a(l— r). 
 
 To a quantity of silver, a quantity of copper equal to 20 per 
 cent, of the silver is to be added, and the mass is to weigh 22 
 ounces. What weight of silver is required ? 
 
 a = 5-7- (l-}-r) = 22-^-1.2 = 18£ ounces. Ans. 
 
 What weight of copper is required ? 
 
 s — — . — = r-7— = 34 ounces. Ans. 
 1 -f- r 1-f-r 8 
 
 To a quantity of copper, a quantity of nickel equal to 62£ per 
 cent, of the copper, a quantity of zinc equal to 33£ per cent, of the 
 copper, and a quantity of lead equal to 5 per cent, of the copper, 
 are to be added; and the whole is to weigh 40£ pounds. The 
 weight of each constituent of the alloy is required. 
 
 _ s _ 40 $ 
 
 a — i j^r + ri + rH ~ i _|_. 62^+. 33£+. 05 
 
 =r 20 lbs. of copper, 
 b = 20 r = 1 2£ lbs. of nickel, . 
 6'=20r'=6§lbs.ofzinc, 
 b r, _ 20 r" = l lb. of lead. 
 
 INTEREST. 
 
 Universal for any rate per cent. 
 
 T = time in months and decimal parts of a month ; t= time in days ; 
 P as principal ; r = rate per cent., expressed decimally; i= interest. 
 
 PXTXr TxtXr 
 
 
 12 365 
 
 p _i2_t_365i T _i2_* j_ 365 * xti^aegj 
 
 — Tr~~" tr ' ~~Pr* ~Pr' "~"PT Ft ' 
 Example. — A promissory note, made April 27, 1864, for 
 
INTEREST. 121 
 
 $825 A^j- and interest at 6 per cent, matured Oct. 6, 1865 : what 
 was the interest? 
 
 Oct. is 10th month. 
 April is itii month. 
 
 j: m, d. 
 
 1865 . 10 . 6 
 
 '64 . 4 . 27 
 
 Time from April 27 to Oct. 6 (one of 
 the dates always included) ss 162 days, 
 which, added to the 865 days in the year 
 preceding = 527 days. 
 
 Note. — One day's interest at least is gener- 
 ally lost by computing the time in years and 
 months, or months, instead of days. 
 
 Time= 1.5.9 
 
 825.25 X 17.3 X -06 — 12 = $71.38. Ans. 
 825.25 X 527 X-06 -7- 365 = $71.49. Ans. 
 
 To find a constant divisor, fc, for any given rate -per cent* 
 
 When the time is taken in months, k = 1 2 -7- r. 
 
 When the time is taken in days, k s= 365 -7- r ; thus, 
 
 P X t 
 When the rate is 6 per cent. -^-^-= Interest. 
 
 P X t 
 
 When the rate is 7 per cent. ~ sa Interest, &c. 
 
 Example. — Required the interest on $750 for 93 days, at 7 
 per cent. 
 
 750 X 93 -7- 5214 = $13.38. Ans. 
 
 Example. — What is the rate per cent, when $450 gains $94} 
 in 3 years ? 
 
 450 : 100 *.: 94.5 : 3x=7 per cent. Ans. 
 
 94.5 -f- 3 X 450 = .07. Ans. 
 
 Example. — In what time will $125 at 6 per cent, gain $18|? 
 
 6 : 100 ;: 18.75 : 125 X »= 2} years. Ans. 
 
 18.75 -f- 125 X-06 = 2} years. Ans. 
 
 Example. — What principal at 5 per cent, interest will gain 
 $16} in 18 months? 
 
 5 : 100 ;: 16.875: 1.5 X a: = 8225. Ans. 
 
 16.875 X 12-f-18 X-05 = $225. Ans. 
 11 
 
122 COMPOUND INTEREST. 
 
 WJien partial payments have been made. 
 
 Rule. — Find the amount (sum of the principal and interest) 
 up to the time of the first payment, and deduct the payment there- 
 from ; then find the interest on the remainder up to the next pay- 
 ment, add it to the remainder, or new principal, and from the sum 
 subtract the next payment ; and so on for all the payments ; then 
 find the amount up to the time of final payment for the final 
 amount. 
 
 COMPOUND INTEREST. 
 
 If we calculate the interest on a debt for one year, and then on 
 the same debt for another year, and again on the same debt for 
 still another year, the sum will be the simple interest on the debt 
 for three years. But, on the contrary, if we calculate the interest 
 on the debt for one year, and then on the amount (sum of the prin- 
 cipal and interest) for the next year, and then on the second 
 amount for the third year, the sum of the interest so calculated 
 will be the compound interest, or yearly compound interest, on the 
 debt for three years ; equal to the simple interest on the debt for 
 three years, plus the yearly compound interest on the first year's 
 interest for two years, plus the simple interest on the second year's 
 interest for one year. So, if we divide the time into shorter 
 •periods than a year, and proceed for the interest as last suggested, 
 the interest will be compound. Thus we have half-yearly com- 
 pound interest, or compound interest semi-annually, quarter- 
 yearly compound interest, or compound interest quarterly, &c. 
 
 This method of computing interest is predicated upon the 
 natural idea, that interest, when it becomes due by stipulation and 
 is withheld, commences to draw interest, and continues at use to 
 the holder, at the same rate as the principal, until it is paid, like 
 other over-due demands; and that the interest so made matures 
 and becomei due as often, and at the same periods, as that on the 
 principal. 
 
 It will be perceived by the foregoing that the >rorkin(/-t>'me in 
 
 compound interest is the interval between th«* stipulated payments 
 
 of toe interest, or between one stipulated payment of the interest 
 
 and that of another; and that the wurkiiKj-rate is pro rata to -the 
 rate per annum. 
 
 Thus the amount of $10o at semi-annual compound interest for 
 2 years, at G per cent, per annum, is 
 
COMPOUND INTEREST. 123 
 
 100 X (1.03)* = $112.550881 =$112.55, or 
 100. 
 .03 
 
 3. 
 
 100. 
 
 103. 
 .03 
 
 3.09 
 103 1 _ 
 
 106^09 
 .03 
 
 3.1827 
 106.09 
 
 109.2727 
 .03 
 
 3.278181 
 109.2727 
 
 SI 12.550881, as before. 
 
 If we let P = principal or debt at interest, 
 r = working-rate of interest, 
 
 n = number of intervals into which the whole time is 
 divided for the payment of interest, or number of consecutive 
 intervals for the payment of interest that have transpired without 
 a payment having been made, 
 
 i = compound interest, 
 A = P -j- i or amount, then 
 
 A = P( H - r) .;P=^ ;r =^-l i 
 
 ^-=(l + r)»;« = A-P. 
 
 Example. — What is the compound interest, or yearly com- 
 pound interest, on $100 for 1£ years, at 6 per cent, a year ? 
 
 100X 1.06X 1-03 = 109.18 — 100 = $9.18. Ans. 
 
 Example. — What is the amount of $560.46, at 7 percent, 
 compound interest per year, for 6 years and 57 days ? 
 
 560.46 X (1.07)6 x(l + '° 7 3 ^ 5 57 ) = $850.29. Ans. 
 
124 COMPOUND INTEREST. 
 
 Example. — The principal is $250, the rate 8 per cent, a year, 
 the time 2 years, and the interest compound per quarter year: 
 required the amount. 
 
 250 X (l. — ) =$292.91. Ans. 
 
 ('•t) 8 = 
 
 When Partial Payments have been made. 
 
 Rule. — Find the amount up to the first payment, and deduct 
 the payment therefrom ; then find the amount up to the next pay- 
 ment, and therefrom deduct that payment ; and so on for all the 
 payments ; then find the amount up to the time of final payment, 
 tor the final amount. 
 
 Example. — A note of hand for $500 and interest from date, 
 at 6 per cent, a year, has been paid in part as follows ; viz., two 
 years and four months from the date of the note, by an indorse- 
 ment of $50 ; and three years from that indorsement, by an in- 
 dorsement of $150. It is now eight months since the last payment 
 was made, and the demand is to be settled in full : required the 
 amount at the present time, interest being compound per year. 
 
 500 X (1.06)2 x 1.02 — 50=523.036 
 
 (1.06) 8 
 
 622.944 
 150 
 
 472.944 
 1.04 
 
 $491.86. Ans. 
 
 The following table shows (1 -f- r) raised to all the integer 
 powers from 1 to 12 inclusive ; r being taken at 4, 5, 6, 7, 8, and 10 
 per cent. If the numbers in the column headed years are taken 
 to represent years, then 4 per cent., 5 per cent., &c, at the head 
 of the columns of powers, will stand for per cent, per annum : if 
 they are taken to represent half-years, then 4 percent, 5 percent., 
 &c, will stand for per cent, per half-year, &c. The quantities in 
 the columns are powers of (1 -f~ r )> °f ^hich the numbers referred 
 to and standing opposite, respectively, are the exponents. Thus, 
 1.26248, in the 6 per cent, column, and against 4 in the column 
 marked vears, = (1.06) 4 ; and so with the others. The powers 
 or quantities in the columns are co-efficients in the calculations. 
 
COMPOUND INT! 
 
 125 
 
 Years. 
 
 4 p«r cent. 
 
 5 per cent. 
 
 e per cent. 
 
 7 per cent. 
 
 S ]..T C.llt. 
 
 io percent 
 
 1 
 
 1.04 
 
 1.08 
 
 1.06 
 
 1.07 
 
 1.08 
 
 1.10 
 
 2 
 
 1.081G 
 
 1.1025 
 
 l.ri:;.; 
 
 1.1449 
 
 1.1664 
 
 1.21 
 
 3 
 
 1.12486 
 
 1.15762 
 
 1.11)102 
 
 1.22504 
 
 1.25971 
 
 1.881 
 
 4 
 
 1.16986 
 
 1.21551 
 
 1.26248 
 
 1.3108 
 
 1.36049 
 
 1.4641 
 
 5 
 
 1.21668 
 
 1.27628 
 
 1.38828 
 
 1.40255 
 
 1.46933 
 
 1.61051 
 
 6 
 
 1.26532 
 
 1.3401 
 
 1.41852 
 
 1.50073 
 
 1.58687 
 
 1.77156 
 
 7 
 
 1.31593 
 
 1.1071 
 
 1.50363 
 
 L.60578 
 
 1.71382 
 
 1.94872 
 
 8 
 
 1.36857 
 
 1.47746 
 
 1.59385 
 
 1.71819 
 
 1.85098 
 
 2.14359 
 
 9 
 
 1.42331 
 
 1.55133 
 
 1.68948 
 
 1.88846 
 
 1.999 
 
 2.35795 
 
 10 
 
 1.48024 
 
 1.62889 
 
 1.79085 
 
 1.96715 
 
 2.15892 
 
 2.59374 
 
 11 
 
 1.53945 
 
 1.71034 
 
 1.8983' 
 
 2.10485 
 
 2.33164 
 
 2.85812 
 
 12 
 
 1.60103 
 
 1.79586 
 
 2.0122 
 
 2.25219 
 
 2.51817 
 
 3.13843 
 
 Note. — If a co-efficient is wanted for a greater number of years or intervals 
 of time than is given in the table, square the tabular co-efficient opposite half 
 that number of intervals, or cube the tabular co-efficient opposite oue-tbird 
 that number of intervals, &c, for the co-efficient required. Thus, 
 
 1. 91)92=1. 586S7 3 =1. OS 12 X 1.08°= 1.08^ = 3.990, 
 
 the co-efficient for 18 years or intervals at 8 per cent, per interval, &c. 
 
 It* the compound interest alone is sought on a given principal, subtract 1 
 from the tabular power corresponding to the time and rate, and multiply the 
 remainder by the given principal ; the product will be the compound interest. 
 Thus (1.26532— 1)X 100 = $26,632, the yeprly compound interest, at 4 per 
 cent, per annum, on $100 for years, or the half-yearly compound interest, at 
 8 per cent, per annum, on $100'i'or :5 years, or the half-yearly compound inter- 
 est, at 4 per cent, per half year, on $100 for half-years. 
 
 Example. — What is the amount of $125.54, at 5 per cent, 
 compound interest, for 7 years, 21 days? 
 
 21 X 05 
 
 1-1 ~; — =z 1.00288, the co-efficient for the odd days; and, 
 
 1 365 
 
 turning to the 5 per cent, column in the table, we find against 7, in 
 
 the column of years, 1.40 71, the co-efficient for 7 years : then 
 
 1 25.54 X 1.4071 X 1.00288 =: $1 78.20. Ans. 
 
 Example. — In -what time, at 7 per cent, compound interest 
 per annum, will $1000 gain $462? A-^-P=r (1 -f-r) n : then 
 146 2 -j- 1000 = 1.462, the co-efficient demanded. Turning now 
 to the 7 per cent, column in the table, we find the nearest less 
 co-efficient there (there being none that exactly corresponds) to 
 
 be that for 5 years ; viz., 1.40255. And ( 4Q255 — !) "T- - 07 = 
 .60553, the fraction of a year over 5 years to the answer. 
 
 .60553 X 365 = 221 days: 5 years, 221 days. Ana. 
 11* 
 
126 
 
 COMPOUND INTEREST. 
 
 The following table is of the same nature as the preceding, 
 and is applicable when the interest becomes due at regular inter- 
 vals short of a year, or when the working-rate in compound inter- 
 est is less than 4 per cent. 
 
 The quantities in the If per cent, column apply to quarter-yearly 
 compound interest when the rate is 7 per cent, a year ; and those 
 in the 1£ per cent, column, to quarterly compound interest when 
 the rate is 5 per cent, a year ; also the former are applicable to 
 monthly compound interest at 21 per cent, per annum, and the 
 latter to monthly compound interest at 15 per cent, per annum ; 
 and so relatively, throughout the table. 
 
 
 1 
 
 u 
 
 a 
 
 s 
 
 1 
 
 ■ 
 
 s 
 8 
 
 •J 
 
 a 
 S 
 
 ■ 
 
 i 
 
 1 
 
 
 1 
 
 % 
 
 V 
 
 I 
 
 B 
 
 1 
 
 1 
 
 1 
 
 
 1 
 
 s 
 
 A 
 
 S 
 
 ft 
 
 M 
 
 £ 
 
 £ 
 
 3 
 
 ft 
 
 * 
 
 1 
 
 1.035 
 
 1.03 
 
 1.025 1.02 
 
 1.0175 
 
 1.015 
 
 1.0125 
 
 1.01 
 
 1.005 
 
 2 
 
 1.07123 1.0609 
 
 1.05063 1.0404 
 
 1.03531 1.03023 
 
 1.025161.0201 
 
 1.01003 
 
 3 
 
 1.10872 1.09273 
 
 1.076891.06121 
 
 1.05342- 1.04568 
 
 l.o:37L»7 1.0303 
 
 1.01508 
 
 4 
 
 1.1475211.12561 
 
 1.10381 1.08243 
 
 1.07186il.0t3136 
 
 1.05095 1.0406 
 
 1.02015 
 
 6 
 
 1.1876911.15927 
 
 1.13141 1.10408 
 
 1.09062 
 
 1.07728 
 
 1.06408 
 
 1.05101 
 
 L.02525 
 
 6 
 
 1.22925 
 
 1.19405 
 
 1.15969.1.12616 
 
 1.1077 
 
 1.09344 
 
 1.0774 
 
 1.06152 
 
 1.03038 
 
 7 
 
 1.27228 
 
 1.22987 
 
 1.18869|l.l4869 
 
 1.12709 
 
 1.109S4 
 
 1.09087 
 
 1.07214 
 
 
 8 
 
 1.31681 
 
 1.26677 
 
 1.2184 11.17166 
 
 1.14681 
 
 1.12G49 
 
 1.10451 
 
 1.08888 
 
 1.04071 
 
 9 
 
 1.3629 
 
 1.30477 
 
 1.248861.19509 
 
 1.16688 
 
 1.14339 
 
 1.11831 
 
 1.09369 
 
 1.04591 
 
 10 
 
 1.4106 
 
 1.34392 
 
 1.280081.21899 
 
 1.1873 
 
 1.16054 
 
 1.18229 
 
 L10462 
 
 1.05114 
 
 11 
 
 1.45997 
 
 1.38423 
 
 1.312091.24337 
 
 1.20808 
 
 1.17795 
 
 1.146461.11567 
 
 1.0564 
 
 12 1.51107 1.42576 
 
 1.34489!l.26824 
 
 1.22922 
 
 1.19562 
 
 1.160781.12683 
 
 1.06168 
 
 Example. — What is the amount of $750 for 4 years and 40 
 days, allowing half-yearly compound interest, at 7 per cent, a year ? 
 
 In this case, the working-rate for the full periods of time is 3£ per 
 cent, and there are 8 such full periods ; then, seeking the co-efficient 
 in the 3£ per cent, column, we find against 8, in the column of 
 
 times, the quantity or co-efficient 1.31681 ; and 1 -f- — ~ — = 
 
 1.00767 : therefore 
 
 750 X 1.31681 X 1.00767 = $995.18. 4ft* 
 
 Example. — What is the amount of $1000 at compound inter- 
 est per quarter-year, at 1£ per cent, per quarter-year, for 4£ years ? 
 
 1000 X 1.12649 2 X 1.015 = $1288.01. Ans. 
 
HANK INTEltKST. 127 
 
 BANK INTEREST OR BANK DISCOUNT. 
 
 A bank loans money on a promissory note made payable with- 
 out interest at a future period. The operation is called discounting 
 the note at bank, and is as follows : The bank takes the note, funis 
 the interest on it for three days more time than by its own tenor it 
 has to run, subtracts it from the principal, and hands the balance, 
 called the avails of the note, in its own bills, to the party soliciting 
 the loan, or offering the note for discount, as it is called ; whereby 
 the note becomes the property of the bank, and the maker and 
 indorscrs are held for its payment when it matures. 
 
 The three days mentioned are called days of grace, and the 
 note does not become due to the bank until three days after it 
 becomes due by its own tenor. These proceedings are sanctioned 
 by usage, and protected by law. 
 
 Bank interest, then, is bank discount, and bank discount is bank 
 interest. But bank discount is not discount, nor is it what is called 
 legal interest on the money loaned. It is the interest on the money 
 loaned, plus the interest on the interest of the loan, plus the inter- 
 est on the difference of the sum taken and the interest on the loan 
 for the time of the loan ! A kind of interest more onerous, if any 
 description of interest be onerous, than compound interest, rate 
 for rate and time for time, as may be readily perceived. 
 
 Let P = principal or face of the note. 
 
 r = working-rate of the interest for the time of the loan. 
 a = avails of the note or sum borrowed. 
 i = bank interest. 
 t = time of the loan. 
 
 R : r : : T : t. R being the rate per cent, per annum, and T 
 one year. 
 
 P = a-Hl— r). a = Y — Pr. i = Vr. r = (P — a)-j-P. 
 
 If we let n represent the time of the note in months, 
 _ R n , 3 R 
 
 r — ~Y2 ~T ggj=' But it is the practice with many banks to count 
 
 the days of grace as so many 3G0ths of a year. 
 
 Putting d to represent the time of the note in days, 
 
 Rrf-f3R . . 
 
 r = , true time and rate. 
 
 365 
 
 "With some banks, it is the practice, in calculating interest, to take 
 the time, when it does not exceed 93 days, as so many 360ths of a 
 year. 
 
 A note having 3 months to run from Aug. 10, for instance, will 
 
128 
 
 BANK INTEREST. 
 
 fall due Nov. 10-13; but one having 90 days to run from Aug. 
 10 will fall Nov. 8-11. The time including grace of the former 
 is 3 mo. 3 ds., and that of the latter 3 mo. 2 ds., mean time. Never- 
 theless, the former embraces 95 days, or one day more than mean 
 time, and the latter but 93 days. 
 
 The following table shows 1 — r, mean time, for the intervals of 
 time set down in the left-hand column ; B, being taken at 4, 5, 6, 7, 
 and 8 per cent, per annum, as set down at the top of the columns. 
 
 Time. 
 
 
 4 
 
 6 
 
 6 
 
 7 
 
 8 
 
 mo. 
 
 da. 
 
 per cent. 
 
 per cent. 
 
 per cent. 
 
 percent. 
 
 per cent. 
 
 1 
 
 3 
 
 .996333 
 
 .995417 
 
 .9945 
 
 .993583 
 
 .992667 
 
 2 
 
 3 
 
 .993 
 
 .99125 
 
 .9895 
 
 .98775 
 
 .986 
 
 3 
 
 3 
 
 .989667 
 
 .987083 
 
 .9845 
 
 .981917 
 
 .979333 
 
 4 
 
 3 
 
 .986333 
 
 .982917 
 
 .9795 
 
 .976083 
 
 .972667 
 
 5 
 
 3 
 
 .983 
 
 .97875 
 
 .9745 
 
 .97025 
 
 .966 
 
 6 
 
 3 
 
 .979667 
 
 .974583 
 
 .9695 
 
 .964417 
 
 .959333 
 
 7 
 
 3 
 
 .976333 
 
 .970417 
 
 .9645 
 
 .958583 
 
 .952667 
 
 8 
 
 3 
 
 .973 
 
 .96625 
 
 .9595 
 
 .95275 
 
 .946 
 
 9 
 
 3 
 
 .969667 
 
 .962083 
 
 .9545 
 
 .946917 
 
 .939333 
 
 10 
 
 3 
 
 .966333 
 
 .957917 
 
 .9495 
 
 .941083 
 
 .932667 
 
 11 
 
 3 
 
 .963 
 
 .95375 
 
 .9445 
 
 .93525 
 
 .926 
 
 12 
 
 3 
 
 .959667 
 
 .949583 
 
 .9395 
 
 .929417 
 
 .919333 
 
 Putting k to represent the tabular quantity 1 — r, 
 
 a= Pit, P=^ a -f- fc, i = P — a = P— Pfc 
 
 Example. — What will be the avails of a note for $1,250 
 payable in 4 months if discounted at a bank, interest being 7 per 
 cent, a year ? 
 
 The tabular constant 1 — r, in the 7 per cent, column, against 4 
 months and 3 days in the time column, is .976083, and 
 $1,250 X .976083 = $1,220.10. Ans. 
 
 Example. — For what sum must I make a note having 6 months 
 to run, in order that the avails at bank, If discounted on the day 
 of the date of the note, may amount to $956.38, interest being 6 
 percent, per annum? 
 
 By the table, $956.38 -f- .9695 = $986.4 7. A m. 
 
 Example. — What is the rate of bank interest when the nomi- 
 nal or legal rate is 7 per cent.? 
 
 .07 -f- (1 — .07) = .07527 = 7f + rffo per cent. 
 
 .i — A note living 5 BMmthfl 1<> run from Kelt. 1 will fall due July 
 
 tnd Hi. time, lnelu<finc graoe, is ■:, mo. 8 da. 156 days, mean time. 
 
 r.ui the time In days from Feb. l to Julj «. when February has but iittdays, 
 
 is 163 days only, or 2 days short of mean time. 
 
DISCOUNT. — COMI»OUND DISCOUNT. 129 
 
 DISCOUNT. 
 
 Discount is a deduction of the interest on the present worth or 
 availability of a debt not yet due, in consideration of its present 
 payment * The principal is the present nominal value of the debt, 
 interest included, if any interest lias accrued The time is the 
 interval from the present to the date at which the debt will become 
 due. The rate, is the legal rate of interest, if no other rate is speci- 
 fied; and the present /corf// is that sum of money, which, if put at 
 interest at the same rate and for the same time as the discount, will 
 amount to the principal. 
 
 Let a represent the principal, d the discount, If the present 
 worth, and i the interest on one dollar for the time and at the rate 
 of the discount. 
 
 w = a-±- (1 -\-i) =: a — d. d = fltf-f- (1-|- i) — a — w. 
 a = d (1 -j- 1) -7- i =2 d -j- w. 
 
 Example. — Required the discount on $250 for 8 months at 6 
 per cent. 
 
 The interest on $1 for 8 months at 6 per cent, is .04 of a dollar, 
 or 4 cts. ^ and 
 
 250 X -04-4- (1 -j-. 04) = $9.6154. Ans. 
 
 Example. — Required the present worth of $1272.62 due 247 
 days hence, discount 7 per cent. 
 
 The interest on $1 for 247 days at 7 per cent. = 247X-07 -f-365 
 = 0.04737, and 
 
 1272.62-^- 1.04737 =$1215.06. Ans. 
 
 Note. — " Talcing off, in common parlance, a certain per centum from 
 the face of a demand, is equal to deducting the interest, at that rate per cent- 
 turn, on the present worth for 1 year, plus the interest on the interest of the 
 present worth, at the same rate per centum for 1 year. 
 
 COMPOUND DISCOUNT. 
 
 Compouxd Discount is to compound interest what simple dis- 
 count is to simple interest. In both cases of discount, the differ- 
 ence between the principal and the discount is that sum of money, 
 which, if put at interest for the same length of time, at the same 
 rate, and in the same general manner as the discouut, will amount 
 to the principal. 
 
 Rule. — Add 1 to the rate per cent, of the discount for the 
 
130 COMPOUND DISCOUNT. 
 
 working-time, and raise the sum to a power corresponding with the 
 number of working-times ; divide the principal by the power, and 
 the quotient will be the present worth ; subtract the present worth 
 from the principal, and the remainder will be the compound 
 discount. 
 
 Note. — The tables of the powers of 1 + r, applicable to compound in- 
 terest, are equally applicable to compound discount. 
 
 Example. — Required the present worth of a debt of $250, 
 allowing yearly compound discount, at 7 per cent, a year, for 
 8 years 84 days. 
 
 1 _l_ - 7 X 8 * — 1.01611, the working-rate for the 84 days, and 
 '365 ' c J ' 
 
 250 -f- (1.078 x 1.01611) b= $200.84. Ans. 
 
 Example. — What is the present worth of a debt of $150.25, 
 due 3 years, 3 months, and 10 days hence, without interest, allow- 
 ing compound discount per quarter-year, at 1^ per cent, per quar- 
 ter-year ? 
 
 150.25 -^(l.015 13 X l.- 06 X 10 )=Ans. 
 \ 365 / 
 
 By table, 150.25-^(1.19562 X 1-015 X 1.00164)= I 
 
 $123.61. Ans. 
 
 Note.— What is here denominated the debt, or principal, represents the 
 debt at the close of the time of the discount; that is, if the debt be on in- 
 terest, the interest must be included in what is here called the debt, or 
 principal. 
 
 PROFIT AND LOSS. 
 
 The term "Profit and Loss," as intimated in treating of 
 Percentage, relates to the positive and negative interests in 
 business, and embraces the idea of both. 
 
 Both profit and loss are absolute quantities, and are expressed by 
 the difference of the cost price and selling price that limit them. 
 They are usually, however, estimated by percentage, predicated 
 upon the first-mentioned price or prime cost. 
 
 When the selling price is greater than the cost price, or when 
 tin- money obtained by the disposal of property exceeds what the 
 property cost, the difference is positive, and denotes increase, 
 
 profit, or gain. Conversely, when the cost price is greater than the 
 selling price, or when property is disposed of for less money than 
 it cost, the difference is negative, and denotes decrease, loss, or 
 
PROFIT AND LOSS. 131 
 
 waste. So, the difference of the two prices, divided by the cost 
 price, expresses the rate of gain on the cost when the selling price 
 is the greater, -—expresses the rate of loss on the cost when tin- 
 cost price is the greater. 
 
 Let c represent the cost price, purchase price, par value, or sum 
 of money paid for the property; s, the selling price, trade price, 
 premium price, or sum of money received in exchange for the 
 property ; r, the rate of the profit or loss ; p, the rate per cent, of 
 the profit or loss. 
 
 To find the rate or rate per cent, of the profit or loss. 
 
 r ■=. ■ ~ . p — >. ~ ' . Moreover, when the difference is 
 
 e ■ * c 
 
 s s 
 positive, r = 1 ; and, when it is negative, r — 1 
 
 Example. — Paid $4 for an article, and sold it for $5. What 
 
 ?er cent, was gained ? 5 is more than 4 by what per cent, of 4 ? 
 ne difference of 5 and 4 is what percent, of 4? 5 — 4 = $1, 
 
 gained; and —^—z=:. 25 = £ — 1. 25 per cent. Ans. 
 
 Example. — Paid $5 for an article, and sold it for $4. What 
 
 per cent, was lost ? 4 is less than 5 by what per cent, of 5 ? The 
 
 difference of 4 and 5 is what per cent, of 5? 4 — 5=r — lz=$l, 
 
 5 ~ 4 
 lost ; and — - — = .20 zzr 1 — £. 20 per cent. Ans. 
 o 
 
 Example. — A whistle that cost 3 cents was sold for 20 cents 1 
 The profit was how much per cent ? (20 ~ 3) -f- 3 = 5f or 566§ 
 per cent. Ans. 
 
 Example. — A fop paid $10 for a well-made and well-fitting 
 pair of boots for his own wear, that were worth what they cost him ; 
 but, being told that they were unfashionably large, sold them for 
 $4. His vanity cost him what per cent, of the purchase price ? 
 1 — ^= .6 or 60 per cent. Ans. 
 
 To find a price long a given per cent, of the cost, or to find a sell- 
 ing price that shall be the sum of the cost price and a given per 
 cent, of it. 
 
 s = c -\- cr = c (1 -f- r) = c (100 -f-^) -^- 100. 
 
 Example. — At what price must I sell an article that cost 
 $2.35 to gain 25 per cent. V 2.35, more 25 per cent, of it, is how 
 much ? The sum of $2.35 and 25 per cent, of it is how much ? 
 2.35 -4- 2.35 X -25 = 2.35 X 1-25 = $2.93f. Ans. 
 
132 EQUATION OF PAYMENTS. 
 
 To find a price short a given per cent, of the cost, or to find a sett- 
 ing price that shall be the difference of the cost price and a given 
 per cent, of it. 
 
 s=ic — cr=c(l — r)z=c (100 — ;>)-^-100. 
 
 Example. — I have a damaged article of merchandise that cost 
 $2.75, and I wish to mark it for sale at 30 per cent, below cost. 
 At what price shall I mark it ? 2.75 less 30 per cent, of it is how 
 much? The difference of S2.75 and 30 per cent, of it is how 
 much? 2.75 (1—. 30) = 2.75 X -7 = $1,925. Ans. 
 
 To find the cost price when the selling price and profit per cent, are 
 
 given. 
 s = c-\-cr = c (1+r) . • . c =zs ~ (1 -J- ?•) =: 100 8 -f- (100 -f-;>). 
 
 Example. — What cost that article whose selling price, $4, is 
 long 25 per cent, of the cost ? What price, more 25 per cent, of 
 it, is equal to S4 ? $4 is the sum of what price and 25 per cent, 
 of it? 400 -j- 125 = $3.20. Ans. 
 
 To find the cost price when the selling price and loss per cent, are 
 
 given. 
 
 sr=c — cr = c(l — r) .-. c = 5~(l— 7-) = 100s-f-(100 — p) 
 
 Example. — What cost that article whose selling price, $375, 
 is short 7 per cent, of the cost ? What price less 7 per cent, of it 
 is equal to $375 ? $375 is the difference of what price and 7 per 
 cent, of it ? 
 375 -J- (1 — .07) = 375 -^- .93 = 375 X 100 -^- (100 — 7) = 
 
 $403,226. Ans. 
 
 EQUATION OF PAYMENTS, OR AVERAGE. 
 
 Average consists in finding the time at which several sums, 
 foiling due at different dates, become due if taken collectively. 
 
 Rule. — Multiply each sum respectively by the number of 
 days it falls due later than that failing due at the earliest date, and 
 divide the sum of the products by the sum of the several sums. 
 The quotient will be the number of days subsequent to the earliest 
 date at which the whole will mature, or averages due. 
 
 . : .— .w i i: \<.i. gtn - 1 no '• interest on i"t< >■<.<(" to the creditor. l\ 
 not give 1 1 i in his just due. It estimates by waj of the fnft /•« ri on both ride*, on 
 the Minis falling due prior to the average date, and on those falling due - 
 quently, and not by the Interest <>n those (ailing due prior, and by the dUotmnt 
 on those (ailing due subsequent, as would be strict iv correct. The praetl 
 against the creditor or holder of the demands, in like manner and relati 
 tent, as shown in note under DlW oi N >. 
 
EQUATION OF PAYMENTS. I:;;; 
 
 The following exhibits the face of an account in the ledger, and 
 the time (date) at which it averages due is required. 
 
 36C 
 
 ), April 10 $250.26 — 6 mo. 
 
 Due Oct. 
 
 10. 
 
 u 
 
 June 25 320.56 — 6 " 
 
 " Dec. 
 
 25. 
 
 it 
 
 July 10 50.02 — 3 " 
 
 " Oct. 
 
 10. 
 
 u 
 
 Aug. 1 210.84 — 4 " 
 
 u Dec. 
 
 1. 
 
 (( 
 
 " 18 73.40 — 5 " 
 
 " Jan. 
 
 18. 
 
 (( 
 
 Oct. 15 100. — cash* 
 
 " Oct. 
 
 15. 
 
 Example. — Practical method of stating and working. 
 1860. Due Oct. 10, $301 
 
 " " Dec.25, 321 X 76 =■ 24396. 
 
 " ■ " « 1, 211 X 52= 10972. 
 
 " " Jan. 18, 73 X 100 = 7300. 
 
 " " Oct. 15, 100 X 5 a 500. 
 
 1006 ) 43168 ( 43 days, = Nov. 22, 1860. 
 
 Ans. 
 COMPOUND AVERAGE. 
 
 Compound Average consists in finding the time at which the bal- 
 ance of an account or demand averages due, whose sides — the debit 
 and the credit — average due at different dates. 
 
 Rule. — Multiply the less sum or side by the difference in days 
 between the two dates — that at which the debit side averages due 
 and that at which the credit side averages due — and divide the prod- 
 uct by the difference of the sums or sides ; the quotient will be the 
 number of days that one of the dates must be set back, or the other 
 forward, to mark the time sought ; for which last, 
 
 SPECIAL RULE. 
 
 Earlier date with larger sum, set back from earlier. 
 Later, date with larger sum, set forward from later. 
 
 Example. — The debit side of an account in the ledger foots up 
 $400, and averages due Oct. 12, 1860 ; the credit side of the same 
 account foots $300, and averages due Nov. 16, 1860. At what date 
 does the balance or difference between the two sides average due 1 
 400 300 
 
 300 35 
 
 "TOO ) 10500 ( 105 days earlier than Oct. 12, = June 29, 1860. Ans. 
 
 Example. — The debit side of an obligation foots $250, and aver- 
 ages due May 17, 1860 ; the credit side of the same obligation foots 
 $175, and averages due May 1, 1860. At what date does the differ- 
 ence of the sides average due 1 
 250 175 
 
 175 _J6 
 
 75 ) 2800 ( 37J days later than May 17, = June 23, 1860. Ans. 
 12 
 
134 GENERAL AVERAGE. 
 
 GENERAL AVERAGE. 
 
 It is the established usage that whatever of either of the three 
 commercial interests — the ship, the cargo, or the freight — is 
 voluntarily sacrificed or destroyed for the general good, or with 
 the view of saving the most that may be saved when all is in immi- 
 nent danger of being lost, is matter of general loss to the respec- 
 tive interests, and not more especially to the interest voluntarily 
 abandoned than to the others. So, too, the losses and damages inci- 
 dent to the voluntary sacrifice, and collateral therewith, together 
 with the expenditures which the master has been compelled to 
 make for the general good, in consequence of disaster, are matters 
 of general average, or are to be contributed for, pro rata, by the 
 several interests. 
 
 The contributory interests are the ship, the cargo, and the 
 freight, at their net values, independent of charges, premiums 
 paid for insurance, &c. 
 
 The contributory value of the ship, generally, is her value at the 
 port of departure at the time of leaving, less the premium paid for 
 her insurance. 
 
 The contributory value of the cargo is its net value, in a sound 
 state, at the port of destination, if the voyage be completed ; or its 
 invoice value if the voyage be broken up and the cargo returned 
 to the port whence it was shipped ; or its market-value at any in- 
 termediate port, where of necessity it is discharged and disposed of. 
 The value of the goods jettisoned, and to be contributed for, is 
 their value after the same manner ; and that value is a part of the 
 contributory value of the cargo, as well as a matter of general 
 average. 
 
 The contributory value of the freight, generally, is the gross 
 amount or amount per freight-list, less one-third part thereof, in 
 most of the States ; but, in the State of New York, one-half thereof, 
 for seamen's wages and other expenses. The loss of freight by 
 "jettison, when any freight is earned, is matter of general average. 
 If the cargo is transshipped on board another vessel, and in that 
 way sent to the port of destination, the contributory value of the 
 freight is the gross amount, less the sum paid the other vessel. 
 
 The voluntary damage to the ship, with a view to the general 
 good, — such as throwing over her furniture, destroying bet equip- 
 ments, cutting away her masts, breaking up her decks to L r «t .it toe 
 cargo for the purpose of throwing it over, &c, — is contributed for 
 at two-thirds the cost of repairing and restoring ; the new articles 
 being supposed one-half better, or worth one-half more, than the 
 old. 
 
GENERAL AVERAGE. 135 
 
 If we let V = contributory value of the vessel, 
 C = contributory value of the cargo, 
 F = contributory value of the freight, 
 d z=. aggregate amount of losses to be averaged, then 
 d -J- ( V -f- C -f- F) = r, the per cent, of each interest that each 
 must contribute, and 
 
 VX r = Vessel's share of the loss, 
 C X t ■=. Cargo's share of the loss, 
 F X t = Freight's share of the loss. 
 When a contributory interest's share of the loss is to be distrib- 
 uted among the several owners of that interest, the same pro rata 
 method is to be observed : thus 
 
 A X r = sum A- must contribute, 
 B X r = sum B must contribute, 
 D X t = sum D must contribute ; 
 A, B, and D being A's, B's, and D's respective shares in that 
 interest. 
 
136 ASSESSMENT OF TAXES. — INSURANCE. 
 
 ASSESSMENT OF TAXES. 
 
 G = amount of taxable property, real and personal, as per 
 grand list. 
 
 A = amount of money to be raised, including the whole poll-tax. 
 
 T = amount of money to be raised on property alone. 
 
 n = number of ratable polls. 
 
 h = poll-tax per head. 
 
 r = rate per cent, to be raised on taxable property. 
 
 P = an individual's taxable property, as per grand list. 
 
 b = P's poll-tax. 
 
 Tz=A — hn. r = T -f- G. P r -f b = Fs tax, including poll. 
 
 INSURANCE. 
 
 Insurance is a written contract of indemnity, called the policy, 
 by which one party (the insurer or underwriter) engages, for a 
 stipulated sum, called the premium (usually a per cent, on the 
 value of the property insured), to insure another against a risk or 
 loss to which he is exposed. 
 
 Let P= Principal, or amount insured on, 
 r = rate per cent, of insurance, 
 a = premium for insurance. 
 
 a = Pr. r = a -f- P. P = a -f- r. 
 
 Example. — What is the premium for insuring on &4500 at lj 
 per cent. ? 
 
 4500 X -015 = $67.50. Ans. 
 
 LIFE-INSURANCE. 
 
 Life-insurance is predicated upon the even chance in years, 
 called the expectation of life, that an individual in general health 
 at any given age appears by the rates of mortality to have of living 
 beyond that age. 
 
 The Carlisle Tables of Expectation, column C in the following 
 tables, are used almost or quite exclusively in England, and by 
 some insurance-companies in the United States; while tli<»e by 
 Dr. Wiggleiwtiirth, column \V, computed with special re f e re nce to 
 the rates of mortality in this country, arc used by others. 
 
 The Supreme Court of Massachusetts has adopted the Wiggles- 
 

 
 worth rates of expectation in estimating the value of life-annuities 
 and life-estates. 
 
 TABLE 
 
 Of Ages and Expectations jrom Birth to 103 Years. 
 
 Age. 
 
 C. 
 
 W. 
 
 Age. 
 
 0. 
 
 w. 
 
 Age. 
 52 
 
 c. 
 
 w. 
 
 
 0. 
 
 w. 
 6.59 
 
 
 
 38.72 
 
 28.15 
 
 26 
 
 87.14 
 
 31.93 
 
 19.68 
 
 20.05 
 
 78 
 
 6.12 
 
 1 
 
 44.68 
 
 
 27 
 
 36.41 
 
 31.50 
 
 53 
 
 18.97 
 
 L9.46 
 
 79 
 
 
 6.21 
 
 2 
 
 47.55 
 
 88.74 
 
 28 
 
 35.69 
 
 31.08 
 
 54 
 
 18.28 
 
 L8.92 
 
 80 
 
 5.51 
 
 
 3 
 
 
 40.01 
 
 29 
 
 35.0030.66 
 
 55 
 
 l 7.58 
 
 18.35 
 
 81 
 
 5.21 
 
 5.50 
 
 4 
 
 50.76 
 
 10.79 
 
 30 
 
 30.25 
 
 56 
 
 16.89 
 
 17.78 
 
 82 
 
 4.93 
 
 5.16 
 
 5 
 
 51.25 
 
 40.88; 
 
 31 
 
 33.68 
 
 29.88 
 
 57 
 
 L6.2J 
 
 17.20 
 
 83 
 
 4.65 
 
 4.S7 
 
 6 
 
 51.17 
 
 40.69 
 
 32 
 
 83.03 
 
 29.48, 
 
 58 
 
 15.55 
 
 16.68 
 
 84 
 
 4.39 
 
 1.66 
 
 7 
 
 
 40.47 
 
 33 
 
 82.86 
 
 29.02 
 
 59 
 
 14.92 
 
 L6.04 
 
 85 
 
 4.12 
 
 4.57 
 
 8 
 
 50.84 
 
 40.14 
 
 34 
 
 31.68 
 
 28.62 
 
 60 
 
 14.34 
 
 15.45 
 
 '86 
 
 3.90 
 
 4.21 
 
 9 
 
 19.57 
 
 39.72 
 
 35 
 
 31.00 
 
 28.22 
 
 61 
 
 13.82 
 
 14.86 
 
 87 
 
 8.71 
 
 8.90 
 
 10 
 
 48.82 
 
 39.23 
 
 36 
 
 30.32 
 
 27.78 
 
 62 
 
 13.81 
 
 14.26 
 
 88 
 
 3.59 
 
 3.67 
 
 11 
 
 48.04 
 
 38.64 
 
 37 
 
 29.64 
 
 27.34 
 
 63 
 
 12.81 
 
 13.66 
 
 89 
 
 3.47 
 
 8.66 
 
 12 
 
 47.27 
 
 38.02 
 
 38 
 
 28.96 
 
 26.91 
 
 64 
 
 12.30 
 
 13.05 
 
 90 
 
 8.28 
 
 3.43 
 
 13 
 
 46.51 
 
 37.41 
 
 39 
 
 28.28 
 
 26.4 7 
 
 65 
 
 11.79 
 
 12.43 
 
 91 
 
 3.26 
 
 3.32 
 
 14 
 
 i. ->.:;. 
 
 36.79 
 
 40 
 
 27.61 
 
 26.04 
 
 66 
 
 11.27 
 
 11.96 
 
 92 
 
 3.37 
 
 3.12 
 
 15 
 
 45.00 
 
 36.17 
 
 41 
 
 26.97 
 
 25.61 
 
 67 
 
 ID. 7.") 
 
 11.48 
 
 93 
 
 3.48 
 
 2.40 
 
 16 
 
 44.27 
 
 35.76 
 
 42 
 
 26.34 
 
 25.19 
 
 68 
 
 10.23 
 
 11.01 
 
 94 
 
 3.53 
 
 1.98 
 
 17 
 
 43.57 
 
 35.37 
 
 43 
 
 25.71 
 
 21.77 
 
 69 
 
 9.70 
 
 10.50 
 
 95 
 
 3.53 
 
 1.62 
 
 18 
 
 42.87 
 
 34.98 
 
 44 
 
 25.09 
 
 24.35 
 
 70 
 
 9.18 
 
 10.06 
 
 96 
 
 3.46 
 
 
 19 
 
 42.17 
 
 34.59 
 
 45 
 
 24.46 
 
 23.92 
 
 71 
 
 8.65 
 
 9.60 
 
 97 
 
 3.28 
 
 
 20 
 
 41.46 
 
 34.22 
 
 46 
 
 23.82 
 
 23.37 
 
 72 
 
 8.16 
 
 9.14 
 
 98 
 
 3.07 
 
 
 21 
 
 40.75 
 
 33.84 
 
 47 
 
 23.17 
 
 22.83 
 
 73 
 
 7.72 
 
 8.69 
 
 99 
 
 2.77 
 
 
 22 
 
 40.04 
 
 33.46 
 
 48 
 
 22.50 
 
 22.27 
 
 74 
 
 7.33 
 
 8.25 
 
 100 
 
 2.28 
 
 
 23 
 
 39.31 
 
 33.08 
 
 49 
 
 21.81 
 
 21.72 
 
 75 
 
 7.01 
 
 7.83 
 
 101 
 
 1.79 
 
 
 24 
 
 38.59 
 
 32.70 
 
 50 
 
 21.11 
 
 21.17 
 
 76 
 
 6.69 
 
 7.40 
 
 102 
 
 1.30 
 
 
 25 
 
 37.86 
 
 32.33 
 
 51 
 
 20.39 
 
 20.61 
 
 77 
 
 6.40 
 
 6.99 
 
 103 
 
 0.83 
 
 
 Thus, by the tables, a man in general good health at 21 years of 
 age has an even chance, by the Carlisle rate of mortality, of living 
 40! years longer; by the Wigglesworth rate, of living 33^- 
 years longer. So a man in general good health, at 60 years of 
 age, has, by the Carlisle rate, an even chance of living 14.34 years 
 longer; by the Wigglesworth rate, an even chance of living 15.45 
 years longer, etc. 
 12* 
 
138 
 
 FELLOWSHIP. 
 
 FELLOWSHIP. 
 
 Fellowship calls for the distribution of a given effect to each 
 of the several causes associated in its production, proportional to their 
 respective magnitudes one with another. 
 
 It is a rule, therefore, adapted to the use of partners associated in 
 business, in achieving a. pro rata distribution among themselves as indi- 
 viduals, of the profits or losses pertaining to the company. 
 
 Rule. — Multiply each partner's investment or share of the capital 
 stock, by the whole gain or loss, and divide the product by the sum 
 of all the shares, or gross capital. 
 
 Example. — Three men, A, B, and C, enter into partnership. A 
 invests $500, B $700, and C $300. They trade and gain $400. 
 What is each partner's share of the profits * 
 
 A, $500 
 
 B, 700 
 
 C, 300 
 
 500 X 400 + 1500 = $133. 33£ = A's share. 
 700 X 400 -J- 1500 = I86.66jf = B's " 
 300 X 400 -f- 1500 = 80.00 = C's " 
 
 $1500 = gross capital. $400.00 Proof. 
 
 Example. — D's investment of $600 has been employed eight 
 months ; E's, of $500, five months ; and F's, of $300, five months ; 
 the profits of the company are $500, and are to be divided pro rata 
 among the partners. What is each partner's share ? 
 
 D, $600 X 8 = 4800 X 500 -r- 8800 = $272.73, D's share. 
 
 E, 500 X 5 = 2500 X 500 -f- 8800 = 142.05, E's " 
 
 F, 300 X 5 = 1500 X 500 -r- 8800 = 85.22 , F's " 
 
 8800 $500. Proof. 
 
 Example. — Of $120 distributed, there were given to A, J ; to B, 
 £ ; to C, £ ; and to D, £, and there was nothing remaining. 
 What sum did each receive 1 
 
 J of 120 = 40 X 120 -T- 114 = $42 T \ = A's share, 
 j of 120 = 30 X 120 -r- 114= 31-f^ = B's " 
 £ of 120 = 21 X 120 -h 114 = 25^ 9 = C's " 
 I of 120 = 20 X 120 -J- 114 = 21^ = D'a " 
 Til $120. Proof. 
 
 Example. — Divide the number 180 into 3 parts, which shall 
 be to each other as 2, 3, 4. 
 
 J of 180 = 90 X 180 4-195 = 83.08 
 of 180 = GO X 180 -f- 195 = 55.88 
 of 180 = 45 X 180 4-195 = 41.54 
 
 195 180.00 Proof. 
 
ALLIGATION. 189 
 
 Example. — $400 are to be divided between A, B, and C, in 
 the ratio of £ to A, £ to B, and | to C; how much will each 
 receivg ? 
 
 4 of 400 = 200, and 200 X 400-^-500 = $160 = A's share. 
 
 X of 400 = 200, and 200 X 400 -^- 500 = 160 = B's share. 
 
 J of 400 = 100, and 100 X 400 -f- 500 = 80 = C's share. 
 
 500 $400. Proof. 
 
 ALLIGATION. 
 
 Alligation Medial is a method by which to find the mean price of 
 a mixture or compound, consisting of two or more articles or ingre- 
 dients, the quantity and price of each being given. 
 
 Rule. — Multiply each quantity by its price, and divide the sum of 
 the products by the sum of the quantities ; the quotient will be the 
 price per unity of measure of the mixture ; and, having found tha 
 price of the given quantities as mixed, any quantities of the same 
 materials, taken in like proportions, will be at the same price. 
 
 Example. — If 20 lbs. of sugar at 8 cents, 40 lbs. at 7 cents, and 
 80 lbs. at 5 cents per pound, be mixed together, what will be the mean 
 price, or price per pound, of the mixture? 
 20 X 8 = 160 
 
 40X7 = 280 
 80X5 = 400 
 
 140 ) 840 ( 6 cents. Ans. 
 
 The several kinds, then, at their respective prices, taken in the 
 proportion of 1 at 8, 2 at 7, and 4 at 5 cts., will form a mixture worth 
 6 cts. a pound. 
 
 Example. — If 10 lbs. of nickel are worth $2, and 24 lbs. of copper 
 are worth $4£, , and 8 lbs. of zinc are worth 40 cts., and 1 lb. of lead is 
 worth 5 cts., what are 5 lbs. of pretty good German silver worth? 
 (iiUL±JLiJ^+4JL±_a)Ki = 81 cents. Ans. 
 
 Alligation Alternate is a method by which to find what quantity 
 of each of two or more articles or ingredients, whose prices or quali- 
 ties are given, must be taken to form a mixture or compound that 
 shall be at a given price or of a given quality between the two 
 extremes. It also'applies to the finding of relative quantities when 
 the quantity of one or more of the articles is limited. 
 
 Rule. — Connect the given prices or qualities — a less than the 
 given mean with that one or either one that is greater — and to the 
 extent that all be thus connected ; then plaee the difference between 
 
140 
 
 ALLIGATION. 
 
 each given and the given mean opposite, not the given, or the 
 given mean, but the given with which it is alligated ; the num- 
 ber standing opposite each price or quality will be the quantity that 
 must be taken at that price, or of that quality, to form a mixture or 
 compound at the price or of the quality desired. And, being propor- 
 tions respectively to each other, they may be taken in ratio greater 
 or less, as desired. 
 
 Example. — In what proportions shall I mix teas at 48 cents a 
 pound and 54 cents a pound, that the mean price may be 50 cents a 
 pound? 
 
 In the proportions 
 
 , A 5 48i ( 4 lbs at 48 cts. ) A 
 50 > 54J ) 2 lbs. at 54 cts. J^ 15 ' 
 Or, as 2 at 48 to 1 at 54. 
 
 Proof. 5 2 X 48 -f 1 X 54 = 150. 
 
 3 X 50 
 
 = 150. 
 
 Example. — In what proportions shall I mix teas at 48, 54, and 72 
 cents a pound, that the mixture may average 60 cents a pound ? 
 (481 12, 12 at 48) ( 2 at 48 
 
 60 { 54-|| 12, 12 at 54 > = < 2 at 54 V 
 
 72J 
 
 18 
 
 y avcidgc uu i.cuis <i jr 
 
 at 48 ) ( 2 at 48 ) 
 at 54 } = < 2 at 54 V 
 at 72 ) ( 3 at 72 J 
 
 12 + 6, 
 
 Example. — A wine dealer has received an order for a quantity of 
 wine at 50 cts. a gallon. He has none ready manufactured at that 
 price. He has it at 40 cts., at 56 cts., and at 80 cents a gallon, and 
 he has water that cost him nothing. He wishes to fill the order 
 with a mixture composed of the four materials — the water and the 
 three different priced wines. In what proportions must he mix them, 
 that the mean or average price may be 50 cents? 
 
 Ans. 
 
 30 = 301 
 
 6 + 30 = 36 I 
 
 10 =10 f 
 
 80=^50 -{-10 = 60 J 
 
 Or, 50 
 
 176 gals. 
 
 66J 
 80- 
 
 = 136 gals. 
 Ans. 
 
 6 1 
 
 | 6 4- 30 1 
 
 50 -f 10 f 
 J 10 J 
 
 
 = 1 12 gals. 
 
 If, now, having found the proportions desired, it is wished to limit 
 \e of the articles in quantity — say the best wine to 8 gallons in the 
 
INVOLUTION — EVOLUTION. 141 
 
 mixture — the pioportions of the remaining articles thereto are found 
 thus : — 
 
 Instance, 1st example, — 
 
 10 
 
 10 
 
 10 
 
 ;, 1st example, — 
 
 8 :: 50 =10 ) . . . .„ . ~ 
 
 o .. on o i (And the mixture will consist of 
 
 8 :: 6= 44 ( 8 + 40 + 24 + 4 t = 76 t S allons - 
 
 If, instead, it is desired to mix a given quantity, say 100 gallons, 
 and proportioned, say as in first example, the quantity to be taken of 
 
 each is ascertained by the following 
 
 Rule. — As the sum of the relative quantities is to the quantity 
 required, so is each relative quantity to the quantity required of it 
 respectively. 
 
 The sum of the relative quantities alluded to is 6 + 30 -J- 50 -\- 10 
 — 96; then, 
 
 96 : 100 :: 6 = 6| 
 y« : 100 :: 30=314 
 96 : 100 :: 50 = 52^ 
 96 : ioo :: io=io T * 2 
 
 INVOLUTION. 
 
 Involution consists in involving, that is, in multiplying a number 
 one or more tines into itself. The number so involved is called the 
 root, and the produet arising from such involution, its power. 
 
 The second power, or square, of the root, is obtained by multiplying 
 the root once into itself, as4 X 4=»16; 4 being the root and 16 its 
 square. 
 
 The third poiver, or cube, of a number, is obtained by multiplying 
 the number twice into itself, as4 X 4X 4 = 64; and so on for any 
 power whatever. 
 
 When a number is to be involved into itself, a small figure called 
 the index or exponent is placed at its right, indicating the number of 
 times it is to be so involved, or the power to which it is to be raised. 
 Thus, 3 1 = 3 X 3 X 3 X 3 = 81; and4 3 = 4 X 4 X 4 = 64. 
 
 EVOLUTION. 
 
 Evolution is the opposite of Involution. It consists in finding a 
 toot of a given number, instead of a power of a given root. 
 
 When the root of a number is required or indicated, the number is 
 A'ritten witb the V before it : and the character or denomination of 
 the root, if it be other than the square root, is defined by an index 
 
142 EVOLUTION. 
 
 figure placed over the sign. When the square root of a number is 
 required, the sign (V) is placed before the number, but the index 
 (2) is usually omitted. Thus, V25, shows that the square root of 
 25 is required, or to be taken ; and /^25 shows that the cube root 
 is required. The operation is usually called extracting the root. 
 
 TO EXTRACT THE SQUARE ROOT. 
 
 Rule — 1. Separate the given number into periods of two figures 
 each, by placing a point over the first figure, third, fifth, &c, counting 
 from right to left — the root will consist of as many figures as there 
 are periods. 
 
 2. Find the greatest square in the left hand period, and place its 
 root in the quotient ; subtract the square of the root from the left 
 hand period, and to the remainder bring down the next period for a 
 dividend. 
 
 3. Multiply the root so far found — the figure in the quotient — by 
 2, for a divisor ; see how many times the divisor is contained in the 
 divided, except the right hand figure, and place the result (the num- 
 ber of times it is contained) in the quotient, to the right of the figure 
 already there, and also to the right of the divisor ; multiply the divi- 
 sor, thus increased, by the last figure in the quotient, and subtract the 
 product from the dividend, and to the remainder bring down the next 
 period for a dividend. 
 
 4. Multiply the quotient — the root so far found (now consisting of 
 two figures) — by 2, as before, and take the product for a divisor ; 
 see how many times the divisor is contained in the dividend, except 
 the right hand figure, and place the result in the quotient, and to the 
 right of the divisor, as before ; multiply the divisor, as it now stands, 
 by the figure last placed in the quotient, and subtract the product from 
 the dividend, and to the remainder bring down the next period for a 
 dividend, as before. 
 
 5. Multiply the quotient (now consisting of 3 figures) by 2, as 
 before, and take the product for a divisor, and in all respects proceed 
 as when seeking for the last two figures in the quotient. The quo- 
 tient, when all the periods have been brought down and divided, will 
 be the root sought. 
 
 Notb. — 1. If there is a remainder after finding the integer of a root, annex periods of 
 ciphers thereto, and proceed as when seeking for the integer. The quotient figures will 
 be the decimal portion of the root. 
 
 2. If the given number is a decimal, or consists of a whole number and decimal, point 
 off the decimal from left to right, by placing the point over the secomi, fourth, sixth, &.c, 
 figures therein, aiwl fill the last period, if incomplete, bjf ipher. 
 
 3. If the dividend does not contain the divisor, a Cipher must he placed in the quotient, 
 and also at the right of the divisor, and the next period brought down ; then the dividend 
 must be divided by the divisor as increased. 
 
 4. If the quotient figure, obtained by dividing by the double of the root, is too large, as 
 will sometimes be the case, (see 3d Example) it must be dropped, and a lees — one which 
 m the truo measure — taken in its stead. 
 
EVOLUTION. 143 
 
 Example. — Required the square root of 123456.432. 
 
 123456.4320 ( 351.3636-f-. Ans. 
 9 
 
 65 ) 334 
 325 
 
 70 . ) 956 
 701 
 
 7023 ) 25543 
 21069 
 
 70266 ) 447420 
 4 21596 
 
 702723 ) 2582400 
 2108169 
 
 7027266 ) 47423100 
 42163596 
 
 5259504 
 
 Example. — Required the square root of 10621. Also, of 28561. 
 
 10621 ( 103.05+. Ans. 
 
 1 
 
 203 ) 00621 
 609 
 20605 ) 120000 
 103025 
 16975 
 
 28561 ( 169. Ans. 
 
 1 
 
 26 ) 185 
 156 
 
 329 ) 2961 
 2961 
 
 TO EXTRACT THE CUBE ROOT. 
 
 Rule — 1. Separate the given number into periods of three figures 
 each, by placing a point over the first, fourth, seventh, &c, counting 
 from right to left — the root will consist of as many figures as there 
 are periods. 
 
 2. Find the greatest cube in the left hand period, and place its root 
 in the quotient ; subtract the cube of the root from the left hand pe- 
 riod, and to the remainder bring down the next period for a dividend. 
 
 3. Multiply the square of the quotient by 300, for a divisor ; see 
 how many times the divisor is contained in the dividend, and place 
 the result (except that the remainder is large, diminished by one or 
 two units) in the quotient. 
 
 4. Multiply the divisor by the figure last placed in the quotient, 
 and to the product add the square of the same figure, multiplied by the 
 other figure, or figures, in the quotient, and by 30 ; and add also thereto 
 
144 EVOLUTION. 
 
 the cube of the same figure, and take the sum for the subtrahend ; sufr. 
 tract the subtrahend from the dividend, and to the remainder bring 
 down the next period for a dividend, with which proceed as with the 
 preceding, so continuing until the whole is completed. 
 
 Note — 1. Decimals must be pointed from left to right, by placing a point over the 
 third, sixth, &c, figures in that direction. 
 
 2. If the divisor is not contained by the dividend, place a cipher in the quotient, and 
 annex two ciphers to the divisor, and bring down the next period for a dividend, and use 
 the divisor, as thus increased, for finding the next quotient figure. 
 
 3. If there is a remainder after finding the integer of the root, annex a period of three 
 ciphers thereto, and proceed for the decimal of the root as if seeking for the integer, an- 
 nexing a period of three ciphers to each remainder until the decimal is carried to as many 
 places of figures as desired. 
 
 Example. —Required the cube root of 47421875.6324. 
 
 4742i875.632400 ( 361.959-J- . 
 27 Am. 
 
 3 2 X 300 = 2700) 20421 
 6 
 
 16200 
 6 s X 3 X 30 = 3240 
 
 6 3 = 216=19656 
 
 36 2 X 300 = 388800 ) 765875 
 1 
 
 388800 
 l 2 X 36 X 30 = 1080 
 
 I 3 = 1 = 389881 
 
 36 1 2 X 300 = 390963Q0 ) 375994632 
 9 
 
 351866700 
 B 2 X 361 X 30 = 877230 
 
 93= 729 = 352744659 
 
 3619 2 X 300 = 3929148300 ) 23249973400 
 5 
 
 19615711500 
 5 s X 3619 X 30 = 2714250 
 
 5^= 125 = 19648455875 
 
 36195 2 X 300 = 393023107500 ) 3601517525000 
 9 
 
 3537210667500 
 S* X 36195 X 30 a 87953850 
 3 =- 729 » 3537298622079 
 
 64218902921 
 
EVOLUTION. 145 
 
 Example. - - Required the cube root of 32768. Also, of 8489664. 
 
 32768(32. 
 27 Ans. 
 
 32X300 = 2700 ) 5768 
 2 
 
 5400 
 2 2 X 3X30=360 
 
 23= 8 = 5768 
 
 8489664(204. 
 8 Ans. 
 
 2 s X 300 = 120000 ) 489664 
 4 
 
 480000 
 4 2 X 20X30 =9600 
 
 4 3 = 64=480664 
 
 General Rule for extracting the roots of all powers, or for finding 
 any proposed root of a given number. 
 
 1. Point off the given number into periods of as many figures 
 each, counting from right to left, as correspond with the denomina- 
 tion of the root required ; that is, if the cube root be required, into 
 periods of three figures, if the fourth root, into periods of four fig- 
 ures, &c. 
 
 2. find the first figure of the root by inspection or trial, and place 
 it at the right of the number, in the form of a quotient ; raise this 
 quotient figure to a power corresponding with the denomination of 
 the root sought, and subtract that power from the left hand period, 
 and to the remainder bring down the first figure of the next period, 
 for a dividend. 
 
 3. Raise the root thus far found (the quotient figure) to a power 
 next inferior in denomination to that of the root required, multiply 
 this power by the number or index figure of the root required, and 
 take the product for a divisor ; find the number of times the divisor 
 is contained in the dividend, and place the result (except that the 
 remainder is large, diminished by one or two units) in the quotient, 
 for the second figure of the root. 
 
 4. Raise the root thus far found (now consisting of two figures) to 
 a power corresponding in denomination with the root required, and 
 subtract that power from the two left hand periods, and to the re- 
 mainder bring down the first figure of the third period, for a divi- 
 dend ; find a new divisor, as before, and so proceed until the whole 
 root is extracted. 
 
 Example. — Required the fifth root of 45435424. 
 
 45435424(34. Ans. 
 3 5 = 243. 
 
 3^X5)2113 
 345= 45435424 
 
 13 
 
146 AKITHMETICAL PROGRESSION. 
 
 Example. — Required the fifth root of 432040.0o54. 
 
 432040.03540 ( 13.4 -f. Arts. 
 
 1 4 X5)33 
 13 5 = 371293 
 
 13 4 X5) 607470 
 13.4 5 = 43204003424 
 
 116 
 
 For instructions touching special cases, see Notes relative to the 
 extraction of the square root, and to the extraction of the cube root. 
 
 The a/ of the a/ of any number = /s/ of that number 
 " Vofthe^ = /y. 
 " V of the V of the s/ = £/ . 
 " # of the a/ = a/. 
 " V of the & =&, &c. 
 
 ARITHMETICAL PROGRESSION. 
 
 A series of three or more numbers, increasing or decreasing by 
 equal differences, is called an arithmetical progression. If the num- 
 bers progressively increase, the series is called an ascending arith- 
 metical progression ; and if they progressively decrease, the series is 
 called a descending arithmetical progression. 
 
 The numbers forming the series are called the terms of the 
 progression, of which the first and the last are called the extremes, 
 and the others the means. 
 
 The difference between the consecutive terms, or that quantity by 
 which the numbers respectively increase upon each other, or decrcaso 
 from each other, is called the common difference. 
 
 Thus, 3, 5, 7, 9, 11, *C., is an ascending arithmetical progression, 
 and 11, 9, 7, 5, 3, is a descending arithmetical progression. In these 
 professions, in both instances, 11 and 3 are the extremes, of whick 
 11 is the greater extreme, and 3 is the less extreme. The Humbert 
 between these, (9, 7, 5,) arc the means. 
 
 In every arithmetical progression, the sum of the extremes is 
 equal to the sum of any two moans that arc equally distant from the 
 extremes; and is, therefore, equal to twice the middle term, \v lion 
 the series consists of an odd Dumber of terms. Thus, in the fore- 
 going series, 3 + 11 = 5 -f 9 = 7 X 2. 
 
 The greater extreme, the less extreme, the nund>er of terms, the 
 
ARITHMETICAL PROGRESSION. 147 
 
 common difference, and the sum of the terms, are called the Jive prop- 
 erties of an arithmetical progression, of which, any three being given, 
 the other two may be found. 
 
 Let s represent the sum of the terms. 
 ' ' E " the greater extreme. 
 " e " the less extreme. 
 lt d " the common difference. 
 " n " the number of* terms. 
 
 The extremes of an arithmetical progression and the number of terms 
 being given, to find the sum of the terms. 
 
 (E 4- e) X n 
 
 2 ■■ 8um °f tne terms. 
 
 Example. — What is the sum of all the even numbers from 2 to 
 100, inclusive ? 
 
 102 X 50-4-2 = 2550. Ans. 
 
 Example. — How many times does the hammer of a common clock 
 strike in 12 hours 1 
 
 (1 -J- 12) X 12 -r- 2 = 78 times. Ans. 
 I ~~ e + 1 j x T =•» s um of tn o terms. 
 
 (E X 2 — w—1 X d) X h n = sum of the terms. 
 
 (2e-\~n — lX.d) X £ w = sum of the terms. 
 
 The greater extreme, the common difference, and the number of terms 
 of an arithmetical progression being given, to find the less extreme. 
 
 E — (d X n — 1) == less extreme. 
 
 Example. — A man travelled 18 days, and every day 3 miles far- 
 ther than on the preceding ; on the last day he travelled 56 miles ; 
 how many miles did he travel the first day ? 
 
 56 — (18 — 1 X 3) = 5 miles. Ans. 
 
 — { ) = less extreme. 
 
 n V 2 / 
 
 5 
 
 - X 2 — E = less extreme. 
 
148 ARITHMETICAL PROGRESSION. 
 
 V (EX2 + d)> — s X dX$-\- <* =lesa extreme, when 
 2 
 W (2 E -\-.d ) 2 — 8 s d is equal to, or greater than d. 
 
 a/ {2^ t -\-dy i — 8 sd^d = less extreme, when 
 2 
 V (2E-j-rf) 2 — 85«? is less than d. 
 
 A/(2e^d) 2 -±-8sd — < f=» greater extreme 
 2 
 
 rfX» — l-|-e = greater extreme. 
 
 —■ -{- o ■■ greater extreme. 
 
 25-fn — e = greater extreme. 
 
 Tfe extremes of an arithmetical progression and the common difference 
 being given, to find the member of terms. 
 
 E — e-r-d-\-l=i number of terms. 
 
 Example. — As a heavy body, falling freely through spaee, de- 
 ■cends 16^- feet in the first second of its descent, 48^ feet in the 
 next second, 80^- in the third second, and so on ; how many sec- 
 onds had that body been falling, that descended 305^. z fcet in the 
 last second of its descent ? 
 
 305^ — 16^ = 289£ -5- 32£ = 9 + 1 = 10 seconds. Ans. 
 
 */(2e^dy + 8sd — d — e -e- <* -f 1 = number of terms. 
 
 25-j.E-f V(2E-f</)t — 8srf-f </ 2= number of terms when 
 2 
 V (2 E -\- d) 2 — 8 5 d is equal to, or greater than d. 
 
 2 5 -f- E -f V(2E-f<f)2 — Ssd^d — number of terms when 
 2 
 
 //(2E4-^/) 2 — 8*rf is less than rf. 
 *X2 
 
 »+« 
 
 = number of terms. 
 
ARITHMETICAL PROGRESSION. 140 
 
 The extremes of an arithmetical progression, and the number of terms 
 being given, to find the common difference, 
 
 E — e 
 
 7 = common difference. 
 
 n — l 
 
 Example. — One of the extremes of an arithmetical progression is 
 28 and the other is 100, and there are 19 terms in the series ; re- 
 quired the common difference. 
 
 100^28-j-lool9=a4. Arts. 
 
 AX 2 \ 
 
 — e "5" \ E4-e — * J ™ comm011 difference. 
 
 E 
 
 2*-5-n — 2e 
 
 n — 1 
 
 2E— (2 5-J-n) 
 
 common difference. 
 
 = common difference, 
 n — I 
 
 Example. — The less extreme of an arithmetical progression is 28, 
 the sum of the terms 1216, and the number of terms 19 ; required 
 the 7th term in the series, descending. • 
 
 1216 X 2 -f- 19 = 128 = sum of the extremes. 
 128 — 28 = 100 — greater extreme. 
 100 — 28 = 72 = difference of extremes. 
 
 72-j-w — 1 (18) = 4 = common difference. 
 100 — (7 — 1 X 4) = 76 = 7th term descending. Ans. 
 Required the 5th term from the less extreme, in an arithmetical 
 progression, whose greatest extreme is 100, common difference 4, 
 and number of terms 19. 
 
 100 — (19 — 5 X 4) = 44. Ans. 
 
 To find any Assigned number of arithmetical means, between two given 
 numbers or extremes. 
 
 Rule. — Subtract the less extreme from the greater, divide the 
 remainder by 1 more than the number of means required, and the 
 quotient will be the common difference between the extremes ; 
 which, added to the loss extreme, gives the least mean, and, added 
 to that, gives the next greater, and so on. 
 
 Or, K — ~e -f- ra + 1 = d, E being the greater extreme, e the less 
 extreme, m the number of means required, and d the common differ- 
 
 1 e -f- d, e -f 2 d, e+'dd, &c. ; or, E — d, E — 2d, E — 3 d, 
 fcc., will give the means required. 
 13* 
 
150 GJOMETRICAL PROGRESSION. 
 
 Example. — Required to find 5 arithmetical mean* between the 
 numbers 18 and 3. 
 
 18 — 3 = 15 H- 6 = 24, and 
 3-^2i=-5i-f.2i=»8-f-24=-104-f2i = 13-f-24 = 15i. 
 5£, 8, 10£, 13, 15£, therefore, are 5 arithmetical means, between the 
 extremes, 3 and 18. 
 
 Note. — The arithmetical mean between any two numbers maybe found by dividing 
 the sum of those numbers by 2 ; thus, the arithmetical mean of and & is (&-^-&)-^2=8±. 
 
 GEOMETRICAL PROGRESSION. 
 
 A series of three or more numbers, increasing by a common mul- 
 tiplier, or decreasing by a common divisor, is called a geometrical 
 progression. If the greater numbers of the progression are to the 
 right, the progression is called an ascending geometrical progression, 
 but, on the contrary, if they are to the left, it is called a descending 
 geometrical progression. The number by which the progression is 
 Formed, that is,*the common multiplier, or divisor, is called the 
 ratio. 
 
 The numbers forming the series are called the terms of the pro- 
 gression, of which the first and the last are called the extremes, and 
 the others the means. The greater of the extremes is called tho 
 greater extreme, and the less the less extreme. 
 
 Thus, 3, 6, 12, 24, 48, is an ascending geometrical progression, 
 because 48 is as many times greater than 24, as 24 is greater 
 than 12, <Sbc. ; and 250, 50, 10, 2, is a descending geometrical pro- 
 gression, because 2 is as many times less than 10, as 10 is less than 
 50, &c. 
 
 In the first mentioned series, (3, 6, 12, 24, 48,) 48 is the greater 
 extreme, and 3 is the less extreme ; the numbers 6, 12, 24 are tho 
 means in that progression. 
 
 So, too, of the progression 250, 50, 10, 2 ; 250 and 2 are the ex- 
 tremes, and 50 and 10 are the means. 
 
 In the first mentioned progression, 2 is the ratio, and in the last, 
 or in the progression 2, 10, 50, 250, 5 is the ratio. 
 
 In a geometrical progression, the product of the two extremes is 
 equal to tho product of any two means that are equally distant from 
 the extremes, and, also, equal to the square of the middle term, 
 when the progression consists of an odd number of t< ; 
 
 Thus, in tho progression 2, 6, 18, 54, 102 ; 102 X 2 = 5 1 X r 
 = 18 X 18. 
 
 When a geometrical progression has but 3 terms, cither of the 
 
GEOMETRICAL PROGRESSION. 151 
 
 extremes is called a third proportional to the other two ; and the 
 middle term, consequently, is a mean proportional between them. 
 
 Thus, in the progression 48, 12, 3, 3 is a third proportional to 48 
 and 12, because 48 divided by the ratio = 12, and 12 divided by the 
 ratio = 3 ; or 3 X ratio = 12, and 12 X ratio = 48 : 12 is the mean 
 proportional, because 12 X 12 = 48 X 3. 
 
 Of the 5 properties of a geometrical progression, viz., the greater 
 extreme, the less extreme, the number of terms, the ratio, and the sum 
 of the terms, any three being given, the other two may be found. 
 
 Let s represent the sum of the terms. 
 
 E " the greater extreme. 
 
 e " the less extreme. 
 
 r " the ratio. 
 
 n " the number of terms. 
 
 n when affixed as an index or exponent, represent that the 
 term, number, or quantity, to which it is affixed, is to be raised 
 to a power equal to the number of terms in the respective progres- 
 sion, &c. 
 
 Any three of tliefive parts of a geometrical progression being given, to 
 find the remaining two parts. 
 
 E — e 
 -, -(-Eat sum of the terms. 
 
 — * r e — sum of the terms, 
 r— 1 
 
 r n X c — e 
 
 r— 1 
 
 sum of the terms. 
 
 -\- E = sum of the terms. 
 E — e 
 
 ^(E-he)-! 
 
 ■f- E = sum of the terms. 
 
 Example. — The greater extreme of a geometrical progression is 
 162, the less extreme is 2, and there are 5 terms in the progression ; 
 required the sum of the series. 
 
 80 + 162 = 242. Ans. 
 
 ^(162-s-2)-r 
 
 sXr-l +e 
 
 = greater extreme. 
 
152 GEOMETRICAL PROGRESSION. 
 
 — X c = greater extreme, 
 r n_l X c = greater extreme. 
 
 = greater extreme. 
 
 r :i 
 
 5 — (5 — E) X t = less extreme. 
 E -f- r n_1 = less extreme. 
 
 sXr^Xr-L . n-1 
 
 -£-r = less extreme. 
 
 r°— 1 
 * — e 
 
 s — E 
 
 ratio. 
 
 E 
 n 7j/- = ratio. 
 
 *Xr 
 
 1 = r n ; n, therefore, is equal to the number of timei 
 
 sXr — l 
 
 that r must be multiplied into itself to equal -f- L 
 
 -x— 1 +1.,.. 
 
 s— (5 — E)Xr 
 
 Example. — A farmer proposed to a drover that he would sell 
 him 12 sheep and allow him to select them from his flock, provided 
 the drover would pay 1 cent for the first selected, 3 cents for the 
 -second, 9 cents for the third, and so on ; what sum of money would 
 12 sheep amount to, at that rate? 
 
 r n X e — e 
 
 r _l — = s } then 
 
 312x1 — 1 
 
 jj^Tj— = $2657.20. Arts. 
 
 Note. — Ratio 4 , cubed = ratio 12 ; ratio 6 , squared = ratio' ' : , &c. 
 
 When it is required to find a high power of a ratio, it is conven- 
 ient to proceed as follows, viz. : write down a few of the lower or 
 leading powers of the ratio, successively as they arise, in a line, one 
 after another, and placo their respective indices over them ; then 
 
 I J 
 
GEOMETRICAL PROGRESSION. 153 
 
 will the product of such of those powers as stand under such indices 
 whose sum is equal to the index of the required power, equal the 
 power required. 
 
 Example. — Required the 11th power of 3. 
 
 12 3 4 5 
 3 9 27 81 243 
 
 Here 5 + 4-f-2 = ll, consequently, 
 
 243 X 81 X 9 = 11th power of 3, or 
 
 5X24-1 = U» consequently, 
 243 X 243 X 3 = 11th power of 3, or 
 
 4X2 + 3 = 11, consequently, 
 81 X 81 X 27 = 11th power of 3, or 
 
 3 X 3-f-2 = ll, consequently, 
 
 27 3 X 9 = r 11 = 177147. Ans. 
 
 To find any assigned number of geometrical means, between two given 
 numbers or extremes. 
 
 Rule. — Divide the greater given number by the less, and from 
 the quotient extract that root whose index is 1 more than the 
 number of means required ; that is, if 1 mean be required, extract 
 the square root ; if two, the cube root, &c, and the root will be the 
 common ratio of all the terms ; which, multiplied bv the less given 
 extreme, will give the least mean ; and that, multiplied by the said 
 root, will give the next greater mean, and so on, for all the means 
 required. Or the greater extreme may be divided by the common" 
 ratio, for the greatest mean ; that by the same ratio, for the next 
 less, and so on. 
 
 Example. — Required to find 5 geometrical means between the 
 numbers 3 and 2187. 
 
 2187 -7- 3 = 729, and ^729 — 3, then — 
 3X3 = 9X3 = 27X3=81X3 = 243 X 3-= 729, that is, the 
 numbers 9, 27, 81, 243, 729 are the 5 geometrical means between 
 3 and 2187. 
 
 Notb. — The geometrical mean between any two given numbers is equal to the square 
 root of the product of those numbers. Thus the geometrical mean between 5 and 20, =» 
 
 V( 5 X20)=io. 
 
154 ANNUITIES. 
 
 ANNUITIES. 
 
 An annuity, strictly speaking and practically, is a certain sum 
 of money by the year ; payable, usually, either in a single pay- 
 ment yearly, or in half, half-yearly, quarter, quarter-yearly, &c, 
 and for a succession of years, greater or less, or forever. Pensions, 
 awards, bequests, and the like, that are made payable in fixed 
 sums for a succession of payments, are commonly rated by the 
 year, and denominated annuities. 
 
 A current annuity that has already commenced, or that is to 
 commence after an interval of time not greater than that between 
 the stipulated payments, is said to be in possession. 
 
 One that is to commence or cease on the occurrence of an 
 indeterminate event, as upon the death of an individual, is a re- 
 versionary, contingent, or life annuity. 
 
 One that is to commence at a given period, and to continue for a 
 given number of years or payments, is a certain annuity. 
 
 One that is to continue from a given time, forever, is a perpetual 
 annuity, or & perpetuity. 
 
 Annuity payments do not exist fractionally : they mature, and 
 exist only in that state, and are then due. 
 
 A current annuity commences with a payment, and terminates 
 with a payment. 
 
 One current in the past is measured from a present included pay- 
 ment, closes with an included payment, and is said to be in arrears 
 or forborne, from a supposed cancelled payment one regular inter- 
 val or time beyond. 
 
 One current in the future is measured from the present to the 
 first included payment of the series, and from thence is said to con- 
 tinue to the close ; but if the interval from the present to the first 
 included payment is equal to that between the successive pay- 
 ments, it is supposed to continue from the present. 
 
 Annuities in negotiation are adjusted, with regard to time, by 
 interest, or discount, or both. 
 
 The tables applicable to compound interest and compound dis- 
 count are applicable in adjusting annuities at compound rates. 
 
 To find the Amount of a Current Annuity in Arrears. 
 
 Lemma. — The amount of an annuity that has been fo r borne 
 for a given time is equal to the sum of the several payments that 
 have become due in that time, plus the interest on each, from the 
 time it became due, until the close of the time. 
 
ANNUITIES. 155 
 
 Then the amount of an annuity of $100, payable in a single 
 payment annually, but delayed of payment 4 years, allowing sim- 
 ple interest at 6 per cent, on the payments, is 
 
 100 X 1.18= 118 
 100 X 1.12= 112 
 
 100 X 1.06= 106 
 
 100 X 1 = 100 = $436. 
 
 And at 6 per cent, compound interest on the payments, it is 
 
 100 X (1.06)8 = 119.10 
 100 X (1.06) 2 = 112.36 
 100 X (1.06)! = 106.00 
 100 X 1 =100.00 =$437.46. 
 
 At 6 per cent, simple interest, when payable in half, half- 
 yearly, it is 
 
 50 X 1.21=60.50 
 50 X 1.18 = 59.00 
 50 X 1-15 = 57.50 
 50 X 1.12 = 56.00 
 50 X 1.09 = 54.50 
 50 X 1.06 = 53.00 
 50 X 1.03 = 51.50 
 50 X 1 = 50.00 = $442. 
 
 And at 6 per cent, compound interest per annum, when payable 
 in half-yearly instalments, it is 
 
 50 X (1.06)8 X 1.03=61.34 
 
 50 X (1.06)8 =59.55 
 
 50 X (1.06) 2 X 1.03=57.86 
 
 50 X (1.06)2 =56.18 
 50 X (1.06)1 x 1.03 = 54.59 
 
 50 X 1-06 =53.00 
 
 50 X 1-03 =51.50 
 
 50 X 1. =50.00 = $444.02. 
 
 From the foregoing, we derive the following general Rules: — 
 
 Let P = annuity or yearly sum, 
 
 r = rate of interest per annum, 
 
 a = rate of discount per annum, 
 
 n or n = nominal time of the annuity in full years, 
 
 A = amount for the full years, 
 
 D =present worth for the full years. 
 
156 ANNUITIES. 
 
 When the annuity is payable in a single payment yearly, 
 A = P/i (l -j- ^f^)y Simple Interest 
 A = P — ~ i Compound Interest 
 
 When payable in equal half-yearly instalments, 
 
 A = Pn ( 1 -f r -^~^ + "f )' Simple Interest. 
 
 A = P X (1+r i.'" 1 X ( 1 + 0' Compound Interest 
 When payable in equal third-yearly instalments, 
 
 A = Pn ( 1 + ^Hz± -j- -f ), Simple Interest 
 
 A = P — £ — (i_j_r^ Compound Interest. 
 When payable in quarter-yearly instalments, 
 
 A = Pn ( 1 + r -^f^+ ~ ), Simple Interest. 
 
 A = P ( 1+r ^~ 1 ( l -f ^- ), Compound Interest. 
 When there are odd payments, to find the amount, S. 
 
 When 1 half-yearly, S == A(l 
 
 1 third-yearly, S = A(l + £ r) 
 
 *') + *?• 
 
 S = A(l--}r)--JP. 
 
 S = A(l-|-fr)-JP(l + W+JP 
 
 ,S = A(l-^r)-iP. , ^ 
 
 ±r) + P(8 + r)-^16. 
 
 1 quarter-yearly, 
 
 2 ". S = A(1 
 
 3 « S = A(l + |r) + P(3 + |r)-f-4. 
 
 For any number of equal and regular payments at compound 
 interest per interval between the payments, S = P' ( — - — j, and 
 for any number of equal and regular payments at simple interest 
 per interval between the payments, S = P'n' (l -\- r ' lH '~ 1) ) ; P' 
 being a payment, n 1 or n ' the number of payments, and r 1 the rate 
 of interest per interval between the payments. But this must not 
 be confounded with compound interest annually, on payments oc- 
 curring semi-annually, quarterly, &c. 
 
 Example. — What is the amount of an annuity of $150, paya- 
 ble in half, half-yearly, but delayed of payment 2 years and 72 
 days, allowing compound interest per annum at 7 per cent. V 
 
 150 x l ^~= $310.50, the amount for 2 years, if payable 
 in yearly payments, and 
 
ANNUITIES. 157 
 
 810.50X 0-^) =$315.93, the amount for 2 years, if payable 
 in half-yearly payments, and 
 
 815.93 X O'^^O =$320.29, the amount for 2 years and 72 
 days, if payable in half-yearly payments. Ans. 
 
 Example. — What is the amount of an allowance, pension, or 
 award, of $100 a year, payable quarterly, but forborne 3£ years, 
 interest compound per annum at 6 per cent. ? 
 
 100 X ( -^— X ( 1 -f 1 ^) = $325.52*, the amount for 3 years, 
 
 and 
 
 325.52 (1 -{- .03) -J-100X 8.06 -f- 16= $385.66. Ans. 
 
 Example. — What is the amount of $100 a year, payable in 
 quarterly payments, and in arrears 4 years, interest being com- 
 pound per quarter-year, at 6 per cent, a year ? 
 
 25 [(1 -f-f) 1 - 1] X ~m • Bv taDular powers of (1 + r), page 
 
 125, =$448.30. Ans. 
 
 To find the Present Worth of an Annuity Current. 
 
 Lemma. — The present worth of an annuity that is to continue 
 for a given time is equal to that sum of money, which, if put at 
 interest from the present time to the close of the payments, will 
 amount to the amount of the payments at that time ; and therefore, 
 the times being full, is equal to the sum of the several payments, 
 discounted, respectively, at the rate of interest for their respective 
 times. 
 
 Note. —If the foregoing proposition is tenable, it follows, since simple 
 interest is due and payable annually, that the true present worth of an annuity 
 having more than one year to run cannot be found by simple interest and dis- 
 count. By simple interest and discount, at 6 per cent., predicating the rule 
 upon the foregoing lemma, the amount of $100, payable annually, and in 
 arrears for 4 years, is $436 5 and the present worth, at 6 per cent., is 
 
 jpo ioo_ wo 100 
 
 1.24^1.18 1.12^1.06 * 
 
 But $349 at 6 per cent, interest for 4 years, with the payments of interest annu- 
 ally, will amount to $440.60; and at interest simply for 4 years it will amount 
 to only $432.76. 
 
 Then the present worth of an annuity of $100, payable in a 
 single payment yearly, and to continue 4 years, or to become due 
 1, 2, 3, and 4 years hence, interest and discount being compound 
 per annum, and each at 6 per cent. = 
 14 
 
158 ANNUITIES. 
 
 P P P P 
 
 U + /T-L-TT3 + n-j-^2 + i-T- = S346.51 =z 
 
 (1+r)* ' (l+r) s ' (i+r)»^l+r- 
 
 100 X (1.06) 3 = 119.10 
 
 100 X (1.06) 2 = 112.36 
 
 100 X (1.06) =106.00 
 
 100 X 1 = 100.00 = 437.46 -t-(1.06) 4 z= $346.51. 
 
 And interest at 6 per cent, and discount at 10, both compound, it is 
 100 X (1.06) 3 = 119.10 
 100 X (1.06) 2 = 112.36 
 100 X 1-06 =106.00 
 100 X 1 =100.00 = 437.46 -f-(1.10) 4 = $298.79. 
 
 Therefore, when the annuity is payable in a single payment 
 yearly from the present time, 
 
 D = P ( "^ r) ~ 1 »= n when r and a are equal. 
 
 ra + af a + rr ^ 
 
 When payable in half-yearly payments, 
 
 D = Px< w x(1 + ir >- 
 
 When payable in third-yearly payments, 
 
 -p __ PxCd+D'-llxd-Hr^ 
 r(l + a) s 
 When payable in quarter-yearly payments, 
 
 D = rftl + r)*-l](l + jr) . 
 r(l + a) n 
 
 When there are odd payments, to find the present worth, S. 
 There being a half-yearly, S = l -^r- -f- ,-4^— 
 « 1 third-yearly, 8 = ,-^-+^. 
 
 « 9 « S J — I 2P(l+$r) . 
 
 o-_ 1 + |a - r 8(1 + fa) 
 
 « 1 quarter-yearly, S = q^+ r^Ta 
 
 Ml " S — -5- _L Z&±i!$* 
 
 For any number of equal payments, at equal intervals between 
 the payments, S = P'X ( ~^ri P' being a payment, n ' the 
 
ANNUITIES. 159 
 
 number of payments, and r' and a' the rates per interval between 
 the payments. 
 
 Note.— Since ( 1 ~*" r) 7 1 is the co-efficient of V, for its present worth, at 
 
 compound interest and discount, for the time » , at the rates r, «, it follows 
 that tables of co-efficients of 1* lor its present worth, at given rates, for any 
 number of years, may be easily made. Thus (1-06* — n-s-i.oe 4 x.06 = :u(;r>n, 
 the co-efficient of an annuity, P, for 4 years' continuance, interest and discount 
 being compound per annum, at 6 percent.; and (1.06 2 — D-Ml.06 2 X -06) = 
 1.83339, the co-efficient for 2 years, &c. 
 
 If the annuity is deferred, then the diflerenceof two of these co-efficients 
 (one of them that for the time deferred, and the other that for the sum of the 
 time deferred and the time of the annuity) will be the co-efficient of P for 
 its present worth. Thus 3.4051 1 — 1.83339*= 1.63172, the co-efficient of an annuity, 
 P, for its present worth, when it is to commence two years hence, and to con- 
 tinue 2 years, interest and discount being compound per annum, at G per 
 cent, each; or D= 1.03172 P. 
 
 In like manner, tables of other co-efficients, such as the formulae suggest, 
 may be made that will greatly assist in calculating annuities. 
 
 Example. — What is the present worth of an award of $500 a 
 year, payable in half-yearly instalments, the 1st payment to mature 
 6 months hence, and the annuity to continue three years; interest 
 and discount being 7 per cent., compounded yearly ? 
 
 500 X [(1.07) 3 — 1]X (l.f) 
 
 >oyx(1>07) , -^—^ =$1888.18. Ans. 
 
 Example. — What is the present worth of an annuity of $100, 
 payable in half-yearly payments, and to continue 1£ years; interest 
 and discount being 6 per cent, per annum ? 
 
 100 X [1.06 — l]Xl-4 6 
 
 D — - 95 755 ana 
 
 U — .06X1.06 XW,7W ' 
 
 95.755 , 50 
 
 Tor+roa^* 141 - 61 - Ans - 
 
 Example. — What is the present worth of an annuity of $500, 
 payable in semi-annual instalments, and to continue 10| years, 
 interest and discount being compound per annum, the former at 6 
 per cent., and the latter at 8 ? 
 
 500 [(1.06)*- 1] (I..*) 5QQ 
 
 .06(1.08y(l.f) + 2(l.f) 
 
 A 250 
 
 1.08 10 X 1-04 + 1.04 — AnS ' 
 
160 ANNUITIES. 
 
 KDwers of 1 -}- r, page 12 
 = $3052.64, the present worth for 10 years' con- 
 
 By tabular powers of 1 -}- r, page 125 : 
 500 X -79085 
 
 .06 X 2.15892 
 
 tinuance, if payable in yearly payments, and 
 
 3052.64 X 1-015 = $3098.43, 
 
 the present worth for 10 years' continuance, if payable in half- 
 yearly payments, and 
 
 3098.43 -7- 1.04 -|- 500 -+- 2 X 1-04 = $321 9.64. Ans. 
 
 When the interval of time from the present to the 1st payment 
 is shorter than that between the consecutive payments, and the 
 annuity is payable in a single payment yearly, 
 
 A= P[(l+r)--l](l+£) 
 
 r 
 
 A P [(! + »•)■- !](!+£) 
 
 d being the time in days from the present to the 1st payment. 
 
 So, if the annuity is payable in half-yearly, third-yearly, or quar- 
 ter-yearly instalments, multiply by 1 4- £ r, 1 -J- ^ r, or 1 -}- f r, as 
 before directed ; and if there are odd payments proceed for the 
 present worth, S, as already directed. 
 
 Example. — Required the present worth of an annuity of $100, 
 payable yearly, to commence 4 months hence, and to continue 4 
 years ; interest and discount being 6 per cent annually. 
 
 100 X (1.06 4 — 1) X (l- 1 ^) 
 
 .06 X 1-06 3 x (i.--2^r^) 
 
 To find the Present Worth of a Deferred Current Annuity ■, or of 
 an Annuity in Reversion. 
 
 When the annuity is payable in a single payment yearly, and the 
 deferred time embraces full years only, 
 
 D = P i 1 ~r r ) "" n ' being the deferred time. 
 r(l + o) <B+B) 
 
 If it is payable in half-yearly, third-yearly, or quarter-yearly 
 instalments, multiply by 1 -f \ r, 1 + | r, or 1 + § r, as already 
 
ANNUITIES. 161 
 
 directed ; and, if there are odd payments, find the present worth, S, 
 as already directed. 
 
 Example. — What is the present worth of an annuity of $150, 
 payable yearly, to commence 2 years hence, and to continue 4 
 years ; interest and discount being compound per annum, at 6 per 
 cent. ? 
 
 150 X (1-06 4 — 1) -r .06 X 1-06 6 = $462.59. Am. 
 
 Example. — Required the present worth of an annuity of $500, 
 payable in semi-annual instalments, to commence 2£ years hence, 
 and to continue 6 years ; allowing compound interest and discount 
 annually at 7 per cent. 
 
 500 X (1.07 8 — 1) X l. ,J j- 
 .07 X 1.07 8 X 1. '°' 
 
 $2046.44. Ans. 
 
 2 
 
 Example. — Required the present worth of an allowance, 
 pension, or award of $125 a year, payable in half every half-year, 
 to commence 7 months 24 days hence, and to continue 6£ years ; 
 interest and discount being compound per annum at 5 per cent. 
 
 1 25 X (1.05° -1)X 1.0125 125 
 
 .05 X 1-05 6 X 1-03247 X 1025 ~ 2 X 1-025 
 
 0r ^^ ^xaow^ = S634,47 ' the P resenfc worth for 6 
 years' continuance, if payable in yearly instalments ; and 
 
 634.47 X l-x = &642.40, 
 
 the present worth for 6 years' continuance, if payable in half-yearly 
 instalments ; and 
 
 642.40^(1 + ^^?) = 622.20, 
 
 the present worth for 6 years' continuance, if payable in half-yearly 
 instalments, and to commence 7 months, 24 days hence ; and 
 
 622.20 -^(l + -5i) +2 _^_ = $668. Ans. 
 
 To jind the Present Worth of a Perpetuity. 
 
 Lemma. — The present worth* of an annuity to commence one 
 year hence, and to continue forever, is expressed by that sum of 
 money whose interest for 1 year is equal to the amount of the 
 14* 
 
*62 annuities. 
 
 annuity for 1 year ; and so, pro rata, for perpetuities otherwise 
 
 regularly affected. 
 
 Then when the annuity is to commence 1 year hence, and is 
 
 payable in a single payment yearly . . . D = P -J- r. 
 
 P(l -4- ±r) 
 Payable in half-yearly instalments . . D = ~ . 
 
 Payable in third-yearly instalments 
 
 Pfl + fr) 
 
 PCl 4- #r) 
 Payable in quarter-yearly instalments . D = v ' g ■ 
 
 r 
 
 Example. — What is the present worth of a perpetuity of $150 
 a year, payable in a single payment yearly from the present time ; 
 interest at 6 per cent ? 
 
 150 -f-.06 =$2500. Ans. 
 
 Example. — What is the present worth of a perpetuity, of $150 
 a year, payable in semi-annual instalments, and to commence 4 
 months hence ; interest 7 per cent ? 
 
 PO+iO- 07(12^ =3( , Am _ 
 r ' 12 
 
 Example. — Required the present worth of a perpetuity of 
 $400 a year, payable in quarterly payments, and to commence 6 
 years hence ; interest and discount being 5 per cent., compound 
 per year. 
 
 P(l-J-fr) 400 Xl. 3 -^ 
 
 D = — — £-r = $6081.65. Ans. 
 
 u — r(l-f-a) B .05X1-05 8 
 
 The Amount, Time, and Rate given, to find the Annuity. 
 When payable in a single payment yearly from the present time, 
 
 * = ( i+^=r « hM -y^' p - Ki+ry-i] <!+*■) ; 
 
 third-yearly, P = y+^+^q i quarterly, 
 
 P = 
 
 (l + if<-)[(l + r)--l] ' 
 
ANNUITIES. 163 
 
 and so, pro rata, for other fractional units of the integral unit. 
 
 ™. x Ar Ar Ar 
 
 Therefore (l + r).-l= ir , „__, OTf -_ 
 
 or pTTF)' &c - 
 
 Example. — What annuity, payable in quarterly payments 
 from the present time, will amount to $3000 in 12 years; interest, 
 being compound per annum, at 8 per cent. ? 
 
 3000 X -08 -|- [(108 12 — 1) X 1. 3 - J V £ \l = $ 153 - 48 - Ans - 
 
 Example. — What length of time must a current annuity of 
 $400, payable in quarterly payments, remain unpaid, that it may 
 amount to $2500 ; interest being 7 per cent, yearly ? 
 
 2500 X .07 = ,4263094 = 5 4- years, and 5 years by table of 
 400 XL ^x 27 
 
 (l+*-l- .402552 : therefore fgjg- 1 ) 3 J£= 308 
 
 days, 5 years, 308 days. Ans. 
 
 The Present Worth, Time, and Rate given, to find the Annuity. 
 
 When payable in a single payment yearly from the present time, 
 _ Dr(l+r) n .' . „ Dr(l4-r) n .... 
 
 *~ 0+ JL-1 » half ^ P - T(l+r)^l](l+ir) 5 third " 
 
 yearly, P = [(l ^^+^ + , r) 5 quarter-yearly, P = 
 
 [(1+ y^( ) l + IO - &C - Therefore, (l+^=p^ = 
 P(l+jr) _ P(l + |r) 
 P(l_L.i r )_Dr~~P(l + fr) — Dr ' ' 
 
 Example. — What annuity, payable in half-yearly instalments, 
 and to continue 3 years, is at present worth $1335.13 ; discount and 
 interest being compound per year, at 7 per cent ? 
 
 1335.13X.07X1-07 3 ..^ . 
 
 — w = $500. Ans. 
 
 (1.07 3 — 1)X1-^ 
 
164 ANNUITIES. 
 
 OF INSTALMENTS GENERALLY. 
 
 Any certain sum of money to be paid on a debt periodically 
 until the debt is paid is called an instalment ; and a debt so made 
 payable is said to be payable by instalments. 
 
 Let D = principal or debt to be paid, 
 
 n = number of years in which the debt is to be paid, 
 
 r a= rate of interest per annum, 
 
 p = instalment or periodical payment. 
 
 When the instalments are payable yearly, and the debt u at 
 interest, 
 
 When payable half-yearly, 
 
 Dr(l-fr)" 
 
 2[(l+r)--l](l + ir] 1 
 
 1 f* "[^(1+ W+rf -Dr ' " - r(l + r)« 
 
 When the debt is not on interest, and the instalments are pay- 
 able yearly, 
 
 f- ( i + f) ..i '(! + r ) =-7-' D - F * 
 
 Example. — What yearly instalment will pay a debt of $4000 
 in 4 years, the debt being on interest the while, at 6 per cent, 
 annually ? 
 
 4000 X -06 X 1.06 4 -7- (1.06 4 — 1) =$1154.37. Ans. 
 
 Example. — What semi-annual instalment will pay a debt of 
 $4500 in 3 years, the debt bearing interest at 7 per cent, yearly ? 
 
 4500 X .07 X 1.07' _ $842 . 62 . Am . 
 
 2 X (1-07* — 1)X 1-0175 
 
ANNUITIES. 165 
 
 When a debt has been diminished at regular intervals by the 
 payment of a constant sum, to find the remaining debt at the close 
 of the last payment. 
 
 When the debt is on interest, and the payments have been made 
 yearly from the date of the debt, 
 
 P— (i_j_ r )»_i ' 
 
 When the payments have been made half-yearly, 
 
 d=p+p(l + $r)-(l + ry[p + p(l+ i r)-Dr] + r,lkc. 
 
 Example. — On a debt of $1000, drawing interest the while 
 at 8 per cent, a year, there has been paid yearly, from the date of 
 the debt, $200 for 6 years : required the unpaid debt at the close 
 of the last payment. 
 
 [200— 1.08 6 (200 — .08 X 1000)] + .08 = $119.69. Ans. 
 
 Example. — On a note of hand for $1000, and interest from 
 date, at 8 per cent, annually, the following payments have been 
 made; viz., $100 at the close of every half-year from the date of 
 the note, for 6 years. How much remained unpaid at the close 
 of the last payment ? 
 
 [204 — 1.08 8 (204 — .08 X 1000)] -f- .08 = $90.34. Ans. 
 
166 PERMUTATION. 
 
 PERMUTATION. 
 
 Permutation, in the mathematics, has reference to the greatest 
 number of unlike relative positions, that a given number of things, 
 either wholly unlike, or unlike only in part; may be placed in. It 
 considers the number of changes, therefore, that may be made, in 
 the arrangement of the things, under different given circumstances. 
 
 To find the number of changes that can be made in the order of arrange- 
 ment of a given number of things, when the things are all different. 
 
 Rule. — Find the product of the natural series of numbers, from 
 1 up to the given number of things, inclusive ; and that product will 
 be the number of changes or permutations that may be made. 
 
 Example. — In how many different relative positions may 12 per- 
 sons be seated at a table ? 
 
 1X2X3X4X5X6X7X8X9X10X11X12 = 
 
 479,001,000. Am. 
 
 To find the number of changes that can be made in the order of arrange- 
 ment of a given num/jer of things, when that number is composed of 
 several different things, and of several which are alike. 
 
 Rule. — Find the number of changes that could be made if the 
 things were all unlike, as in first example. Then find the number 
 of changes that could be made with the several things of each kind, 
 if they were unlike. Lastly, divide the number first found by the 
 product of the numbers last found, and the quotient will be the 
 number of permutations or changes that the collection admits of. 
 
 I a ample. — Required the number of permutations that can be 
 made with the letters a, bb, ccc, dddd, = 10 letters. 
 
 1X2X3X4X5X6X7X8X9X10 = 3028800 
 
 1 X 2 X 6 X 24 = 288 - u T n ' Ans ' 
 
 To find the number of permutations that can be made with a given num- 
 ber of different things, by taking an assigned number of them at 
 a time. 
 
 Rule. — Take a series of numbers beginning with the number of 
 things givrn, :ind decreasing by 1 continually, until the number of 
 t this is equal to the number of things that are to be taken :it :i 
 time ; then will the product of the scries be the number of changes 
 that may be made. 
 
COMBINATION. ' 1()7 
 
 Example. — What number of changes can be made with the 
 numbers 1, 2, 3, 4, 5, 6, taking three of them at a time? 
 
 G — 1 = 5, 5 — 1 = 4, then 0X5X4 = 120. Ans. 
 What number, by taking 4 of them at a time 1 
 0X5x4X3 = 3C0. Ans. 
 
 Example. — Arrange the three letters a, b, c, into the greatest 
 number of permutations possible. 
 
 abc, acb, bac, bca, cab, cba, = 6 permutations. Ans. 
 
 Example. — Arrange the four letters a, b, a, b, into the greatest 
 number of permutations possible. 
 
 abab, aabbf abba, bbaa, baba, baab, = G permutations. Ans 
 
 COMBINATION. 
 
 Combination, in the mathematics, lias reference to the number of 
 unlike groups, which may be formed from a given number of differ- 
 ent things, by taking any assigned number of them, less than the 
 whole at a time. It does not regard the relative positions of the 
 things, one with another, in any of the collections or groups. But 
 it exacts that each group, in all instances, shall have the assigned 
 number of members in it, and that, in every group, in every instance, 
 there shall be a like number of members. It exacts, therefore, that 
 no two groups shall be composed of precisely the same members. 
 
 To find the number of combinations that can be made from a given 
 number of different things, by taking any given number of them at a 
 time. 
 
 Rule. — Take a series of numbers beginning with that which is 
 equal to the number of things from which the combinations are to 
 be made, and decreasing by 1, continually, until the number of 
 tonus is equal to the number of things that are to be taken at a time, 
 and find the product of those numbers or terms. Then take the natural 
 series, 1, 2, 3, 4, &c, up to the number of things that are to be taken 
 at a time, and find the product of that series. Lastly, divide the 
 product first found by the product last found, and the quotient will 
 express the number of combinations that can be made. 
 
 Example. — What number of combinations can be made from 8 
 different things, by taking 4 of them at a time? 
 8 X 7 X G X 5 _ 1680 
 IX 2X3X4"" 24 — 70 - Ans - 
 
56. Ans. 
 
 168 COMBINATION. 
 
 What number, by taking 5 of them at a time % 
 
 8X7X6X5X4 6720 
 
 1X2X3X4X5" 120 
 What number, by taking 3 of them at a time ? 
 
 8 X 7 X 6 = 336 
 
 1X2X3 6 - &b * Ans ' 
 
 Example. — What number of combinations can be made from 5 
 different things, by taking three of them at a time ? 
 
 5X4X3 60 
 1 X 2 X 3 = 6"" 10 * Ans ' 
 What number, by taking 2 of them at a time ? 
 
 A*i-?!UlO. Ans. 
 1X2 2 
 
 Example. — Form 5 letters, a, b, c, d, e, into 10 combinations of 2 
 letters each ; that is, into 10 unlike groups of two letters each. 
 
 ab, aCj ad, ae, be, bd, be, cd, ce, de. Ans. 
 
 Form them into the greatest number of combinations possible, in 
 collections of three each. 
 
 abc, obi, abe, acd, ace, ode, bcd f bee, bde, cde. Ans. 
 
FOREIGN MONEYS OF ACCOUNT: 
 
 THEIR DENOMINATIONS, RELATIVE VALUES, AND VALUES IN FEDERAL 
 
 MONEY. 
 
 The value in Federal money, affixed to any particular denomina- 
 tion of a Foreign money of account, in the following tables, is the 
 intrinsic par thereof, as near as practicable. It is based upon the 
 standard weight and purity of the coins coined especially to repre- 
 sent that denomination, compared with the standard weight and 
 purity of the coins of the United States that represent the dollar, 
 and is the United States Customs value of that denomination for 
 computing duties. The denomination itself, to which the Federal 
 value is immediately affixed, is usually the unit or ultimate money 
 of account of the country especially referred to. It is a money of 
 account in that country always ; but not always in that country 
 the name of a national coin. It is not always, even, represented by 
 a single national coin. Thus, in Great Britain, until comparatively 
 recently, there was no single British coin of the value of one pound. 
 That denomination is now represented by a single gold coin, called 
 a sovereign. 
 
 Foreign. U. States. 
 
 ALGIERS. — Algiers, Bona, &c. : 100 centimes = 1 Li- 
 
 vre, = $0,187 
 
 29 aspers = 1 tomin, 8 tomins = 1 pataka-chicas, 
 
 3 patakas-chicas = 1 Piastre, - - =0.21 
 
 ARABIA. —Mocha, Jidda : 80 caveers = 1 Piastre, - = 0.823 
 
 1 wakega/or gold and silver = 480 troy grains. 
 AUSTRIA. — 100 centesimi = 1 Lira Austriache, - = 0.1622 
 
 Vienna, Trieste, Prague (Commercial) : 4 pfennige 
 = 1 kreuzer, GO k. = 1 Gulden or Florin Austri- 
 ache = j\y of a Cologne mark of fine silver = 
 180-fVb- troy grains, - - - - = 0.4858 
 
 6 hellers = 1 groschen, 80 g. = 1 Florin, - = 0.4858 
 
 1 J groschen = 1 kreuzer. 
 
 l| florins = 1 current Thaler. 
 
 2 florins = 1 Specie Thaler. 
 
 1 florin Austriache = 5fy lire^de Trieste = 5yV lire 
 
 di piazza. 
 1 mark Austrian = 4332| troy grains. 
 
2 a FOREIGN MONEYS OP ACCOUNT. 
 
 Foreign. U. States. 
 
 AZORE ISLANDS. — Corvo, Fayal, Flores, Graciosa, 
 Pico, Terceira, St. Michael, St. Mary's: 1000 
 reas = 1 Milrea, = $0.83 J 
 
 BALEARIC ISLANDS. — Majorca I. — Palma : Mi- 
 norca I. — Port Mahon : same as Cadiz, Spain. 
 
 BELGIUM. — Antwerp, Brussels, Liege, Mechlin, 
 Ghent, &c. : 
 10 centimes = 1 decime, 10 d. = 1 Franc, - ■■ 0.187 
 24 mitres or 8 Brabant penning or 6 liarde or 2 
 groote = 1 stuiver, 6 stuivers = 1 scheiling, 20 s. 
 = 1 Pond Flemish, - - - ' - = 2.377 
 
 6 gulden or 2£ daalder = 1 Pond Flemish. 
 
 BERMUDAS I. —4 farthings = 1 penny, 12 pence = 1 
 
 shilling, 20 shillings = 1 Pound, - - = 3.00 
 
 BOURBON ISLANDS. — 100 centimes = 1 Franc, - = 0.187 
 
 BRAZIL. — Aracati, Bahia, Maranharn, Para, Pernam- 
 buco, Portalegra, Rio Janeiro, &c. : 1000 reas = 
 1 Milrea, = 1.042 
 
 BONAIRE I. — 48 stuivers or 8 reals = 1 Piastre, = 0.73 
 
 Central and South America. 
 
 Balize, Campeche, Guatimala, Honduras, Laguna, Leon, 
 
 Nicaragua, San Juan, San Salvador, Sisal, &c. : 
 Buenos Ay res, Callao, Carthagena, Coquimbo, Guayaquil, 
 Laguayra, Lima, Maracaybo, Montevideo, Rio 
 Hacha, Truxillo, Valparaiso, &c. : 
 2 cuartilli = 1 medio, 2 medios = 1 Real, - = 0.12^ 
 8 reale = 1 Peso, - - - - -= 1.00 
 
 Pound of Honduras, - - - - = 3.00 
 
 Berbice, Demerara, Essequibo, Surinam : 
 
 8 duyt = 1 stuiver, 20 s. = 1 Florin or Gulden, = 0.33J 
 Cayenne: 100 centimes = 1 Franc or Livre, - - = 0.187 
 
 CANARY ISLANDS. — Grand Canary, Teneriffe, 
 Palma, &c. : 
 34 maraw.li a 1 Real (current), - - = 0.074 
 
 CAND1A I. — 80 aspers or 33 niedini = 1 Piastre, = 0.048 
 CAPE VERD I. — 1000 reds = 1 Milrea, - - = 
 
 CHILL — Coquimbo, San Carlos, Santiago, Valdiiia, 
 Valparaiso, &c. : 
 4 cuartilli = 1 medio, 2m. = l real, 8r. = l Peso, = 1.00 
 CHINA. — Amoy, Canton, Macao, Nankin, Pckin, 
 Shanghae, &c. : 
 10 cash = 1 < amlarine, 10 candarines= 1 mace, 10 
 
 bum* = 1 Tael, ----■■ 1.48 
 
 Hong Kong I. — Same as Great Britain. 
 
FOREIGN MONEYS OF ACCOUNT. a 3 
 
 Foreign. U. States. 
 
 CORSICA I. — 100 centimes «= 1 Franc, - - = $0,187 
 
 CYPRESS I.— Same as Constantinople (Turkey). 
 DENMARK. — Copenhagen, &c. : 12 pfennige == 1 skil- 
 ling, 16 s. = 1 mark, G m. = 1 Ry ksbankdaler = 
 ■fir of a Cologne marc, or 194.98 troy grains of 
 pure silver, - - ■■ - - = 0.5252 
 
 2 Ryksbankdalers = 1 Speciesdaler, - - =1.05 
 
 EGYPT. —Alexandria and the Delta : 8 borbi or 6 fiorli 
 
 or 3 aspers =* 1 medimne, 40 m. = 1 Piastre, = 0.048 
 20 piastres = 1 real (a gold coin), - - - = 0.908 
 
 Cairo : 80 aspers or 33 medimni = 1 Piastre, - = 0.048 
 FRANCE. — Standard for gold and silver coins = ^ 
 fine, each : Relative values — gold to silver as 15 
 to 1. 
 10 centimes =» 1 decime, 10 d. =* 1 Franc = stkt^ 
 
 kilogrammes of fine silver = G9.449 troy grains, = 0.18706 
 12 deniers = 1 sou, 20 s. = 1 Livre tournois (old) 
 = |$ franc. 
 GERMANY. —The mark of Cologne, divided into 8 unze = 64 
 quent = 256 pfennig « 512 heller = 4352 eschen = 65536 richt- 
 pfennig, is employed at the mints, for weighing gold and silver 
 coins, throughout Germany : this mark = 3607| troy grains. 
 
 The standard for the Ducat, at present, throughout Germany, is 
 yj- or 23| carats fine, its weight, ^V of a Cologne mark. This piece, 
 therefore, should weigh 53.84 troy grains, and contain 53.09 troy 
 grains of fine gold = $2,286. 
 
 The standard for the Pistole or Zehn Gulden piece, of the Con- 
 vention of 1753, is f £ or 21| carats fine ; its weight, ^V of a Cologne 
 mark. This piece, therefore, should weigh 103.06 troy grains, and 
 contain 93.4 troy grains of fine gold = $4,022. 
 
 The standard for the Specie ThaJer, or Rixdollar affective, of the 
 Convention of 1753, is | or 13 loth 6 gran fine, its weight 2 \ Co- 
 logne mark = $0.9716 ; and the species Florin is £ thereof =* 
 $0.4858. 
 
 The standard value of the Current Thaler or Rixdollar of account, 
 established about 1775, is | Rixdollar affective = l£ specie Florins 
 = $0.7287. 
 
 The Thaler of the Convention of 1838 contains yj- Cologne mark 
 of fine silver = $0,694 ; and the Gulden or Florin of that Conven- 
 tion = f thereof = $0.3966 : 1| gulden = 1 Thaler. 
 
 The standard of purity for the coins established by the Convention 
 of 1838, are : Two Thaler piece = T 9 ^ ; thaler, f thaler, £ thaler, 
 each, = | ; florin, £ florin, each = T 9 g, less fractions = J. 
 
4fl FOREIGN MONEYS OF ACCOUNT* 
 
 Three Thalers of the Convention of 1838, by the estimate of rela* 
 tive values then established (gold to silver as 14. 5G to 1), = 1 Ducat j 
 while five of the current llixdollars, established in 1775, by the then 
 existing estimate of relative values (gold to silver as 14.483 to 1), 
 = 1 Pistole, or 10 guilder piece, above referred to. 
 
 Most of the moneys of account throughout Germany, including 
 Austria and Prussia, are based upon some portion of the fore- 
 going. 
 
 Foreign. U. Slates. 
 
 Bremen : 5 schwaren =*= 1 groot, 72 g. or 2 florins =■= 1 
 
 Rixdollar « £ standard Carl d'or, - - = $0,781 
 
 Frankfort : 4 pfennig = 1 kreuzer, 60 k. =» 1 Gulden = 
 
 tV Convention pistole, * - - - »= 0.4022 
 
 90 kreuzer = 1 Rixdollar of account, - «= 0.0033 
 
 1£ albus = 1 kraiser-groschen, 30 k. = 1 Rixdollar, = 0.6033 
 4 kreuzer = 1 batzen, 22^ b. mt 1 Rixdollar, - == 0.6033 
 
 120 kreuzer or 2 gulden or 1 J Rixdollar *a 1 Species 
 Rixdollar; -----«= 0.8044 
 Hamburg, Lubec : 12 pfennig =» 1 schilling, 16 schillinge 
 
 — 1 mark. 
 
 1 mark current ■■ $0.28. 1 mark banco, - = 0.35 
 3 marks banco = 1 Specie Rixdollar, - - s= 1.05 
 
 Baden. — Carlsruhe, Heidelberg, &c. : Same as Bavaria. 
 
 Bavaria. — Augsburg, Bamberg, Bayreuth, Munich, 
 Nuremberg, Ratisbon, Wurtzburg , &e. : 4 denari 
 = 1 kreuzer, 60 k. — 1 Florin, - - - = 0.4858 
 
 2 kreuzer = 1 albus, 2a.»l batzen, 15 batzens 
 = 1 Florin. 
 
 Ik florins = 1 Rixdollar current, - - =*= 0.7287 
 
 2 florins = 1 Specie Rixdollar. 
 
 Hanover. — EmJcn, Gottcngcn, Hanover, Osnaburg, &c. : 
 
 12 pfennig = 1 gute groschen, 24 g. s=a 1 Rixdollar, = 0.7287 
 
 lj Rixdollar == 1 Specie Rixdollar. 
 
 60 kreuzer = 1 gulden, 1| g. «■ 1 Thaler, - = 0.094 
 
 — 12 hellers or 9 pfennig = 1 albus, 32 albus 
 
 = 1 Rixdollar, - - - - -— 0.7281 
 
 24 mari a = 1 reiuhsflorin, l£ r. = 1 Rix- 
 
 dollar. 
 60 kreuzer = 1 golden, L| £ = 1 Thaler, - m 0.094 
 iv, Alton*, Kul, &c. : 12 pfennig = 1 schilling 
 lubs, lf> ■ohillinge [of I^ilm-) = 1 mark, - - =s 0.35 
 
 3 marks = 1 Specieedaler of Denmark. 
 
 Mi:< KUNBDBO. — Rostock, Wismar, &C. : Same U Han«>- 
 
 Oldenhurg. — Same as Bremen; also, same as Ham- 
 burg. 
 
FOREIGN MONEYS OF ACCOUNT. a 5 
 
 Foreign. U. States. 
 
 Saxony. — Dresden, Leipsic, &c. : 12 pfennig = 1 gute • 
 
 groschen, 24 g. = 1 Species Thaler, - = $0.7287 
 
 16 gute groschen =*= 1 reiehilorin, 2 r. =* 1 Specie 
 Kixdollar. 
 Saxe. — Gotha, Weimar : Same as Hanover. 
 Saxe generally and Nassau : 4 hellers *■ 1 kreuzer, 60 
 
 kreuzers = 1 Gulden, - - - - am 0.4022 
 
 l£ gulden = 1 Rixdollar current. 
 Wurtemburg. — Halle, Stuttgard, Vim, &c. : Same as 
 
 Saxe and Nassau. 
 GREAT BRITAIN. — Sterling money: Standard for 
 silver coins = £ J line ; for gold coins ■» \% fine. 
 Relative values, gold to silver as 14.288 to 1. 
 4 farthings = 1 penny, 12 p. = 1 shilling, 20 s. = 
 
 1 Pound = (4.866.* U. S. Customs value, - = 4.84 
 GREECE. — 12 denari = 1 soldo, 20 s. = * Lira or 
 
 Drachma, - - - - -= 0.163 
 
 HOLLAND. — Standard for silver coins = tnVu - fine. 
 Standard for gold coins — Gouden Willem (10 
 florins) fractions and multiples = i 9 o d p <j fine — 
 Ducat and multiples = tVtfff nn0 5 weight of 
 Ducat = 3.494 grammes am $2.2827. Relative 
 values — gold to silver as 15.604 to 1. 
 100 centimes = 1 Florin or Gulden = 9.45 grammes 
 
 of fine silver = 145.843 troy grains, - -= 0.3928 
 
 2£ florins = 1 Ryksdaalder, = 0.982 
 
 10 florins in gold = 6.056 grammes fine gold = 
 $4.0251. Custom-House value of Florin = $0.40. 
 
 India and Malaysia or East Indies. 
 
 British Possessions. — Standard of purity for gold 
 and silver coins = T £ fine, each. 
 Hindostan. — Bombay, Sural, Tatta : 100 reas = 1 quar- 
 ter, 4 q. = 1 Rupee = 165 troy grains of fine 
 silver, - - - - - - = 0.4444 
 
 * For all time since 1816, the government of Great Britain has estimated gold and silver 
 as 14.2879 to 1. The pound starling of mint silver weighs 1745.454 grains, and contains 
 1014.545 grains of fine silver. The value of the pound sterling of silver, therefore, rated 
 by the United States standard of 371} grains of fine silver to the dollar. Is $4<849. The 
 value of the silver shilling, of full weight, is $0.2174 'Hn; pound sterling of mint gold 
 weighs 123.274 grains, and contains 113.001 grains of fine gold. The value of the pound 
 sterling of gold, rated by t' ie United States standard of 23.22 grains of fine gold to the 
 dollar, is $4,866. At the old intrinsic par between the two currencies, viz., 4 shillings 
 and 6 pence sterling to the dollar, or $4,444 to the £, the par of exchange is 9^ per 
 cent. Gold is the money standard in Great Britain, and the silver coins of that country 
 are not legal tender at home in sums exceeding £2. 
 A* 
 
6* FOREIGN MONEYS OP ACCOUNT. 
 
 Foreign. U. States. 
 
 Calcutta : 12 pice = 1 anna, 16 annas = 1 Rupee, «s $0.4444 
 1 Arcot rupee = 1 Sicca rupee *= $0.44^f f . 
 1 Mohur or Gold Rupee » 165 troy grains fine gold 
 
 = $7.1033. 
 A Lac of rupees = 100.000 rupees. 
 A Crore of rupees = 100 lacs of rupees. 
 Madras. — 12 pice = 1 anna, 16 annas = 1 Rupee, = 0.4444 
 80 cash = 1 fanam, 42 fanams = 1 Pagoda, - = 1.851 
 3£ old Sicca rupees = 1 Pagoda. 
 1 Sicca rupee less 16 per cent. = 1 current rupee. 
 Cochin : 12 pice = 1 anna, 16 annas = 1 Rupee, = 0.4444 
 
 4 fanams = 1 schilling, 5 schillings = 1 Rupee. 
 Goa : 18 budgerooks = 1 vintim, 4 v. = 1 tanga, 5 t. 
 
 = 1 Pardo, - - - - m 0.96 
 
 Pondicherry : 60 cash = 1 fanam, 24 f . = 1 Pagoda, = 1.84 
 Banca I. — Same as Batavia {Java I.) 
 Borneo I. — Borneo, Pentaniah, Sambos, &c. : Same as 
 
 Batavia (Java I.) 
 Celebes I. — Macassar: Same as Batavia (Java I.) 
 Ceylon I. — Colombo : 4 pice = 1 fanam, 12 fanams = 
 
 1 Ryksdaalder, = 0.3928 
 
 Java I. — Batavia, Samarang, Sarakarta : 5 duyt = 1 
 stuiver, 2 stuivers = 1 dubbel, 3 dubbele = 1 
 schilling, 4 schillinge = 1 Florin, - - = 0.3928 
 
 U. S. Customs value of the Florin = $0.40. 
 Malacca. — Malacca : 4 duyt = 1 stuiver, 6 stuivers = 
 
 1 schilling, 8 schillinge = 1 Ryksdaalder, - = 0.795 
 Molucca Islands or Spice I. — Same as Batavia, Java I. 
 Philippine I. — Luzon I. — Manilla, &c. : 34 mara- 
 
 vedi = 1 real, 8 reals = 1 Peso, - - = 1.00 
 
 Siam. — Bangkok, &c. : 4 tical or bats = 1 tael, 100 t. 
 
 = lPecul, = 0.617 
 
 Singapore I. — Same as Malacca. 
 Sooloo Islands. — Same as China. 
 Sumatra I. — Achcen: 4 copangs = 1 mace, 4 m. =1 
 
 pardo, 4 p. = 1 Tael, - - - - = 4.1G 
 
 Bencoolen : 8 satellers = 1 soocoo, 4 s. = 1 Real, m 1.10 
 IONIAN ISLANDS. — Cephalonia, Corfu, Ithaca, 
 Paxos, Zante, &c. : 12 denari = 1 soldo, 20 s. w 
 1 Lira, - - - - =** 
 
 ITALY. — 100 centesimi = 1 Lira Italiani, - - = 0.187 
 
 Ecclesiastical States. — Standard for silver coins =- 
 ffjjfinc; for goldoomm ,'oVo fiue\ Relative 
 values, gold to silver as 15.526 to 1* 
 
FOREIGN MONEYS OP ACCOUNT. a 7 
 
 Foreign. U. States. 
 
 Ancona: 12 denari = 1 soldo, 20 s. =» 1 Scudo, - = $1,007 
 
 100 bajochi or 80 bologni or 10 paoli = 1 Scudo. 
 Bologna, Ferrara : 12 denari = 1 soldo, 20 s. = 1 Lira, = 0.201 
 5 lire or 10 paoli or 100 baiochi or 500 quattrini = 
 
 1 Scudo, = 1.007 
 
 Rome : 5 quattrini = 1 baiocho, 10 b. = 1 paolo, 10 p. 
 = 1 Scudo = T V libbra (373.78 troy grains) of 
 fine silver, - = 1.007 
 
 Sequin = T ff fine = T ^ libbra of fine gold. 
 Lucca. — 12 denari = 1 soldo, 20 s. = 1 Lira, - *m 0.243 
 12 denari = 1 soldo, 20 s. = 1 Scudo correnta, = 1.007 
 1 scudo d'oro of Lucca = $1,127. 
 12 denari di cambia = 1 soldo di cambia, 20 s. = 1 
 Scudo di cambia, - - - - = 1.068 
 
 Lombardy and Venice. — Standard for silver coins = ^ 
 fine ; for gold coins = f $ fine. Relative values, 
 gold to silver as 16 to 1. 
 Bergamo, Mantua, Milan, Padua, Verona, Venice, &c. : 
 
 100 centesimi = 1 Lira Italiani, - = 0.187 
 
 100 centesimi = 1 Lira Austriache, - - = 0.162 
 
 12 denari = 1 soldo, 20 s. = 1 Lira correnta di Mi- 
 lan = -^f jj marcs of fine silver = 52.531 troy 
 grains, - - - - = 0.1415 
 
 1 Lira picola di Bergamo, di Verona or di Venice, = 0.098 
 1 Lira di Mantua, - - - - - = 0.058 
 
 Modena, Parma. — 100 centesimi = 1 Lira, - = 0.187 
 
 Naples. — Naples, Salerno, &c. : 7200 accini = 360 
 trapesi = 12 oncie= 1 marco or libbra = 4950.53 
 troy grains. 
 Standard for gold and silver coins = -^uutj fine, each. 
 Relative values, gold to silver as 15.373 — to 1. 
 10 grani = 1 carlino, 10 c. = 1 Ducato = ^ Nea- 
 politan libbra of fine silver = 295.55-f- troy 
 grains, ----.= 0.796 
 
 1| ducati = 1 scudo or crown. 
 Sardinia : 4608 grani of 24 granottini, each = 1152 
 carati = 192 denari = 8 oncie =■ 1 marco = 3795 
 troy grains. 
 Standard for gold and silver coins = f £ fine, each. 
 Relative values, gold to silver as 15.545-[- to 1. 
 100 centesimi = 1 Lira Italiani, - = 0.187 
 
 12 denari = 1 soldo, 20 s. = 1 Lira di Sardinia =* 
 * ^V marco of fine silver = 130.86 troy grains, -= 0.3525 
 Genoa ; 5| lire fuori banco = 1 Pezza, - = 0.8854 
 
8tf FOREIGN MONEYS OF ACCOUNT. 
 
 Foreign. U. States. 
 
 4f lire di cambio = 1 scudo of Exchange, - - — $0.7187 
 
 lOjVtf lire moneta buona = 1 Scudo d'oro, - = 1.6663 
 
 Tuscany. — Florence — moneta buona: 12 denari = 1 
 
 soldo, 20 soldi = 1 Lira, = 0.1566 
 
 12 denari di ducato = l soldo di ducato, 20 s. = 
 
 1 Ducato or scudo correnta, - - - = 1.0962 
 
 7 lire = 1 ducato. 7£ lire = 1 scudo d'oro. 
 Leghorn. — moneta lunga : 12 denari di lira= 1 soldo 
 
 di lira, 20 soldi di lira = 1 Lira, - = 0.15 
 
 12 denari di pezza = 1 soldo di pezza, 20 soldi di 
 
 pezza = 1 Pezza,- - - - -= 0.9004 
 
 6 lira = 1 pezza. 
 
 7 lire moneta buona = 1 Scudo corrente, - = 1.0962 
 7£ lire moneta buona = 1 Scudo d'oro, - - = 1.1745 
 
 JAPAN. — Mats/nay, Miaco, Nangasaki, Osaca, Yedo, &c. : 
 10 cash = 1 candarine, 10 c. = 1 mace, 10 m. = 1 
 Tael, _--_-= 1.4074 
 
 MADEIRA ISLANDS.— 1000 reas = 1 Milrea, -= 1.00 
 
 MALTA I. — 20 grani = 1 taro, 12 t. = Scudo, - = 0.406 
 6 piccioli = 1 carlino, 2 c. = 1 taro, 12 t. = 1 
 
 Scudo, = 0.406 
 
 2£ scudi = 1 Pezza, = 1.015 
 
 MAURITIUS I. — Port Louis, &c. : 100 cents = 1 Dol- 
 lar, - - - - - -= 0.9353 
 
 20 sols = 1 Livre colonial = £ Franc of France, = 0.09353 
 10 livres = 1 Dollar. 
 MEXICO. — Acapulco, Tampico, Vera Cruz, &c. : 
 
 6 grani = leuarto, 2 c. = 1 medio, 2 m. = 1 Real, = 0.125 
 
 8 reals = 1 Peso, - - - - = 1.00 
 MOROCCO. — Fez, Mogadore, &c. : 24 fluce = 1 blan- 
 ked, 4 b. = 1 once, 10 onces = 1 Mitkul, = 0.7407 
 
 NORWAY. — Bergen : 10 skillinge = 1 mark, 6 m. = 
 
 1 Ryksdaler, = 0.5252 
 
 2 Ryksdalers = 1 Speciesdaler. 
 Christiania, &c. : 12 pfennige=l skilling, 6 s. = 1 
 ort, 4 orte = 1 Ryksdaler = 1 mark banco of 
 
 Hamburg, = 0.3501 
 
 .*> Ryksdaler = 1 Sj.r.irsdaler. 
 PERSIA. — Bushirc, &o. : 5 denari = 1 kasbeque, 10 k. 
 = 1 Bhafree, lis. = l mainoode, 2 m. = 1 abasse, 
 50 a. = 1 Toman, = 2.233 
 
 2 kasbequi = 1 denaro-biste. 
 PORTUGAL: Standard for silver coins = §£| fine — for 
 gold ooinao* \\ line. Relative values, gold to 
 silver as 15.3504- to 1. 
 
FOREIGN MONEYS OF ACCOUNT. a 9 
 
 Foreign. U. States 
 
 Method of writing and reading quantities: Ex. — 
 rs. 5 : COO 750 = 5,000 inilreas and 750 reas. 
 l(i(IO reas a* 1 Milrea = the silver coroa = $%% 
 
 mareo of lino silver = 415.435 troy grains, - *= $1,119 
 1000 reas = 1 Milrea current — fluctuating, about 
 
 = ,s().%. 
 1 Milrea, paper — fluctuating, about = $0.81. 
 480 reus = 1 Crusado. 
 PRUSSIA. — Standards and relative values, same as 
 given under Germany. 
 Berlin, Brandenburg, Dantzic, Potsdam, Magdeburg, 
 Stetin, &c. : 
 12 pfennig = 1 gute groschen, 24 g. = 1 Rixdollar 
 
 or Thaler current = lgV specie thaler, - = 0.7287 
 
 H Rixdollar = 1 Thaler banco = $0.91 H V 
 1$ florins — 1 Thaler specie, - - - = 0.694 
 
 Cologne: 12 hellers = 1 albus, 80 a. = 1 Rixdollar 
 
 = 2 3 (j Convention pistole = 1£ florins d'or, - = 0.6033 
 78 albus = 1 Rixdollar current. 
 120 fettmangen = 90 kreuzer = 30 groschen = 20 
 blafferts = 3£ Cologne florins = 2 heron florins 
 = l£ rader florins. 
 Aix la Chapelle, Crevelt, Elberfeldt, &c. : 
 
 4 pfennig = 1 kreuzer, 60 k. = 1 florin, 1| f. = 1 
 
 Thaler, ...-.= 0.694 
 
 Brunswick: 8 pfennig = 1 marien-groschen, 36 m. 
 
 = 1 Thaler, = 0.694 
 
 Konigsberg : 6 pfennig = 1 schilling, 3 s. = 1 gros- 
 chen, 30 groschen = 1 florin, 3 f . = 1 Thaler, = 0.694 
 8 specie gute groschen of Berlin = 30 groschen of 
 Konigsberg. 
 PRINCE OF WALES I. — 10 pice = 1 copang, 10 c. 
 
 = 1 Dollar, = 1.00 
 
 PROVINCES of New Brunswick, Nova Scotia, New- 
 foundland, AND THE CANADAS : 
 4 farthings = 1 penny, 12 p. = 1 shilling, 20 s. = 
 
 1 Pound, = 4.00. 
 
 RUSSIA. — Standard for silver coins = £ fine, for gold, 
 coins = -fj fine. Relative values, gold to silver 
 as 15^$- to 1. 
 Archangel, Cronstadt, Helsingfors, Odessa, Revel, Se- 
 vastopol, St. Petersburg, &c. : 
 10 kopecs = 1 grieven, 10 g. = 1 Rublyu (ruble) 
 
 = B 3 ff funt of fine silver = 278.47 troy grains, = 0.75 
 
10 a FOREIGN MONEYS OF ACCOUNT. 
 
 Foreign. U. States. 
 
 2 denushkas or 4 polushkas =* 1 kopec. 33 J altins 
 = 1 ruble. 
 Riga. — Same as St. Petersburg, also — 
 
 30 groschen = 1 florin, 3 f. = 1 Kixdollar. 1 Alber- 
 
 tus dollar, - - - - - = $1.00 
 
 SARDINIA I. — 100 centesimi — 1 Lira Italiani, = 0.187 
 
 1 Lira di Sardinia, - = 0.354 
 
 SICILY I. — Standards of purity and relative values, 
 same as Naples. 
 G picioli = 1 grano, 20 g. = 1 taro, 30 t. = 1 Oncia 
 
 = £f Neapolitan libbra of fine silver, - - = 2.388 
 
 8 picioli = 1 ponti, 15 p. = 1 taro, 10 t. = 1 ducato. 
 6 tari = 1 fiorino or florin, 2 f . = 1 scudo,- 2£ s. = 
 
 1 oncia. 
 
 SPAIN. — Standard for silver coins since 1786, peso and 
 £ peso = y§ fine ; peseta, real and £ real = f | 
 fine ; for gold coins = % fine, except the coronilla 
 (gold dollar) = T f $ fine. Relative values, since 
 1786, gold to silver as 16.39 to 1. 
 Real velldn = ^V peso duro, - - - = 0.05 
 
 Real de plata nuevo = y 1 ^ peso duro, - = 0.10 
 
 Real de plata Mexicana = $ peso duro, - - = 0.125 
 
 Real de plata antiquas = j^ 5 peso duro, - = 0.0943 
 
 Real d'Alicant = j 3 ? 2 F peso duro, - - - = 0.0754 
 
 Re£l de Valencia = ■££■$ peso duro, - = 0.0566 
 
 Real currante de Gibraltar = T ^- peso duro, - = 0.0835 
 
 Real de Catalonia = 5V5 P eso duro, - - = 0.0808 
 
 Real ardita de Catalonia = -5^ peso duro, - = 0.0539 
 
 8 reale de plata antiquas = 1 Piastre or peso of ex- 
 change = g£ peso duro, - - = 0.7543 
 Peso duro = y 1 ^ marco of fine silver = 371.9 troy 
 
 grain*, - - - - - = 1.0018 
 
 40 dineri = 16 comadi = 8 bland = 4 maravedi = 
 
 2 ochavi = 1 quarto, 4$ quarti = 1 sualdo, 2 s. 
 = 1 Real. 
 
 Alkaut : 34 maravedi = 1 real, 10 r. = 1 Piastre, = 0.7543 
 Barcelona, Tortosa^2 malli » idinero, 1 12 <1. = 1 
 BOaldo, 20 s. = 1 Libra = 10 reule ardita de 
 Catalan, - - - - - = 0.5388 
 
 liilboa, Carlhagcna, Madrid, Malaga, Santander, 
 Toledo: 
 34 maravedi = 1 real, 15 r. = 1 Peso sencillo. 
 
FOKEION MONEYS OS ACCOUNT. all 
 
 Foreign. U. States. 
 
 15jV reiile = 1 peso de plata or Piastre, - = $0.7543 
 
 4 piastres = 1 doubloon de plata or pistole of ex- 
 change. 
 Cadiz, Sevilla : 34 maravedi or 16 quarti = 1 Real, = 0.0943 
 
 8 mile = 1 Piastre, 10| reale = 1 Peso duro. 
 Gibraltar : 34 maravedi = 1 real, 9 r. = 1 Piastre, = 0.7543 
 
 12 mile = 1 Peso duro. 
 Valencia : 12 dineri = 1 sualdo, 2 s. = 1 real, 10 r. 
 
 « 1 Libra, = 0.5657 
 
 lj- libra = 1 Piastre or peso of account, - - = 0.7543 
 
 24 diueri = 1 real, 10 r. = 1 Peso duro, - = 1.0018 
 
 SW EDEN. — Standard for gold coins (ducats, multiples 
 and fractions) = f fs nne i f° r silver coins = %fy 
 fine. Kelative values, gold to silver as 14.692 to 1. 
 Carlscrona, Gefle, Gottenburg, Stockholm, &c. : 
 
 12 rundstycken or ore = 1 skilling, 48 s. = 1 Riks- 
 daler = ifg mark of fine silver = 393.68 troy 
 grains, - - - - - -= 1.0604 
 
 100 centimes or skillings = 1 Riksdaler, - = 1.0604 
 
 SWITZERLAND. — 1 Livre de Suisse, of the convention 
 of 1814, = l£ litres tournois of France = f^ 
 francs of France, - - - - = 0.2771 
 
 Berne, Basle, Lausanne, Lucerne, Pay de Vaud : 
 10 rappen = 1 batz, 10 batzen = 1 Livre de Suisse. 
 12 deniers = 1 sou, 20 sols de Suisse = 1 Livre. 
 10 rappen = 1 batz, 15 b. = 1 Florin or Guilder, m$ 0.4156 
 8 hellers = 1 kreuzer, 60 k. = 1 Florin. 
 Geneva : 12 deniers = 1 sou, 20 s. = 1 Livre = 3£ 
 
 florins petite monnie = 1% francs of France, = 0.3117 
 
 3 livres== 1 Ecu or Patagon, - *m 0.8313 
 
 ISeufchatfrr 100 rappen = 1 Franc or Livre de Suisse. 
 12 deniers =1 sol, 20 s. = 1 Livre tournois de 
 
 Neufchatel = 2£ livers foible, - - - = 0.2628 
 
 St.' Gaul: 480 heller = 240 pfennig = 60 kreuzer = 
 15 batzen = 10 skilling = 1 Florin or Guilder. 
 1 florin current = 2£ francs of France, - = 0.4365 
 
 1 florin specie, r - - - - = 0.5187 
 
 Zurich: 60 kreuzer of 8 hellers each, or 16 batzen of 
 10 augsters each, or 40 skillings of 12 hellers each 
 = 1 Guilder or Florin, = 0.4365 
 
 TRIPOLI. — 100 paras = 1 Piastre or Ghersch, ghersch 
 
 of 1832, = 0.10 
 
 TUNIS. — Tunis, Biserta, Susa, &c. : 2 burbine = 1 
 
12 a TORSION MONEYS Off ACCOUNT, 
 
 Foreign. U. States. 
 
 asper, 52 a. or 16 carobas =» 1 Piastre,* piastre 
 
 of 1838, =$0,128 
 
 TURKEY. — Constantinople : 3 aspers = 1 para, 40 p. 
 =* 1 Piastre or Ghersch.* 
 With the Dutch, French and Venetians, 100 aspers = 1 
 
 Piastre. 
 With the English and Swedes, 80 aspers = 1 Piastre. 
 500 piastres = 1 chise ; 30,000 piastres = 1 kitz ; 
 100,000 piastres = 1 juck. 
 Smyrna : 40 paras or medini = 1 Piastre or Gooroosh. 
 12 tomans = 1 Piastre or Gooroosh. 
 
 West Indies. 
 
 Cuba I. — Cardenas, Cienfuegos, Havana, Matanzas, 
 Mariel, Nuevitas, Porto Principe, Sagua laGrande, 
 St. Jago, &c. : 
 34 maravedi = 1 real, 8 r. = 1 Peso, - - = 1.00 
 
 Hayti I. — Aux Cages, Cape Haytien, Port au Prince, 
 San Domingo, &c. : 
 100 centesimi = 1 Dollar or Peso duro = 11 eseu- 
 
 lini, .-_--= 1.00 
 
 1 dollar Haytien currency = 7J esculini, - - = 0.66 
 
 Porto Rico I. — Guayama, Mayaguez, St. Johns, 
 Ponce, &c. : 
 34 maravedi = 1 real, 8 r. = 1 Peso, - - =1.00 
 
 British Islands. — Anguilla, Antigua, Barbuda, Do- 
 minica, Grenada, Montscrrat, Nevis, St. Kitts, St. 
 Lucia, St. Vincent, Tobago, Tortola, Trinidad, 
 Virgin Gorda: 
 4 farthings = 1 penny, 12 p. = 1 shilling, 20 s. = 
 
 1 pound, - - - - - = 2.222 
 
 Nassau and the Bahamas generally : 
 4 farthings = 1 penny, 12 p. = 1 shilling, 20 s. = 
 
 1 Pound, = 2.485 
 
 Pound of Turks I. - - - - -= 3.00 
 
 Barbadoks I. — Bridgetown, &u. : 1 Pound, - = 3.20 
 
 Jamaica I. — Falmouth, Kingston, Morant Bay, Savan- 
 nah la Mar, &c. : 
 4 farthings = 1 penny, 12 p. = 1 shilling, 20 s. = 
 
 1 Pound, = 3.00 
 
 * The coins of tin- Turkish government, owing to frequent and oft-repeated deterioration 
 by enactments, have no definable standard value whatever. Bills of exchange on Turkey 
 arc usually drawn in Spanish dollars. The rains, of the lOrer piastre "t Turkey, of full 
 w.-ixht, of 1775, is $0,446 ; of that minted it. Tunis in 1787, $0,259 ; of that of Turkey of 
 1818. $0,182, and of that of 1836, $0,128, while that issued only a few years since, id 
 worth, intrinsically, but about 4 cents. 
 
FOREIGN MONEYS OF ACCOUNT. ft 13 
 
 Foreign. U. States. 
 
 Danish Islands. — Santa Cruz, St. John, St. Thomas, 
 St. Bartholomew : 
 12 skillings = 1 bit, 8 b. = 1 Ryksdaler, - =» $0.64 
 100 cents = 1 Ryksdalor. 
 12£ bits = 1 Spanish dollar. 
 Dutch Islands. — Saba, St. Eustatius, St. Martin: 
 
 6 stuivers = 1 redl, 8 r. = 1 Piastre, - - = 0.73 
 
 11 reiils or Esculins = 1 Spanish dollar. 
 French Islands. — Deseada, Guadeloupe, Mariega- 
 
 lante, Martinique: 
 
 12 deniers = 1 sol, 20 s. = 1 Livre = § livre tour- 
 
 nois, ------ a 0.1232 
 
 4 farthings = 1 penny, 12 p. = 1 shilling, 20 s. = 
 
 1 Pound, - - - - - = 2.222 
 
 Little Antilles, generally, Same as Mexico. 
 B 
 
14 
 
 FOREIGN LINEAR AND SURFACE MEASURES 
 REDUCED TO UNITED STATES. 
 
 Foreign. 
 ABYSSINIA. — Massuah : 8 robl= I derah or pic, 
 ALGIERS. — 10 decimetres = 1 metre, - 
 
 8 robi = 1 pic. Pic, Moorish, for linens, - 
 
 Pic, Turkish, for silks, &c, - 
 ARABIA . — 1 kassaba = 12.31 ft. Mile, 
 Aden : 8 robi= 1 yard or pic, - 
 Jidda : 8 robi = 1 pic, • 
 
 Mocha : 8 gheria = 1 covid. Covid (land), 
 Covid (for iron, <J* c -)> 
 8 robi = 1 gez, - 
 
 AUSTRIA. — (Imperial, or legal and general) : 
 Vienna, Trieste, Prague, Lmtz, $c. : 
 
 12 7011=1^ - - 
 
 29£zoll = lelle, - 
 
 6 fus = 1 klafter, 4000 k. = 1 meile, 
 
 10fus=lruth (builders , ) 1 - 
 
 3 metzen = l joeh, - 
 (Special and local) — 
 Upper Austria. — Lintz, dfc. : 1 elle, - 
 Bohemia. — Prague, 4fc. : 2 fus — 1 elle, 
 
 4 elle = 1 dumplachter, ... 
 Hungary. — 1 fus = 1.037 feet. 1 elle, 
 Moravia. — 2§ fus = 1 elle, ... 
 
 AZORE ISLANDS. — Same as Lisbon (Portugal). 
 BALEARIC ISLANDS. — 3 pie or 4 palma = l 
 vara, 2 vara = l cana. 
 Majorca. — 1 cana, 
 Minorca. — 1 cana, - 
 BELGIUM. — 10 streep = 1 duhn, 10 d. = 1 palm, 
 10 p. = 1 el. = 1 metre of France, 
 10 el = 1 roed, 100 r. = 1 mijl, 
 2£ fus = 1 aune. 
 Antwerp : Aune for cloths, - 
 
 . Aune for silks, - 
 
 Brussels: 1 aune =0.761 yards. Vaem, - = 2.- 
 
 U. i 
 
 States. 
 
 0.682 
 
 yard . 
 
 1.094 
 
 i< 
 
 0.519 
 
 M 
 
 0.092 
 
 (( 
 
 1.22 
 
 miles* 
 
 0.95 
 
 yard. 
 
 0.743 
 
 a 
 
 1.58 
 
 feet. 
 
 2.25 
 
 u 
 
 0.694 
 
 yard. 
 
 1.037 
 
 feet. 
 
 0.852 
 
 yard- 
 
 4.712 miles- 
 
 L0.37 
 
 feet. 
 
 1.422 
 
 acres* 
 
 0.874 
 
 yard. 
 
 0.65 
 
 i« 
 
 2.598 
 
 it 
 
 0.874 
 
 it 
 
 0.865 
 
 u 
 
 1.711 
 
 yards. 
 
 1.754 
 
 M 
 
 1.003 
 
 yards. 
 
 0.621 "mile. 
 
 0.749 
 
 yard. 
 
 0.761 
 
 M 
 
FOREIGN LINEAR AND SURFACE MEASURES. a 15 
 
 Foreign. U. States. 
 
 Mechlin: 1 aun<\ - - - -= 0.753 yard. 
 
 BERMUDAS I. — Same M Gkeat Britain. 
 BOURBON I.— 3 pied = 1 aune, - - — 1.298 " 
 
 BRAZIL. — 12 pollegada = l pe, 5 pes = 1 passo, 
 52 passi = 1 cstadio, 24 estadi = 1 milha, 3 
 milhe = 1 legoa, - - • -«= 3.836 miles. 
 
 8 pollegada = 1 palmo, 5 palmi = 1 vara, 2 
 
 vare, or 3^ covadi, or 1£ passi = 1 braca, = 7.214 feet. 
 
 1 geira, .----= 1.428 acres. 
 Bahia, Rio Janeiro; 3 palmi = 1 covado, -= 0.713 yard. 
 
 Central and South America. 
 
 Balize, Bolivia, Buenos Ayres, Chili, Equador, 
 Guatimala, New Granada, Peru, Uruguay, 
 Venezuela, Yucatan : 
 Nomenclatures and legal values, same as Castile 
 
 ( Spain). 
 Guiana. — Berbice, Demerara, Essequibo, Surinam: 
 
 Same as Holland. 
 Cayenne. — Same as France. 
 CANARY I. — 12 onza= 1 pie, 3 p. = 1 vara, = 0.920 yard. 
 
 2 vara = 1 braza, - - - -= 5.522 feet. 
 52 braza cuadrada=l celemin, 12 c.= l fa- 
 
 negada, - - - - = 0.5 acre. 
 
 CANDIA I. — 8 robi = l pic, - - -= 0.697 yard. 
 
 CAPE COLONY. — Same as Great Britain. 
 CAPE VERDE I. — Same as Lisbon (Portugal). 
 CHINA. — 10 fan=l tsun or punt, 10 tsun=l 
 kong-pu or chik, 10 kong-pu = 1 cheung, 
 10 cheung = 1 yan, 18 yan = 1 li, - - = 0.346 mile. 
 
 Chik (mathematical) = 1.094 ft. Chik (en- 
 gineers'), - - - = 
 Chik (tradesmen' s) = 1.218 ft. Kong-pu, - = 
 l£ chik (engineers' 1 ) = 1 thuoc, 3£ thuoc 
 
 = 1 po, - - - - = 
 
 10 punts =1 covid or cobre, If c. = 1 thuoc 
 
 {mercers''), - - - - = 
 
 Pekin : 10 chik (math.) = 1 cheung, - - = 
 
 CYPRUS I. — 8 robi= 1 pic, - - - = 
 
 DENMARK. — 24 tomme or 2 fod = 1 aln, - = 
 
 3 aln = 1 favn, If f. = 1 rode, 2400 r. = 1 miil, = 
 
 96 album or 8 skiepper = 1 toende, - - = 
 
 EGYPT. — 2 derah = 1 fedan, 3 f . = 1 gasab, = 
 
 8 rob = 1 pic, - - - =* 
 
 1.058 
 1.014 
 
 feet. 
 
 n 
 
 5.025 
 
 it 
 
 0.711 
 
 10.937 
 
 0.696 
 
 0.688 
 
 yard. 
 
 feet. 
 
 yard. 
 
 4.681 miles. 
 
 5.45 acres. 
 
 12.67 feet. 
 
 0.74 yard. 
 
16 a JOREIGN LINEAR AND SURFACE MEASURES. 
 
 • 
 
 Foreign. U. Slates. 
 
 1 fedan al rieach, - - - - = 4. acres 
 
 Alexandria, Rosctta: 1 pic stambuli, - = 0.733 yard. 
 
 Pic for muslins, &c, - = 0.686 " 
 
 Pic for cloths, - - = 0.613 M 
 FRANCE. — 100 centimetres or 10> decimetres = 1 
 
 metre, - - - - - = 1.094 " 
 
 100 metres or 10 decametres = 1 hectometre, = 19.883 rods. 
 100 hectometres or 10 kilometres = 1 myria- 
 
 metre, - - - - = 6.214 miles. 
 
 100 square metres = 1 are, 100 a. = 1 hectare, = 2.471 acres. 
 
 3 T 6 ^ pied metrique = 1 aune = 47 £ inches, - = 1 .312 yards. 
 GERMANY.— Baden {legal) : 20 zoll or 2 fus = 
 
 lelle, = 0.656 " 
 
 5 elle = 1 ruthe = 3 metres of France, - = 3.281 " 
 
 2 stunden = 1 meile, - - - - = 5.524 miles. 
 1 jauchart = 0.82 acre. 1 morgen, - = 0.889 acre. 
 
 Manheim : 1 fus = 0.952 ft. 1 elle, - - = 0.610 yard. 
 
 Bavaria (legal) : 120 zoll or 10 fus=l ruthe, = 9.575 feet. 
 
 2400 ruthe = 1 meile, = 4.352 miles. 
 
 34^ zoll = lelle, - - -= 0.911 yard. 
 
 1 jauchart or morgen, - - = 0.841 acre. 
 
 5 cubic fus= 1 klafter = 110.62 cubic feet. 
 
 Augsburg: 2 fus = lelle, - - -= 0.648 yard. 
 
 1 elle (mercers'), - - = 0.666 " 
 Nuremberg : 2$ fus = 1 elle, - - -= 0.718 " 
 Hanover (legal) : 12 zoll = l fus, - = 0.943 foot. 
 
 2 fus = 1 elle = 0.638 yard. 8 e. = 1 ruthe, = 15.328 feet. 
 1462£ ruthe =1 meile, - - - = 4.246 miles. 
 2 vierling = 1 morgen, - - = 0.647 acre. 
 
 Bremen : 24 zoll or 2 fus = l elle, - - = 0.633 yard. 
 
 6 fus= 1 klafter, 2f k. = l ruthe, - = 15.188 feet. 
 20000 Rhineland fus = 1 meile, - - = 3.896 miles. 
 120 square ruthe = 1 morgen, - = 0.636 acre. 
 1 reif = 96.52 cub. ft. 1 faden = 61.6 cub. ft. 
 
 Emdcn, Osnaburg : 2{ fus = lelle, - -= 0.(V.»S yard. 
 
 Hesse Cassel. — 24 zoll or 2 fus =1 elle, - = 0.623 " 
 
 14 fus = l ruthe, - - - -=13.088 feet. 
 
 lklafter = 126.089 cubic feet. 
 Hesse Darmstadt (legal)'. 100 /.oil or 10 fus = 
 
 1 klafter = 2£ mUrcs of France, - = 8.202 feet. 
 
 32 zoll = 1 elle, - - - -= 0.875 jard. 
 
 400 square klafter or 4 viertel = 1 morgen, = 0.618 acre. 
 
 Frankfort: 12 zoll = 1 fus or werksi-huh, - — 0.934 foot. 
 
 2fus=l elle, 2e. = l stab, - - - = 1.245 jorae. 
 
 10 feldfus=l ruthe, - - - =11.672 feet. 
 
FOREIGN LINEAR AND SURFACE MEASURES. 
 
 «17 
 
 Foreign. 
 Holstein. — Hamburg, Altona : 
 
 24 zoll or 6 palm or 2 fus a 1 ello, - 
 3 ello = 1 klafter, 2\ k. = 1 marschruthe, 
 2§ klafter (16 fus) = 1 geestruthe, 
 24000 Rhineiand fus (2000 R. ruthe) «= 1 
 meile, - - - - - 
 
 1 Brabant elle for woollens, 
 COO square marschruthe = 1 morgen, 
 Lubec : Denominations and relative values, same 
 as at Hamburg. — 1 elle, - 
 
 Mecklenburg. — Rostock, dfc. — Same as Ham- 
 burg. 
 Saxony. — Dresden, Leipsic: 12 linie = 1 zoll, 12 
 
 zoll = 1 fus, 2 fus = 1 elle, 
 • 2 elle = 1 stab, 4 stab = 1 ruthe, - - i 
 
 3 elle = 1 klafter, - 
 
 1500 ruthe = 1 meile, - 
 
 300 square ruthe = 1 acker, 
 Freyburg : 2 fus = 1 elle, 5 e. = 1 ruthe, 
 Oldenburg. — 24 zoll or 2 fus = 1 elle, 
 
 9 elle = 1 ruthe, 1850 r. = 1 meile, - 
 GREAT BRITAIN. — Same as United States. 
 GREECE. — Patras : 8 robi = 1 pic for silks, 
 
 1 pic for woollens, dj^c., 
 HOLLAND (legal) : 10 streep = 1 duim, 10 d. = 
 1 palm, 10 p. = 1 el = 1 metre of France, 
 
 10 el = 1 roed, 100 r. = 1 mijl, 
 Previous to 1820 — 2& fus= 1 el, - 
 
 El of Flanders, - 
 
 Hague — Brabant el, - 
 
 U. States. 
 
 m 0.G266 yard. 
 = 13.159 feet. 
 = 5.013 yards. 
 
 = 4.68 miles. 
 = 0.761 .yard. 
 — 2.385 acres. 
 
 = 0.63 yard. 
 
 0.618 
 4.943 
 5.561 
 4.213 
 1.515 
 9.619 
 0.648 
 6.133 
 
 yard. 
 
 M 
 
 feet, 
 miles, 
 acres. 
 
 feet, 
 yard, 
 miles. 
 
 0.694 yard. 
 0.75 " 
 
 1.093 
 0.621 
 
 0.747 
 0.776 
 0.761 
 
 mile, 
 yard. 
 
 India and Malaysia or East Indies. 
 
 An-nam. — Same as China. 
 
 Birmah. — 4 taim = 1 sadang, 7 s. = 1 bambou, = 4.208 yards. 
 
 Ceylon I. — Colombo : 5 palmi= 1 covid, - = 0.516 " 
 Hindostan. — Bombay : 2 tussoo = 1 gheria, 8 g., 
 
 = 1 haut or covid, - - - - = 0.503 " 
 
 1 J- haut = 1 guz, = 0.755 " 
 Calcutta : 3 jaob = 1 angulla, 3 a. = 1 gheria, 
 
 8 g. = 1 haut or covid, 2 h. = 1 ghes or guz, = 1. " 
 
 3 palgat= 1 hand, 5 h. = l cubit, - - = 1.25 foot. 
 
 3 cubits = 1 corah, 1728 c. = 1 coss, - = 1.227 miles. 
 
 Goa: 12pollegada=lpe, - - - = 1.082 feet. 
 
 B* 
 
18 a 
 
 EOBEIGN LINEAR AND SURFACE MEASURES. 
 
 Foreign. 
 
 24f pollegada = 1 covado avantejado, - = 
 
 13^ pollegada = 1 tcrca, 3 t. = 1 vara, - = 
 
 Madras : 8 gheria em 1 covid, - = 
 
 1 cassency or cawney, - - - = 
 
 Massulipatam, 2 palm = 1 span, 3 8. = 1 cubit, = 
 
 Mysore, Sringapatam : 8 gerah = 1 haut, 2 h. 
 
 = 1 gugah, = 
 
 Pondiclv rry : 8 gheria = 1 haut or covid, - = 
 
 Sural : 84 tussoo or 20 wiswusa = 1 wusa, = 
 
 18 tussoo = 1 cubit or haut/or matting, - = 
 Tatta : 10 garca — 1 guz, - - = 
 
 Tranquebar, Serampore (legal) : same as Den- 
 mark, 
 Java I. — Batavia : 8 gheria = 1 covid, cubit or el, = 
 1 fus (Rhenish), - - = 
 
 Malacca. — Malacca : 8 gheria = 1 covid, - - = 
 
 8 covid = 1 jumba, - - = 
 
 Philippine I. — Luzon J. — Manilla. — Same as 
 
 Cadiz, Spain. 
 Siam. — 12 nion = 1 keub, 2 k. = 1 sok, 
 
 2sok=l ken, 2 k. = 1 vouah, 20 v. = l sen 
 40 s.= 1 jod, 25 jod= 1 roeneng, 
 Bangkok : -8 gheria = 1 covid, - 
 Singapore I. — 8 gheria = 1 hasta, 
 Sumatra I. — 4 tempoh or 2 jankal = 1 etto, 2 etto 
 
 = 1 hailoh, 
 IONIAN ISLANDS. — Ccphalonia, Corfu, Illiaca, 
 Paxos, St. Maura, Zantc, &c. : 
 12 onue = 1 pie, 5 pes = 1 passo, 
 1 braccio for silks, - 
 1 braccio /or woollens, - 
 1 moggio (linear) , 
 30 inches or 3 feet = 1 yard, 
 
 ITALY. — LOHBAKDY AM> VENICE : 
 Government and Customs Measure — 
 10 atome= 1 dito, 10 d. = 1 palmo, 10 p. = 1 
 
 metro or braccio — 1 metft of FranoOj 
 1000 metre = 1 miglio, - 
 100 square metre=l tavnla, 100 t. =1 torna- 
 tura, ----- 
 
 Special and local — 
 
 Venice: 2 palmi= 1 braccio, 2£ b. = 1 
 1£ passi = 1 pertica. 
 44 pede — 1 chebbo, l£ c. = 1 QMttBO 
 1 passo, geometrical, 
 1 braccio for woollens, 
 
 U. States. 
 
 0.744 
 
 yard. 
 
 1.203 
 
 M 
 
 0.515 
 
 « 
 
 1.32 
 
 acres. 
 
 1.594 
 
 feet. 
 
 1.072 yards. 
 
 0.5 
 
 ii 
 
 2.712 
 
 u 
 
 0.581 
 
 ii 
 
 0.943 
 
 M 
 
 0.75 
 
 II 
 
 1.03 
 
 feet. 
 
 0.5 
 
 yard, 
 
 12.— 
 
 feet. 
 
 -= 0.525 yard. 
 
 2.388 miles. 
 1.5 feet. 
 
 1.5 
 
 -= 1.08 yard. 
 
 5.455 feet. 
 0.705 yard. 
 0.7.M » 
 2.4 miles. 
 
 1. yard. 
 
 3.281 feet. 
 0.621 mfle. 
 
 12. iT 1 acres. 
 
 5.099 feet. 
 
 5 » 
 0.73'J " 
 
FOREIGN LINEAR AND SURFACE MEASURES. a 19 
 
 Foreign. U. States. 
 
 1 braccio, for silks, - - = 0.693 feet. 
 
 Naples. — 5 minuto= 1 oncia, 12 o. = 1 palmo, 8 
 
 palrni= 1 carina, - - - - = 6.92 " 
 
 7£ palnii = l passo or pertica, 8 pertica=l 
 
 catena, 11 6| catene= 1 miglio, - = 1.147 milea. 
 
 900 square passi = 1 moggio, - - - = 0.87 acre. 
 
 1 braccio (2§ palmi in theory), - = 0.764 yard. 
 
 Sardinia. — Genoa : 8 oncie = I pie, 10 p. or 12 
 
 palmi = 1 canna (surveyors'), - - = 9.715 feet. 
 
 2 J palmi = 1 braccio, - - - =0.63 yard. 
 
 9 palmi = 1 canna picolo, - - - = 2.429 " 
 
 10 palmi = 1 canna, for linens. 
 12 oncia = 1 pie liprando. 
 
 Nice : 12 oncia = 1 palmo. 25 oncia = 1 raso, = 0.600 " 
 Turin; 8 oncia = 1 pie manual, - - =1.19 feet. 
 
 12 oncia = 1 pie liprando. 
 
 14 oncia = 1 raso, - - - -= 0.649 yard. 
 
 5 pie manual = 1 tesa. 
 
 6 pie lip. = 1 trabucco, 2 t. = 1 pertica. 
 
 States of the Chruch. — Ancona: 1 braccio, = 0.704 " 
 10 pie = 1 pertica, - - - =13.438 feet. 
 
 Rome: 10 decline or 5 minuto= 1 oncia, 16 o. 
 
 = 1 pie, 5 piede = 1 passo, - - = 4.884 feet. 
 
 5 linea = 1 parto, 24 p. = 1 palmo, 8 palmi = 
 
 1 canna, - - = 2.176 yards. 
 
 Tuscany. — Leghorn, Florence, Pisa: 
 
 12 denari or 3 quattrini = 1 soldo, 20 soldi or 2 
 
 palmi = 1 braccio, 4 b. = 1 canna, - - = 2.552 '* 
 
 8 braccia=l passo, 2 p. = l cavezzo, - = 11.484 feet. 
 
 5 braccia= 1 pertica, 566J p. = 1 miglio, = 1.027 miles. 
 
 JAPAN. — 5 Kupera sasi = 1 ink, = 2.072 yds. 
 
 l£ sasi = lk. sasi, 2\ sasi = 1 ikje, - - = 2.32 feet. 
 
 MALTA I. — 12 oncie = 1 palmo, 8 palmi or 7 J 
 
 piede = 1 canna, - - - - = 2.275 " 
 
 MADEIRA I. — Standard same as Lisbon, Porl- 
 
 MAURITIUS I. — Standard same as Great Brit- 
 ain. 
 MEXICO. — Same as Cadiz, Spain. 
 MOROCCO. — Mogadore: 1 cadee, - - = 1.695 feet. 
 
 1 covado = 1.654 feet. 1 pic, - -= 0.723 yard. 
 
 NORWAY. — Same as Denmark. 
 PERSIA. — 1 archiii- ariscli, - - - =1.063 " 
 
 1 arc-bin schah, - - - - = 0.874 " 
 
 1 gueza (royal) = 3 T \y feet. 1 gueza (com- 
 mon), = 0.692 " 
 
20a 
 
 FOREIGN LINEAR AND SURFACE MEASURES. 
 
 Foreign. 
 1 monkelzer, - - - - - = 
 
 Bushire : 1 guz, = 
 
 PORTUGAL. — Lisbon, St. Ubes, fc. : 
 
 80 pollegada, or 10 palmi do craveira, or 6§ 
 pes, or 3 J covado, or 2 vara, or 1 J passo = 1 
 braca, - - - - - = 
 
 780 pes = l estadio, 8 estadi = l milha, - = 
 3 milha = 1 legua. 
 
 8 pollegada = 1 palma, 3 p. = 1 covado, - = 
 
 24f pollegada = 1 covado avantejado, - = 
 
 13 J pollegada = 1 terca, 3 t. =1 vara, - = 
 
 Oporto ; & palma = 1 covado, - = 
 
 PRUSSIA (legal since 1820) : 
 
 12 zolle= 1 fus (Rhein-fus), - - - = 
 
 10 zolle a 1 land-fus, 10 land-fus or 12 Rhine- 
 
 fus = 1 ruth, 2000 r. = 1 meile, - = 
 
 25£ zolle (Rhein-zolle) = lelle, - - = 
 
 180 square ruthe = 1 morgen. 
 
 Dantzic (special) : 75 am = 1 seil, - = 
 
 Konigsberg ; 1 elle, - - - - = 
 
 RUSSIA (legal for the Empire) : 
 
 16 verschok = 1 archine, - - = 
 
 3 archines or 7 feet =* 1 sachine, - - = 
 
 500 sachines = 1 verst, - - = 
 
 2400 square sachine = 1 deciatine, - - = 
 
 Crimea. — Sevastopol, dfc. : 1 halebi, - = 
 
 SARDINIA I. — 12 oncia = 1 palma, - - == 
 
 22 oncia = 1 pie, = 
 
 25^ oncia = 1 raso, - - - - = 
 
 12 palmi = 1 trabucco. 10 palmi = 1 canna, = 
 
 SICILY I. — Messina : 8 palmi = 1 canna, - = 
 
 Palermo : 8 palmi = 1 canna, - - - = 
 
 SPAIN. — Alicant : 9 pulgada = 1 palmo, 4 palmi 
 
 = 1 vara, 2 vara = 1 hraza, - = 
 
 12 pulgada or lj palmi = I pie, - - = 
 
 Barcelona : 4 palmi = 1 vara or matja-cana, = 
 
 2 vara = 1 cana, = 
 
 Cadiz (Standard of Castile) : — 6 nulgada = l 
 
 sesma, 2 s. = 1 pie or tercia, 3 pie = 1 vara, = 
 
 5 pie =3 1 passo. 
 
 2 octava = 1 quarta or palma, 4 q. = 1 vara, = 
 12 ]»ulgada=l pic, 1£ i»ie = l codo, 2 c. = 1 
 vara, 2 v. = 1 estado, braza, brazada or 
 toesa, 2 e. = 1 cuurda, 2 c. =» 1 cordel, 500 
 cordcle=*l legua, - - - -■■ 
 
 U. Stales. 
 2.351 feet. 
 0.557 yard. 
 
 7.214 feet. 
 1.279 miles. 
 
 0.722 
 0.744 
 1.203 
 0.707 
 
 yard. 
 
 »<. 
 
 ft 
 
 u 
 
 1.03 
 
 feet. 
 
 4.68 miles. 
 0.7293 yard. 
 
 47.062 
 0.628 
 
 M 
 M 
 
 0.777 
 
 7.— 
 
 0.663 
 
 2.7 
 
 0.799 
 
 0.286 
 
 1.571 
 
 feet. 
 
 mile. 
 
 acres. 
 
 yard. 
 
 a. 
 
 feet. 
 
 0.6 
 
 2.87 
 
 2.311 
 
 2.07 
 
 yard. 
 
 M 
 
 l.r.77 
 0.833 
 0.849 
 5.094 
 
 foot. 
 
 yard. 
 
 feet 
 
 2.782 
 
 u 
 
 0.928 
 
 yard 
 
 4.215 miles. 
 
FOREIGN LINEAE AND SURFACE MEASURES. U 21 
 
 Foreign. U. States, 
 
 192 vara cuadrada = 1 quartillo, 4 q. = 1 ce- 
 lemin, 7£ c. = 1 arancada, 1§ a. = 1 fane- 
 gada, ----- = 1.587 acres; 
 50 fanegada = 1 vugada. 
 Corunna, Ferrol : 4 palma op 8 octava wm 1 vara, = 0.928 yard. 
 Gibraltar. — As at Caaiz ; also, as in Great Britain. 
 Malaga. — Same as Cadiz . 
 
 Santander : 8 octava or 4 palma = 1 vara, - = 0.913 " 
 
 Valencia : 9 onze= 1 palmo, l£ p. = 1 pie, = 0.992 feet. 
 
 3 pie = 1 vara, 2\ v. = 1 braza reale, - = 2.232 yards. 
 SWEDEN. — 12 tuin = l fot, 2 f. = lain, -= 0.648 '* 
 
 3 aln = 1 Famn, 2§ famn = 1 stang, - = 15.553 feet. 
 2250 stang=l mil, - - - -= 6.627 miles. 
 
 4 kappland = 1 fjerding, 4 f. .= 1 spannland, 2 
 
 s. = 1 tunnland = 218i| square stang, - = 1.211 acres. 
 SWITZERLAND. — Legal, since 1823, for the 
 Cantons of Aarau, Basle, Betne, Freiburg, 
 Lucerne, Solothurn, Vaud ; but not in gen- 
 eral use : 
 10 zoll = 1 fuss, 4 f . = 1 stab mm 1 aune of 
 
 France, - - - - -= 1.3124 yards. 
 
 2k stab = 1 toise or ruthe, - - =3.2809 " 
 
 Special and local — 
 
 Basle : 12 zoll = 1 schuh or fuss, 10 s. * 1 ruthe, = 3.33 " 
 
 21A zoll = 1 braccio, - - - =0.5966 " 
 
 44£ » = 1 elle, = 1.2348 " 
 
 40^ " =1 klafter. 
 Berne : 12 zoll = 1 fuss, 6 f. = 1 klafter, If k. or 
 
 10 fuss=l ruthe, - - - -=9.6215 feet. 
 
 UJ fuss = l elle, - - - - = 0.5933 yard. 
 
 Geneva : 12 zoll = 1 pied, 5 J p.= 1 toise, - = 8.528 feet. 
 
 1 aune (wholesale), - - - -= 1.299 yards. 
 
 1 aune (retail), - - - = 1.25 " 
 
 Lausanne : 3f piede = 1 aune (metrical, of 
 
 France), - - - - -= 1.3123 " 
 
 9 ])iL'de = 1 ruthe. 
 Neufchatcl ; 12 zoll = 1 fuss, 10 f. = 1 tois, - = 
 22| zoll = 1 elle, - - - - = 
 
 St. Gall : 10 zoll= 1 fus, 4 f . = 1 stab, - = 
 Zurich : 12 zoll = 1 fus, 2 f . = 1 elle, - - = 
 
 a elle = l ruthe. 
 TRIPOLI (N. Africa) : 8 robi= 1 pic, - = 
 
 1 pic for ribbons, - - - - = 
 
 TUNIS. — 8 robi = 1 pic, for woollens, - = 
 
 1 pic, for silks, - - - - = 
 
 1 pic, for linens, - - = 
 
 9.621 
 
 feet. 
 
 0.608 
 
 yard. 
 
 1.3123 
 
 <( 
 
 0.6561 
 
 ii 
 
 0.6Q41 
 
 tt 
 
 0.5285 
 
 (< 
 
 0.736 
 
 a 
 
 0.690 
 
 M 
 
 0.5173 
 
 a 
 
22 a FOREIGN LINEAR AND SURFACE MEASURES. 
 
 Foreign. U. States. 
 
 TURKEY. — Aleppo : 8 robi — 1 pic, - - = 0.7396 yard. 
 
 1 dra mesrour, ----=» 0.6089 " 
 
 1 dra stambouli, - - - - = 0.7079 " 
 
 Bagdad ; 1 guz, - ==0.8796 " 
 
 Bussorah: lguz=* 2.6389 ft. l,hadid, -=0.9502 " 
 
 Constantinople : 1 halebi, - - = 2.325 feet. 
 
 1 endrasi or archim, - - - - = 2.255 u 
 
 1 pic stambouli, = 0.7079 yard. 
 
 1 pic for silks, - - - - = 0.7317 " 
 
 Damascus : 1 pic, - =• 0.637 " 
 
 Smyrna : 1 indise, - - - - = 0.6846 " 
 
 8 rob = 1 pic, - =0.7302 " 
 
 West Indies. 
 
 In the islands of Antigua, the Bahamas, Barbadoes, 
 
 Barbuda, Dominica, Grenada, Jamaica, Les 
 
 Saints, Montserrat, Nevis, Santa Cruz, St. 
 
 John, St. Kitts\ St. Thomas, St. Vincent, 
 
 Tobago, Tortola, the Measures of Length are 
 
 the same as in Great Britain. 
 In Deseade, Guadeloupe, Mariegalante, Martinique, 
 
 St. Lucia : 
 12 ponce = 1 pied de Roy, 3§ p. = 1 aune, - =» 1.3 yard* 
 This being the old system of France, or system 
 
 previous to 1812. 
 In Bonaire, Saba, St. Eustatius, St. Martin, Same 
 
 as Holland. 
 In St. Bartholomew, Same as Sweden. 
 In Curacoa, Trinidad, Same as Castile (Spain). 
 Cuba I. — Cardenas, Cienfuegos, Havana, Matan- 
 
 zas, Nuevitas, Porto Principe, St. Jago, &c. ; 
 
 Same as Castile (Spain). 
 Hatti I. — Aux Cayes, Cape Haytien, Jeremie, Port 
 
 au Prince, Port Platte, &c. : Same as France, 
 
 before 1812. 
 Savanna, <Sf. Dmingo, &c. : Same as Castile 
 
 (Spain). 
 Porto Rico I. — Ponce, St. Johns, &c. : Same as 
 
 Castile (Spain). 
 
23 a 
 
 FOREIGN WEIGHTS REDUCED TO UNITED STATES. 
 
 Foreign. U. States. 
 
 Avoirdupois 
 pounds. 
 
 ABYSSINIA. — Massuah : 10 dirhem = 1 wakea, 12 
 
 w. or 10 mocha = 1 rotl or liter, - - = 0.688 
 
 ALGIERS. —8 mitkal — 1 wakea, 10 wakea =» 1 rotl 
 
 attari {for spices and drugs) , - - = 1.190 
 
 18 wakea = 1 rotl gheddari (for fruits, oil, &c.), = 1.339 
 27 wakea = 1 rotl khebir {market pound), - = 2.008 
 
 100 rotl = 1 cantaro or quantar. 
 
 1000 grammes = 1 kilogramme, - = 2.205 
 
 ARABIA. — Hodeida : 30 vakia = 1 maon, 10 maon = 
 
 1 frazil, 40 frazils = 1 bahar, - - - = 813. 
 
 Jidda: 15 vakia = 1 rotolo, 5 rotoli = 1 maund, = 1.83 
 
 10 maunds = 1 frazil, 10 f. = 1 bahar, - = 183. 
 
 Mocha: 15 vakia or wakega = 1 rotolo or rotl, - = 1.5 
 
 2 rotolo = 1 maund or maon, 10 maunds = 1 frazil, 
 
 15 frazils = 1 bahar, - - - - = 450. 
 
 100 miscals = 1 vakia, 22£ v. = 1 maund copra, = 2.25 
 At the Bazaar, for coffee — 
 
 14£ vakia = 1 rotolo, and a bahar, - = 435. 
 
 Muscat : 24 cucha = 1 maund, - - - = 8.75 
 
 AUSTRIA. — Trieste, Vienna: 2 lothe = 1 unze, 4 u. 
 = 1 vierding, 2 v. = 1 mark, 2 m. = 1 pfund, 20 
 p. = 1 stein, 5 s. = 1 centner, - = 123.47 
 
 4 centner = 1 karch. 1 saum, - - -=339.5 
 
 1 saum for steel, - - - = 308.666 
 
 Trieste (Venice weight) : 1 pfund (peso grosso) , - = 1.052 
 1 pfund (peso sottile) — apothecaries' weight, - = 0.665 
 Bohemia. — 100 pfund = 1 centner, - - -= 113.4 
 
 Prague: 16 unze = 1 pfund, - - = 1.26 
 
 18 pfund = 1 stein, 6 s. = 1 centner, - - = 136.08 
 
 Hungary. — 1 oka, - - - - - = 2.78 
 
 AZORE ISLANDS. — Same as Lisbon (Portugal). 
 BALEARIC ISLANDS. — Majorca. — 25 rotoli = 1 
 
 arroba, - - - - - -= 22.37 
 
 4 arroba = 1 quintal, 112 rotoli = 1 oder, - = 100.217 
 100 rotoli barbaresco = 1 quintal, - - - — 92.794 
 
24 a FOREIGN WEIGHTS REDUCED TO UNITED STATES. 
 
 Foreign. U. States. 
 
 Avoirdupois 
 pounds. 
 
 Minorca. — 100 libra = 1 cantaro, - - -= 88.2 
 
 100 rotoli barbaresco = 1 quintal, . - = 81.727 
 
 3 quintals = 1 carga, - - - - = 275.18 
 
 BELGIUM. — Same as Holland. 
 Previous to 1820 — 
 8 pond = 1 stein, 12£ s. = 1 centner, - = 103.659 
 
 3 centner = 1 schippond, 4 centner = 1 charge. 
 
 Waeg of coals, - - - -= 150. 
 
 BERMUDAS I. — Same as Great Britain. 
 
 BOURBON I. — 100 livres=l quintal, 3 q. = l charge, = 323.765 
 
 BRAZIL. — 16 onca = 1 arratel, 32 arratel = 1 arroba, = 32.501 
 
 4 arrobas = 1 quintal, 13£ q. = 1 tonelada. 
 
 Central and South America. 
 Balize, Campeche, Guatimala, Honduras, Laguna, Leon, 
 
 Nicaragua, San Juan, San Salvador, Sisal, <3fC. 
 Buenos Ayres, Callao, Carlhagena, Coquimbo, Guaya- 
 quil, Laguayra, Lima, Maracaybo, Montevideo, Rio 
 Hacha, Truxillo, Valparaiso, &c. : 
 16 onza = 1 libra, 25 1. = 1 arroba, 4 a. = 1 quin- 
 tal, = 101.546 
 
 Berbice, Demcrara, Essequibo, Surinam. — Same as 
 
 Holland. 
 Cayenne. — Same as France. 
 CANARY [SLA N I >S. — Same as Castile (Spain) . 
 OANDIA I. — 44 oka = 1 cantaro, - - =116.568 
 
 CAPE COLONY. — ( tope Town. — 32 loot = 1 pond, = 1.03 
 CAPE VER DE ISLANDS.— Same as Lisbon ( Portugal) . 
 CHINA. — 10 lis = 1 tael or Leung, 16 taels = 1 catty 
 
 $T kan, LOO catties = 1 pecul or tarn, - -= 133.333 
 
 ■2-2\ oka = 1 leang, 10 1. = 1 catty, 2 c. = 1 yin, 
 
 15 y. = 1 kwan, 3£ k. = 1 tarn, 1£ t. = 1 shik, = 160. 
 
 CORSICA I. — 1 Itae, - - - - - = 0.76 
 
 CYPRl'S I. — 4<)0<lrachmi = loka,40 oka=lmoosa, = 112. 
 
 l$oka=] rotolo, = 5.25 
 
 DENMARK. — 32 lod = 16 unze = 2 mark = 1 pund, = 1.101 
 I no pound = 1 centner, ... -=110.11 
 
 12 pond = 1 biamertmnd, lj b. = 1 lispund, 20 1. 
 = 1 drippund, - - - - -= 862.364 
 
 2| lisjumd ■■ 1 waag, - - = 39.639 
 
 EGYPT. — 144 drachm i or 100 miscali = 1 rotolo for- 
 
 fora, = 0.95 
 
 ■ldti dnchmi ■■ 1 harsela, - - - = 2.639 
 
 420 drachmi = 1 oka, - - - - = 2.771 
 
FOREIGN WEiailTS REDUCED TO UNITED STATES. O 29 
 
 Foreign. , U. States. 
 
 Avoirdupota 
 pounds. 
 
 100 rotoli or 36 harseli = 1 cantaro forfora, - = 95. 
 
 105 " or 36 oka = 1 cantaro, for coffee, - = 99.75 
 1 rotolo mina, for spices, - - - -== 1.403 
 
 1 " zaidino, for dye-woods, - = 1.138 
 
 1 " zauro, for iron, - - - -= 2.216 
 
 102 rotoli = 1 cantaro, for quicksilver and vermilion, = 96.9 
 
 115 " =1 " for almonds and fruit, - =109.25 
 125 " =1 " for drugs, - - -=118.75 
 133 " =1 " for gum arabic, - =126.35 
 150 " =1 " for plumbago, - -=142.5 
 
 FRANCE. — 1000 milligrammes = 100 centigrammes = 
 10 decigrammes = 1 gramme = 15.43315 troy 
 grains. 
 100 grammes = 10 decagrammes = 1 hectogramme, = . 0.22 
 10 hectogrammes = 1 kilogramme, - - = 2.205 
 
 10 kilogrammes = 1 myriagramme, - - = 22.047 
 
 100 myriagrammes = 10 quintal = 1 tonneau. 
 1 livre poids de marc, - =1.07922 
 
 1 livre metrique = £ kilogramme, - = 1.10237 
 
 GERMANY. — Baden.— Heidelberg, Manheim, &c. : 
 1000 as = 100 pfennig = 10 centas = 1 zehnling. 
 1000 z. = 100 pfund = 10 stein = 1 centner, „ - = 110.237 
 8 quentchen = 2 loth = 1 unze. 
 
 16 unze = 2 mark = 1 pfund, - = 1.102 
 
 Bavaria. — 20 pfund {legal) = 1 stein, - - = 24.693 
 
 Augsburg : 512 pfennig = 128 quentchen = 32 loth 
 
 = 16 unze = 2 mark = 1 pfund or frohngewicht, = 1.082 
 100 pfund = 1 centner, - - - - = 108.262 
 
 3 centner = 1 pfundschwer or schiffpfund, - = 324.786 
 7£ pfundschwer or 100 stein = 1 tonne. 
 
 22£ pfund = 1 stein, 5j stein = 1 wage, - - = 129.914 
 
 Nuremberg : Denominations and relative value, same 
 as Augsburg. 
 100 pfund = 1 centner, = 112.432 
 
 Hanover (legal) : 32 ortchen = 16 drachma or quent- 
 chen = 2 loth = 1 unze, 8u. = l mark, 2 m. = 
 
 1 pfund, = 1.079 
 
 14 pfund = 1 liespfund, - - - =15.11 
 
 24 liespfund = 1 pfundschwer or last, - - = 362.648 
 
 20 pfund = 1 stein for flax, = 21.586 
 
 Bremen : 32 ortchen = 8 quentchen = 2 loth =» 1 unze, 
 
 8 u. = 1 mark, 2 m. = 1 pfund, - - = 1.099 
 
 116 pfund = 1 centner, - - - - = 127.516 
 2£ centner — 1 schiffpfund, = 318.791 
 
 
 
26(1 FOREIGN WEIGHTS REDUCED TO UNITED STATES. 
 
 Foreign. U. Stales. 
 
 Avoirdupois 
 pounds. 
 
 300 pfund = 1 pfundschwer or last, - - = 329.784 
 
 14 pfund = 1 liespfund. 1 wage, for iron, - = 131.913 
 1 stein, for fax = 21.985 lbs. 1 stein, for wool, = 10.993 
 Ernden, Osnaburg : 10 unze = 2 mark = 1 pfund, 100 
 
 pfund = 1 centner, - - - - = 109 J041 
 
 3 centner = 1 pfundschwer. 
 Hesse Cassel. — 16 unze = 1 pfund, 100 pfund = 1 
 
 centner, -----= 106.762 
 
 21 pfund = 1 kleuder. 
 
 Hesse Darmstadt {legal) : 100 pfund = 1 centner, = 110.236 
 
 Frankfort : 16 unze or 2 mark = 1 pfund, - - = 1.114 
 
 I 100 pfund = 1 centner, - - - =111.407 
 
 22 pfund = 1 stein, - - - - = 24.509 
 HoLSTfiiN. — Hamburg, Lubcc, Altona, Kiel: 
 
 16 unze = 2 mark = 1 pfund, - - - = 1.068 
 
 14 pfund = 1 liespfund, 8 1. = 1 centner, - = 119.6 
 
 2£ centner = 1 schiffpfund, - - - = 299. 
 
 7f schiffpfund or 100 stein = 1 tonne, - = 2135.72 
 
 90 pfund = 1 last, - - - -= 96.11 
 
 1 stein , for feathers and ivool, - - = 10 679 
 
 . 320 pfunds {land freight) = 1 schiffpfund, - = 341.72 
 
 Mecklenburg ^generally) : 16 unze = 2 mark = 1 
 pfund, 15 pfund = 1 liespfund, 20 1. = 1 schiff- 
 pfund, ....-= 313.723 
 Rostock: 16 pfund = 1 liespfund, 20 1.= 1 s.-hi tip fund, « 868 64 
 280 pfund = 1 schiffpfund, /or iron and had. - = 313.723 
 22 pfund = 1 stein, y or wool and fax, - - =24.65 
 Saxony. — Dresden, Lcipsic: 32 pfennig = 8 drachma or 
 quentlein = 2 loth = 1 unze, 8 u. = 1 mark, 2 
 mark =1 pfund, - - - -= 1.03 
 22 pfund — 1 stein, 2 s. = 1 wage, - - — 46.324 
 110 pfund = 1 centner, - - - -=113.31 
 114 M «■ 1 " berg-gewfcht. 
 118 " =1 " Btafl-gewioht 
 Fni/hirg: 1 pfund, ... == 1.165 
 Oldenburg. — Denominations and relative values, same 
 
 as Bremen, but weight vahu « li.'.>4 % less. 
 GREAT BRITAIN.* — Bee United States. 
 
 * In Gnat Britain, in addition to the denominations of weights used in the United 
 States (the values of which Bit tin- MMM), 1 1 i . - 
 
 Stone oi Inii'-h-r.s' ni.at or lli-.-h, = 8 lbs. 
 
 St ofcheoMj = 16 ** 
 
 : 'lass, B 
 
 = ISO •• 
 
 BtootofMnm, m 
 
 Fotbxr of lead, .... • . . . = 19i cwt. 
 
 of WOOl, 
 
 = 7 lbs 
 
 ' " iron, flour, 
 
 = 14 - 
 
 Tod « " 
 
 = i 
 
 Weigh " " 
 
 = 182 " 
 
 Sack " " 
 
 = 864 « 
 
 L»gt « »t 
 
 b=4368 " 
 
FOREIGN WEIGHTS REDUCED TO UNITED STATES. a 27 
 
 Foreign. U. States. 
 
 ▲tolrdapoii 
 ptwnflfi 
 
 GREECE. —Athens : 400 draclimi = 1 oka, - - = 3.137 
 
 44 oka = 1 eantaro, - = 148.3 
 
 Morea. — 1 eantaro, generally, - - - -■■123.75 
 
 Patras : 400 draclimi = 1 oka, - - = 2. 043 
 
 44 oka = 1 eantaro or quintal, - - -=110.3 
 
 HOLLAND (legal) : 10" korrel = 1 wigtjc, 10 w. = 1 
 
 lood, 10 1. = 1 onz, 10 o. = 1 pond = 1 kilogramme 
 
 of France, - - - - -= 2.204 
 
 2000 ponds = 1 vat (shipping), - - =2204.74 
 
 Previous to 1820 — 
 
 300 ponds = 1 schippond, - - - - = 32G.77 
 
 8 ponds = 1 steen, = 8.71 
 
 India and Malaysia or East Indies. 
 
 An-nam. — Cochin China — Saigon : 16 luong = 1 can, 
 
 10 can = 1 yen, 5.y. = 1 binh, - - - = 68.876 
 
 2 binh = 1 ta, 5 ta = 1 quan, - - = 688.76 
 
 Tonquin — Kesho : 100 catties = 1 pecul, - -= 132. 
 
 Birmah. — Pegu : 12^ tical = 1 abucco, 2 a. = 1 agito, 
 
 4 agiti = 1 vis, - - - = 3.393 
 
 33 tical = 1 catty, 3 c. = 1 vis, - - - = 3.393 
 
 Rangoon : 2 small rwes = 1 large nve, 4 large rwes = 
 1 bai, 2 b. = 1 mu, 2 m. = 1 mat'h, 4 niat'hs 
 = 1 kyat or ticul, 100 k. = 1 paitktlia or vis, = 3.65 
 Borneo I. — 100 catty = 1 pecul, - - -==135.633 
 
 Ceylon I. — Colombo : 500 pond = 1 bahar or candy, = 500. 
 
 Celebes I. — Macassar: 100 catty = 1 pecul, - = 135.633 
 Hindostan — Bengal, generally (bazar weight) : 
 
 10 mace = 1 khanelia, 3 k. = 1 chattac, 10 c. = 1 
 dhurra or pussaree, 8 d. = 1 maon or maund, = 82.133 
 Calcutta (factory weight) : 5 sicca = 1 chattac, 16 c. 
 
 = 1 seer, 40 s. = 1 maund, - - - = 74.666 
 
 Bombay : 36 tanks or 15 pice = 1 tipprce, 2 t. = 1 
 
 seer, 40 s. = 1 maund, 20 m. = 1 candy, - = 560. 
 
 2± tank-seers = 1 rupee-seer, for liquids = 1.54 lbs. 
 
 Goa : 32 seers = 1 maund, 20 in. = 1 bahar, - = 495. 
 
 Madras: 10 pagodas or varahuns = 1 pollam, 8 p. = 
 1 seer, 5 s. = 1 vis or visay, 8 v. = 1 maund or 
 
 maon, - - - - - - <= 25. 
 
 20 maunds = 1 candy or baruay. - = 500. 
 
 Malabar Coast: 40 polams = 1 vis, 8 v. = 1 maon, = 30. 
 
 20 m. = 1 candy, 20 c. = 1 garce. 
 Malabar (interior) : 20 maon = 1 candy, - - = 095. 
 
28 a FOREIGN WEIGHTS REDUCED TO UNITED STATES. 
 
 Foreign. {J. States. 
 
 Avoirdupois 
 pounds. 
 
 Mangalore : 6 sida= 1 vis, 8 v. = 1 maund, 20 maunds 
 
 • = 1 candy, = 564.72 
 
 Massulipatam : 1£ nawtauk = 1 chittac, 6 c. = 1 
 yabbolain, 2 y. = 1 puddalum, 2£ p. = 1 vis, 6| 
 
 v. = maund, 20 m. = 1 candy, - - - = 500. 
 
 21j vis = 1 pucca maund, - - - = 80. 
 
 Mysore, Seringapatam : 10 varahuns — 1 pollani, 40 
 
 p. = 1 pussaree, 8 pussaree= 1 maon or maund, = 24.276 
 20 maund = 1 bahar or candy. 
 Pondicherry : 10 varahuns = 1 poloin, 40 p. = 1 vis, 
 
 8 v. = 1 maund, 20 m. = 1 candy, - - = 588 
 
 Serampore, Tranquebar {legal) : Same as Denmark. 
 Sinde: 2 pice = 1 anna, 2 a. = 1 chittac, 16 c. = 1 
 
 seer, 40 seers = 1 maund, - - - = 74.666 
 
 Sural (new measure) : 8 pice = 1 tippree, 2 t. = 1 
 
 seer, 40 s. = 1 maund, 21 m. = 1 candy, - = 300. 
 
 3 candi = 1 bhaur. 
 Tatta : 4 pice = 1 anna, 16 a. = 1 seer, 40 s. = 1 
 
 maund, - - - - - - = 74.32 
 
 Java I. — Batavia : 16 tael = 1 catty, l£ c. = 1 goelak, 
 66| g. or 100 catty = 1 pecul, 3 p. = 1 bahar = 
 16 m. 1 vis, 24 pollams of Madras, - - = 405.333 
 
 4£ pecul = 1 great bahar. 
 
 5 pecul = 1 timbang, for grain, - = 675.555 
 
 Bantam : 24 tael = 1 goelak, 100 g. = 1 catty, 2 
 
 catty = 1 bahar, for pepper, - - - = 405.333 
 Malacca. — Malacca: 16 tael = 1 catty, 100 c. = 1 pe- 
 cul, 3 peculs= 1 bahar, - - - =405. 
 
 2£ pinga = 1 tampang, 2 t. = 1 bedoor, 12 b. = 1 
 
 hali, 14 h. = 1 kip,ybr tin, - - - = 40.677 
 
 2 buncals = 1 catty, for gold and silver, - = 2.049 
 
 Philippine I. — Manilla, &c. : 
 
 22 piastres = 1 catty, 100 c. = 1 pecul, - = 139.443 
 
 1 caban of rice (usual) , - - - -= 133. 
 
 1 caban of cocoa, = 83.5 
 
 Siam. — Bangkok, &c. : 4 tical = 1 tael, 2 t. = 1 catty, 
 
 100 catty = 1 pecul, - - - - = 135.238 
 
 Singapore I. — Same as Malacca. 
 Sooloo Islands. — 10 mace = 1 tael, 16 t. = 1 catty, 
 
 50 c. = 1 lachsa, 2 1. = 1 pecul, - - = 133.333 
 
 Sumatra I. — 62 catties = 1 pecul, - - -=132.587 
 
 24 tael = 1 salup, 2 s. = 1 ootan, 7J o. = 1 nelli, 
 for camphor, - - - - =* 29.333 
 
Avoirdupois 
 pounds. 
 
 FOREIGN WEIGHTS REDUCED TO UNITED STATES. a 29 
 
 Foreign. U. States. 
 
 Achecn : 10 mace = 1 tael, 20 t. = 1 goclak, 1£ g. = 
 
 1 catty, 36 c. = 1 maund, - - - = 76.986 
 
 5£ inaund = 1 candil or bahar. 
 Bencoolen: 46 catties = 1 maund, - = 98.371 
 
 5§ maunds = 1 bahar, - - - - = 557.416 
 
 IONIAN ISLANDS. — Cephalonia, Corfu, Ithaca, 
 Paxos, Zante, &c. : 
 
 Legal since 1817 : 100 libbra = 1 talento, - = 100. 
 
 100 oke = 385 marcs. 
 
 44 oke = 1 cantaro, - - - - = 118.807 
 
 Cephalonia: 04 libbra = 1 barile,/or salt, - = 67.262 
 
 Corfu : 100 libbra = 1 talento, - - -= 90.034 
 
 ITALY. — Carrara. — 1 carrata, for marble, = 25 
 
 cubic palma = 12.764 cubic feet = 31f centi- 
 
 najo or 29 J quintale of Modena, - - =2240. 
 
 LOMBARDY AND VENICE. 
 
 Government and Customs Measure : 
 10 grani = 1 denaro, 10 d. = 1 grosso, 10 g. = 1 
 oncia, 10 o. = 1 libbra, 10 1. = 1 rubbio, 10 r. 
 = 1 centinajo = 10 myriagrammes of France, = 220.474 
 Special and local : 
 
 Venice. — Peso grosso : 4 grani = 1 carato, 32 c. = 1 
 saggio, 6 s. = 1 oncia, 6 o. = 1 marco, 2 m. = 
 
 1 libbra, = 1.052 
 
 25 libbre = 1 miro, 40 m. = 1 migliajo, - - =1051.86 
 
 Peso sottile : 4 grani = 1 carato, 24 c. = 1 saggio, 
 
 6 s. = 1 oncia, 12 o. = 1 libbra, - = 0.666 
 
 100 libbre = 1 quintale, 4 q. = 1 carica, - - = 266.332 
 
 Naples. — 20 acini = 1 trapeso, 30 t. = 1 oncia, 12 o. 
 
 = 1 libbra, 26 1. = 1 rubbio, - - = 18.387 
 
 150 libbra = 1 cantaro piccole, - - - = 106.08 
 
 33J onci = 1 rotolo, 100 r. = 1 cantaro grosso, = 196.45 
 Sardinia. — Genoa : 24 grani = 1 denaro, 24 d. = 1 oncia, 
 12 o. = 1 libbra, l£ 1. = 1 rotolo, 16% r. 
 (25 libbre) = 1 rubbio, 4 r. = 1 centinajo, l£ c. = 
 
 1 cantaro. 
 Peso grosso : 1 centinajo, - - = 76.863 
 
 Peso scarso : 1 centinajo, - - - - = 69.875 
 
 Nice : 12 oncia = 1 libbra, 25 1. = 1 rubbio, 4 rubbi 
 
 = 1 centinajo, :.-_== 68.694 
 
 Turin: 25 libbre = 1 rubbio, - - -= 20.329 
 
 States of the Church. — 1 libbra Italiana, - = 2.204 
 
 Ancona: 12 oncia = 1 lira, 100 1. = 1 cantaro, - = 72.942 
 
 C* 
 
30 a FOREIGN WEIGHTS REDUCED TO UNITED STATES. 
 
 Foreign. U. States, 
 
 Avoidupois 
 
 pounds. 
 
 Rome: 12 oncia = 1 libbra, 10 1. = 1 decina, 10 d. — 
 
 1 cantaro, - - - - - = 74.763 
 
 160 libbre = 1 cantaro. 250 libbre = 1 cantaro. 
 
 1000 libbre = 1 migliajo, - = 747.633 
 
 Tuscan y. — Leghorn, Florence, Pisa : 
 
 72 grani or 3 donuri= 1 draimna, 96 draninie or 12 
 
 oncia = 1 libbra, 100 1. = 1 centinajo, - - = 74.857 
 
 10 centinaje = 1 migliajo. 
 
 160 libbre = 1 cantaro or carara, for wool, fish, <Sfc, = 119.771 
 50 rottoli = 1 cantaro generale (old), - - = 112.29 
 
 JAPAN. — 160 rin = 10 pun = 1 its-go - - = 1.333 lbs. 
 2,500 pun = 1 00 ischo = 1 itho = 1 its 'ko-koo == 333£ lbs. 
 MALTA I. — 30 trapesi = 1 oncia, 30 o. == 1 rotl, 
 
 100 rotl = 1 cantaro sottile, = 174.504 
 
 110 rotl = 1 cantaro grosso. 
 MADEIRA I. — Denominations and relative values, 
 . same as Lisbon, Portugal: 
 
 32 arratel or libbra = 1 arroba, - - - = 32.349 
 
 MAI Kill US I. — Port Louis : 16 onces = 1 livre, = 1.08 
 MEXICO. — Standard same as Cadiz, Spain. 
 
 MOROCCO. — 100 rotl == 1 cantaro, - - « 118.723 
 
 Tangier s : 1 rotl { mine r s '), - - - -= 1.06 
 
 1 rotl (market), - - - = 1.701 
 
 MOZ AMBlQ U E (Africa) . — Mozambique : Same as Port- 
 ugal. 
 NORWAY. — Same as Denmark. 
 
 PERSIA. 1 — Bushire: 3 clieki = 1 ratal, 7£ r. 1 maund 
 tabree, 2 m. tabree = 1 maund show. 
 1 maund show, bazar, - = 12.5 
 
 1 " copra, " - - - -=7.3 
 
 1 " show, factory, - - = 13.5 
 
 1 " copra, " - - - - = 7-75 
 
 Tauris: 2 mascais = 1 dirhem, 50 d. = 1 ratel, 6 
 
 ratcl = 1 batman, = 5. 017 
 
 K/iiraz: 1 batman, - - - - -= 10.123 
 
 POBTUGAL. — 576 grao or 24 escropulo or 8 oatuava, 
 = 1 onca, 16 o. = 4 quarto = 2 maroa = 1 arra- 
 tel, - - - - - = 1.016 
 32 arratel — 1 arroba, 4 arrobe = 1 quintal, - = 130.06 
 13^ quintale = 1 fcoaelada. 
 PR1 8SL4 {Irgal stare 1820): 4 quentchen = 1 loth, 
 
 21. — J un/.e, 8 u. = 1 mark, 2 m. 1 piund, = 1.0312 
 I64 pfund = 1 li.spiund, 1| 1. = 1 stein, - - = 22.687 
 
 5 stein = 1 centner, 3 0, = 1 schillplund, - = 340.31 
 
FOREIGN WEIGHTS REDUCED TO UNITED STATES. a 31 
 
 Foreign. U. States. 
 
 Avoirdupois 
 pounds. 
 100 pfunds = 1 lagel, for steel, - - - = 103.116 
 
 1 Prussian mark = 1 Cologne mark. 
 
 Dantzic: 33 pfund = 1 Btein, for fax, - = 34.029 
 
 RUSSIA (bgal throughout the Umpire) : 
 
 3 zolotnik = 1 loth, 32 loth or 12 lana = 1 funt, 
 
 40 font mm 1 pud, - - - - = 30.067 
 
 10 pud = 1 berkowitz, 3 b. = 1 paken, - =1082.02 
 
 2 paken = 1 last. 
 
 Libau: 20 funt = 1 licspfunt, 20 1. = 1 schiffpfunt, = 364.168 
 
 Hamburg weights arc also used here. 
 Riga : 20 pfunde = 1 liespfund, 5 1. = 1 lof, - = 92.158 
 
 4 lof = 1 berkowitz or gehiffpfund, - - = 368.633 
 SARDINIA I. — Cagliari, &c. : 12 oncia = 1 libbra, 
 
 26 1. = 1 rubbio, 4 r. = 1 cantarello, - - = 93.082 
 
 SICILY I.— Messina: 12 oncia = 1 libbra, - = 0.707 
 
 2£ libbre = 1 rotolo sottile, - - -= 1.768 
 
 33 oneia = 1 rotolo grosso, - - = 1.945 
 
 100 rotoli = 1 cantaro (gross or net) . 
 
 Palermo : 250 libbre or 100 rotoli sottile = 1 cantaro 
 
 sottile, - - - - -= 175.04 
 
 275 libbre or 100 rotoli grosso = 1 cantaro grosso, = '192.556 
 Syracuse : 250 libbre or 100 rotoli sottile = 1 cantaro 
 
 sottile, - - - - = 180.125 
 275 libbre or 100 rotoli grosso = 1 cantaro grosso, = 198.137 
 SPAIN. — 16 Castilian onze = 1 Castilian libra ( Cus- 
 toms'), = 1.01546 
 
 Alicant: 12 onze = 1 libra menor (minor). 
 
 18 onze = 1 libra mayor (major), - = 1.144 
 
 24 1. mayor or 36 1. menor = 1 arroba, - - = 27.456 
 
 4 arrobe = 1 quintal, 2£ q. = 1 carga, - = 274.567 
 8 carga = 1 tonelada. 
 
 24 Castilian libre = 1 arroba,/or vermilion, - = 24.371 
 
 25 Castilian libre = 1 arroba of the Customs, - = 25.386 
 'Barcelona: 25 libre = 1 arroba, - - -= 22.14 
 Bilboa : 25 libre = 1 arroba, - = 26.97 
 Cadiz (Standard of Castile) : 8 onza = 1 marco, 
 
 2 m. = 1 libra, 25 1. = 1 arroba, 4 a. = 1 quintal, = 101.546 
 20 quintale = tonelada. 
 Corunna, Ferrol : 16 onze = 1 libra sutil, 100 libre 
 
 sutil = l quintal (Castilian), - - -=101.546 
 
 20 onze = 1 libra gallega, 100 1. g. = 1 quintal, = 126.933 
 
 25 libre = 1 arroba. 
 
 Gibraltar : 16 onze = 1 libra ( Castilian) , - =1.01546 
 
 16 ounces = 1 pound, 25 p. = 1 arroba, - - = 25. 
 
32 a 
 
 FOREIGN WEIGHTS REDUCED TO UNITED STATES. 
 
 Foreign. 
 
 U. Slates. 
 
 Avoirdupois 
 pounds. 
 
 = 177.7 
 = 152.28 
 = 0.784 
 = 1.176 
 
 - = 338.413 
 
 Malaga. — Same as Cadiz. 
 
 1| quintal, or 3£ barrile = 1 carga of raisins, 
 Santander: 100 libre = 1 quintal, 
 Valencia : 12 onze = 1 libreta or libra menor, 
 18 onze = 1 libra gruesa, - 
 
 35 libre menor = 1 arroba, 4 a. = 1 quintal, 
 12j arobe = 1 carga, - 
 SWEDEN. — Stockholm, &c. : 
 
 Viktualie-wigt or skal-wigt : 4 quintin = 1 lod, 2 1. 
 
 = 1 untz, 16 u. = 1 skalpund, - - = 0.9375 
 
 20 skalpund = 1 lispund, 20 1. = 1 skeppund, - mm 375. 
 
 32 skalpund = 1 sten, - - = 30. 
 
 12 skeppund = 1 last. 
 Metall-wigt or jern-wigt (for iron, steel, &c.) : 
 20 mark = 1 markpund, 20 m. = 1 lispund, 
 
 20 1. = 1 skeppund, - - - - = 300. 
 
 15 skeppund = 1 last. 
 
 8£ lispund = 1 waag or vog, for tin, - - = 123.75 
 
 Uppstadt-wigt (inland weight) : 
 
 400 pund or 20 lispund = 1 skeppund, - - = 315.674 
 
 Tachjern-wigt : 400 pund or 20 liap. = l skeppund, = 453.47 
 Berg-wigt : 400 pund or 20 lisp. = 1 skeppund, = 348.822 
 SWITZERLAND (legal, since 1823, for the Cantons of 
 Aarau, Basle, Berne, Freiburg, Lucerne, Solothum, 
 Vaud ; but not in general use) : 
 8 gros = 1 unze, 8 u. = 1 mark, 2 m. = 1 livre or 
 
 pfund = 1 livre poids de marc of France, = 1.07922 
 
 10 livres = 1 stein, 10 s. = 1 centner, - - = 107.922 
 
 Special and local : 
 
 Berne: 100 pfunde = 1 centner, - = 114.9 
 
 Geneva : 24 grani = 1 denier, 24 d. = 1 once, 15 o. 
 
 = 1 livre foible, = 1.0118 
 
 18 once — 1 livre /brt, - - - - =1.2141 
 
 Lausanne : 16 onces = 1 livre = 1 livre poids de metrique 
 
 of France, - - - - - = 1.10237 
 
 Neufchatel: 8 onces = 1 marc, 2 m. = 1 livre, • = 1.14682 
 St. Gall : 10 unze = 1 loth, 2 1. = 1 pfund, - = 1.2&14 
 
 Zurich: 18 unze = 1 pfund, - - = 1.1637 
 
 Poids foible (for silks, &c.) : 2 lothe = 1 unze, 8 u. 
 
 = 1 mark, 2 m. = 1 pfund, - - - = 1.0344 
 
 TRIPOLI. — (N. Africa) : S termini = 1 usano, 16 u. 
 
 = 1 rotolo, 100 rotoli = 1 cantaro, - - = 111.214 
 
 400 drachmi = 1 oke, « 2.7429 
 
FOREIGN WEIGHTS REDUCED TO UNITED STATES. a 33 
 
 Foreign. U. States, 
 
 Avoirdupois 
 pounds. 
 
 TUNIS. — 8 metical = 1 usano, 16 u. = 1 rotolo, 100 
 
 rotoli = 1 eantaro, - = 109.155 
 
 TURKEY. — Aleppo : 266| meticals — 1 okc, - - = 2.81349 
 
 480 meticals = 1 rotolo, 5 r. = 1 vesno, 20 v. = 1 
 
 eantaro, - ■■ 506.428 
 
 3J rotoli = 1 batman, 10£ b. — 1 cola, - - = 177.249 
 
 30£ rotoli = 1 eantaro zurlo, - - = 154.46 
 
 400 meticals = 1 rotolo for Dainacene, - - = 4.22023 
 
 453J meticals = 1 rotolo for Persian silks, - = 4.78293 
 460^ meticals = 1 rotolo Tripolitan, - - = 4.92361 
 
 Bagdad: 2£ vakia = 1 oke, = 2.74286 
 
 Bussorah: J 00 miseals = 1 cheko, - - -=1.02857 
 
 24 vakia = 1 maund, - = 116. 
 
 46 oke = 1 cuttra, - - - - — 136.482 
 
 24 vakia attaree = 1 maund attaree, - = 28. 
 
 76 vakia attaree = 1 maund sessee, - - = 88.6666 
 
 4f vakia attaree = 1 vakia. 
 Constantinople: 16 kara, kilot or taim = 1 dirhem, 
 100 dirhem or 06j meticals = 1 cheki or yusdrum, 
 2 cheki = 1 rottel, 100 r. = 1 eantaro, - = 140.3 
 
 13 T 7 T rottel = 1 batman, 7£ b. = 1 eantaro. 
 266^ meticals or 2 rottel = 1 oka. 
 
 1 16| meticals = 1 cheki, for opium, - - = 1.7578 
 
 Damascus : 400 meticals or 60 peso = 1 rotolo, 100 
 
 rotoli = 1 eantaro, - = 395.673 
 
 Smyrna: 100 drachmi or 66f miseals = 1 cheko, 2£ 
 
 cheki = 1 cequi, - - - - - = 1.7578 
 
 180 drachmi or 120 miseals = 1 rotolo, 13J r. = 1 
 
 batman, 7£ b. or 100 rotoli = 1 eantaro, - = 126.571 
 4 cheki = 1 oka, 45 o. = 1 eantaro. 
 44 oke = 1 eantaro, for tin, &c., - - - = 123.758 
 
 West Indies. 
 
 In the Islands of Antigua, The Bahamas, Barbadoes, 
 Barbuda, Dominica, Grenada, Jamaica, Les 
 Saints, Montserrat, Nevis, St. Kitts, St. Vincent, 
 Tobago, Tortola, the commercial weights are the 
 same as in Great Britain. 
 
 In Deseade, Guadeloupe, Mariegalante, Martinique, St. 
 Lucia : 2 quartiers = 1 marc, 2 m. = 1 livre, 100 
 1. = 1 quintal, - - - -=107.922 
 
 3 quintals = 1 charge, 3£ c. = 1 millier. 
 This being the old system, poids de marc, of France. 
 
34 a FOREIGN WEIGHTS REDUCED TO UNITED STATES. 
 
 Foreign. U. States. 
 
 Aroirdupois 
 pounds. 
 
 In Saba, St. Eustatia, St. Martin, the commercial weights 
 
 are the same as in Holland, old system. 
 In Santa Cruz, St. John, St. Thomas, Same as Denmark. 
 In St. Bartholomew, Same as Sweden. 
 In Curacoa, Trinidad, Same as Castile (Spain). 
 In Bonaire: 100 pond = 1 centenaar, - - - s 103.659 
 
 3 centenaar = 1 schippond. 
 This being the old weight of Brabant, Holland. 
 Cuba I. — Cardenas, Cienfuegos, Havana, Matanzas, 
 
 Nuevitas, Porto Principe, St. Jago, &c. : Same as 
 
 Castile (Spain). 
 Hayti I. — Aux Cayes, Cape Haytien, Jeremie, Port au 
 
 Prince, Port Platte, &c. : Same as France, before 
 
 1812. 
 Savanna, St. Domingo, &c. : Same as Castile (Spam). 
 Porto Rico I. — Ponce, St. Johns, &c. : Same as Castile. 
 
35 a 
 
 FOREIGN LIQUID MEASURES REDUCED TO UNI- 
 TED STATES. 
 
 Foreign. U. States 
 
 Wine 
 gallons 
 
 ABYSSINIA.— Massuah: 1 cuba, - - - m 0.268 
 ALGIERS. — 16| litres — 1 khoulle, 6 k. = 1 hectoli- 
 tre, = 26.418 
 
 ARABIA. — Mocha: 20 vacias {weight) = 1 nusfiah, 8 
 
 n. = 1 cuda or gudda = 10 lbs. Av. , or of oil, &c. = 2.07 
 AUSTRIA {legal and general for the Empire) : 
 Vienna, Trieste, Lintz, Prague, Pesth, &c. : 
 
 4 seidel — 1 mass, 10 mass = 1 viertel, - = 3.738 
 
 4 viertel = 1 eimer or orna, - - - = 14.952 
 
 32 eimer = 1 fuder, . - - - = 478.48 
 Special and local — 
 
 Trieste : 4| caffiso = 1 orna, - - - = 14.952 
 
 Bohemia. — 32 pinte = 1 eimer, - - = 16.141 
 
 4 eimer = 1 fass, - - - - - = 64.56 
 Prague: 60 mass = 1 eimer, - - - =16.591 
 Hungary. = 4 r impel = 1 halbe or icze, 100 icze = 1 
 
 czeber, - - - - - - = 22. 
 
 1 an thai = 13.352 gals. 1 ako, - = 18.495 
 
 Buda, Pesth, &c. : 1 eimer, - - - - = 15.028 
 
 Presburg : 1 eimer, - - - = 19.368 
 
 Moravia. — 40 mass = 4 viertel =» 1 eimer, - - = 11.282 
 
 AZORE ISLANDS. — Same as Lisbon {Portugal). 
 
 BALEARIC ISLES.— Majorca. — 4 quarta = 1 quartes, 
 
 6 quartes = 1 cuartin, 4 cuartin = 1 carga, = 28.666 
 3 carga = 1 pelexo. 1 quartinello, - - =1.8 
 Minorca. — 4 quarta = 1 quartes, 3 quartes = 1 gerrah, 
 
 10 g. = 1 carga, 4 c. = 1 botta, - - = 133.379 
 
 1 barrel, = 8.344 
 
 BELGIUM. — 3 J canette = 1 uper, 10 u. = 1 emmer, 
 
 3 e. = 1 vat = 1 hectolitre of France, - - = 26.418 
 
 36.578 
 
 2 pinte = 1 pot or mingle, 2 p. = 1 stoop or gelte, 
 
 2 s. = 1 schreef, 25 schreef = 1 aam, - = 
 
 6£ aam = 1 ton of spirits, for shipping, - - = 237.76 
 
 21 stoop = 1 velte, = 2.011 
 
36fl FOREIGN LIQUID MEASURES REDUCED TO UNITED STATES. 
 
 Foreign. U. States. 
 
 Wine 
 gallons. 
 
 BERMUDAS ISLANDS. —Same as United States. 
 
 BRAZIL. — Bahia : 10 garrafa = 1 canada, - = 18.734 
 
 10 canada = 1 pipa of molasses, - - - = 187.342 
 
 7£ Canada = 1 pipa of spirits, - - = 134.885 
 Rio Janeiro : 4 quartilho = 1 medida, 3 m. = 1 pote, = 2.185 
 
 16 pote = 1 pipa, 2. p. = 1 tonelada, - - = 262.178 
 
 1 frasco, - - - - = 0.562 
 
 Central and South America. 
 
 Balize, Guatimala, Yucatan, Bolivia, Buenos Ayres, 
 Equador, New Granada, Paraguay, Peru, Uru- 
 guay, Venezuela. Denominations and values, 
 same as Castile (Spain.) 
 
 Guiana. — Berbice, Demerara, Essequibo, Surinam : Same 
 as Holland. 
 Cayenne. — Same as France. 
 
 CANARY ISLANDS. — Grand Canary, Teneriffe, &c. : 
 
 4 cuartilla = 1 arroba, 28£ a. = 1 pipa, - = 120.06 
 
 CANDIA I.— By weight — 1 oke = 2.649 lbs. Av. 
 
 CAPE COLONY. — Cape Town: 16 flask = 1 anker, 
 
 4 anker = 1 aain, 4 aam = 1 legger, - - = 152. 
 
 CAPE VERDE I. — Same as Lisbon (Portugal). 
 
 CHILI. — Valparaiso, Coquimbo, &c. : 4 copa = 1 quar- 
 
 tilla, 4 q. = 1 arroba, - - = 9.906 
 
 CHINA. — By weight. See Weights. Also — 
 
 10 kop tsong = 1 shing tsong, 10 shing tsong = 1 
 tau tsong, 5 tau tsong = 1 nok tsong, 2 hok tsong 
 = 1 shik tsong, If shik tsong = 1 yu, 5 yu = 1 
 
 ping = 832 lbs. Av. 
 [CA I. — 
 
 CORSICA I. — 4 cuarto = 1 boccale, 9 b. = 1 zucca, 
 
 12 z. = 1 barile, - - - - = 36.985 
 
 CYPRUS I. — By weight. See Weights. 
 J ) IA.M ARK. — 155 pagel or 38| potte or 19| kande = 
 
 1 anker, -...-== 9.889 
 4 anker = 1 aam, 1£ a. = 1 oxehoved, 4 o. = 1 
 
 fader, 1| f. = 1 stykfad, - - - = 296.672 
 
 60 vi.rt.l = 1 piba, = 122.499 
 
 17 vii-rti-1 = 1 toende, for beer, - - -= 34.708 
 
 EGYPT. — By weight. See Weights. 
 FRANCE. — 1000 millilitres — 100 centilitres = 10 de- 
 cilitre* = 1 litre, = 0.264 
 I001itren= HI decalitres =1 hectoliter - - = 26.418 
 100 hectolitres = 10 kilolitres = 1 myrialitre. 
 
FOEEIGN LIQUID MEASURES REDUCED TO UNITED STATES. « 37 
 
 Foreign. U. State$, 
 
 Wiuo 
 gallons. 
 
 GERMANY. — Baden {legal) : 4 schoppen = 1 mass, 
 12£ m. = 1 stutz, 8 s. = 1 ohm = 1^ hectolitres of 
 
 l-Yance, m 39.626 
 
 10 ohm = 1 fuder. 
 Manheim : 16 schoppen or 4 eich-niass = 1 viertel, 12 
 
 vicrtel = 1 ohm, - - - - an 25.285 
 
 16 schoppen or 4 wirths-mass = 1 viertel, 24 viertel 
 = 1 ohm = 16 decalitres of France, - =* 42.268 
 
 Bavaria {legal) : 4 quartil = 1 mas or masskanne, 60 
 
 masskanne = 1 eimer, - - - - = 16.944 
 
 |S4 M =1 eimer, for beer, - = 18.075 
 
 , Augsburg, Wurtzburg : 4 achtel = 1 seidel, 16 s. = 1 
 
 boson, 8 beson = 1 eimer, 12 e. = 1 fuder, - = 238.745 
 Nuremberg: visir-niass : 4 seidel = 1 viertel, 32 v. 
 
 = 1 eimer, 12 e. = 1 fuder, = 232.348 
 
 Schenk-mass : 32 viertel = 1 eimer, - - = 18.244 
 
 12 eimer = 1 fuder, = 218.924 
 
 Ratisbon : 32 viertel = 1 eimer, 12 e. = 1 fuder, - = 158.507 
 
 Hanover {legal) : 8 nossel = 4 quartier = 2 kanne = 1 
 
 stubchen, - - - - = 1.036 
 
 10 stubchen = 5 viertel = 1 anker, - - = 10.36 
 4 anker or 2£ eimer = 1 ahm, - - = 41.439 
 6 ahm or 4 oxhoft = 1 fuder, - - - = 248.637 
 4 ahm or tonne, for beer, = 1 fass, - = 165.756 
 
 Bremen : 180 mingel = 90 versel '= 45 quartier or 
 
 , vierling = ll£ stubchen = 5 viertel = 1 anker, = 9.574 
 24 anker = 6 ohm = 1 fuder, - - = 229.779 
 
 16 mingles = 1 stubchen, 6 s. = 1 stechkanne, 6 
 
 stechkanne = 1, tonne, for whale oil, - -= 30.64 
 
 44 stubchen {beer measure) = 1 tonne, - = 43.836 
 
 Hesse Cassel : 4 schoppen = 1 mass, 4 m. = 1 viertel 
 
 or quartlein, 20 v. = 1 ohm, 6 ohm = 1 fuder, = 251.547 
 20 viertel {beer measure) = 1 ohm, - - = 46.128 
 
 Hesse Darmstadt {legal) : Denominations and relative 
 values, same as H. Cassel. 
 1 ohm = 16 decalitres of France, - = 42.27 
 
 Frankfort: 4 schoppen = 1 mass, 4£ neu-mass = 1 
 
 viertel, 20 v. = 1 ohm, 6 ohm = 1 fuder, - = 227.352 
 
 8 alt-mass = 9 neu-mass. 
 
 11 fuder = 1 stiickfass, = 303.136 
 Holstein. — Hamburg, Altona, Lubec : 8 oessel, plank or 
 
 nossel = 4 quartier = 2 kanne = 1 stubchen, = 0.955 
 
 8 stubchen = 4 viertel = 1 eimer, - - - = 7.644 
 
 • 5 eimer or 4 anker = 1 ahm or fass, - - =38.22 
 
 D 
 
38 a FOREIGN LIQUID MEASURES REDUCED TO UNITED STATES. 
 
 Foreign. 77. States. 
 
 Wine 
 gallons. 
 
 l£ ahm or l£ tonne = 1 oxhoft, - - - = 57. 33 
 
 4 oxhoft or 2 pipe = 1 fuder, = 229.32 
 16 margel or melgel = 1 stechkanne, 6 8. = 1 tonne, 
 
 2 t. = 1 quarteel,/or whale oil, - - - = 61.548 
 
 1 tonne, for beer, = 45.804 
 Mecklenburg. — Rostock, &c. : Same as Holstein. 
 
 Saxony. — Dresden : 8 quartier or 2 nossel = 1 kanne, 
 
 quart or shenkkanne, 3 kanne = 1 viertel, - = 0.743 
 
 18 v. = 1 anker, lj a. = 1 eimer, - = 17.833 
 
 2 e. = 1 anker, l£ a. = 1 oxhoft, - - - = 53.499 
 1| o. = 1 fass, 2f f. = 1 fuder, - - = 213.996 
 4 tonne or 2 viertel = 1 fass, beer measure, - - = 104.026 
 
 L'eipsic : Denominations and relative values same as 
 Dresden, but capacity values = 12.53 °/ greater. 
 24 viertel = 1 eimer, = 20.067 
 
 Freyburg : 100 schoppen or viertel = 1 brente, - = 10.312 
 
 16 brente = 1 fass, = 165. 
 
 GREAT BRITAIN : Imperial measure : Denominations 
 
 and relative values same as wine measure, U. S., 
 
 but capacity values 20 T 3 -rV P er cent « greater. See 
 
 Liquid Measures, U. S. 
 
 GREECE. — Patras : 24 boccale = 1 barile, - - = 13.54 
 
 HOLLAND (legal) : 10 vingerhoed = 1 maatje, 10 m. 
 
 = 1 kan, 10 k. = 1 vat = 1 hectolitre of F., = 26.418 
 
 Previous to 1820 — 
 2 mutsje = 1 pint, 2 p. = 1 mingle, 2 m. = 1 stoop, 
 3Jj- s. = 1 viertel, 2$ v. 1 steekan, 2 s. = 1 anker, 
 
 4 a. = 1 aam, 1£ aam = 1 okshoofd, - = 61. 
 
 1 aam, for oil, - - - * - - = 37.64 
 
 1 legger, /or beer, - =153.57 
 
 India and Malaysia or East Indies. 
 
 Ceylon I. — Colombo : 4 aams = 1 legger, - - = 150.— 
 
 IIi.mxotan. — Jiuinhay : 60 rupees =1 seer, 50 seers = 
 1 inauiid fluid as 77 U»s. Av. 
 Calcutta: 5 sicca = 1 chattac, 4 c. = 1 pouah, 4 p. 
 = 1 seer, 5 s. = 1 BoaBaree, 8 p. = 1 bazar 
 maund weight = 82.18 lbs. Av. 
 Madras: By weight. See Weights. 
 Seramporc, JWwflwftflr, {l<y<il) \ Same as Denmark. 
 Java I. — Batana : ") kau = 1 barile, - - = 13.207 
 
 Luzon I. — Manilla: Same as Cadiz (Spain). 
 
FOREIGN LIQUID MEASURES REDUCED TO UNITED STATES, a 39 
 Foreign. U. States. 
 
 Wine 
 
 gallons. 
 
 Siam. — Bangkok : 20 canan = 1 cohi = 5 decalitres of 
 
 France, - -= 13.209 
 
 Sumatra I. — 8 pakha or 2 culah = 1 koolah, 15 koolah 
 
 — 1 tub, = 17.44 
 
 IONIAN ISLANDS. — Cephalonia : 2 quartucci = 1 
 boccale, 8 b. = 1 pagliazza, 1£ p. = 1 secchio, G 
 
 s. = 1 barile, - - - - - = 18. 
 
 Corfu, Paxos : l£ miltre = 1 boccale, 12 b. = 1 sec- 
 chio, G s. = 1 barile, - - = 18. 
 
 Zante : 1G quartucci or 8 boccale = 1 lira, 1£ 1. mm 1 
 
 secchio, G s. = 1 barile, - - - - = 18. 
 
 ITALY. — Lombard? and Venice. — Government and 
 Customs measure: 10 coppi = 1 pinta, 10 p. = 1 
 mina, 10 m. = 1 soma = 1 hectolitre of France, »= 26.418 
 Special and local — 
 Venice : 1£ quart uzzi = 1 boccale, 2g b. = 1 bozza, 4 
 
 bozzi = 1 secchio, G s. = 1 inastello or concia = 17.119 
 2 niastclli = 1 bigoncia, 4 b. = 1 anfora, - =s 136.95 
 14 anfori = 1 botta, - - - - = 171.187 
 
 16 iniri = 1 bigoncia, 2£ b. = 1 migliajo, 2m.= 
 
 1 botta, for oil, ...-== 322.22 
 
 Naples: GO carraffa = 1 barile, - - - = 11.581 
 
 3£ barile = 1 salina, 4 s. = 1 pipa, - = 162.137 
 
 12 barile = 1 botta, 2 botte = 1 carro. • 
 
 6 misurella or l£ pignata = 1 quarto, 16 q. = 1 
 
 stajo, 16 s. = lmlma,, for oil, - = 42.538 
 
 11 salina = 1 last for shipping. 
 Sardinia. — Genoa : 90 amola or 5 foglietta or pinta = 
 
 1 barile, 2 b. = 1 niezzaruola, - - - = 39.218 
 
 16 quarteroni = 1 quarto, 4 q. = 1 barile,/or oil, = 17.084 
 Turin : 20 quartine = 1 boccale, 2 b. = 1 pinta, 6 p. 
 
 = 1 rubbio, 6 r. = 1 brenta, 10 b. = 1 carro, — 148.806 
 States of the Church. — Ancona: 
 
 . 4 fogliette = 1 boccale, 24 b. = 1 barile, - = 11.35 
 
 1 soma of oil, - - - - -= 18.494 
 
 Rome: Wine measure: 4 cartocci = 1 quartuccio, 4 
 
 q. = 1 foglietta, 4 f . = 1 boccale, - - = 0.481 
 
 32 boccali = 1 barile, 16 b. = 1 botta, - - = 246.544 
 
 Oil measure: 4 boccali = 1 cugnatello, 10 c. = 1 
 
 mastello or pello, 2 m. = 1 soma, - - =» 43.333 
 
 Tuscany. — Leghorn, Florence, Pisa : 
 
 4 quartucci or 2 mezette = 1 boccale, 40 b. or 20 
 fiasco = 1 barile = 133J libbra or 99.81 lbs. Av. 
 
40 FOREIGN LIQUID MEASURES REDUCED TO UNITED STATES. 
 
 Foreign. U. States 
 
 "Wine 
 gallons 
 
 16 fiasco = 1 barile, 2 b. = 1 botta, for oil = 240 
 libbra or 179§ lbs. U. S. 
 MALTA I. — 2 caffisi = 1 barile = 50 rotl or 87| lbs. 
 
 Av. 
 MADEIRA I. — Standard same as Lisbon (Portugal) . 
 
 M A I rEmUS I. — Port Louis : 1 velt. - - = 2. 
 
 MEXICO. — Same as Cadiz (Spain). 
 
 NORWAY. — Same as Denmark. 
 
 PORTUGAL. — Lisbon, &c. : 24 quartilhi or 6 Canada 
 
 = 1 alqueire or cantaro, - - - - = 2.185 
 
 2 alqueire = 1 almude, 26 a. = 1 bota or pipa, = 113.627 
 2 bota = 1 tonelada. 
 31 almudes = 1 pipa, London gauge. 
 Oporto : 2 alqueire = 1 almude, 21 a. = 1 pipa, = 139.134 
 
 PRUSSIA (legal throughout the kingdom since 1820 :) 
 
 2 ossel = 1 quart, 30 q. = 1 anker, 2 a. = 1 eimer 
 = 3840 cubic Rhein-zolle or 4192 cubic inches, 
 
 U.S., - — 18.146 
 
 3 eimer or 1£ ohm = 1 oxhoft, 4 o. = 1 fuder, - = 217.758 
 3 J eimer = 1 fass. 
 
 Dantzie: 3 \ eimer = 1 fass, - - = 60.487 
 
 6 eimer = 1 pipe, - - - - - = 108.876 
 
 Konigsberg : 4£ eimer = 1 pipe, - - = 81.658 
 
 RUSSIA (legal for the Empire since 1820) : 
 
 12£ tscharka = 1 osmuschka or krashka, 2 o. = 1 
 
 tschet-vverk, 4 t. = 1 vedro or wedro, - - = 3.240 
 
 40 vedro = 1 botsclika or anker, - = 129.86 
 
 13J botschka = 1 sarokowaja. 
 Revel, Riga: 30 stof = 5 viertel = 1 anker, - - = 10.311 
 
 4 ankor = 1 alim, 6 a. = 1 fuder, - = 247.46 
 SARDINIA I. — 4 quartucci = 1 quartaro, 8 q. = 1 
 
 barile, - - - - - -= 8.874 
 
 2 barile = 1 inezzaruola. 
 SICILY I. — Palermo : 20 quartucci = 1 quartaro, 8 
 
 <|iiartari = 1 barile, - = 9.430 
 
 12 barile or 5 salma = 1 botta or pipa, - - = 113.237 
 
 12 salma = 1 toiinrllata. 
 
 1 nMBOffor oil** 12| rotoli grosso, - =» 3.09 
 
 Messina: 12 barile or 5 salma = 1 pipa, - - = 108.— 
 
 1 cattBOffor oil = 12£ rotoli groat 
 Syracuse: I - salma = I tonnellata, - - -= 247. — 
 
 SPAIN. — F"i- Customs values, nee Cadiz. 
 
 Alicant: 4 copa = I cuartilla, 4 c. = 1 cuarto, 4 
 cuarti = 1 cantaro = 1 Castilian am>l>a = 25.38 
 
FOREIGN LIQUID MEASURES REDUCED TO UNITED STATES, fl 41 
 
 Foreign. 
 
 lbs. = 3.04 gallons of wine or 3.642 gallons of 90 
 per cent, alcohol. United State- measure. 
 40 arrobe = 1 pipa, 2 p. = 1 toneladft. 
 Barcelona: 4 petricon = 1 mitadclla or porrone, 4 m. 
 = 1 quartern, 2 q. » 1 cortan or mitjera, 2 e. = 
 1 mallah, 8 m. = 1 carga = 12 arrobe or 205.08 
 lbs. Av. 
 4 carga = 1 pipa. 
 
 4 quarta = 1 cuarto, 4 c. = 1 cortan, 30 cortan = 
 1 carga, for oil =11 arrobe or 243.54 lbs. Av. 
 Cadiz (Standard of Castile) : 2 copa = 1 azumbra, 2 
 a. = 1 cuartilla, 4 c. = 1 cantaro or arroba. 
 1 arroba major = 35 libre or 35.541 lbs. Av., or 
 
 984| cubic inches of distilled water at 00°, 
 1 arroba menor, /<?;■ oil = 27.', libre, 
 10 arrobe = 1 mayo, 27 arrobe = 1 pipa, 30 arrobe 
 = 1 bota, 2 bote = 1 tonelada. 
 Corunna, Fcrrol: 10 quartilli = 1 olla, 4 o. = 1 can- 
 ado, 4 c. = 1 mayo = 14 arroba sutil, - 
 Gibraltar : Same as the United States. 
 Malaga: 8 azumbre = 1 cantaro or arroba (34J 1.), 
 Santander : 8 azumbre = 1 cantaro = 20 libre, - 
 Valencia: 1 arroba = 38 libre menor, 
 
 1 arroba, for oil= 29^ libre menor, 
 SWEDEN. — Stockholm, &c. : 4 jungfru or ort 
 
 quarter, 4 q. = 1 stop, 2 s. = 1 kanna, - 
 6 kanne = 1 atting or ottingar, 2 a. = 1 fjerding, 
 
 1\ f . = 1 ankare, 2 a. = 1 embar, If e. = 1 
 
 tunna, - 
 
 14 tunna = 1 am, 1£ a. = 1 oxhufwud, 
 
 2 oxhufwud = 1 pipa, 2 p. = 1 fuder, 
 SWITZERLAND (legal since 1823, for the Cantons of 
 
 Aarau, Basle, Berne, Freiburg, Lucerne, Solothurn, 
 Vaud ; but not in general use) : 
 10 emine = 1 mass or pot, 10 m. = 1 gelt = lj^y 
 decalitres of France, - 
 
 Special and local — 
 Basle : 4 schoppen = 1 mass, 4 m. = 1 viertel, 2f v. 
 
 = 1 setier, 1§ s. = 1 ohm, 3 o. = 1 saum, - 
 Berne: 8 becher or 2 viertel = 1 mass, 25 m. = 1 
 brente or eimer, 4 b. = 1 saum, - 
 ' 4 saum = 1 fass, 1£ f. = 1 landfass, - 
 Geneva : 2 pot = 1 quarteron, 24 q. = 1 setier, 
 D* 
 
 U. States. 
 
 Wine 
 gallons. 
 
 4.263 
 3.319 
 
 -== 42.533 
 
 = 1 
 
 4.182 
 4.739 
 3.500 
 2.737 
 
 -= 0.089 
 
 33.174 
 02.202 
 248.81 
 
 = 3.5004 
 
 = 40 337 
 
 44.1G1 
 
 204. 9G6 
 
 11.942 
 
42 <Z FOREIGN LIQUID MEASURES REDUCED TO UNITED STATES. 
 
 Foreign. IT. States. 
 
 Wine 
 gallons. 
 
 12 setier = 1 char. 
 Lausanne : 10 verre = 1 mass, 10 m. = 1 broc, 3 b. 
 
 = 1 setier or eimer, - - - - = 10.G99 
 
 Neufchatel: 8 pote or mass = 1 brochet or stutz, = 4.024 
 
 2£ brochet = 1 brande, 2§ brande = 1 gerl, - = 26.159 
 
 24 brochet = 1 muid, 24 m. = 1 bosse. 
 St. Gall: lauter-mass : 8 mass = 1 viertel, - = 2.773 
 
 4 viertel = 1 eimer, 4e. = 1 saum, - - = 44.37 
 
 7£ saum = 1 fuder. 
 
 Schenk-mass : 8 mass = 1 viertel, - = 2.465 
 
 4 viertel = 1 eimer, &c. 
 
 8 mass = 1 viertel, for oil, - - - = 2.867 
 
 Zurich: lauter-mass: 8 statz or 2 mass = 1 kopf, = 0.9637 
 7£ kopf = 1 viertel, 4 v. = 1 eimer, 1£ e. = 1 saum, = 43.368 
 Schenk-mass : 2 quartli = 1 mass, 2 m. = 1 kopf, = 0.86746 
 7£ kopf = 1 viertel, &c. 
 TRIPOLI (N. Africa) : 14 caraffa = 1 mataro, for oil 
 = 42 rotoli = 46^ lbs. Av. 
 1 barril = 116| rotoli. 
 TUNIS. — 2 mettar,/or wine = 1 mettar, for oil = 36 
 rotoli = 39 T 3 <j lbs. Av. 
 1 millerolle = 120 rotoli. 
 TURKEY. — 1 almud, = 1.38 
 
 West Indies. 
 
 In the islands of Antigua, the Bahamas, Barbadoes, Bar- 
 buda, Dominica, Grenada, Les Saints, Montserrat, 
 Nevis, St. Kitts\ St. Vincent, Tobago, Tortola, 
 the pleasures for Liquids are the same as those of 
 the United States, or the same as those of Great 
 Britain, previous to 1825. 
 
 In Jamaica: 85 Imperial gallons = 1 puncheon, - = 102.03 
 
 In the Islands of Deseade, Guadeloupe, Mariegalante, Mar- 
 tinique, St. Lucia : 8 muces = 4 roquilles = 2 
 chopines = 1 pinte, 8 pintes = 4 pots = 2 gallons 
 
 = 1 velt, - - - - - - to 2. 
 
 35 veltes = 1 muid. 
 This was the system for Liquid Measures in France, 
 before 1812, except that the value of the muid 
 was 70.855 gallons, U. S. 
 
 In Bonaire, Curacoa, Saba, St. Eustatius, St. Martin : 
 Same at Holland old measure, or measure before 
 1820. 
 
FOREIGN LIQUID MEASURES SEDUCED TO UNITED STATES, a 43 
 Foreign. U. States. 
 
 Wine 
 gallons 
 
 In St. Bartholomew : Same as Sweden. 
 
 In Trinidad: Same as Castile (Spain). 
 
 In Santa Cruz, St. John, St. Thomas : Same as Denmark. 
 
 Cuba I. — Cardenas, Cienfuegos, Matanzas, Nuevitas, 
 
 Porto Principe, St. Jago, &o. : Same as Castile 
 
 ( Spain) . 
 Havana: 1 arroba = 4.1 gallons. 1 bocoy, - =» 36.— 
 Hayti I. — Aux Cayes, Cape Haytien, Jeremie, Port au 
 
 Prince, Port Platte, &c. : Same as France before 
 
 1812. 
 Savanna, St. Dmingo, &c. : Same as Castile. 
 Poeto Rico I. — Same as Castile. 
 
Ua 
 
 FOREIGN DRY MEASURES REDUCED TO UNITED 
 STATES. 
 
 Foreign. U. States. 
 
 Winchester 
 bushels. 
 
 ABYSSINIA. — Massuah : 24 madcga =* 1 ardeb, - =* 0.333 
 
 ALGIERS. — 2 tarrie = 1 saa or aaha, - - - = 1.125 
 
 8 saa = 1 caffiso, - - - - 'em 9. 
 
 100 litres = 1 hectolitre, - - - - = 2.838 
 
 ARABIA. — Mocha: 40 kella = 1 tomaun (for rice) = 
 168 lbs. Av. 
 
 AUSTRIA (legal and general) : 
 
 2 becher = 1 fudermassel, 2 f.= l muhlmassel, 2 
 m. = 1 achtel, 2 a. = 1 viertel, 4v. = l metze, 
 
 30 m. = 1 muth, = 52.354 
 Local and special — 
 
 Trieste: 2 polonic = 1 metze, 1£ m. = 1 stajo, - = 2.156 
 Bohemia. — Prague: 12 seidel = 1 massel, 4 in. = 1 
 
 viertel, 4 v. = 1 strich, = 2.656 
 
 3 viertel = 1 metze, - - - -= 1.992 
 Hungary : 32 halbe = 1 viertel, 4 v. = 1 metze, - = 1.745 
 
 Buda and Pesth : 1 metze, - - - - = 2.-7 
 
 Moravia : 1 metze, - - - - = 2.— 
 
 AZORE I. — 2 meio = 1 alqueire, 4 a. = 1 fanga, - = 1.359 
 
 BALEARIC I. — Majorca : 6 barcella = 1 quartern, = 2.042 
 
 Minorca: 6 barcella = 1 quartera, - = 2.156 
 BELGIUM. — 100 uper = 10 setier = 3 mudde = 1 
 
 muid = 3 hectolitres of France, - - -= 8.513 
 
 10 muid = 1 last, = 85.134 
 Antwerp, Brussels, &c. (old measures) — 
 
 Jo mftlfltar vat = 1 halster, 10 h. = 1 sac, - = 6.918 
 
 108 gelte = 1 muid, = 8.302 
 
 Ghent : 1 halster, - - - - -= 1.4W9 
 
 4 meuke = 1 raziere, - = l > -<» 
 Mechlin: 1 Bteake, - - - - -= 0.014 
 
 BERM1 DAS I. — Same as United States. 
 
 BRAZIL. — 10 quarta = 1 iun-a, 15 f. = 1 moio, - = 23.02 
 I in Ian : 1 alqueire, - - - - -■■0.863 
 
 Rio Janeiro : 1 alqueire, = 1.135 
 
FOREIGN DRY MEASURES REDUCED TO UNITED STATES, a 45 
 Foreign. U. States. 
 
 Winchester 
 bushels. 
 
 Central and South America. 
 
 Balize, Campeche, Nicaragua, San Salvador, Sisal, &c. 
 Buenos Ay res, Callao, Carthagena, Laguayra, Mara- 
 caybo, Montevideo, Truxillo, Valparaiso, &c. : Samo 
 as Cadiz, generally. 
 Buenos Ayres : 1 fanega, - - = 3.752 
 
 Montevideo : 1 fanega, - - - sss 3.868 
 
 Valparaiso : 1 fanega, - - - - «= 2.572 
 
 Berbice, Demerara, Essequibo, Surinam: Same as Hol- 
 land before 1820. 
 Cayenne : Same as France. 
 CANARY ISLANDS. — 12 celemine — 1 fanega, — 1.776 
 
 17 celemine = 1 fanaga (heaped) . 
 CANADA EAST. — 1 minot, = 1.111 
 
 CANDIA I. — lcarga, - - - -— 4.323 
 
 CAPE COLONY. — Cape Town : 4 schepel = 1 muid, 
 
 10 muid = 1 load, ----=: 30.65 
 CHINA. — By weight. See Weights. 
 
 CORSICA I. — 6 bacino = 1 mezzino, 2 m. = 1 stajo, = 4.256 
 CYPRESS I. — By weight. See Weights. ' 
 DENMARK. — 4 sextingkar or fjerdingkar =* 1 otting- 
 kar or skieppe, 2 o. = 1 fjerding or stubchen, 4 
 f. = 1 toende, - - - - -= 3.947 
 
 22 toende = 1 last, = 86.836 
 
 EGYPT. — Alexandria, Rosetta : 1 kisloz, - - == 4.85 
 
 24 robi = 1 rebeb, = 4.462 
 
 Cairo : 24 robi = 1 ardeb, - - - - « 5.165 
 
 FRANCE. — 100 litres = 10 decalitres = 1 hectolitre, = 2.838 
 100 hectolitres = 10 kilolitres = 1 myrialitre, - = 283.782 
 GERMANY .— Baden (legal) : 1000 becher or 100 mas- 
 
 sel or masslein or 10 sester = 1 malter, - = 4.256 
 10 malter = 1 zober = 15 hectolitres of France, - = 42.567 
 Manheim, Heidelberg : 32 masschel or 4 immel or invel 
 or 2 kumpf or vierling = 1 simmer, 2 s. = 1 vi- 
 ernzel, 8 v. = 1 malter, for wheat, - = 3.152 
 
 1 malter, minim, - - - - - = 2.922 
 
 1 " for barley and oats, - - = 3.546 
 
 Bavaria (legal) : 8 masslein or 4 dreissiger = 1 achtel 
 
 or massel, 4 achtel = 1 viertel, - - - = 0.526 
 
 12 viertel = 1 scheffel, ----=» 6.31 
 144 metzen or 12 mass = 1 scheffel, /or oats, &c, = 7.363 
 4 kubel = 1 seidel, 6 s. or 4 scheffel = 1 muth,/or 
 
 coals and lime, - - - - - = 25.24 
 
46 FOREIGN DRY MEASURES REDUCED TO UNITED STATES. 
 
 Foreign. 
 
 Bamberg : 40 gaissil = 1 simra, 3 s. = 1 sheffel, 
 Bayreuth : 16 mass = 1 simmer, - 
 Nuremberg : 16 mass or 2 diethaufe = 1 metze, 16 
 metzen = 1 malter or simmer, - 
 16 hafer-mass = 1 hafer-metze, 32 hafer-metzen = 
 1 hafer-simmer, - - 
 
 Ratisbon: 4 massel a 1 strich, - 
 
 1 strich, for salt, &c., - » 
 
 Wurzberg : 144 massel = 12 mass = 2 achtel = 1 
 scheffel, ------ 
 
 1 scheffel, /or oats, &c., - - - 
 Hanover (legal) : 144 krus = 24 vierfas = 18 drittel or 
 
 metzen = 6 hhnten = 1 malter, 
 8 malter = 1 wispel, 2 w. = 1 last, 
 12 malter = 1 fuder, - 
 Bremen : 16 spirit = 4 viertel = 1 scheffel, - 
 40 scheffel = 1 last, - 
 Hesse Cassel : 64 kopfchen = 32 masschen = 8 metzen 
 = 4 mass = 2 himten = 1 scheffel, 
 
 3 scheffel or 1£ viertel or butte = 1 malter, 
 Hesse Darmstadt (legal) : 64 kopfchen = 32 masschen 
 
 = 8 gescheid = 2 kumpf = 1 metze, 
 
 2 metzen = 1 simmer, 4 s. = 1 malter, 
 
 4 butte (coal measure) = 1 mass, - - - 
 Frankfort: 4 schrott = 1 mass, .4 m. = 1 gescheid, 4 
 
 g. = 1 sechter, 2 s. = 1 metze, 2 m. = 1 simmer, 
 4 s. = 1 achtel or malter, - 
 Holstein. — Hamburg, Altona: 4 masschen = 1 spint, 
 4 s. = 1 hinit, 2 h. = 1 fass, - - - 
 
 20 fass = 10 scheffel = 1 wispel, 
 4£ wispel or 1£ last = 1 stock, - - - 
 
 10 scheffel (for barley and oats) = 1 wispel, - 
 45 tonne (for coals) or 30 sacks = 1 fass, - 
 Lubec: 4 fass = 1 scheffel, 4 s. = 1 tonne, 
 
 3 tonne = 1 dromt, 8 d. = 1 last, - - - 
 96 scheffel or 24 tonno = 1 last, for oats, 
 
 Kiel: 4 scheffel = 1 tonne or barril, - - - 
 
 Mecklenburg. — Rostock, &c. : 16 spint = 4 fass = 1 
 scheffel, 2 s. = 1 dromt, - 
 2| dromt = 1 wispel, 3 w. = 1 last, 
 45 viertel or 15 stubchen = 1 drum t, for oats, - 
 Saxon v. — Dresden, Jsipsic: 4 BMWohcn— 1 metze, 4 
 m. = 1 viertel, 4 v. = 1 sclitflel, 
 12 s. = 1 malter, 2 m. = 1 wispel, 
 
 U. States. 
 
 Winchester 
 bushels. 
 
 = 6.618 
 = 14.044 
 
 - = 9.028 
 
 16.696 
 0.756 
 1.51 
 
 5.183 
 8.533 
 
 5.296 
 84.736 
 63.552 
 
 2.021 
 80.834 
 
 2.28 
 6.482 
 
 0.452 
 
 3.632 
 
 17.736 
 
 = 3.256 
 
 — 1.495 
 = 29.892 
 = 134.514 
 = 44.831 
 = 179.6 
 = 3.796 
 = 91.1 
 = 106.918 
 = 3.367 
 
 = 13.243 
 
 = 105.944 
 
 = 14.9 
 
 = 2.963 
 
 — 71.11 
 
FOREIGN DRY MEASURES REDUCED TO UNITED STATUS, <X 47 
 
 Foreign. U. States. 
 
 Winchester 
 busheli. 
 GREAT BRITAIN: Imperial measure: See Dry Meas- 
 ures of the United States ; 1 bushel, - - = 1.0315 
 GREECE. — Pair as : 2 medimni = 1 staro, - =2.23 
 lbachel, - - - = 0.85 
 HOLLAND (legal) : 10 maatje = 1 kop, 10 k. t= 1 
 scheppel, 10 s. = 1 mudde or zac, 30 m. = 1 last 
 = 3 kilolitres of France, = 85.134 
 
 India and Malaysia or East Indies. 
 
 Birmah. — Rangoon : 2 lamyet = 1 lame, 2 1. = 1 said, 
 4 s. = 1 pyis, 2 p. = 1 sarot, 2 s. = 1 sait, 4 
 sait = 1 ten or basket = 16 vis = 58.4 lbs. Av. 
 Ceylon I. — Colombo : 24 seers = 1 parah, - - = 0.721 
 
 Hindostan. — Bombay : Salt measure — 
 
 10£ adowlies = 1 parah, 100 p. = 1 anna = 93.033 
 cub. feet, 1G anna = 1 rash, - - ==1196. 13 
 
 Grain measure — 2 tipprees = 1 seer, 4 s. = 1 adoulio, 
 16 a. or 7 pallie = 1 para = 186| lbs. Av. 
 8 para = 1 candy. 
 Calcutta : 5 chattac = 1 khoonka, 16 k. = 1 raik, 4 r. 
 = 1 pallie, 20 p. = 1 soallie = 154 lbs. Av. 
 8 soallie = 1 morah or maund bazar. 
 16 morah = 1 kahoon. 
 lg bazar maunds = 1 soallie. 
 Madras : 8 ollock = 1 puddy, 8 p. = 1 marcal, 5 m. 
 
 = 1 para, - - - = 1.744 
 
 80 para = 1 garce, - - - - - = 139.535 
 
 Serampore, Tranquebar (legal) : Same as Denmark. 
 Tatta : 4 puttoes = 1 twier, 4 t. = 1 cossa, 60 c. = 
 1 carvel = 5£ Tatta maunds or 408$ lbs. Av. 
 Java I. — Batavia : 22 mudden = 1 coyang, - = 62.432 
 
 Bantam : 1600 bambou = 400 gantang = 52 mudde 
 
 = 1 coyang, for rice, - -=147.565 
 
 Luzon I. — Manilla: Same as Cadiz (Spain). 
 Malacca. — 32 mudde = 1 coyang, - - = 90.81 
 
 Siam. — 40 sat = 1 scsti, 40 s. = 1 cohi, 10 c. = 1 co- 
 yang = 32 hectolitres of France, - - - = 90.81 
 Sumatra I. — 4 pakha = 1 culah, 2 c. = 1 koolah, 15 
 
 koolah = 1 tub, = 1.872 
 
 IONIAN ISLANDS. — Corfu, Paxos: 2 misura = 1 
 
 bacile, 4 b. = 1 moggio, - - - - = 4.777 
 
 Cephalonia : 8 misure = 4 bacile = 1 moggio, - = 5.6 
 Zante: 8 misure or 4 bacile = 1 moggio, - - = 5.116 
 
48 a FOREIGN DRY MEASURES SEDUCED 70 UNITED STATES. 
 
 Foreign. U. States. 
 
 Winchester 
 bushels. 
 
 Ithaca: 5 bacile =* 1 moggio, - - - -= 5. 
 
 ITALY. — Lombardy and Venice. — Government and 
 Customs Measure: 10 coppi = 1 pinta, 10 p. = 
 
 1 mina, 10 m. = 1 soma = 1 hectolitre of France, = 2.838 
 Special and local — 
 
 Venice : 4 quartaroli = 1 quarto, 4 q. = 1 stajo or 
 
 staro, 4 8. = 1 moggio, - - = 9.08 
 
 Naples. — 3 misura = 1 stopello, 4 s. = 1 mezetta, 2 m. 
 
 = 1 tomolo, 36 t, = 1 carro, - - - = 54.81 
 
 Sardinia. — Genoa: 12 gombetti — 1 ottaro or quarto, 
 
 8 quarto = 1 mina, - = 3.426 
 
 8 mine = 1 niondino, /or salt. 
 Nice: 4 motureau = 1 quartier, 4 q. = 1 stajo, 4 staji 
 
 = 1 sacco, - - - - - = 3.405 
 
 Turin : 20 cucchiari = 1 copello, 4 c. = 1 quartiere, 
 
 2 q. = 1 mina, 2 m. = 1 stajo, 3 s. = 1 6acco, = 3.263 
 States of the Church. — Ancona : 
 
 4 provenda = 1 coppa or lappa, 2 c. = 1 corba, = 2.03 
 Rome: 5£ quartucci or lg scorzi = 1 starello, 2 starelli 
 
 or 1£ staji = 1 quartarello, - - - = 1.044 
 
 4 quartarelli or 2 quarte = 1 rubbiatilla, 2 rubbia- 
 
 tille = 1 rubbio, - - = 8.356 
 
 4£ rubbi = 1 tonnellata {shipping) . 
 Tuscany. — Florence, Leghorn, Pisa : 
 
 8 bussole = 4 quartucci = 2 mezette = 1 metadella, 
 4 m. = 1 quarto, 4 q. or 2 mina = 1 stajo, 3 s. 
 = 1 sacco, 8 sacci = 1 maggio, - - - = 16.592 
 
 JAPAN. — 10 gantang = 1 ickoga, 100 ickoga = 1 
 
 icmagoga, 100 icmagoga = 1 managoga. 
 MALTA. — 1 salma (rasa), = 8.22 
 
 1 sidma (colina), - - - - = 9.56 
 
 MADEIRA I. — Standard same as Lisbon (Portugal). 
 MEXICO. — Same as Cadiz (Spain). 
 
 MOROCCO. — Mogadore: 1 mud, - - - =* 5.184 
 
 NORWAY. — Same as Denmark. 
 PORTUGAL. — Lisbon, St. Ubes, &c. : 
 
 16 quarto = 8 meio = 4 alqueire = 1 fanga, - = 1.534 
 
 15 boga = I majo, 4 m. = 1 lust, - - =* 92.087 
 
 27 fanga = 1 toneladft, for shipping. 
 
 1 l>:ilde, for coals, - - - - -= 12.69 
 
 1 fanga, " " ... = 21.167 
 
 Oporto : 1 fanga = 1.937 bus. 1 raze, for salt, = 1.25 
 
 PRUSSIA (legal since 1820) : 4 masschen == 1 metzo, 4 
 
FORJBHJN DRY MEASURES REDUCED TO UNITED STATES, a 49 
 
 Foreign. U. States. 
 
 Winchester 
 bushels. 
 
 metze = 1 viertel, 4 v. = 1 scheffel = 3072 cubic 
 Rhein zolle or 3353f cubic inches, U. S., - - = 1.559 
 
 12 scheffel = 1 malter or dromt, 2 in. = 1 wispel, = 37.431 
 
 3 wispel = 1 last 
 
 2 wispel = 1 last, for barley and oats. 
 RUSSIA (legal for the Empire) : 
 
 8 garnetz = 1 tschetwerik, 2 t. = 1 payak, - = 1.438 
 2 p. = 1 osmin, 2 o. = 1 tschetwerk, - - = 5.952 
 
 14 tschetwerk = 1 kuhl, 16 tschetwerk = 1 last. 
 Libau, Revel, Riga : 12 stof = 1 kulmet, 3 k. s= 1 lof, 
 24 1. = 1 tonne, 2 t. = 1 last. 
 SARDINIA I. — Cagliari, &c. : 4 imbuto = 1 carbula, 
 
 4 c. = 1 starello, 3 s. = 1 restiere or rasiera, = 4.166 
 SICILY I. — Palermo, Messina : 2 stari = 1 modello, 4 
 
 m. = 1 tomolo, 4 t. = 1 bisaccia, 4 b. = 1 salma, = 7.81 
 16 tomoli grosso = 1 sahna grosso, - - =9.72 
 
 SPAIN. — Alicant : 2 medio = 1 celemin, 4 c. = 1 bar- 
 
 cella, 12 b. = 1 cahiz, - - - - = 6.992 
 
 Barcelona : 4 picolin = 1 cortain, 12 c. = 1 quartera, 
 
 2£ q. = 1 carga, if c. = 1 salma, - = 8.191 
 
 Cadiz (Standard of Castile) : 2 medio = 1 celemin, 12 
 
 c. = 1 fanega, 12 f. = 1 cahiz, - - - <-» 19.189 
 
 4 cahiz = 1 last, =* 76.759 
 Corunna, Ferrol: 4 celemine = 1 ferrado, 3 f . = 1 
 
 fanega, 12 fanega = 1 cahiz, - - - =* 19.189 
 
 Gibraltar : Same as Cadiz. 
 Malaga : Same as Cadiz. 
 
 Santander : 144 celemin = 12 fanega = 1 cahiz - = 24.984 
 Valencia : 8 medio = 4 celemin = 1 barchilla, 12 bar- 
 
 chille = 1 cahiz, - - - - - = 5.758 
 
 SWEDEN. — Stockholm, &c. : 2 stop = 1 kanna, 11 k. 
 = 1 kappe, 4 kappe = 1 fjerding, 4 f . = 1 spann, 
 2 spann = 1 tunna, = 4.158 
 
 24 tunne = 1 last. 
 SWITZERLAND (legal, since. 1823, for the Cantons of 
 Aarau, Basle, Berne, Freiburg, Lucerne, Solothurn t 
 Vaud ; but not in general use) : 
 10 emine = 1 gelt or quarteron, 10 g. = 1 sac = 
 
 L/tj- hectolitres of France, - - - -= 3.831 
 
 Special and local — 
 Basle : 2 bacher = 1 kopflein, 8 k. = 1 sester, - = 0.97 
 
 4 sester = 1 sack, 2 s. = 1 vierzel, - - - = 7.756 
 
 Berne : 4 achterli or 2 immi = 1 massli, 2 m. = 1 
 
 mass, 12 mass = 1 mut, - - = 4.771 
 
 E 
 
50 a J OREIGN DRY MEASURES REDUCED TO UNITED STATES. 
 
 Foreign. U. States. 
 
 Winchester 
 bushels. 
 
 Geneva : 2 bichet = 1 coupe or sac, - - - — 2.203 
 
 Lausanne : 10 copet = 1 emine, 10 e. = 1 sac, - = 3.831 
 
 Neufchatel : 3 copet = 1 emine, 8 e. = 1 sac, - - = 3.459 
 
 3 sacks = 1 muid. 
 
 St. Gall : 4 massli = 1 vierling, 4 v. = 1 viertel, 4 
 
 viertel = 1 mutt, 2 m. = 1 malter, - = 4.688 
 
 Zurich : 16 massli or 4 vierlmg = 1 viertel, 4 v. = 1 
 
 mutt, 4 m. = 1 malter, - - - - = 9.333 
 
 1 mass, for salt, = 2.622 
 
 4 mass = 1 korb. 
 
 TRIPOLI (N. Africa) : 20 tiberi = 1 caffiso, - - = 1.15*4 
 
 4 orbah = 1 tomen, 3 J t. = 1 nusfiah, - = 1.0157 
 3 n. = 1 ueba. 
 
 TUNIS. — 12 zah or saha =- 1 quiba, 16 q. = 1 caffiso 
 
 = 18 wage, - - - - - = 14.954 
 
 TURKEY. — Constantinople : 4 kibz = 1 fortin, - = 3.764 
 
 Latakia, Aleppo : 1 garave, - - - -= 41.15 
 
 Smyrna: 4 kilo = 1 fortin, = 5.824 
 
 West Indies. 
 
 In the Islands of Antigua, the Bahamas, Barbadoes, Bar- 
 buda, Dominica, Grenada, Jamaica, Les Saints, 
 Montserrat, Nevis, St. Kitts\ St. Vincent, Tobago, 
 Tor tola, the Dry Measures are the same as those 
 of the United States. 
 
 In Deseade, Guadeloupe, Mariegalante, Martinique, St. 
 Lucia : 3 boisseau = 1 minot, 2 m. = 1 mine, 12 
 mines = 1 setier, 2 s. = 1 muid, - - = 53.153 
 
 This being the system of France before 1812. 
 
 In Bonaire, Curacoa, Saba, St. Eustatius, St. Martin: 
 Same as in Holland before 1820 : See Holland. 
 
 In Santa Cruz, St. John, St. Thomas : Same as Denmark. 
 
 In St. Bartholomew : Same as Swkdkx. 
 
 In Trinidad: Same as Castile (Spain). 
 
 Cuba I. — Same as Castile, generally. 
 
 Havana: 4 arrobas = 1 fanega, ... . = 3.114 
 
 Hayti I. — Aux Cayes, Cape Haytien, Port au Prince, 
 Port Platte, &c. : Same as France before 1812. 
 Savanna, St. Domingo, &c. : Same as Castile. 
 
 Porto Rico I. — Same as Castile (Spain). 
 
CUSTOM HOUSE ALLOWANCES ON DUTIABLE GOODS. a 51 
 
 CUSTOM HOUSE ALLOWANCES ON DUTIABLE GOODS. 
 
 Draft, or Tret, is an allowance of weight for supposed waste on 
 articles paying duty by the pound. It is deducted from the actual 
 gross weight of the article, and is established as follows : — 
 
 Cv/t. Cwt. Draft. 
 
 . On 1 (112 lbs.) lib. 
 
 Above 1 and under . . 2, . 2 " 
 
 On 2 " " . . . 3, . 3 " 
 " 3 " " . . . 10, . 4 " 
 
 10 " " . . . 18, . 7 " 
 " 18 " upwards, 9 " 
 
 Tare is the weight — actual or assumed by law — of the cask, 
 sack, &c, in which the article paying duty is contained. It is de- 
 ducted from the actual gross weight less the draft. The remainder 
 is the net weight on which the duty is assessed, and the weight at 
 which the heavy purchasers receive the goods. 
 
 Leakage is an allowance on the gauge of molasses, oils, wines, and 
 ail liquids in casks. It is established at 2 per cent., and is deducted 
 from the actual gross gauge, less the real wants of the cask. 
 
 Breakage is an allowance of 10 per cent, on ale, beer and porter, in 
 bottles, and 5 per cent, on all other liquors in bottles ; or, if the 
 importer prefer, the duties are assessed by actual count, he so electing 
 at the time of making the entry. Common sized bottles are computed 
 to contain 1\ gallons per dozen. 
 
 On bottles in which wine is imported there is assessed a duty of 
 two dollars per gross, in addition to the duty on the wine. 
 
 The following articles, whether intended for sale or otherwise, are 
 admitted into the United States, from foreign ports, free of duty ; but 
 nevertheless must pass through the Custom House in manner the 
 same as goods on which a duty is assessed. • 
 
 Animals imported for breed. 
 
 Antiquities. 
 
 Bulbs or bulbous roots. 
 
 Bullion, silver or gold. 
 
 Canary seed. 
 
 Cardamon seed. 
 
 Coins, gold, silver, or copper. 
 
 Copper sheathing, 14 by 48 inch, 
 
 and from 14 oz. to 34 oz. per 
 
 square foot. 
 Copper ore. 
 Cotton. 
 
 Cummin seed. 
 Fossils. 
 Gold dust. 
 Guano. 
 
 Gypsum, unground. 
 Oakum and old junk. 
 Oysters. 
 
 Platina, unmanufactured. 
 Silver, old, fit only for re-manu- 
 facturing. 
 Vanilla, plant of. 
 
52 a CT7ST0M HOUSE ALLOWANCES ON DUTIABLE GOODS, 
 
 TABLE OF ESTABLISHED TARES. 
 
 (a=by custom; c=Iegal. 
 Almonds, in bags, 
 Alum, casks, 
 Beef, jerked, drums, 
 " hhds., 
 Bristles, Archangel, 
 
 " Cronstadt, 
 
 Camphor, crude, tubs, 
 Candles, boxes, 
 
 " chests, 160 lbs. 
 
 Candy, sugar, baskets, 
 
 " " boxes, 
 
 Cheese, hps. or baskets, 
 
 " boxes, 
 Chocolate, boxes, 
 Cinnamon, mats, 
 
 " chests, 
 
 Cloves, casks, 
 Cocoa, bags, {actual 2) 
 
 " casks, 
 
 " zeioons, 
 Coffee, E.I. , grass bags, 
 
 " " bales, 
 
 " " casks, 
 
 " W.I.,bags, 
 Copperas, casks, 
 Cordage, lines, bales, 
 Cordage, mats, 
 Corks, bales, light, 
 
 11 heavy, 
 Cotton, bales, 
 
 " zeroons, 
 Currants, casks, 
 Figs, boxes, 60 lbs., 
 
 " £ " 30 " 
 
 t< li 15 m 
 
 " drums, 
 
 " frails, 75 lbs., 
 Glue, Russia, boxes, 
 Indigo, bags or mats, 
 
 " barrels, 
 
 Per 
 
 lb*. 
 
 
 cent. 
 
 per 
 
 
 a 4 
 
 Pkg- 
 
 Indigo, casks, 
 
 alO 
 
 
 " zeroons. 
 
 
 70 
 
 Looking-glasses, Fr., 
 
 
 112 
 
 Mace, kegs, 
 
 all 
 
 
 Nails, casks, 
 
 al2 
 
 
 Nutmegs, " 
 
 Ochre, French, casks, 
 
 a35 
 
 
 c 8 
 
 
 Pepper, bales, 
 
 «20 
 
 
 " bags, 
 
 a 5 
 
 
 M casks, 
 
 clO 
 
 
 Pimento, bales, 
 
 «10 
 
 
 " bags, 
 
 «20 
 
 
 " casks, 
 
 clO 
 
 
 Prunes, boxes, 
 
 alO 
 
 
 Raisins, Malaga, boxes, 
 
 
 16 
 
 " " casks, 
 
 al2 
 
 
 jars, 
 
 c I 
 
 
 M Smyrna, casks, 
 
 clO 
 
 
 Salts, glauber, casks, 
 
 a 8 
 
 
 Shot, casks, 
 
 
 2 
 
 Soap, French, boxes. 
 
 c 3 
 
 
 " boxes, (a more) 
 
 cl2 
 
 
 Steel, bundles, 
 
 c 2 
 
 
 " cases, 
 
 alO 
 
 
 Sugar, bags or mats, 
 
 c 3 
 
 
 11 boxes, 
 
 a\\ 
 
 
 " casks, 
 
 
 5 
 
 " canisters, 
 
 «20 
 
 
 " Java, willow > 
 baskets, J 
 
 c 2 
 
 
 c 6 
 
 
 Tallow, casks, 
 
 «12 
 
 
 " zeroons, 
 
 alO 
 a 6 
 
 
 Tea, caddies, K ctaa ,< 
 li «"»*». ) weight.} 
 
 alO 
 
 
 Twine, bales, 
 
 a 4 
 
 
 11 casks, 
 
 al5 
 
 
 Wool, Germany, bale, 
 
 c 3 
 
 
 " S. Amer., bale, 
 
 cl2 
 
 
 " Smyrna, " 
 
 «15 
 
 
 

YB 18482 
 
 284302 
 
 UNIVERSITY OF CALIFORNIA LIBRARY