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Digitized by tine Internet Arciiive 
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 littp://www.arcliive.org/details/foundersmanualprOOpayn 
 
THE 
 
 FOUNDER'S MANUAL 
 
 A PRESENTATION OF MODERN 
 FOUNDRY OPERATIONS 
 
 FOR THE USE OF 
 
 lOUNDRYMEN, FOREMEN, STUDENTS 
 AND OTHERS 
 
 BY 
 
 DAVID W. PAYNE 
 
 EDITOR OF "steam" 
 
 245 ILLUSTRATIONS 
 
 NEW YORK 
 
 D. VAN NOSTRAND COMPANY 
 
 25 Park Place 
 
 1917 
 
t6 
 
 ■Tj 
 
 30 
 
 Copyright, 191 7, by 
 D. VAN NOSTRAND COMPANY 
 
 in- It 
 
 b 
 
 APR -5 1917 
 
 PRICE, $Jr^O-()....- ™l^ 
 
 ©GI.A460168 
 
PREFACE 
 
 While there is Kttle a foundryman needs to know 
 which has not been fully treated by competent authori- 
 ties, there is not, so far as I am aware, any summary of 
 this great mass of publications. 
 
 In a foundry experience covering many years, I have 
 frequently spent hours at a time in searching for special 
 information. Believing, therefore, that a compilation of 
 this matter, with authoritative instruction for the solu- 
 tion of the many problems which are continually pre- 
 sented in the foundry, all properly arranged for ready 
 reference, would receive a favorable reception, an attempt 
 has been made to meet this need by the production of 
 this book. 
 
 The material for the Manual has been drawn from 
 every available source. The proceedings of the American 
 Foundrymen's Association have furnished no end of 
 information. The publications of Professors Turner, 
 Porter, Reis, Dr. Moldenke, Messrs. Keep, Longmuir, 
 Outerbridge, West and others have been most carefully 
 searched. Much has been taken from '' The Foundry, '^ 
 '' Castings " and '' Iron Age." A great many of the 
 " Foundry " records are given in full. 
 
 Possibly, in some cases, special credit for extracts 
 has not been accorded; for such omissions indulgence 
 is asked, as there has been no intentional neglect or 
 lack of courtesy. 
 
 iii 
 
iv Preface 
 
 In the selection of the material for the book, proper 
 consideration has been taken of beginners and others 
 who may have not gotten very far in their acquisition 
 of foundry information. For such men, it is also hoped 
 the book will be of good service. 
 
 As regards the price Ksts and discounts which are 
 given in connection with many foundry supplies, it 
 should be stated that these are not quoted as current 
 prices. They are offered simply as furnishing a guide 
 to close approximation of costs. 
 
 The matter for the preHminary portion of the book 
 relating to elementary Mathematics, Mechanics, etc., 
 has been taken in large part from such authorities as 
 Rankine, Bartlett, Wentworth, Trau twine, Kent, Jones 
 and Laughlin, Carnegie Steel Co., and the Encyclopedia 
 Britannica. 
 
 D. W. P. 
 
 New York, Jan., 1917. 
 
CONTENTS 
 
 CHAPTER I 
 
 Elementary Mathematics i 
 
 Ratio and Proportion, i. Root of Numbers, 3. Percentage, 
 5. Algebra, 7. Equations, 11. Plane Geometry, 15. The 
 Parabola, 22. The Hyperbola, 23. Properties of Plane Fig- 
 ures, 24. Mensuration, Plane Surfaces, 26. Solids, 30. 
 
 CHAPTER II 
 
 Weights and Measures 35 
 
 Commercial Weights and Measures, 36. Metric Weights and 
 Measures, 40. Measures of Work, Power and Duty, 45. 
 Mathematical Tables, 46. 
 
 CHAPTER III 
 
 Natural Sines, Tangents, Etc 107 
 
 Solution of the Right-angled Triangle, 109. Solution of Ob- 
 lique-angled Triangles, 109. Tables of Sines, Tangents and 
 Secants, no. Approximate Measurement of Angles, 115. 
 Tapers per foot and Corresponding Angles, 117. 
 
 CHAPTER IV 
 
 Materials 
 
 Wire and Sheet Metal Gauges, 119. Weights of Iron and 
 Steel, 122. Cold-rolled Steel Shafting, 140. Galvanized and 
 Corrugated Sheet Iron, 141. Sheet Tin, 142. Copper and 
 Brass, 143. Metal Fillets, 145. Iron Wire, 146. Nails and 
 Tacks, 148. Threads, 149. Bolts, Nuts and Washers, 150. 
 Set Screws, 160. Turnbuckles, 162. Cotters, 164. Thumb- 
 screws, 165. Rivets, 166. Iron Pipe, 167. Tin and Zinc, 
 169. Lead Pipe, 171. Chains and Cables, 173. Sprocket- 
 wheels, 176. Modulus of Elasticity, 181. Deflections, 184. 
 Modulus of Rupture, 185. Moment of Inertia, 187. Strength 
 of Beams, 188. 
 
 V 
 
 119 
 
vi Contents 
 
 Page 
 CHAPTER V 
 
 Mechanics 191 
 
 Acceleration of Falling Bodies, I'gi. Center of Gravity, 194. 
 Radius of Gyration, 197. Specific Gravities, 108. Physical 
 Constants, 202. Expansion of Solids, 205. Measurement 
 of Heat, 207. Radiation of Heat, 208. Equivalent Tem- 
 peratures, 211. Strength of Materials, 213. Properties of 
 Air, 215. Pressure of Water, 219. Electrical and Mechanical 
 Units, 220. 
 
 CHAPTER VI 
 
 Alloys 222 
 
 Alloys of Copper, Tin and Zinc, 222. Aluminum bronze, 226. 
 Bearing Metals, 226. 
 
 Belting 227 
 
 Formulas for Width of Belts, 228. Speed of Belts, 229. Rules 
 for Speeds and Diameters of Pulleys, 231. Formulas for Cast 
 Iron Fittings, 232. 
 
 CHAPTER VII 
 
 Useful Information 234 
 
 Shrinkage of Castings, 234. Window Glass, 236. Fire Clays, 
 236. Weight of Metals, 239. Iron Ores, 240. 
 
 CHAPTER VIII 
 
 Iron 241 
 
 Physical Properties of Iron, 241. Grading Pig Iron, 242. 
 Standard Specifications for Pig Iron, 246. Machine-cast Pig 
 Iron, 248. Charcoal Iron, 250. Grading Scrap Iron, 250. 
 
 CHAPTER IX 
 
 Chemical Constituents of Cast Iron 252 
 
 Influence of Carbon, 252. Loss or Gain of Carbon in Re- 
 melting, 254. Influence of Silicon^ 256. Influence of Sulphur, 
 260. Influence of Phosphorus, 263. Influence of Manganese, 
 265. Aluminum, 266. Nickel, 267. Titanium, 267. Vana- 
 dium, 268. Thermit, 270. Oxygen, 270. Nitrogen, 271. 
 
 CHAPTER X 
 
 Mixing Iron 275 
 
 Mixing by Fracture, 273. Mixing Iron by Analysis, 274. 
 Castings for Agricultural Machinery, Cylinders and Fly- 
 wheels, 277. Castings for Chills, Motor Frames and Gas En- 
 
Contents vii 
 
 Page 
 gines, 278. Castings for Gears, Hydraulic Machinery and 
 Locomotives, 280. Castings for Pulleys, Radiators and Heat- 
 ers, 284. Castings for Weaving, Woodworking Machinery, 
 etc., 287. 
 
 CHAPTER XI 
 
 Steel Scrap in Mixtures of Cast Iron 290 
 
 Recovering and Melting Shot Iron, 291. Burnt Iron, 293. 
 Melting Borings and Turnings, 293. 
 
 CHAPTER XII , 
 
 Test Bars 294 
 
 Report of Committee on Test Bars of American Foundry- 
 man's Association, 294. Proposed Specifications for Gray 
 Iron, 296. Patterns for Test Bars of Cast Iron, 297. Erratic 
 Results, 298. Table of Moduli of Rupture, 299. Comparison 
 of Test Bars, 302. Casting Defects, 304. Circular Test Bars, 
 304. Effect of Structure of Cast Iron Upon its Physical Prop- 
 erties, 306. Mechanical Tests, 307. Chemical Analysis, 308. 
 Chilled and Unchilled Bars, 310. Forms of Combination of 
 Iron and Carbon, 313. 
 
 CHAPTER XIII 
 
 Chemical Analyses 315 
 
 Strength, 315. Elastic Properties, 322. Hardness, 324. 
 Grain Structure, 329. Shrinkage, 329. Fusibility, 332. 
 Fluidity, 334. Resistance to Heat, 335. Electrical Proper- 
 ties, 338. Resistance to Corrosion, 340. Resistance to Wear, 
 •342. Coefficient of Friction, 342. Casting Properties, 343. 
 Micro-structure of Cast Iron, 345. 
 
 CHAPTER XIV 
 
 Standard Specifications for Cast Iron Car Wheels 350 
 
 Chemical Properties, 350. Drop Tests, 350. Marking, 351. 
 Measures, 351. Finish, 351. Material and Chili, 351. In- 
 spection and Shipping, 352. Retaping, 353. Thermal Test, 
 353. Storing and Shipping, 354. Rejections, 354. 
 
 Standard Specifications for Locomotive Cylinders 355 
 
 Process of Manufacture, 355. Chemical Properties, 355. 
 Physical Properties, 355. Test Pieces, 355. Character of 
 Castings, 355. Inspector, 355. 
 
vm Contents 
 
 Page 
 
 Standard Specifications for Cast Iron Pipe 356 
 
 Allowable Variations, 356. Defective Spigots, 357. Special 
 Castings, 357. Tables of General Dimensions, 358. Marking, 
 360. Quality of Iron, 360. Tests, 361. Cleaning and Coat- 
 ing, 361. Contractor, Engineer, Inspector, 362. Tables of 
 Weight of Pipe, 364. 
 
 CHAPTER XV 
 
 Mechanical Analysis 371 
 
 Shrinkage Chart, 372. Keep's Strength Table, 375. Stand- 
 ard Methods for Determining the Constituents of Cast Iron, 
 
 377- 
 
 CHAPTER XVI 
 
 Malleable Cast Iron 382 
 
 Black Heart, 382. Ordinary or Reaumur Malleable Iron, 385. 
 Temperature Curve for Annealing Oven, 386. Analysis Be- 
 fore and After Annealing, 387. American Practice, 389. 
 . Specifications, 392. Comparison of Tests, 392. 
 
 CHAPTER XVII 
 
 Steel Castings in the Foundry . 1 394 
 
 Normal Steels, 396. Bessemer Process, 396. The Baby Con- 
 verter, 397. Annealing, 400. Tropenas Process, 401. Chem- 
 istry in the Process, 403. Converter Linings, 404. Standard 
 Specifications, 409. Open Hearth Methods, 411. Compara- 
 tive Cost of Steel Castings, 417. Basic Open Hearth, 418. 
 Acid Open Hearth, 419. Converter, 420. Converter with 
 Large Waste, 421. Crucible Castings, 423. Electric Fur- 
 nace, 424. 
 
 CHAPTER XVIII 
 
 Foundry Fuels 425 
 
 Anthracite Coal, 425. Coke, 425. By-product Coke, 426. 
 Effect of Atmospheric Moisture Upon Coke, 427. Specifica- 
 tions for Foundry Coke, 428. Fluxes, 429. Comparison of 
 Slags, 432. Fire Brick and Fire Clay, 434. Fire Sand, 435. 
 Magnesite, 436. Bauxite, 436. 
 
 CHAPTER XIX 
 
 The Cupola 437 
 
 The Lining, 437. Tuyeres, 439. The Breast, 440. Sand 
 Bottom, 441. Zones of Cupola, 442. Chemical Reaction in 
 
Contents ix 
 
 Page 
 Cupola, 443. Wind box, 445. The Blast, 446. Sturtevant 
 Blowers, 448. Buffalo Blowers, 449. Root Blowers, 449. 
 Diameter of Blast Pipe, 450. Dimensions of Cupolas, 451. 
 Charging and Melting, 452. The Charging Floor, 453. Melt- 
 ing Losses, 454. Melting Ratio, 461. Appliances About 
 Cupola, 462. Ladles, 462. Tapping Bar, 463. Bod Stick, 
 463. Capacities of Ladles, 464. Applying Metalloids in La- 
 dles, 465. Cranes, 466. Spill Bed, 466. Gagger Moulds, 467. 
 
 CHAPTER XX 
 
 Moulding Sand 468 
 
 Bonding Power, 468. Permeability and Porosity, 468. Re- 
 fractoriness, 469. Durability, 469. Texture, 469. Grades, 
 470. Sandfor Brass, 472. Testing Sand, 473. For Dry Sand 
 Moulding, 477. Skin Drying, 469. Core Sand, 479. Core 
 Mixtures, 480. Dry Binders, 481. Parting Sand, 486. 
 Facings, 486. 
 
 CHAPTER XXI 
 
 The Core Room and Appurtenances 492 
 
 Core Oven Carriages, 496. Mixing Machines, 497. Sand 
 Conveyors, 497. Rod Straighteners, 497. Wire Cutter, 497. 
 Sand Driers, 498. Core Plates, 498. Core Machines, 499. 
 Cranes and Hoists, 499. 
 
 CHAPTER XXII 
 
 The Moulding Room 501 
 
 Cranes, 502. Hooks, Slings and Chains, 502. Lifting Beams, 
 503. Safe Loads, 504. Binder Bars, 505. Clamps, 506. 
 Flasks, 506. Iron Flasks, 510. Sterling Steel Flasks, 515. ^ 
 Snap Flasks, 517. Slip Boxes, 519. Pins, Plates and Hinges, 
 519. Sweeps, 522. Anchors, Gaggers and Soldiers, 523. 
 Sprues, Risers and Gates, 524. Top Pouring Gates, 526. 
 Whirl Gates, 527. Skim Gates, 527. Horn Gates,' 527. 
 Strainers and Spindles, 528. Weights, 528. Chaplets, 528. 
 Liquid Pressure on Moulds, 529. Nails, 536. Sprue Cutters, 
 537- 
 
 CHAPTER XXIII 
 
 Moulding Machines 538 
 
 Jigs, 540. Flasks, 547. Moulding Operations, 549. 
 
X Contents 
 
 Page 
 CHAPTER XXIV 
 
 Continuous Melting 551 
 
 Multiple Moulds, 555. Permanent Moulds, 558. Centrif- 
 ugal Castings, 561. Castings Under Pressure, 562. Direct 
 Casting, 562. Carpenter Shop and Tool Room, 562. The 
 Cleaning Room, 563. Tumbling Mills, 563. Chipping, 566. 
 Grinding, 566. Sand Blast, 566. Pickling, 567. 
 
 CHAPTER XXV 
 
 Determination of Weight of Castings ... , 569 
 
 By Weight of Patterns, 569. Weight of Pattern Lumber, 569. 
 Formulas for Finding Weight of Castings, 570. Formulas 
 for Weight on Cope, 575. 
 
 CHAPTER XXVI 
 
 Water, Lighting, Heating and Ventilation 577 
 
 Water Supply, 577. Lighting, 578. Heating and Ventila- 
 tion, 579. 
 
 CHAPTER XXVII 
 
 Foundry Accounts 587 
 
 Foundry Requisition, 588. Pattern Card, 589. Pig Iron 
 Card, 590. Core Card, 591. Heat Book, 592. Cleaning 
 Room Report, 597. Weekly Foundry Report, 600. Monthly 
 Expenditure of Supplies, 601. Comparison of Accounts, 605. 
 Transmission of Orders, 611. American Foimdrymen's As- 
 sociation Methods, 612. Cost of Metal, 617. Moulding, 619. 
 Cleaning and Tumbling, 620. Pickling, 621. Sand Blast- 
 ing, 622. Core Making, 623. A Successful Foundry Cost 
 System, 625. Castings Returned, 629. 
 
 CHAPTER XXVIII 
 
 Pig Iron Directory 633 
 
 Classification and Grades of Foundry Iron, 633. Coke and 
 Anthracite Irons, 635. Charcoal Irons, 655. 
 
 Authorities 66c 
 
 Index 663 
 
Most readers of this book will, without doubt, be familiar with the 
 ordinary mathematical processes; to them, such brief references as may- 
 appear, will, perhaps, seem superfluous. There may be, however, those 
 who, from disuse or otherwise, are not so circumstanced. For their 
 convenience such information will be given as may facilitate the inter- 
 pretation of the formulas and calculations herein. 
 
 SIGNS AND ABBREVIATIONS 
 
 A prime mark ' above a nimiber 
 means minutes or linear feet; 
 as lo' means ten minutes or ten 
 linear feet. 
 
 Two prime marks " likewise mean 
 seconds; or linear inches; as lo" 
 indicates lo seconds or lo linear 
 inches. 
 
 The sign D means square, as D' 
 square foot, D " square inch. 
 
 The sign O means round or cir- 
 cular, as O" circvilar inch. 
 
 The sign / means an angle. 
 
 The sign L means a right angle. 
 
 The sign -L means a perpendicular. 
 
 The sign x, called Pi, means the 
 ratio of the circumference of a 
 circle to the diameter, and is 
 equal to 3. 141 59. 
 
 The sign g means acceleration due 
 to gravity and equals 32.16 foot 
 pounds per second. 
 
 The sign E indicates the coefl&cient 
 
 of elasticity. 
 The sign / indicates the coefl&cient 
 
 of friction. 
 The sign M indicates modulus of 
 
 rupture. 
 The sign log indicates the common 
 
 logarithm. 
 The sign log e ) hyperbolic 
 or log hyp. \ logarithm. 
 R.p.m. revolutions per minute. 
 H.P. horse power. 
 K.W. Hr. Kilowatt hours. 
 A.W.G. American wire gauge. 
 B.W.G. Birmingham wire gauge. 
 A.S.M.E. American Society of 
 
 Mechanical Engineers. 
 A.F.A. American Foundrymen's 
 
 Association. 
 B.F. A. Birmingham Foundry- 
 men's Association. 
 I.S.I. Iron and Steel Institute. 
 
FOUNDERS MANUAL 
 
 ELEMENTARY MATHEMATICS 
 
 CHAPTER I 
 SECTION I 
 ARITHMETIC 
 
 It is deemed unnecessary to present anything under this branch of 
 mathematics, except Ratio and Proportion, Square and Cube Roots, 
 Alligation and Percentage. These operations are applied so frequently 
 in the foundry that, it is believed, a simple explanation of them will not 
 be out of place. 
 
 Ratio and Proportion 
 
 The ratio of two numbers is the relation which the first bears to the 
 second and is equivalent to a fraction obtained by dividing the first 
 number by the second. 
 
 Thus: S : 7 = f or 7:5 = 1- 
 
 When the first of four numbers is the same fraction of the second, as 
 the third is of the fourth, the first has the same ratio to the second as the 
 third has to the fourth, and the four numbers are in proportion. Pro- 
 portion, therefore, is the equality of two ratios. 
 
 Thus: 
 
 t = T3 = I- 
 
 The proportion is expressed, 4 : 6 :: lo : 15, and is read, 4 is to 6 as 10 
 • is to 15. The first and fourth terms are called the extremes; the second 
 and third the means. 
 
 The product of the extremes is equal to the product of the means; 
 thus in the above proportion 4 X 15 = 6 X 10 = 60. Hence where 
 three terms of the proportion are known the fourth can be found. 
 
2 Arithmetic 
 
 Thus: Find the number to which lo bears the same ratio as 4 does to 6. 
 4 : 6 :: 10 : required number. 
 
 Required number equals -\°- =15. 
 
 Where one extreme and both means are known, to find the other 
 extreme, divide the product of the means by the known extreme. 
 
 Where both extremes and one mean are known, to find the other mean, 
 divide the product of the extremes by the known mean. 
 
 For the purpose of illustrating these rules replace the figures in a 
 proportion, by the letters A, B, C, D, and write A : B :: C : D; then, 
 
 AD-BC,^--^,A-—,D--j-,B-—,C.-—. 
 
 To state the terms ot a simple proportion where three are given; 
 place that as the third term which is of the same kind as the required 
 term; then consider whether the required term should be greater or less 
 than the third term; if greater, make the greater of the two remaining 
 terms the second and the other the first term. But if the required term 
 should be less than the third term, place the smaller of the first two as 
 the second term and the greater as the first. 
 
 Thus: What is the price, per net ton, of pig iron sold at $17.50 gross 
 ton? 
 
 As the price is required, $17.50 becomes the third term. Since the 
 net price is less than the gross, 2000 is the second term and 2240 the first. 
 The proportion is then written: 
 
 2240 : 2000 :: $17.50 : answer. 
 
 2000 X $17.50 
 2240 
 
 $15.62 = required price. 
 
 Therefore, the net 
 price is equal to the gross multiplied by 0.892 +; or $17.50 X .892 = 
 $15.62; or the net price being known the gross is equal to the net multi- 
 
 Compound Proportion 
 
 Where the ratio of two quantities depends upon a combination of 
 other ratios, the proportion becomes a compound proportion. In this 
 as in simple proportion, there is but one third term, and it is of the same 
 kind as the required term; there may be two or more first and second 
 terms. Set down the third term as in simple proportion; consider each 
 pair of terms of the same kind separately and as terms of a simple pro- 
 portion, and arrange them in the same manner, making the greater of 
 
Roots of Numbers 3 
 
 the pair the second term, if the answer considered with reference to this 
 pair alone should be greater than the tishd term; or the reverse if it 
 should be less. 
 
 Set down the terms under each other in their order of first and second 
 terms. Multiply the product of all the second terms by the third term 
 and divide this product by that of all the first terms. 
 
 Example. — If 36 men working 10 hours per day perform | of a piece 
 of work in 17 days, how long must 25 men work daily to complete the 
 work in 16 days? 
 
 The length of the day will be greater the fewer the men, and the fewer 
 the days are; and less, the less the work is; hence, the above problem 
 is stated as follows: 
 
 Men 25 : 36 :: 10 
 
 Days 16 : 17 :: 
 
 Fifths of work 3 : 2 
 
 36 X 17 X 2 X 10 
 25 X 16 X 3 
 
 5J. = 10.2 hours per day. 
 
 Roots of Numbers 
 
 To Extract the Square Root of a Given Number 
 
 Point off the nuniber into periods of two figures each, beginning with 
 units; if there are decimals, begin at the decimal point, separating the 
 whole number to the left and the decimal to the right into such periods, 
 supplying as many ciphers in groups of two, as may be desired. 
 
 Find the greatest number whose square is less than the first left hand 
 period and place this to the right of the given nimiber as the first figure 
 of the root. Subtract its square from the first left hand period and to 
 the remainder annex the second period for a dividend. 
 
 Place before this as a partial divisor, double the root figure just found. 
 Find how many times the dividend, exclusive of its right hand figure, 
 contains the divisor, and place the quotient as the second figure of the 
 root, and also at the right of the partial divisor. 
 
 Multiply the divisor thus completed, by the second root figure and 
 subtract the product from the dividend. To this remainder annex the 
 next period for a new dividend, and double the two root figures for a 
 new partial divisor. Proceed as before until all the periods have been 
 brought down. 
 
Arithmetic 
 
 Example. — Extract the square root of 7840.2752 -f. 
 
 78'40.27'52/88.S453 
 64 
 
 168)1440 
 1344 
 
 1765)9627 
 8825 
 
 17704)80252 
 70816 
 
 77085)943600 
 885425 
 
 1770903)5817500 
 5312709 
 
 To Extract the Square Root of a Fraction 
 Find the roots of the numerator and denominator separately; or 
 reduce to a decimal and take its root. 
 
 Example.— y ^ = — ^ = ^ ; or ^ = 0.5625, V0.5625 = 0.75. 
 
 To Extract the Cube Root of a Number 
 Beginning at the right, point off the number into periods of three 
 figures each. If there are decimals, begin at the decimal point, separate 
 the whole number to the left, and the decimal at the right into such 
 periods; find the greatest cube contained in the left-hand period, and 
 write its root as the first figure of the root required. 
 
 Subtract the cube of the first root figure from the left-hand period, 
 and to the remainder annex the next period for a dividend. Then 
 multiply the square of the first figure of the root by 300 and use the prod- 
 uct as a trial divisor; write the quotient as the second root figure. 
 Complete the trial divisor by adding to it 30 times the product of the 
 first root figure by the second, and the square of the second; multiply 
 the completed divisor by the second root figure and subtract the product 
 from the dividend. To the remainder annex the next period and proceed 
 as before, to find the third figure of the root, i.e., square the first two 
 figures of the root and multiply by 300 for a trial divisor. To this add 
 30 times the product of the first two root figures by the third, and the 
 square of the third for the completed divisor, etc. 
 
 The cube root will always contain as many figures as there are periods 
 in the given number. 
 
Percentage 
 
 Example. — Extract the cube root of 7^-402^ 752 
 
 78'402'752/428. 
 64 
 
 4^ X 300 = 4800 14402 
 4 X 2 X 30 = 240 
 4 
 
 5044 10088 
 
 422 X 300 = 529200 4314752 
 
 42 X 8 X 30 = 10080 
 82 = 64 
 
 539344 4314752 
 
 Alligation 
 
 Alligation is the process of determining the value of a mixture of 
 different substances, when the quantity and value of each substance 
 is known. 
 
 Rule. — Take the sum of all the products of the quantity of each 
 substance by its respective price, and divide it by the total quantity; 
 the result is the value of one unit of the mixture. 
 
 Example. — What is the value per ton of a mixture containing 500 lbs. 
 of pig iron at $18.00 per ton, 275 lbs. at $16.50 and 800 lbs. of scrap at 
 $14.00? 
 
 500 X 18 = 9000 
 
 275 X 16.5 = 4537-50 
 
 800 X 14 = 11200.00 
 
 i57S 24737-50 
 
 — = $15,706 per ton. 
 
 1575 
 
 Percentage 
 Per cent means so many parts of 100, and is expressed decimally 
 as three per cent .03, meaning jf q; one-fourth of one per cent .0025 = 
 ToVoo- 
 
 Percentage covers the operations of finding the part of a given 
 number at a given rate per cent; as 6 per cent of 2750, 2750 X .06 = 
 165.00; of finding what per cent one number is of another as:. What 
 per cent of 780 is 39? 
 
 39 ^ 780 = .05 per cent; 
 of ascertaining a number when an amount is given, which is a given 
 per cent of that number; as 62.5 is .04 per cent of what nimiber? 
 62.5 -^ .04 = 1562.5. 
 
Arithmetic 
 
 
 Decimal Equivalents of Parts of One Inch 
 
 
 1-64 
 
 .015625 
 
 17-64 
 
 .265625 
 
 33-64 
 
 .515625 
 
 49-64 
 
 .576625 
 
 1-32 
 
 .031250 
 
 9-32 
 
 .281250 
 
 17-32 
 
 .531250 
 
 25-32 
 
 .781250 
 
 3-64 
 
 .046875 
 
 19-64 
 
 .296875 
 
 35-64 
 
 .546875 
 
 51-64 
 
 .796875 
 
 I-I6 
 
 .062500 
 
 S-16 
 
 .312500 
 
 9-16 
 
 .562500 
 
 13-16 
 
 .812500 
 
 5-64 
 
 .078125 
 
 21-64 
 
 .328125 
 
 37-64 
 
 .578125 
 
 53-64 
 
 .828125 
 
 3-32 
 
 .093750 
 
 11-32 
 
 .343750 
 
 19-32 
 
 .593750 
 
 27-32 
 
 .843750 
 
 7-64 
 
 .109375 
 
 23-64 
 
 .359375 
 
 39-64 
 
 .609375 
 
 55-64 
 
 .859375 
 
 1-8 
 
 .125000 
 
 3-8 
 
 .375000 
 
 5-8 
 
 . 625000 
 
 7-8 
 
 .875000 
 
 ^ 9-64 
 
 .140625 
 
 25-64 
 
 .390625 
 
 41-^4 
 
 .640625 
 
 57-64 
 
 .890625 
 
 5-32 
 
 . 156250 
 
 13-32 
 
 .406250 
 
 21-32 
 
 .656250 
 
 29-32 
 
 .906250 
 
 11-64 
 
 .171875 
 
 27-64 
 
 .421875 
 
 43-64 
 
 .671875 
 
 59-64 
 
 .921875 
 
 3-16 
 
 . 187500 
 
 7-16 
 
 .437500 
 
 11-16 
 
 .687500 
 
 IS-16 
 
 .937500. 
 
 13-64 
 
 .203125 
 
 29-64 
 
 .453125 
 
 45-64 
 
 .703125 
 
 61-64 
 
 .953125 
 
 7-32 
 
 .218750 
 
 15-32 
 
 .468750 
 
 23-32 
 
 .718750 
 
 31-32 
 
 .968750 
 
 15-64 
 
 .234375 
 
 31-64 
 
 .484375 
 
 47-64 
 
 .734375 
 
 63-64 
 
 .984375 
 
 1-4 
 
 .250000 
 
 1-2 
 
 .500000 
 
 3-4 
 
 .750000 
 
 I 
 
 I 
 
 
 
 
 Inches to 
 
 Decimals 
 
 OF A 
 
 Foot 
 
 
 
 
 
 
 
 
 I 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 10 
 
 II 
 
 
 
 .0833 
 
 .1667 
 
 .2500 
 
 .3333 
 
 .4167 
 
 .5000 
 
 •5833 
 
 .6667 
 
 • 7500 
 
 • 8333 
 
 .9167 
 
 3^1 
 
 .0026 
 
 .0859 
 
 .1693 
 
 .2526 
 
 .3359 
 
 .4193 
 
 .5026 
 
 •5859 
 
 • 6693 
 
 .7526 
 
 .8359 
 
 .9193 
 
 X^B 
 
 .0052 
 
 .0885 
 
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Algebra 
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 SECTION II 
 ALGEBRA 
 
 In algebra quantities of every kind are denoted by letters of the 
 alphabet. . 
 
 The first letters of the alphabet are used to denote known quantities, 
 and the last letters unknown quantities. 
 
 The sign + (plus) denotes that the quantity before which it is placed 
 is to be added to some other quantity. Thus: a + b denotes the sum 
 of a and b. 
 
 The sign — (minus) denotes that the quantity before which it is 
 placed is to be subtracted from some other quantity. Thus: a — b 
 denotes that b is to be subtracted from a. 
 
 When no sign is prefixed to a quantity, + is always understood. 
 
 Quantities are said to have like or unlike signs, according as their 
 signs are like or unlike. 
 
8 Algebra 
 
 A quantity which consists of one term is said to be simple; but if it 
 consists of several terms connected by the signs + or — , it is said to be 
 compound. Thus: a or — b are simple quantities; but — a — & is a 
 compound quantity. 
 
 Addition of Like Quantities 
 
 Add together the coefi&cients of the quantities having like signs, and 
 subtract the negative sum from the positive. Thus: Add 7 a -\- 2 Oy 
 2, a — a, and 6 a — 4 a. 
 
 y a — a 
 
 2 a — 4a 
 
 3^ 
 6 a 
 
 18 a — 5 a = 13 a. 
 
 Addition of Unlike Quantities 
 
 If some of the quantities are unlike, proceed as before with each like 
 'quantity, and write down the algebraic sum of all the quantities. Thus: 
 Add 7a-\-2b, ^a — b,6b — 4a and 5^ — 46. 
 
 y a — 4a 2b — b 
 S a — 6b — 4b 
 
 5a 
 
 1$ a — 4a 86 — 56 
 — 4a — 5& 
 
 II a 36 
 
 Answer = 11 a + 3 J. 
 
 The process is the same with compound quantities. Thus: Add 
 a^b + 2 cd^ to - 2 a?b + cJ^ = 3 c(P - a^b. 
 
 Subtraction 
 
 Change the sign of the subtrahend and proceed as in addition. Thus: 
 Subtract ^ a^b — g c from 4 a^b + c; changing the signs of the subtra- 
 hend and adding, the expressions may be written 
 
 4a^b — ^a^b -\- c-\- gc or a^b + 10 c. 
 
 Multiplication 
 
 If the quantities to be multiplied have like signs, the sign of the 
 product is + ; if they have unlike signs, that of the product is — . 
 
Powers of Quantities g 
 
 Of Simple Quantities 
 
 Multiply the coefficients together and prefix the + or — sign, accord- 
 ing as the signs of the quantities are like or unlike. Thus: 
 Multiply -\- ahy -\- b. Product equals -f- ab. 
 Multiply + 5 5 by — 4 c. Product equals — 20 be. 
 Multiply — ^axhy -\- yab. Product equals — 21 a^x. 
 
 Of Compound Quantities 
 
 Multiply each term of the multiplicand by all the terms of the multi- 
 plier, one after the other as by former rule; collect their products into 
 one sum for the required product. 
 Example. — 
 
 Multiply a — b + c 
 by a + b — c 
 
 
 a^ — /lifS -\- flc 
 
 
 
 + aif 
 
 - 62 + he 
 
 
 — a-c 
 
 + be -c^ 
 
 
 a^ 
 
 -b^ + 2be- c^ 
 
 Multiply 
 
 2X+ y 
 
 
 by 
 
 X — 2 y 
 
 
 2x^ -\- xy 
 
 — 4 xy — 2 y^ 
 
 20^— TyXy— 2'f 
 
 Powers of Quantities 
 
 The products arising from the continued multiplication of the same 
 quantity by itself are called powers of that quantity; and the quantity 
 itself is called the root. 
 
 The product of two or more powers of any quantity is the quantity 
 with an exponent equal to the sum of the exponents of the powers. 
 
 Thus: 
 
 a2 X a^ = flS. fl2j X aJ = aW\ 4 a6 X — 3 ac = — i.2a^be. 
 
 The square of the sum of two quantities equals the sum of their 
 squares plus twice their product. 
 
 {a + 6)2 = a2 + 62 + 2 ab. 
 
 The square of the difference of two quantities is the sum of their 
 squares minus twice their product. 
 
 (a - 6)2 = a2 + 62 - 2 ab. 
 
10 Algebra 
 
 The product of the sum and difference of two quantities is equal to 
 the difference of their squares. 
 
 (a + b) (a-b) =0"- ¥. 
 
 The squares of half the sum of two quantities is equal to their product 
 plus the square of half their difference. 
 
 Thus: ia + hY , , {a - h^ 
 
 = ab -] 
 
 2 2 
 
 The square of a trinomial is equal to the sum of the squares of each 
 
 term plus twice the product of each term by each of its following terms- 
 
 Thus: {a + b + cy = a^ + b^ + c^ + 2ab-\-2ac-\-2bc. 
 
 (a — b — cf = a^ -\- b^ -{- c^ — 2 ab — 2 ac -{- 2 be. 
 
 Parenthesis ( ) 
 
 When a parenthesis is preceded by a plus sign, it may be removed 
 without changing the value of the expression. 
 
 Thus: {a + b)-}-(a + b) = 2a+2b. 
 
 But if preceded by a minus sign,' if removed, the signs of all the terms 
 within the parenthesis must be changed. 
 
 Thus: (a + b) — {a — b)=a + b — a + b = 2b. 
 
 When a parenthesis is within a parenthesis, remove the inner one first. 
 
 Thus: a-[b-[c-{d- e)]] = a - [b - [c - d + e]] = 
 
 a — [b — c + d — e] = a — b + c — d -{- e. 
 
 Where the sign of multiplication ( X ) appears, the operation indicated 
 by it must be performed before that of addition or subtraction. 
 
 Division 
 
 If the sign of the divisor and dividend be like, the sign of the quotient 
 is plus (+); but if they be unlike the sign of the quotient is minus (— ). 
 
 To Divide a Monomial by a Monomial 
 
 Write the dividend over the divisor with a line between them. If the 
 expressions have common factors remove them. 
 
 Thus: ,, , a^bx ax a^ 1 „ 
 
 a^x -V- aby = —r— = — ;i = "i = ^~ 
 aby y a^ a^ 
 
 To Divide a Polynomial by a Monomial 
 
 Divide each term of the polynomial by the monomial. 
 Thus: (8 a6 — 12 ac) 4- 4 a = 2 6 — 3 c. 
 
Simple Equations ii 
 
 To Divide a Polynomial by a Polynomial 
 
 Arrange the terms of both dividend and divisor according to the as- 
 cending or descending powers of some letter, and keep this arrangement 
 throughout the operation. Divide the first term of the dividend by 
 the first term of the divisor, and write the result as the first term of the 
 quotient. 
 
 Multiply all the terms of the divisor by the first term of the quotient 
 and subtract the product from the dividend. If there is a remainder 
 consider it as a new dividend and proceed as before. 
 
 Thus: 
 
 {a' - b') 
 
 -^ia + b) 
 
 a + b)a^ 
 
 -b\a 
 
 -b 
 
 a^ 
 
 + ab 
 
 
 
 -ab- 
 
 -62 
 
 
 -ab- 
 
 -62 
 
 (i) The difference between two equal powers of the same quantities 
 is divisible by their difference. 
 
 (2) The difference between two equal even powers of the same quan- 
 tities is divisible by their sum or difference. 
 
 (3) The sum of two equal even powers of the same quantities is not 
 divisible by their sum or difference. 
 
 (4) The sum of two equal odd powers of the same quantities is 
 divisible by their sum, 
 
 (5) The sum of two equal even powers, whose exponents are composed 
 of odd and even factors, is divisible by the sum of the powers of the 
 quantities expressed by the even factor. 
 
 Thus: {x^ + y) is divisible by (x^ + y^). 
 
 Simple Equations 
 
 An equation is a statement of equahty between two expressions; as 
 a-\-b = c -{- d. 
 
 A simple equation, or equation of the first degree, is one which contains 
 only the first power of the unknown quantity. 
 
 If both sides of the equation be changed equally, by addition, sub- 
 traction, multiplication or division, the equality will not be disturbed. 
 
 Any term of an equation may be changed from one side to the other 
 provided its sign be changed. 
 
 Thus: a-]-b = c-{-d, a = c + d — b. 
 
1^ Algebra 
 
 To Solve an Equation Having One Unknown Quantity 
 
 Transpose all the terms containing the unknown quantity to one side 
 of the equation, and aU the other terms to the other side. 
 
 Combine like terms, and divide both sides by the coefi&cient of the 
 unknown quantity. 
 
 Thus: 8 .T — 29 = 26 — 3 X, 11 a; = 55, a; = 5. 
 
 Simple algebraic problems containing one unknown quantity, are 
 solved by making x equal the unknown quantity, and stating the con- 
 ditions of the problem in the form of an algebraic equation, then solving 
 the equation. 
 
 Thus : What two nmnbers are those whose sum is 48 and difference 14? 
 
 Let 
 
 X = the smaller nmnber. 
 
 Then 
 
 a? -1- 14 = the greater number. 
 
 
 ic + a; + 14 = 48, 
 
 
 2x = 2>A- 
 
 Therefore 
 
 x= IT, 
 
 and 
 
 a; + 14 = 31, 
 
 
 31 + 17 = 48. 
 
 Find the number whose treble exceeds 50 by as much as its double 
 falls short of 40. 
 
 Let X = the number. 
 
 Then 3 a; — 50 = 40 — 2 x, 
 
 5 a; = 90, X = 18. 
 
 Equations Containing Two Unknown Quantities 
 
 If one equation contains two unknown quantities, an indefinite number 
 of pairs of values for them may be found, which will satisfy the equation; 
 but if a second equation be given, only one pair of values can be found 
 that will satisfy both equations. Simultaneous equations, or those 
 which may be satisfied by the same values of the unknown quantity, 
 are solved by combining the equations so as to obtain a single equation 
 containing only one unknown quantity. 
 
 This process is called elimination. 
 
 Elimination by Addition or Subtraction 
 
 Multiply the equations by such a number as will make the coefficients 
 of one of the unknown quantities equal in both. Add or subtract 
 according as they have like or unlike signs. 
 
Elimination by Comparison 13 
 
 Solve 2x-\- sy = 7 
 
 4X- 5y= 3 
 
 Multiply by 2 4^ + 6 y = 14 
 
 Subtract 4-^— 5 y = 3 
 
 II y = II 
 y = ^^ 
 Substituting the value of y in the first equation 
 
 2X -\- $ = 7, .'. X = 2. 
 
 Elimination by Substitution 
 
 From one of the equations obtain the value of one of the unknown 
 quantities in terms of the other. Substitute this value of this imknown 
 quantity for it, in the other equation, and reduce the resulting equations. 
 
 Solve . 2 a: + 3 y = 8 (i) 
 
 3 X + 7 y = 7 (2) 
 
 From (i) x = ^~^^ 
 
 2 
 
 Substituting this value in (2) 
 
 (8 — ^ y) 
 3- — -^ 1-73' = 7, 24-93;+ i4y= 14, .••y=--2. 
 
 Substituting this value in (i); 
 
 2 a; — 6 = 8, :. x = 7. 
 
 Elimination by Comparison 
 
 From each equation obtain the value of one of the unknown quantities, 
 in terms of the other. Form an equation from these equal values of the 
 same unknown quantity and reduce. 
 
 Solve 2a; — gy = II (i) 
 
 3^-4^= 7 (2) 
 
 From (i) x = =^^ 
 
 2 
 
 From (2) X = ^-^^l^ 
 
 3 
 Placing the values of i»; in a new equation 
 
 ii + gy 7 + 4y 
 
 — ^= ^ , 19^=- 19, .-. y=-i. 
 
 Substituting this value of 3; in (i) 
 
 2« + 9 = II, .'. X = I. 
 
14 Algebra 
 
 If three simultaneous equations are given containing three unknown 
 quantities, one of the unknown quantities must be eliminated between 
 two pairs of the equations, then a- second between the two resulting 
 equations. 
 
 Quadratic Equations or Equations of the Second Degree 
 
 A quadratic equation contains the square of the unknown quantity, 
 but no higher power. A pure quadratic contains the square only; an 
 adfected quadratic contains both the square and the first power. 
 
 To Solve a Pure Quadratic * 
 
 Collect the unknown quantities on one side, and the known quantities 
 on the other; divide by the coefficient of the unknown quantity and 
 extract the square root of each side of the resulting equation. 
 
 Solve 3 ^c^ — 15 = o. _ 
 
 Sx- = 15, .'. x^ = s, x = V5. 
 
 A root which is indicated, but can only be found approximately is 
 called a surd. 
 
 Solve 3 a;2 + 15 = o. 
 
 3 a;2 = — 15, x^ = - 5, .'. X = V- 5. 
 
 The square root of a negative quantity cannot be found even approxi- 
 mately, for the square of any number is positive; therefore, a root which 
 is indicated, but cannot be found approximately is called imaginary. 
 
 To Solve an Adfected Quadratic 
 
 First. — Carry all the terms involving the unknown quantities to one 
 side of the equation and the known quantities to the other side. Arrange 
 the unknown quantities in the order of their exponents, changing the 
 signs of the equation if necessary, so that the sign of the term containing 
 the square of the unknown quantity shall be positive. 
 
 Second. — Divide both terms by the coefficient of the square of the 
 unknown quantity. 
 
 Third. — To complete the square. 
 
 Add to both sides of the equation, the square of half the coefficient 
 of the unknown quantity. The side containing the unknown quantity 
 will now be a perfect square. 
 
 Fourth. — Extract the square root of both sides of the equation and 
 solve the resulting simple equation. 
 
 Example. — a;^ + 2 a: = 35. 
 
 Add the square of half the coefficient of x, which is i, to both sides; 
 then x^ + 2 x -\- 1 = $s + ^ = 3^' 
 
Plane Geometry 15 
 
 Extracting the square root 
 
 x + i = V^ = rb 6 
 
 X = 6 - 1 = s 
 
 x=— 6 — i = — y. 
 Example: 3 rc^ — 4^ = 32. 
 Divide by the coefficient of x^ 
 
 x^-^ = ^. 
 3 3 
 
 Add the square of half the coefficient of x, which equals {^Y = f ; 
 then ^2_|^ + i=3_2_|.4, 
 
 Extracting the square root, the equation becomes 
 x-i = VI^ = V- 
 ^ = ¥ + f = 4, or X = - -1/ + I = - f = - 2f. 
 
 Since the square of a quantity has two roots =t, a quadratic equation 
 has apparently two solutions. Both solutions may be correct; but in 
 some cases one may be correct and the other inconsistent with the con- 
 ditions of the problem. 
 
 For the solution of quadratic equations containing two unknown 
 quantities, or for that of equations of a higher order, a more extended 
 treatment of the subject is required, than is permissible in a book of this 
 character. 
 
 SECTION III 
 
 PLANE GEOMETRY 
 
 Problem 1 
 
 To Bisect a Straight Line, or an Arc of a Circle 
 
 With any radius greater than half AB and with 
 A and B as centers, describe arcs cutting each other 
 at C and D. Draw the hne CD, which will bisect 
 the straight line at E and the arc at F. 
 
 Problem 2 
 
 To Draw a Perpendicular to a Straight Line, or a Radial Line to the Arc 
 of a Circle 
 This is the same as Problem i, Fig. i. 
 CD is perpendicular to AB, ox is radial to the arc. 
 
l6 Plane Geometry 
 
 Problem 3 
 
 To Draw a Ferpendicular to a Straight Line, from a Given Point on that 
 
 Line 
 
 KXi 
 
 Fig. 2. 
 
 With any convenient radius and the given point C, 
 as a center, cut the line AB, at A and B. Then 
 with a radius longer than AC, describe arcs from A 
 and B intersecting each other at D and E. Draw 
 DC, perpendicular to AB. 
 
 In laying out work on the ground or in places where the straight edge 
 and dividers are inapplicable: 
 
 Set off six feet from A to B. Then with ^, as a cen- S 
 
 ter and AC = 2>' taken on a tape hne, describe an arc at / 
 
 C; with B, as a center and a radius BC = lo', cut the / 
 
 other arc at C. A line through CA, will be perpendicu- ^/- 'a. 
 
 IsiT to AB. 3, 4 and 5 may be used instead of 6, 8 and ^ 
 
 10; or any multiples of 6, 8, 10 will serve. 
 
 Problem 4 
 
 From a Point at the End of a Given Line to Draw a Perpendicular 
 
 From any point C, above the line, with the radius 
 AC, describe an arc, cutting the given line at B. 
 Draw BC, and prolong until it intersects the arc at D. 
 Then, DA will be perpendicular to AB,ait A. 
 
 Fig. 4. 
 
 Problem 5 
 
 From Any Point Without a Given Straight Line, to Draw a Perpendicular 
 to the Line 
 
 Let BC, be the given line; then from any point A, 
 with any radius AB, describe arcs cutting the line at y 
 B and C. From B and C as centers and any radius ^ 
 greater than half of BC, describe arcs intersecting at :1:d 
 
 D. Draw AD, perpendicular to BC. (Fig. 5.) Fjg. 5. 
 
Plane Geometry 
 
 17 
 
 Fig. 6. 
 
 ProblemTB 
 
 To Draw a Straight Line Parallel to a Given Line at a Given Distance 
 from That Line 
 
 D r> 
 
 From any two points on the given line as - 
 
 centers and the given distance as a radius, 
 describe the arcs B and D. Draw BD parallel 
 to AC. (Fig. 6.) 
 
 Problem 7 
 To Divide a Given Straight Line into Any Nunber of Equal Parts 
 
 Let AB he the given Hne. Draw any 
 — c Hne AC, intersecting the given line and lay 
 off on it, say, 5 equal parts. Join the last 
 point 5 with B. Then through each of the 
 other divisions on AC, draw lines parallel to 
 
 Fig. 7. 
 
 B 5, dividing AB into 5 equal parts. (Fig. 7.) 
 
 4^ 
 
 Problem 8 
 
 To Draw an Angle of 60°, also One of 30° 
 
 From A with any radius describe the arc CB, then 
 with the same radius and B, as a center, cut the arc at 
 C. Then the angle CAB = 60°. 
 
 From C drop CD perpendicular to AB. The angle 
 ACD = 30^ 
 
 Problem 9 
 
 To Draw an Angle of 45° 
 
 Draw BC, perpendicular to AB. Make BC = AB, 
 and draw AC. The angle CAB = 45°. (Fig. 9.) 
 
 Fig. 8. 
 
 Fig. 9- 
 
 Problem 10 
 
 To Bisect an Angle 
 
 Let ABC be the given angle. With 5 as a center and 
 any radius, draw the arc AC. Then with A and C as 
 centers and a radius greater than one-half AC, describe 
 arcs cutting each other at D. Draw BD, which will 
 bisect the angle ABC. (Fig. 10.) 
 
 ::D 
 
 Fig. 10. 
 
l8 Plane Geometry 
 
 Problem 11 
 
 Through Two Given Points and With a Given Radius Describe the Arc 
 of a Circle 
 
 Referring to Fig. lo. Let A and C be the given points and a distance 
 AB the given radius. 
 
 From A and C, with ^5 as a radius describe arcs cutting each other 
 at B, then with 5 as a center strike AC. 
 
 All Angles in a semicircle are Right Angles. 
 
 Problem 12 
 
 An Angle at the Center of a Circle is Twice the Angle at the Circumference 
 when Both Stand on the same Arc 
 
 P Thus the angle BAC is equal to twice the angle 
 BDC. (Fig. II.) 
 
 Problem 13 
 
 All the Angles Between an Arc and its Chord, the Sides of the Angle Pass- 
 ing Through the Extremities of the Chord, are Equal. (Fig, 12.) 
 
 h 
 
 F 
 
 Thus, the angle EFG = EEC. 
 
 Fig. 12. 
 Problem 14 
 
 To Find the Center of a Circle or of an Arc. (Fig. 13.) 
 
 Take any three convenient points on the circum- 
 ference, and with any radius greater than half the 
 distance between any two points, describe arcs cut- 
 ting each other at d, e, f and g. Through d, f and 
 e, g, draw the Hues df and eg; the center is at their 
 Fig. 13. intersection H. 
 
 Problem 15 
 
 To Pass a Circle Through Three Given Points 
 Referring to Problem 14, let a, h and c be the three given points. 
 Proceed in the same way as to find the center H. 
 
Plane Geometry 
 
 19 
 
 Problem 16 
 
 To Describe an Arc of a Circle Passing Through Three Given Points 
 when the Center is not Accessible. (Fig. 14.) 
 
 Let A , B and C be the three given points. 
 
 From A and B as centers and with yl5 as a radius, describe the arcs 
 AEdiudBD. 
 
 Draw AD and BE through C Lay off on 
 the arc AE, any number of equal parts 
 above E and on BD, the same number be- 
 low D, numbering the points i, 2, 3, etc., in 
 the order in which they are taken. Draw 
 from A, lines through i, 2, 3, etc., on the 
 arc BD; and from B, lines through i, 2, 3, 
 etc., on the arc AE. The intersections of 
 lines having corresponding numbers will be points on the required arc 
 between C and B. 
 
 Proceed in the same manner to find points between C and A . Then 
 draw the arc through the points. 
 
 Fig. 14. 
 
 Problem 17 
 
 From a Point on the Circumference of a Circle Draw a Tangent to 
 the Circle. (Fig. 15.) 
 
 Through the given point A draw the radial line 
 AC. Then on ^C erect the perpendicular BE, as 
 in Problem 3. 
 
 Fig. 15. 
 
 Problem 18 
 
 From a Point Without a Circle Draw a Tangent to the Circle. (Fig. 16.) 
 
 Let A be the center of the circle, and B the 
 given point. Join A and B, and on the hne AB 
 describe a semicircle, with a radius equal to one- 
 half oi AB. Through the intersection of the 
 semicircle and the given circle draw the tangent 
 BC. 
 
 Fig. 16. 
 
Plane Geometry 
 
 Problem 19 
 
 Through a Point on a Line, Bisecting the Angle Between Two Lines, Draw 
 a Circle Which Shall he Tangent to the Given Lines. (Fig. 17.) 
 
 Fig. 17. 
 
 Let A be the point on a line bisect- 
 ing the angle between BC and DE. 
 Through A draw CE perpendicular to 
 AF. Bisect the angles at C and E. 
 The intersection G of the bisecting 
 lines will be on ^F and at the center 
 of the required circle. 
 
 Problem 20 
 
 Describe an Arc, Tangent to Two Given Arcs and at a Given Point 
 on one of the Arcs. (Fig. 18.) 
 
 Let A and B be the centers of the given arcs 
 and C the point of tangency on the arc, whose 
 center is B. Join A and B and draw BC through 
 the given point. Make CE equal to the radius 
 AD. 
 
 Bisect AE, draw a perpendicular at its middle 
 point and prolong to intersection with BC at F, 
 which is the center of the arc required. 
 
 Fig. 18. 
 
 Problem 21 
 
 To Construct a Pentagon having a Given Side AB. (Fig. 19.) 
 
 At B erect a perpendicular BC, equal to one-half AB. Draw AC and 
 make CD equal BC. Then BD is the radius of the 
 circle circumscribing a pentagon having sides equal 
 to AB. 
 
 The radius of a given circle is the side of an in- 
 scribed hexagon. 
 
 The radius of a circle circumscribing a hexagon, 
 is equal to the distance from the center of the hexa- 
 gon to the extremity of one of its sides. 
 
 Fig. 19. 
 
Plane Geometry 
 
 21 
 
 Problem 22 
 
 To Construct an Ellipse when the Transverse and Conjugate Axes 
 are Given. (Fig. 20.) 
 
 Draw the axes AB and CD intersecting at G. From C, with one- 
 half ^5 as a radius, cut AB dit E and F. Divide GB into any number 
 of parts as at i, 2, 3, 4, 5. 
 
 With £ as a center and ^ i as a 
 radius, and with i^ as a center and 
 radius B i, strike arcs cutting each 
 other at i, i, above and below the 
 transverse axis. 
 
 Again with E and F as centers 
 and A 2 and B 2, respectively as 
 radii, describe arcs cutting each 
 other at 2, 2. Find as many points as desired in the same way in both 
 halves of the ellipse, then trace the curve. 
 
 This construction depends on the property of an ellipse; that the sum 
 of the distances from the foci to any point on the ellipse is equal to the 
 transverse axis. 
 
 Problem 23 
 
 To Describe an Ellipse Mechanically when the Transverse and Con- 
 jugate Axes are Known. (Fig. 21.) 
 
 Draw the axes and determine the foci as in Problem 22. Drive two 
 pins at the foci E and F. Fasten to each of the pins one end of a cord 
 
 whose length is equal to that of the 
 transverse axis. 
 
 Then with a pencil, so placed 
 within the loop of the cord as 
 always to keep it taut and uniformly 
 strained, trace one-half of the curve, 
 from one extremity of the trans- 
 verse axis to the other. The other 
 half of the curve is traced by chang- 
 ing the cord and pencil to the oppo- 
 site side of the transverse axis. This 
 method is seldom satisfactory on 
 account of the unequal stretching 
 of the cord. 
 
 A better mechanical method of describing an ellipse is to place a 
 straight edge along and above the transverse axis and another along and 
 
 1° 
 
 1 
 
 A 
 
 B C 
 
 
 Fig. 21. 
 
22 
 
 Plane Geometry 
 
 at one side of the conjugate axis, as at AB and CD (Fig. 21), leaving a 
 slight opening between the end of the straight edge CD and the transverse 
 axis. 
 
 There must also be a thin strip of wood with a hole for pencil point at 
 A and small pins at B and C; AB being equal to one-half of the conju- 
 gate axis; and AC equal to one-half the transverse axis. By moving 
 this strip so that the pin B is always in contact with AB and the pin C 
 in like contact with CD the upper half of the ellipse may be de- 
 scribed. 
 
 The straight edges are placed in corresponding positions on the 
 opposite side of the transverse axis to describe the other half of the 
 ellipse. 
 
 Except where extreme accuracy is required, it is more convenient to 
 approximate the ellipse with circular arcs. 
 Thus: Lay o& AB and CD (Fig. 22) 
 equal to the transverse and conjugate axes 
 respectively. Make Oa and Oc equal to 
 the difference between the serai-transverse 
 and semi-conjugate axes, and ad equal to 
 one-half ac. Set off Oe equal to Od. Draw 
 di parallel to ac; join e and i and draw. the 
 parallel lines dm and em. From m, with a 
 radius mC, strike an arc cutting md and me. From i, with iD as a 
 radius, strike an arc cutting id and ie. Then from d and e, with radius 
 Ad, strike arcs closing the figure. 
 
 The Parabola 
 
 A parabola is a curve every point of which is equidistant from a line 
 called the directrix and from a point on its axis called the focus. The 
 directrix is a line perpendicular to the axis and at the same distance as 
 the focus from the apex of the curve. 
 
 A line perpendicular to the axis, drawn through the focus to the curve, 
 is called the parameter. 
 
 If a line be drawn from any point of the curve, perpendicular to the 
 axis, the distance from the apex to the intersection of the perpendicular 
 with the axis is called the abscissa of that point and the distance from 
 the intersection at the axis to the curve is called the ordinate of that 
 point. 
 
 Abscissae of a parabola are as the squares of corresponding ordl- 
 nates. 
 
The HypeTholsL 
 
 23 
 
 Problem 24 
 
 To Construct a Parabola when the Focus and Directrix 
 are Given. (Fig. 23.) 
 Let AB he the directrix, and C the 
 focus of a parabola. Bisect CD at E, which 
 point is the apex of the curve. 
 
 Then with C as a center and any radii, 
 as C I, C 2, etc., strike arcs at i, 2 and 3, 
 etc. From Z> as a center and with the 
 radii equal to C i, C 2, C 3, etc., cut the 
 axis at i', 2', 3', etc. Through these points 
 draw lines parallel to AB. 
 
 The intersection of corresponding parallels and arcs are points on the 
 required curve. 
 
 Problem 25 
 
 To Construct a Parabola when an Abscissa and Its Corre- 
 sponding Ordinate are Given. (Fig. 24.) 
 
 Fig. 23. 
 
 A 
 
 ^ 
 
 A 
 
 \\ 
 
 / 
 
 TA. 
 
 /■ 
 
 \ A 
 
 / . 
 
 \\ 
 
 '^' F 
 
 .^-^E Ad 
 
 Fig. 24. 
 
 Let BA be the given abscissa and AD 
 the ordinate. 
 
 Bisect AD at E. Draw EB, and EF 
 perpendicular to EB. Set off BG and BK, 
 each equal to AF. Then will G be the 
 focus and LM (through K) perpendicular 
 to AB, the directrix. Construct the curve 
 as in Problem 24. 
 
 The Hyperbola 
 
 An hyperbola is a curve, such that the difference of the distances from 
 any point of it to two fixed points is always equal to a given distance. 
 
 The two fixed points are called the foci and the given distance is the 
 transverse axis. The conjugate axis is a line perpendicular to the trans- 
 verse axis at its middle point; and its length is equal to the side of a 
 rectangle, of which the transverse axis is the other side and the distance 
 between the foci, the diagonal. 
 
 Problem 26 
 
 To Construct an Hyperbola when the Foci and Transverse Axis are Given 
 
 Let A and B be the foci and EF the transverse axis. From A set off 
 
 AG equal to EF. Then, from ^ as a center and with any distance 
 
 greater than AF z.°, 3. radius, strike an arc CD, cutting the transverse 
 
24 
 
 Plane Geometry 
 
 axis (prolonged) at H. From 5 as a center and HG as a radius, describe 
 arcs cutting the arc CD at C and D. C and D will be points on the curve; 
 in like manner any number of points are determined, through which the 
 curve may be traced. 
 
 Proceeding in the- same way on the opposite side 
 of the conjugate axis, the other branch of the curve 
 is constructed. 
 
 The diagonals of a rectangle constructed on the 
 transverse and conjugate axes are called the 
 asymptotes and are lines to which the curve is 
 tangent at an infinite distance. When the asymp- 
 totes are at right angles the curve is called an equi- 
 ^'^- ^5- lateral hyperbola. 
 
 It is a property of the equilateral hyperbola, that if the asymptotes 
 be taken as the co-ordinate axes the product of the abscissa and ordinate 
 of any point of the curve is equal to the corresponding product of the 
 co-ordinates at any other point; or that the diagonal of a rectangle con- 
 structed by the ordinate and abscissa of any point of the curve passes 
 through the intersection of the axes. 
 
 Problem 27 
 
 Given the Asymptotes and any Point on the Curve, to Construct 
 the Curve. (Fig. 26.) 
 
 Let AB and ^G be the asymptotes and D the given 
 point. Multiply AB by AE and divide the product 
 
 AB XAE 
 
 by any other distance AF; then AG 
 
 AF 
 
 and the intersection at / of lines through F and G, 
 parallel to the axes, is another point on the curve. 
 
 
 / 
 
 / 
 
 I 
 
 / 
 
 \ 
 
 \ 
 
 n 
 
 ^ 
 
 \ 
 
 
 \\ 
 
 
 ^-^ 
 
 ^ 
 
 ^s 
 
 ^ 
 
 F 
 
 Fig. 
 
 26. 
 
 Properties of Plane Figures 
 
 (i) In a right angle triangle, the square of the hypothenuse is equal 
 to the sum of the squares of the other two sides. 
 
 (2) In an equilateral triangle all the angles are equal. 
 
 (3) In an isosceles triangle a line drawn from the vertex perpendicular 
 to the base bisects the base and also the angle at the vertex. 
 
 (4) An exterior angle of a triangle equals the sum of the two opposite 
 angles. 
 
 (5) Similar triangles have equal angles and the sides opposite to 
 corresponding angles are proportional. 
 
Properties of Plane Figures 25 
 
 (6) In any polygon, the sum of all the interior angles is equal to twice 
 as many right angles as the figure has sides, less four right angles. 
 
 (7) In any polygon the sum of all the exterior angles is equal to four 
 right angles, or 360°. 
 
 (8) The diagonals of any regular polygon intersect at the center 
 of the figure. 
 
 (9) A circle may be passed through any three points, not on the same 
 straight line. 
 
 (10) In the same circle, arcs are proportional to the angles at the 
 center. 
 
 (11) Any two arcs having the same angle at the center are propor- 
 tional to their radii. 
 
 (12) Areas of circles are proportional to the squares of their diameters 
 or the squares of the radii, 
 
 (13) A radius perpendicular to the chord of an arc bisects the arc 
 and its chord. 
 
 (14) A straight line tangent to a circle is perpendicular to the radius 
 at the point of tangency. 
 
 (15) An angle at the center of the circle is equal to twice the angle 
 afthe circumference subtended by the same arc. 
 
 (16) Angles at the circumference of a circle, standing on the same 
 arc, are equal. 
 
 (17) Any triangle inscribed in a semicircle is a right angled tri- 
 angle. 
 
 (18) In any triangle inscribed in a segment of a circle, the angles at 
 the circumference are equal. 
 
 (19) Parallel chords or a chord and a parallel tangent intercept 
 equal arcs. 
 
 (20) If two chords of a circle intersect, the rectangles made by the 
 segments of the respective chords are equal. 
 
 (21) If one of the chords is a diameter of the circle and the other is 
 perpendicular to it, then one-half of the chord is a mean proportional 
 between the segments of the diameter. 
 
 (22) In any circle, with the center as the origin of co-ordinates, the 
 sum of the squares of the abscissa and ordinate of any point is equal to 
 the square of the radius, or x^ -\- y^ =^ R^. 
 
 (23) In any ellipse with same origin, the square of the abscissa of any 
 point multiplied by the square of the semi-conjugate axis plus the square 
 of the ordinate of same point multiplied by the square of the semi- 
 transverse axis is equal to the square of the product of the semi-axes. 
 
 Thus: -BV _j_ j^2y2 = ^2^2^ where A and B are the semi-transverse 
 and semi-conjugate axes. 
 
26 
 
 Mensuration 
 
 (24) In an ellipse, lines drawn from any point to the foci make equal 
 angles with a tangent at that point. 
 
 (25) The sum of the distances from any point of an ellipse to the foci 
 is equal to the transverse axis. 
 
 (26) If from any point of a parabola a line be drawn to the focus, and 
 one parallel to the axis, they will make equal angles with the tangent at 
 that point. 
 
 (27) The apex of a parabola bisects the distance on the axis from the 
 focus to the directrix. 
 
 (28) The angle between two tangents to a parabola is equal to half 
 the angle at the focus, subtended by the chord joining the points of 
 tangency. 
 
 (29) The area included between any chord of a parabola and the curve 
 is equal to two-thirds that of the triangle formed by the chord and 
 tangents through its extremities. 
 
 (30) The difference between the focal distances of any point of an 
 hyperbola is equal to the transverse axis. 
 
 (31) The product of the perpendiculars from the foci to any tangent 
 of an hyperbola is constant. 
 
 (32) A tangent at any point of an hyperbola makes equal angles with 
 the focal distances of the point. 
 
 SECTION IV 
 MENSURATION 
 
 PLANE SURFACES 
 Triangles 
 
 The area of any triangle is equal to half the 
 base multiplied by the altitude. (Fig. 27.) 
 AB 
 
 Area = 
 
 XCD. 
 
 To solve a triangle, three sides, two angles 
 and one side or two sides and one angle must 
 be given. 
 
 The area of a parallelogram is equal to the 
 base multiplied by the perpendicular distance 
 between the sides =- AB X CD. (Fig. 28.) 
 
 Fio. 2$. 
 
Triangles 
 
 The area of a trapezoid is equal to half the 
 sum of the parallel sides multiplied by the per- 
 pendicular distance between them. (Fig. 29.) 
 
 27 
 
 A \. 
 
 Area 
 
 AB + CD 
 
 X CE. 
 
 Fig. 29. 
 
 Fig. 30. 
 
 The area of a trapezium is equal to the 
 diagonal multiplied by half the sum of the 
 perpendiculars dropped to it from the vertices 
 of the opposite angles. (Fig. 30.) 
 
 The area of any quadrilateral is found 
 by multiplying the diagonal by one-half the 
 sum of the perpendiculars dropped from the 
 vertices of the opposite angles. (Fig. 31.) 
 DE + BF 
 
 Area = AC X 
 
 Fig. 31. 
 
 F E 
 Fig. 32. 
 
 If the diagonal falls without the figure, the 
 area is equal to the product of the diagonal 
 by half the difference of the perpendiculars. 
 (Fig. 32.) 
 
 Area =ABCD = AC X ^^~^^ . 
 
 A polygon is a plane figure bounded by three or more straight lines; 
 it is regular or irregular according as the lines bounding it are equal or 
 unequal. 
 
 If straight lines be drawn from the center of a regular polygon to each 
 of the vertices of the interior angles, the polygon will be divided into as 
 many isosceles triangles as it has sides. Each triangle will have for its 
 base one of the sides of the polygon and for its altitude the perpendicular 
 distance from the center of the polygon to that side. The area of the 
 polygon is equal to the sum of the areas of all the triangles, and is 
 found by multiplying one-half the sum of all the 
 sides of the polygon by the perpendicular distance 
 from the center to one of its sides. 
 
 To find the area of an irregular polygon, divide 
 
 the polygon into triangles and take the sum of 
 
 their areas. 
 
 Fig. 33. 
 
 To Find the Area of Any Irregular Plane Figure 
 Let C D EF G he any irregular figure. Draw any straight line AB 
 as a base; through the ^extremities of the figure drop perpendiculars 
 
 £3^56789 10 
 
28 Mensuration 
 
 CA and FB to the base. Divide AB into any number of equal parts, 
 say lo. Through the middle points of each of the equal divisions draw 
 perpendiculars cutting the boundaries of the figure on opposite sides. 
 Take the sum of the lengths of all these lines within the figure and divide 
 such sum by the number of divisions; the' quotient is the mean width of 
 the figure which multipHed by its length AB gives the area. 
 
 TJ 
 
 Thus: ab -{- cd + ef etc. = H; then — X AB equals the area of 
 CDEFG. 
 
 The Circle 
 
 The ratio of the circumference of a circle to its diameter is equal to 
 3.14159. This is represented by the Greek letter x, pronounced Pi. 
 
 Let C = the circumference of any circle. 
 D = the diameter of any circle. 
 r = the radius of any circle. 
 A = area of any circle. 
 
 The areas of circles are as the squares of their diameters, or as the 
 squares of their radii. 
 
 C = 7rZ> = 3-14159 X D. 
 C = 2-n-r = 6.28318 X r. 
 A = irr"^ = 3.14159 X r^. 
 ^ = i,rZ>2 = 0.7854 X D\ 
 
 A = — = 0.07958 X (?. 
 47r 
 
 A = 0.7854 X 4 r^' 
 
 24' 
 
 C 
 D = - = 0.3183 X C. 
 
 D = 2 Y - = 1.1284 Va. 
 
 r = — = 0.5642 y/A, 
 
 2ir 
 
The Ellipse 
 
 59 
 
 The Ellipse 
 
 The ellipse is a curve formed by the intersection of a plane inclined 
 to the axis of a cone or cyHnder, where the plane does not cut the base. 
 
 (^ 
 
 
 
 G 
 
 V ' ■■ 
 
 
 
 V 
 
 
 -> 
 
 ^ 
 
 
 Fig 
 
 ■ 34. 
 
 
 To Find the Length of any Ordinate, HK or LM, Knowing the Two 
 Diameters AB and CD, and the Abscisses OK and OM 
 
 HK 
 
 LM 
 
 AB^ : CD^ :: AK X KB : HK^, 
 
 ./ CD^ X (AK X KB) 
 V ' AB^ 
 
 ./AB^ {CM X MD) _ 
 
 CD^ 
 
 = ^ 
 AB 
 
 AB 
 CD 
 
 VAKxKBy 
 
 VCM X MD. 
 
 The circumference of an ellipse is found from the formula below, 
 wherein D = transverse diameter and d = conjugate diameter. C = 
 
 circumference = $.1415 d + 2 {D — d) '^ 
 
 V{D + d) X {D + 2d) 
 
 ^ »/Z)2 + # (D - dY 
 C = 3.i4i5V-- g;g— 
 
 These formulas apply where large D is not more than five times as 
 long as d. 
 
 The area of an ellipse is equal to that of an annular ring of which the 
 sum and difference of the radii of the limiting circles are respectively 
 equal to the semi-axes of the ellipse. 
 
 Thus TT (r2 - r'^) =Tr{r + r')X{r- r') ; then if {r + r') equals the semi- 
 transverse axis equals A, and (r — r') equals the semi-conjugate axis 
 equals B, the area of the ellipse equals tt {AB) or tt into the product of 
 the semi-axes or into the product of the axes, divided by four. 
 
30 Mensuration 
 
 SOLIDS 
 The Prism 
 
 A prism is a solid whose bases or ends are similar, equal and parallel 
 polygons and whose sides are parallelograms. The prism is right or 
 oblique according as the sides are perpendicular to or inclined to the ends; 
 regular or irregular, as the ends are regular or irregular polygons. 
 
 The surface of any prism is the sum of the areas of the sides added to 
 that of the ends. 
 
 To find the surface of a right prism, multiply the perimeter of its base 
 by its altitude; to this product add the areas of the ends. 
 
 The volume of any prism is equal to the area of its base multiplied 
 by its altitude, or perpendicular distance between the ends. 
 
 The volume of any frustum of a prism is equal to the product of the 
 sum of all the edges (divided by their number), and the area of the cross 
 section perpendicular to those edges. 
 
 The Pyramid 
 
 A p5n'amid is a solid having any polygon for its base; and for its sides 
 triangles, terminating at one point called the apex 
 
 The axis of a pyramid is a straight line from the apex to the center of 
 gravity of its base. 
 
 A pyramid is right or oblique according as the axis is perpendicular 
 or inclined to the base; regular or irregular, as the base is a regular or 
 irregular figure. 
 
 The slant height is the distance from the vertex of any of the tri- 
 angular sides to the middle point of its base. 
 
 The surface of any pyramid is equal to the sum of the areas of all the 
 triangles of which it is composed plus the area of the base. 
 
 The surface of a right regular pyramid is equal to the perimeter of its 
 base multiplied by half the slant height plus the area of the base. 
 
 The volimie of any pyramid is equal to the area of the base multiplied 
 by one-third of the altitude; or the perpendicular distance from the apex 
 to the base. It is also equal to one-third the volume of a cylinder having 
 the same base and altitude; or to one-half the volume of a hemisphere 
 having the same base and altitude. 
 
 The volumes of a pyramid, hemisphere and cylinder, having the same 
 base and altitude are to each other as i, 2 and 3. 
 
 Frustrum of a Pyramid 
 
 The frustrum of a pyramid is the section between two planes which 
 may or may not be parallel. 
 
folyhedra 31 
 
 The slant height of any side of a frustrum of a p)nramid is measured 
 from the middle points of the top and bottom sides of the trapezium 
 • forming that side. 
 
 To find the surface of any frustrum of apyramid, take the sum of the 
 areas of all the trapeziums forming the sides, to which add the sum of 
 the top and base. 
 
 The surface of a frustrum of a right regular pyramid, where the top 
 and base are parallel planes, is equal to one-half the sum of the perimeters 
 of top and base multiphed by the slant height plus the sum of the areas 
 of the top and base. 
 
 The volume of any frustrvmi of any pyramid, with top and base 
 parallel, is equal to one-third the perpendicular distance between top 
 and base multiplied by the sums of the areas of top and base, and the 
 square root of the product of those areas. 
 
 Thus H, being the perpendicular and A and A' the areas of top and 
 base, respectively, then the volume equals \ H X {A -{- A' -{- Va X A') 
 or A" being equal to the area of a section midway between and parallel 
 to base and top, the volume = V = I H {A +A' + 4A"). 
 
 A prismoid is a solid having six sides, two of which are parallel but 
 unequal quadrangles, and the other sides trapeziums. 
 
 To find the Volume of a Prismoid 
 
 Let A = area of one of the parallel sides. 
 a = area of the other parallel side. 
 M = area of cross section midway between and parallel to 
 
 the parallel sides. 
 L = perpendicular distance between the two parallel sides. 
 
 Then . Volmne = LX (^A+^+AK"^ . 
 
 The Wedge 
 
 The wedge is a frustrum of a triangular prism. Its volimie is equal 
 to the area of a right section multiplied by one-third the sum of the 
 lengths of the three parallel edges. 
 
 Let A equal area of section perpendicular to the axis of the prism and 
 BC, DE and FG, the lengths of the parallel edges respectively. 
 
 Then Volume of wedge = A (BC + DE+FG) ^ 
 
 3 
 Polyhedra 
 
 A polyhedron is a solid bounded by plane surfaces. 
 A regular polyhedron is one whose bounding faces are all equal and 
 regular polygons. 
 
32 Mensuration 
 
 There are five regular polyhedra as follows: 
 
 Name 
 
 Bounded by 
 
 Surface 
 = sum of sur- 
 faces of all the 
 faces 
 = square of 
 the length of 
 one edge by 
 
 Volume 
 = product of 
 cube of length 
 of one edge by 
 
 
 4 Equilateral triangles. . . 
 
 6 squares 
 
 8 Equilateral triangles.. . 
 • 12 Equilateral pentagons. 
 20 Equilateral triangles. . 
 
 I . 7320 
 6.000 
 3.4641 
 20.6458 
 8.6602 
 
 .1178 
 
 Cube or hexahedron 
 
 1. 000 
 
 
 7 6631 
 
 
 2.1817 
 
 
 
 The Cylinder 
 
 A cylinder may be defined as a prism, of which a section perpendicular 
 to its axis is a circle. It may be right or oblique. 
 
 The base of a right cylinder is a circle, that of an oblique cylinder an 
 ellipse. 
 
 The surface of any cylinder is equal to the product of the circumference 
 of a circle whose plane is perpendicular to the axis of the cylinder, by 
 the length of the axis, plus the area of the ends. 
 
 The volume of a cylinder is equal to the area of a circle perpendicular 
 to the axis multiplied by its altitude. 
 
 The Cone 
 
 A cone is a pyramid having an infinite number of sides. 
 
 Cones are right or oblique according as their axes are perpendicular 
 or inchned to their bases. 
 
 The surface of a right cone is equal to the product of the perimeter 
 of the base by half the slant height, plus the area of the base. 
 
 The surface of an oblique cone, cut from a right cone having a circular 
 
 base, is equal to the area of the base, multiplied by the altitude and 
 
 divided by the perpendicular distance from the axis at the point where 
 
 it pierces the base, to the surface of the cone, plus the area of the base; 
 
 AH 
 or the curved surface of the cone equals -zz-- Wherein A is the area 
 
 K 
 
 of the base, H the altitude and R the perpendicular. 
 
 The volume of any cone is equal to the area of the base multiplied by 
 one-third of the altitude. 
 
 The volume of a cone is equal to one-third that of a cylinder, or one- 
 half that of an hemisphere having same base and altitude. 
 
The Sphere 33 
 
 The surface of a right circular frustrum of a cone with top and base 
 parallel is found by adding together the circumferences of top and base, 
 multiplying this sum by one-half the slant height; to this product add 
 the area of top and base to get the total surface. 
 
 The volume of a frustrum of any cone, with top and base parallel, is 
 equal to one-third of the altitude multiplied by the sum of the areas of 
 top and base plus the square root of the product of those areas, or equals 
 i the altitude 
 
 X (area of top + area of base + V^area of top X area of base). 
 
 The Sphere 
 
 A sphere is a solid generated by revolving a semicircle about its 
 diameter. 
 
 The intersection of a sphere with any plane is a circle. 
 A circle cut by the intersection of the surface of a sphere and a plane 
 passing through its center is a great circle. 
 
 The volume of a sphere is greater than that of any other solid having 
 an equal surface. 
 
 The surface of a sphere equals that of four great circles. 
 Surface = /^.Trr"^. 
 = ttDK 
 " = curved surface of a circumscribing cyhnder. 
 " = area of a circle having twice the diameter of the sphere. 
 
 The surface of a sphere is equal to that of a circumscribing cube 
 multiplied by 0.5236. 
 
 Surfaces of spheres are to each other as the squares of their diameters. 
 
 Volume of a Sphere 
 
 Volume = f7ry3 = 4.1888^3 
 " =i7r2)3 = 0.52362)3 
 " =1 volume of circumscribing cylinder. 
 " = 0.5236 volume of circumscribing cube. 
 
 Volumes of spheres are to each other as the cubes of their diameters. 
 
 Radius of a sphere = 0.62035 "V^ volume. 
 
 Circumference of sphere = v^59.2i76 volume. 
 
 = V3.1416 X area of surface. 
 _ Area of surface 
 Diameter 
 
34 Mensuration 
 
 The area of the curved surface of a spherical segment is equal to the 
 product of the circumference of a great circle by the height of the seg- 
 ment = ttDH, where D is the diameter of the sphere and H the height 
 of the spherical segment. 
 
 The curved surface of a segment of a sphere is to the whole surface 
 of the sphere as the height of the segment is to the diameter of the 
 sphere. 
 
 To Find the Volume of a Spherical Segment 
 
 Let R = radius of base of segment. 
 
 H = height. 
 
 Then volume of segment = ^TrH{2,B? + H^). 
 
 To find the curved surface of a spherical zone, multiply the circum- 
 ference of the sphere by the height of the zone. 
 
 To find the volume of a spherical zone, let A and^' be the radii of 
 the ends of the zone and H be the height and V the volume. 
 
 Then V -- 
 
 Guldin's Theorems 
 
 (i) If any plane curve be revolved about any external axis situated 
 in its plane, the surface generated is equal to the product of the perimeter 
 of the curve and the length of the path described by the center of gravity 
 of that perimeter. 
 
 (2) If any plane surface be revolved about any external axis situated 
 in its plane, the volume generated is equal to the area of the revolving 
 surface multiplied by the path described by its center of gravity. 
 
CHAPTER II 
 
 WEIGHTS AND MEASURES 
 
 In the United States and Great Britain measures of length and weight 
 are, for the same denomination, essentially equal; but liquid and dry 
 measures for same denomination differ widely. The standard measure 
 of length for both countries is that of the simple seconds pendulum, 
 at the sea level, in the latitude of Greenwich; in vacuum and at a tem- 
 perature of 62° F. 
 
 The length of such a pendulum is 39.1393 inches; 36 of these inches 
 constitute the standard British Imperial yard. This is also the stand- 
 ard in the United States. 
 
 The Troy pound at the U, S, Mint of Philadelphia is the legal standard 
 of weight in the United States. 
 
 It contains 5760 grains and is exactly the same as the Imperial Troy 
 pound of Great Britain. 
 
 The avoirdupois pound (commercial) of the United States contains 
 7000 grains, and agrees with the British avoirdupois pound within o.ooi 
 of a grain. 
 
 The metric system was legalized by the United States in 1866 but its 
 use is not obligatory. 
 
 The metre is the unit of the metric system of lengths and was supposed 
 
 to be one ten millionth, , of that portion of a meridian between 
 
 10,000,000 
 
 either pole and the equator. 
 
 The metric measures of surface and volume are the squares and cubes 
 of the metre, and of its decimal fractions and multiples. 
 
 The metric unit of weight is the gramme or grain, which is the weight 
 of a cubic centimeter of pure water at a temperature of 40° F. 
 
 The legal equivalent of the metre as established by Act of Congress 
 is 39-37 inches = 3.28083 ft. = 1.093611 yards. 
 
 The legal equivalent of the gramme is 15.432 grains. 
 
 The systems of weights used for commercial purposes in the United 
 States are as follows: 
 
 35 
 
36 Weights and Measures 
 
 Troy Weight 
 
 For Gold, Silver, Platinum and Jewels, except Diamonds and Pearls 
 24 grains = i pennyweight (dwt.).' 
 
 20 pennyweights = i ounce = 480 grains. 
 12 ounces = i pound = 5760 grains. 
 
 Apothecaries Weight 
 
 {For Prescriptions only.) 
 20 grains = i scruple O) 
 
 3 scruples = i drachm (3) = 60 grains. 
 
 8 drachms = i ounce (S) = 480 " 
 12 ounces. = i pound (lb) = 5760 " 
 
 Avoirdupois Weight 
 
 For all Materials except those above named 
 16 drachms or 437.5 grains = i ounce (oz.). 
 16 ounces = i pound (lb.) = 7000 grains. 
 
 28 pounds = I quarter (qr.). 
 
 4 quarters ' = i hundredweight (cwt.) = 
 
 112 lbs. 
 20 hundredweight = i long or gross ton = 2240 lb. 
 
 2000 pounds = I short or net ton. 
 
 2204.6 pounds = I metric ton. 
 
 I stone =14 pounds. 
 
 I quintal =100 pounds. 
 
 The weight of the grain is the same for all systems of weights. 
 A troy ounce = i .097 avoirdupois ounces. 
 
 An avoirdupois ounce = .91146 troy or apoth. ounce. 
 A troy pound = .82286 avoirdupois pound. 
 
 An avoirdupois pound = i . 21528 troy or apoth. pounds. 
 The standard avoirdupois pound is equal to the weight of 27.7015 cu. 
 in. distilled water at 39.2° F., at sea level and at the latitude of Green- 
 wich. 
 
 Long Measure 
 
 12 inches = i foot = .3047973 metre. 
 
 3 feet = I yard = 36 in. = .9143919 metre. 
 
 5I yards = i rod, pole, perch = i6| feet = 198 in. 
 40 rods = I furlong = 220 yards = 660 ft. 
 
 8 furlongs = i statute mile = 320 rods = 1760yds. = 5280 ft. 
 
 3 miles = I league = 24 furlongs =960 rods = 5 280 yds. 
 
Square Measure 37 
 
 Land Measure 
 
 7.92 inches = i link; 100 links (66 ft.) = i chain = 4 rods. 
 
 10 chains = i furlong; 8 furlongs (80 chains) = i mile. 
 
 10 square chains = i acre. 
 
 Measures occasionally used 
 
 y^5 inch = I point; 6 points-y^a in. = i Hne. 
 1000 mils = I inch; 3 in. = i palm; 4 in. = i hand; 9 in. = i span. 
 2 yards = i fathom = 6 feet; 120 fathoms = i cable length. 
 A geographical (nautical) mile or knot = 6087.15 ft. = 1855.345 
 
 metres = 1. 15287 statute miles. 
 I knot = I minute of longitude or latitude at the equator. 
 
 1° latitude at the equator = 68 . 70 statute miles. 
 1° " " latitude 20° =68.78 
 1° " " " 40° =69.00 " 
 '1° " " " 60° =69.23 " 
 1° " " " 90° =69.41 " 
 
 Square Measure 
 
 144 square inches = i square foot. 
 9 " feet =1 " yard. 
 30^ " yards =1 " rod, perch or pole = 272J sq. ft. 
 40 " rods = I rood = 1210 sq. yds. = 108,908 sq. ft. 
 4 roods (10 sq. chains) = i acre = 160 sq. rods = 4840 sq. yds = 
 43,560 sq. ft. 
 640 acres = i sq. mile = i section. 
 An acre = a square whose side is 208.71 ft. 
 A half acre = a square whose side is 147.581 ft. 
 A quarter acre = a square whose side is 104.355 ft. 
 A circular inch is the area of a circle i inch in diameter and = .7854 
 sq. inches. 
 
 I square inch = 1.2732 circular inches. 
 
 A circular mil is the area of a circle i mil or .001 in. in diameter. 
 
 looo^ mils or 1,000,000 circular mils = i circular inch. 
 
 I square inch = 1,273,239 circular mils. 
 
 A cylinder, i inch in diameter and i foot high, contains: 
 1 . 3056 U. S. gills. 
 .2805 U. S. dry pints. 
 .3246 U. S. liquid pints. 
 A cylinder, one foot in diameter and i foot high, contains: 
 1357-1712 cubic inches. i'8S.oo64 U. S. liquid gills. 
 
 .7854 " feet. ^ 47.0016 U.S. " pints. 
 
 .02909 " yards. 23.5008 U.S. " quarts. 
 
38 
 
 Weights and Measures 
 
 5.8752 U. S. liquid gallons. 
 40.3916 U. S. dry pints. 
 20.1958 U. S. " quarts. 
 
 2.5254 U. S. dry pecks. 
 0.63112U.S. " bushels. 
 
 Liquid Measure 
 
 {United States only) 
 4 gills = I pint = 28.875 cubic inches. 
 
 2 pints = I quart= 57.75 cu. ins. = 8 gills. 
 
 4 quarts = i gallon =231 cu. in. = 8 pts. = 32 gills. 
 31I gallons = I barrel = 126 quarts = 4.211 cu. ft. 
 63 gallons = I hogshead. 
 - 2 hogsheads = i pipe or butt. 
 2 pipes = I tun. 
 
 A puncheon contains 84 gallons. 
 A tierce contains 42 gallons. 
 
 A cube 1. 615 ft. on edge contains 3.384 U. S. struck bushels; or 31I 
 gallons = I bbl.; or 4.21 1 cu. ft. 
 
 Approximate 
 measure 
 
 Diameter 
 
 Height 
 
 Approximate 
 measure 
 
 Diameter 
 
 Height 
 
 I Gill 
 i Pint 
 I Pint 
 I Quart 
 
 Inches 
 1.7s 
 2.25 
 3-50 
 3.50 
 
 Inches 
 3 
 31 
 3 
 6 
 
 1 Gallon 
 
 2 Gallons 
 8 Gallons 
 
 10 Gallons 
 
 Inches 
 
 7 
 
 7 
 14 
 14 
 
 Inches 
 6 
 12 
 12 
 15 
 
 The basis of this measure is the old British wine gallon of 231 cubic 
 inches; or 8.3388 lbs. of distilled water at 39° F. and 30" barometer. 
 A cubic foot contains 7.48 gallons. 
 
 Apothecaries' or Wine Measure 
 
 Measure 
 
 Symbol 
 
 Pints 
 
 Fluid 
 ounces 
 
 Fluid 
 drachms 
 
 Minims 
 
 Cubic 
 inches 
 
 Weight of water 
 
 Ounces 
 avoir. 
 
 Grains ' 
 
 I Minim 
 
 I fluid drachm . 
 I fluid ounce... 
 
 I pint 
 
 m 
 
 % 
 
 
 Cong. 
 
 I 
 8 
 
 I 
 
 16 
 128 
 
 I 
 8 
 
 128 
 1024 
 
 I 
 60 
 480 
 
 7680 
 61440 
 
 0.0038 
 0.2256 
 1.8047 
 
 28.875 
 231 
 
 I 043 
 Pounds 
 avoir. 
 1.043 
 8.345 
 
 0-95 
 
 57.05 
 
 456.4 
 
 7301.9 
 
 I gallon 
 
 S8415 
 
r 
 
 British Imperial Liquid and Dry Measures 
 
 Dry Measure 
 
 {United States only) 
 
 39 
 
 2 pints = I quart = 67.2006 cubic inches = 1. 163 65 liquid quarts. 
 4 quarts = i gallon = 8 pints = 268.80 cubic inches = 1. 16365 liq. gal. 
 2 gallons = I peck = 16 pints = 8 qts. = 537.60 cu, inches. 
 4 pecks = I struck bu. = 64 pints = 32 qts. = 8 gallons = 2150.42 cu. in. 
 The old Winchester struck bushel containing 2150.42 cubic inches or 
 77.627 pounds, avoirdupois, of distilled water at its maximum density- 
 is the basis of this table. 
 
 Its legal dimensions are those of a cylinder 18^ inches in diameter and 
 8 inches deep. When heaped, the cone must not be less than 6 inches 
 high; (the bushel) containing 1.5555 cubic feet and equal to i| struck 
 bushels. 
 
 Miscellaneous Measures 
 
 12 pieces = i dozen. 20 pieces = i score. 
 
 12 dozen = i gross. 24 sheets = i quire. 
 
 12 gross = I great gross. 20 quires = i ream. 
 
 2 pieces = i pair. 
 
 Weights of Given Volumes of Distilled Water at 70° F, 
 
 United States Liquid Measure 
 I gill = . 26005 lbs. 
 I pint = 1 . 1402 " 
 I quart = 2.0804 " 
 I gallon = 8 lbs. 5 J oz. = 8.345 lbs. 
 I barrel = 31I gals. = 262.1310 lbs. 
 
 United States Dry Measure 
 
 I pint 
 
 I quart 
 
 I gallon 
 
 I peck 
 
 I bushel (struck) 
 
 = 1. 2 104 lbs. 
 = 2.4208 " 
 
 = 9.6834 " 
 = 19.3668 " 
 = 77-4670 " 
 
 British Imperial Liquid and Dry Measures 
 
 Liquid and Dry Measures 
 .31214 lbs. avoir, of distilled water. 
 1.24858 
 
 I gill = 
 
 I pint = 
 
 I quart = 
 
 I gallon = 
 
 I peck = 19.977^ 
 
 I bushel = 79.9088 
 
 2.49715 
 9.9886 
 
40 
 
 Weights and Measures 
 
 This system supersedes the old ones throughout Great Britain, and, 
 is based on the Imperial gallon of 277.274 cubic inches, equal to 10 pounds 
 avoirdupois of pure water at 62° F., 30 in. Bar. 
 
 I Utre 
 
 I centilitre 
 
 I decilitre 
 
 I decalitre 
 
 I metre or stere =2198.0786 
 
 Metric Measures 
 
 = 2. 1 98 1 lbs. avoir, of pure water. 
 
 .02198 " " " " "= 153,866 gr. 
 .2198 '* " " " " = 3.516902. 
 
 i-».^ It tc IC t c 
 
 = 21 .' 
 
 Metric Measures of Length in U. S. Standard 
 
 
 Inches 
 
 Feet 
 
 Yards 
 
 Miles 
 
 Millimetre* 
 
 .039370 
 .393704 
 3-93704 
 39-3704 
 393-704 
 Road 
 measiires 
 
 .003281 
 .032809 
 .328087 
 3.28087 
 32.80869 
 328.0869 
 3280.869 
 32808.69 
 
 .1093623 
 1.093623 
 10.93623 
 109.3623 
 1093.623 
 10936.23 
 
 
 
 
 Decimetre 
 
 MetreJ 
 
 
 Decametre 
 Hectometre 
 Kilometre 
 Myriametre i 
 
 .062137s 
 .6213750 
 
 
 
 About 5V of an inch. t About I of an inch. t About 3 feet 3§ inches. 
 
 Metric Square Measure by U. S. Standard 
 
 Measures 
 
 Square millimetre 
 
 Square centimetre — 
 Square decimetre. . . . 
 Square meter or cen- 
 
 taf e 
 
 Square decametre or 
 
 • aire 
 
 Square decare* 
 
 Hectare 
 
 Square kilometre 
 
 Square myriametre . . 
 
 Square inches Square feet Square yards Acres 
 
 .001550 
 .155003 
 15.5003 
 
 1550.03 
 155003 
 
 Square miles 
 .3861090 
 38.61090 
 
 .00001076 
 .00107641 
 . 10764101 
 
 10.764101 
 
 1076. 4101 
 10764. lOI 
 107641.01 
 10764101 
 
 .0000012 
 .0001196 
 .0119601 
 
 I . 19601 
 
 119.6011 
 1196.011 
 11960.11 
 1196011 
 
 .000247 
 
 .024711 
 .247110 
 2.47110 
 247.110 
 24711.0 
 
 Seldom used. 
 
Metric Weights, Reduced to Avoirdupois 
 
 41 
 
 Metric, Cubic or Solid Measure by U. S. Standard 
 
 Millilitre or cubic cen- 
 timetre 
 
 Centilitre . 
 
 Decilitre , 
 
 Litre or cubic decimetre 
 Decalitre or centistere . . 
 
 Hectolitre or decistere . 
 
 Kilolitre or cubic metre 
 or stere 
 
 Myrialitre or decastere. 
 
 Cubic inches 
 .0610254 
 
 .610254 
 6.10254 
 
 61.0254 
 610.254 
 
 Cubic feet 
 .353156 
 
 3-53156 
 
 35.3156 
 
 353.156 
 
 Liquid 
 
 Dry 
 Liquid 
 
 Dry 
 Liquid 
 
 Dry 
 Liquid 
 
 Dry 
 
 Liquid 
 
 Dry 
 Liquid 
 
 Dry 
 
 Liquid 
 
 Dry 
 Liquid 
 
 Dry 
 
 .0084537 gill. 
 
 .0018162 pint. 
 .084537 gill. 
 
 .018162 pint. 
 .84537 gill. 
 
 . 18162 pint. 
 
 1. 05671 quart = 2.1134 pints. 
 
 ,11351 peck = .9031 qt. = 1.816 pts. 
 
 2.64179 gallons 
 
 .283783 bu. = I.1351 pks. = 9.081 qts. 
 26.4179 gallons. 
 
 2.83783 bushel. 
 264.179 gallons 
 
 28.3783 bushels 
 2641.79 gallons 
 
 5.78 bushels 
 
 = 1.3080 cu. yd. 
 = 13.080 cu. yd. 
 
 Metric Weights, Reduced to Avoirdupois 
 
 Measure 
 
 Avoirdupois 
 
 Milligramme 
 
 Centigramme 
 
 Decigramme 
 
 Gramme. . . 
 
 .015432 grains 
 .15432 
 1.5432 
 15.432 " 
 
 
 
 Decagramme 
 
 Hectogramme 
 
 Kilogramme 
 
 Myriagramme 
 
 Quintal ' .. ... 
 
 .022046 lbs. 
 .22046 " 
 2.2046 " 
 22.046 
 220.46 " 
 
 Tonneau, millier or tonne 
 
 2204.6 " 
 
 The base of the French system of weights is the gramme; which is 
 the weight of a cubic centimeter of distilled water at maximum density, 
 at the sea level and at the latitude of Paris, Barometer 29.922 inches. 
 
4^ 
 
 Weights and Measures 
 
 Metric Lineal Measure 
 
 
 Metres 
 
 Inches 
 
 Feet 
 
 Yards 
 
 Miles 
 
 Millimetre 
 
 .001 
 .01 
 
 .1 
 
 I 
 
 10 
 
 lOO 
 
 lOOO 
 
 lOOOO 
 
 .03937 
 -3937 
 3-937 
 39-3685 
 
 .00328 
 .0328 
 .3280 
 3.2807 
 32.807 
 328.07 
 3280.7 
 32807 
 
 
 
 Centimetre 
 
 
 
 Decimetre 
 
 Metre 
 
 . 10936 
 1.0936 
 10.936 
 109.36 
 1093-6 
 10936 
 
 
 
 
 
 
 
 
 
 
 
 
 Metric Square Measure 
 
 Measures 
 
 V 
 
 Square 
 metres 
 
 Square 
 inches 
 
 Square 
 feet 
 
 Square 
 yards 
 
 Acres 
 
 Square centimetre.... 
 
 decimetre 
 
 " centare 
 
 Are 
 
 .01 
 .1 
 I 
 10 
 100 
 
 .155 
 15.5 
 1,549-88 
 154,988 
 
 . 10763 
 10.763 
 1,076.3 
 107,630 
 
 .01196 
 1.196 
 119. 6 
 11,959 
 
 .00025 
 .0247 
 
 
 
 
 
 
 
 Acres 
 
 Square miles 
 
 Square kilometre 
 
 " myriametre. . 
 
 
 
 247 
 24,708 
 
 .3860' 
 38.607 
 
 I 
 
 Metric, Cubic or Solid Measure 
 
 Measures 
 
 Cubic 
 metres 
 
 Cubic 
 inches 
 
 Cubic feet 
 
 Cubic 
 yards 
 
 OiiHif rpntimp+rf 
 
 .0001 
 
 .001 
 
 .01 
 
 I 
 
 10 
 100 
 
 .0610165 
 61.0165 
 610.165 
 6101.6s 
 
 .353105 
 3.53105 
 35.3105 
 353. los 
 3531.05 
 
 
 
 
 
 
 Decimstere 
 
 . 13078 
 
 Stere 
 
 1.3078 
 
 
 
 13.078 
 
 
 
 130.78 
 
 
 
 
Circular Measure 
 
 43 
 
 Metric Weights 
 
 Weight 
 
 Grammes 
 
 Troy grains 
 
 Avoirdupois 
 ounces 
 
 Avoirdupois 
 pounds 
 
 
 .001 
 .01 
 .1 
 I 
 
 10 
 
 100 
 
 1,000 
 
 10,000 
 
 100,000 
 
 1,000,000 
 
 .01543 
 .1543 
 1.543 
 15.43316 
 
 .03528 
 .3528 
 3.52758 
 35.2758 
 
 
 
 
 
 
 Gramme 
 
 Decagramme 
 
 Hectogram.me 
 
 .0022047 
 .022047 
 
 
 .2204737 
 
 Kilogramme 
 
 Myriagramme 
 
 Quintal 
 
 
 2 . 204737 
 
 
 22.04737 
 
 
 
 220.4737 
 
 
 
 
 2204.737 
 
 
 
 
 
 Metric Dry and Liquid Measures 
 
 
 Measures 
 
 Litres 
 
 Cubic inches 
 
 Cubic feet 
 
 Millilitre 
 
 Centilitre 
 
 Decilitre 
 
 .001 
 .01 
 .1 
 I 
 10 
 100 
 i,ooo- 
 10,000 
 
 .061 
 
 .61 
 
 6.1 
 
 61.02 
 
 610.16 
 
 
 Litre 
 
 
 
 
 Hectolitre 
 
 3-531 
 
 Kilolitre 
 
 
 35.31 
 
 Myrialitre 
 
 
 353.1 
 
 
 
 
 Circular Measure 
 
 60 seconds (") i minute ('). 
 
 60 minutes (') i degree (°). 
 
 90 degrees (°) i quadrant. 
 
 360 degrees (°) circumference. 
 
 Time 
 
 60 seconds i minute. 
 
 60 minutes i hour. 
 
 24 hours I day. 
 
 7 days I week. 
 
 365 days, s hours, 48 minutes, 48 seconds = i year. 
 Every year whose number is divisible by 4 is a leap year and contains 
 366 days. 
 
 The Centismal years are leap years only when the number of the year 
 is divisible by 400. 
 
44 
 
 Weights and Measures 
 
 Board and Timber Measure 
 
 The unit of measurement is a board 12 inches square by one inch thick. 
 
 To ascertain the number of feet board measure in a plank or piece of 
 square timber, multiply the length by the breadth in feet and by the 
 thickness in inches. 
 
 To find the cubic contents of a stick of timber (all the measurements 
 being reduced to feet), take one-fourth the product of the mean girth by 
 the diameter and the length. 
 
 To find the cubic contents of square timber, reduce all measurements 
 to feet, then the product of the length by the breadth and thickness will 
 be the volume in cubic feet. 
 
 Miscellaneous Measures and Weights 
 
 I barrel of flour weighs 196 pounds. 
 
 I barrel of salt weighs 280 " 
 
 I barrel of beef or pork weighs 200 " 
 
 I bushel of salt (Syracuse) weighs 56 " 
 
 Anthracite coal (broken) averages 54 lbs. to the cubic foot. 
 
 Bituminous coal (broken) averages 49 " " " " " 
 
 Cement (Portland) 
 Gypsum (ground) 
 Lime (loose) 
 Lime (well-shaken) 
 Sand 
 
 weighs 
 
 96 lbs. 
 
 to the bushel, 
 
 70 " 
 
 a a c< 
 
 70 " 
 
 a t. a 
 
 80 " 
 
 u i( a 
 
 98 " 
 
 " " cubic : 
 
 or 1, 181 tons 
 to the cu. yd. 
 
 Useful Factors 
 
 Inches X 
 
 " X 
 
 " X 
 
 Square inches X 
 
 " X 
 
 Cubic inches x 
 
 " X 
 
 " X 
 
 Feet X 
 
 " X 
 
 Square feet X 
 
 " X 
 
 Cubic feet X 
 
 " X 
 
 " X 
 
 0.08333 = feet 
 
 0.02778 = yards 
 
 0.00001578 = miles 
 
 0.00695 
 0.0007716 
 
 0.00058 
 
 0.0000214 
 
 0.004329 
 
 o 3334 
 0.00019 
 
 144.0 
 0.II12 
 
 1728 
 
 o 03704 
 7.48 
 
 = square feet 
 = square yards 
 
 = cubic feet 
 = cubic yards 
 = U. S. gallons 
 
 = yards 
 = miles 
 
 = square inches 
 = square yards 
 
 = cubic inches 
 = cubic yards 
 = U. S. gallons 
 
Measures of Work, Power and Duty 45 
 
 Useful Factors — {Continued) 
 
 Yards X 36 = inches 
 
 " ., X 3 =feet 
 
 " X 0.0005681 = miles 
 
 Square yards X i ,296 = square inches 
 
 " " X 9 = square feet 
 
 Cubic yards X 46,656 = cubic inches 
 
 " X 27 = cubic feet 
 
 Miles X 63,360 = inches 
 
 " X 5,280 =feet 
 
 " X 1 ,760 = yards 
 
 Avoirdupois ounces X .0.0625 = pounds 
 
 X 0.0000312s =tons 
 
 " pounds X 16 = ounces 
 
 " " X .001 = hundredweight 
 
 " " X .oooS = tons 
 
 *' " 27.681 = cubic inches of 
 
 water at 39.2° F 
 
 " tons X 32,000 = ounces 
 
 " " X 2,000 = pounds 
 
 Watts X 0.00134 = horse power 
 
 Horse power X 746 = watts 
 
 Weight of round iron per foot = square of diameter in quarter inches -f- 6. 
 
 Weight of flat iron per foot = width X thickness X io-3- 
 
 Weight of flat plates per square foot = 5 pounds for each 1-8 inch thickness. 
 
 Measures of Work, Power and Duty 
 
 Work is the result of expenditure of energy in overcoming resistance. 
 
 The unit of work is the pressure of one pound exerted through a distance 
 
 of one foot and is called one foot pound. 
 
 Horse Power. — Term employed to measure the quantity of work. 
 
 The unit is one horse power; or the quantity of work performed in 
 
 raising 33,000 lbs., one foot in one minute 
 
 = 33,000 foot pounds per minute 
 
 = 550 foot pounds per second 
 
 = 1,980,000 foot pounds per hour. 
 
 A heat unit is the amount of heat required to raise one pound of water 
 
 at maximum density 1° F., or i pound of water from 39"^ F. to 40** F. = 
 
 778 foot pounds. 
 
 One horse power = 2545 heat units per hour 
 
 33,000 . , 
 
 = z— = 42.146 heat units per mmute 
 
 s= .7021 heat units per second. 
 
46 
 
 Mathematical Tables 
 
 Table of Squares, Cubes, Square Roots and Cube 
 Roots of Numbers from .i to io 
 
 No. 
 
 Square 
 
 Cube 
 
 Square 
 root 
 
 Cube 
 root 
 
 No. 
 
 Square 
 
 Cube 
 
 Square 
 root 
 
 Cube 
 root 
 
 .1 
 
 .OI 
 
 .001 
 
 .3162 
 
 .4642 
 
 4.1 
 
 16.81 
 
 68.921 
 
 2.025 
 
 1. 601 
 
 .15 
 
 .0225 
 
 .0034 
 
 .3873 
 
 .5313 
 
 4.2 
 
 17.64 
 
 74.088 
 
 2.049 
 
 1. 613 
 
 .2 
 
 .04 
 
 .008 
 
 .4472 
 
 .5848 
 
 4.3 
 
 18.49 
 
 79.507 
 
 2.074 
 
 1.626 
 
 .25 
 
 .0625 
 
 .0156 
 
 .500 
 
 .6300 
 
 4.4 
 
 19.36 
 
 85.184 
 
 2.098 
 
 1.639 
 
 .3 
 
 .09 
 
 .027 
 
 ■ 5477 
 
 .6694 
 
 4.5 
 
 20.25 
 
 91 . 125 
 
 2. 121 
 
 1. 651 
 
 .35 
 
 .1225 
 
 .0429 
 
 .5916 
 
 .7047 
 
 4.6 
 
 21.16 
 
 97.336 
 
 2.145 
 
 1.663 
 
 .4 
 
 .16 
 
 .064 
 
 .6525 
 
 .7368 
 
 4.7 
 
 22.09 
 
 103.823 
 
 2.168 
 
 1.675 
 
 ■ 45 
 
 .2025 
 
 .0911 
 
 .6708 
 
 .7663 
 
 4.8 
 
 23.04 
 
 110.592 
 
 2. 191 
 
 1.687 
 
 .5 
 
 .25 
 
 .125 
 
 .7071 
 
 .7937 
 
 4-9 
 
 24.01 
 
 117.649 
 
 2.214 
 
 1.698 
 
 • 55 
 
 .3025 
 
 .1664 
 
 .7416 
 
 .8193 
 
 5 
 
 25 
 
 125 
 
 2.2361 
 
 1. 710 
 
 .6 
 
 .36 
 
 .216 
 
 .7746 
 
 .8434 
 
 5.1 
 
 26.01 
 
 132.651 
 
 2.258 
 
 1. 721 
 
 .65 
 
 • 4225 
 
 .2746 
 
 .8062 
 
 .8662 
 
 5.2 
 
 27.04 
 
 140.608 
 
 2.280 
 
 1.732 
 
 .7 
 
 .49 
 
 .343 
 
 .8367 
 
 .8879 
 
 5.3 
 
 28.09 
 
 148.877 
 
 2.302 
 
 1.744 
 
 .75 
 
 .562s 
 
 .4219 
 
 ■.8660 
 
 .9086 
 
 5.4 
 
 29.16 
 
 157.464 
 
 2.324 
 
 1. 754 
 
 .8 
 
 .64 
 
 .512 
 
 .8944 
 
 .9283 
 
 5.5 
 
 30.25 
 
 166.375 
 
 2.345 
 
 1.765 
 
 .85 
 
 .7225 
 
 .6141 
 
 .9219 
 
 .9473 
 
 5.6 
 
 31.36 
 
 175.616 
 
 2.366 
 
 1.776 
 
 •9 
 
 .81 
 
 .729 
 
 .9487 
 
 .9655 
 
 5-7 
 
 32.49 
 
 .185.193 
 
 2.387 
 
 1.786 
 
 .95 
 
 .9025 
 
 .8574 
 
 .9747 
 
 .9830 
 
 5.8 
 
 33.64 
 
 195. 112 
 
 2.408 
 
 1.797 
 
 I 
 
 I 
 
 I 
 
 I 
 
 I 
 
 5.9 
 
 34.81 
 
 205.379 
 
 2.429 
 
 1.807 
 
 I-05 
 
 I . 1025 
 
 1. 158 
 
 1.025 
 
 1. 016 
 
 6 
 
 36 
 
 216 
 
 2.4495 
 
 1.8171 
 
 I.I 
 
 I. 21 
 
 I 331 
 
 1.049 
 
 1.032 
 
 6.1 
 
 37.21 
 
 226.981 
 
 2.470 
 
 1.827 
 
 1.15 
 
 1.3225 
 
 1. 521 
 
 1.072 
 
 1.048 
 
 6.2 
 
 38.44 
 
 238.328. 
 
 2.490 
 
 1.837 
 
 1.2 
 
 1.44 
 
 1.728 
 
 1.095 
 
 1.063 
 
 6.3 
 
 39.69 
 
 250.047 
 
 2.510 
 
 1.847 
 
 1.25 
 
 1.5625 
 
 1.953 
 
 1. 118 
 
 1.077 
 
 6.4 
 
 40.96 
 
 262.144 
 
 2.530 
 
 1.857 
 
 1.3 
 
 1.69 
 
 2.197 
 
 1. 140 
 
 1. 091 
 
 6.5 
 
 42.25 
 
 274.625 
 
 2.550 
 
 1.866 
 
 1.35 
 
 1.8225 
 
 2.460 
 
 1. 162 
 
 1. 105 
 
 6.6 
 
 43.56 
 
 287.496 
 
 2.569 
 
 1.876 
 
 1.4 
 
 1.96 
 
 2.744 
 
 1 . 183 
 
 1. 119 
 
 6.7 
 
 44.89 
 
 300.763 
 
 2.588 
 
 I -885 
 
 1-45 
 
 2.1025 
 
 3.049 
 
 1.204 
 
 1. 132 
 
 6.8 
 
 46.24 
 
 314.432 
 
 2.608 
 
 1.89s 
 
 1.5 
 
 2.25 
 
 3.375 
 
 1.2247 
 
 I. 1447 
 
 6.9 
 
 47.61 
 
 328.509 
 
 2.627 
 
 1.904 
 
 1.55 
 
 2.4025 
 
 3.724 
 
 1.245 
 
 1. 157 
 
 7 
 
 49 
 
 343 
 
 2.6458 
 
 I. 9129 
 
 1.6 
 
 2.56 
 
 4.096 
 
 1.265 
 
 1. 170 
 
 7.1 
 
 50.41 
 
 357.911 
 
 2.665 
 
 1.922 
 
 1.65 
 
 2.7225 
 
 4.492 
 
 1.285 
 
 1. 182 
 
 7.2 
 
 51.84 
 
 373.248 
 
 2.683 
 
 1. 931 
 
 1.7 
 
 2.98 
 
 4.913 
 
 1.304 
 
 1. 193 
 
 7.3 
 
 53.29 
 
 389.017 
 
 2.702 
 
 1.940 
 
 1.75 
 
 3 0625 
 
 5.359 
 
 1.323 
 
 1.205 
 
 7.4 
 
 54.76 
 
 405.224 
 
 2.720 
 
 1.949 
 
 1.8 
 
 3.24 
 
 5.832 
 
 1.342 
 
 1. 216 
 
 7.5 
 
 56.25 
 
 421.875 
 
 2.739 
 
 1.957 
 
 1.85 
 
 3 4225 
 
 6.332 
 
 1.360 
 
 1.228 
 
 7.6 
 
 57.76 
 
 438.976 
 
 2.757 
 
 1.966 
 
 1-9 
 
 3.61 
 
 6.859 
 
 1.378 
 
 1.239 
 
 7.7 
 
 59.29 
 
 456.533 
 
 2.775 
 
 1. 975 
 
 1.95 
 
 3.802s 
 
 7.415 
 
 1.396 
 
 1.249 
 
 7.8 
 
 60.84 
 
 474.552 
 
 2.793 
 
 1.983 
 
 2 
 
 4 
 
 8 
 
 I. 4142 
 
 1.2599 
 
 7.9 
 
 62.41 
 
 493.039 
 
 2. 811 
 
 1.992 
 
 2.1 
 
 4.41 
 
 9.26 
 
 1.449 
 
 1. 281 
 
 8 
 
 64 
 
 512 
 
 2.8284 
 
 2 
 
 2.2 
 
 4.84 
 
 10.648 
 
 1.483 
 
 1. 301 
 
 8.1 
 
 65.61 
 
 531.441 
 
 2.846 
 
 2.008 
 
 a. 3 
 
 5.29 
 
 12.167 
 
 1. 517 
 
 1.320 
 
 8.2 
 
 67.24 
 
 551.368 
 
 2.864 
 
 2.017 
 
 2-4 
 
 5. 76 
 
 13.824 
 
 1.549 
 
 1.339 
 
 8.3 
 
 68.89 
 
 571.787 
 
 2.881 
 
 2.025 
 
 2.5 
 
 6.25 
 
 15.625 
 
 1. 581 
 
 1.357 
 
 8.4 
 
 70.56 
 
 592.704 
 
 2.898 
 
 2.033 
 
 2.6 
 
 6.76 
 
 17.576 
 
 1. 612 
 
 1.375 
 
 8.5 
 
 72.25 
 
 614.125 
 
 2.915 
 
 2.041 
 
 2.7 
 
 7.29 
 
 19.683 
 
 1.643 
 
 1.392 
 
 8.6 
 
 73.96 
 
 636.056 
 
 2.933 
 
 2.049 
 
 2.8 
 
 7.84 
 
 21.952 
 
 1-673 
 
 1.409 
 
 8.7 
 
 75.69 
 
 658.503 
 
 2.950 
 
 2. 057 
 
 2.9 
 
 8.41 
 
 24.389 
 
 1.703 
 
 1.426 
 
 8.8 
 
 77.44 
 
 681.472 
 
 2.966 
 
 2.065 
 
 3 
 
 9 
 
 27 
 
 I. 7321 
 
 1.442 
 
 8.9 
 
 79.21 
 
 704.969 
 
 2.983 
 
 2.072 
 
 3.1 
 
 9.61 
 
 29.791 
 
 1. 761 
 
 1.458 
 
 9 
 
 81 
 
 729 
 
 3 
 
 •2.081 
 
 3.2 
 
 10.24 
 
 32.768 
 
 1.789 
 
 1.474 
 
 9.1 
 
 82.81 
 
 753.571 
 
 3.017 
 
 2.088 
 
 33 
 
 10.89 
 
 35.937 
 
 1. 817 
 
 1.489 
 
 9.2 
 
 84.64 
 
 778.688 
 
 3.033 
 
 2.095 
 
 3.4 
 
 11.56 
 
 39.304 
 
 1.844 
 
 1.504 
 
 9.3 
 
 86.49 
 
 804.357 
 
 3.050 
 
 2.103 
 
 35 
 
 12.25 
 
 42.875 
 
 1. 871 
 
 1. 518 
 
 9.4 
 
 88.36 
 
 830.584 
 
 3.066 
 
 2. no 
 
 3.6 
 
 12.96 
 
 46.656 
 
 1.897 
 
 1.533 
 
 9.5 
 
 90.25 
 
 857.375 
 
 3.082 
 
 2. 118 
 
 37 
 
 13.69 
 
 50.653 
 
 1.924 
 
 1.47 
 
 9.6 
 
 92.16 
 
 884.736 
 
 3.098 
 
 2.125 
 
 3.8 
 
 14.44 
 
 54.872 
 
 1.949 
 
 1.560 
 
 9.7 
 
 94.09 
 
 912.673 
 
 3. 114 
 
 2.133 
 
 3-9 
 
 15.21 
 
 59.319 
 
 1.975 
 
 1.574 
 
 9.8 
 
 96.04 
 
 941 . 192 
 
 3.130 
 
 2.140 
 
 4 
 
 16 
 
 64 
 
 2 
 
 1.5874 
 
 9.9 
 
 98.01 
 
 970.299 
 
 3.146 
 
 2.147 
 
V 
 
 Table of Squares, Cubes, Square Roots and Cube Roots 47 
 
 Table of Squares, Cubes, Square Roots and Cube Roots 
 OF Numbers from i to idoo 
 
 Remark on the Following Table. Wherever the effect of a fifth decimal in the 
 roots would be to add i to the fourth and final decimal in the table, the addition has 
 been made. 
 
 No. 
 
 Square 
 
 Cube 
 
 Square 
 root 
 
 Cube 
 root 
 
 No. 
 50 
 
 Square 
 
 Cube 
 
 Square 
 root 
 
 Cube 
 root 
 
 I 
 
 I 
 
 I' 
 
 
 
 2,500 
 
 125,000 
 
 7.0711 
 
 3.6840 
 
 2 
 
 4 
 
 8 
 
 I. 4142 
 
 1.2599 
 
 51 
 
 2,601 
 
 132,651 
 
 
 1414 
 
 3.7084 
 
 3 
 
 9 
 
 27 
 
 I. 7321 
 
 1.4422 
 
 52 
 
 2.704 
 
 140,608 
 
 
 2111 
 
 3.7325 
 
 4 
 
 16 
 
 64 
 
 2 
 
 1.5874 
 
 53 
 
 2,809 
 
 148,877 
 
 
 2801 
 
 3.7563 
 
 s 
 
 25 
 
 125 
 
 2.2361 
 
 I . 7100 
 
 ♦ 54 
 
 2.916 
 
 157.464 
 
 
 3485 
 
 3.7798 
 
 6 
 
 36 
 
 216 
 
 2.4495 
 
 1.8171 
 
 55 
 
 3.02s 
 
 166,375 
 
 
 4162 
 
 3.8030 
 
 7 
 
 49 
 
 343 
 
 2.6458 
 
 I. 9129 
 
 56 
 
 3.136 
 
 175,616 
 
 
 4833 
 
 3.8259 
 
 8 
 
 64 
 
 512 
 
 2.8284 
 
 2 
 
 57 
 
 3.249 
 
 185.193 
 
 
 5498 
 
 3.8485 
 
 9 
 
 81 
 
 729 
 
 3 
 
 2.0801 
 
 58 
 
 3.364 
 
 195,112 
 
 
 6158 
 
 3.8709 
 
 10 
 
 100 
 
 1,000 
 
 3.1623 
 
 2.1544 
 
 59 
 
 3,481 
 
 205.379 
 
 
 6811 
 
 3.8930 
 
 II 
 
 121 
 
 1,331 
 
 3.3166 
 
 2.2240 
 
 60 
 
 3.600 
 
 216,000 
 
 
 7460 
 
 3.9149 
 
 12 
 
 144 
 
 1,728 
 
 3.4641 
 
 2.2894 
 
 61 
 
 3.721 
 
 226,981 
 
 
 8102 
 
 3.9365 
 
 13 
 
 169 
 
 2,197 
 
 3.6056 
 
 2.3513 
 
 62 
 
 3.844 
 
 238,328 
 
 
 8740 
 
 3-9579 
 
 14 
 
 196 
 
 2,744 
 
 3.7417 
 
 2.4101 
 
 63 
 
 3,969 
 
 250,047 
 
 
 9373 
 
 3.9791 
 
 IS 
 
 225 
 
 3,375 
 
 3.8730 
 
 2.4662 
 
 64 
 
 4.096 
 
 262,144 
 
 8 
 
 
 4 
 
 16 
 
 256 
 
 4,096 
 
 4 
 
 2.5198 
 
 65 
 
 4.225 
 
 274,625 
 
 8 
 
 0623 
 
 4.0207 
 
 17 
 
 289 
 
 4,913 
 
 4.1231 
 
 2.5713 
 
 66 
 
 4,356 
 
 287,496 
 
 8 
 
 1240 
 
 4.0412 
 
 18 
 
 324 
 
 5.832 
 
 4.2426 
 
 2.6207 
 
 67 
 
 4,489 
 
 300,763 
 
 8 
 
 1854 
 
 4 -0615 
 
 19 
 
 361 
 
 6,859 
 
 4.3589 
 
 2.6684 
 
 68 
 
 4.624 
 
 314,432 
 
 8 
 
 2462 
 
 4.0817 
 
 20 
 
 400 
 
 8,000 
 
 4.4721 
 
 2.7144 
 
 69 
 
 4,761 
 
 328,509 
 
 8 
 
 3066 
 
 4.1016 
 
 21 
 
 441 
 
 9,261 
 
 4.5826 
 
 2.7589 
 
 70 
 
 4,900 
 
 343.000 
 
 8 
 
 3666 
 
 4.1213 
 
 22 
 
 484 
 
 10,648 
 
 4.6904 
 
 2.8020 
 
 71 
 
 5,041 
 
 357,911 
 
 8 
 
 4261 
 
 4-1408 
 
 23 
 
 529 
 
 12,167 
 
 4.7958 
 
 2.8439 
 
 72 
 
 5,184 
 
 373.248 
 
 8 
 
 4853 
 
 4.1602 
 
 24 
 
 576 
 
 13,824 
 
 4.8990 
 
 2.8845 
 
 73 
 
 5,329 
 
 389,017 
 
 8 
 
 5440 
 
 4.1793 
 
 25 
 
 625 
 
 15,625 
 
 5 
 
 2.9240 
 
 74 
 
 5,476 
 
 405,224 
 
 8 
 
 6023 
 
 4.1983 
 
 26 
 
 676 
 
 17.576 
 
 5.0990 
 
 2.9625 
 
 75 
 
 5,625 
 
 421,875 
 
 8 
 
 6603 
 
 4.2172 
 
 27 
 
 729 
 
 19,683 
 
 5.1962 
 
 3 
 
 76 
 
 5,776 
 
 438,976 
 
 8 
 
 7178 
 
 4.2358 
 
 28 
 
 784 
 
 21,952 
 
 5.2915 
 
 3-0366 
 
 77 
 
 5,929 
 
 456,533 
 
 8 
 
 7750 
 
 4.2543 
 
 29 
 
 841 
 
 24,389 
 
 5.3852 
 
 3.0723 
 
 78 
 
 6,084 
 
 474,552 
 
 8 
 
 8818 
 
 4.2727 
 
 30 
 
 900 
 
 27,000 
 
 5.4772 
 
 3.1072 
 
 79 
 
 6,241 
 
 493.039 
 
 8 
 
 8882 
 
 4.2908 
 
 31 
 
 961 
 
 29,791 
 
 5.5678 
 
 3.1414 
 
 80 
 
 6,400 
 
 512,000 
 
 8 
 
 9443 
 
 4.3089 
 
 32 
 
 1,024 
 
 32,768 
 
 5.6569 
 
 3.1748 
 
 81 
 
 6,561 
 
 531,441 
 
 9 
 
 
 4.3267 
 
 33 
 
 1,089 
 
 35.937 
 
 5.7446 
 
 3.2075 
 
 82 
 
 6,724 
 
 551,368 
 
 9 
 
 05S4 
 
 4.3445 
 
 34 
 
 1,156 
 
 39,304 
 
 5.8310 
 
 3.2396 
 
 83 
 
 6,889 
 
 571,787 
 
 9 
 
 1 104 
 
 4.3621 
 
 35 
 
 1.225 
 
 42.875 
 
 5.9161 
 
 3.2711 
 
 84 
 
 7,056 
 
 592,704 
 
 9 
 
 1652 
 
 4.3795 
 
 36 
 
 1,296 
 
 46.656 
 
 6 
 
 3.3019 
 
 85 
 
 7.225 
 
 614,125 
 
 9 
 
 2195 
 
 4.3968 
 
 37 
 
 1,369 
 
 50.653 
 
 6.0828 
 
 3.3322 
 
 86 
 
 7,396 
 
 636,056 
 
 9 
 
 2736 
 
 4.4140 
 
 38 
 
 1,444 
 
 54.872 
 
 6.1644 
 
 3.3620 
 
 87 
 
 7.S69 
 
 658,503 
 
 9 
 
 3274 
 
 4.4310 
 
 39 
 
 1. 521 
 
 59.319 
 
 6.2450 
 
 3.3912 
 
 88 
 
 7,744 
 
 681,472 
 
 9 
 
 3808 
 
 4.4480 
 
 40 
 
 1,600 
 
 64,000 
 
 6.3246 
 
 3.4200 
 
 89 
 
 7,921 
 
 704,969 
 
 9 
 
 4340 
 
 4.4647 
 
 41 
 
 1,681 
 
 68,921 
 
 6.4031 
 
 3.4482 
 
 90 
 
 8,100 
 
 729,000 
 
 9 
 
 4868 
 
 4.4814 
 
 42 
 
 1,764 
 
 74.088 
 
 6.4807 
 
 3.4760 
 
 91 
 
 8,281 
 
 753,571 
 
 9 
 
 5394 
 
 4.4979 
 
 43 
 
 1,849 
 
 79.507 
 
 6.5574 
 
 3 -5034 
 
 92 
 
 8,464 
 
 778,688 
 
 9 
 
 5917 
 
 4.S144 
 
 44 
 
 1,936 
 
 85.184 
 
 6.6332 
 
 3.5303 
 
 93 
 
 8,649 
 
 804,357 
 
 9 
 
 6437 
 
 4.5307 
 
 45 
 
 2,025 
 
 91.125 
 
 6.7082 
 
 3.5569 
 
 94 
 
 8,836 
 
 830,584 
 
 9 
 
 6954 
 
 4.5468 
 
 46 
 
 2,116 
 
 97.336 
 
 6.7823 
 
 3.5830 
 
 95 
 
 9,025 
 
 857,375 
 
 9 
 
 7468 
 
 4.5629 
 
 47 
 
 2,209 
 
 103,823 
 
 6.8557 
 
 3.6088 
 
 96 
 
 9>2i6 
 
 884,736 
 
 9 
 
 7980 
 
 4.5789 
 
 48 
 
 2,304 
 
 110,592 
 
 6. 9282 \ 
 
 3.6342 
 
 97 
 
 9,409 
 
 912,673 
 
 9 
 
 8489 
 
 4.5947 
 
 49 
 
 2,401 
 
 117,649 
 
 7 
 
 3-6593 
 
 98 
 
 9,604 
 
 941,192 
 
 9 
 
 8995 
 
 4.6104 
 
48 
 
 Mathematical Tables 
 
 Table of Squares, Cubes, Square Roots and Cube Roots 
 OF Numbers from i to iooo — (Continued) 
 
 No. 
 
 Square 
 
 Cube 
 
 Square 
 root 
 
 Cube 
 root 
 
 No. 
 152 
 
 Square 
 
 Cube 
 
 Square 
 root 
 
 Cube 
 root 
 
 99 
 
 9.801 
 
 970,299 
 
 9-9499 
 
 4.6261 
 
 23,104 
 
 3.511.808 
 
 12.3288 
 
 5.3368 
 
 ICXD 
 
 10,000 
 
 1,000.000 
 
 10 
 
 4.6416 
 
 153 
 
 23.409 
 
 3,581.577 
 
 12.3693 
 
 5.3485 
 
 lOI 
 
 10,201 
 
 1.030,301 
 
 10.0499 
 
 4.6570 
 
 154 
 
 23,716 
 
 3,652,264 
 
 12.4097 
 
 5.3601 
 
 I02 
 
 10,404 
 
 1,061,208 
 
 10.0995 
 
 4.6723 
 
 155 
 
 24.025 
 
 3,723,875 
 
 12.4499 
 
 5.3717 
 
 103 
 
 10,609 
 
 1,092,727 
 
 10.1489 
 
 4-6875 
 
 156 
 
 24.336 
 
 3,796,416 
 
 12.4900 
 
 5.3832 
 
 104 
 
 10,816 
 
 1,124.864 
 
 10.1980 
 
 4.7027 
 
 157 
 
 24,649 
 
 3,869,893 
 
 12.5300 
 
 5.3947 
 
 105 
 
 11,025 
 
 1.157,625 
 
 10.2470 
 
 4-7177 
 
 158 
 
 24.964 
 
 3,944.312 
 
 12.5698 
 
 5.4061 
 
 106 
 
 11,236 
 
 1,191,016 
 
 10 . 2956 
 
 4.7326 
 
 159 
 
 25,281 
 
 4,019,679 
 
 12.6095 
 
 5.417s 
 
 107 
 
 11,449 
 
 1,225,043 
 
 10.3441 
 
 4-7475 
 
 160 
 
 25,600 
 
 4.096,000 
 
 12.6491 
 
 5.4288 
 
 108 
 
 11,664 
 
 1.259.712 
 
 10.3923 
 
 4 . 7622 
 
 161 
 
 25.921 
 
 4,173.281 
 
 12.6886 
 
 5.4401 
 
 109 
 
 11,881 
 
 1.295.029 
 
 10.4403 
 
 4.7769 
 
 162 
 
 26,244 
 
 4,251,528 
 
 12.7279 
 
 5.4514 
 
 no 
 
 12,100 
 
 1,331,000 
 
 10 . 4881 
 
 4.7914 
 
 163 
 
 26,569 
 
 4.330,747 
 
 12.7671 
 
 5.4626 
 
 III 
 
 12,321 
 
 1.367,631 
 
 10.5357 
 
 4.8059 
 
 164 
 
 26,896 
 
 4.410,944 
 
 12.8062 
 
 5.4737 
 
 112 
 
 12,544 
 
 1,404,928 
 
 10.5830 
 
 4-8203 
 
 165 
 
 27.225 
 
 4,492.125 
 
 12.8452 
 
 5.4848 
 
 113 
 
 12,769 
 
 1.442,897 
 
 10.6301 
 
 4-8346 
 
 166 
 
 27,556 
 
 4,574.296 
 
 12.8841 
 
 5.4959 
 
 114 
 
 12,996 
 
 1. 481. 544 
 
 10.6771 
 
 4.8488 
 
 167 
 
 27,889 
 
 4.657.463 
 
 12.9228 
 
 5.5069 
 
 115 
 
 13,225 
 
 1.520,875 
 
 10.7238 
 
 4.8629 
 
 168 
 
 28,224 
 
 4.741.632 
 
 12.9615 
 
 5.5178 
 
 116 
 
 13,456 
 
 1.560,896 
 
 10.7703 
 
 4.8770 
 
 169 
 
 28,561 
 
 4.826,809 
 
 13 
 
 5.5288 
 
 117 
 
 13,689 
 
 1,601,613 
 
 10.8167 
 
 4.8910 
 
 170 
 
 28,900 
 
 4,913,000 
 
 13.0384 
 
 5.5397 
 
 118 
 
 13,924 
 
 1.643.032 
 
 10.8628 
 
 4.9049 
 
 171 
 
 29.241 
 
 5.000,211 
 
 13.0767 
 
 5.5505 
 
 119 
 
 14,161 
 
 1.685,159 
 
 10.9087 
 
 4.9187 
 
 172 
 
 29,584 
 
 5.088,448 
 
 13.1149 
 
 5.5613 
 
 120 
 
 14.400 
 
 1,728,000 
 
 10.9545 
 
 4-9324 
 
 173 
 
 29,929 
 
 5,177.717 
 
 13.1529 
 
 5.5721 
 
 121 
 
 14,641 
 
 1,771,561 
 
 II 
 
 4-9461 
 
 174 
 
 30,276 
 
 5,268,024 
 
 13.1909 
 
 5.5828 
 
 122 
 
 14.884 
 
 1,815,848 
 
 11.0454 
 
 4-9597 
 
 175 
 
 30,625 
 
 5.359,375 
 
 13.2288 
 
 5.5934 
 
 123 
 
 15.129 
 
 1,860,867 
 
 11.0905 
 
 4-9732 
 
 176 
 
 30,976 
 
 5,451,776 
 
 13.2665 
 
 5.6041 
 
 124 
 
 15.376 
 
 1,906,624 
 
 II. 1355 
 
 4.9866 
 
 177 
 
 31,329 
 
 5,545,233 
 
 13.3041 
 
 5.6147 
 
 125 
 
 15,625 
 
 1,953,125 
 
 II. 1803 
 
 5 
 
 178 
 
 31.684 
 
 5,639,752 
 
 13.3417 
 
 5.6252 
 
 126 
 
 15.876 
 
 2,000,376 
 
 11.2250 
 
 5.0133 
 
 179 
 
 32,041 
 
 5.735.339 
 
 13.3791 
 
 5.6357 
 
 127 
 
 16,129 
 
 2,048,383 
 
 11.2694 
 
 5.0265 
 
 180 
 
 32,400 
 
 5.832,000 
 
 13.4164 
 
 5.6462 
 
 128 
 
 16.384 
 
 2,097,152 
 
 11-3137 
 
 5.0397 
 
 181 
 
 32,761 
 
 5.929,741 
 
 13.4536 
 
 5.6567 
 
 129 
 
 16,641 
 
 2,146,689 
 
 11.3578 
 
 5.0528 
 
 182 
 
 33.124 
 
 6,028,568 
 
 13.4907 
 
 5.6671 
 
 130 
 
 16,900 
 
 2,197,000 
 
 II. 4018 
 
 5.0658 
 
 183 
 
 33.489 
 
 6,128,487 
 
 13.5277 
 
 5.6774 
 
 131 
 
 17.161 
 
 2,248,091 
 
 11.4455 
 
 5.0788 
 
 184 
 
 33.856 
 
 6,229,504 
 
 13.5647 
 
 5.6877 
 
 132 
 
 17,424 
 
 2.299,968 
 
 I I. 4891 
 
 5-0916 
 
 I8S 
 
 34,225 
 
 6,331,625 
 
 13.6015 
 
 5.6980 
 
 133 
 
 17.689 
 
 2.352,637 
 
 11.5326 
 
 5.1045 
 
 186 
 
 34.596 
 
 6,434,856 
 
 13.6382 
 
 5.7083 
 
 134 
 
 17,956 
 
 2,406,104 
 
 11-5758 
 
 5.1172 
 
 187 
 
 34.969 
 
 6,539,203 
 
 13.6748 
 
 5.7185 
 
 135 
 
 18,225 
 
 2,460,375 
 
 II. 6190 
 
 5.1299 
 
 188 
 
 35.344 
 
 6,644,672 
 
 13.7113 
 
 5.7287 
 
 136 
 
 18,496 
 
 2,515,456 
 
 II. 6619 
 
 5. 1426 
 
 189 
 
 35.721 
 
 6,751,269 
 
 13-7477 
 
 5.7388 
 
 137 
 
 18,769 
 
 2.571,353 
 
 11.7047 
 
 5.1551 
 
 190 
 
 36.100 
 
 6,859,000 
 
 13.7840 
 
 5.7489 
 
 138 
 
 19.044 
 
 2,628,072 
 
 11.7473 
 
 5.1676 
 
 191 
 
 36,481 
 
 6,967,871 
 
 13.8203 
 
 5.7590 
 
 139 
 
 19.321 
 
 2,685,619 
 
 11.7898 
 
 5.1801 
 
 192 
 
 36,864 
 
 7,077,888 
 
 13.8564 
 
 5.7690 
 
 140 
 
 19.600 
 
 2.744,000 
 
 11.8322 
 
 5.1925 
 
 193 
 
 37.249 
 
 7,189,057 
 
 13.8924 
 
 5.7790 
 
 141 
 
 19.881 
 
 2,803,221 
 
 11.8743 
 
 5.2048 
 
 194 
 
 37.636 
 
 7,301,384 
 
 13.9284 
 
 5.7890 
 
 142 
 
 20,164 
 
 2,863,288 
 
 I I. 9164 
 
 5. 2171 
 
 195 
 
 38,025 
 
 7,414,875 
 
 13.9642 
 
 5.7989 
 
 143 
 
 20.449 
 
 2,924,207 
 
 11-9583 
 
 5. 2293 
 
 196 
 
 38,416 
 
 7,529,536 
 
 14 
 
 5.8088 
 
 144 
 
 20,736 
 
 2,985,984 
 
 12 
 
 5.2415 
 
 197 
 
 38,809 
 
 7,645,373 
 
 14.0357 
 
 5.8186 
 
 I4S 
 
 21.025 
 
 3,048,625 
 
 12.0416 
 
 5.2536 
 
 198 
 
 39.204 
 
 7,762,392 
 
 14.0712 
 
 5.8285 
 
 146 
 
 21.316 
 
 3,112,136 
 
 12.0830 
 
 5.2656 
 
 199 
 
 39.601 
 
 7,880,599 
 
 14.1067 
 
 5.8383 
 
 147 
 
 21,609 
 
 3.176,523 
 
 12.1244 
 
 5.2776 
 
 200 
 
 40.000 
 
 8,000,000 
 
 14.1421 
 
 5.8480 
 
 148 
 
 21,904 
 
 3,241.792 
 
 12.1655 
 
 5.2896 
 
 201 
 
 40,401 
 
 8,120,601 
 
 14.1774 
 
 5.8578 
 
 149 
 
 22,201 
 
 3.307.949 
 
 12 2066 
 
 5.3015 
 
 202 
 
 40,804 
 
 8,242,408 
 
 14.2127 
 
 5.8675 
 
 150 
 
 22,500 
 
 3,375,000 
 
 12.2474 
 
 5.3133 
 
 203 
 
 41,209 
 
 8,365.427 
 
 14.2478 
 
 5.8771 
 
 151 
 
 22,801 
 
 3,442,951 
 
 12 . 2882 
 
 5.3251 
 
 204 
 
 41,616 
 
 8,489.664 
 
 14.2829 
 
 5.8868 
 
\ 
 
 Table of Squares, Cubes, Square Roots and Cube Roots 49 
 
 Table of Squares, Cubes, Square Roots and Cube Roots 
 OF Numbers from i to iooo — {Continued) 
 
 Square 
 
 Cube 
 
 Square 
 root 
 
 Cube 
 root 
 
 No. 
 
 Square 
 
 42,02s 
 
 8,615,12s 
 
 14.3178 
 
 5.8964 
 
 258 
 
 66,564 
 
 42,436 
 
 8,741,816 
 
 14.3527 
 
 5.9059 
 
 259 
 
 67,081 
 
 42,849 
 
 8,869,743 
 
 14.3875 
 
 5. 9155 
 
 260 
 
 67,600 
 
 43,264 
 
 8,998,912 
 
 14.4222 
 
 5.9250 
 
 261 
 
 68,121 
 
 43,681 
 
 9,129,329 
 
 14.4568 
 
 5.9345 
 
 262 
 
 68,644 
 
 44,icxD 
 
 9,261,000 
 
 14.4914 
 
 5.9439 
 
 263 
 
 69,169 
 
 44,521 
 
 9.393,931 
 
 14.5258 
 
 5.9533 
 
 264 
 
 69,696 
 
 44,944 
 
 9.528,128 
 
 14.5602 
 
 5.9627 
 
 265 
 
 70,225 
 
 45,369 
 
 9.663,597 
 
 14.5945 
 
 5. 9721 
 
 266 
 
 70,756 
 
 45,796 
 
 9,800,344 
 
 14.6287 
 
 5.9814 
 
 267 
 
 71,289 
 
 46,225 
 
 9.938,375 
 
 14.6629 
 
 5.9907 
 
 268 
 
 7^,824 
 
 46,656 
 
 10,077,696 
 
 14.6969 
 
 6 
 
 269 
 
 72,361 
 
 47,089 
 
 10,218,313 
 
 14.7309 
 
 6.0092 
 
 270 
 
 72,900 
 
 47,524 
 
 10,360,232 
 
 14.7648 
 
 6.018s 
 
 271 
 
 73,441 
 
 47,961 
 
 10,503,459 
 
 14.7986 
 
 6.0277 
 
 272 
 
 73,984 
 
 48.400 
 
 10,648,000 
 
 14.8324 
 
 6.0368 
 
 273 
 
 74,529 
 
 48,841 
 
 10,793,861 
 
 14.8661 
 
 6.0459 
 
 274 
 
 75,076 
 
 49,284 
 
 10,941,048 
 
 14.8997 
 
 6.0550 
 
 275 
 
 75,625 
 
 49,729 
 
 11,089,567 
 
 14.9332 
 
 6.0641 
 
 276 
 
 76,176 
 
 50,176 
 
 11,239,424 
 
 14.9666 
 
 6.0732 
 
 277 
 
 76,729 
 
 50,625 
 
 11,390,62s 
 
 15 
 
 6.0822 
 
 278 
 
 77.284 
 
 51,076 
 
 11,543,176 
 
 15.0333 
 
 6.0912 
 
 279 
 
 77,841 
 
 51,529 
 
 11,697,083 
 
 15.0665 
 
 6.1002 
 
 280 
 
 78,400 
 
 51,984 
 
 11,852,352 
 
 15.0997 
 
 6.1091 
 
 281 
 
 78,961 
 
 52,441 
 
 12,008,989 
 
 15.1327 
 
 6.1180 
 
 282 
 
 79,524 
 
 52,900 
 
 12,167,000 
 
 15.1658 
 
 6.1269 
 
 283 
 
 80,089 
 
 53,361 
 
 12,326,391 
 
 15.19S7 
 
 6.1368 
 
 284 
 
 80,656 
 
 53,824 
 
 12,487,168 
 
 15.2315 
 
 6.1446 
 
 285 
 
 81, 22s 
 
 54,289 
 
 12,649,337 
 
 15.2643 
 
 6.IS34 
 
 286 
 
 81,796 
 
 54,756 
 
 12,812,904 
 
 15.2971 
 
 6.1622 
 
 287 
 
 82,369 
 
 55.225 
 
 12,977,875 
 
 15.3297 
 
 6.1710 
 
 288 
 
 82,944 
 
 55,696 
 
 13,144,256 
 
 15.3623 
 
 6.1797 
 
 289 
 
 83,521 
 
 56,169 
 
 13,312,053 
 
 15.3948 
 
 6.188S 
 
 290 
 
 84,100 
 
 56,644 
 
 13,481,272 
 
 15.4272 
 
 6.1972 
 
 291 
 
 84,681 
 
 57,121 
 
 13,651,919 
 
 15.4596 
 
 6.2058 
 
 292 
 
 85,264 
 
 57,600 
 
 13,824,000 
 
 15.4919 
 
 6.2145 
 
 293 
 
 85,849 
 
 58,081 
 
 13,997.521 
 
 15.5242 
 
 6.2231 
 
 294 
 
 86,436 
 
 58,564 
 
 14,172,488 
 
 15.5563 
 
 6.2317 
 
 295 
 
 87,025 
 
 59,049 
 
 14,348,907 
 
 15.588s 
 
 6 . 2403 
 
 296 
 
 87,616 
 
 59,536 
 
 14,526,784 
 
 15.6205 
 
 6.2488 
 
 297 
 
 88,209 
 
 60,025 
 
 14,706,125 
 
 15.6525 
 
 6.2573 
 
 298 
 
 88,804 
 
 60,516 
 
 14,886,936 
 
 15.6844 
 
 6.2658 
 
 299 
 
 89,401 
 
 61,009 
 
 15,069,223 
 
 15.7162 
 
 6.2743 
 
 300 
 
 90,000 
 
 61,504 
 
 15,252.992 
 
 15.7480 
 
 6.2828 
 
 301 
 
 90,601 
 
 62,001 
 
 15,438,249 
 
 15.7797 
 
 6.2912 
 
 302 
 
 91,204 
 
 62,500 
 
 15,625,000 
 
 1S.8114 
 
 6.2936 
 
 303 
 
 91,809 
 
 63,001 
 
 15,813,251 
 
 15.8430 
 
 6.3080 
 
 304 
 
 92,416 
 
 63,504 
 
 16,003,008 
 
 15.8745 
 
 6.3164 
 
 305 
 
 93,025 
 
 64,009 
 
 16,194,277 
 
 15.9060 
 
 6.3247 
 
 306 
 
 93,636 
 
 64,516 
 
 16,387,064 
 
 15.9374 
 
 6.3330 
 
 307 
 
 94,249 
 
 65,025 
 
 16,581,375 
 
 15.9687 
 
 6.3413 
 
 308 
 
 94,864 
 
 65,536 
 
 16,777,216 
 
 16 V 
 
 6.3496 
 
 309 
 
 95,481 
 
 66,049 
 
 16,974,593 
 
 16.0312 
 
 6.3579 
 
 310 
 
 96,100 
 
 Cube 
 
 17,173,512 
 17,373,979 
 17,576,000 
 17,779,581 
 17,984,728 
 18,191,447 
 18,399,744 
 18,609,625 
 18,821,096 
 19,034,163 
 19,248,832 
 19.46s. 109 
 19.683,000 
 19,902,511 
 20,123,648 
 20,346,417 
 20,570,824 
 20,796,875 
 21,024,576 
 21,253,933 
 21,484,952 
 21,717,639 
 21,952,00c 
 22,188,041 
 22,425,768 
 22,665,187 
 22,906,304 
 23,149,125 
 23,393,656 
 23,639,903 
 23,887,872 
 24,137,569 
 24,389,000 
 24,642,171 
 24,897,088 
 25,153,757 
 25,412,184 
 25,672,375 
 25,934,336 
 26,198,073 
 26,463,592 
 26,730,899 
 27,000,000 
 27,270,901 
 27,543,608 
 27,818,127 
 28,094,464 
 28,372,625 
 28,652,616 
 28,934,443 
 29,218,112 
 29.503,629 
 29,791,000 
 
 Square 
 root 
 
 16.0624 
 
 16.0935 
 
 16.1245 
 
 16.1555 
 
 16.1864 
 
 16.2173 
 
 16.2481 
 
 16.2788 
 
 16.3095 
 
 16.3401 
 
 16.3707 
 
 16.4012 
 
 16.4317 
 
 16.4621 
 
 16 . 4924 
 
 16.5227 
 
 16.5529 
 
 16.5831 
 
 .16.6132 
 
 16.6433 
 
 16.6733 
 
 16.7033 
 
 16.7332 
 
 16,7631 
 
 16.7929 
 
 16.8226 
 
 16.8523 
 
 16.8819 
 
 16.9115 
 
 16.9411 
 
 16.9706 
 
 I? 
 
 17.0294 
 
 17.0587 
 
 17.0880 
 
 17.1172 
 
 17.1464 
 
 17.1756 
 
 17.2047 
 
 17 . 2337 
 
 17.2627 
 
 17.2916 
 
 17. 320s 
 
 17.3494 
 
 17.3781 
 
 17.4069 
 
 17.4356 
 
 17 . 4642 
 
 17.4929 
 
 17.5214 
 
 17-5499 
 
 17.5784 
 
 17.6068 
 
50 
 
 Mathematical Tables 
 
 Table of Squares, Cubes, Square Roots and Cube Roots 
 OF Numbers from i to iooo — {Continued) 
 
 No. 
 
 Square 
 
 Cube 
 
 Square 
 root 
 
 Cube 
 root 
 
 No. 
 364 
 
 Square 
 
 Cube 
 
 Square 
 root 
 
 Cube 
 root 
 
 311 
 
 96.721 
 
 30,080,231 
 
 17.6352 
 
 6.7752 
 
 132,496 
 
 48,228,544 
 
 19.0788 
 
 7.1400 
 
 312 
 
 97.344 
 
 30,371,328 
 
 17.663s 
 
 6.7824 
 
 365 
 
 133,225 
 
 48.627,125 
 
 19.1050 
 
 7.1466 
 
 313 
 
 97,969 
 
 30,664.297 
 
 17.6918 
 
 6.7897 
 
 366 
 
 133,956 
 
 49,027,896 
 
 19.1311 
 
 7.IS3I 
 
 314 
 
 98.596 
 
 30,959.144 
 
 17.7200 
 
 6.7969 
 
 367 
 
 134.689 
 
 49,4.30.863 
 
 19.1572 
 
 7.1596 
 
 31S 
 
 99,225 
 
 31,255.875 
 
 17.7482 
 
 6.8041 
 
 368 
 
 135.424 
 
 49.836,032 
 
 19.1833 
 
 7.1661 
 
 316 
 
 99.856 
 
 31,554.496 
 
 17.7764 
 
 6.8113 
 
 369 
 
 136,161 
 
 50,243,409 
 
 19.2094 
 
 7.1726 
 
 317 
 
 100,489 
 
 31. 85s .013 
 
 17.8045 
 
 6.8185 
 
 370 
 
 136,900 
 
 50,653,000 
 
 19.2354 
 
 7.1791 
 
 318 
 
 101,124 
 
 32,157,432 
 
 17.8326 
 
 6.8256 
 
 371 
 
 137,641 
 
 51,064,811 
 
 19.2614 
 
 7.1855 
 
 319 
 
 101,761 
 
 32,461,759 
 
 17.8606 
 
 6.8328 
 
 372 
 
 138,384 
 
 51,478,848 
 
 19.2873 
 
 7.1920 
 
 320 
 
 102,400 
 
 32,768,000 
 
 17.8885 
 
 6.8399 
 
 373 
 
 139,129 
 
 51 .895.117 
 
 19.3132 
 
 7.1984 
 
 321 
 
 103,041 
 
 33.076,161 - 
 
 17.9165 
 
 6.8470 
 
 374 
 
 139.876 
 
 52,313.624 
 
 19.3391 
 
 7.2048 
 
 322 
 
 103,684 
 
 33.386,248 
 
 17.9444 
 
 6.8541 
 
 375 
 
 140,625 
 
 52,734.375 
 
 19.3649 
 
 7.2112 
 
 323 
 
 104,329 
 
 33.698,267 
 
 17.9722 
 
 6.8612 
 
 376 
 
 141.376 
 
 53.157.376 
 
 19-3907 
 
 7.2177 
 
 324 
 
 104,976 
 
 34.012,224 
 
 18 
 
 6.8683 
 
 377 
 
 142,129 
 
 53.582,633 
 
 19.4165 
 
 7.2240 
 
 325 
 
 105,625 
 
 34,328,125 
 
 18.0278 
 
 6.8753 
 
 378 
 
 142,884 
 
 54.010,152 
 
 19.4422 
 
 7.2304 
 
 326 
 
 106.276 
 
 34.645.976 
 
 18.0555 
 
 6.8824 
 
 379 
 
 143.641 
 
 54.439.939 
 
 19.4679 
 
 7-2368 
 
 327 
 
 106,929 
 
 34.965.783 
 
 18.0831 
 
 6.8894 
 
 380 
 
 144.400 
 
 54.872,000 
 
 19.4936 
 
 7.2432 
 
 328 
 
 107,584 
 
 35,287.552 
 
 18. I 108 
 
 6.8964 
 
 381 
 
 145,161 
 
 55.306,341 
 
 19.5192 
 
 7.2495 
 
 329 
 
 108,241 
 
 35.611,289 
 
 18.1384 
 
 6.9034 
 
 382 
 
 145.924 
 
 55.742.968 
 
 19.5448 
 
 7.2558 
 
 330 
 
 108,900 
 
 35,937.000 
 
 18. 1659 
 
 6.9104 
 
 383 
 
 146,689 
 
 56.181,887 
 
 19.5704 
 
 7.2622 
 
 331 
 
 109,561 
 
 36,264,691 
 
 18.1934 
 
 6.9174 
 
 384 
 
 147,456 
 
 56,623,104 
 
 19-5959 
 
 7.2685 
 
 332 
 
 110,224 
 
 36,594.368 
 
 18.2209 
 
 6.9244 
 
 385 
 
 148,225 
 
 57,066,625 
 
 19-6214 
 
 7.2748 
 
 333 
 
 110,889 
 
 36,926,037 
 
 18.2483 
 
 6.9313 
 
 386 
 
 148,996 
 
 57.512.456 
 
 19.6469 
 
 7.2811 
 
 334 
 
 111,556 
 
 37.259.704 
 
 18.2757 
 
 6.9382 
 
 387 
 
 149.769 
 
 57.960,603 
 
 19-6723 
 
 7.2874 
 
 335 
 
 112,225 
 
 37.595.375 
 
 18.3030 
 
 6.9451 
 
 388 
 
 150,544 
 
 58,411,072 
 
 19.6977 
 
 7-2936 
 
 336 
 
 112,896 
 
 37.933,056 
 
 18.3303 
 
 6.9521 
 
 389 
 
 151. 321 
 
 58,863,869 
 
 19-7231 
 
 7.2999 
 
 337 
 
 113,569 
 
 38.272,753 
 
 18.3576 
 
 6.9589 
 
 390 
 
 152,100 
 
 59.319.000 
 
 19.7484 
 
 7.3061 
 
 338 
 
 114,244 
 
 38,614,472 
 
 18.3848 
 
 6.9658 
 
 391 
 
 152,881 
 
 59,776,471 
 
 19.7737 
 
 7.3124 
 
 339 
 
 114,921 
 
 38,958.219 
 
 18.4120 
 
 6.9727 
 
 392 
 
 153.664 
 
 60,236,288 
 
 19.7990 
 
 7.3186 
 
 340 
 
 115,600 
 
 39-304,000 
 
 18.4391 
 
 6.9795 
 
 393 
 
 154.449 
 
 60,698,457 
 
 19.8242 
 
 7.3248 
 
 341 
 
 116,281 
 
 39.651. 821 
 
 18.4662 
 
 6.9864 
 
 394 
 
 155.236 
 
 61,162,984 
 
 19.8494 
 
 7.3310 
 
 342 
 
 116,964 
 
 40,001,688 
 
 18.4932 
 
 6.9932 
 
 395 
 
 156,025 
 
 61,629,875 
 
 19.8746 
 
 7.3372 
 
 343 
 
 117,649 
 
 40,353.607 
 
 18.5203 
 
 7 
 
 396 
 
 156,816 
 
 62,099,136 
 
 19-8997 
 
 7.3434 
 
 344 
 
 118,336 
 
 40,707,584 
 
 18.5472 
 
 7.0068 
 
 397 
 
 157,609 
 
 62,570,773 
 
 19.9249 
 
 7.3496 
 
 345 
 
 119,025 
 
 41,063,625 
 
 18.5742 
 
 7.0136 
 
 398 
 
 158,404 
 
 63,044,792 
 
 19-9499 
 
 7-3558 
 
 346 
 
 119,716 
 
 41,421,736 
 
 18.6011 
 
 7.0203 
 
 399 
 
 159,201 
 
 63,521,199 
 
 19.9750 
 
 7-3619 
 
 347 
 
 120,409 
 
 41,781,923 
 
 18.6279 
 
 7.0271 
 
 400 
 
 160,000 
 
 64,000,000 
 
 20 
 
 7-3681 
 
 348 
 
 121,104 
 
 42,144,192 
 
 18.6548 
 
 7.0338 
 
 401 
 
 160,801 
 
 64,481,201 
 
 20.0250 
 
 7.3742 
 
 349 
 
 121,801 
 
 42,508,549 
 
 18.6815 
 
 7.0406 
 
 402 
 
 161,604 
 
 64,964,808 
 
 20.0499 
 
 7.3803 
 
 350 
 
 122,500 
 
 42,875.000 
 
 18.7083 
 
 7.0473 
 
 403 
 
 162,409 
 
 65,450,827 
 
 20.0749 
 
 7.3864 
 
 351 
 
 123,201 
 
 43.243.551 
 
 18.7350 
 
 7.0540 
 
 404 
 
 163,216 
 
 65,939,264 
 
 20.0998 
 
 7.3925 
 
 352 
 
 123,904 
 
 43.614,208 
 
 18.7617 
 
 7.0607 
 
 405 
 
 164,025 
 
 66,430,125 
 
 20.1246 
 
 7.3986 
 
 353 
 
 124,609 
 
 43,986,977 
 
 18.7883 
 
 7.0674 
 
 406 
 
 164,836 
 
 66,923,416 
 
 20.1494 
 
 7.4047 
 
 354 
 
 125,316 
 
 44,361,864 
 
 18.8149 
 
 7.0740 
 
 407 
 
 165,649 
 
 67,419,143 
 
 20.1742 
 
 7.4108 
 
 355 
 
 126,025 
 
 44,738,875 
 
 18.8414 
 
 7.0807 
 
 408 
 
 166,464 
 
 67,917,312 
 
 20.1990 
 
 7.4169 
 
 356 
 
 126,736 
 
 45.118,016 
 
 18.8680 
 
 7.0873 
 
 409 
 
 167,281 
 
 68,417,929 
 
 20.2237 
 
 7.4229 
 
 357 
 
 127,449 
 
 45,499,293 
 
 18.8944 
 
 7.0940 
 
 410 
 
 168,100 
 
 68,921,000 
 
 20.2485 
 
 7.4290 
 
 358 
 
 128,164 
 
 45,882,712 
 
 18.9209 
 
 7.1006 
 
 411 
 
 168,921 
 
 69,426,531 
 
 20.2731 
 
 7.4350 
 
 359 
 
 128,881 
 
 46,268,279 
 
 18.9473 
 
 7 . 1072 
 
 412 
 
 169,744 
 
 69,934,528 
 
 20.2978 
 
 7.4410 
 
 360 
 
 129.600 
 
 46,656,000 
 
 18.9737 
 
 7.1138 
 
 413 
 
 170,569 
 
 70,444,997 
 
 20.3224 
 
 7.4470 
 
 361 
 
 130,321 
 
 47,045,881 
 
 19 
 
 7 . 1204 
 
 414 
 
 171,396 
 
 70,957,944 
 
 20.3470 
 
 7.4530 
 
 362 
 
 131,044 
 
 47,437,928 
 
 19.0263 
 
 7.1269 
 
 415 
 
 172,225 
 
 71,473.375 
 
 20.3715 
 
 7.4590 
 
 363 
 
 131,769 
 
 47.832,147 
 
 19.0526 
 
 7.1335 
 
 416 
 
 173,056 
 
 71,991,296 
 
 20.3961 
 
 7.4650 
 
Table of Squares, Cubes, Square Roots and Cube Roots 51 
 
 Table of Squares, Cubes, Square Roots and Cube Roots 
 OF Numbers from i to iooo — {Continued) 
 
 No. 
 
 Square 
 
 Cube 
 
 Square 
 root 
 
 Cube 
 root 
 
 No. 
 
 Square 
 
 Cube 
 
 Square 
 root 
 
 Cube 
 root 
 
 417 
 
 173.889 
 
 72,511,713 
 
 20.4206 
 
 7.4710 
 
 470 
 
 220,900 
 
 103,823,000 
 
 21.6795 
 
 7.7750 
 
 418 
 
 174,724 
 
 73,034,632 
 
 20.4550 
 
 7.4770 
 
 471 
 
 221,841 
 
 104,487,111 
 
 21.702s 
 
 7.7805 
 
 419 
 
 175,561 
 
 73,560,059 
 
 20.469s 
 
 7.4829 
 
 472 
 
 222,784 
 
 105,154,048 
 
 21.7256 
 
 7.7860 
 
 420 
 
 176,400 
 
 74,088,000 
 
 20.4939 
 
 7.4889 
 
 473 
 
 223,729 
 
 105,823,817 
 
 21.7486 
 
 7.791S 
 
 421 
 
 177,241 
 
 74,618,461 
 
 20. s 183 
 
 7.4948 
 
 474 
 
 224,676 
 
 106,496,424. 
 
 21.7715 
 
 7.7970 
 
 422 
 
 178,084 
 
 75,151.448 
 
 20.5426 
 
 7.5007 
 
 475 
 
 225,625 
 
 107,171.875 
 
 21.7945 
 
 7 8025 
 
 423 
 
 178,929 
 
 75.686,967 
 
 20.S670 
 
 7.5067 
 
 476 
 
 226,576 
 
 107,850,176 
 
 21.8174 
 
 7.8079 
 
 424 
 
 179.776 
 
 76,225,024 
 
 20.5913 
 
 7.5126 
 
 477 
 
 227.529 
 
 108,531,333 
 
 21.8403 
 
 7.8134 
 
 42s 
 
 180,62s 
 
 76,765,625 
 
 20.6155 
 
 7.S185 
 
 478 
 
 228,484 
 
 109,215,352 
 
 21.8632 
 
 7.8188 
 
 426 
 
 181,476 
 
 77.308,776 
 
 20.6398 
 
 7.5244 
 
 479 
 
 229,441 
 
 109,902,239 
 
 21.8861 
 
 7.8243 
 
 427 
 
 182,329 
 
 77.854.483 
 
 20.6640 
 
 7.5302 
 
 480 
 
 230,400 
 
 110,592,000 
 
 21.9089 
 
 7.8297 
 
 428 
 
 183,184 
 
 78,402,752 
 
 20.6882 
 
 7.5361 
 
 481 
 
 231,361 
 
 111,284,641 
 
 21.9317 
 
 7.8362 
 
 429 
 
 184,041 
 
 78,953,589 
 
 20.7123 
 
 7.5420 
 
 482 
 
 232,324 
 
 111,980,168 
 
 21.9545 
 
 7.8406 
 
 430 
 
 184,900 
 
 79,507,000 
 
 20.7364 
 
 7.5478 
 
 483 
 
 233,289 
 
 112,678,587 
 
 21.9773 
 
 7.8460 
 
 431 
 
 185.761 
 
 80,062,991 
 
 20.760s 
 
 7.5537 
 
 484 
 
 234,256 
 
 113,379.904 
 
 22 
 
 7.8514 
 
 432 
 
 186,624 
 
 80,621,568 
 
 20.7846 
 
 7.5595 
 
 485 
 
 235.22s 
 
 114.084,12s 
 
 22.0227 
 
 7.8568 
 
 433 
 
 187,489 
 
 81,182,737 
 
 20.8087 
 
 7.5654 
 
 486 
 
 236,196 
 
 114.791,256 
 
 22.0454 
 
 7.8622 
 
 434 
 
 188,356 
 
 81,746,504 
 
 20.8327 
 
 7.5712 
 
 487 
 
 237.169 
 
 115,501,303 
 
 22.0681 
 
 7.8676 
 
 435 
 
 189,225 
 
 82,312,875 
 
 20.8567 
 
 7.5770 
 
 488 
 
 238,144 
 
 116,214,272 
 
 22.0907 
 
 7.8730 
 
 436 
 
 190,096 
 
 82,881,856 
 
 20.8806 
 
 7.5828 
 
 489 
 
 239.121 
 
 116,930,169 
 
 22.1133 
 
 7.8784 
 
 437 
 
 190,969 
 
 83,453.453 
 
 20.9045 
 
 7.5886 
 
 490 
 
 240,100 
 
 117,649,000 
 
 22.1359 
 
 7.8837 
 
 438 
 
 191,844 
 
 84,027,672 
 
 20.9284 
 
 7.5944 
 
 491 
 
 241 -,081 
 
 118,370,771 
 
 22.158s 
 
 7.8891 
 
 439 
 
 192,721 
 
 84,604,519 
 
 20.9523 
 
 7.6001 
 
 492 
 
 242,064 
 
 119,095,488 
 
 22.1811 
 
 7.8944 
 
 440 
 
 193,600 
 
 85,184,000 
 
 20.9762 
 
 7.6059 
 
 493 
 
 243,049 
 
 119,823,157 
 
 22.2036 
 
 7.8998 
 
 441 
 
 194,481 
 
 85,766,121 
 
 21 
 
 7.6117 
 
 494 
 
 244,036 
 
 120,553,784 
 
 22.2261 
 
 7.9051 
 
 442 
 
 195.364 
 
 86,350,888 
 
 21.0238 
 
 7.6174 
 
 495 
 
 245,025 
 
 121,287,37s 
 
 22.2486 
 
 7.9105 
 
 443 
 
 196,249 
 
 86,938,307 
 
 21.0476 
 
 7.6232 
 
 496 
 
 246,016 
 
 122,023,936 
 
 22.2711 
 
 7.9158 
 
 444 
 
 197.136 
 
 87,528,384 
 
 21.0713 
 
 7.6289 
 
 497 
 
 247,009 
 
 122,763,473 
 
 22.2935 
 
 7.9211 
 
 445 
 
 198,025 
 
 88,i2i,i2S 
 
 21.0950 
 
 7.6346 
 
 498 
 
 248,004 
 
 123,505,992 
 
 22.3159 
 
 7.9264 
 
 446 
 
 198,916 
 
 88,716,536 
 
 21.1187 
 
 7.6403 
 
 499 
 
 249,001 
 
 124,251,499 
 
 22.3383 
 
 7.9317 
 
 447 
 
 199.809 
 
 89,314,623 
 
 21 . 1424 
 
 7.6460 
 
 500 
 
 250,000 
 
 125,000,000 
 
 22.3607 
 
 7.9370 
 
 448 
 
 200,704 
 
 89,915,392 
 
 21.1660 
 
 7.6517 
 
 SOI 
 
 251,001 
 
 125,751,501 
 
 22.3830 
 
 7.9423 
 
 449 
 
 201,601 
 
 90,518,849 
 
 21 . 1896 
 
 7.6574 
 
 S02 
 
 252,004 
 
 126,506,008 
 
 22.4054 
 
 7.9476 
 
 450 
 
 202,500 
 
 91,125,000 
 
 21.2132 
 
 7.6631 
 
 503 
 
 253.009 
 
 127,263,527 
 
 22.4277 
 
 7.9528 
 
 451 
 
 203,401 
 
 91,733,851 
 
 21.2368 
 
 7.6688 
 
 S04 
 
 254,016 
 
 128,024,064 
 
 22.4499 
 
 7.9581 
 
 452 
 
 204,304 
 
 92,345,408 
 
 21.2603 
 
 7.6744 
 
 505 
 
 255,025 
 
 128,787,62s 
 
 22.4722 
 
 7.9634 
 
 453 
 
 205,209 
 
 92,959.677 
 
 21.2838 
 
 7.6801 
 
 506 
 
 256,036 
 
 129,554,216 
 
 22.4944- 
 
 7.9686 
 
 454 
 
 206,116 
 
 93.S76.664 
 
 21.3073 
 
 7.6857 
 
 507 
 
 257,049 
 
 130,323,843 
 
 22.S167 
 
 7.9739 
 
 455 
 
 207,02s 
 
 94.196.37S 
 
 21.3307 
 
 7.6914 
 
 S08 
 
 258,064 
 
 131,096,512 
 
 22.5389 
 
 7.9791 
 
 456 
 
 207,936 
 
 94,818,816 
 
 21.3542 
 
 7.6970 
 
 509 
 
 259,081 
 
 131,872,229 
 
 22.5610 
 
 7.9843 
 
 457 
 
 208,849 
 
 95,443,993 
 
 21.3776 
 
 7.7026 
 
 510 
 
 260,100 
 
 132,651,000 
 
 22.5832 
 
 7.9896 
 
 458 
 
 209,764 
 
 96,071,912 
 
 21.4009 
 
 7.7082 
 
 Sii 
 
 261,121 
 
 133,432,831 
 
 22.6053 
 
 7.9948 
 
 459 
 
 210,681 
 
 96,702,579 
 
 21.4243 
 
 7.7138 
 
 512 
 
 262,144 
 
 134,217,728 
 
 22 . 6274 
 
 8 
 
 460 
 
 211,600 
 
 97,336,000 
 
 21.4476 
 
 7.7194 
 
 513 
 
 263,169 
 
 135,005,697 
 
 22.6495 
 
 8.0052 
 
 461 
 
 212,521 
 
 97,972,181 
 
 21.4709 
 
 7.7250 
 
 514 
 
 264,196 
 
 135,796,744 
 
 22.6716 
 
 8.0104 
 
 462 
 
 213,444 
 
 98,611,128 
 
 21.4942 
 
 7.7306 
 
 51S 
 
 265,225 
 
 136,590,875 
 
 22.6936 
 
 8.0156 
 
 463 
 
 214,369 
 
 99,252.847 
 
 21.5174 
 
 7.7362 
 
 516 
 
 266,256 
 
 137,388,096 
 
 22.7156 
 
 8.0208 
 
 464 
 
 215,296 
 
 99,897,344 
 
 21 . 5407 
 
 7.7418 
 
 517 
 
 267,289 
 
 138,188,413 
 
 22.7376 
 
 8.0260 
 
 465 
 
 216,22s 
 
 ioo,S44.62S 
 
 21.5639 
 
 7.7473 
 
 518 
 
 268,324 
 
 138,991,832 
 
 22.7596 
 
 8.0311 
 
 466 
 
 217,156 
 
 101,194,696 
 
 21 . 5870 
 
 7.7529 
 
 519 
 
 269,361 
 
 139,798,359 
 
 22.7816 
 
 8.0363 
 
 467 
 
 218,089 
 
 101,847,563 
 
 21 . 6102 
 
 7.7584 
 
 520 
 
 270,400 
 
 140,608,000 
 
 22.8035 
 
 8.041S 
 
 468 
 
 219,024 
 
 102,503,232 
 
 21.6333 
 
 7.7639 
 
 521 
 
 271,441 
 
 141,420,761 
 
 22.8254 
 
 8.0466 
 
 469 
 
 219,961 
 
 103,161,709 
 
 21.6564 
 
 7.7695 
 
 522 
 
 272,484 
 
 '142,236,648 
 
 22.8473 
 
 8.0517 
 
52 
 
 Mathematical Tables 
 
 Table of Squares, Cubes, Square Roots and Cube Roots 
 OF Numbers from i to iooo — {Continued) 
 
 No. 
 
 Square 
 
 Cube 
 
 Square 
 root 
 
 Cube 
 root 
 
 No. 
 
 Square 
 
 Cube 
 
 Square 
 root 
 
 Cube 
 root 
 
 523 
 
 273.529 
 
 143,055.667 
 
 22.8692 
 
 8.0569 
 
 576 
 
 331,776 
 
 191,102,976 
 
 24 
 
 8.3203 
 
 524 
 
 274,576 
 
 143,877,824 
 
 22 . 8910 
 
 8.0620 
 
 577 
 
 332,929 
 
 192,100,033 
 
 24.0208 
 
 8.3251 
 
 525 
 
 275,62s 
 
 144,703.125 
 
 22.9129 
 
 8.0671 
 
 578 
 
 334,084 
 
 193.100,552 
 
 24.0416 
 
 8.3300 
 
 526 
 
 276,676 
 
 145.531,576 
 
 22.9347 
 
 8.0723 
 
 579 
 
 335,241 
 
 194,104,539 
 
 24.0624 
 
 8.3348 
 
 527 
 
 277,729 
 
 146,363,183 
 
 22.9565 
 
 8.0774 
 
 580 
 
 336,400 
 
 195,112,000 
 
 24.0832 
 
 8.3396 
 
 528 
 
 278,784 
 
 147,197,952 
 
 22.9783 
 
 8.0S25 
 
 581 
 
 337,561 
 
 196,122,941 
 
 24.1039 
 
 8.3443 
 
 529 
 
 279,841 
 
 148,035,889 
 
 23 
 
 8.0876 
 
 582 
 
 338,724 
 
 197,137,368 
 
 24.1247 
 
 8.3491 
 
 530 
 
 280,900 
 
 148,877,000 
 
 23.0217 
 
 8.0927 
 
 583 
 
 339,889 
 
 198.155,287 
 
 24.1454 
 
 8.3539 
 
 531 
 
 281,961 
 
 149,721,291 
 
 23.0434 
 
 8.0978 
 
 584 
 
 341.056 
 
 199.176,704 
 
 24.1661 
 
 8.3587 
 
 532 
 
 283,024 
 
 150,568,768 
 
 23.0651 
 
 8.1028 
 
 585 
 
 342,225 
 
 200,201,625 
 
 24.1868 
 
 8.3634 
 
 533 
 
 284,089 
 
 151,419,437- 
 
 23.0868 
 
 8.1079 
 
 586 
 
 343.396 
 
 201,230,056 
 
 24.2074 
 
 8.3682 
 
 534 
 
 285,156 
 
 152.273,304 
 
 23.1084 
 
 8. I 130 
 
 587 
 
 344,569 
 
 202,262,003 
 
 24.2281 
 
 8.3730 
 
 535 
 
 286,225 
 
 153,130,375 
 
 23.1301 
 
 8.1180 
 
 588 
 
 345,744 
 
 203,297,472 
 
 24.2487 
 
 8.3777 
 
 536 
 
 287,296 
 
 153,990,656 
 
 23.1517 
 
 8.1231 
 
 589 
 
 346,921 
 
 204,336,469 
 
 24 . 2693 
 
 8.3825 
 
 537 
 
 288,369 
 
 154,854,153 
 
 23.1733 
 
 8.1281 
 
 590 
 
 348,100 
 
 205,379-000 
 
 24.2899 
 
 8.3872 
 
 538 
 
 289,444 
 
 155,720,872 
 
 23.1948 
 
 8.1332 
 
 591 
 
 349.281 
 
 206,425,071 
 
 24.3105 
 
 8.3919 
 
 539 
 
 290,521 
 
 156,590,819 
 
 23.2164 
 
 8.1382 
 
 592 
 
 350,464 
 
 207,474,688 
 
 24.3311 
 
 8.3967 
 
 S40 
 
 291,600 
 
 157,464,000 
 
 23.2379 
 
 8.1433 
 
 593 
 
 351,649 
 
 208,526,857 
 
 24.3516 
 
 8.4014 
 
 541 
 
 292,681 
 
 158,340,421 
 
 23.2594 
 
 8.1483 
 
 594 
 
 352,836 
 
 209,584,584 
 
 24.3721 
 
 8.4061 
 
 542 
 
 293,764 
 
 159,220,088 
 
 23.2809 
 
 8.1533 
 
 595 
 
 354,025 
 
 210,644,875 
 
 24.3926 
 
 8.4108 
 
 543 
 
 294,849 
 
 160,103,007 
 
 23.3024 
 
 8.1583 
 
 596 
 
 355,216 
 
 211,708,736 
 
 24.4131 
 
 8.4155 
 
 544 
 
 295,936 
 
 160,989,184 
 
 23.3238 
 
 8.1633 
 
 597 
 
 356,409 
 
 212,776,173 
 
 24.4336 
 
 8.4202 
 
 545 
 
 297,02s 
 
 161,878,625 
 
 23.3452 
 
 8.1683 
 
 598 
 
 357,604 
 
 213,847.192 
 
 24.4540 
 
 8.4249 
 
 546 
 
 298.116 
 
 162,771,336 
 
 23.3666 
 
 8.1733 
 
 599 
 
 358,801 
 
 214.921,799 
 
 24.4745 
 
 8.4296 
 
 547 
 
 299.209 
 
 163.667,323 
 
 23.3880 
 
 8.1783 
 
 600 
 
 360,000 
 
 216,000,000 
 
 24.4949 
 
 8.4343 
 
 548 
 
 300,304 
 
 164,566,592 
 
 23.4094 
 
 8.1833 
 
 601 
 
 361,201 
 
 217,081,801 
 
 24.5153 
 
 8.4390 
 
 549 
 
 301,401 
 
 165,469,149 
 
 23.4307 
 
 8.1882 
 
 602 
 
 362,404 
 
 218,167,208 
 
 24.5357 
 
 8.4437 
 
 550 
 
 302,500 
 
 166,375,000 
 
 23.4521 
 
 8.1932 
 
 603 
 
 363,609 
 
 219,256,227 
 
 24.5561 
 
 8.4484 
 
 551 
 
 303,601 
 
 167,284,151 
 
 23.4734 
 
 8.1982 
 
 604 
 
 364,816 
 
 220,348,864 
 
 24.5764 
 
 8.4530 
 
 552 
 
 304,704 
 
 168,196,608 
 
 23.4947 
 
 8 . 2031 
 
 605 
 
 366,025 
 
 221,445,125 
 
 24.5967 
 
 8.4577 
 
 553 
 
 305,809 
 
 169,112,377 
 
 23.5160 
 
 8 . 2081 
 
 606 
 
 367.236 
 
 222,545.016 
 
 24.6171 
 
 8.4623 
 
 554 
 
 306,916 
 
 170,031,464 
 
 23.5272 
 
 8.2130 
 
 607 
 
 368,449 
 
 223,648,543 
 
 24.6374 
 
 8.4670 
 
 555 
 
 308,025 
 
 170,953,875 
 
 23.5584 
 
 8 . 2180 
 
 608 
 
 369,664 
 
 224,755,712 
 
 24.6577 
 
 8.4716 
 
 556 
 
 309,136 
 
 171,879,616 
 
 23.5797 
 
 8 . 2229 
 
 609 
 
 370,881 
 
 225,866,529 
 
 24.6779 
 
 8.4763 
 
 557 
 
 310,249 
 
 172,808,693 
 
 23.6008 
 
 8.2278 
 
 610 
 
 372,100 
 
 226,981,000 
 
 24.6982 
 
 8.4809 
 
 558 
 
 311,364 
 
 173,741,112 
 
 23 . 6220 
 
 8.2327 
 
 611 
 
 373,321 
 
 228,099,131 
 
 24.7184 
 
 8.4856 
 
 559 
 
 312.481 
 
 174,676,879 
 
 23.6432 
 
 8.2377 
 
 612 
 
 374,544 
 
 229,220,928 
 
 24.7386 
 
 8.4902 
 
 56o 
 
 313,600 
 
 175.616,000 
 
 23.6643 
 
 8.2426 
 
 613 
 
 375,769 
 
 230,346,397 
 
 24.7588 
 
 8.4948 
 
 561 
 
 314.721 
 
 176.558,481 
 
 23.6854 
 
 8.2475 
 
 614 
 
 376,996 
 
 231,475,544 
 
 24.7790 
 
 8.4994 
 
 562 
 
 31S.844 
 
 177.504,328 
 
 23.7065 
 
 8.2524 
 
 61S 
 
 378,22s 
 
 232,608,375 
 
 24.7992 
 
 8.5040 
 
 563 
 
 316,969 
 
 178,453,547 
 
 23.7276 
 
 8.2573 
 
 616 
 
 379,456 
 
 233,744,896 
 
 24.8193 
 
 8.5086 
 
 564 
 
 318,096 
 
 179,406,144 
 
 23.7487 
 
 8.2621 
 
 617 
 
 380,689 
 
 234,885,113 
 
 24.8395 
 
 8.5132 
 
 565 
 
 319,225 
 
 180,362,125 
 
 23.7697 
 
 8.2670 
 
 618 
 
 381,924 
 
 236,029,032 
 
 24.8596 
 
 8.5178 
 
 566 
 
 320,356 
 
 181,321,496 
 
 23.7908 
 
 8.2719 
 
 619 
 
 383,161 
 
 237,176,659 
 
 24.8797 
 
 8.5224 
 
 567 
 
 321,489 
 
 182,284.263 
 
 23.8118 
 
 8.2768 
 
 620 
 
 384,400 
 
 238,328,000 
 
 24.8998 
 
 8.5270 
 
 568 
 
 322,624 
 
 183,250,432 
 
 23.8328 
 
 8.2816 
 
 621 
 
 385,641 
 
 239.483,061 
 
 24.9199 
 
 8.5316 
 
 569 
 
 323,761 
 
 184,220,009 
 
 23.8537 
 
 8.2865 
 
 622 
 
 386,884 
 
 240,641,848 
 
 24.9399 
 
 8.5362 
 
 S70 
 
 324.900 
 
 185,193,000 
 
 23.8747 
 
 8.2913 
 
 623 
 
 388,129 
 
 241,804,367 
 
 24.9600 
 
 8.5408 
 
 571 
 
 326,041 
 
 186,169,411 
 
 23.8956 
 
 8.2962 
 
 624 
 
 389,376 
 
 242,970,624 
 
 24.9800 
 
 8.5453 
 
 572 
 
 327,184 
 
 187,149,248 
 
 23.916s 
 
 8.3010 
 
 625 
 
 390,625 
 
 244,140,62s 
 
 25 
 
 8.5499 
 
 573 
 
 328,329 
 
 188,132,517 
 
 23.9374 
 
 8.3059 
 
 626 
 
 391,876 
 
 245,314.376 
 
 25.0200 
 
 8.5544 
 
 574 
 
 329.476 
 
 189,119,224 
 
 23.9583 
 
 8.3107 
 
 627 
 
 393,129 
 
 246,491.883 
 
 25.0400 
 
 8.5590 
 
 S75 
 
 330,625 
 
 190,109,375 
 
 23.9792 
 
 8.3155 
 
 628 
 
 394,384 
 
 247,673.152 
 
 25.0590 
 
 8.563s 
 
\ 
 
 Table of Squares, Cubes, Square Roots and Cube Roots 53 
 
 Table oe Squares, Cubes, Square Roots and Cube Roots 
 or Numbers from i to iooo — (Continued) 
 
 No. 
 
 Square 
 
 Cube 
 
 Square 
 root 
 
 Cube 
 root 
 
 No. 
 
 Square 
 
 Cube 
 
 Square 
 root 
 
 Cube 
 root 
 
 629 
 
 395,641 
 
 248,858,189 
 
 25.0799 
 
 8.5681 
 
 682 
 
 465.124 
 
 317,214.568 
 
 26.1151 
 
 8.8023 
 
 630 
 
 396,900 
 
 250,047,000 
 
 25.0998 
 
 8.5726 
 
 683 
 
 466,489 
 
 318,611,987 
 
 26.1343 
 
 8 
 
 8066 
 
 631 
 
 398,161 
 
 251,239.591 
 
 25.1197 
 
 8.5772 
 
 684 
 
 467.856 
 
 320,013,504 
 
 26.1534 
 
 8 
 
 8109 
 
 632 
 
 399.424 
 
 252,435.968 
 
 25 . 1396 
 
 8.5817 
 
 685 
 
 469.225 
 
 321,419.125 
 
 26.1725 
 
 8 
 
 8152 
 
 633 
 
 400,689 
 
 253.636,137 
 
 25.1595 
 
 8.5862 
 
 686 
 
 470,596 
 
 322,828,856 
 
 26.1916 
 
 8 
 
 8194 
 
 634 
 
 401,956 
 
 254,840,104 
 
 25 . 1794 
 
 8.5907 
 
 687 
 
 471,969 
 
 324,242,703 
 
 26.2107 
 
 8 
 
 8237 
 
 63s 
 
 403,225 
 
 256,047.875 
 
 25.1992 
 
 8.5952 
 
 688 
 
 473,344 
 
 325,660,672 
 
 26 . 2298 
 
 8 
 
 8280 
 
 636 
 
 404,496 
 
 257,259.456 
 
 25.2190 
 
 8.5997 
 
 689 
 
 474.721 
 
 327,082,769 
 
 26.2488 
 
 8 
 
 8323 
 
 637 
 
 405,769 
 
 258,474,853 
 
 25 . 2389 
 
 8.6043 
 
 690 
 
 476,100 
 
 328,509,000 
 
 26.2679 
 
 8 
 
 8366 
 
 638 
 
 407,044 
 
 259,694,072 
 
 25 . 2587 
 
 8.6088 
 
 691 
 
 477,481 
 
 329,939.371 
 
 26.2869 
 
 8 
 
 8408 
 
 639 
 
 408,321 
 
 260,917,119 
 
 25.2784 
 
 8.6132 
 
 692 
 
 478,864 
 
 331,373.888 
 
 26.3059 
 
 8 
 
 8451 
 
 640 
 
 409,600 
 
 262,144,000 
 
 25.2982 
 
 8.6177 
 
 693 
 
 480,249 
 
 332,812,557 
 
 26.3249 
 
 8 
 
 8493 
 
 641 
 
 410.881 
 
 263,374,721 
 
 25.3180 
 
 8.6222 
 
 694 
 
 481,636 
 
 334.255.384 
 
 26.3439 
 
 8 
 
 8536 
 
 642 
 
 412,164 
 
 264,609,288 
 
 25.3377 
 
 8.6267 
 
 695 
 
 483,025 
 
 335,702,375 
 
 26.3629 
 
 8 
 
 8578 
 
 643 
 
 413,449 
 
 265,847,707 
 
 25.3574 
 
 8.6312 
 
 696 
 
 484.416 
 
 337,153.536 
 
 26.3818 
 
 8 
 
 8621 
 
 644 
 
 414,736 
 
 267,089,984 
 
 25.3772 
 
 8.6357 
 
 697 
 
 485,809 
 
 338,608,873 
 
 26.4008 
 
 8 
 
 8663 
 
 645 
 
 416.025 
 
 268,336,125 
 
 25.3969 
 
 8.6401 
 
 698 
 
 487,204 
 
 340,068,392 
 
 26.4197 
 
 8 
 
 8706 
 
 646 
 
 417,316 
 
 269,586,136 
 
 25.4165 
 
 8.6446 
 
 699 
 
 488,601 
 
 341.532,099 
 
 26.4386 
 
 8 
 
 8748 
 
 647 
 
 418,609 
 
 270,840,023 
 
 25.4362 
 
 8.6490 
 
 700 
 
 490,000 
 
 343.000,000 
 
 26.4575 
 
 8 
 
 8790 
 
 648 
 
 419.904 
 
 272,097,792 
 
 25.4558 
 
 8.6535 
 
 701 
 
 491.401 
 
 344,472,101 
 
 26.4764 
 
 8 
 
 8833 
 
 649 
 
 421,201 
 
 273.359.449 
 
 25.4755 
 
 8.6579 
 
 702 
 
 492,804 
 
 345.948,408 
 
 26.4953 
 
 8 
 
 8875 
 
 650 
 
 422,500 
 
 274,625,000 
 
 25.4951 
 
 8.6624 
 
 703 
 
 494,209 
 
 347.428,927 
 
 26.5141 
 
 8 
 
 8917 
 
 651 
 
 423,801 
 
 275.894,451 
 
 25.5147 
 
 8.6668 
 
 704 
 
 495,616 
 
 348,913,664 
 
 26.5330 
 
 8 
 
 8959 
 
 652 
 
 425,104 
 
 277,167,808 
 
 25.5343 
 
 8.6713 
 
 705 
 
 497,025 
 
 350,402,625 
 
 26.5518 
 
 8 
 
 9001 
 
 653 
 
 426,409 
 
 278,445.077 
 
 25.5539 
 
 8.6757 
 
 706 
 
 498,436 
 
 351,895,816 
 
 26.5707 
 
 8 
 
 9043 
 
 654 
 
 427,716 
 
 279.726,264 
 
 25.5734 
 
 8.6801 
 
 707 
 
 499-849 
 
 353,393,243 
 
 26.5895 
 
 8 
 
 9085 
 
 655 
 
 429,025 
 
 281,011,375 
 
 25.5930 
 
 8.6845 
 
 708 
 
 501,264 
 
 354,894,912 
 
 26.6083 
 
 8 
 
 9127 
 
 656 
 
 430,336 
 
 282,300,416 
 
 25.6125 
 
 8.6890 
 
 709 
 
 502,681 
 
 356,400,829 
 
 26.6271 
 
 8 
 
 9169 
 
 657 
 
 431.649 
 
 283,593,393 
 
 25.6320 
 
 8.6934 
 
 710 
 
 504,100 
 
 357.911.000 
 
 26.6458 
 
 8 
 
 9211 
 
 658 
 
 432,964 
 
 284,890,312 
 
 25.6515 
 
 8.6978 
 
 711 
 
 505,521 
 
 359.425.431 
 
 26.6646 
 
 8 
 
 9253 
 
 659 
 
 434,281 
 
 286,191,179 
 
 25.6710 
 
 8.7022 
 
 712 
 
 506,944 
 
 360,944,128 
 
 26.6833 
 
 8 
 
 9295 
 
 660 
 
 435,600 
 
 287,496,000 
 
 25.6905 
 
 8.7066 
 
 713 
 
 508,369 
 
 362,467.097 
 
 26 . 7021 
 
 8 
 
 9337 
 
 661 
 
 436,921 
 
 288,804,781 
 
 25.7099 
 
 8.7110 
 
 714 
 
 509,796 
 
 363.994.344 
 
 26.7208 
 
 8 
 
 9378 
 
 662 
 
 438,244 
 
 290,117,528 
 
 25.7294 
 
 8.7154 
 
 71S 
 
 511.225 
 
 365,525,875 
 
 26.7395 
 
 8 
 
 9420 
 
 663 
 
 439,569 
 
 291,434,247 
 
 25.7488 
 
 8.7198 
 
 716 
 
 512,656 
 
 367,061,696 
 
 26.7582 
 
 8 
 
 9462 
 
 664 
 
 440,896 
 
 292,754,944 
 
 25.7682 
 
 8.7241 
 
 717 
 
 514,089 
 
 368,601,813 
 
 26.7769 
 
 8 
 
 9503 
 
 665 
 
 442,225 
 
 294,079,625 
 
 25.7876 
 
 8.7285 
 
 718 
 
 515.524 
 
 370,146,232 
 
 26.7955 
 
 8 
 
 9545 
 
 666 
 
 443,556 
 
 295,408,296 
 
 25.8070 
 
 8.7329 
 
 719 
 
 516,961 
 
 371.694.959 
 
 26.8142 
 
 8 
 
 9587 
 
 667 
 
 444.889 
 
 296,740,963 
 
 25.8263 
 
 8.7373 
 
 720 
 
 518,400 
 
 373,248,000 
 
 26.8328 
 
 8 
 
 9628 
 
 668 
 
 446,224 
 
 298,077,632 
 
 25.8457 
 
 8.7416 
 
 721 
 
 519.841 
 
 374.805,361 
 
 26.8514 
 
 8 
 
 9670 
 
 669 
 
 447,561 
 
 299.418,309 
 
 25.8650 
 
 8.7460 
 
 722 
 
 521,284 
 
 375,367,048 
 
 26.8701 
 
 8 
 
 971 1 
 
 670 
 
 448,900 
 
 300,763,000 
 
 25.8844 
 
 8.7503 
 
 723 
 
 522,729 
 
 377,933,067 
 
 26.8887 
 
 8 
 
 9752 
 
 671 
 
 450,241 
 
 302,111,711 
 
 25.9037 
 
 8.7547 
 
 724 
 
 524,176 
 
 379.503.424 
 
 26.9072 
 
 8 
 
 9794 
 
 672 
 
 451,584 
 
 303,464.448 
 
 25.9230 
 
 8.7590 
 
 72s 
 
 525.625 
 
 381,078,125 
 
 26.9258 
 
 8 
 
 9835 
 
 673 
 
 452,929 
 
 304,821,217 
 
 25.9422 
 
 8.7634 
 
 726 
 
 527.076 
 
 382,657,176 
 
 26.9444 
 
 8 
 
 9876 
 
 674 
 
 454,276 
 
 306,182,024 
 
 25.9615 
 
 8.7677 
 
 727 
 
 528,529 
 
 384,240,583 
 
 26 . 9629 
 
 8 
 
 9918 
 
 675 
 
 455.625 
 
 307,546,875 
 
 25.9808 
 
 8.7721 
 
 728 
 
 529.984 
 
 385,828,352 
 
 26.9815 
 
 8 
 
 9959 
 
 676 
 
 456,976 
 
 308,915,776 
 
 26 
 
 8.7764 
 
 729 
 
 531.441 
 
 387,420,489 
 
 27 
 
 9 
 
 
 677 
 
 458,329 
 
 310,288,733 
 
 26.0192 
 
 8.7807 
 
 730 
 
 532,900 
 
 389,017,000 
 
 27.0185 
 
 9 
 
 0041 
 
 678 
 
 459,684 
 
 311,665,752 
 
 26.0384 
 
 8.7850 
 
 731 
 
 534,361 
 
 390,617,891 
 
 27.0370 
 
 9 
 
 0082 
 
 679 
 
 461,041 
 
 313,046,839 
 
 26.0576 
 
 8.7893I 
 
 732 
 
 535,824 
 
 392,223,168 
 
 27.0555 
 
 9 
 
 0123 
 
 680 
 
 462,400 
 
 314,432,000 
 
 26.0768 
 
 a. 7937: 
 
 733 
 
 537,289 
 
 393,832,837 
 
 27.0740 
 
 9 
 
 0164 
 
 681 
 
 463,761 
 
 315,821,241 
 
 26.0960 
 
 8.7980: 
 
 ! 
 
 734 
 
 538,756 
 
 395,446,904 
 
 27.0924 
 
 9 
 
 0205 
 
54 
 
 Mathematical Tables 
 
 Table of Squares, Cubes, Square Roots and Cube Roots 
 OF Numbers from i to iooo — {Continued) 
 
 No. 
 
 Square 
 
 Cube 
 
 Square 
 root 
 
 Cube 
 root 
 
 No. 
 
 Square 
 
 Cube 
 
 Square 
 root 
 
 Cube 
 root 
 
 733 
 
 540,225 
 
 397.065.375 
 
 27.1109 
 
 9.0246 
 
 788 
 
 620,944 
 
 489.303.872 
 
 28.0713 
 
 9-2365 
 
 736 
 
 541.696 
 
 398.688,256 
 
 27.1293 
 
 9.0287 
 
 789 
 
 622,521 
 
 491.169,069 
 
 28.0891 
 
 9 
 
 2404 
 
 737 
 
 543,169 
 
 400,315.553 
 
 27.1477 
 
 9.0328 
 
 790 
 
 624,100 
 
 493,039.000 
 
 28.1069 
 
 9 
 
 2443 
 
 738 
 
 544.644 
 
 401,947.272 
 
 27.1662 
 
 9.0369 
 
 791 
 
 625,681 
 
 494,913,671 
 
 28.1247 
 
 9 
 
 2482 
 
 739 
 
 546.121 
 
 403.583.419 
 
 27.1846 
 
 9.0410 
 
 792 
 
 627,264 
 
 496,793,088 
 
 28.1425 
 
 9 
 
 2521 
 
 740 
 
 547.600 
 
 405,224.000 
 
 27 . 2029 
 
 9.0450 
 
 793 
 
 628,849 
 
 498,677,257 
 
 28.1603 
 
 9 
 
 2560 
 
 741 
 
 549.081 
 
 406,869,021 
 
 27.2213 
 
 9.0491 
 
 794 
 
 630,436 
 
 500,566,184 
 
 28.1780 
 
 9 
 
 2599 
 
 742 
 
 550,564 
 
 408,518,488 
 
 27.2397 
 
 9.0532 
 
 795 
 
 632,025 
 
 502,459,875 
 
 28.1957 
 
 9 
 
 2638 
 
 743 
 
 552,049 
 
 410,172,407 
 
 27.2580 
 
 9.0572 
 
 796 
 
 633,616 
 
 504,358,336 
 
 28.2135 
 
 9 
 
 2677 
 
 744 
 
 553,536 
 
 411,830,784 
 
 27.2764 
 
 9.0613 
 
 797 
 
 635,209 
 
 506,261,573 
 
 28.2312 
 
 9 
 
 2716 
 
 745 
 
 555.025 
 
 413,493,62s 
 
 27.2947 
 
 9.0654 
 
 798 
 
 636,804 
 
 508,169,592 
 
 28.2489 
 
 9 
 
 2754 
 
 746 
 
 556,516 
 
 415.160,936 
 
 27.3130 
 
 9.0694 
 
 799 
 
 638,401 
 
 510,082.399 
 
 28.2666 
 
 9 
 
 2793 
 
 747 
 
 558,009 
 
 416,832,723 
 
 27.3313 
 
 9.0735 
 
 800 
 
 640,000 
 
 512,000,000 
 
 28.2843 
 
 9 
 
 2832 
 
 748 
 
 559.504 
 
 418,508,992 
 
 27.3496 
 
 9.077s 
 
 801 
 
 641,601 
 
 513,922,401 
 
 28.3019 
 
 9 
 
 2870 
 
 749 
 
 561,001 
 
 420,189,749 
 
 27.3679 
 
 9.0816 
 
 802 
 
 643,204 
 
 515,849,608 
 
 28.3196 
 
 9 
 
 2909 
 
 7SO 
 
 562,500 
 
 421,875,000 
 
 27.3861 
 
 9.0856 
 
 803 
 
 644,809 
 
 517,781,627 
 
 28.3373 
 
 9 
 
 2948 
 
 751 
 
 564.001 
 
 423,564,751 
 
 27.4044 
 
 9.0896 
 
 804 
 
 646,416 
 
 519,718,464 
 
 28.3549 
 
 9 
 
 2986 
 
 752 
 
 565,504 
 
 425,259,008 
 
 27.4226 
 
 9.0937 
 
 805 
 
 648,025 
 
 521,660,125 
 
 28.3725 
 
 9 
 
 302s 
 
 753 
 
 567.009 
 
 426,957,777 
 
 27.4408 
 
 9.0977 
 
 806 
 
 649,636 
 
 523,606,616 
 
 28.3901 
 
 9 
 
 3063 
 
 754 
 
 568,516 
 
 428,661,064 
 
 27.4591 
 
 9.1017 
 
 807 
 
 651,249 
 
 525,557,943 
 
 28.4077 
 
 9 
 
 3102 
 
 755 
 
 570.025 
 
 430,368,875 
 
 27.4773 
 
 9.1057 
 
 808 
 
 652,864 
 
 527,514.112 
 
 28.4253 
 
 9 
 
 3140 
 
 756 
 
 571,536 
 
 432,081,216 
 
 27.4955 
 
 9.1098 
 
 809 
 
 654,481 
 
 529,475,129 
 
 28.4429 
 
 9 
 
 3179 
 
 757 
 
 573.049 
 
 433,798.093 
 
 27.5136 
 
 9.1138 
 
 810 
 
 656,100 
 
 531,441,000 
 
 28.4605 
 
 9 
 
 3217 
 
 758 
 
 574,564 
 
 435,519,512 
 
 27.5318 
 
 9.1178 
 
 811 
 
 657,721 
 
 533,411,731 
 
 28.4781 
 
 9 
 
 325s 
 
 759 
 
 576,081 
 
 437,245,479 
 
 27.5500 
 
 9.1218 
 
 812 
 
 659,344 
 
 535,387,328 
 
 28.4956 
 
 9 
 
 3294 
 
 760 
 
 577,600 
 
 438,976,000 
 
 27.5681 
 
 9.1258 
 
 813 
 
 660,969 
 
 537.367.797 
 
 28.5132 
 
 9 
 
 3332 
 
 761 
 
 579,121 
 
 440.71 1. 081 ■ 
 
 27.5862 
 
 9.1298 
 
 814 
 
 662,596 
 
 539,353.144 
 
 28.5307 
 
 9 
 
 3370 
 
 762 
 
 580,644 
 
 442.450,728 
 
 27.6043 
 
 9.1338 
 
 815 
 
 664.225 
 
 541,343.375 
 
 28.5482 
 
 9 
 
 3408 
 
 763 
 
 582,169 
 
 444,194,947 
 
 27.6225 
 
 9.1378 
 
 816 
 
 665,856 
 
 543,338,496 
 
 28.5657 
 
 9 
 
 3447 
 
 764 
 
 583,696 
 
 445,943,744 
 
 27.6405 
 
 9.1418 
 
 817 
 
 667,489 
 
 545,338,513 
 
 28.5832 
 
 9 
 
 3485 
 
 76s 
 
 585,225 
 
 447,697,125 
 
 27.6586 
 
 9.1458 
 
 818 
 
 669,124 
 
 547,343,432 
 
 28.6007 
 
 9 
 
 3523 
 
 766 
 
 586,756 
 
 449,455,096 
 
 27.6767 
 
 9.1498 
 
 819 
 
 670,761 
 
 549,353,259 
 
 28.6182 
 
 9 
 
 3561 
 
 767 
 
 588,289 
 
 451,217,663 
 
 27.6948 
 
 9.1537 
 
 820 
 
 672,400 
 
 551,368.000 
 
 28.6356 
 
 9 
 
 3599 
 
 768 
 
 589,824 
 
 452,984,832 
 
 27.7128 
 
 9-1577 
 
 821 
 
 674,041 
 
 553,387,661 
 
 28.6531 
 
 9 
 
 3637 
 
 769 
 
 591,361 
 
 454.756,609 
 
 27.7308 
 
 9.1617 
 
 822 
 
 675,684 
 
 555,412,248 
 
 28.6705 
 
 9 
 
 3675 
 
 770 
 
 592.900 
 
 456.533,000 
 
 27.74891 
 
 9.1657 
 
 823 
 
 677,329 
 
 557,441,767 
 
 28.6880 
 
 9 
 
 3713 
 
 771 
 
 594,441 
 
 458,314,011 
 
 27.7669 
 
 9.1696 
 
 824 
 
 678,976 
 
 559,476,224 
 
 28.7054 
 
 9 
 
 3751 
 
 772 
 
 595,984 
 
 460,099,648 
 
 27.7849 
 
 9-1736 
 
 825 
 
 680,625 
 
 561,515,62s 
 
 28.7228 
 
 9 
 
 3789 
 
 773 
 
 597,529 
 
 461,889,917 
 
 27 . 8029 
 
 9-1775 
 
 826 
 
 682,276 
 
 563,559,976 
 
 28.7402 
 
 9 
 
 3827 
 
 774 
 
 599.676 
 
 463,684,824 
 
 27.8209 
 
 9-I815 
 
 827 
 
 683,929 
 
 565,609.283 
 
 28.7576 
 
 9 
 
 3865 
 
 775 
 
 600,625 
 
 465,484,37s 
 
 27.8388 
 
 9-1855 
 
 828 
 
 685.584 
 
 567,663,552 
 
 28.7750 
 
 9 
 
 3902 
 
 776 
 
 602,176 
 
 467,288.576 
 
 27.8568 
 
 9-1894 
 
 829 
 
 687,241 
 
 569,722.789 
 
 28.7924 
 
 9 
 
 3940 
 
 777 
 
 603.729 
 
 469,097,433 
 
 27.8747 
 
 9-1933 
 
 830 
 
 688,900 
 
 571,787,000 
 
 28.8097 
 
 9 
 
 3978 
 
 778 
 
 605,284 
 
 470,910,952 
 
 27.8927 
 
 9-1973 
 
 831 
 
 690,561 
 
 573,856,191 
 
 28.8271 
 
 9 
 
 4016 
 
 779 
 
 606,841 
 
 472,729,139 
 
 27.9106 
 
 9.2012 
 
 832 
 
 692,224 
 
 575,930,368 
 
 28.8444 
 
 9 
 
 4053 
 
 780 
 
 608,400 
 
 474,552,000 
 
 27.9285 
 
 9-2052 
 
 833 
 
 693,889 
 
 578,009,537 
 
 28.8617 
 
 9 
 
 4091 
 
 781 
 
 609,961 
 
 476.379.541 
 
 27.9464 
 
 9.2091 
 
 834 
 
 695,556 
 
 580.093,704 
 
 28.8791 
 
 9 
 
 4129 
 
 782 
 
 611,524 
 
 478.211,768 
 
 27.9643 
 
 9.2130 
 
 835 
 
 697,22s 
 
 582,182,875 
 
 28.8964 
 
 9 
 
 4166 
 
 783 
 
 613,089 
 
 480,048,687 
 
 27.9821 
 
 9.2170 
 
 836 
 
 698,896 
 
 584,277,056 
 
 28.9137 
 
 9 
 
 4204 
 
 784 
 
 614,656 
 
 481,890,304 
 
 28 
 
 9.2209 
 
 837 
 
 700,569 
 
 586,376,253 
 
 28.9310 
 
 9 
 
 4241 
 
 785 
 
 616,225 
 
 483,736,625 
 
 28.0179 
 
 9.2248 
 
 838 
 
 702,244 
 
 588,480,472 
 
 28.9482 
 
 9 
 
 4279 
 
 786 
 
 617.796 
 
 485,587,656 
 
 28.0357 
 
 9.2287 
 
 839 
 
 703,921 
 
 590.589,719 
 
 28.9655 
 
 9 
 
 4316 
 
 787 
 
 619,369 
 
 487,443,403 
 
 28.0535 
 
 9.2326 
 
 840 
 
 705,600 
 
 592,704,000 
 
 28.9828 
 
 9 
 
 4354 
 
Table of Squares, Cubes, Square Roots and Cube Roots 55 
 
 Table or Squares, Cxjbes, Square Roots and Cube Roots 
 OF Numbers from i to iooo — {Continued) 
 
 No. 
 
 Square 
 
 Cube 
 
 Square 
 root 
 
 Cube 
 root 
 
 No. 
 
 Square 
 
 , Cube 
 
 Square 
 root 
 
 Cube 
 root 
 
 841 
 
 707,281 
 
 594.823,321 
 
 29 
 
 3.4391 
 
 894 
 
 799,236 
 
 714,516,984 
 
 29.8998 
 
 9.6334 
 
 842 
 
 708,964 
 
 596,947,688 
 
 29.0172 
 
 3.4429 
 
 895 
 
 801,025 
 
 716,917,375 
 
 29.9166 
 
 9.6370 
 
 843 
 
 710,649 
 
 599,077,107 
 
 29-0345 
 
 3.4466 
 
 896 
 
 802,816 
 
 719,323,136 
 
 29.9333 
 
 9.6406 
 
 844 
 
 712,336 
 
 601,211,584 
 
 29.0517 ( 
 
 3.4503 
 
 897 
 
 804,609 
 
 721,734,273 
 
 29.9500 
 
 9.6442 
 
 84s 
 
 714,025 
 
 603,351,125 
 
 29.0689 ( 
 
 ).454i 
 
 898 
 
 806,404 
 
 724,150,792 
 
 29.9666 
 
 9.6477 
 
 846 
 
 715,716 
 
 605,495,736 
 
 29.0861 ( 
 
 )-4578 
 
 899 
 
 808,201 
 
 726,572,699 
 
 29.9833 
 
 9.6513 
 
 847 
 
 717.409 
 
 607,645.423 
 
 29.1033 c 
 
 3.4615 
 
 900 
 
 810,000 
 
 729,000,000 
 
 30 
 
 9.6549 
 
 848 
 
 719,104 
 
 609,800,192 
 
 29.1204 c 
 
 ^.4652 
 
 901 
 
 811,801 
 
 731,432,701 
 
 30.0167 
 
 9.6585 
 
 849 
 
 720,801 
 
 611,960,049 
 
 29.1376 c 
 
 ^.4690 
 
 902 
 
 813,604 
 
 733,870,808 
 
 30.0333 
 
 9.6620 
 
 850 
 
 722,500 
 
 614,125,000 
 
 29.1548 c 
 
 ).4727 
 
 903 
 
 815,409 
 
 736,314,327 
 
 30.0500 
 
 9.6656 
 
 851 
 
 724,201 
 
 616,295,051 
 
 29.1719 c 
 
 ).4764 
 
 904 
 
 817,216 
 
 738,763,264 
 
 30.0666 
 
 9.6692 
 
 852 
 
 725,904 
 
 618,470,208 
 
 29.1890 c 
 
 ).48oi 
 
 905 
 
 819,025 
 
 741.217,625 
 
 30.0832 
 
 9.6727 
 
 853 
 
 727,609 
 
 620,650,477 
 
 29 . 2062 c 
 
 ).4838 
 
 906 
 
 820,836 
 
 743,677,416 
 
 30.0998 
 
 9.6763 
 
 854 
 
 729,316 
 
 622,835.864 
 
 29.2233 c 
 
 .4875 
 
 907 
 
 822,649 
 
 746,142,643 
 
 30.1164 
 
 9-6799 
 
 855 
 
 731,025 
 
 625,026,375 
 
 29.2404 c 
 
 ).49I2 
 
 908 
 
 824,464 
 
 748,613,312 
 
 30.1330 
 
 9.6834 
 
 856 
 
 732,736 
 
 627,222,016 
 
 29.2575 c 
 
 .4949 
 
 909 
 
 826,281 
 
 751,089,429 
 
 30.1496 
 
 9.6870 
 
 857 
 
 734.449 
 
 629,422,793 
 
 29.2746 c 
 
 .4986 
 
 910 
 
 828,100 
 
 753,571,000 
 
 30.1662 
 
 9.6905 
 
 858 
 
 736,164 
 
 631,628,712 
 
 29.2916 c 
 
 .5023 
 
 911 
 
 829,921 
 
 756,058,031 
 
 30.1828 
 
 9.6941 
 
 859 
 
 737.881 
 
 633,839,779 
 
 29.3087 c 
 
 .5060 
 
 912 
 
 831,744 
 
 758,550,528 
 
 30.1993 
 
 9.6976 
 
 860 
 
 739.600 
 
 636,056,000 
 
 29:3258 c 
 
 .5097 
 
 913 
 
 833,569 
 
 761,048,497 
 
 30.2159 
 
 9-7012 
 
 861 
 
 741.321 
 
 638,277,381 
 
 29.3428 c 
 
 .5134 
 
 914 
 
 835,396 
 
 763,551,944 
 
 30.2324 
 
 9.7047 
 
 862 
 
 743.044 
 
 640,503,928 
 
 29.3598 c 
 
 .5171 
 
 915 
 
 837,225 
 
 766,060,875 
 
 30.2490 
 
 9.7082 
 
 863 
 
 744.769 
 
 642,735,647 
 
 29.3769 c 
 
 .5207 
 
 916 
 
 839.056 
 
 768,575,296 
 
 30.2655 
 
 9.7118 
 
 864 
 
 746,496 
 
 644,972,544 
 
 29.3939 c 
 
 .5244 
 
 917 
 
 840,889 
 
 771.095.213 
 
 30.2820 
 
 9.7153 
 
 86s 
 
 748,225 
 
 647,214,625 
 
 29.4109 c 
 
 .5281 
 
 918 
 
 842,724 
 
 773 620,632 
 
 30.2985 
 
 9.7188 
 
 866 
 
 749.956 
 
 649,461,896 
 
 29.4279 c 
 
 .5317 
 
 919 
 
 844.561 
 
 776,151.559 
 
 30.3150 
 
 9.7224 
 
 867 
 
 751.689 
 
 651,714,363 
 
 29.4449 c 
 
 .5354 
 
 920 
 
 846,400 
 
 778,688,000 
 
 30.3315 
 
 9.7259 
 
 868 
 
 753,424 
 
 653,972,032 
 
 29.4618 c 
 
 .5391 
 
 921 
 
 848,241 
 
 781,229,961 
 
 30.3480 
 
 9.7294 
 
 869 
 
 755.161 
 
 656,234,909 
 
 29.4788 c 
 
 • 5427 
 
 922 
 
 850,084 
 
 783,777,448 
 
 30.3645 
 
 9.7329 
 
 870 
 
 756,900 
 
 658,503,000 
 
 29.4958 c 
 
 .5464 
 
 923 
 
 851.929 
 
 786,330,467 
 
 30.3809 
 
 9 7364 
 
 871 
 
 758,641 
 
 660,776,311 
 
 29.5127 c 
 
 .5501 
 
 924 
 
 853.776 
 
 788,889,024 
 
 30.3974 
 
 9.7400 
 
 872 
 
 760,384 
 
 663,054,848 
 
 29.5296 c 
 
 .5537 
 
 925 
 
 855,625 
 
 791,453,125 
 
 30.4138 
 
 9.7435 
 
 873 
 
 762,129 
 
 665,338,617 
 
 29.5466 c 
 
 .5574 
 
 926 
 
 857,476 
 
 794,022,776 
 
 30.4302 
 
 9.7470 
 
 874 
 
 763.876 
 
 667,627,624 
 
 29.5635 c 
 
 .5610 
 
 927 
 
 859,329 
 
 796,597,983 
 
 30.4467 
 
 9 -750s 
 
 87s 
 
 765.625 
 
 669,921,875 
 
 29.5804 c 
 
 .5647 
 
 928 
 
 861,184 
 
 799.178,752 
 
 30.4631 
 
 9.7540 
 
 876 
 
 767,376 
 
 672,221,376 
 
 29.5973 c 
 
 .5683 
 
 929 
 
 863,041 
 
 801,765,089 
 
 30.479s 
 
 9.7575 
 
 877 
 
 769,129 
 
 674,526,133 
 
 29.6142 c 
 
 .5719 
 
 930 
 
 864,900 
 
 804,357.000 
 
 30.4959 
 
 9.7610 
 
 878 
 
 770,884 
 
 676,836,152 
 
 29.6311 c 
 
 ■ 5756 
 
 931 
 
 866,761 
 
 806,954,491 
 
 30.5123 
 
 9.7645 
 
 879 
 
 772,641 
 
 679,151,439 
 
 29.6479 c 
 
 .5792 
 
 932 
 
 868,624 
 
 809,557,568 
 
 30.5287 
 
 9.7680 
 
 880 
 
 774,400 
 
 681,472,000 
 
 29.664S c 
 
 .5828 
 
 933 
 
 870,489 
 
 812,166,237 
 
 30.5450 
 
 9.7715 
 
 881 
 
 776,161 
 
 683,797,841 
 
 29.6816 c 
 
 .5865 
 
 934 
 
 872,356 
 
 814,780,504 
 
 30.5614 
 
 9.7750 
 
 882 
 
 777.924 
 
 686,128,968 
 
 29.6985 c 
 
 .5901 
 
 935 
 
 874,225 
 
 817,400,375 
 
 30.5778 
 
 9.778S 
 
 883 
 
 779.689 
 
 688,465,387 
 
 29.7153 c 
 
 .5937 
 
 936 
 
 876,096 
 
 820,025,856 
 
 30.5941 
 
 9.7819 
 
 884 
 
 781,456 
 
 690,807,104 
 
 29.7321 c 
 
 .5973 
 
 937 
 
 877,969 
 
 822,656,953 
 
 30.610S 
 
 9.7854 
 
 885 
 
 783,225 
 
 693,154,125 
 
 29.7489 c 
 
 .6010 
 
 938 
 
 879,844 
 
 825,293,672 
 
 30.6268 
 
 9.7889 
 
 886 
 
 784.996 
 
 695,506,456 
 
 29.7658 c 
 
 .6046 
 
 939 
 
 881,721 
 
 827,936,019 
 
 30.6431 
 
 9.7924 
 
 887 
 
 786,769 
 
 697,864,103 
 
 29.7825 c 
 
 ).6o82 
 
 940 
 
 883,600 
 
 830,584,000 
 
 30.6594 
 
 9.7959 
 
 888 
 
 788,544 
 
 700,227,072 
 
 29.7993 c 
 
 ).6ii8 
 
 941 
 
 885,481 
 
 833,237,621 
 
 30.6757 
 
 9.7993 
 
 889 
 
 790,321 
 
 702,595,369 
 
 29.8161 c 
 
 ).6i54 
 
 942 
 
 887,364 
 
 835.896,^88 
 
 30 . 6920 
 
 9.8028 
 
 890 
 
 792,100 
 
 704,969,000 
 
 29.8329 c 
 
 ).6i9o 
 
 943 
 
 889,249 
 
 838,561,807 
 
 30.7083 
 
 9.8063 
 
 891 
 
 793.881 
 
 707,347,971 
 
 29 . 8496 c 
 
 ).6226 
 
 944 
 
 891,136 
 
 841,232,384 
 
 ^0 7246 
 
 9.8097 
 
 892 
 
 795,664 
 
 709,732,288 
 
 29.8664 < 
 
 ).6262 
 
 945 
 
 893,025 
 
 843,908,625 
 
 30.7409 
 
 9.8132 
 
 893 
 
 797,449 
 
 712,121,957 
 
 29.8831 c 
 
 ).6298 
 
 946 
 
 894,916 
 
 846,590,536 
 
 30.7571 
 
 9.8167 
 
56 
 
 Mathematical Tables 
 
 Table of Squares, Cubes, Square Roots and Cube Roots 
 OF Numbers from i to iooo — {Continued) 
 
 No. 
 
 Square 
 
 Cube 
 
 Square 
 root 
 
 Cube 
 root 
 
 No. 
 
 974 
 
 Square 
 
 Cube 
 
 Square 
 root 
 
 Cube 
 root 
 
 947 
 
 896,809 
 
 849,278,123 
 
 30.7734 
 
 9 . 8201 
 
 948.676 
 
 924,010,424 
 
 31.2090 c 
 
 ).9i26 
 
 948 
 
 898,704 
 
 851,971.392 
 
 30.7896 
 
 9 . 8236 
 
 975 
 
 950.625 
 
 926,859,375 
 
 31 . 2250 ( 
 
 ).9i6o 
 
 949 
 
 900,601 
 
 854.670,349 
 
 30.8058 
 
 9.8270 
 
 976 
 
 952,576 
 
 929,714,176 
 
 31.2410 ( 
 
 ).9i94 
 
 950 
 
 902,500 
 
 857,375,000 
 
 30.8221 
 
 9.8305 
 
 977 
 
 954,529 
 
 932,574.833 
 
 31.2570 
 
 J. 9227 
 
 951 
 
 904,401 
 
 860,085,351 
 
 30.8383 
 
 9 8339 
 
 978 
 
 956,484 
 
 935.441,352 
 
 31.2730 
 
 ?.926i 
 
 952 
 
 906,304 
 
 862,801,408 
 
 30.854s 
 
 9.8374 
 
 979 
 
 958,441 
 
 938,313,739 
 
 31.2890 
 
 3.9295 
 
 953 
 
 908,209 
 
 865,523,177 
 
 30.8707 
 
 9.8408 
 
 980 
 
 960,400 
 
 941,192,000 
 
 31.3050 
 
 9.9329 
 
 954 
 
 910,116 
 
 868,250,664 
 
 30.8869 
 
 9.8443 
 
 981 
 
 962,361 
 
 944,076,141 
 
 31.3209 
 
 3.9363 
 
 955 
 
 912,02s 
 
 870,983,875 
 
 30.9031 
 
 9.8477 
 
 982 
 
 964,324 
 
 946,966,168 
 
 31.3369 
 
 9.9396 
 
 9S6 
 
 913,936 
 
 873.722,816 
 
 30.9192 
 
 9.8511 
 
 983 
 
 966,289 
 
 949,862,087 
 
 31.3528 
 
 9.9430 
 
 957 
 
 915,849 
 
 876,467,493 
 
 30.9354 
 
 9.8546 
 
 984 
 
 968,256 
 
 952,763,904 
 
 31.3688 
 
 9.9464 
 
 958 
 
 917,764 
 
 879.217.912 
 
 30. 9516 j 9. 8580 
 
 985 
 
 970,225 
 
 955,671.625 
 
 31.3847 
 
 9.9497 
 
 959 
 
 919,681 
 
 881,974,079 
 
 30.9677 
 
 9.8614 
 
 986 
 
 972,196 
 
 958,585.256 
 
 31 . 4006 
 
 9.9531 
 
 960 
 
 921,600 
 
 884,736',ooo 
 
 30.9839 
 
 9.8648 
 
 987 
 
 974,169 
 
 961,504,803 
 
 31.4166 
 
 9.9565 
 
 961 
 
 923,521 
 
 887,503,681 
 
 31 
 
 9.8683 
 
 988 
 
 976,144 
 
 964,430,272 
 
 31.432s 
 
 9.9598 
 
 962 
 
 925,444 
 
 890,277,128 
 
 31.0161 
 
 9.8717 
 
 989 
 
 978,121 
 
 967,361,669 
 
 31.4484 
 
 9.9632 
 
 963 
 
 927.369 
 
 893,056,347 
 
 31-0322 
 
 9.8751 
 
 990 
 
 980,100 
 
 970,299,000 
 
 31.4643 
 
 9.9666 
 
 964 
 
 929,296 
 
 895,841,344 
 
 31.0483 
 
 9.8785 
 
 991 
 
 982,081 
 
 973,242,271 
 
 31.4802 
 
 9.9699 
 
 965 
 
 931,22s 
 
 898,632,125 
 
 31-0644 
 
 9.8819 
 
 992 
 
 984.064 
 
 976,191,488 
 
 31 . 4960 
 
 9.9733 
 
 966 
 
 933,156 
 
 901,428,696 
 
 31.0805 
 
 9.8854 
 
 993 
 
 986,049 
 
 979.146,657 
 
 31.5119 
 
 9.9766 
 
 967 
 
 935,089 
 
 904,231,063 
 
 31.0966 
 
 9.8888 
 
 994 
 
 988,036 
 
 982,107,784 
 
 31.5278 
 
 9.9800 
 
 968 
 
 937,024 
 
 907,039.232 
 
 31.1127 
 
 9.8922 
 
 995 
 
 990,025 
 
 985,074,875 
 
 31.5436 
 
 9.9833 
 
 969 
 
 938,961 
 
 909,853.209 
 
 31.1288l9.8956 
 
 996 
 
 992,016 
 
 988,047,936 
 
 31.5595 
 
 9.9866 
 
 970 
 
 940,900 
 
 912,673,000 
 
 31.1448 
 
 9.8990 
 
 997 
 
 994,009 
 
 991,026,973 
 
 31.5753 
 
 9.9900 
 
 971 
 
 942,841 
 
 915,498.611 
 
 31.1609 
 
 9.9024 
 
 998 
 
 996,004 
 
 994,011,992 
 
 31.5911 
 
 9.9933 
 
 972 
 
 944,784 
 
 918,330,048 
 
 31 . 1769 
 
 9.9058 
 
 999 
 
 998,001 
 
 997,002,999 
 
 31.6070 
 
 9.9967 
 
 973 
 
 946,729 
 
 921,167,317 
 
 31.19299.9092 
 
 IOOO 
 
 1,000,000 
 
 1,000,000,000 
 
 31,6228 
 
 10 
 
 To find the square or cube of any whole number ending 
 with ciphers. First, omit all the final ciphers. Take from the table the 
 square or cube (as the case may be) of the rest of the number. To this 
 square add twice as many ciphers as there were final ciphers in the original 
 number. To the cube add three times as many as in the original number. 
 Thus, for 90,5002, 9052 = 819,025. Add twice 2 ciphers, obtaining 
 8,190,250,000. For 90,500^, 9053 = 741,217,625. Add 3 times 2 ci- 
 phers, obtaining 741,217,625,000,000. 
 
 I 
 
\ 
 
 Table of Square Roots and Cube Roots of Numbers 57 
 
 Table of Square Roots and Cube Roots or Numbers 
 
 FROM 1000 TO 10,000 
 No errors 
 
 No. 
 
 Sq. 
 
 Cube 
 
 No. 
 
 Sq. 
 
 Cube 
 
 No. 
 
 Sq. 
 
 Cube 
 
 No. 
 
 Sq. 
 
 Cube 
 
 root 
 
 root 
 
 root 
 
 root 
 
 root 
 
 root 
 
 root 
 
 root 
 
 1005 
 
 31.70 
 
 10.02 
 
 1270 
 
 35.64 
 
 10.83 
 
 1535 
 
 39.18 
 
 11.54 
 
 1800 
 
 42.43 
 
 12.16 
 
 lOIO 
 
 31 
 
 78 
 
 10.03 
 
 1275 
 
 35 
 
 71 
 
 10.84 
 
 1540 
 
 39-24 
 
 11.55 
 
 180S 
 
 42.49 
 
 12.18 
 
 IOI5 
 
 31 
 
 86 
 
 10.05 
 
 1280 
 
 35 
 
 78 
 
 10.86 
 
 1545 
 
 39.31 
 
 11.56 
 
 1810 
 
 42.54 
 
 12.19 
 
 1020 
 
 31 
 
 94 
 
 10.07 
 
 1285 
 
 35 
 
 85 
 
 10.87 
 
 1550 
 
 39.37 
 
 11.57 
 
 1815 
 
 42.60 
 
 12.20 
 
 1025 
 
 32 
 
 02 
 
 10.08 
 
 1290 
 
 35 
 
 92 
 
 10.89 
 
 1555 
 
 39.43 
 
 11.59 
 
 1820 
 
 42.66 
 
 12.21 
 
 1030 
 
 32 
 
 09 
 
 10.10 
 
 1295 
 
 35 
 
 99 
 
 10.90 
 
 1560 
 
 39 50 
 
 11.60 
 
 1825 
 
 42.72 
 
 12.22 
 
 1035 
 
 32 
 
 17 
 
 10.12 
 
 1300 
 
 36 
 
 06 
 
 10.91 
 
 1565 
 
 39.56 
 
 II. 61 
 
 1830 
 
 42.78 
 
 12.23 
 
 1040 
 
 32 
 
 25 
 
 10.13 
 
 1305' 
 
 36 
 
 12 
 
 10.93 
 
 1570 
 
 29.62 
 
 11.62 
 
 1835 
 
 42.84 
 
 12.24 
 
 1045 
 
 32 
 
 33 
 
 10.15 
 
 1310 
 
 36 
 
 19 
 
 10.94 
 
 1575 
 
 39.69 
 
 11.63 
 
 1840 
 
 42.90 
 
 12.25 
 
 1050 
 
 32 
 
 40 
 
 10.16 
 
 131S 
 
 36 
 
 26 
 
 10.96 
 
 1580 
 
 39.75 
 
 II. 6s 
 
 1845 
 
 42.95 
 
 12.26 
 
 1055 
 
 32 
 
 48 
 
 10.18 
 
 1320 
 
 36 
 
 33 
 
 10.97 
 
 1585 
 
 39.81 
 
 11.66 
 
 1850 
 
 43.01 
 
 12.28 
 
 1060 
 
 32 
 
 56 
 
 10.20 
 
 132s 
 
 36 
 
 40 
 
 10.98 
 
 1590 
 
 39-87 
 
 11.67 
 
 1855 
 
 43.07 
 
 12.29 
 
 106s 
 
 32 
 
 63 
 
 10.21 
 
 1330 
 
 36 
 
 47 
 
 II 
 
 1595 
 
 39.94 
 
 11.68 
 
 i860 
 
 43.13 
 
 12.30 
 
 1070 
 
 32 
 
 71 
 
 10.23 
 
 1335 
 
 36 
 
 54 
 
 II. 01 
 
 1600 
 
 40 
 
 11.70 
 
 1865 
 
 43.19 
 
 12.31 
 
 1075 
 
 32 
 
 79 
 
 10.24 
 
 1340 
 
 36 
 
 61 
 
 11.02 
 
 1605 
 
 40.06 
 
 11.71 
 
 1870 
 
 43.24 
 
 12.32 
 
 1080 
 
 32 
 
 86 
 
 10.26 
 
 1345 
 
 36 
 
 67 
 
 11.04 
 
 1610 
 
 40.12 
 
 11.72 
 
 187s 
 
 43.30 
 
 12.33 
 
 108s 
 
 32 
 
 94 
 
 10.28 
 
 1350 
 
 36 
 
 74 
 
 11.05 
 
 1615 
 
 40.19 
 
 11.73 
 
 1880 
 
 43.36 
 
 12.34 
 
 1090 
 
 33 
 
 02 
 
 10.29 
 
 1355 
 
 36 
 
 81 
 
 11.07 
 
 1620 
 
 40.25 
 
 11.74 
 
 188S 
 
 43.42 
 
 12.35 
 
 1095 
 
 33 
 
 09 
 
 10.31 
 
 1360 
 
 36 
 
 88 
 
 11.08 
 
 1625 
 
 40.31 
 
 11.76 
 
 1890 
 
 43.47 
 
 12.36 
 
 HOC 
 
 33 
 
 17 
 
 10.32 
 
 1365 
 
 36 
 
 95 
 
 11.09 
 
 1630 
 
 40.37 
 
 11.77 
 
 1895 
 
 43.53 
 
 12.37 
 
 1 105 
 
 33 
 
 24 
 
 10.34 
 
 1370 
 
 37 
 
 01 
 
 II. II 
 
 1635 
 
 40.44 
 
 11.78 
 
 1900 
 
 43.59 
 
 12.39 
 
 IIIO 
 
 33 
 
 32 
 
 10.3s 
 
 1375 
 
 37 
 
 08 
 
 II. 12 
 
 1640 
 
 •40.50 
 
 11.79 
 
 1905 
 
 43.65 
 
 12.40 
 
 HIS 
 
 33 
 
 39 
 
 10.37 
 
 1380 
 
 37 
 
 15 
 
 II. 13 
 
 1645 
 
 40.56 
 
 11.80 
 
 1910 
 
 43.70 
 
 12.41 
 
 1 120 
 
 33 
 
 47 
 
 10.38 
 
 1385 
 
 37 
 
 22 
 
 II. 15 
 
 1650 
 
 40.62 
 
 11.82 
 
 1915 
 
 43.76 
 
 12.42 
 
 II25 
 
 33 
 
 54 
 
 10.40 
 
 1390 
 
 37 
 
 28 
 
 II. 16 
 
 1655 
 
 40' 68 
 
 11.83 
 
 1920 
 
 43.82 
 
 12.43 
 
 1 130 
 
 33 
 
 62 
 
 10.42 
 
 1395 
 
 37 
 
 35 
 
 II. 17 
 
 1660 
 
 40.74 
 
 11.84 
 
 1925 
 
 43.87 
 
 12.44 
 
 1 135 
 
 33 
 
 69 
 
 10.43 
 
 1400 
 
 37 
 
 42 
 
 II. 19 
 
 1665 
 
 40.80 
 
 II. 85 
 
 1930 
 
 43.93 
 
 12. 45 
 
 1 140 
 
 33 
 
 76 
 
 10. 45 
 
 1405 
 
 37 
 
 48 
 
 11.20 
 
 1670 
 
 40.87 
 
 11^86 
 
 1935 
 
 43.99 
 
 12.46 
 
 1 145 
 
 33 
 
 84 
 
 10.46 
 
 1410 
 
 37 
 
 55 
 
 II. 21 
 
 1675 
 
 40.93 
 
 11.88 
 
 1940 
 
 44.05 
 
 12.47 
 
 1 150 
 
 33 
 
 91 
 
 10.48 
 
 1415 
 
 37 
 
 62 
 
 11.23 
 
 1680 
 
 40.99 
 
 11.89 
 
 1945 
 
 44.10 
 
 12.48 
 
 1155 
 
 33 
 
 99 
 
 10.49 
 
 1420 
 
 37 
 
 68 
 
 11.24 
 
 1685 
 
 41.05 
 
 II . 90 
 
 1950 
 
 44.16 
 
 12.49 
 
 1160 
 
 34 
 
 06 
 
 10.51 
 
 1425 
 
 37 
 
 75 
 
 11.25 
 
 1690 
 
 41. II 
 
 II. 91 
 
 1955 
 
 44.22 
 
 12.50 
 
 1165 
 
 34 
 
 13 
 
 10.52 
 
 1430 
 
 37 
 
 82 
 
 11.27 
 
 1695 
 
 41.17 
 
 11.92 
 
 i960 
 
 44.27 
 
 12.51 
 
 1 170 
 
 34 
 
 21 
 
 10. 54 
 
 1435 
 
 37 
 
 88 
 
 11.28 
 
 1700 
 
 41.23 
 
 11.93 
 
 1965 
 
 44.33 
 
 12.53 
 
 1175 
 
 34 
 
 28 
 
 10.55 
 
 1440 
 
 37 
 
 95 
 
 11.29 
 
 1705 
 
 41.29 
 
 11.95 
 
 1970 
 
 44.38 
 
 12.54 
 
 1180 
 
 34 
 
 35 
 
 10.57 
 
 1445 
 
 38 
 
 01 
 
 II. 31 
 
 1710 
 
 41.35 
 
 11.96 
 
 1975 
 
 44.44 
 
 12.55 
 
 1 185 
 
 34 
 
 42 
 
 10.58 
 
 1450 
 
 38 
 
 08 
 
 11.32 
 
 1715 
 
 41.41 
 
 11.97 
 
 1980 
 
 44.50 
 
 12.56 
 
 1190 
 
 34 
 
 50 
 
 10.60 
 
 1455 
 
 38 
 
 14 
 
 11.33 
 
 1720 
 
 41.47 
 
 11.98 
 
 1985 
 
 44.55 
 
 12.57 
 
 1195 
 
 34 
 
 57 
 
 10.61 
 
 1460 
 
 38 
 
 21 
 
 11.34 
 
 172s 
 
 41.53 
 
 11.99 
 
 1990 
 
 44.61 
 
 12.58 
 
 1200 
 
 34 
 
 64 
 
 10.63 
 
 1465 
 
 38 
 
 28 
 
 11.36 
 
 1730 
 
 41.59 
 
 12 
 
 1995 
 
 44.67 
 
 12.59 
 
 1205 
 
 34 
 
 71 
 
 10.64 
 
 1470 
 
 38 
 
 34 
 
 11.37 
 
 1735 
 
 41-65 
 
 12.02 
 
 2000 
 
 44.72 
 
 12.60 
 
 1210 
 
 34 
 
 79 
 
 10.66 
 
 1475 
 
 38 
 
 41 
 
 11.38 
 
 1740 
 
 41.71 
 
 12.03 
 
 2005 
 
 44.78 
 
 12.61 
 
 1215 
 
 34 
 
 86 
 
 10.67 
 
 1480 
 
 38 
 
 47 
 
 11.40 
 
 1745 
 
 41.77 
 
 12.04 
 
 2010 
 
 44.83 
 
 12.62 
 
 1220 
 
 34 
 
 93 
 
 10.69 
 
 1485 
 
 38 
 
 54 
 
 II. 41 
 
 1750 
 
 41.83 
 
 12.05 
 
 2015 
 
 44.89 
 
 12.63 
 
 1225 
 
 35 
 
 
 10.70 
 
 1490 
 
 38 
 
 60 
 
 11.42 
 
 1755 
 
 41.89 
 
 12.06 
 
 2020 
 
 44.94 
 
 12.64 
 
 1230 
 
 35 
 
 07 
 
 10.71 
 
 1495 
 
 38 
 
 67 
 
 11.43 
 
 1760 
 
 41.95 
 
 12.07 
 
 2025 
 
 45 
 
 12.65 
 
 1235 
 
 35 
 
 14 
 
 10. "73 
 
 1500 
 
 38 
 
 73 
 
 11.45 
 
 1765 
 
 42.01 
 
 12.09 
 
 2030 
 
 45 06 
 
 12.66 
 
 1240 
 
 35 
 
 21 
 
 10.74 
 
 150s 
 
 38 
 
 79 
 
 11.46 
 
 1770 
 
 42.07 
 
 12.10 
 
 2035 
 
 45.11 
 
 12.67 
 
 1245 
 
 35 
 
 28 
 
 10.76 
 
 1510 
 
 38 
 
 86 
 
 11.47 
 
 1775 
 
 42.13 
 
 12. II 
 
 2040 
 
 45. 17 
 
 12.68 
 
 1250 
 
 35 
 
 36 
 
 10.77 
 
 1515 
 
 38 
 
 92 
 
 11.49 
 
 1780 
 
 42.19 
 
 12.12 
 
 2045 
 
 45.22 
 
 12.69 
 
 I2SS 
 
 35 
 
 43 
 
 10.79 
 
 1520 
 
 38 
 
 99 
 
 11.50 
 
 1785 
 
 42.25 
 
 12.13 
 
 2050 
 
 45.28 
 
 12.70 
 
 1260 
 
 35 
 
 50 
 
 10.80 
 
 152s 
 
 39 
 
 05 
 
 1I.5I 
 
 1790 
 
 42.31 
 
 12.14 
 
 2055 
 
 45.33 
 
 12.71 
 
 1265 
 
 35 
 
 57 
 
 10.82 
 
 1530 
 
 39 
 
 12 
 
 11.52 
 
 1795 
 
 42.37 
 
 12.15 
 
 2060 
 
 45.39 
 
 12.72 
 
58 
 
 Mathematical Tables 
 
 Table or Square Roots and Cube Roots of Numbers from 
 looo to 10,000 — {Continued) 
 
 No. 
 
 Sq. 
 root 
 
 Cube 
 root 
 
 No. 
 
 Sq. 
 root 
 
 Cube 
 root 
 
 No. 
 
 Sq. 
 root 
 
 Cube 
 root 
 
 No. 
 
 Sq. 
 root 
 
 Cube 
 root 
 
 2065 
 
 45-44 
 
 12.73 
 
 2330 
 
 48.27 
 
 13.26 
 
 2740 
 
 52.35 
 
 13-99 
 
 3270 
 
 57.18 
 
 14.84 
 
 2070 
 
 45 
 
 50 
 
 12.74 
 
 2335 
 
 48 
 
 32 
 
 13 
 
 27 
 
 2750 
 
 52.44 
 
 14.01 
 
 3280 
 
 57.27 
 
 14.86 
 
 2075 
 
 45 
 
 55 
 
 12.75 
 
 2340 
 
 48 
 
 37 
 
 13 
 
 28 
 
 2760 
 
 52.54 
 
 14-03 
 
 3290 
 
 57.36 
 
 14.87 
 
 2080 
 
 45 
 
 61 
 
 12.77 
 
 2345 
 
 48 
 
 43 
 
 13 
 
 29 
 
 2770 
 
 52.63 
 
 14.04 
 
 3300 
 
 57.45 
 
 14.89 
 
 2085 
 
 45 
 
 66 
 
 12.78 
 
 2350 
 
 48 
 
 48 
 
 13 
 
 30 
 
 2780 
 
 52.73 
 
 14.06 
 
 3310 
 
 57.53 
 
 14.90 
 
 2090 
 
 45 
 
 72 
 
 12.79 
 
 2355 
 
 48 
 
 53 
 
 13 
 
 30 
 
 2790 
 
 52.82 
 
 14.08 
 
 3320 
 
 57.62 
 
 14.92 
 
 2095 
 
 45 
 
 77 
 
 12.80 
 
 2360 
 
 48 
 
 58 
 
 13 
 
 31 
 
 2800 
 
 52.92 
 
 14.09 
 
 3330 
 
 57.71 
 
 14.93 
 
 2100 
 
 45 
 
 83 
 
 12.81 
 
 2365 
 
 48 
 
 63 
 
 13 
 
 32 
 
 2810 
 
 53.01 
 
 14. II 
 
 3340 
 
 57.79 
 
 14.9s 
 
 210S 
 
 45 
 
 88 
 
 12.82 
 
 2370 
 
 48 
 
 68 
 
 13 
 
 33 
 
 2820 
 
 53. 10 
 
 14.13 
 
 3350 
 
 57.88 
 
 14.96 
 
 21 10 
 
 45 
 
 93 
 
 12.83 
 
 2375 
 
 48 
 
 73 
 
 13 
 
 34 
 
 2830 
 
 53^20 
 
 14.14 
 
 3360 
 
 57.97 
 
 14.98 
 
 2115 
 
 45 
 
 99 
 
 12.84 
 
 2380 
 
 48 
 
 79 
 
 13 
 
 35 
 
 2840 
 
 53^29 
 
 14.16 
 
 3370 
 
 58.05 
 
 14.99 
 
 2120 
 
 46 
 
 04 
 
 12.85 
 
 2385 
 
 48 
 
 84 
 
 13 
 
 36 
 
 2850 
 
 53^39 
 
 14.18 
 
 3380 
 
 58.14 
 
 15.01 
 
 2I2S 
 
 46 
 
 10 
 
 12.86 
 
 2390 
 
 48 
 
 89 
 
 13 
 
 37 
 
 2860 
 
 53^48 
 
 14.19 
 
 3390 
 
 58.22 
 
 15.02 
 
 2130 
 
 46 
 
 15 
 
 12.87 
 
 2395 
 
 48 
 
 94 
 
 13 
 
 38 
 
 2870 
 
 53^57 
 
 14.21 
 
 3400 
 
 58.31 
 
 15.04 
 
 2135 
 
 46 
 
 21 
 
 12.88 
 
 2400 
 
 48 
 
 99 
 
 13 
 
 39 
 
 2880 
 
 53^67 
 
 14.23 
 
 3410 
 
 58.40 
 
 15. OS 
 
 2140 
 
 46 
 
 26 
 
 12.89 
 
 240s 
 
 49 
 
 04 
 
 13 
 
 40 
 
 2890 
 
 53^76 
 
 14.24 
 
 3420 
 
 58.48 
 
 15.07 
 
 2145 
 
 46 
 
 31 
 
 12.90 
 
 2410 
 
 49 
 
 09 
 
 13 
 
 41 
 
 2900 
 
 53.85 
 
 14.26 
 
 3430 
 
 58.57 
 
 15 08 
 
 2150 
 
 46 
 
 37 
 
 12.91 
 
 2415 
 
 49 
 
 14 
 
 13 
 
 42 
 
 2910 
 
 53.94 
 
 14.28 
 
 3440 
 
 58.65 
 
 15.10 
 
 2155 
 
 46 
 
 42 
 
 12.92 
 
 2420 
 
 49 
 
 19 
 
 13 
 
 43 
 
 2920 
 
 54.04 
 
 14.29 
 
 3450 
 
 58.74 
 
 15. II 
 
 2160 
 
 46 
 
 48 
 
 12.93 
 
 242s 
 
 49 
 
 24 
 
 13 
 
 • 43 
 
 2930 
 
 54.13 
 
 14.31 
 
 3460 
 
 58.82 
 
 15.12 
 
 2165 
 
 46 
 
 53 
 
 12.94 
 
 2430 
 
 49 
 
 30 
 
 13 
 
 • 44 
 
 2940 
 
 54.22 
 
 14.33 
 
 3470 
 
 58.91 
 
 15.14 
 
 2170 
 
 46 
 
 58 
 
 12.95 
 
 2435 
 
 49 
 
 35 
 
 13 
 
 • 45 
 
 2950 
 
 54.31 
 
 14.34 
 
 3480 
 
 58.99 
 
 15. IS 
 
 2175 
 
 46 
 
 64 
 
 12.96 
 
 2440 
 
 49 
 
 40 
 
 13 
 
 .46 
 
 2960 
 
 54.41 
 
 14.36 
 
 3490 
 
 59.08 
 
 IS. 17 
 
 2180 
 
 46 
 
 69 
 
 12.97 
 
 2445 
 
 49 
 
 45 
 
 13 
 
 • 47 
 
 2970 
 
 54 -50 
 
 14-37 
 
 3500 
 
 59.16 
 
 IS. 18 
 
 2185 
 
 46 
 
 74 
 
 12.98 
 
 2450 
 
 49 
 
 50 
 
 13 
 
 • 48 
 
 2980 
 
 54.59 
 
 14-39 
 
 3510 
 
 59.25 
 
 15.20 
 
 2190 
 
 46 
 
 80 
 
 12.99 
 
 2460 
 
 49 
 
 60 
 
 13 
 
 • 50 
 
 2990 
 
 54.68 
 
 14.41 
 
 3520 
 
 59.33 
 
 15.21 
 
 219s 
 
 46 
 
 .85 
 
 13 
 
 2470 
 
 49 
 
 70 
 
 13 
 
 • 52 
 
 3000 
 
 54.77 
 
 14.42 
 
 3530 
 
 59.41 
 
 15.23 
 
 2200 
 
 46 
 
 .90 
 
 13.01 
 
 2480 
 
 49 
 
 80 
 
 13 
 
 • 54 
 
 3010 
 
 54.86 
 
 14.44 
 
 3540 
 
 59.50 
 
 15.24 
 
 2205 
 
 46 
 
 96 
 
 13 02 
 
 2490 
 
 49 
 
 90 
 
 13 
 
 • 55- 
 
 3020 
 
 54.95 
 
 14.45 
 
 3550 
 
 59 58 
 
 15.25 
 
 2210 
 
 47 
 
 .01 
 
 13.03 
 
 2500 
 
 50 
 
 
 13 
 
 57 
 
 3030 
 
 55.05 
 
 14.47 
 
 3560 
 
 59.67 
 
 15.27 
 
 2215 
 
 47 
 
 06 
 
 13.04 
 
 2510 
 
 50 
 
 10 
 
 13 
 
 •59 
 
 3040 
 
 55.14 
 
 14.49 
 
 3570 
 
 59-75 
 
 15.28 
 
 2220 
 
 47 
 
 .12 
 
 13-05 
 
 2520 
 
 50 
 
 20 
 
 13 
 
 61 
 
 3050 
 
 55.23 
 
 14.50 
 
 3580 
 
 59-83 
 
 IS. 30 
 
 2225 
 
 47 
 
 • 17 
 
 13.05 
 
 2530 
 
 50 
 
 30 
 
 13 
 
 63 
 
 3060 
 
 55.32 
 
 14.52 
 
 3590 
 
 59.92 
 
 15.31 
 
 2230 
 
 47 
 
 22 
 
 13.06 
 
 2540 
 
 50 
 
 40 
 
 13 
 
 64 
 
 3070 
 
 55.41 
 
 14.53 
 
 3600 
 
 60 
 
 15.33 
 
 2235 
 
 47 
 
 28 
 
 13.07 
 
 2550 
 
 50 
 
 50 
 
 13 
 
 66 
 
 3080 
 
 .55.50 
 
 14.55 
 
 3610 
 
 60.08 
 
 IS. 34 
 
 2240 
 
 47 
 
 .33 
 
 13.08 
 
 2560 
 
 50 
 
 60 
 
 13 
 
 68 
 
 3090 
 
 55.59 
 
 14.57 
 
 3620 
 
 60.17 
 
 IS. 35 
 
 2245 
 
 47 
 
 .38 
 
 13.09 
 
 2570 
 
 50 
 
 70 
 
 13 
 
 70 
 
 3100 
 
 55.68 
 
 14.58 
 
 3630 
 
 60.25 
 
 15.37 
 
 2250 
 
 47 
 
 43 
 
 13.10 
 
 2580 
 
 50 
 
 79 
 
 13 
 
 72 
 
 3110 
 
 55.77 
 
 14.60 
 
 3640 
 
 60.33 
 
 IS. 38 
 
 2255 
 
 47 
 
 •49 
 
 I3-II 
 
 2590 
 
 50 
 
 89 
 
 13 
 
 73 
 
 3120 
 
 55.86 
 
 14.61 
 
 3650 
 
 60.42 
 
 15.40 
 
 2260 
 
 47 
 
 54 
 
 13- 12 
 
 2600 
 
 50 
 
 99 
 
 13 
 
 75 
 
 3130 
 
 55.95 
 
 14.63 
 
 3660 
 
 60.50 
 
 IS. 41 
 
 2265 
 
 47 
 
 59 
 
 13.13 
 
 2610 
 
 51 
 
 09 
 
 13 
 
 77 
 
 3140 
 
 56.04 
 
 14.64 
 
 3670 
 
 60.58 
 
 15.42 
 
 2270 
 
 47 
 
 64 
 
 13.14 
 
 2620 
 
 51 
 
 19 
 
 13 
 
 79 
 
 3150 
 
 56.12 
 
 14.66 
 
 3680 
 
 60.66 
 
 15.44 
 
 2275 
 
 47 
 
 70 
 
 13.15 
 
 2630 
 
 51 
 
 28 
 
 13 
 
 80 
 
 3160 
 
 56.21 
 
 14.67 
 
 3690 
 
 60.75 
 
 15^45 
 
 2280 
 
 47 
 
 75 
 
 13.16 
 
 2640 
 
 51 
 
 38 
 
 13 
 
 82 
 
 3170 
 
 56.30 
 
 14.69 
 
 3700 
 
 60.83 
 
 15-47 
 
 228s 
 
 47 
 
 80 
 
 13.17 
 
 2650 
 
 51 
 
 48 
 
 13 
 
 84 
 
 3180 
 
 56.39 
 
 14.71 
 
 3710 
 
 60.91 
 
 15.48 
 
 2290 
 
 47 
 
 85 
 
 13.18 
 
 i 2660 
 
 51 
 
 58 
 
 13 
 
 86 
 
 3190 
 
 56.48 
 
 14.72 
 
 3720 
 
 60.99 
 
 IS. 49 
 
 2295 
 
 47 
 
 91 
 
 13.19 
 
 2670 
 
 51 
 
 67 
 
 13 
 
 87 
 
 3200 
 
 56.57 
 
 14.74 
 
 3730 
 
 61.07 
 
 IS. SI 
 
 2300 
 
 47 
 
 96 
 
 13 -20 
 
 2680 
 
 51 
 
 77 
 
 13 
 
 89 
 
 3210 
 
 56.66 
 
 14.75 
 
 3740 
 
 61.16 
 
 15.52 
 
 2305 
 
 48 
 
 or 
 
 13-21 
 
 2690 
 
 SI 
 
 87 
 
 13 
 
 91 
 
 3220 
 
 56.75 
 
 14.77 
 
 3750 
 
 61.24 
 
 IS. 54 
 
 2310 
 
 48 
 
 06 
 
 13.22 
 
 2700 
 
 51 
 
 96 
 
 13 
 
 92 
 
 3230 
 
 56.83 
 
 14.78 
 
 3760 
 
 61.32 
 
 IS.SS 
 
 2315 
 
 48 
 
 II 
 
 13.23 
 
 2710 
 
 52. 
 
 06 
 
 13 
 
 94 
 
 3240 
 
 56.92 
 
 14.80 
 
 3770 
 
 61.40 
 
 15.56 
 
 2320 
 
 48 
 
 17 
 
 13.24 
 
 2720 
 
 52. 
 
 15 
 
 13 
 
 9.6 
 
 3250 
 
 57- 01 
 
 14.81 
 
 3780 
 
 61.48 
 
 15. 58 
 
 2325 
 
 48 
 
 22 
 
 13.2s 
 
 2730 
 
 52. 
 
 25 
 
 13. 
 
 98 
 
 3260 
 
 57.10 
 
 14.83 
 
 3790 
 
 61.56 
 
 15.59 
 
Table of Square Roots and Cube Roots 
 
 59 
 
 Table of Square Roots and Cube Roots of Numbers from 
 looo to 10,000" — {Continued) 
 
 No. 
 
 Sq. 
 root 
 
 Cube 
 root 
 
 No. 
 
 Sq. 
 root 
 
 Cube 
 root 
 
 No. 
 
 Sq. 
 root 
 
 Cube 
 root 
 
 No. 
 
 Sq. 
 root 
 
 Cube 
 root 
 
 3800 
 
 61.64 
 
 15.60 
 
 4330 
 
 65.80 
 
 16.30 
 
 4860 
 
 69.71 
 
 16.94 
 
 S390 
 
 73.42 
 
 17.53 
 
 3810 
 
 61.73 
 
 15.62 
 
 4340 
 
 65.88 
 
 16.31 
 
 4870 
 
 69.79 
 
 16.95 
 
 5400 
 
 73.48 
 
 17.54 
 
 3820 
 
 61.81 
 
 15.63 
 
 4350 
 
 65.9s 
 
 16.32 
 
 4880 
 
 69.86 
 
 16.96 
 
 5410 
 
 73.55 
 
 17.55 
 
 3830 
 
 61.89 
 
 15-65 
 
 4360 
 
 66.03 
 
 16.34 
 
 4890 
 
 69.93 
 
 16.97 
 
 5420 
 
 73-62 
 
 17.57 
 
 3840 
 
 61.97 
 
 15.66 
 
 4370 
 
 66.11 
 
 16.35 
 
 4900 
 
 70 
 
 16.98 
 
 5430 
 
 73-69 
 
 17.58 
 
 3850 
 
 62.05 
 
 15.67 
 
 4380 
 
 66. IS 
 
 16.36 
 
 4910 
 
 70.07 
 
 17 
 
 5440 
 
 73-76 
 
 17.59 
 
 3860 
 
 62.13 
 
 15.69 
 
 4390 
 
 66.26 
 
 16.37 
 
 4920 
 
 70.14 
 
 17.01 
 
 5450 
 
 73-82 
 
 17.60 
 
 3870 
 
 62.21 
 
 15.70 
 
 4400 
 
 66.33 
 
 16.39 
 
 4930 
 
 70.21 
 
 17.02 
 
 5460 
 
 73-89 
 
 17.61 
 
 3880 
 
 62.29 
 
 15.71 
 
 4410 
 
 66.41 
 
 16.40 
 
 4940 
 
 70.29 
 
 17.03 
 
 5470 
 
 73-96 
 
 17.62 
 
 3890 
 
 62.37 
 
 15.73 
 
 4420 
 
 66.48 
 
 16.41 
 
 4950 
 
 70.36 
 
 17.04 
 
 5480 
 
 74-03 
 
 17-63 
 
 3900 
 
 62.45 
 
 15.74 
 
 4430 
 
 66.56 
 
 16.42 
 
 4960 
 
 70.43 
 
 17. OS 
 
 5490 
 
 74.09 
 
 17.64 
 
 3910 
 
 62.53 
 
 15.75 
 
 4440 
 
 66.63 
 
 16.44 
 
 4970 
 
 70.50 
 
 17.07 
 
 5500 
 
 74.16 
 
 17.65 
 
 3920 
 
 62.61 
 
 15.77 
 
 44SO 
 
 66.71 
 
 16.45 
 
 4980 
 
 70.57 
 
 17.08 
 
 5510 
 
 74.23 
 
 17.66 
 
 3930 
 
 62.69 
 
 IS. 78 
 
 4460 
 
 66.78 
 
 16.46 
 
 4990 
 
 70.64 
 
 17.09 
 
 5520 
 
 74.30 
 
 17.67 
 
 3940 
 
 62.77 
 
 15.79 
 
 4470 
 
 66.86 
 
 16.47 
 
 Sooo 
 
 70.71 
 
 17.10 
 
 5530 
 
 74.36 
 
 17.68 
 
 3950 
 
 62.85 
 
 15.81 
 
 4480 
 
 66.93 
 
 16.49 
 
 5010 
 
 70.78 
 
 17. II 
 
 5540 
 
 74.43 
 
 17.69 
 
 3960 
 
 62.93 
 
 15.82 
 
 4490 
 
 67.01 
 
 16.50 
 
 5020 
 
 70.85 
 
 17.12 
 
 S5SO 
 
 74.50 
 
 17.71 
 
 3970 
 
 63.01 
 
 15.83 
 
 4500 
 
 67.08 
 
 16.51 
 
 5030 
 
 70.92 
 
 17.13 
 
 5560 
 
 74.57 
 
 17.72 
 
 3980 
 
 63.09 
 
 15.85 
 
 4510 
 
 67.16 
 
 16.52 
 
 5040 
 
 70.99 
 
 17.15 
 
 5S70 
 
 74.63 
 
 17.73 
 
 3990 
 
 63. 17 
 
 15.86 
 
 4520 
 
 67.23 
 
 16.53 
 
 5050 
 
 71.06 
 
 17.16 
 
 5580 
 
 74.70 
 
 17.74 
 
 4000 
 
 63.25 
 
 15.87 
 
 4530 
 
 67.31 
 
 16.55 
 
 5060 
 
 71.13 
 
 17.17 
 
 5590 
 
 74.77 
 
 17.75 
 
 4010 
 
 63.32 
 
 IS. 89 
 
 4540 
 
 67.38 
 
 16.56 
 
 5070 
 
 71.20 
 
 17.18 
 
 5600 
 
 74.83 
 
 17.76 
 
 4020 
 
 63.40 
 
 15.90 
 
 4S50 
 
 67.4s 
 
 16.57 
 
 5080 
 
 71.27 
 
 17.19 
 
 5610 
 
 74.90 
 
 ■17.77 
 
 4030 
 
 63.48 
 
 15.91 
 
 4560 
 
 67.53 
 
 16.58 
 
 5090 
 
 71.34 
 
 17.20 
 
 5620 
 
 74.97 
 
 17.78 
 
 4040 
 
 63.56 
 
 15.93 
 
 4570 
 
 67.60 
 
 16.59 
 
 5100 
 
 71.41 
 
 17.21 
 
 5630 
 
 75.03 
 
 17.79 
 
 4050 
 
 63.64 
 
 15.94 
 
 4580 
 
 67.68 
 
 16.61 
 
 5110 
 
 71.48 
 
 17.22 
 
 5640 
 
 75.10 
 
 17.80 
 
 4060 
 
 63.72 
 
 IS. 95 
 
 4590 
 
 67.75 
 
 16.62 
 
 5120 
 
 71.55 
 
 17.24 
 
 5650 
 
 75.17 
 
 17.81 
 
 4070 
 
 63.80 
 
 15.97 
 
 4600 
 
 67.82 
 
 16.63 
 
 5130 
 
 71.62 
 
 17.25 
 
 5660 
 
 75.23 
 
 17.82 
 
 4080 
 
 63.87 
 
 IS. 98 
 
 4610 
 
 67.90 
 
 16.64 
 
 5140 
 
 71.69 
 
 17.26 
 
 5670 
 
 75.30 
 
 17.83 
 
 4090 
 
 63.95 
 
 15.99 
 
 4620 
 
 67.97 
 
 16.66 
 
 5150 
 
 71.76 
 
 17.27 
 
 5680 
 
 75.37 
 
 17.84 
 
 4100 
 
 64.03 
 
 16.01 
 
 4630 
 
 68.04 
 
 16.67 
 
 5160 
 
 71.83 
 
 17.28 
 
 5690 
 
 75.43 
 
 17.85 
 
 41T0 
 
 64.11 
 
 16.02 
 
 4640 
 
 68.12 
 
 16.68 
 
 5170 
 
 71.90 
 
 17.29 
 
 S700 
 
 75.50 
 
 17.86 
 
 4120 
 
 64.19 
 
 16.03 
 
 4650 
 
 68.19 
 
 16.69 
 
 5180 
 
 71.97 
 
 17.30 
 
 5710 
 
 75.56 
 
 17.87 
 
 4130 
 
 64.27' 
 
 16.04 
 
 4660 
 
 68.26 
 
 16.70 
 
 5190 
 
 72.04 
 
 17.31 
 
 S720 
 
 75.63 
 
 17.88 
 
 4140 
 
 64.34 
 
 16.06 
 
 4670 
 
 68.34 
 
 16.71 
 
 5200 
 
 72.11 
 
 17.32 
 
 5730 
 
 75.70 
 
 17.89 
 
 4150 
 
 64.42 
 
 16.07 
 
 4680 
 
 68.41 
 
 16.73 
 
 5210 
 
 72.18 
 
 17.34 
 
 S740 
 
 75.76 
 
 17.90 
 
 4160 
 
 64.50 
 
 16.08 
 
 4690 
 
 68.48 
 
 16.74 
 
 5220 
 
 72.25 
 
 17.35 
 
 S750 
 
 75.83 
 
 17.92 
 
 4170 
 
 64.58 
 
 16.10 
 
 4700 
 
 68.56 
 
 16.75 
 
 5230 
 
 72.32 
 
 17.36 
 
 5760 
 
 75.89 
 
 17.93 
 
 4180 
 
 64.65 
 
 16. II 
 
 4710 
 
 68.63 
 
 16.76 
 
 5240 
 
 72.39 
 
 17.37 
 
 S770 
 
 75.96 
 
 17.94 
 
 4190 
 
 64.73 
 
 16.12 
 
 4720 
 
 68.70 
 
 16.77 
 
 5250 
 
 72.46 
 
 17.38 
 
 5780 
 
 76.03 
 
 17.95 
 
 4200 
 
 64.81 
 
 16.13 
 
 4730 
 
 68.77 
 
 16.79 
 
 5260 
 
 72.53 
 
 17.39 
 
 S790 
 
 76.09 
 
 17.96 
 
 4210 
 
 64.88 
 
 16. IS 
 
 4740 
 
 68.85 
 
 16.80 
 
 5270 
 
 72.59 
 
 17.40 
 
 5800 
 
 76.16 
 
 17.97 
 
 4220 
 
 64.96 
 
 16.16 
 
 4750 
 
 68.92 
 
 16.81 
 
 5280 
 
 72.66 
 
 17.41 
 
 5810 
 
 76.22 
 
 17.98 
 
 4230 
 
 65.04 
 
 16.17 
 
 4760 
 
 68.99 
 
 16.82 
 
 5290 
 
 72.73 
 
 17.42 
 
 5820 
 
 76.29 
 
 17.99 
 
 4240 
 
 65.12 
 
 16.19 
 
 4770 
 
 69.07 
 
 16.83 
 
 5300 
 
 72.80 
 
 17-44 
 
 5830 
 
 76.35 
 
 18 
 
 4250 
 
 65.19 
 
 16.20 
 
 4780 
 
 69.14 
 
 16.8s 
 
 5310 
 
 72.87 
 
 17.4s 
 
 5840 
 
 76.42 
 
 18.01 
 
 4260 
 
 65.27 
 
 16.21 
 
 4790 
 
 69.21 
 
 16.86 
 
 S320 
 
 72.94 
 
 17.46 
 
 5850 
 
 76.49 
 
 18.02 
 
 4270 
 
 65.35 
 
 16.22 
 
 4800 
 
 69.28 
 
 16.87 
 
 S330 
 
 73.01 
 
 17.47 
 
 5860 
 
 76.55 
 
 18.03 
 
 4280 
 
 65.42 
 
 16.24 
 
 4810 
 
 69.35 
 
 16.88 
 
 S340 
 
 73.08 
 
 17.48 
 
 5870 
 
 76.62 
 
 18.04 
 
 4290 
 
 65.50 
 
 16.25 
 
 4820 
 
 69.43 
 
 16.89 
 
 5350 
 
 73.14 
 
 17.49 
 
 5880 
 
 76.68 
 
 18.05 
 
 4300 
 
 65.57 
 
 16.26 
 
 4830 
 
 69.50 
 
 16.90 
 
 5360" 
 
 73.21 
 
 17.50 
 
 5890 
 
 76.75 
 
 18.06 
 
 4310 
 
 65. 65 
 
 16.27 
 
 4840 
 
 69.57 
 
 16.92 
 
 5370 
 
 73.28 
 
 17.51 
 
 5900 
 
 76.81 
 
 18.07 
 
 4320 
 
 65.73 
 
 16.29 
 
 4850 
 
 69.64 
 
 "16.93 
 
 5380 
 
 73.35 
 
 17.52 
 
 5910 
 
 76.88 
 
 18.08 
 
6o 
 
 Mathematical Tables 
 
 Table of Square Roots and Cube Roots of Numbers from 
 
 looo to 10,000 — (Continued) 
 
 No. 
 
 Sq. 
 
 Cube 
 
 No. 
 
 Sq. 
 
 Cube 
 
 No. 
 
 Sq. 
 
 Cube 
 
 No. 
 
 Sq. 
 
 Cube 
 
 root 
 
 root 
 
 root 
 
 root 
 
 root 
 
 root 
 
 root 
 
 root 
 
 5920 
 
 76.94 
 
 18.09 
 
 6450 
 
 80.31 
 
 18.61 
 
 6980 
 
 83.55 
 
 19. II 
 
 7510 
 
 86.66 
 
 19 58 
 
 S930 
 
 77.01 
 
 18.10 
 
 6460 
 
 80.37 
 
 18.62 
 
 6990 
 
 83.61 
 
 19 
 
 .12 
 
 7520 
 
 86 
 
 .72 
 
 19.59 
 
 5940 
 
 77.07 
 
 18. II 
 
 6470 
 
 80.44 
 
 18.63 
 
 7000 
 
 83.67 
 
 19 
 
 .13 
 
 7530 
 
 86 
 
 78 
 
 19.60 
 
 5950 
 
 77.14 
 
 18.12 
 
 6480 
 
 80.50 
 
 18.64 
 
 7010 
 
 83.73 
 
 19 
 
 14 
 
 7540 
 
 86 
 
 -83 
 
 19.61 
 
 5960 
 
 77.20 
 
 18.13 
 
 6490 
 
 80.56 
 
 18.65 
 
 7020 
 
 83-79 
 
 19 
 
 IS 
 
 7550 
 
 86 
 
 -89 
 
 19.62 
 
 5970 
 
 77.27 
 
 18.14 
 
 6500 
 
 80.62 
 
 18.66 
 
 7030 
 
 83 -8s 
 
 19 
 
 .16 
 
 7560 
 
 86 
 
 95 
 
 19.63 
 
 5980 
 
 77.33 
 
 18.15 
 
 6510 
 
 80.68 
 
 18.67 
 
 7040 
 
 83-90 
 
 19 
 
 .17 
 
 7570 
 
 87 
 
 .01 
 
 19.64 
 
 5990 
 
 77.40 
 
 18.16 
 
 6520 
 
 80.75 
 
 18.68 
 
 7050 
 
 83-96 
 
 19 
 
 .17 
 
 7580 
 
 87 
 
 06 
 
 19.64 
 
 6000 
 
 77.46 
 
 18.17 
 
 6530 
 
 80.81 
 
 18.69 
 
 7060 
 
 84.02 
 
 19 
 
 .18 
 
 7590 
 
 87 
 
 12 
 
 19.65 
 
 6010 
 
 77.52 
 
 18.18 
 
 6540 
 
 80.87 
 
 18.70 
 
 7070 
 
 84.08 
 
 19 
 
 .19 
 
 7600 
 
 87 
 
 18 
 
 19.66 
 
 6020 
 
 77.59 
 
 18.19 
 
 6550 
 
 80.93 
 
 18.71 
 
 7080 
 
 84.14 
 
 19 
 
 20 
 
 7610 
 
 87 
 
 24 
 
 19.67 
 
 6030 
 
 77.65 
 
 18.20 
 
 6560 
 
 80.99 
 
 18.72 
 
 7090 
 
 84.20 
 
 19 
 
 .21 
 
 7620 
 
 87 
 
 29 
 
 19.68 
 
 6040 
 
 77.72 
 
 18.21 
 
 6570 
 
 81.06 
 
 18.73 
 
 7100 
 
 84.26 
 
 19 
 
 22 
 
 7630 
 
 87 
 
 35 
 
 19.69 
 
 6050 
 
 77.78 
 
 18.22 
 
 6580 
 
 81.12 
 
 18.74 
 
 7110 
 
 84.32 
 
 19 
 
 23 
 
 7640 
 
 87 
 
 41 
 
 19.70 
 
 6060 
 
 77.85 
 
 18.23 
 
 6590 
 
 81.18 
 
 18-75 
 
 7120 
 
 84.38 
 
 19 
 
 24 
 
 7650 
 
 87 
 
 46 
 
 19-70 
 
 6070 
 
 77.91 
 
 18.24 
 
 6600 
 
 81.24 
 
 18.76 
 
 7130 
 
 84.44 
 
 19 
 
 25 
 
 7660 
 
 87 
 
 52 
 
 19-71 
 
 6080 
 
 77.97 
 
 18.2s 
 
 6610 
 
 81.30 
 
 18.77 
 
 7140 
 
 84-50 
 
 19 
 
 26 
 
 7670 
 
 87 
 
 58 
 
 19-72 
 
 6090 
 
 78.04 
 
 18.26 
 
 6620 
 
 81.36 
 
 18.78 
 
 7150 
 
 84-56 
 
 19 
 
 26 
 
 7680 
 
 S7 
 
 .64 
 
 19-73 
 
 6100 
 
 78.10 
 
 18.27 
 
 6630 
 
 81.42 
 
 18.79 
 
 7160 
 
 84.62 
 
 19 
 
 27 
 
 7690 
 
 87 
 
 69 
 
 19-74 
 
 6110 
 
 78.17 
 
 18.28 
 
 6640 
 
 81.49 
 
 18.80 
 
 7170 
 
 84.68 
 
 19 
 
 28 
 
 7700 
 
 87 
 
 75 
 
 19-75 
 
 6120 
 
 78.23 
 
 18.29 
 
 6650 
 
 81.55 
 
 18.81 
 
 7180 
 
 84.73 
 
 19 
 
 29 
 
 7710 
 
 87 
 
 81 
 
 19-76 
 
 6130 
 
 78.29 
 
 18.30 
 
 6660 
 
 81.61 
 
 18.81 
 
 7190 
 
 84.79 
 
 19 
 
 30 
 
 7720 
 
 87 
 
 86 
 
 19.76 
 
 6140 
 
 78.36 
 
 18.31 
 
 6670 
 
 81.67 
 
 18.82 
 
 7200 
 
 84-85 
 
 19 
 
 31 
 
 7730 
 
 87 
 
 92 
 
 19.77 
 
 6150 
 
 78.42 
 
 18.32 
 
 6680 
 
 81.73 
 
 18.83 
 
 7210 
 
 84.91 
 
 19 
 
 32 
 
 7740 
 
 87 
 
 98 
 
 19 78 
 
 6160 
 
 78.49 
 
 18.33 
 
 6690 
 
 81.79 
 
 18.84 
 
 7220 
 
 84.97 
 
 19 
 
 33 
 
 7750 
 
 88 
 
 03 
 
 19.79 
 
 6170 
 
 78.55 
 
 18.34 
 
 6700 
 
 81.85 
 
 18.85 
 
 7230 
 
 85.03 
 
 19 
 
 34 
 
 7760 
 
 88 
 
 09 
 
 19.80 
 
 6180 
 
 78.61 
 
 18.35 
 
 6710 
 
 81.91 
 
 18.86 
 
 7240 
 
 85.09 
 
 19 
 
 35 
 
 7770 
 
 88 
 
 15 
 
 19.81 
 
 6190 
 
 78.68 
 
 18.36 
 
 6720 
 
 81.98 
 
 18.87 
 
 7250 
 
 85.15 
 
 19 
 
 35 
 
 7780 
 
 88 
 
 20 
 
 19.81 
 
 6200 
 
 78.74 
 
 18.37 
 
 6730 
 
 82.04 
 
 18.88 
 
 7260 
 
 85.21 
 
 19 
 
 36 
 
 7790 
 
 88 
 
 26 
 
 19.82 
 
 6210 
 
 78.80 
 
 18.38 
 
 6740 
 
 82.10 
 
 18.89 
 
 7270 
 
 85.26 
 
 19 
 
 37 
 
 7800 
 
 88 
 
 32 
 
 19.83 
 
 6220 
 
 78.87 
 
 18.39 
 
 6750 
 
 82.16 
 
 18.90 
 
 7280 
 
 85.32 
 
 19 
 
 38 
 
 7810 
 
 88 
 
 37 
 
 19.84 
 
 6230 
 
 78.93 
 
 18.40 
 
 6760 
 
 82.22 
 
 18.91 
 
 7290 
 
 85.38 
 
 19 
 
 39 
 
 7820 
 
 88 
 
 43 
 
 19-85 
 
 6240 
 
 78.99 
 
 18.41 
 
 6770 
 
 82.28 
 
 18.92 
 
 7300 
 
 85.44 
 
 19 
 
 40 
 
 7830 
 
 88 
 
 49 
 
 19.86 
 
 6250 
 
 79.06 
 
 18.42 
 
 6780 
 
 82.34 
 
 18.93 
 
 7310 
 
 85.50 
 
 19 
 
 41 
 
 7840 
 
 88 
 
 54 
 
 19.87 
 
 6260 
 
 79-12 
 
 18.43 
 
 6790 
 
 82.40 
 
 18.94 
 
 7320 
 
 85.56 
 
 19 
 
 42 
 
 7850 
 
 88 
 
 60 
 
 19-87 
 
 6270 
 
 79-18 
 
 18.44 
 
 6800 
 
 82.46 
 
 18.95 
 
 7330 
 
 85.62 
 
 19 
 
 43 
 
 7860 
 
 88 
 
 66 
 
 19.88 
 
 6280 
 
 79.25 
 
 18.45 
 
 6810 
 
 82.52 
 
 18.95 
 
 7340 
 
 85.67 
 
 19 
 
 43 
 
 7870 
 
 88 
 
 71 
 
 19.89 
 
 6290 
 
 79.31 
 
 18.46 
 
 6820 
 
 82.58 
 
 18.96 
 
 7350 
 
 85.73 
 
 19 
 
 44 
 
 7880 
 
 88 
 
 77 
 
 19.90 
 
 6300 
 
 79.37 
 
 18.47 
 
 6830 
 
 82.64 
 
 18.97 
 
 7360 
 
 85.79 
 
 19 
 
 45 
 
 7890 
 
 88 
 
 83 
 
 19.91 
 
 6310 
 
 79.44 
 
 18.48 
 
 6840 
 
 82.70 
 
 18.98 
 
 7370 
 
 85.85 
 
 19 
 
 46 
 
 7900 
 
 88 
 
 88 
 
 19.92 
 
 6320 
 
 79.50 
 
 18.49 
 
 6850 
 
 82.76 
 
 18.99 
 
 7380 
 
 85.91 
 
 19 
 
 47 
 
 7910 
 
 88 
 
 94 
 
 19.92 
 
 6330 
 
 79-56 
 
 18.50 
 
 6860 
 
 82.83 
 
 19 
 
 7390 
 
 85.97 
 
 19 
 
 48 
 
 7920 
 
 88 
 
 99 
 
 19.93 
 
 6340 
 
 79-62 
 
 18.51 
 
 6870 
 
 82.89 
 
 19.01 
 
 7400 
 
 86.02 
 
 19 
 
 49 
 
 7930 
 
 89 
 
 05 
 
 19.94 
 
 6350 
 
 79.69 
 
 18.52 
 
 6880 
 
 82.95 
 
 19.02 
 
 7410 
 
 86.08 
 
 19 
 
 50 
 
 7940 
 
 89 
 
 II 
 
 19.95 
 
 6360 
 
 79.75 
 
 18.53 
 
 6890 
 
 83-01 
 
 19-03 
 
 7420 
 
 86.14 
 
 19 
 
 50 
 
 7950 
 
 89 
 
 16 
 
 19.96 
 
 6370 
 
 79.81 
 
 18.54 
 
 6900 
 
 83-07 
 
 19-04 
 
 7430 
 
 86.20 
 
 19 
 
 51 
 
 7960 
 
 89 
 
 22 
 
 19.97 
 
 6380 
 
 79.87 
 
 18.55 
 
 6910 
 
 83-13 
 
 19 -05 
 
 7440 
 
 86.29 
 
 19 
 
 52 
 
 7970 
 
 89 
 
 27 
 
 19.97 
 
 6390 
 
 79.94 
 
 18.56 
 
 6920 
 
 83.19 
 
 19.06 
 
 7450 
 
 86.31 
 
 19 
 
 53 
 
 7980 
 
 89 
 
 33 
 
 19.98 
 
 6400 
 
 80 
 
 18.57 
 
 6930 
 
 83.25 
 
 19.07 
 
 7460 
 
 86.37 
 
 19 
 
 54 
 
 7990 
 
 89 
 
 39 
 
 19-99 
 
 6410 
 
 80.06 
 
 18.58 
 
 6940 
 
 83.31 
 
 19-07 
 
 7470 
 
 86.43 
 
 19 
 
 55 
 
 8000 
 
 89 
 
 44 
 
 20 
 
 6420 
 
 80.12 
 
 18.59 
 
 6950 
 
 83.37 
 
 19.08 
 
 7480 
 
 86.49 
 
 19 
 
 56 
 
 8010 
 
 89 
 
 50 
 
 20 01 
 
 6430 
 
 80.19 
 
 18.60 
 
 6960 
 
 83.43 
 
 19.09 
 
 7490 
 
 86.54 
 
 19. 
 
 57 
 
 8020 
 
 89 
 
 55 
 
 20.02 
 
 6440 
 
 80.25 
 
 18.60 
 
 6970 83.49 
 
 19.10 
 
 7500 
 
 86.60 19. 
 
 57 
 
 8030 
 
 89 
 
 61 
 
 20.02 
 
Table of Square Roots and Cube Roots 
 
 6i 
 
 Table of Square Roots and Cube Roots of Numbers from 
 looo to 10,000 — {Contlmied) 
 
 No. 
 
 s,. 
 
 Cube 
 
 No. 
 
 Sq. 
 
 Cube 
 
 No. 
 
 Sq. 
 
 Cube 
 
 No. 
 
 Sq. 
 
 Cube 
 
 root 
 
 root 
 
 root 
 
 root 
 
 root 
 
 root 
 
 root 
 
 root 
 
 8040 
 
 89.67 
 
 20.03 
 
 8540 
 
 92.41 
 
 20.44 
 
 9040 
 
 95.08 
 
 20.83 
 
 9540 
 
 97.67 
 
 21.21 
 
 8050 
 
 89.72 
 
 20.04 
 
 8550 
 
 92 
 
 47 
 
 20.45 
 
 9050 
 
 95 
 
 14 
 
 20.84 
 
 9550 
 
 97 
 
 72 
 
 21.22 
 
 8060 
 
 89.78 
 
 20.05 
 
 8560 
 
 92 
 
 52 
 
 20.46 
 
 9060 
 
 95 
 
 18 
 
 20.85 
 
 9560 
 
 97 
 
 78 
 
 21.22 
 
 8070 
 
 89.83 
 
 20.06 
 
 8570 
 
 92 
 
 57 
 
 20.46 
 
 9070 
 
 95 
 
 24 
 
 20.85 
 
 9570 
 
 97 
 
 83 
 
 21.23 
 
 8080 
 
 89.89 
 
 20.07 
 
 8580 
 
 92 
 
 63 
 
 20.47 
 
 9080 
 
 95 
 
 29 
 
 20.86 
 
 9580 
 
 97 
 
 88 
 
 21.24 
 
 8090 
 
 89.94 
 
 20.07 
 
 8590 
 
 92 
 
 68 
 
 20.48 
 
 9090 
 
 95 
 
 34 
 
 20.87 
 
 9590 
 
 97 
 
 93 
 
 21.25 
 
 8100 
 
 90 
 
 20.08 
 
 8600 
 
 92 
 
 74 
 
 20.49 
 
 9100 
 
 95 
 
 39 
 
 20.88 
 
 9600 
 
 97 
 
 98 
 
 21.25 
 
 8110 
 
 90.06 
 
 20.09 
 
 8610 
 
 92 
 
 79 
 
 20.50 
 
 91 10 
 
 95 
 
 45 
 
 20.89 
 
 9610 
 
 98 
 
 03 
 
 21.26 
 
 8120 
 
 90.11 
 
 20.10 
 
 8620 
 
 92 
 
 84 
 
 20.50 
 
 9120 
 
 95 
 
 50 
 
 20.89 
 
 9620 
 
 98 
 
 08 
 
 21.27 
 
 8130 
 
 90.17 
 
 20.11 
 
 8630 
 
 92 
 
 90 
 
 20.51 
 
 9130 
 
 95 
 
 55 
 
 20.90 
 
 9630 
 
 98 
 
 13 
 
 21.28 
 
 8140 
 
 90.22 
 
 20.12 
 
 8640 
 
 92 
 
 95 
 
 20.52 
 
 9140 
 
 95 
 
 60 
 
 20.91 
 
 9640 
 
 98 
 
 18 
 
 21.28 
 
 8150 
 
 90.28 
 
 20.12 
 
 8650 
 
 93 
 
 01 
 
 20. S3 
 
 9150 
 
 95 
 
 66 
 
 20.92 
 
 9650 
 
 98 
 
 23 
 
 21.29 
 
 8160 
 
 90.33 
 
 20.13 
 
 8660 
 
 93 
 
 06 
 
 20.54 
 
 9160 
 
 95 
 
 71 
 
 20.92 
 
 9660 
 
 98 
 
 29 
 
 21.30 
 
 8170 
 
 90.39 
 
 20.14 
 
 8670 
 
 93 
 
 II 
 
 20.54 
 
 9170 
 
 95 
 
 76 
 
 20.93 
 
 9670 
 
 98 
 
 34 
 
 21.30 
 
 8180 
 
 90.44 
 
 20.15 
 
 8680 
 
 93 
 
 17 
 
 20.55 
 
 9180 
 
 95 
 
 81 
 
 20.94 
 
 9680 
 
 98 
 
 39 
 
 21.31 
 
 8190 
 
 90.50 
 
 20.16 
 
 8690 
 
 93 
 
 22 
 
 20.56 
 
 9190 
 
 95 
 
 86 
 
 20.95 
 
 9690 
 
 98 
 
 44 
 
 21.32 
 
 8200 
 
 90.55 
 
 20.17 
 
 8700 
 
 93 
 
 27 
 
 20.57 
 
 9200 
 
 95 
 
 92 
 
 20.9s 
 
 9700 
 
 98 
 
 49 
 
 21.33 
 
 8210 
 
 90.61 
 
 20.17 
 
 8710 
 
 93 
 
 33 
 
 20.57 
 
 9210 
 
 95 
 
 97 
 
 20.96 
 
 9710 
 
 98 
 
 54 
 
 21.33 
 
 8220 
 
 90.66 
 
 20.18 
 
 8720 
 
 93 
 
 38 
 
 20.58 
 
 9220 
 
 96 
 
 02 
 
 20.97 
 
 9720 
 
 98 
 
 59 
 
 21.34 
 
 8230 
 
 90.72 
 
 20.19 
 
 8730 
 
 93 
 
 43 
 
 20.59 
 
 9230 
 
 96 
 
 07 
 
 20.98 
 
 9730 
 
 98 
 
 64 
 
 21.35 
 
 8240 
 
 90.77 
 
 20.20 
 
 8740 
 
 93 
 
 49 
 
 20.60 
 
 9240 
 
 96 
 
 12 
 
 20.98 
 
 9740 
 
 98 
 
 69 
 
 21.36 
 
 8250 
 
 90.83 
 
 20.21 
 
 8750 
 
 93 
 
 54 
 
 20.61 
 
 9250 
 
 96 
 
 18 
 
 20.99 
 
 9750 
 
 98 
 
 74 
 
 21.36 
 
 8260 
 
 90.88 
 
 20.21 
 
 8760 
 
 93 
 
 59 
 
 20.61 
 
 9260 
 
 96 
 
 23 
 
 21 
 
 9760 
 
 98 
 
 79 
 
 21.37 
 
 8270 
 
 90.94 
 
 20.22 
 
 8770 
 
 93 
 
 65 
 
 20.62 
 
 9270 
 
 96 
 
 28 
 
 21.01 
 
 9770 
 
 98 
 
 84 
 
 21.38 
 
 8280 
 
 90.99 
 
 20.23 
 
 8780 
 
 93 
 
 70 
 
 20.63 
 
 9280 
 
 96 
 
 33 
 
 21.01 
 
 9780 
 
 98 
 
 89 
 
 21.39 
 
 8290 
 
 91.05 
 
 20.24 
 
 8790 
 
 93 
 
 75 
 
 20.64 
 
 9290 
 
 96 
 
 38 
 
 21.02 
 
 9790 
 
 98 
 
 94 
 
 21.39 
 
 8300 
 
 91.10 
 
 20.25 
 
 8800 
 
 93 
 
 81 
 
 20.65 
 
 9300 
 
 96 
 
 44 
 
 21.03 
 
 9800 
 
 98 
 
 99 
 
 21.40 
 
 8310 
 
 91.16 
 
 20.26 
 
 8810 
 
 93 
 
 86 
 
 20.65 
 
 9310 
 
 96 
 
 49 
 
 21.04 
 
 9810 
 
 99 
 
 05 
 
 21.41 
 
 8320 
 
 91.21 
 
 20.26 
 
 8S20 
 
 93 
 
 91 
 
 20.66 
 
 9320 
 
 96 
 
 54 
 
 21.04 
 
 9820 
 
 99 
 
 10 
 
 21.41 
 
 8330 
 
 91.27 
 
 20.27 
 
 8830 
 
 93 
 
 97 
 
 20.67 
 
 9330 
 
 96 
 
 59 
 
 21.05 
 
 9830 
 
 99 
 
 15 
 
 21.42 
 
 8340 
 
 91.32 
 
 20.28 
 
 8840 
 
 94 
 
 02 
 
 20.68 
 
 9340 
 
 96 
 
 64 
 
 21.06 
 
 9840 
 
 99 
 
 20 
 
 21.43 
 
 8350 
 
 91.38 
 
 20.29 
 
 8850 
 
 94 
 
 07 
 
 20.68 
 
 9350 
 
 96 
 
 70 
 
 21.07 
 
 9850 
 
 99 
 
 25 
 
 21.44 
 
 8360 
 
 91.43 
 
 20.30 
 
 8860 
 
 94 
 
 13 
 
 20.69 
 
 9360 
 
 96 
 
 75 
 
 21.07 
 
 9860 
 
 99 
 
 30 
 
 21.44 
 
 8370 
 
 91.49 
 
 20.30 
 
 8870 
 
 94 
 
 18 
 
 20.70 
 
 9370 
 
 96 
 
 80 
 
 21.08 
 
 9870 
 
 99 
 
 35 
 
 21.45 
 
 8380 
 
 91.54 
 
 20.31 
 
 8880 
 
 94 
 
 23 
 
 20.71 
 
 9380 
 
 96 
 
 85 
 
 21.09 
 
 9880 
 
 99 
 
 40 
 
 21.46 
 
 8390 
 
 91.60 
 
 20.32 
 
 8890 
 
 94 
 
 29 
 
 20.72 
 
 9390 
 
 96 
 
 90 
 
 21.10 
 
 9890 
 
 99 
 
 45 
 
 21.47 
 
 8400 
 
 91.65 
 
 20.33 
 
 8900 
 
 94 
 
 34 
 
 20.72 
 
 9400 
 
 96 
 
 95 
 
 21.10 
 
 9900 
 
 99 
 
 50 
 
 21.47 
 
 8410 
 
 91.71 
 
 20.34 
 
 8910 
 
 94 
 
 39 
 
 20.73 
 
 9410 
 
 97 
 
 01 
 
 21. II 
 
 9910 
 
 99 
 
 55 
 
 21.48 
 
 8420 
 
 91.76 
 
 20.34 
 
 8920 
 
 94 
 
 45 
 
 20.74 
 
 9420 
 
 97 
 
 06 
 
 21.12 
 
 9920 
 
 99 
 
 60 
 
 21.49 
 
 8430 
 
 91.82 
 
 20.35 
 
 8930 
 
 94 
 
 50 
 
 20.7s 
 
 9430 
 
 97 
 
 II 
 
 21.13 
 
 9930 
 
 99 
 
 65 
 
 21.49 
 
 8440 
 
 91.87 
 
 20.36 
 
 8940 
 
 94 
 
 55 
 
 20.75 
 
 9440 
 
 97 
 
 16 
 
 21.13 
 
 9940 
 
 99 
 
 70 
 
 21.50 
 
 8450 
 
 91.92 
 
 20.37 
 
 8950 
 
 94 
 
 60 
 
 20.76 
 
 9450 
 
 97 
 
 21 
 
 21.14 
 
 9950 
 
 99 
 
 75 
 
 21.51 
 
 8460 
 
 91.98 
 
 20.38 
 
 8960 
 
 94 
 
 66 
 
 20.77 
 
 9460 
 
 97 
 
 26 
 
 21.15 
 
 9960 
 
 99 
 
 80 
 
 21.52 
 
 8470 
 
 92.03 
 
 20.38 
 
 8970 
 
 94 
 
 71 
 
 20.78 
 
 9470 
 
 97 
 
 31 
 
 21.16 
 
 9970 
 
 99 
 
 85 
 
 21.52 
 
 8480 
 
 92.09 
 
 20.39 
 
 8980 
 
 94 
 
 76 
 
 20.79 
 
 9480 
 
 97 
 
 37 
 
 21.16 
 
 9980 
 
 99 
 
 90 
 
 21.53 
 
 8490 
 
 92.14 
 
 20.40 
 
 8990 
 
 94 
 
 82 
 
 20.79 
 
 9490 
 
 97 
 
 42 
 
 21.17 
 
 9990 
 
 99 
 
 95 
 
 21.54 
 
 85cx> 
 
 92.20 
 
 20.41 
 
 9000 
 
 94 
 
 87 
 
 20.80 
 
 9500 
 
 97 
 
 47 
 
 21.18 
 
 lOOOO 
 
 100 
 
 21.54 
 
 8510 
 
 92.25 
 
 20.42 
 
 9010 
 
 94 
 
 92 
 
 20.81 
 
 9510 
 
 97 
 
 .52 
 
 21.19 
 
 
 
 
 8520 
 
 92.30 
 
 20.42 
 
 9020 
 
 94 
 
 97 
 
 20.82 
 
 9520 
 
 97 
 
 .57 
 
 21.19 
 
 
 
 
 8530 
 
 92.36 
 
 20.43 
 
 9030 
 
 95 
 
 03 
 
 20.82 
 
 9S30 
 
 97 
 
 62 
 
 21.20 
 
 
 
 
62 Mathematical Tables 
 
 To find Square or Cube Roots of large numbers not con- 
 tained in the column of numbers of the table 
 
 Such roots may sometimes be taken at once from the table, by merely 
 regarding the columns of powers as being columns of numbers; and those 
 of numbers as being those of roots. Thus, if the square root of 25281 
 is required, first find that number in the column of squares; and opposite 
 to it, in the column of numbers, is its square root 159. For the cube root 
 of 857375, find that number in the column of cubes; and opposite to it, 
 in the colimin of numbers, is its cube root 95. When the exact number 
 is not contained in the column of squares, or cubes, as the case may be, 
 we may use instead the number nearest to it, if no great accuracy is 
 required. But when a considerable degree of accuracy is necessary, the 
 following very correct methods may be used. 
 
 For the square root 
 
 This rule appHes both to whole numbers and to those which are partly 
 (not wholly) decimal. First, in the foregoing manner, take out the 
 tabular number, which is nearest to the given one; and also its tabular 
 square root. Multiply this tabular number by 3; to the product add 
 the given number. Call the sum A . Then multiply the given number 
 by 3; to the product add the tabular number. Call the sum 5. Then 
 A \ B :'. Tabular root : Required root. 
 
 Example. — Let the given number be 946.53. Here we find the nearest 
 tabular number to be 947; and its tabular square root 30.7734. Hence, 
 
 947 = tabular number 
 3 
 
 ■ and ■ 
 59 " 
 
 946.53 = given number 
 3 
 
 2841 
 946.53 = given number 
 
 2839-59 
 947 = tabular number 
 
 3787.53 - A. 
 
 A B 
 
 en 3787.53 : 3786 
 
 ,3786.59 = B. 
 
 Tab. root Req'd root 
 
 30.7734 : 30.7657+. 
 
 The root as found by actual mathematical process is also 30.7657+. 
 
 For the cube root 
 
 This rule applies both to whole mmabers and to those which are parity 
 decimal. First take out the tabular number which is nearest to the given 
 one; and also its tabular cube root. Multiply this tabular nimiber by 
 2; and to the product add the given number. Call the sum A. Then 
 
Cube Root 
 
 63 
 
 multiply the given number by 2; and to the product add the tabular 
 number. Call the sum B. Then 
 
 A : B :: Tabular root : Required root. 
 
 Example. — Let the given number be 7368. Here we find the nearest 
 tabular number (in the column of cubes) to be 6859; and its tabular cube 
 root 19. Hence, 
 
 6859 = tabular number 
 
 13718 
 7368 = given number 
 
 21086 = A. 
 
 and 
 
 7368 = given number 
 
 2 
 
 14736 
 6859 
 
 tabular number 
 B. 
 
 2159s 
 B Tab. root Req'd root 
 
 Then 21086 : 21595 '■ ^9 * i9-4S85. 
 
 The root as found by correct mathematical process is 19.4588 
 
 A 
 
 21086 
 
64 
 
 Mathematical Tables 
 
 Areas and Circumferences of Circles for Diameters m 
 Units and Eighths, etc., from Yg^ to ioo. 
 
 Diatn- 
 
 Circum- 
 
 Area 
 
 Diam- 
 
 Circum- 
 
 Area 
 
 Diam- 
 
 Circum- 
 
 Area 
 
 eter 
 
 ference 
 
 eter 
 
 ference 
 
 eter 
 
 ference 
 
 1/64 
 
 .049087 
 
 .00019 
 
 21/ 
 
 7.06858 
 
 3.9761 
 
 5Me 
 
 17.4751 
 
 24.301 
 
 H2 
 
 .098175 
 
 .00077 
 
 ■Me 
 
 7.26493 
 
 4.2000 
 
 H 
 
 17.6715 
 
 24.850 
 
 3/64 
 
 .147262 
 
 .00173 
 
 % 
 
 7.46128 
 
 4.4301 
 
 IMe 
 
 17.8678 
 
 25.406 
 
 Me 
 
 .196350 
 
 .00307 
 
 Me 
 
 7.65763 
 
 4.6664 
 
 M 
 
 18.0642 
 
 25.967 
 
 H2 
 
 .294524 
 
 .00690 
 
 1/2 
 
 7.85398 
 
 4.9087 
 
 IMe 
 
 18.2605 
 
 26.535 
 
 H 
 
 .392699 
 
 .01227 
 
 Me 
 
 8.05033 
 
 5.1572 
 
 Ms 
 
 18.4569 
 
 27.109 
 
 %2 
 
 .490874 
 
 .01917 
 
 Ms 
 
 8.24668 
 
 5.4119 
 
 IMe 
 
 18.6532 
 
 27.688 
 
 3/6 
 
 .589049 
 
 .02761 
 
 ii/e 
 
 8.44303 
 
 5.6727 
 
 6 
 
 18.8496 
 
 28.274 
 
 1^2 
 
 .687223 
 
 .03758 
 
 M 
 
 8.63938 
 
 5.9396 
 
 \i 
 
 19.2423 
 
 29.465 
 
 H 
 
 .785398 
 
 .04909 
 
 iMe 
 
 8.83573 
 
 6.2126 
 
 M 
 
 19.6350 
 
 30.680 
 
 %2 
 
 .883573 
 
 .06213 
 
 Ms 
 
 9.03208 
 
 6.4918 
 
 H 
 
 20.0277 
 
 31.919 
 
 Mo 
 
 .981748 
 
 .07670 
 
 iMe 
 
 9.22843 
 
 6.7771 
 
 i/i 
 
 20.4204 
 
 33.183 
 
 IH2 
 
 1.07992 
 
 .09281 
 
 3 
 
 9.42478 
 
 7.0686 
 
 n 
 
 20.8131 
 
 34.472 
 
 % 
 
 I . 17810 
 
 . II04S 
 
 Me 
 
 9.62113 
 
 7.3662 
 
 M 
 
 21.2058 
 
 35.785 
 
 ^H2 
 
 1.27627 
 
 . 12962 
 
 i/i 
 
 9.81748 
 
 7.6699 
 
 % 
 
 21.5984 
 
 37.122 
 
 7/6 
 
 1.37445 
 
 . 15033 
 
 Me 
 
 10.0138 
 
 7.9798 
 
 7 
 
 21. 991 I 
 
 38.485 
 
 15^2 
 
 1.47262 
 
 .17257 
 
 1/ 
 
 10.2102 
 
 8.2958 
 
 i/i 
 
 22.3838 
 
 39.871 
 
 1/ 
 
 1.57080 
 
 .19635 
 
 Me 
 
 10.4065 
 
 8.6179 
 
 M 
 
 22.7765 
 
 41.282 
 
 lj^2 
 
 1.66897 
 
 .22166 
 
 % 
 
 10.6029 
 
 8.9462 
 
 % 
 
 23.1692 
 
 42.718 
 
 ri6 
 
 I . 76715 
 
 .24850 
 
 Me 
 
 10.7992 
 
 9.2806 
 
 M 
 
 23.5619 
 
 44.179 
 
 1%2 
 
 1.86532 
 
 .27688 
 
 1/2 
 
 10.9956 
 
 9.6211 
 
 H 
 
 23.9546 
 
 45.664 
 
 5/i 
 
 1.96350 
 
 .30680 
 
 Me 
 
 11.1919 
 
 9.9678 
 
 3/4 
 
 24.3473 
 
 47.173 
 
 2^2 
 
 2.06167 
 
 .33824 
 
 5.^ 
 
 11.3883 
 
 10.321 
 
 Ms 
 
 24.7400 
 
 48.707 
 
 11/6 
 
 2.15984 
 
 .37122 
 
 i/e 
 
 11.S846 
 
 10.680 
 
 8 
 
 25.1327 
 
 50.265 
 
 ^%2 
 
 2.25802 
 
 .40574 
 
 M 
 
 I I. 7810 
 
 11.045 
 
 i/i 
 
 25.5254 
 
 51.849 
 
 % 
 
 2.35619 
 
 .44179 
 
 iMe 
 
 11.9773 
 
 II. 416 
 
 M 
 
 25.9181 
 
 53.456 
 
 2^2 
 
 2.45437 
 
 .47937 
 
 % 
 
 12.1737 
 
 11.793 
 
 H 
 
 26.3108 
 
 55.088 
 
 13/6 
 
 2.55254 
 
 .51849 
 
 IMe 
 
 12.3700 
 
 12.177 
 
 H 
 
 26.703s 
 
 56.745 
 
 27/^2 
 
 2 . 65072 
 
 ■55914 
 
 4 
 
 12.5664 
 
 12.566 
 
 H 
 
 27.0962 
 
 58.426 
 
 % 
 
 2.74889 
 
 .60132 
 
 He 
 
 12.7627 
 
 12.962 
 
 H 
 
 27.4889 
 
 60.132 
 
 2%2 
 
 2.84707 
 
 .64504 
 
 i/i 
 
 12.9591 
 
 13.364 
 
 % 
 
 27.8816 
 
 61.862 
 
 1-/6 
 
 2.94524 
 
 .69029 
 
 Me 
 
 13.1554 
 
 13.772 
 
 9 
 
 28.2743 
 
 63.617 
 
 3^2 
 
 3.04342 
 
 .73708 
 
 1/ 
 
 13.3518 
 
 14.186 
 
 i/i 
 
 28.6670 
 
 65.397 
 
 I 
 
 3.14159 
 
 .78540 
 
 Me 
 
 13.5481 
 
 14.607 
 
 M 
 
 29.0597 
 
 67.201 
 
 1/6 
 
 3.33794 
 
 .88664 
 
 H 
 
 13.7445 
 
 15.033 
 
 H 
 
 29.4524 
 
 69.029 
 
 'A 
 
 3.53429 
 
 .99402 
 
 Me 
 
 13.9408 
 
 15.466 
 
 H 
 
 29.8451 
 
 70.882 
 
 ?i6 
 
 3.73064 
 
 I . 1075 
 
 1/ 
 
 14.1372 
 
 15.904 
 
 H 
 
 30.2378 
 
 72.760 
 
 M 
 
 3.92699 
 
 I . 2272 
 
 Me 
 
 14.3335 
 
 16.349 
 
 % 
 
 30.6305 
 
 74.662 
 
 5/6 
 
 4.12334 
 
 1.3530 
 
 Ms 
 
 14.5299 
 
 16.800 
 
 % 
 
 31.0232 
 
 76.589 
 
 % 
 
 4.31969 
 
 1.4849 
 
 i/e 
 
 14.7262 
 
 17.257 
 
 IC 
 
 31.4159 
 
 78.540 
 
 Vi6 
 
 4.51604 
 
 1.6230 
 
 % 
 
 14.9226 
 
 17.721 
 
 H 
 
 31.8086 
 
 80.516 
 
 ¥i 
 
 4.71239 
 
 I. 7671 
 
 IMe 
 
 15.1189 
 
 18.190 
 
 M 
 
 32.2013 
 
 82.516 
 
 9/6 
 
 4.90874 
 
 I. 9175 
 
 % 
 
 15.3153 
 
 18.665 
 
 % 
 
 32.5940 
 
 84.541 
 
 H 
 
 5.10509 
 
 2.0739 
 
 IMe 
 
 15.5116. 
 
 19.147 
 
 1/ 
 
 32.9867 
 
 86.590 
 
 1/6 
 
 5.30144 
 
 2.2365 
 
 5 
 
 15.7080 
 
 19.635 
 
 5.^ 
 
 33-3794 
 
 88.664 
 
 3/ 
 
 5. 49779 
 
 2.4053 
 
 Me 
 
 15.9043 
 
 20.129 
 
 3/4 
 
 33.7721 
 
 90.763 
 
 13/6 
 
 5.69414 
 
 2.5802 
 
 % 
 
 16.1007 
 
 20.629 . 
 
 i^i 
 
 34.1648 
 
 92.886 
 
 % 
 
 5.89049 
 
 2.7612 
 
 Me 
 
 16.2970 
 
 21.135 
 
 II 
 
 34.5575 
 
 95.033 
 
 15/6 
 
 6.08684 
 
 2.9483 
 
 M 
 
 16.4934 
 
 21.648 
 
 H 
 
 34.9502 
 
 97.205 
 
 2 
 
 6.28319 
 
 3.1416 
 
 Me 
 
 16.6897 
 
 22.166 
 
 H 
 
 35.3429 
 
 99.402 
 
 1/6 
 
 6.47953 
 
 3.3410 
 
 H 
 
 16.8861 
 
 22.691 
 
 % 
 
 35.7356 
 
 101.62 
 
 ^ 
 
 6.67588 
 
 3.5466 
 
 Me 
 
 17.0824 
 
 23.221 
 
 1/2 
 
 36.1283 
 
 103.87 
 
 Me 
 
 6.87223 
 
 3.7583 
 
 M2 
 
 17.2788 
 
 23.758 
 
 5/i 
 
 36.5210 
 
 106.14 
 
Areas and Circumferences of Circles 
 
 65 
 
 Areas and Circumterences of Circles for Diameters in 
 Units and Eighths, etc. — (Continued) 
 
 Diam- 
 
 Circum- 
 
 Area 
 
 Diam- 
 
 Circum- 
 
 Area 
 
 Diam- 
 
 Circum- 
 
 Area 
 
 eter 
 
 ference 
 
 eter 
 
 ference 
 
 eter 
 
 ference 
 
 im 
 
 36.9137 
 
 108.43 
 
 im 
 
 57-7268 
 
 265-18 
 
 25 
 
 78.5398 
 
 490.87 
 
 ■"yi 
 
 37.3064 
 
 110.75 
 
 Vi 
 
 58.1195 
 
 268.80 
 
 % 
 
 78.9325 
 
 495.79 
 
 12 
 
 37.6991 
 
 113. 10 
 
 % 
 
 58.5122 
 
 272.45 
 
 V 
 
 79-3252 
 
 500.74 
 
 H 
 
 38.0918 
 
 IIS. 47 
 
 % 
 
 58.9049 
 
 276.12 
 
 H 
 
 79-7179 
 
 505.71 
 
 Vi 
 
 38.4845 
 
 117.86 
 
 ^A 
 
 59.2976 
 
 279.81 
 
 V2 
 
 80.1106 
 
 S10.71 
 
 H 
 
 38.8772 
 
 120.28 
 
 19 
 
 59.6903 
 
 283.53 
 
 Vs 
 
 80.5033 
 
 515.72 
 
 H 
 
 39.2699 
 
 122.72 
 
 A 
 
 60.0830 
 
 287.27 
 
 ¥i 
 
 80.8960 
 
 520.77 
 
 % 
 
 39.6626 
 
 125.19 
 
 M 
 
 60.4757 
 
 291.04 
 
 Vs 
 
 81.2887 
 
 525.84 
 
 ¥i 
 
 40.0553 
 
 127.68 
 
 rs 
 
 60.8684 
 
 294.83 
 
 26 
 
 81.6814 
 
 530.93 
 
 % 
 
 40.4480 
 
 ,130.19 
 
 V2 
 
 61.2611 
 
 298.65 
 
 M 
 
 82.0741 
 
 536.0s 
 
 13 
 
 40.8407 
 
 132.73 
 
 Y?, 
 
 61.6538 
 
 302.49 
 
 Vi 
 
 82.4668 
 
 541 • 19 
 
 \i 
 
 41.2334 
 
 135.30 
 
 ¥i 
 
 62.0465 
 
 306.3s 
 
 3/8 
 
 82.8595 
 
 546.35 
 
 H 
 
 41.6261 
 
 137.89 
 
 'A 
 
 62.4392 
 
 310.24 
 
 V2 
 
 83.2522 
 
 551-55 
 
 3/8 
 
 42.0188 
 
 140.50 
 
 20 
 
 62.8319 
 
 314.16 
 
 5/8 
 
 83.6449 
 
 556.76 
 
 H 
 
 42.411S 
 
 143.14 
 
 A 
 
 63 . 2246 
 
 318.10 
 
 % 
 
 84.0376 
 
 562.00 
 
 % 
 
 42.8042 
 
 145-80 
 
 Vi 
 
 63-6173 
 
 322.06 
 
 % 
 
 84.4303 
 
 567.27 
 
 % 
 
 43.1969 
 
 148.49 
 
 H 
 
 64.0100 
 
 326.05 
 
 27 
 
 84.8230 
 
 572.56 
 
 % 
 
 43.S896 
 
 151.20 
 
 y2 
 
 64.4026 
 
 330.06 
 
 A 
 
 85-2157 
 
 577.87 
 
 14 
 
 43.9823 
 
 153-94 
 
 5/8 
 
 64.7953 
 
 334.10 
 
 Vi 
 
 85.6084 
 
 583-21 
 
 i/i 
 
 44.3750 
 
 156-70 
 
 % 
 
 65.1880 
 
 338.16 
 
 y& 
 
 86.0011 
 
 588.57 
 
 \i 
 
 44.7677 
 
 159-48 
 
 A 
 
 65.5807 
 
 342.25 
 
 V2 
 
 86.3938 
 
 593.96 
 
 % 
 
 45.1604 
 
 162.30 
 
 21 
 
 65.9734 
 
 346.36 
 
 n 
 
 86.786s 
 
 599.37 
 
 ¥2 
 
 45.5531 
 
 165.13 
 
 Vs' 
 
 66.3661 
 
 350.50 
 
 Vi 
 
 87.1792 
 
 604.81 
 
 5,i 
 
 45.9458 
 
 167.99 
 
 H 
 
 66.7588 
 
 354.66 
 
 A 
 
 87.5719 
 
 610.27 
 
 % 
 
 46.3385 
 
 170.87 
 
 % 
 
 67.1515 
 
 358.84 
 
 28 
 
 87.9646 
 
 615.7s 
 
 % 
 
 46.7312 
 
 173.78 
 
 ¥2 
 
 67.5442 
 
 363.05 
 
 H 
 
 88.3573 
 
 621.26 
 
 IS 
 
 47-1239 
 
 176.71 
 
 5/g 
 
 67.9369 
 
 367-28 
 
 Vi 
 
 88.7500 
 
 626.80 
 
 H 
 
 47.5166 
 
 179.67 
 
 % 
 
 68.3296 
 
 371-54 
 
 % 
 
 89.1427 
 
 632.36 
 
 Vi 
 
 47.9093 
 
 182.65 
 
 Vs 
 
 68.7223 
 
 375-83 
 
 V2 
 
 89.5354 
 
 637 -94 
 
 % 
 
 48.3020 
 
 185.66 
 
 22 
 
 69.1150 
 
 380.13 
 
 ^A 
 
 89.9281 
 
 643-55 
 
 Vi 
 
 48.6947 
 
 188.69 
 
 Vs 
 
 69.5077 
 
 384.46 
 
 Vi 
 
 90.3208 
 
 649-18 
 
 H 
 
 49.0874 
 
 191-75 
 
 H 
 
 69.9004 
 
 388.82 
 
 % 
 
 90.7135 
 
 654.84 
 
 % 
 
 49-4801 
 
 194-83 
 
 % 
 
 70.2931 
 
 393-20 
 
 29 
 
 91 . 1062 
 
 660.52 
 
 'A 
 
 49.8728 
 
 197-93 
 
 V2 
 
 70.6858 
 
 397-61 
 
 A 
 
 91.4989 
 
 666.23 
 
 16 
 
 50.2655 
 
 201.06 
 
 % 
 
 71.0785 
 
 402.04 
 
 Vi 
 
 91.8916 
 
 671-96 
 
 H 
 
 SO. 6582 
 
 204.22 
 
 % 
 
 71.4712 
 
 406.49 
 
 % 
 
 92.2843 
 
 677.71 
 
 Vi 
 
 51-0509 
 
 207.39 
 
 A 
 
 71.8639 
 
 410.97 
 
 V2 
 
 92.6770 
 
 683.49 
 
 % 
 
 SI -4436 
 
 210.60 
 
 23 
 
 72.2566 
 
 415.48 
 
 % 
 
 93.0697 
 
 689.30 
 
 Vi 
 
 SI -8363 
 
 213.82 
 
 M 
 
 72.6493 
 
 420.00 
 
 % 
 
 93.4624 
 
 695.13 
 
 % 
 
 52.2290 
 
 217.08 
 
 H 
 
 73.0420 
 
 424.56 
 
 li 
 
 93.8551 
 
 700.98 
 
 % 
 
 52.6217 
 
 220.35 
 
 y& 
 
 73.4347 
 
 429.13 
 
 30 
 
 94-2478 
 
 706.86 
 
 % 
 
 53.0144 
 
 223.65 
 
 V2 
 
 73-8274 
 
 433-74 
 
 A 
 
 94-6405 
 
 712.76 
 
 17 
 
 53.4071 
 
 226.98 
 
 ^ 
 
 74 -2201 
 
 438-36 
 
 Vi 
 
 95.0332 
 
 718.69 
 
 \i 
 
 53.7998 
 
 230.33 
 
 % 
 
 74-6128 
 
 443-01 
 
 H 
 
 95.4259 
 
 724.64 
 
 H 
 
 54.1925 
 
 233.71 
 
 li 
 
 75.0055 
 
 447-69 
 
 V2 
 
 95.8186 
 
 730.62 
 
 H 
 
 54.5852 
 
 237.10 
 
 24 
 
 75-3982 
 
 452-39 
 
 5/8 
 
 96.2113 
 
 736.62 
 
 Vi 
 
 54.9779 
 
 240.53 
 
 H 
 
 75-7909 
 
 457-11 
 
 ¥i 
 
 96.6040 
 
 742.64 
 
 % 
 
 55-3706 
 
 243.98 
 
 Vi 
 
 76.1836 
 
 461.86 
 
 li 
 
 96.9967 
 
 748.69 
 
 % 
 
 55.7633 
 
 247.45 
 
 n 
 
 76.5763 
 
 466.64 
 
 31 
 
 97.3894 
 
 754-77 
 
 % 
 
 56 . 1560 
 
 250.95 
 
 V2 
 
 76.9690 
 
 471.44 
 
 A 
 
 97.7821 
 
 760.87 
 
 18 
 
 56.5487 
 
 254-47 
 
 Vs 
 
 77.3617 
 
 476.26 
 
 Vi 
 
 98.1748 
 
 766.99 
 
 H 
 
 56.9414 
 
 258.02 
 
 % 
 
 77-7544 
 
 481. II 
 
 % 
 
 98.5675 
 
 773-14 
 
 H 
 
 57.3341 
 
 261.59 
 
 % 
 
 78.1471 
 
 485.98 
 
 V2 
 
 98.9602 
 
 779-31 
 
66 
 
 Mathematical Tables 
 
 Areas and Circumferences of Circles for Diameters in 
 Units and Eighths, etc. — {Continued) 
 
 Diam- 
 
 Circum- 
 
 Area 
 
 Diam- 
 
 Circum- 
 
 Area 
 
 Diam- 
 
 Circum- 
 
 Area 
 
 eter 
 
 ference 
 
 eter 
 
 ference 
 
 eter 
 
 ference 
 
 3l5^ 
 
 99-3529 
 
 785-51 
 
 H 
 
 120,166 
 
 1149.1 
 
 AA% 
 
 140.979 
 
 1581.6 
 
 % 
 
 99-7456 
 
 791.73 
 
 H 
 
 120.559 
 
 1156.6 
 
 45 
 
 141.372 
 
 1590.4 
 
 % 
 
 100.138 
 
 797.98 
 
 V2 
 
 120.951 
 
 1164.2 
 
 A 
 
 141 . 764 
 
 1599.3 
 
 32 
 
 100.531 
 
 804.25 
 
 H 
 
 121.344 
 
 1171.7 
 
 Vi 
 
 142.157 
 
 1608.2 
 
 H 
 
 100.924 
 
 810,54 
 
 ¥i 
 
 121.737 
 
 1179.3 
 
 % 
 
 142.550 
 
 1617.0 
 
 W • 
 
 loi . 316 
 
 816.86 
 
 li 
 
 122.129 
 
 1186.9 
 
 \^ 
 
 142 . 942 
 
 1626.0 
 
 % 
 
 loi . 709 
 
 823 . 21 
 
 39 
 
 122.522 
 
 1194.6 
 
 % 
 
 143.335 
 
 1634.9 
 
 y2 
 
 102.102 
 
 829.58 
 
 1/8 
 
 122.915 
 
 1202.3 
 
 % 
 
 143.728 
 
 1643.9 
 
 % 
 
 102.494 
 
 835.97 
 
 Vi 
 
 123.308 
 
 1210.0 
 
 A 
 
 144. 121 
 
 1652.9 
 
 % 
 
 102.887 
 
 842.39 
 
 % 
 
 123,700 
 
 1217.7 
 
 46 
 
 144.513 
 
 1661.9 
 
 % 
 
 103.280 
 
 848.83 
 
 . ¥2 
 
 124.093 
 
 1225.4 
 
 A 
 
 144.906 
 
 1670.9 
 
 33 
 
 103.673 
 
 855.30 
 
 % 
 
 124.486 
 
 1233.2 
 
 M 
 
 145.299 
 
 1680.0 
 
 % 
 
 104.065 
 
 861.79 
 
 % 
 
 124.878 
 
 1241.0 
 
 % 
 
 145.691 
 
 1689. I 
 
 H 
 
 104.458 
 
 868.31 
 
 Vs 
 
 125.271 
 
 1248.8 
 
 A 
 
 146.084 
 
 1698.2 
 
 % 
 
 104.851 
 
 874.85 
 
 40 
 
 125.664 
 
 1256.6 
 
 A 
 
 146.477 
 
 1707.4 
 
 H 
 
 105.243 
 
 881.41 
 
 Vs 
 
 126.056 
 
 1264.5 
 
 % 
 
 146.869 
 
 1716.5 
 
 ^A 
 
 105.636 
 
 888.00 
 
 14 
 
 126.449 
 
 1272.4 
 
 A 
 
 147.262 
 
 1725.7 
 
 % 
 
 106.029 
 
 894.62 
 
 H 
 
 126,842 
 
 1280.3 
 
 47 
 
 147.655 
 
 1734.9 
 
 % 
 
 106.421 
 
 901.26 
 
 Vi 
 
 127.235 
 
 1288. 2 
 
 A 
 
 148.048 
 
 1744.2 
 
 34 
 
 106.814 
 
 907.92 
 
 % 
 
 127.627 
 
 1296.2 
 
 A 
 
 148 . 4JO 
 
 1753. 5 
 
 H 
 
 107.207 
 
 914.61 
 
 %. 
 
 128.020 
 
 1304.2 
 
 H 
 
 148.833 
 
 1762.7 
 
 H 
 
 107.600 
 
 921.32 
 
 % 
 
 128.413 
 
 1312.2 
 
 A 
 
 149.226 
 
 1772. I 
 
 % 
 
 107.992 
 
 928.06 
 
 41 
 
 128.805 
 
 1320.3 
 
 A 
 
 149.618 
 
 1781.4 
 
 H 
 
 108.385 
 
 934.82 
 
 M 
 
 129.198 
 
 1328.3 
 
 % 
 
 150. 01 I 
 
 1790.8 
 
 % 
 
 108.778 
 
 941.61 
 
 H 
 
 129.591 
 
 1336.4 
 
 A 
 
 150.404 
 
 1800. I 
 
 % 
 
 109.170 
 
 948.42 
 
 % 
 
 129.983 
 
 1344.5 
 
 48 
 
 150.796 
 
 1809.6 
 
 % 
 
 109.563 
 
 955.25 
 
 Vi 
 
 130.376 
 
 1352.7 
 
 Vs 
 
 151 . 189 
 
 1819.0 
 
 35 
 
 109.956 
 
 962.11 
 
 5/8 
 
 130.769 
 
 1360.8 
 
 A 
 
 151 582 
 
 1828.5 
 
 H 
 
 110.348 
 
 969.00 
 
 M 
 
 131. 161 
 
 1369 
 
 A 
 
 151.975 
 
 1837.9 
 
 H 
 
 no. 741 
 
 975.91 
 
 ''A 
 
 131.554 
 
 1377-2 
 
 V2 
 
 152.367 
 
 1847.5 
 
 % 
 
 III. 134 
 
 982.84 
 
 42 
 
 131.947 
 
 1385.4 
 
 A 
 
 152.760 
 
 1857.0 
 
 ^ 
 
 III. 527 
 
 989.80 
 
 A 
 
 132.340 
 
 1393.7 
 
 % 
 
 153.153 
 
 1866.5 
 
 5i 
 
 III. 919 
 
 996.78 
 
 H 
 
 132.732 
 
 1402.0 
 
 A 
 
 153.545 
 
 1876. I 
 
 % 
 
 112. 312 
 
 1003.8 
 
 Vs 
 
 133.125 
 
 1410.3 
 
 49 
 
 153.938 
 
 1885.7 
 
 ^ 
 
 112.705 
 
 1010.8 
 
 H 
 
 133-518 
 
 1418.6 
 
 A 
 
 154.331 
 
 1895.4 
 
 36 
 
 113-097 
 
 1017.9 
 
 H 
 
 133-910 
 
 1427.0 
 
 Vi 
 
 154.723 
 
 1905.0 
 
 H 
 
 113.490 
 
 1025 . 
 
 % 
 
 134-303 
 
 1435.4 
 
 A 
 
 155. 116 
 
 1914.7 
 
 M 
 
 113.883 
 
 1032 . I 
 
 li 
 
 134.696 
 
 1443.8 
 
 A 
 
 155.509 
 
 1924.4 
 
 % 
 
 114.275 
 
 1039.2 
 
 43 
 
 135.088 
 
 1452.2 
 
 A 
 
 155.902 
 
 1934.2 
 
 J^ 
 
 114.668 
 
 1046.3 
 
 % 
 
 135.481 
 
 1460.7 
 
 % 
 
 156.294 
 
 1943.9 
 
 ^ 
 
 I 15. 061 
 
 1053.5 
 
 Yi 
 
 135.874 
 
 1469. I 
 
 A 
 
 156.687 
 
 1953.7 
 
 14 
 
 115-454 
 
 1060.7 
 
 % 
 
 136.267 
 
 1477.6 
 
 50 
 
 157.080 
 
 1963. 5 
 
 % 
 
 115.846 
 
 1068.0 
 
 V2 
 
 136.659 
 
 1486.2 
 
 A 
 
 157.472 
 
 1973.3 
 
 37 
 
 116.239 
 
 1075.2 
 
 Vs 
 
 137.052 
 
 1494.7 
 
 A 
 
 157.865 
 
 1983.2 
 
 ^ 
 
 116.632 
 
 1082.5 
 
 V 
 
 137.445 
 
 1503.3 
 
 A 
 
 158.258 
 
 1993. I 
 
 M 
 
 117.024 
 
 1089,8 
 
 Vs 
 
 137.837 
 
 1511.9 
 
 I/, 
 
 158.650 
 
 2003.0 
 
 ^ 
 
 II7-417 
 
 1097. I 
 
 44 
 
 138 . 230 
 
 1520.5 
 
 A 
 
 159.043 
 
 2012.9 
 
 J^ 
 
 117. 810 
 
 1104.5 
 
 i/i 
 
 138.623 
 
 1529.2 
 
 % 
 
 159.436 
 
 2022.8 
 
 ^ 
 
 118.202 
 
 nil. 8 
 
 H 
 
 139 015 
 
 1537.9 
 
 A 
 
 159.829 
 
 2032.8 
 
 % 
 
 118.596 
 
 1119.2 
 
 H 
 
 139.408 
 
 1546.6 
 
 51 
 
 160.221 
 
 2042.8 
 
 % 
 
 118.988 
 
 1126.7 
 
 H 
 
 139.801 
 
 1555.3 
 
 A 
 
 160.614 
 
 2052.8 
 
 38 
 
 119 -381 
 
 1134.1 
 
 ^A 
 
 140.194- 
 
 1564.0 
 
 H 
 
 161.007 
 
 2062.9 
 
 H 
 
 119.773 
 
 1141.6 
 
 % 
 
 140.586 
 
 1572.8 
 
 A 
 
 161.399 
 
 2073.0 
 
Areas and Circumferences of Circles 
 
 67 
 
 Areas and Circumferences of Circles for Diameters in 
 Units and Eighths, etc. — {Continued) 
 
 Diam- 
 
 Circum- 
 
 Area 
 
 Diam- 
 
 Circum- 
 
 Area 
 
 Diam- 
 
 Circum- 
 
 
 eter 
 
 ference 
 
 eter 
 
 ference 
 
 eter 
 
 ference 
 
 Area 
 
 51H 
 
 161.792 
 
 2083.1 
 
 5814 
 
 182.605 
 
 2653.5 
 
 64^/4 
 
 203 , 418 
 
 3292.8 
 
 % 
 
 162.185 
 
 2093.2 
 
 H 
 
 182.998 
 
 2664.9 
 
 l^ 
 
 203 811 
 
 3305-6 
 
 % 
 
 162.577 
 
 2103.3 
 
 % 
 
 183.390 
 
 2676.4 
 
 65 
 
 204.204 
 
 3318.3 
 
 % 
 
 162.970 
 
 2II3-5 
 
 H 
 
 183.783 
 
 2687.8 
 
 \^ 
 
 204-596 
 
 3331 -I 
 
 52 
 
 163.363 
 
 2123.7 
 
 H 
 
 184.176 
 
 2699.3 
 
 Yi 
 
 204.989 
 
 3343.9 
 
 % 
 
 163.756 
 
 2133-9 
 
 % 
 
 184.569 
 
 2710.9 
 
 % 
 
 205.382 
 
 3356.7 
 
 H 
 
 164.148 
 
 2144.2 
 
 % 
 
 184.961 
 
 2722.4 
 
 \^ 
 
 205.774 
 
 3369.6 
 
 % 
 
 164.541 
 
 2154.5 
 
 59 
 
 185-354 
 
 2734.0 
 
 % 
 
 206.167 
 
 3382.4 
 
 H 
 
 164.934 
 
 2164.8 
 
 i/i 
 
 185.747 
 
 2745.6 
 
 ¥i 
 
 206.560 
 
 3395.3 
 
 H 
 
 165.326 
 
 2175. I 
 
 H 
 
 186.139 
 
 2757.2 
 
 % 
 
 206.952 
 
 3408.2 
 
 % 
 
 165-719 
 
 2185.4 
 
 % 
 
 186.532 
 
 2768.8 
 
 66 
 
 207.345 
 
 3421.2 
 
 li 
 
 166. 112 
 
 2195-8 
 
 Vi 
 
 186.925 
 
 2780.5 
 
 \i 
 
 207.738 
 
 3434.2 
 
 53 
 
 166.504 
 
 2206.2 
 
 % 
 
 187-317 
 
 2792.2 
 
 Yi 
 
 208.131 
 
 3447.2 
 
 H 
 
 166.897 
 
 2216.6 
 
 % 
 
 187-710 
 
 2803.9 
 
 % 
 
 208.523 
 
 3460.2 
 
 H 
 
 167.290 
 
 2227.0 
 
 % 
 
 188.103 
 
 2815.7 
 
 Yz 
 
 208.916 
 
 3473.2 
 
 % 
 
 167.683 
 
 2237.5 
 
 60 
 
 188.496 
 
 2827-4 
 
 % 
 
 209.309 
 
 3486.3 
 
 \^ 
 
 168.075 
 
 2248.0 
 
 H 
 
 188.888 
 
 . 2839.2 
 
 % 
 
 209.701 
 
 3499.4 
 
 % 
 
 168.468 
 
 2258.5 
 
 Yi 
 
 189.281 
 
 2851.0 
 
 'A 
 
 210.094 
 
 3512.5 
 
 % 
 
 168.861 
 
 2269.1 
 
 H 
 
 189.674 
 
 . 2862.9 
 
 67 
 
 210.487 
 
 3525.7 
 
 % 
 
 169.253 
 
 2279.6 
 
 1/2 
 
 190.066 
 
 2874. 8 
 
 H 
 
 210.879 
 
 3538.8 
 
 54 
 
 169.646 
 
 2290.2 
 
 5/8 
 
 190.459 
 
 2886.6 
 
 Yi 
 
 211.272 
 
 3552.0 
 
 li 
 
 170.039 
 
 2300.8 
 
 % ■ 
 
 190.852 
 
 2898.6 
 
 H 
 
 211.665 
 
 3565.2 
 
 3/4 
 
 170.431 
 
 2311.5 
 
 li 
 
 191.244 
 
 2910.5 
 
 1/2 
 
 212.058 
 
 3578.5 
 
 % 
 
 170.824 
 
 2322.1 
 
 61 
 
 191.637 
 
 2922.5 
 
 H 
 
 212.450 
 
 3591.7 
 
 H 
 
 171. 217 
 
 2332.8 
 
 Yi 
 
 192.030 
 
 2934.5 
 
 % 
 
 212.843 
 
 3605.0 
 
 n 
 
 171.609 
 
 2343-5 
 
 Yi 
 
 192.423 
 
 2946.5 
 
 'A 
 
 213.236 
 
 3618.3 
 
 % 
 
 172.002 
 
 2354-3 
 
 % 
 
 192.815 
 
 2958.5 
 
 68 
 
 213.628 
 
 3631.7 
 
 li 
 
 172.39s 
 
 2365.0 
 
 ' Y2 
 
 193-208 
 
 2970.6 
 
 % 
 
 214.021 
 
 3645.0 
 
 55 
 
 172.788 
 
 2375-8 
 
 H 
 
 193.601 
 
 2982.7 
 
 Yi 
 
 214.414 
 
 3658.4 
 
 H 
 
 173.180 
 
 2386.6 
 
 % 
 
 193.993 
 
 2994.8 
 
 % 
 
 214.806 
 
 3671.8 
 
 H 
 
 173.573 
 
 2397.5 
 
 % 
 
 194.386 
 
 3006.9 
 
 Y2 
 
 215.199 
 
 3685.3 
 
 % 
 
 173.966- 
 
 2408.3 
 
 62 
 
 194.779 
 
 3019. I 
 
 % 
 
 215.592 
 
 3698.7 
 
 Vi 
 
 174.358 
 
 2419.2 
 
 M 
 
 195. 171 
 
 3031.3 
 
 Yi 
 
 215.984 
 
 3712.2 
 
 H 
 
 174.751 
 
 2430.1 
 
 Yi 
 
 195.564 
 
 3043.5 
 
 'A 
 
 216.377 
 
 3725.7 
 
 % 
 
 175.144 
 
 2441 . I 
 
 Yb 
 
 195.957 
 
 3055.7 
 
 ■69 
 
 216.770 
 
 3739.3 
 
 % ■ 
 
 175.536 
 
 2452 
 
 Yi 
 
 196.350 
 
 3068.0 
 
 A 
 
 217.163 
 
 3752.8 
 
 56 
 
 175.929 
 
 2463.0 
 
 5/8 
 
 196.742 
 
 3080.3 
 
 Yi 
 
 217.555 
 
 3766.4 
 
 M 
 
 176.322 
 
 2474.0 
 
 /•4 
 
 197.135 
 
 3092.6 
 
 H 
 
 217.948 
 
 3780.0 
 
 H 
 
 176.715 
 
 2485.0 
 
 l^ 
 
 197.528 
 
 3104.9 
 
 A 
 
 218.341 
 
 3793.7 
 
 H 
 
 177.107 
 
 2496.1 
 
 63 
 
 197.920 
 
 3117.2 
 
 % 
 
 218.733 
 
 3807.3 
 
 H 
 
 177.500 
 
 2507.2 
 
 \i 
 
 198.313 
 
 3129.6 
 
 % 
 
 219.126 
 
 3821.0 
 
 % 
 
 177.893 
 
 2518.3 
 
 Yi 
 
 198.706 
 
 3142.0 
 
 A 
 
 219.519 
 
 3834.7 
 
 % 
 
 178.285 
 
 2529.4 
 
 % 
 
 199.098 
 
 3154.5 
 
 70 
 
 219. 911 
 
 3848.5 
 
 % 
 
 178.678 
 
 2540.6 
 
 Y. 
 
 199.491 
 
 3166.9 
 
 A 
 
 220.304 
 
 3862.2 
 
 57 
 
 179 071 
 
 2551.8 
 
 rs 
 
 199.884 
 
 3179.4 
 
 Yi 
 
 220.697 
 
 3876.0 
 
 H 
 
 179.463 
 
 2563.0 
 
 % 
 
 200.277 
 
 3191.9 
 
 A 
 
 221.090 
 
 3889.8 
 
 Yi 
 
 179.856 
 
 2574.2 
 
 % 
 
 200.669 
 
 3204.4 
 
 Y2 
 
 221.482 
 
 3903.6 
 
 H 
 
 180.249 
 
 2585.4 
 
 64 
 
 201.062 
 
 3217.0 
 
 5/8 
 
 221.875 
 
 3917. 5 
 
 H 
 
 180.642 
 
 2596.7 
 
 M 
 
 201.455 
 
 3229.6 
 
 Yi 
 
 222 . 268 
 
 3931.4 
 
 H 
 
 181.034 
 
 2608.0 
 
 Yi 
 
 -201.847 
 
 3242.2 
 
 A 
 
 222.660 
 
 3945.3- 
 
 H 
 
 181.427 
 
 2619.4 
 
 % 
 
 202.240 
 
 3254.8 
 
 71 
 
 223.053 
 
 3959-2 
 
 % 
 
 181.820 
 
 2630.7 
 
 H 
 
 202.633 
 
 3267.5 
 
 A 
 
 223.446 
 
 3973.1 
 
 58 
 
 182.212 
 
 2642.1 
 
 % 
 
 203.02s 
 
 3280.1 
 
 Yi 
 
 223.838 
 
 3987.1 
 
68 
 
 Mathematical Tables 
 
 Areas and Circumferences of Circles for Diameters in 
 Units and Eighths, etc. — (Continued) 
 
 Diam- 
 
 Circum- 
 
 
 Diam- 
 
 Circum- 
 
 
 Diam- 
 
 Circum- 
 
 
 eter 
 
 ference 
 
 Area 
 
 eter 
 
 ference 
 
 Area 
 
 eter 
 
 ference 
 
 Area 
 
 im 
 
 224.231 
 
 4001. I 
 
 78 
 
 245.044 
 
 4778.4 
 
 84H 
 
 265.857 
 
 5624.5 
 
 H 
 
 224.624 
 
 , 401S.2 
 
 H 
 
 245.437 
 
 4793.7 
 
 3/4 
 
 266.250 
 
 5641.2 
 
 H 
 
 225.017 
 
 4029.2 
 
 H 
 
 245 830 
 
 4809.0 
 
 li 
 
 266.643 
 
 5657.8 
 
 % 
 
 225.409 
 
 4043.3 
 
 3/8 
 
 246.222 
 
 4824.4 
 
 85 
 
 267.035 
 
 5674.5 
 
 ^ 
 
 225 . 802 
 
 4057.4 
 
 1/2 
 
 246.615 
 
 4839 .8 
 
 H 
 
 267.428 
 
 5691.2 
 
 72 
 
 226.195 
 
 4071.5 
 
 H 
 
 247.008 
 
 4855.2 
 
 /4 
 
 267.821 
 
 5707.9 
 
 H 
 
 226.587 
 
 4085.7 
 
 3/4 
 
 247.400 
 
 4870.7 
 
 % 
 
 268.213 
 
 5724.7 
 
 M 
 
 226.980 
 
 4099.8 
 
 li 
 
 247.793 
 
 4886.2 
 
 1/-2 
 
 268.606 
 
 5741 -5 
 
 H 
 
 227.373 
 
 41140 
 
 79 
 
 248.186 
 
 4901.7 
 
 ^A 
 
 268.999 
 
 5758-3 
 
 Vi 
 
 227.765 
 
 4128.2 
 
 H 
 
 248.579 
 
 4917-2 
 
 % 
 
 269.392 
 
 5775 -I 
 
 ^A 
 
 228.158 
 
 4142.5 
 
 Vi 
 
 248.971 
 
 4932 .-7 
 
 % 
 
 269.784 
 
 5791-9 
 
 % 
 
 228.551 
 
 4156.8 ■ 
 
 3/8 
 
 249 364 
 
 4948.3 
 
 86 
 
 270.177 
 
 5808.8 
 
 % 
 
 228.944 
 
 4171.1 
 
 /2 
 
 249-757 
 
 4963.9 
 
 M 
 
 270.570 
 
 5825.7 
 
 73 
 
 229.336 
 
 4185.4 
 
 % 
 
 250.149 
 
 4979-5 
 
 H 
 
 270.962 
 
 5842.6 
 
 ^ 
 
 229.729 
 
 4199.7 
 
 3/4 
 
 250.542 
 
 4995-2 
 
 % 
 
 271.355 
 
 5859-6 
 
 H 
 
 230.122 
 
 4214. I 
 
 li 
 
 250.935 
 
 5010.9 
 
 Vi 
 
 271 . 748 
 
 5876-5 
 
 % 
 
 230.514 
 
 4228.5 
 
 80 
 
 251.327 
 
 5026.5 
 
 rs 
 
 272.140 
 
 5893-5 
 
 Vz 
 
 230.907 
 
 4242.9 
 
 % 
 
 251.720 
 
 5042.3 
 
 3/4 
 
 272.533 
 
 5910 -6 
 
 % 
 
 231.300 
 
 4257.4 
 
 M 
 
 252.113 
 
 5058.0 
 
 Ji 
 
 272.926 
 
 5927-6 
 
 % 
 
 231.692 
 
 4271.8 
 
 % 
 
 252.506 
 
 5073.8 
 
 87 
 
 273.319 
 
 5944-7 
 
 % 
 
 232.085 
 
 4286.3 
 
 /2 
 
 252.898 
 
 5089.6 
 
 \^ 
 
 273.711 
 
 5961.8 
 
 74 
 
 232.478 
 
 4300.8 
 
 54 
 
 253.291 
 
 5105.4 
 
 Vi 
 
 274.104 
 
 5978.9 
 
 \^ 
 
 232.871 
 
 4315.4 
 
 % 
 
 253.684 
 
 5121.2 
 
 % 
 
 274.497 
 
 5996.0 
 
 % 
 
 233.263 
 
 4329.9 
 
 . H 
 
 254.076 
 
 5137.1 
 
 \^ 
 
 274.889 
 
 6013 . 2 
 
 % 
 
 233.656 
 
 4344.5 
 
 81 
 
 254.469 
 
 5153-0 
 
 H 
 
 275.282 
 
 6030.4 
 
 V2 
 
 234.049 
 
 4359.2 
 
 H 
 
 254.862 
 
 5168.9 
 
 % 
 
 275-675 
 
 6047.6 
 
 % 
 
 234.441 
 
 4373.8 
 
 H 
 
 255 . 254 
 
 5184.9 
 
 % 
 
 276.067 
 
 6064.9 
 
 % 
 
 234.834 
 
 4388.5 
 
 % 
 
 255.647 
 
 5200.8 
 
 88 
 
 276.460 
 
 6082.1 
 
 ■"A 
 
 235.227 
 
 4403.1 
 
 1/2 
 
 256.040 
 
 5216.8 
 
 A 
 
 276.853 
 
 6099.4 
 
 75 
 
 235.619 
 
 4417.9 
 
 % 
 
 256.433 
 
 5232.8 
 
 H 
 
 277.246 
 
 6116.7 
 
 H 
 
 236.012 
 
 4432.6 
 
 % 
 
 256.825 
 
 5248.9 
 
 % 
 
 277.638 
 
 6134- I 
 
 H 
 
 236.405 
 
 4447.4 
 
 li 
 
 257.218 
 
 5264.9 
 
 H 
 
 278.031 
 
 6151.4 
 
 3/8 
 
 236.798 
 
 4462.2 
 
 82 
 
 257.611 
 
 5281.0 
 
 H 
 
 278.424 
 
 6168.8 
 
 1/2 
 
 237.190 
 
 4477.0 
 
 M 
 
 258.003 
 
 5297-1 
 
 34 
 
 278.816 
 
 6186.2 
 
 % 
 
 237.583 
 
 4491-8 
 
 M 
 
 258.396 
 
 5313-3 
 
 'A 
 
 279.209 
 
 6203.7 
 
 % 
 
 237.976 
 
 4506.7 
 
 3/8 
 
 258.789 
 
 5329-4 
 
 89 
 
 279 . 602 
 
 6221. I 
 
 H 
 
 238.368 
 
 4521.5 
 
 Vz 
 
 259.181 
 
 5345-6 
 
 A 
 
 279.994 
 
 6238.6 
 
 76 
 
 238.761 
 
 4536.5 
 
 5/i 
 
 259.574 
 
 5361.8 
 
 H 
 
 280.387 
 
 6256.1 
 
 % 
 
 239-154 
 
 4551.4 
 
 M 
 
 259.967 
 
 5378.1 
 
 % 
 
 280.780 
 
 6273 .7 
 
 H 
 
 239.546 
 
 4566.4 
 
 % 
 
 260.359 
 
 5394.3 
 
 H 
 
 281.173 
 
 6291.2 
 
 3/^ 
 
 239.939 
 
 4581.3 
 
 83 
 
 260.752 
 
 5410.6 
 
 % 
 
 281.565 
 
 6308.8 
 
 H 
 
 240.332 
 
 4596.3 
 
 M 
 
 261 . 145 
 
 5426.9 
 
 3/4 
 
 281.958 
 
 6326.4 
 
 5/8 
 
 240.725 
 
 4611.4 
 
 Vi 
 
 261.538 
 
 5443.3 
 
 li 
 
 282.351 
 
 6344.1 
 
 M 
 
 241. 117 
 
 4626.4 
 
 % 
 
 261.930 
 
 5459-6 
 
 90 
 
 282.743 
 
 6361.7 
 
 % 
 
 241.510 
 
 4641.5 
 
 1/^ 
 
 262.323 
 
 5476.0 
 
 A 
 
 283.136 
 
 6379-4 
 
 77 
 
 241.903 
 
 4656.6 
 
 5/8 
 
 262.716 
 
 5492.4 
 
 M 
 
 283.529 
 
 6397.1 
 
 H 
 
 242.295 
 
 4671.8 
 
 3/4 
 
 263.108 
 
 5508.8 
 
 3/i 
 
 283.921 
 
 6414-9 
 
 H 
 
 242.688 
 
 4686.9 
 
 % 
 
 263 . 501 
 
 5525.3 
 
 A 
 
 284.314 
 
 6432.6 
 
 3^ 
 
 243.081 
 
 4702.1 
 
 84 
 
 263.894 
 
 5541.8 
 
 A 
 
 284.707 
 
 6450.4 
 
 1/^ 
 
 243-473 
 
 4717-3 
 
 \i 
 
 264.286 
 
 5558.3 
 
 3/4 
 
 285.100 
 
 6468.2 
 
 5^ 
 
 243.866 
 
 4732.5 
 
 Vi 
 
 264.679 
 
 5574.8 
 
 ''A 
 
 285.492 
 
 6486.0 
 
 % 
 
 244.259 
 
 4747.8 
 
 3,^ 
 
 265.072 
 
 5591-4 
 
 91 
 
 285.88s 
 
 6503.9 
 
 % 
 
 244.652 
 
 4763.1 
 
 /2 
 
 265.465 
 
 5607.9 
 
 A 
 
 286.278 
 
 6521.8 
 
Areas and Circumferences of Circles 
 
 69 
 
 Areas and Circumferences of Circles for Diameters in 
 Units and Eighths, etc. — {Concluded) 
 
 Diam 
 
 Circum- 
 
 
 Diam 
 
 Circum- 
 
 Area 
 
 Diam- 
 
 Circum- 
 
 
 eter 
 
 ference 
 
 Area 
 
 eter 
 
 ference 
 
 eter 
 
 ference 
 
 Area 
 
 91 H 
 
 286.670 
 
 6539.7 
 
 94H 
 
 296.095 
 
 6976.7 
 
 97K 
 
 305.520 
 
 7428.0 
 
 % 
 
 287.063 
 
 6557.6 
 
 H 
 
 296.488 
 
 6995.3 
 
 % 
 
 305.913 
 
 7447-1 
 
 Vi 
 
 287.456 
 
 6575.5 
 
 V2 
 
 296.881 
 
 7013.8 
 
 Vi 
 
 306.305 
 
 7466.2 
 
 % 
 
 287.848 
 
 6593.5 
 
 H 
 
 297.273 
 
 7032.4 
 
 A 
 
 306.698 
 
 748s. 3 
 
 H 
 
 288 . 241 
 
 6611.5 
 
 % 
 
 297.666 
 
 7051.0 
 
 % 
 
 307.091 
 
 7504.5 
 
 "A 
 
 288.634 
 
 6629.6 
 
 ""A 
 
 298.059 
 
 7069.6 
 
 li 
 
 307.483 
 
 7523.7 
 
 92 
 
 289 . 027 
 
 6647.6 
 
 95 
 
 298.451 
 
 7088.2 
 
 98 
 
 307.876 
 
 7543.0 
 
 H 
 
 289.419 
 
 6665.7 
 
 A 
 
 298.844 
 
 7106.9 
 
 A 
 
 308.269 
 
 7562.2 
 
 H 
 
 289.812 
 
 6683.8 
 
 H 
 
 299.237 
 
 7125.6 
 
 H 
 
 308.661 
 
 7581.5 
 
 H 
 
 290.205 
 
 6701.9 
 
 % 
 
 .299.629 
 
 7144.3 
 
 % 
 
 309.054 
 
 7600.8 
 
 H 
 
 290.597 
 
 6720.1 
 
 V2 
 
 300.022 
 
 7163.0 
 
 1/2 
 
 309.447 
 
 7620.1 
 
 % 
 
 290.990 
 
 6738.2 
 
 % 
 
 300.415 
 
 7181.8 
 
 % 
 
 309.840 
 
 7639.5 
 
 H 
 
 291.383 
 
 6756.4 
 
 % 
 
 300.807 
 
 7200.6 
 
 % 
 
 310.232 
 
 7658.9 
 
 % 
 
 291 . 775 
 
 6774.7 
 
 A 
 
 301 . 200 
 
 7219.4 
 
 'A 
 
 310.625 
 
 7678.3 
 
 93 
 
 292.168 
 
 6792.9 
 
 96 
 
 301.593 
 
 7238.2 
 
 99 
 
 311. 018 
 
 7697.7 
 
 Vs 
 
 292.561 
 
 6811.2 
 
 A 
 
 301.986 
 
 7257.1 
 
 Vs 
 
 311. 410 
 
 7717. I 
 
 Vi 
 
 292.954 
 
 6829. 5 
 
 H 
 
 302.378 
 
 7276.0 
 
 H 
 
 311.803 
 
 7736.6 
 
 % 
 
 293.346 
 
 6847.8 
 
 H 
 
 302.771 
 
 7294.9 
 
 H 
 
 312.196 
 
 7756.1 
 
 H 
 
 293.739 
 
 6866.1 
 
 V2 
 
 303.164 
 
 7313.8 
 
 1/2 
 
 312.588 
 
 7775.6 
 
 % 
 
 294.132 
 
 6884.5 
 
 5/8 
 
 303.556 
 
 7332.8 
 
 % 
 
 312.981 
 
 7795.2 
 
 % 
 
 294.524 
 
 6902.9 
 
 -H 
 
 303.949 
 
 7351.8 
 
 Vi 
 
 313.374 
 
 7814.8 
 
 % 
 
 294.917 
 
 6921.3 
 
 % 
 
 304.342 
 
 7370.8 
 
 A 
 
 313.767 
 
 7834.4 
 
 94 
 
 295.310 
 
 6939.8 
 
 97 
 
 304.734 
 
 7389.8 
 
 100 
 
 314.159 
 
 7854.0 
 
 ^ 
 
 295.702 
 
 6958.2 
 
 A 
 
 305.127 
 
 7408.9 
 
 
 
 
70 
 
 Mathematical Tables 
 
 Areas and Circumferences of Circles for Diameters 
 FROM Ho TO loo Advancing by Tenths 
 
 Diameter 
 
 Area 
 
 Circumference Diair 
 
 leter 
 
 Area 
 
 Circumference 
 
 0.6 
 
 
 s 
 
 3 
 
 4 
 
 22.0618 
 22.9022 
 
 16.6504 
 
 .1 
 
 .007854 
 
 .31416 
 
 16.9646 
 
 .2 
 
 .031416 
 
 .62832 
 
 5 
 
 23.7583 
 
 17.2788 
 
 • 3 
 
 .070686 
 
 .94248 
 
 6 
 
 24 - 6301 
 
 17.5929 
 
 .4 
 
 .12566 
 
 1.2566 
 
 7 
 
 25.5176 
 
 17.9071 
 
 .5 
 
 ■1963s 
 
 1.5708 
 
 8 
 
 26.4208 
 
 18.2212 
 
 .6 
 
 .28274 
 
 1.8850 
 
 9 
 
 27-3397 
 
 18-5354 
 
 • 7 
 
 .38485 
 
 2.1991 6 
 
 
 
 28.2743 
 
 18.8496 
 
 .8 
 
 .50266 
 
 2.S133 
 
 I 
 
 29.2247 
 
 19.1637 
 
 • 9 
 
 .63617 
 
 2.8274 
 
 2 
 
 30.1907 
 
 19-4779 
 
 I.O 
 
 .7854 
 
 3.1416 
 
 3 
 
 31.1725 
 
 19.7920 
 
 .1 
 
 .9503 
 
 3-4558 
 
 4 
 
 32.1699 
 
 20.1062 
 
 .2 
 
 I . 1310 
 
 3-7699 
 
 5 
 
 33.1831 
 
 20.4204 
 
 .3 
 
 1-3273 
 
 4-0841 
 
 6 
 
 34.2119 
 
 20. 7345 
 
 .4 
 
 1.5394 
 
 4.3982 
 
 7 
 
 35.2565 
 
 21.0487 
 
 .5 
 
 I . 7671 
 
 4.7124 
 
 8 
 
 36.3168 
 
 21.3628 
 
 .6 
 
 2.0106 
 
 5.0265 
 
 9 
 
 37.3928 
 
 21.6770 
 
 • 7 
 
 2.2698 
 
 5.3407 7 
 
 
 
 38-4845 
 
 21.9911 
 
 .8 
 
 2.5447 
 
 5.6549 
 
 I 
 
 39-5919 
 
 22.3053 
 
 • 9 
 
 2.8353 
 
 5.9690 
 
 2 
 
 40.7150 
 
 22.6195 
 
 2.0 
 
 3.1416 
 
 6.3832 
 
 3 
 
 41-8539 
 
 22.9336 
 
 .1 
 
 3.4636 
 
 6.5973 
 
 4 
 
 43.0084 
 
 23.2478 
 
 .2 
 
 3.8013 
 
 6.911S 
 
 5 
 
 44.1786 
 
 23-5619 
 
 • 3 
 
 4.1548 
 
 7.2257 
 
 6 
 
 45.3646 
 
 23.8761 
 
 ■ 4 
 
 4.5239 
 
 7.5398 
 
 7 
 
 46.5663 
 
 24.1903 
 
 • 5 
 
 4.9087 
 
 7.8540 
 
 8 
 
 47.7836 
 
 24-5044 
 
 .6 
 
 5.3093 
 
 8.1681 
 
 9 
 
 49 -0167 
 
 24-8186 
 
 -7 
 
 5.7256 
 
 8.4823 8 
 
 
 
 50.2655 
 
 25.1327 
 
 .8 
 
 6.1575 
 
 8.7965 
 
 I 
 
 51.5300 
 
 25.4469 
 
 •9 
 
 6.6052 
 
 9.1106 
 
 2 
 
 52.8102 
 
 25.7611 
 
 3.0 
 
 7.0686 
 
 9-4248 
 
 3 
 
 54.1061 
 
 26.0752 
 
 .1 
 
 7.5477 
 
 9-7389 
 
 4 
 
 55.4177 
 
 26.3894 
 
 .2 
 
 8.0425 
 
 10.0531 
 
 5 
 
 56.7450 
 
 26.7035 
 
 .3 
 
 8.5530 
 
 10.3673 
 
 6 
 
 58.0880 
 
 27.0177 
 
 .4 
 
 9 0792 
 
 10.6814 
 
 7 
 
 59.4468 
 
 27.3319 
 
 .5 
 
 9.6211 
 
 10.9956 
 
 8 
 
 60.8212 
 
 27.6460 
 
 .6 
 
 10.1788 
 
 11.3097 
 
 9 
 
 62.2114 
 
 27.9602 
 
 .7 
 
 10.7521 
 
 11.6239 9 
 
 
 
 63.6173 
 
 28.2743 
 
 .8 
 
 II. 341 I 
 
 I I. 9381 
 
 I 
 
 65.0388 
 
 28.588s 
 
 •9 
 
 11.9459 
 
 12.2522 
 
 2 
 
 66.4761 
 
 28.9027 
 
 4.0 
 
 12.5664 
 
 12.5664 
 
 3 
 
 67.9291 
 
 29.2168 
 
 .1 
 
 13.202s 
 
 12.8805 
 
 4 
 
 69.3978 
 
 29.5310 
 
 .2 
 
 13.8544 
 
 13.1947 
 
 5 
 
 70.8822 
 
 29.8451 
 
 .3 
 
 14.5220 
 
 13.5088 
 
 6 
 
 72.3823 
 
 30.1593 
 
 • 4 
 
 15.2053 
 
 13.8230 
 
 7 
 
 73.8981 
 
 30.4734 
 
 .5 
 
 15.9043 
 
 14.1372 
 
 8 
 
 75.4296 
 
 30.7876 
 
 .6 
 
 16.6190 
 
 14.4513 
 
 9 
 
 76.9769 
 
 31 . 1018 
 
 • 7 
 
 17.3494 
 
 14.765s 10 
 
 
 
 78.5398 
 
 31.4159 
 
 .8 
 
 18.0956 
 
 15.0796 
 
 I 
 
 80.1185 
 
 31.7301 
 
 • 9 
 
 18.8574 
 
 15.3938 
 
 2 
 
 81.7128 
 
 32.0442 
 
 S.o 
 
 19-6350 
 
 IS. 7080 
 
 3 
 
 . 83.3229 
 
 32.3584 
 
 .1 
 
 20.4282 
 
 16.0221 
 
 4 
 
 84.9487 
 
 32.6726 
 
 .2 
 
 21.2372 
 
 16.3363 
 
 5 
 
 86.5901 
 
 32.9867 
 
Areas and Circumferences of Circles 
 
 71 
 
 Areas and Circumferences of Circles for Diameters 
 FROM Mo to 100 Advancing by Tenths — {Continued) 
 
 Diameter 
 
 Area 
 
 Circumference 
 
 Diameter 
 
 Area 
 
 Circumference 
 
 10.6 
 
 88.2473 
 
 33.3009 
 
 15.9 
 
 198.5565 
 
 49.9513 
 
 .7 
 
 89.9202 
 
 33.6150 
 
 16.0 
 
 201.0619 
 
 50.2655 
 
 .8 
 
 91.6088 
 
 33.9292 
 
 .1 
 
 203.5831 
 
 50.5796 
 
 .9 
 
 93.3132 
 
 34.2434 
 
 .2 
 
 206.1199 
 
 so. 8938 
 
 «.o 
 
 95.0332 
 
 34.5575 
 
 .3 
 
 208.6724 
 
 SI. 2080 
 
 
 96.7689 
 
 34.8717 
 
 .4 
 
 211.2407 
 
 51.5221 
 
 .2 
 
 98.5203 
 
 35.1858 
 
 .5 
 
 213.8246 
 
 SI. 8363 
 
 .3 
 
 100.2875 
 
 35.5000 
 
 .6 
 
 216.4243 
 
 52.1504 
 
 • 4 
 
 102.0703 
 
 35.8142 
 
 .7 
 
 219.0397 
 
 52.4646 
 
 .5 
 
 103.8689 
 
 36.1283 
 
 .8 
 
 221.6708 
 
 52.7788 
 
 .6 
 
 105.6832 
 
 36.442s 
 
 • 9 
 
 224.3176 
 
 53.0929 
 
 .7 
 
 107.5132 
 
 36.7566 
 
 17.0 
 
 226.9801 
 
 53.4071 
 
 .8 
 
 109.3588 
 
 37.0708 
 
 .1 
 
 229.6583 
 
 53.7212 
 
 • 9 
 
 III. 2202 
 
 37.3850 
 
 .2 
 
 232.3522 
 
 54.0354 
 
 12.0 
 
 113.0973 
 
 37.6991 
 
 .3 
 
 235.0618 
 
 54.3496 
 
 .1 
 
 114. 9901 
 
 38.0133 
 
 .4 
 
 237.7871 
 
 54.6637 
 
 .2 
 
 116.8987 
 
 38.3274 
 
 .5 
 
 240.5282 
 
 54.9779 
 
 .3 
 
 118.8229 
 
 38.6416 
 
 .6 
 
 243.2849 
 
 55.2920 
 
 .4 
 
 120.7628 
 
 38.9557 
 
 .7 
 
 246.0574 
 
 55.6062 
 
 .5 
 
 122.7185 
 
 39.2699 
 
 .8 
 
 248.8456 
 
 55.9203 
 
 .6 
 
 124.6898 
 
 39.5841 
 
 • 9 
 
 251.6494 
 
 56.2345 
 
 •7 
 
 126.6769 
 
 39.8982 
 
 18.0 
 
 254.4690 
 
 56.5486 
 
 .8 
 
 128.6796 
 
 40.2124 
 
 .1 
 
 257.3043 
 
 56.8628 
 
 • 9 
 
 130.6981 
 
 40.5265 
 
 .2 
 
 260.1553 
 
 57 . 1770 
 
 13.0 
 
 132.7323 
 
 40.8407 
 
 .3 
 
 263.0220 
 
 57.4911 
 
 .1 
 
 134.7822 
 
 41.1549 
 
 ■ 4 
 
 265.9044 
 
 57.8053 
 
 .2 
 
 136.8478 
 
 41.4690 
 
 ■ 5 
 
 268.8025 
 
 58.119s 
 
 .3 
 
 138.9291 
 
 41.7832 
 
 .6 
 
 271.7164 
 
 58.4336 
 
 • 4 
 
 141. 0261 
 
 42.0973 
 
 .7 
 
 274.6459 
 
 58.7478 
 
 .5 
 
 143.1388 
 
 42.4115 
 
 .8 
 
 277.5911 
 
 59.0619 
 
 .6 
 
 145.2672 
 
 42.7257 
 
 ■9 
 
 280.5521 
 
 59.3761 
 
 .7 
 
 147.4114 
 
 43.0398 
 
 19.0 
 
 283.5287 
 
 59.6903 
 
 .8 
 
 149.5712 
 
 43.3540 
 
 .1 
 
 286.5211 
 
 60.0044 
 
 • 9 
 
 151.7468 
 
 43.6681 
 
 .2 
 
 289.5292 
 
 60.3186 
 
 14.0 
 
 153.9380 
 
 43.9823 
 
 .3 
 
 292.5530 
 
 60.6327 
 
 .1 
 
 156.1450 
 
 44.2965 
 
 .4 
 
 295.592s 
 
 60.9469 
 
 .2 
 
 158.3677 
 
 44.6106 
 
 .5 
 
 298.6477 
 
 61.2611 
 
 •3 
 
 160.6061 
 
 44.9248 
 
 .6 
 
 301.7186 
 
 61.5752 
 
 .4 
 
 162.8602 
 
 45.2389 
 
 .7 
 
 304.8052 
 
 61.8894 
 
 ■ 5 
 
 165 . 1300 
 
 45.5531 
 
 .8 
 
 307.907s 
 
 62.203s 
 
 .6 
 
 167.4155 
 
 45.8673 
 
 • 9 
 
 311.0255 
 
 62.S177 
 
 .7 
 
 169.7167 
 
 46.1814 
 
 20.0 
 
 314.1593 
 
 62.8319 
 
 .8 
 
 172.0336 
 
 46.4956 
 
 .1 
 
 317.3087 
 
 63 . 1460 
 
 • 9 
 
 174.3662 
 
 46.8097 
 
 .2 
 
 320.4739 
 
 63.4602 
 
 iS.o 
 
 176.7146 
 
 47.1239 
 
 .3 
 
 323.6547 
 
 63.7743 
 
 .1 
 
 179.0786 
 
 47.4380 
 
 .4 
 
 326.8513 
 
 64.088s 
 
 .2 
 
 181.4584 
 
 47.7522 
 
 .5 
 
 330.0636 
 
 64.4026 
 
 .3 
 
 183.8539 
 
 48.0664 
 
 .6 
 
 333.2916 
 
 64.7168 
 
 .4 
 
 186.2650 
 
 48.3805 
 
 .7 
 
 336.5353 
 
 65.03x0 
 
 .5 
 
 188.6919 
 
 48.6947 
 
 .8 
 
 339.7947 
 
 65.3451 
 
 .6 
 
 191 . 1345 
 
 49.0088 
 
 •9 
 
 343.0698 
 
 65.6593 
 
 .7 
 
 193.5928 
 
 49.3230 
 
 21.0 
 
 346.3606 
 
 65.9734 
 
 .8 
 
 196.0668 
 
 49.6372 
 
 .1 
 
 349.6671 
 
 66.2876 
 
72 
 
 Mathematical Tables 
 
 Aeeas and Circumferences of Circles for Diameters 
 FROM Mo TO loo Advancing by Tenths — (Continued) 
 
 Diameter 
 
 Area 
 
 Circumference Diair 
 
 leter 
 
 Area 
 
 Circumference 
 
 21.2 
 
 352.9894 
 
 66.6018 26 
 
 5 
 
 551.5459 
 
 83.2522 
 
 
 3 
 
 356.3273 
 
 66.9159 
 
 6 
 
 555.7163 
 
 83 
 
 S664 
 
 
 4 
 
 359 6809 
 
 67.2301 
 
 7 
 
 559.9025 
 
 83 
 
 8805 
 
 
 5 
 
 363.0503 
 
 67.5442 
 
 8 
 
 564.1044 
 
 84 
 
 1947 
 
 
 6 
 
 366 . 4354 
 
 67.8584 
 
 9. 
 
 568.3220 
 
 84 
 
 5088 
 
 
 7 
 
 369.8361 
 
 68.1726 27 
 
 
 
 572.5553 
 
 84 
 
 8230 
 
 
 8 
 
 373 • 2526 
 
 68.4867 
 
 I 
 
 576.8043 
 
 85 
 
 1372 
 
 
 9 
 
 376.6848 
 
 68.8009 
 
 2 
 
 581.0690 
 
 85 
 
 4513 
 
 22 
 
 o 
 
 380.1327 
 
 69.1150 
 
 3 
 
 585.3494 
 
 85 
 
 7655 
 
 
 I 
 
 383.5963 
 
 69.4292 
 
 .4 
 
 589.6455 
 
 86 
 
 0796 
 
 
 2 
 
 387.0756 ■ 
 
 69.7434 
 
 .5 
 
 593.9574 
 
 86 
 
 3938 
 
 
 3 
 
 390.5707 
 
 70.0575 
 
 .6 
 
 598.2849 
 
 86 
 
 7080 
 
 
 .4 
 
 394.0814 
 
 70.3717 
 
 .7 
 
 602.6282 
 
 87 
 
 0221 
 
 
 • 5 
 
 397.6078 
 
 70.6858 
 
 .8 
 
 606.9871 
 
 87 
 
 3363 
 
 
 .6 
 
 401 . 1500 
 
 71.0000 
 
 .9 
 
 61 I. 3618 
 
 87 
 
 6504 
 
 
 • 7 
 
 404.7078 
 
 71.3142 28 
 
 .0 
 
 615.7522 
 
 87 
 
 9646 
 
 
 .8 
 
 408 . 2814 
 
 71.6283 
 
 .1 
 
 620.1582 
 
 88 
 
 2788 
 
 
 ■ 9 
 
 411.8707 
 
 71.9425 
 
 .2 
 
 624.5800 
 
 88 
 
 5929 
 
 23 
 
 .o 
 
 415.4756 
 
 72.2566 
 
 .3 
 
 629.017s 
 
 88 
 
 9071 
 
 
 .1 
 
 419.0963 
 
 72.5708 
 
 .4 
 
 633.4707 
 
 89 
 
 .2212 
 
 
 .2 
 
 422.7327 
 
 72.8849 
 
 .5 
 
 637.9397 
 
 89 
 
 .5354 
 
 
 .3 
 
 426.3848 
 
 73.1991 
 
 .6 
 
 642.4243 
 
 89 
 
 .8495 
 
 
 • 4 
 
 430.0526 
 
 73.5133 
 
 .7 
 
 646 . 9246 
 
 90 
 
 .1637 
 
 
 .5 
 
 433.7361 
 
 73.8274 
 
 .8 
 
 651.4407 
 
 90 
 
 .4779 
 
 
 .6 
 
 437.4354 
 
 74.1416 
 
 •9 
 
 655.9724 
 
 90 
 
 .7920 
 
 
 ■ 7 
 
 441 . 1503 
 
 74.4557 29 
 
 .0 
 
 660.5199 
 
 91 
 
 .1062 
 
 
 .8 
 
 444.8809 
 
 74.7699 
 
 .1 
 
 665.0830 
 
 91 
 
 .4203 
 
 
 9 
 
 448.6273 
 
 75.0841 
 
 .2 
 
 669.6619 
 
 91 
 
 .7345 
 
 24 
 
 o 
 
 452.3893 
 
 75.3892 
 
 • 3 
 
 674.2565 
 
 92 
 
 .0487 
 
 
 I 
 
 456 . 1671 
 
 75.7124 
 
 .4 
 
 678.8668 
 
 92 
 
 .3628 
 
 
 2 
 
 459.9606 
 
 76.0265 
 
 •5 
 
 683 . 4928 
 
 92 
 
 6770 
 
 
 3 
 
 463.7698 
 
 76.3407 
 
 .6 
 
 688.1345 
 
 92 
 
 991 1 
 
 
 4 
 
 467.5947 
 
 76.6549 
 
 .7 
 
 692.7919 
 
 93 
 
 3053 
 
 
 5 
 
 471.4352 
 
 76.9690 
 
 .8 
 
 697.4650 
 
 93 
 
 6195 
 
 
 6 
 
 475 . 2916 
 
 77.2832 
 
 9 
 
 702 . 1538 
 
 93 
 
 9336 
 
 
 7 
 
 479.1636 
 
 77.5973 30 
 
 
 
 706.8583 
 
 94 
 
 2478 
 
 
 8 
 
 483.0513 
 
 77.9115 
 
 I 
 
 711.5786 
 
 94 
 
 5619 
 
 
 9 
 
 486.9547 
 
 78.2257 
 
 2 
 
 716.314s 
 
 94 
 
 8761 
 
 25 
 
 o 
 
 490.8739 
 
 78.5398 
 
 3 
 
 721.0662 
 
 95 
 
 1903 
 
 
 I 
 
 494.8087 
 
 78.8540 
 
 4 
 
 725.8336 
 
 95 
 
 5044 
 
 
 2 
 
 498.7592 
 
 79.1681 
 
 5 
 
 730.6167 
 
 95 
 
 8186 
 
 
 3 
 
 502 . 7255 
 
 79.4823 
 
 6 
 
 735.4154 
 
 96 
 
 1327 
 
 
 4 
 
 506.7075 
 
 79.796s 
 
 7 
 
 740.2299 
 
 96 
 
 4469 
 
 
 5 
 
 510.7052 
 
 80.1106 
 
 8 
 
 745.0601 
 
 96 
 
 761 1 
 
 
 6 
 
 514.7185 
 
 80.4248 
 
 9 
 
 749.9060 
 
 97 
 
 0752 
 
 
 7 
 
 S18.7476 
 
 80.7389 31 
 
 
 
 754.7676 
 
 97 
 
 3894 
 
 
 8 
 
 522.7924 
 
 81.0531 
 
 I 
 
 759.6450 
 
 97 
 
 7035 
 
 
 9 
 
 526.8529 
 
 81.3672 
 
 2 
 
 764.5380 
 
 98 
 
 0177 
 
 26. 
 
 o 
 
 530.9292 
 
 81.6814 
 
 3 
 
 769.4467 
 
 98 
 
 3319 
 
 
 I 
 
 S35.02II 
 
 81.9956 
 
 4 
 
 774.3712 
 
 98 
 
 6460 
 
 
 2 
 
 539.1287 
 
 82.3097 
 
 5 
 
 779.3113 
 
 98 
 
 9602 
 
 
 3 
 
 543.2521 
 
 82.6239 
 
 6 
 
 784.2672 
 
 99 
 
 2743 
 
 
 4 
 
 547. 391 I 
 
 82.9380 
 
 7 
 
 789.2388 
 
 99. 
 
 5885 
 
Areas and Circumferences of Circles 
 
 73 
 
 Areas and Circumferences of Circles for Diameters 
 FROM Ho TO loo Advancing by Tenths — {Continued) 
 
 Diameter 
 
 Area 
 
 Circumference Diarr 
 
 eter 
 
 Area 
 
 Circumference 
 
 31.8 
 
 794-2260 
 
 99.9026 37. 
 
 I 
 
 1081.0299 
 
 116. 5531 
 
 
 9 
 
 799 2290 
 
 100.2168 
 
 2 
 
 1086.8654 
 
 116.8672 
 
 32. 
 
 o 
 
 804.2477 
 
 100.5310 
 
 3 
 
 1092. 7166 
 
 117.1814 
 
 
 I 
 
 809.2821 
 
 100.8451 
 
 4 
 
 1098.5835 
 
 117.4956 
 
 
 2 
 
 814.3322 
 
 101.1593 
 
 5 
 
 I 104. 4662 
 
 117.8097 
 
 
 3 
 
 819.3980 
 
 101.4734 
 
 6 
 
 mo. 3645 
 
 118. 1239 
 
 
 4 
 
 824.4796 
 
 101.7876 
 
 7 
 
 1116.2786 
 
 118.4380 
 
 
 5 
 
 829.5768 
 
 102 . 1018 
 
 8 
 
 I 122. 2083 
 
 118.7522 
 
 
 6 
 
 834.6898 
 
 102.4159 
 
 9 
 
 I 128. 1538 
 
 119.0664 
 
 
 7 
 
 839.8185 
 
 102 . 7301 38 
 
 
 
 1134.1149 
 
 119.3805 
 
 
 8 
 
 844.9628 
 
 103.0442 
 
 I 
 
 1140.0918 
 
 119.6947 
 
 
 9 
 
 850.1229 
 
 103.3584 
 
 2 
 
 I 146. 0844 
 
 120.0088 
 
 33 
 
 o 
 
 855.2986 
 
 103.6726 
 
 3 
 
 I 152. 0927 
 
 120.3230 
 
 
 I 
 
 860.4902 
 
 103.9867 
 
 4 
 
 1158.1167 
 
 120.6372 
 
 
 2 
 
 865.6973 
 
 104 . 3009 
 
 5 
 
 1164.1564 
 
 120.9513 
 
 
 3 
 
 870.9202 
 
 104.6150 
 
 6 
 
 1170.2118 
 
 121.2655 
 
 
 4 
 
 876.1588 
 
 104.9292 
 
 7 
 
 I 176. 2830 
 
 121.5796 
 
 
 S 
 
 881.4131 
 
 105 . 2434 
 
 8 
 
 I 182. 3698 
 
 121.8938 
 
 
 6 
 
 886.6831 
 
 105.5575 
 
 9 
 
 I 188. 4724 
 
 122 . 2080 
 
 
 7 
 
 891.9688 
 
 105.8717 39 
 
 
 
 I 194. 5906 
 
 122.5221 
 
 
 8 
 
 897.2703 
 
 106.1858 
 
 I 
 
 1200.7246 
 
 122.8363 
 
 
 9 
 
 902.5874 
 
 106 . 5000 
 
 2 
 
 1206.8742 
 
 123.1504 
 
 34 
 
 o 
 
 907.9203 
 
 106.8142 
 
 3 
 
 1213.0396 
 
 123.4646 
 
 
 I 
 
 913.2688 
 
 107.1283 
 
 4 
 
 1219.2207 
 
 123.7788 
 
 
 2 
 
 918.6331 
 
 107.4425 
 
 5 
 
 1225. 4175 
 
 124.0929 
 
 
 3 
 
 924.0131 
 
 107.7566 
 
 6 
 
 1231.6300 
 
 124.4071 
 
 
 4 
 
 929.4088 
 
 108.0708 
 
 7 
 
 1237.8582 
 
 124.7212 
 
 
 5 
 
 934.8202 
 
 108.3849 
 
 8 
 
 1244. 1021 
 
 125.0354 
 
 
 6 
 
 940.2473 
 
 108.6991 
 
 9 
 
 1250. 3617 
 
 125.3495 
 
 
 7 
 
 945.6901 
 
 109.0133 40 
 
 
 
 1256. 6371 
 
 125.6637 
 
 
 8 
 
 951.1486 
 
 109.3274 
 
 I 
 
 1262. 9281 
 
 125.9779 
 
 
 9 
 
 956.6228 
 
 109.6416 
 
 2 
 
 1269.2348 
 
 126.2920 
 
 35 
 
 o 
 
 962.1128 
 
 109.9557 
 
 3 
 
 1275.5573 
 
 126.6062 
 
 
 I 
 
 967.6184 
 
 110.2699 
 
 4 
 
 1281.8955 
 
 126.9203 
 
 
 2 
 
 973.1397 
 
 no. 5841 
 
 5 
 
 1288.2493 
 
 127.2345 
 
 
 3 
 
 978 . 6768 
 
 110.8982 
 
 .6 
 
 1294. 6189 
 
 127.5487 
 
 
 4 
 
 984.2296 
 
 III. 2124 
 
 7 
 
 1301.0042 
 
 127.8628 
 
 
 5 
 
 989.7980 
 
 III. 5265 
 
 8 
 
 1307 . 4052 
 
 128.1770 
 
 
 .6 
 
 995.3822 
 
 II I. 8407 
 
 9 
 
 1313.8219 
 
 128. 491 I 
 
 
 .7 
 
 1000. 9821 
 
 112. 1549 41 
 
 .0 
 
 1320.2543 
 
 128.8053 
 
 
 .8 
 
 1006.5977 
 
 112.4690 
 
 .1 
 
 1326.7024 
 
 129. I 195 
 
 
 • 9 
 
 1012 . 2290 
 
 112.7832 
 
 .2 
 
 1333. 1663 
 
 129.4336 
 
 36 
 
 o 
 
 1017.8760 
 
 113.0973 
 
 .3 
 
 1339.6458 
 
 129.7478 
 
 
 .1 
 
 1023.5387 
 
 113.4115 
 
 4 
 
 1346 . 1410 
 
 130.0619 
 
 
 .2 
 
 1029. 2172 
 
 113.7257 
 
 5 
 
 1352 . 6520 
 
 130.3761 
 
 
 .3 
 
 1034. 91 13 
 
 114.0398 
 
 .6 
 
 1359. 1786 
 
 130.6903 
 
 
 • 4 
 
 1040. 6212 
 
 114.3540- 
 
 .7 
 
 1365. 7210 
 
 131.0044 
 
 
 .5 
 
 1046.3467 
 
 114. 6681 
 
 .8 
 
 1372. 2791 
 
 131. 3186 
 
 
 .6 
 
 1052.0880 
 
 114.9823 
 
 ■ 9 
 
 1378.8529 
 
 131.6327 
 
 
 .7 
 
 1057.8449 
 
 115.2965 42 
 
 .0 
 
 1385.4424 
 
 131.9469 
 
 
 .8 
 
 1063. 6176 
 
 115. 6106 
 
 .1 
 
 1392.0476 
 
 132. 261 I 
 
 
 •9 
 
 1069.4060 
 
 115.9248 
 
 .2 
 
 1398.6685 
 
 132.5752 
 
 37. o 
 
 1075. 2 lOI 
 
 116.2389 
 
 .3 
 
 140S.3051 
 
 132.8894 
 
74 
 
 Mathematical Tables 
 
 Areas and Circumferences of Circles for Diameters 
 FROM Mo TO loo Advancing by Tenths — {Continued) 
 
 Diameter 
 
 Area 
 
 Circumference Diarr 
 
 leter 
 
 Area 
 
 Circumference 
 
 42.4 
 
 141 I. 9574 
 
 133.2035 47 
 
 7 
 
 1787.0086 
 
 149-8540 
 
 
 5 
 
 1418.6254 
 
 133-5177 
 
 8 
 
 1794.5091 
 
 150.1681 
 
 
 6 
 
 1425.3092 
 
 133.8318 
 
 9 
 
 1802.0254 
 
 150.4823 
 
 
 7 
 
 1432.0086 
 
 134.1460 48 
 
 
 
 1809.5574 
 
 150.7964 
 
 
 8 
 
 1438.7238 
 
 134.4602 
 
 I 
 
 1817.1050 
 
 151.1106 
 
 
 9 
 
 1445.4546 
 
 134.7743 
 
 2 
 
 1824.6684 
 
 ISI.4248 
 
 43 
 
 
 
 1452 . 2012 
 
 135.0885 
 
 3 
 
 1832 . 2475 
 
 151.7389 
 
 
 I 
 
 1458.9635 
 
 135.4026 
 
 4 
 
 1839.8423 
 
 152.0531 
 
 
 2 
 
 1465. 741S . 
 
 135.7168 
 
 5- 
 
 1847.4528 
 
 152.3672 
 
 
 3 
 
 1472.5352 
 
 136.0310 
 
 6 
 
 1855 -0790 
 
 152.6814 
 
 
 4 
 
 1479-3446 
 
 136.3451 
 
 7 
 
 1862. 7210 
 
 152.9956 
 
 
 5 
 
 i486. 1697 
 
 136.6593 
 
 8 
 
 1870 . 3786 
 
 153-3097 
 
 
 6 
 
 1493 oios 
 
 136.9734 
 
 9 
 
 1878. 0519 
 
 153.6239 
 
 
 7 
 
 1499-8670 
 
 137.2876 49 
 
 
 
 1885.7409 
 
 153.9380 
 
 
 8 
 
 1506.7393 
 
 137.6018 
 
 I 
 
 1893.4457 
 
 154-2522 
 
 
 9 
 
 1513-6272 
 
 137-9159 
 
 2 
 
 1901 . 1662 
 
 154-5664 
 
 44 
 
 
 
 1520.5308 
 
 138.2301 
 
 3 
 
 1908.9024 
 
 154-8805 
 
 
 I 
 
 1527.4502 
 
 138.5442 
 
 4 
 
 1916.6543 
 
 155.1947 
 
 
 2 
 
 1534.3853 
 
 138.8584 
 
 5 
 
 1924. 4218 
 
 155-5088 
 
 
 3 
 
 154I-3360 
 
 139-1726 
 
 6 
 
 1932 . 2051 
 
 155-8230 
 
 
 4 
 
 1548.3025 
 
 139-4867 
 
 7 
 
 1940.0042 
 
 156.1372 
 
 
 5 
 
 1555-2847 
 
 139-8009 
 
 8 
 
 1947. 8189 
 
 156.4513 
 
 
 6 
 
 1562.2826 
 
 140.1153 
 
 9 
 
 1955.6493 
 
 156.7655 
 
 
 7 
 
 1569.2962 
 
 140.4292 So 
 
 
 
 1963-4954 
 
 157-0796 
 
 
 8 
 
 1576.3255 
 
 140.7434 
 
 I 
 
 1971.3572 
 
 157.3938 
 
 
 9 
 
 1583.3706 
 
 141.0575 
 
 2 
 
 1979.2348 
 
 157.7080 
 
 45 
 
 
 
 1590. 4313 
 
 141. 3717 
 
 3 
 
 1987 . 1280 
 
 158.0221 
 
 
 I 
 
 1597.5077 
 
 141.6858 
 
 4 
 
 1995-0370 
 
 158.3363 
 
 
 2 
 
 1604.5999 
 
 142.0000 
 
 5 
 
 2002.9617 
 
 158.6504 
 
 
 3 
 
 1611.7077 
 
 142.3142 
 
 6 
 
 2010 . 9020 
 
 158.9646 
 
 
 4 
 
 1618.8313 
 
 142.6283 
 
 7 
 
 2018. 8581 
 
 159-2787 
 
 
 5 
 
 1625.9705 
 
 142.9425 
 
 8 
 
 2026.8299 
 
 159-5929 
 
 
 6 
 
 1633. 1255 
 
 143.2566 
 
 9 
 
 2034-8174 
 
 159-9071 
 
 
 7 
 
 1640.2962 
 
 143.5708 51 
 
 
 
 2042.8206 
 
 160.2212 
 
 
 8 
 
 1647.4826 
 
 143.8849 
 
 I 
 
 2050.839s 
 
 160.5354 
 
 
 9 
 
 1654.6847 
 
 144.1991 
 
 2 
 
 2058.8742 
 
 160.849s 
 
 46 
 
 
 
 1661.9025 
 
 144.5133 
 
 3 
 
 2066.9245 
 
 161 . 1637 
 
 
 I 
 
 1669. 1360 
 
 144.8274 
 
 4 
 
 2074.990s 
 
 161.4779 
 
 
 2 
 
 1676.3853 
 
 145.1416 
 
 5 
 
 2083.0723 
 
 161.7920 
 
 
 3 
 
 1683.6502 
 
 145-4557 
 
 6 
 
 2091 . 1697 
 
 162.1062 
 
 
 4 
 
 1690.9308 
 
 145.7699 
 
 7 
 
 2099.2829 
 
 162.4203 
 
 
 5 
 
 1698.2272 
 
 146.0841 
 
 8 
 
 2107. 4118 
 
 162.734s 
 
 
 6 
 
 170S.5392 
 
 146.3982 
 
 9 
 
 21 15. 5563 
 
 163.0487 
 
 
 7- 
 
 1712.8670 
 
 146.7124 52 
 
 
 
 2123. 7166 
 
 163.3628 
 
 
 .8 
 
 1720. 2105 
 
 147.0265 
 
 I 
 
 2131.8926 
 
 163.6770 
 
 
 •9 
 
 1727.5697 
 
 147.3407 
 
 2 
 
 2140.0843 
 
 163.9911 
 
 47 
 
 
 
 1734.9445 
 
 147.6550 
 
 3 
 
 2148. 2917 
 
 164.3053 
 
 
 .1 
 
 1742. 3351 
 
 147.9690 
 
 4 
 
 2156.5149 
 
 164.6195 
 
 
 .2 
 
 1749. 7414 
 
 148.2832 
 
 5 
 
 2164.7537 
 
 164.9336 
 
 
 .3 
 
 1757. 1635 
 
 148.5973 
 
 6 
 
 2173.0082 
 
 165.2479 
 
 
 .4 
 
 1764. 6012 
 
 148.9115 
 
 7 
 
 2181.2785 
 
 165.5619 
 
 
 .5 
 
 1772.0546 
 
 149.2257 
 
 8 
 
 2189.5644 
 
 165.8761 
 
 .6 
 
 1779.5237 
 
 149.5398 
 
 9 
 
 2197. 8661 
 
 166.1903 
 
Areas and Circiimferences of Circles 
 
 7^ 
 
 Areas and Circumferences of Circles for Diameters 
 FROM Ho to ioo Advancing by Tenths — {Continued) 
 
 Diameter 
 
 Area 
 
 Circumference 
 
 Diameter 
 
 Area 
 
 Circumference 
 
 53. o 
 
 2206.1834 
 
 166.5044 
 
 58.3 
 
 2669.4820 
 
 183.5914 
 
 .1 
 
 2214. 5165 
 
 166.8186 
 
 .4 
 
 2678.6476 
 
 183.4690 
 
 .2 
 
 2222 . 8653 
 
 167.1327 
 
 .5 
 
 2687.8289 
 
 183.7832 
 
 .3 
 
 2231 . 2298 
 
 167.4469 
 
 6 
 
 2697.0259 
 
 184.0973 
 
 • 4 
 
 2239 . 6100 
 
 167.7610 
 
 .7 
 
 2706.2386 
 
 184.411S 
 
 .5 
 
 2248.0059 
 
 168.0752 
 
 .8 
 
 2715.4670 
 
 184.7256 
 
 . .6 
 
 2256.4175 
 
 168.3894 
 
 • 9 
 
 2724. 7112 
 
 185.0398 
 
 .7 
 
 2264.8448 
 
 168.703s 
 
 59.0 
 
 2733.9710 
 
 185.3540 
 
 .8 
 
 2273.2879 
 
 169.0177 
 
 .1 
 
 2743.2466 
 
 185.6681 
 
 .9 
 
 2281.7466 
 
 169.3318 
 
 .2 
 
 2752.5378 
 
 185.9823 
 
 54. o 
 
 2290.2210 
 
 169 . 6460 
 
 .3 
 
 2761.8448 
 
 186.2964 
 
 .1 
 
 2298. 7112 
 
 169.9602 
 
 .4 
 
 2771. 1675 
 
 186.6106 
 
 .2 
 
 2307. 2171 
 
 170.2743 
 
 .5 
 
 2780.5058 
 
 186.9248 
 
 .3 
 
 231S.7386 
 
 170.5885 
 
 .6 
 
 2789.8599 
 
 187.2389 
 
 • 4 
 
 2324.2759 
 
 170.9026 
 
 .7 
 
 2799.2297 
 
 187.5531 
 
 .5 
 
 2332.8289 
 
 171. 2168 
 
 .8 
 
 2808.6152 
 
 187.8672 
 
 .6 
 
 2341.3976 
 
 171. 5310 
 
 • 9 
 
 2818. 0165 
 
 188.1814 
 
 • 7 
 
 2349.9820 
 
 171. 8451 
 
 60.0 
 
 2827.4334 
 
 188.4956 
 
 .8 
 
 2358.5821 
 
 172.1593 
 
 .1 
 
 2836.8660 
 
 188.8097 
 
 •9 
 
 2367 . 1979 
 
 172.4735 
 
 .2 
 
 2S46.3144 
 
 189.1239 
 
 55. o 
 
 2375.8294 
 
 172.7876 
 
 .3 
 
 2855.7784 
 
 189.4380 
 
 .1 
 
 2384.4767 
 
 173.1017 
 
 .4 
 
 286s . 2582 
 
 189.7522 
 
 .2 
 
 2393.1396 
 
 173.4159 
 
 .5 
 
 2874.7536 
 
 190.0664 
 
 .3 
 
 2401. 8183 
 
 173.7301 
 
 .6 
 
 2884.2648 
 
 190.3805 
 
 • 4 
 
 2410. 5126 
 
 174.0442 
 
 .7 
 
 2893.7917 
 
 190.6947 
 
 .5 
 
 2419.2227 
 
 174.3584 
 
 .8 
 
 2903.3343 
 
 191.0088 
 
 .6 
 
 2427.9485 
 
 174.6726 
 
 • 9 
 
 2912.8926 
 
 191.3230 
 
 .7 
 
 2436.6899 
 
 174.9867 
 
 61.0 
 
 2922.4666 
 
 191.6372 
 
 .8 
 
 2445.4471 
 
 175.3009 
 
 .1 
 
 2932.0563 
 
 191. 9513 
 
 •9 
 
 2454.2200 
 
 175.6150 
 
 .2 
 
 2941. 6617 
 
 192.2655 
 
 56.0 
 
 2463.0086 
 
 175.9292 
 
 3 
 
 2951 . 2828 
 
 192.5796 
 
 .1 
 
 2471. 8130 
 
 176.2433 
 
 4 
 
 2960.9197 
 
 192.8938 
 
 .2 
 
 2480.6330 
 
 176.5575 
 
 5 
 
 2970.5722 
 
 193.2079 
 
 .3 
 
 2489.4687 
 
 176.8717 
 
 6 
 
 2980.2405 
 
 193.5221 
 
 .4 
 
 2498.3201 
 
 177.1858 
 
 ■ 7 
 
 2989.9244 
 
 193.8363 
 
 .5 
 
 2507.1873 
 
 177.5000 
 
 .8 
 
 2999.6241 
 
 194.1504 
 
 .6 
 
 2516. 0701 
 
 177.8141 
 
 • 9 
 
 3009.3395 
 
 194.4646 
 
 .7 
 
 2524.9687 
 
 178.1283 
 
 62.0 
 
 3019.0705 
 
 194.7787 
 
 .8 
 
 2533.8830 
 
 178.4425 
 
 .1 
 
 3028.8173 
 
 195.0929 
 
 .9 
 
 2542.8129 
 
 178.7566 
 
 .2 
 
 3038.5798 
 
 195.4071 
 
 57. 
 
 2551.7586 
 
 179.0708 
 
 .3 
 
 3048.3580 
 
 195.7212 
 
 .1 
 
 2560.7200 
 
 179.3849 
 
 .4 
 
 3058.1520 
 
 196.0354 
 
 .2 
 
 2569.6971 
 
 179.6991 
 
 .5 
 
 3067.9616 
 
 196.349s 
 
 .3 
 
 2578.6899 
 
 180.0133 
 
 .6 
 
 3077.7869 
 
 196.6637 
 
 .4 
 
 2587.6985 
 
 180.3274 
 
 .7 
 
 3087.6279 
 
 196.9779 
 
 .5 
 
 2596.7227 
 
 180.6416 - 
 
 .8 
 
 3097.4847 
 
 197.2920 
 
 .6 
 
 2605.7626 
 
 180.9557 
 
 •9 
 
 3107. 3571 
 
 197.6062 
 
 .7 
 
 2614. 8183 
 
 181.2699 
 
 63.0 
 
 3117.2453 
 
 197.9203 
 
 .8 
 
 2623.8896 
 
 181. 5841 
 
 .1 
 
 3127. 1492 
 
 198.2345 
 
 •9 
 
 2632 . 9767 
 
 181 , 8982 
 
 .2 
 
 3137.0688 
 
 198.5487 
 
 S8.0 
 
 2642.0794 
 
 182.2124 
 
 .3 
 
 3147.0040 
 
 198.8628 
 
 .1 
 
 2651 . 1979 
 
 182.5265 
 
 .4 
 
 3156.9550 
 
 199.1770 
 
 .2 
 
 2660.3321 
 
 182.8407 
 
 .5 
 
 3166. 9217 
 
 199.4911 
 
76 
 
 Mathematical Tables 
 
 Areas and Circumferences of Circles for Diameters 
 FROM Ho TO loo Advancing by Tenths — (Continued) 
 
 Diameter 
 
 Area 
 
 1 
 Circumference Diam 
 
 eter 
 
 Area 
 
 Circumference 
 
 63.6 
 
 3176.9043 
 
 199.8053 68 
 
 9 
 
 3728.4500 
 
 216.4556 
 
 
 7 
 
 3186.9023 
 
 200.1195 69 
 
 
 
 3739.2807 
 
 216.7699 
 
 
 8 
 
 3196 . 9161 
 
 200.4336 
 
 I 
 
 3750.1270 
 
 217.0841 
 
 
 9 
 
 3206.9456 
 
 200.7478 
 
 2 
 
 3760.9891 
 
 217.3982 
 
 64 
 
 
 
 3216.9909 
 
 201.0620 
 
 3 
 
 3771.8668 
 
 217.7124 
 
 
 I 
 
 3227.0518 
 
 201.3761 
 
 4 
 
 3782.7603 
 
 218.0265 
 
 
 2 
 
 3237 . 128s 
 
 201 . 6902 
 
 5 
 
 3793.669s 
 
 218.3407 
 
 
 3 
 
 3247 ■ 2222 
 
 202.0044 
 
 6 
 
 3804.5944 
 
 218.6548 
 
 
 4 
 
 3257.3289 . 
 
 202.3186 
 
 7 
 
 3815.5350 
 
 218.9690 
 
 
 5 
 
 3267.4527- 
 
 202.6327 
 
 8 
 
 3826.4913 
 
 219.2832 
 
 
 6 
 
 3277.5922 
 
 202.9469 
 
 9 
 
 3837 • 4633 
 
 219.5973 
 
 
 7 
 
 3287.7474 
 
 203.2610 70 
 
 
 
 3848.4510 
 
 219.9115 
 
 
 8 
 
 3297.9183 
 
 203.5752 
 
 I 
 
 3859.4544 
 
 220.2256 
 
 
 9 
 
 3308.1049 
 
 203.8894 
 
 2 
 
 3870.4736 
 
 220.5398 
 
 65 
 
 
 
 3318.3072 
 
 204.2035 
 
 3 
 
 3881. S084 
 
 220.8540 
 
 
 I 
 
 3328.5253 
 
 204.5176 
 
 4 
 
 3892.5590 
 
 221.1581 
 
 
 2 
 
 3338.7590 
 
 204.8318 
 
 5 
 
 3903.6252 
 
 221.4823 
 
 
 3 
 
 3349.008s 
 
 205.1460 
 
 6 
 
 3914.7072 
 
 221.7964 
 
 
 4 
 
 3359-2736 
 
 205.4602 
 
 7 
 
 3925.8049 
 
 222.1106 
 
 
 5 
 
 3369.5545 
 
 205.7743 
 
 8 
 
 3936.9182 
 
 222 . 4248 
 
 
 6 
 
 3379.8510 
 
 206.0885 
 
 9 
 
 3948.0473 
 
 222.7389 
 
 
 7 
 
 3390.1633 
 
 206.4026 71 
 
 
 
 3959.1921 
 
 223.0531 
 
 
 8 
 
 3400.4913 
 
 206.7168 
 
 I 
 
 3970.3526 
 
 223.3672 
 
 
 9 
 
 3410.8350 
 
 207.0310 
 
 2 
 
 3981.5289 
 
 223.6814 
 
 66 
 
 
 
 3421 . 1944 
 
 207.3451 
 
 3 
 
 3992.7208 
 
 223.9956 
 
 
 .1 
 
 3431.5695 
 
 207.6593 
 
 4 
 
 4003.9284 
 
 224.3097 
 
 
 .2 
 
 3441.9603 
 
 207.9734 
 
 5 
 
 4015. 1518 
 
 224.6239 
 
 
 .3 
 
 3452.3669 
 
 208.2876 
 
 6 
 
 4026.3908 
 
 224.9380 
 
 
 .4 
 
 3462.7891 
 
 208.6017 
 
 .7 
 
 4037 . 6456 
 
 225.2522 , 
 
 
 .5 
 
 3473.2270 
 
 208.9159 
 
 .8 
 
 4048.9160 
 
 225.5664 
 
 
 .6 
 
 3483.6807 
 
 209 . 2301 
 
 9 
 
 4060.2022 
 
 225.8805 
 
 
 .7 
 
 3494. iSoo 
 
 209.5442 72 
 
 
 
 4071. 5041 
 
 226 . 1947 
 
 
 .8 
 
 3504.6351 
 
 209.8584 
 
 .1 
 
 4082.8217 
 
 226.5088 
 
 
 .9 
 
 3515. 1359 
 
 210.1725 
 
 .2 
 
 4094.1550 
 
 226.8230 
 
 ■ 67 
 
 .0 
 
 3525.6524 
 
 210.4867 
 
 .3 
 
 4105.5040 
 
 227.1371 
 
 
 .1 
 
 3536.1845 
 
 210.8009 
 
 ■4 
 
 41 16. 8687 
 
 227.4513 
 
 
 .2 
 
 3546.7324 
 
 211.1150 
 
 .5 
 
 4128. 2491 
 
 227.765s 
 
 
 .3 
 
 3557 . 2960 
 
 211.4292 
 
 .6 
 
 4139.6452 
 
 228.0796 
 
 
 •4 
 
 3567.8754 
 
 211.7433 
 
 .7 
 
 4151.0571 
 
 228.3938 
 
 
 .5 
 
 3578.4704 
 
 212.0575 
 
 .8 
 
 4162 . 4846 
 
 228 . 7079 
 
 
 .6 
 
 3589. 0811 
 
 212.3717 
 
 • 9 
 
 4173.9279 
 
 229.0221 
 
 
 •7 
 
 3599.7075 
 
 212.6858 73 
 
 
 
 4185.3868 
 
 229.3363 
 
 
 .8 
 
 3610.3497 
 
 213.0000 
 
 .1 
 
 4196. 861S 
 
 229.6504 
 
 
 • 9 
 
 3621.0075 
 
 213.3141 
 
 .2 
 
 4208.3519 
 
 229.9646 
 
 68 
 
 .0 
 
 3631. 6811 
 
 213.6283 
 
 .3 
 
 4219.8579 
 
 230.2787 
 
 
 .1 
 
 3642.3704 
 
 213.9425 
 
 • 4 
 
 4231.3797 
 
 230.5929 
 
 
 .2 
 
 3653.0754 
 
 214.2566 
 
 .5 
 
 4242.9172 
 
 230.9071 
 
 
 .3 
 
 3663.7960 
 
 214.5708 
 
 .6 
 
 4254.4704 
 
 231.2212 
 
 
 •4 
 
 3674.5324 
 
 214.8849 
 
 .7 
 
 4266.0394 
 
 231.5354 
 
 
 .5 
 
 3685.2845 
 
 215.1991 
 
 .8 
 
 4277.6240 
 
 231.849s 
 
 
 .6 
 
 3696.0523 
 
 215.5133 
 
 .9 
 
 4289.2243 
 
 232.1637 
 
 
 • 7 
 
 3706.8359 
 
 215.8274 74 
 
 
 
 4300.8403 
 
 232.4779 
 
 
 .8 
 
 3717. 6351 
 
 216.1416 
 
 .1 
 
 4312. 4721 
 
 232.7920 
 
Areas and Circumferences of Circles 
 
 77 
 
 Areas and Circumferences of Circles for Diameters 
 FROM Mo TO loo Advancing by Tenths — {Continued) 
 
 Diameter 
 
 Area 
 
 Circumference Dian 
 
 aeter 
 
 Area 
 
 Circumference 
 
 74.2 
 
 4324. II95 
 
 233.1062 79 
 
 5 
 
 4963.9127 
 
 249.7566 
 
 
 3 
 
 4335.7827 
 
 233.4203 
 
 6 
 
 4976.4084 
 
 250.0708 
 
 
 4 
 
 4347.4616 
 
 233.7345 
 
 7 
 
 4988.9198 
 
 250.3850 
 
 
 5 
 
 4359.1562 
 
 234.0487 
 
 8 
 
 5001 . 4469 
 
 250.6991 
 
 
 6 
 
 4370.8664 
 
 234.3628 
 
 9 
 
 5013 . 9897 
 
 251.0133 
 
 
 7 
 
 4382.5924 
 
 234.6770 80 
 
 
 
 5026 . 5482 
 
 251.3274 
 
 
 8 
 
 4394-3341 
 
 234.9911 
 
 I 
 
 5039.1225 
 
 251.6416 
 
 
 9 
 
 4406.0916 
 
 235.3053 
 
 2 
 
 5051 . 7124 
 
 251.9557 
 
 75 
 
 o 
 
 4417.8647 
 
 235.6194 
 
 3 
 
 5064.3180 
 
 252.2699 
 
 
 I 
 
 4429.6535 
 
 235.9336 
 
 4 
 
 5076.9394 
 
 252.5840 
 
 
 2 
 
 4441 4580 
 
 236.2478 
 
 5 
 
 5089.5764 
 
 252.8982 
 
 
 3 
 
 4453.2783 
 
 236.5619 
 
 6 
 
 5102 . 2292 
 
 253.2124 
 
 
 4 
 
 4465. I 142 
 
 236.8761 
 
 7 
 
 5114.8977 
 
 253.5265 
 
 
 5 
 
 4476.9659 
 
 237.1902 
 
 8 
 
 5127. 5819 
 
 253.8407 
 
 
 6 
 
 4488.8332 
 
 237.5044 
 
 9 
 
 5140. 2818 
 
 254.1548 
 
 
 7 
 
 4500.7163 
 
 237.8186 81 
 
 
 
 5152.9973 
 
 254.4690 
 
 
 8 
 
 4512. 6151 
 
 238.1327 
 
 I 
 
 5165.7287 
 
 254 7832 
 
 
 9 
 
 4524.5296 
 
 238.4469 
 
 2 
 
 5178.4757 
 
 255.0973 
 
 76 
 
 o 
 
 4536.4598 
 
 238 . 7610 
 
 3 
 
 5191 . 2384 
 
 255. 41 IS 
 
 
 I 
 
 4548.4057 
 
 239.0752 
 
 4 
 
 5204.0168 
 
 255.7256 
 
 
 2 
 
 4560.3673 
 
 239.3894 
 
 5 
 
 5216. 8110 
 
 256.0398 
 
 
 3 
 
 4572.3446 
 
 239.7035 
 
 6 
 
 5229 . 6208 
 
 256.3540 
 
 
 4 
 
 4584.3377 
 
 240.0177 
 
 7 
 
 5242 . 4463 
 
 256.6681 
 
 
 5 
 
 4596.3464 
 
 240.3318 
 
 8 
 
 5255 . 2876 
 
 256.9823 
 
 
 6 
 
 4608.3708 
 
 240.6460 
 
 9 
 
 5268.1446 
 
 257.2966 
 
 
 7 
 
 4620. 41 10 
 
 240.9602 82 
 
 
 
 5281. 0173 
 
 257.6106 
 
 
 8 
 
 4632 . 4669 
 
 241.2743 
 
 I . 
 
 5293.9056 
 
 257.9247 
 
 
 9 
 
 4644.5384 
 
 241.5885 
 
 2 
 
 5306.8097 
 
 258.2389 
 
 77 
 
 o 
 
 4656.6257 
 
 241 . 9026 
 
 3 
 
 5319.7295 
 
 258.5531 
 
 
 I 
 
 4668.7287 
 
 242.2168 
 
 4 
 
 5332.6650 
 
 258.8672 
 
 
 2 
 
 4680.8474 
 
 242.5310 
 
 5 
 
 5345.6162 
 
 259.1814 
 
 
 3 
 
 4692.9818 
 
 242.8451 
 
 6 
 
 5358.5832 
 
 259.4956 
 
 
 4 
 
 4705 . 1319 
 
 243.1592 
 
 7 
 
 5371.5658 
 
 259.8097 
 
 
 5 
 
 4717.2977 
 
 243.4734 
 
 8 
 
 5384.5641 
 
 260.1239 
 
 
 6 
 
 4729.4792 
 
 243.7876 
 
 9 
 
 5397.5782 
 
 260.4380 
 
 
 7 
 
 4741.6756 
 
 244.1017 83 
 
 
 
 5410.6079 
 
 260.7522 
 
 
 8 
 
 4753.8894 
 
 244.4159 
 
 I 
 
 5423.6534 
 
 261.0663 
 
 
 9 
 
 4766. 1181 
 
 244.7301 
 
 2 
 
 5436.7146 
 
 261. 380s 
 
 78 
 
 o 
 
 4778.3624 
 
 245.0442 
 
 3 
 
 5449.7915 
 
 261.6947 
 
 
 I 
 
 4790.6225 
 
 245.3584 
 
 4 
 
 5462.8840 
 
 262.0088 
 
 
 2 
 
 4802.8983 
 
 245.6725 
 
 5 
 
 5475.9923 
 
 262.3230 
 
 
 3 
 
 4815. 1897 
 
 245.9867 
 
 6 
 
 5489.1163 
 
 262.6371 
 
 
 4 
 
 4827.4969 
 
 246.3009 
 
 7 
 
 5502 . 2561 
 
 262.9513 
 
 
 5 
 
 4839.8198 
 
 246.6150 
 
 8 
 
 5515. 4115 
 
 263.265s 
 
 
 6 
 
 4852.1584 
 
 246.9292 
 
 9 
 
 5528.5826 
 
 263.5796 
 
 
 7 
 
 4864 . 5128 
 
 247.2433 84 
 
 
 
 5541.7694 
 
 263.8938 
 
 
 8 
 
 4876.8828 
 
 247.5575 
 
 I 
 
 5554.9720 
 
 264.2079 
 
 
 9 
 
 4889.2685 
 
 247.8717 
 
 2 
 
 5568.1902 
 
 264.5221 
 
 79 
 
 o 
 
 4901.6699 
 
 248.1858 
 
 3 
 
 5581.4242 
 
 264.8363 
 
 
 I 
 
 4914. 0871 
 
 248.5000 
 
 4 
 
 5594.6739 
 
 265 . 1414 
 
 
 2 
 
 4926.5199 
 
 248.8141 
 
 5 
 
 5607.9392 
 
 265 . 4646 
 
 
 3 
 
 4938.9685 
 
 249.1283 
 
 6 
 
 5621.2203 
 
 265.7787 
 
 
 4 
 
 4951.4328 
 
 249.4425 
 
 7 
 
 5634. 5171 
 
 266.0929 
 
78 
 
 Mathematical Tables 
 
 Areas and Circumferences of Circles for Diameters 
 FROM Ho TO loo Advancing by Tenths — {Continued) 
 
 Diameter 
 
 Area 
 
 Circumference Diarr 
 
 leter 
 
 Area 
 
 Circumference 
 
 84.8 
 
 5647.8296 
 
 266.4071 90 
 
 I 
 
 6375.8701 
 
 283.057s 
 
 
 9 
 
 5661 . 1578 
 
 266.7212 
 
 2 
 
 _ 6390.0309 
 
 283.3717 
 
 85 ; 
 
 
 
 5674-5017 
 
 267.0354 
 
 3 
 
 6404.2073 
 
 283.6858 
 
 
 I 
 
 5687.8614 
 
 267.349s 
 
 4 
 
 6418.3995 
 
 284.0000 
 
 
 2 
 
 5701 . 2367 
 
 267.6637 
 
 5 
 
 6432.6073 
 
 284.3141 
 
 
 3 
 
 5714.6277 
 
 267.9779 
 
 6 
 
 6446.8309 
 
 284.6283 
 
 
 4 
 
 5728.0345 
 
 268.2920 
 
 7 
 
 6461. 0701 
 
 284.942s 
 
 
 S 
 
 5741.4569 
 
 268.6062 
 
 8 
 
 6475.3251 
 
 285.2566 
 
 
 6 
 
 5754.8951 
 
 268.9203 
 
 9 
 
 6489.5958 
 
 285.5708 
 
 
 7 
 
 5768.3490 
 
 269.2345 91 
 
 
 
 6503.8822 
 
 285.8849 
 
 
 8 
 
 5781. 8185 
 
 269.5486 
 
 I 
 
 6518. 1843 
 
 286.1991 
 
 
 9 
 
 5795.3038 
 
 269.8628 
 
 2 
 
 6532 . 5021 
 
 286.5133 
 
 86 
 
 
 
 5808.8048 
 
 270.1770 
 
 3 
 
 6546.8356 
 
 286.8274 
 
 
 I 
 
 5822.3215 
 
 270.4911 
 
 4 
 
 6561 . 1848 
 
 287 . 1416 
 
 
 2 
 
 5835.8539 
 
 270.8053 
 
 5 
 
 6575.5498 
 
 287.4557 
 
 
 3 
 
 5849.4020 
 
 271.1194 
 
 6 
 
 6589.9304 
 
 287.7699 
 
 
 4 
 
 5862.9659 
 
 271.4336 
 
 7 
 
 6604.3268 
 
 288.0840 
 
 
 5 
 
 5876.5454 
 
 271.7478 
 
 8 
 
 6618.7388 
 
 288.3982 
 
 
 6 
 
 5890.1407 
 
 272.0619 
 
 9 
 
 6633.1666 
 
 288.7124 
 
 
 7 
 
 5903.7516 
 
 272.3761 92 
 
 
 
 6647. 6101 
 
 289.0265 
 
 
 8 
 
 5917.3783 
 
 272 . 6902 
 
 I 
 
 6662.0692 
 
 289.3407 
 
 
 9 
 
 5931.0206 
 
 273.0044 
 
 2 
 
 6676.5441 
 
 289.6548 
 
 87 
 
 
 
 5944.6787 
 
 273.3186 
 
 3 
 
 6691.0347 
 
 289.9690 
 
 
 I 
 
 5958.3525 
 
 273.6327 
 
 4 
 
 6705.5410 
 
 290.2832 
 
 
 2 
 
 5972.0420 
 
 273.9469 
 
 5 
 
 6720.0630 
 
 290.5973 
 
 
 3 
 
 5985.7472 
 
 274.2610 
 
 6 
 
 6734.6008 
 
 290.9115 
 
 
 4 
 
 5999.4681 
 
 274.5752 
 
 7 
 
 6749.1542 
 
 291 . 2256 
 
 
 5 
 
 6013.2047 
 
 274.8894 
 
 8 
 
 6763.7233 
 
 291.5398 
 
 
 6 
 
 6026 . 9570 
 
 275.2035 
 
 9 
 
 6778.3082 
 
 291.8540 
 
 
 7 
 
 6040.7250 
 
 275.5177 93 
 
 
 
 6792.9087 
 
 292.1681 
 
 
 8 
 
 6054.5088 
 
 275.8318 
 
 I 
 
 6807.5250 
 
 292.4823 
 
 
 9 
 
 6068.3082 
 
 276.1460 
 
 2 
 
 6822 . 1569 
 
 292.7964 
 
 88 
 
 
 
 6082 . 1234 
 
 276.4602 
 
 3 
 
 6836.8046 
 
 293.1106 
 
 
 I 
 
 6095.9542 
 
 276.7743 
 
 4 
 
 6851.4680 
 
 293.4248 
 
 
 2 
 
 6109.8008 
 
 277.0885 
 
 5 
 
 6866. 1471 
 
 293.7389 
 
 
 3 
 
 6123. 6631 
 
 277.4026 
 
 6 
 
 6880.8419 
 
 294.0531 
 
 
 4 
 
 6137. 5411 
 
 277.7168 
 
 7 
 
 6895.5524 
 
 294.3672 
 
 
 5 
 
 6151.4348 
 
 278.0309 
 
 8 
 
 6910.2786 
 
 294.6814 
 
 
 6 
 
 6165.3442 
 
 278.3451 
 
 9 
 
 6925.0205 
 
 294.9956 
 
 
 7 
 
 6179.2693 
 
 278.6593 94 
 
 
 
 6939.7782 
 
 295.3097 
 
 
 8 
 
 6193. 2101 
 
 278.9740 
 
 I 
 
 6954.5515 
 
 295.6239 
 
 
 9 
 
 6207 . 1666 
 
 279.2876 
 
 2 
 
 6969.3106 
 
 295.9380 
 
 89 
 
 
 
 6221 . 1389 
 
 279.6017 
 
 3 
 
 6984.1453 
 
 296.2522 
 
 
 I 
 
 6235 . 1268 
 
 279.9159 
 
 4 
 
 6998.9658 
 
 296.5663 
 
 
 .2 
 
 6249.1304 
 
 280.2301 
 
 5 
 
 7013. 8019 
 
 296.8805 
 
 
 .3 
 
 6263 . 1498 
 
 280.5442 
 
 6 
 
 7028.6538 
 
 297.1947 
 
 
 .4 
 
 6277.1849 
 
 280.8584 
 
 7 
 
 7043.5214 
 
 297.5088 
 
 
 5 
 
 6291 . 2356 
 
 281 . 1725 
 
 .8 
 
 7058.4047 
 
 297.8230 
 
 
 .6 
 
 6305.3021 
 
 281.4867 
 
 •9 
 
 7073.3033 
 
 298.1371 
 
 
 •7 
 
 6319.3843 
 
 281.8009 95 
 
 
 
 7088 . 2184 
 
 298.4513 
 
 
 .8 
 
 6333.4822 
 
 282.1150 
 
 .1 
 
 7103. 1488 
 
 298.765s 
 
 
 •9 
 
 6347.5958 
 
 282.4292 
 
 .2 
 
 71 18. 1950 
 
 299.0796 
 
 90 
 
 .0 
 
 6361 . 7251 
 
 282.7433 
 
 .3 
 
 7133.0568 
 
 299.3938 
 
Areas and Circumferences of Circles 
 
 79 
 
 Areas and Circumferences of Circles for Diameters 
 FROM Ho TO loo Advancing by Tenths — {Concluded) 
 
 Diameter 
 
 Area 
 
 Circumference Dian 
 
 leter 
 
 Area 
 
 Circumference 
 
 95.4 
 
 7148.0343 
 
 299.7079 97 
 
 8 
 
 7512.2078 
 
 397.2478 
 
 
 5 
 
 7163.0276 
 
 300.0221 
 
 9 
 
 7527.5780 
 
 307.5619 
 
 
 6 
 
 7178.0366 
 
 300.3363 98 
 
 
 
 7542.9640 
 
 307.8761 
 
 
 7 
 
 7193. 0612 
 
 300.6504 
 
 I 
 
 7558.3656 
 
 308 . 1902 
 
 
 8 
 
 7208 . 1016 
 
 300.9646 
 
 2 
 
 7573.7830 
 
 308.5044 
 
 
 9 
 
 7223.1577 
 
 301.2787 
 
 3 
 
 7589. 2161 
 
 308.8186 
 
 96 
 
 
 
 7238.2295 
 
 301.5929 
 
 4 
 
 7604.6648 
 
 309.1327 
 
 
 I 
 
 7253.3170 
 
 301.9071 
 
 5 
 
 7620.1293 
 
 309.4469 
 
 
 2 
 
 7268.4202 
 
 302 . 2212 
 
 6 
 
 7635.609s 
 
 309.7610 
 
 
 3 
 
 7283.5391 
 
 302.5354 
 
 7 
 
 7651 . 1054 
 
 310.0752 
 
 
 4 
 
 7298.6737 
 
 302.8405 
 
 8 
 
 7666.6170 
 
 310.3894 
 
 
 S 
 
 7313.8240 
 
 303.1637 
 
 9 
 
 7682.1444 
 
 310.7035 
 
 
 6 
 
 7328.9901 
 
 303.4779 99 
 
 
 
 7697.6893 
 
 31 I. 0177 
 
 
 1 
 
 7344. 1718 
 
 303.7920 
 
 I 
 
 7713. 2461 
 
 31 I. 3318 
 
 
 8 
 
 7359.3693 
 
 304.1062 
 
 2 
 
 7728.8206 
 
 ■ 311.6460 
 
 
 9 
 
 7374-5824 
 
 304.4203 
 
 3 
 
 7744.4107 
 
 311.9602 
 
 97 
 
 
 
 7389. 8113 
 
 304.7345 • 
 
 4 
 
 7760.0166 
 
 312.2743 
 
 
 I 
 
 7405.0559 
 
 305.0486 
 
 5 
 
 7775.6382 
 
 312. 588s 
 
 
 2 
 
 7420.3162 
 
 305.3628 
 
 6 
 
 7791-2764 
 
 312.9026 
 
 
 3 
 
 7435.5922 
 
 305.6770 
 
 7 
 
 7806.9284 
 
 313.2168 
 
 
 4 
 
 7450.8839 
 
 305.9911 
 
 8 
 
 7822.5971 
 
 313.5309 
 
 
 5 
 
 7466. 1913 
 
 306.3053 
 
 9 
 
 7838. 281S 
 
 313.8451 
 
 
 6 
 
 7481 . 5144 
 
 306.6194 100 
 
 
 
 7853.9816 
 
 314.1593 
 
 
 7 
 
 7496.8532 
 
 306.9336 
 
 
 
 
 To compute the area or circumference of a circle of a diameter greater than 
 100 and less than looi; 
 
 Take out the area or circumference from table as though the number 
 had one decimal, and move the decimal point two places to the right for 
 the area, and one place for the circumference. 
 
 Example. — Wanted the area and circumference of 567. The tabular 
 area for 56.7 is 2524.9687, and circumference 178.1283. Therefore area 
 for 567 = 252496.87 and circumference = 1781.283. 
 
 To compute the area or circumference of a circle of a diameter greater than 
 1000, 
 
 Divide by a factor, as 2, 3, 4, 5, etc., if practicable, that will leave a 
 quotient to be found in table, then multiply the tabular area of the 
 quotient by the square of the factor, or the tabular circumference by the 
 factor. 
 
 Example. — Wanted the area and circumference of 2109, Dividing 
 by 3, the quotient is 703, for which the area is 388150.84 and the circum- 
 ference 2208.54. Therefore area of 2109 = 388150.84 X 9 = 3493357-56 
 and circumference = 2208.54 X 3 = 6625.62. 
 
So 
 
 Mathematical Tables 
 
 Table of Circular Arcs 
 
 Length of circular arcs when the chord and the height of the arc are given. 
 
 Divide the height by the chord. Find in the column of Heights the number 
 equal to this quotient. 
 
 Take out the corresponding number from the column of lengths. 
 Multiply this last number by the length of the given chord. 
 
 Heights 
 
 Lengths 
 
 Heights 
 
 Lengths 
 
 Heights 
 
 Lengths 
 
 Heights 
 
 Lengths 
 
 .001 
 
 1.00002 
 
 .049 
 
 1.00638 
 
 .097 
 
 I. 02491 
 
 .145 
 
 I. 05516 
 
 .002 
 
 1.00002 
 
 .050 
 
 1.00665 
 
 .098 
 
 1.02542 
 
 .146 
 
 I -05591 
 
 .003 
 
 1.00003 
 
 .051 
 
 1.00692 
 
 •099 
 
 1.02593 
 
 • 147 
 
 1.05667 
 
 .004 
 
 1.00004 
 
 .052 
 
 1.00720 
 
 .100 
 
 1.02646 
 
 .148 
 
 1.05743 
 
 .005 
 
 1.00007 
 
 .CS3 
 
 1.00748 
 
 .101 
 
 1.02698 
 
 -149 
 
 I. 05819 
 
 .006 
 
 I.OOOIO 
 
 •OS4 
 
 I .00776 
 
 .102 
 
 1.02752 
 
 .150 
 
 1.05896 
 
 .007 
 
 I. 00013 
 
 .055 
 
 1.00805 
 
 .103 
 
 1.02806 
 
 ■ 151 
 
 I OS973 
 
 .008 
 
 I. 00017 
 
 .056 
 
 1.00834 
 
 .104 
 
 1.02860 
 
 .152 
 
 I. 06051 
 
 .009 
 
 1.00022 
 
 .057 
 
 1.00864 
 
 .105 
 
 I. 02914 
 
 • 153 
 
 I. 06130 
 
 .010 
 
 1.00027 
 
 .058 
 
 1.00895 
 
 .106 
 
 1.02970 
 
 -154 
 
 1.06209 
 
 .011 
 
 1.00032 
 
 .059 
 
 1.00926 
 
 .107 
 
 1.03026 
 
 • 155 
 
 1.06288 
 
 .012 
 
 1.00038 
 
 .060 
 
 1.00957 
 
 .108 
 
 1.03082 
 
 .156 
 
 1.06368 
 
 .013 
 
 1.00045 
 
 .061 
 
 1.00989 
 
 .109 
 
 I 03139 
 
 • 157 
 
 1.06449 
 
 .014 
 
 1.00053 
 
 .062 
 
 1.01021 
 
 .110 
 
 I. 03196 
 
 .158 
 
 1.06530 
 
 •ois 
 
 I. 00061 
 
 .063 
 
 I. 01054 
 
 .III 
 
 1.03254 
 
 ■159 
 
 1.06611 
 
 .016 
 
 1.00069 
 
 .064 
 
 I. 01088 
 
 .112 
 
 I. 03312 
 
 .160 
 
 1.06693 
 
 .017 
 
 1.00078 
 
 .065 
 
 1.01123 
 
 -113 
 
 I 03371 
 
 .161 
 
 1.0677s 
 
 .018 
 
 1.00087 
 
 .066 
 
 I. 01 158 
 
 .114 
 
 I 03430 
 
 .162 
 
 1.06858 
 
 .019 
 
 1.00097 
 
 .067 
 
 I. 01 193 
 
 • 115 
 
 1.03490 
 
 .163 
 
 I. 06941 
 
 .020 
 
 I. 00107 
 
 .068 
 
 I. 01228 
 
 .116 
 
 I. 03551 
 
 .164 
 
 1.07025 
 
 .021 
 
 1.00117 
 
 .069 
 
 I. 01264 
 
 .117 
 
 I. 0361 I 
 
 .16s 
 
 I. 07109 
 
 .022 
 
 I. 00128 
 
 .070 
 
 I. 01302 
 
 .iiS 
 
 1.03672 
 
 .166 
 
 I. 07194 
 
 .023 
 
 I. 00140 
 
 .071 
 
 I. 01338 
 
 .119 
 
 1.03734 
 
 .167 
 
 1.07279 
 
 .024 
 
 I. 00153 
 
 .072 
 
 I. 01376 
 
 .120 
 
 1-03797 
 
 .168 
 
 1.07365 
 
 .025 
 
 I. 00167 
 
 .073 
 
 1.01414 
 
 .121 
 
 1.03860 
 
 .169 
 
 I. 07451 
 
 .026 
 
 I. 00182 
 
 .074 
 
 I -01453 
 
 .122 
 
 1.03923 
 
 .170 
 
 I.07S37 
 
 .027 
 
 I. 00196 
 
 .075 
 
 I. 01493 
 
 .123 
 
 1.03987 
 
 .171 
 
 1.07624 
 
 .028 
 
 I. 002 10 
 
 .076 
 
 I -01533 
 
 .124 
 
 I. 04051 
 
 .172 
 
 I.077H 
 
 .029 
 
 1.00225 
 
 .077 
 
 I -01573 
 
 .125 
 
 I. 041 16 
 
 .173 
 
 1.07799 
 
 .030 
 
 I .00240 
 
 .078 
 
 1.01614 
 
 .126 
 
 1.04181 
 
 .174 
 
 1.07888 
 
 .031 
 
 1.00256 
 
 .079 
 
 I. 01656 
 
 .127 
 
 1.04247 
 
 .175 
 
 1.07977 
 
 .032 
 
 1.00272 
 
 .080 
 
 I. 01698 
 
 .128 
 
 1.04313 
 
 .176 
 
 1.08066 
 
 .033 
 
 1.00289 
 
 .081 
 
 1.01741 
 
 .129 
 
 1.04380 
 
 .177 
 
 I. 08156 
 
 -034 
 
 1.00307 
 
 .082 
 
 I. 01784 
 
 .130 
 
 1.04447 
 
 .178 
 
 1.08246 
 
 .035 
 
 1.00327 
 
 .083 
 
 I. 01828 
 
 .131 
 
 I. 04515 
 
 ■ .179 
 
 1.08337 
 
 .036 
 
 I.C034S 
 
 .0S4 
 
 I. 01872 
 
 .132 
 
 1.04584 
 
 .180 
 
 1.08428 
 
 .037 
 
 1.00364 
 
 .085 
 
 1.01916 
 
 • 133 
 
 1.04652 
 
 .181 
 
 I. 08519 
 
 .038 
 
 1.00384 
 
 .086 
 
 1.01961 
 
 .134 
 
 I .04722 
 
 .182 
 
 1.08611 
 
 .039 
 
 1.00405 
 
 .087 
 
 I .02006 
 
 • 135 
 
 I .04792 
 
 .183 
 
 1.08704 
 
 .040 
 
 1.00426 
 
 .088 
 
 1.02052 
 
 .136 
 
 1.04862 
 
 .184 
 
 1.08797 
 
 .041 
 
 1.00447 
 
 .089 
 
 1.02098 
 
 • 137 
 
 1.04932 
 
 .185 
 
 1.08890 
 
 .042 
 
 I .00469 
 
 .090 
 
 I. 02146 
 
 .138 
 
 1.05003 
 
 .186 
 
 1.08984 
 
 •043 
 
 1.00492 
 
 .091 
 
 I .02192 
 
 .139 
 
 1.05075 
 
 .187 
 
 1.09079 
 
 .044 
 
 I. 00515 
 
 .092 
 
 1.02240 
 
 .140 
 
 I. 05147 
 
 .188 
 
 I. 09174 
 
 .045 
 
 I.C50539 
 
 .093 
 
 1.02CS9 
 
 .141 
 
 1.05220 
 
 .189 
 
 1.09269 
 
 .046 
 
 1.00563 
 
 .094 
 
 1.02339 
 
 .142 
 
 1.05293 
 
 .190 
 
 1.0936s 
 
 .047 
 
 1.00587 
 
 .095 
 
 1.02389 
 
 .143 
 
 1.05367 
 
 .191 
 
 I. 09461 
 
 .048 
 
 I. 00612 
 
 .096 
 
 1.02440 
 
 .144 
 
 I. 05441 
 
 .192 
 
 I.09SS7 
 
Table of Circular Arcs 
 Table of Circular Arcs — (Contimied) 
 
 8i 
 
 Heights 
 
 Lengths 
 
 Heights 
 
 Lengths He 
 
 ights 
 
 Lengths He 
 
 ights L 
 
 engths 
 
 .193 
 
 1.09654 
 
 .248 
 
 I. 15670 
 
 303 
 
 1.22920 
 
 358 I 
 
 31276 
 
 .194 
 
 1.09752 
 
 .249 
 
 1.15791 
 
 304 
 
 1.23063 
 
 359 I 
 
 31437 
 
 .195 
 
 1.09850 
 
 .250 
 
 1.15912 
 
 30s 
 
 I . 23206 
 
 360 I 
 
 31599 
 
 .196 
 
 1.09949 
 
 .251 
 
 I. 16034 
 
 306 
 
 1.23349 
 
 361 I 
 
 31761 
 
 .197 
 
 I . 10048 
 
 .252 
 
 1.16156 
 
 307 
 
 1.23492 
 
 362 I 
 
 31923 
 
 .198 
 
 1 . 10147 
 
 .253 
 
 I. 16279 
 
 308 
 
 1.23636 
 
 363 I 
 
 32086 
 
 • 199 
 
 1. 10247 
 
 .254 
 
 I . 16402 
 
 309 
 
 I. 23781 
 
 364 I 
 
 32249 
 
 .200 
 
 I. 10347 
 
 .255 
 
 I . 16526 
 
 310 
 
 1.23926 
 
 365 I 
 
 32413 
 
 .201 
 
 I. 10447 
 
 .256 
 
 I . 16650 
 
 311 
 
 1.24070 
 
 366 I 
 
 32577 
 
 .202 
 
 I. 10548 
 
 .257 
 
 I . 16774 
 
 312 
 
 I. 24216 
 
 357 I 
 
 32741 
 
 .203 
 
 I. 10650 
 
 .258 
 
 I. 16899 
 
 313 
 
 I. 24361 
 
 368 I 
 
 3290s 
 
 .204 
 
 I.I07S2 
 
 .259 
 
 I . 17024 
 
 314 
 
 1.24507 
 
 369 I 
 
 33069 
 
 .205 
 
 I. 10855 
 
 .260 
 
 I . 17150 
 
 315 
 
 1.24654 
 
 370 I 
 
 33234 
 
 .206 
 
 I . 10958 
 
 .261 
 
 I. 17276 
 
 316 
 
 I . 24801 
 
 371 I 
 
 33399 
 
 .207 
 
 I.11062 
 
 .262 
 
 1.17403 
 
 317 
 
 1.24948 
 
 372 I 
 
 33564 
 
 .208 
 
 1.1116s 
 
 .263 
 
 I. 17530 
 
 318 
 
 1.25095 
 
 373 I 
 
 33730 
 
 .209 
 
 1.11269 
 
 .264 
 
 I . 17657 
 
 319 
 
 1.25243 
 
 374 I 
 
 33896 
 
 .210 
 
 I.11374 
 
 .265 
 
 I . 17784 
 
 320 
 
 I. 25391 
 
 375 I 
 
 34063 
 
 .211 
 
 I.I1479 
 
 .266 
 
 1.17912 
 
 321 
 
 1.25540 
 
 376 I 
 
 34229 
 
 .212 
 
 1.11S84 
 
 .267 
 
 I . 18040 
 
 322 
 
 1.25689 
 
 377 I 
 
 34396 
 
 .213 
 
 1.11690 
 
 .268 
 
 I . 18169 
 
 323 
 
 1.25838 
 
 378 I 
 
 34563 
 
 .214 
 
 1.I1796 
 
 .269 
 
 I . 18299 
 
 324 
 
 1.25988 
 
 379 I 
 
 34731 
 
 .215 
 
 I. I 1904 
 
 .270 
 
 I. 18429 
 
 325 
 
 I. 26138 
 
 380 I 
 
 34899 
 
 .216 
 
 1.12011 
 
 .271 
 
 I . 18559 
 
 326 
 
 1.26288 
 
 381 I 
 
 35068 
 
 .217 
 
 1.12118 
 
 .272 
 
 I. 18689 
 
 327 
 
 1.26437 
 
 382 I 
 
 35237 
 
 .218 
 
 I . 12225 
 
 .273 
 
 I . 18820 
 
 328 
 
 1.26588 
 
 383 I 
 
 35406 
 
 .219 
 
 I. 12334 
 
 .274 
 
 1.18951 
 
 329 
 
 I . 26740 
 
 384 I 
 
 35575 
 
 .220 
 
 I . 12444 
 
 .275 
 
 I. 19082 
 
 330 
 
 1.26892 
 
 385 I 
 
 35744 
 
 .221 
 
 I. 12554 
 
 .276 
 
 1.19214 
 
 331 
 
 1.27044 
 
 386 I 
 
 35914 
 
 .222 
 
 I. 12664 
 
 .277 
 
 I. 19346 
 
 332 
 
 1.27196 
 
 387 I 
 
 36084 
 
 .223 
 
 I. 12774 
 
 .278 
 
 I. 19479 
 
 333 
 
 1.27349 
 
 388 I 
 
 36254 
 
 .224 
 
 1.1288s 
 
 .279 
 
 1.19612 
 
 334 
 
 1.^502 
 
 389 I 
 
 36425 
 
 .225 
 
 I. 12997 
 
 .280 
 
 I . 19746 
 
 335 
 
 1.27656 
 
 390 I 
 
 36596 
 
 .226 
 
 I . 13108 
 
 .281 
 
 I . 19880 
 
 336 
 
 I. 27810 
 
 391 I 
 
 36767 
 
 .227 
 
 I . 13219 
 
 .282 
 
 I. 20014 
 
 337 
 
 1.27964 
 
 392 I 
 
 36939 
 
 .228 
 
 I.13331 
 
 .283 
 
 I. 20149 
 
 338 
 
 1.28118 
 
 393 I 
 
 37111 
 
 .229 
 
 I. 13444 
 
 .284 
 
 1.20284 
 
 339 
 
 1.28273 
 
 394 I 
 
 37283 
 
 .230 
 
 I. 13557 
 
 .28s 
 
 I . 20419 
 
 340 
 
 1.28428 
 
 395 I 
 
 37455 
 
 .231 
 
 1.13671 
 
 .286 
 
 I.20S5S 
 
 341 
 
 1.28583 
 
 396 I 
 
 37628 
 
 .232 
 
 I. 13785 
 
 .287 
 
 I. 20691 
 
 342 
 
 1.28739 
 
 397 I 
 
 37801 
 
 .233 
 
 I. 13900 
 
 .288 
 
 1.20827 
 
 343 
 
 1.28895 
 
 398 I 
 
 37974 
 
 .234 
 
 I-I4015 
 
 .279 
 
 1.20964 
 
 344 
 
 1.29052 
 
 399 I 
 
 38148 
 
 .235 
 
 I.14131 
 
 .290 
 
 I. 21 102 
 
 345 
 
 1.29209 
 
 400 I 
 
 .38322 
 
 .236 
 
 I. 14247 
 
 .291 
 
 I. 21239 
 
 346 
 
 1.29366 
 
 401 I 
 
 38496 
 
 .237 
 
 I. 14363 
 
 .292 
 
 I. 21377 
 
 347 
 
 1.29523 
 
 402 I 
 
 38671 
 
 .238 
 
 I. 14480 
 
 .293 
 
 1.21515 
 
 348 
 
 I. 29681 
 
 403 I 
 
 38846 
 
 .239 
 
 I. 14597 
 
 .294 
 
 1.21654- 
 
 349 
 
 1.29839 
 
 404 I 
 
 39021 
 
 .240 
 
 I.14714 
 
 .295 
 
 I. 21794 
 
 350 
 
 1.29997 
 
 405 I 
 
 39196 
 
 .241 
 
 I. 14832 
 
 .296 
 
 I. 21933 
 
 351 
 
 1.30156 
 
 406 I 
 
 39372 
 
 .242 
 
 I . 14951 
 
 .297 
 
 1.22073 
 
 352 
 
 1.3031S 
 
 407 I 
 
 .39548 
 
 .243 
 
 I . 15070 
 
 .298 
 
 I. 22213 
 
 .353 
 
 1.30474 
 
 408 I 
 
 39724 
 
 .244 
 
 1.IS189 
 
 .299 
 
 1.22354 
 
 .354 
 
 1.30634 
 
 409 I 
 
 39900 
 
 .245 
 
 I . 15308 
 
 .300 
 
 1.22495 
 
 .355 
 
 1.30794 
 
 410 I 
 
 .40077 
 
 .246 
 
 I. 15428 
 
 .301 
 
 1.22636 
 
 .356 
 
 1.30954 
 
 411 I 
 
 40254 
 
 .247 
 
 I . 15549 
 
 .302 
 
 1.22778 
 
 .357 
 
 I.3111S 
 
 .412 I 
 
 .40432 
 
82 
 
 Mathematical Tables 
 Table of Circular Arcs — {Concluded) 
 
 Heights 
 
 Lengths 
 
 Heights 
 
 Lengths 
 
 Heights 
 
 Lengths He 
 
 ights 
 
 Lengths 
 
 .413 
 
 1. 40610 
 
 .435 
 
 1.44589 
 
 .457 
 
 1.48699 
 
 479 
 
 1.52931 
 
 .414 
 
 
 40788 
 
 .436 
 
 
 44773 
 
 .458 
 
 1.48889 
 
 480 
 
 1. 53126 
 
 .415 
 
 
 40966 
 
 .437 
 
 
 44957 
 
 .459 
 
 1.49079 
 
 481 
 
 1.53322 
 
 .416 
 
 
 41145 
 
 .438 
 
 
 45142 
 
 .460 
 
 1.49269 
 
 482 
 
 I. 53518 
 
 .417 
 
 
 41324 
 
 .439 
 
 
 45327 
 
 .461 
 
 1.49460 
 
 483 
 
 I. 53714 
 
 .418 
 
 
 41503 
 
 .440 
 
 
 45512 
 
 .462 
 
 I. 49651 
 
 484 
 
 I. 53910 
 
 .419 
 
 
 41682 
 
 .441 
 
 
 45697 
 
 .463 
 
 1.49842 
 
 485 
 
 I . 54106 
 
 .420 
 
 
 41861 
 
 .442 
 
 
 45883 
 
 .464 
 
 1.50033 
 
 486 
 
 1.54302 
 
 .421 
 
 
 42041 
 
 .443 
 
 
 46069 
 
 .465 
 
 1.50224 
 
 487 
 
 1.54499 
 
 .422 
 
 
 42221 
 
 -.444 
 
 
 46255 
 
 .466 
 
 I. 50416 
 
 488 
 
 1.54696 
 
 .423 
 
 
 42402 
 
 .445 
 
 
 46441 
 
 .467 
 
 1.50608 
 
 489 
 
 1.54893 
 
 .424 
 
 
 42583 
 
 .446 
 
 
 46628 
 
 .468 
 
 1.50800 
 
 490 
 
 I. 55091 
 
 .42s 
 
 
 42764 
 
 .447 
 
 
 46815 
 
 .469 
 
 1.50992 
 
 491 
 
 1.55289 
 
 .426 
 
 
 42945 
 
 .448 
 
 •'• 
 
 47002 
 
 .470 
 
 1.51185 
 
 492 
 
 1.55487 
 
 .427 
 
 
 43127 
 
 .449 
 
 
 47189 
 
 .471 
 
 I. 51378 
 
 493 
 
 1.5568s 
 
 .428 
 
 
 43309 
 
 .450 
 
 
 47377 
 
 .472 
 
 1.51571 
 
 494 
 
 1.55884 
 
 .429 
 
 
 43491 
 
 .451 
 
 
 4756s 
 
 .473 
 
 I. 51764 
 
 495 
 
 1.56083 
 
 .430 
 
 
 43673 
 
 .452 
 
 
 47753 
 
 .474 
 
 I. 51958 
 
 496 
 
 1.56282 
 
 .431 
 
 
 43856 
 
 .453 
 
 
 47942 
 
 .475 
 
 I. 52152 
 
 497 
 
 1.56481 
 
 .432 
 
 
 44039 
 
 .454 
 
 
 48131 
 
 .476 
 
 1.52346 
 
 498 
 
 1.56681 
 
 .433 
 
 
 44222 
 
 .455 
 
 
 48320 
 
 .477 
 
 I. 52541 
 
 499 
 
 I. 56881 
 
 .434 
 
 
 44405 
 
 .456 
 
 
 48509 
 
 .478 
 
 1.52736 
 
 500 
 
 1.57080 
 
 Lengths of Circular Arcs to Radius 1 
 
 To find the length of a circular arc by the following table 
 
 Knowing the radius of the circle and the measure of the arc in deg., 
 min., etc. 
 
 Rule. — Add together the lengths in the table found respectively 
 opposite to the deg., min., etc., of the arc. Multiply the sum by the 
 radius of the circle. 
 
 Example. — In a circle of 12.43 f^et radius, is an arc of 13 deg., 27 min., 
 8 sec. How long is the arc? 
 
 Here, opposite 13 deg. in the table, we find .2268928 
 
 " 27 min. " " " " .0078540 
 " • 8 sec. " " " " .0000388 
 
 Sum =.2347856 
 
 And .2347856 X 12.43, or radius = 2.918385 feet, the required length 
 of arc. 
 
Lengths of Circular Arcs to Radius i 83 
 
 Lengths of Circular Arcs to Radius i 
 
 Deg. 
 
 Length 
 
 Deg. 
 
 Length 
 
 Deg. 
 
 Length 
 
 Deg. 
 136 
 
 Length 
 
 I 
 
 .0174533 
 
 46 
 
 .8028515 
 
 91 
 
 1.5882496 
 
 2.3736478 
 
 2 
 
 .0349066 
 
 47 
 
 .8203047 
 
 92 
 
 1.6057029 
 
 137 
 
 2. 391 ion 
 
 3 
 
 .0523599 
 
 48 
 
 .8377580 
 
 93 
 
 I. 6231562 
 
 138 
 
 2.4085544 
 
 4 
 
 .0698132 
 
 49 
 
 .8552113 
 
 94 
 
 I . 6406095 
 
 139 
 
 2 . 4260077 
 
 5 
 
 087266s 
 
 50 
 
 .8726646 
 
 95 
 
 1.6580628 
 
 140 
 
 2.4434610 
 
 6 
 
 .1047198 
 
 SI 
 
 .8901179 
 
 96 
 
 1.6755161 
 
 141 
 
 2 . 4609142 
 
 7 
 
 .1221730 
 
 52 
 
 .9075712 
 
 97 
 
 1.6929694 
 
 142 
 
 2.4783675 
 
 8 
 
 .1396263 
 
 53 
 
 .9250245 
 
 98 
 
 I. 7104227 
 
 143 
 
 2.4958208 
 
 9 
 
 .1570796 
 
 54 
 
 .9424778 
 
 99 
 
 I . 7278760 
 
 144 
 
 2.5132741 
 
 10 
 
 .1745329 
 
 55 
 
 .9593911 
 
 100 
 
 1.7453293 
 
 145 
 
 2.5307274 
 
 II 
 
 . 1919862 
 
 56 
 
 .9773844 
 
 lOI 
 
 1.762782s 
 
 146 
 
 2.5481807 
 
 12 
 
 .2094395 
 
 57 
 
 .9948377 
 
 102 
 
 1.7802358 
 
 147 
 
 2.5656340 
 
 13 
 
 .2268928 
 
 58 
 
 1.0122910 
 
 103 
 
 I. 7976891 
 
 148 
 
 2.5830873 
 
 14 
 
 .2443461 
 
 59 
 
 1.0297443 
 
 104 
 
 1.8151424 
 
 149 
 
 2.6005406 
 
 IS 
 
 .2617994 
 
 60 
 
 I. 047 1976 
 
 105 
 
 1.8325957 
 
 150 
 
 2.6179939 
 
 16 
 
 . 2792527 
 
 61 
 
 1.0646508 
 
 106 
 
 1.8500490 
 
 151 
 
 2.6354472 
 
 17 
 
 . 2967060 
 
 62 
 
 1.0821041 
 
 107 
 
 1.8675023 
 
 152 
 
 2.6529005 
 
 18 
 
 .3141593 
 
 63 
 
 1.0995574 
 
 108 
 
 1.8849556 
 
 153 
 
 2.6703538 
 
 19 
 
 .3316126 
 
 64 
 
 I . 1170107 
 
 109 
 
 1.9024089 
 
 154 
 
 2.6878070 
 
 20 
 
 .3490659 
 
 65 
 
 I. 1344640 
 
 no 
 
 I. 9198622 
 
 I5S 
 
 2.7052603 
 
 21 
 
 .3665191 
 
 66 
 
 1.1519173 
 
 III 
 
 I. 9373155 
 
 156 
 
 2.7227136 
 
 22 
 
 .3839724 
 
 67 
 
 I . 1693706 
 
 112 
 
 1.9547688 
 
 157 
 
 2 . 7401669 
 
 23 
 
 .4014257 
 
 68 
 
 I . X868239 
 
 113 
 
 1,9722221 
 
 158 
 
 2 . 7576202 
 
 24 
 
 .4188790 
 
 69 
 
 1.2042772 
 
 114 
 
 1.9896753 
 
 159 
 
 2.7750735 
 
 25 
 
 .4363323 
 
 70 
 
 I. 2217305 
 
 115 
 
 2.0071286 
 
 160 
 
 2.7925268 
 
 26 
 
 .4537856 
 
 71 
 
 I. 2391838 
 
 116 
 
 2.0245819 
 
 161 
 
 2 . 8099801 
 
 27 
 
 .4712389 
 
 72 
 
 I. 2566371 
 
 117 
 
 2.0420352 
 
 162 
 
 2.8274334 
 
 28 
 
 .4886922 
 
 73 
 
 1.2740904 
 
 118 
 
 2.0594885 
 
 163 
 
 2 . 8448867 
 
 29 
 
 .5061455 
 
 74 
 
 I. 2915436 
 
 119 
 
 2.0769418 
 
 164 
 
 2.8623400 
 
 30 
 
 .5235988 
 
 75 
 
 1.3089969 
 
 120 
 
 2.0943951 
 
 165 
 
 2.8797933 
 
 31 
 
 .5410521 
 
 76 
 
 1.3264502 
 
 121 
 
 2. I I 18484 
 
 166 
 
 2.8972466 
 
 32 
 
 .5585054 
 
 77 
 
 1.343903s 
 
 122 
 
 2.1293017 
 
 167 
 
 2.9146999 
 
 33 
 
 .5759587 
 
 78 
 
 I. 3613568 
 
 123 
 
 2 . 1467550 
 
 168 
 
 2.9321531 
 
 34 
 
 .5934119 
 
 79 
 
 1.3788101 
 
 124 
 
 2 . 1642083 
 
 169 
 
 2.9496064 
 
 35 
 
 .6108652 
 
 80 
 
 1.3962634 
 
 125 
 
 2.1816616 
 
 170 
 
 2.9670597 
 
 36 
 
 .6283185 
 
 81 
 
 1.4137167 
 
 126 
 
 2.1991149 
 
 171 
 
 2.9845130 
 
 37 
 
 .6457718 
 
 82 
 
 1.4311700 
 
 127 
 
 2.2165682 
 
 172 
 
 3.0019663 
 
 38 
 
 .6632251 
 
 83 
 
 1.4486233 
 
 128 
 
 2.2340214 
 
 173 
 
 3.0194x96 
 
 39 
 
 .6806784 
 
 84 
 
 1.4660766 
 
 129 
 
 2.2514747 
 
 174 
 
 3.0368729 
 
 40 
 
 .6981317 
 
 . 85 
 
 1.4835299 
 
 130 
 
 2.2689280 
 
 175 
 
 3.0543262 
 
 41 
 
 .7155850 
 
 86 
 
 1.5009832 
 
 131 
 
 2.2863813 
 
 176 
 
 3.0717795 
 
 42 
 
 .7330383 
 
 87 
 
 I. 5184364 
 
 132 
 
 2.3038346 
 
 177 
 
 3.0892328 
 
 43 
 
 .7504916 
 
 88 
 
 1.5358897 
 
 133 
 
 2.3212879 
 
 178 
 
 3.1066861 
 
 44 
 
 .7679449 
 
 89 
 
 I • 5533430 
 
 134 
 
 2.3387412 
 
 179 
 
 3.1241394 
 
 45 
 
 .7853982 
 
 90 
 
 1.5707963 
 
 135 
 
 2.3561945 
 
 180 
 
 3.1415927 
 
 Min. 
 
 Length 
 
 Min. 
 
 Length 
 
 Min. 
 
 Length 
 
 Min. 
 
 Length 
 
 I 
 
 .0002909 
 
 6 
 
 .OOI74S3 
 
 II 
 
 .0031998 
 
 16 
 
 .0046542 
 
 2 
 
 .0005818 
 
 7 
 
 .0020362 
 
 12 
 
 .0034907 
 
 17 
 
 .0049451 
 
 3 
 
 .0008727 
 
 8 
 
 .0023271 
 
 13 
 
 .0037815 
 
 18 
 
 .0052360 
 
 4 
 
 .0011636 
 
 9 
 
 .0026180 
 
 14 
 
 .0040724 
 
 19 
 
 .0055269 
 
 5 
 
 .0014544 
 
 10 
 
 .0029089 
 
 15 
 
 .0043633 
 
 20 
 
 .0058178 
 
84 Mathematical Tables 
 
 Lengths or Circular Aecs to Radius i — {Continued) 
 
 Min. 
 
 Length 
 
 Min. 
 
 Length 
 
 Min. 
 
 Length 
 
 Min. 
 
 Length 
 
 21 
 
 .0061087 
 
 31 
 
 .0090175 
 
 • 
 41 
 
 .0119264 
 
 SI 
 
 0148353 
 
 22 
 
 .0063995 
 
 32 
 
 .0093084 
 
 42 
 
 .0122173 
 
 52 
 
 .0151262 
 
 23 
 
 .0066904 
 
 33 
 
 .0095993 
 
 43 
 
 .0125082 
 
 53 
 
 .0154171 
 
 24 
 
 .0069813 
 
 34 
 
 .0098902 
 
 44 
 
 .0127991 
 
 54 
 
 0157080 
 
 25 
 
 .0072722 
 
 35 
 
 .0101811 
 
 45 
 
 .0130900 
 
 55 
 
 .0159989 
 
 26 
 
 .0075631 
 
 36 
 
 .0104720 
 
 46 
 
 .0133809 
 
 56 
 
 .0162897 
 
 27 
 
 .0078540 
 
 37 
 
 .0107629 
 
 47 
 
 .0136717 
 
 57 
 
 .0165806 
 
 28 
 
 .00S1449 
 
 38 
 
 .0110538 
 
 48 
 
 .0139626 
 
 58 
 
 .0168715 
 
 29 
 
 .0084358 
 
 39 
 
 .0113446 
 
 49 
 
 .0142535 
 
 59 
 
 .0171624 
 
 30 
 
 .oc^7266 
 
 40 
 
 .0116355 
 
 50 
 
 .0145444 
 
 1 
 
 60 
 
 .0174533 
 
 Sec. 
 
 Length 
 
 Sec. 
 
 Length 
 
 Sec. 
 
 Length 
 
 Sec. 
 
 Length 
 
 I 
 
 .0000048 
 
 16 
 
 .0000776 
 
 31 
 
 .0001503 
 
 46 
 
 .0002230 
 
 2 
 
 0000097 
 
 17 
 
 .0000824 
 
 32 
 
 .0001551 
 
 47 
 
 .0002279 
 
 3 
 
 .0000145 
 
 18 
 
 .0000873 
 
 33 
 
 .0001600 
 
 48 
 
 .0002327 
 
 4 
 
 .0000194 
 
 19 
 
 .0000921 
 
 34 
 
 .0001648 
 
 49 
 
 .0002376 
 
 5 
 
 0000242 
 
 20 
 
 .0000970 
 
 35 
 
 .0001697 
 
 50 
 
 .0002424 
 
 6 
 
 0000291 
 
 21 
 
 .0001018 
 
 36 
 
 .0001745 
 
 51 
 
 .0002473 
 
 7 
 
 0000339 
 
 22 
 
 .0001067 
 
 37 
 
 .0001794 
 
 52 
 
 .0002521 
 
 8 
 
 0000388 
 
 23 
 
 .0001115 
 
 38 
 
 .0001842 
 
 53 
 
 .0002570 
 
 9 
 
 0000430 
 
 24 
 
 .0001164 
 
 39 
 
 .0001891 
 
 54 
 
 .0002618 
 
 10 
 
 0000485 
 
 25 
 
 .0001212 
 
 40 
 
 .0001939 
 
 55 
 
 .0002666 
 
 II 
 
 0000533 
 
 26 
 
 .0001261 
 
 41 
 
 .0001988 
 
 56 
 
 .0002715 
 
 12 
 
 0000582 
 
 27 
 
 .0001309 
 
 42 
 
 .0002036 
 
 . 57 
 
 .0002763 
 
 13 
 
 0000630 
 
 28 
 
 .0001357 
 
 43 
 
 .0002085 
 
 58 
 
 .0002812 
 
 14 
 
 0000679 
 
 29 
 
 .0001406 
 
 44 
 
 .0002133 
 
 59 
 
 .0002860 
 
 15 
 
 0000727 
 
 30 
 
 .0001454 
 
 45 
 
 .0002182 
 
 1 
 
 60 
 
 .0002909 
 
 Table of Areas of Circular Segments 
 
 If the segment exceeds a semicircle, its area = area of circle — area of a segment 
 whose rise = (diam. of circle — rise of given segment). Diam. of circle = (square 
 of half chord -^ rise) + rise, whether the segment exceeds a semicircle or not. 
 
 Rise 
 divided 
 by diam. 
 
 Area = 
 
 (square 
 
 of diam.) 
 
 multi- 
 
 Rise 
 divided 
 by diam. 
 
 Area = 
 
 (square 
 
 of diam.) 
 
 multi- 
 
 Rise 
 divided 
 by diam. 
 
 Area = 
 
 (square 
 
 of diam.) 
 
 multi- 
 
 Rise 
 divided 
 by diam. 
 
 Area = 
 
 (square 
 
 of diam.) 
 
 of circle 
 
 plied by 
 
 of circle 
 
 plied by 
 
 of circle 
 
 plied by 
 
 of circle 
 
 plied by 
 
 .001 
 
 .000042 
 
 .010 
 
 .001329 
 
 .019 
 
 .003472 
 
 .028 
 
 .006194 
 
 .002 
 
 .000119 
 
 .011 
 
 .001533 
 
 .020 
 
 .003749 
 
 .029 
 
 .006527 
 
 .003 
 
 .000219 
 
 .012 
 
 .001746 
 
 .021 
 
 .004032 
 
 .030 
 
 .006866 
 
 .004 
 
 .000337 
 
 .013 
 
 .001969 
 
 .022 
 
 .004322 
 
 .031 
 
 .007209 
 
 .005 
 
 .000471 
 
 .014 
 
 .002199 
 
 .023 
 
 .004619 
 
 .032 
 
 .007559 
 
 .006 
 
 .000619 
 
 .015 
 
 .002438 
 
 .024 
 
 .004922 
 
 .033 
 
 .007913 
 
 .007 
 
 .000779 
 
 .016 
 
 .002685 
 
 .025 
 
 .005231 
 
 .034 
 
 .008273 
 
 .008 
 
 .000952 
 
 .017 
 
 .002940 
 
 .026 
 
 .005546 
 
 .035 
 
 .008638 
 
 .009 
 
 .001135 
 
 .018 
 
 .003202 
 
 .027 
 
 .005867 
 
 .036 
 
 .009008 
 
Table of Areas of Circular Segments 
 
 8s 
 
 
 Table of 
 
 Areas of Circular Segments — 
 
 {Continued) 
 
 Rise 
 divided 
 by diam. 
 
 Area = 
 
 (square 
 
 of diam.) 
 
 Rise 
 divided 
 by diam. 
 
 Area = 
 
 (square 
 
 of diam.) 
 
 multi- 
 
 _ . Area = 
 
 ^^}f^ (square 
 divided ^f^i^^_) 
 
 by diam. ^^j^.. 
 
 Rise 
 divided 
 by diam. 
 
 Area= 
 
 (square 
 
 of diam.) 
 
 multi- 
 
 of circle 
 
 plied by 
 
 of circle 
 
 plied by 
 
 °f"^^^« plied by 
 
 of circle 
 
 plied by 
 
 .037 
 
 .009383 
 
 .087 
 
 .033308 
 
 .137 
 
 .064761 
 
 .187 
 
 . IOISS3 
 
 
 .038 
 
 .009764 
 
 .088 
 
 .033873 
 
 .138 
 
 .065449 
 
 .188 
 
 ■ 102334 
 
 
 .039 
 
 .010148 
 
 .089 
 
 .034441 
 
 .139 
 
 .066140 
 
 .189 
 
 • 103116 
 
 
 .040 
 
 .010538 
 
 .090 
 
 .035012 
 
 .140 
 
 .066833 
 
 .190 
 
 .103900 
 
 
 .041 
 
 .010932 
 
 .091 
 
 .035586 
 
 .141 
 
 067528 
 
 .191 
 
 . 104686 
 
 
 .042 
 
 .011331 
 
 .092 
 
 .036162 
 
 ,142 
 
 068225 
 
 .192 
 
 . 105472 
 
 
 •043 
 
 .011734 
 
 .093 
 
 .036742 
 
 .143 
 
 068924 
 
 .193 
 
 . 106261 
 
 
 .044 
 
 .012142 
 
 .094 
 
 •037324 
 
 .144 
 
 069626 
 
 .194 
 
 . 107051 
 
 
 04s 
 
 .012555 
 
 .095 
 
 .037909 
 
 .145 
 
 070329 
 
 • 195 
 
 .X07843 
 
 
 .046 
 
 .012971 
 
 .096 
 
 , .038497 
 
 .146 
 
 071034 
 
 .196 
 
 .108636 
 
 
 .047 
 
 .013393 
 
 .097 
 
 .039087 
 
 • 147 
 
 071741 
 
 .197 
 
 -109431 
 
 
 .048 
 
 .013818 
 
 .098 
 
 .039681 
 
 .148 
 
 072450 
 
 .198 
 
 . 110227 
 
 
 .049 
 
 .014248 
 
 .099 
 
 .040277 
 
 .149 
 
 073162 
 
 .199 
 
 . 111025 
 
 
 .oso 
 
 .014681 
 
 .100 
 
 .040875 
 
 .ISO 
 
 073875 
 
 .200 
 
 . 111824 
 
 
 .051 
 
 .015119 
 
 .101 
 
 .041477 
 
 .151 
 
 074590 
 
 .201 
 
 .112625 
 
 
 .052 
 
 .015561 
 
 .102 
 
 .042081 
 
 .152 
 
 075307 
 
 .202 
 
 .113427 
 
 
 053 
 
 .016008 
 
 .103 
 
 .042687 
 
 .153 
 
 076026 
 
 .203 
 
 .114231 
 
 
 OS4 
 
 .016458 
 
 .104 
 
 .043296 
 
 .154 
 
 076747 
 
 .204 
 
 .115036 
 
 
 055 
 
 .016912 
 
 .105 
 
 .043908 
 
 .155 
 
 077470 
 
 .205 
 
 .115842 
 
 
 056 
 
 .017369 
 
 .106 
 
 •044523 
 
 .156 
 
 078194 
 
 .206 
 
 .116651 
 
 
 057 
 
 .017831 
 
 .107 
 
 .045140 
 
 .157 
 
 078921 
 
 .207 
 
 .117460 
 
 
 058 
 
 .018297 
 
 .108 
 
 •0457S9 
 
 .158 
 
 079650 
 
 .208 
 
 .118271 
 
 
 059 
 
 .018766 
 
 .109 
 
 .046381 
 
 .159 
 
 080380 
 
 .209 
 
 .119084 
 
 
 060 
 
 .019239 
 
 .110 
 
 .047006 
 
 .160 
 
 081 I 12 
 
 .210 
 
 .119898 
 
 
 061 
 
 .019716 
 
 .III 
 
 •047633 
 
 .161 
 
 081847 
 
 .211 
 
 .120713 
 
 
 062 
 
 .020197 
 
 .112 
 
 .048262 
 
 .162 
 
 082582 
 
 .212 
 
 •121530 
 
 
 063 
 
 .020681 
 
 .113 
 
 .048894 
 
 .163 
 
 083320 
 
 .213 
 
 .122348 
 
 
 064 
 
 .021168 
 
 .114 
 
 .049529 
 
 .164 
 
 084060 
 
 .214 
 
 .r23i67 
 
 
 065 
 
 .021660 
 
 .115 
 
 .050165 
 
 .165 
 
 084801 
 
 .215 
 
 .123988 
 
 
 066 
 
 .022155 
 
 .116 
 
 .050805 
 
 .166 
 
 085545 
 
 .216 
 
 . 124811 
 
 
 067 
 
 .0236S3 
 
 .117 
 
 .051446 
 
 .167 
 
 086290 
 
 .217 
 
 •125634 
 
 
 068 
 
 .023155 
 
 .118 
 
 .052090 
 
 .168 
 
 087037 
 
 .218 
 
 . 126459 
 
 
 069 
 
 .023660 
 
 .119 
 
 .052737 
 
 .169 
 
 087785 
 
 .219 
 
 . 127286 
 
 
 070 
 
 .024168 
 
 .120 
 
 •053385 
 
 .170 
 
 088536 
 
 .220 
 
 .128114 
 
 
 071 
 
 .024680 
 
 .121 
 
 •054037 
 
 .171 
 
 089288 
 
 .221 
 
 .128943 
 
 
 072 
 
 .025196 
 
 .122 
 
 .054690 
 
 .172 
 
 090042 
 
 .222 
 
 .129773 
 
 
 073 
 
 .025714 
 
 .123 
 
 •055346 
 
 .173 
 
 090797 
 
 .223 
 
 .13060S 
 
 
 074 
 
 .026236 
 
 .124 
 
 .056004 
 
 .174 
 
 091555 
 
 .224 
 
 .131438 
 
 
 075 
 
 .026761 
 
 .125 
 
 .056664 
 
 .175 
 
 092314 
 
 .225 
 
 .132273 
 
 
 076 
 
 .027290 
 
 .126 
 
 .057327 
 
 .176 
 
 093074 
 
 .226 
 
 .133109 
 
 
 077 
 
 .027821 
 
 .127 
 
 •057991 
 
 .177 
 
 093837 
 
 .227 
 
 .133946 
 
 
 078 
 
 .028356 
 
 .128 
 
 .058658 
 
 .178 
 
 094601 
 
 .228 
 
 .134784 
 
 
 079 
 
 .028894 
 
 .129 
 
 .059328 
 
 .179 
 
 095367 
 
 .229 
 
 .135624 
 
 
 080 
 
 .029435 
 
 -.130 
 
 ■059999 
 
 .180 
 
 096135 
 
 .230 
 
 .13646S 
 
 
 081 
 
 .029979 
 
 .131 
 
 .060673 
 
 .181 
 
 096904 
 
 .231 
 
 .137307 
 
 
 082 
 
 .030526 
 
 .132 
 
 .061349 
 
 .182 
 
 097675 
 
 .232 
 
 .138151 
 
 
 083 
 
 .031077 
 
 .133 
 
 .062027 
 
 .183 
 
 098447 
 
 .233 
 
 .138996 
 
 
 084 
 
 .031630 
 
 .134 
 
 .062707 
 
 .184 
 
 099221 
 
 .234 
 
 .139842 
 
 
 085 
 
 .032186 
 
 .1.35 
 
 .063389 
 
 .185 
 
 099997 
 
 .235 
 
 .140689 
 
 !o86 
 
 .032746 
 
 .136 
 
 .064074 
 
 .186 
 
 100774 
 
 .236 
 
 .141538 
 
S6 
 
 Mathematical Tables 
 
 Table of 
 
 Areas 
 
 DF Circular Segments — 
 
 (Continued) 
 
 Rise 
 divided 
 by diam. 
 
 Area = 
 
 (square 
 
 of diam.) 
 
 multi- 
 
 Rise 
 divided 
 by diam. 
 
 Area = 
 
 (square 
 
 of diam.) 
 
 multi- 
 
 Rise 
 divided 
 by diam. 
 
 Area = 
 (square 
 of diam.) 
 multi- 
 
 Rise 
 divided 
 by diam. 
 
 Area = 
 
 (square 
 
 of diam.) 
 
 multi- 
 
 of circle 
 
 plied by 
 
 of circle 
 
 plied by 
 
 of circle 
 
 plied by 
 
 of circle 
 
 pUed by 
 
 .237 
 
 .142388 
 
 .287 
 
 . 186329 
 
 .337 
 
 .232634 
 
 .387 
 
 .280669 
 
 .238 
 
 .143239 
 
 .288 
 
 . 187235 
 
 .338 
 
 .233580 
 
 .388 
 
 .281643 
 
 .239 
 
 . 144091 
 
 .289 
 
 . 188141 
 
 .339 
 
 .234526 
 
 .389 
 
 .282618 
 
 ..240 
 
 .144945 
 
 .290 
 
 .189048 
 
 .340 
 
 .235473 
 
 .390 
 
 .283593 
 
 .241 
 
 .145800 
 
 .291 
 
 .189956 
 
 .341 
 
 .236421 
 
 .391 
 
 .284569 
 
 .242 
 
 .146656 
 
 .292 
 
 .190865 
 
 .342 
 
 .237369 
 
 .392 
 
 .285545 
 
 .243 
 
 .147513 
 
 .293 
 
 .191774 
 
 .343 
 
 .238319 
 
 .393 
 
 .286521 
 
 .244 
 
 .148371 
 
 .294 
 
 . 192685 
 
 .344 
 
 .239268 
 
 .394 
 
 .287499 
 
 .245 
 
 .149231 
 
 .295 
 
 .193597 
 
 .345 
 
 .240219 
 
 .395 
 
 .288476 
 
 .246 
 
 .150091 
 
 .296 
 
 .194509 
 
 .346 
 
 .241170 
 
 .396 
 
 .289454 
 
 .247 
 
 .150953 
 
 .297 
 
 .195423 
 
 .347 
 
 .242122 
 
 .397 
 
 .290432 
 
 .248 
 
 .151816 
 
 .298 
 
 .196337 
 
 .348 
 
 .243074 
 
 .398 
 
 .291411 
 
 .249 
 
 . 152681 
 
 .299 
 
 .197252 
 
 .349 
 
 .244027 
 
 -399 
 
 .292390 
 
 .250 
 
 .153546 
 
 .300 
 
 .198168 
 
 .350 
 
 .244980 
 
 .400 
 
 .293370 
 
 .251 
 
 .154413 
 
 .301 
 
 .199085 
 
 .351 
 
 .245935 
 
 .401 
 
 .294350 
 
 .252 
 
 .155281 
 
 .302 
 
 .200003 
 
 .352 
 
 .246890 
 
 .402 
 
 .295330 
 
 .253 
 
 .156149 
 
 .303 
 
 .200922 
 
 .353 
 
 .247845 
 
 .403 
 
 .296311 
 
 .254 
 
 .157019 
 
 .304 
 
 . 201841 
 
 .354 
 
 .248801 
 
 .404 
 
 .297292 
 
 .255 
 
 .157891 
 
 .305 
 
 .202762 
 
 .355 
 
 .249758 
 
 .40s 
 
 .298274 
 
 .256 
 
 .158763 
 
 .306 
 
 .203683 
 
 .356 
 
 .250715 
 
 .406 
 
 .299256 
 
 .257 
 
 .159636 
 
 .307 
 
 . 204605 
 
 .357 
 
 .251673 
 
 .407 
 
 .300238 
 
 .258 
 
 .160511 
 
 .308 
 
 . 205528 
 
 .358 
 
 .252632 
 
 .408 
 
 .301221 
 
 .259 
 
 .161386 
 
 .309 
 
 .206452 
 
 .359 
 
 .253591 
 
 .409 
 
 .302204 
 
 .260 
 
 . 162263 
 
 .310 
 
 .207376 
 
 .360 
 
 .254551 
 
 .410 
 
 .303187 
 
 .261 
 
 . 163141 
 
 .311 
 
 .208302 
 
 .361 
 
 .255511 
 
 .411 
 
 .304171 
 
 .262 
 
 . 164026 
 
 .312 
 
 .209228 
 
 .362 
 
 .256472 
 
 .412 
 
 .305156 
 
 .263 
 
 .164900 
 
 .313 
 
 .2IOI5S 
 
 .363 
 
 .257433 
 
 .413 
 
 .306140 
 
 .264 
 
 .165781 
 
 .314 
 
 .211083 
 
 .364 
 
 .258395 
 
 .414 
 
 .307125 
 
 .26s 
 
 .166663 
 
 .315 
 
 .212011 
 
 .365 
 
 .259358 
 
 .415 
 
 .308110 
 
 .266 
 
 .167546 
 
 .316 
 
 .212941 
 
 .366 
 
 .260321 
 
 .416 
 
 .309096 
 
 .267 
 
 .168431 
 
 .317 
 
 .213871 
 
 .367 
 
 .261285 
 
 .417 
 
 .310082 
 
 .268 
 
 . 169316 
 
 .318 
 
 . 214802 
 
 .368 
 
 .262249 
 
 .418 
 
 .311068 
 
 .269 
 
 .170202 
 
 .319 
 
 .215734 
 
 .369 
 
 .263214 
 
 .419 
 
 .312055 
 
 .270 
 
 .171090 
 
 .320 
 
 .216666 
 
 .370 
 
 .264179 
 
 .420 
 
 .313042 
 
 .271 
 
 .171978 
 
 .321 
 
 .217600 
 
 .371 
 
 .265145 
 
 .421 
 
 .314029 
 
 .272 
 
 .172868 
 
 .322 
 
 .218534 
 
 .372 
 
 .266111 
 
 .422 
 
 .315017 
 
 .273 
 
 .173758 
 
 .323 
 
 .219469 
 
 .373 
 
 .267078 
 
 .423 
 
 .316005 
 
 .274 
 
 . 174650 
 
 .324 
 
 .220404 
 
 .374 
 
 .268046 
 
 .424 
 
 .316993 
 
 .275 
 
 .175542 
 
 .325 
 
 .221341 
 
 .375 
 
 .269014 
 
 .425 
 
 .317981 
 
 .276 
 
 . 176436 
 
 .326 
 
 . 222278 
 
 .376 
 
 .269982 
 
 .426 
 
 .318970 
 
 .277 
 
 .177330 
 
 .327 
 
 .223216 
 
 .377 
 
 .270951 
 
 .427 
 
 .319959 
 
 .278 
 
 .178226 
 
 .328 
 
 .224154 
 
 .378 
 
 .271921 
 
 .428 
 
 .320949 
 
 .279 
 
 .179122 
 
 .329 
 
 .225094 
 
 .379 
 
 .272891 
 
 .429 
 
 .321938 
 
 .280 
 
 .180020 
 
 .330 
 
 .226034 
 
 .380 
 
 .273861 
 
 .430 
 
 .322928 
 
 .281 
 
 . 180918 
 
 .331 
 
 .226974 
 
 .381 
 
 .274832 
 
 .431 
 
 .323919 
 
 .282 
 
 .181818 
 
 .332 
 
 .227916 
 
 .382 
 
 .275804 
 
 .432 
 
 .324909 
 
 .283 
 
 . 182718 
 
 .333 
 
 .228858 
 
 .383 
 
 .276776 
 
 .433 
 
 .325900 
 
 .284 
 
 . 183619 
 
 .334 
 
 .229801 
 
 .384 
 
 .277748 
 
 .434 
 
 .326891 
 
 .285 
 
 . 184522 
 
 .335 
 
 .230745 
 
 .385 
 
 .278721 
 
 .435 
 
 .327883 
 
 .286 
 
 .185425 
 
 .336 
 
 .231689 
 
 .386 
 
 .279695 
 
 .436 
 
 .328874 
 
Table of Areas of Circular Segments 
 
 87 
 
 Table of' Areas of Circular Segments — {Continued) 
 
 Rise 
 divided 
 
 Area = 
 (square 
 
 Rise 
 divided 
 
 Area= j 
 (square ^^ 
 
 lise 
 ^ided 
 
 Area = j 
 (square ^j, 
 
 Use 
 
 /ided 
 
 Area = 
 (square 
 
 by diam. 
 of circle 
 
 of diam.) 
 multi- 
 
 by diam. 
 of circle 
 
 of diam.) , 
 multi- J 
 
 diam. 
 circle 
 
 of diam.) , 
 multi- q£ 
 
 diam. 
 circle 
 
 of diam.) 
 multi- 
 
 
 plied by 
 
 
 plied by 
 
 
 plied by 
 
 
 plied by 
 
 .437 
 
 .329866 
 
 .453 
 
 .345768 
 
 .469 
 
 .361719 
 
 485 
 
 .377701 
 
 .438 
 
 .330858 
 
 .454 
 
 .346764 
 
 470 
 
 .362717 
 
 486 
 
 .378701 
 
 .439 
 
 .331851 
 
 .455 
 
 .347760 
 
 471 
 
 .363715 
 
 487 
 
 .379701 
 
 .440 
 
 .332843 
 
 .456 
 
 .348756 
 
 472 
 
 .364714 
 
 488 
 
 .380700 
 
 .441 
 
 .333836 
 
 .457 
 
 .349752 
 
 473 
 
 .365712 
 
 489 
 
 .381700 
 
 .442 
 
 .334829 
 
 .458 
 
 .350749 
 
 474 
 
 .366711 
 
 490 
 
 .382700 
 
 .443 
 
 .335823 
 
 .459 
 
 .351745 
 
 475 
 
 .367710 
 
 491 
 
 .383700 
 
 • .444 
 
 .336816 
 
 .460 
 
 .352742 
 
 476 
 
 .368708 
 
 492 
 
 .384699 
 
 -445 
 
 .337810 
 
 .461 
 
 .353739 
 
 477 
 
 .369707 
 
 493 
 
 .385699 
 
 .446 
 
 .338804 
 
 .462 
 
 .354736 
 
 478 
 
 .370706 
 
 494 
 
 .386699 
 
 .447 
 
 .339799 
 
 .463 
 
 .355733 
 
 479 
 
 .371705 
 
 495 
 
 .387699 
 
 .448 
 
 .340793 
 
 .464 
 
 .356730 
 
 480 
 
 .372704 
 
 496 
 
 .388699 
 
 .449 
 
 .341788 
 
 .465 
 
 .357728 
 
 481 
 
 .373704 
 
 497 
 
 .389699 
 
 .450 
 
 .342783 
 
 .466 
 
 .358725 
 
 482 
 
 .374703 
 
 498 
 
 .390699 
 
 .451 
 
 .343778 
 
 .467 
 
 .359723 
 
 483 
 
 .375702 
 
 499 
 
 .391699 
 
 .452 
 
 .344773 
 
 .468 
 
 .360721 
 
 484 
 
 .376702 
 
 500 
 
 .392699 
 
88 
 
 Mathematical Tables 
 
 Chords of Arcs from One to Ninety Degrees 
 
 Dimensions given in inches. 
 
 Ang. 
 
 18-inch 
 
 36-inch 
 
 72-inch 
 
 Ang. 
 Deg. 
 
 18-inch 
 
 36-inch 
 
 72-inch 
 
 radius 
 
 radius 
 
 radius 
 
 radius 
 
 radius 
 
 radius 
 
 Deg. 
 
 chord 
 
 chord 
 
 chord 
 
 chftrd 
 
 chord 
 
 chord 
 
 I 
 
 Vi6 
 
 % 
 
 iH 
 
 46 
 
 14 1/1 6 
 
 281/i 
 
 561/64 
 
 2 
 
 ^A 
 
 iV^ 
 
 2/2 
 
 47 
 
 1423/64 
 
 2823/32 
 
 572/64 
 
 3 
 
 1^6 
 
 m 
 
 33/4 
 
 48 
 
 14^/64 
 
 29%2 
 
 583/64 
 
 4 
 
 iH 
 
 2V, 
 
 5 
 
 49 
 
 145 %4 
 
 2955/4 
 
 5923/2 
 
 5 
 
 l3%4 
 
 3%4 
 
 6?^2 
 
 50 
 
 I5%2 
 
 302 %4 
 
 6055/64 
 
 6 
 
 lli 
 
 34 %4 
 
 7I/32 
 
 51 
 
 15/2 
 
 31 
 
 62 
 
 7 
 
 21^64 
 
 42"5/64 
 
 851/^4 
 
 52 
 
 1525/32 
 
 319/6 
 
 63% 
 
 8 
 
 2H 
 
 5/64 
 
 IO%4 
 
 53 
 
 16/16 
 
 32% 
 
 641/4 
 
 9 
 
 253/^4 
 
 5^/64 
 
 Ill%4 
 
 54 
 
 16I/32 
 
 321/6 
 
 653/ 
 
 lO 
 
 39/64 
 
 6^32 
 
 123 %4 
 
 55 
 
 l65/^ 
 
 33/ 
 
 66/2 
 
 II 
 
 32 9/64 
 
 62 9/32 
 
 135/64 
 
 56 
 
 162 9/32 
 
 33^/64 
 
 6739/4 
 
 12 
 
 34 %4 
 
 71/32 
 
 IS%4 
 
 57 
 
 I7IH4 
 
 3423/64 
 
 6823/2 
 
 13 
 
 4^/64 
 
 8/32 
 
 l61%4 
 
 58 
 
 172/64 
 
 3429/2 
 
 6913/6 
 
 14 
 
 42 %4 
 
 825/32 
 
 1735/64 
 
 59 
 
 1723/32 
 
 3529/4 
 
 7029/2 
 
 15 
 
 4^5/64 
 
 925/64 
 
 1851/64 
 
 60 
 
 18 
 
 36 
 
 72 
 
 i6 
 
 5 
 
 10^4 
 
 20H2 
 
 61 
 
 181/64 
 
 3635/4 
 
 735/64 
 
 17 
 
 521/64 
 
 104^4 
 
 21%2 
 
 62 
 
 1835/64 
 
 37/64 
 
 74II/64 
 
 i8 
 
 SH 
 
 Ill%4 
 
 22l%2 
 
 63 
 
 181 /l 6 
 
 37% 
 
 7514 
 
 19 
 
 5^5/16 
 
 11% 
 
 234%4 
 
 64 
 
 19/64 
 
 385/2 
 
 765/6 
 
 20 
 
 6I/4 
 
 12/2 
 
 25 
 
 65 
 
 I9IH2 
 
 38II/16 
 
 7734 
 
 21 
 
 6^16 
 
 T-zY^ 
 
 2615/64 
 
 66 
 
 1939/64 
 
 39%2 
 
 782 %4 
 
 22 
 
 674 
 
 134 %4 
 
 273/64 
 
 67 
 
 19% 
 
 39^/64 
 
 7915/2 
 
 23 
 
 7"/64 
 
 142/64 
 
 28* %4 
 
 68 
 
 2ol,i 
 
 4oi%4 
 
 8oi%2 
 
 24 
 
 73/64 
 
 143/32 
 
 291 5/6 
 
 69 
 
 2o2 5/^4 
 
 4o2%2 
 
 8x9/6 
 
 25 
 
 7^/64 
 
 153/64 
 
 311/64 
 
 70 
 
 20*1/64 
 
 4ii%4 
 
 82l%2 
 
 26 
 
 83/^2 
 
 161^^4 
 
 3225/64 
 
 71 
 
 2o2%2 
 
 4I13/6 
 
 835/^ 
 
 27 
 
 813/^2 
 
 16I/16 
 
 33^^ 
 
 72 
 
 2iyz2 
 
 4221.^4 
 
 84*1/64 
 
 28 
 
 845/64 
 
 1713/32 
 
 3413/16 
 
 73 
 
 2ll%2 
 
 425 %4 
 
 8521/2 
 
 29 
 
 9/64 
 
 l81/^2 
 
 36/16 
 
 74 
 
 2l21y^2 
 
 432/64 
 
 8621/2 
 
 30 
 
 9^6 
 
 1841/64 
 
 371/64 
 
 75 
 
 2X5 %4 
 
 4353/4 
 
 8721/2 
 
 31 
 
 9% 
 
 191^^4 
 
 3831/64 
 
 76 
 
 225,^2 
 
 442/64 
 
 8821/32 
 
 32 
 
 95 %4 
 
 192^2 
 
 391/6 
 
 77 
 
 22I/32 
 
 4453/4 
 
 894/64 
 
 33 
 
 io7;^2 
 
 202%4 
 
 405/64 
 
 78 
 
 2221/^2 
 
 45/1 6 
 
 9054 
 
 34 
 
 I0l%2 
 
 2I%4 
 
 423/^2 
 
 79 
 
 2257/64 
 
 455/64 
 
 9ii%2 
 
 35 
 
 105^4 
 
 2l21/^2 
 
 43i%4 
 
 80 
 
 239/64 
 
 469/2 
 
 92?l6 
 
 36 
 
 JlM 
 
 22l.i 
 
 44/2 
 
 81 
 
 233/8 
 
 463/ 
 
 933^4 
 
 37 
 
 iimi 
 
 222 %2 
 
 451/6 
 
 82 
 
 2339/4 
 
 4715/64 
 
 94i%2 
 
 38 
 
 Il2 3/^2 
 
 23/6 
 
 465.^ 
 
 83 
 
 2355/64 
 
 4745/4 
 
 9513/^2 
 
 39 
 
 12^4 
 
 24H2 
 
 48/16 
 
 84 
 
 243/32 
 
 481/64 
 
 9623/4 
 
 40 
 
 I2M6 
 
 245/i 
 
 49H 
 
 85 
 
 2421/4 
 
 4841/4 
 
 97?^2 
 
 41 
 
 123 9/64 
 
 25%2 
 
 50^6 
 
 86 
 
 2435/4 
 
 493/32 
 
 9813/4 
 
 42 
 
 122 %2 
 
 255/64 
 
 513 9/64 
 
 87 
 
 2425/2 
 
 49?i6 
 
 99% . 
 
 43 
 
 133/6 
 
 2625/64 
 
 522 5/fe 
 
 88 
 
 25 
 
 50/64 
 
 IOO%2 
 
 44 
 
 1331/^4 
 
 2631/^2 
 
 531 /l 6 
 
 89 
 
 251 5/4 
 
 501/32 
 
 I0015/6 
 
 45 
 
 1325/^2 
 
 273^^4 
 
 55^/^4 
 
 90 
 
 2529/64 
 
 502 %2 
 
 1015^4 
 
Chords 
 
 89 
 
 Fig. 35. 
 
 To Find the Length of a Chord which will Divide the Circumference of 
 a Circle into N Equal Parts Multiply S by the Diameter 
 
 N 
 
 5 
 
 N 
 
 5 
 
 N 
 
 5 
 
 N 
 
 5 
 
 I 
 
 
 26 
 
 . 12054 
 
 51 
 
 .061560 
 
 76 
 
 041325 
 
 2 
 
 
 27 
 
 .11609 
 
 52 
 
 .060379 
 
 77 
 
 040788 
 
 3 
 
 '! 86603" 
 
 28 
 
 .11197 
 
 53 
 
 .059240 
 
 78 
 
 040267 
 
 4 
 
 .70711 
 
 29 
 
 . 10812 
 
 54 
 
 .058145 
 
 79 
 
 039757 
 
 5 
 
 .58779 
 
 30 
 
 .10453 
 
 55 
 
 .057090 
 
 80 
 
 039260 
 
 6 
 
 .50000 
 
 31 
 
 .10117 
 
 56 
 
 .056071 
 
 81 
 
 038775 
 
 7 
 
 .43388 
 
 32 
 
 .098018 
 
 57 
 
 .055089 
 
 82 
 
 038303 
 
 8 
 
 .38268 
 
 33 
 
 .095056 
 
 58 
 
 .054139 
 
 83 
 
 037841 
 
 9 
 
 .34202 
 
 34 
 
 .092269 
 
 59 
 
 .053222 
 
 84 
 
 037391 
 
 10 
 
 .30902 
 
 35 
 
 .089640 
 
 60 
 
 .052336 
 
 85 
 
 036953 
 
 II 
 
 .28173 
 
 36 
 
 .087156 
 
 61 
 
 .051478 
 
 86 
 
 036522 
 
 12 
 
 .25882 
 
 37 
 
 .084804 
 
 62 
 
 .050649 
 
 87 
 
 036103 
 
 13 
 
 .23932 
 
 38 
 
 .082580 
 
 63 
 
 .049845 
 
 88 
 
 035692 
 
 14 
 
 .22252 
 
 39 
 
 .080466 
 
 64 
 
 .049068 
 
 89 
 
 035291 
 
 IS 
 
 .20791 
 
 40 
 
 .078460 
 
 65 
 
 .048312 
 
 90 
 
 034899 
 
 16 
 
 .19509 
 
 41 
 
 .076549 
 
 66 
 
 .047582 
 
 91 
 
 034516 
 
 17 
 
 .18375 
 
 42 
 
 .074731 
 
 67 
 
 .046872 
 
 92 
 
 034141 
 
 18 
 
 .17365 . 
 
 43 
 
 .072995 
 
 68 
 
 .046184 
 
 93 
 
 033774 
 
 19 
 
 .16460 
 
 44 
 
 .071339 
 
 69 
 
 .045515 
 
 94 
 
 033415 
 
 20 
 
 .15643 
 
 45 
 
 .069756 
 
 70 
 
 .044865 
 
 95 
 
 033064 • 
 
 21 
 
 .14904 
 
 46 
 
 .06S243 
 
 71 
 
 .044232 
 
 96 
 
 032719 
 
 22 
 
 .14232 
 
 47 
 
 .066793 
 
 72 
 
 .043619 
 
 97 
 
 032381 
 
 23 
 
 .13617 
 
 48 
 
 .065401 
 
 73 
 
 .043022 
 
 98 
 
 032051 
 
 24 
 
 .13053 
 
 49 
 
 .064073 
 
 74 
 
 .042441 
 
 99 
 
 031728 
 
 25 
 
 .12533 
 
 50 
 
 .062791 
 
 75 
 
 .041875 
 
 100 
 
 031411 
 
90 
 
 Mathematical Tables 
 
 Lengths of Chords for Spacing Circle whose Diameter is i 
 
 For circles of other diameters multiply length given in table by diameter of circle. 
 
 No. of 
 
 Length of 
 
 No. of 
 
 Length of 
 
 No. of 
 
 Length of 
 
 No. of 
 
 Length of 
 
 spaces 
 
 chord 
 
 spaces 
 
 chord 
 
 spaces 
 
 chord 
 
 spaces 
 
 chord 
 
 
 
 26 
 
 .1205 
 
 51 
 
 .0616 
 
 76 
 
 .0413 
 .0408 
 .0403 
 
 
 
 27 
 
 .1161 
 
 52 
 
 .0604 
 
 77 
 
 3 
 
 "'■.8660" 
 
 28 
 
 .1120 
 
 53 
 
 .0592 
 
 78 
 
 4 
 
 .7071 
 
 29 
 
 .1081 
 
 54 
 
 .0581 
 
 79 
 
 .0398 
 
 s 
 
 .5878 
 
 30 
 
 .1045 
 
 55 
 
 .0571 
 
 80 
 
 .0393 
 
 6 
 
 .5000 
 
 31 
 
 .1012 
 
 56 
 
 .0561 
 
 81 
 
 .0388 
 
 7 
 
 .4339 
 
 32 
 
 .0980 
 
 57 
 
 .0551 
 
 82 
 
 .0383 
 
 8 
 
 .3827 
 
 33 
 
 .0951 
 
 58 
 
 .0541 
 
 83 
 
 .0378 
 
 9 
 
 .3420 
 
 34 
 
 .0923 
 
 59 
 
 .0532 
 
 84 
 
 .0374 
 
 lo 
 
 .3090 
 
 35 
 
 .0896 
 
 60 
 
 .0523 
 
 85 
 
 .0370 
 
 II 
 
 .2817 
 
 36 
 
 .0872 
 
 61 
 
 .0515 
 
 86 
 
 .0365 
 
 12 
 
 .2588 
 
 37 
 
 .0848 
 
 62 
 
 .0507 
 
 87 
 
 .0361 
 
 13 
 
 .2393 
 
 38 
 
 .0826 
 
 63 
 
 .0499 
 
 88 
 
 .0357 
 
 14 
 
 .2225 
 
 39 
 
 .0805 
 
 64 
 
 .0491 
 
 89 
 
 .0353 
 
 15 
 
 .2079 
 
 40 
 
 .0785 
 
 65 
 
 .0483 
 
 90 
 
 .0349 
 
 i6 
 
 .1951 
 
 41 
 
 .0765 
 
 66 
 
 .0476 
 
 91 
 
 .0345 
 
 17 
 
 .1838 
 
 42 
 
 .0747 
 
 67 
 
 .0469 
 
 92 
 
 .0341 
 
 I8 
 
 .1736 
 
 43 
 
 •0730 
 
 68 
 
 .0462 
 
 93 
 
 .0338 
 
 19 
 
 .1646 
 
 44 
 
 .0713 
 
 69 
 
 .0455 
 
 94 
 
 .0334 
 
 20 
 
 .1564 
 
 45 
 
 .0698 
 
 70 
 
 .0449 
 
 95 
 
 .0331 
 
 21 
 
 .1490 
 
 46 
 
 .0682 
 
 71 
 
 .0442 
 
 96 
 
 .0327 
 
 22 
 
 .1423 
 
 47 
 
 .0668 
 
 72 
 
 .0436 
 
 97 
 
 .0324 
 
 23 
 
 .1362 
 
 48 
 
 .0654 
 
 73 
 
 .0430 
 
 98 
 
 .0321 
 
 24 
 
 .1305 
 
 49 
 
 .0641 
 
 74 
 
 .0424 
 
 99 
 
 .0317 
 
 25 
 
 .1253 
 
 50 
 
 .0628 
 
 75 
 
 .0419 
 
 TOO 
 
 .0314 
 
 Computed by W. I. Mann, Pittsburg, Pa. 
 Supplement to Machinery, February, 1903. 
 
Board Measure 
 
 91 
 
 Board Measure 
 
 
 
 
 
 Length 
 
 in feet 
 
 
 
 Size 
 
 12 
 
 14 
 
 16 
 
 18 
 
 20 
 
 22 
 
 24 
 
 26 
 
 
 Square feet 
 
 IX 8 
 
 8 
 
 9\i 
 
 I02/^ 
 
 12 
 
 n\i 
 
 142/^ 
 
 16 
 
 17% 
 
 IX 10 
 
 10 
 
 11% 
 
 132/^ 
 
 15 
 
 16% 
 
 18% 
 
 20 
 
 21% 
 
 1X12 
 
 12 
 
 14 
 
 16 
 
 18 
 
 20 
 
 22 
 
 24 
 
 26 
 
 1X14 
 
 14 
 
 16I/6 
 
 182/3 
 
 21 
 
 233'^ 
 
 252/^ 
 
 28 
 
 30% 
 
 IX16 
 
 16 
 
 I82/^ 
 
 21H 
 
 24 
 
 262/^ 
 
 29/3 
 
 32 
 
 34% 
 
 2X 3 
 
 6 
 
 7 
 
 8 
 
 9 
 
 10 
 
 II 
 
 12 
 
 13 
 
 2X 4 
 
 8 
 
 m 
 
 1024 
 
 12 
 
 I3H 
 
 142% 
 
 16 
 
 17% 
 
 2X 6 
 
 12 
 
 14 
 
 16 
 
 18 
 
 20 
 
 22 
 
 24 
 
 26 
 
 2X 8 
 
 16 
 
 18% 
 
 21/3 
 
 24 
 
 262/^ 
 
 29% 
 
 32 
 
 34% 
 
 2X10 
 
 20 
 
 231/^ 
 
 26% 
 
 30 
 
 33H 
 
 3624 
 
 40 
 
 43% 
 
 2X12 
 
 24 
 
 28 
 
 32 
 
 36 
 
 40 
 
 44 
 
 -48 
 
 52 
 
 2X14 
 
 28 
 
 322/^ 
 
 37^ 
 
 42 
 
 4624 
 
 51% 
 
 56 
 
 60% 
 
 2X16 
 
 32 
 
 375^ 
 
 42% 
 
 48 
 
 53H 
 
 582% 
 
 64 
 
 69% 
 
 3X 4 
 
 12 
 
 14 
 
 16 
 
 18 
 
 20 
 
 22 
 
 24 
 
 26 
 
 3X 6 
 
 18 
 
 21 
 
 24 
 
 27 
 
 30 
 
 33 
 
 36 
 
 39 
 
 3X 8 
 
 24 
 
 28 
 
 32 
 
 36 
 
 40 
 
 44 
 
 48 
 
 52 
 
 3X10 
 
 30 
 
 35. 
 
 40 
 
 45 
 
 50 
 
 55 
 
 60 
 
 65 
 
 3X12 
 
 36 
 
 42 
 
 48 
 
 54 
 
 60 
 
 66 
 
 72 
 
 78 
 
 3X14 
 
 42 
 
 49 
 
 S6 
 
 63 
 
 70 
 
 77 
 
 84 
 
 91 
 
 3X16 
 
 48 
 
 56 
 
 64 
 
 72 
 
 80 
 
 88 
 
 96 
 
 104 
 
 4X 4 
 
 16 
 
 I82/^ 
 
 2m 
 
 24 
 
 26% 
 
 29% 
 
 32 
 
 34% 
 
 4X 6 
 
 24 
 
 28 
 
 32 
 
 2,^ 
 
 40 
 
 44 
 
 48 
 
 52 
 
 4X 8 
 
 32 
 
 37H 
 
 42% 
 
 48 
 
 53H 
 
 58% 
 
 64 
 
 69% 
 
 4X10 
 
 40 
 
 46% 
 
 53H 
 
 60 
 
 66% 
 
 73% 
 
 80 
 
 86% 
 
 4X12 
 
 48 
 
 56 
 
 64 
 
 72 
 
 80 
 
 88 
 
 96 
 
 104 
 
 4X14 
 
 56 
 
 65!/^ 
 
 742/3 
 
 84 
 
 93% 
 
 I022/^ 
 
 112 
 
 121% 
 
 4X16 
 
 64 
 
 742/3 
 
 8sH 
 
 96 
 
 106% 
 
 117% 
 
 128 
 
 138% 
 
 6X 6 
 
 36 
 
 42 
 
 48 
 
 54 
 
 60 
 
 66 
 
 72 
 
 78 
 
 6X 8 
 
 48 
 
 56 
 
 64 
 
 72 
 
 80 
 
 88 
 
 96 
 
 104 
 
 6X10 
 
 60 
 
 70 
 
 80 
 
 90 
 
 100 
 
 no 
 
 120 
 
 130 
 
 6X12 
 
 72 
 
 84 
 
 96 
 
 108 
 
 120 
 
 132 
 
 144 
 
 156 
 
 6X14 
 
 84 
 
 98 
 
 112 
 
 126 
 
 140 
 
 154 
 
 168 
 
 182 
 
 6X16 
 
 96 
 
 112 
 
 128 
 
 144 
 
 160 
 
 176 
 
 192 
 
 208 
 
 8X 8 
 
 64 
 
 74% 
 
 851/3 
 
 96 
 
 10624 
 
 117% 
 
 128 
 
 138% 
 
 8X10 
 
 80 
 
 93H 
 
 106% 
 
 120 
 
 133% 
 
 1462% 
 
 160 
 
 173% 
 
 8X12 
 
 96 
 
 112 
 
 128 
 
 144 
 
 160 
 
 176 
 
 192 
 
 208 
 
 8X14 
 
 ■112 
 
 I302/^ 
 
 149^/^ 
 
 168 
 
 1862/3 
 
 205% 
 
 224 
 
 242% 
 
 8X16 
 
 128 
 
 I49V^ 
 
 I702/^ 
 
 192 
 
 213% 
 
 234% 
 
 256 
 
 277% 
 
 loXio 
 
 100 
 
 116% 
 
 133^/^ 
 
 150 
 
 1662/3 
 
 183% 
 
 200 
 
 216% 
 
 10X12 
 
 120 
 
 140 
 
 160 
 
 .180 
 
 200 
 
 220 
 
 240 
 
 260 
 
 10X14 
 
 140 
 
 163H 
 
 1862/^ 
 
 210 
 
 233% 
 
 256% 
 
 280 
 
 303% 
 
 10X16 
 
 160 
 
 1862/^ 
 
 213H 
 
 240 
 
 2662/3 
 
 293% 
 
 320 
 
 346% 
 
 12X12 
 
 144 
 
 168 
 
 192 
 
 216 
 
 240 
 
 264 
 
 288 
 
 312 
 
 12X14 
 
 168 
 
 196 
 
 224 
 
 252 
 
 280 
 
 308 
 
 336 
 
 364 
 
 12X16 
 
 192 
 
 224 
 
 256 
 
 288 
 
 320 
 
 352 
 
 384 
 
 416 
 
 14X14 
 
 196 
 
 22m 
 
 2(>m 
 
 294 
 
 326% 
 
 359% 
 
 392 
 
 424% 
 
 14X16 
 
 224 
 
 261H 
 
 2982/i 
 
 336 
 
 373/3 
 
 4io2/^ 
 
 448 
 
 485% 
 
 16x16 
 
 256 
 
 2982/3 
 
 341H 
 
 384 
 
 4262/^ 
 
 469% 
 
 512 
 
 554% 
 
92 
 
 Mathematical Tables 
 Board Measure — {Continued) 
 
 
 Length in feet 
 
 Size 
 
 28 
 
 30 
 
 32 
 
 34 
 
 36 
 
 38 
 
 40 
 
 
 Square feet 
 
 IX 8 
 
 i8H 
 
 20 
 
 21 1/^ 
 
 22% 
 
 24 
 
 2534 
 
 26% 
 
 IXIO 
 
 23H 
 
 25 
 
 262/^ 
 
 28H 
 
 30 
 
 312/6 
 
 33H 
 
 IXI2 
 
 28 
 
 30 ■ 
 
 32 
 
 34 
 
 36 
 
 38 
 
 40 
 
 1X14 
 
 322/^ 
 
 35 
 
 37H 
 
 39% 
 
 42 
 
 44I/6 
 
 46% 
 
 1X16 
 
 37H 
 
 40 
 
 42^^ 
 
 45H 
 
 48 
 
 502/6 
 
 53H 
 
 2X 3 
 
 14 
 
 15 
 
 16 
 
 17 
 
 18 
 
 19 
 
 20 
 
 2X 4 
 
 I82/^ 
 
 20 
 
 2ll/i 
 
 222/^ 
 
 24 
 
 25H 
 
 26% 
 
 2X 6 
 
 28 
 
 30 
 
 32 
 
 34 
 
 36 
 
 38 
 
 40 
 
 2X 8 
 
 37^/^ 
 
 40 
 
 422/3 
 
 45H 
 
 48 
 
 502/6 
 
 53% 
 
 2X10 
 
 462/^ 
 
 50 
 
 53H 
 
 56% 
 
 60 
 
 63H 
 
 66% 
 
 2X12 
 
 56 
 
 60 
 
 64 
 
 68 
 
 72 
 
 76 
 
 80 
 
 2X14 
 
 65H 
 
 70 
 
 722/3 
 
 7954 
 
 84 
 
 882/6 
 
 93% 
 
 2X16 
 
 74^i 
 
 80 
 
 85H 
 
 90% 
 
 96 
 
 loii^ 
 
 106% 
 
 3X 4 
 
 28 
 
 30 
 
 32 
 
 34 
 
 36 
 
 38 
 
 40 
 
 3X 6 
 
 42 
 
 45 
 
 48 
 
 51 
 
 54 
 
 57 
 
 60 
 
 3X 8 
 
 56 
 
 60 
 
 64 
 
 68 
 
 72 
 
 76 
 
 80 
 
 3X10 
 
 70 
 
 75 
 
 80 
 
 85 
 
 90 
 
 95 
 
 100 
 
 3X12 
 
 84 
 
 90 
 
 96 
 
 102 
 
 108 
 
 114 
 
 120 
 
 3X14 
 
 98 
 
 los 
 
 112 
 
 119 
 
 126 
 
 133 
 
 140 
 
 3X16 
 
 112 
 
 120 
 
 128 
 
 136 
 
 144 
 
 152 
 
 160 
 
 4X 4 
 
 37H 
 
 40 
 
 42^ 
 
 45H 
 
 48 
 
 50% 
 
 53% 
 
 4X 6 
 
 56 
 
 60 
 
 64 
 
 68 
 
 72 
 
 76 
 
 80 
 
 4X 8 
 
 74^/3 
 
 80 
 
 85!/^ 
 
 9o2/i 
 
 96 
 
 loiH 
 
 106% 
 
 4X10 
 
 93H 
 
 100 
 
 I062/^ 
 
 113H 
 
 120 
 
 126% 
 
 133% 
 
 4X12 
 
 112 
 
 120 
 
 128 
 
 136 
 
 144 
 
 152 
 
 160 
 
 4X14 
 
 130^^ 
 
 140 
 
 ugH 
 
 1582/^ 
 
 168 
 
 177)4 
 
 186% 
 
 4X16 
 
 149H 
 
 160 
 
 \io% 
 
 i8ii/^ 
 
 192 
 
 202% 
 
 213% 
 
 6X 6 
 
 84 
 
 90 
 
 96 
 
 102 
 
 108 
 
 114 
 
 120 
 
 6x 8 
 
 112 
 
 120 
 
 128 
 
 136 
 
 144 
 
 152 
 
 160 
 
 6x10 
 
 140 
 
 150 
 
 160 
 
 170 
 
 180 
 
 190 
 
 200 
 
 6X12 
 
 168 
 
 180 
 
 192 
 
 204 
 
 216 
 
 228 
 
 240 
 
 6x14 
 
 196 
 
 210 
 
 224 
 
 238 
 
 252 
 
 266 
 
 280 
 
 6X16 
 
 224 
 
 240 
 
 256 
 
 272 
 
 288 
 
 304 
 
 320 
 
 8X 8 
 
 U9H 
 
 160 
 
 170^^ 
 
 i8ii.^ 
 
 192 
 
 202% 
 
 213% 
 
 8X10 
 
 1862/^ 
 
 200 
 
 213H 
 
 226% 
 
 240 
 
 253H 
 
 266% 
 
 8X12 
 
 224 
 
 240 
 
 256 
 
 272 
 
 288 
 
 304 
 
 320 
 
 8X14 
 
 261 1/^ 
 
 280 
 
 29824 
 
 317^/^ 
 
 336 
 
 354% 
 
 373% 
 
 8X16 
 
 298^^ 
 
 320 
 
 341I4 
 
 3622/ 
 
 384 
 
 405H 
 
 426% 
 
 loXio 
 
 2335'^ 
 
 250 
 
 266^^ 
 
 283H 
 
 300 
 
 316% 
 
 333% 
 
 10X12 
 
 280 
 
 300 
 
 320 
 
 340 
 
 360 
 
 380 
 
 400 
 
 10X14 
 
 3262/i 
 
 350 
 
 373H 
 
 3962/6 
 
 410 
 
 443H 
 
 466% 
 
 10X16 
 
 373H 
 
 400 
 
 4262yi 
 
 453H 
 
 480 
 
 So6% 
 
 533% 
 
 12x12 
 
 336 
 
 360 
 
 384 
 
 408 
 
 432 
 
 456 
 
 480 
 
 12X14 
 
 392 
 
 420 
 
 448 
 
 476 
 
 504 
 
 532 
 
 560 
 
 12X16 
 
 448 
 
 480 
 
 512 
 
 544 
 
 576 
 
 608 
 
 640 
 
 14X14 
 
 457!/^ 
 
 490 
 
 5222/^ 
 
 S55I/6 
 
 588 
 
 620% 
 
 6S3% 
 
 14X16 
 
 522^/^ 
 
 560 
 
 597H 
 
 634% 
 
 672 
 
 709H 
 
 746% 
 
 16X16 
 
 597I4 
 
 640 
 
 682H 
 
 725H 
 
 768 
 
 810% 
 
 853% 
 
 Note. — By simply multiplying or dividing the above amounts, the number of 
 feet contained in other dimensions can be obtained. 
 
Surface and Volumes of Spheres 93 
 
 Weight of Lumber per iooo Feet Board Measure 
 
 Character of lumber 
 
 Dry 
 
 Partly 
 seasoned 
 
 Green • 
 
 Pine and. hemlock 
 
 Pounds 
 2500 
 3000 
 4000 
 3SOO 
 
 Pounds 
 2750 
 4000 
 5000 
 4CXX) 
 
 Pounds 
 3000 
 
 Norway and. yellow pine 
 
 5000 
 
 Oak and walnut ... 
 
 
 
 
 
 
 Surface and Volumes of Spheres 
 
 Spheres. (Original.) Trautwine. 
 Some errors of i in the last figure only. 
 
 Diam. 
 
 Surface 
 
 Solidity 
 
 Diam. 
 
 Surface 
 
 Solidity 
 
 Diam. 
 
 Surface 
 
 Solidity 
 
 K4 
 
 .0C077 
 
 
 13/^2 
 
 3.7583 
 
 .68511 
 
 2%2 
 
 15.466 
 
 5.7190 
 
 H2 
 
 .00307 
 
 .00002 
 
 % 
 
 3.9761 
 
 .74551 
 
 M 
 
 15.904 
 
 5. 9641 
 
 %4 
 
 .00690 
 
 .00005 
 
 5/2 
 
 4.2000 
 
 .80939 
 
 %2 
 
 16.349 
 
 6.2161 
 
 Me 
 
 .01227 
 
 .00013 
 
 Me 
 
 4.4301 
 
 .87681 
 
 Me 
 
 16.800 
 
 6. 4751 
 
 3.^2 
 
 .02761 
 
 .00043 
 
 %2 
 
 4.6664 
 
 .94786 
 
 1H2 
 
 17.258 
 
 6.7412 
 
 H 
 
 .04909 
 
 .00102 
 
 M 
 
 4.9088 
 
 1.0227 
 
 % 
 
 17.721 
 
 7.0144 
 
 5i2 
 
 .07670 
 
 .00200 
 
 %2 
 
 5.1573 
 
 I . 1013 
 
 13/^2 
 
 18.190 
 
 7.2949 
 
 3/16 
 
 .11045 
 
 .00345 
 
 Me 
 
 5.4119 
 
 I. 1839 
 
 Me 
 
 18.666 
 
 7.5829 
 
 %2 
 
 . 1S033 
 
 .00548 
 
 1/32 
 
 5.6728 
 
 1.2704 
 
 15/32 
 
 19.147 
 
 7.8783 
 
 }i 
 
 .19635 
 
 .00818 
 
 3/i 
 
 5. 9396 
 
 1.3611 
 
 1/^ 
 
 19.635 
 
 8.1813 
 
 %2 
 
 .24851 
 
 .01165 
 
 13/^2 
 
 6.2126 
 
 I. 4561 
 
 li^2 
 
 20.129 
 
 8.4919 
 
 Me 
 
 .30680 
 
 .01598 
 
 Me 
 
 6.4919 
 
 1-5553 
 
 9/16 
 
 20 . 629 
 
 8.8103 
 
 1H2 
 
 .37123 
 
 .02127 
 
 15^2 
 
 6.7771 
 
 1.6590 
 
 19/^2 
 
 21.135 
 
 9.1366 
 
 H 
 
 .44179 
 
 .02761 
 
 ¥2 
 
 7.0686 
 
 I. 7671 
 
 % 
 
 21.648 
 
 9.4708 
 
 m2 
 
 51848 
 
 .03511 
 
 1%2 
 
 7.3663 
 
 1.8799 
 
 2H2 
 
 22.166 
 
 9.8131 
 
 Ma 
 
 .60132 
 
 .04385 
 
 9/6 
 
 7.6699 
 
 1.9974 
 
 iMe 
 
 22.691 
 
 10.164 
 
 15^2 
 
 .69028 
 
 .05393 
 
 19/32 
 
 7.9798 
 
 2.1196 
 
 23/2 
 
 23 . 222 
 
 10.522 
 
 Yi 
 
 .78540 
 
 .06545 
 
 % 
 
 8.2957 
 
 2.2468 
 
 % 
 
 23.758 
 
 10.889 
 
 ^%2 
 
 88664 
 
 .07850 
 
 21/2 
 
 8.6180 
 
 2.3789 
 
 25/2 
 
 24.302 
 
 11.265 
 
 9/16 
 
 .99403 
 
 .09319 
 
 iMe 
 
 8.9461 
 
 2.5161 
 
 IMe 
 
 24.850 
 
 11.649 
 
 1%2 
 
 1 . 1075 
 
 . 10960 
 
 23^^2 
 
 9.2805 
 
 2.6586 
 
 2%2 
 
 25.405 
 
 12.041 
 
 ^A 
 
 I . 2272 
 
 .12783 
 
 3/ 
 
 9.6211 
 
 2.8062 
 
 % 
 
 25.967 
 
 12.443 
 
 21/^2 
 
 1.3530 
 
 . 14798 
 
 2^2 
 
 9.9678 
 
 2.9592 
 
 2 9/2 
 
 26.535 
 
 12.853 
 
 iMe 
 
 1.4849 
 
 .17014 
 
 iMe 
 
 10.321 
 
 3.1177 
 
 IMe 
 
 27.109 
 
 13.272 
 
 2 3/^2 
 
 I . 6230 
 
 .19442 
 
 ^^2 
 
 10.680 
 
 3.2818 
 
 31/2 
 
 27.688 
 
 13.700 
 
 % 
 
 I. 7671 
 
 . 22089 
 
 % 
 
 11.044 
 
 3.4514 
 
 3 
 
 28.274 
 
 14.137 
 
 25/^2 
 
 I. 9175 
 
 .24967 
 
 2 9/32 
 
 II. 416 
 
 3.6270 
 
 Me 
 
 29.465 
 
 15.039 
 
 13/16 
 
 2.0739 
 
 .28084 
 
 1M6 
 
 11.793 
 
 3.8083 
 
 H 
 
 30.680 
 
 15.979 
 
 ^%2 
 
 2.236s 
 
 .31451 
 
 31/32 
 
 12.177 
 
 3.9956 
 
 Me 
 
 31.919 
 
 16.957 
 
 % 
 
 2.4053 
 
 .35077 
 
 2 
 
 12.566 
 
 4.1888 
 
 M 
 
 33.183 
 
 17.974 
 
 ^%2 
 
 2.5802 
 
 .38971 
 
 H2 
 
 12.962 
 
 4.3882 
 
 Me 
 
 34.472 
 
 19.031 
 
 15/6 
 
 2.7611 
 
 .43143 
 
 Me 
 
 13.364 
 
 4.5939 
 
 3/8 
 
 35.784 
 
 20.129 
 
 3^2 
 
 2.9483 
 
 .47603 
 
 3/^2 
 
 13.772 
 
 4.8060 
 
 Me 
 
 37.122 
 
 21.268 
 
 I 
 
 3.1416 
 
 .52360 
 
 H 
 
 14.186 
 
 5.0243 
 
 1/ 
 
 38.484 
 
 22.449 
 
 H2 
 
 3.3410 
 
 .57424 
 
 ^2 
 
 14.607 
 
 5.2493 
 
 9/6 
 
 39.872 
 
 23.674 
 
 He 
 
 3.5466 
 
 .62804 
 
 Me 
 
 15.033 
 
 5. 4809 
 
 5/ 
 
 41.283 
 
 24.942 
 
94 
 
 Mathematical Tables 
 
 Spheres — {Continued) 
 
 Diam. 
 
 Surface 
 
 Solidity 
 
 Diam. 
 
 Surface 
 
 Solidity 
 ■268.08 
 
 Diam. 
 
 Surface 
 
 Solidity 
 
 31 He 
 
 42.719 
 
 26.254 
 
 8 
 
 201.06 
 
 14^/^ 
 
 671.9s 
 
 1637.9 
 
 % 
 
 44.179 
 
 27.611 
 
 H 
 
 207.39 
 
 280.85 
 
 3/ 
 
 683.49 
 
 1680.3 
 
 1^6 
 
 45.664 
 
 29.016 
 
 H 
 
 213.82 
 
 294.01 
 
 ^i 
 
 695.13 
 
 ■ 1723.3 
 
 ^i 
 
 47.173 
 
 30.466 
 
 % 
 
 220.36 
 
 307.58 
 
 15 
 
 706.85 
 
 1767.2 
 
 15/16 
 
 48.708 
 
 31.96s 
 
 1/2 
 
 226.98 
 
 321.56 
 
 i/i 
 
 718.69 
 
 1811.7 
 
 4 
 
 50.265 
 
 33.510 
 
 % 
 
 233.71 
 
 335.9s 
 
 1/4 
 
 730.63 
 
 1857.0 
 
 Me 
 
 51.848 
 
 35.106 
 
 3/4 
 
 240.53 
 
 350.77 
 
 3/i 
 
 742.65 
 
 1903.0 
 
 5^ 
 
 53.456 
 
 36.751 
 
 'A 
 
 247.45 
 
 366.02 
 
 H2 
 
 754.77 
 
 1949.8 
 
 3/16 
 
 55.089 
 
 38.448 
 
 9 
 
 254.47 
 
 381.70 
 
 5/i 
 
 767.00 
 
 1997.4 
 
 i/i 
 
 56.745 
 
 40.195 
 
 ^ 
 
 261.59 
 
 397.83 
 
 3/ 
 
 779-32 
 
 2045.7 
 
 Me 
 
 58.427 
 
 41.994- 
 
 H 
 
 268.81 
 
 414.41 
 
 Ji 
 
 791.73 
 
 2094.8 
 
 ?i 
 
 60.133 
 
 43.847 
 
 % 
 
 276.12 
 
 431.44 
 
 16 
 
 804.25 
 
 2144.7 
 
 7/16 
 
 61.863 
 
 45 . 752 
 
 H 
 
 283.53 
 
 448.92 
 
 \i 
 
 816.85 
 
 2195. 3 
 
 1/^ 
 
 63.617 
 
 47.713 
 
 5/i 
 
 291.04 
 
 466.87 
 
 H 
 
 829.57 
 
 2246.8 
 
 9/16 
 
 65.397 
 
 49.729 
 
 3/ 
 
 298.65 
 
 485.31 
 
 % 
 
 842.40 
 
 2299.1 
 
 54 
 
 67.201 
 
 51.801 
 
 % 
 
 306.36 
 
 504.21 
 
 ^'i 
 
 855.29 
 
 2352.1 
 
 11/6 
 
 69.030 
 
 53.929 
 
 10 
 
 314.16 
 
 523.60 
 
 % 
 
 868.31 
 
 2406.0 
 
 M 
 
 70.883 
 
 56.116 
 
 % 
 
 322.06 
 
 543.48 
 
 % 
 
 881.42 
 
 2460.6 
 
 13/6 
 
 72.759 
 
 58.359 
 
 H 
 
 330.06 
 
 S63.86 
 
 'A 
 
 894.63 
 
 2516. I 
 
 Ji 
 
 74.663 
 
 60.663 
 
 3/i 
 
 338.16 
 
 S84.74 
 
 17 
 
 907.93 
 
 2572.4 
 
 15/6 
 
 76.589 
 
 63.026 
 
 H 
 
 346.36 
 
 606.13 
 
 i/i 
 
 921.33 
 
 2629.6 
 
 5 
 
 78.540 
 
 65.450 
 
 5/i 
 
 354.66 
 
 628.04 
 
 H 
 
 934.83 
 
 2687.6 
 
 He 
 
 80.516 
 
 67.935 
 
 3/ 
 
 363.05 
 
 650.46 
 
 % 
 
 948.43 
 
 2746.5 
 
 H 
 
 82.516 
 
 70.482 
 
 % 
 
 371.54 
 
 673.42 
 
 Vi 
 
 962.12 
 
 2806.2 
 
 3/16 
 
 84.541 
 
 73.092 
 
 II 
 
 380.13 
 
 696.91 
 
 % 
 
 975-91 
 
 2866.8 
 
 H 
 
 86.591 
 
 75.767 
 
 % 
 
 388.83 
 
 720,95 
 
 % 
 
 989.80 
 
 2928.2 
 
 5/6 
 
 88.664 
 
 78.505 
 
 H 
 
 397.61 
 
 745.51 
 
 'A 
 
 1003.8 
 
 2990. 5 
 
 3.i 
 
 90.763 
 
 81.308 
 
 % 
 
 406.49 
 
 770.64 
 
 18 
 
 1017.9 
 
 3053.6 
 
 7l6 
 
 92.887 
 
 84.178 
 
 1/2 
 
 41S.48 
 
 796.33 
 
 i/i 
 
 1032. I 
 
 3117.7 
 
 H 
 
 95.033 
 
 87.113 
 
 % 
 
 424.56 
 
 822.58 
 
 H 
 
 1046.4 
 
 3182.6 
 
 «/6 
 
 97.205 
 
 90.118 
 
 3/ 
 
 433.73 
 
 849.40 
 
 % 
 
 1060.8 
 
 3248.5 
 
 5/i 
 
 99.401 
 
 93.189 
 
 li 
 
 443.01 
 
 876.79 
 
 H 
 
 1075.2 
 
 3315.3 
 
 iHe 
 
 101.62 
 
 96.331 
 
 12 
 
 452.39 
 
 904.78 
 
 5/i 
 
 1089.8 
 
 3382.9 
 
 % 
 
 103.87 
 
 99.541 
 
 M 
 
 461.87 
 
 933.34 
 
 % 
 
 1104.5 
 
 3451. 5 
 
 13/6 
 
 106.14 
 
 102.82 
 
 Vi 
 
 471.44 
 
 962.52 
 
 % 
 
 1119.3 
 
 3521.0 
 
 % 
 
 108.44 
 
 106.18 
 
 % 
 
 481. II 
 
 992.28 
 
 19 
 
 1134.1 
 
 3591.4 
 
 15/6 
 
 110.75 
 
 109.60 
 
 H2 
 
 490.87 
 
 1022.7 
 
 i/i 
 
 I149.1 
 
 3662.8 
 
 6 
 
 113. 10 
 
 113. 10 
 
 fi 
 
 S00.73 
 
 1053.6 
 
 H 
 
 1164.2 
 
 3735. 
 
 M 
 
 117.87 
 
 120.31 
 
 % 
 
 510.71 
 
 1085.3 
 
 % 
 
 1179.3 
 
 3808.2 
 
 H 
 
 122.72 
 
 127.83 
 
 % 
 
 520.77 
 
 1117.S 
 
 H2 
 
 1194.6 
 
 3882.5 
 
 3/i 
 
 127.68 
 
 135.66 
 
 13 
 
 530.93 
 
 1IS0.3 
 
 A 
 
 1210.0 
 
 3957.6 
 
 1/^ 
 
 132.73 
 
 143.79 
 
 H 
 
 541.19 
 
 1183.8 
 
 % 
 
 1225.4 
 
 4033. 5 
 
 5/^8 
 
 137.89 
 
 152.25 
 
 H 
 
 551.55 
 
 1218.0 
 
 A 
 
 1241.0 
 
 4110.8 
 
 3/4 
 
 143.14 
 
 161.03 
 
 % 
 
 562.00 
 
 1252.7 
 
 20 
 
 1256.7 
 
 4188.8 
 
 j^^ 
 
 148.49 
 
 170.14 
 
 1/2 
 
 572.55 
 
 1288.3 
 
 H 
 
 1272.4 
 
 4267.8 
 
 7 
 
 153.94 
 
 179.59 
 
 % 
 
 583.20 
 
 1324.4 
 
 H 
 
 1288.3 
 
 4347.8 
 
 H 
 
 159.49 
 
 189.39 
 
 % 
 
 593.95 
 
 1361.2 
 
 % 
 
 1304.2 
 
 4428.8 
 
 H 
 
 165.13 
 
 199.53 
 
 % 
 
 604 . 80 
 
 1398.6 
 
 V2 
 
 1320.3 
 
 4510.9 
 
 % 
 
 170.87 
 
 210.03 
 
 14 
 
 615.75 
 
 1436.8 
 
 % 
 
 1336.4 
 
 4593.9 
 
 H 
 
 176.71 
 
 220.89 
 
 % 
 
 626.80 
 
 1475.6 
 
 % 
 
 1352.7 
 
 4677.9 
 
 5/^ 
 
 182.66 
 
 232.13 
 
 H 
 
 637.95 
 
 1515.1 
 
 li 
 
 1369.0 
 
 4763.0 
 
 3/ 
 
 188.69 
 
 243.73 
 
 % 
 
 649.17 
 
 1555-3 
 
 21 
 
 1385. 5 
 
 4849.1 
 
 ^i 
 
 194.83 
 
 255.72 
 
 Vi 
 
 660.52 
 
 1596.3 
 
 \i 
 
 1402.0 
 
 4936.2 
 
Spheres 
 
 Spheres — (Continued) 
 
 95 
 
 Diam. 
 
 Surface 
 
 Solidity 
 
 Diam. 
 
 Surface 
 
 Solidity 
 
 Diam. 
 
 Surface 
 
 Solidity 
 
 2lH 
 
 1418.6 
 
 5,024.3 
 
 21A 
 
 2441. I 
 
 11,341 
 
 345^2 
 
 3739.3 
 
 21,501 
 
 n 
 
 1435.4 
 
 5.113.5 
 
 28 
 
 2463.0 
 
 11.494 
 
 A 
 
 3766.5 
 
 21,736 
 
 H 
 
 1452.2 
 
 5.203.7 
 
 A 
 
 2485.1 
 
 11,649 
 
 % 
 
 3793.7 
 
 21,972 
 
 ^A 
 
 1469.2 
 
 5,295.1 
 
 M 
 
 2507.2 
 
 11,805 
 
 A 
 
 3821 . I 
 
 22,210 
 
 % 
 
 1486.2 
 
 5,397.4 
 
 % 
 
 2529.5 
 
 11,962 
 
 35 
 
 3848.5 
 
 22,449 
 
 ^ 
 
 1S03.3 
 
 5.480.8 
 
 Vi 
 
 2551. 8 
 
 12,121 
 
 A 
 
 3876.1 
 
 22,691 
 
 22 
 
 1520.5 
 
 5,575.3 
 
 % 
 
 2574.3 
 
 12,281 
 
 H 
 
 3903.7 
 
 22,934 
 
 H 
 
 1537.9 
 
 5,670.8 
 
 % 
 
 2596.7 
 
 12,443 
 
 A 
 
 3931.5 
 
 23,179 
 
 H 
 
 1555.3 
 
 5,767.6 
 
 A 
 
 2619.4 
 
 12,606 
 
 A 
 
 3959.2 
 
 23,425 
 
 % 
 
 1572.8 
 
 5,865.2 
 
 29 
 
 2642 . I 
 
 12,770 
 
 A 
 
 3987.2 
 
 23,674 
 
 H 
 
 1590.4 
 
 5,964.1 
 
 A 
 
 2665.0 
 
 12,936 
 
 % 
 
 4015.2 
 
 23,924 
 
 % 
 
 1608.2 
 
 6,064.1 
 
 }i 
 
 2687.8 
 
 13,103 
 
 A 
 
 4043.3 
 
 24,176 
 
 % 
 
 1626.0 
 
 6,165.2 
 
 34 
 
 2710.9 
 
 13.272 
 
 36 
 
 4071.5 
 
 24,429 
 
 ^i 
 
 1643.9 
 
 6,267.3 
 
 A 
 
 2734.0 
 
 13.442 
 
 A 
 
 4099.9 
 
 24,685 
 
 23 
 
 1661.9 
 
 6,370.6 
 
 H 
 
 2757.3 
 
 13.614 
 
 34 
 
 4128.3 
 
 24,942 
 
 H 
 
 1680.0 
 
 6,475.0 
 
 M 
 
 2780.5 
 
 13.787 
 
 A 
 
 4156.9 
 
 25,201 
 
 M 
 
 1698.2 
 
 6,580.6 
 
 A 
 
 2804.0 
 
 13.961 
 
 A 
 
 4185.5 
 
 25,461 
 
 ?^ 
 
 1716.5 
 
 6,687.3 
 
 30 
 
 2827.4 
 
 14.137 
 
 A 
 
 4214. I 
 
 25,724 
 
 H 
 
 1735.0 
 
 6,795.2 
 
 A 
 
 2851 . I 
 
 14.315 
 
 % 
 
 4243.0 
 
 25,988 
 
 % 
 
 1753.5 
 
 6,904.2 
 
 A 
 
 2874.8 
 
 14.494 
 
 A 
 
 4271.8 
 
 26,254 
 
 % 
 
 1772. I 
 
 7,014 3 
 
 H 
 
 2898.7 
 
 14.674 
 
 37 
 
 4300.9 
 
 26,522 
 
 % 
 
 1790.8 
 
 7,125.6 
 
 A 
 
 2922.5 
 
 14.856 
 
 A 
 
 4330.0 
 
 26,792 
 
 24 
 
 1809.6 
 
 7,238.2 
 
 % 
 
 2946.6 
 
 15.039 
 
 1/4 
 
 4359.2 
 
 27,063 
 
 ?^ 
 
 1828.5 
 
 7,351.9 
 
 % 
 
 2970.6 
 
 15,224 
 
 % 
 
 4388.5 
 
 27,337 
 
 Vi 
 
 1847.5 
 
 7,466.7 
 
 A 
 
 2994.9 
 
 15,411 
 
 A 
 
 4417.9 
 
 27,612 
 
 % 
 
 1866.6 
 
 7,583.0 
 
 31 
 
 3019. I 
 
 15,599 
 
 A 
 
 4447.5 
 
 27,889 
 
 Vi 
 
 1885.8 
 
 7,700.1 
 
 A 
 
 3043.6 
 
 15,788 
 
 % 
 
 4477.1 
 
 28,168; 
 
 H 
 
 1905. I 
 
 7,818.6 
 
 A 
 
 3068.0 
 
 15,979 
 
 A 
 
 4506.8 
 
 28.449 
 
 % 
 
 1924.4 
 
 7,938.3 
 
 y& 
 
 3092.7 
 
 16,172 
 
 38 
 
 4536.5 
 
 28,731 
 
 % 
 
 1943.9 
 
 8,059.2 
 
 Vi 
 
 3117.3 
 
 16,366 
 
 A 
 
 4566.5 
 
 29,016 
 
 25 
 
 1963.5 
 
 8,181.3 
 
 A 
 
 3142. I 
 
 16,561 
 
 H 
 
 4596.4 
 
 29,302 
 
 li 
 
 1983.2 
 
 8,304.7 
 
 % 
 
 3166.9 
 
 16,758 
 
 3/8 
 
 4626.5 
 
 29,590 
 
 H 
 
 2002.9 
 
 8,429.2 
 
 A 
 
 3192.0 
 
 16,957 
 
 A 
 
 4656.7 
 
 29,880 
 
 % 
 
 2022 . 9 
 
 8,554.9 
 
 32 
 
 3217.0 
 
 17.157 
 
 5/8 
 
 4686.9 
 
 30,173 
 
 ^ 
 
 2042.8 
 
 8,682.0 
 
 A 
 
 3242.2 
 
 17.359 
 
 3/4 
 
 4717.3 
 
 30,466 
 
 5,^ 
 
 2062 . 9 
 
 8.810.3 
 
 Vi 
 
 3267.4 
 
 17.563 
 
 A 
 
 4747.9 
 
 30,762 
 
 ^4 
 
 2083.0 
 
 8,939.9 
 
 % 
 
 3292.9 
 
 17.768 
 
 39 
 
 4778.4 
 
 31,059 
 
 ?^ 
 
 2103.4 
 
 9,070.6 
 
 Vi 
 
 3318.3 
 
 17.974 
 
 A 
 
 4809.0 
 
 31,359 
 
 26 
 
 2123.7 
 
 9,202.8 
 
 A 
 
 3343.9 
 
 18,182 
 
 H 
 
 4839.9 
 
 31,661 
 
 \i 
 
 2144.2 
 
 9,336.2 
 
 % 
 
 3369.6 
 
 18,392 
 
 A 
 
 4870.8 
 
 31,964 
 
 H 
 
 2164.7 
 
 9.470.8 
 
 A 
 
 3395.4 
 
 18,604 
 
 A 
 
 4901.7 
 
 32,270 
 
 ?i 
 
 2185.5 
 
 9,606.7 
 
 33 
 
 3421.2 
 
 18,817 
 
 A 
 
 4932.7 
 
 32,577 
 
 1/^ 
 
 2206.2 
 
 9,744.0 
 
 A 
 
 3447.3 
 
 19.032 
 
 % 
 
 4964.0 
 
 32,886 
 
 5/i 
 
 2227.1 
 
 9,882.5 
 
 A 
 
 3473.3 
 
 19,248 
 
 % 
 
 4995.3 
 
 33,197 
 
 % 
 
 2248.0 
 
 10,022 
 
 A 
 
 3499.5 
 
 19.466 
 
 40 
 
 5026.5 
 
 33,510 
 
 ''A 
 
 2269.1 
 
 10,164 
 
 A 
 
 3525.7 
 
 19,685 
 
 A 
 
 5058.1 
 
 33,826 
 
 27 
 
 2290.2 
 
 10,306 
 
 A 
 
 3552.1 
 
 19.907 
 
 Yi 
 
 5089.6 
 
 34.143 
 
 H 
 
 2311.5 
 
 10,450 
 
 % 
 
 3578.5 
 
 20,129 
 
 A 
 
 5121.3 
 
 34.462 
 
 H 
 
 2332.8 
 
 10,595 
 
 A 
 
 3605.1 
 
 20,354 
 
 A 
 
 5153. I 
 
 34.783 
 
 % 
 
 2354.3 
 
 10,741 
 
 34 
 
 3631.7 
 
 20,580 
 
 A 
 
 5184.9 
 
 35.106 
 
 H 
 
 2375.8 
 
 10,889 
 
 A 
 
 36S8.5 
 
 20,808 
 
 A 
 
 5216.9 
 
 35.431 
 
 5^ 
 
 2397.5 
 
 11,038 
 
 Vi 
 
 3685.3 
 
 21,037 
 
 A 
 
 5248.9 
 
 35,758 
 
 % 
 
 2419.2 
 
 11,189 
 
 A 
 
 3712.3 
 
 21,268 
 
 41 
 
 5281 . I 
 
 36.087 
 
96 
 
 Mathematical Tables 
 Spheres — {Continued) 
 
 Diam. 
 
 Surface 
 
 Solidity 
 
 Diam 
 
 Surface 
 
 Solidity. 
 
 Diam. 
 
 Surface 
 
 Solidity 
 
 41^ 
 
 S313.3 
 
 36.418 
 
 47% 
 
 7163. I 
 
 57,006 
 
 5A% 
 
 9,288.5 
 
 84.177 
 
 % 
 
 5345.6 
 
 36,751 
 
 % 
 
 7200.7 
 
 57,455 
 
 i/i 
 
 9,331.2 
 
 84,760 
 
 % 
 
 5378.1 
 
 37,086 
 
 48 
 
 7238.3 
 
 57,906 
 
 H 
 
 9,374.1 
 
 85,344 
 
 ^ 
 
 5410.7 
 
 37.423 
 
 H 
 
 7276.0 
 
 58,360 
 
 % 
 
 9,417.2 
 
 85.931 
 
 % 
 
 5443.3 
 
 37.763 
 
 Vi 
 
 7313.9 
 
 58.815 
 
 A 
 
 9,460.2 
 
 86,521 
 
 % 
 
 5476.0 
 
 38,104 
 
 % 
 
 7351.9 
 
 59,274 
 
 55 
 
 9.503.2 
 
 87.114 
 
 % 
 
 5508.9 
 
 38,448 
 
 V2 
 
 7389.9 
 
 59.734 
 
 H 
 
 9.546.5 
 
 87.709 
 
 42 
 
 5541.9 
 
 38,792 
 
 % 
 
 7428.0 
 
 60,197 
 
 H 
 
 9,590.0 
 
 88,307 
 
 % 
 
 5574.9 
 
 39.140 
 
 H 
 
 7466.3 
 
 60,663 
 
 H 
 
 9.633.3 
 
 88.908 
 
 H 
 
 5608.0 
 
 39,490 
 
 % 
 
 7504.5 
 
 61,131 
 
 Yi 
 
 9.676.8 
 
 89.511 
 
 H 
 
 5641.3 
 
 39.841 . 
 
 49 
 
 7543.1 
 
 61,601 
 
 n 
 
 9.720.6 
 
 90.117 
 
 Vi 
 
 5674.5 
 
 40,194 
 
 H 
 
 7581.6 
 
 62,074 
 
 % 
 
 9,764.4 
 
 90,726 
 
 % 
 
 5708.0 
 
 40.551 
 
 H 
 
 7620.1 
 
 62,549 
 
 A 
 
 9,808.1 
 
 91,338 
 
 % 
 
 5741.5 
 
 40,908 
 
 H 
 
 7658.9 
 
 63,026 
 
 56 
 
 9,852.0 
 
 91,953 
 
 'A 
 
 5775.2 
 
 41,268 
 
 H 
 
 7697.7 
 
 63,506 
 
 H 
 
 ■9.896.0 
 
 92.570 
 
 43 
 
 5808.8 
 
 41,630 
 
 % 
 
 7736.7 
 
 63,989 
 
 M 
 
 9,940.2 
 
 93,190 
 
 i/i 
 
 5842.7 
 
 41,994 
 
 % 
 
 7775 • 7 
 
 64.474 
 
 % 
 
 9.984.4 
 
 93.812 
 
 H 
 
 5876. 5 
 
 42,360 
 
 li 
 
 7814.8 
 
 64,961 
 
 ¥2 
 
 10,029 
 
 94.438 
 
 % 
 
 5910.7 
 
 42,729 
 
 50 
 
 7854.0 
 
 65,450 
 
 % 
 
 10,073 
 
 95,066 
 
 Vi 
 
 5944.7 
 
 43,099 
 
 H 
 
 7893.3 
 
 65,941 
 
 % 
 
 10.118 
 
 95,697 
 
 H 
 
 5978.9 
 
 43,472 
 
 Vi 
 
 7932.8 
 
 66,436 
 
 ■A 
 
 10,163 
 
 96.330 
 
 H 
 
 6013.2 
 
 43,846 
 
 3/8 
 
 7972.2 
 
 66,934 
 
 SI 
 
 10,207 
 
 96,967 
 
 li 
 
 6047.7 
 
 44.224 
 
 V2 
 
 8011.8 
 
 67.433 
 
 H 
 
 10,252 
 
 97,606 
 
 44 
 
 6082.1 
 
 44,602 
 
 ^A 
 
 8051 . 6 
 
 67,935 
 
 H 
 
 10,297 
 
 98,248 
 
 H 
 
 6116.8 
 
 44,984 
 
 % 
 
 8091.4 
 
 68,439 
 
 % 
 
 10,342 
 
 98.893 
 
 'A 
 
 6151.5 
 
 45,367 
 
 A 
 
 8131.3 
 
 68,946 
 
 V2 
 
 10.387 
 
 99,541 
 
 H 
 
 6186.3 
 
 45.753 
 
 51 
 
 8171.2 
 
 69.456 
 
 % 
 
 10,432 
 
 100,191 
 
 H 
 
 6221 . 2 
 
 46.141 
 
 % 
 
 8211.4 
 
 69,967 
 
 % 
 
 10.478 
 
 100,84s 
 
 % 
 
 6256.1 
 
 46,530 
 
 M 
 
 8251 . 6 
 
 70,482 
 
 7/8 
 
 10.523 
 
 101,501 
 
 % 
 
 6291 . 2 
 
 46,922 
 
 ^/i 
 
 8292.0 
 
 70,999 
 
 58 
 
 10,568 
 
 102,161 
 
 % 
 
 6326.5 
 
 47,317 
 
 Vi 
 
 8332.3 
 
 71,519 
 
 H 
 
 10,614 
 
 102,823 
 
 45 
 
 6361.7 
 
 47.713 
 
 5/8 
 
 8372.8 
 
 72,040 
 
 H 
 
 10,660 
 
 103,488 
 
 % 
 
 6397.2 
 
 48,112 
 
 % 
 
 8413.4 
 
 72,56s 
 
 % 
 
 10,706 
 
 104,155 
 
 H 
 
 6432.7 
 
 48,513 
 
 % 
 
 8454.1 
 
 73,092 
 
 /2 
 
 10,751 
 
 104,826 
 
 % 
 
 6468.3 
 
 48,916 
 
 52 
 
 8494.8 
 
 73,622 
 
 % 
 
 10,798 
 
 105.499 
 
 H 
 
 6503.9 
 
 49.321 
 
 Vs 
 
 8535.8 
 
 74,154 
 
 % 
 
 10,844 
 
 106,17s 
 
 54 
 
 6539.7 
 
 49.729 
 
 H 
 
 8576.8 
 
 74.689 
 
 % 
 
 10,890 
 
 106.854 
 
 H 
 
 6575.5 
 
 50,139 
 
 y& 
 
 8617.8 
 
 75.226 
 
 59 
 
 10,936 
 
 107,536 
 
 % 
 
 6611.6 
 
 50,551 
 
 K2 
 
 8658.9 
 
 75,767 
 
 i/i 
 
 10,983 
 
 108,221 
 
 46 
 
 6647.6 
 
 50,965 
 
 5/8 
 
 8700.4 
 
 76,309 
 
 H 
 
 11,029 
 
 108,909 
 
 H 
 
 6683.7 
 
 51,382 
 
 % 
 
 8741.7 
 
 76.854 
 
 % 
 
 11,076 
 
 109,600 
 
 H 
 
 6720.0 
 
 51,801 
 
 % 
 
 8783.2 
 
 77,401 
 
 V2 
 
 11,122 
 
 110,294 
 
 % 
 
 6756.5 
 
 52,222 
 
 53 
 
 8824.8 
 
 77,952 
 
 54 
 
 11,169 
 
 110,990 
 
 Vi 
 
 6792.9 
 
 52,645 
 
 Ks 
 
 8866.4 
 
 78,505 
 
 % 
 
 11,216 
 
 111,690 
 
 H 
 
 6829.5 
 
 53,071 
 
 Vi 
 
 8908.2 
 
 79,060 
 
 A 
 
 11,263 
 
 112,392 
 
 % 
 
 6866.1 
 
 53,499 
 
 % 
 
 8950.1 
 
 79,617 
 
 60 
 
 11,310 
 
 113,098 
 
 % 
 
 6902.9 
 
 53,929 
 
 Vi 
 
 8992.0 
 
 80,178 
 
 /8 
 
 11.357 
 
 113.806 
 
 47 
 
 6939 -9 
 
 54.362 
 
 % 
 
 9034.1 
 
 80,741 
 
 /4 
 
 11,404 
 
 114,518 
 
 % 
 
 6976.8 
 
 54,797 
 
 % 
 
 9076.4 
 
 81,308 
 
 34 
 
 11.452 
 
 115,232 
 
 H 
 
 7013.9 
 
 55,234 
 
 % 
 
 9118.5 
 
 81,876 
 
 /2 
 
 11,499 
 
 115,949 
 
 H 
 
 7050.9 
 
 55,674 
 
 54 
 
 9160.8 
 
 82,448 
 
 % 
 
 11.547 
 
 116,669 
 
 H 
 
 7088.3 
 
 56,115 
 
 i/i 
 
 9203.3 
 
 83,021 
 
 M 
 
 11,595 
 
 117.392 
 
 ^ 
 
 7125.6 
 
 56.559 
 
 Yi 
 
 9246.0 
 
 83,598 
 
 ^i 
 
 11,642 
 
 118,118 
 
Spheres 
 Spheres — (Continued) 
 
 97 
 
 Diam. 
 
 Surface 
 
 Solidity 
 
 Diam. 
 
 Surface 
 
 Solidity 
 
 Diam. 
 
 Surface 
 
 Solidity 
 
 6i 
 
 11,690 
 
 118,847 
 
 67^^ 
 
 14,367 
 
 161,927 
 
 74H 
 
 17,320 
 
 214.333 
 
 H 
 
 11,738 
 
 "9,579 
 
 M 
 
 14.420 
 
 162,827 
 
 % 
 
 17,379 
 
 215,417 
 
 H 
 
 11,786 
 
 120,315 
 
 % 
 
 14,474 
 
 163.731 
 
 Vi 
 
 17,437 
 
 216,505 
 
 H 
 
 11,834 
 
 121,053 
 
 68 
 
 14,527 
 
 164.637 
 
 % 
 
 17,496 
 
 217,597 
 
 H 
 
 11,882 
 
 121,794 
 
 H 
 
 14,580 
 
 165,547 
 
 % 
 
 17,554 
 
 218,693 
 
 H 
 
 11,931 
 
 122,538 
 
 H 
 
 14,634 
 
 166,460 
 
 % 
 
 17,613 
 
 219,792 
 
 Yi 
 
 11,980 
 
 123,286 
 
 H 
 
 . 14,688 
 
 167,376 
 
 75 
 
 17,672 
 
 220,894 
 
 % 
 
 12,028 
 
 124,036 
 
 H 
 
 14,741 
 
 168,295 
 
 \i 
 
 17.731 
 
 222,001 
 
 62 
 
 12,076 
 
 124,789 
 
 5/i 
 
 14,795 
 
 169,218 
 
 M 
 
 17,790 
 
 223.111 
 
 i/i 
 
 12,126 
 
 125,545 
 
 H 
 
 14,849 
 
 170,145 
 
 % 
 
 17,849 
 
 224,224 
 
 H 
 
 12,174 
 
 126,305 
 
 % 
 
 14,903 
 
 171,074 
 
 H 
 
 17.908 
 
 225,341 
 
 H 
 
 12,223 
 
 127,067 
 
 69 
 
 14,957 
 
 172,007 
 
 ^A 
 
 17,968 
 
 226,463 
 
 \i 
 
 12,272 
 
 127,832 
 
 H 
 
 15,012 
 
 172,944 
 
 % 
 
 18,027 
 
 227,588 
 
 % 
 
 12,322 
 
 128,601 
 
 H 
 
 15.066 
 
 173,883 
 
 'A 
 
 18,087 
 
 228,716 
 
 % 
 
 12,371 
 
 129,373 
 
 H 
 
 15,120 
 
 174,828 
 
 76 
 
 18,146 
 
 229,848 
 
 % 
 
 12,420 
 
 130,147 
 
 H 
 
 15,175 
 
 175,774 
 
 \^ 
 
 18,206 
 
 230,984 
 
 63 
 
 12,469 
 
 130,925 
 
 ■H 
 
 15,230 
 
 176,723 
 
 M 
 
 18,266 
 
 232,124 
 
 i/i 
 
 12,519 
 
 131,706 
 
 H 
 
 15,284 
 
 177,677 
 
 H 
 
 18,326 
 
 233.267 
 
 M 
 
 12,568 
 
 132,490 
 
 n 
 
 15,339 
 
 178,635 
 
 H 
 
 18,386 
 
 234,414 
 
 % 
 
 12,618 
 
 133,277 
 
 70 
 
 15,394 
 
 179.595 
 
 H 
 
 18,446 
 
 235.566 
 
 H 
 
 12,668 
 
 134,067 
 
 Vs 
 
 15,449 
 
 180,559 
 
 H 
 
 18,506 
 
 236,719 
 
 H 
 
 12,718 
 
 134,860 
 
 H 
 
 15,504 
 
 181,525 
 
 Vs 
 
 18,566 
 
 237,879 
 
 % 
 
 12,768 
 
 135,657 
 
 H 
 
 15,560 
 
 182,497 
 
 77 
 
 18,626 
 
 239,041 
 
 % 
 
 12,818 
 
 136,456 
 
 V2 
 
 15,615 
 
 183,471 
 
 Vs 
 
 18,687 
 
 240,206 . 
 
 64 
 
 12,868 
 
 137,250 
 
 5/8 
 
 15,670 
 
 184,449 
 
 \i 
 
 18,748 
 
 241.376 
 
 H 
 
 12,918 
 
 138,065 
 
 % 
 
 15,726 
 
 185,430 
 
 H 
 
 18,809 
 
 242.551 
 
 H 
 
 12,969 
 
 138,874 
 
 Vs 
 
 15,782 
 
 186,414 
 
 H 
 
 18,869 
 
 243,728 
 
 3/i 
 
 13,019 
 
 139,686 
 
 71 
 
 15,837 
 
 187,402 
 
 5/8 
 
 18,930 
 
 244,908 
 
 V^ 
 
 13,070 
 
 140,501 
 
 H 
 
 15,893 
 
 188,394 
 
 M 
 
 18,992 
 
 246,093 
 
 H 
 
 13,121 
 
 141,320 
 
 H 
 
 15,949 
 
 189,389 
 
 % 
 
 19.053 
 
 247,283 
 
 % 
 
 13,172 
 
 142,142 
 
 H 
 
 16,005 
 
 190,387 
 
 78 
 
 19,114 
 
 248,47s 
 
 H 
 
 13,222 
 
 142,966 
 
 3/2 
 
 16,061 
 
 191,389 
 
 Vs 
 
 19-175 
 
 249.672 
 
 6s 
 
 13,273 
 
 143,794 
 
 ^yi 
 
 16,117 
 
 192,395 
 
 Vi 
 
 19,237 
 
 250,873 
 
 H 
 
 13,324 
 
 144,625 
 
 M 
 
 16,174 
 
 193,404 
 
 % 
 
 19,298 
 
 252,077 
 
 H 
 
 13,376 
 
 145,460 
 
 % 
 
 16,230 
 
 194,417 
 
 H 
 
 19.360 
 
 253.284 
 
 H 
 
 13,427 
 
 146,297 
 
 72 
 
 16,286 
 
 195,433 
 
 % 
 
 19,422 
 
 254.496 
 
 H 
 
 13,478 
 
 147,138 
 
 H 
 
 16,343 
 
 196,453 
 
 % 
 
 19,483 
 
 255.713 
 
 % 
 
 13,530 
 
 147,982 
 
 H 
 
 16,400 
 
 197,476 
 
 'A 
 
 19,545 
 
 256,932 
 
 % 
 
 13,582 
 
 148,828 
 
 % 
 
 16,456 
 
 198,502 
 
 79 
 
 19,607 
 
 258,15s 
 
 % 
 
 13,633 
 
 149,680 
 
 1/2 
 
 16,513 
 
 199,532 
 
 \^ 
 
 19,669 
 
 259.383 
 
 66 
 
 13,685 
 
 150,533 
 
 5/i 
 
 16,570 
 
 200,566 
 
 M 
 
 19,732 
 
 260,613 
 
 H 
 
 13,737 
 
 151,390 
 
 % 
 
 16,628 
 
 201,604 
 
 % 
 
 19,794 
 
 261,848 
 
 M 
 
 13,789 
 
 152,251 
 
 78 
 
 16,685 
 
 202,645 
 
 Yi 
 
 19,856 
 
 263,088 
 
 % 
 
 13,841 
 
 153,114 
 
 73 
 
 16,742 
 
 203,689 
 
 H 
 
 19-919 
 
 264.330 
 
 H 
 
 13,893 
 
 153,980 
 
 H 
 
 16,799 
 
 204,737 
 
 H 
 
 19,981 
 
 265.577 
 
 5i 
 
 13,946 
 
 154,850 
 
 H 
 
 16,857 
 
 205,789 
 
 li 
 
 20,044 
 
 266,829 
 
 % 
 
 13,998 
 
 155,724 
 
 % 
 
 16,914 
 
 206,844 
 
 80 
 
 20,106 
 
 268,083 
 
 % 
 
 14,050 
 
 156,600 
 
 H 
 
 16,972 
 
 207,903 
 
 A 
 
 20,170 
 
 269.342 
 
 67 
 
 14,103 
 
 157,480 
 
 % 
 
 17,030 
 
 208,966 
 
 H 
 
 20,232 
 
 270,604 
 
 H 
 
 14,156 
 
 158,363 
 
 M 
 
 17,088 
 
 210,032 
 
 H 
 
 20,296 
 
 271,871 
 
 M 
 
 14,208 
 
 159,250 
 
 li 
 
 17,146 
 
 211,102 
 
 H 
 
 20,358 
 
 273,141 . 
 
 % 
 
 14.261 
 
 160,139 
 
 74 
 
 17,204 
 
 212,175 
 
 H 
 
 20,422 
 
 274,416 
 
 H 
 
 14,314 
 
 161,032 
 
 H 
 
 17,262 
 
 213,252 
 
 % 
 
 20,485 
 
 275,694 
 
98 
 
 Mathematical Tables 
 Spheres — {Continued) 
 
 Diam. 
 
 Surface 
 
 Solidity 
 
 Diam. 
 
 Surface 
 
 Solidity 
 
 Diam. 
 
 Surface 
 
 Solidity 
 
 8o7^ 
 
 2o,549 
 
 276,977 
 
 s^% 
 
 23,984 
 
 349,269 
 
 93^/^ 
 
 27,686 
 
 433.160 
 
 81 
 
 20,6l2 
 
 278,263 
 
 H 
 
 24,053 
 
 350,771 
 
 94 
 
 27.759 
 
 434.894 
 
 H 
 
 20,676 
 
 279-553 
 
 % 
 
 24,122 
 
 352,277 
 
 H 
 
 27.833 
 
 436,630 
 
 y. 
 
 20,740 
 
 280,847 
 
 % 
 
 24,191 
 
 353,785 
 
 H 
 
 27.907 
 
 438,373 
 
 % 
 
 20,804 
 
 282,14s 
 
 7/i 
 
 24,260 
 
 355.301 
 
 % 
 
 27,981 
 
 440,118 
 
 H 
 
 20,867 
 
 283.447 
 
 88 
 
 24,328 
 
 356,819 
 
 H 
 
 28,055 
 
 441,871 
 
 H 
 
 20,932 
 
 284,754 
 
 H 
 
 24,398 
 
 358,342 
 
 % 
 
 28,130 
 
 443,62s 
 
 % 
 
 20,996 
 
 286,064 
 
 H 
 
 24,467 
 
 359,869 
 
 % 
 
 28,204 
 
 445,387 
 
 ^ 
 
 21,060 
 
 287,378 
 
 H 
 
 24.536 
 
 361,400 
 
 % 
 
 28,278 
 
 447,151 
 
 82 
 
 21,124 
 
 288,696 • 
 
 H 
 
 24.606 
 
 362,935 
 
 95 
 
 28,353' 
 
 448,920 
 
 H 
 
 21,189 
 
 290,019- 
 
 % 
 
 24,676 
 
 364,476 
 
 H 
 
 28,428 
 
 450,69s 
 
 H 
 
 21,253 
 
 291.34s 
 
 % 
 
 24,745 
 
 366,019 
 
 \i 
 
 28,503 
 
 452,475 
 
 H 
 
 21,318 
 
 292,674 
 
 A 
 
 24,815 
 
 367,568 
 
 % 
 
 28,577 
 
 454,259 
 
 H 
 
 21,382 
 
 294,010 
 
 89 
 
 24,885 
 
 369,122 
 
 Vi 
 
 28,652 
 
 456,047 
 
 % 
 
 21,448 
 
 295,347 
 
 }i 
 
 ' 24,955 
 
 370,678 
 
 n 
 
 28,727 
 
 457,839 
 
 % 
 
 21,512 
 
 296,691 
 
 H 
 
 25,025 
 
 372,240 
 
 % 
 
 28,802 
 
 459,638 
 
 % 
 
 21,578 
 
 298,036 
 
 9i 
 
 25,095 
 
 373,806 
 
 % 
 
 28,878 
 
 461,439 
 
 83 
 
 21,642 
 
 299,388 
 
 i/i 
 
 25.165 
 
 375,378 
 
 96 
 
 28,953 
 
 463,248 
 
 H 
 
 21,708 
 
 300,743 
 
 H 
 
 25,236 
 
 376,954 
 
 % 
 
 29,028 
 
 465,059 
 
 H 
 
 21,773 
 
 302,100 
 
 % 
 
 25,306 
 
 378,531 
 
 H 
 
 29,104 
 
 466,87s 
 
 . % 
 
 21,839 
 
 303.463 
 
 % 
 
 25,376 
 
 380,11s 
 
 H 
 
 29,180 
 
 468,697 
 
 H 
 
 21,904 
 
 304,831 
 
 90 
 
 25,447 
 
 381,704 
 
 V2 
 
 29,25s 
 
 470,524 
 
 % 
 
 21,970 
 
 306,201 
 
 H 
 
 25,518 
 
 383.297 
 
 n 
 
 29,331 
 
 472,354 
 
 H 
 
 22,036 
 
 307,576 
 
 H 
 
 25,589 
 
 384,894 
 
 % 
 
 29.407 
 
 474,189 
 
 Vs 
 
 22,102 
 
 308,957 
 
 H 
 
 25,660 
 
 386,496 
 
 A 
 
 29,483 
 
 476,029 
 
 84 
 
 22,167 
 
 310,340 
 
 H 
 
 25,730 
 
 388,102 
 
 97 
 
 29,559 
 
 477,874 
 
 H 
 
 22,234 
 
 311,728 
 
 5/i 
 
 25,802 
 
 389,711 
 
 H 
 
 29,636 
 
 479.725 
 
 H 
 
 22,300 
 
 313.118 
 
 H 
 
 25,873 
 
 391,327 
 
 H 
 
 29,712 
 
 481,579 
 
 % 
 
 22,366 
 
 314.514 
 
 li 
 
 25,944 
 
 392,945 
 
 % 
 
 29,788 
 
 483,438 
 
 H 
 
 22,432 
 
 315.915 
 
 91 
 
 26,016 
 
 394,570 
 
 H 
 
 29,865 
 
 485,302 
 
 ^A 
 
 22,499 
 
 317.318 
 
 Vs 
 
 26,087 
 
 396,197 
 
 5/i 
 
 29,942 
 
 487,171 
 
 % 
 
 22,565 
 
 318,726 
 
 H 
 
 26,159 
 
 397,831 
 
 % 
 
 30,018 
 
 489,04s 
 
 % 
 
 22,632 
 
 320,140 
 
 H 
 
 26,230 
 
 399.468 
 
 % 
 
 30.09s 
 
 490,924 
 
 8s 
 
 22,698 
 
 321,556 
 
 H 
 
 26,302 
 
 401,109 
 
 98 
 
 30,172 
 
 492,808 
 
 H 
 
 22,765 
 
 322,977 
 
 ^A 
 
 26,374 
 
 402,756 
 
 % 
 
 30.249 
 
 494,695 
 
 H 
 
 22,832 
 
 324.402 
 
 % 
 
 26,446 
 
 404,406 
 
 H 
 
 30.326 
 
 496,588 
 
 H 
 
 22,899 
 
 325,831 
 
 A 
 
 26,518 
 
 406,060 
 
 34 
 
 30,404 
 
 498,486 
 
 H 
 
 22,966 
 
 327.264 
 
 92 
 
 26,590 
 
 407,721 
 
 H 
 
 30,481 
 
 500,388 
 
 ^A 
 
 23.034 
 
 328,702 
 
 H 
 
 26,663 
 
 409,384 
 
 H 
 
 30,558 
 
 502,296 
 
 H 
 
 23,101 
 
 330,142 
 
 M 
 
 26,735 
 
 4II.OS4 
 
 % 
 
 30,636 
 
 S04.208 
 
 % 
 
 23,168 
 
 331.588 
 
 H 
 
 26,808 
 
 412,726 
 
 78 
 
 30.713 
 
 506,12s 
 
 86 
 
 23.23s 
 
 333.039 
 
 V2 
 
 26,880 
 
 414,405 
 
 99 
 
 30,791 
 
 508,047 
 
 H 
 
 23,303 
 
 334,492 
 
 H 
 
 26,953 
 
 416,086 
 
 A 
 
 30,869 
 
 S09.975 
 
 H 
 
 23.371 
 
 335,951 
 
 % 
 
 27,026 
 
 417,774 
 
 Vi 
 
 30,947 
 
 511,906 
 
 H 
 
 23,439 
 
 337,414 
 
 % 
 
 27.099 
 
 419,464 
 
 % 
 
 31,025 
 
 S13.843 
 
 H 
 
 23.506 
 
 338,882 
 
 93 
 
 27.172 
 
 421,161 
 
 H 
 
 31,103 
 
 SIS. 78s 
 
 H 
 
 23,575 
 
 340,352 
 
 H 
 
 27.245 
 
 422,862 
 
 H 
 
 31,181 
 
 517,730 
 
 H 
 
 23,643 
 
 341.829 
 
 H 
 
 27,318 
 
 424,567 
 
 H 
 
 31.259 
 
 S19.682 
 
 % 
 
 23.711 
 
 343,307 
 
 H 
 
 27,391 
 
 426,277 
 
 % 
 
 31.338 
 
 521,638 
 
 87 
 
 23.779 
 
 344,792 
 
 H 
 
 27,464 
 
 427,991 
 
 100 
 
 31.416 
 
 523.598 
 
 H 
 
 23.847 
 
 346,281 
 
 % 
 
 27,538 
 
 429,710 
 
 
 
 
 H 
 
 23.916 
 
 347,772 
 
 H 
 
 27,612 
 
 431,433 
 
 
 
 
Capacity of Rectangular Tanks 
 
 99 
 
 Capacity of Rectangular Tanks in U. S. Gallons for 
 Each Foot in Depth 
 
 Width of 
 tank 
 
 Ft. Ins. 
 
 2 
 
 2 6 
 3 
 
 3 6 
 4 
 
 4 6 
 5 
 
 5 6 
 6 
 
 Length of tank 
 
 2 feet 
 
 2 feet, 
 6 ins. 
 
 3 feet 
 
 3 feet, 
 6 ins. 
 
 52.36 
 65.45 
 78.54 
 91.64 
 
 4 feet 
 
 4 feet, 
 6 ins. 
 
 67.32 
 84.16 
 100.99 
 117.82 
 134.65 
 151.48 
 
 Sfeet 
 
 74.81 
 93.51 
 112. 21 
 130.91 
 149.61 
 168.31 
 187.01 
 
 5 feet, 
 
 6 ins. 
 
 82.29 
 102.86 
 123.43 
 144.00 
 164.57 
 185.14 
 205.71 
 226.28 
 
 6 feet 
 
 89.77 
 112. 21 
 134.65 
 157.09 
 179.53 
 201.97 
 224.41 
 246.86 
 269.30 
 
 
 
 
 Length of tank 
 
 
 
 Width of 
 
 
 
 
 
 
 
 tank 
 
 
 
 
 
 
 
 
 6 feet, 6 ins. 
 
 7 feet 
 
 7 feet, 6 ins. 
 
 8 feet 
 
 8 feet, 6 ins. 
 
 9 feet 
 
 Ft. Ins. 
 
 
 
 
 
 
 
 2 
 
 97.2s 
 
 104.73 
 
 112. 21 
 
 119.69 
 
 127.17 
 
 134.6s 
 
 2 6 
 
 121.56 
 
 130.91 
 
 140.26 
 
 149.61 
 
 158.96 
 
 168.31 
 
 3 
 
 145.87 
 
 157.09 
 
 168.31 
 
 179-53 
 
 190.75 
 
 202.97 
 
 3 6 
 
 170.18 
 
 183.27 
 
 196.36 
 
 209.45 
 
 222.54 
 
 235.63 
 
 4 
 
 194.49 
 
 209.45 
 
 224.41 
 
 239-37 
 
 254.34 
 
 269.30 
 
 4 6 
 
 218.80 
 
 235.63 
 
 252.47 
 
 269.30 
 
 286.13 
 
 302.96 
 
 5 
 
 243.11 
 
 261.82 
 
 280.52 
 
 299-22 
 
 317.92 
 
 336.62 
 
 5 6 
 
 267.43 
 
 288.00 
 
 308.57 
 
 329-14 
 
 349.71 
 
 370.28 
 
 6 
 
 291.74 
 
 314.18 
 
 336.62 
 
 359 06 
 
 381.50 
 
 403.94 
 
 6 6 
 
 316.05 
 
 340.36 
 
 364.67 
 
 388.98 
 
 413.30 
 
 437.60 
 
 7 
 
 
 366.54 
 
 392 . 72 
 
 418 91 
 
 455.09 
 
 476 88 
 
 471.27 
 S04.93 
 538.59 
 572.25 
 605.92 
 
 7 6 
 
 
 
 420 . 78 
 
 448 83 
 
 8 
 
 
 
 
 478 75 
 
 508.67 
 540.46 
 
 8 6 
 
 
 
 
 
 9 
 
 
 
 
 
 
 
 
 
 
 
lOO 
 
 Mathematical Tables 
 
 Capacity of Rectangular Tanks in U. S. Gallons for 
 Each Foot in Depth — {Continued) 
 
 
 Length of tank 
 
 Width of 
 
 
 
 
 
 
 
 tank 
 
 9 feet, 
 
 
 10 feet, 
 
 
 II feet. 
 
 
 
 6 ins. 
 
 10 feet 
 
 6 ins. 
 
 II feet 
 
 6 ins. 
 
 12 feet 
 
 Ft. Ins. 
 
 
 
 
 
 
 
 2 
 
 142.13 
 
 149.61 
 
 157.09 
 
 164-57 
 
 172. OS 
 
 179. S3 
 
 2 6 
 
 177.66 
 
 187.01 
 
 196.36 
 
 205.71 
 
 215.06 
 
 224.41 
 
 3 
 
 213.19 
 
 224.41 
 
 235.68 
 
 246.86 
 
 258.07 
 
 269.03 
 
 3 6 
 
 248.73 
 
 261.82 
 
 274.90 
 
 288.00 
 
 301.09 
 
 314.18 
 
 4 
 
 284.26 
 
 299.22 
 
 314.18 
 
 329-14 
 
 344- 10 
 
 359 -06 
 
 4 6 
 
 319.79 
 
 336.62 
 
 353-45 
 
 370.28 
 
 385.10 
 
 403-94 
 
 5 
 
 355-32 
 
 374.03 
 
 392.72 
 
 411-43 
 
 430.13 
 
 448.83 
 
 5 6 
 
 390. 85 
 
 411.43 
 
 432.00 
 
 452.57 
 
 473-14 
 
 493-71 
 
 6 
 
 426.39 
 
 448.83 
 
 471-27 
 
 493-71 
 
 S16.15 
 
 538.59 
 
 6 6 
 
 461.92 
 
 486.23 
 
 510.54 
 
 534.85 
 
 559.16 
 
 ■583.47 
 
 7 
 
 497.45 
 
 523.64 
 
 549.81 
 
 575-99 
 
 602.18 
 
 628.36 
 
 7 6 
 
 523.98 
 
 561.04 
 
 589.08 
 
 617.14 
 
 645.19 
 
 673.24 
 
 8 
 
 568. SI 
 
 598.44 
 
 628.36 
 
 658.28 
 
 688.20 
 
 718.12 
 
 8 6 
 
 604.05 
 
 635.84 
 
 667.63 
 
 699-42 
 
 713-21 
 
 763.00 
 
 9 
 
 639.58 
 
 673.25 
 
 706.90 
 
 740.56 
 
 774-23 
 
 807.89 
 
 9 6 
 
 675.11 
 
 710.65 
 
 746.17 
 
 781.71 
 
 817.24 
 
 852.77 
 
 lO 
 
 
 748.05 
 
 785.45 
 
 822.86 
 
 860.26 
 
 897.66 
 
 lo 6 
 
 
 
 824.73 
 
 864.00 
 
 903-26 
 
 942.56 
 
 II 
 
 
 
 
 905.14 
 
 946 . 27 
 
 987 . 43 
 
 II 6 
 
 
 
 
 
 989.29 
 
 1032 3 
 
 12 
 
 
 
 
 
 
 1077 . 2 
 
 
 
 
 
 
 
 Number of Barrels (31.5 Gallons) in Cisterns and Tanks 
 
 I Bbl. 31.S Gallons 4-2109 Cubic Feet. 
 
 
 Diameter in feet 
 
 Depth in 
 
 
 
 
 
 
 
 
 
 feet 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 10 
 
 II 
 
 12 
 
 I 
 
 4.663 
 
 6.714 
 
 9.139 
 
 11.937 
 
 15.108 
 
 18.652 
 
 22.659 
 
 26.859 
 
 S 
 
 23.3 
 
 36.6 
 
 45. 7 
 
 59.7 
 
 75.5 
 
 93.3 
 
 112. 8 
 
 134.3 
 
 6 
 
 28.0 
 
 40.3 
 
 54.8 
 
 71.6 
 
 90.6 
 
 III. 9 
 
 135.4 
 
 161. 2 
 
 7 
 
 32.6 
 
 47.0 
 
 64.0 
 
 83.6 
 
 105.10 
 
 130.6 
 
 158.0 
 
 188.0 
 
 8 
 
 37.3 
 
 53.7 
 
 73.1 
 
 95.5 
 
 120.9 
 
 149.2 
 
 180.6 
 
 214.9 
 
 9 
 
 42.0 
 
 60.4 
 
 82.3 
 
 107.4 
 
 136.0 
 
 167.9 
 
 203.1 
 
 241.7 
 
 10 
 
 46.6 
 
 67.1 
 
 91.4 
 
 II9-4 
 
 151. 1 
 
 186.5 
 
 225.7 
 
 268.6 
 
 II 
 
 51.3 
 
 73.9 
 
 100.5 
 
 131. 3 
 
 166.3 
 
 205.2 
 
 248.3 
 
 295.4 
 
 12 
 
 56.0 
 
 80.6 
 
 109.7 
 
 143.2 
 
 181. 3 
 
 223.8 
 
 270.8 
 
 322.3 
 
 13 
 
 60.6 
 
 87.3 
 
 118. 8 
 
 152.2 
 
 196.4 
 
 242.5 
 
 293.4 
 
 349.2 
 
 14 
 
 65.3 
 
 94.0 
 
 127.9 
 
 167. 1 
 
 211. s 
 
 261. 1 
 
 316.0 
 
 376.0 
 
 15 
 
 69. Q 
 
 100.7 
 
 137. 1 
 
 179. 1 
 
 226.6 
 
 289.8 
 
 338.5 
 
 402.9 
 
 16 
 
 74.6 
 
 107.4 
 
 146.2 
 
 191. 
 
 241.7 
 
 298.4 
 
 361. 1 
 
 429.7 
 
 17 
 
 79.3 
 
 114. 1 
 
 155.4 
 
 202.9 
 
 256.8 
 
 317. 1 
 
 383.7 
 
 456.6 
 
 18 
 
 83.9 
 
 120.9 
 
 164. 5 
 
 214.9 
 
 271.9 
 
 335.7 
 
 406.2 
 
 483.5 
 
 19 
 
 88.6 
 
 127.6 
 
 173.6 
 
 226.8 
 
 287.1 
 
 354.4 
 
 428.8 
 
 510.3 
 
 20 
 
 93.3 
 
 134.3 
 
 182.8 
 
 238.7 
 
 302.2 
 
 373.0 
 
 451.4 
 
 537.2 
 
Number of Barrels in Cisterns and Tanks 
 
 lOI 
 
 Number of Barrels (31.5 Gallons) in Cisterns and 
 Tanks — {Continued) 
 
 
 
 
 
 Diameter in feet 
 
 
 
 
 Depth 
 
 
 
 
 
 
 
 
 
 
 in feet 
 
 
 
 
 
 
 
 
 
 
 
 13 
 
 14 
 
 15 
 
 16 
 
 17 
 
 18 
 
 19 
 
 20 
 
 21 
 
 I 
 
 31.522 
 
 36.557 
 
 41.9 
 
 47-7 
 
 53.9 
 
 60.4 
 
 67-3 
 
 74.6 
 
 82.2 
 
 5 
 
 157.6 
 
 182.8 
 
 209.8 
 
 238.7 
 
 269.5 
 
 203.2 
 
 336.7 
 
 373.0 
 
 441.3 
 
 6 
 
 199. 1 
 
 219.3 
 
 251.8 
 
 286.5 
 
 323.4 
 
 362.6 
 
 404.0 
 
 447.6 
 
 493.6 
 
 7 
 
 220.7 
 
 255.9 
 
 293.8 
 
 334.2 
 
 377.3 
 
 423.0 
 
 471.3 
 
 522.2 
 
 575.8 
 
 8 
 
 252 2 
 
 292. 5 
 
 335.7 
 
 382.0 
 
 431-2 
 
 483.4 
 
 538.7 
 
 590.8 
 
 658.0 
 
 9 
 
 283.7 
 
 329.0 
 
 377.7 
 
 429.7 
 
 485.1 
 
 543.9 
 
 606.0 
 
 671.5 
 
 740.3 
 
 10 
 
 315.2 
 
 365.6 
 
 419.7 
 
 477.5 
 
 539.0 
 
 604.3 
 
 673.3 
 
 746.1 
 
 822.5 
 
 II 
 
 346.7 
 
 402.1 
 
 461.6 
 
 525.2 
 
 592.9 
 
 664.7 
 
 740.7 
 
 820.7 
 
 904.8 
 
 12 
 
 378.3 
 
 438.7 
 
 503.6 
 
 573.0 
 
 646.8 
 
 725.2 
 
 808.0 
 
 895.3 
 
 987.0 . 
 
 13 
 
 409.8 
 
 475.2 
 
 545.6 
 
 620.7 
 
 700.7 
 
 785.6 
 
 875.3 
 
 969.9 
 
 1069.3 
 
 14 
 
 441.3 
 
 5II.8 
 
 587.5 
 
 668.5 
 
 754.6 
 
 846.0 
 
 942.6 
 
 1044.5 
 
 II5I.S 
 
 IS 
 
 472.8 
 
 548.4 
 
 629. s 
 
 716.2 
 
 808.5 
 
 906.5 
 
 lOIO.O 
 
 III9.I 
 
 1223.8 
 
 16 
 
 504.4 
 
 584.9 
 
 671.5 
 
 764.0 
 
 862.4 
 
 966.9 
 
 1077.3 
 
 II93.7 
 
 I3I6.0 
 
 17 
 
 535.9 
 
 621.5 
 
 713.4 
 
 811. 7 
 
 916.4 
 
 1027.4 
 
 II44.6 
 
 1268.3 
 
 1398.3 
 
 18 
 
 567.4 
 
 658.0 
 
 755.4 
 
 859.5 
 
 970.3 
 
 1087.8 
 
 I2I2.0 
 
 1342.9 
 
 1480.6 
 
 19 
 
 598.9 
 
 694.6 
 
 797.4 
 
 907.2 
 
 1024.2 
 
 1148.2 
 
 1279-3 
 
 I4I7.5 
 
 1562.8 
 
 20 
 
 630.4 
 
 731. 1 
 
 839-3 
 
 955.0 
 
 1078. I 
 
 1208.6 
 
 1346.6 
 
 1492. I 
 
 1645-1 
 
 
 
 
 
 Diameter 
 
 nfeet 
 
 
 
 Depth in 
 
 
 
 
 
 
 
 
 feet 
 
 
 
 
 
 
 
 
 
 
 
 22 
 
 23 
 
 24 
 
 25 
 
 26 
 
 27 
 
 28 
 
 29 
 
 30 
 
 I 
 
 90-3 
 
 98.6 
 
 107.4 
 
 116. 6 
 
 126. 1 
 
 136.0 
 
 148.2 
 
 157.9 
 
 167.9 
 
 5 
 
 451 -4 
 
 483.3 
 
 537-2 
 
 582.9 
 
 630.4 
 
 679.8 
 
 731. 1 
 
 784.3 
 
 839.3 
 
 6 
 
 541.6 
 
 592.0 
 
 644.6 
 
 699.4 
 
 756.5 
 
 815.8 
 
 877.4 
 
 941 -I 
 
 1007.2 
 
 7 
 
 631.9 
 
 690.7 
 
 752.0 
 
 816.0 
 
 882.6 
 
 951.8 
 
 1023.6 
 
 1098.0 
 
 1175.0 
 
 8 
 
 722.2 
 
 789.3 
 
 859.5 
 
 932.6 
 
 1008.7 
 
 1087.7 
 
 1169.8 
 
 1254.9 
 
 1342.9 
 
 9 
 
 812.5 
 
 888.0 
 
 966.9 
 
 1049. I 
 
 1134.7 
 
 1223.7 
 
 1316.0 
 
 1411.7 
 
 1510.8 
 
 10 
 
 902.7 
 
 986.7 
 
 1074.3 
 
 1165.7 
 
 1260.8 
 
 1359.7 
 
 1462.2 
 
 1568.6 
 
 1678.6 
 
 II 
 
 993.0 
 
 1085.3 
 
 1181.8 
 
 1282.3 
 
 1386.9 
 
 1495.6 
 
 1608.5 
 
 1725.4 
 
 1846.5 
 
 12 
 
 1083.3 
 
 1184.0 
 
 1289.2 
 
 1398.8 
 
 1513.0 
 
 1631.6 
 
 1764.7 
 
 1882.3 
 
 2014.0 
 
 13 
 
 1173.5 
 
 1282.7 
 
 1396.6 
 
 1515.4 
 
 '1639. 1 
 
 1767.6 
 
 1900.9 
 
 2039.2 
 
 2182.2 
 
 14 
 
 1263.8 
 
 1381.3 
 
 1504.0 
 
 1632.6 
 
 1765.2 
 
 1903.6 
 
 2047.2 
 
 2196.0 
 
 2350.1 
 
 15 
 
 1354. I 
 
 1480.0 
 
 1611.5 
 
 1748.6 
 
 1891.2 
 
 2039.5 
 
 2193-4 
 
 2352.9 
 
 2517.9 
 
 16 
 
 1444.4 
 
 1578.7 
 
 1718.9 
 
 1865. I 
 
 2017.3 
 
 2175.5 
 
 2339.6 
 
 2509.7 
 
 2685.8 
 
 17 
 
 1534.5 
 
 1677.3 
 
 1826.3 
 
 1981.7 
 
 2143.4 
 
 2311.5 
 
 2485.8 
 
 2666.6 
 
 2853-7 
 
 18 
 
 1624.9 
 
 1776.0 
 
 1933.8 
 
 2098.3 
 
 2269.5 
 
 2447.4 
 
 2632.0 
 
 2823.4 
 
 3021.5 
 
 19 
 
 1715.2 
 
 1874.7 
 
 2041 . 2 
 
 2214.8 
 
 2395.6 
 
 2583.4 
 
 2778.3 
 
 2980.3 
 
 3189-4 
 
 20 
 
 180S.5 
 
 1973.3 
 
 2148.6 
 
 2321.4 
 
 2521.7 
 
 2719.4 
 
 2924.5 
 
 3137.2 3357-3 
 
I02 
 
 Mathematical Tables 
 
 Contents of Cylinders, or Pipes 
 Contents for one foot in length, in cubic feet, and in U. S. 
 gallons of 231 cubic inches, or 7.4805 gallons to a cubic foot. A cubic 
 foot of water weighs about 62H lbs.; and a gallon about 8H lbs. Diams. 
 2, 3, or 10 times as great give 4, 9, or 100 times the content. 
 
 
 
 For I foot 
 
 in 
 
 
 
 For I foot in 
 
 
 
 length 
 
 
 
 
 length 
 
 
 Diam- 
 eter in 
 decimals 
 of a foot 
 
 
 
 Diam- 
 eter in 
 inches 
 
 Diam- 
 eter in 
 decimals 
 of a foot 
 
 
 
 Diam- 
 eter in 
 inches 
 
 Cubic p 
 feet. Also \ 
 
 allons 
 f 231 
 
 Cubic 
 feet. Also 
 
 Gallons 
 of 231 
 
 
 
 area in 
 square -^ 
 feet 
 
 ubic 
 iches 
 
 
 
 area in 
 
 square 
 
 feet 
 
 cubic 
 inches 
 
 H 
 
 .0208 
 
 .0003 
 
 .0025 
 
 ^ 
 
 .6250 
 
 .3068 
 
 2.29s 
 
 Me 
 
 .0260 
 
 .0005 
 
 .0040 
 
 Vi 
 
 .6458 
 
 .3276 
 
 2.450 
 
 % 
 
 .0313 
 
 .0008 
 
 .0057 
 
 8 
 
 .6667 
 
 .3491 
 
 2.6X1 
 
 Me 
 
 .0365 
 
 .0010 
 
 .0078 
 
 Vi 
 
 .6875 
 
 .3712 
 
 2.777 
 
 \^ 
 
 .0417 
 
 .0014 
 
 0102 
 
 H 
 
 .7083 
 
 .3941 
 
 2.948 
 
 9i6 
 
 .0469 
 
 .0017 
 
 0129 
 
 Vi 
 
 .7292 
 
 .4176 
 
 3.12s 
 
 % 
 
 .0521 
 
 .0021 
 
 0159 • 
 
 9 
 
 .7500 
 
 .4418 
 
 3.30s 
 
 iMe 
 
 .0573 
 
 .0026 
 
 0193 
 
 Vi 
 
 .7708 
 
 .4667 
 
 3.491 
 
 % 
 
 .0625 
 
 .0031 
 
 0230 
 
 H 
 
 .7917 
 
 .4922 
 
 3.682 
 
 m^ 
 
 .0677 
 
 .0036 
 
 0269 
 
 Vi 
 
 .8125 
 
 .5185 
 
 3.879 
 
 li 
 
 .0729 
 
 .0042 
 
 0312 
 
 10 
 
 .8333 
 
 .5454 
 
 4.080 
 
 1^6 
 
 .0781 
 
 .0048 
 
 0359 
 
 Vi 
 
 .8542 
 
 .5730 
 
 4.286 
 
 I 
 
 .0833 
 
 .0055 
 
 0408 
 
 1/2 
 
 .8750 
 
 .6013 
 
 4.498 
 
 M 
 
 .1042 
 
 .0085 
 
 0638 
 
 % 
 
 .8958 
 
 .6303 
 
 4.71S 
 
 H 
 
 .1250 
 
 .0123 
 
 0918 
 
 II 
 
 .9167 
 
 .6600 
 
 4.937 
 
 % 
 
 .1458 
 
 .0167 
 
 1249 
 
 Vi 
 
 ■ 9375 
 
 .6903 
 
 5.164 
 
 2 
 
 .1667 
 
 .0218 
 
 1632 
 
 H 
 
 .9583 
 
 .7213 
 
 S.396 
 
 Vi ■ 
 
 .1875 
 
 .0276 
 
 2066 
 
 Vi 
 
 .9792 
 
 .7530 
 
 5.633 
 
 H 
 
 .2083 
 
 .0341 
 
 2550 
 
 12 
 
 I foot 
 
 .7854 
 
 5.87s 
 
 ¥i 
 
 .2292 
 
 .0412 
 
 3085 
 
 Vi 
 
 1.042 
 
 .8522 
 
 6. 375 
 
 3 
 
 .2500 
 
 .0491 
 
 3672 
 
 13 
 
 1.083 
 
 .9218 
 
 6.89s 
 
 Vi 
 
 .2708 
 
 .0576 
 
 4309 
 
 \i 
 
 1. 125 
 
 .9940 
 
 7.436 
 
 H 
 
 .2917 
 
 .0668 
 
 4998 
 
 14 
 
 1. 167 
 
 1.069 
 
 7.997 
 
 % 
 
 .3125 
 
 .0767 
 
 5738 
 
 J-i 
 
 1.208 
 
 1. 147 
 
 8.578 
 
 4 
 
 .3333 
 
 .0873 
 
 6528 
 
 15 
 
 1.250 
 
 1.227 
 
 9.180 
 
 H 
 
 .3542 
 
 .0985 
 
 7369 
 
 H 
 
 1.292 
 
 1. 310 
 
 9.801 
 
 Vi 
 
 .3750 
 
 .1104 
 
 8263 
 
 16 
 
 1.333 
 
 1.396 
 
 10.44 
 
 H 
 
 .3958 
 
 .1231 
 
 9206 
 
 1/2 
 
 1.375 
 
 1.485 
 
 II. II 
 
 5 
 
 .4167 
 
 . 1364 I 
 
 020 
 
 17 
 
 1. 417 
 
 1.576 
 
 11.79 
 
 »H 
 
 .4375 
 
 .1503 I 
 
 125 
 
 1/^ 
 
 1-458 
 
 1.670 
 
 12.49 
 
 5^ 
 
 .4583 
 
 . 1650 I 
 
 234 
 
 18 
 
 1.500 
 
 1.767 
 
 13.22 
 
 H 
 
 .4792 
 
 .1803 I 
 
 349 
 
 \^ 
 
 1.542 
 
 1.867 
 
 13.96 
 
 6 
 
 .5000 
 
 .1963 I 
 
 469 
 
 19 
 
 1.583 
 
 1.969 
 
 14.73 
 
 Vi 
 
 .5208 
 
 .2131 I 
 
 594 
 
 M 
 
 1.625 
 
 2.074 
 
 15.51 
 
 \i 
 
 .5417 
 
 .2304 I 
 
 724 
 
 20 
 
 1.667 
 
 2.182 
 
 16.32 
 
 Vi 
 
 .5625 
 
 .2485 I 
 
 859 
 
 H 
 
 1.708 
 
 2.292 
 
 17. IS 
 
 7 
 
 .5833 
 
 .2673 I 
 
 999 
 
 21 
 
 1.750 
 
 2.405 
 
 17.99 
 
 Vi 
 
 .6042 
 
 .2867 2 
 
 145 
 
 M 
 
 1.792 
 
 2. 521 
 
 18.86 
 
Contents of Cylinders, or Pipes 103 
 
 Contents of Cylinders^ or Pipes — {Continued) 
 
 
 
 For I 
 
 foot in 
 
 
 
 For I foot in 
 
 
 
 length 
 
 
 
 length 
 
 
 Diam- 
 eter in 
 
 
 
 Diam- 
 eter in 
 
 
 Diam- 
 
 
 
 Diam- 
 
 
 
 eter in 
 inches 
 
 decimals 
 of a foot 
 
 Cubic 
 feet. Also 
 
 Gallons 
 of 231 
 
 eter in 
 inches 
 
 decimals 
 of a foot 
 
 Cubic 
 feet. Also 
 
 Gallons 
 of 231 
 
 
 
 area m 
 
 cubic 
 
 
 
 area in 
 
 cubic 
 
 
 
 square 
 feet 
 
 inches 
 
 
 
 square 
 feet 
 
 inches 
 
 22 
 
 1.833 
 
 2.640 
 
 19.75 
 
 35 
 
 2.917 
 
 6.681 
 
 49.98 
 
 M 
 
 1.87s 
 
 2.761 
 
 20.66 
 
 36 
 
 3.000 
 
 7-069 
 
 52.88 
 
 23 
 
 1. 917 
 
 2.88s 
 
 21.58 
 
 37 
 
 3.083 
 
 7.467 
 
 55.86 
 
 ^^ 
 
 1.958 
 
 3 012 
 
 22.53 
 
 38 
 
 3.167 
 
 7.876 
 
 58.92 
 
 24 
 
 2.000 
 
 3.142 
 
 23 -SO 
 
 39 
 
 3.250 
 
 8.296 
 
 62.06 
 
 25 
 
 2.083 
 
 3.409 
 
 25.50 
 
 40 
 
 3.333 
 
 8.727 
 
 65.28 
 
 26 
 
 2.1^7 
 
 3.687 
 
 27.58 
 
 41 
 
 3.417 
 
 9.168 
 
 68.58 
 
 27 
 
 2.250 
 
 3.976 
 
 29.74 
 
 42 
 
 3.500 
 
 9.621 
 
 71.97 
 
 28 
 
 2.333 
 
 4.276 
 
 31.99 
 
 43 
 
 3-583 
 
 10.085 
 
 75.44 
 
 29 
 
 2.417 
 
 4.587 
 
 34.31 
 
 44 
 
 3-667 
 
 10. 559 
 
 78.99 
 
 30 
 
 2.500 
 
 4.909 
 
 36.72 
 
 45 
 
 3.750 
 
 II. 04s 
 
 82.62 
 
 31 
 
 2.583 
 
 5.241 
 
 39-21 
 
 46 
 
 3.833 
 
 II. 541 
 
 86.33 
 
 32 
 
 2.667 
 
 5.585 
 
 41.78 
 
 47 
 
 3.917 
 
 12.048 
 
 90.13 
 
 33 
 
 2.750 
 
 5.940 
 
 44-43 
 
 48 
 
 4.000 
 
 12.566 
 
 94.00 
 
 34 
 
 2.833 
 
 6.305 
 
 47-16 
 
 
 
 
 
 
 Table 
 
 Continued, but with 
 
 THE DlATVTF.TERS IN FeET 
 
 Diam., 
 
 Cubic 
 
 U.S. 
 
 Diam., 
 
 Cubic 
 
 U.S. 
 
 Diam., 
 
 Cubic 
 
 U.S. 
 
 feet 
 
 feet 
 
 gallons 
 
 feet 
 
 feet 
 
 gallons 
 
 feet 
 
 feet 
 
 gallons 
 
 4 
 
 12.57 
 
 94.0 
 
 8 
 
 50.27 
 
 376.0 
 
 20 
 
 314-2 
 
 2350 
 
 H 
 
 14.19 
 
 106. 1 
 
 H 
 
 56.75 
 
 424.5 
 
 21 
 
 346.4 
 
 2591 
 
 H 
 
 15.90 
 
 119. 
 
 9 
 
 63 .'62 
 
 475-9 
 
 22 
 
 380.1 
 
 2844 
 
 % 
 
 17.72 
 
 132.5 
 
 ^A 
 
 70.88 
 
 S30-2 
 
 23 
 
 415-5 
 
 3108 
 
 5 
 
 19.64 
 
 146.9 
 
 10 
 
 78.54 
 
 587-5 
 
 24 
 
 452.4 
 
 3384 
 
 Vi 
 
 21.65 
 
 161. 9 
 
 1/2 
 
 86.59 
 
 647-7 
 
 25 
 
 490.9 
 
 3672 
 
 Vi 
 
 23.76 
 
 177.7 
 
 II 
 
 95.03 
 
 710.9 
 
 26 
 
 530.9 
 
 3971 
 
 H 
 
 25-97 
 
 194.3 
 
 H 
 
 103.90 
 
 777 -o 
 
 27 
 
 572.6 
 
 4283 
 
 6 
 
 28.27 
 
 211. 5 
 
 12 
 
 113. 1 
 
 846.1 
 
 28 
 
 615.8 
 
 4606 
 
 Vi 
 
 30.68 
 
 229.5 
 
 13 
 
 132.7 
 
 992.8 
 
 29 
 
 660.5 
 
 4941 
 
 H 
 
 33-18 
 
 248.2 
 
 14 
 
 153.9 
 
 1152 
 
 30 
 
 706.9 
 
 5288 
 
 H 
 
 35.79 
 
 267.7 
 
 15 
 
 176.7 
 
 1322 
 
 31 
 
 754.8 
 
 5646 
 
 7 
 
 38.49 
 
 287.9 
 
 16 
 
 201. 1 
 
 1S04 
 
 32 
 
 804. » 
 
 6017 
 
 H 
 
 41.28 
 
 308.8 
 
 17 
 
 227.0 
 
 1698 
 
 33 
 
 855.3 
 
 6398 
 
 H 
 
 44.18 
 
 330.5 
 
 18 
 
 254.5 
 
 1904 
 
 34 
 
 907.9 
 
 6792 
 
 H 
 
 47.17 
 
 352.9 
 
 19 
 
 283.5 
 
 2121 
 
 35 
 
 963.1 
 
 7197 
 
I04 
 
 Mathematical Tables 
 
 Contents of Linings of Wells 
 
 For diameters twice as great as those in the table, for the cubic yards 
 of digging, take out those opposite one half of the greater diameter; and 
 multiply them by 4. Thus, for the cubic yards in each foot of depth of 
 a well 31 feet in diameter, first take out from the table those opposite the 
 diameter of 153'^ feet; namely, 6.989. Then 6.989 X 4 = 27.956 cubic 
 yards required for the 31 feet diameter. But for the stone lining or 
 walling, bricks or plastering, multiply the tabular quantity opposite 
 half the greater diameter by 2. Thus, the perches of stone walling for 
 each foot of depth of a well of 31 feet diameter will be 2.073 X 2 = 
 4.146. If the wall is more or less than one foot thick, within usual 
 moderate limits, it will generally be near enough for practice to assume 
 that the number of perches, or of bricks, will increase or decrease in the 
 same proportion. 
 
 The size of the bricks is taken at 8K X 4 X 2 inches; and to be laid 
 dry, or without mortar. In practice an addition of about 5 per cent 
 should be made for waste. The brick Hning is supposed to be i brick 
 thick, or 8^ ins. 
 
 Caution. — Be careful to observe that the diameters to be used for 
 the digging are greater than those for the walling, bricks, or plastering. 
 
 
 For each foot of depth 
 
 
 For each foot of depth 
 
 
 For this 
 
 For these three col- 
 
 For this 
 
 For these three col- 
 
 
 column 
 
 umns use the diameter 
 
 
 column ^ 
 
 imns use the diameter 
 
 
 use the 
 
 in clear of the lining 
 
 
 use the 
 
 in clear of the lining 
 
 Diam- 
 
 diam- 
 eter of 
 
 
 
 Diam- 
 eter 
 
 diam- 
 
 
 
 eter 
 
 
 
 
 eter of 
 
 
 
 
 in 
 
 feet 
 
 the digT 
 
 Stone 
 lining 
 
 No. of 
 
 
 in 
 feet 
 
 the dig- j^ 
 
 Jtone 
 ning 
 
 No. of 
 
 
 
 ging 
 
 I foot 
 
 bricks 
 
 Square 
 
 
 ging ^ 
 
 foot 
 
 bricks 
 
 Square 
 
 
 
 thick. 
 
 - in a 
 
 yards of 
 plaster- 
 
 
 
 lick. 
 
 • 
 
 yards of 
 plaster- 
 
 
 
 Perches 
 
 lining 
 
 
 ^ u- P^ 
 
 rches 
 
 lining 
 
 
 Cubic 
 
 of 25 
 
 I brick 
 
 ing 
 
 
 Cubic 
 
 3f2S 
 
 I brick 
 
 ing 
 
 
 yards of 
 
 cubic 
 
 thick 
 
 
 
 yards of ^ 
 
 ubic 
 
 thick 
 
 
 
 digging 
 
 feet 
 
 
 
 
 digging 
 
 feet 
 
 
 
 1 
 
 .0291 
 
 .2513 
 
 57 
 
 .3491 
 
 4 
 
 .4654 
 
 6283 
 
 227 
 
 1.396 
 
 H 
 
 .0455 
 
 .2827 
 
 71 
 
 .4364 
 
 H 
 
 .5254 
 
 6597 
 
 241 
 
 1.484 
 
 \i 
 
 .0654 
 
 .3142 
 
 85 
 
 .5236 
 
 1/2 
 
 .5890 
 
 6912 
 
 255 
 
 1. 571 
 
 H 
 
 .0891 
 
 .3456 
 
 99 
 
 .6109 
 
 H 
 
 :6563 
 
 7226 
 
 269 
 
 1.658 
 
 2 
 
 .1164 
 
 .3770 
 
 114 
 
 .6982 
 
 5 
 
 .7272 
 
 7540 
 
 283 
 
 1-745 
 
 H 
 
 .1473 
 
 .4084 
 
 128 
 
 .7855 
 
 u 
 
 .8018 
 
 7854 
 
 297 
 
 1.833 
 
 H 
 
 .1818 
 
 .4398 
 
 142 
 
 .8727 
 
 1/2 
 
 .8799 
 
 8168 
 
 311 
 
 1.920 
 
 H 
 
 .2200 
 
 .4712 
 
 156 
 
 .9600 
 
 H 
 
 ■9617 
 
 8482 
 
 326 
 
 2.007 
 
 3 
 
 .2618 
 
 .5027 
 
 170 
 
 1.047 
 
 6 
 
 1.047 
 
 8796 
 
 340 
 
 2.09s 
 
 H 
 
 • 3073 
 
 .5341 
 
 184 
 
 1. 135 
 
 H 
 
 1. 136 
 
 9111 
 
 354 
 
 2.182 
 
 H 
 
 • 3563 
 
 5655 
 
 198 1.222 
 
 H 
 
 1.229 
 
 9425 
 
 368 
 
 2.269 
 
 H 
 
 .4091 
 
 ■5969 
 
 212 1.309 
 
 % 
 
 1.325 
 
 9739 
 
 382 2.356 
 
 A cubic yard = 203 U. S. gallons. 
 
Contents of Linings of Wells 
 Contents or Linings of Wells 
 
 105 
 
 
 For each foot of depth 
 
 
 For each foot of depth 
 
 
 For this 
 
 For these three col- 
 
 For this 
 
 For these three col- 
 
 
 column 
 
 umns use the diameter 
 
 
 column 
 
 umns use the diameter 
 
 
 use the 
 
 in clear of the lining 
 
 Diam- 
 eter 
 
 use the 
 
 in clear of the lining 
 
 Diam- 
 
 diam- 
 eter of 
 
 
 
 
 diam- 
 eter of 
 
 
 
 eter 
 
 
 
 
 
 
 
 in 
 feet 
 
 the dig- 
 
 Stone 
 lining 
 
 No. of 
 
 
 in 
 feet 
 
 the dig- 
 
 Stone 
 lining 
 
 . No. of 
 
 
 
 ging 
 
 I foot 
 
 bricks 
 
 Square 
 
 
 ging 
 
 I foot 
 
 bricks 
 
 Square 
 
 
 
 thick. 
 
 in a 
 
 yards of 
 
 
 
 thick. 
 
 in a 
 
 yards of 
 
 
 
 
 
 
 Perches 
 
 lining 
 
 plaster- 
 
 
 
 Perches 
 
 lining 
 
 plaster- 
 
 
 Cubic 
 
 of 25 
 
 I brick 
 
 ing 
 
 
 Cubic 
 
 of 25 
 
 I brick 
 
 ing 
 
 
 yards of 
 
 cubic 
 
 thick 
 
 
 
 yards of 
 
 cubic 
 
 thick 
 
 
 
 digging 
 
 feet 
 
 
 
 
 digging 
 
 feet 
 
 
 
 7 
 
 1.42s 
 
 1.005 
 
 396 
 
 2.444 
 
 16H 
 
 7.681 
 
 2.168 
 
 919 
 
 5. 673 
 
 Vi 
 
 1.529 
 
 1.037 
 
 410 
 
 2.531 
 
 1/2 
 
 7.919 
 
 2.199 
 
 933 
 
 5.760 
 
 Vi 
 
 1.636 
 
 1.068 
 
 425 
 
 2.618 
 
 V^ 
 
 8. 161 
 
 2.231 
 
 948 
 
 5.847 
 
 % 
 
 1.747 
 
 1. 100 
 
 439 
 
 2.705 
 
 17 
 
 8.407 
 
 2.262 
 
 962 
 
 5.934 
 
 8 
 
 1.862 
 
 1. 131 
 
 453 
 
 2.793 
 
 H 
 
 8.656 
 
 2.293 
 
 976 
 
 6.022 
 
 K 
 
 1.980 
 
 1. 162 
 
 467 
 
 2.880 
 
 Vi 
 
 8.908 
 
 2.325 
 
 990 
 
 6.109 
 
 H 
 
 2.102 
 
 1. 194 
 
 481 
 
 2.967 
 
 % 
 
 9.165 
 
 2.356 
 
 1004 
 
 6.196 
 
 % 
 
 2.227 
 
 1.225 
 
 495 
 
 3.054 
 
 18 
 
 9.425 
 
 2.388 
 
 1018 
 
 6.283 
 
 9 
 
 2.356 
 
 1.257 
 
 509 
 
 3-142 
 
 M 
 
 9.688 
 
 2.419 
 
 1032 
 
 6.371 
 
 % 
 
 2.489 
 
 1.288 
 
 523 
 
 3.229 
 
 \^ 
 
 9.956 
 
 2.450 
 
 1046 
 
 6.458 
 
 H 
 
 2.625 
 
 1. 319 
 
 538 
 
 3.316 
 
 K 
 
 10.23 
 
 2.482 
 
 1061 
 
 6.545 
 
 % 
 
 2.76s 
 
 1. 351 
 
 552 
 
 3.404 
 
 19 
 
 10.50 
 
 2.513 
 
 I07S 
 
 6.633 
 
 10 
 
 2.909 
 
 1.382 
 
 566 
 
 3.491 
 
 Vi 
 
 10.78 
 
 2.545 
 
 1089 
 
 6.720 
 
 Yi 
 
 3.056 
 
 1. 414 
 
 580 
 
 3.578 
 
 ^2 
 
 11.06 
 
 2.576 
 
 1 103 
 
 6.807 
 
 "■A 
 
 3.207 
 
 1.445 
 
 594 
 
 3.665 
 
 % 
 
 11.35 
 
 2.608 
 
 1117 
 
 6.894 
 
 % 
 
 3 362 
 
 1.477 
 
 608 
 
 3.753 
 
 20 
 
 11.64 
 
 2.639 
 
 1131 
 
 6.982 
 
 II 
 
 3.520 
 
 1.508 
 
 622 
 
 3.840 
 
 H 
 
 11.93 
 
 2.670 
 
 1145 
 
 7.069 
 
 Vi ■ 
 
 3.682 
 
 1.539 
 
 637 
 
 3.927 
 
 H 
 
 12.22 
 
 2.702 
 
 1160 
 
 7.156 
 
 1/^ 
 
 3.847 
 
 1. 571 
 
 651 
 
 4.014 
 
 % 
 
 12.52 
 
 2.733 
 
 1174 
 
 -7.243 
 
 ¥i 
 
 4.016 
 
 1.602 
 
 665 
 
 4.102 
 
 21 
 
 12.83 
 
 2.765 
 
 1 188 
 
 7.331 
 
 12 
 
 4.189 
 
 1.634 
 
 ■679 
 
 4.189 
 
 M 
 
 13.14 
 
 2.796 
 
 1202 
 
 7.418 
 
 • M 
 
 4.36s 
 
 1.665 
 
 693 
 
 4.276 
 
 1/2 
 
 13.45 
 
 2.827 
 
 1216 
 
 7.505 
 
 Vi 
 
 4.545 
 
 1.696 
 
 707 
 
 4.364^ 
 
 % 
 
 13.76 
 
 2.859 
 
 1230 
 
 7.593 
 
 % 
 
 4.729 
 
 1.728 
 
 721 
 
 4.451 
 
 22 
 
 14.08 
 
 2.890 
 
 1244 
 
 7.680 
 
 13 
 
 4.916 
 
 1.759 
 
 736 
 
 4.538 
 
 Yi 
 
 14.40 
 
 2.922 
 
 1259 
 
 7.767 
 
 H 
 
 5. 107 
 
 1. 791 
 
 750 
 
 4.625 
 
 Yi 
 
 14.73 
 
 2.953 
 
 1273 
 
 7.854 
 
 1/^ 
 
 5.301 
 
 1.822 
 
 764 
 
 4.713 
 
 % 
 
 15.06 
 
 2.985 
 
 1287 
 
 7.942 
 
 % 
 
 S-Soo 
 
 1.854 
 
 778 
 
 4.800 
 
 23 
 
 15.39 
 
 3.016 
 
 1301 
 
 8.029 
 
 14 
 
 5.701 
 
 1.885 
 
 792 
 
 4.887 
 
 Yi 
 
 15.72 
 
 3.047 
 
 1315 
 
 8. 116 
 
 \i 
 
 S.907 
 
 1. 916 
 
 806 
 
 4.974 
 
 Yi 
 
 16.06 
 
 3.079 
 
 1329 
 
 8.203 
 
 Y^ 
 
 6. 116 
 
 1.948 
 
 820 
 
 5.062 
 
 % 
 
 16.41 
 
 3. no 
 
 1343 
 
 8.291 
 
 % 
 
 6.329 
 
 1.979 
 
 834 
 
 5.149 
 
 24 
 
 16.76 
 
 3.142 
 
 1357 
 
 8.378 
 
 IS 
 
 6.545 
 
 2. on 
 
 849 
 
 5.236 
 
 H 
 
 17. II 
 
 3.173 
 
 1372 
 
 8.465 
 
 H 
 
 6.765 
 
 2.042 
 
 863 
 
 5.323 
 
 Y. 
 
 17.46 
 
 3.204 
 
 1386 
 
 8.552 
 
 1/^ 
 
 6.989 
 
 2.073 
 
 877 
 
 5. 411 
 
 % 
 
 17.82 
 
 3.236 
 
 1400 
 
 8.640 
 
 % 
 
 7.216 
 
 2.105 
 
 891 
 
 5.498 
 
 25 
 
 18.18 
 
 3.267 
 
 1414 
 
 8.727 
 
 16 
 
 7.447 
 
 2.136 
 
 90s 
 
 5.585 
 
 
 
 
 
 
 A cubic yard = 202 U. S. gallons. 
 
lo6 Mathematical Tables 
 
 If perches are named in a contract, it is necessary, in order to prevent 
 fraud, to specify the number of cubic feet contained in the perch; for 
 stone-quarriers have one perch, stone-masons another, etc. Engineers, 
 on this account, contract by the ctibic yard. The perch should be done 
 away with entirely; perches of 25 cubic feet X 0.926 = cubic yards; and 
 cubic yards -i- 0,926 = perches of 25 cubic feet. 
 
CHAPTER III 
 
 NATURAL SINES, TANGENTS, ETC. 
 
 Sine 
 
 The sine of any angle acb or the sine of any circular arc ab is the 
 perpendicular distance, as, from one end of the arc a to the radius 
 passing through the other end b of the arc. It 
 is equal to one-half the chord of the arc abn, 
 which is twice the arc ab; or the chord of the 
 arc abn is equal to twice the sine of half the arc, 
 or twice the sine oi ab. 
 
 The sine of the angle tcb, if tcb equals 90", is 
 equal to the radius of the circle. 
 
 t 
 
 u/ 
 
 w 
 
 c 
 
 / 
 
 eV 
 
 Vers.' 
 
 
 c 
 
 n 
 
 s 
 
 
 Fig. 36. 
 
 Cosine 
 
 The cosine of an arc ab is the distance cs from 
 the center of the circle c to the intersection of the 
 sine as with the radius cb, and is equal to ya or the sine of the arc ta. 
 But the angle tea is equal to the difference between 90° and the angle 
 acb; or the difference between the arcs tab and ab; and is the comple- 
 ment of acb. Hence the cosine of an angle or arc is equal to the sine of 
 its complement, and vice versa. 
 
 Versed Sine 
 
 The versed sine of an arc is the distance sb from the foot 5 of the sine 
 to the arc at b, measured on the radius cb. 
 
 Natural Sines, Tangents, etc. 
 
 The versed sine of an arc ab is equal to the rise of twice the arc; or 
 equal to the rise of abn. 
 
 Tangent 
 
 The tangent bw of an arc ab is the perpendicular .distance from the 
 radius at one extremity of the arc b to the intersection w of the perpen- 
 dicular bw with the prolongation of a radius drawn through the other 
 extremity of the arc at a. 
 
 107 
 
lo8 Mathematical Tables 
 
 The Secant 
 
 The secant of an arc is the distance cw from the center of the arc to 
 the intersection of the tangent at w of the prolonged radius ca. 
 
 If the angle tch equals 90 degrees and tea be the complement of achy 
 the sine ya of this complement, its versed sine ty, tangent to and secant 
 CO become respectively the cosine, coversed sine, cotangent and co- 
 secant of the angle ach, and vice versa. 
 
 When the radius ah is equal to unity the corresponding sines, cosines, 
 tangents, etc., are called natural sines, cosines, etc.; and the table con- 
 taining their lengths for different angles is the table of natural sines, etc. 
 
 The lengths of the sines, etc., for the arcs of any other circle, whose 
 radius may be greater or less than i, are found by multiplying the tabu- 
 lar values by such radius. 
 
 The following table contains only natural sines, tangents and secants; 
 the other lengths may be found for any angle not exceeding 90 degrees 
 as follows: 
 
 Cosine = sine of the complement of the given angle. 
 
 Versed sine = i — cosine. 
 
 Coversed sine = i — sine. 
 
 Cotangent = tangent of the complement. 
 
 Cosecant = i divided by natural sine. 
 
 Sine = = — 7 = V (i — cos^). 
 
 cosec cot 
 
 Tangent 
 
 sm _ _i_ 
 cos cot 
 tan 
 
 Secant = -^ = i?£ = Vb? + tangent^, 
 
 cos sm 
 
 Cosine = V(i — sin^) = — = sine X cotangent = 
 
 tan sec 
 
 Cotangent 
 
 _ cos _ I 
 sin tan 
 Versed sine = radius — cosine. 
 Coversed sine = radius — sine. 
 
 Radius = tangent X cotangent = v sine^ + cosine^. 
 
 The formulae for the solution of the right-angled and the oblique- 
 angled triangle are given; for further information the reader is referred 
 to works on Trigonometry, 
 
Solution of Oblique-angled Triangles 
 
 109 
 
 Solution of the Right-angled Triangle 
 
 LetA,B and C be the angles of the triangle and a, h and c the sides 
 opposite those angles respectively. 
 
 Then (i) 
 
 «, 
 
 = sine^, a = c sine^. 
 
 <^)! 
 
 = cosine A, h = c cosine A. 
 
 (3)^ 
 
 = tangent A, a = b tangent A 
 
 ^^^l 
 
 = cot A, b = a cot A. 
 
 , . Sin ^ 
 
 ^^^ C^^ = tangents. 
 
 ,,^ Cosyl 
 
 (0). ^^ = cotangent A. 
 
 (7) Sine A + cos^ A = i 
 
 (8) Sine^ = Vi — cosM. 
 
 (9) Cos A = Vi - sind^A. 
 
 Solution of Oblique-angled Triangles 
 
 h 
 
 Fig. 38. 
 Value of any side c is: 
 
 a sin C b sin C 
 
 sin^ 
 
 sin 5 
 
 Value of any angle A : 
 
 o sin C a sin B 
 
 Sin^ 
 Cos 4 
 
 c b 
 
 b — a cos C c — a cos B 
 
 Tan 4 
 
 C2 ■!■ ^,2 _ ^2 
 
 2 be 
 asinC 
 
 a sin 5 
 
 b — aco^C c — acosB' 
 
no 
 
 Mathematical Tables 
 
 Natural Sines, Tangents and Secants 
 
 Advancing by lo min. 
 
 Deg. 
 
 Min. 
 
 Sine 
 
 Tan- 
 gent 
 
 Secant 
 
 Deg. 
 
 Min. 
 
 Sine 
 
 Tan- 
 gent 
 
 Secant 
 
 
 
 oo 
 
 .0000 
 
 .OCX)0 
 
 I.CX300 
 
 
 SO 
 
 .IS36 
 
 .1554 
 
 I. 0120 
 
 
 lO 
 
 .0029 
 
 .0029 
 
 I. 0000 
 
 9 
 
 00 
 
 .1564 
 
 .1584 
 
 I.OI2S 
 
 
 20 
 
 .0058 
 
 .0058 
 
 I. 0000 
 
 
 10 
 
 .1593 
 
 .1614 
 
 I. 0129 
 
 
 30 
 
 .0087 
 
 .0087 
 
 I. 0000 
 
 
 20 
 
 .1622 
 
 .1644 
 
 I. 0134 
 
 
 40 
 
 .0116 
 
 .0116 
 
 I. 0001 
 
 
 30 
 
 .1650 
 
 .1673 
 
 I. 0139 
 
 
 so 
 
 .0145 
 
 .0145 
 
 I.OCXJI 
 
 
 40 
 
 .1679 
 
 .1703 
 
 I. 0144 
 
 I ■ 
 
 00 
 
 .0175 
 
 .0175 
 
 1.0002 
 
 
 SO 
 
 .1708 
 
 .1733 
 
 I. 0149 
 
 
 10 
 
 .0204 
 
 ■ .0204 
 
 1.0002 
 
 10 
 
 00 
 
 .1736 
 
 .1763 
 
 I. 0154 
 
 
 20 
 
 .0233 
 
 . .0233 
 
 1.0003 
 
 
 10 
 
 .1765 
 
 .1793 
 
 I. 0160 
 
 
 30 
 
 .0262 
 
 .0262 
 
 1.0003 
 
 
 20 
 
 .1794 
 
 .1823 
 
 I. 0165 
 
 
 40 
 
 .0291 
 
 .0291 
 
 i.Sbo4 
 
 
 30 
 
 .1822 
 
 .1853 
 
 I. 0170 
 
 
 50 
 
 .0320 
 
 .0320 
 
 i.ooos 
 
 
 40 
 
 .1851 
 
 .1883 
 
 I. 0176 
 
 2 
 
 00 
 
 .0349 
 
 .0349 
 
 1.0006 
 
 
 SO 
 
 .1880 
 
 .1914 
 
 1.0181 
 
 
 10 
 
 .0378 
 
 .0378 
 
 1.0007 
 
 II 
 
 00 
 
 .1908 
 
 .1944 
 
 I. 0187 
 
 
 20 
 
 .0407 
 
 .0407 
 
 1.0008 
 
 
 10 
 
 .1937 
 
 .1974 
 
 I. 0193 
 
 
 30 
 
 .0436 
 
 .0437 
 
 I. 00 10 
 
 
 20 
 
 . 1965 
 
 .2004 
 
 1. 0199 
 
 
 40 
 
 .0465 
 
 .0466 
 
 I.OOII 
 
 
 30 
 
 .1994 
 
 .2035 
 
 1.0205 
 
 
 50 
 
 .0494 
 
 .049s 
 
 I. 0012 
 
 
 40 
 
 .2022 
 
 .2065 
 
 1.0211 
 
 3 
 
 00 
 
 .0523 
 
 .0524 
 
 I. 0014 
 
 
 SO 
 
 .2051 
 
 .2095 
 
 I. 0217 
 
 
 10 
 
 .0552 
 
 .0553 
 
 I. 0015 
 
 12 
 
 00 
 
 .2079 
 
 .2126 
 
 1.0223 
 
 
 20 
 
 .0581 
 
 .0582 
 
 I. 0017 
 
 
 10 
 
 .2108 
 
 .2156 
 
 1.0230 
 
 
 30 
 
 .0610 
 
 .0612 
 
 I. 0019 
 
 
 20 
 
 .2136 
 
 .2186 
 
 1.0236 
 
 
 40 
 
 .0640 
 
 .0641 
 
 I. 0021 
 
 
 30 
 
 .2164 
 
 .2217 
 
 1.0243 
 
 
 50 
 
 .0669 
 
 .0670 
 
 1.0022 
 
 
 40 
 
 .2193 
 
 .2247 
 
 1.0249 
 
 4 
 
 00 
 
 .0698 
 
 .0699 
 
 1.0024 
 
 
 SO 
 
 .2221 
 
 .2278 
 
 1.0256 
 
 
 10 
 
 .0727 
 
 .0729 
 
 1.0027 
 
 13 
 
 00 
 
 .2250 
 
 .2309 
 
 1.0263 
 
 
 20 
 
 .0756 
 
 .0758 
 
 1.0029 
 
 
 10 
 
 .2278 
 
 .2339 
 
 1.0270 
 
 
 30 
 
 .0785 
 
 .0787 
 
 I. 0031 
 
 
 20 
 
 .2306 
 
 .2370 
 
 1.0277 
 
 
 40 
 
 .0814 
 
 .0816 
 
 1.0033 
 
 
 30 
 
 .2334 
 
 .2401 
 
 1.0284 
 
 
 50 
 
 .0843 
 
 .0846 
 
 1.0036 
 
 
 40 
 
 .2363 
 
 .2432 
 
 I. 0291 
 
 5 
 
 00 
 
 .0872 
 
 .0875 
 
 1.0038 
 
 
 SO 
 
 .2391 
 
 .2462 
 
 1.0299 
 
 
 10 
 
 .0901 
 
 .0904 
 
 I. 0041 
 
 14 
 
 00 
 
 .2419 
 
 .2493 
 
 1.0306 
 
 
 20 
 
 .0929 
 
 .0934 
 
 1.0043 
 
 
 10 
 
 .2447 
 
 .2524 
 
 I. 0314 
 
 
 30 
 
 .0958 
 
 .0963 
 
 1.0046 
 
 
 20 
 
 .2476 
 
 .2555 
 
 I. 0321 
 
 
 40 
 
 .0987 
 
 .0992 
 
 1.0049 
 
 
 30 
 
 .2504 
 
 .2586 
 
 1.0329 
 
 
 50 
 
 .1016 
 
 .1022 
 
 1.0052 
 
 
 40 
 
 .2532 
 
 .2617 
 
 1.0337 
 
 6 
 
 00 
 
 .1045 
 
 .1051 
 
 I. 005s 
 
 
 50 
 
 .2560 
 
 .2648 
 
 1.0345 
 
 
 10 
 
 .1074 
 
 .1080 
 
 1.0058 
 
 15 
 
 00 
 
 .2588 
 
 .2679 
 
 I.03S3 
 
 
 20 
 
 .1103 
 
 .1110 
 
 I. 0061 
 
 
 10 
 
 .2616 
 
 .2711 
 
 I. 0361 
 
 
 30 
 
 .1132 
 
 .1139 
 
 1.0065 
 
 
 20 
 
 .2644 
 
 .2742 
 
 1.0369 
 
 
 40 
 
 .1161 
 
 .1169 
 
 1.0068 
 
 
 30 
 
 .2672 
 
 .2773 
 
 1.0377 
 
 
 50 
 
 .1190 
 
 .1198 
 
 1.0072 
 
 
 40 
 
 .2700 
 
 .2805 
 
 1.0386 
 
 7 
 
 00 
 
 .1219 
 
 .1228 
 
 1.0075 
 
 
 SO 
 
 .2728 
 
 .2836 
 
 1.0394 
 
 
 10 
 
 .1248 
 
 .1257 
 
 1.0079 
 
 16 
 
 00 
 
 .2756 
 
 .2867 
 
 1.0403 
 
 
 20 
 
 .1276 
 
 .1287 
 
 1.0082 
 
 
 10 
 
 .2784 
 
 .2899 
 
 I. 0412 
 
 
 30 
 
 .1305 
 
 .1317 
 
 1.0086 
 
 
 20 
 
 .2812 
 
 .2931 
 
 I. 0421 
 
 
 40 
 
 .1334 
 
 .1346 
 
 1.0090 
 
 
 30 
 
 .2840 
 
 .2962 
 
 1.0429 
 
 
 50 
 
 .1363 
 
 .1376 
 
 1.0094 
 
 
 40 
 
 .2868 
 
 .2994 
 
 1.0439 
 
 8 
 
 00 
 
 .1392 
 
 .I40S 
 
 1.0098 
 
 
 SO 
 
 .2896 
 
 .3026 
 
 1.0448 
 
 
 10 
 
 .1421 
 
 .1435 
 
 I. 0102 
 
 17 
 
 00 
 
 .2924 
 
 .3057 
 
 I.04S7 
 
 
 20 
 
 .1449 
 
 .1465 
 
 I. 0107 
 
 
 10 
 
 .2952 
 
 .3089 
 
 1.0466 
 
 
 30 
 
 .1478 
 
 .1495 
 
 I.OIII 
 
 
 20 
 
 .2979 
 
 .3121 
 
 1.0476 
 
 
 40 
 
 .1507 
 
 .1524 
 
 I.0II6 
 
 
 30 
 
 .3007 
 
 .3153 
 
 1.0485 
 
Natural Sines, Tangents and Secants iii 
 
 Natural Sines, Tangents and Secants — {Continued) 
 
 Deg. 
 
 Min. 
 
 Sine 
 
 Tan- 
 gent 
 
 Secant 
 
 Deg. 
 
 Min. 
 
 Sine 
 
 Tan- 
 gent 
 
 Secant 
 
 
 40 
 
 .3035 
 
 .3185 
 
 1.0495 
 
 
 SO 
 
 .4514 
 
 .5059 
 
 I . 1207 
 
 
 SO 
 
 .3062 
 
 .3217 
 
 1.0505 
 
 27 
 
 00 
 
 .4540 
 
 .5095 
 
 I . 1223 
 
 i8 
 
 00 
 
 .3090 
 
 .3249 
 
 I. 0515 
 
 
 10 
 
 .4566 
 
 .5132 
 
 I . 1240 
 
 
 10 
 
 .3118 
 
 .3281 
 
 1.0525 
 
 
 20 
 
 .4592 
 
 .5169 
 
 I. 1257 
 
 
 20 
 
 .3145 
 
 .3314 
 
 1.0535 
 
 
 30 
 
 .4617 
 
 .5206 
 
 I. 1274 
 
 
 30 
 
 .3173 
 
 .3346 
 
 I. 054s 
 
 
 40 
 
 .4643 
 
 .5243 
 
 1.1291 
 
 
 40 
 
 .3201 
 
 .3378 
 
 1.0555 
 
 
 50 
 
 .4669 
 
 .5280 
 
 I . 1308 
 
 
 50 
 
 .3228 
 
 .3411 
 
 1.0566 
 
 28 
 
 00 
 
 .4695 
 
 .5317 
 
 I . 1326 
 
 19 
 
 00 
 
 .32S6 
 
 .3443 
 
 1.0576 
 
 
 10 
 
 .4720 
 
 .5354 
 
 I. 1343 
 
 
 10 
 
 .3283 
 
 .3476 
 
 1.0587 
 
 
 20 
 
 .4746 
 
 • 5392 
 
 1.1361 
 
 
 20 
 
 .3311 
 
 .3508 
 
 1.0598 
 
 
 30 
 
 .4772 
 
 .5430 
 
 I . 1379 
 
 
 30 
 
 .3338 
 
 .3541 
 
 1.0608 
 
 
 40 
 
 .4797 
 
 .5467 
 
 I . 1397 
 
 
 40 
 
 .336s 
 
 .3574 
 
 I. 0619 
 
 
 SO 
 
 .4823 
 
 .5505 
 
 1.1415 
 
 
 SO 
 
 .3393 
 
 .3607 
 
 I. 0631 
 
 29 
 
 00 
 
 .4848 
 
 .5543 
 
 I. 1434 
 
 20 
 
 00 
 
 .3420 
 
 .3640 
 
 1.0642 
 
 
 10 
 
 .4874 
 
 .5581 
 
 I. 1452 
 
 
 10 
 
 .3448 
 
 .3673 
 
 1.0653 
 
 
 20 
 
 .4899 
 
 .5619 
 
 1.1471 
 
 
 20 
 
 .3475 
 
 .3706 
 
 1.0665 
 
 
 30 
 
 .4924 
 
 .5658 
 
 I. 1490 
 
 
 30 
 
 .3502 
 
 .3739 
 
 1.0676 
 
 
 40 
 
 .4950 
 
 .5696 
 
 I. 1509 
 
 
 40 
 
 .3529 
 
 .3772 
 
 1.0688 
 
 
 SO 
 
 .4975 
 
 .5735 
 
 I . 1528 
 
 
 50 
 
 .3SS7 
 
 .3805 
 
 1.0700 
 
 30 
 
 00 
 
 .5000 
 
 .5774 
 
 I. 1547 
 
 21 
 
 00 
 
 .3584 
 
 .3839 
 
 1.0711 
 
 
 10 
 
 .5025 
 
 .5812 
 
 I . 1566 
 
 
 10 
 
 .3611 
 
 .3872 
 
 1.0723 
 
 
 20 
 
 .5050 
 
 .5851 
 
 I. 1586 
 
 
 20 
 
 .3638 
 
 .3906 
 
 1.0736 
 
 
 30 
 
 .5075 
 
 .5890 
 
 I . 1606 
 
 
 30 
 
 .3665 
 
 .3939 
 
 1.0748 
 
 
 40 
 
 .5100 
 
 .5930 
 
 I . 1626 
 
 
 40 
 
 .3692 
 
 .3973 
 
 1.0760 
 
 
 50 
 
 .5125 
 
 .5969 
 
 I . 1646 
 
 
 SO 
 
 .3719 
 
 .4006 
 
 1.0773 
 
 31 
 
 00 
 
 .5150 
 
 .6009 
 
 I. 1666 
 
 22 
 
 00 
 
 .3746 
 
 .4040 
 
 1.0785 
 
 
 10 
 
 .5175 
 
 .6048 
 
 I. 1687 
 
 
 10 
 
 .3773 
 
 .4074 
 
 1.0798 
 
 
 20 
 
 .5200 
 
 .6088 
 
 I. 1707 
 
 
 20 
 
 .3800 
 
 .4108 
 
 1.0811 
 
 
 30 
 
 .5225 
 
 .6128 
 
 I. 1728 
 
 
 30 
 
 .3827 
 
 .4142 
 
 1.0824 
 
 
 40 
 
 .5250 
 
 .6168 
 
 I. 1749 
 
 
 40 
 
 .3854 
 
 .4176 
 
 1.0837 
 
 
 50 
 
 .5275 
 
 .6208 
 
 I . 1770 
 
 
 50 
 
 .3881 
 
 .4210 
 
 1.0850 
 
 32 
 
 00 
 
 .5299 
 
 .6249 
 
 I . 1792 
 
 23 
 
 00 
 
 .3907 
 
 .4245 
 
 1.0864 
 
 
 10 
 
 .5324 
 
 .6289 
 
 1.1813 
 
 
 10 
 
 .3934 
 
 .4279 
 
 1.0877 
 
 
 20 
 
 .5348 
 
 .6330 
 
 I. 1835 
 
 
 20 
 
 .3961 
 
 .4314 
 
 1.0891^ 
 
 
 30 
 
 .5373 
 
 .6371 
 
 I. 1857 
 
 
 30 
 
 .3987 
 
 .4348 
 
 1.0904 
 
 
 40 
 
 .5398 
 
 .6412 
 
 I. 1879 
 
 
 40 
 
 .4014 
 
 .4383 
 
 I. 0918 
 
 
 50 
 
 .5422 
 
 .6453 
 
 1.1901 
 
 
 50 
 
 .4041 
 
 .4417 
 
 1.0932 
 
 33 
 
 00 
 
 .5446 
 
 .6494 
 
 I. 1924 
 
 24 
 
 00 
 
 .4067 
 
 .4452 
 
 1.0946 
 
 
 10 
 
 .5471 
 
 .6536 
 
 I . 1946 
 
 
 10 
 
 .4094 
 
 .4487 
 
 I. 0961 
 
 
 20 
 
 .5495 
 
 .6577 
 
 I. 1969 
 
 
 20 
 
 .4120 
 
 .4522 
 
 1.0975 
 
 
 30 
 
 .5519 
 
 .6619 
 
 I. 1992 
 
 
 30 
 
 .4147 
 
 .4557 
 
 1.0989 
 
 
 40 
 
 .5544 
 
 .6661 
 
 1.201S 
 
 
 40 
 
 .4173 
 
 .4592 
 
 I. 1004 
 
 
 50 
 
 .5568 
 
 .6703 
 
 1.2039 
 
 
 SO 
 
 .4200 
 
 .4628 
 
 1.1019 
 
 34 
 
 00 
 
 .5592 
 
 .6745 
 
 1.2062 
 
 25 
 
 00 
 
 .4226 
 
 .4663 
 
 I . 1034 
 
 
 10 
 
 .5616 
 
 .6787 
 
 1.2086 
 
 
 10 
 
 .4253 
 
 .4699 
 
 I. 1049 
 
 
 20 
 
 .5640 
 
 .6830 
 
 1.2110 
 
 
 20 
 
 .4279 
 
 .4734 
 
 I . 1064 
 
 
 30 
 
 .5664 
 
 .6873 
 
 I. 2134 
 
 
 30 
 
 .4305 
 
 .4770 
 
 I. 1079 
 
 
 40 
 
 .5688 
 
 .6916 
 
 I. 2158 
 
 
 40 
 
 .4331 
 
 .4806 
 
 I. 1095 
 
 
 SO 
 
 .5712 
 
 .6959 
 
 I. 2183 
 
 
 50 
 
 .4358 
 
 .4841 
 
 I.IIIO 
 
 35 
 
 00 
 
 .5736 
 
 .7002 
 
 1.2208 
 
 26 
 
 00 
 
 .4384 
 
 .4877 
 
 1.1126 
 
 
 10 
 
 .5760 
 
 .7046 
 
 I . 2233 
 
 
 10 
 
 .4410 
 
 .4913 
 
 1.1142 
 
 
 20 
 
 .5783 
 
 .7089 
 
 1.2258 
 
 
 20 
 
 .4436 
 
 .4950 
 
 1.1158 
 
 
 30 
 
 .5807 
 
 .7133 
 
 1.2283 
 
 
 30 
 
 .4462 
 
 .4986 
 
 1.1174 
 
 
 40 
 
 .5831 
 
 .7177 
 
 1.2309 
 
 
 40 
 
 .4488 
 
 .5022 
 
 1.1190 
 
 
 SO 
 
 .5854 
 
 .7221 
 
 1.233s 
 
112 
 
 Mathematical Tables 
 
 
 Natural Sines 
 
 , Tangents 
 
 AND Secants 
 
 — {Continued) 
 
 
 Deg. 
 
 Min. 
 
 Sine ^ 
 
 ran- 
 ;ent 
 
 Secant 
 
 Deg. 
 
 Min. 
 
 Sine 
 
 Tan- 
 gent 
 
 Secant 
 
 36 
 
 00 
 
 .5878 
 
 7265 
 
 I. 2361 
 
 
 10 
 
 .7092 
 
 1.0058 
 
 I . 4183 
 
 
 10 
 
 .5901 
 
 7310 
 
 I . 2387 
 
 
 20 
 
 .7112 
 
 1.0117 
 
 1.422s 
 
 
 20 
 
 .5925 
 
 735S 
 
 I. 2413 
 
 
 30 
 
 .7133 
 
 I. 0176 
 
 1.4267 
 
 
 30 
 
 .5948 
 
 7400 
 
 1.2440 
 
 
 40 
 
 .7153 
 
 1.0235 
 
 I. 4310 
 
 
 40 
 
 .5972 
 
 7445 
 
 1.2467 
 
 
 50 
 
 .7173 
 
 1.0295 
 
 1.4352 
 
 
 50 
 
 .5995 
 
 7490 
 
 I . 2494 
 
 46 
 
 00 
 
 .7193 
 
 I.03SS 
 
 1.4396 
 
 37 
 
 00 
 
 .6018 
 
 7536 
 
 I . 2521 
 
 
 10 
 
 .7214 
 
 I. 0416 
 
 1.4439 
 
 
 10 
 
 .6041 
 
 7581 
 
 I . 2549 
 
 
 20 
 
 .7234 
 
 1.0477 
 
 1.4483 
 
 
 20 
 
 .6065 
 
 7627 
 
 1-2577 
 
 
 30 
 
 .7254 
 
 1.0538 
 
 1.4527 
 
 
 30 
 
 .6088 
 
 7673 
 
 1.2605 
 
 
 40 
 
 .7274 
 
 1.0599 
 
 1.4572 
 
 
 40 
 
 .6111 
 
 7720 
 
 1.2633 
 
 
 50 
 
 .7294 
 
 I. 0661 
 
 I. 4617 
 
 
 50 
 
 .6134 
 
 7766 
 
 I. 2661 
 
 47 
 
 00 
 
 .7314 
 
 1.0724 
 
 1.4663 
 
 38 
 
 00 
 
 .6157 
 
 7813 
 
 I . 2690 
 
 
 10 
 
 .7333 
 
 1.0786 
 
 1.4709 
 
 
 10 
 
 .6180 
 
 7860 
 
 I. 2719 
 
 
 20 
 
 .7353 
 
 1.0850 
 
 1.4755 
 
 
 20 
 
 .6202 
 
 7907 
 
 1.2748 
 
 
 30 
 
 .7373 
 
 I. 0913 
 
 1.4802 
 
 
 30 
 
 .6225 
 
 7954 
 
 1.2778 
 
 
 40 
 
 .7392 
 
 1.0977 
 
 1.4849 
 
 
 40 
 
 .6248 
 
 8002 
 
 1.2808 
 
 
 so 
 
 .7412 
 
 I . 1041 
 
 1.4987 
 
 
 50 
 
 .6271 
 
 8050 
 
 1.2837 
 
 48 
 
 00 . 
 
 .7431 
 
 1.II06 
 
 1.4945 
 
 39 
 
 00 
 
 .6293 
 
 8098 
 
 1.2868 
 
 
 10 
 
 .7451 
 
 I.1171 
 
 1.4993 
 
 
 10 
 
 .6316 
 
 8146 
 
 I . 2898 
 
 
 20 
 
 .7470 
 
 I . 1237 
 
 1.S042 
 
 
 20 
 
 .6338 
 
 8195 
 
 1.2929 
 
 
 30 
 
 .7490 
 
 I. 1303 
 
 1.S092 
 
 
 30 
 
 .6361 
 
 8243 
 
 I . 2960 
 
 
 40 
 
 .7509 
 
 I. 1369 
 
 1.5141 
 
 
 40 
 
 .6383 
 
 8292 
 
 I. 2991 
 
 
 SO 
 
 .7528 
 
 I. 1436 
 
 1.S192 
 
 
 50 
 
 .6406 
 
 8342 
 
 1.3022 
 
 49 
 
 00 
 
 .7547 
 
 I . 1504 
 
 1.5243 
 
 40 
 
 00 
 
 .6428 
 
 8391 
 
 I -3054 
 
 
 10 
 
 .7566 
 
 1.1571 
 
 1.5294 
 
 
 10 
 
 .6450 
 
 8441 
 
 1.3086 
 
 
 20 
 
 .7585 
 
 I . 1640 
 
 I . 5345 
 
 
 20 
 
 .6472 
 
 8491 
 
 1.3118 
 
 
 30 
 
 .7604 
 
 I . 1708 
 
 1.5398 
 
 
 30 
 
 .6494 
 
 8541 
 
 1.3151 
 
 
 40 
 
 .7623 
 
 I. 1778 
 
 I.S450 
 
 
 40 
 
 .6517 
 
 8591 
 
 I. 3184 
 
 
 SO 
 
 .7642 
 
 I. 1847 
 
 1.SS04 
 
 
 SO 
 
 .6539 
 
 8642 
 
 I. 3217 
 
 SO 
 
 00 
 
 .7660 
 
 I.1918 
 
 I. 5557 
 
 41 
 
 00 
 
 .6561 
 
 8693 
 
 1.3250 
 
 
 10 
 
 .7679 
 
 I. 1988 
 
 1.5611 
 
 
 10 
 
 .6583 
 
 8744 
 
 1.3284 
 
 
 20 
 
 .7698 
 
 1.2059 
 
 1.5666 
 
 
 20 
 
 .6604 
 
 8796 
 
 I. 3318 
 
 
 30 
 
 .7716 
 
 I.2131 
 
 I. 5721 
 
 
 30 
 
 .6626 
 
 8847 
 
 1.3352 
 
 
 40 
 
 .7735 
 
 1.2203 
 
 1.5777 
 
 
 40 
 
 .6648 
 
 8899 
 
 1.3386 
 
 
 50 
 
 .7753 
 
 1.2276 
 
 1.5833 
 
 
 SO 
 
 .6670 
 
 8952 
 
 I. 3421 
 
 51 
 
 00 
 
 .7771 
 
 1.2349 
 
 1.5890 
 
 42 
 
 00 
 
 .6691 
 
 9004 
 
 1.3456 
 
 
 10 
 
 .7790 
 
 1.2423 
 
 1.5948 
 
 
 10 
 
 .6713 
 
 9057 
 
 1.3492 
 
 
 20 
 
 .7808 
 
 1.2497 
 
 1.6005 
 
 
 20 
 
 .6734 
 
 91 10 
 
 1.3527 
 
 
 30 
 
 .7826 
 
 I . 2572 
 
 1.6064 
 
 
 30 
 
 .6756 
 
 9163 
 
 1.3563 
 
 
 40 
 
 .7844 
 
 I . 2647 
 
 I. 6123 
 
 
 40 
 
 .6777 
 
 9217 
 
 1.3600 
 
 
 50 
 
 .7862 
 
 I . 2723 
 
 I. 6183 
 
 
 50 
 
 .6799 
 
 9271 
 
 1.3636 
 
 52 
 
 00 
 
 .7880 
 
 1.2799 
 
 1.6243 
 
 43 
 
 00 
 
 .6820 
 
 9325 
 
 1.3673 
 
 
 10 
 
 .7898 
 
 1.2876 
 
 1.6303 
 
 
 10 
 
 .6841 
 
 9380 
 
 I.3711 
 
 
 20 
 
 .7916 
 
 1.2954 
 
 1.636s 
 
 
 20 
 
 .6862 
 
 9435 
 
 1.3748 
 
 
 30 
 
 .7934 
 
 1.3032 
 
 1.6427 
 
 
 30 
 
 .6884 
 
 9490 
 
 1.3786 
 
 
 40 
 
 .7951 
 
 1.1311 
 
 1.6489 
 
 
 40 
 
 .6905 
 
 9545 
 
 1.3824 
 
 
 SO 
 
 .7969 
 
 I. 3190 
 
 1.6553 
 
 
 SO 
 
 .6926 
 
 9601 
 
 1.3863 
 
 S3 
 
 00 
 
 .7986 
 
 1.3270 
 
 I. 6616 
 
 44 
 
 00 
 
 .6947 
 
 9657 
 
 1.3902 
 
 
 10 
 
 .8004 
 
 I. 3351 
 
 I. 6681 
 
 
 10 
 
 .6967 
 
 9713 
 
 I. 3941 
 
 
 20 
 
 .8021 
 
 1.3432 
 
 1.6746 
 
 
 20 
 
 .6988 
 
 9770 
 
 1.3980 
 
 
 30 
 
 .8039 
 
 I. 3514 
 
 I. 6812 
 
 
 30 
 
 .7009 
 
 9827 
 
 I . 4020 
 
 
 40 
 
 .8056 
 
 1.3597 
 
 1.6878 
 
 
 40 
 
 .7030 
 
 9884 
 
 I . 4061 
 
 
 50 
 
 .8073 
 
 1.3680 
 
 1.6945 
 
 
 50 
 
 .70S0 
 
 9942 
 
 1.4101 
 
 54 
 
 00 
 
 .8090 
 
 1.3764 
 
 I. 7013 
 
 45 
 
 00 
 
 .7071 I 
 
 CXXXJ 
 
 I. 4142 
 
 
 10 
 
 .8107 
 
 1.3848 
 
 I. 7081 
 
Natural Sines, Tangents and Secants 
 
 "3 
 
 
 Natural Sines 
 
 , Tangents 
 
 AND Secants — {Co 
 
 ntinued] 
 
 
 Deg. 
 
 Min. 
 
 Sine 
 
 ran- 
 jent 
 
 Secant 
 
 Deg. 
 
 Min. 
 
 Sine 
 
 Tan- 
 gent 
 
 Secant 
 
 
 20 
 
 .8124 I 
 
 3924 
 
 1.7151 
 
 
 30 
 
 .8949 
 
 2.0057 
 
 2.2412 
 
 
 30 
 
 .8141 I 
 
 4019 
 
 I . 7221 
 
 
 40 
 
 .8962 
 
 2.0204 
 
 2.2543 
 
 
 40 
 
 .8158 I 
 
 4106 
 
 I. 7291 
 
 
 SO 
 
 .8975 
 
 2.0353 
 
 2.2677 
 
 
 SO 
 
 .817s I 
 
 4193 
 
 1.7362 
 
 64 
 
 00 
 
 .8988 
 
 2.0503 
 
 2.2812 
 
 55 
 
 00 
 
 .8192 I 
 
 4281 
 
 1-7434 
 
 
 10 
 
 .9001 
 
 2.0655 
 
 2.2949 
 
 
 10 
 
 .8208 I 
 
 4370 
 
 1.7507 
 
 
 20 
 
 .9013 
 
 2.0809 
 
 2.3088 
 
 
 20 
 
 .8225 I 
 
 4460 
 
 1.7581 
 
 
 30 
 
 .9026 
 
 2.0965 
 
 2.3228 
 
 
 30 
 
 .8241 I 
 
 4550 
 
 1.7655 
 
 
 40 
 
 .9038 
 
 2.I123 
 
 2.3371 
 
 
 40 
 
 .8258 I 
 
 4641 
 
 I . 7730 
 
 
 50 
 
 .9051 
 
 2 . 1283 
 
 2.3515 
 
 
 50 
 
 .8274 I 
 
 4733 
 
 I . 7806 
 
 6s 
 
 00 
 
 .9063 
 
 2.1445 
 
 2.3662 
 
 S6 
 
 00 
 
 .8290 I 
 
 4826 
 
 1.7883 
 
 
 10 
 
 .9075 
 
 2.1609 
 
 2.3811 
 
 
 10 
 
 .8307 I 
 
 4919 
 
 1.7960 
 
 
 20 
 
 .9088 
 
 2.1775 
 
 2.3961 
 
 
 20 
 
 .8323 I 
 
 S013 
 
 1.8039 
 
 
 30 
 
 .9100 
 
 2.1943 
 
 2.4114 
 
 
 30 
 
 .8339 I 
 
 5108 
 
 1.8118 
 
 
 40 
 
 .9112 
 
 2.2113 
 
 2.4269 
 
 
 40 
 
 .835s I 
 
 5204 
 
 I. 8198 
 
 
 SO 
 
 .9124 
 
 2.2286 
 
 2.4426 
 
 
 50 
 
 .8371 I 
 
 S30I 
 
 1.8279 
 
 66 
 
 00 
 
 .9135 
 
 2.2460 
 
 2.4586 
 
 57 
 
 00 
 
 .8387 I 
 
 5399 
 
 I. 8361 
 
 
 10 
 
 .9147 
 
 2.2637 
 
 2.4748 
 
 
 10 
 
 .8403 I 
 
 5497 
 
 1.8443 
 
 
 20 
 
 .9159 
 
 2.2817 
 
 2.4912 
 
 
 20 
 
 .8418 I 
 
 5597 
 
 1.8527 
 
 
 30 
 
 .9171 
 
 2.2998 
 
 2.5078 
 
 
 30 
 
 .8434 I 
 
 5697 
 
 I. 8612 
 
 
 40 
 
 .9182 
 
 2.3183 
 
 2.5247 
 
 
 40 
 
 .8450 I 
 
 5798 
 
 1.8699 
 
 
 SO 
 
 .9194 
 
 2.3369 
 
 2.5419 
 
 
 50 
 
 .8465 I 
 
 5900 
 
 1.8783 
 
 67 
 
 00 
 
 .9205 
 
 2.3559 
 
 2.5593 
 
 58 
 
 00 
 
 .8480 I 
 
 6003 
 
 I. 8871 
 
 
 10 
 
 .9216 
 
 2.37SO 
 
 2.S570 
 
 
 10 
 
 .8496 I 
 
 6107 
 
 1.8959 
 
 
 20 
 
 .9228 
 
 2.3945 
 
 2.5949 
 
 
 20 
 
 .8511 I 
 
 6213 
 
 1.9048 
 
 
 30 
 
 .9239 
 
 2.4141 
 
 2.6131 
 
 
 30 
 
 .8S26 I 
 
 6319 
 
 I. 9139 
 
 
 40 
 
 .9250 
 
 2.4342 
 
 2.6316 
 
 
 40 
 
 .8542 I 
 
 6426 
 
 1.9230 
 
 
 50 
 
 .9261 
 
 2.4545 
 
 2.6504 
 
 
 50 
 
 .8557 I 
 
 6534 
 
 1.9323 
 
 68 
 
 00 
 
 .9272 
 
 2.4751 
 
 2.6695 
 
 59 
 
 00 
 
 .8572 I 
 
 6643 
 
 I. 9416 
 
 
 10 
 
 .9283 
 
 2.4960 
 
 2.6888 
 
 
 10 
 
 .8587 I 
 
 6753 
 
 1.9511 
 
 
 20 
 
 .9293 
 
 2.S172 
 
 2.708s 
 
 
 20 
 
 .8601 I 
 
 6864 
 
 1.9606 
 
 
 30 
 
 .9304 
 
 2.5386 
 
 2.7285 
 
 
 30 
 
 .8616 I 
 
 6977 
 
 1.9703 
 
 
 40 
 
 .931S 
 
 2.5605 
 
 2.7488 
 
 
 40 
 
 .8631 I 
 
 7090 
 
 I . 9801 
 
 
 SO 
 
 .9325 
 
 2.5826 
 
 2.7695 
 
 
 50 
 
 .8646 I 
 
 7205 
 
 i.99<io. 
 
 69 
 
 00 
 
 .9336 
 
 2.6051 
 
 2.7904 
 
 6o 
 
 00 
 
 .8660 I 
 
 7321 
 
 2.0000 
 
 
 10 
 
 .9346 
 
 2.6279 
 
 2.8117 
 
 
 10 
 
 .8675 I 
 
 7437 
 
 2.0101 
 
 
 20 
 
 .9356 
 
 2.6511 
 
 2.8334 
 
 
 20 
 
 .8689 I 
 
 7556 
 
 2.0204 
 
 
 30 
 
 .9367 
 
 2.6746 
 
 2.8S55 
 
 
 30 
 
 .8704 I 
 
 767s 
 
 2.0308 
 
 
 40 
 
 .9377 
 
 2.6985 
 
 2.8779 
 
 
 40 
 
 .8718 I 
 
 7796 
 
 2.0413 
 
 
 SO 
 
 .9387 
 
 2.7228 
 
 2.9006 
 
 
 SO 
 
 .8732 I 
 
 7917 
 
 2.0S19 
 
 70 
 
 00 
 
 .9397 
 
 2.7475 
 
 2.9238 
 
 6i 
 
 00 
 
 .8746 I 
 
 8040 
 
 2.0627 
 
 
 10 
 
 .9407 
 
 2.772s 
 
 2.9474 
 
 
 10 
 
 .8760 I 
 
 8165 
 
 2.0736 
 
 
 20 
 
 .9417 
 
 2.7980 
 
 2.9713 
 
 
 20 
 
 .8774 I 
 
 8291 
 
 2.0846 
 
 
 30 
 
 .9426 
 
 2.8239 
 
 2.9957 
 
 
 30 
 
 .8788 I 
 
 8418 
 
 2.0957 
 
 
 40 
 
 .9436 
 
 2.8502 
 
 3.0206 
 
 
 40 
 
 .8802 I 
 
 8546 
 
 2 . 1070 
 
 
 SO 
 
 .9446 
 
 2.8770 
 
 3.0458 
 
 
 SO 
 
 .8816 I 
 
 8676 
 
 2.118s 
 
 71 
 
 00 
 
 -9455 
 
 2.9042 
 
 3.0716 
 
 62 
 
 00 
 
 .8829 I 
 
 8807 
 
 2.1301 
 
 
 10 
 
 .9465 
 
 2.9319 
 
 3.0977 
 
 
 10 
 
 .8843 I 
 
 8940 
 
 2.1418 
 
 
 20 
 
 .9474 
 
 2.9600 
 
 3.1244 
 
 
 20 
 
 .8857 I 
 
 9074 
 
 2.1537 
 
 
 30 
 
 .9483 
 
 2.9887 
 
 3.1515 
 
 
 30 
 
 .8870 I 
 
 9210 
 
 2.i6S7 
 
 
 40 
 
 .9492 
 
 3.0178 
 
 3.1792 
 
 
 40 
 
 .8884 I 
 
 9347 
 
 2.1786 
 
 
 SO 
 
 .9502 
 
 3.047s 
 
 3.2074 
 
 
 50 
 
 .8897 I 
 
 9486 
 
 2.1902 
 
 72 
 
 00 
 
 .9511 
 
 3.0777 
 
 3.2361 
 
 63 
 
 GO 
 
 .8910 I 
 
 9626 
 
 2.2027 
 
 
 10 
 
 .9520 
 
 3.1084 
 
 3.2653 
 
 
 10 
 
 .8923 I 
 
 9768 
 
 2.2153 
 
 
 20 
 
 .9528 
 
 3.1397 
 
 3.2951 
 
 
 20 
 
 .8936 I 
 
 9912 
 
 2.2282 
 
 
 30 
 
 .9537 
 
 3.1716 
 
 3.3255 
 
114 Mathematical Tables 
 
 Natural Sines, Tangents and Secants — (Continiied) 
 
 Deg. 
 
 Min. 
 
 Sine 
 
 Tan- 
 gent 
 
 Secant 
 
 Deg. 
 
 Min. 
 
 Sine 
 
 Tan- 
 gent 
 
 Secant 
 
 
 4o 
 
 .9546 
 
 3.2041 
 
 3.3565 
 
 
 30 
 
 .9890 
 
 6.6912 
 
 6.76SS 
 
 
 SO 
 
 .9SSS 
 
 3.2371 
 
 3.3881 
 
 
 40 
 
 .9894 
 
 6.8269 
 
 6.8998 
 
 73 
 
 oo 
 
 .9563 
 
 3.2709 
 
 3.4203 
 
 
 50 
 
 .9899 
 
 6.9682 
 
 7.0396 
 
 
 lO 
 
 9S72 
 
 3.3052 
 
 3.4532 
 
 82 
 
 00 
 
 .9903 
 
 7.1154 
 
 7.1853 
 
 
 20 
 
 9580 
 
 3.3402 
 
 3.4867 
 
 
 10 
 
 .9907 
 
 7.2687 
 
 7.3372 
 
 
 30 
 
 9588 
 
 3.3759 
 
 3.5209 
 
 
 20 
 
 9911 
 
 7.4287 
 
 7-4957 
 
 
 40 
 
 9596 
 
 3.4124 
 
 3.5559 
 
 
 30 
 
 9914 
 
 7-5958 
 
 7.6613 
 
 
 so 
 
 960s 
 
 3.4495 
 
 3.5915 
 
 
 40 
 
 9918 
 
 7.7704 
 
 7.8344 
 
 74 
 
 c» 
 
 9613 
 
 3.4874 
 
 3.6280 
 
 
 50 
 
 9922 
 
 7-9S30 
 
 8.0156 
 
 
 10 
 
 9621 
 
 3.5261 
 
 3.6652 
 
 83 
 
 00 
 
 9925 
 
 8-1443 
 
 8.20S5 
 
 
 20 
 
 9628 
 
 3.5656 
 
 3.7032 
 
 
 10 
 
 9929 
 
 8.3450 
 
 8-4047 
 
 
 30 
 
 9636 
 
 3.6059 
 
 3.7420 
 
 
 20 
 
 9932 
 
 8.5555 
 
 8.6138 
 
 
 40 
 
 9644 
 
 3.6470 
 
 3 7817 
 
 
 30 
 
 9936 
 
 8.7769 
 
 8.8337 
 
 
 50 
 
 9652 
 
 3.6891 
 
 3.8222 
 
 
 40 
 
 9939 
 
 9-0098 
 
 9-0652 
 
 75 
 
 CX) 
 
 9659 
 
 3-7321 
 
 3.8637 
 
 
 50 
 
 9942 
 
 9-2553 
 
 9-3092 
 
 
 10 
 
 9667 
 
 3.7760 
 
 3.9061 
 
 84 
 
 00 
 
 9945 
 
 9.5144 
 
 9-5668 
 
 
 20 
 
 9674 
 
 3.8208 
 
 3.9495 
 
 
 10 
 
 9948 
 
 9.7882 
 
 9-8391 
 
 
 30 
 
 9681 
 
 3.8667 
 
 3.9939 
 
 
 20 
 
 9951 
 
 10.0780 
 
 10.1275 
 
 
 40 
 
 9689 
 
 3.9136 
 
 4.0394 
 
 
 30 
 
 9954 
 
 10.3854 
 
 10.4334 
 
 
 so 
 
 9696 
 
 3.9617 
 
 4.0859 
 
 
 40 
 
 9957 
 
 10.7119 
 
 10.758S 
 
 76 
 
 00 
 
 9703 
 
 4.0108 
 
 4.1336 
 
 
 so 
 
 9959 
 
 11.0594 
 
 II. 1045 
 
 
 10 
 
 9710 
 
 4.0611 
 
 4- 1824 
 
 85 
 
 00 
 
 9962 
 
 11.430 
 
 11-474 
 
 
 20 
 
 9717 
 
 4.1126 
 
 4-2324 
 
 
 10 
 
 9964 
 
 11.826 
 
 11.868 
 
 
 30 
 
 9724 
 
 4.1653 
 
 4.2837 
 
 
 20 
 
 9967 
 
 12.251 
 
 12.291 
 
 
 40 
 
 9730 
 
 4.2193 
 
 4.3362 
 
 
 30 
 
 9969 
 
 12.706 
 
 12.745 
 
 
 so 
 
 9737 
 
 4-2747 
 
 4.3901 
 
 
 40 
 
 9971 
 
 13.197 
 
 13.23s 
 
 77 
 
 00 
 
 9744 
 
 4.3315 
 
 4.4454 
 
 
 SO 
 
 9974 
 
 13-727 
 
 13-763 
 
 
 10 
 
 9750 
 
 4.3897 
 
 4.5022 
 
 86 
 
 00 
 
 9976 
 
 14-301 
 
 14-336 
 
 
 20 
 
 97S7 
 
 4.4494 
 
 4.5604 
 
 
 10 
 
 9978 
 
 14-924 
 
 14.958 
 
 
 30 
 
 9763 
 
 4.S107 
 
 4.6202 
 
 
 20 
 
 9980 
 
 15-605 
 
 15.637 
 
 
 40 
 
 9769 
 
 4.5736 
 
 4.6817 
 
 
 30 
 
 9981 
 
 16.350 
 
 16.380 
 
 
 SO 
 
 9775 
 
 4.6382 
 
 4.7448 
 
 
 40 
 
 9983 
 
 17.169 
 
 17.198 
 
 78 
 
 00 
 
 9781 
 
 4.7046 
 
 4.8097 
 
 
 50 
 
 998s 
 
 18.075 
 
 18.103 
 
 
 10 
 
 9787 
 
 4.7729 
 
 4.8765 
 
 87 
 
 00 
 
 9986 
 
 19.081 
 
 19.107 
 
 
 20 
 
 9793 
 
 4.8430 
 
 4. 9452 
 
 
 10 
 
 9988 
 
 20 . 206 
 
 20.230 
 
 
 30 
 
 9799 
 
 4.9152 
 
 5.0159 
 
 
 20 
 
 9989 
 
 21.470 
 
 21.494 
 
 
 40 
 
 980s 
 
 4.9894 
 
 5.0886 
 
 
 30 
 
 9990 
 
 22.904 
 
 22.926 
 
 
 SO 
 
 981 1 
 
 5.0658 
 
 5 . 1636 
 
 
 40 
 
 9992 
 
 24.542 
 
 24.562 
 
 79 
 
 00 
 
 9816 
 
 5.1446 
 
 5. 2408 
 
 
 50 
 
 9993 
 
 26.432 
 
 26.451 
 
 
 10 
 
 9822 
 
 5.2257 
 
 5. 3205 
 
 88 
 
 00 
 
 9994 
 
 28.636 
 
 28.654 
 
 
 20 
 
 9827 
 
 5. 3093 
 
 5. 4026 
 
 
 10 
 
 9995 
 
 31.242 
 
 31.258 
 
 
 30 
 
 9833 
 
 5.3955 
 
 5.4874 
 
 
 20 
 
 9996 
 
 34.368 
 
 34.382 
 
 
 40 
 
 9838 
 
 5.4845 
 
 5.5749 
 
 
 30 
 
 9997 
 
 38.188 
 
 38.202 
 
 
 SO 
 
 9843 
 
 5.5764 
 
 5.6653 
 
 
 40 
 
 9997 
 
 42.964 
 
 42.976 
 
 8o 
 
 00 
 
 9848 
 
 5. 6713 
 
 5. 7588 
 
 
 50 
 
 9998 
 
 49.104 
 
 49.114 
 
 
 10 
 
 9853 
 
 5. 7694 
 
 5.8554 
 
 89 
 
 00 
 
 9998 
 
 57.290 
 
 57.299 
 
 
 20 
 
 9858 
 
 S.8708 
 
 5.9554 
 
 
 10 
 
 9999 
 
 68.750 
 
 68.757 
 
 
 30 
 
 9863 
 
 5.9758 
 
 5. 0589 
 
 
 20 
 
 9999 
 
 85.940 
 
 85.946 
 
 
 40 
 
 9868 
 
 6.0844 
 
 6.1661 
 
 
 30 I 
 
 0000 
 
 114.589 
 
 I 14. 593 
 
 
 SO 
 
 9872 
 
 6.1970 
 
 6.2772 
 
 
 40 I 
 
 0000 
 
 171.885 
 
 171.888 
 
 8i 
 
 00 
 
 9877 
 
 6.3138 
 
 6.3925 
 
 
 SO I 
 
 0000 
 
 343.774 
 
 343.775 
 
 
 10 
 
 9881 
 
 6.4348 
 
 6.5121 
 
 90 
 
 00 I 
 
 0000 
 
 Infi- 
 
 Infi- 
 
 
 20 
 
 9886 
 
 6.5606 
 
 6.6363 
 
 
 
 
 nite 
 
 nite 
 
Approximate Measurement of Angles / 
 
 115 
 
 Approximate Measurement of Angles 
 (i) The four fingers of the hand, held at right angles to the arm 
 and at arm's length from the eye, cover about 7 degrees; and an angle 
 of 7 degrees corresponds to about 12.2 feet in 100 feet; or to 36.6 feet in 
 100 yards; or to 645 feet in a mile. 
 
 (2) By means of a two-foot rule, either on a drawing or between 
 distant objects in the field. If the inner edges of a common two-foot 
 rule be opened to the extent shown in the column of inches, they will be 
 incHned to each other at the angles shown in the column of angles. 
 Since an opening of H inch (up to 19 inches or about 105 degrees) corre- 
 sponds to from about ]'i degree to i degree, no great accuracy is to be 
 expected, and beyond 105 degrees still less, for the liability to error then 
 increases very rapidly as the opening becomes greater. Thus, the last 
 J-i inch corresponds to about 1 2 degrees. 
 
 Angles for openings intermediate of those given may be calculated to 
 the nearest minute or two, by simple proportion, up to 23 in'^hes of 
 opening, or about 147 degrees. 
 
 Table of Angles Corresponding to Openings oe a 2-foot 
 Rule. (Original.) Trautwine. 
 
 Ins. 
 
 Deg. 
 
 Min. 
 
 Ins. 
 
 Deg. 
 
 Min. 
 
 Ins. 
 
 Deg. 
 
 Min. 
 
 Ins. 
 
 Deg. 
 
 Min. 
 
 H 
 
 I 
 
 12 
 
 3'A 
 
 16 
 
 46 
 
 mi 
 
 32 
 
 40 
 
 10 
 
 49 
 
 15 
 
 
 I 
 
 48 
 
 
 17 
 
 22 
 
 
 33 
 
 17 
 
 
 49 
 
 54 
 
 H 
 
 2 
 
 24 
 
 H 
 
 17 
 
 59 
 
 7 
 
 33 
 
 54 
 
 Yi 
 
 50 
 
 34 
 
 
 3 
 
 00 
 
 
 18 
 
 35 
 
 
 34 
 
 33 
 
 
 51 
 
 13 
 
 % 
 
 3 
 
 36 
 
 4 
 
 19 
 
 12 
 
 Yi 
 
 35 
 
 10 
 
 Y2 
 
 51 
 
 53 
 
 
 4 
 
 II 
 
 
 19 
 
 48 
 
 
 35 
 
 47 
 
 
 52 
 
 33 
 
 I 
 
 4 
 
 47 
 
 H 
 
 20 
 
 24 
 
 ¥1 
 
 36 
 
 25 
 
 % 
 
 53 
 
 13 
 
 
 5 
 
 23 
 
 
 21 
 
 
 
 37 
 
 3 
 
 
 53 
 
 53 
 
 H 
 
 5 
 
 58 
 
 V2 
 
 21 
 
 37 
 
 % 
 
 37 
 
 41 
 
 II 
 
 54 
 
 34 
 
 
 6 
 
 34 
 
 
 22 
 
 13 
 
 
 38 
 
 19 
 
 
 55 
 
 14 
 
 H 
 
 7 
 
 10 
 
 % 
 
 22 
 
 50 
 
 8 
 
 38 
 
 57 
 
 H 
 
 55 
 
 55 
 
 
 7 
 
 46 
 
 > 
 
 23 
 
 27 
 
 
 39 
 
 35 
 
 
 56 
 
 35 
 
 H 
 
 8 
 
 22 
 
 5 
 
 24 
 
 3 
 
 1/4 
 
 40 
 
 13 
 
 H 
 
 57 
 
 16 
 
 
 8 
 
 58 
 
 
 24 
 
 39 
 
 
 40 
 
 51 
 
 
 57 
 
 57 
 
 2 
 
 9 
 
 34 
 
 H 
 
 25 
 
 16 
 
 ¥2 
 
 41 
 
 29 
 
 H 
 
 58 
 
 38 
 
 
 10 
 
 10 
 
 
 25 
 
 53 
 
 
 42 
 
 7 
 
 
 59 
 
 19 
 
 H 
 
 10 
 
 46 
 
 H 
 
 26 
 
 30 
 
 % 
 
 42 
 
 46 
 
 12 
 
 60 
 
 00 
 
 
 II 
 
 22 
 
 
 27 
 
 7 
 
 
 43 
 
 24 
 
 
 60 
 
 41 
 
 H 
 
 II 
 
 58 
 
 % 
 
 27 
 
 44 
 
 9 
 
 44 
 
 3 
 
 H 
 
 61 
 
 23 
 
 
 12 
 
 34 
 
 
 28 
 
 21 
 
 
 44 
 
 42 
 
 
 62 
 
 5 
 
 H 
 
 13 
 
 10 
 
 6 
 
 28 
 
 58 
 
 Vi 
 
 45 
 
 21 
 
 Y2 
 
 62 
 
 47 
 
 
 13 
 
 46 
 
 
 29 
 
 35 
 
 
 45 
 
 59 
 
 
 63 
 
 28 
 
 3 
 
 14 
 
 22 
 
 M 
 
 30 
 
 II 
 
 V2 
 
 46 
 
 38 
 
 H 
 
 64 
 
 II 
 
 
 14 
 
 58 
 
 
 30 
 
 49 
 
 
 47 
 
 17 
 
 
 64 
 
 53 
 
 H 
 
 15 
 
 34 
 
 M 
 
 31 
 
 26 
 
 % 
 
 47 
 
 56 
 
 13 
 
 65 
 
 35 
 
 
 16 
 
 10 
 
 
 32 
 
 3 
 
 
 48 
 
 35 
 
 
 66 
 
 18 
 
ii6 
 
 Mathematical Tables, 
 
 Tables of Angles Corresponding to Openings of a 2-foot 
 Rule — {Continued) 
 
 Ins. 
 
 Deg. 
 
 Min. 
 
 Ins. 
 
 Deg. 
 
 Min. 
 
 Ins.. 
 
 Deg. 
 
 Min.- 
 
 Ins. 
 
 Deg. 
 
 Min. 
 
 13M 
 
 67 
 
 I 
 
 16 
 
 83 
 
 37 
 
 1834 
 
 102 
 
 45 
 
 21H 
 
 127 
 
 14 
 
 
 67 
 
 44 
 
 
 84 
 
 26 
 
 
 103 
 
 43 
 
 
 128 
 
 35 
 
 H 
 
 68 
 
 28 
 
 H 
 
 85 
 
 14 
 
 19 
 
 104 
 
 41 
 
 H 
 
 129 
 
 59 
 
 
 69 
 
 12 
 
 
 86 
 
 3 
 
 
 los 
 
 40 
 
 
 131 
 
 25 
 
 % 
 
 69 
 
 55 
 
 K2 
 
 86 
 
 52 
 
 34 
 
 106 
 
 39 
 
 22 
 
 132 
 
 53 
 
 
 70 
 
 38 
 
 
 87 
 
 41 
 
 
 107 
 
 40 
 
 
 134 
 
 24 
 
 14 
 
 71 
 
 22 
 
 % 
 
 88 
 
 31 
 
 Vi 
 
 108 
 
 41 
 
 H 
 
 135 
 
 58 
 
 
 72 
 
 6 
 
 
 89 
 
 21 
 
 
 109 
 
 43 
 
 
 137 
 
 35 
 
 % 
 
 72 
 
 51 
 
 17 
 
 90 
 
 12 
 
 % 
 
 no 
 
 46 
 
 ^A 
 
 139 
 
 16 
 
 
 73 
 
 36 
 
 
 91 
 
 3 
 
 
 III 
 
 49 
 
 
 141 
 
 I 
 
 yi 
 
 74 
 
 21 
 
 H 
 
 91 
 
 54 
 
 20 
 
 112 
 
 53 
 
 H 
 
 142 
 
 51 
 
 
 75 
 
 6 
 
 
 92 
 
 46 
 
 
 113 
 
 58 
 
 
 144 
 
 46 
 
 % 
 
 75 
 
 51 
 
 i'^ 
 
 93 
 
 38 
 
 Vi 
 
 115 
 
 5 
 
 23 
 
 146 
 
 48 
 
 
 76 
 
 36 
 
 
 94 
 
 31 
 
 
 116 
 
 12 
 
 
 148 
 
 58 
 
 15 
 
 77 
 
 22 
 
 % 
 
 95 
 
 24 
 
 V2 
 
 117 
 
 20 
 
 H 
 
 151 
 
 17 
 
 
 78 
 
 8 
 
 
 96 
 
 17 
 
 
 118 
 
 30 
 
 
 153 
 
 48 
 
 H 
 
 78 
 
 54 
 
 18 
 
 97 
 
 II 
 
 H 
 
 119 
 
 40 
 
 H 
 
 156 
 
 34 
 
 
 79 
 
 40 
 
 
 98 
 
 5 
 
 
 120 
 
 52 
 
 
 159 
 
 43 
 
 \^ 
 
 80 
 
 27 
 
 H 
 
 99 
 
 00 
 
 21 
 
 122 
 
 6 
 
 % 
 
 163 
 
 27 
 
 
 81 
 
 14 
 
 
 99 
 
 55 
 
 
 123 
 
 20 
 
 
 168 
 
 18 
 
 % 
 
 82 
 
 2 
 
 ^/^ 
 
 100 
 
 51 
 
 H 
 
 124 
 
 36 
 
 24 
 
 180 
 
 00 
 
 
 82 
 
 49 
 
 
 lOI 
 
 48 
 
 
 125 
 
 54 
 
 
 
 
 (3) With the same table, using feet instead of inches. — 
 
 From any point measure 1 2 feet -toward* each object and place marks. 
 Measure the distance in feet between these marks. Suppose the first 
 column in the table to be feet instead of inches. Then opposite the 
 distance in feet will be the angle. 
 
 Vs foot =1.5 inches. 
 
 1 in. = .083 ft. 
 
 2 ins. = .167 ft. 
 
 3 ins. = .25 ft. 
 
 4 ins. = .333 ft. 
 
 5 ins. = .416 ft. 
 
 6 ins. = .5 ft. 
 
 7 ins. = .583 ft. 
 
 8 ins. = .667 ft. 
 
 9 ins. = .75 ft. 
 
 10 ins. = .833 ft. 
 
 11 ins. = .917 ft. 
 
 12 ins. = i.o ft. 
 
 (4) Or, measure toward* each object 100 or any other number 
 of feet and place marks. Measure the distance in f.eet between the 
 marks. Then 
 
 Sine of half _ • half the distance between the marks 
 
 the angle the distance measured toward one of the objects * 
 
 Find this sine in the table, etc.; take out the corresponding angle and 
 multiply it by 2. 
 
 If it is inconvenient to measure toward the objects, measure directly from them. 
 
Tapers per Foot and Corresponding Angles 
 
 117 
 
 Tapers per Foot and Corresponding Angles 
 
 Computed by E. M. Willson 
 
 Taper 
 per 
 foot 
 
 Included 
 
 Angle with 
 
 Taper 
 
 Included 
 
 Angle with 
 
 angle 
 
 center line 
 
 per 
 foot 
 
 angle 
 
 center line 
 
 
 Deg. Min. Sec. 
 
 Deg. Min. Sec. 
 
 
 Deg. Min. Sec. 
 
 Deg. Min. Sec. 
 
 1/64 
 
 4 28 
 
 2 14 
 
 23/^ 
 
 II 18 10 
 
 5 39 5 
 
 H2 
 
 8 58 
 
 4 29 
 
 2/2 
 
 II 53 36 
 
 5 56 48 
 
 Me 
 
 17 54 
 
 8 57 
 
 2% 
 
 12 29 2 
 
 6 14 31 
 
 ?i2 
 
 26 52 
 
 13 26 
 
 2% 
 
 13 4 24 
 
 6 32 12 
 
 ^i 
 
 35 48 
 
 17 54 
 
 2A 
 
 13 39 42 
 
 6 49 51 
 
 ^A2 
 
 44 44 
 
 22 22 
 
 3 
 
 14 15 
 
 7 7 30 
 
 Me 
 
 53 44 
 
 26 52 
 
 3H 
 
 14 SO 14 
 
 7 25 7 
 
 %2 
 
 I 2 34 
 
 31 17 
 
 3H 
 
 15 25 24 
 
 7 42 42 
 
 M 
 
 I II 36 
 
 35 48 
 
 33/i 
 
 16 34 
 
 8 17 
 
 %2 
 
 I 20 30 
 
 40 15 
 
 3I/2 
 
 16 35 40 
 
 8 17 50 
 
 5/16 
 
 I 29 30 
 
 44 45 
 
 3H 
 
 17 10 40 
 
 8 35 20 
 
 1^2 
 
 I 38 22 
 
 49 II 
 
 33/ 
 
 17 45 40 
 
 8 52 50 
 
 H 
 
 I 47 24 
 
 53 42 
 
 3A 
 
 18 20 34 
 
 9 10 17 
 
 m2 
 
 I 56 24 
 
 58 12 
 
 4 
 
 18 55 28 
 
 9 27 44 
 
 Vie 
 
 2 5 18 
 
 I 2 39 
 
 4Vs 
 
 19 30 18 
 
 9 45 9 
 
 m2 
 
 2 14 16 
 
 I 7 8 
 
 4I/4 
 
 20 5 2 
 
 10 2 31 
 
 }i 
 
 2 23 10 
 
 I II 35 
 
 43/^ 
 
 20 39 44 
 
 10 19 52 
 
 m2 
 
 2 32 4 
 
 I 16 2 
 
 4I/2 
 
 21 14 2 
 
 10 37 I 
 
 rie 
 
 2 41 4 
 
 I 20 32 
 
 4H 
 
 21 48 54 
 
 10 54 27 
 
 l?i2 
 
 2 50 2 
 
 I 25 I 
 
 43/ 
 
 22 23 22 
 
 II II 41 
 
 ^A 
 
 2 59 42 
 
 I 29 51 
 
 4/8 
 
 22 57 48 
 
 II 28 54 
 
 m2 
 
 3 7 56 
 
 I 33 58 
 
 5 
 
 23 32 12 
 
 II 46 6 
 
 ii/e 
 
 3 16 54 
 
 I 38 27 
 
 5% 
 
 24 6 28 
 
 12 3 14 
 
 m2 
 
 3 25 50 
 
 I 42 55 
 
 5I/4 
 
 24 40 42 
 
 12 20 21 
 
 H 
 
 3 34 44 
 
 I 47 22 
 
 5% 
 
 25 14 48 
 
 12 37 24 
 
 25/^2 
 
 3 43 44 
 
 I 51 52 
 
 5I/2 
 
 25 48 48 
 
 12 54 24 
 
 13/16 
 
 3 52 38 
 
 I 56 19 
 
 sH 
 
 26 22 52 
 
 13 II 26 
 
 2^32 
 
 4 I 36 
 
 2 48 
 
 53/ 
 
 26 56 46 
 
 13 28 23 
 
 li 
 
 4 10 32 
 
 2 5 16 
 
 5% 
 
 27 30 34 
 
 13 45 17 
 
 2%2 
 
 4 19 34 
 
 2 9 47 
 
 6 
 
 28 4 2 
 
 14 2 I 
 
 1^6 
 
 4 28 24 
 
 2 14 12 
 
 6/8 
 
 28 37 58 
 
 14 18 59 
 
 31/^2 
 
 4 37 20 
 
 2 18 40 
 
 61/ 
 
 29 II 34 
 
 14 35 47 
 
 I 
 
 4 46 18 
 
 2 23 9 
 
 63/^ 
 
 29 45 18 
 
 14 52 39 
 
 iHe 
 
 5 4 12 
 
 2 32 6 
 
 6/2 
 
 30 18 26 
 
 15 9 13 
 
 iH 
 
 5 21 44 
 
 2 40 52 
 
 6H 
 
 30 51 48 
 
 IS 25 54 
 
 iMe 
 
 5 39 54 
 
 2 49 57 
 
 63/ 
 
 31 25 2 
 
 15 42 31 
 
 iH 
 
 5 57 48 
 
 2 58 54 
 
 6% 
 
 31 58 10 
 
 IS 59 5 
 
 iMe 
 
 6 15 38 
 
 3 7 49 
 
 7 
 
 32 31 12 
 
 16 IS 36 
 
 l3/i 
 
 6 33 26 
 
 3 16 43 
 
 7% 
 
 33 4 8 
 
 16 32 4 
 
 1^6 
 
 6 51 20 
 
 3 25 40 
 
 7/4 
 
 33 36 40 
 
 16 48 20 
 
 iH 
 
 7 9 10 
 
 3 34 35 
 
 73/^ 
 
 34 9 50 
 
 17 4 55 
 
 I?'! 6 
 
 7 26 58 
 
 3 43 29 
 
 71/2 
 
 34 42 30 
 
 17 21 15 
 
 154 
 
 7 44 48 
 
 3 52 24 
 
 7% 
 
 35 15 2 
 
 17 37 31 
 
 iiMe 
 
 8 2 38 
 
 4 I 19 
 
 7% 
 
 35 47 32 
 
 17 53 46 
 
 iH 
 
 8 20 26 
 
 4 10 13 
 
 7A 
 
 36 19 54 
 
 18 9 57 
 
 113/6 
 
 8 38 16 
 
 4 19 8 
 
 8 
 
 36 52 12 
 
 18 26 6 
 
 1% 
 
 8 56 2 
 
 4 28 I 
 
 8/8 
 
 37 24 22 
 
 18 42 II 
 
 I15/6 
 
 9 13 50 
 
 4 36 55 
 
 m 
 
 37 56 26 
 
 18 58 13 
 
 2 
 
 9 31 36 
 
 4 45 48 
 
 m 
 
 38 28 16 
 
 19 14 8 
 
 2H 
 
 10 7 io 
 
 5 3 35 
 
 81/^ 
 
 39 16 
 
 19 30 8 
 
 2H 
 
 10 42 42 
 
 5 21 21 
 
 85,^ 
 
 39 31 52 
 
 19 45 56 
 
Ii8 Mathematical Tables, 
 
 Tapers per Foot and Corresponding Angles — (Continued) 
 
 Taper 
 
 Included 
 
 Angle with 
 
 Taper 
 
 Included 
 
 Angle with 
 
 per 
 foot 
 
 angle 
 
 center line 
 
 per 
 foot 
 
 angle 
 
 center line 
 
 
 Deg. Min. Sec. 
 
 Deg. Min. Sec. 
 
 
 Deg. Min. Sec. 
 
 Deg. Min. Sec. 
 
 83/4 
 
 4o 3 42 
 
 20 I SI 
 
 I03/i 
 
 46 45 24 
 
 23 22 42 
 
 8Ji 
 
 4o 35 i6 
 
 20 17 38 
 
 10I/2 
 
 47 15 32 
 
 23 37 46 
 
 9 
 
 41 6 44 
 
 20 33 22 
 
 I05/i 
 
 47 45 30 
 
 23 52 45 
 
 9H 
 
 41 38 28 
 
 20 49 14 
 
 I03^ 
 
 48 15 24 
 
 24 7 42 
 
 9H 
 
 42 9 i8 
 
 21 4 39 
 
 loji 
 
 48 45 10 
 
 24 22 35 
 
 9H 
 
 42 40 26 
 
 21 20 13 
 
 II 
 
 49 14 48 
 
 24 37 24 
 
 9H 
 
 43 II 24 . 
 
 21 35 42 
 
 I1I4 
 
 49 44 20 
 
 24 52 10 
 
 9% 
 
 43 42 20 
 
 21 51 10 
 
 iiH 
 
 50 13 46 
 
 25 6 53 
 
 9% 
 
 44 13 6 
 
 22 6 33 
 
 ii^i 
 
 50 43 4 
 
 25 21 32 
 
 9^ 
 
 44 43 48 
 
 22 21 54 
 
 iiJ-^ 
 
 51 12 14 
 
 25 36 7 
 
 lo 
 
 45 14 22 
 
 22 37 II 
 
 ii^i 
 
 51 41 18 
 
 25 SO 39 
 
 loi^ 
 
 45 44 52 
 
 22 52 26 
 
 iiH 
 
 52 10 16 
 
 26 5 8 
 
 loH 
 
 46 15 46 
 
 23 7 53 
 
 im 
 
 52 39 2 
 
 26 19 31 
 
CHAPTER IV 
 
 DIFFERENT STANDARDS FOR WIRE GAUGES 
 
 Different Standards for Wire Gauges in Use in the 
 United States 
 
 Dimensions of sizes in decimal parts of an inch 
 
 II 
 
 ^ .tl 
 
 H., S. & Co. 
 "F.&G." 
 
 steel music 
 wire gauge 
 
 1 
 
 U.S. 
 standard 
 for plate 
 
 American or 
 
 Brown & 
 
 Sharpe 
 
 all 
 
 t4 
 
 las 
 
 03 <U P 
 
 
 1 
 
 OS 
 
 II 
 
 oooooo 
 
 
 
 .46875 
 
 
 
 
 .464 
 
 
 oooooo 
 
 ooooo 
 
 
 
 .4375 
 
 
 
 
 .432 
 
 
 ooooo 
 
 OGOO 
 
 
 
 .40625 
 
 .46 
 
 .454 
 
 .3938 
 
 .400 
 
 
 0000 
 
 coo 
 
 
 
 • 375 
 
 .40964 
 
 .42s 
 
 .3625 
 
 .372 
 
 
 000 
 
 oo 
 
 .0087 
 
 
 .34375 
 
 .3648 
 
 .38 
 
 .3310 
 
 .348 
 
 
 00 
 
 o 
 
 .0093 
 
 .0578 
 
 .312s 
 
 .32486 
 
 .34 
 
 .3065 
 
 .324 
 
 
 
 
 I 
 
 .0098 
 
 .0710 
 
 .28125 
 
 .2893 
 
 .3 
 
 .2830 
 
 .300 
 
 .227 
 
 I 
 
 2 
 
 .0106 
 
 .0842 
 
 .265625 
 
 .25763 
 
 .284 
 
 .2625 
 
 .276 
 
 .219 
 
 2 
 
 3 
 
 .0114 
 
 .0973 
 
 .25 
 
 .22942 
 
 .259 
 
 .2437 
 
 .252 
 
 .212 
 
 3 
 
 4 
 
 .0122 
 
 .1105 
 
 .234375 
 
 . 20431 
 
 .238 
 
 .2253 
 
 .232 
 
 .207 
 
 4 
 
 5 
 
 .0138 
 
 .1236 
 
 .21875 
 
 .18194 
 
 .22 
 
 .2070 
 
 .212 
 
 .204 
 
 5 
 
 6 
 
 .0157 
 
 .1368 
 
 .203125 
 
 . 16202 
 
 .203 
 
 .1920 
 
 .192 
 
 .201 
 
 6 
 
 7 
 
 .0177 
 
 .1500 
 
 .1875 
 
 .14428 
 
 .18 
 
 .1770 
 
 .176 
 
 .199 
 
 7 
 
 8 
 
 .0197 
 
 .1631 
 
 .171875 
 
 .12^49 
 
 .165 
 
 .1620 
 
 .160 
 
 .197 
 
 8 
 
 9 
 
 .0216 
 
 .1763 
 
 . 15625 
 
 .11443 
 
 .148 
 
 .1483 
 
 .144 
 
 .194 
 
 9 
 
 ID 
 
 .0236 
 
 .1894 
 
 . 14062s 
 
 . 10189 
 
 .134 
 
 .1350 
 
 .128 
 
 .191 
 
 10 
 
 II 
 
 .0260 
 
 .2026 
 
 .125 
 
 .090742 
 
 .12 
 
 .1205 
 
 .116 
 
 .188 
 
 II 
 
 12 
 
 .0283 
 
 .2158 
 
 .109375 
 
 .080808 
 
 .109 
 
 .1055 
 
 .104 
 
 .185 
 
 12 
 
 13 
 
 .0303 
 
 .2289 
 
 .09375 
 
 .071961 
 
 .09s 
 
 .0915 
 
 .092 
 
 .182 
 
 13 
 
 14 
 
 .0323 
 
 .2421 
 
 .078125 
 
 .064084 
 
 .083 
 
 .0800 
 
 .080 
 
 .180 
 
 14 
 
 IS 
 
 .0342 
 
 .2552 
 
 .0703125 
 
 .057068 
 
 .072 
 
 .0720 
 
 .072 
 
 .178 
 
 IS 
 
 i6 
 
 .0362 
 
 .2684 
 
 .0625 
 
 .05082 
 
 .06s 
 
 .0625 
 
 .064 
 
 .175 
 
 16 
 
 17 
 
 .0382 
 
 .2816 
 
 .05625 
 
 .045257 
 
 .058 
 
 .0540 
 
 .056 
 
 .172 
 
 17 
 
 i8 
 
 .04 
 
 .2947 
 
 .05 
 
 .040303 
 
 .049 
 
 .0475 
 
 .048 
 
 .168 
 
 18 
 
 19 
 
 .042 
 
 
 .04375 
 
 .03589 
 
 .042 
 
 .0410 
 
 .040 
 
 .164 
 
 19 
 
 20 
 
 .044 
 
 .3210 
 
 .0375 
 
 .031961 
 
 .035 
 
 .0348 
 
 .036 
 
 .161 
 
 20 
 
 21 
 
 .046 
 
 
 .034375 
 
 .028462 
 
 .032 
 
 .03175 
 
 .032 
 
 .157 
 
 21 
 
 22 
 
 .048 
 
 .3474 
 
 .03125 
 
 .025347 
 
 .028 
 
 .0286 
 
 .028 
 
 .155 
 
 22 
 
 23 
 
 .051 
 
 
 .028125 
 
 .022571 
 
 .02s 
 
 .0258 
 
 .024 
 
 .153 
 
 23 
 
 24 
 
 • OSS 
 
 3737 
 
 .025 
 
 .0201 
 
 .022 
 
 .0230 
 
 .022 
 
 .151 
 
 24 
 
 25 
 
 .059 
 
 
 .021875 
 
 .0179 
 
 .02 
 
 .0204 
 
 .020 
 
 .148 
 
 25 
 
 26 
 
 .063 
 
 .4000 
 
 .01875 
 
 .01594 
 
 .018 
 
 .0181 
 
 .018 
 
 .146 
 
 26 
 
 27 
 
 .067 
 
 
 .0171875 
 
 .014195 
 
 .016 
 
 .0173 
 
 .0164 
 
 .143 
 
 27 
 
 28 
 
 .071 
 
 .4263 
 
 .015625 
 
 .012641 
 
 .014 
 
 .0162 
 
 .0149 
 
 .139 
 
 28 
 
 119 
 
I20 
 
 Materials 
 
 Deffeeent Standards for Wire Gauges in Use in the 
 United States — {Continued) 
 
 
 &Co. 
 
 music 
 gauge 
 
 
 . S. 
 
 dard 
 
 plate 
 
 
 1:1 -tt 
 
 
 2J 
 
 1 
 
 OS, 
 
 u 3 
 
 '1 
 
 
 
 ^sa 
 
 1" 
 
 
 
 
 
 
 29 
 
 .074 
 
 
 .0140625 
 
 .011257 
 
 .013 
 
 .0150 
 
 .0136 
 
 .134 
 
 29 
 
 30 
 
 .078 
 
 •452 
 
 3 OI2S 
 
 .010025 
 
 
 012 
 
 .0141 
 
 .0124 
 
 .127 
 
 30 
 
 31 
 
 .082 
 
 
 •0109375 
 
 .008928 
 
 
 01 
 
 .0132 
 
 .0116 
 
 .120 
 
 31 
 
 32 
 
 .086 
 
 
 .01015625 
 
 .00795 
 
 
 009 
 
 .0128 
 
 .0108 
 
 .115 
 
 32 
 
 33 
 
 
 
 - .009375 
 
 .00708 
 
 
 008 
 
 .0118 
 
 .0100 
 
 .112 
 
 33 
 
 34 
 
 
 
 .00859375 
 
 .006304 
 
 
 007 
 
 .0104 
 
 .0092 
 
 .110 
 
 34 
 
 35 
 
 
 
 .0078125 
 
 .005614 
 
 
 005 
 
 .0095 
 
 .0084 
 
 .108 
 
 35 
 
 36 
 
 
 
 .00703125 
 
 .005 
 
 
 004 
 
 .0090 
 
 .0076 
 
 .106 
 
 36 
 
 37 
 
 
 
 .006640625 
 
 .004453 
 
 
 
 
 .0068 
 
 .103 
 
 37 
 
 38 
 
 
 
 .00625 
 
 .003965 
 
 
 
 
 .0060 
 
 .101 
 
 38 
 
 39 
 
 
 
 
 .003531 
 
 
 
 
 .0052 
 
 .099 
 
 39 
 
 40 
 
 
 
 
 .003144 
 
 
 
 
 .0048 
 
 .097 
 
 40 
 
 Birmingham Gauge for Sheet Brass, Silver, Gold and all 
 Metals except Steel and Iron 
 
 
 Thick- 
 
 
 Thick- 
 
 
 Thick- 
 
 
 Thick- 
 
 
 Thick- 
 
 
 Thick- 
 
 No. 
 
 ness, 
 
 No. 
 
 ness, 
 
 No. 
 
 ness, 
 
 No. 
 
 ness, 
 
 No. 
 
 ness, 
 
 No. 
 
 ness, 
 
 
 inch 
 
 
 inch 
 
 13 
 
 inch 
 
 
 inch 
 
 
 inch 
 
 
 inch 
 
 I 
 
 .004 
 
 7 
 
 .015 
 
 .036 
 
 19 
 
 .064 
 
 25 
 
 .095 
 
 31 
 
 .133 
 
 2 
 
 .005 
 
 8 
 
 .016 
 
 14 
 
 .041 
 
 20 
 
 .067 
 
 26 
 
 .103 
 
 32 
 
 .143 
 
 3 
 
 .008 
 
 9 
 
 .019 
 
 15 
 
 .047 
 
 21 
 
 .072 
 
 27 
 
 .113 
 
 33 
 
 .145 
 
 4 
 
 .010 
 
 10 
 
 .024 
 
 16 
 
 .051 
 
 22 
 
 .074 
 
 28 
 
 .120 
 
 34 
 
 .148 
 
 5 
 
 .012 
 
 II 
 
 .029 
 
 19 
 
 .057 
 
 23 
 
 .077 
 
 29 
 
 .124 
 
 35 
 
 .158 
 
 6 
 
 .013 
 
 12 
 
 .034 
 
 18 
 
 .061 
 
 24 
 
 .082 
 
 30 
 
 .126 
 
 36 
 
 .167 
 
 ^ Gauges Generally used by Mills in the U. S. Rolling Sheet 
 Iron. (Vary Slightly from Birmingham Gauge) 
 
 No. 
 
 Pounds per 
 
 No. 
 
 Pounds per 
 
 No. 
 
 Pounds per 
 
 No. 
 
 Pounds per 
 
 square foot 
 
 square foot 
 
 square foot 
 
 square foot 
 
 I 
 
 12.50 
 
 8 
 
 6.86 
 
 15 
 
 2.81 
 
 22 
 
 1. 25 
 
 2 
 
 12.00 
 
 9 
 
 6.24 
 
 16 
 
 2.50 
 
 23 
 
 1. 12 
 
 3 
 
 11.00 
 
 10 
 
 5.62 
 
 17 
 
 2.18 
 
 24 
 
 1. 00 
 
 4 
 
 10.00 
 
 II 
 
 5.00 
 
 18 
 
 1.86 
 
 25 
 
 .90 
 
 5 
 
 8.75 
 
 12 
 
 4.38 
 
 19 
 
 1.70 
 
 26 
 
 .80 
 
 6 
 
 8.12 
 
 13 
 
 3.75 
 
 20 
 
 1-54 
 
 27 
 
 .72 
 
 7 
 
 7.50 
 
 14 
 
 3.12 
 
 21 
 
 1.40 
 
 28 
 
 .64 
 
Band and Hoop Iron Weights per Lineal Foot 
 Band and Hoop Iron Weights per Lineal Foot 
 
 
 
 
 
 Width 
 
 in inches 
 
 
 
 
 No. of 
 
 
 
 
 
 
 
 
 
 
 gauge 
 
 
 
 
 
 
 
 
 
 
 
 % 
 
 % 
 
 % 
 
 I 
 
 ii/i 
 
 ii/4 
 
 1% 
 
 m 
 
 1% 
 
 
 lbs. 
 
 lbs. 
 
 lbs. 
 
 lbs. 
 
 lbs. 
 
 lbs. 
 
 lbs. 
 
 lbs. 
 
 lbs. 
 
 6 
 
 .4231 
 
 .5078 
 
 .5924 
 
 674 
 
 762 
 
 846 
 
 .931 I 
 
 016 
 
 1. 10 
 
 8 
 
 .3581 
 
 .4296 
 
 .5013 
 
 5729 
 
 64s 
 
 716 
 
 .788 
 
 859 
 
 .931 
 
 lo 
 
 .2929 
 
 .3515 
 
 .4101 
 
 4689 
 
 527 
 
 586 
 
 .645 
 
 703 
 
 .762 
 
 II 
 
 
 
 
 
 469 
 
 521 
 
 .573 
 
 625 
 
 .677 
 
 12 
 
 .2278 
 
 .2734 
 
 .3190 
 
 364s 
 
 41 
 
 456 
 
 .501 
 
 547 
 
 .592 
 
 13 
 
 
 
 
 
 352 
 
 391 
 
 .430 
 
 469 
 
 .508 
 
 14 
 
 .1628 
 
 .1953 
 
 .2278 
 
 2604 
 
 293 
 
 326 
 
 .358 
 
 391 
 
 .423 
 
 15 
 
 
 
 
 
 264 
 
 293 
 
 .322 
 
 352 
 
 .381 
 
 i6 
 
 .1302 
 
 .1562 
 
 .1822 
 
 2083 
 
 234 
 
 26 
 
 .286 
 
 313 
 
 .339 
 
 17 
 
 .1139 
 
 .1367 
 
 .1595 
 
 1822 
 
 205 
 
 229 
 
 .251 
 
 273 
 
 .269 
 
 i8 
 
 .0976 
 
 .1171 
 
 .1367 
 
 1562 
 
 176 
 
 195 
 
 .215 
 
 234 
 
 .254 
 
 19 
 
 .0895 
 
 .1074 
 
 .1253 
 
 1432 
 
 161 
 
 179 
 
 .197 
 
 215 
 
 
 20 
 
 .0814 
 
 .0976 
 
 .1139 
 
 1302 
 
 146 
 
 163 
 
 .179 
 
 195 
 
 
 21 
 
 ■0731 
 
 .0877 
 
 .1023 
 
 1169 . 
 
 
 
 
 
 
 22 
 
 .0651 
 
 .0781 
 
 .0911 
 
 104 1 
 
 
 
 
 
 
 23 
 
 .0588 
 
 .0705 
 
 .0822 
 1 
 
 0939 . 
 
 
 
 
 
 
 
 
 
 
 
 
 Width in inches 
 
 
 
 
 
 No. of 
 
 
 
 
 
 
 
 
 
 
 
 gauge 
 
 
 
 
 
 
 
 
 
 
 
 
 1% 
 
 m 
 
 2 
 
 2}i 
 
 2H 
 
 2% 
 
 2I/2 
 
 2% 
 
 234 
 
 2% 
 
 
 lbs. 
 
 lbs. 
 
 lbs.' 1 
 
 bs. 
 
 lbs. 
 
 lbs. 
 
 lbs. 
 
 lbs. 
 
 lbs. 
 
 lbs. 
 
 4 
 
 1.367 
 
 1.465 
 
 1.562 I 
 
 660 
 
 i.^S8 
 
 1.855 
 
 1.953 
 
 2.051 
 
 2.148 
 
 2.246 
 
 6 
 
 1. 185 
 
 1.270 
 
 1.354 I 
 
 439 
 
 1.523 
 
 1.608 
 
 1.693 
 
 1.777 
 
 1.862 
 
 1-947 
 
 8 
 
 1.003 
 
 1.074 
 
 I . 146 I 
 
 217 
 
 1.289 
 
 1. 361 
 
 1.432 
 
 1.504 
 
 1.576 
 
 1.647 
 
 9 
 
 .914 
 
 .977 
 
 1.042 I 
 
 107 
 
 1. 172 
 
 1.237 
 
 1.302 
 
 1.367 
 
 1.423 
 
 1-497 
 
 10 
 
 .820 
 
 .897 
 
 .938 
 
 996 
 
 1.055 
 
 1. 113 
 
 1. 172 
 
 1. 231 
 
 1.289 
 
 1.348 
 
 II 
 
 .729 
 
 .781 
 
 .833 
 
 88s 
 
 .938 
 
 ■990 
 
 1.042 
 
 1.094 
 
 1. 146 
 
 1. 198 
 
 12 
 
 .638 
 
 .684 
 
 .729 
 
 775 
 
 .820 
 
 .866 
 
 .911 
 
 • 957 
 
 1.003 
 
 1.048 
 
 13 
 
 .547 
 
 .586 
 
 .625 
 
 664 
 
 .703 
 
 .742 
 
 .781 
 
 .820 
 
 .859 
 
 .898 
 
 14 
 
 .456 
 
 .488 
 
 .521 
 
 553 
 
 .586 
 
 .618 
 
 .651 
 
 .684 
 
 .716 
 
 .749 
 
 ♦ 15 
 
 .410 
 
 .439 
 
 .469 
 
 498 
 
 .527 
 
 .557 
 
 .586 
 
 
 
 
 16 
 
 .36s 
 
 .391 
 
 .417 
 
 443 
 
 .469 
 
 .495 
 
 .521 
 
 
 
 
 17 
 
 .319 
 
 .342 
 
 .365 . 
 
 
 
 
 
 
 
 
 
 18 
 
 .273 
 
 .293 
 
 .313 . 
 
 
 
 
 
 
 
 
22 Materials 
 
 Band and Hoop Iron Weights per Lineal Foot — {Continued) 
 
 
 
 
 
 
 Width in inches 
 
 
 
 
 
 No. of 
 
 
 
 
 
 
 
 
 
 
 gauge 
 
 
 
 
 
 
 
 
 
 
 
 
 3 
 
 3H 
 
 3H 
 
 3% 
 
 4 
 
 4H 
 
 4H 
 
 5 
 
 SH 
 
 6 
 
 
 lbs. 
 
 lbs. 
 
 lbs. 
 
 lbs. 
 
 lbs. 
 
 lbs. 
 
 lbs. 
 
 lbs. 
 
 lbs. 
 
 lbs. 
 
 4 
 
 2.344 
 
 2.539 
 
 2.734 
 
 2.930 
 
 3.125 
 
 3.321 
 
 3.516 
 
 3.906 
 
 4.297 
 
 4.688 
 
 5 
 
 2.188 
 
 2.370 
 
 2.552 
 
 2.734 
 
 2.917 
 
 3.099 
 
 3.281 
 
 3.646 
 
 4. on 
 
 4.37s 
 
 6 
 
 2.031 
 
 2.201 
 
 2.370 
 
 2.539 
 
 2.708 
 
 2.878 
 
 3 047 
 
 3.385 
 
 3.724 
 
 4.063 
 
 7 
 
 1.875 
 
 2.031 
 
 2.188 
 
 2.344 
 
 2.500 
 
 2.656 
 
 2.813 
 
 3.125 
 
 3.437 
 
 3 -750 
 
 8 
 
 1. 719 
 
 1.862 
 
 2.005 
 
 2.148 
 
 2.292 
 
 2.435 
 
 2.578 
 
 2.864 
 
 3. 151 
 
 3.438 
 
 9 
 
 1.563 
 
 1.693 
 
 1.823 
 
 1.953 
 
 2.083 
 
 2.214 
 
 2.344 
 
 2.604 
 
 2.865 
 
 3.12s 
 
 lo 
 
 1.406 
 
 1.523 
 
 1. 641 
 
 1.758 
 
 1.875 
 
 1.992 
 
 2.109 
 
 2.344 
 
 2.578 
 
 2.813 
 
 II 
 
 1. 250 
 
 1.354 
 
 1.458 
 
 1.563 
 
 1.667 
 
 1. 771 
 
 1.87s 
 
 2.083 
 
 2.292 
 
 2.500 
 
 13 
 
 1.094 
 
 1. 185 
 
 1.276 
 
 1.367 
 
 1.458 
 
 1.549 
 
 1. 641 
 
 1.823 
 
 2.00S 
 
 2.188 
 
 13 
 
 .938 
 
 1. 016 
 
 1.094 
 
 
 
 
 
 
 
 
 
 
 
 14 
 
 .781 
 
 .846 
 
 .911 
 
 
 
 
 
 
 
 
 
Weights of Flat Rolled Iron per Lineal Foot 
 
 123 
 
 Weights or Flat Rolled Iron per Lineal Foot 
 
 For thicknesses from He inch to 2 inches and widths from i inch to 
 
 12% inches. 
 
 Iron weighing 480 pounds per cubic foot. 
 
 Thick- 
 
 I 
 
 iH 
 
 m 
 
 1% 
 
 2 
 
 2H 
 
 2H 
 
 3% 
 
 12 
 
 ness in 
 inches 
 
 inch 
 
 inches 
 
 inches 
 
 inches 
 
 inches 
 
 inches 
 
 inches 
 
 inches 
 
 inches 
 
 Ms 
 
 .208 
 
 .260 
 
 .313 
 
 .36s 
 
 .417 
 
 .469 
 
 .521 
 
 .573 
 
 2.50 
 
 H 
 
 .417 
 
 .521 
 
 .625 
 
 .729 
 
 .833 
 
 .938 
 
 1.04 
 
 1. 15 
 
 5.00 
 
 ?l6 
 
 .625 
 
 .781 
 
 .938 
 
 1.09 
 
 1.25 
 
 1. 41 
 
 1.56 
 
 1.72 
 
 7.50 
 
 H 
 
 .833 
 
 1.04 
 
 1.25 
 
 1.46 
 
 1.67 
 
 1.88 
 
 2.08 
 
 2.29 
 
 10.00 
 
 Me 
 
 1.04 
 
 1.30 
 
 1.56 
 
 1.82 
 
 2.08 
 
 2.34 
 
 2.60 
 
 2.86 
 
 12.50 
 
 H 
 
 1. 25 
 
 1:56 
 
 1.88 
 
 2.19 
 
 2.50 
 
 2.81 
 
 3.13 
 
 3.44 
 
 I5-00 
 
 Viti 
 
 1.46 
 
 1.82 
 
 2.19 
 
 2.55 
 
 2.92 
 
 3.28 
 
 3.65 
 
 4.01 
 
 17. SO 
 
 H 
 
 1.67 
 
 2.08 
 
 2.50 
 
 2.92 
 
 3.33 
 
 3.75 
 
 4.17 
 
 4.58 
 
 20.00 
 
 %6 
 
 I 88 
 
 2.34 
 
 2.81 
 
 3.28 
 
 3. 75 
 
 4.22 
 
 4.69 
 
 5.16 
 
 22.50 
 
 H 
 
 2.08 
 
 2.60 
 
 3.31 
 
 3.65 
 
 4.17 
 
 4.69 
 
 5.21 
 
 5.73 
 
 25.00 
 
 iMe 
 
 2.29 
 
 2.86 
 
 3-44 
 
 4.01 
 
 4.58 
 
 5.16 
 
 5.73 
 
 6.30 
 
 27.50 
 
 % 
 
 2.50 
 
 3.13 
 
 3.75 
 
 4.38 
 
 500 
 
 5.63 
 
 6.25 
 
 6.88 
 
 30.00 
 
 1^6 
 
 2.71 
 
 3.39 
 
 4.06 
 
 4-74 
 
 5.42 
 
 6.09 
 
 6.77 
 
 7.45 
 
 32.50 
 
 % 
 
 2.92 
 
 3.65 
 
 4.38 
 
 5.10 
 
 5.83 
 
 6.56 
 
 7.29 
 
 8.02 
 
 35.00 
 
 iMe 
 
 3.13 
 
 3.91 
 
 4.69 
 
 5.47 
 
 6.25 
 
 7.03 
 
 7.81 
 
 8.59 
 
 37.50 
 
 I 
 
 3.33 
 
 4.17 
 
 5.00 
 
 5.83 
 
 6.67 
 
 7.50 
 
 8.33 
 
 9.17 
 
 40.00 
 
 iHe 
 
 3.54 
 
 4.43 
 
 5.31 
 
 6.20 
 
 7.08 
 
 7.97 
 
 8.85 
 
 9.74 
 
 42.50 
 
 iH 
 
 3.75 
 
 4.69 
 
 5.63 
 
 6.56 
 
 7.50 
 
 8.44 
 
 9-38 
 
 10.31 
 
 45.00 
 
 iMe 
 
 3.96 
 
 4.95 
 
 5. 94 
 
 6.93 
 
 7-92 
 
 8.91 
 
 9.90 
 
 10.89 
 
 47.50 
 
 iH 
 
 4 17 
 
 5.21 
 
 6.25 
 
 7.29 . 
 
 8.33 
 
 9.38 
 
 10.42 
 
 11.46 
 
 50.00 
 
 1^6 
 
 4.37 
 
 5. 47 
 
 6.56 
 
 7.66 
 
 8.75 
 
 9.84 
 
 10.94 
 
 12.03 
 
 52.50 
 
 l3/6 
 
 4. 58 
 
 5.73 
 
 6.88 
 
 8.02 
 
 917 
 
 10.31 
 
 11.46 
 
 12.60 
 
 55.00 
 
 1M5 
 
 4.79 
 
 5.99 
 
 7.19 
 
 8.39 
 
 958 
 
 10.78 
 
 11.98 
 
 13 18 
 
 57.50 
 
 i3^ 
 
 S.oo 
 
 6.25 
 
 7-So 
 
 8.75 
 
 10.00 
 
 11.25 
 
 12.50 
 
 13-75 
 
 60.00 
 
 iMe 
 
 5. 21 
 
 6.51 
 
 7.81 
 
 9. II 
 
 10.42 
 
 11.72 
 
 13.02 
 
 14.32 
 
 62.50 
 
 i5i 
 
 5.42 
 
 6.77 
 
 8.13 
 
 948 
 
 10.83 
 
 12.19 
 
 13.54 
 
 14.90 
 
 65.00 
 
 iiHe 
 
 5.63 
 
 7-03 
 
 8.44 
 
 9.84 
 
 11.25 
 
 12.66 
 
 14.06 
 
 15.47 
 
 67.50 
 
 zVi 
 
 6.83 
 
 7.29 
 
 8.75 
 
 10.21 
 
 11.67 
 
 13.13 
 
 14.58 
 
 16.04 
 
 70.00 
 
 i^ie 
 
 6.04 
 
 7.5s 
 
 9.06 
 
 10.57 
 
 12.08 
 
 13.59 
 
 15.10 
 
 16.61 
 
 72.50 
 
 1% 
 
 6.25 
 
 7.81 
 
 9.38 
 
 10.94 
 
 12.50 
 
 14.06 
 
 15.63 
 
 17.19 
 
 75 -00 
 
 iiMe 
 
 6.46 
 
 8.07 
 
 9.69 
 
 11.30 
 
 12.92 
 
 14.53 
 
 16. IS 
 
 17.76 
 
 77.50 
 
 2 
 
 6.67 
 
 8.33 
 
 10.00 
 
 11.67 
 
 13-33 
 
 15.00 
 
 16.67 
 
 18.33 
 
 80.00 
 
124 Materials 
 
 Weights of Flat Rolled Iron per Lineal Foot — {Continued) 
 
 Thick- 
 
 3 
 
 314 
 
 _ 3^2 
 
 ._ 3% 
 
 4 
 
 4M 
 
 1 
 
 4V^ 
 
 4% 
 
 12 
 
 ness in 
 inches 
 
 inches 
 
 inches 
 
 inches 
 
 inches 
 
 inches 
 
 inches 
 
 inches 
 
 inches 
 
 inches 
 
 Me 
 
 .625 
 
 .677 
 
 .729 
 
 .781 
 
 .833 
 
 .885 
 
 .938 
 
 .990' 
 
 2.50 
 
 H 
 
 1.25 
 
 1. 35 
 
 1.46 
 
 1.56 
 
 1.67 
 
 1.77 
 
 1.88 
 
 1.98 
 
 5.00 
 
 He 
 
 1.88 
 
 2.03 
 
 2.19 
 
 2.34 
 
 2.50 
 
 2.66 
 
 2.81 
 
 2.97 
 
 7.50 
 
 H 
 
 2.50 
 
 2.71 
 
 2.92 
 
 3.13 
 
 3.33 
 
 3-54 
 
 3.75 
 
 3.96 
 
 10.00 
 
 Me 
 
 3.13 
 
 3.39 
 
 3.65 
 
 3.91 
 
 4.17 
 
 4.43 
 
 4.69 
 
 4-95 
 
 12.50 
 
 % 
 
 3.75 
 
 4.06 
 
 4.38 
 
 4.69 
 
 S-oo 
 
 5. 31 
 
 5. 63 
 
 5.94 
 
 15.00 
 
 Me 
 
 4.38 
 
 4.74 
 
 S.io 
 
 5.47 
 
 5.83 
 
 6.20 
 
 6.56 
 
 6.93 
 
 17.50 
 
 H 
 
 5.00 
 
 S.42 
 
 5.83 
 
 6.25 
 
 6.67 
 
 7.08 
 
 7.50 
 
 7.92 
 
 20.00 
 
 Vis 
 
 5. 63 
 
 6.09 
 
 6.56 
 
 7.03 
 
 7. So 
 
 7.97 
 
 8.44 
 
 8.91 
 
 22.50 
 
 5/i 
 
 6.25 
 
 6.77 
 
 7.29 
 
 7.81 
 
 8.33 
 
 8.85 
 
 9.38 
 
 9.90 
 
 25.00 
 
 iMe 
 
 6.88 
 
 7-45 
 
 8.02 
 
 8.59 
 
 9.17 
 
 9.74 
 
 10.31 
 
 10.89 
 
 27.50 
 
 % 
 
 7.50 
 
 8.13 
 
 8.75 
 
 9.38 
 
 10.00 
 
 10.63 
 
 11.25 
 
 11.88 
 
 30.00 
 
 me 
 
 8.13 
 
 8.80 
 
 9.48 
 
 10.16 
 
 10.83 
 
 II. SI 
 
 12.19 
 
 12.86 
 
 32.50 
 
 li 
 
 8.75 
 
 9.48 
 
 10.21 
 
 10.94 
 
 11.67 
 
 12.40 
 
 13.13 
 
 13.85 
 
 35.00 
 
 iMe 
 
 9.38 
 
 10,16 
 
 10.94 
 
 11.72 
 
 12.50 
 
 13 .28 
 
 14.06 
 
 14.84 
 
 37.50 
 
 I 
 
 10.00 
 
 10.83 
 
 11.67 
 
 12.50 
 
 13.33 
 
 14.17 
 
 15.00 
 
 15.83 
 
 40.00 
 
 iMa 
 
 10.63 
 
 II. 51 
 
 12.40 
 
 13.28 
 
 14. 17 
 
 15. OS 
 
 15.94 
 
 16.82 
 
 42.50 
 
 i\i 
 
 11.25 
 
 12.19 
 
 13.13 
 
 14.06 
 
 15.00 
 
 IS. 94 
 
 16.88 
 
 17.81 
 
 45.00 
 
 xVie 
 
 11.88 
 
 12.86 
 
 13.85 
 
 14.84 
 
 15.83 
 
 16.82 
 
 17.81 
 
 18.80 
 
 47.50 
 
 iM 
 
 12.50 
 
 13.54 
 
 14.58 
 
 15.63 
 
 16.67 
 
 17.71 
 
 18.75 
 
 19.79 
 
 50.00 
 
 iVie 
 
 13.13 
 
 14.22 
 
 IS. 31 
 
 16.41 
 
 17.50 
 
 18.59 
 
 19.69 
 
 20.78 
 
 52.50 
 
 l3/i 
 
 13.75 
 
 14.90 
 
 16.04 
 
 17.19 
 
 18.33 
 
 19.48 
 
 20.63 
 
 21.77 
 
 55. 00 
 
 iMe 
 
 14.38 
 
 15.57 
 
 16.77 
 
 17.97 
 
 19.17 
 
 20.36 
 
 21.56 
 
 22.76 
 
 57.50 
 
 iH 
 
 15.00 
 
 16.25 
 
 17.50 
 
 18.7s 
 
 20.00 
 
 21.25 
 
 22.50 
 
 23.75 
 
 60.00 
 
 i%e 
 
 IS. 63 
 
 16.93 
 
 18.23 
 
 19.53 
 
 20.83 
 
 22.14 
 
 23.44 
 
 24.74 
 
 62.50 
 
 iH 
 
 16.25 
 
 17.60 
 
 18.96 
 
 20.31 
 
 21.67 
 
 23.02 
 
 24.38 
 
 25.73 
 
 65.00 
 
 iiHe 
 
 16.88 
 
 18.28 
 
 19.69 
 
 21.09 
 
 22.50 
 
 23.91 
 
 25.31 
 
 26.72 
 
 67.50 
 
 1% 
 
 17. SO 
 
 18.96 
 
 20.42 
 
 21.88 
 
 23.33 
 
 24.79 
 
 26.25 
 
 27.71 
 
 70.00 
 
 Il3/i6 
 
 18.13 
 
 19.64 
 
 21.15 
 
 22.66 
 
 24.17 
 
 25.68 
 
 27.19 
 
 28.70 
 
 72.50 
 
 x-'A 
 
 18.75 
 
 20.31 
 
 21.88 
 
 23.44 
 
 25.00 
 
 26.56 
 
 28.13 
 
 29.69 
 
 75. 00 
 
 iiMe 
 
 19.38 
 
 20.99 
 
 22.60 
 
 24.22 
 
 25.83 
 
 27.45 
 
 29.06 
 
 30.68 
 
 77.50 
 
 2 
 
 20.00 
 
 21.67 
 
 23.33 
 
 25.00 
 
 26.67 
 
 28.33 
 
 30.00 
 
 31.67 
 
 80.00 
 
Weights of Flat Rolled Iron per Lineal Foot 125 
 
 Weights of Flat Rolled Iron per Lineal Foot — {Continued). 
 
 Thick- 
 
 5 
 
 sH 
 
 5\^ 
 
 5% 
 
 6 
 
 6H 
 
 6^2 
 
 m 
 
 12 
 
 ness in 
 inches 
 
 inches 
 
 inches 
 
 inches 
 
 inches 
 
 inches 
 
 inches 
 
 inches 
 
 inches 
 
 inches 
 
 He 
 
 1.04 
 
 1.09 
 
 1. 15 
 
 1.20 
 
 1.25 
 
 1.30 
 
 1.35 
 
 1. 41 
 
 2.50 
 
 H 
 
 2.08 
 
 2.19 
 
 2.29 
 
 2.40 
 
 2.50 
 
 2.60 
 
 2.71 
 
 2.81 
 
 5-00 
 
 ^ie 
 
 3.13 
 
 3.28 
 
 3.44 
 
 3.59 
 
 3.75 
 
 3.91 
 
 4.06 
 
 4.22 
 
 7-50 
 
 Yi 
 
 4.17 
 
 4.38 
 
 4.58 
 
 4.79 
 
 5.00 
 
 5.21 
 
 5.42 
 
 5.63 
 
 10.00 
 
 M6 
 
 5.21 
 
 5.47 
 
 S.73 
 
 S.99 
 
 6.2s 
 
 6.51 
 
 6.77 
 
 7.03 
 
 12.50 
 
 ^i 
 
 6.25 
 
 6.56 
 
 6.88 
 
 7.19 
 
 7.50 
 
 7.81 
 
 8.13 
 
 8.44 
 
 15 00 
 
 ^6 
 
 7.29 
 
 7.66 
 
 8.02 
 
 8.39 
 
 8.75 
 
 9. II 
 
 948 
 
 9.84 
 
 17-50 
 
 H 
 
 8.33 
 
 8.75 
 
 9.17 
 
 9.58 
 
 10.00 
 
 10.42 
 
 10.83 
 
 11.25 
 
 20.00 
 
 ^M 
 
 9- 38 
 
 9.84 
 
 10.31 
 
 10.78 
 
 11.25 
 
 11.72 
 
 12.19 
 
 12.66 
 
 22.50 
 
 H 
 
 10.42 
 
 10.94 
 
 11.46 
 
 11.98 
 
 12.50 
 
 13.02 
 
 13-54 
 
 14.06 
 
 25.00 
 
 1^6 
 
 11.46 
 
 12.03 
 
 12.60 
 
 13.18 
 
 13.75 
 
 14.32 
 
 14.90 
 
 15.47 
 
 27.50 
 
 % 
 
 12.50 
 
 13.13 
 
 13.75 
 
 14-38 
 
 1500 
 
 15.63 
 
 16.25 
 
 16.88 
 
 30.00 
 
 13/i6 
 
 13.54 
 
 14.22 
 
 14.90 
 
 15.57 
 
 16.25 
 
 16.93 
 
 17.60 
 
 18.28 
 
 32.50 
 
 ^ 
 
 14.58 
 
 15.31 
 
 16.04 
 
 16.77 
 
 17.50 
 
 18.23 
 
 18.96 
 
 19.69 
 
 35.00 
 
 15/6 
 
 IS. 63 
 
 16.41 
 
 17.19 
 
 17.97 
 
 18.75 
 
 19 53 
 
 20.31 
 
 21.09 
 
 37. so 
 
 I 
 
 16.67 
 
 17.50 
 
 18.33 
 
 19.17 
 
 20.00 
 
 20.83 
 
 21.67 
 
 22.50 
 
 40.00 
 
 iMe 
 
 17.71 
 
 18.59 
 
 19-48 
 
 20.36 
 
 21.25 
 
 22.14 
 
 23.02 
 
 23.91 
 
 42.50 
 
 iH 
 
 18.75 
 
 19.69 
 
 20.63 
 
 21.56 
 
 22.50 
 
 23.44 
 
 24.38 
 
 25. 31 
 
 45.00 
 
 iMe 
 
 19-79 
 
 20.78 
 
 21.77 
 
 22.76 
 
 23.75 
 
 24.74 
 
 25.73 
 
 26.72 
 
 47. SO 
 
 iH 
 
 20.83 
 
 21.88 
 
 22.92 
 
 23.96 
 
 25.00 
 
 26.04 
 
 27.08 
 
 28.13 
 
 50.00 
 
 iMe 
 
 21.88 
 
 22.97 
 
 24.06 
 
 25.16 
 
 26.25 
 
 27.34 
 
 28.44 
 
 29.53 
 
 52.50 
 
 1% 
 
 22.92 
 
 24.06 
 
 25.21 
 
 26.35 
 
 27.50 
 
 28.65 
 
 29.79 
 
 30.94 
 
 55. 00 
 
 l7/i6 
 
 23.96 
 
 25.16 
 
 26.35 
 
 27.55 
 
 28.75 
 
 29.9s 
 
 31.15 
 
 32.34 
 
 57.50 
 
 l^^ 
 
 25.00 
 
 26.25 
 
 27.50 
 
 28.75 
 
 30.00 
 
 31.25 
 
 32.50 
 
 33.75 
 
 60.00 
 
 I9i6 
 
 26.04 
 
 27.34 
 
 28.6s 
 
 29.95 
 
 . 31.25 
 
 32.55 
 
 33.85 
 
 35.16 
 
 62.50 
 
 IH 
 
 27.08 
 
 28.44 
 
 29.79 
 
 31.15 
 
 32.50 
 
 33.85 
 
 35.21 
 
 36.56 
 
 65.00 
 
 liHe 
 
 28.13 
 
 29.53 
 
 30.94 
 
 32.34 
 
 33.75 
 
 35. 16 
 
 36.56 
 
 37.97 
 
 67.50 
 
 iVi 
 
 29.17 
 
 30.63 
 
 32.08 
 
 33.54 
 
 35. 00 
 
 36.46 
 
 37.92 
 
 39.38 
 
 70.00 
 
 Il?i6 
 
 30.21 
 
 31.72 
 
 33.23 
 
 34.74 
 
 36.25 
 
 37.76 
 
 39-27 
 
 40.78 
 
 72.50 
 
 i^i 
 
 31.25 
 
 32.81 
 
 34.38 
 
 35.94 
 
 37.50 
 
 39.06 
 
 40.63 
 
 42.19 
 
 75 -00 
 
 11^6 
 
 32.29 
 
 33.91 
 
 35. 52 
 
 37.14 
 
 38.75 
 
 40.36 
 
 41.98 
 
 43.59 
 
 77 SO 
 
 2 
 
 33.33 
 
 35.00 
 
 36.67 
 
 38.33 
 
 40.00 
 
 41.67 
 
 43.33 
 
 45.00 
 
 80.00 
 
126 . Materials 
 
 Weights of Flat Rolled Iron per Lineal Foot — (Continued) 
 
 Thick- 
 
 7 
 
 7H 
 
 7H 
 
 7M 
 
 8 
 
 8K 
 
 8^ 
 
 8% 
 
 12 
 
 inches 
 
 inches 
 
 inches 
 
 inches 
 
 inches 
 
 inches 
 
 inches 
 
 inches 
 
 inches 
 
 inches 
 
 Me 
 
 1.46 
 
 1. 51 
 
 I.S6 
 
 1. 61 
 
 1.67 
 
 1.72 
 
 1.77 
 
 1.82 
 
 2.S0 
 
 H 
 
 2.92 
 
 3.02 
 
 3.13 
 
 3.23 
 
 3.33 
 
 3.44 
 
 3.54 
 
 3.65 
 
 S.oo 
 
 Me 
 
 4.38 
 
 4.53 
 
 4.69 
 
 4.84 
 
 5.00 
 
 5.16 
 
 5.31 
 
 5.47 
 
 7.50 
 
 H 
 
 5.83 
 
 6.04 
 
 6.25 
 
 6.46 
 
 6.67 
 
 6.88 
 
 7.08 
 
 7.29 
 
 10.00 
 
 Me 
 
 7.29 
 
 7.55 
 
 7.81 
 
 8.07 
 
 8.33 
 
 8.59 
 
 8.85 
 
 9. II 
 
 12.50 
 
 H 
 
 8.75 
 
 9.06 
 
 9.38 
 
 9.69 
 
 10.00 
 
 10.31 
 
 10.63 
 
 10.94 
 
 15.00 
 
 Me 
 
 10.21 
 
 10.57 
 
 10.94 
 
 11.30 
 
 11.67 
 
 12.03 
 
 12.40 
 
 12.76 
 
 17.50 
 
 H 
 
 11.67 
 
 12.08 
 
 12.50 
 
 12.92 
 
 13.33 
 
 13.75 
 
 14.17 
 
 14^58 
 
 20.00 
 
 Me 
 
 13.13 
 
 13.59 
 
 14.06 
 
 14.53 
 
 15.00 
 
 15.47 
 
 15.94 
 
 16.41 
 
 22.50 
 
 H 
 
 14.58 
 
 15.10 
 
 15.63 
 
 16.15 
 
 16.67 
 
 17.19 
 
 17.71 
 
 18.23 
 
 25.00 
 
 iMe 
 
 16.04 
 
 16.61 
 
 17.19 
 
 17.76 
 
 18.33 
 
 18.91 
 
 19.48 
 
 20.05 
 
 27.50 
 
 % 
 
 17-50 
 
 18.13 
 
 18.75 
 
 19.38 
 
 20.00 
 
 20.63 
 
 21.25 
 
 21.88 
 
 30.00 
 
 iMe 
 
 18.96 
 
 19.64 
 
 20.31 
 
 20.99 
 
 21.67 
 
 22.24 
 
 23.02 
 
 23.70 
 
 32.50 
 
 ^i 
 
 20.42 
 
 21.15 
 
 21.88 
 
 22.60 
 
 23.33 
 
 24.06 
 
 24.79 
 
 25.52 
 
 35.00 
 
 iM« 
 
 21.88 
 
 22.66 
 
 23.44 
 
 24.22 
 
 25.00 
 
 25.78 
 
 26.56 
 
 27.34 
 
 37.50 
 
 I 
 
 23.33 
 
 24.17 
 
 25.00 
 
 25.83 
 
 26.67 
 
 27.50 
 
 28.33 
 
 29.17 
 
 40.00 
 
 iMe 
 
 24.79 
 
 25.68 
 
 26.56 
 
 27.45 
 
 28.33 
 
 29.22 
 
 30.10 
 
 30.99 
 
 42.50 
 
 tH 
 
 26.25 
 
 27.19 
 
 28.13 
 
 29.06 
 
 30.00 
 
 30.94 
 
 31.88 
 
 32.81 
 
 45.00 
 
 iMe 
 
 27.71 
 
 28.70 
 
 29.69 
 
 30.68 
 
 31.67 
 
 32.66 
 
 33.65 
 
 34.64 
 
 47.50 
 
 iH 
 
 29.17 
 
 30.21 
 
 31.25 
 
 32.29 
 
 33.33 
 
 34.38 
 
 35.42 
 
 36.46 
 
 SO. 00 
 
 iMe 
 
 30.62 
 
 31.72 
 
 32-81 
 
 33.91 
 
 35-00 
 
 36.09 
 
 37.19 
 
 38.28 
 
 52. so 
 
 m 
 
 32.08 
 
 33.23 
 
 34.38 
 
 35.52 
 
 36.67 
 
 37.81 
 
 38.96 
 
 40.10 
 
 55. 00 
 
 iMe 
 
 33.54 
 
 34-74 
 
 35.94 
 
 37.14 
 
 38.33 
 
 39.53 
 
 40.73 
 
 41.93 
 
 57.50 
 
 I^ 
 
 35.00 
 
 36.25 
 
 37.50 
 
 38.75 
 
 40.00 
 
 41.25 
 
 42.50 
 
 43-75 
 
 60.00 
 
 iMe 
 
 36.46 
 
 37.76 
 
 39-06 
 
 40.36 
 
 41.67 
 
 42.97 
 
 44.27 
 
 45.57 
 
 62. so 
 
 iH 
 
 37.92 
 
 39.27 
 
 40.63 
 
 41.98 
 
 43.33 
 
 44.69 
 
 46.04 
 
 47.40 
 
 65.00 
 
 I»H6 
 
 39.38 
 
 40.78 
 
 42.19 
 
 43.59 
 
 45-00 
 
 46.41 
 
 47-81 
 
 49.22 
 
 67. so 
 
 iM 
 
 40.83 
 
 42.29 
 
 43.75 
 
 45.21 
 
 46.67 
 
 48.13 
 
 49.58 
 
 51.04 
 
 70. CO 
 
 i^Me 
 
 42.29 
 
 43.80 
 
 45.31 
 
 46.82 
 
 48.33 
 
 49.84 
 
 51.35 
 
 52.86 
 
 72. so 
 
 iji 
 
 43.75 
 
 45.31 
 
 46.88 
 
 48.44. 
 
 50.00 
 
 51.56 
 
 53.13 
 
 54.69 
 
 75. 00 
 
 iiMfl 
 
 45.21 
 
 46.82 
 
 48.44 
 
 50.05 
 
 51.67 
 
 53.28 
 
 54.90 
 
 56.51 
 
 77.50 
 
 2 
 
 46.67 
 
 48.33 
 
 50.00 
 
 51.67 
 
 53.33 
 
 55. 00 
 
 56.67 
 
 58.33 
 
 80.00 
 
Weights of Flat Rolled Iron per Lineal Foot 127 
 
 Weights of Flat Rolled Iron per Lineal Foot — {Continued) 
 
 Thick- 
 
 9 
 
 9^/4 
 
 9H 
 
 9% 
 
 10 
 
 loH 
 
 loj'^ 
 
 1034 
 
 12 
 
 ness in 
 inches 
 
 inches 
 
 inches 
 
 inches 
 
 inches 
 
 inches 
 
 inches 
 
 inches 
 
 inches 
 
 inches 
 
 He 
 
 1.88 
 
 1.93 
 
 1.98 
 
 2.03 
 
 2.08 
 
 2.14 
 
 2.19 
 
 2.24 
 
 2. so 
 
 \^ 
 
 3.75 
 
 3.85 
 
 3.96 
 
 4.06 
 
 4.17 
 
 4.27 
 
 4.38 
 
 4.48 
 
 S.oo 
 
 3/6 
 
 5.63 
 
 5.78 
 
 5. 94 
 
 6.09 
 
 6.25 
 
 6.41 
 
 6.56 
 
 6.72 
 
 7.50 
 
 M 
 
 7. SO 
 
 7.71 
 
 7.92 
 
 8.13 
 
 8.33 
 
 8.54 
 
 8.7s 
 
 8.96 
 
 10.00 
 
 Me 
 
 9.38 
 
 9-64 
 
 9.90 
 
 10.16 
 
 10.42 
 
 10.68 
 
 10.94 
 
 11.20 
 
 12.50 
 
 ?i 
 
 11.25 
 
 11.56 
 
 11.88 
 
 12.19 
 
 12.50 
 
 12.81 
 
 13.13 
 
 13.44 
 
 15.00 
 
 ^6 
 
 13.13 
 
 13.49 
 
 13.8s 
 
 14.22 
 
 14.58 
 
 14.95 
 
 15.31 
 
 15.68 
 
 17.50 
 
 \^ 
 
 15.00 
 
 15.42 
 
 15.83 
 
 16.25 
 
 16.67 
 
 17.08 
 
 17.50 
 
 17.92 
 
 20.00 
 
 %6 
 
 16.88 
 
 17.34 
 
 17.81 
 
 18.28 
 
 18.7s 
 
 19.22 
 
 19.69 
 
 20.16 
 
 22.50 
 
 H 
 
 18.75 
 
 19.27 
 
 19.79 
 
 20.31 
 
 20.83 
 
 21.35 
 
 21.88 
 
 22.40 
 
 25.00 
 
 iMe 
 
 20.63 
 
 21.20 
 
 21.77 
 
 22.34 
 
 22.92 
 
 23-49 
 
 24.06 
 
 24.64 
 
 27.50 
 
 % 
 
 22.50 
 
 23.13 
 
 23.75 
 
 24.38 
 
 25.00 
 
 25.62 
 
 26.25 
 
 26.88 
 
 30.00 
 
 13/16 
 
 24.38 
 
 25.05 
 
 25.73 
 
 26.41 
 
 27.08 
 
 27.76 
 
 28.44 
 
 29.11 
 
 32.50 
 
 % 
 
 26.25 
 
 26.98 
 
 27.71 
 
 28.44 
 
 29.17 
 
 29.90 
 
 30.63 
 
 31.3s 
 
 35.00 
 
 1^6 
 
 28.13 
 
 28.91 
 
 29.69 
 
 30.47 
 
 31.2s 
 
 32.03 
 
 32.81 
 
 33.59 
 
 37. SO 
 
 I 
 
 30.00 
 
 30.83 
 
 31.67 
 
 32.50 
 
 33.33 
 
 34.17 
 
 35.00 
 
 35.83 
 
 40.00 
 
 iMe 
 
 31.88 
 
 32.76 
 
 33.65 
 
 34.53 
 
 35.42 
 
 36.30 
 
 37.19 
 
 38.07 
 
 42.50 
 
 1% 
 
 33.75 
 
 34.69 
 
 35.63 
 
 36.56 
 
 37 SO 
 
 38.44 
 
 39-38 
 
 40.31 
 
 45.00 
 
 lYie 
 
 35.63 
 
 36.61 
 
 37.60 
 
 38.59 
 
 39.58 
 
 40.57 
 
 41.56 
 
 42.55 
 
 47.50 
 
 m 
 
 37.50 
 
 38.54 
 
 39-58 
 
 40.63 
 
 41.67 
 
 42.71 
 
 43-75 
 
 44.79 
 
 50.00 
 
 iMe 
 
 39 38 
 
 40.47 
 
 41 56 
 
 42.66. 
 
 43.75 
 
 44.84 
 
 45-94 
 
 47.03 
 
 52.50 
 
 134 
 
 41.25 
 
 42.40 
 
 43.54 
 
 44.69 
 
 45.83 
 
 46.98 
 
 48.13 
 
 49-27 
 
 55. 00 
 
 iMe 
 
 43.13 
 
 44.32 
 
 45.52 
 
 46.72 
 
 47.92 
 
 49.11 
 
 SO. 31 
 
 51-51 
 
 57.50 
 
 1I/2 
 
 45.00 
 
 46.2s 
 
 47-50 
 
 48.7s 
 
 50.00 
 
 51.25 
 
 52.50 
 
 53-75 
 
 60.00 
 
 l9/l6 
 
 46.88 
 
 48.18 
 
 49-48 
 
 so. 78 
 
 52.08 
 
 53.39 
 
 54.69 
 
 55.99 
 
 62.50 
 
 15^ 
 
 48.75 
 
 SO. 10 
 
 SI. 46 
 
 52.81 
 
 54.17 
 
 55.52 
 
 56.88 
 
 58.23 
 
 65.00 
 
 iiMe 
 
 50.63 
 
 52.03 
 
 53-44 
 
 54.84 
 
 56.25 
 
 57.66 
 
 59 -06 
 
 60.47 
 
 67.50 
 
 iH 
 
 52.50 
 
 53.96 
 
 55.42 
 
 56.88 
 
 58.33 
 
 59-79 
 
 61.25 
 
 62.71 
 
 70.00 
 
 mis 
 
 54.38 
 
 55.89 
 
 57.40 
 
 58.91 
 
 60.42 
 
 61.93 
 
 63.44 
 
 64.9s 
 
 72. SO 
 
 1% 
 
 56.25 
 
 57.81 
 
 59-38 
 
 60.94 
 
 62.50 
 
 64.06 
 
 65.63 
 
 67.19 
 
 75. 00 
 
 115/16 
 
 58.13 
 
 59-74 
 
 61.35 
 
 62.97 
 
 64.58 
 
 66.20 
 
 67.81 
 
 69.43 
 
 77.50 
 
 2 
 
 60.00 
 
 61.67 
 
 63.33 
 
 65.00 
 
 66.67 
 
 68.33 
 
 70.00 
 
 71.67 
 
 80.00 
 
128 Materials 
 
 Weights of Flat Rolled Iron per Lineal Foot — {Continued) 
 
 Thick- 
 
 II 
 
 11% 
 
 iiH 
 
 11% 
 
 12 
 
 12H 
 
 I2l/^ 
 
 1234 
 
 ness in 
 inches 
 
 inches 
 
 inches 
 
 inches 
 
 inches 
 
 inches 
 
 inches 
 
 inches 
 
 inches 
 
 He 
 
 2.29 
 
 2.34 
 
 2.40 
 
 2.45 
 
 2.50 
 
 2.55 
 
 2.60 
 
 2.66 
 
 ^i 
 
 4.58 
 
 4.69 
 
 4.79 
 
 4.90 
 
 5.00 
 
 5-10 
 
 5-21 
 
 S-31 
 
 Yit 
 
 6.88 
 
 7.03 
 
 7.19 
 
 7-34 
 
 7.50 
 
 7-66 
 
 7.81 
 
 7.97 
 
 H 
 
 917 
 
 9.38 
 
 9.58 
 
 9-79 
 
 10.00 
 
 10.21 
 
 10.42 
 
 10.63 
 
 Me 
 
 11.46 
 
 11.72 
 
 11.98 
 
 12.24 
 
 12.50 
 
 12.76 
 
 13 02 
 
 13.28 
 
 3/i 
 
 13.75 
 
 14.06 
 
 14.38 
 
 14.69 
 
 15.00 
 
 IS- 31 
 
 15-63 
 
 15.94 
 
 Me 
 
 16.04 
 
 16.41 
 
 16.77 
 
 17-14 
 
 17.50 
 
 17-86 
 
 18.23 
 
 18-59 
 
 Yi 
 
 18.33 
 
 18.75 
 
 19.17 
 
 19-58 
 
 20.00 
 
 20.42 
 
 20.83 
 
 21.25 
 
 »/e 
 
 20.63 
 
 21.09 
 
 21.56 * 
 
 21.94 
 
 22.50 
 
 22.97 
 
 23.44 
 
 23-91 
 
 5i 
 
 22.92 
 
 23.44 
 
 23.96 
 
 24.48 
 
 25.00 
 
 25-52 
 
 26.04 
 
 26.56 
 
 iHe 
 
 25.21 
 
 25.78 
 
 26.35 
 
 26.93 
 
 27.50 
 
 28.07 
 
 28.65 
 
 29.22 
 
 H 
 
 27.50 
 
 28.13 
 
 28.75 
 
 29-38 
 
 30.00 
 
 30-63 
 
 31-25 
 
 31.88 
 
 13/(6 
 
 29.79 
 
 30.47 
 
 31.15 
 
 31-82 
 
 32.50 
 
 33.18 
 
 33.85 
 
 34-53 
 
 ?i 
 
 32.08 
 
 32-81 
 
 33. 54 
 
 34.27 
 
 3500 
 
 35.73 
 
 36-46 
 
 37.19 
 
 15i6 
 
 34.38 
 
 35-16 
 
 35.94 
 
 36.72 
 
 37.50 
 
 38-28 
 
 39-06 
 
 39-84 
 
 I 
 
 36.67 
 
 37.50 
 
 38.33 
 
 39.17 
 
 40.00 
 
 40.83 
 
 41-67 
 
 42.50 
 
 iHe 
 
 38.96 
 
 39.84 
 
 40.73 
 
 41.61 
 
 42.50 
 
 43-39 
 
 44.27 
 
 45.16 
 
 iH 
 
 41.25 
 
 42.19 
 
 43.13 
 
 44-06 
 
 45.00 
 
 45-94 
 
 46.88 
 
 47-81 
 
 I?i6 
 
 43.54 
 
 44.53 
 
 45-52 
 
 46-51 
 
 47-50 
 
 48.49 
 
 49-48 
 
 50.47 
 
 iH 
 
 45.83 
 
 46.88 
 
 47.92 
 
 48.96 
 
 50.00 
 
 51 04 
 
 52-08 
 
 53-13 
 
 iMe 
 
 48.13 
 
 49.22 
 
 50.31 
 
 51-41 
 
 52-50 
 
 53-59 
 
 54-69 
 
 55. 78 
 
 l3/i 
 
 50.42 
 
 51 56 
 
 52.71 
 
 53.85 
 
 55 00 
 
 56.15 
 
 57-29 
 
 58.44 
 
 1^6 
 
 52.71 
 
 53.91 
 
 55.10 
 
 56.30 
 
 57-50 
 
 58.70 
 
 S9-90 
 
 61.09 
 
 iH 
 
 55.00 
 
 56.25 
 
 57 -50 
 
 58.75 
 
 60.00 
 
 61.25 
 
 62.50 
 
 63.7s 
 
 i?ie 
 
 57.29 
 
 58.59 
 
 5990 
 
 61.20 
 
 62.50 
 
 63.80 
 
 65.10 
 
 66.41 
 
 l5i 
 
 59.98 
 
 60.94 
 
 62.29 
 
 63-65 
 
 65.00 
 
 66.35 
 
 67.71 
 
 69.06 
 
 i^Me 
 
 61.88 
 
 63.28 
 
 64-69 
 
 66.09 
 
 67-50 
 
 68.91 
 
 70.31 
 
 71.72 
 
 l3/i 
 
 64.17 
 
 65.63 
 
 67.08 
 
 68.54 
 
 70.00 
 
 71.46 
 
 72.92 
 
 74.38 
 
 Il3/i6 
 
 66.46 
 
 67.97 
 
 69.48 
 
 70.99 
 
 72.50 
 
 74 -01 
 
 75.52 
 
 77.03 
 
 1% 
 
 68.75 
 
 70.31 
 
 71.88 
 
 73-44 
 
 75.00 
 
 76-56 
 
 78.13 
 
 79.69 
 
 i^Me 
 
 71.04 
 
 72.66 
 
 74.27 
 
 75.89 
 
 77.50 
 
 79-11 
 
 80 73 
 
 82.34 
 
 2 
 
 73.33 
 
 75.00 
 
 76.67 
 
 78.33 
 
 80.00 
 
 81.67 
 
 83.33 
 
 85.00 
 
 The weights for 12-inch width are repeated on each page to facilitate making the 
 additions necessary to obtain the weights of plates wider than 12 inches. Thus, to 
 find the weight of I5}4"X%", add the weights to be found in the same line for zM X% 
 and 12x3^=9.48 + 35.00 = 44.48 pounds. 
 
Areas of Flat Rolled Iron 
 
 129 
 
 Areas of Flat Rolled Iron 
 
 For thicknesses from Me inch to 2 inches and widths from i inch to 12% inches. 
 
 Thick- 
 
 I 
 
 m 
 
 iH 
 
 m 
 
 2 
 
 21/4 
 
 21/2 
 
 2% 
 
 12 
 
 ness in 
 inches 
 
 inch 
 
 ■ 
 
 inches 
 
 inches 
 
 inches 
 
 inches 
 
 inches 
 
 inches 
 
 inches 
 
 inches 
 
 He 
 
 .063 
 
 .078 
 
 .094 
 
 .109 
 
 .125 
 
 .141 
 
 .156 
 
 .172 
 
 .750 
 
 H 
 
 .125 
 
 .156 
 
 .188 
 
 .219 
 
 .250 
 
 .281 
 
 .313 
 
 .344 
 
 I. SO 
 
 ri6 
 
 .188 
 
 .234 
 
 .281 
 
 .328 
 
 .375 
 
 .422 
 
 .469 
 
 .516 
 
 2.25 
 
 M 
 
 .250 
 
 .313 
 
 .375 
 
 .438 
 
 .500 
 
 .563 
 
 .625 
 
 .688 
 
 • 3.00 
 
 Me 
 
 .313 
 
 .391 
 
 .469 
 
 .547 
 
 .625 
 
 .703 
 
 .781 
 
 .859 
 
 3.7s 
 
 H 
 
 • 375 
 
 ' .469 
 
 .563 
 
 .656 
 
 .750 
 
 .844 
 
 .938 
 
 1.03 
 
 4.50 
 
 He 
 
 .438 
 
 .547 
 
 .656 
 
 .766 
 
 .875- 
 
 .984 
 
 1.09 
 
 1.20 
 
 5.25 
 
 H 
 
 .500 
 
 .625 
 
 .750 
 
 .875 
 
 1. 00 
 
 1. 13 
 
 1. 25 
 
 1.38 
 
 6.00 
 
 9/i6 
 
 .563 
 
 .703 
 
 .844 
 
 .984 
 
 1. 13 
 
 X.27 
 
 1. 41 
 
 1.55 
 
 6.75 
 
 % 
 
 .625 
 
 .781 
 
 .938 
 
 1.09 
 
 1.25 
 
 1. 41 
 
 1.56 
 
 1.72 
 
 7.50 
 
 ^yie 
 
 .688 
 
 .859 
 
 1.03 
 
 1.20 
 
 1.38 
 
 1.55 
 
 1.72 
 
 1.89 
 
 8.25 
 
 H 
 
 .750 
 
 .938 
 
 1. 13 
 
 1. 31 
 
 1.50 
 
 1.69 
 
 1.88 
 
 2.06 
 
 9.00 
 
 13/ie 
 
 .813 
 
 1.02 
 
 1.22 
 
 1.42 
 
 1.63 
 
 1.83 
 
 2.03 
 
 2.23 
 
 9.75 
 
 li 
 
 .875 
 
 1.09 
 
 1.31 
 
 1.53 
 
 1.75 
 
 1.97 
 
 2.19 
 
 2.41 
 
 10.50 
 
 15/ie 
 
 .938 
 
 1. 17 
 
 1. 41 
 
 1.64 
 
 1.88 
 
 2. II 
 
 2.34 
 
 2.58 
 
 11.25 
 
 I 
 
 1. 00 
 
 1. 25 
 
 1.50 
 
 1.7s 
 
 2.00 
 
 2.25 
 
 2.50 
 
 2.75 
 
 12.00 
 
 iMe 
 
 1.06 
 
 1.33 
 
 1.59 
 
 1.86 
 
 2.13 
 
 2.39 
 
 2.66 
 
 2.92 
 
 12.75 
 
 iH 
 
 1. 13 
 
 1. 41 
 
 1.69 
 
 1.97 
 
 2.25 
 
 2.53 
 
 2.81 
 
 3.09 
 
 13.50 
 
 iHe 
 
 1. 19 
 
 1.48 
 
 1.78 
 
 2.08 
 
 2.38 
 
 2.67 
 
 2.97 
 
 3.27 
 
 14.25 
 
 m 
 
 1.25 
 
 i.S6 
 
 1.88 
 
 2.19- 
 
 2.50 
 
 2.81 
 
 3.13 
 
 3.44 
 
 15 00 
 
 iHe 
 
 1. 31 
 
 1.64 
 
 1.97 
 
 2.30 
 
 2.63 
 
 2.95 
 
 3.28 
 
 3.61 
 
 15.75 
 
 l3/i 
 
 1.38 
 
 1.72 
 
 2.06 
 
 2.41 
 
 2.75 
 
 3.09 
 
 3.44 
 
 3.78 
 
 16.50 
 
 iHe 
 
 1.44 
 
 1.80 
 
 2.16 
 
 2.52 
 
 2.88 
 
 3.23 
 
 3.59 
 
 3.95 
 
 17.25 
 
 iV^ 
 
 I. SO 
 
 1.88 
 
 2.25 
 
 2.63 
 
 3.00 
 
 3.38 
 
 3.75 
 
 4.13 
 
 18.00 
 
 I?i6 
 
 i.S6 
 
 1. 95 
 
 2.34 
 
 2.73 
 
 3.13 
 
 3.52 
 
 3.91 
 
 4.30 
 
 18.75 
 
 iH 
 
 1.63 
 
 2.03 
 
 2.44 
 
 2.84 
 
 3.25 
 
 3.66 
 
 4.06 
 
 4-47 
 
 19 50 
 
 iiHe 
 
 1.69 
 
 2. II 
 
 2.53 
 
 2.9s 
 
 3.38 
 
 3.80 
 
 4.22 
 
 4.64 
 
 20.25 
 
 13/4 
 
 1.75 
 
 2.19 
 
 2.63 
 
 3.06 
 
 3.50 
 
 3.94 
 
 4.38 
 
 4.81 
 
 21.00 
 
 iiHe 
 
 1. 81 
 
 2.27 
 
 2.72 
 
 3.17 
 
 3.63 
 
 4.08 
 
 4.53 
 
 4.98 
 
 21.75 
 
 m 
 
 1.88 
 
 2.34 
 
 2.81 
 
 3.28 
 
 3.75 
 
 4.22 
 
 4.69 
 
 5. 16 
 
 22.50 
 
 iiMe 
 
 1.94 
 
 2.42 
 
 2.91 
 
 3.39 
 
 3.88 
 
 4.36 
 
 4.84 
 
 S.33 
 
 23.25 
 
 2 
 
 2.00 
 
 2.50 
 
 3.00 
 
 3. SO 
 
 4.00 
 
 4.50 
 
 5.00 
 
 S.50 
 
 24.00 
 
I30 
 
 Materials 
 
 Weights of Flat Rolled Steel per Lineal Foot 
 
 For thicknesses from Vie inch to 2 inches and widths from i inch to 12% inches. 
 
 Thick- 
 ness in 
 inches 
 
 I 
 
 iH 
 
 1I/2 
 
 lU 
 
 2 
 
 2H 
 
 2H 
 
 2?4 
 
 12 
 
 inch 
 
 inches 
 
 inches 
 
 inches 
 
 inches 
 
 inches 
 
 inches 
 
 inches 
 
 inches 
 
 Me 
 
 .638 
 
 .797 
 
 . .957 
 
 I. II 
 
 1.28 
 
 1.44 
 
 1.59 
 
 1.75 
 
 7.65 
 
 H 
 
 .850 
 
 1.06 
 
 1.28 
 
 1.49 
 
 1.70 
 
 1. 91 
 
 2.12 
 
 2.34 
 
 10.20 
 
 Me 
 
 1.06 
 
 1.33 
 
 1-59 
 
 1.86 
 
 2.12 
 
 2.39 
 
 2.65 
 
 2.92 
 
 12.7s 
 
 % 
 
 1.28 
 
 1.59 
 
 1.92 
 
 2.23 
 
 2.55 
 
 2.87 
 
 3.19 
 
 3.51 
 
 15.30 
 
 Me 
 
 1.49 
 
 1.86 
 
 2.23 
 
 2.60 
 
 2.98 
 
 3.35 
 
 3.72 
 
 4.09 
 
 17.85 
 
 H 
 
 1.70 
 
 2.12 
 
 2.55 
 
 2.98 
 
 3.40 
 
 3.83 
 
 4.25 
 
 4.67 
 
 20.40 
 
 Me 
 
 1.92 
 
 2.39 
 
 2.87 
 
 3.35 
 
 3.83 
 
 4-30 
 
 4.78 
 
 5.26 
 
 22.95 
 
 % 
 
 2.12 
 
 2.65 
 
 3.19 
 
 3.72 
 
 4.25 
 
 4.78 
 
 5.31 
 
 5.84 
 
 25 50 
 
 iMe 
 
 2.34 
 
 2.92 
 
 3.51 
 
 4.09 
 
 4.67 
 
 5.26 
 
 5.84 
 
 6.43 
 
 28.0s 
 
 M 
 
 2.55 
 
 3.19 
 
 3.83 
 
 4-47 
 
 5.10 
 
 5.75 
 
 6.38 
 
 7.02 
 
 30.60 
 
 13/(6 
 
 2.76 
 
 3-45 
 
 4.14 
 
 4.84 
 
 5.53 
 
 6.21 
 
 6.90 
 
 7.60 
 
 33. IS 
 
 li 
 
 2.98 
 
 3-72 
 
 4-47 
 
 5.20 
 
 5.95 
 
 6.69 
 
 7.44 
 
 8.18 
 
 35.70 
 
 iMe 
 
 3.19 
 
 3.99 
 
 4.78 
 
 5. 58 
 
 6.38 
 
 7.18 
 
 7.97 
 
 8.77 
 
 38.25 
 
 I 
 
 3-40 
 
 4-25 
 
 5.10 
 
 5.95 
 
 6.80 
 
 7.65 
 
 8.50 
 
 9-35 
 
 40.80 
 
 iMe 
 
 3.61 
 
 4-52 
 
 5-42 
 
 6.32 
 
 7.22 
 
 8.13 
 
 903 
 
 9-93 
 
 43-35 
 
 i^ 
 
 3.83 
 
 4.78 
 
 5-74 
 
 6.70 
 
 7.65 
 
 8.61 
 
 9-57 
 
 10.52 
 
 45-90 
 
 iMe 
 
 4.04 
 
 5.0s 
 
 6.06 
 
 7.07 
 
 8.08 
 
 9.09 
 
 10.10 
 
 II. II 
 
 48.45 
 
 iH 
 
 4-25 
 
 5.31 
 
 6.38 
 
 7-44 
 
 8.50 
 
 9-57 
 
 10.63 
 
 11.69 
 
 51 00 
 
 iMe 
 
 4.46 
 
 5.58 
 
 6.69 
 
 7.81 
 
 8.93 
 
 10.04 
 
 II. 16 
 
 12.27 
 
 53.55 
 
 l3/i 
 
 4.67 
 
 5.84 
 
 7.02 
 
 8.18 
 
 9.35 
 
 10.52 
 
 11.69 
 
 12.85 
 
 56.10 
 
 iMe 
 
 4.89 
 
 6.11 
 
 7-34 
 
 8.56 
 
 9-78 
 
 11.00 
 
 12.22 
 
 13.44 
 
 58.65 
 
 iH 
 
 5.10 
 
 6.38 
 
 7.65 
 
 8.93 
 
 10.20 
 
 11.48 
 
 12.75 
 
 14.03 
 
 61.20 
 
 iMe 
 
 5.32 
 
 6.64 
 
 7.97 
 
 930 
 
 10.63 
 
 11.95 
 
 13.28 
 
 14.61 
 
 63.7s 
 
 i5i 
 
 5-52 
 
 6.90 
 
 8.29 
 
 9.67 
 
 11.05 
 
 12.43 
 
 13.81 
 
 15.19 
 
 66.30 
 
 iii/ie 
 
 5.74 
 
 7.17 
 
 8.61 
 
 10.04 
 
 11.47 
 
 12.91 
 
 14.34 
 
 15.78 
 
 68.8S 
 
 1% 
 
 5.9s 
 
 7.44 
 
 8.93 
 
 10.42 
 
 11.90 
 
 13.40 
 
 14.88 
 
 16.37 
 
 71.40 
 
 Il3/i6 
 
 6.16 
 
 7.70 
 
 9-24 
 
 10.79 
 
 12.33 
 
 13.86 
 
 15.40 
 
 16.95 
 
 73. 95 
 
 i^i 
 
 6.38 
 
 7.97 
 
 9-57 
 
 II. 15 
 
 12.75 
 
 14.34 
 
 15.94 
 
 17.53 
 
 76.50 
 
 iiMe 
 
 6.59 
 
 8.24 
 
 9.88 
 
 11.53 
 
 13.18 
 
 14.83 
 
 16.47 
 
 18.12 
 
 79 05 
 
 2 
 
 6.80 
 
 8.50 
 
 10.20 
 
 11.90 
 
 13.60 
 
 15.30 
 
 17.00 
 
 18.70 
 
 81.60 
 
Weights of Flat Rolled Steel per Lineal Foot 131 
 
 Weights of Flat Rolled Steel per Lineal Foot — (Continued) 
 
 Thick- 
 
 3 
 
 3H 
 
 3H 
 
 3M 
 
 4 
 
 4H 
 
 4^2 
 
 43/4 
 
 12 
 
 ness in 
 inches 
 
 inches 
 
 inches 
 
 inches 
 
 inches 
 
 inches 
 
 inches 
 
 inches 
 
 inches 
 
 inches 
 
 M« 
 
 1. 91 
 
 2.07 
 
 2.23 
 
 2-39 
 
 2.55 
 
 2.71 
 
 2.87 
 
 3.03 
 
 7-65 
 
 V* 
 
 2.55 
 
 2.76 
 
 2.98 
 
 3-19 
 
 3-40 
 
 3-61 
 
 3-83 
 
 4.04 
 
 10.20 
 
 Me 
 
 3.19 
 
 3.45 
 
 3-72 
 
 3-99 
 
 4-25 
 
 4-52 
 
 4-78 
 
 5.05 
 
 12.75 
 
 H 
 
 3.83 
 
 4.15 
 
 4-47 
 
 4.78 
 
 5-10 
 
 5-42 
 
 5-74 
 
 6.06 
 
 15-30 
 
 Mo 
 
 4.46 
 
 4.83 
 
 5. 20 
 
 5-58 
 
 5-95 
 
 6.32 
 
 6.70 
 
 7-07 
 
 17.85 
 
 H 
 
 5.10 
 
 5.53 
 
 5-95 
 
 6.38 
 
 6.80 
 
 7.22 
 
 7-65 
 
 8.08 
 
 20.40 
 
 Mo 
 
 5. 74 
 
 6.22 
 
 6.70 
 
 7-17 
 
 7-65 
 
 8.13 
 
 8.61 
 
 9-09 
 
 22.95 
 
 H 
 
 6.38 
 
 6.91 
 
 7-44 
 
 7-97 
 
 8.50 
 
 9-03 
 
 9-57 
 
 10.10 
 
 25.50 
 
 iMo 
 
 7.02 
 
 7.60 
 
 8.18 
 
 8.76 
 
 9-35 
 
 9-93 
 
 10.52 
 
 II. II 
 
 28.05 
 
 H 
 
 7.6s 
 
 8.29 
 
 8.93 
 
 9-57 
 
 10.20 
 
 10.84 
 
 11.48 
 
 12.12 
 
 30.60 
 
 13/6 
 
 8.29 
 
 8.98 
 
 9.67 
 
 10.36 
 
 11.05 
 
 11.74 
 
 12.43 
 
 13-12 
 
 33. IS 
 
 ^ 
 
 8.93 
 
 967 
 
 10.41 
 
 II. 16 
 
 11.90 
 
 12.65 
 
 13-39 
 
 14-13 
 
 35-70 
 
 iMe 
 
 957 
 
 10.36 
 
 II. 16 
 
 XI. 95 
 
 12.75 
 
 13-55 
 
 14.34 
 
 15-14 
 
 38-25 
 
 I 
 
 10.20 
 
 11.05 
 
 11.90 
 
 12.75 
 
 13-60 
 
 14-45 
 
 15-30 
 
 16.15 
 
 40.80 
 
 1H6 
 
 10.84 
 
 11.74 
 
 12.65 
 
 13-55 
 
 14-45 
 
 15 -35 
 
 16.26 
 
 17.16 
 
 43-35 
 
 IH 
 
 11.48 
 
 12.43 
 
 13.39 
 
 14-34 
 
 15-30 
 
 16.26 
 
 17.22 
 
 18.17 
 
 45 -90 
 
 IM6 
 
 12.12 
 
 13.12 
 
 14-13 
 
 15 -i4 
 
 16.15 
 
 17.16 
 
 18.17 
 
 19.18 
 
 48.45 
 
 I^ 
 
 12.75 
 
 13-81 
 
 14-87 
 
 15-94 
 
 17.00 
 
 18.06 
 
 19-13 
 
 20.19 
 
 51.00 
 
 iMe 
 
 13.39 
 
 14.50 
 
 15-62 
 
 16.74 
 
 17-85 
 
 18.96 
 
 20.08 
 
 21.20 
 
 53-55 
 
 l3/i 
 
 1403 
 
 15.20 
 
 16.36 
 
 17 -"53 
 
 18.70 
 
 19-87 
 
 21.04 
 
 22.21 
 
 56.10 
 
 iMe 
 
 1466 
 
 15-88 
 
 17.10 
 
 18.33 
 
 19-55 
 
 20.77 
 
 21-99 
 
 23.22 
 
 S8-6S 
 
 iH 
 
 15.30 
 
 16. S8 
 
 17-85 
 
 19.13 
 
 20-40 
 
 21.68 
 
 22.9s 
 
 24.23 
 
 61.20 
 
 1^6 
 
 15-94 
 
 17-27 
 
 18.60 
 
 19-92 
 
 21.25 
 
 22.58 
 
 23-91 
 
 25.24 
 
 63.75 
 
 1% 
 
 16.58 
 
 17-96 
 
 19-34 
 
 20.72 
 
 22.10 
 
 23.48 
 
 24.87 
 
 26.25 
 
 66.30 
 
 iiHe 
 
 17.22 
 
 18.65 
 
 20.08 
 
 21.51 
 
 22.95 
 
 24-38 
 
 25.82 
 
 27.26 
 
 68.85 
 
 1% 
 
 17.85 
 
 19-34 
 
 20.83 
 
 22.32 
 
 23.80 
 
 25-29 
 
 26.78 
 
 28.27 
 
 71.40 
 
 iiMe 
 
 18.49 
 
 20.03 
 
 21.57 
 
 23.11 
 
 24.6s 
 
 26.19 
 
 27.73 
 
 29.27 
 
 73-95 
 
 1% 
 
 19- 13 
 
 20.72 
 
 22.31 
 
 23.91 
 
 25.50 
 
 27.10 
 
 28.69 
 
 30.28 
 
 76 -SO 
 
 iiS/ie 
 
 19.77 
 
 21.41 
 
 23.06 
 
 24-70 
 
 26.3s 
 
 28.00 
 
 29.64 
 
 31-29 
 
 7905 
 
 2 
 
 20.40 
 
 22.10 
 
 23-80 
 
 25 -SO 
 
 27.20 
 
 28.90 
 
 30.60 
 
 32-30 
 
 81.60 
 
132 Materials 
 
 Weights of Flat Rolled Steel per Lineal Foot -^ {Continued) 
 
 Thick- 
 
 5 
 
 5H 
 
 s'A 
 
 .5% 
 
 6 
 
 6H 
 
 6H 
 
 63/4 
 
 12 
 
 ness in 
 inches 
 
 inches 
 
 inches 
 
 inches 
 
 inches 
 
 inches 
 
 inches 
 
 inches 
 
 inches 
 
 inches 
 
 3/i6 
 
 3.19 
 
 3.35 
 
 3-51 
 
 3.67 
 
 3.83 
 
 3.99 
 
 4.14 
 
 4-30 
 
 7.6s 
 
 H 
 
 4.25 
 
 4-46 
 
 4-67 
 
 4-89 
 
 5- 10 
 
 5-31 
 
 5.53 
 
 5-74 
 
 10.20 
 
 Me 
 
 5.31 
 
 5-58 
 
 5.84 
 
 6. II 
 
 6.38 
 
 6.64 
 
 6.90 
 
 7-17 
 
 12.75 
 
 H 
 
 6.38 
 
 6.69 
 
 7.02 
 
 7-34 
 
 7.65 
 
 7-97 
 
 8.29 
 
 8.61 
 
 15.30 
 
 Me 
 
 7.44 
 
 7.81 
 
 8.18 
 
 8.56 
 
 8.93 
 
 9-29 
 
 9-67 
 
 10.04 
 
 17.85 
 
 H 
 
 8.S0 
 
 8.93 
 
 9-35 
 
 9-77 
 
 10.20 
 
 10.63 
 
 11-05 
 
 11.48 
 
 20.40 
 
 ri6 
 
 9.57 
 
 10.04 
 
 10.52 
 
 11.00 
 
 11.48 
 
 11-95 
 
 12-43 
 
 12.91 
 
 22.95 
 
 % 
 
 10.63 
 
 II. 16 
 
 11.69 
 
 12.22 
 
 12.75 
 
 13-28 
 
 13-81 
 
 14-34 
 
 25.50 
 
 iHe 
 
 11.69 
 
 12.27 
 
 12.85 
 
 13-44 
 
 14 -03 
 
 14-61 
 
 15 20 
 
 15-78 
 
 28.05 
 
 % 
 
 12.75 
 
 13-39 
 
 14.03 
 
 14.67 
 
 15.30 
 
 15-94 
 
 16.58 
 
 17.22 
 
 30.60 
 
 iMe 
 
 13-81 
 
 14.50 
 
 15.19 
 
 15-88 
 
 16.58 
 
 17.27 
 
 17.95 
 
 18.65 
 
 33. IS 
 
 % 
 
 14.87 
 
 15-62 
 
 16.36 
 
 17.10 
 
 17.85 
 
 18.60 
 
 19-34 
 
 20.08 
 
 35.70 
 
 1^6 
 
 15.94 
 
 16.74 
 
 17-53 
 
 18.33 
 
 19 -13 
 
 19.92 
 
 20.72 
 
 21.51 
 
 38.2s 
 
 I 
 
 17.00 
 
 17-85 
 
 18.70 
 
 19-55 
 
 20.40 
 
 21.25 
 
 22.10 
 
 22.95 
 
 40.80 
 
 iMa 
 
 18.06 
 
 18.96 
 
 19-87 
 
 20.77 
 
 21.68 
 
 22.58 
 
 23-48 
 
 24.39 
 
 43.35 
 
 iH 
 
 19-13 
 
 20.08 
 
 21.04 
 
 21.99 
 
 22.95 
 
 23.91 
 
 24-87 
 
 25.82 
 
 45.90 
 
 iMe 
 
 20.19 
 
 21.20 
 
 22.21 
 
 23-22 
 
 24-23 
 
 25.23 
 
 26.24 
 
 27 25 
 
 48.45 
 
 iH 
 
 21.25 
 
 22.32 
 
 23-38 
 
 24.44 
 
 25-50 
 
 26.56 
 
 27.62 
 
 28.69 
 
 51.00 
 
 iMe 
 
 22.32 
 
 23-43 
 
 24-54 
 
 25.66 
 
 26.78 
 
 27.90 
 
 29.01 
 
 30.12 
 
 53.55 
 
 iH 
 
 23.38 
 
 24-54 
 
 25.71 
 
 26.88 
 
 28.05 
 
 29.22 
 
 30.39 
 
 31.56 
 
 56.10 
 
 I7l6 
 
 24.44 
 
 25-66 
 
 26.88 
 
 28.10 
 
 29.33 
 
 30.55 
 
 31.77 
 
 32.99 
 
 58.65 
 
 ii/^ 
 
 25.50 
 
 26.78 
 
 28.05 
 
 29-33 
 
 30.60 
 
 31.88 
 
 33.15 
 
 34.43 
 
 61.20 
 
 I9i6 
 
 26.57 
 
 27-89 
 
 29.22 
 
 30-55 
 
 31.88 
 
 33.20 
 
 34.53 
 
 35.86 
 
 63.75 
 
 l5/i 
 
 27.63 
 
 29.01 
 
 30-39 
 
 31-77 
 
 33.15 
 
 34.53 
 
 35.91 
 
 37.29 
 
 66.30 
 
 iiMe 
 
 28.69 
 
 30.12 
 
 31.55 
 
 32.99 
 
 34.43 
 
 35.86 
 
 37.30 
 
 38.73 
 
 68.85 
 
 l3/i 
 
 29.75 
 
 31-24 
 
 32.73 
 
 34.22 
 
 35.70 
 
 37.19 
 
 38.68 
 
 40.17 
 
 71.40 
 
 113/16 
 
 30.81 
 
 32.35 
 
 33.89 
 
 35.43 
 
 36.98 
 
 38.52 
 
 40.05 
 
 41.60 
 
 73.95 
 
 1% 
 
 31.87 
 
 33-47 
 
 35.06 
 
 36.65 
 
 38.25 
 
 39.85 
 
 41-44 
 
 43.03 
 
 76.50 
 
 iiMe 
 
 32.94 
 
 34-59 
 
 36.23 
 
 37.88 
 
 39.53 
 
 41.17 
 
 42.82 
 
 44.46 
 
 79.0s 
 
 2 
 
 34.00 
 
 35-70 
 
 37.40 
 
 39-10 
 
 40.80 
 
 42.50 
 
 44-20 
 
 45.90 
 
 81.60 
 
Weights of Flat Rolled Steel per Lineal Foot 133 
 
 Weights of Flat Rolled Steel per Lineal Foot — {Continmd) 
 
 Thick- 
 ness in 
 inches 
 
 7 
 
 7H 
 
 7!/^ 
 
 73/ 
 
 8 
 
 8H 
 
 81^ 
 
 8% 
 
 12 
 
 inches 
 
 inches 
 
 inches 
 
 inches 
 
 inches 
 
 inches 
 
 inches 
 
 inches 
 
 inches 
 
 3/i6 
 
 4.46 
 
 4.62 
 
 4.78 
 
 4.94 
 
 5.10 
 
 5.26 
 
 5. 42 
 
 5. 58 
 
 7.6s 
 
 K4 
 
 5. 95 
 
 6.16 
 
 6.36 
 
 6.58 
 
 6.80 
 
 7.01 
 
 7.22 
 
 7-43 
 
 10.20 
 
 Me 
 
 7.44 
 
 7.70 
 
 7.97 
 
 8.23 
 
 8.50 
 
 8.76 
 
 9.03 
 
 9.29 
 
 12.75 
 
 % 
 
 8.93 
 
 9.25 
 
 9.57 
 
 9.88 
 
 10.20 
 
 10.52 
 
 10.84 
 
 II. 16 
 
 15.30 
 
 Vie 
 
 10.41 
 
 10.78 
 
 II. 16 
 
 11.53 
 
 11.90 
 
 12.27 
 
 12.64 
 
 13.02 
 
 17.8S 
 
 H 
 
 11.90 
 
 12.32 
 
 12 75 
 
 13.18 
 
 13.60 
 
 14.03 
 
 14.44 
 
 14.87 
 
 20.40 
 
 Vie 
 
 13.39 
 
 13.86 
 
 14.34 
 
 14.82 
 
 15.30 
 
 15.78 
 
 16.27 
 
 16.74 
 
 22.95 
 
 % 
 
 14.87 
 
 15.40 
 
 15.94 
 
 16.47 
 
 17.00 
 
 17.53 
 
 18.06 
 
 18.59 
 
 25.50 
 
 iMe 
 
 16.36 
 
 16.94 
 
 17.53 
 
 18.12 
 
 18.70 
 
 19.28 
 
 19.86 
 
 20.45 
 
 28.05 
 
 M 
 
 17.85 
 
 18.49 
 
 19.13 
 
 19.77 
 
 20.40 
 
 21.04 
 
 21.68 
 
 22.32 
 
 30.60 
 
 13/16 
 
 19.34 
 
 20.03 
 
 20.72 
 
 21.41 
 
 22.10 
 
 22.79 
 
 23.48 
 
 24.17 
 
 33. IS 
 
 % 
 
 20.83 
 
 21.57 
 
 22.32 
 
 23.05 
 
 23.80 
 
 24-55 
 
 25.30 
 
 26.04 
 
 35.70 
 
 1^6 
 
 22.32 
 
 23.11 
 
 23.91 
 
 24.70 
 
 25.50 
 
 26.30 
 
 27.10 
 
 27.89 
 
 38.25 
 
 I 
 
 23.80 
 
 24.6s 
 
 25.50 
 
 26.35 
 
 27.20 
 
 28.05 
 
 28.90 
 
 29.75 
 
 40.80 
 
 iHe 
 
 25.29 
 
 26.19 
 
 27.10 
 
 28.00 
 
 28.90 
 
 29.80 
 
 30.70 
 
 31.61 
 
 43-35 
 
 iH 
 
 26.78 
 
 27.73 
 
 28.68 
 
 29.64 
 
 30.60 
 
 31.56 
 
 32.52 
 
 33-47 
 
 45-90 
 
 I3/16 
 
 28.26 
 
 29.27 
 
 30.28 
 
 31.29 
 
 32.30 
 
 33.31 
 
 34.32 
 
 35-33 
 
 48.4s 
 
 i>i 
 
 29.75 
 
 30.81 
 
 31.88 
 
 32.94 
 
 34.00 
 
 35.06 
 
 36.12 
 
 37.20 
 
 SI .00 
 
 I5/16 
 
 31.23 
 
 32.35 
 
 33.48 
 
 34-59 
 
 35.70 
 
 36.81 
 
 37.93 
 
 39 -05 
 
 53.55 
 
 l3/i 
 
 32.72 
 
 33.89 
 
 35.06 
 
 36.23" 
 
 37.40 
 
 38.57 
 
 39-74 
 
 40.91 
 
 56.10 
 
 I7/16 
 
 34.21 
 
 35.44 
 
 36.66 
 
 37.88 
 
 39- 10 
 
 40.32 
 
 41.54 
 
 42.77 
 
 58.6s 
 
 IH 
 
 35.70 
 
 36.98 
 
 38.26 
 
 39.53 
 
 40.80 
 
 42.08 
 
 43-35 
 
 44.63 
 
 61.20 
 
 I?l6 
 
 37.19 
 
 38.51 
 
 39.84 
 
 41.17 
 
 42.50 
 
 43.83 
 
 45-16 
 
 46.49 
 
 63.7s 
 
 i-H 
 
 38.67 
 
 40.05 
 
 41.44 
 
 42.82 
 
 44.20 
 
 45.58 
 
 46.96 
 
 48.34 
 
 66.30 
 
 iiMe 
 
 40.16 
 
 41.59 
 
 43.03 
 
 44.47 
 
 45.90 
 
 47.33 
 
 48.76 
 
 50.20 
 
 68.85 
 
 l3/4 
 
 41-65 
 
 43.14 
 
 44.63 
 
 46.12 
 
 47.60 
 
 49.09 
 
 50.58 
 
 52.07 
 
 71.40 
 
 113/6 
 
 43.14 
 
 44.68 
 
 46.22 
 
 47.76 
 
 49.30 
 
 SO. 84 
 
 52.38 
 
 53.92 
 
 73.95 
 
 1% 
 
 44.63 
 
 46.22 
 
 47.82 
 
 49.40 
 
 5100 
 
 52.60 
 
 54. 20 
 
 55.79 
 
 76.50 
 
 115/6 
 
 46.12 
 
 47.76 
 
 49.41 
 
 51 -OS 
 
 52.70 
 
 54.35 
 
 56.00 
 
 57.64 
 
 79.05 
 
 2 
 
 4760 
 
 49.30 
 
 51 00 
 
 52.70 
 
 54.40 
 
 56.10 
 
 57.80 
 
 59.50 
 
 81.60 
 
134 Materials 
 
 Weights or Flat Rolled Steel per Lineal Foot — (Continued) 
 
 Thick- 
 ness in 
 inches 
 
 9 
 
 9M 
 
 9H 
 
 9% 
 
 10 
 
 loH 
 
 loi/^ 
 
 I03/4 
 
 12 
 
 inches 
 
 inches 
 
 inches 
 
 inches 
 
 inches 
 
 inches 
 
 inches 
 
 inches 
 
 inches 
 
 Me 
 
 5.74 
 
 5.90 
 
 6.06 
 
 6.22 
 
 6.38 
 
 6.54 
 
 6.70 
 
 6.86 
 
 7.6s 
 
 H 
 
 7.65 
 
 7.86 
 
 8.08 
 
 8.29 
 
 8.50 
 
 8.71 
 
 8.92 
 
 9.14 
 
 10.20 
 
 Me 
 
 9.56 
 
 9.83 
 
 10.10 
 
 10.36 
 
 10.62 
 
 10.89 
 
 II. 16 
 
 11.42 
 
 12.75 
 
 % 
 
 11.48 
 
 11.80 
 
 12.12 
 
 12.44 
 
 12.75 
 
 13.07 
 
 13.39 
 
 13. 71 
 
 1S.30 
 
 Vl6 
 
 13.40 
 
 13.76 
 
 14.14 
 
 14.51 
 
 14.88 
 
 15.25 
 
 15.62 
 
 15.99 
 
 17.8S 
 
 H 
 
 15.30 
 
 15.73 
 
 16.16 
 
 16.58 
 
 17.00 
 
 17.42 
 
 17.85 
 
 18.28 
 
 20.40 
 
 Me 
 
 17.22 
 
 17.69 
 
 18.18 
 
 18.65 
 
 19.14 
 
 19.61 
 
 20.08 
 
 20.56 
 
 22.95 
 
 % 
 
 19.13 
 
 19.65 
 
 20.19 
 
 20.72 
 
 21.25 
 
 21.78 
 
 22.32 
 
 22.85 
 
 25.50 
 
 iMe 
 
 21.04 
 
 21.62 
 
 22.21 
 
 22.79 
 
 23.38 
 
 23.96 
 
 24.54 
 
 25.13 
 
 28.0s 
 
 H 
 
 22.96 
 
 23.59 
 
 24.23 
 
 24.86 
 
 ■ 
 
 25.50 
 
 26.14 
 
 26.78 
 
 27.42 
 
 30.60 
 
 iMe 
 
 24.86 
 
 25.55 
 
 26.24 
 
 26.94 
 
 27.62 
 
 28.32 
 
 29.00 
 
 29.69 
 
 33.15 
 
 Ti 
 
 26.78 
 
 27.52 
 
 28.26 
 
 29.01 
 
 29.75 
 
 30.50 
 
 31.24 
 
 31.98 
 
 35.70 
 
 15/16 
 
 28.69 
 
 29.49 
 
 30.28 
 
 31.08 
 
 31.88 
 
 32.67 
 
 33.48 
 
 34.28 
 
 38.2s 
 
 I 
 
 30.60 
 
 31.4s 
 
 32.30 
 
 33.15 
 
 34.00 
 
 34.85 
 
 35.70 
 
 36.55 
 
 40.80 
 
 iMe 
 
 32.52 
 
 33.41 
 
 34.32 
 
 35.22 
 
 36.12 
 
 37.03 
 
 37.92 
 
 38.83 
 
 4335 
 
 iH 
 
 34.43 
 
 35.38 
 
 36.34 
 
 37.29 
 
 38.25 
 
 39.21 
 
 40.17 
 
 41.12 
 
 45.90 
 
 iMe 
 
 36.34 
 
 37.35 
 
 38.36 
 
 39.37 
 
 40.38 
 
 41.39 
 
 42.40 
 
 43.40 
 
 48.4s 
 
 iH 
 
 38.26 
 
 39.31 
 
 40.37 
 
 41.44 
 
 42.50 
 
 43.56 
 
 44.63 
 
 45.69 
 
 SI. 00 
 
 iMe 
 
 40.16 
 
 41.28 
 
 42.40 
 
 43.52 
 
 44.64 
 
 45.75 
 
 46.86 
 
 47.97 
 
 53.55 
 
 iH 
 
 42.08 
 
 43.25 
 
 44.41 
 
 45.58 
 
 46.75 
 
 47.92 
 
 4908 
 
 50.25 
 
 56.10 
 
 iMe 
 
 44.00 
 
 45.22 
 
 46.44 
 
 47.66 
 
 48.88 
 
 50.10 
 
 51.32 
 
 52.54 
 
 S8.6S 
 
 iH 
 
 45.90 
 
 47.18 
 
 48.45 
 
 49-73 
 
 51.00 
 
 52.28 
 
 53.55 
 
 54.83 
 
 61.20 
 
 iMe 
 
 47.82 
 
 49.14 
 
 50.48 
 
 51.80 
 
 53.14 
 
 54.46 
 
 55.78 
 
 57.11 
 
 63.7s 
 
 iH 
 
 49.73 
 
 51.10 
 
 52.49 
 
 53.87 
 
 55.25 
 
 56.63 
 
 58.02 
 
 59.40 
 
 66.30 
 
 iiMe 
 
 51.64 
 
 53.07 
 
 54. SI 
 
 SS. 94 
 
 57.38 
 
 58.81 
 
 60.24 
 
 61.68 
 
 68.85 
 
 IM 
 
 53.56 
 
 55.04 
 
 56.53 
 
 58.01 
 
 59.50 
 
 60.99 
 
 62.48 
 
 63.97 
 
 71.40 
 
 Il3/i6 
 
 55.46 
 
 57.00 
 
 58.54 
 
 60.09 
 
 61.62 
 
 63.17 
 
 64.70 
 
 66.24 
 
 73.9s 
 
 I7/^ 
 
 57.38 
 
 58.97 
 
 60.56 
 
 62.16 
 
 63.75 
 
 65.35 
 
 66.94 
 
 68.53 
 
 76.50 
 
 liMe 
 
 59.29 
 
 60.94 
 
 62.58 
 
 64.23 
 
 65.88 
 
 67.52 
 
 69.18 
 
 70.83 
 
 79.0s 
 
 2 
 
 61.20 
 
 62.90 
 
 64.60 
 
 66.30 
 
 68.00 
 
 69.70 
 
 71.40 
 
 73.10 
 
 81.60 
 
Weights of Flat Rolled Steel per Lineal Foot 135 
 
 Weights of Flat Rolled Steel pee Lineal Foot — (Continued) 
 
 Thick- 
 
 II 
 
 iiH 
 
 iii/^ 
 
 II3/4 
 
 12 
 
 121/4 
 
 I2l/^ 
 
 12?^ 
 
 ness in 
 inches 
 
 inches 
 
 inches 
 
 inches 
 
 inches 
 
 inches 
 
 inches 
 
 inches 
 
 inches 
 
 Me 
 
 7.02 
 
 7.17 
 
 7.32 
 
 7.49 
 
 7.65 
 
 7-82 
 
 7.98 
 
 8.13 
 
 H 
 
 9-34 
 
 9. 57 
 
 9.78 
 
 10.00 
 
 10.20 
 
 10.42 
 
 10.63 
 
 10.84 
 
 V16 
 
 11.68 
 
 11.95 
 
 12.22 
 
 12.49 
 
 12.75 
 
 1301 
 
 13.28 
 
 13.5s 
 
 % 
 
 14 03 
 
 14.35 
 
 14.68 
 
 14.99 
 
 15.30 
 
 15-62 
 
 15.94 
 
 16.26 
 
 Vl6 
 
 16.36 
 
 16.74 
 
 17.12 
 
 17.49 
 
 17.85 
 
 18.23 
 
 18.60 
 
 18.97 
 
 H 
 
 18.70 
 
 19.13 
 
 19.55 
 
 19.67 
 
 20.40 
 
 20.82 
 
 21.25 
 
 21.67 
 
 He 
 
 21.02 
 
 21.51 
 
 22.00 
 
 22.48 
 
 22.95 
 
 23.43 
 
 23.90 
 
 24.39 
 
 H 
 
 23.38 
 
 23.91 
 
 24.44 
 
 24-97 
 
 25.50 
 
 26.03 
 
 26.56 
 
 27.09 
 
 iHe 
 
 25.70 
 
 26.30 
 
 26.88 
 
 27.47 
 
 28.05 
 
 28.64 
 
 29.22 
 
 29.80 
 
 % 
 
 28.05 
 
 28,68 
 
 29.33 
 
 29.97 
 
 30.60 
 
 31-25 
 
 31.88 
 
 32.52 
 
 1^16 
 
 30.40 
 
 31.08 
 
 31.76 
 
 32.46 
 
 33.15 
 
 33-83 
 
 34.53 
 
 35.22 
 
 ^ 
 
 32.72 
 
 33.47 
 
 34.21 
 
 34.9s 
 
 35.70 
 
 36.44 
 
 37.19 
 
 37.93 
 
 15/16 
 
 35.06 
 
 35.86 
 
 36.66 
 
 37.46 
 
 38.25 
 
 39 05 
 
 39.84 
 
 40.64 
 
 I 
 
 37.40 
 
 38.25 
 
 39- 10 
 
 39.95 
 
 40.80 
 
 41.65 
 
 42.50 
 
 43.35 
 
 iMe 
 
 • 39-74 
 
 40.64 
 
 41.54 
 
 42.45 
 
 43.35 
 
 44-25 
 
 45.16 
 
 46.06 
 
 ii/i 
 
 42.08 
 
 43.04 
 
 44.00 
 
 44.94 
 
 45.90 
 
 46.86 
 
 47.82 
 
 48.77 
 
 iMe 
 
 44.42 
 
 45.42 
 
 46.44 
 
 47.45 
 
 48.45 
 
 49-46 
 
 50.46 
 
 SI. 48 
 
 iH 
 
 46.76 
 
 47.82 
 
 48.88 
 
 49.94 
 
 51 00 
 
 52.06 
 
 ■ 53.12 
 
 54.19 
 
 iMe 
 
 49.08 
 
 50.20 
 
 51.32 
 
 52.44 
 
 53-55 
 
 54-67 
 
 55.78 
 
 56.90 
 
 iH 
 
 51.42 
 
 52.59 
 
 53.76 
 
 54.93 
 
 56.10 
 
 57-27 
 
 58.44 
 
 59.60 
 
 1^6 
 
 53.76 
 
 54.99 
 
 56.21 
 
 57.43 
 
 58.65 
 
 59.87 
 
 61.10 
 
 62.32 
 
 I1/2 
 
 56.10 
 
 57.37 
 
 58.65 
 
 59.93 
 
 61.20 
 
 62.48 
 
 63.75 
 
 65.03 
 
 i^ie 
 
 58.42 
 
 59.76 
 
 61.10 
 
 62.43 
 
 63-75 
 
 65.08 
 
 66.40 
 
 67.74 
 
 iH 
 
 60.78 
 
 62.16 
 
 63 -54 
 
 64.92 
 
 66.30 
 
 67.68 
 
 69.06 
 
 70.44 
 
 iiMe 
 
 63.10 
 
 64.55 
 
 65.98 
 
 67.42 
 
 68.85 
 
 70.29 
 
 71.72 
 
 73. IS 
 
 l3/4 
 
 65.45 
 
 66.93 
 
 68.43 
 
 69.92 
 
 71.40 
 
 72.90 
 
 74.38 
 
 75.87 
 
 11^6 
 
 67.80 
 
 69.33 
 
 70.86 
 
 72.41 
 
 73-95 
 
 75.48 
 
 77.03 
 
 78.57 
 
 1% 
 
 70.12 
 
 71.72 
 
 73.31 
 
 74.90 
 
 76.50 
 
 78.09 
 
 79.69 
 
 81.28 
 
 11^6 
 
 72.46 
 
 74.11 
 
 75.76 
 
 77.41 
 
 79-05 
 
 80.70 
 
 82.34 
 
 83.99 
 
 2 
 
 74.80 
 
 76.50 
 
 78.20 
 
 79.90 
 
 81.60 
 
 83.30 
 
 85.00 
 
 86.70 
 
 The weights. for 12-inch width are repeated on each page to facilitate making the 
 additions necessary to obtain the weights of plates wider than 12 inches. Thus to 
 find the weight of 15H" X%", add the weights to be found in the same line for 3H X^i 
 and 12x^^ = 10.41-1-35.70 = 46.11 pounds. 
 
136 
 
 Materials 
 
 Weights and Areas of Square and Round Bars of Wrought 
 Iron and Circumference of Round Bars. 
 
 One cubic foot weighing 480 lbs. 
 
 Thickness 
 
 
 
 Area of 
 
 Area of 
 
 Circum- 
 
 or diam- 
 
 Weight of 
 
 n bar 
 I foot long 
 
 Weight of 
 
 bar 
 I foot long 
 
 D bar 
 
 bar 
 
 ference of 
 
 eter in 
 inches 
 
 in square 
 inches 
 
 in square 
 inches 
 
 bar 
 in inches 
 
 
 
 Me 
 
 .013 
 
 .010 
 
 .0039 
 
 .0031 
 
 .1963 
 
 H 
 
 .052 
 
 .041 
 
 .0156 
 
 .0123 
 
 .3927 
 
 3/i6 
 
 .117 
 
 .092 
 
 .0352 
 
 .0276 
 
 .5890 
 
 H 
 
 .208 
 
 .164 
 
 .0625 
 
 .0491 
 
 .7854 
 
 Me 
 
 .326 
 
 .256 
 
 .0977 
 
 .0767 
 
 .9817 
 
 % 
 
 .469 
 
 .368 
 
 .1406 
 
 .1104 
 
 1.1781 
 
 Me 
 
 .638 
 
 .501 
 
 .1914 
 
 .1503 
 
 •1.3744 
 
 H 
 
 .833 
 
 .654 
 
 .2500 
 
 .1963 
 
 1.5708 
 
 %6 
 
 1. 055 
 
 .828 
 
 .3164 
 
 .2485 
 
 I. 7671 
 
 % 
 
 1.302 
 
 1.023 
 
 .3906 
 
 .3068 
 
 1.963s 
 
 iHe 
 
 1.576 
 
 1.237 
 
 .4727 
 
 .3712 
 
 2.1598 
 
 % 
 
 1.875 
 
 1.473 
 
 .5625 
 
 .4418 • 
 
 2.3562 
 
 13/i6 
 
 2.201 
 
 1.728 
 
 .6602 
 
 .5185 
 
 2.SS2S 
 
 ^ 
 
 2.552 
 
 2.004 
 
 .7656 
 
 .6013 
 
 2.7489 
 
 iMe 
 
 2.930 
 
 2.301 
 
 .8789 
 
 .6903 
 
 2.9452 
 
 I 
 
 3.333 
 
 2.618 
 
 I. 0000 
 
 .7854 
 
 3.1416 
 
 He 
 
 3.763 
 
 2.955 
 
 I. 1289 
 
 .8866 
 
 3.3379 
 
 M 
 
 4.219 
 
 3.313 
 
 I . 2656 
 
 .9940 
 
 3.5343 
 
 ?i6 
 
 4.701 
 
 3.692 
 
 I . 4102 
 
 I. 1075 
 
 3.7306 
 
 Vi 
 
 5.208 
 
 4.091 
 
 1-5625 
 
 I . 2272 
 
 3.9270 
 
 Me 
 
 5. 742 
 
 4-510 
 
 1.7227 
 
 1.3530 
 
 4.1233 
 
 % 
 
 6.302 
 
 4-950 
 
 1.8906 
 
 1.4849 
 
 4.3197 
 
 Me 
 
 6.888 
 
 5.410 
 
 2.0664 
 
 1.6230 
 
 4.5160 
 
 >i 
 
 7.500 
 
 5.890 
 
 2.2500 
 
 I. 7671 
 
 4.7124 
 
 Me 
 
 8.138 
 
 6.392 
 
 2.4414 
 
 I -9175 
 
 4.9087 
 
 S/^ 
 
 8.802 
 
 6.913 
 
 2.6406 
 
 2.0739 
 
 5.1051 
 
 iMe 
 
 9.492 
 
 7.455 
 
 2.8477 
 
 2.2365 
 
 5.3014 
 
 % 
 
 10.21 
 
 8.018 
 
 3.0625 
 
 2.4053 
 
 5. 4978 
 
 13/(6 
 
 10-95 
 
 8.601 
 
 3.2852 
 
 2.5802 
 
 5 -6941 
 
 H 
 
 11.72 
 
 9.204 
 
 3-5156 
 
 2.7612 
 
 5.890s 
 
 iMe 
 
 12.51 
 
 9.828 
 
 3-7539 
 
 2.9483 
 
 6.0868 
 
 2 
 
 13.33 
 
 10.47 
 
 4.0000 
 
 3.1416 
 
 6.2832 
 
 He 
 
 14.18 
 
 II. 14 
 
 4-2539 
 
 3.3410 
 
 6. 4795 
 
 H 
 
 15 OS 
 
 11.82 
 
 4.5156 
 
 3.5466 
 
 6.6759 
 
 Me 
 
 15-95 
 
 12.53 
 
 4-7852 
 
 3.7583 
 
 6.8722 
 
 H 
 
 16.88 
 
 13.25 
 
 5-0625 
 
 3.9761 
 
 7.0686 
 
 Me 
 
 17.83 
 
 14.00 
 
 5.3477 
 
 4.2000 
 
 7.2649 
 
 ?^ 
 
 18.80 
 
 14-77 
 
 5.6406 
 
 4.4301 
 
 7.4613 
 
 Me 
 
 19.80 
 
 15-55 
 
 5.9414 
 
 4.6664 
 
 7.6576 
 
 H 
 
 20.83 
 
 16.36 
 
 6.2500 
 
 4.9087 
 
 7.8540 
 
 Me 
 
 21.89 
 
 17.19 
 
 6.5664 
 
 5.1572 
 
 8.0S03 
 
 5i 
 
 22.97 
 
 18.04 
 
 6.8906 
 
 S.4119 
 
 8.2467 
 
 iHe 
 
 24.08 
 
 18.91 
 
 7.2227 
 
 5.6727 
 
 8.4430 
 
 % 
 
 25.21 
 
 19.80 
 
 7.562s 
 
 5.9396 
 
 8.6394 
 
 iMe 
 
 26.37 
 
 20.71 
 
 7.9102 
 
 6.2126 
 
 8.8357 
 
 % 
 
 27.55 
 
 21.64 
 
 8.2656 
 
 6.4918 
 
 9-0321 
 
 iMe 
 
 28.76 
 
 22.59 
 
 8.6289 
 
 6.7771 
 
 9.2284 
 
Weight of Square and Round Bars 
 
 137 
 
 Weight of Square and Round Bars — (Continued) 
 
 Thickness 
 or diam- 
 
 . Weight of 
 D bar 
 I foot long 
 
 Weight of 
 
 bar 
 I foot long 
 
 Area of 
 a bar 
 
 Area of 
 bar 
 
 Circum- 
 ference of 
 
 eter in 
 inches 
 
 in square 
 inches 
 
 in square 
 inches 
 
 bar 
 in inches 
 
 3 
 
 30.00 
 
 23.56 
 
 9.0000 
 
 7.0686 
 
 9.4248 
 
 Me 
 
 31 26 
 
 24.55 
 
 9.3789 
 
 7.3662 
 
 9.6211 
 
 H 
 
 32.55 
 
 25.57 
 
 9-7656 
 
 7.6699 
 
 9.8175 
 
 3/16 
 
 33.87 
 
 26.60 
 
 10.160 
 
 7.9798 
 
 10.014 
 
 H 
 
 35.21 
 
 27.65 
 
 10.563 
 
 8.2958 
 
 10.210 
 
 ^16 
 
 36.58 
 
 28.73 
 
 10.973 
 
 8.6179 
 
 10.407 
 
 H 
 
 37.97 
 
 29.82 
 
 II. 391 
 
 8.9462 
 
 10.603 
 
 Vxo 
 
 39-39 
 
 30.94 
 
 II. 816 
 
 9.2806 
 
 10.799 
 
 
 40.83 
 
 32.07 
 
 12.250 
 
 9.6211 
 
 10.996 
 
 42.30 
 
 33.23 
 
 12.691 
 
 9-9678 
 
 II. 192 
 
 % 
 
 43.80 
 
 34.40 
 
 13. 141 
 
 10.321 
 
 11.388 
 
 iMe 
 
 45. 33 
 
 35.60 
 
 13.598 
 
 X0.680 
 
 II. 58s 
 
 % 
 
 46.88 
 
 36.82 
 
 14.063 
 
 II.04S 
 
 II. 781 
 
 13/16 
 
 48.45 
 
 38.05 
 
 14-535 
 
 II. 416 
 
 11.977 
 
 ^^ 
 
 50.0s 
 
 39-31 
 
 IS.016 
 
 11-793 
 
 12.174 
 
 15/6 
 
 51.68 
 
 40.59 
 
 15.504 
 
 12.177 
 
 12.370 
 
 4 
 
 53.33 
 
 41.89 
 
 16.000 
 
 12.566 
 
 12.566 
 
 Me 
 
 55. 01 
 
 43-21 
 
 16.504 
 
 12.962 
 
 12.763 
 
 1/^ 
 
 56.72 
 
 44.55 
 
 17.016 
 
 13.364 
 
 12.959 
 
 3/6 
 
 58.45 
 
 45.91 
 
 17.535 
 
 13-772 
 
 13.ISS 
 
 M 
 
 60.21 
 
 47.29 
 
 18.063 
 
 14.186 
 
 13 352 
 
 5/6 
 
 61.99 
 
 48.69 
 
 18.598 
 
 14.607 
 
 13.548 
 
 % 
 
 63.80 
 
 50.11 
 
 19. 141 
 
 15.033 
 
 13.744 
 
 VlQ 
 
 65.64 
 
 51.55^ 
 
 19.691 
 
 15.466 
 
 13.941 
 
 Vl 
 
 67.50 
 
 53.01 
 
 20.250 
 
 IS -904 
 
 14.137 
 
 %6 
 
 69.39 
 
 54.50 
 
 20.816 
 
 16.349 
 
 14.334 
 
 ^A 
 
 71-30 
 
 56.00 
 
 21.391 
 
 16.800 
 
 14.530 
 
 iMe 
 
 73.24 
 
 57.52 
 
 21.973 
 
 17-257 
 
 14.726 
 
 % 
 
 75.21 
 
 59.07 
 
 22.563 
 
 17.721 
 
 14.923 
 
 1^6 
 
 77.20 
 
 60.63 
 
 23.160 
 
 18.190 
 
 15. 119 
 
 ^ 
 
 79.22 
 
 62.22 
 
 23.766 
 
 18.665 
 
 15.31S 
 
 IMe 
 
 81.26 
 
 63.82 
 
 24.379 
 
 19-147 
 
 15.512 
 
 5 
 
 83.33 
 
 65.45 
 
 25.000 
 
 19-635 
 
 15.708 
 
 Me 
 
 85.43 
 
 67.10 
 
 25.629 
 
 20.129 
 
 15.904 
 
 H 
 
 87.55 
 
 68.76 
 
 26.266 
 
 20.629 
 
 16.101 
 
 Me 
 
 89.70 
 
 70.45 
 
 26.910 
 
 21 . 135 
 
 16.297 
 
 M 
 
 91.88 
 
 72.16 
 
 27-563 
 
 21.648 
 
 16.493 
 
 Me 
 
 94.08 
 
 73.89 
 
 28.223 
 
 22.166 
 
 16.690 
 
 % 
 
 96.30 
 
 75.64 
 
 28.891 
 
 22.691 
 
 16.886 
 
 ^6 
 
 98.55 
 
 77.40 
 
 29.566 
 
 23.221 
 
 17.082 
 
 H 
 
 100.8 
 
 79.19 
 
 30.250 
 
 23.758 
 
 17.279 
 
 Me 
 
 103. 1 
 
 81.00 
 
 30.941 
 
 24-301 
 
 17-475 
 
 H 
 
 105.5 
 
 82.83 
 
 31.641 
 
 24.850 
 
 17.671 
 
 iMe 
 
 107.8 
 
 84.69 
 
 32.348 
 
 25.406 
 
 17.868 
 
 % 
 
 no. 2 
 
 86.56 
 
 33.063 
 
 25.967 
 
 18.064 
 
 13/6 
 
 112. 6 
 
 88.45 
 
 33.785 
 
 26.535 
 
 18.261 
 
 ^ 
 
 115. 1 
 
 90.36 
 
 34.516 
 
 27.109 
 
 18.457 
 
 iMe 
 
 117. S 
 
 92.29 
 
 35.254 
 
 27.688 
 
 18.653 
 
 6 
 
 120.0 
 
 94.25 
 
 36.000 
 
 28.274 
 
 18.8S0 
 
 M« 
 
 122. 5 
 
 96.22 
 
 36.754 
 
 28.866 
 
 19.046 
 
 ^ 
 
 125. 1 
 
 98.22 
 
 37.516 
 
 29.465 
 
 19.242 
 
 Me 
 
 127.6 
 
 100.2 
 
 38.28s 
 
 30.069 
 
 19.439 
 
138 
 
 Materials 
 
 Weight of Square and 
 
 Round Bars — {Continued) 
 
 Thickness 
 or diam- 
 
 Weight of 
 
 D bar 
 I foot long 
 
 Weight of 
 
 bar 
 
 I foot long 
 
 Area of 
 D bar 
 
 Area of 
 bar 
 
 Circum- 
 ference of 
 
 eter in 
 inches 
 
 in square 
 inches 
 
 in square 
 inches 
 
 bar 
 in inches 
 
 m 
 
 130.2 
 
 102.3 
 
 39-063 
 
 30.680 
 
 19.635 
 
 Me 
 
 132.8 
 
 104.3 
 
 39.848 
 
 31.296 
 
 19.831 
 
 ?^ 
 
 135.5 
 
 106.4 
 
 40.641 
 
 31-919 
 
 20.028 
 
 Mo 
 
 138. 1 
 
 108.5 
 
 41.441 
 
 32.548 
 
 20.224 
 
 H 
 
 140.8 
 
 no. 6 
 
 42.250 
 
 33.183 
 
 20 . 420 
 
 %6 
 
 143.6 
 
 112. 7 
 
 43.066 
 
 33.824 
 
 20.617 
 
 % 
 
 146.3 
 
 114. 9 
 
 43.891 
 
 34.472 
 
 20.813 
 
 1H6 
 
 149. 1 
 
 117. 1 
 
 44-723 
 
 35-125 
 
 21.009 
 
 % 
 
 151. 9 
 
 II9-3 
 
 45.563 
 
 35-785 
 
 21.206 ^ 
 21.402 ^ 
 
 13/(6 
 
 154.7 
 
 121. 5 
 
 46.410 
 
 36.450 
 
 % 
 
 157.6 
 
 123.7 
 
 47.266 
 
 37-122 
 
 21.598 
 
 1^6 
 
 160.4 
 
 126.0 
 
 48.129 
 
 37-800 
 
 21.795 
 
 7 
 
 163.3 
 
 128.3 
 
 49000 
 
 38-485 
 
 21.991 
 
 Me 
 
 166.3 
 
 130.6 
 
 49.879 
 
 39-175 
 
 22.187 
 
 H 
 
 169.2 
 
 132.9 
 
 50.766 
 
 39-871 
 
 22.384 
 
 M« 
 
 172.2 
 
 135.2 
 
 51.660 
 
 40-574 
 
 22.580 
 
 M 
 
 175.2 
 
 137.6 
 
 52.563 
 
 41.282 
 
 22.777 
 
 Ma 
 
 178.2 
 
 140.0 
 
 53.473 
 
 41.997 
 
 22.973 
 
 H 
 
 181. 3 
 
 142.4 
 
 54-391 
 
 42.718 
 
 23.169 
 
 M« 
 
 184.4 
 
 144.8 
 
 55-316 
 
 43.445 
 
 23.366 
 
 H 
 
 187.5 
 
 147.3 
 
 56.250 
 
 44.179 
 
 23.562 
 
 9i6 
 
 190.6 
 
 149-7 
 
 57.191 
 
 44.918 
 
 23.758 
 
 5i 
 
 193.8 
 
 152.2 
 
 58.141 
 
 45 664 
 
 23.955 
 
 iMe 
 
 197.0 
 
 154.7 
 
 59 098 
 
 46.415 
 
 24.151 
 
 % 
 
 200.2 
 
 157.2 
 
 60.063 
 
 47.173 
 
 24.347 
 
 1^6 
 
 203.5 
 
 159-8 
 
 61.035 
 
 47.937 
 
 24.544 
 
 % 
 
 206.7 
 
 162.4 
 
 62.016 
 
 48.707 
 
 24.740 
 
 »M6 
 
 210.0 
 
 164.9 
 
 63.004 
 
 49-483 
 
 24.936 
 
 8 
 
 213.3 
 
 167.6 
 
 64.000 
 
 50.265 
 
 25.133 
 
 Mfl 
 
 216.7 
 
 170.2 
 
 65.004 
 
 51.054 
 
 25.329 
 
 H 
 
 220.1 
 
 172.8 
 
 66.016 
 
 51-849 
 
 25.52s 
 
 Ms 
 
 223.5 
 
 175.5 
 
 67-035 
 
 52.649 
 
 25.722 
 
 M 
 
 226.9 
 
 178.2 
 
 68.063 
 
 53.456 
 
 25-918 
 
 Ms 
 
 230.3 
 
 180.9 
 
 69.098 
 
 54.269 
 
 26.114 
 
 ?i 
 
 233.8 
 
 183.6 
 
 70.141 
 
 55-088 
 
 26.311 
 
 Me 
 
 237.3 
 
 186.4 
 
 71. 191 
 
 55-914 
 
 26.507 
 
 H 
 
 240.8 
 
 189.2 
 
 72.250 
 
 56.745 
 
 26.704 
 
 Me 
 
 244.4 
 
 191-9 
 
 73.316 
 
 57.583 
 
 26.900 
 
 % 
 
 248.0 
 
 194-8 
 
 74.391 
 
 58.426 
 
 27.096 
 
 iHe 
 
 251.6 
 
 197-6 
 
 75.473 
 
 59.276 
 
 27.293 
 
 % 
 
 255.2 
 
 200.4 
 
 76.563 
 
 60.132 
 
 27-489 
 
 iMo 
 
 258.9 
 
 203.3 
 
 77-660 
 
 60.994 
 
 27.685 
 
 ^ 
 
 262.6 
 
 206.2 
 
 78.766 
 
 61.862 
 
 27.882 
 
 »M6 
 
 266.3 
 
 209.1 
 
 79.879 
 
 62.737 
 
 28.078 
 
 9 
 
 270.0 
 
 212. 1 
 
 81.000 
 
 63.617 
 
 28.274 
 
 Me 
 
 273.8 
 
 215.0 
 
 82.129 
 
 64.504 
 
 28.471 
 
 H 
 
 277.6 
 
 218.0 
 
 83.266 
 
 65.397 
 
 28.667 
 
 Me 
 
 281.4 
 
 221.0 
 
 84.410 
 
 66.296 
 
 28.863 
 
 M 
 
 285.2 
 
 224.0 
 
 85.563 
 
 67.201 
 
 29.060 
 
 Me 
 
 289 I 
 
 227.0 
 
 86.723 
 
 68.112 
 
 29.256 
 
 ?^ 
 
 293.0 
 
 230.1 
 
 87.891 
 
 69.029 
 
 29.452 
 
 Me 
 
 296.9 
 
 233.2 
 
 89.066 
 
 69.953 
 
 29.649 
 
Weight of Square and Round Bars 
 
 130 
 
 Weight of Square and Round Bars — {Continued) 
 
 Thickness 
 or diam- 
 
 Weight of 
 D bar 
 
 Weight of 
 bar 
 
 Area of 
 D bar 
 
 Area of 
 bar 
 
 Circum- 
 ference of 
 
 eter in 
 inches 
 
 I foot long 
 
 I foot long 
 
 in square 
 inches 
 
 in square 
 inches 
 
 bar 
 in inches 
 
 m 
 
 300.8 
 
 236.3 
 
 90.250 
 
 70.882 
 
 29.845 
 
 ri6 
 
 304.8 
 
 239.4 
 
 91.441 
 
 71.818 
 
 30.041 
 
 % 
 
 308.8 
 
 242.5 
 
 92.641 
 
 72.760 
 
 36.238 
 
 iMe 
 
 312.8 
 
 245.7 
 
 93.848 
 
 73.708 
 
 30.434 
 
 % 
 
 316.9 
 
 248.9 
 
 95.063 
 
 74.662 
 
 30.631 
 
 1^6 
 
 321.0 
 
 252.1 
 
 96.285 
 
 75.622 
 
 30.827 
 
 % 
 
 325.1 
 
 255.3 
 
 97.516 
 
 76.589 
 
 31.023 
 
 1^6 
 
 329.2 
 
 258.5 
 
 98.754 
 
 77.561 
 
 31.200 
 
 lO 
 
 333.3 
 
 261.8 
 
 100.00 
 
 78.540 
 
 31.416 
 
 H8 
 
 337.5 
 
 265.1 
 
 101.25 
 
 79.525 
 
 31.612 
 
 H 
 
 341.7 
 
 268.4 
 
 102 . 52 
 
 80.516 
 
 31.809 
 
 ^6 
 
 346.0 
 
 271.7 
 
 103.79 
 
 81.513 
 
 32.005 
 
 H 
 
 3S0.2 
 
 275.1 
 
 105.06 
 
 82.516 
 
 32.201 
 
 Me 
 
 354.5 
 
 278.4 
 
 106.35 
 
 83.525 
 
 32.398 
 
 % 
 
 358.8 
 
 281.8 
 
 107.64 
 
 84.541 
 
 32.594 
 
 ^8 
 
 363.1 
 
 285.2 
 
 108.94 
 
 85.562 
 
 32.790 
 
 H 
 
 367.5 
 
 288.6 
 
 110.25 
 
 86.590 
 
 32.987 
 
 916 
 
 371.9 
 
 292.1 
 
 III. 57 
 
 87.624 
 
 33.183 
 
 % 
 
 376.3 
 
 295.5 
 
 112.89 
 
 88.664 
 
 33.379 
 
 »M6 
 
 380.7 
 
 299.0 
 
 114.22 
 
 89.710 
 
 33.576 
 
 % 
 
 385.2 
 
 302.5 
 
 115.56 
 
 90.763 
 
 33.772 
 
 1^6 
 
 389.7 
 
 306.1 ^ 
 
 116. 91 
 
 91.821 
 
 33.968 
 
 % 
 
 394.2 
 
 309.6 
 
 118.27 
 
 92.886 
 
 34.165 
 
 1^6 
 
 398.8 
 
 313.2 
 
 119.63 
 
 93.956 
 
 34.361 
 
 II 
 
 403.3 
 
 316.8 
 
 121.00 
 
 95.033 
 
 34.558 
 
 He 
 
 407.9 
 
 320.4 
 
 122.38 
 
 96.116 
 
 34.754 
 
 H 
 
 412.6 
 
 324.0 
 
 123.77 
 
 97.205 
 
 34.950 
 
 5i6 
 
 417.2 
 
 327.7 
 
 125.16 
 
 98.301 ■ 
 
 35.147 
 
 H 
 
 ^21.9 
 
 331.3 
 
 126.56 
 
 99.402 
 
 35.343 
 
 Me 
 
 426.6 
 
 335.0 
 
 127.97 
 
 100. .51 
 
 35.539 
 
 % 
 
 431.3 
 
 338.7 
 
 129.39 
 
 101.62 
 
 35.736 
 
 ^6 
 
 436.1 
 
 342.5 
 
 130.82 
 
 102.74 
 
 35.932 
 
 ^ 
 
 440.8 
 
 346.2 
 
 132.25 
 
 103.87 
 
 36.128 
 
 Ma 
 
 445.6 
 
 350.0 
 
 133.69 
 
 105.00 
 
 36.32s 
 
 5i 
 
 4S0.5 
 
 353.8 
 
 135.14 
 
 106.14 
 
 36.521 
 
 »Me 
 
 455.3 
 
 357.6 
 
 136.60 
 
 107.28 
 
 36.717 
 
 % 
 
 460.2 
 
 361.4 
 
 138.06 
 
 108.43 
 
 36.914 
 
 iMe 
 
 465.1 
 
 365.3 
 
 139.54 
 
 109.59 
 
 37.110 
 
 ?i 
 
 470.1 
 
 369.2 
 
 141.02 
 
 110.75 
 
 37.306 
 
 iMe 
 
 475.0 
 
 373.1 
 
 142. so 
 
 III. 92 
 
 37.503 
 
140 Materials 
 
 Weights and Areas of Cold Rolled Steel Shafting 
 
 Diam- • 
 
 Area, 
 
 Circum- 
 
 Weight 
 
 Diam- 
 
 Area, 
 
 Circum- 
 
 Weight 
 
 eter, 
 
 square 
 
 ference, 
 
 per foot, 
 
 eter, 
 
 square 
 
 ference, 
 
 per foot. 
 
 inches 
 
 inches 
 
 inches 
 
 pounds 
 
 inches 
 
 inches 
 
 inches 
 
 pounds 
 
 He 
 
 .0276 
 
 .5890 
 
 .095 
 
 23/6 
 
 3.7583 
 
 6.8722 
 
 12.80 
 
 H . 
 
 .0491 
 
 :7854 
 
 .167 
 
 2yi 
 
 3.9761 
 
 7.0686 
 
 13.52 
 
 Vie 
 
 .0767 
 
 .9817 
 
 .260 
 
 25/6 
 
 4.2000 
 
 7.2749 
 
 14.35 
 
 H 
 
 .1104 
 
 1.1781 
 
 .375 
 
 2H 
 
 4.4301 
 
 7.4613 
 
 15.07 
 
 ^6 
 
 .1503 
 
 1.3744 
 
 .511 
 
 2^6 
 
 4.6664 
 
 7.6576 
 
 IS. 89 
 
 H 
 
 .1963 
 
 1.5708 
 
 .667 
 
 21/ 
 
 4.9087 
 
 7.8540 
 
 16.70 
 
 9i6 
 
 .2485 
 
 I. 7671 
 
 .845 
 
 2916 
 
 5.1572 
 
 8.0503 
 
 17.55 
 
 H 
 
 .3068 
 
 1.9635 
 
 1.05 
 
 25i 
 
 5.4119 
 
 8.2467 
 
 18.41 
 
 ^Me 
 
 .3712 
 
 2.1598 
 
 1.26 
 
 211/6 
 
 5.6727 
 
 8.4430 
 
 19.31 
 
 H 
 
 .4418 
 
 2.3562 
 
 1.50 
 
 2% 
 
 5.9396 
 
 8.6394 
 
 20.21 
 
 1^6 
 
 .5185 
 
 2.5525 
 
 1.77 
 
 21 %6 
 
 6.2126 
 
 8.8357 
 
 21.15 
 
 % 
 
 .6013 
 
 2.7489 
 
 2.05 
 
 2% 
 
 6.4918 
 
 9.0321 
 
 22.09 
 
 1^6 
 
 .6903 
 
 2.9452 
 
 2.35 
 
 215/6 
 
 6.7771 
 
 9.2284 
 
 23.06 
 
 I 
 
 .7854 
 
 3.1416 
 
 2.68 
 
 3 
 
 7.0686 
 
 9.4248 
 
 24.05 
 
 iHe 
 
 .8866 
 
 3.3379 
 
 3.02 
 
 31/ 
 
 7.6699 
 
 9.8175 
 
 26.09 
 
 iH 
 
 .9940 
 
 3.5343 
 
 3.38 
 
 33/6 
 
 7.9798 
 
 10.014 
 
 27.16 
 
 I3/16 
 
 I . 1075 
 
 3.7306 
 
 3.77 
 
 3/4 
 
 8.2958 
 
 10.210 
 
 28.22 
 
 m 
 
 1.2272 
 
 3.9270 
 
 4.17 
 
 33/ 
 
 8.9462 
 
 10.603 
 
 30.43 
 
 iMe 
 
 I.3S30 
 
 4.1233 
 
 4.61 
 
 3M6 
 
 9.2806 
 
 10.799 
 
 31.58 
 
 1% 
 
 1.4849 
 
 4.3197 
 
 5.05 
 
 31/ 
 
 9.6211 
 
 10.996 
 
 32.73 
 
 17/16 
 
 1.6230 
 
 4.5160 
 
 5.52 
 
 3% 
 
 10.321 
 
 11.388 
 
 35.20 
 
 iH 
 
 I. 7671 
 
 4.7124 
 
 6.01 
 
 311/6 
 
 10.680 
 
 11.585 
 
 36.40 
 
 I9i6 
 
 I. 9175 
 
 4.9087 
 
 6.52 
 
 33/i 
 
 II. 04s 
 
 11.781 
 
 37.57 
 
 I5i 
 
 2.0739 
 
 5.1051 
 
 7.06 
 
 3H 
 
 11.793 
 
 12.174 
 
 39.40 
 
 iiHe 
 
 2.2365 
 
 5.3014 
 
 7.61 
 
 315/6 
 
 12.177 
 
 12.370 
 
 41.04 
 
 134 
 
 2.4053 
 
 5.4978 
 
 8.18 
 
 4 
 
 12.566 
 
 12.566 
 
 42.75 
 
 113/16 
 
 2.5802 
 
 5.6941 
 
 8.78 
 
 4K 
 
 14.186 
 
 13.352 
 
 48.26 
 
 m 
 
 2.7612 
 
 5.8905 
 
 9.39 
 
 4^6 
 
 IS. 466 
 
 13.941 
 
 52.62 
 
 11^6 
 
 2.9483 
 
 6.0868 
 
 10.03 
 
 41/ 
 
 15.904 
 
 14.137 
 
 54.11 
 
 2 
 
 3.1416 
 
 6.2832 
 
 10.69 
 
 43/ 
 
 17.728 
 
 14.923 
 
 60.88 
 
 2H6 
 
 3.3410 
 
 6.479s 
 
 11.35 
 
 41 Me 
 
 19.147 
 
 15.512 
 
 65.50 
 
 2>i 
 
 3.5466 
 
 6.6759 
 
 12.07 
 
 5 
 
 19.635 
 
 15.708 
 
 67.4s 
 
Corrugated Iron Roofing 
 
 141 
 
 Sheet Iron 
 
 Weight of a superficial foot. 
 
 Number of 
 
 Weight per 
 
 Number of 
 
 Weight per 
 
 gauge 
 
 foot 
 
 gauge 
 
 foot 
 
 I 
 
 11.25 
 
 l6 = M6 
 
 2.5 
 
 2 
 
 10.625 
 
 17 
 
 2.1875 
 
 3=Vi 
 
 10.00 
 
 18 
 
 1.875 
 
 4 
 
 9-375 
 
 19 
 
 I. 7188 
 
 5 
 
 8.750 
 
 20 
 
 1.562s 
 
 6 
 
 8.125 
 
 21 
 
 1.4063 
 
 7 
 
 7.50 
 
 22=1.^2 
 
 I . 2500 
 
 8 
 
 6.875 
 
 23 
 
 1. 120 
 
 9 
 
 6.250 
 
 24 
 
 1. 000 
 
 10 
 
 5.625 
 
 25 
 
 .900 
 
 II =H 
 
 5000 
 
 26 
 
 .800 
 
 12 
 
 4.375 
 
 27 
 
 .720 
 
 13 
 
 3.750 
 
 28 
 
 .640 
 
 14 
 
 3.125 
 
 29 
 
 .560 
 
 15 
 
 2.8125 
 
 30 
 
 .500 
 
 Galvanized Sheet Iron 
 
 Am. Galv. Iron Ass'n. B. W. G. 
 
 No. 
 
 Ounces 
 avoir. 
 
 per 
 
 square 
 
 foot 
 
 Square 
 feet per 
 
 2240 
 pounds 
 
 No. 
 
 Ounces 
 avoir. 
 
 per 
 
 square 
 
 foot 
 
 Square 
 feet per 
 
 2240 
 pounds 
 
 No. 
 
 Ounces 
 avoir. 
 
 per 
 
 square 
 
 foot 
 
 Square 
 feet per 
 . 2240 
 pounds 
 
 29 
 28 
 27 
 26 
 25 
 
 12 
 13 
 14 
 IS 
 16 
 
 2987 
 2757 
 2560 
 2389 
 2240 
 
 24 
 23 
 22 
 
 21 . 
 20 
 
 17 
 19 
 21 
 24 
 28 
 
 2108 
 1886 
 1706 
 1493 
 1280 
 
 19 
 18 
 17 
 16 
 14 
 
 33 
 38 
 43 
 48 
 60 
 
 1084 
 943 
 833 
 746 
 597 
 
 Corrugated Iron Roofing 
 
 B. W. 
 gauge 
 
 Weight per square 
 
 (100 square feet). 
 
 Plain 
 
 Galvanized 
 
 Number 
 28 
 26 
 24 
 22 
 20 
 18 
 16 
 
 Pounds 
 97 
 los 
 128 
 150 
 18S 
 270 
 340 
 
 Weighs from 5 to 15 per cent 
 heavier than plain, accord- 
 ing to the number B. W. G. 
 
 Allow one-third the net width for lapping and for corrugations. 
 2}i to 3}^ pounds for rivets will be required per square. 
 
 From 
 
142 
 
 Materials 
 Sizes and Weight of Sheet Tin 
 
 
 Number of 
 
 sheets in 
 
 box 
 
 Dimension 
 
 Weight of 
 
 Mark 
 
 Length, 
 inches 
 
 Breadth, 
 inches 
 
 box, 
 pounds 
 
 iC 
 
 225 
 225 
 225 
 225 
 225 
 225 
 225 
 
 lob 
 
 ICO 
 ICO 
 IOC 
 lOO 
 200 
 20O 
 200 
 200 
 225 
 
 13H 
 
 13)4 
 
 12% 
 
 13% 
 
 13% 
 
 13% 
 
 13% 
 
 i6% 
 
 i6% 
 
 i6% 
 
 i6% 
 
 l6% 
 
 15 
 
 15 
 
 15 
 
 15 
 
 13% 
 
 lo 
 9% 
 
 lO 
 
 lO 
 
 lO 
 
 lO 
 
 I2l/^ 
 
 12^ 
 
 I2l^ 
 
 I2l^ 
 
 I2l^ 
 
 II 
 
 II 
 
 II 
 
 II 
 
 lO 
 
 112 
 
 iiC 
 
 loS 
 
 iiiC 
 
 98 
 
 iX 
 
 140 
 
 iXX 
 
 161 
 
 iXXX 
 
 182 
 
 iXXXX 
 
 203 
 
 DC 
 
 los 
 
 DX 
 
 126 
 
 DXX 
 
 147 
 
 DXXX 
 
 168 
 
 DXXXX 
 
 189 
 
 SDC 
 
 168 
 
 5DX 
 
 189 
 
 SDXX 
 
 21Q 
 
 SDXXX 
 
 231 
 
 iCW . 
 
 112 
 
 
 
 A box containing 225 sheets, 13% by 10, contains 214.84 square feet; 
 but allowing for seams it will cover only 150 square feet of roof. 
 A roof covered with metal should slope not less than i inch to the foot. 
 
 Weights of Sheet Metals per Square Foot 
 
 Thick- 
 
 Wrought 
 
 Cast 
 
 Steel, 
 
 Copper. 
 
 Brass, 
 
 Lead, 
 
 Zinc, 
 
 inches 
 
 pounds 
 
 pounds 
 
 pounds 
 
 pounds 
 
 pounds 
 
 pounds 
 
 pounds 
 
 Me 
 
 2.53 
 
 2.34 
 
 2.55 
 
 2.89 
 
 2.73 
 
 3.71 
 
 2.34 
 
 H 
 
 5.05 
 
 4.69 
 
 5.10 
 
 5.78 
 
 5.47 
 
 7.42 
 
 4.69 
 
 %6 
 
 7.58 
 
 7.03 
 
 7.66 
 
 8.67 
 
 . 8.20 
 
 II. 13 
 
 7.03 
 
 H 
 
 10.10 
 
 9.38 
 
 10.21 
 
 11.56 
 
 10.94 
 
 14.83 
 
 9.38 
 
 Me 
 
 12.63 
 
 11.72 
 
 12.76 
 
 14.45 
 
 13.67 
 
 18.54 
 
 11.72 
 
 H 
 
 15 16 
 
 14.06 
 
 15.31 
 
 17.34 
 
 16.41 
 
 22.25 
 
 14.06 
 
 Me 
 
 17.68 
 
 16.41 
 
 17.87 
 
 20.23 
 
 19.14 
 
 25.96 
 
 16.41 
 
 ^ 
 
 20.21 
 
 18.75 
 
 20.42 
 
 23.13 
 
 21.88 
 
 29.67 
 
 18.7s 
 
 H 
 
 25.27 
 
 23.44 
 
 25.52 
 
 28.91 
 
 27.34 
 
 37.08 
 
 23-44 
 
 % 
 
 30.31 
 
 28.13 
 
 30.63 
 
 34.69 
 
 32.81 
 
 44.50 
 
 28.13 
 
 -"A 
 
 35-37 
 
 32.81 
 
 35.73 
 
 40.47 
 
 38.28 
 
 51.92 
 
 32.81 
 
 I 
 
 40.42 
 
 37.50 
 
 40.83 
 
 46.2s 
 
 43.75 
 
 59-33 
 
 37-50 
 
Weight of Copper and Brass Wire and Plates 
 
 143 
 
 Weight or Copper and Brass Wire and Plates 
 
 Brown and Sharpe Gauge. 
 
 
 
 Weight of wire per 
 
 Weight of plates per 
 
 No. of 
 
 Size of 
 
 1000 lineal feet 
 
 square foot 
 
 
 each no.. 
 
 
 
 
 
 gauge 
 
 
 
 
 
 
 inch 
 
 Copper, 
 
 Brass, 
 
 Copper, 
 
 Brass, 
 
 
 
 pounds 
 
 pounds 
 
 pounds 
 
 pounds 
 
 0000 
 
 .46000 
 
 640.5 
 
 605-28 
 
 20.84 
 
 19.69 
 
 000 
 
 .40964 
 
 508.0 
 
 479-91 
 
 18.55 
 
 17.53 
 
 00 
 
 .36480 
 
 402.0 
 
 380.77 
 
 16.52 
 
 15.61 
 
 
 
 .32476 
 
 319-5 
 
 301.82 
 
 14-72 
 
 13.90 
 
 I 
 
 .28930 
 
 253-3 
 
 239-45 
 
 13.10 
 
 12.38 
 
 2 
 
 .25763 
 
 200.9 
 
 189.82 
 
 11.67 
 
 11.03 
 
 3 
 
 .22942 
 
 159-3 
 
 150.52 
 
 10.39 
 
 9.82 
 
 4 
 
 .20431 
 
 126.4 
 
 119.48 
 
 9.25 
 
 8.74 
 
 5 
 
 .18194 
 
 100.2 
 
 94-67 
 
 8.24 
 
 7.79 
 
 6 
 
 . 16202 
 
 79-46 
 
 75.08 
 
 7.34 
 
 6.93 
 
 7 
 
 .14428 
 
 63.01 
 
 59. 55 
 
 6.54 
 
 6.18 
 
 8 
 
 .12849 
 
 49.98 
 
 47.22 
 
 5.82 
 
 5.50 
 
 9 
 
 .11443 
 
 39-64 
 
 37.44 
 
 5.18 ^ 
 
 4-90 
 
 10 
 
 .10189 
 
 31-43 
 
 29-69 
 
 4-62 
 
 4-36 
 
 II 
 
 .090742 
 
 24.92 
 
 23.55 
 
 4. II 
 
 3-88 
 
 12 
 
 .080808 
 
 19-77 
 
 18.68 
 
 3-66 
 
 3-46 
 
 13 
 
 .071961 
 
 15-65 
 
 14.81 
 
 3-26 
 
 3.08 
 
 14 
 
 .064084 
 
 12.44 
 
 11.75 
 
 2.90 
 
 2.74 
 
 15 
 
 .057068 
 
 9.86 
 
 9.32 
 
 2.59 
 
 2.44 
 
 16 
 
 .050820 
 
 7.82 
 
 7.59 
 
 2.30 
 
 2.18 
 
 17 
 
 .045257 
 
 6.20 
 
 5.86 
 
 2.05 
 
 1.94 
 
 18 
 
 .040303 
 
 4.92 
 
 4.65 
 
 1.83 
 
 1.72 
 
 19 
 
 .035890 
 
 390 
 
 3.68 
 
 1.63 
 
 1.54 
 
 20 
 
 .031961 
 
 3.09 
 
 2.92 
 
 1-45 
 
 1.37 
 
 21 
 
 .028462 
 
 2.45 
 
 2.317 
 
 1.29 
 
 1.22 
 
 22 
 
 .025347 
 
 1.94 
 
 1.838 
 
 1. 15 
 
 1.08 
 
 23 
 
 .022571 
 
 1.54 
 
 1.457 
 
 1.02 
 
 .966 
 
 24 
 
 .020100 
 
 1.22 
 
 1. 155 
 
 -911 
 
 .860 
 
 25 
 
 .017900 
 
 .699 
 
 .916 
 
 .811 
 
 .766 
 
 26 
 
 .01494 
 
 .769 
 
 .727 
 
 .722 
 
 .682 
 
 27 
 
 .014195 
 
 .610 
 
 .576 
 
 .643 
 
 .608 
 
 28 
 
 .012641 
 
 .484 
 
 .457 
 
 .573 
 
 .541 
 
 29 
 
 .011257 
 
 .383 
 
 .362 
 
 .510 
 
 .482 
 
 30 
 
 .010025 
 
 .304 
 
 .287 
 
 .454 
 
 .429 
 
 31 
 
 .008928 
 
 .241 
 
 .228 
 
 .404 
 
 .382 
 
 32 
 
 .007950 
 
 .191 
 
 .181 
 
 .360 
 
 .340 
 
 33 
 
 .007080 
 
 .152 
 
 .143 
 
 .321 
 
 .303 
 
 34 
 
 .006304 
 
 .120 
 
 .114 
 
 .286 
 
 .270 
 
 35 
 
 .005614 
 
 .096 
 
 .0915 
 
 .254 
 
 .240 
 
 36 
 
 .005000 
 
 .0757 
 
 .0715 
 
 .226 
 
 .214 
 
 37 
 
 .004453 
 
 .0600 
 
 .0567 
 
 .202 
 
 .191 
 
 38 
 
 .003965 
 
 .0467 
 
 .0450 
 
 .180 
 
 170 
 
 39 
 
 .003531 
 
 .0375 
 
 .0357 
 
 .160 
 
 iSi ' 
 
 40 
 
 .003144 
 
 .0299 
 
 .0283 
 
 .142 
 
 .135 
 
 Specific gravit 
 
 y 
 
 8.880 
 
 8.386 
 
 8.698 
 
 8.218 
 
 Weight per cu 
 
 oicfoot 
 
 555 
 
 524.16 
 
 543.6 
 
 513.6 
 
144 
 
 Materials 
 Weight of Sheet and Bar Brass 
 
 
 Sheets 
 
 Square 
 
 Round 
 
 
 Sheets 
 
 Square 
 
 Round 
 
 Thick- 
 
 per 
 
 bars 
 
 bars 
 
 Thick- 
 
 per 
 
 bars 
 
 bars 
 
 ness, 
 
 square 
 
 I foot 
 
 I foot 
 
 ness, 
 
 square 
 
 I foot 
 
 I foot 
 
 inches 
 
 foot, 
 
 long, 
 
 long, 
 
 inches 
 
 foot. 
 
 long, 
 
 long, 
 
 
 pounds 
 
 pounds 
 
 pounds 
 
 
 pounds 
 
 pounds 
 
 pounds 
 
 Me 
 
 2.7 
 
 .015 
 
 .011 
 
 iHe 
 
 45.95 
 
 4.08 
 
 3.20 
 
 H 
 
 5.41 
 
 .055 
 
 .045 
 
 iH 
 
 48.69 
 
 4.55 
 
 3 
 
 57 
 
 3/16 
 
 8.12 
 
 .125 
 
 .1 
 
 I^/ls 
 
 51.4 
 
 5.08 
 
 3 
 
 97 
 
 H 
 
 10.76 
 
 .225 
 
 .175 
 
 iM 
 
 54.18 
 
 5.65 
 
 4 
 
 41 
 
 Ms 
 
 13.48 
 
 .350 
 
 .275 
 
 1M6 
 
 65.85 
 
 6.22 
 
 4 
 
 86 
 
 H 
 
 16.25 
 
 .51 
 
 .395 
 
 1% 
 
 59.55 
 
 6.81 
 
 5 
 
 35 
 
 ViO 
 
 19 
 
 .69 
 
 .54 
 
 iMe 
 
 62.25 
 
 7.45 
 
 5 
 
 85 
 
 Vi 
 
 21.65 
 
 .90s 
 
 .71 
 
 1K2 
 
 65 
 
 8.13 
 
 6 
 
 37 
 
 9i6 
 
 24.3 
 
 1. 15 
 
 ■ 9 
 
 l9/i6 
 
 67.75 
 
 8.83 
 
 6 
 
 92 
 
 5/i 
 
 27.13 
 
 1.4 
 
 I.I 
 
 \% 
 
 70.35 
 
 9-55 
 
 7 
 
 48 
 
 ^He 
 
 29.77 
 
 1.72 
 
 1.35 
 
 iiMe 
 
 73 
 
 10.27 
 
 8 
 
 05 
 
 % 
 
 32.46 
 
 2.05 
 
 1.66 
 
 1% 
 
 75.86 
 
 II 
 
 8 
 
 65 
 
 iS/'ie 
 
 35.18 
 
 2.4 
 
 1.85 
 
 iiMe 
 
 78.55 
 
 11.82 
 
 9 
 
 29 
 
 ?i 
 
 37.85 
 
 2.75 
 
 2.15 
 
 -I'A 
 
 81.25 
 
 12.68 
 
 9 
 
 95 
 
 iMe 
 
 40.55 
 
 3.15 
 
 2.48 
 
 iiMe 
 
 84 
 
 13. 5 
 
 10 
 
 58 
 
 I 
 
 43.29 
 
 3.65 
 
 2.85 
 
 2 
 
 86.75 
 
 14.35 
 
 II 
 
 25 
 
 Weight of Round Bolt Copper per Foot 
 
 Diameter, 
 inches 
 
 Pounds 
 
 Diameter, 
 inches 
 
 Pounds 
 
 Diameter, 
 inches 
 
 Pounds 
 
 % 
 
 .425 
 
 .756 
 
 1. 18 
 
 1.70 
 
 2.31 
 
 I 
 1% 
 
 3.02 
 3.83 
 4.72 
 5-72 
 6.81 
 
 m 
 
 Hi 
 
 2 
 
 7.99 
 9.27 
 10.64 
 12.10 
 
 
 
 
Areas and Weights of Fillets of Steel, Cast Iron and Brass 145 
 
 Areas and Weights of Fillets of Steel, Cast Iron 
 AND Brass 
 
 Calculations are based on the following weights: 
 
 Steel 489 . 6 pounds per cubic foot. 
 
 Cast iron 45° 
 
 Cast brass S04 
 
 Fig. 39. 
 
 Contributed by Ernest J. Lees. 
 
146 
 
 Materials 
 
 Gauges and Weights of Iron Wire 
 
 The sizes and weights from No. 20 to No. 40 are those of the Trenton Iron Co. 
 Trenton, N. J. 
 
 No. 
 
 Diameter, 
 
 Lineal feet 
 
 No. 
 
 Diameter, 
 
 Lineal feet 
 
 inches 
 
 to the pound 
 
 inches 
 
 to the pound 
 
 21 
 
 .031 
 
 392.772 
 
 31 
 
 .013 
 
 2232.653 
 
 22 
 
 .028 
 
 481.234 
 
 32 
 
 .012 
 
 2620.607 
 
 23 
 
 .025 
 
 603.863 
 
 33 
 
 .011 
 
 31 19 092 
 
 24 
 
 .0225 
 
 745.710 
 
 34 
 
 .010 
 
 3773.584 
 
 25 
 
 .020 
 
 943.396 
 
 35 
 
 .0095 
 
 4182.508 
 
 26 
 
 .018 
 
 1164.689 
 
 36 
 
 .009 
 
 4657.728 
 
 27 
 
 .017 
 
 1305.670 
 
 37 
 
 .0085 
 
 5222.035 
 
 28 
 
 .016 
 
 1476.869 
 
 38 
 
 .008 
 
 5896.147 
 
 29 
 
 •ois 
 
 1676.989 
 
 39 
 
 .0075 
 
 6724.291 
 
 30 
 
 .014 
 
 1925.321 
 
 40 
 
 .007 
 
 7698.253 
 
 American Steel & Wire Company 
 
 Full sizes of plain wire 
 
 Fig. 40. 
 
 Gauge 
 
 Diameter 
 of Amer- 
 ican Steel 
 
 «&Wire 
 Co. 's gauge 
 
 .2830 
 .2625 
 .2437 
 
 .2253 
 
 .2070 
 .1920 
 .1770 
 .1620 
 .1483 
 .1350 
 .1205 
 .1055 
 .0915 
 .0800 
 .0720 
 .0625 
 .0540 
 .0475 
 .0410 
 .0348 
 
 Weight 
 
 one mile, 
 
 pounds 
 
 1128.0 
 970.4 
 836.4 
 714.8 
 603.4 
 519.2 
 441.2 
 369.6 
 309 -7 
 256.7 
 204.5 
 156.7 
 117. 9 
 90.13 
 73.01 
 55.01 
 41.07 
 31.77 
 23.67 
 17.05 
 
 Feet to 
 pound 
 
 4.681 
 5.441 
 6.313 
 7.386 
 8.750 
 
 11.97 
 
 14.29 
 
 17.05 
 20.57 
 25.82 
 33.69 
 44.78 
 58.58 
 72.32 
 95.98 
 128.6 
 166.2 
 223.0 
 309.6 
 
Iron Wire 
 
 147 
 
 Iron Wire 
 
 Measured by Washburn & Moen gauge. List prices per pound. 
 
 No. 
 
 -Bright Galv^j 
 market wire "'^f^ 
 
 lized 
 iet 
 
 Annealed 
 stone wire, 
 bright or 
 
 Tinned 
 market 
 
 Tinned 
 stone 
 
 
 
 
 black 
 
 wire 
 
 wire 
 
 ooooto9 
 
 $0.10 $0 
 
 10 
 
 
 $o.is 
 
 
 lo and II 
 
 .11 
 
 II 
 
 
 .16 
 
 
 12 
 
 • iii/i 
 
 11I/2 
 
 
 .17 
 
 
 13 and 14 
 
 .12}-^ 
 
 12H 
 
 
 .17 
 
 
 15 
 
 .14 
 
 14 
 
 
 .I7i/i 
 
 
 16 
 
 .14 
 
 14 
 
 $0.14 
 
 .17}-^ 
 
 
 17 . 
 
 IS 
 
 15 
 
 .15 
 
 .18 
 
 
 18 
 
 .16 
 
 16 
 
 .16 
 
 .18^ 
 
 $o.i8H 
 
 19 
 
 • 19 
 
 19 
 
 • 19 
 
 
 .19 
 .19 
 .20 
 
 20 
 
 .20 
 .21 
 .22 
 .23 
 
 20 
 21 
 22 
 23 
 
 .20 
 
 .21 
 
 .22 
 
 / .23 
 
 
 21 
 
 
 22 
 
 
 .20 
 
 23 
 
 
 .21 
 
 24 
 
 ■ 24 
 
 24 
 
 .24 
 
 
 21 
 
 25 
 
 .25 
 
 25 
 
 .25 
 
 
 .22 
 
 26 
 
 .26 
 
 .28 
 
 26 
 28 
 
 .26 
 .28 
 
 
 .23 
 
 27 
 
 
 .24 
 
 28 
 
 .29 
 
 29 
 
 .29 
 .30 
 
 
 
 29 
 
 •30 
 
 30 
 
 
 .26 
 
 30 
 
 • 32 
 
 32 
 
 ,32 
 
 
 .27 
 
 31 
 
 .33 
 
 33 
 
 .33 
 
 
 .28 
 
 32 
 
 • 35 
 
 35 
 
 .35 
 
 
 .32 
 
 33 
 
 .37 
 
 37 
 
 .37 
 
 
 .33 
 
 ' 34 
 
 .40 
 
 40 
 
 .40 
 
 
 .34 
 
 35 
 
 • 45 
 
 45 
 
 .45 
 
 
 36 
 
 .55 
 
 55 
 
 .55 
 
 
 .48 
 
 
 
 
 • Coppered Market Wire and Coppered Bessemer Spring Wire take same list prices 
 Bright Market Wire. 
 
148 
 
 Materials 
 
 Nails and Tacks 
 
 Common Wire Nails 
 Measured by Washburn & Moen Gauge 
 
 
 Length and gauge 
 
 Approx. 
 
 Size 
 
 
 no. to 
 
 
 
 
 Inch 
 
 No. 
 
 pound 
 
 ■ 2d 
 
 I 
 
 IS 
 
 876 
 
 3d 
 
 iH 
 
 14 
 
 568 
 
 4d 
 
 iH 
 
 12^ 
 
 316 
 
 5d 
 
 l3/i 
 
 I2l/^ 
 
 271 
 
 6d 
 
 2 
 
 Il^i 
 
 181 
 
 7d 
 
 2l/i 
 
 II3/2 
 
 161 
 
 8d 
 
 2\<l 
 
 ioi/4 
 
 106 
 
 9d 
 
 2% 
 
 ioi/4 
 
 96 
 
 lod 
 
 3 
 
 9 
 
 69 
 
 I2d 
 
 3^/4 
 
 9 
 
 63 
 
 i6d 
 
 3^2 
 
 8 
 
 49 
 
 20d 
 
 4 
 
 6 
 
 31 
 
 3od 
 
 4K2 
 
 5 
 
 24 
 
 4od 
 
 5 
 
 4 
 
 18 
 
 5od 
 
 51/2 
 
 3 
 
 14 
 
 6od 
 
 6 
 
 2 
 
 II 
 
 Length and Number of Tacks to the Pound 
 
 Name, 
 
 Length, 
 
 No. to the 
 
 Name, 
 
 Length, 
 
 No. to the 
 
 ounces 
 
 inches 
 
 pound 
 
 ounces 
 
 inches 
 
 pound 
 
 I 
 
 % 
 
 16,000 
 
 10 
 
 iMs 
 
 1600 
 
 m 
 
 3/i6 
 
 10,666 
 
 12 
 
 % 
 
 1333 
 
 2 
 
 H 
 
 8,000 
 
 14 
 
 1^6 
 
 1143 
 
 2M 
 
 Me 
 
 6,400 
 
 16 
 
 % 
 
 1000 
 
 3 
 
 % 
 
 5,333 
 
 18. 
 
 me 
 
 888 
 
 4 
 
 7/i6 
 
 40,000 
 
 20 
 
 I 
 
 800 
 
 6 
 
 9/6 
 
 2,666 
 
 22 
 
 iHe 
 
 727 
 
 8 
 
 5/i 
 
 2,000 
 
 24 
 
 i\i 
 
 666 
 
United States Standard Threads 
 United States Standard Threads 
 
 149 
 
 
 
 
 
 Size of tap 
 
 
 Safe load 
 
 
 
 Diametet of 
 
 drill, giving a 
 clearance of 
 
 
 on threaded 
 bolt on 
 
 Nominal 
 
 No. of 
 
 tap at root of 
 
 i/i the height of 
 
 Area at 
 
 basis of 
 
 diarneter of 
 
 threads 
 
 thread 
 
 the original 
 
 root of 
 
 6000 pounds 
 
 screw, 
 
 per 
 
 
 
 thread triangle 
 
 thread. 
 
 stress per 
 
 inches 
 
 inch 
 
 
 
 
 square 
 inches 
 
 sq. in. of 
 section at 
 
 
 
 
 
 
 
 
 root of 
 
 ' 
 
 
 Inches 
 
 Nearest 
 64ths 
 
 Inches 
 
 Nearest 
 64ths 
 
 
 . thread, 
 pounds 
 
 H 
 
 .250 
 
 20 
 
 .185 
 
 3/i6 - 
 
 .196 
 
 13/64- 
 
 .027 
 
 162 
 
 Me 
 
 .312 
 
 18 
 
 .240 
 
 15/64 + 
 
 .252 
 
 H + 
 
 .045 
 
 270 
 
 % 
 
 .375 
 
 16 
 
 .294 
 
 1%4- 
 
 .307 
 
 5/6 - 
 
 .068 
 
 408 
 
 ^6 
 
 .437 
 
 14 
 
 .345 
 
 11/^2 + 
 
 .360 
 
 23/64 + 
 
 .093 
 
 558 
 
 H 
 
 .500 
 
 13 
 
 .400 
 
 13/32- 
 
 .417 
 
 2/64- 
 
 .126 
 
 756 
 
 Me 
 
 .562 
 
 12 
 
 .454 
 
 2%4 + 
 
 .472 
 
 15/^2 + 
 
 .162 
 
 997 
 
 ^A 
 
 .62s 
 
 II 
 
 .507 
 
 y2 "+ 
 
 .527 
 
 1%2- 
 
 .202 
 
 1,210 
 
 iHe 
 
 .687 
 
 II 
 
 .569 
 
 ri6 + 
 
 .589 
 
 19^2- 
 
 .254 
 
 1,520 
 
 % 
 
 .750 
 
 10 
 
 .620 
 
 5/8 - 
 
 .642 
 
 *l/64 + 
 
 .302 
 
 1,810 
 
 1^6 
 
 .812 
 
 10 
 
 .683 
 
 11/16- 
 
 .704 
 
 4%4 + 
 
 .366 
 
 2,190 
 
 % 
 
 .875 
 
 9 
 
 .731 
 
 4^64- 
 
 .755 
 
 3/4 + 
 
 .420 
 
 2,520 
 
 iMe 
 
 .937 
 
 9 
 
 .793 
 
 51/64- 
 
 .817 
 
 13/16 + 
 
 .494 
 
 2,960 
 
 I 
 
 1. 000 
 
 8 
 
 .838 
 
 27/^2- 
 
 .865 
 
 55/64 + 
 
 .551 
 
 3,300 
 
 iHe 
 
 1.062 
 
 8 
 
 .900 
 
 2%2- 
 
 .927 
 
 59/64 + 
 
 .636 
 
 3,810 
 
 iH 
 
 1. 125 
 
 7 
 
 .939 
 
 15/6 + 
 
 .970 
 
 31/32 + 
 
 .694 
 
 4,160 
 
 iMe 
 
 1. 187 
 
 7 
 
 1.002 
 
 I + 
 
 1.032 
 
 1H2 + 
 
 .788 
 
 4,720 
 
 iH 
 
 1.250 
 
 7 
 
 1.064 
 
 IM5 + 
 
 1.095 
 
 13/32 + 
 
 .893 
 
 5,3So 
 
 iH 
 
 1.375 
 
 6 
 
 1. 158 
 
 15/32 + 
 
 1. 215 
 
 I%2 - 
 
 1.057 
 
 6,340 
 
 i^ 
 
 1.500 
 
 6 
 
 1.283 
 
 19/32 + 
 
 1.345 
 
 111/^2 + 
 
 1.295 
 
 7.770 
 
 iH 
 
 1.625 
 
 51/2 
 
 1.389 
 
 125/64- 
 
 1.428 
 
 12/64 + 
 
 1. 515 
 
 9.090 
 
 m 
 
 I.7SO 
 
 5 
 
 1.490 
 
 131/64 + 
 
 1.534 
 
 117/^2 + 
 
 1.746 
 
 10,470 
 
 m 
 
 1.875 
 
 5 
 
 1. 615 
 
 13 9/64 + 
 
 1.659 
 
 121/32 + 
 
 2.051 
 
 12,300 
 
 2 
 
 2.000 
 
 4^2 
 
 1. 711 
 
 12^32- 
 
 1.760 
 
 14^64 - 
 
 2.302 
 
 13,800 
 
 2H 
 
 2.250 
 
 4K2 
 
 1. 961 
 
 161/64 + 
 
 2.010 
 
 2I.64 - 
 
 3.023 
 
 18,100 
 
 2K 
 
 2.500 
 
 4 
 
 2.175 
 
 211/64 + 
 
 2.230 
 
 215/64- 
 
 3.719 
 
 22,300 
 
 2% 
 
 2.750 
 
 4 
 
 2.425 
 
 22/64 + 
 
 2.480 
 
 231/64- 
 
 4.620 
 
 27,700 
 
 3 
 
 3.000 
 
 3^2 
 
 2.629 
 
 25/8 + 
 
 2.691 
 
 211/6 + 
 
 5.428 
 
 32,500 
 
 3H 
 
 3.250 
 
 3^2 
 
 2.879 
 
 2% + 
 
 2.941 
 
 215/6 + 
 
 6.510 
 
 39,000 
 
 SVi 
 
 3.500 
 
 3H 
 
 3- 100 
 
 33/32 + 
 
 3.167 
 
 31^64- 
 
 7.548 
 
 45,300 
 
 3% 
 
 3.750 
 
 3 
 
 3.317 
 
 35/6 + 
 
 3.389 
 
 325/64- 
 
 8.641 
 
 51,800 
 
 4 
 
 4.000 
 
 3 
 
 3.567 
 
 39/16 + 
 
 3.639 
 
 3*1/64- 
 
 9.963 
 
 59.700 
 
150 
 
 Materials 
 
 to 
 
 M 
 
 1 
 
 •ui -bs 
 J9d -sqi 
 OOO'OI :^v 
 
 M M ei fO ^ .o<0 « O t. JO t^ O r^ g t^jO 
 
 •m -bs 
 jad -sqi 
 oo£A :^v 
 
 
 1 
 
 3 
 fo 
 
 •ui -bs 
 
 jad -sqi 
 
 ooo'oi '^v 
 
 MMM^,ro^Ot^a.^^^^O^^^M^O;0^ 
 
 •UT •bs 
 jad -sqi 
 ooSi W 
 
 H M M of ro -* .O t^ C^ M ro tooo O JO a>0 5 
 
 1 
 
 •UT -bs jad 
 
 '^t-MO <N0O lOM rOO M lD-*<0 lOU^OO (NOO OOO 
 
 M M ^^ N ro -? t: <^ of JO 00 gj O O JO g N ^^- 
 
 •UT -bs jsd 
 •sqi ooS'zi ^V 
 
 
 ■ut -bs jad 
 •sqt ooo'oi q.v 
 
 M H (N ro '^f lO <0 oo" O N JO t^ O ro g^ t;^ <0 
 
 i 
 
 JO uionog 
 
 Oi^oOrOI>wooorOOw0^i-iooa>MQMfOrO<0 
 (O lor-roiON M <N O^H rOa>TfrO'*^*0 mO 0> 
 
 OOOOi-<MCsr0^iO<0000<N'iOt^OroOt~>0 
 
 HHHHNNfOfO-^ 
 
 ^pa 
 
 
 HWMNtNNfOro-^tO 
 
 
 
 CTioO^OiO^i^O OOiorO OOioro OOtO >0 
 
 MHHMHMHIHt-lN 
 
 
 VO lO lO 
 
 (N10I> Olio lO lO >0 lO »0 
 lOwt^fJ lOtN10I> CS10t> tSlOt^ »0 lO 
 <NOOrO'*iOiO<Ot--00 M(NroiOOt--00 C^lOl> 
 
 M W C-i H H l-i H H N n' Cq «' 
 
 Q 
 
 p^ajq^ 
 JO mo^^^og; 
 
 05oo^M^a>M^o^5^;ooog«,r<,rjc.N 
 
 OO^oi^S lOO 0^ r5^rorO<OIooooO CT.mm<o I>0< 
 M (N <N rO-*^iO<OI>OOOiO w !N ro^Ot^OiM'^r 
 
 W H H M M M H W ei pi 
 
 
 gls^Sa^sgl^HlstSSISi 
 
 HHMHMMCsiNiNrorOrorO'*-*-* »o »0 
 
 
 MHMMHHoiiNiNiNoiroi^ro-^'i-'t 
 
 
 OOlOfOOOlO lO lO lO lO lO 
 
 HMMHiHN(S<N<NiN(NrororC'^ 
 
 1 
 
 qout 
 jad spBajqx 
 
 lO lO lO 
 
 ooo^O'*rc<Nw oa>oot-t^<ovoioioiO'*-<t'*-* 
 
 jaq 
 
 aUIBTQ 
 
 OllOt^ (NIO lO lO lO lO lO 
 
 H hI M M H M M M (N N N W 
 
United States Standard Bolts and Nuts 
 
 iSi 
 
 t^<5^a»M<N o o o>o'*t^N 
 
 a> M (N TT uo i> a> 
 
 es 
 
 00 ooo c5>t^i--'^'^-*a>o^»'JO 
 OMi-iQ'^r~"^>^'*oo<OM 
 f; 00^ « 00 q> q> "2 o ^1 oo ic "* n 
 O 00* vo" ■* "* -^ "1 <o 00 w" ■^ oi r^ 
 
 001HJ>'^fO<^>OOlOt^<NfO 
 00 a»M <N ■*ir)t^O%i-i rOtOOO 
 
 ioa»oo looo i>(N •^r'jvo t--* 
 
 Mwiopo-^a^oo 6 '■o m oo in 
 
 P. "^^ "i. °°. ^. "^ 'I H! '^. "^ '^. "v 
 
 f<5 N (N n" -^ O cS pT t^ pT 00 -^ 
 
 lOO t^oo a>o M ro-^vo t^Oi 
 
 00MONl^l^iOlOQ<O0000lO 
 
 oiOiiHNoqNqjoo&io-w Q."-! 
 
 ^f<5<NM'<JoCcioOlOt^I>N'^ 
 
 (£5 lO'^lOMOO'OO ■^woo uo^r 
 •«tvO<0 H H (N i/^iot^oo rrt^oo 
 
 iC m" T? oo~ tJ m" cfi t^ i> a> o" »o 00 
 ^ooo a>o N -^tot^cyvM ■<^»ooo 
 
 t;-(N M cqcftMuiiDo^inoo Ot^ 
 
 rfuiioo cfir<5t>pft-tioPrNO 
 lOvD t^OO OiM (N 'tiot^Oiw t^ 
 
 MMtHMMMPJN 
 
 l>eiwNO>P«i/5i0O»V500 0t^ 
 r^Oi<y.i-ifs O O Oir>'*J><N'* 
 W O •^•^iJirO'^M'O t-io lOCTi 
 
 Ttioio<o a>ror~N t^iiioi <m o 
 
 iJi\0- 1> o6 Cr»i-i IN Tt-ioi>-Cr>i-i ro 
 
 OOO M t~Ti-ro<^ir)Oi^fON fO 
 qoiCMrfOvO-^OiOt^OOt-'* 
 ^OOICS '*<O00 O IN rO'*>oy3l> 
 
 o <Nvo o lOH a>t-.io'o t~o»(N 
 i>oda>w N «^i/^t-lcrii-I rr> in 00 
 
 MMMMMWC^NOIN 
 
 xf> in m m m m m 
 
 N t^VO<N l>lON t^WPJ 
 
 M oot~-»oio(r)<NM oot^"0 
 
 fOli^>0000<M'<t>000 MfOlO 
 
 N IN ei(N rororOfCPO''*'*-'*--^ 
 
 INlflt^ (NlOt^ NlOt^ 
 
 rr>n^n'^-rf-rt-'rtinininin\o 
 
 §8 
 
 §8 
 
 
 
 
 
 
 „ 
 
 ^ 
 
 
 ^ 
 
 ^ 
 
 
 H 
 
 
 -s- 
 
 ^ 
 
 J:r 
 
 f^ 
 
 rn 
 
 H, 
 
 in 
 
 8 
 
 SI 
 
 
 CO 
 
 
 
 
 
 o 
 
 
 ■^ 
 
 » 
 
 O^ 
 
 •* 
 
 N 
 
 M 
 
 ro 
 
 fC 
 
 r^ 
 
 PO 
 
 ■* 
 
 "* 
 
 '^ 
 
 ^ 
 
 •<t 
 
 m 
 
 m 
 
 n 
 
 O 
 
 1 
 
 „ 
 
 M 
 
 M 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 ^ 
 
 
 8. 
 
 
 O 
 
 
 
 
 
 
 
 ro 
 
 rr, 
 
 <£> 
 
 t^ 
 
 J> 
 
 00 
 
 OO 
 
 0-. 
 
 o^ 
 
 o 
 
 O 
 
 M 
 
 ^ 
 
 w 
 
 M 
 
 s 
 
 in 
 
 N 
 
 l_l 
 
 'Jl- 
 
 m 
 
 ^ 
 
 ^ 
 
 r^ 
 
 O 
 
 ro 
 
 2 
 
 Oi 
 
 f: 
 
 J^^'o 
 
 6^ 
 
 s 
 
 ?^ 
 
 & 
 
 ^ 
 
 ^ 
 
 ^ 
 
 to 
 
 io<o 
 
 VO 
 
 1^ 
 
 t^ 
 
 «>00 
 
 00 
 
 a> 
 
 O^ 
 
 O 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 •"i-lOUlUHo'vOO t^t>OOodoo' GTi 
 
 in in f^ I 
 
 rO ro t>6 PO f<5 
 
 t^ "O lO »A) ro ro IN 
 ei cq <N pi IN cs oi 
 
 fjrorOP^'^-^'t'^iOio 
 
152 
 
 Materials 
 
 Nuts and Washers, Number to the Pound 
 
 United States Standard Nuts 
 
 Approximate Number in One Hundred Pounds 
 
 
 Hot pressed 
 
 Cold punched 
 
 Size of 
 bolt, 
 inches 
 
 Blank 
 
 Tapped 
 
 Plain 
 
 Chamfered, 
 
 trimmed and 
 
 reamed 
 
 
 Square 
 
 Hexagon 
 
 Square 
 
 Hexagon 
 
 Square 
 blank 
 
 Hexa- 
 gon 
 blank 
 
 Square 
 blank 
 
 Hexa- 
 gon 
 blank 
 
 Mo 
 % 
 
 % 
 
 I 
 
 l3/4 
 
 1% 
 
 2 
 
 2H 
 2^ 
 23^ 
 2l^ 
 2% 
 
 3 
 
 7200 
 
 40I0 
 
 2540 
 
 1750 
 
 II7S 
 
 910 
 
 6SS 
 
 387 
 
 260 
 
 172 
 
 133 
 
 98 
 
 73 
 
 58 
 
 44 
 
 38 
 
 31 
 
 25 
 
 20 
 
 18 
 
 15 
 
 12 
 
 9 
 7 
 
 8400 
 
 5300 
 
 3070 
 
 2080 
 
 1430 
 
 1030 
 
 798 
 
 479 
 
 315 
 
 216 
 
 155 
 
 114 
 
 91 
 
 73 
 
 57 
 
 41 
 
 39 
 
 32 
 
 25 
 
 21 
 
 20 
 
 16 
 
 II 
 
 8H 
 
 7500 
 4500 
 2720 
 1900 
 1250 
 
 980 
 
 700 
 
 408 
 
 264 
 
 176 
 
 139 
 
 lOI 
 
 77 
 
 61 
 
 49 
 
 40 
 
 33 
 
 27 
 
 21 
 
 181/^ 
 
 15% 
 
 I2l/i 
 
 9H 
 7% 
 
 9000 
 
 5500 
 
 3200 
 
 2170 
 
 1512 
 
 I ISO 
 
 850 
 
 528 
 
 332 
 
 230 
 
 180 
 
 129 
 
 96 
 
 77 
 
 60 
 
 44 
 
 40 
 
 33 
 
 26 
 
 22 
 
 20H 
 
 1X3/4 
 
 9 
 
 6700 
 4100 
 2400 
 1550 
 
 IIOO 
 
 825 
 
 580 
 
 348 
 
 228 
 
 156 
 
 122 
 
 88 
 
 65 
 
 54 
 
 42 
 
 33 
 
 27 
 
 23 
 
 19 
 
 17 
 
 7500 
 
 4700 
 
 2800 
 
 1830 
 
 1300 
 
 990 
 
 700 
 
 438 
 
 290 
 
 198 
 
 140 
 
 103 
 
 77 
 
 63 
 
 50 
 
 39 
 
 31 
 
 28 
 
 24 
 
 20 
 
 7400 
 
 4000 
 
 2730 
 
 1700 
 
 1160 
 
 900 
 
 653 
 
 386 
 
 260 
 
 170 
 
 122 
 
 90 
 
 69 
 
 54 
 
 43 
 
 35 
 
 29 
 
 24 
 
 2oV4 
 
 17 
 
 IS 
 12 
 
 8880 
 
 4800 
 
 3276 
 
 2040 
 
 1392 
 
 1080 
 
 784 
 
 463 
 
 312 
 
 204 
 
 146 
 
 108 
 
 83 
 
 65 
 
 52 
 
 42 
 
 35 
 
 29 
 
 26 
 
 23 
 
 20 
 
 16 
 
Wrought Steel Plate Washers 
 Wrought Steel Plate Washers 
 
 153 
 
 Fig. 41. 
 In 200-pound Kegs. List prices per 100 pounds. 
 
 Size of 
 bolt, 
 inches 
 
 Outside 
 
 diameter, 
 
 inches 
 
 Size of hole, 
 inches 
 
 Thickness, 
 
 English 
 
 standard 
 
 wire gauge 
 
 Approximate 
 number in 
 100 pounds 
 
 Per 100 
 
 pounds 
 
 
 
 
 No. 
 
 „ 
 
 
 Me 
 
 Me 
 
 H 
 
 18 
 
 44.07S 
 
 $14.00 
 
 Vx 
 
 M 
 
 Mfl 
 
 16 
 
 13,84s 
 
 12.20 
 
 Me 
 
 % 
 
 ^ 
 
 16 
 
 11,220 
 
 11.40 
 
 % 
 
 I 
 
 Me ^ 
 
 14 
 
 6,573 
 
 10. so 
 
 Me 
 
 iH 
 
 H 
 
 14 
 
 4,261 
 
 9.70 
 
 Vi 
 
 l3/i 
 
 Me 
 
 12 
 
 2.683 
 
 9.20 
 
 Me 
 
 ^Vi 
 
 H 
 
 12 
 
 2,249 
 
 9.10 
 
 5.^ 
 
 x% 
 
 iHe 
 
 10 
 
 1,31s 
 
 9.00 
 
 M 
 
 2 
 
 iMe 
 
 10 
 
 1,013 
 
 8.80 
 
 ^i 
 
 2H 
 
 iMe 
 
 9 
 
 858 
 
 8.80 
 
 I 
 
 2l/^ 
 
 iH 
 
 9 
 
 617 
 
 8.80 
 
 x\^ 
 
 23/4 
 
 iH 
 
 9 
 
 S16 
 
 8.80 
 
 iH 
 
 3 
 
 x% 
 
 9 
 
 403 
 
 9.00 
 
 iH 
 
 3V4 
 
 iH 
 
 8 
 
 320 
 
 9.00 
 
 iH 
 
 35'^ 
 
 l^yi 
 
 8 
 
 278 
 
 9.20 
 
 iH 
 
 3M 
 
 m 
 
 8 
 
 247 
 
 9.20 
 
 l3/4 
 
 4 
 
 iH 
 
 8 
 
 224 
 
 9-So • 
 
 I^i 
 
 4i/i 
 
 2 
 
 8 
 
 200 
 
 9.50 
 
 2 
 
 45^ 
 
 2}i 
 
 8 
 
 180 
 
 9- SO 
 
 In ordering, always specify size of bolt. 
 
 Fig. 42. 
 Showing Lock Washer on Bolt. 
 
 When the nut is screwed upon the bolt, it first strikes the rib on the 
 lock washer, which, being harder than the nut, progressively upsets 
 and forces some of the metal of the nut into the thread of the bolt, 
 thereby preventing the nut from backing off or loosening. 
 
 Can be used on any make of bolt or nut. The same bolt, nut and lock 
 washer can be used as often as required. 
 
 Prices upon receipt of specifications. 
 
154 
 
 Materials 
 
 Fig. 43. 
 
 The positive lock washer is so constructed that the "body" of the 
 washer carries the load of compression and the tapered ends are thus 
 relieved and the spring is constant. The barbs, being free to move when 
 subjected to vibration, force themselves deeply into the nut and metal 
 backing. 
 
 Are reversible and can be used many times. Do not injure the nut, 
 its thread, or the threads of the bolt. 
 
Machine Bolts 
 
 155 
 
 Machine Bolts 
 
 Approximate Weight per ioo or Machine Bolts with Square 
 Heads and Square Nuts 
 
 Yi 
 
 Me 
 
 % 
 
 Pound 
 
 Pound 
 
 Pound 
 
 2.55 
 
 4-4 
 
 7.71 
 
 2.64 
 
 4.65 
 
 8.04 
 
 2.73 
 
 4.9 
 
 8.36 
 
 2.9 
 
 5.4 
 
 9.01 
 
 3.08 
 
 5.9 
 
 9.66 
 
 3-43 
 
 6.8 
 
 10.94 
 
 4-45 
 
 7.8 
 
 12.74 
 
 5. 45 
 
 8.7 
 
 14-37 
 
 6.46 
 
 9-7 
 
 15.83 
 
 7.09 
 
 10.7 
 
 17-3 
 
 7.7 
 
 II. 7 
 
 18.76 
 
 8.3 
 
 12.7 
 
 20.2 
 
 8.9 
 
 13-7 
 
 21.58 
 
 9-5 
 
 14.7 
 
 22.95 
 
 10.2 
 
 15-7 
 
 24.42 
 
 10.8 
 
 16.7 
 
 25.9 
 
 11-5 
 
 17.7 
 
 27.37 
 
 12. 1 
 
 18. 7 
 
 28.84 
 
 13.4 
 
 20.8 
 
 31.8 
 
 14.6 
 
 22.9 
 
 34.75 
 
 15.8 
 
 24.9 
 
 37.7 
 
 17 
 
 26.9 
 
 40.65 
 
 18.2 
 
 28.9 
 
 43.6 
 
 19-4 
 
 31.0 
 
 46.55 
 
 20.6 
 
 33 
 
 49-5 
 
 21.8 
 
 35 
 
 52.45 
 
 23 
 
 37 
 
 55.4 
 
 24.2 
 
 39 
 
 58.35 
 
 25.4 
 
 41 
 
 61.3 
 
 26.6 
 
 43 
 
 64.25 
 
 27.8 
 
 45 
 
 67.20 
 
 29 
 
 47 
 
 70.15 
 
 30.2 
 
 49 
 
 73.1 
 
 31.4 
 
 51 
 
 76.05 
 
 32.6 
 
 S3 
 
 79 
 
 33.8 
 
 55 
 
 81.95 
 
 35 
 
 57 
 
 84.9 
 
 36.2 
 
 59 
 
 87.8 
 
 37.4 
 
 61 
 
 90.75 
 
 38.6 
 
 63 
 
 93-7 
 
 1 
 
 He 
 
 i/i 
 
 9/i6 
 
 % 
 
 Pound 
 
 Pound 
 
 Pound 
 
 Pound 
 
 10 
 
 
 
 
 10.53 
 
 
 
 
 11.03 
 
 15-5 
 
 ■■i9;8" 
 
 28.9s 
 
 II. 9 
 
 16.7 
 
 21.6 
 
 30.89 
 
 12.8 
 
 17.9 
 
 23.4 
 
 31.83 
 
 14.5 
 
 20.4 
 
 27 
 
 36.7 
 
 17.25 
 
 24.91 
 
 31-5 
 
 41.55 
 
 18.75 
 
 27.64 
 
 33-1 
 
 45.4 
 
 20.90 
 
 29-74 
 
 36.7 
 
 49.28 
 
 23.09 
 
 32.89 
 
 40.3 
 
 53.16 
 
 25.27 
 
 34-98 
 
 43 
 
 57.04 
 
 27.50 
 
 36.01 
 
 47.3 
 
 61.9 
 
 29-59 
 
 38.61 
 
 50.9 
 
 65.77 
 
 31.68 
 
 41.22 
 
 52.9 
 
 68.9 
 
 33.9 
 
 43.82 
 
 56.5 
 
 72.77 
 
 35.73 
 
 46.42 
 
 60.7 
 
 76.71 
 
 37-56 
 
 49.02 
 
 64-3 
 
 80.58 
 
 39 
 
 51.64 
 
 67.9 
 
 84.45 
 
 43-18 
 
 56.84 
 
 75-1 
 
 92.19 
 
 47.36 
 
 62.04 
 
 82.3 
 
 99-94 
 
 51.6 
 
 67.24 
 
 89-5 
 
 107.69 
 
 55.-^6 
 
 72.44 
 
 96-7 
 
 115-44 
 
 59-92 
 
 77.64' 
 
 103.9 
 
 123.19 
 
 64.20 
 
 82.84 
 
 III. I 
 
 130.94 
 
 68.36 
 
 88.04 
 
 118. 3 
 
 138.69 
 
 72.52 
 
 93.24 
 
 125-5 
 
 146.44 
 
 76.68 
 
 98.44 
 
 132.7 
 
 154-19 
 
 80.84 
 
 103.64 
 
 139-9 
 
 161.94 
 
 85 
 
 108.83 
 
 147. 1 
 
 169.69 
 
 89.16 
 
 114.04 
 
 154.3 
 
 177-44 
 
 93-32 
 
 119.20 
 
 161. 5 
 
 185-19 
 
 97-48 
 
 124.44 
 
 168.7 
 
 192.94 
 
 lOI . 64 
 
 129.6s 
 
 175.9 
 
 200.69 
 
 105.80 
 
 134.80 
 
 183. 1 
 
 208.44 
 
 109.96 
 
 140.04 
 
 190.3 
 
 216.19 
 
 114. 12 
 
 145-24 
 
 197.5 
 
 224.94 
 
 118.28 
 
 150.44 
 
 204.7 
 
 232.19 
 
 122.44 
 
 155.64 
 
 211. 9 
 
 240.44 
 
 126.60 
 
 160.84 
 
 219. 1 
 
 248.24 
 
 130.76 
 
 166.04 
 
 226.3 
 
 254.94 
 
156 
 
 Materials 
 
 Approximate Weight per ioo of Machine Bolts with Square 
 Heads and Square Nuts — (Continued) 
 
 Length 
 
 H 
 
 % 
 
 I 
 
 iH 
 
 iH 
 
 iH 
 
 Pound 
 
 Pound 
 
 Pound 
 
 Pounds 
 
 Pounds 
 
 Pounds 
 
 H 
 
 
 
 
 
 
 
 I 
 
 
 
 
 
 
 
 47.63 
 
 
 
 
 
 
 iH 
 
 50.10 
 
 
 
 
 
 
 iH 
 
 52.57 
 
 81.25 
 
 
 
 
 
 3 
 
 57.6 
 
 90.63 
 
 . 137.50 
 
 178.00 
 
 235.37 
 
 
 2H 
 
 63.44 
 
 98.63 
 
 149.10 
 
 192.87 
 
 253.75 
 
 
 3 
 
 69.84 
 
 106.3 
 
 160.75 
 
 207.7s 
 
 272.12 
 
 '"'458" 
 
 3H 
 
 75.93 
 
 114.30 
 
 171.55 
 
 222.62 
 
 290.50 
 
 483 
 
 4 
 
 81.77 
 
 122.30 
 
 182.35 
 
 237.50 
 
 308.88 
 
 508 
 
 4W 
 
 87.61 
 
 130.30 
 
 193.15 
 
 252.38 
 
 327.2s 
 
 533 
 
 S 
 
 93. 45 
 
 138.30 
 
 203.90 
 
 267.2s 
 
 345.62 
 
 558 
 
 sH 
 
 99.46 
 
 146.30 
 
 214.75 
 
 282.13 
 
 364-00 
 
 583 
 
 6 
 
 105.13 
 
 154.30 
 
 225.65 
 
 297.00 
 
 382.37 
 
 608 
 
 \6H 
 
 III. 14 
 
 162.30 
 
 236.35 
 
 311 -87 
 
 399.22 
 
 633 
 
 7 
 
 117. 15 
 
 170.30 
 
 247.15 
 
 316.7s 
 
 416.07 
 
 658 
 
 7H 
 
 123.16 
 
 178.30 
 
 257.95 
 
 321.62 
 
 432.92 
 
 683 
 
 8 
 
 129.17 
 
 186.30 
 
 268.75 
 
 336.49 
 
 449-77 
 
 708 
 
 9 
 
 141. 19 
 
 202.30 
 
 290.3s 
 
 366.23 
 
 483.47 
 
 758 
 
 lo 
 
 153.21 
 
 218.30 
 
 311.95 
 
 395.98 
 
 517.17 
 
 808 
 
 II 
 
 165.23 
 
 234.30 
 
 333. 55 
 
 425.73 
 
 550.87 
 
 858 
 
 13 
 
 177.25 
 
 250.30 
 
 355.15 
 
 455.48 
 
 584-57 
 
 908 
 
 13 
 
 189.27 
 
 266.30 
 
 376.75 
 
 485.33 
 
 618.27 
 
 958 
 
 14 
 
 201.29 
 
 282.30 
 
 398.35 
 
 514.98 
 
 651.97 
 
 1008 
 
 IS 
 
 213.31 
 
 298.30 
 
 419.9s 
 
 544.73 
 
 685.67 
 
 1058 
 
 i6 
 
 225.33 
 
 314.30 
 
 441.55 
 
 574.48 
 
 719.37 
 
 1108 
 
 17 
 
 237.35 
 
 330.30 
 
 463.15 
 
 604.23 
 
 753.07 
 
 IIS8 
 
 i8 
 
 249.37 
 
 346.30 
 
 484.75 
 
 633.98 
 
 786.77 
 
 1208 
 
 19 
 
 361.39 
 
 362.30 
 
 506.35 
 
 663.73 
 
 610.47 
 
 1358 
 
 20 
 
 273.41 
 
 378.30 
 
 527.95 
 
 693.48 
 
 844.17 
 
 1308 
 
 31 
 
 285.43 
 
 394.30 
 
 549-55 
 
 723.23 
 
 877.17 
 
 1358 
 
 32 
 
 297-45 
 
 410.30 
 
 571. 15 
 
 752.98 
 
 911.57 
 
 1408 
 
 33 
 
 309.47 
 
 426.30 
 
 592-75 
 
 782.73 
 
 945.27 
 
 I4S8 
 
 34 
 
 321.49 
 
 442.30 
 
 614.35 
 
 812.48 
 
 978.97 
 
 1508 
 
 35 
 
 333.51 
 
 458.30 
 
 635.9s 
 
 842.23 
 
 1012.67 
 
 1558 
 
 36 
 
 345.53 
 
 464.30 
 
 657.55 
 
 871.98 
 
 1046.37 
 
 1608 
 
 37 
 
 357.55' 
 
 480.30 
 
 679.15 
 
 901.73 
 
 1080.07 
 
 1658 
 
 38 
 
 369.57 
 
 496.30 
 
 700.75 
 
 931.48 
 
 1113.77 
 
 1708 
 
 29 
 
 381.59 
 
 512. 30 
 
 722.35 
 
 961.23 
 
 1147.47 
 
 1758 
 
 30 
 
 393.61 
 
 528.30 
 
 743.95 
 
 990.98 
 
 1181.17 
 
 1808 
 
 These weights are for bolts with bolt size nuts, and with heads of diameter equal 
 to iH times diameter of bolt, and thickness equal to % times diameter of bolt. 
 
Machine Bolts 
 
 157 
 
 Machine Bolts with Square or Button Heads, Square Nuts 
 AND Finished Points 
 
 Adopted Sept. 20, 1899, to take effect Oct. i, 1899. List prices per 100. 
 
 
 
 
 
 
 
 
 Diameter, inches 
 
 
 
 
 
 Length, — 
 
 
 
 
 
 
 
 
 
 
 
 
 inches 
 
 
 
 
 
 
 %6 
 
 
 
 
 
 
 
 Yi 
 
 Me 
 
 % 7/ 
 
 ie 
 
 ¥2 
 
 and 
 
 % 
 
 'A 
 
 I 
 
 iH 
 
 iH 
 
 1I/2 $1 
 
 .70 $ 
 
 2.00 
 
 $2.40 $2 
 
 80 
 
 $3.60 
 
 $5.20 
 
 $7.20 
 
 $10.50 
 
 $15.10 
 
 $22.50 
 
 $30.00 
 
 2 I 
 
 .78 
 
 2.12 
 
 2 
 
 .56 3 
 
 00 
 
 3.86 
 
 5. 58 
 
 7.70 
 
 11.20 
 
 16.00 
 
 23.70 
 
 31. so 
 
 21^ I 
 
 .86 
 
 2.24 
 
 2 
 
 .72 3 
 
 20 
 
 4.12 
 
 5. 96 
 
 8.20 
 
 11.90 
 
 16.90 
 
 24.90 
 
 33.00 
 
 3 I 
 
 ■ 94 
 
 2.36 
 
 2 
 
 .88 3 
 
 40 
 
 4.38 
 
 6.34 
 
 8.70 
 
 12.60 
 
 17.80 
 
 26.10 
 
 34-50 
 
 zVi 2 
 
 .02 
 
 2.48 
 
 3 
 
 .04 3 
 
 60 
 
 4.64 
 
 6.72 
 
 9.20 
 
 13.30 
 
 18.70 
 
 27.30 
 
 36.00 
 
 4 2 
 
 .10 
 
 2.60 
 
 3 
 
 .20 3 
 
 80 
 
 4.90 
 
 7.10 
 
 9- 70 
 
 14.00 
 
 19.60 
 
 28.50 
 
 37. so 
 
 4K2 2 
 
 .18 
 
 2.72 
 
 3 
 
 .36 4 
 
 00 
 
 5.16 
 
 7.48 
 
 10.20 
 
 14.70 
 
 20.50 
 
 29.70 
 
 39.00 
 
 5 2 
 
 .26 
 
 2.84 
 
 3 
 
 .52 4 
 
 20 
 
 5.42 
 
 7.86 
 
 10.70 
 
 15.40 
 
 21.40 
 
 30.90 
 
 40.50 
 
 53^ 2 
 
 .34 
 
 2.96 
 
 3 
 
 68 4 
 
 40 
 
 -5.68 
 
 8.24 
 
 11.20 
 
 16.10 
 
 22.30 
 
 32.10 
 
 42.00 
 
 6 2 
 
 .42 
 
 3.08 
 
 3 
 
 84 4 
 
 60 
 
 5.94 
 
 8.62 
 
 11.70 
 
 16.80 
 
 23.20 
 
 33.30 
 
 43. SO 
 
 m 2 
 
 .50 
 
 3.20 
 
 4 
 
 00 4 
 
 80 
 
 6.20 
 
 9.00 
 
 12.20 
 
 17.50 
 
 24.10 
 
 34.50 
 
 45.00 
 
 7 2 
 
 .58 
 
 3-32 
 
 4 
 
 16 5 
 
 00 
 
 6.46 
 
 9.38 
 
 12.70 
 
 18.20 
 
 25.00 
 
 35.70 
 
 46. SO 
 
 7!/^ 2 
 
 .66 
 
 3-44 
 
 4 
 
 32 5 
 
 20 
 
 6.72 
 
 9.76 
 
 13.20 
 
 18.90 
 
 25.90 
 
 36.90 
 
 48.00 
 
 8 2 
 
 .74 . 
 
 J.S6 
 
 4 
 
 48 5 
 
 40 
 
 6.98 
 
 10.14 
 
 13.70 
 
 19.60 
 
 26.80 
 
 38.10 
 
 49. SO 
 
 9 2 
 
 .90 > 
 
 3.80 
 
 4 
 
 80 5. 
 
 80 
 
 7.50 
 
 10.90 
 
 14.70 
 
 21.00 
 
 28.60 
 
 40.50 
 
 52.50 
 
 10 3 
 
 .06 
 
 ^04 
 
 5 
 
 12 6 
 
 20 
 
 8.02 
 
 11.66 
 
 15.70 
 
 22.40 
 
 30.40 
 
 42.90 
 
 55.50 
 
 II 3 
 
 .22 ^ 
 
 t.28 
 
 5 
 
 44 6 
 
 60 
 
 8.54 
 
 12.42 
 
 16.70 
 
 23.80 
 
 32.20 
 
 45 30 
 
 58.50 
 
 12 3 
 
 .38 
 
 ^52 
 
 5 
 
 76 7. 
 
 00 
 
 9.06 
 
 13.18 
 
 17.70 
 
 25.20 
 
 34.00 
 
 47.70 
 
 61.50 
 
 13 
 
 
 
 6 
 
 08 7. 
 
 40 
 
 958 
 
 13.94 
 
 18.70 
 
 26.60 
 
 35.80 
 
 50.10 
 
 64.50 
 
 14 
 
 
 
 
 6 
 
 40 7- 
 
 80 
 
 10.10 
 
 14.70 
 
 19.70 
 
 28.00 
 
 37.60 
 
 52.50 
 
 67.50 
 
 IS 
 
 
 
 
 6 
 
 72 8. 
 
 20 
 
 10.62 
 
 15.46 
 
 20.70 
 
 29.40 
 
 39 40 
 
 54.90 
 
 70.50 
 
 16 
 
 
 
 
 7 
 
 04 8. 
 
 60 
 
 II. 14 
 
 16.22 
 
 21.70 
 
 30.80 
 
 41.20 
 
 57.30 
 
 73.50 
 
 17 
 
 
 
 
 7 
 
 2,(> 9- 
 
 00 
 
 11.66 
 
 16.98 
 
 22.70 
 
 32.20 
 
 43.00 
 
 59.70 
 
 76.50 
 
 18 
 
 
 
 
 7 
 
 68 9- 
 
 40 
 
 12.18 
 
 17.74 
 
 23.70 
 
 33.60 
 
 44.80 
 
 62.10 
 
 79.50 
 
 19 
 
 
 
 
 8 
 
 00 9. 
 
 80 
 
 12.70 
 
 18.50 
 
 24.70 
 
 3500 
 
 46.60 
 
 64.50 
 
 82.50 
 
 20 
 
 
 
 
 8 
 
 32 10. 
 
 20 
 
 13.22 
 
 19.26 
 
 25.70 
 
 36.40 
 
 48.40 
 
 66.90 
 
 85.50 
 
 21 
 
 
 
 
 
 
 
 13.74 
 
 20.02 
 
 26.70 
 
 37.80 
 
 50.20 
 
 69.30 
 
 88.50 
 
 22 
 
 
 
 
 
 
 
 14.26 
 
 20.78 
 
 27.70 
 
 39.20 
 
 52.00 
 
 71.70 
 
 91.50 
 
 23 
 
 
 
 
 
 
 
 14.78 
 
 21.54 
 
 28.70 
 
 40.60 
 
 53.80 
 
 74.10 
 
 94.50 
 
 24 
 
 
 
 
 
 
 
 15.30 
 
 22.30 
 
 29.70 
 
 42.00 
 
 55.60 
 
 76.50 
 
 97. SO 
 
 25 
 
 
 
 
 
 
 
 15.82 
 
 23.06 
 
 30.70 
 
 43.40 
 
 57.40 
 
 78.90 
 
 100.50 
 
 26 
 
 
 
 
 
 
 
 
 
 31.70 
 
 44.80 
 
 59.20 
 
 81.30 
 
 103.50 
 
 27 
 
 
 
 
 
 
 
 
 
 32.70 
 
 46.20 
 
 61.00 
 
 83.70 
 
 106.50 
 
 28 
 
 
 
 
 
 
 
 
 
 33.70 
 
 47.60 
 
 62.80 
 
 86.10 
 
 109.50 
 
 29 
 
 
 
 
 
 
 
 
 .... 
 
 34.70 
 
 49.00 
 
 64.60 
 
 88.50 
 
 112.50 
 
 30' 
 
 
 
 
 
 
 
 
 
 35.70 
 
 50.40 
 
 66.40 
 
 90.90 
 
 115.50 
 
 Bolts with hexagon heads or hexagon nuts, 10 per cent advance. 
 
 If both hexagon heads and hexagon nuts, 20 per cent advance. 
 
 Machine bolts with countersunk head, joint bolts with oblong nuts, bolts with 
 tee heads, askew heads, and eccentric heads, 10 per cent advance. 
 
 Bolts with cube heads, 20 per cent advance. 
 
 Bolts requiring extra upsets to form the head, 20 per cent advance for each extra 
 upset. 
 
 Special bolts with irregular threads and unusual dimensions of heads or nuts will 
 be charged extra at the discretion of the manufacturer. 
 
 Bolts with cotter pin hole, prices upon application. In ordering bolts with cotter 
 pin hole, state size of hole, and distance from end of bolt to center of hole. 
 
158 
 
 Materials 
 
 Bolt Ends and Lag Screws 
 
 Bolt Ends Fitted with Square Nuts* 
 
 Adopted Jan. 30, 1895, to take effect Feb. 14, 1895. 
 List prices per pound. 
 
 Fig. 44. 
 
 
 
 
 
 Fig 
 
 •45. 
 
 Size of 
 iron, 
 inches 
 
 Length, 
 inches 
 
 Length 
 
 of thread, 
 
 inches 
 
 Price per 
 pound 
 
 Size of 
 iron, 
 inches 
 
 Length, 
 inches 
 
 Length 
 
 of thread, 
 
 inches 
 
 Price 
 
 per 
 
 pound 
 
 Me 
 
 6 
 
 I 
 
 $0.20 
 
 x\^ 
 
 13 
 
 4H 
 
 $0.10 
 
 % 
 
 7 
 
 iH 
 
 .18 
 
 xM 
 
 14 
 
 5 
 
 .11 
 
 Me 
 
 7 
 
 1K2 
 
 .16 
 
 x% 
 
 15 
 
 sV^ 
 
 .11 
 
 ^ 
 
 8 
 
 2H 
 
 .14 
 
 m 
 
 16 
 
 6 
 
 .11 
 
 H 
 
 9 
 
 3 
 
 .12 
 
 1% 
 
 17 
 
 6H 
 
 .12 
 
 H 
 
 10 
 
 3H 
 
 .10 
 
 1% 
 
 18 
 
 7 
 
 .12 
 
 n 
 
 II 
 
 ZV2 
 
 .10 
 
 m 
 
 19 
 
 7^ 
 
 .12 
 
 I 
 
 12 
 
 4 
 
 .10 
 
 2 
 
 20 
 
 8 
 
 .12 
 
 * With hexagon nuts, 10 per cent advance. 
 
 Prices of bolt ends shorter than above standard lengths will be quoted upon appli- 
 cation. 
 
Weights of Nuts and Bolt Heads in Pounds 
 
 159 
 
 Coach Screws with * Square or Washer Heads; Gimlet Points 
 
 List prices per 100, 
 
 
 Diameter, inches 
 
 Length, 
 
 Yi 
 
 
 
 
 Yis 
 
 
 
 
 inches 
 
 and 
 Me 
 
 % 
 
 7/6 
 
 1/^ 
 
 and 
 
 5/8 
 
 % 
 
 li 
 
 I 
 
 1I/2 
 
 $2.25 
 
 $2.70 
 
 $3.15 
 
 $3.75 
 
 
 
 
 
 2 
 
 2.45 
 
 2.96 
 
 3-47 
 
 4. II 
 
 $6.00 
 
 
 
 
 2K2 
 
 2.6s 
 
 3.22 
 
 3.79 
 
 4.47 
 
 6.50 
 
 $9.20 
 
 
 
 3 
 
 2.85 
 
 3.48 
 
 4. II 
 
 4.83 
 
 7.00 
 
 9.90 
 
 $15.00 
 
 
 sH 
 
 3.0s 
 
 3.74 
 
 4.43 
 
 5.19 
 
 7.50 
 
 10.60 
 
 16.00 
 
 $22.00 
 
 4 
 
 3.25 
 
 4.00 
 
 4.7s 
 
 5.55 
 
 8.00 
 
 11.30 
 
 17.00 
 
 23.30 
 
 4K2 
 
 3.45 
 
 4.26 
 
 5.07 
 
 5.91 
 
 8. SO 
 
 12.00 
 
 18.00 
 
 24.60 
 
 5 
 
 3.65 
 
 4.52 
 
 5.39 
 
 ,6.27 
 
 9.00 
 
 12.70 
 
 19.00 
 
 25.90 
 
 S'A 
 
 3.85 
 
 4.78 
 
 5.71 
 
 6.63 
 
 950 
 
 13.40 
 
 20.00 
 
 27.20 
 
 6 
 
 4.05 
 
 5. 04 
 
 6.03 
 
 6.99 
 
 10.00 
 
 14.10 
 
 21.00 
 
 28.50 
 
 61/2 
 
 
 
 6.35 
 
 7.35 
 
 10.50 
 
 14.80 
 
 22.00 
 
 29.80 
 
 7 
 
 
 
 6.67 
 
 7.71 
 
 11.00 
 
 15.50 
 
 23.00 
 
 31.10 
 
 7^ 
 
 
 
 6.99 
 
 8.07 
 
 11.50 
 
 16.20 
 
 24.00 
 
 32.40 
 
 8 
 
 
 
 7.31 
 
 8.43 
 
 12.00 
 
 16.90 
 
 25.00 
 
 33.70 
 
 9 
 
 
 
 7.95 
 
 9. IS 
 
 13.00 
 
 18.30 
 
 27.00 
 
 36.30 
 
 10 
 
 
 
 
 9.87 
 
 14.00 
 
 19.70 
 
 29.00 
 
 38.90 
 
 II 
 
 
 
 
 10.59 
 
 15.00 
 
 21.10 
 
 31.00 
 
 41.50 
 
 12 
 
 
 
 
 II. 31 
 
 16.00 
 
 22.50 
 
 33.00 
 
 44.10 
 
 * Coach screws with hexagon and tee heads, 10 per cent advance. 
 
 Weights of Nuts and Bolt Heads in Pounds. Kent 
 
 For calculating the weight of long bolts. 
 
 Diameter of bolt, in inches 
 
 Weight of hexagon nut and head 
 
 Weight of square nut and head 
 
 
 .017 
 .021 
 
 .057 
 .069 
 
 1/ 
 
 .128 
 
 .164 
 
 .267 
 .320 
 
 .43 
 ■ 55 
 
 .73 
 
 .88 
 
 
 I 
 
 1. 10 
 1. 31 
 
 iH 
 
 2.14 
 
 2.56 
 
 3.78 
 4.42 
 
 1% 
 
 5.6 
 7.0 
 
 2 
 
 8.75 
 10.50 
 
 2H 
 17 
 21 
 
 3 
 
 Weight of hexagon nut and head 
 
 Weight of square nut and head 
 
 28.8 
 36.4 
 
i6o 
 
 Materials 
 
 to (N O 
 
 
 %5 
 
 <o o <r) t- 
 
 
 
 
 ^^SiS^S isa^g K^a^S 
 
 
 
 
 1"^^ o j:5^<^^5^^£i>;;5^ 
 
 
 
 .gcg ^8 R^i2^^l?^^e=^K 
 
 
 
 ^S-^JfJ^^^^f^JJ^S^^^^^ 
 
 
 2 2 8 2^a^^8^ i!?^ft8 i2g 
 
 
 ??J^^^°2S"?5??^^^g't^?:^^ 
 
 t2 
 
 ^ 
 
 ^ 
 
 8 
 
 i2 
 
 S 
 
 s^ 
 
 fttg 
 
 ^ 
 
 o 
 
 ^ 
 
 ^ 
 
 ^ 
 
 2 
 
 ^ 
 
 H 
 
 00 
 
 o» 
 
 o 
 
 2 
 
 M 
 
 N 
 
 M 
 
 ^ 
 
 i? 
 
 l> 
 
 ^ 
 
 h" 
 
 8 
 
 - 
 
 r^ 
 
 i?^i;?&^^ 8 a^R^s ^R^S 
 
 
 ovovoo t^r-oooo 0>0^0 M w cs rO'* 
 
 
 ^^^a^^^i;?2^!$ir?^ag 
 
 
 
 inioioio"Ovo<^t^oooo o^o o i-i N 
 
 
 
 a 
 
 J??>K 8 ^?^&Ji?^^^RJ^S 
 
 
 
 
 ^"^•^loioioioovo t^oooo o>a> 
 
 
 
 
 o oiooiomoioo>oo o o 
 
 rofO"^'4-4'4iOiO<OtO I>l>od 
 
 fO ro ro ro ro •^ ■* 
 
 lo lo "O vd 
 
 ro CO 00 fO 
 
 N N pi fOrororO'<i-'i-'4 
 
 Q ^ 
 
 
 c«N(N<NrorororO-^ 
 
 
 1-2 
 
 < 
 
Cap Screws 
 
 i6i 
 
 Fig. 46. 
 
 On all screws of one inch and less in diameter, and less than four inches 
 long, threads are cut f of the length. Beyond four inches, threads are 
 cut half the length. 
 
 Regular cap screws are soft and have ground heads. Special prices 
 on black heads, extra finished and case hardened screws. 
 
 Cap screws with over-sized heads take the list of regular cap screws 
 with the same-sized heads. 
 
 Price of steel screws will be 25 per cent above the price of iron. 
 
l62 
 
 Materials 
 Drop-Forged Turn-Buckles 
 
 Without Stubs 
 
 With Stubs 
 Fig. 47. 
 
 With right and left U. S. Standard thread. 
 List prices with and without stubs. 
 
 Diameter of 
 stub, inches 
 
 Inside opening 
 
 of buckle, 
 
 inches 
 
 Length over all 
 
 (including 
 stubs), inches 
 
 Each 
 
 M 
 
 3 
 
 14 
 
 $0.36 
 
 Me 
 
 3 
 
 14 
 
 .38 
 
 % 
 
 5 
 
 19K2 
 
 .40 
 
 ^16 
 
 5 
 
 19^2 
 
 .42 
 
 \^ 
 
 6 
 
 21 
 
 .45 
 
 Vi 
 
 9 
 
 24 
 
 .56 
 
 9/16 
 
 6 
 
 22 
 
 .48 
 
 ^A 
 
 6 
 
 23 
 
 .50 
 
 % 
 
 9 
 
 26 
 
 .63 
 
 % 
 
 6 
 
 23 
 
 .63 
 
 % 
 
 9 
 
 26 
 
 -79 
 
 'A 
 
 6 
 
 23 
 
 .75 
 
 n 
 
 9 
 
 26 
 
 • 94 
 
 I 
 
 6 
 
 23 
 
 .88 
 
 I 
 
 9 
 
 26 
 
 I. ID 
 
 iH 
 
 6 
 
 24 
 
 I. GO 
 
 iH 
 
 9 
 
 27 
 
 1.25 
 
 iH 
 
 6 
 
 25 
 
 1.25 
 
 m 
 
 9 
 
 28 
 
 1.56 
 
 m 
 
 6 
 
 26 
 
 1.38 
 
 iH 
 
 9 
 
 29 
 
 1.73 
 
 iH 
 
 6 
 
 26 
 
 I. SO 
 
 m 
 
 9 
 
 29 
 
 1.88 
 
 iH 
 
 6 
 
 26 
 
 1.75 
 
 m 
 
 6 
 
 27 
 
 2.00 
 
 iii 
 
 6 
 
 28 
 
 2.25 
 
 2 
 
 6 
 
 29 
 
 2.65 
 
Drop-Forged Turn-Buckles 
 
 163 
 
 Drop-Forged Turn-Buckles 
 
 With One Eye and On? Hook 
 
 n 
 
 Wi'-th Two Eyes 
 
 (^sai^^^^^gJjEs;:;;^^ 
 
 With Two Hooks 
 
 Fig. 48. 
 
 With right and left U. S. Standard thread. 
 List prices with either one hook and one eye, two eyes, or two hooks. 
 
 Diameter 
 of 
 
 Inside opening of buckle, inches 
 
 
 threaded 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 end, 
 inches 
 
 3 
 
 5 
 
 6 
 
 9 
 
 12 
 
 IS 
 
 18 
 
 24 
 
 36 
 
 48 
 
 72 
 
 H 
 
 $0.40 
 
 
 
 
 
 
 
 
 
 
 
 Me 
 
 .45 
 
 
 
 
 
 
 
 
 
 
 
 % 
 
 
 $0.6.=; 
 
 
 
 
 
 
 
 
 
 
 y% 
 
 
 
 $0.72 
 
 $0.85 
 
 $0.95 
 
 $1.15 
 
 
 
 
 
 
 v% 
 
 
 
 .80 
 
 • 95 
 
 1.05 
 
 1.30 
 
 Si. 55 
 
 $2.05 
 
 
 
 
 % 
 
 
 
 1. 10 
 
 1.25 
 
 1. 00 
 
 1.70 
 
 2.00 
 
 2.65 
 
 
 
 
 % 
 
 
 
 1. 35 
 
 1-55 
 
 1.70 
 
 2.10 
 
 2.45 
 
 3.20 
 
 
 
 
 I 
 
 
 
 1.65 
 
 1.85 
 
 2.0s 
 
 2. so 
 
 2.9s 
 
 3.80 
 
 $4.25 
 
 
 
 ^\i 
 
 
 
 2.10 
 
 2.35 
 
 2.55 
 
 3.0s 
 
 3.55 
 
 4.55 
 
 5.0s 
 
 
 
 iH 
 
 
 
 2.65 
 
 2.9s 
 
 3.2s 
 
 3.90 
 
 4. SO 
 
 5.75 
 
 6.40 
 
 $8.90 
 
 
 ^% 
 
 
 
 3.15 
 
 3.45 
 
 3.80 
 
 4.50 
 
 5.20 
 
 6.60 
 
 7.2s 
 
 10.00 
 
 
 i^ 
 
 
 
 3.70 
 
 4.05 
 
 4.4s 
 
 5.20 
 
 5. 95 
 
 7-45 
 
 8.20 
 
 11.20 
 
 $14.20 
 
 iH 
 
 
 
 4.6s 
 
 
 5.50 
 
 6.40 
 
 7-25 
 
 9.00 
 
 9.90 
 
 13.40 
 
 16.90 
 
 134 
 
 
 
 5. 30 
 
 
 6.40 
 
 7.40 
 
 8.40 
 
 10.40 
 
 11.40 
 
 15.40 
 
 19.40 
 
 x% 
 
 
 
 6.50 
 
 
 7.60 
 
 8.75 
 
 9.«5 
 
 12.10 
 
 13.25 
 
 17.7s 
 
 22.25 
 
 2 
 
 
 
 7-75 
 
 
 9.10 
 
 10.40 
 
 11.75 
 
 14.40 
 
 15.75 
 
 21.00 
 
 26.30 
 
164 
 
 Materials 
 
 P 
 
 ftftftftftS 
 SSftSSooo|oo 
 
 10 10 lO >0 10 N 
 
 •* 
 
 '■'.'.'.'.'.'.'.'. -^ So 
 
 i 
 
 :::::::: :ftft 
 
 : ; :' : : ! : ; :"^ 
 
 
 
 ::::::::: 8 8 
 
 ::::::::: "^ ^ 
 
 "r^ 
 
 
 ::::::::: ftft 
 
 
 
 n 
 
 :::::: 8 8 8 88 
 
 : : : : : :j!?ft"^^^ 
 
 i 
 
 :::::: ^8ftft8 
 
 : : : : : :^^?55^ 
 
 
 : : =2 8 8 ^^ 8 8 88 
 
 : : t^ l^-S^ f^"S J^i^'ft 
 
 
 : :S8 ^2 a Sftftft 
 
 : :2 J?If?^g^^S;t;^ 
 
 IN 
 
 ^8 2 8a.c8^ 8 8 8 8 
 
 ^ «= 2 2 J? Ji? ^ ?5 'S ;^ ^ 
 
 ;^ 
 
 i2{C^8i2ft8 8 ftfta 
 
 ^^^-^^t^^i^f^a??^^ 
 
 
 2 8^8^8^8888 
 
 ^ *-«> 2 G Si?^ S 5r"S 
 
 "S- 
 
 ^i?i^8^a^ 8ftftft 
 
 >rnO t^OiO w fOOoO rrjfO 
 
 - 
 
 eg ftR 8 ^.8 88888 
 
 rtiovoooa. cs ■sJ-VO oo» 
 
 1 
 
 ;^k^;s^i^#^|js:^;I 
 
Thumb Screws 165 
 
 Thumb Screws, Drop-Forged Steel, Threaded, U.S. Standard 
 
 Fig. so. 
 
 Can be furnished in styles A to F. 
 List prices per loo. 
 
 Diameter, 
 inches 
 
 1/^ 
 
 3/1 6 
 
 H 
 
 Me 
 
 ,« 
 
 7/16 
 
 H 
 
 ?i6 
 
 % 
 
 % 
 
 Threads 
 
 
 
 
 
 
 
 
 
 
 
 per inch 
 
 40 
 
 24 
 
 20 
 
 18 
 
 16 
 
 14 
 
 13 
 
 12 
 
 II 
 
 10 
 
 
 r ^4 
 
 S3. 20 
 
 $3.6 
 
 3 $4-10 
 
 $4. 80 
 
 I5.90 
 
 
 
 
 
 
 
 ^! 
 
 3.40 
 
 3.8 
 
 D 4 
 
 30 
 
 5-00 
 
 6.10 
 
 $7.60 
 
 $9.50 
 
 $11.70 
 
 
 
 
 M 
 
 3.60 
 
 4.CX 
 
 D 4 
 
 50 
 
 S.20 
 
 6.40 
 
 8.00 
 
 10.00 
 
 12.40 
 
 
 
 S 
 
 I 
 
 3.80 
 
 4.2 
 
 3 4 
 
 70 
 
 5. 50 
 
 6.80 
 
 8. SO 
 
 10.60 
 
 13.10 
 
 $16.00 
 
 $23.10 
 
 -s 
 
 iH 
 
 4.00 
 
 4-4 
 
 3 4 
 
 90 
 
 5.80 
 
 7.20 
 
 9.00 
 
 11.20 
 
 13.80 
 
 16.80 
 
 24.40 
 
 .s 
 
 ii^ 
 
 4.20 
 
 4.6 
 
 3 5 
 
 10 
 
 6.20 
 
 7.6c 
 
 9.50 
 
 11.90 
 
 14.60 
 
 17.80 
 
 25.80 
 
 "S 
 
 13/4 
 
 
 4.8 
 
 3 5 
 
 40 
 
 6.60 
 
 8.10 
 
 10.10 
 
 12.60 
 
 15.50 
 
 18.80 
 
 27.20 
 
 1' 
 
 2 
 
 
 
 S.o 
 
 3 5 
 
 70 
 
 7.00 
 
 8.60 
 
 10.70 
 
 13.30 
 
 16.40 
 
 19.90 
 
 28.60 
 
 2H 
 
 
 
 
 6 
 
 10 
 
 7.40 
 
 9.20 
 
 11.40 
 
 14.10 
 
 17.30 
 
 21.00 
 
 30.10 
 
 2I/2 
 
 
 
 
 
 6 
 
 SO 
 
 7.90 
 
 9.80 
 
 12.10 
 
 14.90 
 
 18.30 
 
 22.10 
 
 31.60 
 
 § 
 
 2% 
 
 
 
 
 
 6 
 
 90 
 
 8.40 
 
 10.40 
 
 12.80 
 
 15.80 
 
 19.30 
 
 23.30 
 
 33.10 
 
 J3 
 
 3 
 
 
 
 
 
 7 
 
 40 
 
 8.90 
 
 11.00 
 
 13.50 
 
 16.70 
 
 20.30 
 
 24.50 
 
 34.70 
 
 ft 
 
 3H 
 
 
 
 
 
 
 
 10.00 
 
 12.30 
 
 15.10 
 
 18.50 
 
 22.50 
 
 27.00 
 
 38.10 
 
 J 
 
 4 
 
 
 
 
 
 
 
 11.20 
 
 13.80 
 
 16.90 
 
 20.50 
 
 24.80 
 
 29.70 
 
 41.50 
 
 4'A 
 
 
 
 
 
 
 
 
 15.40 
 
 18.70 
 
 22.70 
 
 27.40 
 
 32.70 
 
 45. 20 
 
 
 5 
 
 
 
 
 
 
 
 
 17.00 
 
 20.70 
 
 25.20 
 
 30.. 30 
 
 36.00 
 
 49.60 
 
 
 sVi 
 
 
 
 
 
 
 
 
 18.80 
 
 22.90 
 
 27.80 
 
 33.30 
 
 39.60 
 
 54.30 
 
 
 .6 
 
 
 
 
 
 
 
 
 
 
 30.40 
 
 36.60 
 
 43.60 
 
 60.00 
 
i66 
 
 Materials 
 
 Round Head Iron Rivets 
 
 Approximate number in one pound. 
 
 
 
 
 
 Diameter of 
 
 wire 
 
 
 
 
 
 Length, 
 
 
 
 
 
 
 
 
 
 
 
 
 inches 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 3/i 
 
 
 
 Me 
 
 I 
 
 2 
 
 3 
 
 Yi 
 
 4 
 
 S 
 
 6 
 154 
 
 Me 
 188 
 
 7 
 221 
 
 8 
 256 
 
 9 
 
 % 
 
 
 
 
 
 
 
 
 
 
 334 
 
 H 
 
 32 
 
 42 
 
 SI 
 
 57 
 
 65" 
 
 75 
 
 80 
 
 89' 
 
 108 
 
 131 
 
 ■IS9 
 
 18S 
 
 215 
 
 278 
 
 . H 
 
 29 
 
 37 
 
 45 
 
 SO 
 
 57 
 
 67 
 
 70 
 
 78 
 
 94 
 
 114 
 
 138 
 
 158 
 
 185 
 
 238 
 
 % 
 
 26 
 
 33 
 
 41 
 
 45 
 
 51 
 
 59 
 
 63 
 
 70 
 
 84 
 
 lOI 
 
 122 
 
 139 
 
 163 
 
 208 
 
 ^ 
 
 24 
 
 30 
 
 37 
 
 41 
 
 46 
 
 54 
 
 57 
 
 63 
 
 75 
 
 91 
 
 109 
 
 123 
 
 145 
 
 185 
 
 I 
 
 22 
 
 28 
 
 34 
 
 39 
 
 42 
 
 49 
 
 52 
 
 57 
 
 68 
 
 82 
 
 98 
 
 III 
 
 131 
 
 166 
 
 iH 
 
 20 
 
 26 
 
 31 
 
 34 
 
 39 
 
 45 
 
 47 
 
 53 
 
 63 
 
 75 
 
 90 
 
 lOI 
 
 119 
 
 ISI 
 
 iH 
 
 19 
 
 24 
 
 29 
 
 32 
 
 36 
 
 42 
 
 44 
 
 49 
 
 58 
 
 69 
 
 83 
 
 93 
 
 109 
 
 138 
 
 l3/i 
 
 18 
 
 22 
 
 27 
 
 29 
 
 33 
 
 39 
 
 41 
 
 45 
 
 54 
 
 64 
 
 76 
 
 86 
 
 lOI 
 
 127 
 
 IH 
 
 17 
 
 21 
 
 25 
 
 28 
 
 31 
 
 37 
 
 38 
 
 42 
 
 SI 
 
 59 
 
 71 
 
 80 
 
 94 
 
 119 
 
 13/4 
 
 IS 
 
 18 
 
 22 
 
 24 
 
 27 
 
 33 
 
 34 
 
 40 
 
 44 
 
 55 
 
 63 
 
 70 
 
 82 
 
 104 
 
 2 
 
 13 
 
 17 
 
 20 
 
 22 
 
 25 
 
 29 
 
 30 
 
 35 
 
 40 
 
 47 
 
 S6 
 
 62 
 
 73 
 
 92 
 
 2H 
 
 12 
 
 IS 
 
 18 
 
 19 
 
 22 
 
 27 
 
 28 
 
 32 
 
 36 
 
 42 
 
 50 
 
 56 
 
 66 
 
 83 
 
 2>^ 
 
 II 
 
 14 
 
 17 
 
 18 
 
 20 
 
 24 
 
 25 
 
 29 
 
 33 
 
 39 
 
 46 
 
 50 
 
 60 
 
 75 
 
 23/i 
 
 10 
 
 13 
 
 IS 
 
 17 
 
 19 
 
 22 
 
 23 
 
 26 
 
 30 
 
 36 
 
 42 
 
 46 
 
 55 
 
 67 
 
 3 
 
 9 
 
 12 
 
 14 
 
 IS 
 
 17 
 
 21 
 
 22 
 
 24 
 
 28 
 
 33 
 
 39 
 
 43 
 
 51 
 
 64 
 
 3H 
 
 81^ 
 
 II 
 
 13 
 
 14 
 
 16 
 
 19 
 
 20 
 
 23 
 
 26 
 
 31 
 
 36 
 
 40 
 
 47 
 
 59 
 
 3>^ 
 
 8 
 
 loi/^ 
 
 12 
 
 laVi 
 
 IS 
 
 18 
 
 19 
 
 21 
 
 24 
 
 29 
 
 34 
 
 38 
 
 44 
 
 55 
 
 334 
 
 7Vi 
 
 93/4 
 
 II3/4 
 
 123/4 
 
 14 
 
 17 
 
 18 
 
 20 
 
 23 
 
 27 
 
 32 
 
 35 
 
 41 
 
 52 
 
 4 
 
 7H 
 
 9H 
 
 II 
 
 12 
 
 13 
 
 16 
 
 17 
 
 18 
 
 21 
 
 25 
 
 30 
 
 33 
 
 38 
 
 49 
 
 4H 
 
 7 
 
 83/4 
 
 loi/^ 
 
 iiH 
 
 123/4 
 
 15 
 
 16 
 
 17 
 
 20 
 
 24 
 
 
 
 
 
 4^ 
 
 6^^ 
 
 81/4 
 
 10 
 
 I03/4 
 
 12 
 
 14 
 
 15 
 
 16 
 
 19 
 
 23 
 
 
 
 
 
 4% 
 
 614 
 
 8 
 
 9H 
 
 10 
 
 IlH 
 
 133/4 
 
 143/4 
 
 IS3/4 
 
 18 
 
 22 
 
 
 
 
 
 5 
 
 6 
 
 7H 
 
 9 
 
 m 
 
 II 
 
 13 
 
 14 
 
 15 
 
 17 
 
 21 
 
 
 
 
 •• 
 
 SM 
 
 53/4 
 
 7I/4 
 
 81/^ 
 
 9M 
 
 loi/^ 
 
 12^ 
 
 13H 
 
 T-AVi 
 
 16^ 
 
 20 
 
 
 
 
 
 5H 
 
 SH 
 
 7 
 
 8/4 
 
 9 
 
 10 
 
 12 
 
 13 
 
 14 
 
 16 
 
 19 
 
 
 
 
 
 5% 
 
 5H 
 
 63/4 
 
 73/4 
 
 m 
 
 9\^ 
 
 IlH 
 
 12H 
 
 I3i/i 
 
 IS 
 
 18 
 
 
 
 
 .. 
 
 6 
 
 5 
 
 6H 
 
 7^ 
 
 m 
 
 9% 
 
 II 
 
 12 
 
 13 
 
 14 
 
 17 
 
 
 
 
 
 3}^ cents per pound, net. 
 
Dimensions of Standard Wrot Pipe 
 
 167 
 
 Dimensions of Standard Wrot Pipe 
 
 12 
 
 'it 
 
 3. 
 II 
 
 gT3 
 
 u 
 
 2 
 
 < 
 
 Ins. 
 
 Ins. 
 
 H 
 
 .269 
 
 H 
 
 .364 
 
 H 
 
 .493 
 
 H 
 
 .622 
 
 H 
 
 .824 
 
 I 
 
 1.047 
 
 iM 
 
 1.38 
 
 ii/i 
 
 1. 61 
 
 2 
 
 2.067 
 
 2l/4 
 
 2.467 
 
 3 
 
 3.066 
 
 3^^ 
 
 3.548 
 
 4 
 
 4.026 
 
 45'^ 
 
 4.508 
 
 5 
 
 5. 045 
 
 6 
 
 6.065 
 
 7 
 
 7.023 
 
 8 
 
 7.981 
 
 9 
 
 8.937 
 
 10 
 
 10.018 
 
 II 
 
 II 
 
 12 
 
 12 
 
 13 
 
 13.2s 
 
 14 
 
 14.25 
 
 IS 
 
 15.25 
 
 16 
 
 16.25 
 
 17 
 
 17.25 
 
 18 
 
 18.25 
 
 19 
 
 19.2s 
 
 20 
 
 20.25 
 
 r 
 
 .405 
 
 .54 
 .675 
 .84 
 
 I. OS 
 
 1. 315 
 1.66 
 
 1.90 
 
 2.375 
 2.875 
 
 3.50 
 
 4.00 
 
 4.50 
 
 S.oo 
 
 5.563 
 6.625 
 7.625 
 8.625 
 9.625 
 
 10. 75 
 
 11-75 
 
 12.75 
 
 14 
 
 IS 
 16 
 
 17 
 18 
 
 19 
 
 20 
 
 21 
 
 Ins. 
 
 H + H2 
 
 11/16 
 M6+H2 
 
 iMe 
 
 iMe 
 
 iii/ie 
 
 iiMe 
 
 2% 
 
 2% 
 
 3I/2 
 
 4- 
 
 4V2 
 
 5 
 
 5^/1 6 
 
 m 
 
 10% 
 
 11% 
 
 12% 
 
 14 
 15 
 16 
 17 
 18 
 19 
 
 
 X. 
 
 'rt 
 
 
 
 Q.'O 
 
 
 
 
 ,., <U 1) 
 
 
 
 G 
 
 i 
 
 •o.S 
 a3 <o 
 
 l-^-i 
 
 -S 
 
 § 
 X3X1 
 
 
 ^ 
 
 JD 0. 
 
 "S ° 
 
 *(=! 
 
 "S 
 
 feTj'o. 
 
 .a 
 
 XI 
 
 
 .ii§ 
 
 
 
 0^ 
 
 1 i ° 
 
 
 A 
 
 0^ 
 
 
 P. 
 
 si 
 
 
 
 
 Ins. 
 
 
 
 .068 
 
 27 
 
 .334 
 
 21/64 
 
 .19 
 
 •393 
 
 
 088 
 
 18 
 
 .433 
 
 7/16 
 
 .29 
 
 .522 
 
 
 091 
 
 18 
 
 .567 
 
 ?i6 
 
 .3 
 
 .658 
 
 
 109 
 
 -14 
 
 .701 
 
 11/16 
 
 • 39 
 
 • 815 
 
 
 113 
 
 14 
 
 .911 
 
 2%2 
 
 •4 
 
 1.025 
 
 
 134 
 
 iii/^ 
 
 1. 144 
 
 15^2 
 
 • SI 
 
 1.283 
 
 
 140 
 
 111/2 
 
 1.488 
 
 1I542 
 
 .54 
 
 1.627 
 
 
 145 
 
 111/2 
 
 1.727 
 
 l23/^2 
 
 .55 
 
 1.866 
 
 
 154 
 
 iii/i 
 
 2.2 
 
 27/^2 
 
 •58 
 
 2.339 
 
 
 204 
 
 8 
 
 2.62 
 
 2% 
 
 • 89 
 
 2.82 
 
 
 217 
 
 8 
 
 3.24 
 
 3/4 
 
 • 95 
 
 3.441 
 
 
 226 
 
 8 
 
 3.738 
 
 32%2 
 
 I 
 
 3.938 
 
 
 237 
 
 8 
 
 4.233 
 
 4W 
 
 1.05 
 
 4.434 
 
 
 246 
 
 8 
 
 4.733 
 
 4% 
 
 I.I 
 
 4.931 
 
 
 259 
 
 8 
 
 5.289 
 
 5%2 
 
 1. 16 
 
 5.489 
 
 
 280 
 
 8 
 
 6.347 
 
 61^2 
 
 1.26 
 
 6.547 
 
 
 301 
 
 8 
 
 7.34 
 
 71 H2 
 
 1.36 
 
 7.54 
 
 
 322 
 
 8 
 
 8.332 
 
 81 H2 
 
 1.46 
 
 8.534 
 
 
 344 
 
 8 
 
 9.324 
 
 9% 
 
 1.56 
 
 9.527 
 
 
 366 
 
 8 
 
 10.445 
 
 10^16 
 
 1.68 
 
 10.645 
 
 
 375 
 
 8 
 
 11.439 
 
 II!/l6 
 
 1.80 
 
 11.639 
 
 
 375 
 
 8 
 
 12.433 
 
 1227/64 
 
 1.90 
 
 12.633 
 
 
 375 
 
 8 
 
 13.675 
 
 13* %4 
 
 1.98 
 
 13.875 
 
 
 375 
 
 8 
 
 14.668 
 
 142 H2 
 
 2.15 
 
 14.869 
 
 
 375 
 
 8 
 
 15.662 
 
 152 H2 
 
 2.21 
 
 15.863 
 
 
 375 
 
 8 
 
 16.656 
 
 I62H2 
 
 2.30 
 
 16.856 
 
 
 375 
 
 8 
 
 17.65 
 
 172^2 
 
 2.40 
 
 17.8s 
 
 
 375 
 
 8 
 
 18.644 
 
 1841/64 
 
 2.50 
 
 18.844 
 
 
 375 
 
 8 
 
 19.637 
 
 195/i 
 
 2.59 
 
 19-837 
 
 
 375 
 
 8 
 
 20.631 
 
 20^i 
 
 2.72 
 
 20.831 
 
 
 .27 
 
 •36 
 
 • 49 
 .62 
 .82 
 I. OS 
 1.38 
 1. 61 
 2.07 
 2.47 
 3.07 
 3. 55 
 4.07 
 4. SI 
 5. 04 
 6.06 
 7.02 
 7.98 
 8.93 
 10.02 
 II 
 12 
 
 13.25 
 14.25 
 15^25 
 16.25 
 17.2s 
 18.2s 
 19.25 
 20.25 
 
 Taper of conical tube ends % inch in diameter in 12 inches. 
 
 Contributed by Louis H. Frick. No. 74, Extra Data Sheet, Machinery, October, 
 1907. 
 
 Seamless drawn brass and copper tubes are made by American 
 Tube Works, Boston, Mass.; Ansonia Brass and Copper Co., Ansonia, 
 Conn., office 19 and 21 Cliff St., New York; Benedict & Burnham Mfg. 
 Co., Waterbury, Conn., office 13 Murray St., New York; Randolph & 
 Clowes, Waterbury, Conn., and Bridgeport Brass Co., Bridgeport, 
 Conn. The following sizes are kept in stock, in 12 feet lengths, by 
 Merchant & Co., 517 Arch St., Philadelphia. The five columns signify 
 as follows: 
 
 A = outside diameter of tube in inches. 
 
i68 
 
 Materials 
 
 B = thickness of side by Stubs' (or Birmingham) gauge. When 
 seamless tubes are ordered to gauge number, it is understood that this 
 gauge is intended unless otherwise specified. 
 
 C = thickness of sides of tube in decimals of an inch. 
 
 D = weight, in pounds per lineal foot, of brass tube for columns A, 
 B and C. (For copper, add one-nineteenth). 
 
 Tubes will be furnished hard, unless ordered annealed or soft. 
 
 A 
 
 B 
 
 c 
 
 D 
 
 A 
 
 B 
 
 C 
 
 D 
 
 A 
 
 B 
 
 C 
 
 D 
 
 H 
 
 i8 
 
 .049 
 
 II 
 
 1% 
 
 13 
 
 .095 
 
 1.68 
 
 2I/2 
 
 12 
 
 109 
 
 3.02 
 
 Me 
 
 IS 
 
 .049 
 
 15 
 
 1% 
 
 II 
 
 .120 
 
 2.10 
 
 2I/2 
 
 10 
 
 134 
 
 3.68 
 
 % 
 
 17 
 
 .058 
 
 22 
 
 1% 
 
 15 
 
 .072 
 
 1.40 
 
 2H 
 
 14 
 
 083 
 
 2.44 
 
 He 
 
 17 
 
 .058 
 
 25 
 
 1% 
 
 14 
 
 .083 
 
 1. 61 
 
 2% 
 
 12 
 
 109 
 
 3.18 
 
 H 
 
 17 
 
 .058 
 
 29 
 
 m 
 
 13 
 
 .095 
 
 1.82 
 
 2% 
 
 10 
 
 134 
 
 3.87 
 
 9/16 
 
 17 
 
 .058 
 
 34 
 
 m 
 
 II 
 
 .120 
 
 2.27 
 
 2H 
 
 14 
 
 083 
 
 2.57 
 
 H 
 
 i6 
 
 .06s 
 
 42 
 
 xli 
 
 15 
 
 .072 
 
 I -50 
 
 23/4 
 
 12 
 
 109 
 
 3.37 
 
 % 
 
 i6 
 
 .065 
 
 51 
 
 m 
 
 14 
 
 .083 
 
 1.72 
 
 23/4 
 
 10 
 
 134 
 
 4.07 
 
 ''yi 
 
 i6 
 
 .065 
 
 61 
 
 m 
 
 13 
 
 .09s 
 
 1.96 
 
 2% 
 
 12 
 
 109 
 
 3.50 
 
 I 
 
 i6 
 
 .065 
 
 70 
 
 m 
 
 II 
 
 .120 
 
 2.44 
 
 2% 
 
 10 
 
 134 
 
 4.26 
 
 1% 
 
 i6 
 
 .065 
 
 79 
 
 2 
 
 14 
 
 .083 
 
 1.84 
 
 3 
 
 10 
 
 134 
 
 4.46 
 
 iH 
 
 i6 
 
 .065 
 
 88 
 
 2 
 
 13 
 
 .095 
 
 2.10 
 
 3H 
 
 10 
 
 134 
 
 4.8s 
 
 iH 
 
 14 
 
 .083 I 
 
 12 
 
 2 
 
 10 
 
 .134 
 
 2.91 
 
 3^/i 
 
 10 
 
 134 
 
 5.24 
 
 iH 
 
 II 
 
 .120 I 
 
 57 
 
 2^ 
 
 14 
 
 .083 
 
 1.97 
 
 Z% 
 
 10 
 
 134 
 
 5. 62 
 
 1% 
 
 15 
 
 .072 I 
 
 08 
 
 2}i 
 
 13 
 
 .095 
 
 2.23 
 
 4 
 
 10 
 
 134 
 
 6.00 
 
 m 
 
 14 
 
 .083 I 
 
 25 
 
 2H 
 
 10 
 
 .134 
 
 3.10 
 
 4H 
 
 10 
 
 134 
 
 6.39 
 
 x% 
 
 11 
 
 .120 I 
 
 76 
 
 2I/4 
 
 14 
 
 .083 
 
 2.08 
 
 AV2 
 
 10 
 
 134 
 
 6.78 
 
 iH 
 
 IS 
 
 .072 I 
 
 19 
 
 2l/4 
 
 13 
 
 .095 
 
 2.38 
 
 aH 
 
 10 
 
 134 
 
 7.17 
 
 iH 
 
 14 
 
 .083 I 
 
 36 
 
 2H 
 
 10 
 
 .134 
 
 3.29 
 
 5 
 
 10 
 
 134 
 
 7.56 
 
 iH 
 
 13 
 
 .095 I 
 
 55 
 
 2% 
 
 14 
 
 .083 
 
 2.20 
 
 5H 
 
 10 
 
 134 
 
 7.94 
 
 iH 
 
 II 
 
 .120 I 
 
 92 
 
 2% 
 
 13 
 
 .095 
 
 2.51 
 
 5!/^ 
 
 10 
 
 134 
 
 8.33 
 
 iH 
 
 15 
 
 .072 I 
 
 29 
 
 2% 
 
 10 
 
 .134 
 
 3.49 
 
 5M 
 
 10 
 
 134 
 
 8.72 
 
 iH 
 
 14 
 
 .083 I 
 
 48 
 
 2H 
 
 14 
 
 .083 
 
 2.33 
 
 6 
 
 10 
 
 134 
 
 9. II 
 
 Merchant & Co. supply sizes up to 7 inches outside or inside diameter, 
 and up to 16 inches inside diameter, of other gauges as well as those given 
 in the table; also tubes of special shapes, such as square, triangular, 
 octagonal, etc. ; and bronze tubes. 
 
 They also have in stock, in lengths of 12 feet, the following sizes of 
 seamless brass and copper tubing, made of same outside diameter as 
 standard sizes of iron piping, so as to be used with the same fittings as 
 the iron pipe. 
 
 A = nominal inside diameter of iron pipe, in inches. For actual 
 inside diameters. 
 
 B = outside diameter of iron pipe and of seamless tube, in inches. 
 
 C = inside diameter of seamless tube, in inches. 
 
 D = weight per foot of brass pipe. cols. B ajod C. For copper, add 
 one-nineteenth. 
 
Tin and Zinc 
 
 169 
 
 A 
 
 B 
 
 c 
 
 D 
 
 A 
 
 S 
 
 C 
 
 £> 
 
 A 
 
 B 
 
 C 
 
 D 
 
 % 
 
 1^2 
 
 H 
 
 .28 
 
 % 
 
 iHe 
 
 2%2 
 
 1.15 
 
 2 
 
 2% 
 
 2M« 
 
 4.15 
 
 H 
 
 lji2 
 
 11/^2 
 
 .43 
 
 I 
 
 iMe 
 
 I%2 
 
 I. so 
 
 2H 
 
 2yi 
 
 27l6 
 
 4. SO 
 
 % 
 
 21.^2 
 
 ^%2 
 
 .58 
 
 iVI 
 
 154 
 
 IIH2 
 
 2.25 
 
 3 
 
 ?,\^ 
 
 3M6 
 
 8.00 
 
 Vi 
 
 1^6 
 
 % 
 
 .80 
 
 11/2 
 
 l7/i 
 
 Il%2 
 
 2.55 
 
 4 
 
 Wi 
 
 4H 
 
 12.24 
 
 TIN AND ZINC 
 
 The pure metal is called block tin. — When perfectly pure (which 
 it rarely is, being purposely adulterated, frequently to a large proportion, 
 with the cheaper metals lead or zinc), its specific gravity is 7.29; and its 
 weight per cubic foot is 455 pounds. It is sufi&ciently malleable to be 
 beaten into tin foil, only Hooo of an inch thick. Its tensile strength is 
 but about 4600 pounds per square inch; or about 7000 pounds when made 
 into wire. It melts at the moderate temperature of 442° F. Pure block 
 tin is not used for common building purposes; but thin plates of sheet 
 iron covered with it on both sides constitute the tinned plates, or, as they 
 are called, the tin, used for covering roofs, rain pipes and many domestic 
 utensils. For roofs it is laid on boards. 
 
 The sheets of tin, are united as shown in this Fig. First, several 
 sheets are joined together in the shop, end for end, as at tt, by being first 
 bent over, then hammered 
 flat, and then soldered. 
 These are then formed into 
 a roll to be carried to the 
 roof, a roll being long 
 enough to reach from the 
 peak to the eaves. Dif- 
 
 FiG. SI. 
 
 ferent rolls being spread up and down the roof are then united along 
 their sides by simply being bent as at a and s, by a tool for that purpose. 
 The roofers call the bending at 5 a double groove, or double lock; arid the 
 more simple ones at t, a single groove, or lock. 
 
 To hold the tin securely to the sheeting boards, pieces of the tin 3 or 4 
 inches long, by 2 inches wide, called cleats, are nailed to the boards at 
 about every 18 inches along the joints of the rolls that are to be united, 
 and are bent over with the double groove s. This will be understood 
 from y, where the middle piece is the cleat, before being bent over. The 
 nails should be 4-penny slating nails, which have broader heads than 
 common ones. As they are not exposed to the weather, they may be of 
 plain iron. 
 
1 70 Materials 
 
 Much use is made of what is called leaded tin, or ternes, for roofing. 
 It is simply sheet iron coated with lead, instead of the more costly metal 
 tin. It is not as durable as the tinned sheets, but is somewhat cheaper. 
 
 The best plates, both for tinning and for ternes, are made of charcoal 
 iron, which, being tough, bears bending better. Coke is used for 
 cheaper plates, but inferior as regards bending. In giving orders, it is 
 important to specify whether charcoal plates or coke ones are required; 
 also whether tinned plates, or ternes. 
 
 Tinned and leaded sheets of Bessemer and other cheap steel are now 
 much used. They are sold at about the price of charcoal tin and terne 
 plates. 
 
 There are also in use for roofing, certain compound metals which resist 
 tarnish better than either lead, tin, or zinc but which are so fusible as to 
 be liable to be melted by large burning cinders falling on the roof from a 
 neighboring conflagration. 
 
 A roof covered with tin or other metal should, if possible. Slope not 
 much less than five degrees, or about an inch to a foot; and at the eaves 
 there should be a sudden fall into the rain-gutter, to prevent rain from 
 backing up so as to overtop the double-groove joint s, and thus cause 
 leaks. When coal is used for fuel, tin roofs should receive two coats of 
 paint when first put up, and a coat at every 2 or 3 years after. Where 
 wood only is used, this is not necessary; and a tin roof, with a good pitch, 
 will last 20 or 30 years. 
 
 Two good workmen can put on, and paint outside, from 250 to 300 
 square feet of tin roof, per day of 8 hours. 
 
 Tinned iron plates are sold by the box. These boxes, unUke glass, have 
 not equal areas of contents. They may be designated or ordered either 
 by their names or sizes. Many makers, however, have their private 
 brands in addition; and some of these have a much higher reputation 
 than others. 
 
Sizes and Weights of Lead Pipes 
 Sizes and Weights of Lead Pipes 
 
 171 
 
 Inner 
 diameter, 
 
 Thickness, 
 
 Weight per 
 
 Inner 
 diameter. 
 
 Thickness, 
 
 Weight per 
 
 inches 
 
 inches 
 
 foot, ounces 
 
 inches 
 
 inches 
 
 foot, pounds 
 
 % 
 
 .08 
 
 .10 
 Pounds 
 
 i3^ 
 
 .14 
 
 3.5 
 
 % 
 
 .12 
 
 1. 00 
 
 ii/^ 
 
 .17 
 
 4.2s 
 
 % 
 
 .16 
 
 1. 25 
 
 lYi 
 
 • 19 
 
 5.00 
 
 % 
 
 ■ 19 
 
 1-5 
 
 11/2 
 
 .23 
 
 6.5 
 
 H 
 
 .09 
 
 .75 
 
 iH 
 
 .27 
 
 8.0 
 
 Yi 
 
 .11 
 
 I.O 
 
 m 
 
 .13 
 
 4.0 
 
 Vi 
 
 .13 
 
 1.25 - 
 
 x% 
 
 ■ 17 
 
 S.o 
 
 Vi 
 
 .16 
 
 1.75 
 
 m 
 
 .21 
 
 6.5 
 
 Vi. 
 
 • 19 
 
 2.0 
 
 m 
 
 .27 
 
 8.5 
 
 H 
 
 .25 
 
 3.0 
 
 2 
 
 .15 
 
 4.75 
 
 54 
 
 .09 
 
 1.0 
 
 2 
 
 .18 
 
 6.0 
 
 5i 
 
 .13 
 
 1.5 
 
 2 
 
 .22 
 
 7.0 
 
 ^ 
 
 .16 
 
 2.0 
 
 2 
 
 .27 
 
 9.0 
 
 % 
 
 .20 
 
 2.5 
 
 2l/i 
 
 3/16 
 
 8.0 
 
 % 
 
 .22 
 
 2.75 
 
 2H 
 
 1/4 
 
 II. 
 
 H 
 
 .25 
 
 3-5 
 
 2I/2 
 
 Me 
 
 14.0 
 
 H 
 
 .10 
 
 1.25 
 
 2H 
 
 3/i 
 
 17.0 
 
 % 
 
 .12 
 
 1.75 
 
 3 
 
 3/i6 
 
 9.0 
 
 % 
 
 .16 
 
 2.25 
 
 3 
 
 H 
 
 12.0 
 
 % 
 
 .20 
 
 3.0 
 
 3 
 
 Me 
 
 16.0 
 
 % 
 
 .23 
 
 3-5 
 
 3 
 
 % 
 
 20.0 
 
 % 
 
 .30 
 
 4.75 
 
 3\i 
 
 3/16 
 
 9.5 
 
 I 
 
 .11 
 
 2.0 
 
 3H 
 
 H 
 
 iS.o 
 
 I 
 
 .14 
 
 2.5 
 
 35/2 
 
 Me 
 
 18.S 
 
 I 
 
 .17 
 
 3.25 
 
 3I/2 
 
 % 
 
 22.0 
 
 I 
 
 .21 
 
 4.0 
 
 4 
 
 Me 
 
 12. 5 
 
 I 
 
 .24 
 
 4-75 
 
 4 
 
 H 
 
 16.0 
 
 m 
 
 .10 
 
 2.0 
 
 4 
 
 Me 
 
 21.0 
 
 iH 
 
 .12 
 
 2.5 
 
 4 
 
 % 
 
 25.0 
 
 iH 
 
 .14 
 
 3.0 
 
 4M 
 
 Me 
 
 14.0 
 
 iH 
 
 .16 
 
 3-75 
 
 4H 
 
 H 
 
 18.0 
 
 iH 
 
 .19 
 
 4.75 
 
 5 
 
 M 
 
 20.0 
 
 iH 
 
 .25 
 
 6.00 
 
 5 
 
 % 
 
 31.0 
 
172 
 
 Materials 
 
 K--x^ k-A->| 
 
 1 1 -i^;. 
 
 •>lN|<-o4---af> 
 
 . 8 
 
 c 
 
 ^, 
 
 Vl- -^ -«^ -<«-#> X-* S*« ^ X-* Nf* 
 
 ^x rex t-(X 1-.X rnx rex »-.x f-<x rex ..^ 
 
 ^ 
 
 
 H^ 
 
 rex sjo mx spo vr- sj* sw vpi rex NflO v^ 
 
 ^ 
 
 
 ts 
 
 spO-,,)lv<lOv(IOx-*NP)s50sp» S« V* 
 
 -ix ,-.x rex t^x «x ,jx _hX «x rex mx 
 
 ^ 
 
 fO(^<^>0^>0000>0 o o o 
 
 <D CO to to 
 
 i-<X V* lOX N^ ~x-. USX v^ s^ fix se« x* 
 
 i-<x Nrf lox V!* NT- >nN. v^ sr- rex vpi Xj!< 
 rt rex rt ^x ojx rt a>x c<Sx „ -ix rK 
 
 M M M N Ol M ro -"^ rl- VO "O 
 
 *><0 Ntf5 N^ (D Ntf> v^ -^J* NO 
 
 ,-,X KX ^X spO v-" OJ"X NX N^ vpO NflO vfO S(-i 
 
 M •• m .-•X lox M £4 NX rex u5x ,-x tix 
 
 v-.spO—XvflOvr-'sjJisSO vpOx-*^^vS" 
 
 oix lox ^ tOv P.K r-fx icx reX reX r-ix .-^x 
 
 tt> N^ NSC s(0 <e N^ vjo • 
 
 M l-l i-H W M 
 
 »-hX NPO NflO Sjf N^-t V 
 
 V-< N^ N^ nP^ WS 
 rnX ,-iX U5X r-ix ^ 
 
 M IN ro CO 
 
 . i-N st-« spa s^ 
 CO t-(N NX reN. 
 
 
 2~"rt^; 
 
 v* x-i sF< rex -.^ vpo 
 
 - rex rex r-«x ^ ,-.x i^x 
 
 M M (N ts ro fO 
 
 CS N N (N 
 
 I s^ to N50 N^ vJD sp V* 
 
 . NX Sr-- rex NX U3X NX Nja* ,mX 
 Cq OSn «3 „ re IN .-hX rf 
 
 wwuMMNcoro 
 
 I NFS ^ 
 
 I vpq ,-«x S50 rex \rS- 
 
 N IN cq ro'oo °?0 
 
 .ox r^x ( 
 
 (N PJ PO fO fO •n- 
 
 ^ NSO NSO to NSO 
 
 rex se>i nn ^x v-- »ox n^o v^ 
 
 -IN -Tn lo „ NX ,(1 ^X ,-X 
 
 
 to --fO to CO nW N^ 
 
 . v-i ^N v-i vpq v-t NpO rex 05X 
 lOX _i NX «X 0>X lOX M ^ 
 
 H N ro "S- <0 
 
 O N VO O 
 
 ::S^:5;; 
 
 W ro t 10«0 00 O 
 
Chains and Cables 
 
 173 
 
 Chains and Cables 
 
 (United States Navy Standard.) 
 
 
 
 
 
 
 Load in 
 
 pounds 
 
 A 
 
 B 
 
 c 
 
 D 
 
 Pounds per 
 
 
 
 
 
 
 
 foot 
 
 Ultimate 
 
 Working 
 
 Inches 
 
 Inches 
 
 Inches 
 
 Inches 
 
 
 
 
 H 
 
 ^/i 
 
 iMe 
 
 25/32 
 
 .875 
 
 3,360 
 
 670 , 
 
 5/16 
 
 iHe 
 
 1I/2 
 
 2%2 
 
 1. 000 
 
 5,040 
 
 1,000 
 
 H 
 
 iH 
 
 l3/4 
 
 31/^2 
 
 1.70 
 
 7,280 
 
 1,460 
 
 ^6 
 
 l3/i 
 
 2M6 
 
 I%2 
 
 2.00 
 
 10,080 
 
 2,020 
 
 ^ 
 
 iiHe 
 
 2?^ 
 
 IIH2 
 
 2.50 
 
 13,440 
 
 2.690 
 
 9i6 
 
 l7/i 
 
 25/i- 
 
 Il%2 
 
 3.20 
 
 16,800 
 
 3,360 
 
 H 
 
 2M6 
 
 3 
 
 l2 3/^2 
 
 4.125 
 
 20,720 
 
 4,140 
 
 iMe 
 
 2l/i 
 
 31/4 
 
 . I2%2 
 
 S.co 
 
 25,200 
 
 5,040 
 
 M 
 
 2^ 
 
 3}^ 
 
 13^2 
 
 5.875 
 
 30,240 
 
 6,050 
 
 1%6 
 
 2IH6 
 
 3% 
 
 23/^2 
 
 6.70 
 
 35,280 
 
 7.060 
 
 % 
 
 2ji 
 
 4 
 
 27/^2 
 
 8.00 
 
 40,880 
 
 8,180 
 
 1^6 
 
 3M6 
 
 4% 
 
 215/^2 
 
 9.00 
 
 47,040 
 
 9,410 
 
 I 
 
 3H 
 
 4% 
 
 2l%2 
 
 10.70 
 
 53,760 
 
 10,750 
 
 iMe 
 
 39i6 
 
 4% 
 
 22 %2 
 
 11.20 
 
 60,480 
 
 12,100 
 
 iH 
 
 3% 
 
 5H 
 
 22 %2 
 
 12.50 
 
 68,320 
 
 13,660 
 
 1^6 
 
 3li 
 
 5%^ 
 
 3542 
 
 13.70 
 
 76,160 
 
 15,230 
 
 iH 
 
 4H 
 
 5% 
 
 3%2 
 
 16.00 
 
 84,000 
 
 17,000 
 
 iHe 
 
 4% 
 
 6H 
 
 315/^2 
 
 16.50 
 
 91,840 
 
 18,400 
 
 iH 
 
 49i6 
 
 6% 
 
 35i 
 
 18.40 
 
 101,360 
 
 20,300 
 
 i^a 
 
 4% 
 
 61 He 
 
 325/^2 
 
 19.70 
 
 109,760 
 
 21,900 
 
 i^ 
 
 5 
 
 7 
 
 33^2 
 
 21.70 
 
 120,960 
 
 24,200 
 
174 
 
 Materials 
 
 Chain End Link and Narrow Shackle 
 
 (U.S. Navy 
 Standard) 
 
 
 Standard Hexagonal Nut 
 and Head. 
 
 Fig. 54. 
 
 A 
 
 Ai 
 
 B 
 
 C 
 
 D 
 
 E 
 
 F 
 
 G 
 
 H 
 
 7 
 
 K 
 
 L 
 
 M 
 
 N 
 
 
 
 Ins. 
 
 Ins. 
 
 Ins. 
 
 Ins. 
 
 Ins. 
 
 Ins. 
 
 Ins. 
 
 Ins. 
 
 Ins. 
 
 Ins. 
 
 Ins. 
 
 Ins. 
 
 Ins. 
 
 Ins. 
 
 Ins. 
 
 %6 
 
 ^ie 
 
 1% 
 
 3H 
 
 2^^ 
 
 H 
 
 1 1/6 
 
 34 fi 
 
 iH 
 
 -lU 
 
 34 fi 
 
 o3,^ 
 
 o3^ 
 
 
 
 H 
 
 2H6 
 
 M 
 
 
 3/ 
 
 1/6 
 
 3/6 
 
 ii/ 
 
 13/ 
 
 3/6 
 
 25/ 
 
 27/ 
 
 
 
 % 
 
 11/16 
 
 21/ 
 
 4% 
 
 3 
 
 I 
 
 17/ 6 
 
 H 
 
 2 
 
 l7/ 
 
 3/6 
 
 3 
 
 33/ 
 
 
 
 iMe 
 
 34 
 
 2V^ 
 
 454 
 
 31/ 
 
 I 
 
 17/ 6 
 
 1/ 
 
 2 
 
 17/ 
 
 3/6 
 
 M 
 
 35/ 
 
 
 
 ¥i 
 
 1^6 
 
 2IM6 
 
 5 
 
 3I/ 
 
 IH 
 
 i^ie 
 
 H 
 
 21/ 
 
 2I/ 
 
 3/fp 
 
 zH 
 
 4 
 
 
 
 1%6 
 
 % 
 
 2% 
 
 5I4 
 
 3% 
 
 IH 
 
 i^ie 
 
 Me 
 
 21/ 
 
 21-^ 
 
 34 P 
 
 3% 
 
 4I/ 
 
 
 
 % 
 
 I 
 
 31/ 
 
 53/ 
 
 4H 
 
 ll/ 
 
 1II/6 
 
 5/6 
 
 21/ 
 
 23/ 
 
 1/ 
 
 41/ 
 
 45/ 
 
 5/ 
 
 3^ 
 
 15/16 
 
 1M6 
 
 39/6 
 
 6 
 
 43/ 
 
 ll/ 
 
 iii/e 
 
 5/6 
 
 21/ 
 
 23/ 
 
 1/ 
 
 4H 
 
 .■> 
 
 5/ 
 
 3H 
 
 I 
 
 iH 
 
 33/ 
 
 65,^ 
 
 45/i 
 
 II/ 
 
 2/6 
 
 3/ 
 
 3 
 
 23/ 
 
 1/ 
 
 47/ 
 
 .S3/ 
 
 5/ 
 
 37/ 
 
 iMe 
 
 l3/6 
 
 37/i 
 
 6% 
 
 aU 
 
 ll/ 
 
 21/ 6 
 
 3/ 
 
 3 
 
 23/ 
 
 H 
 
 5 
 
 5H 
 
 5/i 
 
 4 
 
 iH 
 
 ii/4 
 
 4H 
 
 7^ 
 
 51/ 
 
 l3/ 
 
 25/16 
 
 7/6 
 
 31/ 
 
 31/ 
 
 5/6 
 
 51/ 
 
 6 
 
 3/ 
 
 4^ 
 
 13/16 
 
 l5/l6 
 
 43/ 
 
 73/ 
 
 53/ 
 
 13/ 
 
 25/6 
 
 Vie 
 
 31/ 
 
 31/ 
 
 5/6 
 
 53/ 
 
 61/ 
 
 3/ 
 
 4H 
 
 T% 
 
 1% 
 
 49/6 
 
 81/ 
 
 53/ 
 
 1% 
 
 27/6 
 
 7/6 
 
 33/ 
 
 31/ 
 
 5/6 
 
 6 
 
 65/ 
 
 3/ 
 
 4^ 
 
 iMe 
 
 l7/l6 
 
 43/ 
 
 83/ 
 
 5% 
 
 l7/ 
 
 27/6 
 
 1/ 
 
 33/ 
 
 31/ 
 
 5/6 
 
 61/ 
 
 63/ 
 
 3/ 
 
 47/ 
 
 l3/i 
 
 iH 
 
 5 
 
 83/ 
 
 6I4 
 
 2 
 
 211/6 
 
 1/ 
 
 4 
 
 31/ 
 
 5/6 
 
 61/ 
 
 7H 
 
 7/ 
 
 5H 
 
 lM6 
 
 iri6 
 
 53/6 
 
 9 
 
 61/ 
 
 2 
 
 211/ 6 
 
 1/ 
 
 4 
 
 31/ 
 
 5/6 
 
 63/ 
 
 73/ 
 
 7/ 
 
 5^ 
 
 I^ 
 
 iH 
 
 5'A 
 
 95/ 
 
 67/ 
 
 2I4 
 
 3I/6 
 
 9/6 
 
 41/ 
 
 4 
 
 3/ 
 
 7 
 
 73/ 
 
 7/ 
 
 sH 
 
 1^6 
 
 iiHe 
 
 5% 
 
 9% 
 
 71/ 
 
 21/ 
 
 3I/6 
 
 ri6 
 
 41/ 
 
 4 
 
 3/ 
 
 7H 
 
 8 
 
 7/ 
 
 sH 
 
 iH 
 
 l3/i 
 
 5IM6 
 
 loi/ 
 
 73/ 
 
 21/ 
 
 37/6 
 
 5/ 
 
 5 
 
 41/ 
 
 3/ 
 
 71/ 
 
 81/ 
 
 
 6H 
 
 iiHe 
 
 113/6 
 
 6 
 
 10% 
 
 73/ 
 
 21/ 
 
 37/6 
 
 5/ 
 
 S 
 
 41/ 
 
 3/ 
 
 73/ 
 
 83/ 
 
 
 6H 
 
 l3/4 
 
 174 
 
 61/ 
 
 11% 
 
 8 
 
 23/ 
 
 31 1/6 
 
 11/6 
 
 51/ 
 
 5 
 
 7/6 
 
 8 
 
 qi/ 
 
 
 6H 
 
 113/16 
 
 115/6 
 
 6^i6 
 
 Il5/ 
 
 81/ 
 
 23/ 
 
 311/ 6 
 
 11/6 
 
 5H 
 
 5 
 
 7/6 
 
 81/ 
 
 03/ 
 
 
 6H 
 
 1^4 
 
 2 
 
 61 He 
 
 Il3/ 
 
 81/ 
 
 23/ 
 
 3IM6 
 
 11/6 
 
 51/ 
 
 5 
 
 7/6 
 
 8H 
 
 95/ 
 
 ll/ 
 
 6H 
 
 115/16 
 
 2M6 
 
 61-^ 
 
 12 
 
 83/ 
 
 23/ 
 
 311/6 
 
 11/6 
 
 51/ 
 
 5 
 
 7/6 
 
 83/ 
 
 9% 
 
 iH 
 
 6% 
 
 No. 33. Supplement to Machinery, June, 1904. 
 
Table for Eye Bolts 
 
 175 
 
 Table for Eye Bolts 
 
 (Contributed by H. A. H.) 
 
 
 
 ^_„^^ 
 
 
 r^ 
 
 
 ^ 
 
 TJ 
 
 a 
 
 
 ^ 
 
 ^ 
 
 
 
 
 '£ 
 
 
 i 
 
 c 
 
 B 
 
 ■a 
 
 II 
 
 
 
 w 
 
 
 w 
 
 
 rt 
 ^ 
 M 
 
 n 
 
 1^ 
 
 3 
 
 
 
 hi 
 
 
 
 
 
 
 -^•b 
 •^^ 
 
 
 
 
 Fig. 55- 
 
 
 XI 
 
 |co 
 
 cl 
 
 
 
 
 
 
 
 S 
 
 ^ 
 
 2h 
 
 
 
 
 
 
 
 
 12; 
 
 +J 
 
 
 A 
 
 B 
 
 c 
 
 D 
 
 E 
 
 F 
 
 G 
 
 
 M 
 
 C/3 
 
 .375 
 
 2 
 
 .75 
 
 .625 
 
 .1875 
 
 • 375 
 
 .25 
 
 16 
 
 677 
 
 750 
 
 • 5 
 
 2.125 
 
 I 
 
 .75 
 
 .25 
 
 .5 
 
 .3125 
 
 13 
 
 1,257 
 
 1,172 
 
 .625 
 
 2.25 
 
 1-25 
 
 I 
 
 .3125 
 
 .625 
 
 .4375 
 
 II 
 
 2,018 
 
 2,296 
 
 .75 
 
 2.375 
 
 I • 4375 
 
 1. 125 
 
 .3125 
 
 .6875 
 
 .5 
 
 10 
 
 3,020 
 
 3.000 
 
 .875 
 
 2.5 
 
 1.6875 
 
 1-375 
 
 .375 
 
 .75 
 
 .625 
 
 9 
 
 4,194 
 
 4,687 
 
 I 
 
 2.75 
 
 1.87s 
 
 1. 5 
 
 .4875 
 
 .875 
 
 .75 
 
 8 
 
 5,509 
 
 6,750 
 
 1. 125 
 
 2.87s 
 
 2.125 
 
 1.62s 
 
 .5 
 
 I 
 
 .8125 
 
 7 
 
 6,931 
 
 7,921 
 
 1.25 
 
 3 
 
 2.375 
 
 1.75 
 
 .5 
 
 1. 125 
 
 .875 
 
 7 
 
 8.899 
 
 9.188 
 
 1.375 
 
 3.125 
 
 2.625 
 
 1.875 
 
 .5625 
 
 I. 1875 
 
 I 
 
 6 
 
 10,541 
 
 12,000 
 
 1.5 
 
 3.25 
 
 2.75 
 
 2 
 
 .625 
 
 1.25 
 
 1.0625 
 
 6 
 
 12,938 
 
 13,546 
 
 1.625 
 
 3.375 
 
 3 
 
 2.125 
 
 .6825 
 
 1.375 
 
 1. 125 
 
 5.5 
 
 15,149 
 
 15,187 
 
 1.75 
 
 3.5 
 
 3.2s 
 
 2.25 
 
 .75 
 
 i-S 
 
 1.25 
 
 5 
 
 17,441 
 
 i8,7So 
 
 1.875 
 
 3.62s 
 
 3.5 
 
 2.375 
 
 .8125 
 
 1.62s 
 
 1.312s 
 
 5 
 
 20,490 
 
 20,671 
 
 2 
 
 3.75 
 
 3.75 
 
 2.5 
 
 .875 
 
 1-75 
 
 1.375 
 
 4.5 
 
 23,001 
 
 22.686 
 
176 
 
 Materials 
 
 Sprocket Wheels for Ordinary Link Chains 
 
 
 R=4- 
 
 Section E-F. 
 Pitch Chain Sheave. 
 
 « "= ^ (Hutfe Pag. 502-1) B 
 
 '^~\^ 
 
 Section 
 A-B. 
 
 Fig. 56. 
 
Sprocket Wheels for Ordinary Link Chains 
 
 177 
 
 
 
 ?% 
 
 Sfx^^;^^:;^.2.2.2.2.2^^2 :::::: 
 
 H 
 
 |:;"iif^j|:g:s:s^.:s:s:s^:s:sifff 
 
 «> 
 
 
 1 
 
 a 
 .2 
 
 
 
 •a 
 II 
 
 ^^S"ft&^ S;S J^lCS ^<5?J?^^ : : 
 
 2 2 2 C'^'S^ ^ S'^J(??^^g'jqS5^ : : 
 
 ^ 
 
 
 8 S^'RSa^^^-S'S^C^cS^^bf;; : : 
 
 2 2 S S ;:rt?J:8 ^ ^^^^^^^ ^^% : : 
 
 1/2 
 
 
 C^K-^-g-S ^?:?^S^SSf:?u t?>g^ . 
 
 0>0>OHrO'*tOO^Oi-(!Nroioy3>-ifOi/10 • 
 i-iMHwiHMCNiM(N(N!NCSrOroi^^ • 
 
 ^ 
 
 
 ss^^^^^8>gj"€??JJ?^^^^s^s;^ 
 
 ««>2S22>^&^a^?3S?^S'.f?,?5P5^ 
 
 ro 
 
 5d 
 
 g'S'f^^^^J^^^S Fl'Rcg^Si^ ^S"^ 
 
 °=«'^2S2^'2J:'2S^RSS!^g'f^!i5<^ 
 
 IN 
 
 
 VD<0<0 VJOUO-^-^rOM 0) N M M c?ioo r^iO'l- 
 t-^t^odoio'i-i roiovD i>-odod M 4<Oo6 pi 10 
 
 - 
 
 a. 
 
 2 
 
 So 
 
 S'S'S.^^^t^^^&^^^iS^J^^^^S.:^ 
 
 t-t^t-00 OiO P) •^•^lOVO 1^00 0-. P^ '^O C^P» 
 
 
 
 a. 
 
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 -*-^M 5 l>vO MOOVO '^TP) OOOIOOO '^O P^O 
 
 '£>'£> t^oOOO C?iM p] rOTfio<OvO t>0 PI '*l>0^ 
 
 o> 
 
 ^0 
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 -^■^^ s ?^=§ s:;^^ ^ ?i !5 J^^'^ 8 <^ s,.g 
 
 iO>/1<OI>t~OOOMPlPIPOtiiDir>OOOMrfU3 
 
 00 
 
 M 
 W 
 
 j?n?{^^'§fis?Ts.^a<!?g>n?ti§!^^f: 
 
 loioioo t^ooo M p^ P) roTfo j>a^iH po 
 
 t^ 
 
 M 
 
 ae>^5'^'&se3%^fifT^^g^3>'s^ 
 
 ■<*-rruoio<o<£> t^ooo M w P) -*ioo a>o 
 
 VO 
 
 
 
 ^^^^f?)cg?^KJ??2^R2"S5^'^5!^ 
 
 n<r)rfTti/)u-jvoj>ooooo%cno m <r!^<oi> 
 
 m 
 
 ^0 
 
 00 
 
 ^ ^^f ^S S> ^ 3. ?:^ J2 ^ ^^% ^ ?3 ^^ 
 
 fCrcro-^'^'^io^'O l^l>oooooo M PI roio 
 
 II 
 
 1 
 6 
 
 e 
 
 -a 
 c 
 
 ll 
 
 to to to 
 ^-^ HWMMMMPip^pqPtrOfOrorcifCTfioio 
 
 II "o 
 
 hHi-iMWP«P)cqNrOfOf<)';f-*-:f^iOO<Ot-t^ 
 
 II 
 
 |j|:?::I;^^;si^";^?^^'^;^2" ^:g^;g:si|: 
 
178 
 
 Materials 
 
 « ^ ;§i ;S il^ ;i^ :s: :s: s s :$: 5: 5: :s: 
 
 
 ^ 
 
 J? 
 
 % 
 
 
 °cO 
 
 ^ 
 
 ■'^ 
 
 
 fo 
 
 » M 
 
 as8 
 
 ??s 
 
 7^S ■ . . 
 
 
 
 
 o» 0^ 
 
 f^ fj-s-s 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 <g^ 
 
 §ri 
 
 
 
 
 
 •* -tt 
 
 
 
 
 
 
 
 
 
 00 00 
 
 a.?? 
 
 ^?r 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 ^^ 
 
 "S^ 
 
 
 S^a? : : 
 
 
 
 
 l> t^ 
 
 8 ?5 
 
 ^^a 
 
 P>y:i^^ : : 
 
 
 
 
 R a 
 
 ;^e> 
 
 ^s 
 
 2 ^]^g^ . 
 
 
 
 
 M M 
 
 M ?3 
 
 ^j? 
 
 9>^%%^- : 
 
 
 
 
 -ft^SR 
 
 {^^ 
 
 ^j?a ^^^ 
 
 : 
 
 
 
 ■ 
 
 
 
 •o <o 
 
 ^ a 
 
 s ^^ ^^^^^ 
 
 
 
 
 
 
 
 M l-H 
 
 ^s>?i 5? 
 
 00 00 00 00 00 00 
 
 
 
 
 
 
 g'g' 
 
 a s 
 
 g S"^^^^^?? 
 
 10 
 
 
 
 
 
 J> Ol 
 
 ^s 
 
 'S 9>P>Pi%% 
 
 ^ 
 
 
 
 
 5SS 
 
 
 j^s. 
 
 fo w CM» <0 ^ 
 
 ^ 
 
 
 "* Tj-VD 00 
 
 as; 
 
 ^^^P,^% 
 
 ^ 
 
 % 
 
 
 ss 
 
 f:J^ 
 
 ST? 
 
 ^^^)^9>^ 
 
 <2"ft 
 
 
 ■* Tl- 
 
 M m" 
 
 M C3 
 
 n'^^P>^Y^% 
 
 ^ 
 
 
 %% 
 
 ^^ 
 
 ^& 
 
 ^J^^Sgi'^ 
 
 fj 
 
 00 
 
 
 fO re 
 
 \rno 
 
 ^ a 
 
 J^'S^ 9>^^ 
 
 J^*^ 
 
 
 12 i2 
 
 ^% 
 
 :?.^ 
 
 PsftS^^-SSg 
 
 ■^ 
 
 ^ 
 
 •c^ - ■ • • 
 
 2 2 
 
 Tj- ly^ 
 
 t^ a\ 
 
 ?J J?5T^ ^f^ 
 
 ^ 
 
 ^ 
 
 ^ I ; : I 
 
 M M 
 
 ^'S 
 
 ^"2 
 
 S^SP^f^S' 
 
 eg 
 
 fo 
 
 •^ : : : : 
 
 M M 
 
 rO >rnO 00 
 
 ?5 ^^^T's a, 
 
 fo 
 
 p? 
 
 ^ ; ; ; ; 
 
 'S- Tl- 
 
 S.'^ 
 
 ^S 
 
 ? s^c^'a R 
 
 S" 
 
 r~ 
 
 ??,<s . . . 
 
 1 
 
 N-^lOt^ON-^lOt^OOOl-ll^ 
 
 MtHl-ll-l(N<N(NNN(NnrOrO 
 
 J3 
 
 II 
 
 
 .2 J3 
 
 II " 
 
 wMMMMMNC^MrrjPOroPO-cfTrioifl 
 
 C CCN «\ c*v ^X ^X tOx ^N «X CCX «\ «X COX rnX ^X W^ t~X 
 
Transmission or Standing Cables 
 
 179 
 
 Pliable Hoisting Rope 
 
 With 6 strands of 19 wires each. 
 
 Trade 
 
 
 Cir- 
 cum- 
 
 Weight 
 per foot 
 
 Breaking 
 
 strain in 
 
 tons of 2000 
 
 Proper 
 
 working 
 
 load in 
 
 tons of 2000 
 
 Circumfer- 
 ence of 
 Manila 
 rope of 
 
 Minimum 
 
 size of 
 
 drum or 
 
 sheave in 
 
 feet 
 
 num- 
 
 eter 
 
 ference 
 
 with 
 
 pounds 
 
 pounds 
 
 equal 
 
 ber 
 
 
 in 
 inches 
 
 hemp 
 center 
 
 " 
 
 
 strength 
 
 
 Iron 
 
 Steel 
 
 Iron 
 
 Steel 
 
 Iron 
 
 Steel 
 
 Iron 
 
 Steel 
 
 I 
 
 2H 
 
 6H 
 
 8.00 
 
 74.0 
 
 155.0 
 
 15.0 
 
 31.0 
 
 14.0 
 
 
 13.0 
 
 8.5 
 
 2 
 
 2 
 
 6.0 
 
 6.3 
 
 65.0 
 
 125.0 
 
 13.0 
 
 25.0 
 
 13.0 
 
 
 12.0 
 
 8.0 
 
 3 
 
 1% 
 
 5.5 
 
 5.25 
 
 54.0 
 
 106.0 
 
 II. 
 
 21.0 
 
 12.0 
 
 
 10. 
 
 7.25 
 
 4 
 
 M 
 
 S.o 
 
 4.10 
 
 44.0 
 
 86.0 
 
 9.0 
 
 17.0 
 
 II. 
 
 15.0 
 
 8.5 
 
 6.25 
 
 5 
 
 m 
 
 4.75 
 
 3.6s 
 
 39.0 
 
 77.0 
 
 8.0 
 
 iS.o 
 
 10. 
 
 14.0 
 
 7.5 
 
 5. 75 
 
 5l^ 
 
 1% 
 
 4.38 
 
 3.00 
 
 33.0 
 
 63.0 
 
 6.5 
 
 12.0 
 
 9.5 
 
 13.0 
 
 7.0 
 
 55 
 
 6 
 
 iH 
 
 4.0 
 
 2.5 
 
 27.0 
 
 52. 
 
 5.5 
 
 10. 
 
 8.5 
 
 12.0 
 
 6.5 
 
 5.0 
 
 7 
 
 iH 
 
 3-5 
 
 2.0 
 
 20.0 
 
 42.0 
 
 4.0 
 
 8.0 
 
 7.5 
 
 II. 
 
 6.0 
 
 4.5 
 
 8 
 
 1 
 
 3.13 
 
 1. 58 
 
 16.0 
 
 33.0 
 
 3.0 
 
 6.0 
 
 6.5 
 
 9.5 
 
 5.25 
 
 4.0 
 
 9 
 
 % 
 
 2.75 
 
 1.20 
 
 11.5 
 
 25.0 
 
 2.5 
 
 5.0 
 
 5.5 
 
 8.5 
 
 4.5 
 
 3.5 
 
 ID 
 
 % 
 
 2.25 
 
 0.88 
 
 8.64 
 
 18.0 
 
 1.75 
 
 3.5 
 
 4.75 
 
 7.0 
 
 4.0 
 
 3.0 
 
 loH 
 
 H 
 
 2.0 
 
 0.60 
 
 5.13 
 
 12.0 
 
 1.25 
 
 2.5 
 
 3.75 
 
 5.75 
 
 3.5 
 
 2.25 
 
 loi^ 
 
 ?i6 
 
 1.63 
 
 0.44 
 
 4.27 
 
 9.0 
 
 0.75 
 
 1.5 
 
 3.5 
 
 5.0 
 
 2.75 
 
 1.75 
 
 loH 
 
 H 
 
 1.5 
 
 0.35 
 
 3.48 
 
 7.0 
 
 0.5 
 
 i.o 
 
 3.0 
 
 4.5 
 
 2.25 
 
 1.5 
 
 loa 
 
 7/16 
 
 1.38 
 
 0.29 
 
 3.00 
 
 5.5 
 
 0.38 
 
 0.75 
 
 2.7 
 
 3.75 
 
 2.0 
 
 1. 25 
 
 lov.^ 
 
 % 
 
 1. 25 
 
 0.26 
 
 2.50 
 
 4.5 
 
 0.2s 
 
 0.5 
 
 2.5 
 
 3.5 
 
 1. 5 
 
 1.0 
 
 Transmission or Standing Cables 
 
 With 6 strands of 7 wires each. 
 
 IX 
 
 1.5 
 
 4.63 
 
 3.37 
 
 36.0 
 
 62.0 
 
 9.0 
 
 13.0 
 
 lo.o 
 
 13.0 
 
 13.0 
 
 8.5 
 
 12 
 
 1.38 
 
 4.25 
 
 2.77 
 
 30.0 
 
 52.0 
 
 7.5 
 
 10. 
 
 9.0 
 
 12.0 
 
 12.0 
 
 8.0 
 
 13 
 
 1.25 
 
 3.75 
 
 2.28 
 
 25.0 
 
 44.0 
 
 6.25 
 
 9.0 
 
 8.5 
 
 II. 
 
 10.75 
 
 7.25 
 
 14 
 
 1. 13 
 
 3.37 
 
 1.82 
 
 20.0 
 
 36.0 
 
 S.o 
 
 7.5 
 
 7-5 
 
 10. 
 
 9.5 
 
 6.25 
 
 15 
 
 1.0 
 
 3.0 
 
 1.5 
 
 16.0 
 
 30.0 
 
 4.0 
 
 6.0 
 
 6.5 
 
 9.0 
 
 8.5 
 
 5.75 
 
 16 
 
 0.88 
 
 2.62 
 
 1. 12 
 
 12.3 
 
 22.0 
 
 3.0 
 
 4.5 
 
 5.75 
 
 8.0 
 
 7.5 
 
 5.0 
 
 17 
 
 0.75 
 
 2.38 
 
 0.88 
 
 8.8 
 
 17.0 
 
 2.25 
 
 3.5 
 
 4.75 
 
 7.0 
 
 6.75 
 
 4.5 
 
 18 
 
 0.69 
 
 2.13 
 
 0.70 
 
 7.6 
 
 14.0 
 
 2.0 
 
 3.0 
 
 4.5 
 
 6.0 
 
 6.0 
 
 4.0 
 
 19 
 
 0.63 
 
 1.88 
 
 0.57 
 
 5.8 
 
 II. 
 
 1.5 
 
 2.25 
 
 4.0 
 
 5.5 
 
 5.25 
 
 3.5 
 
 20 
 
 0.56 
 
 1.63 
 
 0.41 
 
 4.1 
 
 8.0 
 
 1.0 
 
 1.75 
 
 3.25 
 
 4.75 
 
 4.5 
 
 3.0 
 
 21 
 
 0.5 
 
 1.38 
 
 0.31 
 
 2.83 
 
 6.0 
 
 0.75 
 
 1.5 
 
 2.75 
 
 4.0 
 
 4.0 
 
 2.5 
 
 22 
 
 0.44 
 
 1.25 
 
 0.23 
 
 2.13 
 
 4.5 
 
 0.50 
 
 1.25 
 
 2.5 
 
 3.5 
 
 3.25 
 
 2.25 
 
 23 
 
 0.38 
 
 1. 13 
 
 0.9 
 
 1.65 
 
 4.0 
 
 
 1.0 
 
 2.25 
 
 3.25 
 
 2.75 
 
 2.0 
 
 24 
 
 0.31 
 
 1.0 
 
 16 
 
 1.38 
 
 3.0 
 
 
 0.75 
 
 2.0 
 
 2.75 
 
 2.5 
 
 1.75 
 
 25 
 
 0.28 
 
 0.88 
 
 0.T3 
 
 1.03 
 
 2.0 
 
 
 0.5 
 
 1. 75 
 
 2.25 
 
 2.25 
 
 1.5 
 
i8o 
 
 Materials 
 
 loco f ion for Afax/'mum Mom en f. 
 
 ^ t 
 
 1 i II 
 
 -Oh- 
 
 ^-^--•fltfJ- 
 
 CS denofes center of span, 
 
 Ca cfenofes cenfer of ffrayfft/ of /oads, 
 
 fV/j denotes hea^/es f /oad od/acenf fo CG. 
 
 Let yY= fofaf /oad and //- moment. 
 
 For M a maximum p/ace CS midrvai/ 
 bettveen tV/, and CG and f/nd M under 
 W/,. Forreacf/ons, /?/- ^^ and /?r' 
 iV- Ri. For maximum moment /■f-f^i 
 0/,-(i%Z,ty*iiB), ors/nce Dc'Df,. M' 
 "^-(mi/t^Vzlz). 
 
 Iwo yVhee/s Equa// i / Loacfecf. 
 
 tfre/oad 
 
 For B'or exceeds a S3S8L, y/= ^• 
 and Rr'T^^rtj). 
 
 Notation: /ill ya/aes in/ncfjes andpounds. 
 kit =■ to fa/ /oad. >^ - /oad on one nr/>ee/. 
 L ' /engrf/7 of span. B - tynee/ l/ase. 
 Rl'/effreacf/on, /fr'r/^nfreacf/on. 
 ^' yerf/ca/ shear Teacf/'on nearest fo 
 the point under considerafion. 
 Of distance to front /yhee/ ) 
 Or = distance to rear rvhee/ > ! 
 coming on from the /eff, fff/ 'fnomenf 
 under front tvheet, one ^hee/ on tfie spafi. 
 fifs "moment under front tvhee/ nifh both 
 ivtiee/s on fhe span. /^/-/ ~ /nomenf under rear 
 trheel, one yyheel on the Span. Mrz - niomenf 
 under rear fvheet, both tfhee/s on the span. 
 CC" ya/ue of Or for ffrz a maximum. 
 M- maximum moment. Z'-seciion modu/t>S. 
 Si, 'Stress due fo bencf/ncf. 
 
 Mrz- ^''(L-Dr -§) For yalues of 3 /ess than 
 O.S8S8L, cC'i-^ and M' ^ (/-£ f. 
 
 For t>oth yyhee/s on the span, f^'Z (^^'^r-f) 
 
 Jyvo IVhee/ s Equalti / Loac/ec/, Ob//< ;/t/e ffeac//'o/7. 
 
 ..^ Notation: Same asaboye m'th addition of ; a 'Oncf/e of the reaction 
 
 "■^»s.^^^ mth beam. A" cross secfionat area of beam. T' thrust or 
 
 -(^^-^^^^•^yg pull due to oblique reaction. S" direct s/ress cfue to T 
 - -— • — - -- - — ^"^^ (tension or compression). 
 
 ■ T^CDrfj), or r'f(Drf^)cota 
 ^'i'mi(Ortih or S'^COrr§)cofa. 
 Afe, /*2, JC, M end 4> - same aS abot^e. 
 
 , . - _ W , (Drt-'/zB)cotcx . Dr(L-Dr~''^BK 
 
 ot 51,' i_ ( 2 -t- — 2r ' ' 
 
 S*St,'a maximum ivhen Df • ^ *^ k - i' in^ot a-f-^ -J. 
 ~For light y/eifft?t I- beams f' about 3 depth of beany' 
 
 Figs. 57, 58, 59. 
 
Modulus of Elasticity i8i 
 
 Modulus of Elasticity 
 
 The modulus of elasticity of any body is the ratio, within the elastic 
 limit, of the stress per unit of area to the stretch per unit of length. 
 
 Let S = stress per square inch, and 
 
 L = elongation per unit of length. 
 
 S' = total stress. 
 
 L' = total elongation. 
 
 O = original length. 
 
 A — area of cross section in square inches. 
 
 E = modulus of elasticity. 
 
 Then E = j, which is found to be practically constant, and is a 
 
 measure of the resistance which a body can oppose to change of shape. 
 
 S' 
 
 -J = S = stress per square inch, (i) 
 
 A. 
 
 u 
 
 jr = L = elongation per unit of length 
 
 Hence the modulus of elasticity is equal to the total stress, multiplied 
 by the original length, divided by the area in square inches, multiplied 
 by the total elongation. 
 
 From equation (2), 
 
 
 
 
 
 
 
 
 
 S' = 
 
 EL'A 
 
 : 
 
 
 (3) 
 
 and since 
 
 
 
 
 
 
 
 
 !- 
 
 and 
 
 V 
 = 
 
 = L, then S = 
 
 EL; 
 
 (4) 
 
 or the stress \ 
 
 per unit of 
 
 area 
 
 is equal to the modulus multipUed by 
 
 the 
 
 elongation per unit of length. 
 
 
 
 
 
 From (3), 
 
 
 
 
 
 
 
 
 
 V 
 
 S'O 
 EA 
 
 SO 
 E 
 
 
 (5) 
 
 and 
 
 
 L 
 
 5. 
 
 
 
 (6) 
 
 or the elongation per unit of length equals the stress per unit of area 
 divided by the modulus. 
 
l82 
 
 Materials 
 
 Table of Moduli of Elasticity and of Elastic Limits for 
 Different Materials 
 
 The values here given are approximate averages compiled from many sottrces. 
 Authorities differ considerably in their data on this subject. 
 
 Material 
 
 Modulus or 
 coefliciency 
 of elasticity 
 
 Stretch or compression 
 
 in a length of lo feet, 
 
 under a load of 
 
 looo lbs. per 
 sq. in. 
 
 I ton per 
 sq. in. 
 
 Ash 
 
 Beech 
 
 Birch 
 
 •Brass, cast . . 
 Brass wire... 
 
 Chestnut 
 
 Copper, cast. 
 Copper wire . 
 
 Elm 
 
 Glass 
 
 Iron, cast 
 
 Iron, cast, average 
 
 Iron, wrought, in either bars, 
 
 sheets or plates . 
 
 Iron bars, sheets, average. 
 
 Iron wire, hard 
 
 Iron wire ropes 
 
 Larch 
 
 Lead, sheet 
 
 Lead wire 
 
 Mahogany 
 
 Oak. 
 
 Oak, average 
 
 Pine, white or yellow. 
 
 Slate 
 
 Spruce 
 
 Steel bars . 
 
 Steel bars, average. 
 
 Sycamore 
 
 Teak 
 
 Tin, cast 
 
 Lbs. per 
 sq. in. 
 1,600,000 
 1,300,000 
 1,400,000 
 
 9,200,0C0 
 
 14,200,000 
 1,000,000 
 18,000,000 
 18,000,000 
 1,000,000 
 8,000,000 
 12,000,000 
 
 to 
 23,000,000 
 17.500,000 
 18,000,000 
 
 to 
 40,000,000 
 29,000,000 
 26,000,000 
 15,000,000 
 1,100,000 
 720,000 
 1,000,000 
 1 ,400,000 
 1,000,000 
 
 to 
 2,000,000 
 1,500,000 
 1,600,000 
 14,500,000 
 1,600,000 
 29,000,000 
 
 to 
 42,000,000 
 35,500,000 
 
 1,000,000 
 
 2,000,000 
 4,600,000 
 
 Ins. 
 
 .075 
 .092 
 .086 
 • 013 
 .009 
 .120 
 .007 
 .007 
 .120 
 .015 
 .010 
 to 
 
 .005 
 
 .007 
 .006 
 to 
 .003 
 .004 
 .005 
 .008 
 .109 
 .167 
 .120 
 .086 
 .120 
 to 
 .060 
 .080 
 •075 
 .008 
 .075 
 .004 
 to 
 .003 
 .003 
 .120 
 .060 
 .026 
 
 Ins. 
 
 .168 
 .207 
 .192 
 .029 
 .019 
 .269 
 .015 
 .015 
 .269 
 .034 
 .022 
 
 to 
 .012 
 .015 
 .015 
 
 to 
 .007 
 .009 
 .010 
 .018 
 .244 
 
 .192 
 .269 
 to 
 
 .134 
 
 .179 
 .168 
 .018 
 .168 
 
 .009 
 to 
 .006 
 .007 
 
Table of Deflections 
 
 183 
 
 Table of Deflections 
 
 The formulae are based on the assumption that the increase of deflec- 
 tion is proportional to the increase of load. 
 The values of the letters in the table are as follows: 
 
 d = deflection of beam in inches. 
 W — weight of extraneous load in pounds. 
 w = weight of clear span of beam in pounds. 
 / = clear span of beam in inches. 
 E = modulus of elasticity in pounds per square inch. 
 / = moment of inertia of cross section of beam in inches. . 
 
 Moduli 
 
 OF 
 
 Elasticity 
 
 OJ 
 
 Various Materials 
 
 Materials 
 
 Moduli 
 
 
 9,170,000 
 14,230,000 
 
 Brass wire 
 
 Copper 
 
 15,000,000 to 18 000 000 
 
 Lead 
 
 1,000 000 
 
 Tin cast 
 
 4,600 000 
 
 
 12,000,000 to 27,000,000 (?) 
 22,000,000 to 29,000,000 
 26,000,000 to 32 000 000 
 
 
 Steel 
 
 Marble 
 
 25,000,000 
 
 Slate 
 
 14,500,000 
 
 Glass 
 
 
 Ash 
 
 
 Beech 
 
 
 Oak 
 
 974,000 to 2,283,000 
 1,119,000 to 3,117,000, 1,926,000 
 
 306 000 
 
 Pine, longleaf 
 
 Walnut 
 
 
 
 
 
 
 
i84 
 
 Materials 
 
 S g -S .2 ^ g i^ 
 pq -2 -Si ^ G 
 
 S|=- 
 
 
 'i' 
 
 
 + 
 
 
 1 
 
 
 ? 
 
 
 
 
 "i" 
 
 
 ►^ 
 ^ 
 
 ^ 
 
 
 5 
 
 + 
 ^ 
 
 ^ 
 
 t 
 
 ^ 
 
 + 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 rO 
 
 H 
 
 CO 
 
 H 
 
 ^ 
 
 ^ 
 
 % 
 
 M 
 
 M 
 
 ^ 
 
 H 
 
 ■r! cS 
 
 pq j3 
 
 1^ 11^ IIS lis 
 
 lO 00 1/5 
 
 IS 
 
 113 IIS lia lla 
 
 lla lis 
 -Is -i« 
 
Modulus of Rupture 
 
 i8S 
 
 From the table, it is found that for beams of similar cross section and 
 of same material, and within the elastic limit, the load and deflections 
 (neglecting the weight of the beam itself) are as follows: 
 
 Deflections Under Given Extraneous Loads 
 
 With same span. 
 
 With same span and breadth ... 
 
 With same span and depth 
 
 With same breadth and depth . . . 
 
 Inversely as the breadths and as the cubes of 
 
 the depths 
 Inversely as the cubes of the depths 
 Inversely as the breadths 
 Directly as the cube of the span 
 
 Extraneous Loads eor a Given Deflection 
 
 With the same span 
 
 Directly as the breadths and as the cubes of 
 
 With the same span and breadth . 
 With the same span and depth — 
 With the same breadth and depth . 
 
 the depths 
 Directly as the cubes of the depths 
 Directly as the breadth 
 Inversely as the cubes of the spans 
 
 Modulus of Rupture 
 
 The modulus of rupture is the total resistance, in pounds per square 
 inch, of the fibres of a beam farthest from the neutral axis; and is iS 
 times the center breaking load in pounds, of a beam of the given material, 
 I inch square by i foot span. The values of the modulus of rupture, 
 which is usually denoted by "C," may be obtained from the following 
 table of transverse strengths, by multiplying the values therein by i8. 
 
 One-third part of any of these constants (except those for 
 wrought iron and steel) may be taken in ordinary practice as about the 
 average constant for the greatest center load within the elastic limit. The 
 loads here given for wrought iron and steel are already the greatest 
 within elastic limits. 
 
 Transverse strengths, in pounds 
 
 li 
 
 II 
 
 11 
 
 WOODS 
 
 Ash: 
 
 English 
 
 Amer. White (Traut.) 
 
 Swamp 
 
 Black 
 
 Arbor VitcB, Amer 
 
 Balsam, Canada 
 
 Beech, Amer 
 
 Birch: 
 
 Amer. Black 
 
 Amer. Yellow 
 
 Cedar: 
 
 Bermuda 
 
 Guadaloupe 
 
 Amer. White or Arbor 
 
 Vitae 
 
 Chestnut 
 
 Elm: 
 
 Amer. White 
 
 Rock, Canada 
 
 Hemlock 
 
 650 
 650 
 400 
 600 
 250 
 350 
 850 
 
 550 
 850 
 
 400 
 600 
 
 250 
 
 450 
 
 650 
 800 
 500 
 
 Hickory: 
 
 Amer 
 
 Amer. Bitter nut 
 
 Iron Wood, Canada , 
 
 Locust , 
 
 Lignum Vitce 
 
 Larch 
 
 Mahogany 
 
 Mangrove: 
 
 White 
 
 Black 
 
 Maple: 
 
 B"lack 
 
 Soft 
 
 Oak- 
 English 
 
 Amer. White (by Traut.). . . 
 
 Amer. Red, Black, Basket. 
 
 Live 
 
 Pine: 
 
 Amer. White (by Traut.). . . 
 
 Amer. Yellow* (by Traut.). 
 
 800 
 800 
 600 
 700 
 650 
 400 
 750 
 
 650 
 SSO 
 
 750 
 750 
 
 SSO 
 600 
 850 
 600 
 
 450 
 500 
 
i86 
 
 Materiak 
 
 Transverse strengths, in pounds — (Continued) 
 
 Pine: 
 
 Amer. Pitch* (by Traut.) 
 
 Georgia* 
 
 Poplar 
 
 Poon 
 
 Spruce: 
 
 (By Traut.).. 
 
 Black 
 
 Sycamore 
 
 Tamarack 
 
 Teak 
 
 Walnut 
 
 Willow 
 
 Metals 
 
 Brass 
 
 Iron, cast: 
 
 1500 to 2700, average 
 
 Common pig 
 
 Castings from pig 
 
 Employed in our tables 
 
 For castings 2}^ or 3 ins. thick. . 
 Iron, wrought, 1900 to 2600, average 
 
 Wrought iron does not break; 
 but at about the average of 2250 
 pounds its elastic limit is reached. 
 Steel, hammered or rolled; elas- 
 ticity destroyed by 3000 to 7000. 
 
 Under heavy loads hard steel 
 snaps like cast iron , and soft steel 
 bends like wrought iron. 
 
 Stones, etc. 
 Blue stone flagging, Hudson River. 
 Brick: 
 
 Common, 10 to 30, average 
 
 Good Amer. pressed, 30 to 50, 
 
 average 
 
 Caen Stone 
 
 Cement, Hydraulic: 
 
 English Portland, artificial, 
 7 days in water 
 
 I year in water 
 
 Portland, Kingston, N. Y., 7 
 days in water 
 
 550 
 700 
 
 450 
 550' 
 500 
 400 
 750 
 550 
 350 
 
 850 
 
 2100 
 2000 
 2300 
 2025 
 1800? 
 2250 
 
 30 
 
 days 
 
 Cement Hydraulic: 
 
 Saylor's Portland, 7 
 water 
 
 Common U. S. cements, 7 
 days in water 
 
 The following hydraulic ce- 
 ments were made into prisms, in 
 vertical moulds, under a pressure 
 of 32 pounds per square inch, and 
 were kept in sea water for i year. 
 Portland Cement, English, pure, 
 
 I year old 
 
 Roman Cement, Scotch, pure 
 
 American Cements, pure, average 
 
 about 
 
 Granite: 
 
 50 to 150, average 
 
 Qtiincy 
 
 Glass, Millville, New Jersey, 
 
 thick flooring (by Traut.) 
 
 Mortar: 
 
 Of lime alone, 60 days old 
 
 I measure of slacked lime in 
 powder, i sand 
 
 I measure of slacked lime in 
 
 powder, 2 sand 
 
 Marble: 
 
 Italian, White. 
 
 Manchester, Vt., White 
 
 East Dorset, Vt., White 
 
 Lee, Mass., White 
 
 Montgomery Co., Pa., Gray. .. . 
 
 Montgomery Co., Pa., Clouded. 
 
 Rutland, Vt., Gray 
 
 Glenn's Falls, N. Y., Black. . . . 
 
 Baltimore, Md., White coarse. . . 
 
 Oolites, 20 to 50 
 
 Sandstones: 
 
 20 to 70, average 
 
 Red of Connecticut and New 
 
 Jersey 
 
 Slate, laid on its bed, 200 to 450, 
 
 average 
 
 100 
 100 
 
 170 
 10 
 
 116 
 
 95 
 III 
 
 86 
 103 
 142 
 
 70 
 155 
 102 
 
 35 
 
 45 
 
 45 
 
 32s 
 
 Trautwine. 
 
Moment of Inertia 187 
 
 Moment of Inertia 
 
 The moment of inertia of the weight of a body, with respect to any 
 axis, is the algebraic sum of the products obtained by multiplying the 
 weight of each elementary particle by the square of its distance from 
 the axis. 
 
 If the moment of inertia with respect to any axis be denoted by /; the 
 weight of any elementary particle by w; and its distance from the axis 
 by r; the sum of all the particles by 2, then I = 'E(wr^). 
 
 The moment of inertia of a rod or bar of uniform thickness, with 
 respect to an axis perpendicular to the length of the rod, is 
 
 =«'G+^ 
 
 in which W equals the weight of rod, 2 I equals length and d equals the 
 distance of the center of gravity of the section from the axis. 
 
 For thin circular plates with the axis in its own plane, when r equals 
 the radius of the plate. 
 
 For circular plate, axis perpendicular to the plate. 
 
 Circular ring, axis perpendicular to its own plane, 
 
 r and / being the exterior and interior radii of the ring. 
 Cylinder, axis perpendicular to the axis of the cylinder, 
 
 r = radius of base and 2I — length of the cylinder. 
 
 By making d equal to o in any of the above formulae, the moment of 
 inertia for a parallel axis passing through the center of gravity is found. 
 
 The term moment of inertia is also used in respect to areas, as the 
 cross section of beams under strain. 
 
 In this case, I = S(ar)2, in which a is the elementary area and r its 
 distance from the center. 1 
 
i88 
 
 Materials 
 
 
 
 
 
 
 
 
 
 
 
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Formulae for Transverse Strength of Beams 189 
 
 Formulae for Transverse Strength of Beams 
 
 P = load at middle. 
 
 W = total load distributed uniformly. 
 
 I = length, b = breadth, d = depth in inches. 
 E = modulus of elasticity. 
 R = stress per square inch of extreme fibre. 
 
 / = moment of inertia. 
 
 C = distance between neutral axis and extreme fibre. 
 
 For breaking load of circular section replace bd"^ by 0.59 d^. 
 
 For good wrought iron the value of R is about 80,000; for steel about 
 120,000. For cast iron the value of R varies greatly. Thurston found 
 45,740 for No. 2 and 67,980 for No. i. 
 
190 
 
 Materials 
 
 General Formulae for Transverse Strength, Etc. 
 
 The following table gives the values of W, etc., without introducing 
 the modulus of elasticity or the moment of inertia. 
 
 Formula for Round and Rectangular Solid Beams 
 
 
 
 III 
 
 5 so 
 
 i 
 
 ^1? 
 
 a 
 .HI 
 
 Sts 
 
 
 Icvj 
 
 
 
 ^1 
 
 ^1 
 
 
 r 
 
 4!5 
 
 
 11^ 
 
 
 •til 
 
 IP 
 
 ^N 
 
 Jok 
 
 lb 
 
 5: 
 
 5" r> 
 
 >l< 
 
 
 ^1 
 
 II 
 
 
 •h 
 
 On- 
 
 f^ 
 
 ■-^ 
 
 ^ 
 
 t^- 
 
 ^ 
 
 _<3-t 
 
CHAPTER V 
 
 ACCELERATION OF FALLING BODIES 
 
 The change in velocity of a falling body which occurs in a unit of time 
 is its acceleration. 
 
 That due to gravity is 32.16 feet per second, in one second and is 
 denoted by g. 
 
 Let t = number of seconds during which a body falls. 
 
 V = velocity acquired in feet per second at the expiration of 
 
 t seconds. 
 u = space fallen through in each second. 
 h = total space fallen through in t seconds. 
 
 Then 
 
 gt = 32.16, t 
 
 S.oiVh = 
 
 2 2 2 g D4-32 
 
 t = '- 
 
 32.16 ▼ 8 V 
 
 The table below gives the values of h, v and u, for values of t up to ten 
 seconds. 
 
 
 Space fallen 
 
 Velocity 
 
 Space fallen 
 
 Time in . 
 
 through in 
 
 acquired in 
 
 through in 
 
 seconds. 
 
 feet in 
 
 feet per 
 
 feet in 
 
 t 
 
 time t, 
 
 second at end 
 
 each second, 
 
 
 h 
 
 of time t, 
 
 V 
 
 M 
 
 I 
 
 16 
 
 32 
 
 16 
 
 2 
 
 64 
 
 64 
 
 48 
 
 3 
 
 145 
 
 96 
 
 80 
 
 4 
 
 257 
 
 129 
 
 113 
 
 5 
 
 402 
 
 161 
 
 145 
 
 6 
 
 580 
 
 193 
 
 177 
 
 7 
 
 789 
 
 225 
 
 209 
 
 8 
 
 1030 
 
 257 
 
 241 
 
 9 
 
 1303 
 
 290 
 
 273 
 
 10 
 
 1609 
 
 322 
 
 306 
 
 191 
 
192 
 
 Mechanics 
 
 ISec 
 3" 
 
 \\ 
 
 The graphical method of ascertaining the values of t, v, u and h is 
 easily remembered and is often of service. 
 
 In the triangle, Fig. 6i, let the vertical divisions on 
 the left of the perpendicular represent the number of 
 seconds through which the body falls = t. 
 
 Let the base of each small triangle equal the velocity 
 at the end of the first second = 32.16. Then the 
 number of bases on each of the horizontal lines at 
 I, 2, 3, etc., multiplied by 32.16 will equal the ac- 
 quired velocity for the corresponding time = v. 
 
 Let the area of each small triangle = 16.08. Then 
 the number of such areas between o and any hori- 
 zontal line multiplied by 16.08 will equal the height in feet fallen through 
 in the number of seconds corresponding to that line = h. 
 
 And the number of small triangles between each pair of horizontal 
 lines, multiplied by 16.08 will equal the number of feet fallen through in 
 
 ^k 
 
 Fig. 61. 
 
 each second = u. 
 
 
 Thus: 
 
 / = I, 2, 3, 4, 5, 6. 
 
 
 V = 32.16 X I, 2, 3, 4, 5, 6. 
 
 
 h = 16.08 X I, 4, 9, 16, 25, 36. 
 
 
 u = 16.08 X I, 3, 5, 7, 9, II. 
 
 Fig. 62. 
 
 Parallelogram of Forces 
 
 If two forces are applied to the same point, their resultant will be 
 represented in intensity and direction by the diagonal of a parallelo- 
 gram of which the adjacent sides represent the 
 intensities and directions of the given forces. 
 
 Let AB and AC represent, in intensity and 
 direction, any two forces applied to the point 
 A; then AD will correspondingly represent 
 their resultant. 
 
 Conversely, ii ADhe the known force acting at ^, it may be resolved 
 into two components, in any direction in the same plane; which com- 
 ponents will be the adjacent sides of a parallelogram having AD for its 
 diagonal. 
 
 Parallelopipedon of Forces 
 
 If three forces, not in the same plane, act on the same point, they may 
 be represented by the edges of a parallelopipedon and the diagonal 
 through the point of application is their resultant. 
 
Height Corresponding to a. Given Acquired Velocity 193 
 Height Corresponding to a Given Acquired Velocity 
 
 Velocity. 
 
 Height, 
 
 Velocity, 
 
 Height, 
 
 Velocity, 
 
 Height, 
 
 V 
 
 h 
 
 V 
 
 h 
 
 V 
 
 k 
 
 Feet per 
 second 
 
 Feet 
 
 Feet per 
 secondr 
 
 Feet 
 
 Feet per 
 second 
 
 Feet 
 
 .25 
 
 .0010 
 
 34 
 
 17.9 
 
 76 
 
 89.8 
 
 .50 
 
 .0039 
 
 35 
 
 19.0 
 
 77 
 
 92.2 
 
 .75 
 
 .0087 
 
 36 
 
 20.1 
 
 78 
 
 94.6 
 
 1. 00 
 
 .016 
 
 37 
 
 21.3 
 
 79 
 
 97.0 
 
 1. 25 
 
 .024 
 
 38 
 
 22.4 
 
 80 
 
 99. 5 
 
 1.50 
 
 •035 
 
 39 
 
 23.6 
 
 81 
 
 102.0 
 
 1.75 
 
 .048 
 
 40 
 
 24.9 
 
 82 
 
 104.5 
 
 2.0 
 
 .062 
 
 ■ 41 
 
 26.1 
 
 83 
 
 107. 1 
 
 2.5 
 
 .097 
 
 42 
 
 27.4 
 
 84 
 
 109.7 
 
 3.0 
 
 .140 
 
 43 
 
 28.7 
 
 85 
 
 112. 3 
 
 3.5 
 
 .190 
 
 44 
 
 30.1 
 
 86 
 
 iiS.o 
 
 4.0 
 
 .248 
 
 45 
 
 31.4 
 
 87 
 
 117. 7 
 
 4.5 
 
 .314 
 
 46 
 
 32.9 
 
 88 
 
 120.4 
 
 5.0 
 
 .388 
 
 47 
 
 34.3 
 
 89 
 
 123.2 
 
 6.0 
 
 .559 
 
 . 48 
 
 35.8 
 
 90 
 
 125.9 
 
 7.0 
 
 .761 
 
 49 
 
 37.3 
 
 91 
 
 128.7 
 
 8.0 
 
 .994 
 
 50 
 
 38.9 
 
 92 
 
 131. 6 
 
 9.0 
 
 1.26 
 
 51 
 
 40.4 
 
 93 
 
 134. 5 
 
 lO.O 
 
 1. 55 
 
 52 
 
 42.0 
 
 94 
 
 137.4 
 
 II. 
 
 1.88 
 
 53 
 
 43.7 
 
 95 
 
 140.3 
 
 12.0 
 
 2.24 
 
 54 
 
 45.3 
 
 96 
 
 143.3 
 
 13.0 
 
 2.62 
 
 55 
 
 47.0 
 
 97 
 
 146.0 
 
 14.0 
 
 3.04 
 
 56 
 
 48.8 
 
 98 
 
 149.0 
 
 15.0 
 
 3.49 
 
 57 
 
 50.5 
 
 99 
 
 152.0 
 
 16.0 
 
 3.98 
 
 58 
 
 52.3 
 
 100 
 
 15s 
 
 17.0 
 
 4.49 
 
 59 
 
 54.1 
 
 105 
 
 171. 
 
 18.0 
 
 5.03 
 
 60 
 
 56.0 
 
 no 
 
 188.0 
 
 19.0 
 
 5. 61 
 
 61 
 
 57.9 
 
 115 
 
 205.0 
 
 20.0 
 
 6.22 
 
 62 
 
 59.8 
 
 120 
 
 224.0 
 
 21.0 
 
 6.8s 
 
 63 
 
 61.7 
 
 130 
 
 263.0 
 
 • 22.0 
 
 7.52 
 
 64 
 
 63.7 
 
 140 
 
 304.0 
 
 23.0 
 
 8.21 
 
 65 
 
 65.7 
 
 150 
 
 3SO.O . 
 
 24.0 
 
 8.94 
 
 66 
 
 67.7 
 
 175 
 
 476.0 
 
 25.0 
 
 9.71 
 
 67 
 
 69.8 
 
 200 
 
 622.0 
 
 26.0 
 
 10. 5 
 
 68 
 
 71.9 
 
 300 
 
 1,399.0 
 
 27.0 
 
 11.3 
 
 69 
 
 74.0 
 
 400 
 
 2,488.0 
 
 28.0 
 
 12.2 
 
 70 
 
 76.2 
 
 500 
 
 3,887.0 
 
 29.0 
 
 13. 1 
 
 71 
 
 78.4 
 
 ■6a. 
 
 5,597.0 
 
 30.0 
 
 14.0 
 
 72 
 
 80,6 
 
 700 
 
 7,618.0 
 
 31.0 
 
 14.9 
 
 73 
 
 82.9 
 
 800 
 
 9,952. 
 
 32.0 
 
 15.9 
 
 74 
 
 85.1 
 
 900 
 
 12.593.0 
 
 33.0 
 
 16.9 
 
 75 
 
 87.5 
 
 1000 
 
 15.547.0 
 
194 Mechanics 
 
 The Lever 
 
 The lever is a solid bar of any form, supported at a fixed point, about 
 which it may turn freely. 
 
 -^ -j The fixed point is the fulcrum. There are 
 
 '^' "'pi three orders of levers. In those of the first 
 
 order the points of application of the power 
 ^" and resistance are on opposite sides of the 
 
 fulcrum. 
 
 In the second order the resistance is ap- 
 pKed between the fulcrum and the power. 
 
 In the third order the power is apphed 
 between the fulcrum and the resistance. 
 
 ± 
 
 In any order ^^^- ^4- 
 
 the weight W multiplied by the distance 
 WF from the fulcrum must equal the 
 power P multiplied by PF, to establish 
 ^^' ^' equilibrium. 
 
 Whatever may be the shape of the lever, the power or resistance acts 
 at the end of a hne drawn through the fulcrum and perpendicular to the 
 line of direction of the power or resistance. This perpendicular is called 
 the lever arm of its corresponding force, and the product of the lever arm 
 and its force is called the moment of that force. When the moments are 
 equal the forces are in equilibrium. 
 
 If one moment exceeds the other, rotation will occur about the ful- 
 crum in the direction of the force having the greater moment. 
 
 The Wheel and Axle 
 
 This is simply such an appUcation of the lever of the first order, that 
 the power and resistance may act through greater distances; the radius 
 of the wheel is the lever arm of the power and that of the drum the lever 
 arm of the resistance. 
 
 When the resistance is a weight, it will be raised if the moment of the 
 power is the greater and vice versa. 
 
 The Inclined Plane 
 
 If a force P acts in the direction of C 
 AB, to overcome the resistance R, then p 
 P:R::a:b. "*" 
 
 b a Fig. o6. 
 
Center of Gravity 1 95 
 
 The Wedge 
 
 The wedge is simply a double inclined plane, placed i- 
 
 back to back. _t±iX^ 
 
 If the force applied to "a wedge be represented by P t \ 
 and the resistance to be overcome by R, the base of the 
 wedge by a and its length by&;"then b 
 
 P:R::a:b P = ^ and R = ^ 
 
 a 
 
 Fig. 67. 
 
 Center of Gravity 
 
 The center of gravity of a body is that point through which the effort 
 of its weight always passes. If a body be suspended from any point, 
 the direction of the hne of suspension will pass through its center of 
 gravity. 
 
 Therefore, the center of gravity of any body may be determined by 
 finding the intersection of the hnes of suspension passing through points 
 not on the same vertical hne. 
 
 The center of gravity of two bodies is on a hne joining their respective 
 centers of gravity and the distances from the center of gravity of either 
 body to that of both of them (combined) are inversely proportional to 
 the weights of the bodies respectively. 
 
 To find the center of gravity of any irregular plane surface, divide it 
 into triangles of any convenient areas. Find the center of gravity and 
 the area of each triangle. Then assimiing any coordinate axes X and 
 Y, multiply the area of each triangle by the abscissa of its center of gravity 
 and divide the product by the sum of the areas of all the triangles. The 
 quotient is the abscissa of the center of gravity of the entire figure. Find 
 its ordinate in the same way; then the point determined by this abscissa 
 and ordinate is the center of gravity of the figure. 
 
 This method is precisely that shown by Fig. 61, Machinery Supplement 
 No. 5. 
 
 In addition to the formulae taken from Machinery Supplement No. 5, 
 others are given as follows : 
 
 Semiellipse 
 
 The center of gravity of a semiellipse is on the semiaxis perpendiciilar 
 to the base and at a distance from the base equal to the product of that 
 semiaxis and the decimal 0.4244. 
 
196 Mechanics 
 
 The Center of Gravity of Solids of Uniform Density 
 Throughout 
 
 Sphere and spheroid at center of the body. 
 
 Hemisphere on the radius perpendicular to the base and at H its 
 length from the base. 
 
 Spherical Sector. — On the radius passing through the center of the 
 circle cut from the sphere by the sector and at a distance from the center 
 of the sphere, equal to three-fourths of the difference between the radius, 
 and one-half the rise of the sector. Or G, representing the distance from 
 center of sphere to center of gravity, R = radius of sphere and H the 
 
 rise of the sector; then G = hIr j • 
 
 Spherical Segment 
 
 {2R- Hy 
 
 G=% 
 
 3R-H 
 
 Spherical Zone 
 
 Take the difference between the two segments whose difference is 
 the zone. Find the center of gravity of each segment; then, by inverse 
 proportion, find that of their difference. 
 
 Frustrum of a Cone 
 
 Let G = distance from base to center of gravity measured on 
 
 the axis. 
 A = area of large end. 
 a = area of small end. 
 H = height of frustrum measured on the axis. 
 
 Then a = «fA+^^Aa + sa\ 
 
 4 V ^ + VAa -\-a J 
 
 The center of gravity of a paraboloid is on the axis and at a distance 
 from the vertex equal to two-thirds that from vertex to base. 
 
 A body suspended from center of gravity has no tendency to rotate. 
 
 Center of gravity of regular figures is at geometrical center; of a triangle 
 two-thirds distance from any angle to middle of opposite side; of semicircle 
 
 on middle radius, 4244 r from center; of sector — r- from center; oi seg- 
 
 3 ^ 
 
 ment, from center (where c = chord and a = area); of cone or 
 
 12 a 
 
 pyramid, \i distance from center of base to apex a,. 02, az = areas of 
 respective triangles. 
 
 Center of gravity of two bodies, x = — 7-^^ 
 
Radius of Gyration 
 
 197 
 
 General formulae x 
 
 aixi + (12X2 + azXz 
 <Ji + <i2 + 0,3 
 
 aiji + cgyi + azjz 
 ai + a2 + az 
 
 <vf 
 
 ^ 
 
 O/ 
 
 "^ 
 
 \ 
 
 \ 
 
 ~~-- 
 
 
 \ 
 
 <.x,- 
 
 \--:f^ 
 
 
 ''^^\ 
 
 c-Xj- 
 
 T"!^- 
 
 --^^_\^ 
 
 
 ^ 
 
 ^- 
 
 ^ 
 
 
 
 
 
 
 
 
 
 Y 
 
 Fig. 69. 
 
 Volume of a solid generated by the revolution of a surface about an axis 
 in the same plane with it = area of the surface X circumference de- 
 scribed by its center of gravity. 
 
 Moment of Inertia 
 
 Moment of inertia of rotating body = products of weights of particles 
 X squares of distances from the axis = I = Wir^ + W2ri + Wzr^, etc. 
 K'l, W2, etc. = weights of particles; Vi, Vi, etc. = distances from axis in 
 same imits as the volumes of the particles of which weights are taken. 
 
 Radius of Gyration 
 
 Center of gjnration of rotating body is point at which weight itnay be 
 assumed concentrated. Radius of gyration = k = distance from center 
 
 of rotation to center of gyration. For circular disc, k = -^=. For 
 
 circular ring, k 
 1899.) 
 
 -\/ 
 
 r 
 
 i?2 + r2 
 
 (No. 5 Supplement to Machinery, Sept., 
 
 Specific Gravity of Gases 
 Air = I. 
 
 Hydrogen 0.069 
 
 Marsh gas o . 559 
 
 Steam o. 623 
 
 Carbonic oxide o . 968 
 
 Nitrogen o . 971 
 
 defiant gas o . 978 
 
 Oxygen i . 106 
 
 Sulphuretted hydrogen i .191 
 
 Nitrous oxide i . 527 
 
 Carbonic acid i . 529 
 
 Sulphuric acid 2 . 247 
 
 Chlorine 2 . 470 
 
igS 
 
 Mechanics 
 
 Specific Gravity of Various Substances 
 
 Water = i. 
 
 Substances 
 
 Air at 60° F. under pressure of one atmosphere weighs 
 
 Hi 5 part as much as water at 60° F 
 
 Alcohol 
 
 Ash, American, white, dry 
 
 Aluminum 
 
 Antimony 
 
 Asphaltum 
 
 Basalt 
 
 Bismuth 
 
 Copper and zinc, cast 
 
 Copper and zinc, rolled. . . 
 
 Bronze, copper 8, tin i 
 
 Brick, pressed 
 
 Brick, common, hard 
 
 Brick, soft 
 
 Box wood 
 
 Carbonic acid '. . 
 
 Charcoal, of pines and oaks. 
 Chalk 
 
 Clay, dry, in lump, loose 
 
 Coke: 
 
 Loose 
 
 A heaped bushel 35 to 42 pounds. A ton occupies 
 from 40 to 43 cubic feet. 
 
 Cherry, dry 
 
 Coal: 
 
 Anthracite , 
 
 Anthracite, broken, loose , 
 
 Bituminous 
 
 Bituminous, broken, loose 
 
 A heaped bushel weighs from 70 to 78 pounds. 
 A ton occupies from 43 to 48 cubic feet. 
 Cement: 
 
 Rosendale, ground, loose 
 
 Rosendale, struck bushel , 
 
 English Portland 
 
 French Portland 
 
 Copper, cast , 
 
 Copper, rolled , 
 
 Diamond 
 
 Earth: 
 
 Dry loam, loose 
 
 Dry loam, shaken 
 
 Dry loam, moderately rammed 
 
 Loam, moist, loose 
 
 Loam, moist, shaken 
 
 Soft mud : 
 
 Elm, dry 
 
 Ebony 
 
 Average 
 specific 
 gravity 
 
 0.00123 
 
 0.834 
 
 0.61 
 
 2.6 
 
 6.70 
 
 1-4 
 
 2.9 
 
 9-74 
 
 8.1 
 8.4 
 8.5 
 
 0.96 
 0.00187 
 
 0.672 
 
 i.S 
 
 1-35 
 
 8.7 
 8.9 
 3. S3 
 
 0.56 
 1.22 
 
Specific Gravity of- Various Substances 199 
 
 Specific Gravity of Various Substances — {Continued) 
 
 Substances 
 
 Fat 
 
 Flint 
 
 Feldspar 
 
 Glass 
 
 Glass, common window. 
 
 Granite 
 
 Gneiss, common 
 
 Gypsum, plaster Paris. . 
 
 Greenstone, trap 
 
 Gravel 
 
 Gold, pure ^ 
 
 Gutta percha 
 
 Hornblende, black 
 
 Hydrogen is 14}^ times lighter than air and 16 times 
 
 lighter than oxygen 
 
 Hemlock, dry 
 
 Hickory, dry 
 
 Iron, cast 
 
 Iron, pure 
 
 Iron, wrought, rolled 
 
 Iron, sheets 
 
 Ivory 
 
 Ice 
 
 India rubber 
 
 Lignum Vitse, dry. 
 Lard 
 
 Lead 
 
 Limestones and marbles 
 
 Lime, quick 
 
 Lime, quick, ground loose, per struck bushel. 
 Mahogany: 
 
 Dry, San Domingo 
 
 Dry, Honduras 
 
 Maple, dry 
 
 Marbles, see Limestone 
 Masonry: 
 
 Granite or limestone 
 
 Granite or limestone rubble 
 
 Brick, ordinary quality 
 
 Mercury at 32° F 
 
 Mercury at 212° F 
 
 Mica 
 
 Mortar, hardened . . 
 Mud: 
 
 Dry 
 
 Moist 
 
 Wet, fluid 
 
 Naphtha 
 
 Nitrogen 
 
 Oak live, dry 
 
 Oak white 
 
 Oak, red and black. 
 
 Average 
 specific 
 gravity 
 
 • 93 
 2.6 
 2.65 
 2.98 
 2.52 
 2.72 
 2.69 
 2.27 
 30 
 
 19.258 
 
 3-25 
 
 • 4 
 .85 
 
 7.218 
 
 7-77 
 
 7.69 
 
 7.73 
 
 1.82 
 
 • 92 
 •93 
 
 1-33 
 
 • 95 
 11.38 
 
 2.7 
 1^5 
 
 13^62 
 
 13.38 
 
 2.93 
 
 1.65 
 
 .848 
 .001194 
 .95 
 • 77 
 
 Average 
 weight per 
 cubic foot 
 in pounds 
 
 58.0 
 162.0 
 166.0 
 186.0 
 157^0 
 170.0 
 168.0 
 141. 6 
 187.0 
 90 to 106 
 1204.0 
 
 61. 1 
 203.0 
 
 .00527 
 
 25.0 
 
 53.0 
 450.0 
 485.0 
 480.0 
 485.0 
 114. o 
 
 57.4 
 58.0 
 83.0 
 
 59.3 
 709.6 
 168.0 
 
 95.0 
 
 S3 
 
 53 -o 
 35 •o 
 49 o 
 
 165.0 
 154 o 
 125.0 
 849.0 
 836.0 
 183.0 
 103.0 
 
 80 to no 
 no to 130 
 104 to 120 
 
 52.9 
 .0744 
 
 59-3 
 
 48.0 
 
 32 to 45 
 
200 
 
 Mechanics 
 
 Specific Gravity of Various Substances — {Continued) 
 
 Substances 
 
 Average 
 specific 
 gravity 
 
 Average 
 weight per 
 cubic foot 
 in pounds 
 
 Oil: 
 Whale 
 
 • 92 
 .92 
 •94 
 
 • 969 
 .860 
 
 • 87 
 
 • 914 
 .926 
 
 2.2 
 
 4.129 
 4-344 
 5 -452 
 4.057 
 4.789 
 4-9 
 5-00 
 4.029 
 5-218 
 3-81 
 3.863 
 7.20 
 7.22 
 6.45 
 3.525 
 .00136 
 
 57^3 
 
 Olive 
 
 
 
 Palm 
 
 
 
 
 
 54-3 
 
 Rape seed 
 
 Sunflower 
 
 
 Oolites 
 
 137 
 
 Ores: 
 
 Copper, vitreous 
 
 
 Copper, pyrites 
 
 
 Copper, Cornish 
 
 
 Iron, chromate 
 
 
 Iron, pyrites 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 Tin, Cornish 
 
 
 Zinc, calamine 
 
 
 Oxygen 
 
 0846 
 
 Peat, dry 
 
 20 to 30 
 
 Pine, white, dry. 
 
 .40 
 .55 
 -72 
 
 I-15 
 
 1. 176 
 
 1.0 
 
 2.73 
 21.5 
 
 2.65 
 
 3.9 
 
 I.I 
 
 25 
 
 
 34-3 
 
 
 
 Pitch 
 
 
 Plaster Paris 
 
 
 
 
 
 62.3 
 
 
 
 
 
 
 
 
 
 
 68.6 
 
 Salt: 
 
 Coarse, Syracuse struck bushel, 56 pounds 
 
 Coarse, Turk's Island struck bushel, 76 to 80 
 
 Coarse, Liverpool struck bushel, 50 to 55 
 
 Sand, dry and loose, average 98 
 
 Sand, wet 
 
 45-0 
 62.0 
 42.0 
 
 goto 106 
 118 to 129 
 
 Sand stones 
 
 2.41 
 2.6 
 
 151 
 
 Serpentines . 
 
 162.0 
 
 Snow: 
 Freshly fallen 
 
 5 to 12 
 
 
 
 IS to so 
 
 
 .59 
 2.6 
 2.8 
 
 37-0 
 
 
 162.0 
 
 Slate 
 
 I7S-0 
 
 
 
Specific Gravity of Various Substances 201 
 
 Specefic Gravity of Various Substances — {Continued) 
 
 Substances 
 
 Silver 
 
 Soapstone (steatite) 
 
 Steel 
 
 Sutphur 
 
 Spruce, dry 
 
 Spelter, zinc 
 
 Tallow 
 
 Tar ; 
 
 Trap 
 
 Topaz 
 
 Tin 
 
 Water: 
 
 Distilled at 32° F. , barometer 30" 
 
 Distilled at 62° F., barometer 30" 
 
 Distilled at 212° F., barometer 30" 
 
 At 60° F. a cubic inch of water weighs .03607 pounds 
 or .57712 ounces, avoirdupois 
 
 Sea — 
 
 Dead Sea 
 
 Wax, bees 
 
 Wines 
 
 Walnut, black, dry 
 
 Zinc 
 
 Zircon 
 
 Asbestos 
 
 Acid: 
 
 Acetic 
 
 Carbolic 
 
 Hydrochloric 
 
 Nitric 
 
 Sulphuric 
 
 Barytes 
 
 Brick: 
 
 Common 
 
 Fire 
 
 Clay, fire 
 
 Carbon, graphite 
 
 Manganese 
 
 Magnesium 
 
 Nickel 
 
 Potassium 
 
 Phosphorus 
 
 Silicon 
 
 Stone (building) 
 
 Titanium 
 
 Tungsten 
 
 Uranium 
 
 Vanadium 
 
 Average 
 specific 
 gravity 
 
 10.5 
 2.73 
 7.8s 
 2.0 
 
 • 4 
 7.0 
 
 •94 
 i.o 
 3.0 
 3.55 
 7-35 
 
 1.240 
 
 •97 
 
 .998 
 
 .61 
 
 7.0 
 
 4.45 
 
 Average 
 weight per 
 cubic foot 
 in pounds 
 
 655 o 
 170.0 
 490.0 
 125.0 
 
 25.0 
 437.5 
 
 58.6 
 
 62.4 
 187.0 
 
 459 o 
 
 62.417 
 62.355 
 59-7 
 
 64.08 
 
 60.5 
 
 62.3 
 
 38.0 
 
 437.5 
 
 .993 
 
 1.063 
 1.065 
 1.270 
 1. 554 
 1.970 
 4.86 
 
 1.90 
 2.2 
 2.16 
 2.585 
 8.01 
 2.04 
 8.80 
 .865 
 1.863 
 2.493 
 2.9 
 5.3 
 
 19.26 
 
 18.4 
 55 
 
 499 .o 
 548.7 
 
50^ 
 
 Mechanics 
 Table of Physical Constants 
 
 Name 
 
 Aluminum . . . 
 Antimony — 
 
 Arsenic 
 
 Bismuth 
 
 Calcium 
 
 Carbon 
 
 Chlorine 
 
 Chromium.. . 
 
 Copper 
 
 Gold 
 
 Hydrogen 
 
 Iodine '. . . 
 
 Iron 
 
 Lead 
 
 Magnesium. . . 
 Manganese . . . 
 
 Mercury 
 
 Molybdenum. 
 
 Nickel 
 
 Nitrogen 
 
 Oxygen 
 
 Phosphorus . . 
 
 Platinum 
 
 Potassium — 
 
 Silicon 
 
 Silver 
 
 Sodium 
 
 Sulphur 
 
 Tellurium 
 
 Titanium 
 
 Tin 
 
 Tungsten 
 
 Uranium 
 
 Vanadium . . . 
 Zinc 
 
 Sym- 
 bol 
 
 Al 
 
 Sb 
 
 As 
 
 Bi 
 
 Ca 
 
 C 
 
 CI 
 
 Cr 
 
 Cu 
 
 Au 
 
 H 
 
 I 
 
 Fe 
 
 Pb 
 
 Mg 
 
 Mn 
 
 Hg 
 
 Mo 
 
 Ni 
 
 N 
 
 O 
 
 P 
 
 Pt 
 
 K 
 
 Si 
 
 Ag 
 
 Na 
 
 S 
 
 Te 
 
 Ti 
 
 Sn 
 
 W 
 
 u 
 
 V 
 Zn 
 
 Atomic 
 weight 
 
 27.3 
 
 122.0 
 74-9 
 
 207. 5 
 39-9 
 11-97 
 35.36 
 52.4 
 63.3 
 
 196.2 
 i.o 
 
 126.53 
 55-9 
 
 206.4 
 23.94 
 54.8 
 
 199.8 
 95.8 
 58.6 
 14.01 
 15.96 
 30.94 
 
 196.7 
 39.04 
 28.0 
 
 107.66 
 23.0 
 31.98 
 
 117. 8 
 184.0 
 180.0 
 51.2 
 64.9- 
 
 Specific 
 
 heat, 
 
 water 
 
 = I 
 
 .214 
 
 .0508 
 
 .0814 
 
 .0308 
 
 .170 
 
 .214 
 
 .0952 
 .0324 
 3.2963 
 .0541 
 .114* 
 .0314 
 .25 
 .122 
 •0317 
 .0722 
 .109 
 .244 
 .218 
 .190 
 .0324 
 .166 
 .2029 
 .0570 
 .293 
 .203 
 .0474 
 
 .0562 
 .0334 
 
 .0955 
 
 Specific 
 
 gravity, 
 
 water 
 
 = I 
 
 2.6 
 6.7 
 5. 95 
 9.74 
 1.578 
 2.35 
 2.43 
 6.8 
 8.90 
 19.258 
 
 4.94 
 7.80 
 
 11.38 
 1.70 
 8.0 
 
 13.62 
 8.64 
 8.90 
 
 1.83 
 
 21.53 
 
 .865 
 
 2.49 
 
 10.50 
 
 .972 
 
 2.00 
 
 6.6s 
 
 5.3 
 
 7-35 
 
 17.50 
 
 18.40 
 
 5.54 
 
 7.00 
 
 Specific 
 gravity, 
 
 air 
 
 = I 
 
 .069 
 
 .971 
 1. 106 
 
 (5. so) 
 
 Melting 
 point 
 
 Latent 
 heat of 
 fusion 
 
 1182° F. 
 
 I973°-Ii34° F. 
 
 774° F. 
 
 497°-484° F. 
 
 >Pt. 
 1994° F. 
 2ois° F. 
 
 22S° F. 
 
 i9oo°-279o° F. 
 
 6i7°-588° F. 
 
 1139° F. 
 
 2240° F. 
 
 39° F. 
 
 2610° F. 
 
 115° F. 
 
 3150° F. 
 
 I44.5°-I36° F. 
 
 2574° F. 
 
 1732° F. 
 
 207.7°-i9o° F. 
 
 226° F. 
 
 700° F. 
 
 4000° F. 
 
 442°-4i7* F. 
 
 >Mn 
 
 4300° F. 
 773°-754° F. 
 
 28.5 
 40.0 
 
 43.0 
 16.0 
 
 88.69 
 
 II. o 
 
 5.09 
 68.0 
 
 9.06 
 24.00 
 16.0 
 128.0 
 23.0 
 32.0 
 16.86 
 19.0 
 
 25.65 
 
 48.36 
 
 * Cast iron specific heat at 
 
 212° F. is .109. 
 572° F. is .140. 
 2x50° F. is .190. 
 
Table of Physical Constants 
 Table of Physical Constants 
 
 203 
 
 
 Air = I 
 
 Specific heat at 
 constant pressure 
 
 Specific 
 heat at 
 constant 
 volume 
 
 Pounds 
 
 per 
 
 cubic 
 
 foot 
 
 Cubic 
 
 Substances 
 
 Specific 
 gravity 
 
 For 
 
 equal 
 
 weight, 
 
 water 
 
 = 1 
 
 For 
 
 equal 
 
 volumes 
 
 feet 
 
 per 
 
 pound 
 
 Air 
 
 I 
 
 I . 1056 
 
 .4713 
 
 .0692 
 
 .9670 
 
 1.5210 
 
 .5527 
 
 .9672 
 
 .6220 
 
 .5894 
 
 I. 5241 
 
 1.0384 
 
 I . 1746 
 
 2.2112 
 
 2.4502 
 
 5. 4772 
 
 2.6258 
 
 1.2596 
 
 .2377 
 .2175 
 .2438 
 3.4090 
 .2450 
 .2169 
 .5929 
 .4040 
 .4805 
 .5084 
 .2262 
 .2317 
 .2432 
 .1544 
 .1210 
 .0555 
 .1569 
 .1882 
 .335 
 .700 
 .450 
 .426 
 
 2:^77 
 
 ■ 
 .1689 
 .1550 
 .1730 
 2.4060 
 .1730 
 .1710 
 .4670 
 .3320 
 
 .080728 
 .089210 
 .078420 
 .005610 
 .078100 
 . 123430 
 .044880 
 .079490 
 
 12.387 
 
 
 
 2405 
 2368 
 2359 
 2370 
 3307 
 3277 
 4106 
 2989 
 2996 
 0447 
 2406 
 2857 
 3414 
 2965 
 3040 
 4122 
 2333 
 
 11.209 
 
 
 12.752 
 
 Hydrogen 
 
 Carbon monoxide 
 
 Carbon dioxide .... 
 
 178.230 
 12.804 
 8.102 
 
 Marsh gas 
 
 defiant gas (ethylene) . . . 
 
 Aqueous vapor 
 
 Ammonia 
 
 Nitrous monoxide 
 
 Nitrous dioxide 
 
 22.301 
 12.580 
 
 
 
 
 
 
 
 Bromine vapor 
 
 
 Carbon bisulphide vapor . 
 
 Hydrochloric acid 
 
 Sulphuric acid 
 
 
 Alcohol 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
204 ^ Mechanics 
 
 Weight of Air Required for Combustion of Coal 
 
 Substances 
 
 Pounds of 
 air 
 
 B.t.u. from 
 combustion 
 of one pound 
 
 Carbon 
 
 12.30 
 35.00 
 18.00 
 15.60 
 
 14,500 
 61,524 
 24,021 
 21,524 
 18,260 
 
 
 
 
 
 
 
 Boiling Points at Sea Level 
 
 Water 100 ° C. 
 
 Alcohol 78.4 " 
 
 Ether 34.9 " 
 
 Carbon bisulphide 46. i " 
 
 Nitric acid (strong) 120.0 " 
 
 Sulphuric acid 326.6 " 
 
 Oil turpentine 157 . o " 
 
 Mercury : 35o.o " 
 
 Aldehyde 20.8 " 
 
 Combining Equivalents 
 
 Oxygen 
 
 Hydrogen i 
 
 Nitrogen 14 
 
 Carbon 6 
 
 Sulphtir 8 
 
 Phosphorus 10 
 
 Chlorine 35 
 
 Iodine 25 
 
 Potassium 39 
 
 Iron 28 
 
 Copper 31 
 
 Lead 103 
 
 Silver 108 
 
 Bromine 80 
 
 Sodium 23 , 
 
 Fluorine 19. 
 
 Lithium 7 , 
 
 Rubidium 85. 
 
 8.0 "C. 
 
Lineal Expansion for Solids 
 
 205 
 
 Lesteal Expansion for Solids at Ordinary Temperature 
 FOR i°F. 
 
 Solids 
 
 Aluminum, cast 
 
 Antimony, cryst 
 
 Brass, cast 
 
 Brass, plate 
 
 Brick 
 
 Bronze (copper, 17; tin, 2}^; zinc, i). . 
 
 Bismuth 
 
 Cement, Portland (mixed), pure 
 
 Concrete: cement, mortar and pebbles 
 
 Copper 
 
 Ebonite 
 
 Glass, English flint 
 
 Glass, hard 
 
 Glass, thermometer 
 
 Granite (gray, dry) 
 
 Granite (red, dry) 
 
 Gold, pure 
 
 Iron (wrought) 
 
 Iron (cast) 
 
 Lead 
 
 Marbles, various j ^^ 
 
 Masonry, brick w^ 
 
 Merctiry (cubic expansion) 
 
 Nickel 
 
 Pewter 
 
 Plaster, white 
 
 Platinum 
 
 Porcelain 
 
 Silver, pure 
 
 Slate 
 
 Steel, cast 
 
 Steel, tempered 
 
 Stone, sand, dry 
 
 Tin 
 
 Wedgewood (ware) 
 
 Wood, pine 
 
 Zinc 
 
 Zinc 8 ) 
 
 Tin I 
 
 From 1° F. 
 
 Length 
 
 00001234 
 
 00000627 
 
 00000957 
 
 00001052 
 
 00000306 
 
 00000986 
 
 00000975 
 
 00000594 
 
 00000795 
 
 00000887 
 
 00004278 
 
 00000451 
 
 00000397 
 
 00000499 
 
 00000438 
 
 00000498 
 
 00000786 
 
 00000648 
 
 00000556 
 
 00001571 
 
 00000308 
 
 00000786 
 
 00000256 
 
 00000494 
 
 00009984 
 
 00000695 
 
 00001129 
 
 00000922 
 
 00000479 
 
 00000200 
 
 00001079 
 
 00000577 
 
 00000636 
 
 00000689 
 
 00000652 
 
 00001163 
 
 00000489 
 
 00000276 
 
 00001407 
 
 00001496 
 
 Coefficient 
 
 of expansion 
 
 from 32° to 
 
 212° F. 
 
 .002221 
 .001129 
 .001722 
 .001894 
 .000550 
 .001774 
 •OOI75S 
 .001070 
 .001430 
 .001596 
 . 007700 
 .000812 
 .000714 
 . 000897 
 .000789 
 . 000897 
 .00141S 
 .001166 
 
 . OOIOOI 
 
 .002828 
 .000554 
 .001415 
 .000460 
 .000890 
 .017971 
 .001251 
 .002033 
 .001660 
 .000863 
 .000360 
 .001943 
 .001038 
 .001144 
 .001240 
 .001174 
 .002094 
 .000881 
 .000496 
 .002532 
 . 002692 
 
 Cubical expansion or expansion of volume equals lineal expansion multiplied by 3. 
 The coefficient of expansion from 32° to 212° F. divided by 100 gives the lineal 
 expansion for corresponding solid for 1° C. 
 The expansion of metals above 212° F. is irregular and more rapid. 
 
2o6 Mechanics 
 
 Furnace Temperatures 
 
 M. Le Chatelier finds the melting heat of white cast iron 2075° F., 
 and that of gray cast iron at 2228° F. Mild steel melts at 2687° F., semi- 
 mild at 2651° F. and hard steel at 2570° F. 
 
 The furnace for hard porcelain at the end of the baking has a heat of 
 2498° F. The heat of a normal incandescent lamp is 3272° F., but it 
 may be pushed beyond 3812° F. 
 
 The following are some of the temperatures determined by Professor 
 Roberts-Austin. 
 
 Ten-ton Open-hearth Furnace {Woolwich Arsenal) 
 Temperature of steel, 0.3 per cent carbon, pouring into ladle . . . 2993° F. 
 Temperature of steel, 0.3 per cent carbon, pouring into large 
 
 mold 2876° F. 
 
 Reheating furnace, Woolwich Arsenal, temperature of interior. . 1 706° F. 
 Cupola furnace, temperature of No. 2 cast iron pouring into 
 
 ladle 2912° F. 
 
 Determinations by M. Le Chatelier. Bessemer Process. 
 Six-ton Converter 
 
 Bath of slag 2876° F. 
 
 Metal in ladle 2984° F. 
 
 Metal in ingot mold 2876° F. 
 
 Ingot in reheating furnace . . 2192° F. 
 
 Ingot imder the hammer 1976° F. 
 
 Open-hearth Furnace {Siemans) Semi-mild Steel 
 
 Fuel gas near gas generator 1328° F. 
 
 Fuel gas entering into bottom of regenerator chamber . . . 752"° F. 
 
 Fuel gas issuing from regenerator chamber 2192° F. 
 
 Air issuing from regenerator chamber 1832° F. 
 
 Chimney Gases 
 Furnace in perfect condition 590° F. 
 
 Open-hearth Furnace 
 
 End of the melting of pig charge 2588° F. 
 
 Completion of conversion 2732° F. 
 
 Fownes Elementary Chemistry gives relative conductivity of metals 
 
 asfoUows: silver 1000 
 
 Copper 736 
 
 Gold 532 
 
 Brass 236 
 
 Tin 14s 
 
 Iron 119 
 
 Steel 116 
 
 Lead 85 
 
 Platinum 84 
 
 German silver 63 
 
 Bismuth 18 
 
Measurement of Heat 
 
 207 
 
 MEASUREMENT OF HEAT 
 Unit of Heat 
 
 The British thermal unit (B.t.u.) is the quantity of heat required to 
 raise the temperature of one pound of pure water one degree Fahrenheit 
 at 39.1° F. 
 
 The French thermal unit, or calorie, is the quantity of heat required to 
 raise the temperature of one kilogram of pure water one degree Centi- 
 grade at 4° C, which is equivalent to 39.1° F. The French calorie is 
 equal to 3.968 British thermal units; one B.t.u, is equal to .252 calories. 
 
 Mechanical Equivalent of Heat 
 
 This is the number of foot pounds equivalent to one B.t.u. Joule's 
 experiments gave the figure 772, which is known as Joule's equivalent. 
 Recent experiments give higher figures and the average is now taken 
 to be 778. 
 
 Heat of Combustion in Oxygen oe Various Substances 
 
 Substance 
 
 Hydrogen to liquid water at 0° C 
 
 Hydrogen to steam at 100° C 
 
 Carbon (wood charcoal) to carbonic acid (CO2); ordinary 
 temperatures 
 
 Carbon graphite to CO2 •. 
 
 Carbon to carbonic oxide, CO 
 
 Carbonic oxide to CO2 per unit of CO ■ 
 
 CO to CO2 per unit of C = 2H X 2403 
 
 Marsh gas, CH4 to water and CO2 
 
 defiant gas, C2H4 and water and CO2 
 
 Heat 
 
 units 
 
 Cent. 
 
 Fahr. 
 
 ( 34,462 
 
 62,032 
 
 S 33,808 
 
 60,854 
 
 ( 34,342 
 
 61.816 
 
 28,732 
 
 51,717 
 
 ( 8.080 
 
 14,544 
 
 < 7,900 
 
 14,220 
 
 ( 8,137 
 
 14,647 
 
 7,901 
 
 14,222 
 
 2,473 
 
 4,451 
 
 ( 2,403 
 
 4,325 
 
 < 2,431 
 
 4,376 
 
 ( 2.38s 
 
 4,293 
 
 5,607 
 
 10,093 
 
 ( 13,120 
 
 23,616 
 
 < 13,108 
 
 23,594 
 
 ( 13,063 
 
 23,513 
 
 ( 11,858 
 
 21,344 
 
 < 11,942 
 
 21,496 
 
 ( 11.957 
 
 21,523 
 
 If one pound of carbon is burned to CO2, generating 14,544 B.t.u., and the CO2 
 thus formed is immediately reduced to CO in the presence of glowing carbon, by the 
 reaction CO2 + C = 2 CO. the result is the same as if the two pounds of C had been 
 burned directly to 2 CO. generating 2 X 4451 = 8902 heat units; consequently 
 14,544 — 8902 = 5642 heat units have disappeared or become latent and the reduction 
 of CO2 to CO is thus a cooling operation. 
 
 Kent, 4S6. 
 
208 
 
 Heat 
 
 RADIATION OF HEAT 
 
 Relative Radiating and Reflecting Power of Different 
 
 Substances 
 
 Substances 
 
 Radiating 
 or absorb- 
 ing power 
 
 Reflecting 
 power 
 
 Lampblack 
 
 lOO 
 
 loo 
 98 
 93 to 98 
 90 
 85 
 25 
 23 
 
 2^ 
 
 19 , 
 
 17 
 
 24 
 
 15 
 
 II 
 
 7 
 
 14 
 7 
 3 
 
 
 Water - 
 
 
 Writing paper 
 
 
 
 7 to 2 
 
 
 Ice 
 
 15 
 75 
 77 
 77 
 81 
 
 Cast iron, bright polished 
 
 Mercury, about 
 
 Wrought iron, polished 
 
 Zinc, polished 
 
 Steel, polished 
 
 83 
 76 
 85 
 89 
 93 
 86 
 
 Platinum, polished 
 
 Tin 
 
 Brass, cast, dead polish 
 
 Brass, bright polished 
 
 Copper, varnished 
 
 Copper, hammered 
 
 93 
 97 
 
 Silver, polished, bright 
 
 
 Experiments of Dr. A. M. Mayer give the following: The relative 
 radiations from a cube of cast iron, having faces rough, as from the 
 foundry, planed, drawfiled and polished; and from the same surfaces 
 oiled, are as below (Professor Thurston). 
 
 Surface 
 
 Oiled 
 
 Dry 
 
 Rough 
 
 100 
 60 
 
 49 
 45 
 
 
 Planed 
 
 32 
 20 
 
 Drawfiled 
 
 Polished 
 
 18 
 
 
 
 
Relative Nonconducting Power of Materials 
 Relative Heat-Conducting Power of Metals 
 
 209 
 
 Metals 
 
 Conduc- 
 tivity 
 
 Metals 
 
 Conduc- 
 tivity 
 
 
 1000 
 981 
 84s 
 811 
 677 
 66s 
 641 
 608 
 628 
 
 
 436 
 
 Gold 
 
 Tin 
 
 
 Steel 
 
 397 
 380 
 359 
 287 
 
 
 
 Mercury 
 
 Cast iron 
 
 Aluminum 
 
 Lead 
 
 Zinc. 
 
 Antimony, cast, horizontal. . . 
 
 Antimony, cast, vertical 
 
 Bismuth 
 
 215 
 
 Zinc, cast, horizontal. 
 
 192 
 61 
 
 Zinc, cast, vertical 
 
 
 
 
 Relative Nonconducting Power of Materials 
 
 (Professor Ordway) 
 
 Substance i inch thick. Heat applied 
 310° F. 
 
 Pounds of 
 water heated 
 
 10° F. per 
 
 hour through 
 
 I square 
 
 foot 
 
 Solid 
 
 matter in 
 
 I square 
 
 foot I inch 
 
 thick, parts 
 
 in 1000 
 
 Air 
 included, 
 parts in 
 
 1000 
 
 
 8.1 
 9.6 
 10.4 
 10.3 
 9.8 
 10.6 
 13.9 
 35.7 
 12.4 
 42.6 
 13-7 
 15.4 
 14. 5 
 20.6 
 30.9 
 49 -o 
 48.0 
 62.1 
 13.0 
 14.0 
 21.0 
 21.7 
 18.0 
 18.7 
 16.7 
 22.0 
 21.0 
 27.0 
 
 56 
 
 SO 
 
 20 
 185 
 
 56 
 244 
 119 
 S06 
 
 23 
 285 
 
 60 
 150 
 
 60 
 253 
 368 
 
 81 
 
 
 
 527 
 
 944 
 950 
 980 
 8iS 
 944 
 7S6 
 
 2. Live geese feathers 
 
 3. Carded cotton wool 
 
 4. Hair felt 
 
 S. Loose lampblack . . 
 
 
 
 881 
 
 
 494 
 977 
 715 
 940 
 850 
 940 
 747 
 632 
 
 
 10. Compressed calcined magnesia 
 
 12. Compressed carbonate of magnesia . . . 
 
 13. Loose fossil meal 
 
 14. Ground chalk 
 
 
 
 919 
 
 
 18. Sand 
 
 471 
 
 19. Best slag wool 
 
 20. Paper 
 
 
 
 
 
 
 
 
 
 
 
 
 24. Loose rice chaff 
 
 
 
 25. Paste of fossil meal with hair 
 
 
 
 26. Paste of fossil meal with asbestos 
 
 
 
 27. Loose bituminous coal ashes 
 
 
 
 
 
 
 
 
 
2IO Heat 
 
 Professor Ordway states that later experiments niade with still air 
 gave results which differ Uttle from cotton wool, hair felt or compressed 
 lampblack. Asbestos is one of the poorest conductors. 
 
 Heat-Conducting Power of Covering Materials 
 
 (J. J. Coleman) 
 
 Mineral wool loo Charcoal 140 
 
 Hair felt 117 Sawdust 163 
 
 Cotton wool ■ . 122 Gas works breeze 230 
 
 Sheep's wool 136 Wood and air space 280 
 
 Infusorial earth 136 
 
 Boiling Points at Atmospheric Pressure 
 
 Ether, sulphuric 100° F. Average sea water 213.2° F. 
 
 Carbon bisulphide 118° F. Saturated brine 226° F. 
 
 Ammonia 140° F. Nitric acid 248° F. 
 
 Chloroform 140° F. Oil of turpentine 315° F. 
 
 Bromine 145° F. Phosphorus 554° F. 
 
 Wood-spirit 150° F. Sulphur 570° F. 
 
 Alcohol 173° F. Sulphuric acid 590° F. 
 
 Benzine 176° F. Linseed oil 597° F. 
 
 Water 212° F. Mercury 676° F. 
 
 The boiling points of liquids increase as the pressure increases. 
 
Table of Equivalent Temperatures 
 
 211 
 
 Table of Equivalent Temperatures, Centigrade to 
 Fahrenheit 
 
 Rule to change the values: Fahr. = " C. + 3.2° 
 
 
 
 
 Cent. = (F. - 32°) 
 
 9' 
 
 
 
 
 Degrees 
 
 Degrees 
 
 Degrees 
 
 Degrees 
 
 Degrees 
 
 Cent. 
 
 Fahr. 
 
 Cent! 
 
 Fahr. 
 
 Cent. 
 
 Fahr. 
 
 Cent. 
 
 Fahr. 
 
 Cent. 
 
 Fahr. 
 
 -10 
 
 +14.0 
 
 22 
 
 71.6 
 
 54 
 
 129.2 
 
 86 
 
 186.8 
 
 190 
 
 374 
 
 - 9 
 
 +15. 8 
 
 23 
 
 73.4 
 
 55 
 
 131. 
 
 87 
 
 188.6 
 
 195 
 
 383 
 
 - 8 
 
 +17.6 
 
 24 
 
 75.2 
 
 56 
 
 132.8 
 
 88 
 
 190.4 
 
 200 
 
 392 
 
 - 7 
 
 +19-4 
 
 25 
 
 77.0 
 
 57 
 
 134.6 
 
 89 
 
 192.2 
 
 20s 
 
 401 
 
 - 6 
 
 +21.2 
 
 26 
 
 78.8 
 
 58 
 
 136.4 
 
 90 
 
 194 
 
 210 
 
 410 
 
 - 5 
 
 +23 
 
 27 
 
 80.6 
 
 59 
 
 138.2 
 
 91 
 
 195.8 
 
 215 
 
 419 
 
 - 4 
 
 +24.8 
 
 28 
 
 82.4 
 
 60 
 
 140.0 
 
 92 
 
 197.6 
 
 220 
 
 428 
 
 - 3 
 
 +26.6 
 
 29 
 
 84.2 
 
 61 
 
 141. 8 
 
 53 
 
 199.4 
 
 225 
 
 437 
 
 — 2 
 
 +28.4 
 
 30 
 
 86.0 
 
 62 
 
 143.6 
 
 94 
 
 201.2 
 
 230 
 
 446 
 
 — I 
 
 +30.2 
 
 31 
 
 87.8 
 
 63 
 
 145.4 
 
 95 
 
 203.0 
 
 235 
 
 455 
 
 
 
 +32.0 
 
 32 
 33 
 
 89.6 
 91.4 
 
 64 
 65 
 
 147.2 
 149.0 
 
 96 
 97 
 
 204.8 
 206.6 
 
 240 
 245 
 
 464 
 
 + 1 
 
 33.8 
 
 473 
 
 2 
 
 35.6 
 
 34 
 
 93.2 
 
 66 
 
 150.8 
 
 98 
 
 208.4 
 
 250 
 
 482 
 
 3 
 
 37.4 
 
 35 
 
 95. 
 
 67 
 
 152.6 
 
 99 
 
 210.2 
 
 255 
 
 491 
 
 4 
 
 39-2 
 41.0 
 
 36 
 37 
 
 96.8 
 98.6 
 
 68 
 69 
 
 154.4 
 156.2 
 
 100 
 
 212 
 
 260 
 265 
 
 500 
 
 
 
 
 
 5 
 
 105 
 
 221 
 
 509 
 
 6 
 
 42.8 
 
 38 
 
 100.4 
 
 70 
 
 158.0 
 
 no 
 
 230 
 
 270 
 
 518 
 
 7 
 
 44.6 
 
 39 
 
 102.2 
 
 71 
 
 159-8 
 
 115 
 
 239 
 
 275 
 
 527 
 
 8 
 
 46.4 
 
 40 
 
 104.0 
 
 72 
 
 161. 6 
 
 120 
 
 248 
 
 280 
 
 536 
 
 9 
 
 48.2 
 
 41 
 
 105.8 
 
 73 
 
 163.4 
 
 125 
 
 257 
 
 285 
 
 545 
 
 10 
 
 50.0 
 
 42 
 
 107.6 
 
 74 
 
 165.2 
 
 130 
 
 266 
 
 290 
 
 554 
 
 II 
 
 51.8 
 
 43 
 
 109.4 
 
 75 
 
 167.0 
 
 135 
 
 275 
 
 295 
 
 563 
 
 12 
 
 53.6 
 
 44 
 
 III. 2 
 
 76 
 
 168.8 
 
 140 
 
 284 
 
 300 
 
 572 
 
 13 
 
 55. 4 
 
 45 
 
 113. 
 
 77 
 
 170.6 
 
 145 
 
 293 
 
 305 
 
 581 
 
 14 
 
 57.2 
 
 46 
 
 114. 8 
 
 78 
 
 172.4 
 
 150 
 
 302 
 
 310 
 
 590 
 
 IS 
 
 59. 
 
 47 
 
 116. 6 
 
 79 
 
 174.2 
 
 155 
 
 311 
 
 315 
 
 599 
 
 16 
 
 60.8 
 
 48 
 
 118. 4 
 
 80 
 
 176.0 
 
 160 
 
 320 
 
 320 
 
 608 
 
 17 
 
 62.6 
 
 49 
 
 120.2 
 
 81 
 
 177.8 
 
 165 
 
 329 
 
 325 
 
 617 
 
 18 
 
 64.4 
 
 50 
 
 122.0 
 
 82 
 
 179.6 
 
 170 
 
 338 
 
 330 
 
 626 
 
 19 
 
 66.2 
 
 51 
 
 123.8 
 
 83 
 
 181. 4 
 
 175 
 
 347 
 
 335 
 
 635 
 
 20 
 
 68.0 
 
 52 
 
 125.6 
 
 84 
 
 183.2 
 
 180 
 
 356 
 
 340 
 
 644 
 
 21 
 
 69.8 
 
 53 
 
 127.4 
 
 85 
 
 185.0 
 
 185 
 
 365 
 
 345 
 
 653 
 
 Data Sheet No. 53, The Foundry, November, 1909. 
 
212 
 
 Heat 
 
 Table of Equivalent Temperatures, Centigrade to 
 Fahrenheit — (Continued) 
 
 Degrees 
 
 Degrees 
 
 Degrees 
 
 Degrees 
 
 Degrees 
 
 Cent. 
 
 Fahr. 
 
 Cent. 
 
 Fahr. 
 
 Cent. 
 
 Fahr. 
 
 Cent. 
 
 Fahr. 
 
 Cent. 
 
 Fahr. 
 
 3SO 
 
 662 
 
 510 
 
 9SO 
 
 670 
 
 1238 
 
 830 
 
 1526 
 
 990 
 
 1814 
 
 355 
 
 671 
 
 515 
 
 959 
 
 675 
 
 1247 
 
 835 
 
 I53S 
 
 995 
 
 1823 
 
 360 
 
 680 
 
 520 
 
 968 
 
 680 
 
 1256 
 
 840 
 
 1544 
 
 1000 
 
 1832 
 
 36s 
 
 689 
 
 525 
 
 977 
 
 68s 
 
 126s 
 
 845 
 
 1553 
 
 loos 
 
 1841 
 
 370 
 
 698 
 
 530 
 
 986 
 
 690 
 
 1274 
 
 850 
 
 1562 
 
 lOIO 
 
 1850 
 
 375 
 
 707 
 
 535 
 
 995 
 
 695 
 
 1283 
 
 855 
 
 1571 
 
 lois 
 
 1859 
 
 380 
 
 716 
 
 540 
 
 1004 
 
 700 
 
 1292 
 
 860 
 
 1580 
 
 1020 
 
 1868 
 
 38s 
 
 725 
 
 545 
 
 1013 
 
 705 
 
 1301 
 
 86s 
 
 IS89 
 
 1025 
 
 1877 
 
 390 
 
 734 
 
 550 
 
 1022 
 
 710 
 
 1310 
 
 870 
 
 1598 
 
 1030 
 
 1886 
 
 395 
 
 743 
 
 555 
 
 1031 
 
 715 
 
 1319 
 
 875 
 
 1607 
 
 1035 
 
 189s 
 
 4CX) 
 
 752 
 
 560 
 
 1040 
 
 720 
 
 1328 
 
 880 
 
 1616 
 
 1040 
 
 1904 
 
 405 
 
 761 
 
 565 
 
 1049 
 
 725 
 
 1337 
 
 885 
 
 162s 
 
 104s 
 
 1913 
 
 410 
 
 770 
 
 570 
 
 1058 
 
 730 
 
 1346 
 
 890 
 
 1634 
 
 1050 
 
 1922 
 
 415 
 
 779 
 
 575 
 
 1067 
 
 735 
 
 1355 
 
 895 
 
 1643 
 
 loss 
 
 1931 
 
 420 
 
 788 
 
 580 
 
 1076 
 
 740 
 
 1364 
 
 900 
 
 1652 
 
 1060 
 
 1940 
 
 425 
 
 797 
 
 585 
 
 1085 
 
 745 
 
 1373 
 
 905 
 
 1661 
 
 1065 
 
 1949 
 
 430 
 
 806 
 
 590 
 
 1094 
 
 ' 750 
 
 1382 
 
 910 
 
 1670 
 
 1070 
 
 1958 
 
 435 
 
 815 
 
 595 
 
 1103 
 
 755 
 
 1391 
 
 915 
 
 1679 
 
 107s 
 
 1967 
 
 440 
 
 824 
 
 600 
 
 1112 
 
 760 
 
 1400 
 
 920 
 
 1688 
 
 1080 
 
 1976 
 
 445 
 
 833 
 
 60s 
 
 1121 
 
 765 
 
 1409 
 
 92s 
 
 1697 
 
 1085 
 
 1985 
 
 450 
 
 842 
 
 610 
 
 1130 
 
 770 
 
 1418 
 
 930 
 
 1706 
 
 1090 
 
 1994 
 
 455 
 
 851 
 
 615 
 
 1139 
 
 775 
 
 1427 
 
 935 
 
 1715 
 
 109s 
 
 2003 
 
 460 
 
 860 
 
 620 
 
 1 148 
 
 780 
 
 1436 
 
 940 
 
 1724 
 
 1 100 
 
 2012 
 
 46s 
 
 869 
 
 625 
 
 1157 
 
 785 
 
 1445 
 
 945 
 
 1733 
 
 iios 
 
 2021 
 
 470 
 
 878 
 
 630 
 
 1166 
 
 790 
 
 1454 
 
 9SO 
 
 1742 
 
 mo 
 
 2030 
 
 475 
 
 887 
 
 635 
 
 1175 
 
 795 
 
 1463 
 
 955 
 
 1751 
 
 1115 
 
 2039 
 
 480 
 
 896 
 
 640 
 
 1 184 
 
 800 
 
 1472 
 
 960 
 
 1760 
 
 1 120 
 
 2048 
 
 485 
 
 90s 
 
 64s 
 
 1193 
 
 80s 
 
 1481 
 
 96s 
 
 1769 
 
 1125 
 
 20S7 
 
 490 
 
 914 
 
 650 
 
 1202 
 
 810 
 
 1490 
 
 970 
 
 1778- 
 
 1130 
 
 2066 
 
 495 
 
 923 
 
 655 
 
 1211 
 
 815 
 
 1499 
 
 975 
 
 1787 
 
 1 135 
 
 207s 
 
 500 
 
 932 
 
 660 
 
 1220 
 
 820 
 
 1508 
 
 980 
 
 1796 
 
 1 140 
 
 2084 
 
 S05 
 
 941 
 
 665 
 
 1229 
 
 825 
 
 1517 
 
 985 
 
 1805 
 
 1 145 
 I150 
 
 2093 
 2102 
 
 Data Sheet No. 54. The Foundry, November, 1909. 
 
Strength of Materials 
 Comparison of Thermometer Scales 
 
 213 
 
 Centi- 
 grade 
 
 Reaumur 
 
 Fahren- 
 heit 
 
 Centi- 
 grade 
 
 Reaumur 
 
 Fahren- 
 heit 
 
 Centi- 
 grade 
 
 Reaumur 
 
 Fahren- 
 heit 
 
 -30 
 
 -24.0 
 
 —22.0 
 
 14 
 
 II. 2 
 
 57.2 
 
 58 
 
 46.4 
 
 136.4 
 
 -28 
 
 -22.4 
 
 — 18.4 
 
 16 
 
 12.8 
 
 60.8 
 
 60 
 
 48.0 
 
 140.0 
 
 -26 
 
 -20.8 
 
 -14.8 
 
 18 
 
 14.4 
 
 64.4 
 
 62 
 
 49-6 
 
 143-6 
 
 -24 
 
 -19.2 
 
 -II. 2 
 
 20 
 
 16.0 
 
 68.0 
 
 64 
 
 51.2 
 
 147-2 
 
 —22 
 
 -17.6 
 
 - 7.6 
 
 22 
 
 17.6 
 
 71.6 
 
 66 
 
 52.8 
 
 150.8 
 
 —20 
 
 -16.0 
 
 - 4-0 
 
 24 
 
 19.2 
 
 75-2 
 
 68 
 
 54-4 
 
 154-4 
 
 -18 
 
 -14.4 
 
 - 0.4 
 
 26 
 
 20.8 
 
 78.8 
 
 70 
 
 56.0 
 
 158.0 
 
 -16 
 
 -12.8 
 
 3.2 
 
 28 
 
 22.4 
 
 82.4 
 
 72 
 
 57.6 
 
 161. 6 
 
 -14 
 
 —II. 2 
 
 6.8 
 
 30 
 
 24.0 
 
 86.0 
 
 74 
 
 59-2 
 
 165.2 
 
 — 12 
 
 - 9.6 
 
 10.4 
 
 32 
 
 25.6 
 
 89.6 
 
 76 
 
 60.8 
 
 168.8 
 
 -10 
 
 - 8.0 
 
 14.0 
 
 34 
 
 27.2 
 
 93.2 
 
 78 
 
 62.4 
 
 172.4 
 
 - 8 
 
 - 6.4 
 
 17.6 
 
 36 
 
 28.8 
 
 96.8 
 
 80 
 
 64.0 
 
 176.0 
 
 - 6 
 
 - 4.8 
 
 21.2 
 
 38 
 
 30.4 
 
 100.4 
 
 82 
 
 65.6 
 
 179.6 
 
 - 4 
 
 - 3.2 
 
 24.8 
 
 40 
 
 32.0 
 
 104.0 
 
 84 
 
 67.2 
 
 183.2 
 
 — 2 
 
 - 1.6 
 
 28.4 
 
 42 
 
 33.6 
 
 107.6 
 
 86 
 
 68.8 
 
 186.8 
 
 
 
 0.0 
 
 32.0 
 
 44 
 
 35.2 
 
 III. 2 
 
 88 
 
 70.4 
 
 190.4 
 
 2 
 
 1.6 
 
 35.6 
 
 46 
 
 36.8 
 
 114. 8 
 
 90 
 
 72.0 
 
 194.0 
 
 4 
 
 3.2 
 
 39.2 
 
 48 
 
 38.4 
 
 118. 4 
 
 92 
 
 73.6 
 
 197.6 
 
 6 
 
 4.8 
 
 42.8 
 
 SO 
 
 40.0 
 
 122.0 
 
 94 
 
 75-2 
 
 201.2 
 
 8 
 
 6.4 
 
 46.4 
 
 52 
 
 41.6 
 
 125.6 
 
 96 
 
 76.8 
 
 204.8 
 
 10 
 
 8.0 
 
 50.0 
 
 54 
 
 43.2 
 
 129.2 
 
 98 
 
 78.4 
 
 208.4 
 
 12 
 
 9.6 
 
 53.6 
 
 56 
 
 44.8 
 
 132.8 
 
 100 
 
 80.0 
 
 212.0 
 
 No. 21, Supplement to Machinery, June, 1903. 
 
 Strength of Materials 
 
 (From notes on Machine Design, by permission of the author, Prof. Chas. H. 
 Benjamin, Cleveland, O.) 
 
 
 Ultimate strength 
 
 Elastic 
 limit, 
 tension 
 
 Modu- 
 lus of 
 rupture, 
 trans- 
 verse 
 
 Modu- 
 lus of 
 
 Kind of metal 
 
 Ten- 
 sile 
 
 Com- 
 pression 
 
 Shear- 
 ing 
 
 elastic- 
 ity, 
 tension 
 
 Wrought iron, small bars 
 
 Wrought iron, plates. .... 
 
 55 ,000 
 50,000 
 45,000 
 60,000 
 90,000 
 90,000 
 120,000 
 
 18,000 
 36,000 
 38,000 
 18,000 
 24,000 
 36,000 
 85,000 
 58,000 
 28,000 
 
 38,000 
 100,000 
 
 75.000 
 
 125,000 
 
 12,000 
 
 75,000 
 
 100,000 
 
 132,000 
 
 13.000 
 
 45,000 
 40,060 
 35,000 
 50,000 
 
 80,000 
 
 25,000 
 42,000 
 
 24,000 
 
 43,000 
 
 28,000 
 25,000 
 22,500 
 32,000 
 
 50,000 
 60,000 
 Un- 
 certain 
 16,000 
 18,000 
 
 20,000 
 14,000 
 
 40,000 
 30,000 
 
 36,000 
 30,000 
 
 26,000,000 
 25,000,000 
 25,000,000 
 28,000,000 
 
 29,000,000 
 40,000,000 
 
 18,000,000 
 
 Wrought iron, large forgings. . 
 Steel, 0. H. plate . . . 
 
 Steel, Bessemer 
 
 
 Cast iron 
 
 Malleable castings 
 
 Steel castings 
 
 30,000,000 
 9,000,000 
 15,000,000 
 10,000,000 
 
 Brass castings . . 
 
 Copper castings 
 
 
 Bronze, 10 Al, 90 Cu 
 
 
 14.000,000 
 11,000,000 
 
 
 
214 
 
 Strength of Materials 
 
 Material 
 
 Tension 
 
 per square 
 
 inch 
 
 Compres- 
 sion per 
 square inch 
 
 Shear per 
 
 square 
 
 inch 
 
 
 
 103,272 
 318,823 
 59.246 
 97,908 
 37.607 
 46,494 
 81,114 
 98,578 
 78,049 
 81,735 
 92,224 
 
 11,000 
 17,207 
 ii,Soo 
 18,000 
 13,500 
 8,700 
 12,800 
 18,000 
 10,500 
 10,250 
 19.500 
 
 
 
 
 
 
 
 
 
 
 Iron wire 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 Bronze wire 
 
 
 
 
 
 
 
 
 
 
 
 Woods: 
 Ash......; 
 
 6800 
 
 6280 
 
 Beech 
 
 7000 
 
 5223 
 
 Elm 
 
 7700 
 5300 
 8000 
 
 
 Hemlock 
 
 
 Hickory 
 
 1 
 
 2750 
 604s 
 
 Maple 
 
 6800 
 7000 
 
 7285 
 
 Oak (white) 
 
 ! 
 
 4425 
 
 
 } 
 
 
 Oak (live) 
 
 6850 
 
 5400 
 
 8500 
 
 5700 
 
 8000 
 
 Tons per 
 
 square foot 
 
 40 
 
 300 
 
 300 
 
 1200 
 
 250 
 
 1000 
 
 8480 
 
 Pine (white) 
 
 11,000 
 15,900 
 14,500 
 12,500 
 
 2450 
 5735 
 5255 
 47SO 
 
 
 
 Walnut (black) 
 
 Brick (pressed) 
 
 i 
 
 ! 
 
 1 
 
 
 Granite 
 
 
 
 
 
 
 
 
 Limestone 
 
 
 
 
 
 
Properties of Air 215 
 
 Strength of Lime and Cement Mortar 
 
 Tensile Strength, Pounds per Square Inch 
 Age 7 days. 
 
 Lime mortar 8 
 
 20 per cent Rosendale 8.5 
 
 20 per cent Roseland 8.5 
 
 30 per cent Rosendale 11 
 
 30 per cent Portland 16 
 
 40 per cent Rosendale 12 
 
 40 per cent Portland 39 
 
 60 per cent Rosendale 13 
 
 60 per cent Portland 58 
 
 80 per cent Rosendale 18.5 
 
 80 per cent Portland 91 
 
 100 per cent Rosendale 23 
 
 100 per cent Portland 120 
 
 Coefficient of Friction 
 
 If two bodies have plane surfaces in contact and the plane of contact 
 be inclined so that one body just begins to slide upon the other, the angle 
 made by this plane with a horizontal plane is called the angle of repose. 
 
 The coefficient of friction is the ratio of the ultimate friction to the 
 pressure perpendicular to the plane of contact, and is equal to the 
 tangent of the angle of repose. 
 
 Thus, if R denotes the friction between the surfaces, Q the perpendicu- 
 lar pressure and F the coefficient of friction. Then 
 
 F = ^ and R = FQ. 
 
 Centrifugal Force 
 
 In a revolving body the force expended to deflect it from a rectilinear 
 to a curved path is called centrifugal force and is equal to the weight of 
 the body multiplied by the square of its velocity in feet per second, 
 divided by 32.6 times the radius; or, if F equals centrifugal force, W 
 equals weight of body, V equals velocity in feet per second and R equals 
 
 the radius, then F = ;r-^ . If N equals the number of revolutions 
 
 32.16 i? 
 
 per minute, the formula is reduced to F = .000341 WN^R. 
 
 Properties of Air 
 
 Air is a mechanical mixture of the gases, oxygen and nitrogen; 21 
 parts oxygen and 79 parts nitrogen by volume, or 23 parts oxygen and 
 77 parts nittogen by weight. The weight of pure air at 32° F. and 29.9 
 barometer, or 14.6963 pounds per square inch; or 21 16.3 pounds per 
 
2l6 
 
 Air 
 
 square foot is .080728 pounds. The volume of one pound is 12.387 cubic 
 feet. 
 
 Air expands 1/491.2 of its volume for every increase of 1° F., and its 
 volume varies inversely as the pressure. 
 
 Volume, Density and Pressure of Air at Various Temperatures 
 
 (D. K. Clark.) 
 
 
 Volume at 
 
 atmospheric 
 
 
 Pressure at constant 
 
 
 pressure 
 
 Density, lbs. 
 
 volume 
 
 
 
 
 per cubic foot 
 at atmospheric 
 
 
 Fahr. 
 
 
 
 
 
 
 Cubic feet 
 
 Comparative 
 
 pressure 
 
 Pounds per 
 
 Comparative 
 
 
 in I pound 
 
 volume 
 
 
 square inch 
 
 pressure 
 
 
 
 11.583 
 
 .881 
 
 .086331 
 
 12 . 96 
 
 .881 
 
 32 
 
 12.387 
 
 .943 
 
 .080728 
 
 13.86 
 
 .943 
 
 40 
 
 12.586 
 
 .958 
 
 .079439 
 
 14.08 
 
 • 958 
 
 SO 
 
 12.840 
 
 ■ 977 
 
 .077884 
 
 14.36 
 
 .977 
 
 62 
 
 13. 141 
 
 1. 000 
 
 .076097 
 
 14.70 
 
 1. 000 
 
 70 
 
 13.342 
 
 1. 015 
 
 .074950 
 
 14.92 
 
 1. 015 
 
 80 
 
 13.593 
 
 1.034 
 
 .073565 
 
 15.21 
 
 1.034 
 
 90 
 
 13.845 
 
 T.OS4 
 
 .072230 
 
 15.49 
 
 I OS4 
 
 100 
 
 14.096 
 
 1.073 
 
 .070942 
 
 15.77 
 
 1.073 
 
 no 
 
 14.344 
 
 1.092 
 
 .069721 
 
 16. OS 
 
 1.092 
 
 120 
 
 14.592 
 
 I. Ill 
 
 .068500 
 
 16.33 
 
 I. Ill 
 
 130 
 
 14.846 
 
 1. 130 
 
 .067361 
 
 16.61 
 
 1. 130 
 
 140 
 
 15.100 
 
 1. 149 
 
 .066221 
 
 16.89 
 
 1. 149 
 
 150 
 
 15.351 
 
 1. 168 
 
 .065155 
 
 17.19 
 
 1. 168 
 
 160 
 
 15.603 
 
 1. 187 
 
 .064088 
 
 17.50 
 
 1. 187 
 
 170 
 
 15.854 
 
 1.266 
 
 .063089 
 
 17.76 
 
 1.206 
 
 180 
 
 16 . 106 
 
 1.226 
 
 .062090 
 
 18.02 
 
 1.226 
 
 200 
 
 16.606 
 
 1.264 
 
 .060210 
 
 18.58 
 
 1.264 
 
 210 
 
 16.860 
 
 1.283 
 
 .059313 
 
 18.86 
 
 1.283 
 
 212 
 
 16.910 
 
 1.287 
 
 .059135 
 
 18.92 
 
 1.287 
 
 Pressure of the Atmosphere per Square Inch and per 
 Square Foot at Various Readings of the Barometer 
 
 Rule. — Barometer in inches X .4908 = pressure per square inch; pressure per 
 square inch X 144 = pressure per square foot. 
 
 Barometer, 
 inches 
 
 Pressure per 
 square inch, 
 
 Pressure per 
 square foot. 
 
 Barometer, 
 inches 
 
 Presstire per 
 square inch, 
 
 Pressure per 
 square foot, 
 
 pounds 
 
 pounds 
 
 pounds 
 
 pounds 
 
 28.00 
 
 13.74 
 
 .1978 
 
 29.75 
 
 14.60 
 
 2102 
 
 28.25 
 
 13.86 
 
 1995 
 
 30 
 
 00 
 
 14.72 
 
 2119 
 
 28.50 
 
 13.98 
 
 2013 
 
 30 
 
 25 
 
 14.84 
 
 2136 
 
 28.75 
 
 14. II 
 
 2031 
 
 30 
 
 50 
 
 14.96 
 
 2154 
 
 29.00 
 
 14.23 
 
 2049 
 
 30 
 
 75 
 
 15.09 
 
 2172 
 
 29.25 
 
 14.35 
 
 2066 
 
 31 
 
 00 
 
 15.21 
 
 2190 
 
 29.50 
 
 14.47 
 
 2083 
 
 
 
 
 
 
 
 
 
Properties of Air 
 
 217 
 
 Barometric Readings Corresponding with Different 
 Altitudes (Kent.) 
 
 Altitude, 
 
 Reading of 
 
 Altitude, 
 
 Reading of 
 
 feet 
 
 barometer, 
 inches 
 
 feet 
 
 barometer, 
 inches 
 
 
 
 30.00 
 
 3763.2 
 
 25.98 
 
 68.9 
 
 29.92 
 
 4163.3 
 
 25.59 
 
 416.7 
 
 29.52 
 
 4568.3 
 
 25.19 
 
 767.7 
 
 29.13 
 
 4983.1 
 
 24.80 
 
 1122.1 
 
 28.74 
 
 5403.2 
 
 24.41 
 
 1486.2 
 
 28.35 
 
 5830.2 
 
 24.01 
 
 ■ 1850.4 
 
 27.95 
 
 6243.0 
 
 23.62 
 
 2224.5 
 
 27.55 
 
 6702.9 
 
 23.22 
 
 2599.7 
 
 27.16 
 
 7152.4 
 
 22.83 
 
 2962.1 
 
 26.77 
 
 7605.1 
 
 22.44 
 
 3369. S 
 
 26.38 
 
 8071.0 
 
 22.04 
 
 Horse Power Required to Compress One Cubic Foot of 
 Free Air per Minute to a Given Pressure (Richards.) 
 
 Air not cooled during compression; also the horse power required, supposing the 
 air to be maintained at constant temperature during the compression. 
 
 Gauge 
 pressure 
 
 Air not 
 cooled 
 
 Air at 
 
 constant 
 
 temperature 
 
 100 
 
 .22183 
 
 .14578 
 
 90 
 
 .20896 
 
 .13954 
 
 80 
 
 .19521 
 
 .13251 
 
 70 
 
 .17989 
 
 .12606 • 
 
 60 
 
 .164 
 
 .11558 
 
 50 
 
 .14607 
 
 .10565 
 
 40 
 
 .12433 
 
 .093667 
 
 30 
 
 .10346 
 
 .079219 
 
 20 
 
 .076808 
 
 .061188 
 
 10 
 
 .044108 
 
 .036944 
 
 S 
 
 .024007 
 
 .020848 
 
2l8 
 
 Air 
 
 Horse Power Required to Deliver One Cubic Foot of 
 
 Air per Minute at a Given Pressure (Richards.) 
 
 Air not cooled during compression; also the horse power required, supposing the 
 air to be maintained at constant temperature during the compression. 
 
 Gauge 
 
 Air not 
 
 Air at 
 
 pressure 
 
 cooled 
 
 constant 
 temperature 
 
 lOO 
 
 I. 7317 
 
 i . 13801 
 
 90 
 
 1.4883 
 
 .99387 
 
 80 
 
 1.25779 
 
 .8528 
 
 70 
 
 1.03683 
 
 .72651 
 
 60 
 
 .83344 
 
 .58729 
 
 SO 
 
 .64291 
 
 .465 
 
 40 
 
 .46271 
 
 .34859 
 
 30 
 
 .31456 
 
 .24086 
 
 20 
 
 .181279 
 
 .14441 
 
 10 
 
 .074106 
 
 .06069 
 
 5 
 
 .032172 
 
 .027938 
 
 In computing the above tables an allowance of 10 per cent has been 
 made for friction of the compressor. 
 
Pressure of Water 
 
 219 
 
 Pressure of Water 
 
 Pressure in Pounds per Square Inch for Different 
 Heads of Water (Kent.) 
 
 At 62° F. I foot head 0.433 pound per square inch, 0.433 X 144 = 62.352 pounds 
 per cubic foot. 
 
 Head, 
 feet 
 
 
 
 I 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 
 
 
 0.433 
 
 0.866 
 
 1.299 
 
 1.732 
 
 2.165 
 
 2.598 
 
 3.031 
 
 3.464 
 
 3.897 
 
 10 
 
 4 330 
 
 4.763 
 
 5.196 
 
 5.629 
 
 6.062 
 
 6.49s 
 
 6.928 
 
 7.361 
 
 7.794 
 
 8.227 
 
 20 
 
 8.660 
 
 9 093 
 
 9.526 
 
 9-959 
 
 10.392 
 
 10.825 
 
 11.258 
 
 II. 691 
 
 12 . 124 
 
 12.557 
 
 30 
 
 12.990 
 
 13.423 
 
 13.856 
 
 14.298 
 
 14.722 
 
 IS.I5S 
 
 IS. 588 
 
 16.021 
 
 16.454 
 
 16.887 
 
 40 
 
 17.320 
 
 17.753 
 
 18.186 
 
 18.619 
 
 19.052 
 
 19.48s 
 
 19.918 
 
 20.351 
 
 20.784 
 
 21.217 
 
 SO 
 
 21.650 
 
 22.083 
 
 22.516 
 
 22.949 
 
 23.382 
 
 23.819 
 
 24 . 248 
 
 24.681 
 
 25.114 
 
 25.547 
 
 60 
 
 25.980 
 
 26.413 
 
 26.846 
 
 27.279 
 
 27.712 
 
 28.145 
 
 28.578 
 
 29.011 
 
 29.444 
 
 29.877 
 
 70 
 
 30.310 
 
 30.743 
 
 31.176 
 
 31.609 
 
 32.042 
 
 32.475 
 
 32.908 
 
 33.341 
 
 33.774 
 
 34.207 
 
 80 
 
 34.640 
 
 35.073 
 
 35 506 
 
 35.939 
 
 36.372 
 
 36.805 
 
 37.238 
 
 37.671 
 
 38.104 
 
 38.537 
 
 90 
 
 38.970 
 
 39.403 
 
 39.836 
 
 40.269 
 
 40.702 
 
 41.135 
 
 41.568 
 
 42.001 
 
 42.436 
 
 42.867 
 
 Head in Feet of Water, Corresponding to Pressures in 
 Pounds per Square Inch (Kent.) 
 
 I pound per square inch 2.30947 feet head, i atmosphere 14.71 pounds per square 
 inch 33-94 foot head. 
 
 Pres- 
 sure 
 
 
 
 I 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 
 
 
 2.309 
 
 4.619 
 
 6.928 
 
 9.238 
 
 11.547 
 
 13.857 
 
 16.166 
 
 18.476 
 
 20.78s 
 
 10 
 
 23.0947 
 
 25.404 
 
 27.714 
 
 30.023 
 
 32.333 
 
 34.642 
 
 36.952 
 
 39.261 
 
 41.570 
 
 43.880 
 
 20 
 
 46.1894 
 
 48.499 
 
 50.808 
 
 53.118 
 
 55.427 
 
 57.737 
 
 60.046 
 
 62.356 
 
 64.665 
 
 66.975 
 
 30 
 
 .69.2841 
 
 71.594 
 
 73.903 
 
 76.213 
 
 78.522 
 
 80.831 
 
 83.141 
 
 85.450 
 
 87.760 
 
 90.069 
 
 40 
 
 92.3788 
 
 94.688 
 
 96.998 
 
 99.307 
 
 101.62 
 
 103.93 
 
 106.24 
 
 108.5s 
 
 110.85 
 
 113. 16 
 
 SO 
 
 115.4735 
 
 117.78 
 
 120.09 
 
 122.40 
 
 124.71 
 
 126.02 
 
 129.33 
 
 131.64 
 
 133.95 
 
 136 . 26 
 
 60 
 
 138.5682 
 
 140.88 
 
 143.19 
 
 145.50 
 
 147.81 
 
 150.12 
 
 152.42 
 
 154.73 
 
 157.04 
 
 159. 35 
 
 70 
 
 161.6629 
 
 163.97 
 
 166.28 
 
 168.59 
 
 170.90 
 
 173.21 
 
 175.52 
 
 177.83 
 
 180.14 
 
 182.4s 
 
 80 
 
 184.7576 
 
 187.07 
 
 189.38 
 
 191.69 
 
 194.00 
 
 196.31 
 
 198.61 
 
 200.92 
 
 203.23 
 
 205.54 
 
 90 
 
 207.8523 
 
 210.16 
 
 212.47 
 
 214.78 
 
 217.09 
 
 219.40 
 
 221.71 
 
 224.02 
 
 226.33 
 
 228.64 
 
Electrical and Mechanical Units 
 
 Equivalent Values of Electrical and Mechanical Units 
 
 Units 
 
 Equivalent value in other units 
 
 I kilowatt hour = 
 
 1,000 watt hours. 
 
 1.34 horse-power hours. 
 2,654,200 ft. lbs. 
 3,600,000 joules. 
 3,412 heat units. 
 367,000 kilogram metres. 
 
 .23s lb. carbon, oxidized with perfect efficiency. 
 3.53 lbs. water evap. from and at 212° F. 
 22.75 lbs. of water raised from 62° F., to 212° F. 
 
 I horse-power hour = 
 
 .746 K.W. hours. 
 1,980,000 ft. lbs. 
 2,545 heat units. 
 273,000 kilogram metres. 
 
 .175 lb. carbon oxidized with perfect efficiency. 
 2.64 lbs. water evap. from and at 212° F. 
 17 lbs. of water raised from 62° F. to 212° F. 
 
 I kilowatt = 
 
 1,000 watts. 
 
 1.34 horse power. 
 2,654,200 ft. lbs. per hour. 
 44,240 ft. lbs. per minute. 
 737-3 ft. lbs. per second. 
 3,412 heat units per hour. 
 56.9 heat units per minute. 
 .948 heat unit per second. 
 .2275 lb. carbon oxidized per hour. 
 3.53 lbs. water evap. per hour from and at 212" F. 
 
 I horse power = 
 
 746 watts. 
 .746 K.W. 
 33.000 ft. lbs. per minute. 
 550 ft. lbs. per second. 
 2,545 heat units per hour, 
 42.4 heat units per minute. 
 ,707 heat unit per second. 
 .175 lb. carbon oxidized per hour. 
 2.64 lbs. water evap. per hour from and at 212° F. 
 
 I joule = 
 
 I watt second. 
 .000000278 K.W. hour. 
 .102 k.g.m. 
 
 .0009477 heat units. J^g^Bj^^^^^^Hfl 
 
 1 foot pound = 
 
 1.356 joules. 
 .1383 k.g.m. 
 .000000377 K.W. hour. 
 .001285 heat unit. 
 .0000005 H.P. hour. 
 
Equivalent Values of Electrical and Mechanical Units 221 
 
 Equivalent Values of Electrical and Mechanical 
 Units — {Continued) 
 
 Units 
 
 Equivalent Value in Other Units 
 
 I watt = 
 
 I joule per second. 
 
 .00134 H.P. 
 3.412 heat units per hour. 
 
 .7373 ft. lb. per second. 
 
 .0035 lb. of water evap. per hour. 
 44.24 ft. lbs. per minute. 
 
 I watt per square inch = 
 
 8.19 heat units per sq. ft. per minute. 
 6,371 ft. lbs. per sq. ft. per minute. 
 .193 H.P. per sq. ft. 
 
 I heat unit = 
 
 1,055 watt seconds. 
 778 ft. lbs. 
 107.6 kilogram metres. 
 
 .000293 K.W. hour. 
 
 .000393 H.P. hour. 
 
 .00006S8 lb. of carbon oxidized. 
 
 .001036 lb. water evap. from and at 212° F. 
 
 I heat unit per 
 
 square foot per 
 
 minute = 
 
 . 122 watts per square inch. 
 .0176 K.W. per sq. ft. 
 .0236 H.P. per sq. ft. 
 
 I kilogram metre = 
 
 7.233 ft. lbs. 
 .00000365 H.P. hour. 
 .00000272 K.W. hour. 
 .0093 heat unit. 
 
 I pound carbon 
 
 oxidized with perfect 
 
 efficiency = 
 
 14,544 heat units. 
 
 I . II lbs. of anthracite coal oxidized. 
 2.5 lbs. dry wood, oxidized. 
 21 cubic ft. illuminating gas. 
 4.26 K.W. hours. 
 5.71 H.P. hours. 
 11,315,000 ft. lbs. 
 
 15 lbs. water evap. from and at 212° F. 
 
 I pound water 
 evaporated from 
 and at 212° F. = 
 
 .283 K.W. hour. 
 .379 H.P. hour. 
 965.7 heat units. 
 103,900 k.g.m. 
 1,019,000 joules. 
 751,300 ft. lbs. 
 
 .0664 lb. of carbon oxidized. 
 
CHAPTER VI 
 ALLOYS 
 
 An alloy is a combination by fusion of two or more metals. The com- 
 bination may be a chemical one; generally, however, there is an excess 
 of one or more of the constituents. 
 
 Metals do not unite indifferently, but have certain affinities; thus 
 zinc and lead do not unite, but either will mix with silver in any pro- 
 portion. 
 
 Alloys are generally harder, less ductile and have greater tenacity than 
 the mean of their components. The melting point of an alloy is as a rule 
 below that of any of its components, and it is more easily oxidized. 
 
 The specific gravity of an alloy may be greater, equal to, or less than 
 the mean of its components. 
 
 In alloys of copper and tin the maximum tensile and compressive 
 strength is afforded by a mixture containing 82.7 per cent copper and 
 17.3 per cent tin. The minimum strength is shown by a composition 
 of 62.5 per cent copper and 37.5 per cent tin. 
 
 Alloys of Copper and Tin 
 
 Mean composition by analysis 
 
 Tensile 
 strength in 
 pounds per 
 square inch 
 
 Elastic 
 
 limit in 
 
 pounds per 
 
 square inch 
 
 Crushing 
 strength in 
 
 Copper 
 
 Tin 
 
 pounds per 
 square inch 
 
 
 
 12,760 
 
 24,580 
 
 28,540 
 
 29.430 
 
 32,980 
 
 22,010 
 
 5.585 
 
 2,201 
 
 1.455 
 
 3,010 
 
 6.775 
 
 6,390 
 
 6,4So 
 
 4,780 
 
 3.505 
 
 11,000 
 10,000 
 19,000 
 20,000 
 
 
 97.89 
 92.11 
 87.15 
 80.95 
 76.63 
 69.84 
 65.34 
 
 I 
 7 
 
 12 
 18 
 23 
 29 
 34 
 43 
 55 
 76 
 88 
 91 
 96 
 100 
 
 90 
 80 
 75 
 84 
 24 
 88 
 47 
 17 
 28 
 29 
 47 
 39 
 31 
 00 
 
 34.000 
 42,000 
 53.000 
 
 22,010 
 5,585 
 2,201 
 1,455 
 3.010 
 6.775 
 3.500 
 3.SOO 
 2,750 
 
 144,000 
 147.000 
 84.700 
 
 44.52 
 23.3s 
 11.49 
 
 8.57 
 3.72 
 
 35.800 
 
 10,100 
 9,800 
 9,800 
 6,400 
 
 
 
 
 
 
Composition of Alloys in Common Use in Brass Foundries 223 
 
 Alloys of Copper and Zinc 
 
 Mean composition by analysis 
 
 Tensile 
 strength in 
 pounds per 
 square inch 
 
 Elastic limit 
 per cent of 
 breaking load 
 in pounds per 
 square inch 
 
 Crushing 
 strength in 
 pounds per 
 squaye inch 
 
 Copper 
 
 Zinc 
 
 Q7.83 
 
 1.88 
 16.98 
 23.08 
 28.54 
 33.50 
 38.65 
 44.44 
 50.14 
 52.28 
 56.22 
 66.23 
 77.63 
 86.67 
 94.59 
 100.00 
 
 27,240 
 32,600 
 30,520 
 30,510 
 37,800 
 41,065 
 44,280 
 30,990 
 24,150 , 
 
 9,170 
 
 1.774 
 
 9,000 
 12,413 
 18,065 
 
 5.400 
 
 
 
 82.93 
 
 26.1 
 84.6 
 29.S 
 25.1 
 40.1 
 44.00 
 54.5 
 100. 
 100. 
 100. 
 100. 
 100. 
 100. 
 75.0 
 
 
 76.6s 
 71.20 
 
 42,000 
 
 66.27 
 
 
 60.94 
 55.15 
 49.66 
 47.56 
 43.36 
 
 75.000 
 78,000 
 117,400 
 121,000 
 
 32.94 
 
 
 20.81 
 12.12 
 
 52.152 
 
 4-35 
 
 
 
 
 22,000 
 
 Composition of Alloys in Common Use in Brass Foundries 
 
 (American Machinist.) 
 
 Alloys 
 
 Admiralty metal 
 
 Bell metal 
 
 Brass (yellow)... 
 
 Bush metal 
 
 Gun metal 
 
 Steam metal. . . . 
 
 Hard gun metal . 
 Muntz metal. . . . 
 
 Phosphor bronze 
 
 T, . j metal... 
 ^'■^^^"g I solder.. 
 
 Copper, 
 
 Zinc, 
 
 Tin, 
 
 Lead, 
 
 lbs. 
 
 lbs. 
 
 lbs. 
 
 lbs. 
 
 87 
 
 5 
 
 8 
 
 
 16 
 
 
 4 
 
 
 16 
 
 8 
 
 
 5 
 
 64 
 
 8 
 
 4 
 
 4 
 
 32 
 
 I 
 
 3 
 
 
 20 
 
 I 
 
 1.5 
 
 I 
 
 16 
 
 
 2.5 
 
 
 60 
 
 40 
 
 
 
 92 
 
 
 8.0 
 
 
 90 
 
 
 10. 
 
 
 16 
 
 3 
 
 
 
 50 
 
 50 
 
 
 
 For parts of engines on naval 
 vessels. 
 
 Bells for ships and factories. 
 
 For plumbers, ship and house 
 work. 
 
 Bearing bushes for shafting. 
 
 For pumps and hydraulic work. 
 
 Casting subjected to steam pres- 
 sure. 
 
 For heavy bearings. 
 
 For bolts and nuts, forged. Valve 
 spindles, etc. 
 
 Phos. tin for valves, pumps and 
 general work. 
 
 Phos. tin for cog and worm wheels, 
 bushes and bearings. 
 
 Flanges for copper pipe. 
 
 Solder for above flanges. 
 
224 
 
 x\lloys 
 Alloys of Copper, Tin and Zinc 
 
 Analysis original mixture 
 
 Tensile 
 
 
 
 strength per 
 
 
 
 Cu 
 
 Sn 
 
 Zn 
 
 square inch 
 
 90 
 
 5 
 
 5 
 
 23,660 
 
 85 
 
 5 
 
 10 
 
 28,840 
 
 85 
 
 10 
 
 5 
 
 3S,68o 
 
 80 
 
 5 
 
 15 
 
 37,560 
 
 80 
 
 10 
 
 10 
 
 32,830 
 
 75 
 
 5 
 
 20 
 
 34,960 
 
 75 
 
 7-5 
 
 17. 5 
 
 39.300 
 
 75 
 
 10. 
 
 15.0 
 
 34.000 
 
 75 
 
 15.0 
 
 10. 
 
 28,000 
 
 75 
 
 20.0 
 
 50 
 
 27,660 
 
 70 
 
 5.0 
 
 25.0 
 
 32,940 
 
 70 
 
 7.5 
 
 22.5 
 
 32,400 
 
 70 
 
 10. 
 
 20.0 
 
 26,300 
 
 70 
 
 15.0 
 
 15.0 
 
 27,800 
 
 70 
 
 20.0 
 
 lO.O 
 
 12,900 
 
 67.5 
 
 2.5 
 
 30.0 
 
 45,850 
 
 67.5 
 
 5.0 
 
 27.5 
 
 34,460 
 
 67.5 
 
 7.5 
 
 25.0 
 
 30,000 
 
 65.0 
 
 2.5 
 
 32.5 
 
 38,300 
 
 65.0 
 
 5.0 
 
 30.0 
 
 36,000 
 
 65.0 
 
 10. 
 
 25.0 
 
 22,500 
 
 65.0 
 
 15.0 
 
 20.0 
 
 7.231 
 
 65.0 
 
 20.0 
 
 15.0 
 
 2.665 
 
 60.0 
 
 2.5 
 
 37.5 
 
 57,400 
 
 60.0 
 
 5.0 
 
 35.0 
 
 41,160 
 
 60.0 
 
 10. 
 
 30.0 
 
 21,780 
 
 60.0 
 
 15.0 
 
 25.0 
 
 [ 18,020 
 
 58.22 
 
 2.3 
 
 39-48 
 
 66,500 
 
 55.0 
 
 0.5 
 
 44.5 
 
 68,500 
 
 55.0 
 
 5.0 
 
 40.0 
 
 27,000 
 
 55.0 
 
 lo.o 
 
 35.0 
 
 25.460 
 
 50.0 
 
 5.0 
 
 45.0 
 
 23,000 
 
 Above tables from report of U. S. Test Board, Vol. II, 1881. 
 
 Copper-Nickel Alloys 
 
 (German Silver.) 
 
 Constituents 
 
 Copper, 
 lbs. 
 
 Nickel, 
 lbs. 
 
 Tin, 
 lbs. 
 
 Zinc, 
 lbs. 
 
 German silver i 
 
 51.6 
 50.2 
 75.0 
 
 25.8 
 14.8 
 
 22.6 
 
 3.1 
 
 25.0 
 
 
 Nickel silver 
 
 31.9 
 
 
 
Delta Metal 
 Useful Alloys of Copper, Tin and Zinc 
 
 225 
 
 Alloys 
 
 U. S. Navy Dept., journal boxes, and guide 
 
 gibs 
 
 Tobin bronze 
 
 Naval brass 
 
 Composition, U.S. Navy 
 
 Gun metal 
 
 I 
 
 Tough brass for engines 
 
 Bronze for rod boxes 
 
 Bronze subject to shock 
 
 Bronze for pump castings 
 
 Red brass : . 
 
 Bronze, steam whistles 
 
 Bearing metal < 
 
 Gold bronze 
 
 Copper, 
 
 Tin, 
 
 Zinc, 
 
 lbs. 
 
 lbs. 
 
 lbs. 
 
 6 
 
 I 
 
 .25 
 
 82.8 
 
 13.8 
 
 3.4 
 
 58.22 
 
 2.3 
 
 29.48 
 
 62.0 
 
 I.O 
 
 37.0 
 
 88.0 
 
 10. 
 
 2.0 
 
 92.5 
 
 50 
 
 2.5 
 
 91.0 
 
 7.0 
 
 2.0 
 
 85.0 
 
 5.0 
 
 10. 
 
 83.0 
 
 2.0 
 
 15.0 
 
 76. 5 
 
 II. 8 
 
 II. 7 
 
 82.0 
 
 16.0 
 
 2.0 
 
 83.0 
 
 15.0 
 
 1.5 
 
 88.0 
 
 10. 
 
 2.0 
 
 87.0 
 
 4.4 
 
 4.3 
 
 81.0 
 
 17.0 
 
 
 89.0 
 
 8.0 
 
 3.0 
 
 86.0 
 
 14.0 
 
 
 74-0 
 
 9.5 
 
 9-5 
 
 98.5 
 
 2.1 
 
 5.6 
 
 Other Metals 
 
 .5 lead. 
 
 4.3 lead. 
 
 2.0 antimony. 
 
 7.0 lead. 
 2.8 lead. 
 
 Tobin Bronze 
 
 Constituents 
 
 Pig metal, 
 per cent 
 
 Copper 
 
 Zinc 
 
 59.00 
 
 38.40 
 
 2.16 
 
 .11 
 
 .31 
 
 Tin 
 
 
 Lead 
 
 
 Tensile strength (cast) 66,000 pounds. 
 
 Delta Metal 
 
 Constituents 
 
 Per cent 
 
 Constituents 
 
 Per cent 
 
 
 . I to 5 
 50.0 to 65 
 49-9 to 30 
 
 
 .1 to 5 
 
 
 Tin 
 
 Zinc 
 
 Zinc 
 
 1.8 to 45 
 98.0 to 40 
 
 
 Copper . . . 
 
 
 
 This metal is said to be very strong and tough. 
 
226 
 
 Alloys 
 Aluminum Bronze 
 
 Aluminum, 
 per cent 
 
 Copper, 
 per cent 
 
 Tensile strength, 
 
 pounds per square 
 
 inch 
 
 II 
 lo 
 
 7.5 
 5.0 
 
 89 
 90 
 92.5 
 95-0 
 
 89,600 to 100,800 
 73,920 to 89.600 
 56,000 to 67,200 
 33,600 to 40,320 
 
 Analysis of Bearing-Metal Alloys 
 
 Metal 
 
 Camelia metal 
 
 Anti-friction metal 
 
 White metal 
 
 Salgee anti-friction 
 
 Graphite bearing metal 
 
 Antimonial lead 
 
 Cornish bronze 
 
 Delta metal 
 
 Magnolia metal 
 
 American anti-friction metal 
 
 Tobin bronze 
 
 Graney bronze 
 
 Damascus bronze 
 
 Manganese bronze 
 
 Ajax metal 
 
 Anti-friction metal 
 
 Harrington bronze 
 
 Hard lead .' 
 
 Phosphor bronze 
 
 Extra box metal 
 
 Copper 
 
 70.20 
 1.60 
 
 77.83 
 92.39 
 Trace 
 
 59.00 
 75.80 
 76.41 
 90.52 
 81.24 
 
 55-73 
 
 97.72 
 76.80 
 
 Tin 
 
 4 
 
 25 
 
 98 
 
 13 
 
 9 
 
 91 
 
 14 
 
 38 
 
 9 
 
 60 
 
 2 
 
 37 
 
 
 
 2 
 
 16 
 
 9 
 
 20 
 
 10 
 
 60 
 
 9 
 
 58 
 
 10 
 
 98 
 
 
 97 
 
 10 
 
 92 
 
 8 
 
 00 
 
 Lead 
 
 14-75 
 
 87.92 
 
 i-iS 
 
 67.73 
 
 80.69 
 
 12.40 
 
 5.10 
 
 83.55 
 
 78.44 
 
 .31 
 
 15.06 
 
 12.52 
 
 7.27 
 88.32 
 
 94.40 
 9.61 
 1500 
 
 Zinc 
 
 85.57 
 
 Tn-ce 
 
 .98 
 
 38.44 
 
 42.67 
 
 Anti- 
 mony 
 
 12.08 
 
 16.72 
 18.83 
 
 16.45 
 18.60 
 
 11.93 
 6.03 
 
 Iron 
 
 .07 
 
 Trace 
 
 .65 
 
 .II 
 
 68 
 
 Phos. 
 
 • 94 
 
 .20 
 
 Results of Tests for Wear 
 
 Metal 
 
 Composition 
 
 Rate 
 
 of 
 Wear 
 
 Copper 
 
 Tin 
 
 Lead 
 
 Phos. 
 
 Arsenic 
 
 Rtnnrlprrl 
 
 79.70 
 87.50 
 
 10.00 
 12.50 
 
 10.00 
 10.00 
 
 9.50 
 7.00 
 
 .80 
 
 .80 
 .80 
 
 100 
 
 
 148 
 
 Copper-tin, second experiment, 
 tmmp mptal .... 
 
 153 
 
 Copper-tin, third experiment, 
 
 camp mptal 
 
 
 147 
 
 
 89.20 
 79.20 
 
 142 
 
 
 IIS 
 
Belting 
 
 227 
 
 Concerning the preceding table Dr. Dudley remarks: "We began to 
 find evidences that wear of bearing metal alloys varied in accordance 
 with the following law. That alloy which has the greatest power of dis- 
 tortion without rupture will best resist wear." 
 
 Alloys Containing Antimony 
 
 Various analyses of Babbitt metal. 
 
 Metal 
 
 Babbitt metal 
 
 Babbitt metal for light duty 
 
 Babbitt, hard -I 
 
 Britannia < 
 
 White metal 
 
 Parson's metal 
 
 Richard's metal 
 
 Penton's metal 
 
 French Navy 
 
 German Navy 
 
 Tin 
 
 88.9 
 45-5 
 85.7 
 81.0 
 22.0 
 85.0 
 86.0 
 70.0 
 16.0 
 7.5 
 85.0 
 
 Copper 
 
 I 
 
 1.8 
 
 4.0 
 
 3.7 
 
 1-5 
 
 i.o 
 
 2.0 
 
 lO.O 
 
 5.0 
 
 2.0 
 
 4-5 
 S-o 
 7.0 
 7-5 
 
 Anti- 
 mony 
 
 5 
 
 8.9 
 
 8.0 
 
 7-4 
 
 13.0 
 
 10. 1 
 
 16.0 
 
 62.0 
 
 lo.o 
 
 1.0 
 
 15.0 
 
 Zinc 
 
 2.9 
 1.0 
 6.0 
 
 27.0 
 
 79 o 
 87.5 
 
 Lead 
 
 2.0 
 10. s 
 
 Belting * 
 
 Trautwine gives the ultimate strength of good leather belting at 
 3000 pounds per square inch. 
 
 Jones and Laughlin give the breaking strength per inch of width, 
 Me thick, of good leather belting as follows: 
 
 In the solid leather 675 pounds. 
 
 At the rivet holes of splices 362 pounds. 
 
 At the lacing holes 210 pounds. 
 
 Safe working load 45 pounds per inch of width for single belts, equiva- 
 lent to speed for each inch of width of 720 feet per minute per horse power. 
 The efficiency of the double belt compared to that of a single belt is as 
 10 is to 7. 
 Making D = diameter of pulley in inches. 
 
 R = number of revolutions per minute. 
 
 W = width of belt in inches. 
 
 H = horse power that can be transmitted by the belt; 
 
 th&n for single belts, 
 
 „ DX RXW . 
 j± = , 
 
 2750 
 
228 
 
 and for double belts, 
 
 H = 
 
 Belting 
 
 DXRXW 
 
 1925 
 For Width of Belt in Inches 
 
 Single belt 
 
 Double belt 
 
 i?X275o 
 ^~ DXR 
 
 HX 1925 
 ^~ DXR 
 
 Revolutions per minute 
 
 HX 2750 
 DXW 
 
 HX 1925 
 DXW 
 
 Diameter of pulley 
 
 H X 2750 
 ^= WXR 
 
 ffXi925 
 WXR 
 
 These formulae are for open belts and pulleys of same diameter. If 
 the arc of contact on the smaller pulley is less than 90 degrees, use the 
 following constants for those given in above formulae. 
 
 Degrees 
 contact 
 
 Single belt 
 
 Double belt 
 
 90 
 
 6080 
 
 4250 
 
 112]^^ 
 
 4730 
 
 3310 
 
 120 
 
 4400 
 
 3080 
 
 135 
 
 3850 
 
 2700 
 
 150 
 
 3410 
 
 2390 
 
 rsiH 
 
 3220 
 
 2250 
 
Belt Velocity or Circumferential Speed of Pulleys 229 
 
 Belt Velocity or Circumferential Speed of Pulleys 
 
 i 
 
 Revolutions per minute 
 
 II 
 
 50 
 
 60 
 
 70 
 
 80 
 
 90 
 
 100 
 
 no 
 
 120 
 
 130 
 
 140 
 
 150 
 
 160 
 
 170 
 
 Velocity in feet per minute 
 
 6 
 
 78. 5 
 
 94.2 
 
 no 
 
 126 
 
 141 
 
 157 
 
 173 
 
 188 
 
 204 
 
 220 
 
 235 
 
 251 
 
 267 
 
 7 
 
 91.7 
 
 no 
 
 128 
 
 146 
 
 165 
 
 183 
 
 201 
 
 220 
 
 238 
 
 256 
 
 275 
 
 293 
 
 312 
 
 8 
 
 105 
 
 126 
 
 146 
 
 167 
 
 188 
 
 210 
 
 230 
 
 251 
 
 272 
 
 293 
 
 314 
 
 335 
 
 356 
 
 9 
 
 118 
 
 141 
 
 165 
 
 188 
 
 212 
 
 236 
 
 259 
 
 282 
 
 306 
 
 330 
 
 353 
 
 377 
 
 400 
 
 10 
 
 131 
 
 157 
 
 183 
 
 209 
 
 235 
 
 262 
 
 288 
 
 314 
 
 340 
 
 366 
 
 392 
 
 419 
 
 445 
 
 12 
 
 157 
 
 188 
 
 220 
 
 252 
 
 282 
 
 314 
 
 346 
 
 377 
 
 408 
 
 440 
 
 471 
 
 502 
 
 534 
 
 14 
 
 183 
 
 220 
 
 256 
 
 293 
 
 330 
 
 366 
 
 4oi 
 
 440 
 
 476 
 
 513 
 
 550 
 
 586 
 
 623 
 
 16 
 
 209 
 
 251 
 
 293 
 
 335 
 
 377 
 
 419 
 
 460 
 
 502 
 
 544 
 
 586 
 
 628 
 
 670 
 
 713 
 
 18 
 
 230 
 
 282 
 
 330 
 
 377 
 
 424 
 
 471 
 
 518 
 
 565 
 
 612 
 
 659 
 
 707 
 
 754 
 
 801 
 
 20 
 
 262 
 
 314 
 
 366 
 
 419 
 
 471 
 
 524 
 
 576 
 
 628 
 
 681 
 
 733 
 
 785 
 
 838 
 
 890 
 
 22 
 
 288 
 
 345 
 
 403 
 
 460 
 
 518 
 
 576 
 
 634 
 
 691 
 
 749 
 
 806 
 
 864 
 
 921 
 
 979 
 
 24 
 
 314 
 
 377 
 
 440 
 
 502 
 
 565 
 
 628 
 
 691 
 
 754 
 
 817 
 
 880 
 
 942 
 
 1005 
 
 1068 
 
 26 
 
 340 
 
 408 
 
 476 
 
 545 
 
 622 
 
 681 
 
 749 
 
 817 
 
 885 
 
 953 
 
 1021 
 
 1089 
 
 1157 
 
 28 
 
 380 
 
 440 
 
 513 
 
 586 
 
 659 
 
 733 
 
 806 
 
 880 
 
 ^ 953 
 
 1026 
 
 1 100 
 
 1 173 
 
 1246 
 
 30 
 
 393 
 
 471 
 
 550 
 
 628 
 
 706 
 
 785 
 
 864 
 
 942 
 
 1022 
 
 1 100 
 
 1 178 
 
 1256 
 
 1335 
 
 32 
 
 419 
 
 502 
 
 586 
 
 670 
 
 754 
 
 838 
 
 921 
 
 1005 
 
 1089 
 
 1173 
 
 1257 
 
 1340 
 
 1424 
 
 34 
 
 445 
 
 534 
 
 623 
 
 712 
 
 801 
 
 890 
 
 979 
 
 1068 
 
 IIS7 
 
 1246 
 
 1335 
 
 1424 
 
 1513 
 
 36 
 
 471 
 
 565 
 
 659 
 
 754 
 
 848 
 
 942 
 
 1037 
 
 1131 
 
 1225 
 
 1319 
 
 1414 
 
 1508 
 
 1602 
 
 40 
 
 523 
 
 628 
 
 733 
 
 837 
 
 942 
 
 1047 
 
 1152 
 
 1256 
 
 1361 
 
 1466 
 
 1571 
 
 1675 
 
 1780 
 
 48 
 
 628 
 
 754 
 
 879 
 
 1005 
 
 1131 
 
 1257 
 
 1382 
 
 1508 
 
 1633 
 
 1759 
 
 188s 
 
 2010 
 
 2136 
 
 54 
 
 707 
 
 848 
 
 989 
 
 1 131 
 
 1272 
 
 1414 
 
 1555 
 
 1696 
 
 1838 
 
 1979 
 
 2120 
 
 2262 
 
 2403 
 
 60 
 
 785 
 
 942 
 
 1099 
 
 1256 
 
 1414 
 
 1571 
 
 1728 
 
 1885 
 
 2042 
 
 2199 
 
 2356 
 
 2513 
 
 2670 
 
 66 
 
 864 
 
 1036 
 
 1209 
 
 1382 
 
 1550 
 
 1728 
 
 1900 
 
 2073 
 
 2246 
 
 2419 
 
 2592 
 
 2764 
 
 2937 
 
 72 
 
 942 
 
 1131 
 
 1319 
 
 1508 
 
 1696 
 
 1885 
 
 2073 
 
 2262 
 
 2450 
 
 2639 
 
 2827 
 
 3016 
 
 3204 
 
 78 
 
 1021 
 
 1225 
 
 1429 
 
 1633 
 
 1838 
 
 2042 
 
 2245 
 
 2450 
 
 2655 
 
 2859 
 
 3063 
 
 3267 
 
 3472 
 
 84 
 
 1099 
 
 I3I9 
 
 1539 
 
 1754 
 
 1978 
 
 2199 
 
 2419 
 
 2639 
 
 2859 
 
 3079 
 
 3298 
 
 3518 
 
 3738 
 
 Contributed by W. J. Phillips, No. 117, extra data sheet, Machinery, October, 1909. 
 
230 
 
 Belting 
 
 Belt Velocity or Circumferentl\l Speed of Pulleys 
 — (Continued) 
 
 a s 
 
 
 
 
 
 Revolutions per minute 
 
 
 
 
 
 
 180 
 
 190 
 
 200 
 
 210 
 
 220 
 
 230 
 
 240 
 
 250 
 
 260 
 
 270 
 
 280 
 
 290 
 
 300 
 
 PL. 
 
 Velocity in feet per minute 
 
 6 
 
 282 
 
 298 
 
 311 
 
 330 
 
 346 
 
 361 
 
 377 
 
 392 
 
 408 
 
 424 
 
 440 
 
 455 
 
 471 
 
 7 
 
 330 
 
 348 
 
 367 
 
 385 
 
 403 
 
 421 
 
 440 
 
 458 
 
 477 
 
 495 
 
 513 
 
 531 
 
 5SO 
 
 8 
 
 377 
 
 398 
 
 419 
 
 440 
 
 461 
 
 481 
 
 503 
 
 523 
 
 545 
 
 565 
 
 586 
 
 607 
 
 628 
 
 9 
 
 424 
 
 447 
 
 471 
 
 495 
 
 518 
 
 542 
 
 565 
 
 588 
 
 613 
 
 630 
 
 660 
 
 683 
 
 707 
 
 lo 
 
 471 
 
 497 
 
 524 
 
 549 
 
 576 
 
 602 
 
 628 
 
 654 
 
 681 
 
 707 
 
 733 
 
 759 
 
 785 
 
 12 
 
 S6o 
 
 597 
 
 628 
 
 659 
 
 691 
 
 722 
 
 754 
 
 78s 
 
 817 
 
 848 
 
 880 
 
 911 
 
 942 
 
 14 
 
 6S9 
 
 696 
 
 733 
 
 769 
 
 806 
 
 843 
 
 880 
 
 916 
 
 953 
 
 989 
 
 1026 
 
 1063 
 
 1 100 
 
 i6 
 
 754 
 
 796 
 
 838 
 
 879 
 
 921 
 
 963 
 
 1005 
 
 1046 
 
 1089 
 
 1131 
 
 1173 
 
 1214 
 
 1257 
 
 i8 
 
 848 
 
 895 
 
 942 
 
 989 
 
 1037 
 
 1084 
 
 I131 
 
 1 178 
 
 1225 
 
 1272 
 
 1319 
 
 1366 
 
 1414 
 
 20 
 
 942 
 
 995 
 
 1047 
 
 1099 
 
 1152 
 
 1204 
 
 1256 
 
 1309 
 
 1361 
 
 1414 
 
 1466 
 
 1518 
 
 1571 
 
 22 
 
 1037 
 
 1094 
 
 1152 
 
 1209 
 
 1267 
 
 1325 
 
 1382 
 
 1440 
 
 1497 
 
 1555 
 
 1612 
 
 1670 
 
 1728 
 
 24 
 
 1 131 
 
 1194 
 
 1257 
 
 1319 
 
 1382 
 
 1445 
 
 1508 
 
 1671 
 
 1633 
 
 1696 
 
 1759 
 
 1822 
 
 188S 
 
 26 
 
 1225 
 
 1293 
 
 1361 
 
 1429 
 
 1497 
 
 1565 
 
 1633 
 
 1701 
 
 1770 
 
 1838 
 
 1906 
 
 1974 
 
 2042 
 
 28 
 
 1319 
 
 1393 
 
 1466 
 
 1539 
 
 1613 
 
 1686 
 
 1759 
 
 1832 
 
 1906 
 
 1979 
 
 2052 
 
 2126 
 
 2199 
 
 30 
 
 1413 
 
 1492 
 
 1571 
 
 1649 
 
 1728 
 
 1806 
 
 188s 
 
 1963 
 
 2042 
 
 2120 
 
 2199 
 
 2277 
 
 2356 
 
 32 
 
 IS08 
 
 1592 
 
 1675 
 
 1759 
 
 1843 
 
 1927 
 
 2010 
 
 2094 
 
 2178 
 
 2252 
 
 2345 
 
 2429 
 
 2513 
 
 34 
 
 1602 
 
 1691 
 
 1780 
 
 1869 
 
 1958 
 
 2047 
 
 2136 
 
 2225 
 
 2314 
 
 2403 
 
 2492 
 
 2581 
 
 2670 
 
 36 
 
 1696 
 
 1791 
 
 1885 
 
 1978 
 
 2073 
 
 2168 
 
 2262 
 
 2326 
 
 2450 
 
 2545 
 
 2639 
 
 2733 
 
 2827 
 
 40 
 
 1885 
 
 1989 
 
 2094 
 
 2199 
 
 2304 
 
 2513 
 
 2618 
 
 2723 
 
 2827 
 
 2932 
 
 3037 
 
 3141 
 
 3246 
 
 48 
 
 2262 
 
 2387 
 
 2513 
 
 2639 
 
 276s 
 
 2890 
 
 3016 
 
 3142 
 
 3267 
 
 3393 
 
 3518 
 
 3644 
 
 3769 
 
 54 
 
 2545 
 
 2686 
 
 2827 
 
 2969 
 
 31 10 
 
 3251 
 
 3393 
 
 3534 
 
 3676 
 
 3817 
 
 3959 
 
 4100 
 
 4240 
 
 60 
 
 2827 
 
 2984 
 
 3141 
 
 3298 
 
 3456 
 
 3613 
 
 3770 
 
 3927 
 
 4084 
 
 4251 
 
 4398 
 
 4555 
 
 4712 
 
 66 
 
 31 10 
 
 3283 
 
 3455 
 
 3628 
 
 3801 
 
 3974 
 
 4147 
 
 4319 
 
 4492 
 
 4665 
 
 4838 
 
 5010 
 
 5183 
 
 72 
 
 3392 
 
 3581 
 
 3770 
 
 3958 
 
 4147 
 
 4335 
 
 4524 
 
 4713 
 
 4900 
 
 5059 
 
 5278 
 
 5466 
 
 5654 
 
 78 
 
 3676 
 
 3880 
 
 4084 
 
 4288 
 
 4492 
 
 4696 
 
 4900 
 
 5059 
 
 5309 
 
 5513 
 
 5717 
 
 5921 
 
 6125 
 
 84 
 
 3958 
 
 4178 
 
 4398 
 
 4618 
 
 4838 
 
 5058 
 
 5277 
 
 5497 
 
 5717 
 
 5937 
 
 6157 
 
 6377 
 
 6597 
 
 Contributed by W. J. Phillips, No. 117, extra data sheet, Machinery, October, 1909. 
 
Rules for Calculating Speeds and Diameters of Pulleys 231 
 
 Rules for Calculating Speeds and Diameters of Pulleys 
 
 Proposed speed of grinding spindle being given, to find proper speed 
 of countershaft. 
 
 Rule. — Multiply the number of revolutions per minute of the grinding 
 spindle by the diameter of its pulley and divide the product by the 
 diameter of the driving pulley on the countershaft. 
 
 Speed of countershaft given, to find diameter of pulley to drive grind- 
 ing spindle. 
 
 Rule. — Multiply the number of revolutions per minute of the grinding 
 spindle by the diameter of its pulley and divide the product by the number 
 of revolutions per minute of the countershaft. 
 
 Proposed speed of countershaft given, to find the diameter of pulley 
 for the lineshaft. 
 
 Rule. — Multiply the number of revolutions per minute of the counter- 
 shaft by the diameter of the tight and loose pulleys and divide the 
 product by the number of revolutions per minute of the lineshaft. 
 
 Table of Grinding Wheel Speeds 
 
 
 Revolutions 
 
 Revolutions 
 
 Revolutions 
 
 Diameter 
 
 pef minute 
 
 per minute 
 
 per minute 
 
 of wheel. 
 
 for surface 
 
 for surface 
 
 for surface 
 
 inches 
 
 speed of 
 
 speed of 
 
 speed of 
 
 
 4000 feet 
 
 Sooo feet 
 
 6000 feet 
 
 I 
 
 IS>279 
 
 19,099 
 
 22,918 
 
 2 
 
 7,639 
 
 9,549 
 
 11,459 
 
 3 
 
 5,093 
 
 6,366 
 
 7,639 
 
 4 
 
 3,820 
 
 4,775 
 
 5,730 
 
 5 
 
 3,056 
 
 3,820 
 
 4,584 
 
 6 
 
 2,546 
 
 3,183 
 
 3,820 
 
 7 
 
 2,183 
 
 2,728 
 
 3,274 
 
 8 
 
 1,910 
 
 2,387 
 
 2,865 
 
 10 
 
 1,528 
 
 1,910 
 
 2,292 
 
 12 
 
 1,273 
 
 1,592 
 
 1,910 
 
 14 
 
 1,091 
 
 1,364 
 
 1,637 
 
 16 
 
 955 
 
 1,194 
 
 1,432 
 
 18 
 
 849 
 
 1,061 
 
 1,273 
 
 20 
 
 764 
 
 955 
 
 1,146 
 
 22 
 
 694 
 
 868 
 
 1,042 
 
 24 
 
 637 
 
 796 
 
 955 
 
 30 
 
 509 
 
 637 
 
 764 
 
 36 
 
 424 
 
 531 
 
 637 
 
 The revolutions per minute at which wheels are run is dependent on 
 conditions and style of machine and the work to be ground. 
 Data Sheet, No. 52, The Foundry, October, 1909, 
 
232 
 
 Flanged Fittings 
 
 Rules for Obtaining Surface Speeds, etc. 
 
 To find surface speed in feet per minute, of a wheel. 
 
 Rule. — Multiply the circumference in feet by its revolutions per 
 minute. 
 
 Surface speed and diameter of wheel being given, to find number of 
 revolutions of wheel spindle. 
 
 Rule. — Multiply surface speed in feet per minute by 12, and divide 
 the product by 3.14 times the diameter of wheel in inches. 
 
 Formulae for Dimensions of Cast Iron, Flanged Fittings 
 
 To withstand Hydraulic Pressures of 30, 100 and 200 Pouitds per 
 Square Inch 
 
 
 |-i--Hii<--A-->; 
 
 
 I t±.l.Alz 
 H-E-4 
 
 Fig. 70. 
 
 Diameter of opening A 
 
 r^,, . , r ' ' 7, ^ (pressure in lbs. per sq. inch) , 
 
 Thickness of pipe B= — ^^^ -^ -f 13.25 in. 
 
 3000 
 
 Thickness of flange C= - — Radius of fillet Z) = -approximately. 
 
 Center to face of flange, 
 
 tee and cross : .E= — |- 2 C, or next half-inch. 
 
 2 
 
 Center to face of flange; 
 
 bends, up to 90° F and G = tang, f -^')[ - ) + 2 C, or next 
 
 half inch. 
 Center to face of flange, 
 
 45° Y H = tang. 67^/^° X (-] + 2 C, 
 
 Face to face of flange, 
 
 45° Y 7 = tang. 22H° X ij) 
 
 half inch. 
 
 Diameter of flange /= standard. Number and size of bolts.. . 
 
 K = standard. 
 
 or next half -inch. 
 
 -\- 2 C -\- H, or next 
 
Formulas for Dimensions of Cast Iron, Flanged Fittings 233 
 
 Diameter of bolt circle . . . Z, = standard. 
 Radius on center line of 
 
 bends, up to 90° M and N = ^ r-^* Use first quar- 
 
 (tang.-2S-) 
 
 ter inch below. 
 
 Note. — / and L are alike for 50 and 100 lbs., as both are computed for 100 lbs. Con- 
 tributed. No. 43, Data Sheet, Machinery, April, 1905. 
 
CHAPTER VII 
 USEFUL INFORMATION 
 
 Shrinkage or Castings per Foot 
 
 (By F. G. Walker.) 
 
 Metals 
 
 Fractions 
 of an inch 
 
 Decimals 
 of an inch 
 
 Ptire aluminum , 
 
 Nickel aluminum casting alloy 
 
 " Special Casting Alloy," made by the Pittsburg Reduc- 
 tion Co 
 
 Iron, small cylinders 
 
 Iron, pipes 
 
 Iron, girders, beams, etc 
 
 Iron, large cylinders, contraction of diameter at top 
 
 Iron, large cylinders, contraction of diameter at bottom. 
 
 Iron, large cylinders, contraction in length 
 
 Cast iron 
 
 Steel 
 
 Malleable iron , 
 
 Tin 
 
 Britannia 
 
 Thin brass castings 
 
 Thick brass castings 
 
 Zinc 
 
 Lead 
 
 Copper 
 
 Bismuth 
 
 ^6 
 H6 
 
 Hi 
 M 
 M 
 
 H2 
 1^32 
 13/64 
 ^2 
 
 Me 
 Me 
 
 3/16 
 5^2 
 
 .2031 
 .1875 
 
 .1718 
 
 .0625 
 
 .1250 
 
 .1000 
 
 .6250 
 
 .0830 
 
 .0940 
 
 .1250 
 
 .2500 
 
 .1250 
 
 .0833 
 
 .03125 
 
 .1670 
 
 .1500 
 
 .3125 
 
 .3125 
 
 .1875 
 
 .1563 
 
 Data Sheet, No. 34, The Foundry, January, 1909. 
 
 234 
 
Rapid Conversion of Gross Tons 
 
 235 
 
 This Table Has Been Arranged for the Rapid Conversion 
 OF Gross Tons and Fractions Thereof into Pounds 
 
 Equivalent of gross tons (2240 pounds) in pounds. 
 
 Tons 
 
 Pounds 
 
 Tons 
 
 Pounds 
 
 Tons 
 
 Pounds 
 
 Tons 
 
 Pounds 
 
 15 
 
 33,600 
 
 24 
 
 53,760 
 
 33 
 
 73.920 
 
 42 
 
 94.080 
 
 15^ 
 
 34,160 
 
 24W 
 
 54,320 
 
 33^4 
 
 74.480 
 
 42H 
 
 94,640 
 
 isVii 
 
 34,720 
 
 24!/^ 
 
 54,880 
 
 33i/i 
 
 75.040 
 
 421/^2 
 
 95.200 
 
 15H 
 
 35,280 
 
 24% 
 
 55,440 
 
 333/4 
 
 75,600 
 
 42% 
 
 95.760 
 
 16 
 
 35,840 
 
 25 
 
 56,000 
 
 34 
 
 76,160 
 
 43 
 
 96.320 
 
 mi 
 
 36,400 
 
 25H 
 
 56,560 
 
 mH 
 
 76,720 
 
 431/4 
 
 96.880 
 
 i6i^ 
 
 36,960 
 
 25}^ 
 
 57,120 
 
 Zi>A 
 
 77,280 
 
 431/^ 
 
 97.440 
 
 l63/i 
 
 37,520 
 
 25% 
 
 57,680 
 
 343/4 
 
 77,840 
 
 433/4 
 
 98,000 
 
 17 
 
 38,080 
 
 26 
 
 58,240 
 
 35 
 
 78,400 
 
 44 
 
 98.560 
 
 171/4 
 
 38,640 
 
 261.4 
 
 58,800 
 
 3514 
 
 78,960 
 
 44I/4 
 
 99.120 
 
 17H 
 
 39,200 
 
 261/2 
 
 59.360 
 
 35/2 
 
 79,520 
 
 44 J'^ 
 
 99.680 
 
 17% 
 
 39,760 
 
 263/4 
 
 59.920 
 
 353/4 
 
 80,080 
 
 44% 
 
 100,240 
 
 18 
 
 40,320 
 
 27 
 
 60,480 
 
 36 
 
 80,640 
 
 45 
 
 100,800 
 
 18H 
 
 40,880 
 
 27)'i 
 
 61,040 
 
 361/4 
 
 81,200 
 
 45% 
 
 101,360 
 
 iSi/^ 
 
 41,440 
 
 27H 
 
 61,600 
 
 361/^ 
 
 81,760 
 
 451/^ 
 
 101,920 
 
 183/4 
 
 42,000 
 
 273/4 
 
 62,160 
 
 363/4 
 
 82,320 
 
 453/4 
 
 102,480 
 
 19 
 
 42,560 
 
 28 
 
 62,720 
 
 37 
 
 82,880 
 
 46 
 
 103,040 
 
 19H 
 
 43,120 
 
 281/4 
 
 63,280 
 
 371/4 
 
 83,440 
 
 46% 
 
 103,600 
 
 19H 
 
 43.680 
 
 28K2 
 
 63,840 
 
 37I/2 
 
 84,000 
 
 461-^ 
 
 104,160 
 
 19^4 
 
 44,240 
 
 28% 
 
 64,400 
 
 373/4 
 
 84.560 
 
 46% 
 
 104,720 
 
 20 
 
 44,800 
 
 29 
 
 64,960 
 
 38 
 
 85.120 
 
 47 
 
 105,280 
 
 20H 
 
 45,360 
 
 2914 
 
 65,520 
 
 381/4 
 
 85.680 
 
 47% 
 
 105,840 
 
 20l/i 
 
 45,920 
 
 29!/^ 
 
 66,080 
 
 38/2 
 
 86,240 
 
 47H 
 
 106,400 
 
 20% 
 
 46,480 
 
 29% 
 
 66,640 
 
 383/4 
 
 86,800 
 
 47% 
 
 106,960 
 
 21 
 
 47,040 
 
 30 
 
 67,200 
 
 39 
 
 87,360 
 
 48 
 
 107.520 
 
 21 1/^ 
 
 47,600 
 
 3oJ'4 
 
 67,760 
 
 391/4 
 
 87,920 
 
 481/4 
 
 108,080 
 
 21 1/2 
 
 48,160 
 
 30H 
 
 68,320 
 
 39I/2 
 
 88,480 
 
 481'^ 
 
 108,640 
 
 21% 
 
 48,720 
 
 30% 
 
 68,880 
 
 39% 
 
 89,040 
 
 48% 
 
 109,200 
 
 22 
 
 49,280 
 
 31 
 
 69,440 
 
 40 
 
 89.600 
 
 49 
 
 109,760 
 
 22I/4 
 
 49,840 
 
 31 H 
 
 70,000 
 
 4014 
 
 90,160 
 
 49i/i 
 
 110,320 
 
 22V^ 
 
 50,400 
 
 31V2 
 
 70,560 
 
 40!/^ 
 
 90,720 
 
 49!'^ 
 
 110,880 
 
 22% 
 1 
 
 50,960 
 
 313/4 
 
 71,120 
 
 403/4 
 
 91,280 
 
 49^4 
 
 111,440 
 
 23 
 
 51,520 
 
 32 
 
 71,680 
 
 41 
 
 91,840 
 
 50 
 
 112,000 
 
 231/4 
 
 52,080 
 
 321/4 
 
 72,240 
 
 41I/ 
 
 92,400 
 
 So% 
 
 112,560 
 
 23!/^ 
 
 52,640 
 
 32H 
 
 72,800 
 
 41/2 
 
 92,960 
 
 5oi/i 
 
 113.120 
 
 23% 
 
 53,200 
 
 323/4 
 
 73,360 
 
 41% 
 
 93,520 
 
 50% 
 
 113.680 
 
 Data Sheet No. 2, The Foundry, September, 1907. 
 
236 
 
 Useful Information 
 
 Window Glass 
 
 Table of Number of Panes in a Box 
 
 Size 
 
 Panes 
 
 Size 
 
 Panes 
 
 Size 
 
 Panes 
 
 Size 
 
 Panes 
 
 Size 
 
 Panes 
 
 in 
 
 to a 
 
 m 
 
 to a 
 
 m 
 
 tea 
 
 m 
 
 tea 
 
 m 
 
 to a 
 
 inches 
 
 box 
 
 inches 
 
 box 
 
 inches 
 
 box 
 
 inches 
 
 box 
 
 inches 
 
 box 
 
 8x10 
 
 90 
 
 14X20 
 
 26 
 
 20X42 
 
 9 
 
 26X48 
 
 6 
 
 34X48 
 
 5 
 
 8X12 
 
 75 
 
 14X24 
 
 22 
 
 20X48 
 
 8 
 
 26X60 
 
 5 
 
 34x60 
 
 4 
 
 9X12 
 
 67 
 
 14X36 
 
 14 
 
 22x30 
 
 II 
 
 28X36 
 
 7 
 
 36X40 
 
 5 
 
 9X14 
 
 57 
 
 16X18 
 
 25 
 
 22X36 
 
 9 
 
 28X42 
 
 6 
 
 36X44 
 
 5 
 
 10X12 
 
 60 
 
 16x20 
 
 23 
 
 22X42 
 
 8 
 
 28X56 
 
 5 
 
 36x48 
 
 4 
 
 10X16 
 
 45 
 
 16X24 
 
 19 
 
 22X48 
 
 7 
 
 30X34 
 
 7 
 
 36X54 
 
 4 
 
 12X14 
 
 43 
 
 16X36 
 
 13 
 
 24X30 
 
 10 
 
 30X42 
 
 6 
 
 36X60 
 
 3 
 
 12X18 
 
 34 
 
 18X20 
 
 20 
 
 24X36 
 
 9 
 
 30X48 
 
 5 
 
 40X54 
 
 3 
 
 12X20 
 
 30 
 
 18X24 
 
 17 
 
 24X42 
 
 7 
 
 30X60 
 
 4 
 
 40X72 
 
 3 
 
 12X24 
 
 25 
 
 18x36 
 
 II 
 
 24X48 
 
 6 
 
 32X42 
 
 6 
 
 44X50 
 
 3 
 
 14X16 
 
 32 
 
 20X24 
 
 15 
 
 26X36 
 
 8 
 
 32X48 
 
 5 
 
 44X56 
 
 3 
 
 14X18 
 
 29 
 
 20X30 
 
 12 
 
 26X42 
 
 7 
 
 32X60 
 
 4 
 
 
 
 Box Strapping 
 
 ~<i^ .-»;^, .-^Nv ■■i!SS^\-v»^- ..v^w^N-iS V-.---^'«fi <>^ 
 
 Fig. 71. 
 Improved Trojan Box Strapping 
 
 A soft steel continuous band, without rivets, which allows the nail to 
 be driven anywhere. The surface is studded or embossed, as illustrated, 
 which not only protects the head of the nail, but stiffens and strengthens 
 the strap. Edges are perfectly smooth. Put up in reels of 300 feet. 
 
 Width ■ Yi 5^i Yi I in. 
 
 Per reel $1.00 1.25 1.50 2.00 
 
 Fire Brick and Fire Clay 
 
 An ordinary fire brick measures 9 by 4H by 2}i inches, contains 
 101.25 cubic inches and weighs 7 pounds. Specific gravity, 1.93. From 
 650 to 700 pounds of fire clay are required to lay 1000 bricks. The 
 clay should be used as a thin paste and the joints made as thin as 
 possible. 
 
Fire Clays 237 
 
 Analysis of Fire Clays 
 
 New Jersey Clays: Per cent 
 
 Silica 56 . 80 
 
 Alumina 30 . 08 
 
 Peroxide of iron i . 12 
 
 Titanic acid i . 15 
 
 Potash o. 80 
 
 Water and organic matter 10.50 
 
 100.45 
 
 Pennsylvania Clays: 
 
 Silica 44-395 
 
 Alumina 33-558 
 
 Lime trace 
 
 Peroxide of iron i . 080 
 
 Magnesia o. 108 
 
 Alkalies o . 247 
 
 Titanic acid i . 530 
 
 Water and organic matter 14-575 
 
 95-493 
 
 Stourbridge Clays: 
 
 Silica 40 . 00 
 
 Alumina 37 . 00 
 
 Magnesia 2 . 00 
 
 Potash 9 . 00 
 
 Water 12 . 00 
 
 100.00 
 
 Stourbridge Clays: 
 
 Silica 70 . 00 
 
 Alumina 26 . 60 
 
 Oxide of iron 2 . 00 
 
 Lime i . 00 
 
 Magnesia trace 
 
 100.00 
 
 Fire brick should have a light buff color and when broken present an 
 uniform shade throughout the fracture. Bricks weighing over 7 to 7.5 
 pounds each contain too large a percentage of iron. 
 
 Useful Information 
 
 Velocity of light is 185,844 miles per second. 
 
 Velocity of soimd at 60° F. is 11 20 feet per second. 
 
 The semiaxis of the earth at the poles is 3949.555 miles. 
 
 The terrestrial radius at 45° latitude is equal to 3936.245 miles. 
 
 Radius of a sphere equal to that of the earth is 3958.412 miles. 
 
 Quadrant of the equator is equal to 6224.413 miles. 
 
238 
 
 Useful Information 
 
 Quadrant of the meridian 6214.413 miles. 
 
 One degree of the terrestrial meridian is 69.049 miles. 
 
 One degree of longitude on the equator equals 69.164 miles. 
 
 A degree of longitude upon parallel 45 equals 48.988 miles. 
 
 A nautical mile equals 1.153 statute miles and is equal to one minute 
 of longitude upon the equator. 
 
 Length of a pendulum beating seconds in vacuum at sea level at New 
 York is 39.1012 inches. 
 
 Length of a pendulum beating seconds in vacuum at the equator is 
 39.01817 inches. 
 
 Mean distance of the earth from the sun is 95,364,768 miles. 
 
 Time occupied in transmission of light from the sun to the earth is 
 8 minutes, 13.2 seconds. 
 
 Force Required to Pull Nails from Various Woods 
 
 Kind of wood 
 
 White pine . 
 
 Yellow pine. 
 
 White oak. 
 
 Chestnut . 
 
 Laiirel. 
 
 Size of 
 nail 
 
 8d 
 
 9d 
 
 20 d 
 
 50 d 
 
 6od 
 
 8d 
 10 d 
 50 d 
 60 d 
 
 8d 
 20 d 
 60 d 
 
 50 d 
 6od 
 
 9d 
 20 d 
 
 Holding-power per square inch 
 of surface in wood, pounds 
 
 Wire naU Cut nail 
 
 167 
 
 318 
 
 651 
 
 450 
 455 
 477 
 347 
 363 
 340 
 
 695 
 755 
 596 
 604 
 
 1340 
 1292 
 1018 
 
 664 
 
 702 
 
 1179 
 1221 
 
 Mean 
 
 405 
 
 662 
 
 1216 
 
 683 
 
 Trautwine gives the holding power of 6 d nail driven one inch into oak as 507 pounds; 
 beech, 667 pounds; elm, 327 pounds; pine (white), 187 pounds; % inch square spike 
 driven 4H inches into yellow pine, 2000 pounds; oak, 4000 pounds; locust, 6000 
 pounds; H inch square spike in yellow pine, 3000 pounds; Vie square spike six inches 
 in yellow pine, 4873 pounds. In all cases the nails or spikes were driven across the 
 grain. When driven with the grain the resistance is about one half. 
 
Weights per Cubic Inch of Metals 
 
 239 
 
 Weights per Cubic Inch of Metals 
 
 Lbs. 
 
 Cast iron o . 263 
 
 Wrought iron o . 281 
 
 Cast steel o . 283 
 
 Copper 0.3225 
 
 Brass o. 3037 
 
 Zinc 0.26 
 
 Lead 0.4103 
 
 Mercury o . 4908 
 
 Temperatures Corresponding to Various Colors 
 
 (Taylor & White.) 
 
 Color 
 
 Dark blood red, black red 
 
 Dark red, blood red, low red 
 
 Dark cherry red 
 
 Medium cherry red , 
 
 Cherry, full red 
 
 Light cherry red, bright cherry red, 
 
 Scaling heat,* light red 
 
 Salmon, orange, free scaling heat . . , 
 
 Light salmon, Ught orange 
 
 Yellow 
 
 Light yellow. 
 
 White 
 
 Temperature, 
 degrees F. 
 
 990 
 1050 
 1 17s 
 1250 
 I37S 
 
 I5SO 
 1650 
 1725 
 182s 
 1975 
 2200 
 
 * Heat at which scale forms and adheres, i.e., does not fall away from the piece 
 when allowed to cool in air. 
 
240 
 
 Useful Information 
 
 Iron Ores 
 
 Iron is usually found as an ore in one of the following classifications, 
 oxides, carbonates and sulphides. 
 
 The following table gives the subdivisions of these classes and an idea 
 of the general composition and character of the different varieties. 
 
 . 
 
 Oxides 
 
 Carbonates 
 
 Sulphides 
 
 Component 
 parts 
 
 Anhy- 
 drous: 
 Red 
 hematite 
 
 Hy- 
 drated: 
 Brown 
 
 hematite 
 
 Magnetic 
 
 Spathic 
 
 0-50 
 20-60 
 
 1-25 
 
 O-IO 
 
 0- 5 
 
 0-25 
 
 0- 5 
 35-40 
 Usually 
 absent 
 
 0- 5 
 
 Clay 
 iron 
 stone 
 
 Pyrites 
 
 
 
 50-90 
 
 Usually 
 
 absent 
 
 0- 2 
 
 0- 2 
 
 I-IO 
 
 0- 5 
 1-30 
 0- 5 
 0- 3 
 
 0- I 
 5-20 
 
 Includes: 
 bog iron 
 ore, lake 
 ore and 
 limonite 
 
 30-70 
 15-55 
 
 0- I 
 0- 2 
 
 O-IO 
 
 0- 5 
 0-25 
 0-5 
 0- 2 
 
 0- 2 
 0- 5 
 
 Includes: 
 frank- 
 linite or 
 spiegel- 
 eisen and 
 load 
 stone. 
 
 O-IO 
 
 30-45 
 0- 2 
 
 I-IO 
 I-IO 
 I-IO 
 
 2-25 
 20-3S 
 0- 3 
 
 0- 2 
 0- 4 
 
 Black-' 
 band 
 
 44.28 
 
 Ferric oxide 
 
 Ferrous oxides 
 
 Manganese oxide . . . 
 
 60-95 
 0- 5 
 
 0- 2 
 0- I 
 0- 5 
 0- 3 
 1-25 
 0- 2 
 °- 3 
 
 0- I 
 0- 5 
 
 
 
 
 Lime 
 
 1. 18 
 
 Silica 
 
 2.34 
 
 Carbon dioxide 
 
 Phosphoric anhy- 
 dride. 
 Sulphur 
 
 49.07 
 
 Water 
 
 
 Copper 
 
 2.7s 
 
 Arsenic 
 
 
 .38 
 
 Zinc . 
 
 
 .22 
 
 Lead . 
 
 
 
 
 Includes: 
 specular 
 micace- 
 ous and 
 kidney 
 ores. 
 
 
CHAPTER VIII 
 IRON 
 
 Physical Properties 
 
 Atomic weight 55.9 
 
 Specific gravity 7 . 80 
 
 Specific heat , o.ii 
 
 Melting point 2600° F. 
 
 Coefiicient of linear expansion. 0.0000065 per o" F. 
 
 Thermal conductivity 11. 9 Silver 100 
 
 Electric " 8 . 34 Mercury i 
 
 Latent heat of fusion 88 B.t.u.. 
 
 Pure iron is termed ferrite. 
 
 In the presence of manganese, chromium, etc., hard carbides (double 
 carbides) are formed, known as cementite. 
 
 A mixture of ferrite and cementite is called pearlite. 
 
 Pearhte often consists of alternate layers of ferrite and cementite and 
 in this condition, from its pecuhar iridescence, is termed pearlite. 
 
 As carbon increases, ferrite is replaced by pearlite. 
 
 Pearhte is not found in hardened steels. 
 
 In steels saturated with carbon, a point fixed by Professor Arnold as 
 .89 per cent carbon, the whole structure is represented by pearlite. 
 
 Steels containing less than .89 per cent carbon are known as unsatu- 
 rated; those having over .89 per cent carbon as supersaturated. These 
 degrees refer distinctly to iron-carbon steels; for the double carbides the 
 point of satiuration is slightly lowered. 
 
 Cementite is a hard and brittle compound, but when interspersed with 
 ferrite in the form of pearlite, its brittleness is somewhat neutralized by 
 the adjacent ferrite. 
 
 A steel containing well laminated pearlite possesses high ductility 
 but less tenacity than when found unsegregated. 
 
 Pig Iron 
 
 Pig iron contains from 92 to 96 per cent metallic iron; the remainder 
 is mostly composed of sihcon, sulphur, phosphorus and manganese in 
 greatly varying amounts. Cobalt, copper, chromium, aluminimi, nickel, 
 sodium, titanium and tungsten appear in some brands in minute quan- 
 tities. 
 
 241 
 
242 Iron 
 
 Specific gravity of cast iron is variously given at 7.08, 7.15 and 7.40. 
 
 Atomic weight, 54.5. 
 
 Specific heat from 32° to 212° F., 0.129 Bystrom. 
 
 " " " " at .572° F., 0.1407 " 
 
 " " at 2150° F., 0.190 Oberhoffer. 
 Latent heat of fusion, 88 B.t.u.* 
 Total heat in melted iron, 450 B.t.u. 
 Critical temperature, 1382° F., Stupakoff. 
 Coefi&cient of linear expansion for 32° F., 0.000006. 
 
 " " " " at 1400° F., o.ooooioo. 
 
 Weight per cubic foot, 450 pounds. 
 Weight per cubic inch, 0.2604 pounds. 
 3.84 cubic inches, i pound. 
 
 Grading Pig Iron 
 
 The usual practice of furnaces has been to grade by fracture. 
 
 The grades are designated, Nos. i, 2, 3, 4 or gray forge; mottled and 
 white. 
 
 No. I. — Soft; open grain; dark in color. Used for thin, light 
 castings. Does not possess much strength; has great softening 
 properties; is mixed advantageously with harder grades; carries large 
 percentage of scrap. 
 
 No. 2. — Harder, closer, stronger and color somewhat lighter than No. i. 
 
 No. 3. — Harder, closer, stronger and lighter in color than No. 2; 
 and incHnes to gray. 
 
 No. 4 {Gray forge). — Hard, strong, fine grained and light gray color. 
 
 Mottled. — Hard, very strong and close grained. Color presents mot- 
 tled or imperfectly mingled gray and white colors. 
 
 White. — Hard and brittle, breaks easily imder sledge but has high 
 tensile strength; color white. 
 
 No. I iron running in the spout of the cupola displays few sparks. 
 In the ladle its smrface is lively and broken, sometimes flowery. 
 
 Nos. 2 and 3 present similar appearances but less marked. 
 
 Hard irons running from the cupola throw out innumerable sparks; 
 in the ladle the surface is dull and unbroken; if disturbed the reaction 
 is sluggish. 
 
 One cannot safely be guided by the appearance of the fracture of the 
 
 pig; as when melted it may produce a casting of an entirely different 
 
 character than that indicated. 
 
 * Marker and Oberhoffer have found that the specific heat of iron increases in 
 about the same ratio up to within the region of the critical point (1382° P.). After 
 this it remains practically constant. 
 
Grading Pig Iron 
 
 243 
 
 This method of grading is entirely unreliable as to chemical constit- 
 uents (and physical characteristics) ; the degree of coarseness of fractiure, 
 which affects the grade more than any other property, may be due 
 entirely to the rate of cooling. 
 
 Two pigs from the same cast may produce two grades; pigs from 
 different beds of the same cast may vary as much as i per cent in silicon 
 and .05 in sulphur. 
 
 The character of pig iron is often greatly affected by the accidents of 
 the furnace. 
 
 Irons produced from the same furnace at different times, from identical 
 mixtures, may differ greatly in their constituents, by reason of different 
 thermal conditions existing in the furnace at the time the ores were 
 melted. 
 
 Grading by fracture is so unreliable that most foundrymen specify the 
 characteristics required. 
 
 The following specifications are from Mr. W. G. Scott of the 
 J. I. Case Threshing Machine Co., Racine, Wis. 
 
 No. 
 
 Si, 
 
 not less 
 
 than 
 
 s, 
 
 not over 
 
 P, 
 
 not over 
 
 Mn, 
 not less 
 
 Total 
 carbon 
 
 I 
 
 2.50 
 1.95 
 1. 35 
 
 .03 
 .04 
 •OS 
 
 .60 
 .70 
 .80 
 
 .50 
 .70 
 90 
 
 
 
 
 3 
 
 
 
 
 Below these figures for silicon, or .005 above for sulphur means re- 
 jection. 
 
 Special pig irons 
 
 Silver gray 
 
 Ferro-silicon 
 
 Manganese 
 pig 
 
 
 3.00 to 5.50 
 
 .04 
 
 .00 
 
 .30 
 
 2. so 
 
 7.00 to 12.50 
 .04 
 
 Over 2 . so 
 
 
 
 
 .70 
 
 
 
 
 
 
 
 
 
 
 In calling for charcoal irons, silicon is asked for from .30 to 2.75; 
 sulphur not over .025; phosphorus not over .250; manganese not over 
 .70; carbon with range of from 2.50 to 4,50. 
 
 Phosphoric pig irons, for small thin castings, siHcon not under 1.50; 
 phosphorus not under i.oo; sulphur not over .055; manganese from .30 
 to .90; carbon not under 3.00. 
 
244 
 
 Iron 
 
 Based on a sliding scale for silicon and sulphur and a minimum for carbon. (Mar- 
 shall.) 
 
 No. I Foundry Pig Iron 
 
 Silicon with sulphur 
 
 .1.70 
 
 .010 
 
 to 
 
 to 
 
 3.00 
 
 .050 
 
 Carbon content 
 
 Total carbon over 3 . 20 
 
 Graphitic carbon over 2 . 75 
 
 An increase of .10 silicon for every .003 sulphur. 
 
 Silicon with sulphur 
 
 1.70 
 
 .010 
 
 1.80 
 
 .013 
 
 1.90 
 
 .016 
 
 2.00 
 
 .019 
 
 2.10 
 
 .022 
 
 2.20 
 
 .02s 
 
 2.30 
 
 .028 
 
 2.40 
 
 .031 
 
 2.50 
 
 .034 
 
 2.60 
 
 .037 
 
 2.70 
 
 .040 
 
 2.80 
 
 .043 
 
 2.90 
 
 .046 
 
 3.00 
 
 .050 
 
 No. 2 Foundry Pig Iron 
 
 Silicon with sulphur 
 
 1.20 
 
 .cos 
 
 to 
 
 to 
 
 2.20 
 
 .055 
 
 Carbon content 
 
 Total carbon over 3 00 
 
 Graphitic carbon over 2.50 < 
 
 An increase of .10 silicon for every .005 sulphur. 
 
 Silicon with sulphur 
 
 1.20 
 
 .COS 
 
 1.30 
 
 .010 
 
 1.40 
 
 .CIS 
 
 1.50 
 
 .020 
 
 1.60 
 
 .025 
 
 1.70 
 
 .030 
 
 1.80 
 
 .035 
 
 1.90 
 
 .040 
 
 2.00 
 
 .045 
 
 2.10 
 
 .050 
 
 2.20 
 
 .055 
 
Foundry Pig Iron 
 No. 3 FoxjNDRY Pig Iron 
 
 245 
 
 Silicon with sulphur 
 
 .70 
 
 .COS 
 
 to 
 
 to 
 
 1.70 
 
 .055 
 
 Carbon content 
 
 Silicon with sulphur 
 
 Total carbon over 2.75 
 
 Graphitic carbon over 2 .00 ■ 
 
 An increase of . 10 silicon for every .005 sulphur. 
 
 .70 
 .80 
 .90 
 1. 00 
 1. 10 
 1.20 
 1.30 
 1.40 
 1.50 
 1.60 
 1.70 
 
 .COS 
 .010 
 .015 
 .020 
 .025 
 .030 
 .035 
 .040 
 .045 
 .050 
 .055 
 
 No. 4 Foundry Pig Iron — (Gray Forge) 
 
 Silicon with sulphur 
 
 .50 
 
 .025 
 
 to 
 
 to 
 
 1.50 
 
 .075 
 
 Carbon content 
 
 Total carbon over 2.00 
 
 Graphitic carbon over i . 25 < 
 
 An increase of .10 silicon for every .005 sulphur. 
 
 Silicon with sulphur 
 
 .50 
 
 .025 
 
 .60 
 
 .030 
 
 .70 
 
 .035 
 
 .80 
 
 .040 
 
 .90 
 
 .04s 
 
 1. 00 
 
 .050 
 
 1. 10 
 
 •OSS 
 
 1.20 
 
 .060 
 
 1.30 
 
 .06s 
 
 1.40 
 
 .070 
 
 1.50 
 
 .075 
 
246 
 
 Iron 
 
 The wide variation in silicon and sulphur which may occur in irons 
 graded by fracture is shown in the Transactions of the American Foundry- 
 men's Association, Cleveland Convention; wherein appears a statement 
 as to the range of those elements, in the same grades of iron, made by 
 the same furnace. 
 
 No. I X varies in siHcon from 1.13 to 3.40 per cent. 
 " " " sulphur " 0.013 to 0.053 per cent. 
 
 No. 2 X " " sihcon " 0.67 to 3.30 per cent. 
 
 " " " sulphur " o.oi to 0.049 per cent. 
 
 No. 3 Plain " " sihcon " 1.05 to 3.21 per cent. 
 " " " sulphur " o.oi to 0.069 per cent 
 
 After long consideration, a committee of the American Foundry men's 
 Association, appointed to suggest a uniform system of grading, submitted 
 the following report, which was adopted at the Cincinnati Convention, 
 May, 1909. 
 
 AMERICAN FOUNDRYMEN'S ASSOCIATION 
 
 Standard Specifications for Foundry Pig Iron 
 
 Adopted by the American Fowndrymen's Association in Convention, 
 Cincinnati, May 20, igog. 
 
 It is recommended that foundry pig iron be bought by analysis, and 
 that when so bought these standard specifications be used. 
 
 Percentages and Variations 
 
 In order that there may be uniformity in quotations, the following 
 percentages and variations shall be used. (These specifications do not 
 advise that all five elements be specified in all contracts for pig iron, but 
 do recommend that when these elements are specified that the following 
 percentages be used.) 
 
 Silicon 
 
 Sulphur 
 
 Total carbon 
 
 (.25 allowed either way) 
 
 (maximum) 
 
 (minimum) 
 
 1. 00 (La) Code. 
 
 0.04 (Sa) Code. 
 
 3.00 (Ca) Code. 
 
 1.50 (Le) . 
 
 cos (Se) 
 
 3.20 (Ce) 
 
 2.00 (Li) 
 
 0.06 (Si) 
 
 3.40 (Ci) 
 
 2.50 (Lo) 
 
 0.07 (So) 
 
 3.60 (Co) 
 
 3.00 (Lu) 
 
 0.08 (Su) 
 0.09 (Sy) 
 o.ioi (Sh) 
 
 3.80 (Cu) 
 
Standard Specifications for Foundry Pig Iron 
 
 247 
 
 Manganese 
 
 Phosphorus 
 
 (.20 either way) 
 
 (.150 either way) 
 
 .20 (Ma) Code. 
 
 .20 (Pa) Code. 
 
 .40 (Me) 
 
 .40 (Pe) 
 
 .60 (Mi) 
 
 .60 (Pi) 
 
 .80 (Mo) 
 
 .80 (Po) 
 
 1.00 (Mu) 
 
 1. 00 (Pu) 
 
 1. 25 (My) 
 
 1.25 (Py) 
 
 1.50 (Mh) 
 
 1.50 (Ph) 
 
 Percentages of any element specified half way between the above shall 
 be designated by addition of letter "X" to next lower symbol. 
 
 In case of phosphorus and manganese, the percentages may be used 
 as maximum or minimum figures, but unless so specified they will be 
 considered to include the variation above given. 
 
 Sampling and Analysis 
 
 Each car load, or its equivalent, shall be considered as a unit in 
 sampling. 
 
 One pig of machine-cast, or one-half pig of sand-cast iron shall be taken 
 to every four tons in the car, and shall be so chosen from different parts 
 of the car, as to represent as nearly as possible the average quality of the 
 iron. 
 
 An equal weight of the drilHngs from each pig shall be thoroughly mixed 
 to make up the sample for analysis. 
 
 In case of dispute, the sample and analysis shall be made by an inde- 
 pendent chemist, mutually agreed upon, if practicable, at the time the 
 contract is made. 
 
 It is recomniended that the standard methods of the American 
 Foundrymen's Association be used for analysis. Gravimetric methods 
 shall be used for sulphur analysis, unless otherwise specified in the 
 contract. 
 
 The cost of the resampling and reanalysis shall be borne by the party 
 
 Base or Quoting Price 
 
 The accompanying table may be filled out and may become a part of 
 the contract: "B," or base, represents the price agreed upon for a pig 
 iron running 2.00 in silicon (with allowed variation 0.25 either way), and 
 under 0.05 sulphur. "C" is a constant differential to be determined 
 upon at the time the contract is made. 
 
248 
 
 Iron 
 
 Silicon percentages allow .25 variation either way. Sulphur percentages are maxi- 
 
 mum. 
 
 
 
 
 
 
 Silicon 
 
 3-25 
 
 3.00 
 
 2.75 
 
 2.50 
 
 2.25 
 
 Sulphtir — .04 
 
 B + 6C 
 
 B + sC 
 
 B + 4C 
 
 B + 3C 
 
 B+2C 
 
 Sulphur — .05 
 
 B+sC 
 
 B + 4C 
 
 B+3C 
 
 B + 2C 
 
 B + C 
 
 Sulphur — .06 
 
 B + 4C 
 
 B + 3C 
 
 B + 2C 
 
 B + C 
 
 B 
 
 Sulphur — .07 
 
 B+3C 
 
 B + 2C 
 
 B + C 
 
 B 
 
 B-C 
 
 Sulphur — .08 ■. . 
 
 B + 2C 
 
 B + C 
 
 B 
 
 B-C 
 
 B-2C 
 
 Sulphtu- — .09 
 
 B + C 
 
 B 
 
 B-C 
 
 B-2C 
 
 B-3C 
 
 Sulphur — .10 
 
 B 
 
 B-C 
 
 B-2C 
 
 B-3C 
 
 B-4C 
 
 Silicon 
 
 2.00 
 
 1-75 
 
 1.50 
 
 1.25 
 
 1. 00 
 
 Sulphur — .04 
 
 B + C 
 
 B 
 
 B-C 
 
 B-2C 
 
 B-3C 
 
 Sulphur — .OS 
 
 Base 
 
 B-C 
 
 B-2C 
 
 B-3C 
 
 B-4C 
 
 Sulphur — .06 
 
 B-C 
 
 B-2C 
 
 B-3C 
 
 B-4C 
 
 B-sC 
 
 Sulphur— .07 
 
 B-2C 
 
 B-3C 
 
 B-4C 
 
 B-sC 
 
 B-6C 
 
 Sulphur - .08 
 
 B-3C 
 
 B-4C 
 
 B-sC 
 
 B-6C 
 
 B-7C 
 
 Sulphur — .09 
 
 B-4C 
 
 B-sC 
 
 B-6C 
 
 B-7C 
 
 B-8C 
 
 Sulphur— .10 
 
 B-sC 
 
 B-6C 
 
 • 
 
 B-7C 
 
 B-SC 
 
 B-9C 
 
 (This table is for settling any differences which may arise in filling a 
 contract, as explained under Penalties and Allowances, and may be used 
 to regulate the price of a grade of pig iron which the purchaser desires, 
 and the seller agrees to substitute for the one originally specified.) 
 
 Penalties 
 
 In case the iron, when delivered, does not conform to the specifications, 
 the buyer shall have the option of either refusing the iron, or accepting 
 it on the basis as shown in the table, which must be filled out at the time 
 the contract is made. 
 
 Allowances 
 
 In case the furnace cannot for any good reason deliver the iron as 
 specified, the purchaser may at his option accept any other analysis 
 which the furnace can deliver. The price to be determined by the Base 
 Table herewith, which must be filled in at the time the contract is made. 
 
 Machine- Cast Pig Iron 
 
 Pig iron is usually cast in sand beds. The casting machine has of late 
 years been adopted by some furnaces and the statement is made that 
 machine-cast pig, aside from the freedom from sand, possesses other 
 important advantages. That it is more uniform in character; affords 
 
Machine-Cast Pig Iron 
 
 249 
 
 greater certainty as to its chemical composition; is cleaner and melts 
 more readily. 
 
 Machine-cast pig presents a closer grain and is harder than iron cast 
 in sand, by reason of the greater percentage of combined carbon. 
 
 Upon remelting, this difference disappears and the castings show the 
 same analysis. 
 
 Mr. A. L. Colby, chemist of the Bethlehem Iron Co., gives the follow- 
 ing statement regarding an experiment, made to determine the influence 
 of the mould upon pig iron. 
 
 "One half of a cast was poured into sand moulds and the other half 
 into iron. Equal quantities of drillings from six pigs, selected from 
 different parts of that portion of the cast which had been cast in sand 
 were taken; and similar drillings were obtained from that portion of the 
 cast which had been taken to the casting machine; and each was care- 
 fully analyzed, with the following results: 
 
 Cast No. 7602 
 
 Silicon 
 
 Manganese 
 
 Phosphorus 
 
 Sulphur 
 
 Total carbon ' 
 
 Combined carbon 
 
 Graphitic carbon 
 
 Tensile strength per square inch 
 
 "The high tensile strength of the machine-cast iron is due almost 
 entirely to the higher percentage of its combined carbon. Some of the 
 sand-cast portion of this cast, and some of the machine-cast portion were 
 melted separately in the same cupola, keeping all smelting conditions 
 as nearly uniform as possible; and castings from each melt were made, 
 which were proved by analysis, tensile strength, ability to machine and 
 appearance of fracture to be as nearly alike as different things, made 
 from the same iron, ever are." 
 
 Regarding this experiment, Mr. W. J. Keep in a communication to 
 "The Foundry," remarks: 
 
 "The experiment shows that a pig iron cast in iron moulds with a very 
 close grain and high combined carbon and the same iron cast in a sand 
 pig mould with open grain and low combined carbon, will each, when 
 remelted in a cupola, make castings exactly alike." 
 
2 so 
 
 Iron 
 
 The following report on the test ingots, cast with the experimental 
 castings, supports this statement. 
 
 Constituents 
 
 Sand-cast pig iron ingot 
 
 3H inches square and 
 
 iH feet long 
 
 Machine-cast pig iron 
 
 ingot 3]^ inches square 
 
 and i},^ feet long 
 
 Cast 
 
 horizontally, 
 
 per cent. 
 
 Cast 
 
 vertically, 
 
 per cent 
 
 Cast 
 
 horizontally, 
 
 per cent 
 
 Cast 
 
 vertically, 
 
 per cent 
 
 Silicon 
 
 2.93 
 .84 • 
 .766 
 .071 
 
 3.40 
 .470 
 
 2.930 
 
 18,000 
 G2 Fi 
 
 2.91 
 .85 
 .769 
 .064 
 
 3.390 
 .368 
 
 3.022 
 
 16,300 
 G2 Ei 
 
 2.96 
 .84 
 .772 
 .077 
 
 3.364 
 .336 
 
 3.028 
 
 17,000 
 Gi Fi 
 
 2.9s 
 
 
 .84 
 
 
 .764 
 
 Sulphur 
 
 Total carbon 
 
 Combined carbon 
 
 Graphitic carbon. 
 
 Tensile strength 
 
 .071 
 3.357 
 
 .257 
 3.100 
 17,000 
 
 Mark on ingot 
 
 Gi Fi 
 
 
 
 The coarse open fracture presented by some pig irons, and which under 
 the old system might cause them to be graded as No. i, may be due to 
 an excessive amount of manganese and the iron will be hard upon re- 
 melting. On the other hand, an iron may have a close grain, by reason 
 of the graphitic carbon occurring in a finely divided condition and be 
 graded low; when, since it is soft, it should have a much higher grading. 
 
 Charcoal Iron 
 
 Charcoal iron is graded according to fracture. The grades are desig- 
 nated by numbers and also as soft foundry; low carbon, 2.5 per cent 
 total carbon; medium carbon, 3.5 per cent total carbon; and high car- 
 bon, 4.5 per cent carbon. Purchases are usually made on specifications. 
 
 Comparatively little charcoal iron is now used, since its valuable 
 properties as regards chill and strength may be imparted to coke irons 
 by use of the ferrometalloids and scrap steel. 
 
 Grading Scrap Iron 
 
 Machinery scrap should be free from burnt iron, wrought iron, steel, 
 plow points, brake shoes, sash weights, sleigh shoes, chilled iron, stove 
 plate and fine scrap; should be broken into pieces weighing not over 
 400 pounds. 
 
 Approximately, scrap iron varying in thickness from H inch to i inch, 
 may be compared with pig iron carrying from 1.5 per cent to 2 per cent 
 silicon and .08 per cent sulphur. 
 
Grading Scrap Iron 251 
 
 From I inch to 3 inches thick, as compared with pig iron carrying from 
 I per cent to 1.75 per cent siHcon and .08 per cent sulphur. Above 3 
 inches thick, with an open gray fracture, as ranging in sihcon from .75 
 to 2 per cent. 
 
 In white scrap, sihcon is usually very low and sulphur very high. 
 
 Burnt iron is worthless except for sash weights and similar castings. 
 
 The successful grading of scrap iron can only be accomplished by 
 experience. 
 
CHAPTER IX 
 
 INFLUENCE OF THE CHEMICAL CONSTITUENTS 
 OF CAST IRON 
 
 Carbon 
 
 Combined carbon increases strength, shrinkage, chill and hardness, 
 and closes the gram. 
 
 Graphitic carbon reduces strength, shrinkage, chill, hardness, and tends 
 to produce an open grain. 
 
 Silicon softens iron by promoting the formation of graphitic carbon. 
 It decreases shrinkage and strength; increases fluidity and opens the 
 grain. 
 
 Sulphur hardens iron, increases shrinkage and chill; causes it to set 
 quickly in the ladle ("lose its hfe"); produces blow holes, shrinkage 
 cracks and dirty iron. 
 
 Phosphorus weakens iron, imparts fluidity, decreases shrinkage and 
 lowers the melting point. 
 
 Manganese in large percentages hardens cast iron. It increases 
 shrinkage and chill, reduces deflection and tends to convert graphitic 
 into combined carbon. In small amoimts by reason of its power to 
 remove sulphur and occluded gases, its tendency is to produce sound, 
 dense castings, without increased hardness or shrinkage. 
 
 To raise the strength of castings, increase manganese and reduce 
 silicon ^nd phosphorus. 
 
 To soften iron, increase silicon and phosphorus. 
 
 To reduce shrinkage, increase sihcon and phosphorus and reduce 
 sulphur. 
 
 To prevent blow holes, reduce sulphur and increase manganese. 
 
 To prevent kish (excessive amount of free carbon), increase scrap or 
 increase manganese. 
 
 [W. G. Scott.] 
 
 Properties of the Usual Constituents of Cast Iron 
 Carbon 
 
 Specific gravity (diamond) 3 . 55 
 
 (graphite). 2.35 
 
 Atomic weight 12 . 
 
 252 
 
Properties of the Usual Constituents of Cast Iron 253 
 
 Specific heat at 212° F 0.198 
 
 " " 1800° F 0.459 
 
 " " 3000° F 0.52s 
 
 Carbon exists in cast iron as combined and graphitic. 
 Professor Turner recognizes two different varieties under each of the 
 general subdivisions, as follows: 
 
 (Coarse-grained carbon or graphite. 
 Fine-grained carbon, called amorphous carbon, 
 or temper graphite. 
 P , . /• Combined carbon. 
 
 , J "Missing" carbon, which usually occurs in rela- 
 
 [ tively small quantities in cast iron. 
 
 The amount of carbon which may be absorbed by pure iron at high 
 temperatiues is stated differently by different authorities. 
 
 Turner places the limit of satiuation at 4.25 per cent, and cites Saniter's 
 experiments as follows: 
 
 "At cementation, heat about 1650° F., 2 per cent; by fusion, about 
 2550° F., 4.00 per cent." 
 
 Field states that pure iron at maximum temperatures absorbs 6h 
 per cent carbon. 
 
 Keep gives the saturation of charcoal iron when cold as 4 per cent and 
 that of anthracite or coke irons as 3.50 per cent to 3.75 per cent. 
 
 The saturation point varies according to the temperature. 
 
 As iron cools below the temperature of saturation, carbon separates 
 out in the form of graphitic carbon. At just what temperature this 
 separation ceases is not definitely known; it is variously stated at 
 1300° F., 1650° F., and as high as 1800° F. 
 
 Since the specific heat of carbon is much greater than that of iron, it 
 delays the rate of cooling as the temperature falls. 
 
 In a mixture containing 96 per cent of iron and 4 per cent of carbon, 
 the heat evolved by the carbon, during the process of cooling, retards 
 the rate of cooling one-seventh. 
 
 According to Field, an iron containing 6\i per cent carbon will dis- 
 solve no silicon; and one containing 23 per cent of silicon dissolves no 
 carbon. 
 
 Iron having 3 per cent silicon contains approximately 0.3 per cent 
 combined carbon. 
 
 With 2 per cent silicon the combined carbon is 0.6 per cent and with 
 I per cent silicon 0.9 per cent. 
 
 As the carbon separates out in cooling, it changes from combined to 
 graphitic, producing a softer, weaker iron and one having less shrinkage. 
 
254 Influence of the Chemical Constituents of Cast Iron 
 
 The total carbon in cast iron varies from 2 per cent to 4\i per cent, 
 averaging about 3.4 per cent. 
 
 With silicon as high as 8 to 10 per cent, the total carbon falls to 2 
 per cent. 
 
 Under the same conditions, the higher the total carbon, the softer the 
 iron. A very soft iron may contain as little as 1 per cent combined 
 carbon with 3.4 to 3.5 per cent graphitic. 
 
 An increase of .25 per cent total carbon produces a marked increase 
 in the softness, and a corresponding decrease in strength and shrinkage. 
 
 Combined carbon increases as the grades grow harder. 
 
 Ordinary soft iron contains from .3 to .5 per cent combined carbon. 
 
 Strong irons carry from .45 to .9 per cent. 
 
 The harder grades run from .6 to i per cent. 
 
 The proportion of combined to graphitic carbon is determined: 
 
 First. — By the total carbon present, as the greater the total carbon, 
 the greater will be the proportion of graphitic to combined carbon. 
 
 Second. — By the rate of coohng. Rapid cooling increases the com- 
 bined and slow cooling increases graphitic carbon. 
 
 Third. — By the temperature of the iron when it begins to cool. 
 
 The higher the temperature at which the iron is poured, the longer will 
 be the time elapsed in cooling and the longer the period for conversion 
 of combined to graphitic carbon. 
 
 Fourth. — By the amoimt and kind of other elements present. 
 
 Silicon decreases combined and increases graphitic carbon. With 
 increased silicon all the combined carbon may be changed to graphitic. 
 
 An increase of i per cent silicon in cast iron, other conditions remain- 
 ing the same, will convert from .35 to .47 per cent of combined into 
 graphitic carbon; and imder the same circumstances an increase of 
 .47 per cent combined carbon will cause a corresponding decrease in 
 silicon. 
 
 Sulphur increases combined carbon as also does manganese. 
 
 Phosphorus prolongs the cooling and thereby affords more time for 
 the separation of graphitic carbon. 
 
 Loss or Gain of Carbon in Remelting 
 
 An iron may gain or lose carbon in passing through the cupola. 
 
 There is a tendency to loss of carbon in remelting where the carbon and 
 silicon are high, with heavy blast and low percentage of fuel. 
 
 On the other hand, where the carbon and silicon are low, with low blast 
 and high percentage of fuel, the tendency is to gain in carbon. 
 
 Hard irons melt more readily than soft; the higher the combined 
 carbon, the lower the melting point. 
 
Loss or Gain of Carbon in Remelting 
 
 255 
 
 Hard irons hold their shape in melting. The melted iron runs from 
 bottom and sides of the pig freely, leaving smooth surfaces; while 
 gray irons become soft and drop away in lumps presenting ragged 
 surfaces. 
 
 Hard irons must be melted hotter than gray for pouring as they set 
 much more rapidly. 
 
 In running from the spout of the cupola and in the ladle, hard irons 
 throw off great quantities of sparks, and the surface of the iron in the 
 ladle is dull and inactive when broken; on the other hand, the soft irons 
 seldom emit sparks and present a lively surface in the ladle, breaking 
 with innumerable checks, the soft Scotch irons showing peculiar flowery 
 surfaces. 
 
 The diagram given below taken from the report of Prof. J. J. Porter, 
 "shows the range of combined carbon, which sliould result for each 
 
 1 — I — I — \ — \ — \ — I — I — r 
 
 ^ Doited Lives are Percenfs expected on Basis 
 — ' of Theory. 
 
 Full Lrnes give Percenfs of Combmed Carbon 
 obtained In Actual Castings of Thicknesses 
 given (Approximated) 
 
 Irons plotted are all under I Percent Pand 
 Mn and 0.10 6. and are Cupola Melted. 
 o = Total Carbon, x = Comb. Carbon. 
 
 T/7, 
 
 ?S^ 
 
 Se-i 
 
 §^^ 
 
 3 55:= 
 
 ^/^ 
 
 ,£2 
 
 '^c 
 
 ':irj^ 
 
 percentage of silicon (the cooling being normal, i.e., the castings being 
 neither chilled nor annealed). " The calculations are made on the theory 
 that I per cent of silicon precipitates from solution .45 per cent carbon 
 as graphitic carbon. 
 
256 Influence of the Chemical Constituents of Cast Iron 
 
 For specified purposes Prof. Turner gives the following percentages of 
 combined carbon. 
 
 Character of iron 
 
 Combined 
 carbon 
 
 Extra soft siliceous gray iron 
 
 .08 
 
 
 
 Cast iron of maximum tensile strength 
 
 • 47 
 
 Cast iron of maximum transverse strength 
 
 -47 
 
 Cast iron of maximum crushing strength 
 
 Over 1. 00 
 
 
 
 Silicon 
 
 Full lines show approximately the relation existing between the 
 thickness of section, per cent of silicon and per cent of combined carbon, 
 and are plotted from the actual data there given. 
 
 Atomic weight 28.4 
 
 Specific gravity 2 . 49 
 
 Specific heat .20 B.t.u. 
 
 Pig iron takes up its silicon in the furnace, and the amount so absorbed 
 depends largely upon the working temperatures. 
 
 Pure iron dissolves about 23 per cent of silicon. By means of the 
 electric furnace iron is made to absorb as much as 80 per cent. Those 
 irons containing over 20 per cent are called ferrosilicons; where the 
 silicon content runs from 5 to 10 per cent they are called high silicon 
 irons. 
 
 Iron always loses silicon in passing through the cupola-, and the amount 
 lost depends upon three conditions. 
 
 First. — The amount of oxygen coming in contact with the metal in 
 melting; oxidation increases with the blast. 
 
 Second. — Upon the composition of the iron as it is charged into the 
 cupola, the loss being greater in irons having a high percentage of silicon 
 than in those where the silicon content is low. An iron with 4 per cent 
 silicon may lose as much as 2 per cent in melting, while with one very low 
 in silicon, the loss may be inappreciable. 
 
 The affinity of iron for sihcon decreases as the latter increases, hence 
 the amoimt oxidized increases with increased silicon. 
 
 Third. — The loss of silicon varies also with the percentage of carbon 
 present, being greater in high than in low carbon irons. 
 
 Silicon lowers the solvent power of cast iron for carbon, thereby 
 reducing the amoimt of combined carbon and increasing the graphitic. 
 
 This influence is the more powerful with the lower percentages of 
 silicon; the decrease in combined carbon being particularly rapid as 
 
Silicon 257 
 
 the silicon rises from o to .75 per cent; then as the silicon continues to 
 rise, the decrease in combined carbon grows less and less. 
 
 Silicon and carbon each reduce the solubility of iron for the other. 
 
 The influence of silicon is sometimes rendered less apparent by that 
 of other variable elements. 
 
 Silicon is not of itself a softener of cast iron, nor does it, per se, lessen 
 shrinkage; but it produces a softening effect and reduces shrinkage by 
 changing combined into graphitic carbon; the amount used should be 
 just suflicient to force from solution the amount of carbon desired in the 
 free state for any particular mixture and to furnish the requisite fluidity. 
 
 For every rise of i per cent silicon in cast iron there will be a corre- 
 sponding drop of .45 per cent in combined carbon and vice versa. 
 
 Where iron is melted, very hot silicon unites to some extent with 
 sulphur, forming a very volatile sub-sulphide of silicon, thereby re- 
 ducing the amount of sulphur absorbed by the iron. 
 
 By reason of its specific heat, silicon retards the cooling of iron to a 
 certain extent. It can be made to overcome many difficulties in castings, 
 and to control the quality and cost of mixtures, where scrap iron is 
 largely used. 
 
 An increase of .2 per cent in silicon decreases shrinkage about .01 inch 
 per foot. 
 
 Very high percentages of silicon decrease the fusibility of iron. 
 
 When the percentage of silicon in the casting is above 2 per cent, it has 
 a weakening influence. 
 
 Ferrosilicon is mixed with iron in the ladle for softening and reducing 
 shrinkage. 
 
 Carbide of siHcon is sometimes charged with the iron in the cupola. 
 
 Regarding the use of silicon. Prof. Turner says: "That at one time 
 its presence in cast iron, in all proportions, was regarded as injurious; 
 that there was no accurate knowledge of its influence prior to 1885, when 
 my first paper on 'The Influence of SiHcon on the Properties of Cast 
 Iron' was published in the 'Journal of the Chemical Society.'" 
 
 Summary of Prof. Turner's experiments in the use of silicon. 
 
 Characteristics 
 
 Per cent silicon 
 
 Cast iron yielding maximum hardness 
 
 Cast iron yielding maximum crushing strength 
 
 Cast iron yielding maximum density in mass 
 
 Cast iron yielding maximum crushing tensile and transverse 
 
 strength 
 
 Cast iron yielding maximum tensile strength 
 
 Cast iron yielding maximum softness and general working qualities 
 
 .60 
 
 .80 
 
 1. 00 
 
 1.40 
 1.80 
 2.50 
 
258 Influence of the Chemical Constituents of Cast Iron 
 
 The subjoined chart and table giving the effect of silicon on the proper- 
 ties of cast iron taken from Prof. Turner, show that the influence of 
 silicon is of a uniform character as respects crushing, transverse and 
 tensile strength. 
 
 £ 3 4 5 b 7 
 Silicon, percent. 
 
 Fig. 73. 
 
 60 
 
 60 
 
 40 
 
 20 
 
 \ 
 
 
 
 
 
 \ 
 
 
 
 J^ 
 
 y 
 
 \ 
 
 ^^ 
 
 °>^ 
 
 ^ 
 
 
 2 . 4 
 ^ilicorij percent. 
 
 Fig. 74. 
 
 Chart No. II, showing the hardness of the same series of test bars, 
 was determined by the "Sclerometer." 
 
 The hardness decreased continuously with the additions of silicon until 
 2,5 per cent was reached, when further additions caused an increase of 
 hardness. 
 
 The addition of silicon to iron free from carbon increases the tensile 
 strength and hardness. The influence resembles that of combined car- 
 bon on iron or steel, but is less energetic. 
 
Silicon 
 
 259 
 
 Effects of Silicon on the Properties of Cast Iron 
 
 n 
 
 if 
 
 Cylin- 
 ders 
 
 1 
 1 
 
 If 
 
 Modulus 
 
 of 
 elasticity 
 
 1 
 
 
 
 1 
 
 r 
 
 6 
 
 Chemical analysis 
 
 go 
 
 Is 
 
 1 
 
 4) 
 
 1 
 
 
 
 c 
 
 
 a 
 
 
 
 1 
 1 
 
 i 
 
 i-i 
 
 1 
 
 
 
 .5 
 
 I.O 
 
 1.4 
 
 2.0 
 
 2.5 
 3.0 
 4.0 
 
 S.o 
 7.5 
 10. 
 
 7.560 
 7.510 
 7.641 
 7-555 
 7.518 
 7.422 
 7-258 
 7.183 
 7.167 
 7.128 
 6.978 
 
 72 
 52 
 42 
 
 22 
 
 22 
 22 
 27 
 32 
 42 
 57 
 
 Lbs. 
 
 22,720 
 
 27,580 
 
 28,490 
 
 31,^40 
 
 35,180 
 
 32,760 
 
 27,390 
 
 25,280 
 
 22,750 
 
 11,950 
 
 10,630 
 
 25,790,000 
 28,670,000 
 31,180,000 
 23,500,00c 
 23,560,000 
 25,450,000 
 21,150,000 
 15,640,000 
 18,720,000 
 14,750,000 
 13,930,000 
 
 Lbs. 
 168,700 
 204,800 
 207,300 
 183,900 
 137,300 
 172,900 
 128,700 
 105,900 
 103,400 
 111,000 
 76,380 
 
 Lbs. 
 2702 
 3280 
 3370 
 3498 
 3446 
 3534 
 2850 
 2543 
 2342 
 150S 
 1252 
 
 1.98 
 2.00 
 2.09 
 2.21 
 2.18 
 1.87 
 2.23 
 2.01 
 2.03 
 
 1.86 
 1. 81 
 
 .38 
 
 .10 
 
 .24 
 
 .50 
 
 1.62 
 
 1. 19 
 
 1.43 
 
 I. 81 
 
 1.66 
 1.48 
 1. 12 
 
 1.60 
 
 1.90 
 
 1.85 
 
 1. 71 
 
 .56 
 
 .68 
 
 .80 
 
 .20 
 
 .37 
 
 .38 
 
 .69 
 
 .19 
 .45 
 .96 
 1.37 
 1.96 
 2.51 
 2.96 
 3.92 
 4.74 
 7.33 
 9.80 
 
 .32 
 .33 
 -33 
 .30 
 
 .28 
 .26 
 
 • 34 
 .33 
 .30 
 .29 
 .21 
 
 .14 
 .21 
 .26 
 
 !6o 
 .75 
 .70 
 .84 
 .95 
 1.36 
 1.95 
 
 .05 
 .05 
 .04 
 .05 
 .03 
 .05 
 .04 
 .03 
 -05 
 .03 
 -04 
 
 Bars one foot long, one inch square, loaded in the center. 
 
 Silicon added to hard iron affects the size of the graphite, since the 
 freshly precipitated graphite resulting from such addition is smaller than 
 that found in ordinary soft foundry irons. Consequently, the metal is 
 closer and stronger. 
 
 Prof. Turner favors increasing sihcon in a mixture of cast iron by the 
 use of high silicon pig iron, rather than by that of ferrosilicon, as the 
 latter differs both in fusibility and density from the iron, rendering the 
 product of the mixture uncertain and irregular. "The ideal method is 
 for the founder to have a fairly large stock, including several kinds of 
 iron, each separate kind being a little too hard or a little too soft for the 
 general run of work, but still not very different from what is required. 
 By mixing these irons in suitable proportions, it is then easy to obtain 
 any composition which may be desired, it being asstmied, of course, that 
 the composition of each variety is already known." 
 
 During the period from 1886 to 1888, Mr. Keep made an exhaustive 
 study of the influence of silicon on cast iron. The results of his researches 
 as summarized in "Cast Iron" are: 
 
 SiUcon added to white iron changes it to gray; added to gray iron, low 
 in sihcon, makes the mixture darker. 
 
 It is the influence of silicon, not the percentage, which produces desir- 
 able qualities; and that influence is indirect, acting through the carbon 
 which the iron contains. 
 
'260 Influence of the Chemical Constituents of Cast Iron 
 
 The saturation point of iron for carbon is lowered by the addition of 
 silicon, as the carbon is expelled in the graphitic form and caught between 
 the grains of the iron producing a grayer color. 
 
 If the total carbon is high, or the combined carbon low, the amount 
 of silicon required to produce a particular effect will be correspondingly 
 low. Similar effects are produced by a small amount of sihcon acting 
 through a prolonged period, by reason of slow cooHng of large castings, 
 and by a large amount acting through a short period, as in the rapid 
 cooling of small castings. By regulating the amount of silicon in the 
 mixture the state of carbon as well as the depth of chill can be controlled. 
 The diffusion of silicon is very irregular. Mr. Keep found in a number 
 of experiments that the average variation in diffusion was from .09 to 
 .24 per cent. This average increases and the diffusion is less and less 
 complete as the silicon increases, so that any literal determinatives of 
 silicon are rendered more or less approximative (as showing the per- 
 centage of silicon in a car load of iron) by the unequal diffusion. 
 
 As regards hardness, the addition of 2 to 3H per cent of silicon will 
 convert all the combined into graphitic carbon, which it is possible to 
 change by the use of that element. 
 
 Silicon in itself hardens cast iron, but the softening effect caused by 
 it in producing the change from combined to graphitic carbon, is such as 
 to result in decreased hardness, until the amount of silicon added has 
 reached from 2 to 3 per cent. Further additions are not advantageous. 
 The beneficial influence resulting from the use of silicon in cast iron is not 
 confined to decreased hardness. It imparts fluidity and also tends to 
 produce clear, smooth surfaces on the castings, by reason of the liberated 
 graphite, in part, interposing itself between the sand and the hot iron. 
 
 Sulphur 
 
 Atomic weight 32 . 
 
 Specific gravity 2 . 03 
 
 Specific heat o. 2026 
 
 Melting point 226** F. 
 
 Latent heat of fusion 16.86 B.t.u. 
 
 Weight per cubic foot 125 pounds 
 
 The sulphur in pig iron is taken up in the furnace, from the fuel and 
 flux. Its presence is most injurious and causes the foundryman more 
 difiSculty than any other element. It makes iron hard and brittle, 
 increases shrinkage and chill, causes iron to congeal quickly and by 
 preventing the ready escape of gases, makes blow holes and pin holes. 
 
 It increases the combined carbon and reduces silicon. 
 
Sulphur 
 
 261 
 
 WTien pig iron is remelted, the percentage of sulphur is always in- 
 creased, as it takes up from 20 to 40 per cent of the sulphur in the fuel. 
 Mr. J. B. Neu found in some experiments that as much as 66 per cent 
 of the sulphur in the fuel was absorbed by the iron in melting. 
 
 The sulphur content of the iron at each of three remeltings is given by 
 Mr. Percy Longmuir as follows: 
 
 
 First 
 melt 
 
 Second 
 melt 
 
 Third 
 melt 
 
 Per cent sulphur 
 
 .04 
 
 .10 
 
 .20 
 
 The proportion between the total amount of sulphur present in the 
 fuel, to that absorbed by the iron, is dependent on three conditions. 
 
 First. — The quality and quantity of flux used. 
 
 Second. — The temperature of the melted iron. 
 
 Third. — The composition of the fuel and iron. 
 
 In a hot working cupola, the proper quantity of flux will remove much 
 of the sulphur. That present in the fuel as a sulphuretted hydrocarbon 
 has no appreciable effect upon the percentage retained in the melted iron. 
 
 As sulphur combines with iron at low temperatures, a hot cupola tends 
 to increase the amount carried away by the slag. Where the fuel contains 
 I per cent or over of sulphur, it may add from .04 per cent to .06 per cent 
 to the iron and a casting made from iron having only 2 per cent of sulphur 
 may, when the iron is melted with high sulphur coke, show from .06 
 to .08 per cent. 
 
 A slow melting cupola with low temperature favors the absorption of 
 sulphur. 
 
 An increase of sulphur, the other elements and the rate of cooling 
 remaining constant, hardens iron by increasing the combined carbon and 
 also causes greater shrinkage, contraction and chill. 
 
 Less change in the percentage of sulphur present is required to harden 
 or soften cast iron than in that of any other element. 
 
 Sulphur shortens the time that iron will remain fluid in the ladle, 
 "destroys the life of the iron," and if present to a large extent, makes 
 the production of sound castings very difficult. The molten iron is 
 sluggish and sets quickly, thereby enclosing escaping gases, dross, kish, 
 etc., which cause blow holes and dirty castings. 
 
 Where sulphur is present to any considerable extent, the iron must be 
 poured very hot. 
 
 Iron will absorb as much as .3 per cent sulphur with increasing fusi- 
 bility and decreasing fluidity. 
 
262 Influence of the Chemical Constituents of Cast Iron 
 
 An increase of .01 per cent of sulphur can neutralize the effect of from 
 .08 to .10 per cent silicon. In coke irons, usually, as the silicon decreases 
 the sulphur increases. To maintain a uniform degree of hardness in 
 castings the increase of silicon corresponding to successive increases of 
 .01 per cent sulphur should be about as follows: 
 
 Sulphur, per cent 01 .02 .03 .04 .05 .06 
 
 Silicon, per cent 2 . 00 2.10 2 . 20 2 . 30 2 . 40 2 . 50 
 
 Sulphur may be largely expelled from cast iron by the use of man- 
 ganese, passing off in the slag as sulphide of manganese; the greater the 
 amount of manganese present, the less sulphur will the iron absorb and, 
 it is possible, where the manganese is very high, for the iron to lose 
 sulphur in melting. 
 
 From I to 2 per cent manganese, in addition to that carried by the pig 
 iron, is sometimes used in the ladle, to effect the removal of sulphur; 
 care must be exercised in this respect, however, as manganese in excess 
 of that taken up by the sulphur tends to harden the iron. 
 
 When the fuel does not contain more than .08 per cent sulphur and 
 the iron has about .5 per cent manganese, the sulphur in ordinary gray 
 irons will increase about .025 per cent in melting. 
 
 The injurious effects of sulphur are largely counteracted by the use of 
 phosphorus. Other elements remaining constant, an increase of .1 
 per cent phosphorus produces about the same results in counteracting 
 the effects of sulphur as does an increase of .25 per cent silicon. 
 
 By the use of phosphorus instead of silicon for this purpose, the 
 fluidity of the iron is greatly increased; gases, dross, etc., can come to 
 the surface and greater freedom from blow holes, shrink holes, etc., 
 results. 
 
 Irons with high combined carbon are usually high in sulphur. Long- 
 muir gives the following as the result of examinations of the sulphur 
 content for different amounts of combined carbon. 
 
 Grade 
 
 Combined carbon 
 
 Sulphur 
 
 Silicon 
 
 I 
 
 2 
 
 3 
 
 4 
 
 5 
 
 Mottled 
 
 .50 
 
 .60 
 
 .80 
 
 1. 10 
 
 1.30 
 
 1.80 
 
 .02 
 
 .02 
 
 .04 
 
 .08 
 
 .10 
 
 • IS 
 
 2. so 
 
 2.30 
 
 1.80 
 
 1.50 
 
 1.20 
 
 .70 
 
 White 
 
 3.00 
 .20 
 .30 
 
 The sulphur content of pig iron usually runs from .01 to .08 and some- 
 times higher. 
 
 Prof. J. J. Porter concludes his remarks on the effects of sulphur upon 
 the physical properties of cast iron as follows: "Through the formation 
 
Phosphorus 263 
 
 in the iron sulphide of eutectic films, it causes brittleness and weak- 
 ness, especially to shock. Through its action on the carbon it increases 
 hardness and may either increase or decrease strength according as the 
 combined carbon is already too low or too high. It has a great tendency 
 to cause blow holes, especially near the upper surface of thick castings. 
 So marked is this effect in pig iron that high sulphur pig may nearly 
 always be spotted by the presence of blow holes in the top surfaces. 
 
 "Sulphur probably has a more detrimental effect on low silicon, or 
 chill iron, than on the ordinary foundry grades. All of these effects of 
 sulphur are considerably lessened by the presence of sufficient manganese 
 to insure its being in the form of MnS, but on the other hand, the segre- 
 gation of MnS may cause bad places in the casting, apparently due to 
 dirty iron." 
 
 The statements given above are those generally entertained as regards 
 the deleterious influence of sulphur. They are not, however, entirely 
 confirmed by the investigations of Prof. Turner and Mr. Keep. The 
 former remarks that: "We are still in need of exact information as to the 
 influence of sulphur in cast iron." After a long series of experiments to 
 determine the injurious effect of sulphur on cast iron, Mr. Keep con- 
 cludes that the presence of .05 per cent of that element will not exert any 
 appreciable deleterious influence, and that what little ill effect results 
 is corrected by a slight increase of silicon. Such small percentage of 
 sulphur does not seem to influence the depth of chill, nor does there 
 appear to exist any relation between the sulphur content and the strength 
 of an ordinary casting. 
 
 "While there is no indication that sulphur is in any way beneficial, on 
 the other hand, evidence is lacking to show that its influence is ever any- 
 thing but injurious; and the suggestion arises from the records, that the 
 prevaiUng opinions regarding the deleterious effects of sulphur are partly 
 superstitious, due, largely, to laboratory experiments made under con- 
 ditions never met with in the foundry." 
 
 Phosphorus 
 
 Atomic weight 31 • 00 
 
 Specific gravity i . 83 
 
 Specific heat o . 189 
 
 Melting point 112° F. 
 
 Latent heat of fusion 9 . 06 B.t.u. 
 
 Weight per cubic inch . 066 
 
 The phosphorus content in pig iron comes mostly from the ore, but 
 also in part from the fuel and flux. 
 
264 Influence of the Chemical Constituents of Cast Iron 
 
 Phosphorus weakens cast iron, lowers its melting point, imparts 
 fluidity, tends to soften and decreases shrinkage. 
 
 It has no direct effect on carbon, but since it prolongs the cooling 
 of melted iron it gives more time for graphitic carbon to separate 
 out. 
 
 Its influence in imparting fluidity is greater than that of any other 
 element, hence its presence within moderate limits (i to 1.25 per cent) is 
 especially desirable for light, thin castings. 
 
 After it is once taken up by the iron very little of it escapes, but its 
 percentage is frequently increased if it exists to any extent in the fuel 
 or flux used in melting. 
 
 Phosphorus largely counteracts the influence of sulphur to increase 
 combined carbon, shrinkage, contraction and chill. An increase of 
 .1 per cent phosphorus in the iron will produce about the same physical 
 results in counteracting the effects of sulphur, as an increase of .25 per 
 cent sihcon, all other elements remaining constant. 
 
 Where over .7 per cent phosphorus is present in the iron it tends to 
 make the latter cold short and unless there is necessity for extreme 
 fluidity the phosphorus content should not exceed i per cent. 
 
 By reason of its tendency to increase fusibiUty, it should be kept as low 
 as possible in castings required to stand high temperatures. 
 
 In machinery castings containing 1.5 per cent phosphorus, the tools 
 are quickly heated and worn. 
 
 Where great strength is required of castings, the phosphorus content 
 should not exceed .02 per cent. 
 
 Where blow-holes are formed in castings, by reason of occluded gases, 
 phosphide of iron is frequently extruded into them in the shape of 
 globular masses or shot. 
 
 Ferrophosphorus may contain from 20 to 25 per cent phosphorus and 
 is sometimes used in the ladle where prolonged fluidity is desired. 
 
 Prof. Turner states that the presence of 0.5 phosphorus in cast iron 
 produces excellent results and that where fluidity and soundness are 
 more important than strength, from i to 1.5 per cent may be permitted; 
 it should not be allowed in excess of the higher hmit. According to 
 Prof. Porter, the addition of i per cent phosphorus to iron containing 
 3.5 per cent carbon and 2 per cent silicon approximately: 
 
 Lowers the temperature at which freezing begins from 2200° to 2150° F., 
 or 50° F. 
 
 Lowers the temperature at which freezing ends from 2165° to 1740° F., 
 or 425° F. 
 
 Increases the temperature range of solidification from 50° to 375° F. 
 
Manganese 265 
 
 Manganese 
 
 Atomic weight 55 • 00 
 
 Specific gravity 8.1 
 
 Specific heat .12 
 
 Melting point 2250° F. 
 
 Latent heat of fusion 
 
 Weight per cubic foot ,506. 25 pounds 
 
 Manganese is a white metal, having a brilliant crystalline fracture. 
 It has a strong affinity for oxygen and sulphur, but none for iron; alloys 
 with iron in all proportions. 
 
 The manganese in pig iron comes from the ores. Foundry irons 
 contain from .2 to 2 per cent manganese. 
 
 Manganese pig from 2 to 10 per cent; spiegeleisen from 15 to 40 per 
 cent; ferromanganese from 50 to 90 per cent. 
 
 There is always a loss of manganese in remelting. It escapes by 
 volatilization; by oxidation, and if sulphur is present, by uniting with 
 it to a greater or less extent. The amount of loss depends on the amount 
 of blast and percentage of sulphur present in the fuel. 
 
 With I per cent manganese present in the iron the loss of Mn in re- 
 melting varies from .2 to .3 per cent. 
 
 A peculiarity of manganese is that it may impart to pig iron, or castings, 
 a very open grain, rendering them apparently soft, even though they are 
 quite hard. 
 
 It greatly affects the capacity of iron to retain carbon; where only 
 .75 per cent Mn is present in the iron the carbon content may be as high 
 as 4 per cent. 
 
 It decreases the magnetism of cast iron and when present to the extent 
 of 25 per cent the magnetism disappears. 
 
 As the percentage of manganese in iron increases, that of sulphur 
 decreases. 
 
 On the other hand, the higher the manganese, the greater the combined 
 carbon. 
 
 Manganese hardens cast iron, promotes shrinkage, contraction and 
 chill; but by reason of its affinity for sulphur and its removal of this 
 element, it may produce effects precisely the opposite of those above 
 stated. However, if the amount of manganese is greater than that 
 required for the removal of the sulphur present, the excess causes the 
 iron to take up more carbon in combination, and hardness results. 
 
 Increasing manganese above .75 per cent, the other elements remaining 
 constant, causes greater contraction and chill on accoimt of its hardening 
 influence. These effects may be very pronounced in light castings. 
 
266 Influence of the Chemical Constituents of Cast Iron 
 
 On account of its strong affinity for oxygen it tends greatly to the 
 removal of oxides and occluded gases, thereby preventing blow-holes. 
 
 Manganese pig iron is an ordinary iron, carrying somewhat more 
 manganese than the ordinary foimdry irons. 
 
 It is used to raise the combined carbon, to add strength to the mixture, 
 to prevent blow-holes, to give life to the iron and for the removal of kish. 
 
 Ferromanganese comes to the fomidry in a fine powder. It is used in 
 the ladle in the proportion of about i pound to 600 pounds of iron and 
 acts as a purifier, driving out sulphur, softening the iron where hardness 
 is due to sulphur and reducing the chance of blow-holes. 
 
 When used in this way the iron must be very hot, as with dull iron it 
 does little good. It should be thoroughly incorporated with the iron 
 by stirring. It must be used with caution, as irons with low silicon and 
 carbon and high manganese are hard and shrinky. 
 
 The use of manganese pig iron in the cupola gives better results, and is 
 less expensive than that of ferromanganese in the ladles. 
 
 It is claimed for manganese that it makes hard iron soft and soft iron 
 hard. 
 
 With respect to the influence of Mn upon chill, Mr. Keep's views are 
 at variance with those above given. He states that manganese does not 
 increase chill, but under certain conditions may aid in removing it. 
 
 Aluxmnum 
 
 Atomic weight 27.1 
 
 Specific gravity 2 . 65 
 
 Specific heat o. 212 
 
 Melting point 1182*^ F. 
 
 Latent heat of fusion: 28. 5 B.t.u, 
 
 Weight per cubic foot 165 . 6 pounds 
 
 Almninum is a white metal, resembling silver; very soft and malleable; 
 has a great affinity for oxygen; alloys with iron to an unlimited extent. 
 It does not occur in pig iron. When added to iron in the ladle it 
 should be thoroughly mixed by stirring. 
 
 Its influence on cast iron resembles that of sihcon, in producing a 
 softening effect by the conversion of combined into graphitic carbon. 
 
 A white iron to which from .5 to .75 per cent of aluminum has been 
 added becomes gray. 
 
 Aluminiun decreases shrinkage and chill, and increases fluidity. By 
 reason of its ajffinity for oxygen it tends to prevent the formation of 
 blow-holes. 
 
 It closes the grain of irons high in graphitic carbon, but may render 
 them sluggish and dirty. When used in amounts exceeding 1.5 to 2 
 
Titanium 267 
 
 per cent it has a weakening influence. Hard irons containing from 1.25 
 to 1.4 per cent combined carbon are made stronger by the addition of 
 aluminum. The amount of aluminum which may be used varies from 
 .25 to 1.25 per cent; its action is somewhat uncertain and its alloys with 
 iron are erratic at times, producing results the reverse of those anticipated. 
 
 Nickel 
 
 Atomic weight 58.7 
 
 Specific gravity 8.8 
 
 Specific heat .11 
 
 Melting point 2610° F. 
 
 Latent heat of fusion 
 
 Weight per cubic foot 550 pounds 
 
 Nickel is a white metal having a silvery color; it is highly ductile and 
 does not oxidize readily. Alloys with iron in all proportions. When 
 used in quantities varying from .5 to 5 per cent, its tendency is to 
 harden, render more dense and increase the tensile strength of cast iron. 
 In large amounts it is said to have a softening influence. 
 
 Mr. A. McWilliams found that an alloy of white Sweeds iron with 50 
 per cent nickel gave a soft fine gray metal, even when cast in sections 
 from I to 3 inches thick, in chills. 
 
 Cast iron containing from 25 to 30 per cent nickel resists corrosion. 
 
 Nickel is little used in cast iron, except where great strength is re- 
 quired. It imparts most valuable properties to steel. 
 
 Titanium 
 
 Atomic weight 48 . 00 
 
 Specific gravity 5.3 
 
 Specific heat 
 
 Melting point 4000° F. 
 
 Latent heat of fusion 
 
 Weight per cubic foot 330 pounds 
 
 Titanium is found in many brands of foundry and Bessemer irons, 
 running in percentages from a trace to i per cent. It increases the 
 strength of cast iron to a marked degree. An addition of from .01 to 
 .06 per cent titanium has shown in test bars an increase of 40 per cent 
 in transverse strength. 
 
 It has a strong affinity for oxygen and nitrogen. 
 
 Ferroalloys are made to contain from 10 to 30 per cent titanium. 
 
 When ferrotitanium is added to iron in the ladle, it unites with the 
 oxygen and nitrogen, the resulting oxides and nitrides passing off in the 
 
268 Influence of the Chemical Constituents of Cast Iron 
 
 slag; none of the titanium remains in the iron, except when used in large 
 quantities; its effect then is to harden the iron. 
 
 Formerly titanic irons were carefully avoided and it does not appear 
 that ferrotitanium has as yet been used to any great extent by foundry- 
 
 Investigations by Dr. Richard Moldenke and Mr. G. A. Rossi indicate, 
 however, that the use of ferrotitanium promises a marked improvement 
 as regards strength and the removal of nitrogen and oxygen from cast 
 iron. Mr. Rossi found as the result of his experiments that the addition 
 of 4 per cent of a lo per cent ferrotitanium to cast iron increased the 
 transverse and tensile strength from 25 to 30 per cent. 
 
 Dr. Moldenke gives the following summary of results obtained by him. 
 
 Mixtures 
 
 Gray 
 
 White 
 
 Original iron 
 
 plus .05 T 
 
 " .10 T 
 
 " .05 T. and carb. 
 " .10 " " 
 " .IS " " 
 
 Average 
 
 Tests 
 9 
 4 
 3 
 6 
 6 
 4 
 
 Lbs. 
 2020 
 3100 
 3030 
 3070 
 2990 
 3190 
 
 Tests 
 8 
 II 
 
 9 
 10 
 10 
 
 3070 
 
 Lbs. 
 2030 
 2400 
 
 2420 
 2400 
 2520 
 
 2430 
 
 Increase of strength of treated iron over original 52 per cent — 18 per cent. 
 
 From the above simimary it appears that the greatest increase in 
 strength was found in gray iron. 
 
 With vanadium and cast iron the Doctor found results directly con- 
 trary to the above. He calls attention to the fact that the improve- 
 ment in strength is almost as marked with .05 per cent to .1 per cent 
 titanium as with ,15 per cent, showing that any excess of titanium over 
 that required to produce oxidation is wasted; hence .05 per cent will 
 be sufficient for foundry practice. 
 
 He found that titanium reduces chill but the chill produced is very 
 much harder than that made in the usual way. 
 
 Titanium is of value as preventing blow-holes and producing sound 
 castings. 
 
 Vanadium 
 
 Atomic weight 51.2 
 
 Specific gravity 5.5 
 
 Specific heat 
 
 Melting point 4300° F. 
 
 Latent heat of fusion 
 
 Weight per cubic foot 344 pounds 
 
Vanadium 
 
 269 
 
 As a merchantable product this is obtained as ferrovanadium, con- 
 taining from 10 to 15 per cent vanadium. 
 
 The investigations of Dr. Richard Moldenke furnish about all that is 
 so far known as to the action of this element on cast iron. The follow- 
 ing table gives a summary of his experiments. 
 
 c '3 
 
 Analyses of test bars 
 
 a w 
 
 §21 
 
 Burnt gray iron 
 
 5 
 3 
 
 
 .05 
 
 
 
 2.13 
 2.03 
 
 .094 
 .09s 
 
 .638 
 
 .35 
 
 .370 .... 
 
 2 
 
 7 
 
 1310 
 2220 
 
 .090 
 .100 
 
 70 
 
 Burnt iron, white 
 
 3 
 12 
 
 
 
 •OS 
 
 
 .50 
 
 .41 
 
 .146 
 
 .423 
 
 -43 
 
 .65 .... 
 
 II 
 
 16 
 
 1440 
 1910 
 
 .050 
 .OS5 
 
 33 
 
 
 
 Machinery iron, gray. Melted pig iron. 
 
 No scrap 
 
 
 
 06s 
 
 668 
 
 24 
 
 1980 
 2070 
 2200 
 2740 
 1970 
 1980 
 2130 
 2372 
 2530 
 2360 
 
 .105 
 .105 
 .115 
 .130 
 .100 
 .xoo 
 .100 
 .090 
 .120 
 .100 
 
 
 
 Remelted car wheels, white. No 
 
 pig 
 
 iron 
 
 
 
 
 
 
 
 
 .53 
 
 122 
 
 • 399 
 
 .38 . 
 
 
 82 
 
 
 
 
 5 
 
 
 
 
 
 .60 
 
 138 
 
 
 374 
 
 
 44 
 
 
 85 
 
 1470 
 
 050 
 
 
 s 
 
 •OS 
 
 
 
 
 
 
 
 
 
 
 
 2190 
 
 050 
 
 50 
 
 7 
 
 .10 
 
 
 
 
 
 
 
 
 
 
 
 
 2050 
 
 050 
 
 40 
 
 8 
 
 .15 
 
 
 
 
 
 
 
 
 
 
 
 
 2264 
 
 060 
 
 54 
 
 4 
 
 
 
 
 
 
 
 
 
 
 
 
 
 .... 
 
 2790 
 
 070 
 
 90 
 
 6 
 
 
 •OS 
 
 00 
 
 
 45 
 
 096 
 
 
 423 
 
 
 40 
 
 36 
 
 113 
 
 3020 
 
 060 
 
 los 
 
 6 
 
 .05 
 
 •OS 
 
 50 
 
 
 66 
 
 no 
 
 
 591 
 
 I 
 
 150 
 
 25 
 
 117 
 
 2970 
 
 090 
 
 100 
 
 3 
 
 
 .10 
 
 
 
 45 
 
 119 
 
 
 414 
 
 
 500 
 
 31 
 
 123 
 
 2800 
 
 055 
 
 91 
 
 4 
 
 
 .10 
 
 05 
 
 
 53 
 
 084 
 
 
 431 
 
 
 74 
 
 27 
 
 128 
 
 3030 
 
 090 
 
 106 
 
 6 
 
 
 .IS . 
 
 
 
 42 
 
 112 
 
 
 417 
 
 
 40 
 
 45 
 
 133 
 
 2950 
 
 070 
 
 100 
 
 6 
 
 
 .15 
 
 SO 
 
 
 SO 
 
 082 
 
 
 374 
 
 
 54 
 
 22 
 
 137 
 
 3920 
 
 095 
 
 166 
 
270 Influence of the Chemical Constituents of Cast Iron 
 
 The vanadium alloy used contained : 
 
 Vanadium 14.67 per cent; carbon 4.36 per cent; silicon 0.18 per cent. 
 
 The analyses of the test bars show much more vanadium than was 
 used. This is attributed to errors arising from the dif&culties experienced 
 in making the experiments on too small a scale. 
 
 Dr. Moldenke concludes: "The results shown in the table speak for 
 themselves, and the averages tallied off for each table show a remarkable 
 progression of values. To increase the breaking strength of a test bar 
 from 2000 up to 2500 for gray iron and 1500 up to 3900 for white iron, 
 is sufficient to warrant further investigation on the part of every foundry- 
 man, who has special problems in strength to master." 
 
 Thermit 
 
 Thermit is a mixture of oxide of iron and aluminum, which when 
 ignited burns at an intense heat (resulting temperature is said to be 
 5400° F.) in consequence of the great affinity of aluminum for oxygen. 
 This compound is made by the Goldschmidt Thermit Co. 
 
 Its use in the foundry is to raise the temperature of dull iron; to keep 
 the iron in risers fluid, and for the mending of broken castings. A 
 titanium thermit is also made by same company. 
 
 This is used for the introduction of titanium, to remove nitrogen and 
 oxygen, as well as for its heating effect. The claim is made, that cast 
 iron can be advantageously used in place of steel castings, if titanium 
 thermit is employed in connection with it. Nickel thermit is used for 
 the introduction of nickel. 
 
 Oxygen 
 
 Atomic weight ^5 • 9^ 
 
 Specific gravity (compared to atmos- 
 pheric air 32 °F. and one atmosphere) i . 1056 
 Weight per cubic foot 624 . 8 grains 
 
 No element, perhaps, causes the foundryman more trouble than 
 oxygen. Iron oxidizes very rapidly at high temperatures, in presence of 
 air. The oxides are readily dissolved in molten iron and the gases 
 liberated from them in the castings are the frequent cause of cavities and 
 blow-holes. 
 
 Ferrous oxides, produced in the process of smelting, are found to a 
 greater or less extent in all pig irons. Those irons in which mill cinder 
 has been largely used, often contain high percentages of dissolved 
 oxides. 
 
Nitrogen 271 
 
 Frequently the ends of broken pigs present blow-holes in body of the 
 pig, or worm-holes toward the upper surface. These are certain indi- 
 cations of the presence of oxygen or sulphur and such iron should be used 
 carefully. 
 
 In remelting in the cupola, as the molten iron passes through the 
 tuyere zone, more or less oxidation occurs, especially if the bed is high 
 and the blast strong. 
 
 Rusty scrap (fine scrap particularly) furnishes ferrous oxides in large 
 amounts. 
 
 The removal of ferrous oxides may.be largely effected in the cupola by 
 an abundance of hot slag. 
 
 Ferromanganese and aluminum are used in the ladle for same pur- 
 pose. 
 
 The most effective deoxidizers are the metals in the order named 
 below : 
 
 Titanium Aluminum 
 
 Vanadium Sodium 
 
 Magnesium Manganese 
 
 Calcium Silicon 
 
 Nitrogen 
 
 Atomic weight 14.01 
 
 Specific gravity (air i) . 9713 
 
 Specific heat . 244 
 
 Weight per cubic foot 548 . 8 grains 
 
 Nitrogen is absorbed from the blast as a nitride, by iron in melting; 
 and as the metal cools, the gas is Hberated. 
 
 Very little is known as to the influence of nitrogen upon cast iron; its 
 effect upon steel is very injurious; as little as .03 per cent causing a great 
 loss in tensile strength and nearly eliminating ductility. Gray pig irons 
 show only a trace of nitrogen from .007 to .009 per cent; in white iron 
 it sometimes runs as high as .035 per cent. 
 
 So far as tests have been made it does not appear that, in gray iron, 
 any relation exists between the quality of the iron and the nitrogen 
 content. 
 
 It has a remarkably strong affinity for titanium, combining with it to 
 form a nitride, which is insoluble in molten iron and passes off in the slag. 
 Ground ferrotitanium previously heated is used in the ladle for removal . 
 of nitrogen. 
 
 Arsenic and copper are sometimes found in pig iron, but in amounts so 
 small that the effects produced by them are inappreciable. 
 
272 Influence of the Chemical Constituents of Cast Iron 
 
 In concluding the subject of metalloids, the statement made by Prof. 
 Porter as to the approximate influence of the more important ones on 
 combined carbon must not be omitted. 
 
 I per cent silicon decreases combined carbon 45 per cent. 
 
 I per cent sulphur increases " " 4. 50 per cent. 
 
 I per cent manganese " " " 40 per cent. 
 
 I per cent phosphorus " " " 17 per cent. 
 
CHAPTER X 
 MIXING IRON 
 
 The mixing of iron for the cupola is done either by fracture or by 
 chemical analysis. 
 
 Mixing by Fracture 
 
 The fracture of the freshly broken pig is taken as the index of its com- 
 position. A dark gray color, with coarse open crystalline grain indicates 
 a soft iron, and, as a rule, one capable of carrying a large percentage of 
 scrap. As the color becomes lighter and the grain closer, hardness 
 increases and less scrap can be used. Very hard irons are mottled or 
 white and are used for special work. 
 
 A broken pig may present a dark fracture with open grain, but with a 
 fine white streak showing at the outer edges of the fracture. Such an 
 iron will make hard castings, owing to the presence of too much man- 
 ganese. 
 
 Blow holes and worm holes indicate sulphur or ferrous oxides. Iron 
 showing these with frequency should be used carefully. 
 
 Segregations, much lighter in appearance than the rest of the fracture, 
 frequently appear. These indicate higher percentages of carbon, sulphur 
 or manganese at those particular spots and the iron should be used 
 with care. 
 
 Mixing by fracture is uncertain and is liable to produce irregular and 
 unsatisfactory results. 
 
 The foundryman must always proceed cautiously and can only arrive 
 at the results desired by careful trial. The following mixtures are taken 
 from West's " Foundry Practice." 
 
 Locomotive Cylinders 
 2600 pounds car wheel scrap. 
 600 pounds soft pig. 
 
 Marine and Stationary Cylinders 
 50 per cent No. i charcoal. 
 50 per cent good machinery scrap. 
 33 per cent car wheel scrap. 
 33 per cent good machinery scrap. 
 33 per cent No. i soft pig. 
 273 
 
274 Mixing Iron 
 
 Rolling Mill Rolls 
 50 per cent car wheel scrap. 
 25 per cent No. i charcoal. 
 25 per cent No. 2 charcoal. 
 
 Small Chilled Rolls 
 1300 pounds old car wheels. 
 100 pounds No. I charcoal. 
 300 pounds steel rail butts. 
 
 Kettles to Stand Red Heat 
 1300 pounds No. I charcoal pig. 
 800 pounds car wheel scrap. 
 700 pounds good machinery scrap. 
 
 Chilled Castings to Stand Friction {no strain) 
 200 pounds white iron. 
 200 pounds plow points. 
 100 pounds No. 2 charcoal. 
 100 pounds car wheel scrap. 
 
 Ordinary Castings 
 
 33 per cent No. i soft pig. 
 67 per cent scrap. 
 
 Thin Pulleys 
 
 66 per cent No. i soft pig. 
 
 34 per cent scrap. 
 
 Sash Weight 
 
 67 per cent scrap tin. 
 33 per cent stove scrap. 
 
 The advent of the chemist into the foundry offers means to avoid 
 many of the uncertainties coming from the selection of irons by fracture, 
 and the more advanced foundrymen are now -mixing their irons by 
 analysis. 
 
 Mixing Iron by Analysis 
 
 This method of mixing iron is by no means entirely removed from 
 uncertainties. The chemist is not yet able to insure the production, from 
 irons of known chemical composition, of castings of definite physical 
 characteristics. Analysis should be supplemented by physical tests. 
 
 Again, while the foimdryman may have correct analysis of his pig iron, 
 if scrap is used to any extent, especially foreign scrap, he must approxi- 
 mate the elements contained therein. 
 
Mixing Iron by Analysis 
 
 275 
 
 The statements made on page 307 offer some little assistance, but, in 
 general, reliance must be placed on experience in this respect. Where 
 the scrap comes entirely from previous casts, one can readily arrive at 
 its constituents and much uncertainty is removed. 
 
 The quahties necessary for different grades of castings may be sum- 
 marized as follows: 
 
 1. Hollow Ware, Stove Plate, Sanitary Ware. — Require fluidity, 
 softness; must be high in silicon and phosphorus; low in combined 
 carbon. 
 
 2. Light Machinery Castings. — Require fluidity, softness, strength 
 and absence of shrinkage. Must be high in total carbon and manganese; 
 low in sulphur and contain less silicon and phosphorus than grade No. i. 
 
 3. Heavy Machinery Castings. — Require softness, strength and low 
 shrinkage. Should be lower in silicon, phosphorus and graphitic carbon 
 than No. 2. Higher in combined carbon and manganese; low in sulphur. 
 
 4. Castings requiring great strength should be low in silicon, graphitic 
 carbon, sulphur and phosphorus. Combined carbon should be about 
 .50 per cent; manganese .8 per cent to i.o per cent. 
 
 5. Car Wheels and Chilled Castings. — Require low silicon, phosphorus, 
 graphitic carbon and sulphur. High combined carbon and manganese. 
 
 6. Chilled Rolls. — Require low silicon, graphitic carbon and phos- 
 phorus. High combined carbon. 
 
 The following table is abstracted from "Proceedings of the American 
 Foimdrymen's Association," Vol. X, Part II, which contains the results 
 of a long series of tests made by their committee to standardize test bars. 
 The mixtures are not given as being recommended by the committee for 
 the several purposes, but simply to indicate the practice of some of the 
 larger American foundries. 
 
 Table II 
 
 Character of work 
 
 Silicon 
 
 Sulph. 
 
 Phos. 
 
 Mang. 
 
 Graph, 
 carb. 
 
 Total 
 carb 
 
 Remarks 
 
 Ingot moulds 
 
 Dynamo frames 
 
 Light machinery 
 
 Chilled rolls 
 
 1.67 
 
 1.95 
 
 2.04 
 
 .85 
 
 .72 
 
 .97 
 
 3.19 
 
 1.96 
 
 2.49 
 
 4.19 
 
 2.32 
 
 0.91 
 
 .032 
 .042 
 .044 
 .070 
 .070 
 .060 
 .084 
 .081 
 .084 
 .080 
 .044 
 .218 
 
 I 
 I 
 
 4 
 
 095 
 405 
 578 
 482 
 454 
 301 
 160 
 522 
 839 
 236 
 676 
 441 
 
 ■ IS 
 .17 
 .40 
 .38 
 .48 
 
 ,■2 
 
 .06 
 .00 
 3.43 
 3.08 
 2.99 
 2.99 
 .03 
 2.62 
 
 '2;36' 
 3.04 
 4.17 
 3. .41 
 3.32 
 3.39 
 2.88 
 3.12 
 
 Ton heat 
 60 
 60 
 40 
 30 
 
 
 
 Car wheel iron 
 
 15 
 
 20 
 
 Heavy machinery. . . 
 
 Cylinder iron 
 
 Novelty iron 
 
 Gun iron . 
 
 30 
 10 
 5 
 10 
 
 Sash weights 
 
 IS 
 
276 
 
 Mixing Iron 
 Table III 
 
 Automobile cylinders 
 
 Silicon 
 
 Sulph. 
 
 Phos. 
 
 Mn. 
 
 Graph, 
 carb. 
 
 Total 
 carb. 
 
 25 per cent charcoal iron 
 
 2.46 
 
 .063 
 
 • 531 
 
 .063 
 
 
 
 
 
 Transverse strength, 2901. 
 
 At a later period Prof. J. J. Porter, at the request of the American 
 Foundrymen's Association, undertook the investigation of the composi- 
 tions used for various classes of castings, with a view to formulating 
 standard mixtures. His report embraces every variety of work and 
 contains tabulated analyses of several hundreds of mixtures in use. 
 The averages of the mixtures in each class of work, together with those 
 suggested by Prof. Porter, are subjoined. 
 
 Acid-resisting Castings 
 
 Mixture 
 
 Silicon 
 
 Sulphur 
 
 Phosphorus 
 
 Manganese 
 
 Combined 
 carbon 
 
 Total 
 carbon 
 
 Average 
 
 Per cent 
 
 2.03 
 1.00-2.00 
 
 Per cent 
 
 .033 
 under .05 
 
 Per cent 
 
 .425 
 under .40 
 
 Per cent 
 
 1. 13 
 I. 00-1.50 
 
 Per cent 
 
 Per cent 
 3 33 
 
 Suggested 
 
 
 3. 00-3. SO 
 
 Agricultural Machinery, Ordinary 
 
 Average 
 
 Suggested 
 
 2.33 
 2.00-2.50 
 
 .072 
 .06-. 08 
 
 .766 
 .60-. 80 
 
 .62 
 .60-. 80 
 
 .355 
 
 3.45 
 
 Agricultural Machinery, Very Thin 
 
 Average 
 
 Suggested 
 
 2.70 
 2.25-2.75 
 
 .065 
 .06-. 08 
 
 ■ 75 
 .70-. 90 
 
 .65 
 .SO-. 70 
 
 .20 
 
 3. SO 
 
 Air Cylinders 
 
 Average 
 
 Suggested. . . . 
 
 1.28 
 I. 00-1.75 
 
 .084 
 under .09 
 
 .401 
 .30-.50 
 
 .69 
 .70-. 90 
 
 .633 
 
 3.45 
 3.00-3.30 
 
 
 
 Ammonia Cylinders 
 
 Average 
 
 Suggested 
 
 1. 55 
 I. 00-1.75 
 
 under .095 
 lindpr OQ 
 
 under .70 
 .30-.50 
 
 .70 
 .70-.90 
 
 
 
 
 3.00-3.30 
 
 
 
 
 
Mixing Iron by Analysis 
 Annealing Boxes for Malleable Casting Work 
 
 277 
 
 Mkture 
 
 Silicon 
 
 Sulphur 
 
 Phosphorus Manganese 
 
 Combined 
 carbon 
 
 Total 
 carbon 
 
 Suggested 
 
 Per cent 
 .650 
 
 Per cent 
 • OS 
 
 Per cent 
 .10-. 20 
 
 Per cent 
 .20 
 
 Per cent 
 2.75 
 
 Per cent 
 2.75 
 
 Annealing Boxes, Pots and Pans 
 
 Average . . 
 Suggested 
 
 Average . . 
 Suggested 
 
 Average . . 
 Suggested 
 
 Average . . 
 Suggested 
 
 Average 
 Suggeste 
 
 Average.. 
 Suggested 
 
 Average . . 
 Suggested 
 
 1.52 
 I . 40-1 . 60 
 
 .043 
 under .06 
 
 under .20 
 
 .69 
 .60-1.00 
 
 .58 
 
 3.29 
 
 low 
 
 Automobile Castings 
 
 1.93 
 1.75-2.25 
 
 •059 
 under .08 
 
 ■ 52 
 
 .4o-.5<^ 
 
 .60-. 80 
 
 .52 
 
 Automobile Cylinders 
 
 2.15 
 1.75-2.00 
 
 .091 
 under .08 
 
 .643 
 .40-. so 
 
 .46 
 .60-. 8 
 
 .45 
 .55-. 65 
 
 3.14 
 3.00-3.25 
 
 Automobile Flywheels 
 
 2.73 
 2.25-2.50 
 
 under .07 
 
 .475 
 .4O-.50 
 
 .625 
 .50-. 70 
 
 .335 
 
 
 
 Balls for Ball Mills 
 
 
 
 Average 
 
 Suggested 
 
 1. 00 
 I. 00-1.25 
 
 .10 
 
 under .08 
 
 .30 
 under .20 
 
 .50 
 .60-1.0 
 
 
 low 
 
 
 low 
 
 
 
 Bed-plates 
 
 1. 815 
 I. 25-1. 75 
 
 .07 
 under .10 
 
 .535 
 .3<>--5o 
 
 .60 
 .60-. 80 
 
 .53 
 
 Binders (see Agricultural Machinery) 
 Boiler Castings 
 
 2.38 
 2.00-2 50 
 
 .065 
 under .06 
 
 ■ 41 
 under .20 
 
 .79 
 .60-1.00 
 
278 Mixing Iron 
 
 Car Castings, Gray Iron (see Brake Shoes and Car Wheels) 
 
 Mixture 
 
 Silicon 
 
 Sulphur 
 
 Phosphorus Manganese 
 
 Combined 
 carbon 
 
 Total 
 carbon 
 
 Average 
 
 Suggested.... 
 
 Per cent 
 
 2.03 
 1.50-2.25 
 
 Per cent 
 
 .069 
 under .08 
 
 Per cent 
 
 .65 
 
 .40-. 60 
 
 Per cent 
 
 .62 
 
 .60-. 80 
 
 Per cent 
 
 • 52 
 
 Per cent 
 3.50 
 
 Car Wheels, Chilled 
 
 Average 
 
 Suggested. ... 
 
 .642 
 .60-. 70 
 
 .094 
 .08-. 10 
 
 .38 
 .30-. 40 
 
 .44 
 .50-. 60 
 
 .80 
 .60-. 80 
 
 3.6s 
 3.50-3.70 
 
 Car Wheels, Unchilled (see Wheels) 
 
 Chemical Castings (see Acid-resisting Castings) 
 
 Chilled Castings 
 
 Average . . . 
 Suggested . 
 
 1.04 
 .75-1.25 
 
 .105 
 .08-0.10 
 
 .40 
 .20-. 40 
 
 .76 
 .80-1.2 
 
 1.96 
 
 3.19 
 
 Chills 
 
 Average . . . 
 Suggested . 
 
 2.07 
 1.75-2.25 
 
 .073 
 
 under .07 
 
 .31 
 
 .20-. 4 
 
 .60-1.00 
 
 2.64 
 
 Collars and Couplings for Shafting 
 
 Average.. . 
 Suggested . 
 
 1.60 
 1.75-2.00 
 
 • 04 
 under .08 
 
 .55 
 
 .40-. so 
 
 • 55 
 .60.-80 
 
 3.57 
 
 Cotton Machinery (see also Machinery Castings) 
 
 Average . . . 
 Suggested. 
 
 2.25 
 2.00-2.25 
 
 under .09 
 under .08 
 
 .70 
 .60-. 80 
 
 .60 
 .60-. 80 
 
 3.45 
 
 
 
 Crusher Jaws 
 
 
 
 
 Average 
 
 Suggested 
 
 I. lb 
 .80-1.00 
 
 .127 .45 
 .08-. 100 .20-. 40 
 
 .92 
 .80-1.20 
 
 3.00 
 
 3.125 
 
 Cutting Tools, Chilled Cast Iron 
 
 Average. . . 
 Suggested . 
 
 1.35 
 I. 00-1.25 
 
 .117 
 under .08 
 
 .60 
 .20-. 40 
 
 .54 
 .60-. 80 
 
 .65 
 
 3.00 
 
Mixing Iron by Analysis 
 
 279 
 
 Cylinders 
 
 See Air Cylinders Ammonia Cylinders 
 Automobile " Gas Engine " 
 
 Hydraulic " Locomotive " 
 
 Steam Cylinders 
 
 Cylinder Bushings, Locomotive (see Locomotive Castings) 
 Dies for Drop Hammers 
 
 Mixture 
 
 Silicon 
 
 Sulphur 
 
 Phosphorus 
 
 Manganese 
 
 Combined 
 carbon 
 
 Total 
 carbon 
 
 Average 
 
 Suggested.... 
 
 Per cent 
 
 1.40 
 I. 25-1. 50 
 
 Per cent 
 
 .075 
 under .07 
 
 Per cent 
 
 .25 
 under .20 
 
 Per cent 
 
 .55 
 
 .60-. 80 
 
 Per cent 
 1. 00 
 
 Per cent 
 3.20 
 
 
 
 Diamond Polishing Wheels 
 
 Average 
 
 2.70 
 
 .063 
 
 .30 
 
 .44 
 
 r.60 
 
 2.97 
 
 Dynamo and Motor Frames, Bases and Spiders, Large 
 
 Average 
 
 Suggested 
 
 2.025 
 2.00-2.50 
 
 .0655 
 under .08 
 
 .54 
 .50-. 80 
 
 .49 
 .30-.40 
 
 .56 
 .20-. 30 
 
 3.73 
 low 
 
 Dynamo and Motor Frames, Bases and Spiders, Small 
 
 Average 
 
 Suggested 
 
 2.66 
 2.50-3.00 
 
 .073 
 under .08 
 
 .73 
 .50-. 80 
 
 .45 
 .30-. 40 
 
 .30 
 .20-. 30 
 
 3.4s 
 
 low 
 
 Electrical Castings 
 
 Average 
 
 Suggested 
 
 2.30 
 2.00-3.00 
 
 .068 
 under .08 
 
 .62 .48 
 .50-. 80 .30-. 40 
 
 .48 
 .20-. 30 
 
 3.61 
 
 low 
 
 Eccentric Straps (see Locomotive Castings and Machinery Castings) 
 Engine Castings 
 
 See Bed Plates Engine Frames 
 
 Flywheels Locomotive Castings 
 
 Machinery Castings Steam Cylinders 
 
 Engine Frames (see also Machinery Castings) 
 
 Average.. . 
 Suggested . 
 
 1 72 
 
 .09 
 
 .48 
 
 .60 
 
 1.25-2.00 
 
 under .09 
 
 .3c^.5o 
 
 .60-1.00 
 
28o 
 
 Mixing Iron 
 
 Fans and Blowers . (see Machinery Castings) 
 Farm Implements 
 
 Mixture 
 
 Silicon 
 
 Sulphur Phosphorus 
 
 Manganese 
 
 Combined 
 carbon 
 
 Total 
 carbon 
 
 Average 
 
 Suggested.... 
 
 Per cent 
 
 2. OS 
 
 2.00-2.50 
 
 Per cent 
 
 .078 
 .06-.08 
 
 Per cent 
 
 .78 
 
 .50-. 80 
 
 Per cent 
 
 .455 
 
 .60-.80 
 
 Per cent 
 .48 
 
 Per cent 
 3.35 
 
 Fire Pots 
 
 
 2. so 
 2.00-2.50 
 
 under .07 
 under .06 
 
 under .20 
 under .20 
 
 .90 
 60-1.00 
 
 
 
 Suggested .... 
 
 
 low 
 
 
 
 
 Flywheels ( 
 
 see also Automobile Flywheels and Machinery Castings) 
 
 
 1.85 
 i.so-2.25 
 
 .09 
 under .08 
 
 .525 
 .40-. 60 
 
 .55 
 .50-. 70 
 
 
 
 Suggested 
 
 
 
 Friction Clutches 
 
 Average 
 
 2.25 
 1.75-2.00 
 
 under .15 
 .08-. 10 
 
 under .70 
 under ..30 
 
 under .70 
 .50-. 70 
 
 
 low 
 
 
 
 
 Furnace Castings - 
 
 
 2.125 
 2.00-2.50 
 
 under .06 
 
 .40 
 under .20 
 
 .51 
 .60-1.00 
 
 
 
 Suggested. . . . 
 
 
 low 
 
 
 
 
 
 Gas Engine Cylinders 
 
 Average.. .... 
 
 Suggested. . . . 
 
 1. 18 
 I. 00-1.75 
 
 .082 
 under .08 
 
 .46 
 
 .20-. 40 
 
 .63 
 .70-. 90 
 
 • 93 
 
 3.23 
 
 3 00-3 30 
 
 
 
 
 Gears, Medium 
 
 Average 
 
 Suggested 
 
 1.92 
 1.50-2.00 
 
 .075 
 under .09 
 
 • 47 
 .40-. 60 
 
 .576 
 .70-.90 
 
 .55 
 
 3.79 
 
 Gears, Small 
 
 
 2.72 
 2.00-2.5© 
 
 .08 
 under .08 
 
 ■91 
 
 .50-. 70 
 
 .80 
 .60-. 80 
 
 
 
 Suggested 
 
 
 
Mixing Iron by Analysis 
 Gears, Heavy 
 
 281 
 
 Mixture 
 
 Silicon 
 
 Sulphur 
 
 Phosphorus 
 
 Manganese 
 
 Combined 
 carbon 
 
 Total 
 carbon 
 
 Average 
 
 Per cent 
 
 1.38 
 I. 00-1.50 
 
 Per cent 
 
 .081 
 .08-. 10 
 
 Per cent 
 
 • 39 
 
 .30-. 50 
 
 Per cent 
 
 • 59 
 
 .80-1.0 
 
 Per cent 
 .92 
 
 Per cent 
 3^33 
 low 
 
 
 
 
 Grate Bars 
 
 Average . . 
 
 Suggested 
 
 2.38 
 2.00-2.50 
 
 .08 
 under 1.06 
 
 
 
 
 
 under .20 
 
 .60-1.0 under .30 
 
 low 
 
 Chilled Castings for Grinding Machinery 
 
 Average 
 
 Suggested.... 
 
 .50 
 
 •SO-. 75 
 
 .200 
 .15-. 20 
 
 .45 
 .20-. 40 
 
 1.50 
 1.5-2.0 
 
 300 
 
 3.00 
 
 Gun Carriages 
 
 Average 
 
 Suggested . . . 
 
 .97 
 I. 00-1.25 
 
 • OS 
 under .06 
 
 .37 
 .20-. 30 
 
 .46 
 .80-1.0 
 
 .865 
 
 2.73 
 
 low 
 
 
 
 
 Gun Iron 
 
 Average 
 
 Suggested.... 
 
 1.09 
 
 I.OO-I.2S 
 
 .053 
 under .06 
 
 • 32 
 .20-. 30 
 
 
 .62 
 
 .99 
 .80-1.0 
 
 306 
 
 low 
 
 
 
 Hangers for Shafting 
 
 Average 
 
 Suggested 
 
 1.60 
 
 1.50-2.00 
 
 .04 
 under .08 
 
 • 55 
 .40-. 50 
 
 .55 
 .60-. 80 
 
 .30 
 
 3.57 
 
 
 Hardware, Light 
 
 Average 
 
 Suggested 
 
 2.30 
 
 2.25-2.75 
 
 .06 
 under .08 
 
 • 74 
 .5o-^8o 
 
 .76 
 .SO-. 70 
 
 • 32 
 
 3.39 
 
 Heat-resisting Iron 
 
 Average 
 
 Suggested 
 
 1.95 
 
 1.25-2.50 
 
 .056 
 under .06 
 
 .52 
 under .20 
 
 .68 
 .60-1.00 
 
 .46 
 under .30 
 
 3.46 
 
 low 
 
282 
 
 Mixing Iron 
 Hollow Ware 
 
 Mixture 
 
 Silicon 
 
 Sulphur 
 
 Phosphorus 
 
 Manganese 
 
 Combined 
 carbon 
 
 Total 
 carbon 
 
 Average 
 
 Suggested 
 
 Per cent 
 
 2. SI 
 2.25-2.75 
 
 Per cent 
 
 1. 10 
 under .08 
 
 Per cent 
 
 .62 
 
 .50-. 70 
 
 Per cent 
 
 .41 
 
 .50-. 70 
 
 Per cent 
 .24 
 
 Per cent 
 3.18 
 
 Housings for Rolling Mills 
 
 Average 
 
 Suggested.... 
 
 1. 125 
 
 I. 00-1.25 
 
 .085 
 under .08 
 
 .65 
 .20-. 30 
 
 .75 
 .80-1.0 
 
 
 low 
 
 
 low 
 
 
 
 Hydraulic Cylinders, Heavy 
 
 Average 
 
 Suggested 
 
 1. 19 
 .80-1.20 
 
 .084 
 under .10 
 
 .39 
 .20-. 40 
 
 .82 
 .80-1.0 
 
 ■ 99 
 
 3.12 
 
 low 
 
 
 
 Hydraulic Cylinders, Medium 
 
 Average 
 
 Suggested 
 
 1.67 
 ,1.20-1.60 
 
 .071 
 under .09 
 
 .375 
 .30-. 50 
 
 .55 
 .70-. 90 
 
 
 
 
 low 
 
 
 
 Ingot Moulds and Stools 
 
 Average 
 
 Suggested 
 
 1.43 
 I. 25-1. 50 
 
 .046 .095 
 under .06 under .20 
 
 .345 
 .60-1.0 
 
 
 
 
 
 
 
 Locomotive Castings, Heavy 
 
 Average 
 
 Suggested .... 
 
 1.55 
 I. 25-1. 50 
 
 .081 
 under .08 
 
 .50 
 .30-. 50 
 
 .56 
 .70-. 90 
 
 .60 
 
 3.50 
 
 Locomotive Castings, Light 
 
 Average 
 
 Suggested.... 
 
 1.72s 
 1.50-2.00 
 
 .075 
 under .08 
 
 53 
 .40-. 60 
 
 .58 
 .60-. 80 
 
 .50 
 
 3.50 
 
 Locomotive Cylinders 
 
 Average 
 
 Suggested 
 
 I.4S7 
 I. 00-1.50 
 
 .084 
 .08-. 10 
 
 .58 
 .30-. 50 
 
 .60 
 .80-1.0 
 
 .60 • 
 
 3. so 
 
Mixing Iron by Analysis 
 
 283 
 
 Locks and Hinges (see Hardware, Light) 
 Machinery Castings, Heavy 
 
 Mixture 
 
 Silicon 
 
 Average 
 
 Suggested. . . , 
 
 Per cent 
 
 1.335 
 I. 00-1.50 
 
 Sulphur 
 
 Per cent 
 
 .084 
 under .10 
 
 Phosphorus 
 
 Per cent 
 
 .43 
 
 .30-. 50 
 
 Manganese 
 
 Per cent 
 
 .58 
 
 .80-1.0 
 
 Combined 
 carbon 
 
 Per cent 
 .33 
 
 Total 
 carbon 
 
 Per cent 
 3.21 
 
 low 
 
 
 Machinery Castings, Medium 
 
 
 
 Average 
 
 Suggested 
 
 1.932 
 i.so-2.00 
 
 .078 
 • under .09 
 
 .61 
 .40-. 60 
 
 .53 
 .60-. 80 
 
 .47 
 
 3.33 
 
 Machinery Castings, Light 
 
 Average 
 
 Suggested 
 
 2.57 
 2.00-2.50 
 
 .069 
 under .08 
 
 .74 
 .50-. 70 
 
 .52 
 .50-. 70 
 
 .27 
 
 3.49 
 
 Machine Tool Castings (see Machinery Castings) 
 Motor Frames, Bases and Spiders (see Dynamo) 
 Molding Machines (see Machinery Castings) 
 Mowers (see Agricultural Castings) 
 
 Niter Pots (see Acid-resisting Castings and Heat-resisting 
 Castings) 
 
 Ornamental Work 
 
 Average 
 
 Suggested.... 
 
 2.95 
 
 2.25-2.75 
 
 .095 
 under .08 
 
 .84 
 .60-1.0 
 
 .54 
 .50-. 70 
 
 .135 
 
 3.03 
 
 
 
 Permanent Moulds 
 
 Average 
 
 Suggested.... 
 
 2.085 
 2.00-2.25 
 
 .078 
 under .07 
 
 1 .075 
 .20-. 40 
 
 .35 
 .60-1.0 
 
 .485 
 
 3.4s 
 
 . 
 
 
 Permanent Mould Castings 
 
 Average 
 
 Suggested 
 
 2.5 
 1.50-3.00 
 
 
 
 
 
 350 
 
 under .06 
 
 
 under .40 
 
 ^ 
 
 
 
 
 Piano Plates 
 
 Average 
 
 Suggested 
 
 2.00 
 2.00-2.25 
 
 low- 
 under .07 
 
 .40 
 .40-. 60 
 
 .60 
 .60-.80 
 
 
 
 
 
284 
 
 Mixing Iron 
 Pillow Blocks 
 
 Mixture 
 
 Silicon 
 
 Sulphur 
 
 Phosphorus 
 
 Manganese 
 
 Combined 
 carbon 
 
 Total 
 carbon 
 
 Average 
 
 Suggested 
 
 Per cent 
 
 1.60 
 I. 50-1. 75 
 
 Per cent 
 
 .04 
 under .08 
 
 Per cent 
 
 .55 
 
 .40- .50 
 
 Per cent 
 
 .55 
 
 .60-. 80 
 
 Per cent 
 .30 
 
 Per cent 
 3.50 
 
 Pipe 
 
 Average 
 
 Suggested 
 
 2.00 
 1.50-2.00 
 
 .06 
 under .10 
 
 .60 
 .50-. 80 
 
 .60 
 .60-. 80 
 
 
 
 
 
 Pipe Fittings 
 
 Average 
 
 Suggested 
 
 2.36 
 I. 75-2. 50 
 
 .084 
 under .08 
 
 .51 
 .50-. 80 
 
 .74 
 .6c^.8o 
 
 .70 
 
 3.68 
 
 Pipe Fittings for Superheated Steam Lines 
 
 Average 
 
 Suggested.... 
 
 1.57 
 I. 50-1. 75 
 
 .078 
 under .08 
 
 .49 
 .20-. 40 
 
 .56 
 .70-. 90 
 
 .17 
 
 2.90 
 
 
 
 Piston Rings 
 
 Average 
 
 Suggested 
 
 1. 61 
 i.So-2.00 
 
 .073 
 under .08 
 
 .72 
 .30-. 50 
 
 .45 
 .40-. 60 
 
 .53 
 
 
 
 
 Plow Points, Chilled 
 
 Average 
 
 Suggested.... 
 
 1. 15 
 ■75-1.25 
 
 .086 
 under .08 
 
 .30 
 .20-. 30 
 
 .68 
 .80-1.0 
 
 2.10 
 
 3.30 
 
 
 
 Printing Presses (see Machinery Casting) 
 Propeller Wheels 
 
 Average 
 
 Suggested 
 
 1.28 
 I.OO-I.7S 
 
 low 
 under .10 
 
 .26 
 .20-. 40 
 
 • 455 
 .60-1.0 
 
 .60 
 
 
 
 
 Pulleys, Heavy 
 
 Average 
 
 Suggested 
 
 2.07 
 I. 75-2. 25 
 
 .05 
 under .09 
 
 .575 
 .5<^.7o 
 
 .575 
 .60-. 80^ 
 
 .30 
 
 3.66 
 
Mixing Iron by Analysis 
 
 Pulleys^ Light 
 
 285 
 
 Mixture 
 
 Silicon 
 
 Sulphur 
 
 Phosphorus 
 
 Manganese 
 
 Combined 
 carbon 
 
 Total 
 carbon 
 
 Average 
 
 Suggested 
 
 Per cent 
 
 2.55 
 2.25-2.75 
 
 Per cent 
 
 .069 
 under .08 
 
 Per cent 
 
 .695 
 
 .60-.80 
 
 Per cent 
 
 .62 
 
 .50-.70 
 
 Per cent 
 .35 
 
 Per cent 
 3.48 
 
 Pumps, Hand 
 
 Average 
 
 2.52 
 2.00-2.25 
 
 under .08 
 under .08 
 
 .80 
 .60-.80 
 
 .40 
 .50.-70 
 
 
 
 Suggested 
 
 
 
 Radiators 
 
 Average 
 
 Suggested.... 
 
 2.30 
 2.00-2.25 
 
 low 
 under .08 
 
 .62 
 .60-. 80 
 
 .425 
 •so-. 70 
 
 .425 
 .50- .60 
 
 3.45 
 
 Railroad Castings 
 
 Average 
 
 Suggested 
 
 2.03 
 1.50-2.25 
 
 .065 
 under .08 
 
 .69 
 .40-. 60 
 
 .64 
 .60-. 80 
 
 .525 
 
 3.50 
 
 Retorts (see Heat-resisting Castings) 
 Rolls, Chilled 
 
 Average 
 
 Suggested 
 
 .73 
 .60-. 80 
 
 .055 
 .06-. 08 
 
 .534 
 .20-. 40 
 
 .74 
 1. 0-1.2 
 
 1.75 
 
 3.12 
 3.00-3.25 
 
 Rolls, Unchilled {Sand Cast) 
 
 Average 
 
 .75 
 
 .03 
 
 .25 
 
 .66 
 
 1.20 
 
 4.10 
 
 Scales 
 
 Average 
 
 Suggested.... 
 
 1.83 
 2.00-2.30 
 
 
 1.05 
 .60-1.0 
 
 1.43 
 .50-. 70 
 
 
 
 under .08 
 
 
 
 
 
 Slag Car Castings 
 
 Average 
 
 Suggested 
 
 1.88 
 1.75-2.0 
 
 .058 
 under .07 
 
 .67 
 under .30 
 
 .79 
 .70-.90 
 
 . .56 
 
 3.68 
 
 
 
286 
 
 Mixing Iron 
 
 Smoke Stacks, Locomotive (see Locomotive Castings) 
 Soil Pipe and Fittings 
 
 Mixture 
 
 Silicon 
 
 Sulphur 
 
 Phosphorus 
 
 Manganese 
 
 Combined 
 carbon 
 
 Total 
 carbon 
 
 
 Per cent 
 
 2.00 
 1.75-2.25 
 
 Per cent 
 
 .060 
 under .09 
 
 Per cent 
 
 1. 00 
 •SO-. 80 . 
 
 Per cent 
 
 .60 
 
 .60-80 
 
 ■ Per cent 
 
 Per cent 
 
 Suggested 
 
 
 
 Steam Cylinders, Heavy 
 
 Average 
 
 1.20 
 
 I.OO-I.2S 
 
 .091 
 
 under .10 
 
 .36 
 .20-. 40 
 
 .50 
 .80-1.0 
 
 .81 
 
 3.35 
 
 
 
 
 Steam Cylinders, Medium 
 
 Average 
 
 Suggested 
 
 1.658 
 I. 25-1. 75 
 
 .082 
 under .09 
 
 .55 
 .30-. 50 
 
 .61 
 .70-. 90 
 
 .62 
 
 3.43 
 
 Steam Chests (see Locomotive Castings and Machinery Castings) 
 Stove Plate 
 
 Average 
 
 Suggested 
 
 2.77 
 2.25-2.75 
 
 .076 
 under .08 
 
 .82 
 .60-. 90 
 
 -59 
 .60-. 80 
 
 .28 
 
 3.33 
 
 Valves, Large 
 
 
 1.34 
 I. 25-1. 75 
 
 .095 
 under .09 
 
 .43 
 .20-. 40 
 
 .64 
 .80-1.0 
 
 
 
 Suggested 
 
 
 
 
 
 Valves, Small 
 
 Average 
 
 Suggested 
 
 1.96 ' 
 
 1.1 5-2. 2S 
 
 .067 
 under .08 
 
 .585 
 .30-. 50 
 
 .705 
 .6<^.8o 
 
 1. 16 
 
 4.18 
 low 
 
 
 
 
 Valve Bushings (see Locomotive Castings and Machinery Castings) 
 Water Heaters 
 
 
 2.15 
 2.00-2.25 
 
 .050 
 under .08 
 
 .40 
 .30-. so 
 
 • SO 
 .6<^.8o 
 
 
 
 Suggested 
 
 
 
Mixing Iron by Analysis 
 
 287 
 
 Weaving Machinery (see Machinery Castings) 
 Wheels, Large 
 
 Mixttire 
 
 Silicon 
 
 Sulphur 
 
 Phosphorus 
 
 Manganese 
 
 Combined 
 carbon 
 
 Total 
 carbon 
 
 Average 
 
 Per cent 
 
 2.10 
 1.50-2.00 
 
 Per cent 
 
 .04 
 under .09 
 
 Per cent 
 
 .40 
 .30-. 40 
 
 Per cent 
 
 .70 
 .60-.80 
 
 Per cent 
 
 Per cent 
 
 Suggested 
 
 
 
 
 
 Wheels, Small 
 
 
 
 
 Average 
 
 1.8s 
 I. 75-2. 00 
 
 .0665 
 under .08 
 
 .50 
 ■40-. 50 
 
 • 45 
 .50-. 70 
 
 
 
 Suggested 
 
 
 
 Wheel Centers (see Locomotive Castings) 
 White Iron Castings 
 
 Average. 
 
 .70 
 
 .33 
 
 2.90 
 
 Wood Working Machinery (see Machinery Castings) 
 Brake Shoes 
 
 Average.. . 
 Suggested. 
 
 1-94 
 I. 40-1. 90 
 
 .125 
 .08-. 10 
 
 .675 
 .30 
 
 .556 
 .50-. 70 
 
 .53 
 
 3.16 
 low 
 
 Knowing the desired analysis for any class of casting to be made, the 
 simplest way to arrive at the amounts of the different irons to be used 
 is by percentage. For example, let the requirements be for an iron to 
 produce machinery castings of which the analysis shall be: 
 
 Silicon 
 
 Sulphur 
 
 . Phosphorus 
 
 Manganese 
 
 2.00 
 
 .084 
 
 .350 
 
 .62s 
 
 As previously stated, the loss in silicon in remelting will be from 10 
 to 20 per cent, the same for manganese, and a gain of .03 in sulphur, 
 phosphorus remainuig constant. The mixture then must contain: 
 
 Silicon 
 
 Sulphur 
 
 Phosphorus 
 
 Manganese 
 
 2.22 
 
 .054 
 
 .350 
 
 .687 
 
288 Mixing Iron 
 
 The irons then available are: 
 
 
 Silicon 
 
 Stilphur 
 
 Phosphorus 
 
 Manganese 
 
 No. 2 Southern . 
 
 2.25 
 2.IO 
 4.20 
 
 I. go 
 
 .04 
 .02 
 .02s 
 .080 
 
 .280 
 .350 
 .820 
 .284 
 
 735 * 
 
 No. 2 Northern . . . 
 
 940 
 
 Si] ver gray 
 
 Scrap 
 
 .820 
 .540 
 
 After two or three trials it is found that the desired mixture may be 
 obtained from 
 
 
 Silicon 
 
 Sulphur 
 
 Phosphorus 
 
 Manganese 
 
 20 per cent No. 2 Southern, giving 
 20 per cent No. 2-Northern. giving 
 10 per cent silver gray, giving . . . 
 50 per cent scrap, giving 
 
 .450 
 .420 
 .420 
 .950 
 2.240 
 
 .008 
 .004 
 .0025 
 .0400 
 
 .0545 
 
 .056 
 .070 
 .082 
 .142 
 .350 
 
 .147 
 .188 
 .082 
 270 
 
 
 .687 
 
 Example 2. — Required an iron for pulleys and light castings of 
 following analysis: Silicon, 2.40; sulphur, .09; phosphorus, .700; 
 manganese, .52, and to carry 50 per cent scrap. 
 
 Available irons: 
 
 No. 2 Southern 
 No. 2 Northern 
 
 Silver gray 
 
 Scrap 
 
 Silicon 
 
 2.72 
 2.40 
 5.00 
 2.20 
 
 Sulphur 
 
 .070 
 .020 
 .024 
 
 Phosphorus 
 
 .750 
 .600 
 .960 
 .660 
 
 Manganese 
 
 .56 
 .53 
 .62 
 
 Correcting for losses of sihcon and manganese and gain of sulphiu: the 
 mixture must contain silicon, 2.66, sulphur, .06, phosphorus, .70, man- 
 ganese, .577. 
 
 For reasons of economy no more than 10 per cent of the silver gray 
 iron should be used. This with the 50 per cent scrap supplies: 
 
 
 Silicon 
 
 Sulphur 
 
 Phosphorus 
 
 Manganese 
 
 
 • so 
 1. 10 
 1.60 
 
 1.066 
 
 .0024 
 
 .040 
 
 .0424 
 
 .0176 
 
 .096 
 .330 
 .426 
 
 .274 
 
 .053 
 
 
 .310 
 
 To be supplied by remaining pig 
 iron . ... 
 
 .363 
 .214 
 
 
 
Mixing Iron by Analysis 
 
 289 
 
 By trial it is found that the remaining amounts of the different elements 
 may be obtained by using: 
 
 25 per cent No. 2 Southern 
 
 15 per cent No. 2 Northern 
 
 Giving 
 
 Silicon 
 
 Sulphur 
 
 .0175 
 .0030 
 .0205 
 
 Phosphorus 
 
 .1875 
 .0900 
 
 .2775 
 
 The sUght discrepancies of .02 silicon, .0029 sulphur, .0035 phosphorus 
 and .01 manganese may be neglected. 
 
 Where the scrap is very nearly of uniform quality, the analysis of the 
 castings from any given heat furnishes data from which a very close 
 approximation can be made of the scrap used in the previous heat. 
 
 Assuming such character of scrap, and knowing the mixture used in 
 any heat as well as the analysis of the castings, compute the analysis of 
 scrap used in previous heat. 
 
 Let the castings show the analysis of example 2, viz.: Si, 2.40, S, .09, 
 P, .70, Mn, .52. Then the] mixture must have been as before, Si, 2.66, 
 S, .06, P, .70, Mn, .577. 
 
 The irons having the assumed analysis of example 2, then: 
 
 25 per cent No. 2 Southern gives. 
 15 per cent No. 2 Northern gives. 
 10 per cent silver gray gives . . 
 
 Which subtracted from the mix- 
 ture leaves 
 
 Silicon Sulphur Phosphorus Manganese 
 
 .68 
 
 .36 
 
 ■ 50 
 
 1. 54 
 
 1. 12 
 
 .0175 
 .0030 
 .0024 
 .0229 
 
 .0371 
 
 .1875 
 .0900 
 .0960 
 .3735 
 
 .3265 
 
 ■ 053 
 .257 
 
 .320 
 
 As 50 per cent scrap was used, the analysis of scrap from previous heat 
 is Si, 2.24, S, .0742, P, .653, Mn, .64, giving a very close approxima- 
 tion. 
 
CHAPTER XI 
 
 USE OF STEEL SCRAP IN MIXTURES OF CAST IRON 
 
 Steel scrap, when added to mixtures of cast iron in quantities varying 
 from lo to 40 per cent, closes the grain, increases the toughness and adds 
 greatly to the tensile strength of the castings made from such mixture. 
 
 The steel should be low in carbon, such as boiler plate scrap, machine 
 steel, rail ends, etc. 
 
 Turnings from machine steel are frequently used in the ladle. In this 
 case the steel should be heated quite hot, placed in the ladle and the iron 
 tapped out on it. The mixture should be thoroughly stirred until the 
 steel is melted. In all cases the iron must be very hot. 
 
 Mixing steel in the ladle does not give as satisfactory results as mixing 
 in the cupola. 
 
 As the steel is low in carbon the iron used should be high in total carbon, 
 otherwise the castings will be hard with over 10 per cent steel scrap. 
 
 The following table by Mr. H. E. Diller presents the results of a series 
 of tests, with mixtures made by varying in percentages of steel scrap from 
 i2i/^ to 37!/^ per cent: 
 
 No. 
 
 Sili- 
 con 
 
 Sul- I 
 phur 
 
 'hos- 
 hor- '^ 
 us ga 
 
 lan- 
 
 nese 
 
 Comb, 
 carbon 
 
 Graph- 
 itic 
 carbon 
 
 Total 
 carbon 
 
 Tensile 
 strength 
 
 Trans- 
 verse 
 strength 
 
 Per 
 
 cent 
 steel 
 
 I 
 
 1.43 
 
 .047 
 
 564 
 
 82 
 
 .670 
 
 3.14 
 
 3.81 
 
 23,060 
 
 2550 
 
 
 
 2 
 
 1.50 
 
 .065 
 
 532 
 
 33 
 
 .640 
 
 3-44 
 
 3 
 
 08 
 
 30,500 
 
 2840 
 
 25 
 
 3 
 
 1.76 
 
 .062 
 
 488 
 
 53 
 
 .510 
 
 3.12 
 
 3 
 
 63 
 
 22,180 
 
 2440 
 
 
 
 4 
 
 1.76 
 
 .139 
 
 51S 
 
 57 
 
 .430 
 
 2.94 
 
 3 
 
 37 
 
 37,090 
 
 2770 
 
 I2l/^ 
 
 5 
 
 1.77 
 
 .069 
 
 339 
 
 49 
 
 .560 
 
 2.87 
 
 3 
 
 43 
 
 32,500 
 
 3120 
 
 .121/^ 
 
 6 
 
 1.83 
 
 .100 
 
 610 
 
 55 
 
 .510 
 
 2.44 
 
 2 
 
 95 
 
 36.860 
 
 3280 
 
 25 
 
 7 
 
 1.75 
 
 .089 
 
 598 
 
 35 
 
 .740 
 
 2.12 
 
 2 
 
 86 
 
 30,160 
 
 3130 
 
 37^ 
 
 8 
 
 1.96 
 
 .104 
 
 446 
 
 44 
 
 .630 
 
 3.18 
 
 3 
 
 81 
 
 21,950 
 
 2230 
 
 
 
 9 
 
 2.12 
 
 .037 
 
 410 
 
 26 
 
 .380 
 
 3.26 
 
 3 
 
 64 
 
 21,890 
 
 3470 
 
 121.^ 
 
 10 
 
 2.16 
 
 .060 
 
 31S 
 
 20 
 
 1.060 
 
 2.30 
 
 3 
 
 36 
 
 26,310 
 
 2670 
 
 12H 
 
 II 
 
 1.97 
 
 .093 
 
 470 
 
 48 
 
 .570 
 
 2.83 
 
 3 
 
 40 
 
 32,530 
 
 3050 
 
 2n\'i 
 
 12 
 
 2.35 
 
 .061 
 
 515 
 
 56 
 
 .540 
 
 340 
 
 3 
 
 94 
 
 21,990 
 
 2200 
 
 
 
 13 
 
 2.53 
 
 .104 
 
 490 
 
 54 
 
 .600 
 
 2.56 
 
 3 
 
 16 
 
 33,390 
 
 2850 
 
 25 
 
 14 
 
 2.36 
 
 .064 
 
 327 
 
 24 
 
 1.080 
 
 2.15 
 
 3 
 
 23 
 
 31,560 
 
 3200 
 
 25 
 
 These tests were made with pig iron, ferrosilicon and steel scrap. No 
 cast iron scrap was used. Mr. Diller concludes: "The tests given seem 
 
 290 
 
Recovering and Melting Shot Iron 
 
 291 
 
 to indicate that 25 per cent of steel will add 50 per cent to the strength of 
 the iron, and 12K2 per cent of steel, approximately 25 per cent." 
 
 The tests containing 371/^ per cent steel were hardly as much im- 
 proved in strength as those with 25 per cent of steel; from which we may 
 infer that the limit of the amount of steel it is beneficial to melt with 
 iron in a cupola is between 25 and 371/i per cent. 
 
 Results of experiments made by Mr. C. B. McGahey are embodied 
 below. 
 
 Mr. McGahey used test bars i in. by i in. by 24 in. (distance between 
 supports not stated). 
 
 No. 
 
 Sili- 
 con 
 
 Sul- 
 phur 
 
 Phos- 
 phor- 
 us 
 
 Man- 
 ganese 
 
 Per 
 
 cent 
 steel 
 
 Depth 
 
 of 
 chill 
 
 Trans- 
 verse 
 strength 
 
 Remarks 
 
 I 
 2 
 3 
 4 
 
 .82 
 .88 
 .58 
 ■ 79 
 
 .097 
 .081 
 .097 
 .081 
 
 .23 
 .24 
 .25 
 .239 
 
 .54 
 .67 
 • 44 
 .64 
 
 7 
 20 
 23 
 21.50 
 
 In. 
 .38 
 .40 
 .48 
 
 1800 
 2200 
 2250 
 
 Entirely gray when 
 cast in sand. 
 Depth of chill % in. 
 Steel scrap (struc- 
 tural shapes). 
 
 "I find that to get the strongest bars I have to keep pretty close to 
 these analyses and have made my strongest bar at 2350 pounds with 
 .55 inch deflection. The iron had a fine grain, was low in graphite, but 
 machined nicely. 
 
 When ferromanganese was used, about i per cent was found to be 
 best. The above resulting compositions (the silicons of the mixtures 
 being calculated to bring them about right) are intended for castings 
 ranging from i inch to 2}^ inches in section. 
 
 Should heavier work be required it is better to run the silicon in the 
 pig up to 2.75 and manganese up to 2.00 and use 33!/^ per cent of steel 
 scrap." 
 
 An addition of 10 per cent steel scrap to mixtures for engine cylinders 
 gives excellent results affording a close-grained tough iron. Steel scrap 
 increases shrinkage and causes the iron to set quickly; hence the irons 
 used, should be high in total carbon and must be melted and poured very 
 hot. 
 
 Steel scrap promotes chill and is largely used with coke irons in making 
 car wheels, obviating the use of the expensive charcoal mixtures. 
 
 The charges containing steel should be melted during the first part 
 of the heat, and in each charge the steel should precede the iron. 
 
 Recovering and Melting Shot Iron 
 
 The shot from gangways and cupola bottom is usually recovered by 
 riddling the gangway sand; picking over the dump and by grinding the 
 
292 Use of Steel Scrap in Mixtures of Cast Iron 
 
 bottom in the cinder mill. This is also done by magnetic or hydraulic 
 separators. The amount recovered by machines is much greater than 
 that obtained by hand. 
 
 After charging of the cupola is completed, the shot should be thrown 
 on top of the last charge, using with it some of the coke picked from the 
 dump. Each heat should take care of the shot from the previous one. 
 
 The melted iron coming from the shot can be poured into grate bars, 
 sash weights, or other coarse castings; or it may be run into pigs and 
 used as scrap. 
 
 Mr. W. J. Keep describes his method of recovery as follows: ''After 
 the blast has been shut off and all of the melted iron has been drained 
 from the cupola, make a dam on the floor in front of the cupola spout 
 about 4 inches high, enclosing a semicircular space, having a radius of 
 about 4 feet. Let the melter lay a tapping bar across the spout and have 
 three or four laborers with a piece of old iH inch shafting about 8 feet 
 long ram in the breast. If the bottom and spout have been made right 
 there will be no melted iron in the cupola, but ram back and forth to 
 allow all to drain out. 
 
 All the liquid slag in the cupola will run into the enclosed space 
 underneath the spout and if there is any iron in this, it will run through 
 the slag and lie on the floor in the form of a slab which can be picked up 
 the next morning. 
 
 When the cupola has been emptied of all slag and iron drop the 
 bottom. I like to draw the refuse out from underneath the cupola, 
 turning it- over and cooling it down with water. The pieces of the sand 
 bottom are thrown to one side and all the iron that can be seen is picked 
 up. All the iron taken from the cupola dump, the pig bed, or from the 
 gangways, which is not bad casting, is weighed up and charged as remelt 
 or home scrap. 
 
 All remaining small pieces of coke, iron or slag are shoveled up from 
 the bottom and from all parts of the foundry and placed in boxes on the 
 cupola platform. This includes skulls from the ladles which contain 
 more or less iron. 
 
 When the last charge of iron has been placed in 'the cupola and the 
 heat is near enough to the end to show that there will be no shortage of 
 iron, throw into the cupola any shot iron that may be left over, and all 
 the refuse previously mentioned. The iron and slag will be melted at 
 once and the small bits of coke will hold the blast down and insure hot 
 iron. 
 
 All the finest shot iron is saved in this way, as well as all coke in the 
 form of small pieces and nothing is lost." 
 
 The disposition on the part of many foundrymen is to neglect the 
 
Melting Borings and Turnings 293 
 
 saving of shot iron, preferring to sell to junk dealers what can be readily 
 recovered. Such will not be the case, however, in a well- managed foundry, 
 as by close attention to its recovery the loss in melt can be reduced 
 from I to 2 per cent. 
 
 At one of the large western foundries, through mismanagement, shot 
 had been allowed to accumulate until a portion of the yard was covered 
 to a depth of from 12 inches to 20 inches. This was dug up, milled and 
 melted; 1500 pounds, at each heat, were thrown on top of the last charge, 
 without additional fuel; the melted iron was run into pigs. 
 
 Over 84 tons of No. 4 pig were recovered; 25 per cent of the scrap used 
 in charging was replaced by this iron and the usual mixture was in no 
 other respect changed. 
 
 Burnt Iron 
 
 This class of iron is of no use except for making sash weights. When 
 used for ordinary purposes, the loss caused is greater than the gain. It 
 makes iron hard, causes a great amount of slag and chokes up the cupola. 
 It should be carefully selected and thrown out of the scrap. 
 
 Melting Borings and Turnings 
 
 Cast iron borings and turnings which are usually disposed of to junk 
 dealers at a low price may be advantageously melted by packing them 
 in wood or iron boxes, about 100 pounds to the box. 
 
 The boxes should be charged a few at a time, by throwing them into 
 the center of the charge and covering them with scrap. These will 
 descend to near the melting zone before they are burned or melted. 
 
 Mr. W. F. Prince has patented a process for melting borings, etc., 
 which consists of packing them in sheet iron pipes, with or without 
 bottoms. The pipes are of any convenient length, from 30 to 48 inches; 
 the first one is placed on the coke bed and the others on top of it, with 
 the charges surrounding them. 
 
 This differs little from the method of using boxes, where the latter are 
 piled on each other. In either case the containers prevent the fine 
 material from being blown out of the stack. 
 
 Many attempts have been made to render borings, etc., suitable for 
 melting, by briquetting. So far, these efforts seem to have been only 
 partially successful. 
 
 A process has recently been developed in Germany, by which the 
 borings are made into briquettes under hydraulic pressure. It is claimed 
 that the product successfully meets the purpose and preliminary tests 
 made in America seem to warrant the statement. 
 
CHAPTER XII 
 
 TEST BARS 
 
 TfflS subject has been treated exhaustively by a Committee of the 
 American Foundrymen's Association. Their report was adopted by 
 the Association in June, 1901. 
 
 Extensive extracts from the report are given below. 
 
 The work covered the testing of 1229 bars by 160 1 tests; the following 
 table shows the character of the heats from which the bars were taken. 
 
 Series 
 
 A* 
 B 
 C 
 D 
 
 E 
 
 Ft 
 
 G 
 
 H 
 
 I 
 
 J 
 
 K 
 
 L 
 
 Class of iron 
 
 Ingot mould 
 
 Dynamo frame. . . . 
 Light machinery . . 
 
 Chilled roll 
 
 Sand roll 
 
 Sash Weight 
 
 Car wheel 
 
 Stove plate 
 
 Heavy machinery. 
 
 Cylinder 
 
 Novelty 
 
 Gun metal 
 
 Melted in 
 
 Cupola 
 
 Cupola 
 Air furnace 
 Air furnace 
 
 Cupola 
 
 Cupola 
 Cupola 
 Cupola 
 Cupola 
 Cupola 
 Cupola 
 O. H. furnace 
 
 Pig iron used 
 
 Coke 
 Coke and charcoal 
 Coke and charcoal 
 Cold-blast charcoal 
 Warm-blast char- 
 coal 
 Coke and charcoal 
 Coke and charcoal 
 
 Coke 
 
 Coke 
 
 Coke 
 
 Coke 
 Coke and charcoal 
 
 Size 
 
 
 
 of 
 
 Si 
 
 P 
 
 heat 
 
 
 
 tons 
 
 
 
 60 
 
 1.67 
 
 .095 
 
 60 
 
 1.95 
 
 ■ 40s 
 
 40 
 
 2.04 
 
 .578 
 
 30 
 
 .85 
 
 .482 
 
 30 
 
 .72 
 
 .454 
 
 15 
 
 • 91 
 
 • 441 
 
 10 
 
 • 97 
 
 .301 
 
 20 
 
 3.19 
 
 1. 160 
 
 30 
 
 1.96 
 
 .522 
 
 10 
 
 2.49 
 
 .839 
 
 5 
 
 4.19 
 
 1.236 
 
 10 
 
 2.32 
 
 .676 
 
 .032 
 
 .042 
 .044 
 
 .070 
 .070 
 
 .218 
 
 .060 
 
 .084 
 .081 
 .084 
 .080 
 .044 
 
 * All pig iron. 
 
 t Nearly all burnt scrap, originally from charcoal and coke iron. 
 
 "Throughout the whole line of operations only regularly constituted 
 mixtures were used, the balance of the heats from which these test bars 
 were cast going directly into commercial castings of the classes designated. 
 The results are, therefore, entirely comparable with daily practice. 
 
 For purposes of comparison green sand and dry sand bars were made 
 side by side. 
 
 It was felt that comparison records were wanted just as much as 
 specifications for the separate lines of product. For this reason, we 
 recommend one standard size of test bar for comparative purposes only, 
 each class of iron being given its special treatment for the information 
 wanted in daily practice in addition. 
 
 294 
 
Test Bars 
 
 295 
 
 "Our studies on the shape of the test bar have resulted in the selection 
 of the round form of cross section and this mainly on the score of great- 
 est uniformity in physical structure. . . . There is still a further 
 point of interest, in the preparation of test bars and that is, the making 
 of coupons from which the quality of the castings to which they are 
 attached is to be judged. This method is used extensively in govern- 
 ment work and in the making of cyl- 
 inder castings. 
 
 The idea of obtaining material 
 from the same pour in the same 
 mould as part of the casting itself is 
 good enough in theory. Unfortu- 
 nately, however, this direct connec- 
 tion introduces elements of segrega- 
 tion and temperature changes in the 
 cast iron which make this test less 
 valuable than is generally supposed. 
 At best the iron which has passed 
 through the different parts of a 
 mold before entering the space for 
 the coupon will not be representa- 
 tive of the whole body, but rather 
 one portion of it only. We therefore 
 recommend the method shown later 
 on in Fig. 75. The metal can be 
 poured from crane or hand ladle, 
 clean and speedily, and possesses the 
 temperature of the average iron in 
 the casting more nearly than the 
 coupon method now practiced. 
 
 Your committee while giving spe- 
 cifications for the tensile test of cast 
 iron is of the opinion that the trans- 
 verse test is the more desirable and certainly within reach of even the 
 smallest foundry. 
 
 In selecting the test bars for the purpose of specification, we have 
 followed the cardinal principle of selecting the largest cross section for 
 the iron consistent with a sound physical structure and within the range 
 and structural limits of an ordinary testing machine. 
 
 The following are the sizes of bars selected for tests as a result of 
 our investigations. 
 
 For all tensile tests, a bar turned to .8 inches in diameter, corre- 
 
 FiG. 75. 
 
296 Test Bars 
 
 spending to a cross section of Yi square inch. Results, therefore, multi- 
 phed by two, give the tensile strength per square inch. 
 
 For transverse test, of all classes of iron for general comparison; a 
 bar ii-i inches in diameter, on supports, 12 inches apart; pressure applied 
 in the middle and deflection noted. 
 
 Similarly for ingot mould, light machinery, stove plate and novelty 
 iron, a ii.^-inch diameter bar; that is to say, for irons running from 2 per 
 cent in silicon upward, or from 1.75 per cent silicon upward where but 
 little scrap is in the mixture. 
 
 For dynamo frames, sash weights, cylinders, heavy machinery and 
 gun metal irons; similarly, a 2-inch diameter bar is recommended, that 
 is, for irons running from 1.5 per cent to 2 per cent in silicon or where 
 the silicon is lower and the proportion of scrap is rather large. 
 
 For roll irons, whether chilled or sand, arid car wheel metals, a 214- 
 inch diameter bar is recommended; that is, for all irons below i per cent 
 silicon and which may, therefore, be classed as the chilling irons. 
 
 The method of moulding the test bar we would recommend is given 
 herewith. 
 
 At least three bars of a kind should be made for a given test. 
 
 The sand should not be any damper than to mould well and stand the 
 wash of the iron without cutting, blowing or scabbing. It should be 
 rammed evenly to avoid swells and poured by dropping the metal from 
 the top through gates, or from ladle direct into the open mould. 
 
 After the bars are cast they should remain in their moulds undis- 
 turbed until cool." 
 
 Proposed Standard Specifications for Gray Iron Castings 
 
 1. Unless furnace iron, dry sand, loam moulding, or subsequent 
 annealing is specified, all gray iron castings are understood to be of 
 cupola metal; mixtures, moulds and methods of preparation to be fixed 
 l>y the founder to secure the results required by purchaser. 
 
 2. All castings shall be clean, free from flaws, cracks and excessive 
 shrinkage. They shall conform in other respects to whatever points 
 may be specially agreed upon. 
 
 3. When the castings themselves are to be tested to destruction, the 
 number selected from a given lot and the tests they shall be subjected to 
 are made a matter of special agreement between founder and purchaser. 
 
 4. Castings under these specifications, the iron in which is to be 
 tested for its quality, shall be represented by at least three test bars cast 
 from the same heat. 
 
 5. These test bars shall be subjected to a transverse breaking test, 
 the load applied at the middle with supports 12 inches apart. The 
 
Patterns for Test Bars of Cast Iron 
 
 297 
 
 breaking load and deflection shall be agreed upon specially on placing 
 the contract, and two of these bars shall meet the requirements. 
 
 6. A tensile strength that may be added, in which case at least three 
 bars for this purpose shall be cast with the others, in the same moulds 
 respectively. The ultimate strength shall also be agreed upon specially 
 before placing the contract and two of the bars shall meet the require- 
 ments. 
 
 7. The dimensions of the test bars shall be as given herewith. There 
 is only one size for the tensile bar and three for the transverse. For the 
 light and medium weight castings the i^i inch D bar is to be used; 
 for heavy castings, the 2 inch D bar; and for chilling irons the 2H inch 
 n test bar. 
 
 8. When the chemical composition of the castings is a matter of 
 specification, in addition to the physical tests, borings shall be taken 
 from all the test bars made; they shall be well mixed and any required 
 determination (combined and graphitic carbon alone excepted), made 
 therefrom. 
 
 9. Reasonable facilities shall be given the inspectors to satisfy them- 
 selves that castings are being made in accordance with specifications, 
 and if possible tests shall be made at the place of production prior to 
 shipment." 
 
 Patterns for Test Bars of Cast Iron 
 
 PfC* 
 
 For Transverse Test 
 
 U-2-- 
 
 W t- 
 
 ■='^v 
 
 /3' 
 
 (MC^^ 
 
 ^-2i"-y^ 
 
 loi'- 
 
 For "^y?* Tensile Test 
 
 
 Fig. 76. 
 
 h2|-"*l 
 
 1"^ 
 
 ±:^i::i, 
 
 Steel Socket for Tensile Test of Cast Iron. — Two required 
 
 k- 
 
 1 
 
 13" >l 
 
 Standard Test Bar for Cast-iron Tensile Test. — Cross section equals 
 
 J^ sq. in.; test piece shovdd fit loosely in socket 
 
 Fig. 77- 
 
298 Test Bars 
 
 Modulus of Rupture in Pounds Per Square Inch 
 
 The report of the committee is accompanied by a table giving the 
 moduli of rupture per square inch for bars under the various con- 
 ditions of the tests and from H square inch to 16 square inches. It was 
 found that, with few exceptions, the values decrease as the areas 
 increase. 
 
 In the table on pages 299 and 300, which is extracted from their 
 report, the moduli are given for bars having areas of i square inch, 
 2.25, 4, and 9 square inches. 
 
 "The results show that rough bars are stronger than machined and 
 that there is practically no difference between bars made in green or dry 
 sand. 
 
 An examination of the table shows that the transverse strength is 
 greater in the rough than machined bars, except in two instances, viz. : 
 D bar, series /, in dry sand the rough bar broke with 178 pounds less 
 load than the machined bar. O bar, series L, in dry sand, the rough 
 bar broke with 115 pounds less load than did the machined bar. The 
 average loss in transverse strength of the green sand bar by machining 
 was 12 per cent; that of the dry sand bar 10 per cent. 
 
 The following articles are introduced as showing how little reliance 
 can be placed on the results from test bars. It is shown that bars 
 identical in chemical composition, but made from different brands, differ 
 widely in physical properties; indicating the importance of using in 
 mixtures, irons from different localities, as well as from different furnaces. 
 The micrographs show clearly the variation in structure corresponding 
 to the widely varying results, but it remains for the metallurgist to point 
 out the causes for these differences." 
 
 Erratic Results — Test Bars 
 
 Mr. F. A. Nagle submitted to the American Society of Mechanical 
 Engineers the following report of his investigation of test bars for castings 
 used in the Baltimore Sewage pumps. 
 
 "In machinery castings as well as in cast pipes, separate bars are cast 
 and subjected to tensile or transverse stress to the breaking point, these 
 results being used as evidence of compliance with the contract speci- 
 fications. The writer has examined a large number of such test bars for 
 castings used in the Baltimore Sewage pumps and here reports the results 
 of this examination and study. 
 
 Perhaps the most important conclusion is that the test bar is not to 
 be regarded with too much confidence as indicative of the exact strength 
 of the casting. All transverse bars were nominally 2 inches by i inch by 
 
Modulus of Rupture in Pounds Per Square Inch 299 
 
 
 Rough 
 
 Machined 
 
 Area in 
 square 
 
 Square 
 
 Round 
 
 Square 
 
 Round 
 
 inches 
 
 Green Dry 
 sand sand 
 
 Green 
 sand 
 
 Dry 
 
 sand 
 
 Green 
 sand 
 
 Dry 
 sand 
 
 Green 
 sand 
 
 Dry 
 sand 
 
 Ingot Mould Iron. Series A. Silicoti 1.67 
 
 1. 00 
 
 37.140 
 
 27,530 
 
 44.210 
 
 33.660 
 
 43.200 
 
 38,610 
 
 26,100 
 
 27,840 
 
 2.25 
 
 32,880 
 
 31.320 
 
 34.S70 
 
 33.870 
 
 29.340 
 
 30,790 
 
 39,810 
 
 38.120 
 
 4.00 
 
 29.540 
 
 25,550 
 
 34.900 
 
 31.610 
 
 31.150 
 
 26,500 
 
 34.320 
 
 32,290 
 
 9.00 
 
 26,200 
 
 21,180 
 
 27,280 
 
 26,540 
 
 26,980 
 
 21,690 
 
 26,030 
 
 28,660 
 
 
 Dynamo Frame Iron. 
 
 Series B. Silicon 1.95 
 
 
 1. 00 
 
 39.220 
 
 38,380 
 
 44,300 
 
 49,160 
 
 37,440 
 
 30,240 
 
 40,020 
 
 39.150 
 
 2.25 
 
 39.540 
 
 34,900 
 
 41.270 
 
 44,840 
 
 36.670 
 
 36,180 
 
 44.790 
 
 37.800 
 
 4.00 
 
 33.960 
 
 34,460 
 
 41,680 
 
 39.230 
 
 34.750 
 
 33,250 
 
 38,750 
 
 37.270 
 
 9.00 
 
 29,680 
 
 30,050 
 
 35,600 
 
 35.620 
 
 32,740 
 
 30,880 
 
 35,400 
 
 32,810 
 
 Light Machinery Iron. 
 
 Series C. Silicon 2. 
 
 04 
 
 37.000 
 32,880 
 36,170 
 30,980 
 
 39.190 
 38.780 
 34.550 
 29.230 
 
 48.050 
 38,890 
 42,560 
 38,080 
 
 50.380 
 43.950 
 40,150 
 37.780 
 
 40,230 
 36,990 
 33.290 
 
 38,880 
 35.420 
 32,710 
 
 55.680 
 47,340 
 42,920 
 36.520 
 
 1. 00 
 2.25 
 4.00 
 9.00 
 
 47,850 
 SI. 350 
 37,550 
 36,290 
 
 Chilled Roll (Furnace). Series D. Silicon 0.85 
 
 1. 00 
 2.25 
 4.00 
 9.00 
 
 44,120 
 47.760 
 46,710 
 52,700 
 
 44,010 
 
 67,680 
 43.260 
 54,910 
 
 49.440 
 69.130 
 65,940 
 65.850 
 
 49.850 
 59.010 
 75.000 
 51,660 
 
 
 
 
 1. 00 
 2.25 
 4.00 
 9.00 
 
 Sand Roll Iron (Furnace). Series E. Silicon 0.72 
 
 51,560 
 
 44,180 
 
 51.620 
 
 48,740 
 
 
 
 
 41.740 
 
 46,290 
 
 41.420 
 
 41,960 
 
 
 
 
 34,700 
 
 33,720 
 
 55.110 
 
 61,770 
 
 
 
 
 33,040 
 
 35.760 
 
 53.540 
 
 55,440 
 
 
 
 
 Sash Weight Iron. Series F. Silicon 0.91 
 
 1. 00 
 2.25 
 4.00 
 9.00 
 
 52,920 
 59.170 
 61,870 
 42,710 
 
 42,540 
 51,130 
 
 SI, 810 
 
 39,160 
 
 58,430 
 
 50,050 
 
 
 
 
 39,840 
 
 S3,oio 
 
 
 
 
 50,130 
 
 47.090 
 
 
 
 
 42,370 
 
 4S,73o 
 
 
 
 
300 
 
 Test Bars 
 
 
 Rough 
 
 Machined 
 
 Area in 
 square 
 
 Square 
 
 Round 
 
 Square 
 
 Round 
 
 inches 
 
 Green 
 sand 
 
 Dry 
 sand 
 
 Green 
 sand 
 
 Dry 
 
 sand 
 
 Green 
 sand 
 
 Dry 
 sand 
 
 Green 
 sand 
 
 Dry 
 sand 
 
 Car Wheel Iron. Series G. Silicon 0.97 
 
 1. 00 
 
 47,110 
 
 44,810 
 
 52,600 
 
 61,720 
 
 43,200 
 
 46,080 
 
 64,380 
 
 52,200 
 
 2.25 
 
 32,120 
 
 28,200 
 
 45,880 
 
 39,740 
 
 44,640 
 
 40,680 
 
 43,200 
 
 46,170 
 
 4.00 
 
 35,460 
 
 32,190 
 
 45,970 
 
 39,330 
 
 27,520 
 
 32,760 
 
 41.590 
 
 37 .350 
 
 9.00 
 
 32,050 
 
 32,140 
 
 37,610 
 
 35,150 
 
 28,730 
 
 28,960 
 
 33,930 
 
 28.040 
 
 Stove Plate Iron. Series H. Silicon 3.19 
 
 1. 00 
 
 27,980 
 
 29,360 
 
 42,570 
 
 36,920 
 
 48,960 
 
 43,200 
 
 78,300 
 
 68,600 
 
 2.25 
 
 24,960 
 
 30,710 
 
 42,160 
 
 41,420 
 
 22,500 
 
 24,480 
 
 33.250 
 
 31,550 
 
 4.00 
 
 27,980 
 
 28,930 
 
 40,540 
 
 36,940 
 
 23,400 
 
 28,SlO 
 
 32,290 
 
 21,910 
 
 9.00 
 
 25,620 
 
 25,020 
 
 33,350 
 
 33,550 
 
 23,710 
 
 24,100 
 
 25,540 
 
 23,000 
 
 
 Heavy Machinery Iron 
 
 . Series I. Silicon! 
 
 96 
 
 
 1. 00 
 
 36,000 
 
 44,060 
 
 53,210 
 
 54,180 
 
 43,200 
 
 46,080 
 
 52,200 
 
 55,680 
 
 2.25 
 
 35,290 
 
 35,040 
 
 43,860 
 
 47,100 
 
 33,120 
 
 39,060 
 
 44,900 
 
 43,200 
 
 4.00 
 
 36,120 
 
 33,580 
 
 42,290 
 
 41,330 
 
 30,400 
 
 32,970 
 
 41,670 
 
 42,420 
 
 9.00 
 
 23,850 
 
 20,880 
 
 33,040 
 
 34,970 
 
 37,040 
 
 30,410 
 
 36,030 
 
 38,02a 
 
 
 
 Cylinder Iron. Series J. 
 
 Silicon 2.49 
 
 
 
 1. 00 
 
 43,350 
 
 34,270 
 
 51,690 
 
 55,500 
 
 39,790 
 
 39,790 
 
 52,200 
 
 46,980 
 
 2.25 
 
 30,880 
 
 31,950 
 
 33,400 
 
 41,900 
 
 39,960 
 
 38,520 
 
 51,040 
 
 53.160 
 
 4.00 
 
 32,600 
 
 30,420 
 
 43,180 
 
 41,320 
 
 26,400 
 
 26,610 
 
 38,110 
 
 38,240 
 
 9.00 
 
 27,830 
 
 25,630 
 
 40,900 
 
 40,170 
 
 26,400 
 
 24,890 
 
 34.470 
 
 34.310 
 
 Gun Iron (¥vjnidi.c€). Series L. Silicon 2.^,2 
 
 
 
 Novelty Iron. Series K. 
 
 Silicon 
 
 4.19 
 
 
 
 1. 00 
 
 25.430 
 
 36,490 
 
 39,040 
 
 42,530 
 
 
 
 
 
 2.25 
 
 25.640 
 
 26,290 
 
 37,760 
 
 37,670 
 
 
 
 
 
 4.00 
 
 27,120 
 
 26,860 
 
 33,550 
 
 34,560 
 
 
 
 
 
 9.00 
 
 22,220 
 
 24,130 
 
 30,890 
 
 32,520 
 
 
 
 
 
 1. 00 
 
 52,230 
 
 44,030 
 
 71,570 
 
 67,350 
 
 53,270 
 
 50,400 
 
 80,040 
 
 71.340 
 
 2.25 
 
 49,290 
 
 46,760 
 
 67,060 
 
 66,140 
 
 47,520 
 
 39.600 
 
 59.040 
 
 71,160 
 
 4.00 
 
 50,400 
 
 49,990 
 
 66,980 
 
 66,730 
 
 46,670 
 
 39,680 
 
 61,470 
 
 53.310 
 
 9.00 
 
 41,980 
 
 43,050 
 
 59,010 
 
 59,460 
 
 41,990 
 
 47.830 
 
 56,140 
 
 59.480 
 
Erratic Results — Test Bars 
 
 301 
 
 24 inch centers. . They were cast from two patterns in one mould and 
 made in the same kind of sand as the main casting. The flask was 
 incUned about 30 degrees. There was but one gate for the two bars with 
 suitable risers. The iron for the bars was poured from a small ladle of 
 iron taken as nearly as possible from the middle of the pour of the m^in 
 casting. 
 
 The breaking loads were corrected for varying dimensions of the bars 
 
 by the formula W = , where b and d are the actual dimensions, 
 
 W the actual breaking load and W the corrected load of weight. These 
 results are used throughout this paper. The deflections were not 
 corrected. 
 
 The tensile bars, 1% inches by 6 inches, were cast upright in the same 
 mould as the main castings, within 3 or 4 inches thereof, and connected 
 by an upper and lower gate. The tensile bars were turned to i i/i inches 
 in diameter and threaded, and the middle portion reduced to 1.129 inches 
 in diameter which is equal to i square inch area. Table I gives the 
 results of the chemical analysis of the several bars tested. 
 
 Table I 
 
 
 
 s 
 
 1 
 
 
 
 
 i 
 
 1 
 
 3 
 •a 
 
 
 is 
 
 1^ t 
 
 CO u 
 
 1" 
 
 
 
 1 
 
 
 
 a . 
 
 § 
 
 ^ 
 
 fin 
 
 03 
 
 S 
 
 
 
 0) 
 
 Nov. 21, 
 
 1907.... 
 
 3.580 
 
 2.830 
 
 .75 
 
 • 79 
 
 .485 
 
 .081 
 
 1.59 
 
 24.900 
 
 2440 
 
 .49 
 
 Nov. 26, 
 
 1907.... 
 
 3.396 
 
 2.736 
 
 .66 
 
 .38 
 
 .459 
 
 .124 
 
 1. 91 
 
 22.000 
 
 2075 
 
 .40 
 
 From Aug. 5, 1907 to April 4, 1908 there were made 67 single tensile 
 bars, and the same nurnber of pairs of transverse bars; and the average 
 of the latter was used in this record. From April 4 to Dec. 19, 1908, there 
 were made 91 pairs of tensile bars and an equal number of transverse 
 bars and each piece of the pair is recorded instead of the average. 
 
 Of these 249 tensile bars and their corresponding transverse bars, 32 
 sets — 26 flat and 6 round — were rejected for defects due to blow-holes 
 and four tensile bars were too hard to bear threading, but the companion 
 pieces were used in this record. 
 
 Of the 217 specimens here recorded, 42 were designated as abnormal; 
 that is, the ratio between the tensile and the transverse bars was either 
 considerably greater or smaller than the average. 
 
302 
 
 Test Bars 
 
 By referring to Table II it will be seen that of the 175 specimens of 
 cast iron running from 20,000 to 30,000 pounds tensile strength, the 
 ratio of tensile to breaking loads is practically 10 to i and the deflection 
 
 0.45." 
 
 Table II 
 
 Number of 
 specimens 
 
 Transverse 
 
 Tensile 
 
 Deflection 
 
 Ratio of tensile to 
 transverse 
 
 29 
 36 
 SI 
 43 
 16 
 
 2065 
 2289 
 2523 
 2756 
 2894 
 
 21,630 
 22,940 
 24,880 
 26,500 
 28,460 
 23,732 
 
 Inch 
 .43 
 .45 
 .47 
 • 49 
 .49 
 
 10.47 
 10.02 
 9.86 
 9.61 
 9-83 
 9- 96 
 
 
 175 
 
 Average 2383 
 
 
 45 
 
 
 Comparison of Test Bars 
 
 Table III gives 25 abnormal cases where this average ratio is as high as 
 
 12.56 to I with a deflection of 0.43 inch, also 17 abnormal cases where 
 
 this average ratio is as low as 7.91 to i, with a deflection of 0.44 inch; 
 
 and yet the average of both normal and abnormal bars was again very 
 
 nearly lo to i. 
 
 Table III 
 
 Ahove ratio 10 to i 
 
 Number of 
 
 
 Tensile 
 
 Deflection 
 
 Ratio of tensile to 
 
 specimens 
 
 
 
 
 transverse 
 
 
 
 
 In. 
 
 
 
 10 
 
 2088 
 
 27,143 
 
 .41 
 
 12.95 
 
 
 10 
 
 2294 
 
 28,530 
 
 .43 
 
 12.44 
 
 
 4 
 
 2436 
 
 29,600 
 
 .49 
 
 12.15 
 
 
 I 
 
 2890 
 
 34,000 
 
 .45 
 
 11.76 
 
 
 25 
 
 Average 2258 
 
 28,36s 
 
 .43 
 
 12.56 
 
 
 
 
 Below 10 / 
 
 I 
 
 
 I 
 
 2105 
 
 17,600 
 
 .50 
 
 8.36 
 
 
 4 
 
 2359 
 
 18,825 
 
 .41 
 
 7.98 
 
 
 7 
 
 2487 
 
 18,814 
 
 .43 
 
 7.57 
 
 
 3 
 
 2656 
 
 21,230 
 
 .45 
 
 8.00 
 
 
 2 
 
 2969 
 
 24,500 
 
 .47 
 
 8.2s 
 
 
 17 
 
 2521 
 
 19,954 
 
 .44 
 
 7.91 
 
 
 Breaking loads, presumably alike, varied in pairs of transverse bars 
 and also in pairs of tensile bars as follows: 
 
Comparison of Test Bars 
 
 303 
 
 Out of 65 pairs of flat or transverse bars, 14 or 22 per cent, average 
 variation 18 per cent; 17 or 26 per cent, average variation 5.4 per cent; 
 34 or 52 per cent, average variation less than 2 per cent. 
 
 Out of 65 pairs of round or tensile bars 22 or 34 per cent, average 
 variation 15 per cent; 20 or 31 per cent, average variation 5.5 per cent; 
 23 or 35 per cent, average variation less than 2 per cent. 
 
 61 other pairs of flat bars which had only one companion tensile bar 
 varied in about the same ratios. 
 
 Two special flat bars and two special roimd bars, cast in one mould, one 
 gate and at one pour varied as follows: 
 
 Two flat bars 12 per cent; two round bars 7 per cent. 
 
 In order to get some more definite information on these variations, if 
 possible, I had a pair of transverse and a pair of tensile bars made and 
 cast in the same mould and while the average was again nearly 10 to i as 
 shown in Table III, the same type of bars again varied 12 and 7 per cent 
 respectively. 
 
 Table IV 
 
 Comparison of Cast-iron Test Bars. Special. Two Sets Cast in 
 
 Same Mould at Same Time 
 
 Number of 
 specimens 
 
 Transverse 
 
 Tensile 
 
 Deflection 
 
 Ratio of tensile to 
 transverse 
 
 I 
 
 I 
 
 2 
 
 217 
 
 2350 
 2100 
 
 Average 2225 
 All averages 2380 
 
 23,000 
 21,470 
 
 22,235 
 23,970 
 
 Inch 
 .50 
 • 45 
 
 .47 
 .45 
 
 9-79 
 10.21 
 
 10.04 
 10.07 
 
 I 
 I 
 I 
 I 
 
 I have no satisfactory explanation for the great variation of these test 
 bars and we can only accept the fact that mathematical uniformity in 
 strength of cast-iron bars is not found in the present state of the art. 
 
 To any one questioning the results, I can only say from my own 
 knowledge of the circumstances, that the personal equation did not enter 
 into them. 
 
 Careful observation of broken bars did not show that the so-called 
 "skin of the metal" was of any appreciable thickness and the metal was 
 remarkably homogeneous throughout. 
 
 The tensile bars being turned, the skin, if there was any, of course 
 disappeared. 
 
 It is my opinion that the skin adds practically nothing to the strength 
 in either transverse or tensile bars; other causes, though obscure, produc- 
 ing far greater deviations." 
 
304 Test Bars 
 
 Casting Defects 
 
 Although many castings were condemned for physical defects not a 
 single case of cold-shut was observed. 
 
 In one instance of defect, he says: "To remove all doubt that the test 
 bars were truly representative of the iron in the main casting, two tensile 
 bars were cut out of a large flange which had been at the bottom of the 
 mould. These, from the most favored part of the casting, as v/ill be seen, 
 stood but about 17,350 pounds; 90 per cent of that revealed by the test 
 bars. In this case there was a remarkable agreement between this pair 
 of test bars. 
 
 It may be interesting to apply these results to the formula for the 
 
 strength of cast-iron beams subjected to similar stress. 
 
 T, PI 
 The formula commonly used isR= ^-^-7, , where R is called the modulus 
 
 of rupture, or stress per square inch of extreme fibre, 
 
 P = load at center, 
 I = length between supports in inches, 
 b and d = breadth and depth respectively in inches. 
 
 Make the proper substitutions and we have R = 42,840 pounds. 
 This is not the correct figure, however, for the extreme fibre stress. We 
 know this cannot exceed the tensile strength which we have found to be 
 23,732 pounds. 
 
 I think it is better to use D. K. Clarke's formula given on page 507 of 
 
 WL 
 
 his " Engine Tables." S = r^r , where 5= extreme fibre stress or 
 
 I. 155 bd^ 
 
 tensile strength. If we use the tensile strength found in these tests as 
 23,732 pounds, the breaking load W would become 2284 pounds; the 
 actual breaking load being 2383 pounds. As this is within 4.3 per cent 
 of the average found in these tests, this formula, using the tensile strength 
 for the extreme fibre stress, seems to me to be more intelligible and dis- 
 penses with the "coefficient of rupture." 
 
 Circular Test Bars 
 
 Since the foregoing was written I have had the opportunity to ob- 
 serve two circular test bars, nominally iH inch diameter by 15 inches 
 long, with 12-inch centers. These bars were cast from two separate 
 patterns in one vertical dry sand mould, and poured from a small 
 hand ladle, first one and then the other, with the result shown in 
 Table V. 
 
Circular Test Bars 305 
 
 Table V. — Circular Test Bars in Vertical Dry Sand Moulds 
 
 Bar mark 
 
 Transverse 
 
 Tensile 
 
 Deflection 
 
 Value W by 
 formula 
 
 Original 
 diameter 
 
 H 
 
 3344 
 
 3344 
 
 3026 
 
 2 
 
 23,070 
 
 23,754 
 
 24,670 
 
 3 
 
 .15 
 •IS 
 .12 
 4 
 
 2948 
 
 3036 
 
 3153 
 
 5 
 
 1.305 
 
 H 
 
 1.305 
 
 X 
 
 1.300 
 
 / 
 
 6 
 
 
 
 The tensile bars were taken from the bottom ends of the broken test 
 bars, but I do not know whether H ox X was poured first. 
 
 The first tensile bar H had a small air-hole, which being allowed for, 
 added 7 per cent to its tensile strength, and this is also given in the table. 
 A second bar was then turned up from the immediate joining piece with 
 the result recorded in the table first. The turned bars were 0.937 inch 
 diameter. 
 
 Column six gives the original diameter. Column two was found by 
 reducing the actual breaking loads in the ratio of the cubes of the diam- 
 eters, and column three was reduced to the square inch area. Why the 
 transverse breaking loads should vary 10 per cent and the tensile bars 
 4 to 7 per cent the opposite way, a total variation of 14 to 17 per cent, I 
 leave to the reflection of the reader. If we apply Clarke's formula for 
 
 the breaking weight for circular bars, W = - — - — -, , we find the 
 
 values given in column five. 
 
 While the blow-holes seem to be more frequent in flat transverse bars 
 than in round attached tensile bars, the latter seem liable to a greater 
 abnormal hardness, for which I have no explanation. 
 
 Some indication of the toughness of cast iron may be seen in its deflec- 
 tion, which is not revealed in a direct pull. I would, therefore, be 
 satisfied with two or three transverse test bars 2 in. by i in. by 24 in. 
 centers, and a deflection record poured as near as may be from the middle 
 of the pour of the main casting as giving a fair indication of the iron 
 in the main casting, but mathematical exactness cannot be looked for as 
 yet. 
 
 If we wish to know approximately the corresponding tensile strength 
 of the iron, we can multiply the breaking load of the 2 in. by i in. by 24 
 in. flat bar by 10. 
 
 If the test bar is iM inch diameter by 12-inch centers its breaking 
 load should be multiplied by 8 to obtain the approximate tensile 
 strength. 
 
3o6 
 
 Test Bars 
 
 The general rule seems to be, that where both flat bars agree in break- 
 ing loads, the tensile strength is lo to i of the breaking load, but where 
 they differ the lo to i ratio does not hold. A better practice, therefore, 
 might be to cast three round transverse bars and accept the two that 
 agree, if each is round, as a fair sample of the iron, dispensing with the 
 tensile bars. This concession to the manufacturer, I believe, v/ould 
 entail not only no loss to the city's interests, but a positive gain. 
 
 EFFECT OF STRUCTURE OF CAST IRON UPON ITS 
 PHYSICAL PROPERTIES 
 
 Microscopic Evidence of the Reason why Irons of 
 
 Similar Chemical Composition have Different 
 
 Relative Strengths 
 
 BY 
 
 F. J. Cook and G. Hailstone 
 
 " During daily foundry practice, with work made from mixtures of iron 
 that have the same chemical composition and where tests are frequently 
 taken, it is often found that widely different physical results are obtained. 
 Instances of this have been brought to the notice of this association 
 . . . but in neither case was an explanation of the phenomena given. 
 Attempts have been made to give a satisfactory explanation of these 
 differences, but on the whole the conclusions arrived at have not been 
 generally accepted. 
 
 In the past the instances cited have generally been isolated ones, but 
 a remarkable series of tests over a lengthy period has recently been met 
 with by one of the authors. 
 
 
 1 
 
 
 r~ 
 
 
 
 
 
 
 ^ 
 
 
 
 
 
 -?- v^ 
 
 'h 
 
 
 
 'A ^iLi^v^-5^/... 
 
 J/k? 
 
 J^'l^ 
 
 ^ 
 
 
 ;-° 
 
 ' 3jtD A^""^^^ 
 
 
 ^^L\- 
 
 -^ 
 
 \ 
 
 Zt^ 
 
 V ^L 
 
 T^ 
 
 GJ 
 
 
 >. > 
 
 
 
 
 
 
 V 
 
 
 
 
 X-«- 
 
 
 
 ^\-/ 
 
 A f^ru::?:^ i5^/-,^ 
 
 ^3lJ 
 
 / ' ,' 
 
 -»--^ 
 
 
 t^'^l 
 
 ^^^t 2^2^55 7 
 
 S-^ ' \ 
 
 t^Zu 
 
 1 '-' 
 
 
 7 ' I 
 
 Ac 'n '/nTf^ i oe ;7: ^'c< rf/ o 
 
 V 
 
 r.- jll 
 
 pf — 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 - 
 
 
 
 
 
 
 Fig. 78. 
 
 Fig. 78 is a diagram of tensile test results of two series of casts, each 
 representing 60 consecutive days working with irons mixed to give the 
 
Effect of Structure of Cast Iron upon Its Physical Properties 307 
 
 same chemical composition, but each series made up with different 
 brands of pig iron. 
 
 That the chemical analysis was identical in each case was proved by 
 analyses taken from time to time which, in each instance, for all practical 
 purposes came out ahke. 
 
 The diagram shows that the highest tensile result in the A series was 
 lower than the lowest result in the B series. A summary of the whole 
 of the tests is shown in Table I. 
 
 Table I. - 
 
 - Results of 
 
 Mechanical Tests 
 
 
 
 
 Tensile 
 
 test, tons 
 
 per square 
 
 inch 
 
 Trans- 
 verse test, 
 
 cwts. 
 I in. sq. 
 bar, 12 in. 
 
 center 
 
 Trans- 
 verse test, 
 
 lbs. on 
 H in. sq. 
 bar, 12 in. 
 
 centers, 
 
 Keep's 
 test 
 
 Shrinkage 
 
 in inches 
 
 y2 in. sq. 
 
 bar. 
 
 Keep's 
 
 test 
 
 Hardness 
 
 Blast 
 pressure 
 in ounces 
 
 Series 
 
 A 
 
 B 
 
 A 
 
 B 
 
 A 
 
 B 
 
 A 
 
 B 
 
 A 
 
 68 
 48 
 575'^ 
 60 
 
 B 
 
 78 
 561/^ 
 64H 
 56 
 
 A 
 
 15 
 10 
 
 123/4 
 
 44 
 
 B 
 
 
 
 Highest 
 
 12.9 
 
 8.7 
 10.7 
 60 
 
 18.3 
 13. 1 
 
 15.8 
 60 
 
 28.5 
 19.0 
 23.1 
 33 
 
 32.25 
 25.0 
 29.1 
 30 
 
 5SO 
 390 
 466 
 58 
 
 570 
 
 375 
 
 450 
 
 59 
 
 .182 
 
 .144 
 .140 
 58 
 
 .180 
 .140 
 .155 
 58 
 
 16 
 
 Average 
 
 No test taken . . 
 
 13H 
 39 
 
 Each tensile test bar was i inch square and transverse and hardness 
 bars were cast relatively of the same size, and on the casting they were 
 to represent; while the H-inch transverse bars, which were also used 
 for the shrinkage test, were cast separately by Keep's method. 
 
 The transverse bars were cast iH inch square, machined down to 
 I inch square and tested on 12-inch centers. 
 
 Referring to Table I, it will be seen that the results of the transverse 
 tests on the i inch square bars also show a marked difference, as do the 
 tensile tests. It will be noted, however, that the average result of the 
 transverse test on the 3'^-inch square bars is slightly in favor of the series 
 which gave the weakest tensile, and with the i -inch square bar opposite 
 results. This point will be referred to later. 
 
 As the method of manipulation and the chemical composition of the 
 two series were the same, it was thought that a microscopical analysis 
 would reveal a cause for the vast difference. For the first investigation 
 a low bar of the A series, and the highest bar of the B series were ex- 
 amined. The chemical analysis of the two bars was first taken as 
 shown in Table II. 
 
3o8 Test Bars 
 
 Table U. — Comparative Chemical Analysis of the Two Series 
 
 Series .... 
 
 A 
 
 B 
 
 
 Tensile test 
 
 9.1 tons per 
 
 square inch, 
 
 per cent 
 
 18.3 tons per 
 
 square inch, 
 
 per cent 
 
 Total carbon 
 
 3.250 
 2.397 
 .853 
 1.328 
 .095 
 .923 
 .290 
 
 3.092 
 2.289 
 .903 
 - I. 314 
 .101 
 .909 
 .335 
 
 94.149 
 
 
 
 
 
 
 
 
 
 
 Chemical Analyses 
 
 These analyses will be seen to be practically identical, even to the 
 amount of the combined and graphitic carbon. 
 
 To insure the results being absolutely comparative, a number of 
 micrographs were each taken from the same position at the center of 
 the bars. Fig. 79 shows the polished, but unetched section of the low 
 bar from the A series, Fig. 80 the high bar from the B series. These 
 show the size of the graphite in each case, the one having it in the form 
 of long flakes, the other in very small flakes. 
 
 Fig. 79. 
 
 Figs, 81 and 82 show the same surfaces etched with iodine and magni- 
 fied 120 diameters. In the one case the large flakes of graphite are plainly 
 seen in a matrix of cementite, phosphorus eutectic, pearlite and ferrite; 
 while in the other, the graphitic carbon is scarcely visible and a closer 
 structure is observed. Otherwise, there is nothing very remarkable to 
 account for such widely different physical results. 
 
Chemical Analyses 
 
 309 
 
 The same surfaces were then treated on the lines laid down by Mr. 
 Stead at the 1909 convention, to bring into prominence the phosphorus 
 eutectic. Fig, 83 shows the 9.1 ton bar, and Fig. 84 the 18.3 ton bar. 
 In both cases not only is the phosphorus shown but the cementite as 
 well. 
 
 In Fig. 83 the phosphorus and cementite are evenly distributed, and 
 have not taken up any definite form of structure, the graphite being also 
 shown intermixed with them, but in Fig. 84 a very remarkable arrange- 
 ment of a net-like formation of phosphorus and cementite is shown. As 
 
 Fig. 81. — A Series; tensile strength 
 18,200 pounds per sq. inch; mag- 
 . nifi cation 120 diameters. 
 
 Fig. 83. — A Series; tensile strength 
 18,200 pounds per sq. inch; mag- 
 nification 30 diameters. 
 
 Fig. 82. — B Series; tensile strength 
 36,600 pounds per sq. inch; mag- 
 nification 120 diameters. 
 
 Fig. 84. — B Series; tensile strength 
 36,600 pounds per sq. inch; mag- 
 nification 30 diameters. 
 
 it had been noticed with bars previously examined that those giving 
 high test had also been associated with this particular net-like structure, 
 we were lead to the conclusion that probably strength was associated 
 with this structure independently of what the chemical composition 
 might be; we, therefore, examined a series of bars made by one of the 
 authors a few years ago to show the effect on strength of different rates 
 of cooling. For this experiment four bars had been made in one box, 
 cast from the same ladle of metal, which was ordinary No. 3 foundry- 
 pig iron. 
 
 Taken from " castings," Aug. 1909. 
 
310 
 
 Test Bars 
 
 The rate of cooling was regulated by means of cast iron chills of 
 different thicknesses placed in the moulds for three of the bars, the other 
 having no iron chill. The bar without the chill gave a tensile test result 
 of 8.1 tons per square inch, while the bar at the other end of the series 
 broke at 15.2 tons per square inch. These two bars were selected, the 
 chemical analyses of which are given in Table III. 
 
 Table III. — Analysis of Medium Bar 
 
 Tensile strength 
 
 Total carbon 
 
 Graphitic carbon . 
 Combined carbon 
 
 Silicon 
 
 Sulphur 
 
 Phosphorus 
 
 Manganese 
 
 Iron by difference 
 
 13.9 per cent 
 
 .272 
 .740 
 .532 
 .307 
 .III 
 .948 
 .330 
 
 94.032 
 
 Chilled and Unchilled Bars 
 
 These results are identical, and as there is practically no combined 
 carbon present, there must be an absence of cementite. The bars are 
 also totally different in chemical composition from those previously 
 examined. 
 
 Figs. 85 and 86 show unetched sections from the two bars, with the 
 difference in the formation of the graphite as previously pointed out in 
 
 Fig. 8s. 
 
 Fig. 86. 
 
 connection with the other bars; that is, elongated flakes of graphite in 
 the unchilled bar, and finely divided graphite in that of the chilled 
 
 Figs. 87 and 88 show the formation of the phosphorus eutectic in the 
 case of the weak bar to be broken up and having no distinct pattern, 
 while in the case of the strong bar there is clearly shown that net-like 
 
Chilled and Unchilled Bars 
 
 311 
 
 formation which was the distinguishing feature of the strong bar from 
 the B series, but with this difference, that the structure was rather 
 smaller. 
 
 As there is no cementite present in this specimen, it is proof that the 
 particular formation is not dependent upon cementite. 
 
 Fig. 87. 
 
 Fig. 88. 
 
 There was next examined another bar from B series. This had a 
 tensile strength about half way between the two bars previously selected, 
 and had given a tensile test result of 13.9 tons per square inch. The 
 analysis of this bar is shown in Table III. This showed that while the 
 total carbon and other elements were practically the same as the two 
 bars previously taken, the graphitic carbon was higher by 0.35 per cent, 
 and the combined carbon lower by 0.35 per cent. This was probably 
 due to the fact that this bar had been cast on a much larger casting than 
 the previous two. 
 
 The size of the graphite in this bar is illustrated by an unetched 
 section in Fig. 89 which shows that although it is smaller than that shown 
 in Fig. 79 of the 9.1 ton bar, it is larger and more elongated than that 
 contained in the 18.3 bar, Fig. 80. 
 
 Fig. 89. 
 
 Fig. 90. 
 
 The phosphorus eutectic which is shown in Fig. 90 is the same net-like 
 formation as associated with the previous strong bars, though rather less 
 clearly defined and appears to be getting into the transition stage between 
 the two. 
 
312 Test Bars 
 
 The foregoing results, we think, have been sufl5cient to show that in 
 each case, physical properties have been associated with this net-like 
 formation of the phosphorus, also that the graphite, when in the elongated 
 form, appears to split up phosphorus eutectic and prevent this formation, 
 as clearly shown in Fig. 83. The question of the tendency of the graphite 
 to take either an elongated or finely divided form, we think, is more a 
 question of the way in which the pig iron has been made than of its 
 subsequent treatment in the foundry. The statement of Mr. Pilkington 
 in this respect is very interesting: "Furnace men have always been 
 conversant with the fact that the temperature at which" pig iron leaves 
 the tapping hole of the furnace has a powerful effect on its physical 
 characteristics. The temperature of a large modern blast furnace is 
 very much higher and the metal, therefore, takes very much longer to 
 cool than that which leaves the tapping hole of the smaller furnaces. 
 
 Pig iron from the extreme types could be made practically in a 
 different manner altogether, and would show very different grades, grains 
 and degrees of hardness. 
 
 On referring again to the summary of tests taken with the A and B 
 series it will be seen that the results of the J-^-inch transverse bars of the 
 A series, which gave weak tensile results, are slightly higher than those 
 of the B series, and from this, together with the evidence of the chilled 
 and unchilled bars made from low grade iron, we are of the opinion that 
 no matter what their chemical compositions ma,y be, there is a rate of 
 cooUng which will give high physical properties; the structure of the 
 iron then being associated with the net-like formation of the phosphorus 
 eutectic and the cementite when present. 
 
 Tests reported to the International Association for Testing Materials 
 show: 
 
 -Circular bars showed greater bending and tensile strength than those 
 of rectangular section. 
 
 Test pieces taken from castings showed lower strength figures than bars 
 separately cast. 
 
 Extracts from Prof. Porter's Report 
 Prof. Porter's report contains so much information of value to the 
 foundryman, that extensive extracts are made from those parts relating 
 to the properties and mixtures offcast iron, notwithstanding they may 
 comprise much which has already been considered. 
 
 In treating of the different forms of iron as occurring at differ- 
 ent temperatures, they are designated as the "alpha," "beta" and 
 "gamma." 
 The "alpha" form in the ordinary iron as known in unhardened steel 
 
Chilled and Unchilled Bars 
 
 313 
 
 at ordinary temperatures, is one of the constituents of slowly cooled 
 gray pig iron, and is formed below 1140° F. 
 
 The "beta" form is that between 1440° F. and 1680° F.; it is harder 
 than the "gamma." Prof. Howe suggests its identity with martensite, 
 the chief constituent of hardened tool steels. It is non-magnetic and 
 differs from "alpha" iron in specific heat and density. 
 
 The "gamma" form is the stable one above 1680° F., is very hard, 
 non-magnetic, and differs in specific heat and density from both the 
 "alpha" and "beta." 
 
 It is held that the "gamma" and "beta" forms may be preserved at 
 ordinary temperatures by very rapid coohng, especially in the presence 
 of carbon which is supposed to retard the change from one form into 
 another. 
 
 Table I. — Forms of Combination or Iron and Carbon 
 
 Name 
 
 Synonyms 
 
 Physical characteristics 
 
 Graphite 
 
 
 
 
 size. No strength. 
 
 Kish 
 
 Free carbon . . - 
 
 Graphite in very large flakes. 
 
 Temper carbon 
 
 Free carbon 
 
 Graphite in form of very fine 
 
 
 
 powder. 
 
 Ferrite 
 
 Iron 
 
 Soft, very ductile, low strength. 
 
 Cementite 
 
 Combined carbon. Iron car- 
 
 Very hard and brittle, high static 
 
 
 bide, FeC. 
 
 strength, no ductility. 
 
 Austenite 
 
 Solution carbon in "gam»la" 
 
 Slightly softer than martensite. 
 
 
 iron. 
 
 Also weaker and more brittle. 
 
 Martensite 
 
 Solution carbon in "beta" 
 
 Hard, but less brittle than ce- 
 
 
 iron. Transition product 
 
 mentite. Chief constituent of 
 
 
 austenite to pearlite. 
 
 hardened tool steels. 
 
 Troostite 
 
 Transition product marten- 
 
 Softer than martensite, less 
 
 
 site to sorbite. 
 
 brittle and more ductile. 
 
 Sorbite 
 
 Transition product. Troost- 
 
 Softer than troostite and more 
 
 
 ite to pearlite. 
 
 ductile. Strongest form. 
 
 Pearlite 
 
 An intimate mechanical mix- 
 
 Very strong. Harder than fer- 
 
 
 ture of cementite and fer- 
 
 rite. 
 
 
 rite. 
 
 
 Prof. Porter classifies the more important physical properties of cast 
 iron as follows: 
 
 Static strength, indnding: Tensile strength; compressive strength; 
 transverse strength; torsional strength; shearing strength. 
 
 Dynamic strength, embracing: Resistance to repeated stress; resist- 
 ance to alternating stresses; resistance to shock. 
 
 Elastic properties, embracing: Elastic limit; resilience or elasticity; 
 rigidity; toughness; malleability. 
 
314 Test Bars 
 
 Hardness, embracing: Hardness of mass; ability to chill; hardness 
 of chill. 
 
 Grain structure, including: Fracture or grain size; porosity; specific 
 gravity. 
 
 Shrinkage, embracing: Shrinkage of the hquid mass; shrinkage of the 
 sohd mass; stretch. 
 
 Fluid properties, embracing: Fusibility; fluidity. 
 
 Resistance to heat, embracing: Resistance to continued heat; resist- 
 ance to alternate heating and cooling; resistance to very low temperatures. 
 
 Electrical properties, including: Electrical conductivity; magnetic 
 permeability; hysteresis. 
 
 Miscellaneous properties, including: Resistance to various corrosive 
 agencies; resistance to wear; coefficient of friction. 
 
 Properties of the mass: Soundness, or freedom from blow-holes and 
 shrinkage cavities; cleanness, or freedom from inclusions of dross, etc.; 
 freedom from pin-holes and porous places; homogeneity, or lack of 
 segregation; crystallization; freedom from shrinkage strains; tendency 
 to peel off sand and scale. 
 
CHAPTER XIII 
 CHEMICAL ANALYSES 
 
 Strength 
 
 As regards chemical composition there are nine factors which influence 
 strength of cast iron: (i) Per cent graphite; (2) size of individual graphite 
 flakes; (3) per cent combined carbon; (4) size of primary crystals of 
 solid solution Fe-C-Si; (5) amount of dissolved oxide; (6) per cent 
 phosphorus; (7) per cent sulphur; (8) per cent silicon; (9) per cent 
 manganese. 
 
 1. "Per cent graphite. — The weakening effect of graphite is due to 
 its own extreme softness and weakness, and to the fact that it occurs 
 in small flakes or plates and hence affords a multitude of cleavage planes 
 through the metal. The size of the graphite particles is evidently 
 important as well as the amount but this factor will be discussed under 
 another head. 
 
 Theoretically^ the simplest method of decreasing graphite is to lower 
 the silicon, each decrease on i per cent in silicon lessening the graphite 
 by 0.4s per cent, provided the total carbon remains the same. Practi- 
 cally, however, the fact that all the carbon not graphite becomes combined 
 is an important objection, for when we lower the silicon too much the 
 resulting increase in combined carbon increases the hardness and, beyond 
 a certain point, decreases the strength. The minimum permissible 
 silicon will depend chiefly on the hardness allowable, 
 
 The same objection applies to decreasing the graphite by increas- 
 ing the sulphur and manganese, and in the case of sulphur there is 
 also the objection that its direct effects are injurious. The rate of 
 cooling is, of course, beyond the control of the foundryman in the 
 majority of cases, while even if it were not, the graphite could not 
 be reduced by rapid cooHng without a corresponding increase in com- 
 bined carbon. 
 
 Coming finally to the total carbon, we find here a means of reducing 
 graphite without in any way affecting carbon, and hence, hardness. 
 The only hmitation to this is that as total carbon and graphite are 
 reduced, shrinkage is increased and the metal becomes more liable to 
 oxidation, blow-holes and other defects. 
 
 315 
 
3i6 Chemical Analyses 
 
 There are three ways of reducing total carbon in castings; first, by 
 the use of low carbon pig iron; second, by melting in the air furnace; 
 third, by the use of steel scrap in the cupola mixture. 
 
 In air furnace melting it is easy to reduce total carbon to almost any 
 figure within reason. 2.75 per cent is commonly obtained in melting for 
 malleable castings. Of course the silicon is also burnt out during this 
 process, but were it desired, this could be readily replaced by suitable 
 additions of ferrosilicon. From the standpoint of quality the air 
 furnace is certainly the ideal method of melting, and hence, we find that 
 many lines of castings which must be of particularly high quality are 
 invariably made from air furnace metal. 
 
 The addition of steel scrap to the cupola has now become common 
 practice, the product obtained being known as semi-steel and differing 
 chemically from ordinary cast iron only in being somewhat lower in 
 total carbon and graphite. Physically the metal so made is characterized 
 by greater strength and total shrinkage, hardness remaining about the 
 same. ..." 
 
 The chief points to be watched in melting steel scrap in the cupola 
 mixture are as follows: 
 
 " Trouble with blow-holes. — This is due to the fact that semi-steel being 
 lower in carbon oxidizes more readily than cast iron. The trouble may 
 usually be overcome by correct cupola practice and the use of ferro- 
 manganese or other deoxidizers in the ladle. Owing to the higher 
 melting point of semi-steel mixtures, ferromanganese is much more 
 efficient as a deoxidizer here than in the case of cast iron. . . . 
 
 High shrinkage. — This is due to the decrease in graphite and is 
 hence inevitable. On work where this is an important factor a proper 
 balance must be struck between shrinkage and strength. . . . 
 
 Imperfect mixture of steel and iron resulting in irregular quality of 
 casting, hard spots, etc. — This results from the higher melting point of 
 steel and consequent difficulty of getting perfect solution in the cast 
 iron. It may be largely overcome by careful attention to the charging 
 of the cupola, placing the steel scrap on the coke and the iron on top of 
 the steel (so that the steel will reach the melting zone first and the molten 
 pig will run down over the heated steel instead of away from it as would 
 happen if the order were reversed). A large receiving ladle should, of 
 course, be used also. Another point to be observed is in regard to the 
 size of the steel scrap. Too large scrap is difficult to melt, but, on the 
 other hand, very small scrap is also objectionable as being an abundant 
 source of hard spots in the castings. Apparently very small pieces of 
 steel are Uable to be washed down through the coke bed and out of the 
 cupola spout without being completely melted. 
 
Strength 317 
 
 Regarding the amount of steel scrap to use, it has been found by trial 
 that the best results are obtainable with about 25 per cent. Increase to 
 S3H per cent caused a slight falling ofif in strength. Probably these 
 figures would not hold for every condition of practice, but, in general, 
 20 to 30 per cent steel is a suflQcient amount to give the maximum 
 results. 
 
 2. Size of graphite flakes. — The size of the graphite flakes is prob- 
 ably the most important factor of all those which influence strength, and 
 is the one which most frequently upsets our calculations as to the rela- 
 tion between chemical composition and strength. . . . Recently, how- 
 ever, Messrs. F. J. Cook and G. Hailstone have brought out in a striking 
 manner the great difference in irons in this respect. They give data 
 showing that of two mixtures practically identical in composition the 
 one was invariably much lower in strength (usually about one-half) 
 than the other, this being the case for a great many heats extending over 
 a long period of time." 
 
 Analyses and tests are given as typical of the series. 
 
 "Messrs. Cook and Hailstone have investigated and compared the 
 micro-structure of the strong and weak bars and record two interesting 
 facts: First, that the graphite flakes are invariably much larger in the 
 weak bars; second, that when the polished specimens are treated so as 
 to bring out the phosphide eutectic this eutectic is seen to be arranged 
 in the customary heterogeneous mamner in the weak bars but in a dis- 
 tinct meshwork structure in the strong iron. 
 
 These authors draw the conclusion that it is this meshwork structure 
 which gives great strength to cast iron, but with this conclusion the 
 writer cannot entirely agree. It seems more probable that the increase 
 in strength is caused by the fine state of division of the graphite and that 
 the same influences which have caused this have also caused the meshwork 
 structure. 
 
 We may get some idea of the quantitative relationship between 
 strength and size of graphite by considering the relative strength of 
 malleable cast iron and a very open gray cast iron representing the 
 smallest and largest graphite respectively. Malleable cast iron has a 
 tensile strength of 40,000 pounds and upwards per square inch; open 
 gray iron about 20,000 pounds per square inch. Apparently, then, the 
 increase in the size of the graphite has caused a loss of at least 20,000 
 pounds in tensile strength. 
 
 It is one thing to find that to get strong iron we must have the 
 graphite in finely divided state and another and much more difficult 
 matter to formulate rules whereby we may secure this desired 
 condition. . . .' 
 
3i8 Chemical Analyses 
 
 The factors which influence the size of the graphite flakes in cast 
 iron are as follows : 
 
 A. Factors which certainly exert an influence. 
 
 a. Rate of cooling. 
 
 b. Pouring temperature. 
 
 B. Factors which may possibly exert an influence. 
 
 c. Time which iron has remained in the molten state, 
 
 d. Presence of dissolved oxide. ' - 
 
 e. Presence of steel scrap in the mixture. 
 /. Mixture of different brands. 
 
 g. Nature of ore from which iron is made and treatment in the 
 
 blast furnace. 
 h. Per cent metalloids. 
 
 a. The influence of rate of cooling is undoubted, and an example 
 showing its effect on strength and fitructure is given by Cook and Hail- 
 stone. We have to distinguish here, however, between the rates of 
 cooHng through different ranges of temperature. Evidently the graphite 
 which is separated within the semi-hquid iron will have a much better 
 chance to grow large crystals owing to the greater mobihty of the medium 
 in which it is formed, while that graphite formed within the soUd metal 
 will necessarily be in small particles. Hence, we see that it is the rate 
 of cooling through the soHdificatioti range 2200° to 2000° F., which is 
 of prime importance, and if we can check the formation of graphite 
 through this range and then allow it to form in the solid metal at lower 
 temperatures we will have all the conditions for both the soft and strong 
 iron. This is the principle of Custer's process of casting in permanent 
 moulds and the making of malleable castings is based on the same theory." 
 
 b. The pouring temperature also undoubtedly exerts an influence 
 on the size of the graphite flakes, and hence, on the strength. ..." 
 
 Longmuir finds that iron poured at a medium temperature is stronger 
 than when poured either very hot or very cold. Longmuir' s experi- 
 ments, by the way, are the only ones in which a pyrometer was used and 
 the temperatures of pouring measured in degrees. . . . For this 
 reason we may place the greatest faith in Longmuir's results. 
 
 It is probable that the pouring temperature affects the size of the 
 graphite flakes indirectly through changing the rate of cooling through 
 the solidification range. On this assumption the best results should be 
 obtained from metal poured at as low a temperature as will suffice to 
 give sound castings. 
 
 c. Time which iron has remained in the molten state. This might 
 conceivably have an effect in the case of cast iron high in total carbon, 
 
Strength 319 
 
 since graphite separating in the hquid metal would remain in the metal 
 if poured at once, and this graphite is in the form of large flakes known 
 as kish. 
 
 d. Presence of dissolved oxide. — There is no direct proof that this 
 affects the size of the graphite flakes. However, it is well known that 
 addition of deoxidizing agents almost invariably improves the strength 
 and it is barely possible that a portion of this may be due to change in 
 the size of the graphite. 
 
 e. Presence of steel scrap in the mixture. — Although no exact data 
 are at hand it is the common impression that the addition of steel scrap 
 'closes the grain,' which is equivalent to saying that it reduces the size 
 of the graphite. . . . 
 
 /. Mixture of irons. — It is firmly believed by many foundrymen 
 of the old school that a mixture of brands gives better results than a 
 single brand of the same chemical composition as the average of the 
 mixture. ... 
 
 g. Cook and Hailstone believe that the difference in strength of the 
 two mixtures quoted by them is due to some inherent quality of the pig 
 iron derived from the ores used or their nianner of treatment in the blast 
 furnace. This inherent quahty may have some connection with the 
 presence of oxygen or nitrogen in the metal. . . ." 
 
 h. Per cent metalloids. — This, we know, has a certain effect. For 
 example, high silicon is likely to cause larger graphite as well as more 
 of it. Phosphorus should, theoretically, cause larger graphite since it 
 prolongs the solidification period in which large flakes are free to separate. 
 . . . Sulphur and manganese . . . close the grain, and probably 
 diminish the size of the graphite, as well as its amount. 
 
 3. Per cent combined carbon. — According to Professor Howe the 
 properties of cast iron are the properties of the metallic matrix modified 
 by the presence of the graphite, but since this metallic matrix may be 
 considered as a steel of carbon content equal to the combined carbon of 
 the cast iron, we can predict accurately the effects of combined carbon 
 by the use of the data on steel. 
 
 In the case of steel it is found that the strength increases regularly 
 with the carbon up to about 0.9 per cent, then remains nearly stationary 
 up to about 1.2 per cent, above which it falls off slowly. 
 
 In the case of cast iron the strength is dependent upon so many 
 factors besides combined carbon that it is almost impossible to determine 
 by direct experiment the percentage of combined carbon giving the 
 maximum strength. All indications, however, are that the highest 
 strength is obtained with somewhere between 0.7 per cent and i per cent 
 combined carbon which is in sufficiently close accord with the corre- 
 
320 Chemical Analyses 
 
 spending value for steel. We may, therefore, state tentatively that the 
 maximum strength is obtained with 0.9 per cent carbon, all other factors 
 remaining constant. 
 
 This appb'es only to tensile strength (and approximately to transverse). 
 For compressive strength a somewhat higher value, probably about 1.5 
 per cent combined carbon, would be found to give better results. 
 
 4. Size of primary crystals of solid solution Fe-C-Si. — There is 
 absolutely no data as to the effect of this factor on the strength of cast 
 iron and it is only from analogy with steel that we give it a place in the 
 list of actors influencing strength. ..." 
 
 5. Effect of dissolved oxide. — . . . It is probably a much more 
 important factor than is generally supposed, but there is absolutely no 
 data on which to base a quantitative estimate of its effect." 
 
 To reduce oxide in cast iron to the minimum, the following points 
 may be observed : 
 
 First, get the best brands of pig iron. It is probable that pig made 
 with charcoal fuel contains less oxygen than that made with coke fuel. 
 Cold blast pig is better than hot blast. Pig iron made from easily 
 reducible brown or carbonate ores is lower in oxygen than the pig made 
 from red hematite or magnetic ores, while iron made from mill cinder 
 should never he used in foundries where strength is a prime consideration. 
 Moreover, a pig iron high in manganese is apt to be comparatively free 
 from oxide because of the deoxidizing power of manganese at the high 
 temperature of the blast furnace. It is noteworthy as confirming these 
 observations that most brands of iron which have achieved a reputation 
 for strength are high in manganese and many of them are charcoal irons. 
 The Muirkirk and Salisbury brands which have been known for years 
 as among the strongest irons made in this coimtry answer to every 
 one of these conditions. They are made from readily reducible ores 
 using cold blast and charcoal fuel and contain from i to 2 per cent 
 manganese." 
 
 Second, avoid oxidizing conditions in the cupola, particularly high- 
 blast pressures and wrong methods of charging. Dr. Moldenke's 
 system of using small charges is to be highly recommended in this 
 connection." 
 
 Third, deoxidizing agents may be used, added either to the cupola 
 or to the metal in the ladle. Of the commercially available deoxidizers, 
 ferrotitanium, ferrosihcon and ferromanganese are, perhaps, the most 
 successful, all things considered. Titanium thermite is also extremely 
 valuable in this connection. . . . " 
 
 6. Per cent phosphorus. — Phosphorus lessens both the dynamic and 
 static strength, but the former more than the latter. It weakens be- 
 
' Strength 321 
 
 cause it forms with iron a hard and brittle compound which has but 
 little resistance to shock. The weakness produced is in nearly direct 
 proportion to the amount of this compound present. The effects of 
 phosphorus on strength do not become marked until upward of i per 
 cent is present, but for great strength and particularly strength to shock 
 it should be much lower. Ordinary strong irons may have up to 0.75 
 per cent, while iron which is to withstand shock should not exceed 0.50 
 per cent and is better even lower. . . ." 
 
 7. Per cent sulphur. — The action of sulphur in decreasing the strength 
 of iron is explained in Chap. IX, page 261, and it is also explained 
 there why it is so much less harmful in the presence of manganese. 
 Many tests have been made showing that sulphur has no marked effect 
 on strength and many foundrymen will use sulphur to harden iron and 
 close the grain. It is true that an indirect strengthening effect can be 
 obtained through the use of sulphur in some cases, i.e., if too soft an 
 iron is being used the strength will be increased by the addition of any 
 element which will lessen the graphite, but the hardening is usually better 
 obtained through decrease in silicon than through increase in sulphur. 
 While increased sulphur may not always show in decreased strength of 
 test bars, yet it is a frequent source of blow-holes, dirty iron and various 
 defects caused by high shrinkage, hence, it often causes an indirect 
 weakness in the iron. 
 
 8-9. Per cent silicon and manganese. — These elements act chiefly in 
 an indirect manner and because of their effects on the condition of the 
 carbon; their direct influence in the strength of the metallic matrix is 
 unimportant. From analogy with steel it is probable that sihcon in 
 amounts of over i per cent causes weakness and brittleness in the metal. 
 Similarly, manganese has probably a weakening effect due to its direct 
 action when present in amounts of more than 1.5 per cent. 
 
 The preceding discussion is summarized in the following practical 
 rules for making strong castings: 
 
 Use strong brands of iron. . . . Charcoal irons if cost wiU permit; 
 
 irons made from easily reducible ores; irons high in manganese. 
 Avoid oxidation in melting. Look carefully after the details of 
 
 cupola practice; avoid oxidized scrap; use deoxidizing agents in 
 
 ladle if practicable. . . . 
 Keep the silicon down as low as possible and still have the necessary 
 
 softness. About 1.50 per cent will be right for the ordinary run 
 
 of medium castings; higher for small castings and lower for 
 
 heavy ones. With low total carbon high sihcon has less effect. 
 Keep the phosphorus low, especially when sulphur is high. 0.50 
 
 per cent or under is best. 
 
322 Chemical Analyses 
 
 Keep the sulphur low, especially if phosphorus is high. Under 
 
 o.io per cent is all right for most castings." 
 Keep manganese high, i per cent for large castings, 0.7 per cent 
 
 for medium, 0.5 per cent for small castings. 
 Use from 10 to 25 per cent steel scrap in the mixture. 
 Me. Keep recommends using 10 per cent cast iron borings charged 
 
 in wooden boxes. He states that this is very effective in closing 
 
 the grain and strengthening the castings. 
 
 For iron which is required to have the greatest possible resistance 
 to shock, the points to be especially observed are as follows: 
 
 Keep the phosphorus as low as practicable, still having the necessary 
 fluidity. It should best be below 0.30 per cent. 
 
 Keep the sulphur as low as possible. 
 
 If practicable add vanadium or titanium to the ladle either in the 
 form of ferroalloy or as thermite. ... 
 
 Elastic Properties 
 
 Of the elastic properties of metals, only toughness and its opposite, 
 brittleness, and elasticity and its opposite, rigidity, are ordinarily con- 
 sidered in cast iron. 
 
 Toughness is defined as resistance to breaking after the elastic limit 
 is passed. 
 
 Elasticity is the amount of yield under any stress up to the elastic limit. 
 
 It is unusual for these properties to be determined separately in cast 
 iron, but their sum is given by the deflection which is determined in 
 transverse testing. It is probably true that they nearly always vary- 
 together, and, hence, that deflection is a fairly good measure of either 
 one as well as both. 
 
 Toughness is practically always a desirable quality in cast iron, but 
 the same is not true of elasticity since in many machines great rigidity 
 is a prime requisite. 
 
 The factors influencing toughness and elasticity are about the same 
 as those influencing strength, i.e., the chemical composition, presence of 
 oxide and size of graphite. ... In general, to get a tough elastic 
 iron we should keep sulphur, phosphorus and combined carbon low; 
 manganese, no higher than is necessary to take care of the sulphur; 
 graphite and silicon, the less the better, providing that the combined 
 carbon is not increased; and finally, use metal of good quahty, melted 
 carefully so as to be free from oxide. 
 
 In ordinary gray iron castings it is not practicable to attempt to 
 control the graphite, since the combined carbon needs first attention and 
 
Elastic Properties 
 
 323 
 
 the graphite will necessarily be the difference between total carbon and 
 combined carbon. The silicon also must be adjusted with a view to 
 regulating the combined carbon. Practical rules for getting the maxi- 
 mum toughness and elasticity will then be about as follows: 
 
 Sihcon, 1.5 to 2.0 per cent for castings of average thickness, more or 
 less for very Hght and very heavy castings respectively. 
 
 Sulphur as low as practicable, best under 0.08 per cent. 
 
 Phosphorus as low as practicable considering the necessity for 
 fluidity. Best under 0.50 per cent. 
 
 Manganese from three to five times the sulphur. 
 
 Use good irons and good cupola practice to insure freedom from 
 dissolved oxide. . . . 
 
 "In case steel scrap can be used, i.e., semi-steel made, the toughness 
 may be considerably increased through decrease in the amount of graphite 
 and in the size of the grain. The other elements may remain about as 
 before except that it may be necessary to run the manganese a Uttle 
 higher to counteract the greater tendency of the semi-steel to become 
 oxidized. 
 
 As previously noted, rigidity is desirable in some cases. This is the 
 converse of elasticity and may be obtained by the direct opposite of the 
 rules given for obtaining elasticity. However, to get rigidity with the 
 least sacrifice of strength and toughness it is desirable to use manganese 
 and combined carbon rather -than to increase phosphorus and sulphur. 
 That is, we would lower silicon as much as necessity for softness will 
 allow and raise manganese to about i per cent (or less in very light work). 
 It should be noted that manganese is particularly efficient in increasing 
 rigidity since it accomplishes this end with comparatively little sacrifice 
 of strength and toughness. 
 
 A few examples of very tough and elastic iron are as follows: 
 
 No. 
 
 Silicon 
 
 Sulphur 
 
 Phos- 
 phorus 
 
 Manga- 
 nese 
 
 Com- 
 bined 
 carbon 
 
 Graphite 
 carbon 
 
 Total 
 carbon 
 
 I 
 
 2.5c^2.75 
 
 .80 
 
 2.45 
 
 1. 18 
 
 2.36 
 
 
 050 
 
 
 30 
 
 .43 
 .30 
 
 .24 
 
 .87 
 1,08 
 
 2.34 
 2.15 
 
 3.21 
 
 3 
 
 4 
 5 
 
 
 092 
 084 
 064 
 
 
 063 
 
 27 
 
 33 
 
 3.23 
 
 No. I represents iron which in thin sections can be punched and bent. 
 No. 2 is an analysis of a gray cast iron which is exceedingly malleable. 
 Nos. 3, 4 and 5 are gray irons sho^Adng deflections for the transverse test 
 bars rather higher than usual. 
 
324 Chemical Analyses 
 
 Hardness 
 
 ... It is generally stated that hardness in cast iron is due chiefly 
 to the presence of combined carbon and is only indirectly or to a less 
 extent caused by other elements. The writer believes that this is not 
 altogether true and that there is another factor causing hardness which 
 has not heretofore been generally considered in the case of cast iron." 
 
 It is well known that when steel is hardened by quenching from a 
 temperature above its critical point its carbon is not in the combined 
 state but rather in a form known as hardening or solution carbon, while 
 the iron is retained in the ' gamma ' allotropic form. It is the behef of 
 the present writer that the same is true of cast iron and that many cases 
 of hardness are to be explained in this way. For example, Keep de- 
 scribes a sample of cast iron which was too hard to drill and yet contained 
 only 0.60 per cent combined carbon, and many analyses are on record 
 of irons which have been quenched from comparatively low temperatures 
 and are almost glass hard in spite of the fact that the combined carbons 
 are under i per cent. I think it probable that the hardness of high 
 manganese irons is due chiefly to this same cause since manganese is 
 known to favor the retention of ' gamma ' iron. 
 
 Granting for the present the truth of this theory, the presence of the 
 'gamma' or hard form of iron is controlled by the rate of cooHng and the 
 percentages of metalloids present; so that for aU practical purposes we 
 can say that there are six factors which influence hardness, i.e., the rate 
 and manner of cooling, the combined carbon, silicon, sulphur, man- 
 ganese and phosphorus. The first two of these are of the greatest 
 importance and we will then take up in reverse order, leaving the most 
 important till the last. 
 
 Phosphorus has a shght hardening effect in large quantities but in 
 amoxmts less than i per cent its effects are nearly imperceptible, and it 
 does not become important until the amount exceeds commercial Hmits, 
 or, say, 1.5 per cent. We may, therefore, usually neglect the effects of 
 phosphorus in considering hardness. 
 
 Manganese, although usually regarded as a hardening agent may 
 sometimes soften iron. This anomalous resiilt is explained by the action 
 of manganese on sulphur. If the iron is high in sulphur and low in 
 manganese the first additions of manganese will unite with the sulphur 
 forming the comparatively inert manganese sulphide and thus softening 
 the iron. If, however, the manganese be increased beyond the amount 
 necessary to care for the sulphur, increased hardness will result. 
 
 ... A pig iron containing 3 per cent manganese may have a 
 beautiful open gray fracture and yet be so hard as to be drilled pnly 
 
Hardness 325 
 
 with great difficulty. In addition, the presence of manganese sometimes 
 produces a peculiar kind of gritty hardness, the iron acting as if contain- 
 ing small hard grains. With regard to the amount of manganese re- 
 quired to produce hardness it will be evident that this depends largely 
 on the per cent of sulphur present and also on the rate of cooHng. In 
 general, heavy castings will stand up to i per cent of manganese without 
 noticeable increase of hardness, medium castings about 0.75 per cent 
 and Ught castings 0.50 per cent. 
 
 Sulphur is an exceedingly energetic hardening agent acting, however, 
 chiefly through the carbon. That is, sulphur has a strong tendency to 
 
 keep the carbon in combined form and in that way to harden 
 
 Each o.oi per cent sulphur will increase the combined carbon by about 
 0.045 PSJ" cent, other things being equal. It must be remembered, how- 
 ever, that this applies only to sulphur in the form of iron sulphide, and 
 that in the form of manganese sulphide, i.e., in the presence of about 
 three times its weight of manganese, it acts much less energetically. 
 
 Sulphur also has a direct action in hardening, iron sulphide and 
 manganese sulphide being quite hard substances. Usually this action 
 is imperceptible, but occasionally one meets with hard spots which are 
 due to the segregation of these sulphides. 
 
 SiHcon is generally known as a softening agent and, within reasonable 
 limits, has this effect due to its action in decreasing the combined carbon. 
 The direct effect of silicon, however, is to harden since it forms with iron 
 a compound which is harder than the iron itself. 
 
 When silicon is added to cast iron its first effect, as before stated, is 
 to decrease the combined carbon. This, it does, at the rate of about 
 0.45 per cent for each per cent of silicon added. Actually the rate of 
 decrease is more rapid than this, and, in consequence, by the time we 
 have from 2 to 3 per cent silicon present (depending on the rate of cooHng) 
 we have practically all the combined carbon precipitated out as graphite 
 and, hence, there is no further possibihty of softening in this way. Now; 
 any increase in silicon only increases the amount of the hard iron-silicon 
 alloy, there is no more combined carbon to be decreased, and, hence, the 
 hardness will now be increased again. In other words, it is possible to 
 have too much of a good thing, the good thing in this case being silicon. 
 
 The actual percentage of sihcon which is necessary to secure any 
 given degree of softness will depend upon the size of the casting, the 
 nature of the mold and the amount of sulphur and manganese present. 
 It is, therefore, impossible to give definite silicon standards unless each 
 of these factors is known. . . . 
 
 Combined carbon (or solution carbon) is the chief hardening agent 
 of cast iron, and, under ordinary conditions, the hardness of the metal 
 
326 Chemical Analyses 
 
 will be closely proportional to the percentage present. Of such relative 
 unimportance are the effects of the other elements that it has been found 
 practicable to use the amount of combined carbon as a measure of the 
 hardness of castings and as a means of predicting their behavior in the 
 machine shop. ... 
 
 "To machine easily, cast iron should not contain over 0.75 per cent 
 combined carbon, i.oo per cent combined carbon gives a pretty hard 
 casting and 1.50 per cent is about the upper Hmit for iron to be machined. 
 
 The rate and manner of cooling of the casting are usually supposed 
 to influence its hardness only as it affects the percentage of combined 
 carbon. That it does affect the amount of combined carbon is a well- 
 estabHshed fact. . . . However, we sometimes get hardness in the 
 absence of any considerable amount of combined carbon. Hence, there 
 must be some other factor at work, which, in the writer's opinion, is a 
 solution of carbon in 'gamma' iron, the hard constituent of tool steel. 
 
 According to this theory, combined carbon disappears in the tem- 
 perature range 2200° F. to 1500° F., while 'gamma' or hard iron is not 
 transformed into the ' alpha ' or soft variety until the casting has cooled 
 to about 1300° F. Evidently, then, ordinary rapid cooling of castings 
 from the melted state results in both high combined carbon and high 
 'gamma' ;ron, and hence we have hardness due to both of these causes. 
 The more rapid the cooling, the higher the combined carbon and the 
 higher also the 'gamma' iron, therefore, since both vary together, the 
 percentage of combined carbon is a satisfactory measure of the hardness 
 produced by both factors. 
 
 "If, now, the conditions of cooling are changed, this need no longer 
 be the case. For example, suppose we cool the casting slowly from the 
 molten state down to 1600° and then quench it in water. In this case 
 we would get nearly all combined carbon changed to graphite diuring the 
 slow cooling through the upper range, while the rapid cooling through 
 1300° preserves the ' gamma ' iron solution and hence gives hardness due 
 to this cause. 
 
 Some of the peculiar things noted in connection with Custer's process 
 of casting in permanent moulds are to be explained on this basis. Also, 
 the much greater softness of castings which have been allowed to cool 
 in sand and thereby anneal themselves over those shaken out soon after 
 being poured. 
 
 " Chilled iron is simply white iron, that is, iron in which graphite is 
 absent and the carbon all in the combined or solution state. The same 
 iron may be both gray and white, depending on rate of coohng and hence 
 the exterior of the casting, if rapidly cooled, may be white while the 
 interior which cools more slowly remains gray. Usually there is an 
 
Hardness 
 
 327 
 
 intermediate zone having a mottled structure formed through the inter- 
 lacing and the gradual merging of the gray and white. A chiUing iron, 
 then, is one which when rapidly cooled contains all of its carbon in the 
 combined state. The factors which influence the depth and quahty 
 of chill are the temperature at which the iron is poured, and the amounts 
 of silicon, sulphur and phosphorus, manganese and total carbon, besides 
 some of the elements which are not normally present in cast iron, but 
 which are occasionally added. 
 
 The higher the temperature at which iron is poured the deeper the 
 chill, other things being equal, and it is usually considered advisable to 
 pour chilled castings from hot iron. The quantitative effects of pouring 
 temperature have been studied by Adamson, and while there are some 
 conflicting results, it is in general indicated that in the case of the strongly 
 chilling irons an increase of 50° in the pouring temperature causes an 
 increase of from H to J4 inch in the depth of the chiU. 
 
 The most important element in its effects on chill is silicon, which has 
 the strongest action in precipitating graphite. For chilling iron, silicon 
 should be low, but how low depends on the thickness of the casting, the 
 temperature of pouring and the depth of chill desired as well as on the 
 percentage of other elements in the iron. Table I gives a very approx- 
 imate relationship between the percentage of silicon and depth of chill, 
 other elements bei^ about normal. 
 
 Table I. 
 
 Approximate Relation Between Per Cent 
 Silicon and Depth of Chill 
 
 Silicon, 
 per cent 
 
 Depth of 
 chill, 
 inch 
 
 Silicon, 
 per cent 
 
 Depth of 
 
 ^ chill, 
 
 inch 
 
 I. SO 
 1.25 
 1. 00 
 
 Me 
 
 3/16 
 
 .75 
 .50 
 .40 
 
 ■ 
 
 H 
 H 
 
 I 
 
 Sulphur ^tends to increase the combined carbon, and, hence, the chill. 
 So marked is its influence in this respect that it is sometimes added 
 to cast iron to increase the depth of the chill. This,' however, is not 
 usually good practice since the chill imparted by sulphur is lacking in 
 toughness and strength as well as in resistance to heat strains. Scott 
 cites the case of stamp shoes for mining machinery where sulphur was 
 used to increase the chill. The shoes were very hard at first, but soon 
 went to pieces under the repeated blows. Johnson, also, has noted the 
 great difference between high and low sulphur chilled iron as regards 
 
328 Chemical Analyses 
 
 ability to withstand the strains of sudden cooling without cracking. On 
 the other hand, West states that the chill produced by sulphur is very 
 persistent to frictional wear, and, hence, it may be inferred that sulphur 
 adds to the life of castings which are subject to abrasion. It has been 
 stated that the presence of a small amount of sulphur is essential in order 
 to get the best results in chilled rolls. This, however, is doubtful and 
 it is believed that it is only rarely that sulphur is desirable in chilled 
 castings. The presence of a moderate amount of manganese in cast 
 iron greatly lessens the bad effects of sulphur in chilled as well as in gray 
 iron castings. 
 
 "Phosphorus in the amounts ordinarily present in commercial cast 
 iron has but slight influence on the depth of the chill but does have a 
 more or less injurious effect on its strength. It is generally stated that 
 high phosphorus has the effect of causing a sharp hne of demarkation 
 between the gray and chilled portions of the casting. . . . It is believed 
 that it is best to limit the phosphorus in chilled iron to about 0.4 per cent. 
 
 Manganese, since it tends to increase the combined carbon, also tends 
 to increase the chill; However, it must be remembered that the first 
 effect of manganese is to neutralize sulphur, and, therefore, in small 
 amounts it may indirectly decrease the chill. Manganese very greatly 
 increases the hardness of the chill, and, to a less extent, its strength. It 
 also increases the resistance of the chill to heat stjjain and whence di- 
 minishes the danger of surface cracks in such castings as chilled rolls and 
 car wheels. Still another effect is the promotion of a more gradual 
 merging of the gray and chilled portions of the castings. Manganese 
 is usually considered a desirable constituent of chilled iron and the 
 amounts used vary all the way from 0.40 up to 3.0 per cent. . . . 
 
 Of late years, semi-steel mixtures have been used to some extent for 
 chilled castings, the total carbon being considerably lower than in the 
 ordinary mixture. The effect of low total carbon is to give a deep and 
 comparatively soft chill as compared with the shallow, hard chill obtained 
 with high total carbon. 
 
 "It has been proposed to use nickel as a means of controlling chill, 
 this element having an effect somewhat similar to silicon. Hence, by 
 starting with a strong chilhng iron and adding nickel, the depth of the 
 chill would be lessened in some ratio to the amount of nickel added. 
 Since the same results may be obtained by the use of less expensive 
 sihcon it is difficult to see any advantage in adding nickel. 
 
 The quality of chilled iron may be very greatly improved by the 
 addition of small amounts of titanium or vanadium. The beneficial 
 effects of these elements are probably due chiefly to their deoxidizing 
 power. . . . 
 
Shrinkage 329 
 
 Grain Structure 
 
 "The fracture or grain size and the porosity are closely related and 
 are both dependent primarily on the size of the graphite particles, and, 
 to a less extent, on the percentage of graphite. ... 
 
 Silicon should be kept jvist as low as possible and still have the cast- 
 ings soft enough to machine. The exact percentage will depend on 
 the thickness of the casting, the character of the mould and whether 
 the casting is allowed to anneal itself or is quickly shaken out after 
 pouring. It may range from 0.75 per cent for very heavy work up to 
 2.0 per cent for small valves, etc. It is believed that the majority of 
 founders use more sihcon than is best in work of this character." 
 
 Combined carbon has a powerful action in closing the grain and giving 
 a dense iron and should be just as high as possible and still have the 
 iron machinable. . . . 
 
 Manganese had best be kept moderately high since it appears to have 
 some beneficial effect in closing the grain. 
 
 Sulphur is a powerful agent in closing the grain and is frequently 
 made purposely high for this end. It is, however, a dangerous agent 
 since it may cause trouble in other directions, and as a general proposi- 
 tion it is better to keep the sulphur low and get necessary density by a 
 proper regulation of sihcon and manganese. 
 
 Finally, one of the best, if not the best, means of closing the grain 
 of cast iron and seciuring the maximum density is by means of steel scrap 
 in the mixture. This is now common practice with makers of hydrauhc 
 castings, and is very effective. ... 
 
 Shrinkage 
 
 In considering the shrinkage of cast iron it is necessary to distinguish 
 between the contraction of the fluid mass previous to and during the act 
 of sohdifying and the contraction of the solid mass. The first is that 
 form of shrinkage which necessitates feeding in heavy castings, and which 
 so often results in shrink holes or spongy places in heavy sections of 
 castings which are not fed. West calls this contraction of the fluid mass 
 * shrinkage. ' 
 
 "The contraction of the solid mass represents more nearly what is 
 generally called shrinkage, this term as ordinarily used meaning the 
 difference in size between the casting and its pattern. This contraction 
 of the solid mass West calls ' contraction. ' 
 
 "... It seems necessary to make some distinction between the 
 total amount of fluid contraction and the tendency to form shrink holes 
 in the heavy sections of small castings. At least there seems to be no 
 
33^ Chemical Analyses 
 
 very definite relation between chemical composition and this latter 
 property and it is often the case that an iron low in graphite and, there- 
 fore, having a high fluid contraction, will give sounder castings than 
 another iron high in graphite and which would, therefore, require less 
 feeding in a large casting. . . . " 
 
 "Cook has found that two irons of practically identical chemical 
 composition may give very different results as regards soundness when 
 poured into small castings of heavy section and the writer can confirm 
 this fact from his own experience. A convenient test has been developed 
 by Cook to show the tendency of any particular brand of iron to trouble 
 of this sort. This test consists in making a casting in the shape of a K, 
 the branches having a cross section of one inch square. On breaking 
 off the oblique branches any tendency to sponginess or shrink holes will 
 at once be evident in the fracture." 
 
 "As before stated there has thus far been discovered no important 
 relationship between this property and chemical composition. It rather 
 appears to be something inherent in the brand of iron. . . . It is a 
 curious fact that, in some instances at least, the addition of a small 
 amoimt of steel scrap to the mixture will act as a partial corrective." 
 
 "The contraction of the sohd mass does not take place uniformly as 
 the casting cools but in stages which are separated by periods of less 
 contraction or even of actual expansion. The total shrinkage which 
 perhaps includes also a portion of the shrinkage in the fluid mass is 
 conveniently obtained by Keep's test or by casting a test bar between 
 iron yokes and determining the space between the end of the bar and the 
 yoke after cooling." 
 
 "This, however, tells nothing as to the manner of shrinkage or the 
 temperatiu-e at which it takes place. To get this latter information we 
 must determine the shrinkage curve, or in other words, the length of the 
 test bar at each instant of time during cooling, starting from the instant 
 when the bar has solidified just enough to have some slight strength. 
 West, Keep and Turner have described forms of apparatus for making 
 these curves. Fig. 91 shows some typical shrinkage curves and illus- 
 trates the relationship between chemical composition and the form of 
 these curves." 
 
 "It will be noted that there are three periods of expansion separated 
 by intervals during which the shrinkage takes place. The first of these 
 periods of expansion is due to the separation of graphite and hence is 
 greatest in the softest irons. Note that in the case A , which is a white 
 iron and contains no graphite, this expansion is entirely lacking. This 
 expansion takes place within the temperature range 2200° to 1800° F., 
 or immediately after the iron has solidified." 
 
Shrinkage 
 
 331 
 
 "The second expansion is due to the solidification of the phosphide 
 eutectic with a consequent secondary precipitation of graphite at that 
 time. Evidently, this expansion is only to be expected in high phos- 
 phorus irons and it will be noted that it is lacking in C, which is low in 
 phosphorus, and is well marked in D, which is high in phosphorus. This 
 expansion takes place within the temperature range 1800° to 1500° F." 
 
 "The third expansion is. in the writer's opinion, due to the change of 
 the iron from the 'alpha' to the 'gamma' form, since it takes place 
 
 |20 
 |>P 
 
 X 
 
 iU 
 
 ■-^--0 
 10 
 
 o 
 
 I 40 
 
 -|o50 
 c 
 
 "~ 60 
 v 
 
 CD 
 
 J 70 
 
 c 
 
 \n 
 
 
 
 xi. 
 
 
 ^ 
 
 ^M? 
 
 Vp 
 
 2%^ 
 
 ^ 
 
 ^ 
 
 
 ^ 
 
 ' — 
 
 . 
 
 ■A 
 
 r 
 
 
 
 
 "\ 
 
 
 N 
 
 \ 
 
 \ 
 
 <r 
 
 
 \ 
 
 %sy. 
 
 ?Cf 
 
 
 
 
 \ 
 
 
 
 t^. 
 
 
 
 
 
 
 
 \ 
 
 
 
 ''?? 
 
 ks'' 
 
 
 ^-~.^ 
 
 •..^ 
 
 
 
 
 V 
 
 
 
 
 
 
 
 
 
 
 "^ 
 
 
 
 
 
 
 
 
 
 
 
 
 i 
 
 
 
 
 
 
 
 
 
 
 V 
 
 
 
 
 
 
 
 
 
 
 \ 
 
 ^ 
 
 
 
 
 
 
 
 Ar 
 
 A 
 
 lalyse 
 
 5. 
 
 r 
 
 n 
 
 X 
 
 
 
 
 SiUcon SO/ f.4l 3.4/ 3.98 
 
 Su/phur tr. .01 .OS .03 
 
 ~ Phos. 0.0/ .95 .04 .25- 
 
 Mang. tr. A3 .55 .50 
 
 COffhr/irh ?7? 7<7 Hf, IK 
 
 
 \ 
 
 \ 
 
 
 
 
 
 
 6m 
 
 ipfi.Car 
 L_ 
 
 b. 
 
 Z.73 
 
 2.53 
 1 
 
 ?.60 
 1_„. 
 
 
 
 
 
 50 100 150 
 
 Time- Seconds. 
 
 Fig. qi. 
 
 200. 
 
 within the temperature range 1400° to 1200° F., or about where this 
 change would be expected to take place. Note that this expansion is 
 greatest in high silicon irons C and D, silicon having the effect of acceler- 
 ating the 'gamma' to 'alpha' change. The point at which this third 
 expansion occurs probably marks the lower limit below which iron cannot 
 be hardened by quenching." 
 
 "The study of these curves is very interesting to the experimenter 
 and it is believed that when we understand them better they may 
 become of practical value to the foundryman. At present, however, 
 
33^ Chemical Analyses 
 
 the determination of total shrinkage gives information which is of more 
 
 immediate value." 
 
 "The effect of composition on total shrinkage is given in concise form 
 
 by the following tabular statement: 
 
 Per cent 
 SiHcon Decreases by about .01 inch per foot for each . 20 
 
 Sulphur Increases by about . 01 inch per foot for each . 03 
 
 Phosphorus . . . Decreases by about . 015 inch per foot for each . 10 
 
 Manganese. . . . Increases by about . 01 inch per foot for each . 20 
 
 Total carbon. .Decreases. 
 
 "To get the minimum shrinkage an iron should be high in silicon, 
 from 2 to 3 per cent depending on the thickness, high in phosphorus, say, 
 0.7 s to 1.25 per cent, as low as possible in sulphur, as high as possible in 
 total carbon and with only enough manganese to care for the sulphur, 
 or, say, 0.3 to 0.4 per cent. This will insure high graphite and hence low 
 shrinkage in the casting. The iron will, however, be rather weak and 
 it is something of a problem to get in one and the same iron considerable 
 strength and at the same tim^ very low shrinkage." 
 
 "By the term 'stretch' West describes the power of cast iron to stretch 
 when placed under strain during the cooling process. This property is 
 undoubtedly of much importance in cast iron since there are many 
 castings which are called upon to exhibit it. An extreme case which 
 is commonly cited is that of pulleys, the arms of which are placed in 
 tension due to the quicker coohng of the rim and which must, therefore, 
 either stretch or crack. There is no. data regarding the effect of various 
 metalloids of cast iron on its power of stretching but in general a soft iron 
 will stretch more than a hard one. Almost the only data on this subject 
 is given by West. He finds that the period of greatest stretching of 
 cast iron is within the temperature range 1600° to 1200° F. 
 
 Fusibility- 
 Fusibility, or the melting point of cast iron, must not be confounded 
 with its fluidity, or ease of flow when molten. Fluidity is much the more 
 important of these two properties, but fusibility is of some interest, 
 particularly as it gives us a means of deciding intelligently in what order 
 to charge metals in the cupola. 
 
 The investigations of Dr. Moldenke have shown that the fusibihty of 
 cast iron depends primarily on its combined carbon content, and, to a 
 less extent, on the amount of phosphorus present. . . . We find that 
 cast iron has a melting range varying from 2000° F. for a white iron up 
 to 2300° F. for gray iron containing practically no combined carbon, this 
 
Fusibility 
 
 333 
 
 difference being due probably to the presence of silicon, sulphur, phos- 
 phorus and manganese. 
 
 Since the graphite in gray iron is only in mechanical mixture with the 
 iron we should, perhaps, expect it to have no effect on the melting point. 
 Moreover, it combines with the iron at temperatures below the melting 
 point thus increasing the combined carbon and lowering the melting 
 point. For this reason gray iron melts at a lower temperature than steel 
 having the same percentage of combined carbon. 
 
 2300 
 
 2250 
 
 ^2200 
 
 ft) 
 
 o 
 
 i 
 
 ^ 2150 
 2 
 o. 
 E 
 
 2050 
 
 2000 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 X = 
 
 ResoJ 
 
 tsof 
 
 Dr.M 
 
 7/a'er 
 
 Ae. 
 
 \ 
 
 
 
 
 
 
 
 
 
 
 \ 
 
 
 
 
 
 
 
 
 
 
 
 
 ./'' 
 
 » 
 
 
 
 
 
 
 
 
 P=l.5 
 
 X 
 
 \ 
 
 -^Mh' 
 
 1.4 
 
 
 
 
 
 
 
 
 X5 
 
 
 
 
 
 
 
 
 
 
 
 \< 
 
 ^, 
 
 
 
 
 
 
 
 
 
 
 \ 
 
 P=l. 
 
 \ Mn= 
 
 4- 
 I.I 
 
 
 
 
 
 
 
 
 X 
 
 \ 
 \ 
 
 . \ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 > 
 
 X 
 
 X 
 
 \ 
 
 
 
 
 
 
 
 
 
 
 A^ 
 
 
 
 
 
 
 
 
 
 X 
 
 
 \ 
 \ 
 
 
 2 3 4 
 
 Percent Combined Carbon. 
 
 Fig. 92. 
 
 As previously noted, phosphorus also has the effect of lowering the 
 melting point of cast iron but it is not nearly as powerful in its action as 
 combined carbon. Iron containing 6.7 per cent phosphorus would melt 
 at only 1740° F., but with less phosphorus than this the melting point 
 rises rapidly so that the i or 2 per cent present in commercial high phos- 
 phorus irons makes very little difference in the melting point. 
 
 Fig. 92 gives in graphic form the data of Dr. Moldenke from which 
 is drawn a line representing the approximate melting point of cast iron 
 of any per cent combined carbon. 
 
334 
 
 Chemical Analyses 
 
 "Table I gives the melting points with analyses of some typical 
 irons and ferroalloys selected from the above data. It will be noted 
 that the metalloids other than carbon and phosphorus, i.e., the silicon, 
 sulphur and manganese, seem to have very little effect on the melting 
 point." 
 
 Table I. — Melting Points of Cast Irons 
 
 Melting 
 
 point, 
 
 degrees F. 
 
 Com- 
 bined 
 carbon, 
 per cent 
 
 Graphite, 
 per cent 
 
 vSilicon, 
 per cent 
 
 Man- 
 ganese, 
 per cent 
 
 Phos- 
 phorus, 
 per cent 
 
 Sulphur, 
 per cent 
 
 2030 
 
 3.98 
 
 
 
 .14 
 
 .10 
 
 .22 
 
 .037 pig iron 
 
 2100 
 
 3.52 
 
 .54 
 
 • 47 
 
 .20 
 
 .20 
 
 .036 " 
 
 ' 
 
 2140 
 
 2.27 
 
 1.80 
 
 • 45 
 
 1. 10 
 
 1.46 
 
 .032 " 
 
 * 
 
 2170 
 
 1.93 
 
 1.69 
 
 •52 
 
 .16 
 
 • 76 
 
 .036 " 
 
 ' 
 
 2200 
 
 1.69 
 
 2.40 
 
 1. 81 
 
 •49 • 
 
 1.60 
 
 .060 " 
 
 • 
 
 2210 
 
 1.48 
 
 2.30 
 
 1. 41 
 
 1.39 
 
 • 17 
 
 .033 " 
 
 ' 
 
 2230 
 
 1. 12 
 
 2.66 
 
 1. 13 
 
 .24 
 
 .089 
 
 .027 " 
 
 * 
 
 2210 
 
 .84 
 
 3.07 
 
 2.58 
 
 .47 
 
 2.12 
 
 .051 " 
 
 ' 
 
 2250 
 
 .80 
 
 3.16 
 
 1.29 
 
 .50 
 
 .22 
 
 .020 " 
 
 ' 
 
 2280 
 
 .13 
 
 3.43 
 
 2.40 
 
 .90 
 
 .08 
 
 .032 " " 
 
 2350 
 
 1.32 
 
 
 .21 
 
 .49 
 
 (?) 
 
 (?) steel 
 
 2210 
 
 6.48 
 
 (carbon) 
 
 • 14 
 
 44.59 
 
 (?) 
 
 (?) ferromang. 
 
 2255 
 
 5.02 
 
 (carbon) 
 
 1.65 
 
 81.40 
 
 (?) 
 
 (?) ferromang. 
 
 2190 
 
 3.38 
 
 • 37 
 
 12.30 
 
 16.98 
 
 (?) 
 
 (? ) silicospiegel. 
 
 2040 
 
 1.82 
 
 • 47 
 
 12.01 
 
 1.38 
 
 (?) 
 
 (?) ferrosilicon 
 
 2400 
 
 6.80 
 
 (carbon) 
 
 (chromium 
 
 62.70) 
 
 
 
 (?) ferrochrome 
 
 2280 
 
 
 
 (tungsten 
 39-02) 
 
 
 
 (?) ferrotungsten 
 
 Fluidity 
 
 "Fluidity may be defined as ease of flow. It is synonymous with 
 mobihty and opposed to viscosity. It is a property of far-reaching 
 importance to the foundryman and especially to the manufactiu^er of 
 small and intricate castings. Unfortunately, our means of measuring 
 fluidity are not very satisfactory, and this makes it difficult to determine 
 quantitatively the effect of composition upon this property. About 
 the most satisfactory method is to pour fluidity strips or long strips of 
 perhaps one square inch section (at one end) and tapering to nothing at 
 the other. The distance which the iron runs in a mold of this form is a 
 rough measure of its fluidity." 
 
 "The factors which govern fluidity are percentage of silicon, percent- 
 age of phosphorus, freedom from dissolved oxide and temperature above 
 the melting point." 
 
 "Sihcon perhaps aids fluidity by causing a separation of graphite at 
 the moment of sohdification, thus, according to Field, liberating latent 
 
Resistance to Heat 335 
 
 heat and prolonging the life of the metal. On this basis, high total 
 carbon would also aid fluidity by increasing the amount of graphite 
 separated," 
 
 "Phosphorus is probably the most important element as regards 
 fluidity, high phosphorus causing a marked increase in this property. 
 The best results are obtained with about 1.5 per cent phosphorus, 
 although for other reasons it is seldom desirable to use as much as that." 
 
 "Freedom from oxide is a very important point as its presence makes 
 the metal sluggish and causes it to set quickly. It is a frequent and often 
 unsuspected source of trouble. Dissolved oxide may be eliminated by 
 any of the methods described." 
 
 "The temperature above the freezing point is probably the most 
 important factor of all in connection with fluidity, and it should here be 
 noted that a distinction is made between freezing point and melting 
 point. The two may coincide in the case of white iron, but will not 
 usually, especially with gray iron. This is because, as we have already 
 seen, gray irons have a melting temperature corresponding to their per- 
 centage of combined carbon rather than total carbon. After they are 
 in the molten state, however, all the carbon is in solution (combined as 
 far as melting points are concerned), hence, the freezing point will corre- 
 spond more nearly to the melting point of a white iron having the per- 
 centage of combined carbon equal to the total carbon of the original gray 
 iron. This will be in general from 100° to 300° lower than its melting 
 point. For this reason when gray irons are melted they are always 
 considerably superheated above their solidifying points, and the greater 
 this superheat, the more fluid the iron. Evidently, the superheat due 
 to this cause will be the greater the lower the combined carbon in the 
 iron going into the cupola." 
 
 Practical rules for getting fluid iron are as follows: 
 
 "Keep the phosphorus high, — up to i.oo to 1.25 if possible." 
 
 "If the work will permit, use a soft iron of 2 per cent or over in silicon, 
 and low in combined carbon." 
 
 "Avoid oxidizing conditions in melting and, if necessary, use deoxidiz- 
 ing agents." 
 
 "Use plenty of coke and good cupola practice." 
 
 Resistance to Heat 
 
 "Ability to withstand high temperatures is of paramount importance 
 in several classes of castings such as grate bars, ingot moulds, anneahng 
 boxes, etc., and the factors which affect this ability are, the percentage 
 of phosphorus, sulphur and combined carbon, and the density or close- 
 ness of grain." 
 
336 Chemical Analyses 
 
 "Phosphorus forms with iron an alloy which melts at only 1740° F., or 
 about 400° lower than cast iron free from phosphorus, and each per cent 
 of phosphorus present gives rise to 15 per cent of this easily fusible con- 
 stituent. Now, it will be evident that the presence of a molten con- 
 stituent in a piece of iron must greatly weaken it, and hence it is that the 
 presence of much phosphorus decreases the resistance of cast iron to 
 heat." 
 
 "Sulphur acts in a similar manner to phosphorus since it also forms 
 with iron a constituent of low melting point (1780° F.). It is, therefore, 
 detrimental to castings which have to stand high temperatures." 
 
 "As previously. noted, combined carbon is the element which more than 
 any other determines the melting point of cast iron, this melting point 
 becoming lower with increase in this element. It would seem then, that 
 combined carbon must be very detrimental in this class of castings. 
 However, it should be remembered that the condition of the carbon in 
 the solid iron changes readily at high temperatiures, and, hence, after the 
 casting has been in use for a while its combined carbon content will not 
 in general be the same as when cast. This fact makes the question of 
 combined carb6n of much less practical importance than either phos- 
 phorus or sulphur." 
 
 "Density or close grain is commonly stated to render cast iron con- 
 siderably more resistant to the effects of heat. . . . " 
 
 "One feature of the effect of heat on cast iron which deserves especial 
 mention is the permanent expansion which it imdergoes on repeated 
 heatings. This peculiar behavior was first discovered by Outerbridge 
 and has since been also investigated by Rugan and Carpenter." 
 
 "The extent to which this growth may take place is certainly sur- 
 prising, the increase being in some cases as high as 46 per cent by volume 
 and 1% inches in the length of a 15-inch bar. The strength of the metal 
 is decreased proportionately to the expansion or to about one-half of the 
 original strength. Both the expansion and the decrease in strength are 
 explained by microscopic examination, which shows minute cracks 
 throughout the interior of the metal. . . ." 
 
 "Two conditions are necessary for this growth. First, repeated 
 heatings, and second, a proper composition of the metal." 
 
 "With regard to the heating, a minimum temperature of 1200° F. is 
 necessary. At 1400° to 1600° the rate of growth is more rapid and an 
 increase in temperature beyond 1700° produces no additional effect. 
 Both heating and cooHng are necessary to procure the growth, and the 
 time of heating makes very little difference. No greater growth was 
 produced by 17 hours continuous heating than by 4 hours. The num- 
 ber of heatings required to produce the maximum amount of growth 
 
Resistance to Heat 337 
 
 varies with different irons, but usually lies somewhere between 50 and 
 100." 
 
 "Regarding the effects of composition, it appears that the growth is 
 favored by the presence of graphite and silicon, and also by a large grain 
 or open structure. White iron containing no graphite expands slightly 
 when subjected to this treatment but not sufi&ciently to overcome its 
 original shrinkage. In this case the expansion is due to the conversion 
 of the combined carbon into the temper form, or in other words, to the 
 malleableizing of the casting. Soft irons low in combined carbon and 
 high in silicon show the greatest increase in volume. The effects of 
 sulphur, manganese and phosphorus have not been investigated. Steel 
 and wrought iron are not subject to this growth, but on the contrary 
 undergo a slight permanent contraction when repeatedly heated." 
 
 "It is evident that this property of cast iron is of great importance in 
 many of the applications of the metal and limits its use for many pur- 
 poses. It is, no doubt, the reason why a close-grained iron gives better 
 results when exposed to high temperatures and affords an explanation 
 for the warping of grate bars, annealing boxes and similar castings. It 
 also shows why chills and permanent molds must not be allowed to be 
 heated to redness, such a degree of heat resulting in permanent expansion 
 and the loss of their original dimensions." 
 
 The following is a summary of some of the published statements 
 regarding the proper composition for castings exposed to high tempera- 
 tures: 
 
 "Cast iron to withstand high temperatures should be low in phos- 
 phorus and combined carbon." 
 
 "In car wheels manganese increases the resistance to heat strain." 
 
 "For refractory castings choose a fine grained cast iron, best contain- 
 ing about 2 per cent manganese to retard the separation of amorphous 
 carbon." 
 
 "Castings to resist heat should contain about 1.80 per cent silicon, 
 0.03 per cent sulphur, 0.70 per cent phosphorus, 0.60 per cent%ianganese 
 and 2.90 per cent total carbon. Low sulphur is of chief importance, low 
 silicon, carbon and manganese are also advisable." 
 
 "Close-grained cast iron having the greatest density will invariably 
 be found best to withstand chemical influences and high temperatures," 
 
 "A chill which had given excellent service had the following composi- 
 tion: silicon, 2.07 per cent; sulphur, 0.073 per cent; phosphorus, 0.03 
 per cent; manganese, 0.48 per cent; combined carbon, 0.23 per cent; 
 graphite carbon, 2.41 per cent; total carbon, 2.64 per cent. • 
 
 " Two permanent moulds which had given excellent service analyzed 
 as follows : 
 
338 
 
 Chemical Analyses 
 
 Silicon, 
 per cent 
 
 Sulphvir, 
 per cent 
 
 Phosphorus, 
 per cent 
 
 Manganese, 
 per cent 
 
 Combined 
 carbon, 
 per cent 
 
 Graphite, 
 per cent 
 
 Total 
 carbon, 
 per cent 
 
 2. IS 
 2. 02 
 
 .086 
 .070 
 
 1.26 
 .89 
 
 -41 
 .29 
 
 .13 
 
 .84 
 
 3.17 
 2.76 
 
 3.30 
 3.60 
 
 "Ingot moulds and stools are best made from medium soft iron low in 
 phosphorus, or what is termed a regular Bessemer iron. ... ." 
 
 Electrical Properties 
 
 "Of the three electrical properties, conductivity, permeability and 
 hysteresis, the second only is of importance in connection with cast iron. 
 
 B 
 
 
 
 
 
 
 
 
 
 
 
 12.000 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 10,000 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 ^^' 
 
 ^ 
 
 e;0oo 
 
 
 
 
 
 ^. 
 
 1?..' 
 
 ;;: 
 
 
 ^. 
 
 ^- 
 
 
 
 
 
 :^ 
 
 c 
 
 ^'^ 
 
 
 
 
 '6,000 
 
 
 
 9 
 
 
 ,y^ 
 
 
 
 
 
 
 
 ^y 
 
 / 
 
 > 
 
 
 
 
 
 
 
 4,000 
 
 / 
 / 
 / i 
 
 7 . 
 
 / 
 
 / 
 
 
 
 
 
 
 
 
 // 
 // 
 
 / 
 
 
 
 
 
 
 
 
 
 2,000 
 
 !/ 
 
 
 
 
 
 
 
 
 
 
 ' 
 
 
 
 
 
 
 
 
 
 
 
 V 
 
 
 
 
 
 
 
 
 
 
 20 
 
 40 60 
 
 Fig. 93. 
 
 80 
 
 Little is known regarding the relation between chemical composition 
 and conductivity of cast iron. In the case of steel it has been found that 
 manganese is the element most injurious to this property with carbon 
 a close second. Hence, by analogy, we may infer that to make iron 
 castings of high conductivity we should keep both the manganese and 
 combined carbon as low as possible. 
 
Electrical Properties 
 
 339 
 
 Permeability may be defined as magnetic conductivity and is of 
 importance in many castings used in the construction of electrical 
 machinery. Permeability data are generally given in the form of a 
 curve expressing the relation between the magnetizing force H and the 
 resulting field strength or number of lines of magnetic force per unit 
 area B. This is known as the permeabihty curve. The permeabihty 
 
 is the ratio ^ and it will be noted that it is different for each value of the 
 B 
 
 magnetizing force, H, but approaches a constant or saturation value for 
 
 high values of U. See Fig. 93. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 160 
 
 
 
 
 .,S 
 
 
 924 
 
 
 
 n'2 
 
 
 
 
 
 
 1 
 
 fs 
 
 
 T 
 
 I^^ 
 
 P" 
 
 y 
 
 
 
 
 13, 
 140 
 
 H 
 
 --^ 
 
 f\ 
 
 ^ 
 
 ^J^' 
 
 ^r 
 
 / 
 
 jT 
 
 
 
 
 
 10^ 
 
 n^ 
 
 19 
 
 ►)7 
 
 ^ 
 
 ^ 
 
 
 
 
 
 
 
 
 rfcd 
 
 120 
 
 
 4 
 
 \ 
 
 
 
 
 
 N 
 
 3. Sii. Pho5. Mang. 
 
 1.79 .75 .19 
 
 
 
 ^ 
 
 ^ 
 
 
 
 
 . 
 
 i 1.76 .75 1.73 
 1- 1.81 .75 1.05 
 J 178 75 I 01 
 
 100 
 
 
 
 
 
 i.^^ 
 
 
 
 
 a 1.76 .75 3.46 
 7 1.75 .75 .35 
 i 2.70 ■ .75 .-^fi 
 
 
 
 
 
 \ 
 
 
 
 9 2.61 .75 .35 
 
 10 lis .75 ,36 
 
 11 3.67 .76 .36 
 
 80 
 
 
 
 
 
 
 \ 
 
 
 
 3 1.49.09.75- .46. 
 
 4 1.49 .16 .75 .49 
 
 
 
 
 
 
 
 \ 
 
 
 6 Z,09 .85.75 .4B 
 
 7 2.08 1.35.75 .43 
 
 8 2.14 3.18.75 .43 
 
 60 
 
 
 
 
 
 
 
 6^ 
 
 ^ 9 ).6Z .91 .47 
 
 to 1.69 l.ll .49 
 21 1.63 I.7S .43 
 
 
 
 
 
 
 
 
 
 23 1.84 Z.SS .SZ 
 
 24 1.76 ?.6I • .54 
 
 
 
 
 
 
 
 
 
 
 
 
 1 
 
 1.0 
 
 2.0 3.0 
 
 Fig. 94. 
 
 4.0 
 
 6.0 
 
 The effects of the various elements on permeability are not yet entirely 
 clear although there are some published data along this line. The writer 
 has recentfy done considerable work on the relation between permeability 
 and chemical composition of cast iron, and the resiilts, as yet unpubHshed, 
 are summarized in Fig. 94. It will be noted that the effects of silicon, 
 phosphorus and aluminum are not well marked and are probably not of 
 
340 Chemical Analyses 
 
 any very great importance. On the other hand, manganese has a very 
 detrimental effect on this property. 
 
 Silicon has the opposite effect from manganese in that it accelerates 
 this change in the form of the iron, and we would, therefore, expect 
 it to have a more or less beneficial influence. Silicon steel has 
 achieved a wide reputation as a high permeability material for use in 
 the construction of tran former cores, etc. According to the author's 
 results high silicon is particularly effective in increasing B for low values 
 oiH. 
 
 An important element not considered in the diagram, Fig. 94, is 
 carbon. For high permeability the lower the carbon the better, and 
 excellent results are now being obtained through the use of semi-steel for 
 electrical castings. In this connection, however, it must be remembered 
 that manganese is undesirable and hence must be used cautiously as a 
 deoxidizer in this class of work. 
 
 Some practical rules for obtaining high permeability iron are given 
 herewith. 
 
 Keep the silicon high, best in the neighborhood of 3 per cent. 
 
 Keep the manganese low, preferabl}^ below 0.5 per cent. 
 
 If practicable keep the carbon low by the use of steel scrap or air 
 fiirnace iron. 
 
 Allow the castings to anneal themselves, i.e., cool completely in the 
 sand before shaking out. 
 
 Hysteresis, like conductivity, is seldom or never of importance in cast 
 iron. The property may be defined as the loss of energy due to molecular 
 friction when magnetic polarity is reversed. The effect of composition 
 upon hysteresis is in general about the same as in the case of permeability. 
 
 Resistance to Corrosion 
 
 Although there are a great many corrosive agencies it is not practicable, 
 because of lack of information, to treat of each separately, and so far as 
 we know the effects of composition woiild be relatively the same for the 
 various corroding agents. 
 
 The following is a summary of most of the published information 
 along this line: 
 
 Pig iron which best resists acids contains silicon, i.o per cent; phos- 
 phorus, 0.5 per cent; sulphur, 0.05 per cent; carbon, 3.0 per cent. 
 
 Excellent results with respect to resistance to corrosion by acids were 
 obtained through the use of a mixture of three brands of pig iron.^, B 
 and C in the proportion, two parts of A, one part B and one part C 
 The analysis of the pig irons is thus given: 
 
Resistance to Corrosion 
 
 341 
 
 Fracture 
 
 Silicon, 
 per cent 
 
 Manganese, 
 per cent 
 
 Phosphorus, 
 per cent 
 
 Total 
 carbon, 
 per cent 
 
 A Dark gray 
 
 3. SO 
 I -SO 
 
 .70 
 
 ■ 50 
 .40 
 
 •25 
 
 .20 
 .20 
 .20 
 
 3.80 
 3.50 
 3.50 
 
 B Light Gray . 
 
 C Mottled. 
 
 
 The composition of acid-resistant castings should be about as follows: 
 
 Silicon, 
 per cent 
 
 Sulphur, 
 per cent 
 
 Phosphorus, 
 per cent 
 
 Manganese, 
 per cent 
 
 Total carbon, 
 per cent 
 
 .8 to 2.0 
 
 .02 to .03 
 
 .40 to .60 
 
 I to 2.0 
 
 3.0 to 3.5 
 
 and in addition, the metal should be as free as possible from oxide. 
 
 Cast iron to withstand the corrosive action of molten chemicals 
 should be close grained and dense. The iron having the greatest den- 
 sity will invariably be found to best withstand chemical influences and 
 high temperatures. The addition of deoxidizing agents is of great 
 benefit. 
 
 Gray iron is attacked by acids about three times as fast as white iron. 
 In cases where it is not practicable to use white iron castings it is some- 
 times possible to cast against chills in such a manner as to form a white 
 iron surface to resist corrosion and still leave the body of the casting 
 gray. 
 
 In a series of tests on the acid-resisting properties of some well-known 
 EngHsh brands of iron, the No. i iron, presumably high in silicon, and 
 the "hematite," low in phosphorus and probably high in siUcon, gave the 
 best results. 
 
 Ferrosilicons with high percentages of silicon, 20 per cent and over, are 
 remarkably resistant to the effects of acids and are being made into 
 vessels for use in the chemical industries. 
 
 Sulphur has been found to be a source of corrosion in steel in some 
 instances, causing pitting at points where manganese sulphide has 
 segregated. 
 
 It has been shown that the presence of small amounts of copper in 
 steel and puddled iron diminish their tendency to rust. 
 
 Some practical rules for obtaining castings resistant to corrosion are 
 as follows : 
 
 Use white iron if practicable. 
 
342 Chemical Analyses 
 
 If not practicable to use white iron casting, chill those surfaces which 
 are to be in contact with the corrosive substances. 
 
 If gray iron must be used get dense, close-grained castings through 
 the use of steel scrap or otherwise. 
 
 Avoid oxidized metal, use good cupola practice and good pig irons. 
 
 If possible use deoxidizing agents. 
 
 Keep the sulphur just as low as possible. 
 
 Resistance to Wear 
 
 We must first make some distinction between two cases of wear 
 typified by a grinding roll and a brake shoe. The first case may be 
 dismissed by the simple statement that the greater the hardness the 
 better the wear, providing at the same time that the iron is sufficiently 
 strong. 
 
 In the second case, however, it is necessary that the casting should not 
 be so hard as to unduly wear the material with which it comes in contact. 
 For example, the brake shoe must be softer than the tread of the car 
 wheel. There is no theory to guide us in the matter and the rules given 
 are the results of experiment chiefly with brake shoes. 
 
 Too much silicon gives an open, soft iron which does not wear well. 
 The best results are obtained with silicon about iH per cent in castings 
 of medium thickness. 
 
 Sulphur is claimed by many to be advantageous in castings for fric- 
 tional wear because it closes the grain and hardens somewhat. Diller 
 records a peculiar occurrence of a hard spot which could not be machined, 
 a smooth surface being formed which wore the drill although it could be 
 dented with a center punch. Analysis showed 0.20 per cent sulphur and 
 0.50 per cent combined carbon. 
 
 Phosphorus is best kept moderately low. Most specifications call for 
 0.75 per cent or under. It is injurious probably because it weakens the 
 iron at the high temperature sometimes produced by friction. 
 
 Manganese is best kept moderately high to take care of the sulphur. 
 Most brake shoe specifications call for under 0.70 per cent. 
 
 The addition of steel scrap to the mixture has been found to give 
 excellent results for this class of work, probably owing to the reduction 
 in the total carbon and to its action in closing the grain. 
 
 Coefficient of Friction 
 
 There are no data as to the relation between the composition of cast 
 iron and its coefficient of friction. Since graphite is an excellent lubri- 
 cant it is probable that the percentage of graphite is the controlling 
 factor here, the friction decreasing with increase in this element. From 
 
Casting Properties 343 
 
 theoretical considerations we should expect the best results to be obtained 
 with a very soft iron low in sulphur, manganese and combined carbon 
 and high in graphite. 
 
 Casting Properties 
 
 The properties which remain to be considered pertain more par- 
 ticularly to the casting as a whole and are chiefly influenced by the design, 
 moulding and pouring of the casting, and to a very much less extent, by 
 the composition of the metal. 
 
 Unsoundness due to the presence of blow-holes and shrinkage cavities, 
 while usually resulting from bad practice in moulding may also be caused 
 by poor quality of metal. Blowholes may be caused by oxidized metal 
 or by excessive sulphur. . . . When caused by sulphur the remedy is 
 to decrease this element. Raising the manganese is often effective in 
 preventing blowholes since it acts both as a deoxidizer and desulphurizer. 
 Scott states that manganese below 0.25 per cent often results in blow- 
 holes. High phosphorus sometimes acts as a corrective of blowholes due 
 to its prolonging the fluidity, thus giving the iron more chance to release 
 the dissolved gases. 
 
 Dirty castings are also caused chiefly by poor moulding, pouring or 
 cupola practice. Occasionally, however, it may result from wrong 
 composition of the metal, and the points chiefly to be watched are to keep 
 the sulphur low; to avoid kish or segregated graphite and to avoid 
 oxidized metal. 
 
 Sulphur tends to cause dirty castings because it makes the iron congeal 
 more quickly, and hence any dirt present has less chancy to separate. 
 In addition, the sulphides of iron and manganese themselves form dirt 
 spots when segregated. Kish is usually caused by too much silicon, or 
 sometimes by too much total carbon. Oxidized metal is a prolific source 
 of dirty castings, but the oxidization is usually due to bad cupola practice, 
 or to the use of oxidized scrap. Moderately high manganese and phos- 
 phorus are conducive to clean castings, the first because it takes care of 
 sulphur and oxidation, and the second because it increases the fluidity of 
 the metal and thus gives the dirt a better chance to float out. 
 
 Porosity is usually caused by the presence of kish (see preceding 
 paragraph). Pinholes, another form of porosity, are usually due to 
 excessive sulphiir in the form of iron sulphide. This compound retains 
 gases in solution until the metal is partially frozen and then releases 
 them in the form of tiny bubbles which give rise to this defect. Decrease 
 in sulphur or increase in manganese or both is the remedy. 
 
 Segregation proper is caused by the difference in melting point and 
 specific gravity of the several constituents of cast iron. The constit- 
 
344 Chemical Analyses 
 
 uents of lowest melting point are the phosphorus and sulphur compounds, 
 and it is, therefore, in these cases that we find the greatest tendency 
 towards segregation. It is not unusual to find hard spots in heavy 
 castings high in phosphorus which are caused by the phosphide being 
 squeezed out into blow-holes formed during solidification. Frequently 
 the phosphide does not completely fill the cavity, or fills it as a loose 
 globule. The sulphides, owing to their low specific gravity, usually 
 segregate in the top of the casting and it is not infrequent to find sev- 
 eral times the normal amount of sulphur in the upper part of heavy 
 castings. Manganese sulphide segregates more readily than iron sul- 
 phide. 
 
 Besides segregation proper we sometimes find cases of non-homo- 
 geneity due to other causes. Occasionally spots of white iron are found 
 in the interior of castings. It has always been difficult to account for 
 these but the clew is given by the fact that they are invariably found in 
 castings poured from the first metal tapped. 
 
 Undoiibtedly they are caused by the iron boiling on the sand bed and 
 are connected in some way with the partial Bessemerizing of the metal. 
 Again, hard spots in castings are sometimes due to small pieces of metal 
 (for example, small steel scrap and shot iron) being incompletely melted 
 in their passage through the cupola. Ferromanganese and other ferro- 
 alloys may give rise to this same trouble through incomplete solution 
 when stirred into the ladle. 
 
 Shrinkage strains are caused primarily by wrongly designed castings, 
 but the trouble may be aggravated by the composition of the metal. 
 High sulphur is a particularly prolific source of internal stresses, and, 
 in general, the greater the total shrinkage, the greater the strains due to 
 this cause. 
 
 As all foundrymen know, the fineness of finish and smoothness of skin 
 of a casting depend chiefly on the sands and facings used and the skill 
 of the moulder. High phosphorus in the iron, however, is a consider- 
 able aid in getting the fine skin desired in ornamental work. Another 
 element affecting the skin is manganese which has the rather peculiar 
 action of causing the sand to peel from the castings with extreme readi- 
 ness. With I per cent manganese this tendency is evident and with 
 2 per cent it is very marked. 
 
 Bars, plates and hollow castings were treated, which were permitted 
 to cool in the moulds. The plates cooled more slowly than the bar 
 samples and the material proved somewhat softer, giving smaller values 
 for the bending, tensile and compressive strength, but was better as 
 regards flexure and strength to resist impact. 
 
 Tests reported to the Iron and Steel Institute showed : 
 
Notes on the Micro-structure of Cast Iron 345 
 
 The best tensile and* transverse tests are obtained from bars which 
 have been machined. 
 
 Transverse test bars cast on edge and tested with the "fin" in com- 
 pression give the best results. 
 
 The transverse test is not so reliable or helpful as that of the moment 
 of resistance. 
 
 Cast iron gives the best results when poured as hot as possible. 
 
 As in some measure explanatory of the conflicting results obtained in 
 testing bars of precisely the same chemical combination, and as showing 
 the importance of microscopical examinations of the structure of cast 
 iron in pointing out the causes of difference in its physical properties, the 
 paper of Mr. Percy Longmuir published in the Journal of the American 
 Foundrjrmen's Association, June, 1903 is given in full. 
 
 Notes on the Micro-structure of Cast Iron 
 
 By Percy Longmuir, Sheffield, England 
 
 Journal of the American Foundrymen's Association, Vol. XII, June, IQ03. 
 
 Instances are occasionally found where metal of the right chemical 
 composition goes wrong in practice. It is in cases of this kind that the 
 real value of microscopical examination is most evident, for very often 
 such an examination will locate the trouble and at the same time suggest 
 a remedy. Naturally an examination of diseased samples can only be 
 undertaken after a thorough study of healthy ones, hence a foundation 
 for the study of abnormal samples must necessarily be based on the 
 knowledge gained from a wide series of normal ones, that is, samples of 
 known chemical composition and known physical conditions. 
 
 The structoare of cast iron is very complex — far more so than that of 
 steel — a fact readily shown by the high content of elements present 
 other than iron. By polishing and etching a sample of cast iron, several 
 of the compounds of the elements with iron are, under suitable magni- 
 fication, rendered visible. The structural features, such as the arrange- 
 ment and distribution of the various compounds and their relationship 
 to each other, can then be readily noted and the effect of this combination 
 on the mass then becomes an estimable quantity. 
 
 If the metal under examination contain no impurities it is evident that 
 its mass will be built up of pure crystals. A section cut from such a pure 
 metal will, after polishing and etching, show only the crystal junctions. 
 Crystal junctions of this type are shown in Fig. 95 , which represents the 
 structure of almost pure iron. Even here, although the metal is so pure, 
 the very minute trace of carbon present can be readily detected in the 
 dark knots of which about a dozen are to be seen. As foreign elements 
 
346 
 
 Chemical Analyses 
 
 are added to pure iron the structure becomes more complex and a point 
 is reached when all the pure crystals are replaced by more complex ones. 
 It is to be remembered that all gray irons contain appreciable amounts 
 of two varieties of carbon, silicon, manganese, sulphur and phosphorus. 
 
 =13 
 
 — Magnified 360 diameters 
 
 
 
 0.03 
 0.02 
 0.07 
 
 Sulphur 
 
 Phosphorus 
 
 Iron 
 
 
 
 
 
 99 
 
 01 
 
 01 
 86 
 
 Fig. 95. 
 Carbon 
 Silicon 
 Manganese 
 
 Of these elements graphite is present in its elementary form, that is, as 
 free carbon. The remaining constituents are present in compound form 
 associated either with iron or with other elements. Thus sulphur may 
 occur as sulphide of manganese or as iron sulphide. Carbon occurring 
 
 Fig. 96. — Magnified 60 diameters. 
 Combined Carbon o . 54 Manganese 
 
 Graphite 3 . 1 1 Sulphur 
 
 Silicon 1.77 Phosphorus 
 
 0.63 
 0.04 
 1-34 
 
 in the combined form is present as a definite carbide of iron; or under 
 certain conditions as a double carbide of iron and manganese. Phos- 
 phorus is associated with iron as a definite phosphide. These compounds 
 are all distinguishable under suitable magnification, but the association 
 of silicon and iron is, so far as present knowledge goes, unrecognizable. 
 
Notes on the Micro-structure of Cast Iron 
 
 347 
 
 Microscopically these constituents have received other names — for 
 instance pare iron is known as "ferrite," hence a structure similar to 
 that of Fig. 96 consists almost entirely of ferrite. Combined carbon 
 receives the term "cementite" and a mixture of cementite and ferrite 
 
 Fig. 97. — Magnified 460 diameters. Fig. 98. — Magnified 360 diameters. 
 
 is known as "pearlite." Pearlite often consists of alternate striae of 
 cementite and ferrite and in such a form gives a magnificent play of 
 colors resembling those of mother-of-pearl, consequently this constituent 
 was named by its discoverer, Dr. Sorby, the "pearly constituent," a term 
 now contracted to "pearhte." ' 
 
 Fig. 99. — Magnified 50 diameters. 
 
 Combined Carbon 3 . 25 Sulphur 0.41 
 
 Silicon 0.78 Phosphorus 0.06 
 
 Manganese o . 09 
 
 The classical researches of Professor Arnold have conclusively shown 
 that iron containing 0.89 per cent carbon consists entirely of pearlite. 
 As the content of carbon increases above 0.89 per cent, structurally free 
 cementite appears increasing in quantity with each increment of carbon. 
 It therefore follows that a white cast iron will consist essentially of 
 
34^ Chemical Analyses 
 
 cementite and pearlite. In the majority of gray irons used in the found- 
 ries the conibined carbon is well below 0.89 per cent — cementite is, 
 therefore, only present as a constituent of pearlite. 
 
 Sulphide globules when in the form of manganese sulphide show a light 
 gray color, while iron sulphide shows a hght brown tint. 
 
 In high sulphur irons the sulphide tends to envelop the crystals; a 
 section cut from such an iron would show a network of sulphide following 
 the crystal junctions and destroying their continuity. These siilphides 
 have been thoroughly investigated by Professor Arnold whose researches 
 have thrown much light on the behaviour of both iron and manganese 
 sulphide. 
 
 The relations of iron and phosphorus have been very thoroughly 
 studied by Mr. J. E. Stead. In September, 1900, Mr. Stead presented 
 
 Fig. 100. — Magnified 50 diameters. 
 
 Combined Carbon 0.82 Manganese 0.09 
 
 Graphite 2.07 Sulphur 0.37 
 
 Sihcon 0.75 Phosphorus 0.07 
 
 before the Iron and Steel Institute a most exhaustive research on this 
 subject. With ordinary pig irons the phosphide of iron appears to be 
 rejected to a eutectic of uncertain composition. Eutectic may for our 
 purpose be defined as that portion last to sohdify. This phosphide 
 eutectic may be readily distinguished in all gray irons by an ordinary 
 etching medium, but in white irons containing structurally free cementite, 
 Mr. Stead's "heat tinting" process becomes necessary to distinguish the 
 eutectic from the cementite. 
 
 Fig. 96 reproduces a photo-microscope of an unetched section of gray 
 iron at a magnification of 60 diameters. 
 
 This magnification gives, as it were, a general view only — to get at the 
 ultimate structure higher powers must be used. Fig. 97 represents the 
 structure of an ordinary gray iron magnified 460 diameters. The larger 
 
Notes on the Micro-structure of Cast Iron 
 
 349 
 
 portion of this field consists of pearlite embedded in which are irregular 
 areas of the phosphide eutectic and several notable black plates of 
 graphite. The phosphide eutectic is recognizable by its irregular shape 
 and broken up structure; an area in the center of the photograph enclos- 
 ing an area of pearlite is worthy of notice. 
 
 Fig. 98 reproduces an area of phosphide eutectic from the same section 
 as Fig. 96. 
 
 A typical white cast iron consisting essentially of pearlite and cementite 
 is shown in Fig. 99. This is a type of iron used as a base for the production 
 of malleable cast iron. 
 
 The influences of annealing are shown in Fig. 100, which represents the 
 same iron as Fig. 99, after going through the ordinary malleable iron 
 
 Fig. ioi. — Magnified 60 diameters. 
 
 annealing in ore. This section consists essentially of pearlite and 
 graphite — the analyses appended to each figure showing the change in 
 carbon condition. For the loan of the negatives illustrating Figs. 99 
 and 100, the writer is indebted to the courtesy of Mr. T. Baker, B. Sc. 
 Quite apart from the clear light thrown on what has been aptly termed 
 the internal architecture of a metal, microscopical examination reveals 
 many other features of profitable interest, one notable feature being the 
 examination of minute flaws. Space will not permit of many illustra- 
 tions under this head, but Fig. loi, reproduced from a photo-nlicrograph 
 of a pin-hole in the same section as Fig. 96, will show the range of possi- 
 bility in this direction. Obviously, a study of flaws of this character 
 offers much to the founder producing castings which have to meet a 
 hydraulic or high steam pressure test. 
 
CHAPTER XIV 
 
 Standard Specifications for Cast Iron Car Wheels 
 
 Chemical Properties 
 The wheels furnished under this specification must be made from the 
 best materials and in accordance with the best foundry methods. The 
 following pattern analysis is given for information, as representing 
 the chemical properties of a good cast iron wheel. Successful wheels, 
 varying in some of the constituents quite considerably from the figures 
 given, may be made: 
 
 Analysis 
 
 Per cent 
 
 Analysis 
 
 Per cent 
 
 Total carbon 
 
 3.50 
 
 2.90 
 
 .60 
 
 .70 
 
 Manganese 
 
 Phosphorus 
 
 Sulphur 
 
 40 
 
 Graphitic carbon 
 
 .50 
 08 
 
 Silicon .... 
 
 
 
 
 
 1. Wheels will be inspected and tested at the place of manufacture. 
 
 2. All wheels must conform in general design and in measurements 
 to drawings which will be furnished, and any departure from the stand- 
 ard drawing must be by special permission in writing. Manufacturers 
 wishing to deviate from the standard dimensions must submit duplicate 
 drawings showing the proposed changes, which must be approved. 
 
 Drop Tests 
 
 3. The following table gives data as to weight and tests of various 
 kinds of wheels for different kinds of cars and service: 
 
 Wheel 
 
 33-inch diameter freight and pas- 
 senger cars 
 
 36-inch diameter 
 
 
 
 Kind of service ...\ 
 
 60,000 lbs. 
 
 capacity 
 
 and less 
 
 I 
 
 600 
 
 70,000 lbs. 
 capacity 
 
 2 
 650 
 
 100,000 lbs. 
 capacity 
 
 3 
 
 700 
 
 Passenger 
 cars 
 
 4 
 700 lbs. 
 
 Locomotive 
 tenders 
 
 5 
 750 lbs. 
 
 Desired . . . 
 Weight \ 
 
 Variation . 
 
 Two per cent either way 
 
 Height of drop, feet. 
 Number of blows . . . 
 
 9 
 10 
 
 12 
 10 
 
 12 
 12 
 
 12 
 12 
 
 12 
 14 
 
 350 
 
Material and Chill ^ 351 
 
 Marking 
 
 4. Each wheel must have plainly cast on the outside plate the name 
 of the maker and place of manufacture. Each wheel must also have 
 cast on the inside double plate the date of casting and a serial foundry 
 number. The manufacturer must also provide for the guarantee mark, 
 if so required by the contract. No wheel bearing a dupUcate number, or 
 a number which has once been passed upon, will be considered. Num- 
 bers of wheels once rejected will remain unfilled. No wheel bearing an 
 indistinct number or date, or any evidence of an altered or defaced 
 number will be considered. 
 
 Measures 
 
 5. All wheels offered for inspection must have been measured with a 
 standard tape measure and must have the shrinkage number stenciled 
 in plain figures on the inside of the wheel. The standard tape measure 
 must correspond in form and construction to the "Wheel Circumference 
 Measure" established by the Master Car Builders' Association in 1900. 
 The nomenclature of that measure need not, however, be followed, it 
 being suflQcient if the graduating marks indicating tape sizes are one- 
 eighth of an inch apart. Any convenient method of showing the shrink- 
 age or stencil number may be employed. Experience shows that 
 standard tape measures elongate a little with use, and it is essential to 
 have them frequently compared and rectified. When ready for inspec- 
 tion, the wheels must be arranged in rows according to shrinkage numbers, 
 all wheels of the same date being grouped together. Wheels bearing 
 dates more than thirty days prior to the date of inspection will not be 
 accepted for test, except by permission. For any single inspection and 
 test, only wheels having three consecutive shrinkage or stencil numbers 
 will be considered. The manufacturer will, of course, decide what three 
 shrinkage or stencil numbers he will submit in any given lot of 103 wheels 
 offered, and the same three shrinkage or stencil numbers need not be 
 offered each time. 
 
 Finish 
 
 6. The body of the wheels must be smooth and free from slag and 
 blowholes, and the hubs must be solid. Wheels will not be rejected 
 because of drawing around the center core. The tread and throat of the 
 wheels must be smooth, free from deep and irregular wrinkles, slag, sand 
 wash, chill cracks or swollen rims, and be free from any evidence of hollow 
 rims, and the throat and tread must be practically free from sweat. 
 
 Material and Chill 
 
 7. Wheels tested must show soft, clean, gray iron, free from defects, 
 such as holes containing slag or dirt more than one-quarter of an inch in 
 
352 Standard Specifications for Cast Iron Car Wheels 
 
 diameter, or clusters of such holes, honeycombing of iron in the hub, 
 white iron in the plates or hub, or clear white iron around the anchors of 
 chaplets at a greater distance than one-haK of an inch in any direction. 
 The depth of the clear white iron must not exceed seven-eighths of an 
 inch at the throat and one inch at the middle of the tread, nor must it be 
 less than three-eighths of an inch at the throat or any part of the tread. 
 The blending of the white hon with the gray iron behind must be without 
 any distinct line of demarcation, and the iron must not have a mottled 
 appearance in any part of the wheel at a greater distance than one and 
 five-eighths inches from the tread or throat. The depth of chill will be 
 determined by inspection of the three test wheels described below, all 
 test wheels being broken for this purpose, if necessary. If one only of 
 the three test wheels fails in limits of chill, all the lot under test of the 
 same shrinkage or stencil number will be rejected and the test will be 
 regarded as finished so far as this lot of 103 wheels is concerned. The 
 manufacturer may, however, offer the wheels of the other two shrinkage 
 or stencil numbers, provided they are acceptable in other respects as 
 constituents of another 103 wheels for a subsequent test. If two of the 
 three test wheels fail in limits of chill, the wheels in the lot of 103 of the 
 same shrinkage or stencil number as these two wheels will be rejected, 
 and, as before, the test will be regarded as finished as far as this lot of 
 103 wheels is concerned. The manufacturer may, however, offer the 
 wheels of the third shrinkage or stencil number, provided they are 
 acceptable in other respects, as constituents of another 103 wheels for 
 a subsequent test. If all three test wheels fail in limits of chill, of course 
 the whole hundred will be rejected. 
 
 Inspection and Shipping 
 
 8. The manufacturer must notify when he is ready to ship not less 
 than 100 wheels; must await the arrival of the inspector; must have a 
 car, or cars, ready to be loaded with wheels, and must furnish facilities 
 and labor to enable the Inspector to inspect, test, load and ship the 
 wheels promptly. Wheels offered for inspection must not be covered 
 with any substance which will hide defects. 
 
 9. One himdred or more wheels being ready for test, the inspector will 
 make a list of the wheel numbers, at the same time examining each wheel 
 for defects. Any wheels which fail to conform to specifications by 
 reason of defects must be laid aside, and such wheels will not be accepted 
 for shipment. As individual wheels are rejected, others of the proper 
 shrinkage or stencil number may be offered to keep the number 
 good. 
 
Thermal Test 353 
 
 Retaping 
 
 10. The inspector will retape not less than 10 per cent of the wheels 
 offered for test, and if he finds any showing wrong tape-marking, he will 
 tape the whole lot and require them to be restenciled, at the same time 
 ha\dng the old stencil marks obliterated. He will weigh and make check 
 measurements of at least 10 per cent of the wheels offered for test, and 
 if any of these wheels fail to conform to the specification, he will weigh 
 and measure the whole lot, refusing to accept for shipment any wheels 
 which fail in these respects. 
 
 Drop Tests 
 
 11. Experience indicates that wheels with higher shrinkage or lower 
 stencil numbers are more apt to fail on thermal test; more apt to fail 
 on drop test and more apt to exceed the maximum allowable chill than 
 those with higher stencil or lower shrinkage numbers; while, on the 
 other hand, wheels with higher stencil or lower shrinkage mmibers are 
 more apt to be deficient in chill. For each 103 wheels apparently 
 acceptable, the inspector will select three wheels for test — one from 
 each of the three shrinkage or stencil numbers offered. One of these 
 wheels chosen for this purpose by the inspector must be tested by drop 
 test as follows: The wheel must be placed flange downward in an anvil 
 block weighing not less than 1700 pounds, set on rubble masonry two 
 feet deep and having three supports not more than five inches wide for 
 the flange of the wheel to rest on. It must be struck centrally upon the 
 hub by a weight of 200 pounds, falhng from a height as shown in the 
 table on page 350. The end of the falling weight must be flat, so as to 
 strike fairly on the hub, and when by wear the bottom of the weight 
 assumes a roimd or conical form, it must be replaced. The machine for 
 making this test is shown on drawings which will be furnished. Should 
 the wheel stand, without breaking in two or more pieces, the niraiber of 
 blows shown in the above table, the one hundred wheels represented by 
 it wiU be considered satisfactory as to this test. . Should it fail, the whole 
 hundred will be rejected. 
 
 Thermal Test 
 
 12. The other two test wheels must be tested as follows: The wheels 
 must be laid flange down in the sand, and a channel way one and one-half 
 inches in width at the center of the tread and four inches deep must be 
 molded with green sand around the wheel. The clean tread of the wheel 
 must form one side of this channel way, and the clean flange must form 
 as much of the bottom as its width will cover. The channel way must 
 
354 Standard Specifications for Cast Iron Car Wheels 
 
 then be filled to the top from one ladle with molten cast iron, which must 
 be poured directly into the channel way without previous cooling or 
 stirring, and this iron must be so hot, when poured, that the ring which 
 is formed when the metal is cold shall be sohd or free from wrinkles or 
 layers. Iron at this temperature will usually cut a hole at the point of 
 impact with the flange. In order to avoid spitting during the pouring, 
 the tread and inside of the flange during the thermal test should be 
 covered with a coat of shellac; wheels which are wet or which have been 
 exposed to snow or frost may be warmed sufficiently to dry them or 
 remove the frost before testing, but under no circumstances must the 
 thermal test be applied to a wheel that in any part feels warm to the 
 hand. The time when pouring ceases must be noted, and two minutes 
 later an examination of the wheel under test must be made. If the wheel 
 is found broken in pieces, or if any crack in the plates extends through 
 or into the tread, the test wheel will be regarded as having failed. If 
 both wheels stand, the whole hundred will be accepted as to this test. 
 If both fail, the whole hundred will be rejected. If one only of the ther- 
 mal test wheels fails, all of the lot under test of the same shrinkage or 
 stencil number will be rejected, and the test will be regarded as finished, 
 so far as this lot of wheels is concerned. The manufacturer may, however, 
 offer the wheels of the other two shrinkage or stencil numbers, provided 
 they are acceptable in other respects, as constituents of another 103 
 wheels for a subsequent test. 
 
 Storing and Shipping 
 
 13. All wheels which pass inspection and test will be regarded as 
 accepted, and may be either shipped or stored for future shipment, as 
 arranged. It is desired that shipments should be, as far as possible, in 
 lots of 100 wheels. In all cases the inspector must witness the shipment, 
 and he must give, in his report, the numbers of all wheels inspected and 
 the disposition made of them. 
 
 Rejections 
 
 14. Individual wheels will be considered to have failed and will not 
 be accepted or further considered, which. 
 
 First. Do not conform to standard design and measurement. 
 
 Second. Are under or over weight. 
 
 Third. Have the physical defects described in Section 6. 
 
 15. Each 103 wheels submitted for test will be considered to have 
 failed and will not be accepted or considered further, if. 
 
 First. The test wheels do not conform to Section 7, especially as to 
 limits of white iron in the throat and tread and around chaplets. 
 
Standard Specifications for Locomotive Cylinders 355 
 
 Second. One of the test wheels does not stand the drop test as de- 
 scribed in Section 11. 
 
 Third. Both of the two test wheels do not stand the thermal test as 
 described in Section 12. 
 
 Standard Specifications for Locomotive Cylinders 
 
 Process of Manufacture 
 Locomotive cylinders shall be made from a good quality of close-grained 
 gray iron cast in a dry sand mould. 
 
 Chemical Properties 
 Drillings taken from test pieces cast as hereafter mentioned shall 
 conforrn to the following limits in chemical composition: 
 
 Silicon from 1.25 to 1.75 per cent 
 
 Phosphorus not over o . 90 per cent 
 
 Sulphur not over o. 10 per cent 
 
 Physical Properties 
 
 The minimum physical qualities for cylinder iron shall be as follows: 
 
 The "Arbitration Test Bar," iH inches in diameter, with supports 
 
 12 inches apart, shall have a transverse strength not less than 3000 
 
 pounds, centrally appUed, and a deflection not less than o.io of an inch. 
 
 Test Pieces and Method of Testing 
 
 The standard test-bar shall be iH inches in diameter, about 14 inches 
 long, cast on end in dry sand. The drillings for analysis shall be taken 
 from this test piece, but in case of rejection the manufacturer shall have 
 the option of analyzing drilhngs from the bore of the cylinder, upon 
 which analysis the acceptance or rejection of the cylinder shall be based. 
 
 One test piece for each cylinder shall be required. 
 
 Character of Castings 
 
 Castings shall be smooth, well cleaned, free from blow-holes, shrinkage 
 cracks or other defects, and must finish to blue-print size. 
 
 Each cyhnder shall have cast on each side of saddle, the manufacturer's 
 mark, serial number, date made and mark showing order number. 
 
 Inspector 
 
 The inspector representing the purchaser shall have all reasonable 
 
 facihties afforded to him by the manufacturer to satisfy himself that the 
 
 finished material is furnished in accordance with these specifications. 
 
 All tests and inspections shall be made at the place of the manufacturer. 
 
356 Standard Specifications for Cast Iron Pipe 
 
 Standard Specifications for Cast-Iron Pipe and 
 Special Castings 
 
 Description of Pipes 
 
 The pipes shall be made with hub and spigot joints, and shall accurately 
 conform to the dimensions given in tablss Nos. I and II. They shall be 
 straight and shall be true circles in section, with their inner and outer 
 surfaces concentric, and shall be of the specified dimensions in outside 
 diameter. They shall be at least 12 feet in length, exclusive of socket. 
 For pipes of each size from 4-inch to 24-inch, inclusive, there shall be two 
 standards of outside diameter, and for pipes from 30-inch to 60-inch, 
 inclusive, there shall be four standards of outside diameter, as shown by 
 table No. II. 
 
 All pipes having the same outside diameter shall have the same inside 
 diameter at both ends. The inside diameter of the lighter pipes of each 
 standard outside diameter shall be gradually increased for a distance of 
 about 6 inches from each end of the pipe so as to obtain the required 
 standard thickness and weight for each size and class of pipe. 
 
 Pipes whose standard thickness and weight are intermediate between 
 the classes in table No. II shall be made of the same outside diameter as 
 the next heavier class. Pipes whose standard thickness and weight are 
 less than shown by table No. II shall be made of the same outside diam- 
 eter as the class A pipes, and pipes whose thickness and weight are more 
 than shown by table No. II shall be made of the same outside diameter 
 as the class D pipes. 
 
 For 4-inch to 12-inch pipes, inclusive, one class of special castings 
 shall be furnished, made from class D pattern. Those having spigot 
 ends shall have outside diameters of spigot ends midway between the 
 two standards of outside diameters as shown by table No. II, and shall be 
 tapered back for a distance of 6 inches. For 14-inch to 24-inch pipes, 
 inclusive, two classes of special castings shall be furnished, class B spe- 
 cial castings with classes A and B pipes, and class D special castings 
 with classes C and D pipes, the former to be stamped "AB" and the 
 latter to be stamped "CD." For 30-inch to 60-inch pipes, inclusive, 
 four classes of special castings shall be furnished, one for each class of 
 pipe, and shall be stamped with the letter of the class to which they 
 belong. 
 
 Allowable Variation in Diameter of Pipes and Sockets 
 Especial care shall be taken to have the sockets of the required size. 
 The sockets and spigots will be tested by circular gauges, and no pipe will 
 be received which is defective in joint room from any cause. The diam- 
 eters of the sockets and the outside diameters of the bead ends of the 
 
Special Castings 357 
 
 pipes shall not vary from the standard dimensions by more than 0.06 
 of an inch for pipes 16 inches or less in diameter; 0.08 of an inch for 
 18-inch, 20-inch and 24-inch pipes; o.io of an inch for 30-inch, 36-inch 
 and 42-inch pipes; 0.12 of an inch for 48-inch, and 0.15 of an inch for 
 54-inch and 60-inch pipes. 
 
 Allowable Variation in Thickness 
 
 For pipes whose standard thickness is less than i inch, the thickness of 
 metal in the body of the pipe shall not be more than 0.08 of an inch less 
 than the standard thickness, and for pipes whose standard thickness is 
 I inch or more, the variation shall not exceed o.io of an inch, except that 
 for spaces not exceeding 8 inches in length in any direction, variations 
 from the standard thickness of 0.02 of an inch in excess of the allowance 
 above given shall be permitted. 
 
 For special castings of standard patterns a variation of 50 per cent 
 greater than allowed for straight pipe shall be permitted. 
 
 Defective Spigots may he Cut 
 
 Defective spigot ends on pipes 12 inches or more in diameter may be 
 cut off in a lathe and a half-round wrought-iron band shrunk into a 
 groove cut in the end of the pipe. Not more than 1 2 per cent of the total 
 number of accepted pipes of each size shall be cut and banded, and no 
 pipe shall be banded which is less than 11 feet in length, exclusive of the 
 socket. 
 
 In case the length of a pipe differs from 12 feet, the standard weight 
 of the pipe given in table No. II shall be modified in accordance therewith. 
 
 Special Castings 
 
 All special castings shall be made in accordance with the cuts and the 
 dimensions given in the table forming a part of these specifications. 
 
 The diameters of the sockets and the external diameters of the bead 
 ends of the special castings shall not vary from the standard dimensions 
 by more than 0.12 of an inch for castings 16 inches or less in diameter; 
 0.15 of an inch for 18-inch, 20-Inch and 24-inch castings; 0.20 of an inch 
 for 30-inch, 36-inch and 42-inch castings; and 0.24 of an inch for 48- 
 inch, 54-inch and 60-inch castings. These variations apply only to 
 special castings made from standard patterns. 
 
 The flanges on all manhole castings and manhole covers shall be faced 
 true and smooth, and drilled to receive bolts of the sizes given in the 
 tables. The manufacturer shall furnish and deUver all bolts for bolting 
 on the manhole covers, the bolts to be of the sizes shown on plans and 
 made of the best quality of mild steel, with hexagonal heads and nuts 
 and sound, well-fitting threads. 
 
3S8 
 
 Standard Specifications for Cast Iron Pipe 
 
 Table No. I. — General Dimensions or Pipes 
 
 K PipelZ'-O" '>i 
 
 Fig. I02. 
 
 Nom- 
 
 
 Actual 
 
 Diameter of 
 sockets 
 
 Depth of 
 sockets 
 
 
 
 
 inal 
 diam., 
 
 Classes 
 
 outside 
 diam., 
 
 
 
 
 
 A 
 
 B 
 
 
 Pipe, 
 inches 
 
 Special 
 
 Pipe, 
 inches 
 
 Special 
 
 C 
 
 inches 
 
 
 inches 
 
 castings, 
 inches 
 
 castings, 
 inches 
 
 
 
 
 4 
 
 A-B 
 
 4.80 
 
 5.60 
 
 5.70 
 
 3.50 
 
 4.00 
 
 1.5 
 
 1.30 
 
 .65 
 
 4 
 
 C-D 
 
 500 
 
 5.80 
 
 5.70 
 
 3.50 
 
 4.00 
 
 1.5 
 
 1.30 
 
 .65 
 
 6 
 
 A-B 
 
 6.90 
 
 7.70 
 
 7.80 
 
 3.50 
 
 4 00 
 
 1.5 
 
 1.40 
 
 .70 
 
 6 
 
 C-D 
 
 7.10 
 
 7.90 
 
 7.80 
 
 3.50 
 
 4.00 
 
 1.5 
 
 1.40 
 
 .70 
 
 8 
 
 
 9.05 
 
 9.85 
 
 10.00 
 
 4.00 
 
 4.00 
 
 1.5 
 
 1.50 
 
 75 
 
 8 
 
 'c-D 
 
 9.30 
 
 10.10 
 
 10.00 
 
 4.00 
 
 4.00 
 
 1.5 
 
 1.50 
 
 .75 
 
 lo 
 
 A-B 
 
 II. 10 
 
 11.90 
 
 12.10 
 
 4.00 
 
 4.00 
 
 1.5 
 
 1.50 
 
 .75 
 
 lO 
 
 C-D 
 
 11.40 
 
 12.20 
 
 12.10 
 
 4. CO 
 
 4.00 
 
 1.5 
 
 1.60 
 
 .80 
 
 12 
 
 A-B 
 
 13.20 
 
 14.00 
 
 14.20 
 
 4.00 
 
 4.00 
 
 1.5 
 
 1.60 
 
 .80 
 
 12 
 
 C-D 
 
 13.50 
 
 14.30 
 
 14.20 
 
 4.00 
 
 4.00 
 
 1. 5 
 
 1.70 
 
 .85 
 
 14 
 
 A-B 
 
 15.30 
 
 16.10 
 
 16.10 
 
 4.00 
 
 4.00 
 
 1. 5 
 
 1.70 
 
 .85 
 
 14 
 
 C-D 
 
 15.6s 
 
 16.45 
 
 16.45 
 
 4.00 
 
 4.00 
 
 1.5 
 
 1.80 
 
 .90 
 
 i6 
 
 A-B 
 
 17.40 
 
 18.40 
 
 18.40 
 
 4.00 
 
 4.00 
 
 1. 75 
 
 1.80 
 
 .90 
 
 i6 
 
 C- 
 
 17.80 
 
 18.80 
 
 18.80 
 
 4.00 
 
 4.00 
 
 1.75 
 
 1.90 
 
 1. 00 
 
 i8 
 
 A-B 
 
 19.50 
 
 20.50 
 
 20.50 
 
 4.00 
 
 4.00 
 
 1.75 
 
 1.90 
 
 • 95 
 
 i8 
 
 C-D 
 
 19.92 
 
 20.92 
 
 20.92 
 
 4.00 
 
 4.00 
 
 1.75 
 
 2.10 
 
 1.05 
 
 20 
 
 A-B 
 
 21.60 
 
 22.60 
 
 22.60 
 
 4.00 
 
 4.00 
 
 1. 75 
 
 2.00 
 
 x.oo 
 
 20 
 
 C-D 
 
 22.06 
 
 23.06 
 
 23.06 
 
 4.00 
 
 4.00 
 
 1.75 
 
 2.30 
 
 1. 15 
 
 24 
 
 A-B 
 
 25.80 
 
 26.80 
 
 26.80 
 
 4.00 
 
 4.00 
 
 2.00 
 
 2.10 
 
 1.05 
 
 24 
 
 C-D 
 
 26.32 
 
 27.32 
 
 27.32 
 
 4.00 
 
 4.00 
 
 2.00 
 
 2.50 
 
 1. 25 
 
 30 
 
 A 
 
 31.74 
 
 32.74 
 
 32.74 
 
 4.50 
 
 4.50 
 
 2.00 
 
 2.50 
 
 LIS 
 
 30 
 
 B 
 
 32.00 
 
 33.00 
 
 33.00 
 
 4.50 
 
 4.50 
 
 2.00 
 
 2.30 
 
 I. IS 
 
 30 
 
 C 
 
 32.40 
 
 33.40 
 
 33.40 
 
 4.50 
 
 4.50 
 
 2.00 
 
 2.60 
 
 1.32 
 
 30 
 
 D 
 
 32.74 
 
 33.74 
 
 33.74 
 
 4.50 
 
 4.50 
 
 2.00 
 
 3.00 
 
 1.50 
 
 36 
 
 A 
 
 37.96 
 
 38.96 
 
 38.96 
 
 4.50 
 
 4.50 
 
 2.00 
 
 2.50 
 
 1. 25 
 
 36 
 
 B 
 
 38.30 
 
 39.30 
 
 39.30 
 
 4.50 
 
 4.50 
 
 2.00 
 
 2.80 
 
 1.40 
 
 36 
 
 C 
 
 38.70 
 
 39.70 
 
 39.70 
 
 4.50 
 
 4.50 
 
 2.00 
 
 3.10 
 
 1.60 
 
 36 
 
 D 
 
 39.16 
 
 40.16 
 
 40.16 
 
 4.50 
 
 4.50 
 
 2.00 
 
 3.40 
 
 1.80 
 
 42 
 
 A 
 
 44.20 
 
 45.20 
 
 45. 20 
 
 5.00 
 
 5.00 
 
 2.00 
 
 2.80 
 
 1.40 
 
 42 
 
 B 
 
 44.50 
 
 45.50 
 
 45.50 
 
 5.00 
 
 5.00 
 
 2.00 
 
 3.00 
 
 I. SO 
 
 42 
 
 C 
 
 45.10 
 
 46.10 
 
 46.10 
 
 5.00 
 
 5.00 
 
 2.00 
 
 3.40 
 
 1. 75 
 
 42 
 
 D 
 
 45.58 
 
 46.58 
 
 46.58 
 
 5.00 
 
 5.00 
 
 2.00 
 
 3.80 
 
 1.95 
 
 48 
 
 A 
 
 50.50 
 
 51.50 
 
 51.50 
 
 5.00 
 
 5.00 
 
 2.00 
 
 3.00 
 
 1.50 
 
 48 
 
 B 
 
 50.80 
 
 51.80 
 
 51.80 
 
 5.00 
 
 5.00 
 
 2.00 
 
 3.30 
 
 1. 6s 
 
 48 
 
 C 
 
 51.40 
 
 52.40 
 
 52.40 
 
 5.00 
 
 5.00 
 
 2.00 
 
 3.80 
 
 1.95 
 
 48 
 
 D 
 
 51.98 
 
 52.98 
 
 52.98 
 
 5.00 
 
 500 
 
 2.00 
 
 4.20 
 
 2.20 
 
 54 
 
 A 
 
 56.66 
 
 57.66 
 
 57.66 
 
 5.50 
 
 5.50 
 
 2.25 
 
 3.20 
 
 1.60 
 
 54 
 
 B 
 
 57.10 
 
 58.10 
 
 58.10 
 
 5.50 
 
 5.50 
 
 2.25 
 
 3.60 
 
 1.80 
 
 54 
 
 C 
 
 57.80 
 
 58.80 
 
 58.80 
 
 5.50 
 
 5.50 
 
 2.25 
 
 4.00 
 
 2.15 
 
 54 
 
 D 
 
 58.40 
 
 59.40 
 
 59.40 
 
 5.50 
 
 5.50 
 
 2.25 
 
 4.40 
 
 2.45 
 
 60 
 
 A 
 
 62.80 
 
 63.80 
 
 63.80 
 
 5.50 
 
 5.50 
 
 2.25 
 
 3.40 
 
 1.70 
 
 60 
 
 B 
 
 63.40 
 
 64.40 
 
 64.40 
 
 5.50 
 
 5.50 
 
 2.25 
 
 3.70 
 
 1.90 
 
 60 
 
 C 
 
 64.20 
 
 65.20 
 
 65.20 
 
 5.50 
 
 5.50 
 
 2.25 
 
 4.20 
 
 2.25 
 
 60 
 
 D 
 
 64.82 
 
 65.82 
 
 65.82 
 
 5.50 
 
 5.50 
 
 2.25 
 
 4.70 
 
 2.60 
 
Standard Specifications for Cast Iron Pipe 
 
 359 
 
 Table No. II. — Standard Thicknesses and Weights of 
 Cast Iron Pipe 
 
 
 
 Class A 
 
 
 
 Class B 
 
 
 Nominal 
 
 ICO ft. head. 43 lbs. 
 
 pressure 
 
 200 ft. head. 86 lbs. 
 
 pressure 
 
 inside 
 
 diameter, 
 
 inches 
 
 
 
 
 
 
 
 Thickness, 
 inches 
 
 Weight per 
 
 Thickness, 
 inches 
 
 Weight per 
 
 
 Foot 
 
 Length 
 
 Foot 
 
 Length 
 
 4 
 
 • 42 
 
 20.0 
 
 240 
 
 .45 
 
 21.7 
 
 260 
 
 6 
 
 .44 
 
 30.8 
 
 370 
 
 .48 
 
 33.3 
 
 400 
 
 8 
 
 -.46 
 
 42.9 
 
 515 
 
 .51 
 
 47-5 
 
 570 
 
 lO 
 
 .50 
 
 57.1 
 
 685 
 
 .57 
 
 63.8 
 
 765 
 
 12 
 
 .54 
 
 72.5 
 
 870 
 
 .62 
 
 82.1 
 
 985 
 
 14 
 
 .57 
 
 89.6 
 
 1.075 
 
 .66 
 
 102.5 
 
 1,230 
 
 i6 
 
 .60 
 
 108.3 
 
 1,300 
 
 .70 
 
 125.0 
 
 1,500 
 
 i8 
 
 .64 
 
 129.2 
 
 1,550 
 
 .75 
 
 150.0 
 
 1,800 
 
 20 
 
 .67 
 
 150 
 
 1,800 
 
 .80 
 
 175.0 
 
 2,100 
 
 24 
 
 .76 
 
 204.2 
 
 2,450 
 
 89 
 
 233.3 
 
 2,800 
 
 30 
 
 .88 
 
 291.7 
 
 3,500 
 
 1.03 
 
 333.3 
 
 4,000 
 
 36 
 
 ■ 99 
 
 391.7 
 
 4,700 
 
 1. 15 
 
 454.2 
 
 5,450 
 
 42 
 
 I. ID 
 
 512. 5 
 
 6,150 
 
 1.28 
 
 591.7 
 
 7,100 
 
 48 
 
 1.26 
 
 666.7 
 
 8,000 
 
 1.42 
 
 750.0 
 
 9,000 
 
 54 
 
 1.35 
 
 800.0 
 
 9,600 
 
 1.55 
 
 933.3 
 
 11,200 
 
 6o 
 
 1.39 
 
 916.7 
 
 11,000 
 
 1.67 
 
 1,104.2 
 
 13,250 
 
 
 
 Class C 
 
 
 
 Class D 
 
 
 Nominal 
 
 300 ft. he£ 
 
 id. 130 lbs. 
 
 pressure 
 
 400 ft. he 
 
 ad. 173 lbs 
 
 . pressure 
 
 inside 
 
 diameter, 
 
 inches 
 
 
 
 
 
 
 
 Thickness, 
 inches 
 
 Weig 
 
 ht per 
 
 Thickness, 
 inches 
 
 Weig 
 
 ht per 
 
 
 Foot 
 
 Length 
 
 Foot 
 
 Length 
 
 4 
 
 .48 
 
 23.3 
 
 280 
 
 .52 
 
 25.0 
 
 300 
 
 6 
 
 
 51 
 
 35.8 
 
 430 
 
 .55 
 
 38.3 
 
 460 
 
 8 
 
 
 56 
 
 52.1 
 
 625 
 
 .60 
 
 55.8 
 
 670 
 
 lO 
 
 
 62 
 
 70.8 
 
 850 
 
 .68 
 
 76.7 
 
 920 
 
 12 
 
 
 68 
 
 91.7 
 
 1,100 
 
 .75 
 
 100. 
 
 1,200 
 
 14 
 
 
 74 
 
 116. 7 
 
 1,400 
 
 .82 
 
 129.2 
 
 1,550 
 
 l6 
 
 
 80 
 
 143.8 
 
 1,725 
 
 .89 
 
 158.3 
 
 1,900 
 
 i8 
 
 
 87 
 
 175.0 
 
 2,100 
 
 .96 
 
 191. 7 
 
 2,300 
 
 20 
 
 
 92 
 
 208.3 
 
 2,500 
 
 1.03 
 
 229.2 
 
 2,750 
 
 24 
 
 
 04 
 
 279.2 
 
 3,350 
 
 1. 16 
 
 306.7 
 
 3,680 
 
 30 
 
 
 20 
 
 400.0 
 
 4,800 
 
 1.37 
 
 450.0 
 
 5.400 
 
 36 
 
 
 36 
 
 545.8 
 
 6,550 
 
 1.58 
 
 625.0 
 
 7.500 
 
 42 
 
 
 54 
 
 716.7 
 
 8,600 
 
 1.78 
 
 825.0 
 
 9.900 
 
 48 
 
 
 71 
 
 908.3 
 
 10,900 
 
 1.96 
 
 1050.0 
 
 12,600 
 
 54 
 
 
 90 
 
 1,141.7 
 
 13,700 
 
 2.23 
 
 1341.7 
 
 16,100 
 
 6o 
 
 2 
 
 00 
 
 1,341.7 
 
 16,100 
 
 2.38 
 
 1583.3 
 
 19,000 
 
 The above weights are for 12-feet laying lengths and standard sockets; propor- 
 tionate allowance to be made for any variation therefrom. 
 
360 Standard Specifications for Cast Iron Pipe 
 
 Marking 
 Every pipe and special casting shall have distinctly cast upon it the 
 initials of the maker's name. When cast especially to order, each pipe 
 and special casting larger than 4-inch may also have cast upon it figures 
 showing the year in which it was cast and a number signifying the order 
 in point of time in which it was cast, the figures denoting the year being 
 above and the number below, thus: 
 
 1901 1901 1901 
 
 I 2 3 
 
 etc., also any initials, not exceeding four, which may be required by the 
 purchaser. The letters and figures shall be cast on the outside and shall 
 be not less than 2 inches in length and % of an inch in relief for pipes 
 8 inches in diameter and larger. For smaller sizes of pipes the letters 
 may be i inch in length. The weight and the class letter shall be con- 
 spicuously painted in white on the inside of each pipe and special casting 
 after the coating has become hard. 
 
 Allowable Percentage of Variation in Weight 
 No pipe shall be accepted the weight of which shall be less than the 
 standard weight by more than 5 per cent for pipes 16 inches or less in 
 diameter, and 4 per cent for pipes more than 16 inches in diameter, and 
 no excess above the standard weight of more than the given percentages 
 for the several sizes shall be paid for. The total weight to be paid for 
 shall not exceed, for each size and class of pipe received, the sum of the 
 standard weights of the same number of pieces of the given size and class 
 by more than 2 per cent. 
 
 No special casting shall be accepted the weight of which shall be less 
 than the standard weight by more than 10 per cent for pipes 12 inches 
 or less in diameter, and 8 per cent for larger sizes, except that curves, 
 Y pieces and breeches pipe may be 12 per cent below the standard weight, 
 and no excess above the standard weight of more than the above per- 
 centages for the several sizes will be paid for. These variations apply 
 only to castings made from the standard patterns. 
 
 Quality of Iron 
 All pipes and special castings shall be made of cast iron of good quality 
 and of such character as shall make the metal of the castings strong, 
 tough and of even grain, and soft enough to satisfactorily admit of 
 drilling and cutting. The metal shall be made without any admixtiu"e 
 of cinder iron or other inferior metal, and shall be remelted in a cupola 
 or air furnace. 
 
Coating 361 
 
 Tests of Material 
 Specimen bars of the metal used, each being 26 inches long by 2 inches 
 wide and i inch thick, shall be made without charge as often as the 
 engineer may direct, and, in default of definite instructions, the con- 
 tractor shall make and test at least one bar from each heat or run of 
 metal. The bars, when placed flatwise upon supports 24 inches apart 
 and loaded in the center, shall for pipes 12 inches or less in diameter 
 support a load of 1900 pounds and show a deflection of not less than 0.30 
 of an inch before breaking, and for pipes of sizes larger than 12 inches 
 shall support a load of 2000 pounds and show a deflection of not less than 
 0.32 of an inch. The contractor shall have the right to make and break 
 three bars from each heat or run of metal, and the test shall be based upon 
 the average results of the three bars. Should the dimensions of the bars 
 differ from those above given, a proper allowance therefor shall be made 
 in the results of the tests. 
 
 Casting of Pipes 
 
 The straight pipes shall be cast in dry sand moulds in a vertical position. 
 Pipes 16 inches or less in diameter shall be cast with the hub end up or 
 down, as specified in the proposal. Pipes 18 inches or more in diameter 
 shall be cast with the hub end down. 
 
 The pipes shall not be stripped or taken from the pit while showing 
 color of heat, but shall be left in the flasks for a sufficient length of time 
 to prevent unequal contraction by subsequent exposure. 
 
 Quality of Castings 
 The pipes and special castings shall be smooth, free from scales, lumps, 
 blisters, sand holes and defects of every nature which unfit them for the 
 use for which they are intended. No plugging or filUng will be allowed. 
 
 Cleaning and Inspection 
 All pipes and special castings shall be thoroughly cleaned and sub- 
 jected to a careful hammer inspection. No casting shall be coated unless 
 entirely clean and free from rust, and approved in these respects by the 
 engineer immediately before being dipped. 
 
 Coating 
 
 Every pipe and special casting shall be coated inside and out with coal- 
 tar pitch varnish. The varnish shall be made from coal tar. To this 
 material sufiicient oil may be added to make a smooth coating, tough and 
 tenacious when cold, and not brittle nor with any tendency to scale off. 
 
 Each casting shall be heated to a temperature of 300° F., immediately 
 before it is dipped, and shall possess not less than this temperature at the 
 
362 
 
 Standard Specifications for Cast Iron Pipe 
 
 time it is put in the vat. The ovens in which the pipes are heated shall 
 be so arranged that all portions of the pipe shall be heated to an even 
 temperature. Each casting shall remain in the bath at least five minutes. 
 
 The varnish shall be heated to a temperature of 300° F. (or less if the 
 engineer shall so order), and shall be maintained at this temperature 
 during the time the casting is immersed. 
 
 Fresh pitch and oil shall be added when necessary to keep the mixture 
 at the proper consistency, and the vat shall be emptied of its contents 
 and refilled with fresh pitch when deemed, necessary by the engineer. 
 After being coated the pipes shall be carefully drained of the surplus 
 varnish. Any pipe or special casting that is to be recoated shall first be 
 thoroughly scraped and cleaned. 
 
 Hydrostatic Test 
 
 When the coating has become hard, the straight pipes shall be sub- 
 jected to a proof by hydrostatic pressure, and, if required by the engineer, 
 they shall also be subjected to a hammer test under this pressure. 
 
 The pressures to which the different sizes and classes of pipes shall be 
 subjected are as follows: 
 
 Classes 
 
 20-inch diam- 
 eter and larger, 
 pounds per 
 square inch 
 
 Less than 
 20-inch diam- 
 eter, pounds 
 per square inch 
 
 Class A pipe 
 
 Class B pipe 
 
 Class C pipe 
 
 Class Dpipe 
 
 ISO 
 200 
 250 
 300 
 
 300 
 300 
 300 
 300 
 
 Weighing 
 The pipes and special castings shall be weighed for payment under the 
 supervision of the engineer after the application of the coal-tar pitch 
 varnish. If desired by the engineer, the pipes and special castings shall 
 be weighed after their delivery and the weights so ascertained shall be 
 used in the final settlement, provided such weighing is done by a legalized 
 weighmaster. Bids shall be submitted and a final settlement made upon 
 the basis of a ton of 2000 pounds. 
 
 Contractor to Furnish Men and Materials 
 The contractor shall provide all tools, testing machines, materials and 
 men necessary for the required testing, inspection and weighing at the 
 foundry, of the pipes and special castings; and, should the purchaser have 
 
Engineer or Inspector 363 
 
 no inspector at the works, the contractor shall, if required by the engineer, 
 furnish a sworn statement that all of the tests have been made as specified, 
 this statement to contain the results of the tests upon the test bars. 
 
 Power of Engineer to Inspect 
 
 The engineer shall be at Uberty at all times to inspect the material at 
 the foundry, and the moulding, casting and coating of the pipes and special 
 castings. The forms, sizes, uniformity and conditions of all pipes and 
 other castings herein referred to shall be subject to his inspection and 
 approval, and he may reject, without proving, any pipes or other casting 
 which is not in conformity with the specifications or drawings. 
 
 Inspector to Report 
 
 The inspector at the foundry shall report daily to the foundry office all 
 pipes and special castings rejected, with the causes for rejection. 
 
 Castings to he Delivered Sound and Perfect 
 
 All the pipes and other castings must be delivered in all respects sound 
 and conformable to these specifications. The inspection shall not reheve 
 the contractor of any of his obligations in this respect, and any defective 
 pipe or other castings which may have passed the engineer at the works 
 or elsewhere shall be at all times liable to rejection when discovered imtil 
 the final completion and adjustment of the contract, provided, however, 
 that the contractor shall not be held liable for pipes or special castings 
 found to be cracked after they have been accepted at the agreed point of 
 dehvery. Care shall be taken in handUng the pipes not to injure the 
 coating, and no pipes or other material of any kind shall be placed in the 
 pipes during transportation or at any time after they receive the coating. 
 
 Definition of the Word ^^ Engineer" 
 
 Wherever the word "engineer" is used herein it shall be understood 
 to refer to the engineer or inspector acting for the purchaser and to his 
 properly authorized agents, limited by the particular duties intrusted 
 to them. 
 
364 Standard Specifications for Cast Iron Pipe 
 
 Volume and Weight of Piled, Bell and Spigot Cast Iron Pipe 
 
 Size of 
 
 Head 
 
 Thick- 
 
 Weight 
 
 No. of 
 pipes in 
 
 Cubic 
 feet in 
 
 No. of 
 
 Pounds 
 
 Cubic 
 
 pipe, 
 
 in 
 
 ness of 
 
 of one 
 
 one ton 
 
 one ton 
 
 pipes in 
 
 of pipe 
 
 feet in 
 
 inches 
 
 feet 
 
 metal, 
 inches 
 
 pipe in 
 pounds 
 
 of 2240 
 pounds 
 
 of 2240 
 pounds 
 
 40 cubic 
 
 feet 
 
 in 40 
 cubic feet 
 
 one 
 pipe 
 
 3 
 
 100 
 
 -.38 
 
 167 
 
 I3^4l 
 
 21.414 
 
 24.935 
 
 4164. 121 
 
 1.604 
 
 3 
 
 200 
 
 .42 
 
 18S 
 
 12. II 
 
 19.796 
 
 24.46s 
 
 4523.320 
 
 1.63s 
 
 3 
 
 300 
 
 • 45 
 
 200 
 
 11.20 
 
 18.961 
 
 23.626 
 
 4724.224 
 
 1.693 
 
 3 
 
 400 
 
 • 45 
 
 200 
 
 11.20 
 
 18.961 
 
 23.626 
 
 4724.224 
 
 1.693 
 
 4 
 
 100 
 
 .40 
 
 230 
 
 9.74 
 
 23.646 
 
 16.479 
 
 3787.720 
 
 2.428 
 
 4 
 
 200 
 
 .42 
 
 243 
 
 9.26 
 
 22.953 
 
 16.135 
 
 3920.034 
 
 2.479 
 
 4 
 
 300 
 
 • 45 
 
 260 
 
 8.61 
 
 22.873 
 
 15.754 
 
 4004.480 
 
 2.539 
 
 4 
 
 400 
 
 • 47 
 
 265 
 
 8.45 
 
 21.823 
 
 15.491 
 
 4104.372 
 
 2.S82 
 
 5 
 
 100 _ 
 
 • 42 
 
 29s 
 
 7.59 
 
 26.S37 
 
 11.433 
 
 3376.136 
 
 3.49s 
 
 5 
 
 200 
 
 • 45 
 
 31S 
 
 7. II 
 
 25.356 
 
 11.222 
 
 3534.332 
 
 3.565 
 
 5 
 
 300 
 
 .48 
 
 338 
 
 6.63 
 
 24.13s 
 
 10.983 
 
 3712.000 
 
 3.642 
 
 5 
 
 400 
 
 • 51 
 
 355 
 
 6.31 
 
 23.503 
 
 10.738 
 
 3811.172 
 
 3.725 
 
 6 
 
 100 
 
 • 43 
 
 364 
 
 6. IS 
 
 28.82s 
 
 8.359 
 
 3008.000 
 
 4.684 
 
 6 
 
 200 
 
 • 47 
 
 393 
 
 5.70 
 
 27.28s 
 
 8.356 
 
 3283.240 
 
 4.787 
 
 6 
 
 300 
 
 • 51 
 
 426 
 
 S.2S 
 
 25^764 
 
 8.177 
 
 3477.224 
 
 4.900 
 
 6 
 
 400 
 
 .54 
 
 445 
 
 5. 03 
 
 25.114 
 
 8.017 
 
 3567.092 
 
 4.990 
 
 8 
 
 100 
 
 • 47 
 
 513 
 
 4.36 
 
 33.425 
 
 5.224 
 
 2680.164 
 
 7.656 
 
 8 
 
 200 
 
 .51 
 
 567 
 
 3.95 
 
 30.833 
 
 5. 118 
 
 2906.196 
 
 7.804 
 
 8 
 
 300 
 
 • 56 
 
 624 
 
 3.59 
 
 28.666 
 
 5.009 
 
 3129.392 
 
 7.98s 
 
 8 
 
 400 
 
 .61 
 
 66s 
 
 3.37 
 
 27.456 
 
 4.906 
 
 3262.730 
 
 8.152 
 
 10 
 
 100 
 
 .50 
 
 685 
 
 3.27 
 
 37.400 
 
 3.454 
 
 2366.256 
 
 11.579 
 
 10 
 
 200 
 
 .56 
 
 765 
 
 2.93 
 
 34-676 
 
 3.388 
 
 2587.484 
 
 11.826 
 
 10 
 
 300 
 
 .62 
 
 852 
 
 2.63 
 
 31.800 
 
 3.317 
 
 2826.248 
 
 12.058 
 
 10 
 
 400 
 
 .68 
 
 920 
 
 2.43 
 
 30.266 
 
 3.216 
 
 2959.172 
 
 12.435 
 
 12 
 
 100 
 
 .53 
 
 870 
 
 2.57 
 
 41.230 
 
 2.497 
 
 2172.492 
 
 16.018 
 
 12 
 
 200 
 
 .60 
 
 985 
 
 2.27 
 
 37-218 
 
 2.444 
 
 2407.236 
 
 X6.367 
 
 12 
 
 300 
 
 .68 
 
 IIIO 
 
 2.02 
 
 33.858 
 
 2.384 
 
 2646.288 
 
 16.778 
 
 12 
 
 400 
 
 • 75 
 
 1210 
 
 1.98 
 
 34.839 
 
 2.159 
 
 2612.892 
 
 17.549 
 
 14 
 
 100 
 
 .56 
 
 1074 
 
 2.08 
 
 44-310 
 
 1.882 
 
 2021 . 388 
 
 21 . 252 
 
 14 
 
 200 
 
 .65 
 
 1229 
 
 1.82 
 
 39-798 
 
 1. 831 
 
 2250.592 
 
 21.843 
 
 14 
 
 300 
 
 • 73 
 
 1399 
 
 1.60 
 
 35.699 
 
 1.794 
 
 2509.568 
 
 22.298 
 
 14 
 
 400 
 
 .82 
 
 1540 
 
 1.45 
 
 33.242 
 
 1.757 
 
 2969.184 
 
 22.847 
 
 16 
 
 100 
 
 .60 
 
 1293 
 
 1.73 
 
 47.325 
 
 1.464 
 
 1893.864 
 
 27.308 
 
 16 
 
 200 
 
 •69 
 
 1496 
 
 1.50 
 
 41-829 
 
 1.434 
 
 2145.788 
 
 27.886 
 
 16 
 
 300 
 
 .79 
 
 1723 
 
 1.30 
 
 37.095 
 
 1. 401 
 
 2415.256 
 
 28.535 
 
 16 
 
 400 
 
 .89 
 
 1900 
 
 1. 18 
 
 36.020 
 
 1. 316 
 
 2490.308 
 
 30.578 
 
 18 
 
 100 
 
 • 63 
 
 1532 
 
 1.46 
 
 48.274 
 
 1. 211 
 
 1855.876 
 
 33019 
 
 18 
 
 200 
 
 74 
 
 I7b8 
 
 1.28 
 
 44.456 
 
 1. 157 
 
 2068.864 
 
 34.569 
 
 18 
 
 300 
 
 .85 
 
 2065 
 
 1.08 
 
 38.572 
 
 1. 124 
 
 2321 . 284 
 
 35.583 
 
 18 
 
 400 
 
 .96 
 
 2300 
 
 .974 
 
 35.441 
 
 T.IOO 
 
 2532.076 
 
 36.338 
 
Volume and Weight of Piled, Bell and Spigot Cast Iron Pipe 365 
 
 Volume and Weight of Piled, Bell and Spigot Cast 
 Iron Pipe {Continued) 
 
 Size of 
 
 Head 
 
 Thick- 
 
 Weight 
 
 No. of 
 pipes in 
 
 Cubic 
 feet in 
 
 No. of 
 
 Pounds 
 
 Cubic 
 
 pipe, 
 inches 
 
 in 
 
 feet 
 
 ness of 
 metal, 
 inches 
 
 of one 
 pipe in 
 pounds 
 
 one ton 
 of 2240 
 pounds 
 
 one ton 
 of 2240 
 pounds 
 
 pipes in 
 
 40 cubic 
 
 feet 
 
 of pipe 
 
 in 40 
 
 cubic feet 
 
 feet in 
 one 
 pipe 
 
 20 
 
 100 
 
 .66 
 
 1,788 
 
 1.28 
 
 53.874 
 
 .945 • 
 
 1778.040 
 
 41.893 
 
 20 
 
 200 
 
 .78 
 
 2,104 
 
 1.06 
 
 45.596 
 
 .938 
 
 1963.836 
 
 42.854 
 
 20 
 
 300 
 
 • 91 
 
 2,444 
 
 .916 
 
 39900 
 
 .918 
 
 2240.272 
 
 43.559 
 
 20 
 
 400 
 
 ■03 
 
 2,740 
 
 .814 
 
 36.508 
 
 .891 
 
 2443.188 
 
 44.850 
 
 24 
 
 100 
 
 .75 
 
 2,407 
 
 .931 
 
 55.122 
 
 .679 
 
 1626.132 
 
 59.207 
 
 24. 
 
 200 
 
 .87 
 
 2,803 
 
 .799 
 
 49.463 
 
 .646 
 
 1811.112 
 
 61.906 
 
 24 
 
 300 
 
 1.02 
 
 3,299 
 
 .679 
 
 43-122 
 
 .630 
 
 2080.876 
 
 63.41S 
 
 24 
 
 400 
 
 1. 16 
 
 3,680 
 
 .600 
 
 38.783 
 
 .619 
 
 2277.256 
 
 64.639 
 
 30 
 
 100 
 
 .87 
 
 3.482 
 
 .649 
 
 59.733 
 
 .434 
 
 1513.268 
 
 92.039 
 
 30 
 
 200 
 
 1. 01 
 
 4,027 
 
 .556 
 
 52.760 
 
 .421 
 
 1697.492 
 
 94.892 
 
 30 
 
 300 
 
 1. 19 
 
 4,783 
 
 .468 
 
 45.550 
 
 .411 
 
 1965.660 
 
 97.337 
 
 30 
 
 400 
 
 1.37 
 
 5,420 
 
 .413 
 
 41.047 
 
 .402 
 
 2181.364 
 
 99.387 
 
 36 
 
 100 
 
 .98 
 
 4,699 
 
 .476 
 
 63.567 
 
 .299 
 
 1407.388 
 
 133.544 
 
 36 
 
 200 
 
 1. 14 
 
 5,460 
 
 .410 
 
 55.586 
 
 .295 
 
 1610.884 
 
 135.577 
 
 36 
 
 300 
 
 1.36 
 
 6,543 
 
 .342 
 
 47.019 
 
 .291 
 
 1903.636 
 
 137.484 
 
 36 
 
 400 
 
 1.58 
 
 7,490 
 
 .300 
 
 42.566 
 
 .282 
 
 2111.516 
 
 141.888 
 
 40 
 
 100 
 
 1.09 
 
 5,807 
 
 .386 
 
 63.591 
 
 .242 
 
 1409.936 
 
 164.745 
 
 40 
 
 200 
 
 1.23 
 
 6,525 
 
 .343 
 
 56.997 
 
 .240 
 
 1570.636 
 
 166.174 
 
 40 
 
 300 
 
 1.48 
 
 7,858 
 
 .285 
 
 48.909 
 
 .233 
 
 1831.588 
 
 171. 610 
 
 40 
 
 400 
 
 1.72 
 
 9,050 
 
 .247 
 
 43.413 
 
 .227 
 
 2059.372 
 
 175.763 
 
 42 
 
 100 
 
 1. 10 
 
 6,147 
 
 .364 
 
 66.117 
 
 .225 
 
 1353.628 
 
 181.640 
 
 42 
 
 200 
 
 1.28 
 
 7,100 
 
 .315 
 
 58.179 
 
 .216 
 
 1537.664 
 
 184.695 
 
 42 
 
 300 
 
 1.54 
 
 8,563 
 
 .258 
 
 48.802 
 
 .211 
 
 1810.768 
 
 189.157 
 
 42 
 
 400 
 
 1.79 
 
 9,890 
 
 .248 
 
 48.002 
 
 .206 
 
 2043.812 
 
 193.559 
 
 48 
 
 100 
 
 1.25 
 
 7,982 
 
 .281 
 
 65.246 
 
 .171 
 
 1370.164 
 
 233.023 
 
 48 
 
 200 
 
 1. 41 
 
 8,946 
 
 .250 
 
 59.800 
 
 .167 
 
 1496.000 
 
 239.200 
 
 48 
 
 300 
 
 1. 71 
 
 10,857 
 
 .206 
 
 50.862 
 
 .166 
 
 1758.940 
 
 246.903 
 
 48 
 
 400 
 
 1.99 
 
 12,550 
 
 .179 
 
 44.767 
 
 .163 
 
 2007.856 
 
 250.097 
 
 60 
 
 100 
 
 1.40 
 
 11,000 
 
 .203 
 
 74.817 
 
 .108 
 
 1193.836 
 
 368.559 
 
 60 
 
 200 
 
 1.68 
 
 13,260 ■ 
 
 .169 
 
 63.188 
 
 .107 
 
 1418.568 
 
 373.897 
 
 60 
 
 300 
 
 2.05 
 
 16,040 
 
 .139 
 
 52.903 
 
 .105 
 
 1685 . 760 
 
 380.599 
 
 60 
 
 400 
 
 2.41 
 
 18,970 
 
 .118 
 
 46.253 
 
 .102 
 
 1938.820 
 
 391.978 
 
 Fig. 103. — Pile of 100 Pipe. 
 
366 
 
 Standard Specifications for Cast Iron Pipe 
 
 ^00 — \co 
 
 vro V- v»-i sr" vjl' vS-r^Uj^t- MN(0 «N<0 cSsjO NpOlOv{0(OsflOl/)u§Sl/5 Tt 
 
 cir-.^i>r<i>THr^or^MO rocs i/^^ r-vo O>oo m o ro in r- ■ - - - 
 
 O lO t^^O 00 t~ O>e0 M O MM MM MM MM MM C<CS 0<(M 
 
 ^^-i 
 
 ON O ONVO 
 
 -. i/^ lov tT ION ■^ io\ ro 
 <0 to t-O 00 t^ q>00 
 
 N-i 151 N «N M vJ" ■* v* vD VJ< 00 CON t^ CCN CS 
 
 r-KUriM rOM !N«XM«NOmNCJ»rtOO«00 
 
 0<r)MO PO<M lO'^ t^io oi t^ M a> po m 
 
 
 sio CO to to 
 
 (-^^lO^c-t^Nr-Oi^T-M 
 ^ <N oi\ M Oi\ O osN O 
 <Ci lO r^vO 00 t^ O>00 
 
 io\ ro "O"^ lO c« t^ 
 
 1/) <M M 00 t~ fO 
 
 w M ro N CO f^ 
 
 ON •* U5\ <N 
 rH O) M M 
 
 T}- (^ to ■<d- 
 
 M O —xoo »-N 
 \0 ir> t~ir) " 
 
 t^ vfjto \!;^ vo 
 
 ) vo cm:^ m ( 
 
 O. M M M 
 
 IT) NpO M NpOO ^ CS 
 
 M inN o^ inxto "3N 1^ 
 
 ^00 X^' 
 
 ^ M ,-1 0> 
 
 M 00 f^O> 
 
 (N M N M 
 
 rt t^ eoN CT> _i ej 
 
 «NvO c§^ O 
 
 ;5l, 
 
 N V- O N- 
 
 t^ rO 0» lo 
 
 Oi CNVO lON 
 
 fj "ON o 
 
 rJSOO —N O 
 
 ■-iN O •-*o <J> ^po O ^ < 
 ^ ir^ cc\ <N co\ M wvo 
 <o ■* r- ly^ 00 o oiy 
 
 OO M 
 
 in-soo s?' q> 
 "to O 
 
 O^ rt O ^x ic 
 
 
 O V- t^ N-- IN 
 
 s:a 
 
 Nfovo vmoo 
 t~xio tis (N 
 TT (M lo r<7 
 
 M V* lO vjvo 
 
 t> rtX Tl- wN M 
 
 ^ 00 lO CJi^O 
 
 ;:§^5 
 
 I o t^ M a> ( 
 
 N lo ro 
 
 vo vr' "* sr< ro \- 0> 
 
 c%N tT 
 
 vo fC f^ •» 00 iQ CMC 
 
 6 ^ M M 
 HlO M l> 
 
 L-y- IN >oN 1 
 r-- M a> I 
 
 spo Tf ^50 cri 
 
 «N 0» «\ (M 
 M ro ro IT) 
 
 lOVO 
 
 -^ ■<«■ SOOO 
 nN (N cSnoo 
 •^ M to CM 
 
 NfC M spOO ^ lj> S50 fO 
 
 CON lO -•N M rH\ 1> T->S -^ 
 
 ro i?> lo I 
 
 0» M M M 
 
 V- O N- l> 
 
 U5N M iO\ r) 
 M ro fO ■* 
 
 s.'S is :S'S sS'i-^;5:S- 
 
 rtiN lOiN'OrOt-rOoO'^aiiO 
 
 'oo 
 
 Njl<VO 
 
 ^\ M 
 
 M M 
 
 CO O^ CO ■ 
 ro M rf I 
 
 Q O M 
 
 VO M t>> 
 
 t^ ro 00 ■* 0> ■* 
 
 
 spO NpO M 
 
 r-.\ 0> "N ro 
 
 i> M a» o 
 
 vfO SCO 
 
 CSs t> «v O^ 
 
 CI t^ « <N 
 
 ro M ^ (N 
 
 dfsM irisrOiSNi/jioxi/) 
 imoOm rOr-iOOM ro 
 ION <£>rO t^rOOO'T 
 
 IN O IN M 
 1-0 M Tt IN 
 
 lO N VO ro r~ ro 00 
 
 ION )2n 
 
 0> rt t- CO '^ 
 ^ O Oi <N 0> 
 
 NfO SfO 
 
 iriN t^ io\ M 
 
 M "* IN a> 
 
 ro M -^ M 
 
 lox lo CON o^ CON ro co\ t~ 
 iMrOrfr^--<NMVO 
 lONvOiN t^roooro 
 
 to Nr-' 
 
 c?s M 2 IN 
 
 rt t- O M 
 
 Oi 00 M ri- 
 
 h-rt 
 
 .b-n 
 
 . c 
 
 - a 
 
 <u 3 
 
 m ;j 
 
 •^g 
 
 •ao 
 
 
 .St3 
 
 gs 
 
 fS^ p:^ p:^ 
 
 ^ : ^ _ 
 
 ^01 Mtn ^w 5^03 
 
 .Stj .^'d .S'O .StJ 
 
 (U;3 OJrJ dJW (Ur^ 
 
 .2 o .2 o .N o .S o 
 
 g^- ^^ g+^- g+i' 
 
 i^M ^ M i^ M ^ M 
 
 ^1 ^1 i«l ^'^ 
 
 PL,^ CL,^ Ph^ Oh^ 
 
 cjq c 's CJ2 _c 
 
 
 CI 
 
 3 
 
 w P< 
 
 - G 
 .2 o 
 
 to Q< 
 
 5 a 
 
 "m P- "w 
 
 .G-O 
 - G 
 
 •2 9 
 
 M O. 
 
 fri i-i. C r! 
 
 Ph^ cw^ eu^ 
 
 i^ M ^ M 
 
 III! 
 
 ^.S- g.S- g.& ^.& g.& ^.& ^.2" g.& ^.& ^.2< g.& ^.& g.S- ^.S- g.S< §.2- S.S- 
 ■'fdi -tCm "rPH -vP^ "tPh -vcih -vPh -jcw -rctn "rO, -jPn -vPh -vOi "rfii -7(1, -jfii -vPh 
 
 MWMMMWNNWrO 
 
Pattern Size and Weight of Cast Iron Pipe 
 
 367 
 
 10 00 00 O M 
 
 to ^90 ro ^ O 
 ■<a-oo <o >-> 
 
 V*' I> x* t^ 
 to ■* 00 t^ 
 
 m-^VO m^ 10 M'^ t S« ro ttf^ O 
 - CTi- w - rO'-'^CTi-.tO 
 CsrO'^t^tOO C^CTlOOCTl 
 Mro N(*5 !Nt ro-* roio 
 
 -N M r-x ro — ^ 10 
 
 10 <N t^ ■^ O 
 
 toroooto OOiMro -^tO tO a> <N 00 00 
 MO) Mcs PiM (NroMrOMrr;rO'*!~oi 
 
 O rO 1-1 irj N to "^ 
 
 VO CO 00 "O 
 
 oro 1-iu^ <Nto -^cnto 
 
 MM M (M M CM CM 
 
 inx <N lox (N irSN M ^ o MX o> 
 
 (NM -^^tOt^CMVOOO-* 
 
 CM fO N W IN ro (^ ■* ro >r> 
 
 00 '^ O r~ 
 
 ■00 X— to N-. CM -^ <0 —xto 
 s rO ctX CM cs~- >-< inx t^ ^ -^ 
 
 1/5 Tj-OO to M 00 ro 
 
 - 0> x<>' C^ ^^ 0% 
 ^tO "X T^ wx M 
 
 1^ ^ 
 
 -Jx O O (M M 
 
 spcto Npot^Njao^x-'M X— N s—rovf) 
 
 cox -* rtx M «xoo t^xto t^ fO t-\ O '-'"~^ 
 
 VOOOO^O OiO<Nc» •^Mto^CN 
 
 MN MCM <N(N NM CMCOCMrOfO 
 
 VOtO 
 
 ,-.X Ifl OiX M 
 
 l> t~ 00 0% CJl I 
 
 10 X- 0» xoo 00 
 
 ^ >ox o n'x !>. 
 
 CM O 10 C-) t~ 
 
 CM <N (N <N (M 
 
 • O <£> 
 CT) PJ 
 
 i> r~ 00 00 
 
 :ss 
 
 00 x-tO X" N x-f 
 
 t^ COX Q tOstO ^"x 
 
 ^X M ^X I> ^X O) 
 
 X— O X-IO--90CM S—IO 
 
 lox .;j- uix cji P3X to t~x ro 
 •^OvtOM <Naiool> 
 CM CM IN ro ro ro ro -^ 
 
 SS> SI 
 
 S^:;xv 
 
 C~ t~ 00 c 
 
 ^2t.:i^s :s;^ 
 
 Npooo ^pto 
 ^x 10 lox o 
 IN ro •^to 
 
 O^ x^tO x-i" ■* XTf IN X— -^ Npo ro 
 . -^ i-x cTi ^x ^ _x ov lox ro mxoo 
 ro CM 10 Tf 00 to O CN 00 00 I/; 
 CM iNiN CMiN (NrororOrOTT 
 
 I iA> to t- 00 00 o>g> 
 
 ^x M ^sx 10 
 IN 1^ Tt 10 to t^ 00 
 
 :sg:si 
 
 X— 00 X— 00 X— CJ^ X'* J> sr-i h 
 
 cox O cox Tt cox 00 i-X O lOX ( 
 
 CMIO •>*r~tOOi CMt^OO- 
 
 CM CM CM IN CM M ro (^ ro • 
 
 to to r»oo 
 
 S^tO 
 00 0\ 
 
 O M M IN CM 
 
 Tftot>ooa>OM CM 
 
 - Ol -■X IN r-X to 
 
 tJ5^! 
 
 f3 
 
 IN ■* 
 
 10 in 
 
 t-X |> nSO ov 
 
 iM m t~\to 
 to to t^ l> 
 
 
 isx 10 uoxtj 
 
 O^OM MM rO'^vOtooooo Om 
 
 •^ lO to I> CM ■* 
 
 CM CM CM CM r<^ ro 
 
 rt ■* m \ri 
 
 XCO X— 
 
 inx M coxoo 
 N CO -H fC 
 
 to to r- t^ 
 
 cox Tl- f~xto 
 CftS 2 2 
 
 X— N— V 10 
 
 lox M lox t^ uix M to Tj- 0> X- I> 
 
 „O^M-<rO •* to t^-nXIN 
 
 IDtO t-00 Ov O IN (N Tt-^tOtO <N ro 
 
 MM MM mCM CMIN OJCM CMCM fOCO 
 
 ;l^to ^ 
 
 
 00 00 q> oi 
 
 <tO ^ M 
 
 o o 
 
 , (T) t^X M 
 
 CM M ro 
 
 M CO CO 
 
 spooo ^^ to ^^ ^ 
 Kx ro t'"^ "^ t^"x \n 
 
 (N CM CN <N 
 
 .2 o .2 o 
 
 CO p< 03 p. 
 
 
 lU 3 
 
 .2 o 
 
 .2 o 
 
 
 CJ- C-w" «-m" c. 
 
 d .i3'T3 .S'u .!:;'d .tJ'd .IS'd -"t) , 
 
 C -a -C -C .G -G -G 
 
 M (Urj (d;3 ds (ua 4)3 4;3 
 
 o .2 o .2 o .2 o N o .2 o .2 o 
 
 p. M P< m P< 'w P< ■(« a 'to P< oi P< 
 
 J G +; G ^- C ^- G +r C ^- G +;■ 
 
 S, fe-S «-f S-B, fe-S, fe-S v-E 
 
 fil "t^'lU "'^ *«! "H'ln ■*^*fn "•^'(Tl +:J'(n 
 
 S'd 
 - G 
 
 2 o 
 « a 
 
 G+;- 
 
 .a-d 
 - G 
 
 .2 o 
 w a 
 
 .s-s 
 
 . G 
 
 .2 o 
 
 u Vi 
 
 p:^ ^^ ^^ ^^ ^^ ^^ 
 
 
 rtll rt'lS '^'i. 
 
 PW^ flH^ (1^^ 
 
 bj) ^ M 
 
 fi;^ (i:^ o;^ II 
 
 'f^oj'fiiU'fiiU'fiiD'fiiiJ'fiiU'f^a)'?, iU'?1«'fliU'il4)'fiaj'5liU'5t<U'?l 
 
 S.& ^.2- ^.S" ^.2< ^.2- g.& g.2- S.2- g.2- g.& g.& ^.& g.2< ^.& g-S- S-S- ^.S- 
 veLi -vCLi -rPn -"rC^ -vf^ •■rP^ -tP-i 'rPn -vPh -vPh -vPh -vcw -ypli -vcli -vPh "rf^ -tPh 
 c»5^io«t^ooa>o CM ■^tooo o M Ti-ou" 
 
 MMMWMCSCMCMCOC 
 
368 Standard Specifications for Cast Iron Pipe 
 
 roao 
 
 
 
 P0"O tf> tr~ 
 
 SCO 00 N- P) sp^ 1 
 «N CTi t^\ t- -N lil 
 
 lov o in\ &. n\ Ti- (~s CT> 
 ic lO I>-00 COO 0> M 
 
 ::t§,:5:^. 
 
 
 
 
 -.\00 ^x rt -N O -X'O 
 w ^ 0000 ir. -- ' " 
 
 t^ IT) rovO o> r~ 
 
 _ VP O -\ iJl --s O "^ 
 
 M ro CN ro N ro 
 
 
 ro vo rovo 
 
 00 Oi O ro P0<O 
 
 NfO MTi- «■* roi/5 
 
 O^ v<c lo veo o >oNio mx N ic-sio fi s 
 (N MM (NrONrONr'5(N'rrroir) i 
 
 J2 • ^ .• .^ 
 
 - c 
 
 jj M 4i M 4J bO 
 
 .aT3 
 
 - a 
 
 ,aT3 .S'a .sxi 
 
 p. w P. in 
 
 W ft 
 
 - G 
 
 to 0< 
 
 dJ ;3 
 
 ix! .sts .a-o 
 
 
 N§ §^s sg gg 
 
 
 - c -c 
 .2 o .E2 o 
 
 P< w O. w p. 
 
 i-S, (LI'S, 
 
 
 Ph^ Ph^ Ph^ O,^ Ph^ Cl,^ (Ih^ Ph^ P.^ Ph^ P.^ Ph^ P.^ Ph^ Ah^ Ph^ Ph^ 
 
 OQ.oS.uS-OQ.yp.^p.'Jp.yp.^o.^o.yp.^p.'Jp.^a.Up.WQ.'^Q. 
 C.S' a-S* C.S* C-S C--^ G-s^ G-i- G-- G-- G-- G-- G-- C-" C-- G-" G-"- C-5« 
 
 ••rp^ -tPh -vPh -vPh -rPn -rP^ -vPh -vct, -vp^ -vCu -tPh -tp^ -jPh "tPh -tPh -vi^ -vp^ 
 
Pattern Size and Weight of Cast Iron Pipe 
 
 369 
 
 Pattern Size and Weight of Cast Iron Pipe, % to ii%2 
 Inches Thick 
 
 Thickness, inches 
 
 % 
 
 2542 
 
 1^6 
 
 m2 
 
 5i 
 
 29^2 
 
 1M6 
 
 40-inch 
 Pipe 
 
 Pattern size, inches 
 
 Weight, pounds 
 
 42 
 3910 
 
 42M6 
 407s 
 
 4240 
 
 4440 
 
 42?i6 
 4405 
 
 44?i6 
 4615 
 
 
 42H 
 4737 
 44H 
 4790 
 
 425/16 
 4903 
 
 44Ma 
 496s 
 
 42% 
 4903 
 
 42-inch 
 Pipe 
 
 48-inch 
 Pipe 
 
 60-inch 
 Pipe 
 
 Pattern size, inches 
 
 Weight, pounds 
 
 Pattern size, inches 
 
 Weight, pounds 
 
 Pattern size, inches 
 
 Weight, pounds 
 
 5140 
 5o7ifl 
 5969 
 
 40-inch 
 
 Pipe 
 42-inch 
 
 Pipe 
 48-inch 
 
 Pipe 
 60-inch 
 
 Pipe 
 
 Thickness, inches 
 
 Pattern size, inches. 
 
 Weight, pounds 
 
 Pattern size, inches. 
 
 Weight, pounds 
 
 Pattern size, inches. 
 Weight, pounds. ; . . . 
 Pattern size, inches. 
 Weight, pounds 
 
 ^^i2 
 
 42JI6 
 
 5070 
 
 44^6 
 
 5316 
 
 50/2 
 
 6068 
 
 42'A 
 5237 
 44V^ 
 5492 
 
 6267. 
 
 lj'^2 
 
 42?i6 
 5404 
 449/1 6 
 
 5668 
 6467 
 
 iHe 
 
 42H 
 
 .5572 
 
 44% 
 
 5844 
 
 5011/6 
 
 6667 
 
 627/^ 
 8282 
 
 I%2 
 
 4211/6 
 
 5740 
 
 44IH6 
 
 6021 
 
 50M 
 
 6867 
 
 621^6 
 
 8532 
 
 Il/i 
 
 42M 
 5908 
 
 44% 
 
 6198 
 
 5oiM( 
 
 7067 
 
 63 
 
 8782 
 
 1^2 
 
 421^6 
 6077 
 
 44^ Me 
 
 637s 
 
 50^^ 
 
 7268 
 
 63I/6 
 
 9032 
 
 Thickness, inches 
 
 40-inch 
 
 Pipe 
 42-inch 
 
 Pipe 
 48-inch 
 
 Pipe 
 60-inch 
 
 Pipe 
 
 Pattern size, inches 
 
 Weight, pounds 
 
 Pattern size, inches 
 
 Weight, pounds 
 
 Pattern size, inches 
 
 Weight, pounds 
 
 Pattern size, inches 
 Weight, pounds 
 
 l3/6 
 
 Ili2 
 
 ■ xH 
 
 19^2 
 
 15/ 6 
 
 1IH2 
 
 A2-A 
 
 4215/6 
 
 43 
 
 43M6 
 
 43^/^ 
 
 433/6 
 
 6246 
 
 64IS 
 
 6585 
 
 6755 
 
 6925 
 
 7096 
 
 44^/B 
 
 4415/6 
 
 45 
 
 45/6 
 
 45H 
 
 45M6 
 
 6552 
 
 6730 
 
 6908 
 
 7086 
 
 7264 
 
 7443 
 
 5015/ 6 
 
 51 
 
 51 He 
 
 51^/^ 
 
 51^16 
 
 S1/4 
 
 7469 
 
 7670 
 
 7871 
 
 8073 
 
 827s 
 
 8477 
 
 63>/i 
 
 63^16 
 
 63I/4 
 
 635/6 
 
 63^/^ 
 
 637/6 
 
 9282 
 
 9532 
 
 9782 
 
 10,032 
 
 10,283 
 
 io,S34 
 
 43H 
 
 7267 
 
 45H 
 
 762 
 
 5IM6 
 
 8679 
 
 63!/^ 
 
 10,785 
 
 40-inch 
 
 Pipe 
 
 42-inch 
 
 . Pipe 
 
 48-inch 
 
 Pipe 
 
 60-inch 
 
 Pipe 
 
 Thickness, inches 
 
 Pattern size, inches 
 
 Weight, pounds 
 
 Pattern size, inches 
 
 Weight, pounds 
 
 Pattern size, inches 
 
 Weight , pounds 
 
 Pattern size, inches 
 Weight, pounds — . 
 
 Il?^2 
 
 43M6 
 7438 
 45^16 
 7801 
 
 513/8 
 
 8882 
 639/6 
 11,086 
 
 I7l6 
 
 7610 
 
 453/i 
 7980 
 51M6 
 9083 
 635/i 
 11,337 
 
 115^2 
 
 43V16 
 
 7782 
 
 45^6 
 
 8160 
 
 51^/ 
 
 9288 
 
 6311/ 6 
 11,588 
 
 ll/ 
 
 43^/^ 
 
 7954 
 
 45/2 
 
 8340 
 
 5I?16 
 
 9491 
 
 63% 
 
 11,839 
 
 ^^^2 
 
 43?i6 
 8127 
 459/6 
 8520 
 5i5/i 
 
 9695 
 631^6 
 
 12,091 
 
 iHe 
 
 435/^ 
 8300 
 45H 
 8700 
 
 511/6 
 
 9899 
 
 63^/^ 
 12,343 
 
 119^2 
 
 43IH6 
 
 8473 
 
 4511/6 
 
 8881 
 
 513/ 
 
 10,103 
 
 6315/ 6 
 
 12,545 
 
370 
 
 Standard Specifications for Cast Iron Pipe 
 
 Pattern Size and Weight of Cast Iron Pipe, i^i to 2^2 
 Inches Thick 
 
 40-inch 
 
 Pipe 
 42-inch 
 
 Pipe 
 48-inch 
 
 Pipe 
 60-inch 
 
 Pipe 
 
 Thickness, inches 
 
 Pattern 
 Weight, 
 Pattern 
 Weight, 
 Pattern 
 Weight, 
 Pattern 
 Weight, 
 
 size, inches 
 
 pounds 
 
 size, inches 
 
 pounds 
 
 size, inches 
 
 pounds 
 
 size, inches 
 pounds 
 
 15.^ 
 
 121.^2 
 
 iiHe 
 
 I2-H2 
 
 1% 
 
 43% 
 
 431^6 
 
 43H 
 
 43IM6 
 
 44 
 
 8647 
 
 8821 
 
 8995 
 
 9170 
 
 9345 
 
 45% 
 
 451% 6 
 
 4574 
 
 451^6 
 
 46 
 
 9062 
 
 9243 
 
 9424 
 
 9606 
 
 9788 
 
 5113/16 
 
 sm 
 
 51IM6 
 
 52 
 
 52H6 
 
 10,307 
 
 10,512 
 
 10,717 
 
 10,922 
 
 11,127 
 
 64 
 
 64H6 
 
 641/i 
 
 64% 6 
 
 64H 
 
 12.847 
 
 13.099 
 
 13,357 
 
 13,603 
 
 13,856 
 
 l25'^2 
 
 44H6 
 9520 
 
 46Ha 
 
 9970 
 
 52}^ 
 
 11.333 
 
 645/I9 
 
 14.109 
 
 40-inch 
 
 Pipe 
 42-inch 
 
 Pipe 
 48-inch 
 
 Pipe 
 60-inch 
 
 Pipe 
 
 Thickness, inches 
 
 Pattern size, inches 
 
 Weight, pounds 
 
 Pattern size, inches. 
 
 Weight , pounds 
 
 Pattern size, inches. 
 
 Weight, pounds 
 
 Pattern size, inches. 
 Weight, pounds. . . . . 
 
 ii^ie 
 
 l2J^2 
 
 iH 
 
 129,62 
 
 iiMe 
 
 44H 
 
 44% 6 
 
 uVi 
 
 
 
 9688 
 
 9862 . 
 
 10,048 
 
 
 
 46K8 
 
 46% 6 
 
 46H 
 
 46M6 
 
 463,i 
 
 10,152 
 
 10,335 
 
 10,518 
 
 10,700 
 
 10,885 
 
 52M6 
 
 52^/4 
 
 52% 6 
 
 523/i 
 
 52^6 
 
 11,539 
 
 11,745 
 
 11,951 
 
 12,158 
 
 12,365 
 
 64% 
 
 64% 6 
 
 64M6 
 
 64?'i6 
 
 645/i 
 
 14,362 
 
 14,61s 
 
 14,868 
 
 15,121 
 
 15,374 
 
 13^2 
 
 52^ 
 12,572 
 64IH6 
 15,628 
 
 Thickness, inches 
 
 2 
 
 2}i2 
 
 2/16 
 
 23^2 
 
 2H 
 
 40-inch 
 Pipe 
 
 42-inch 
 Pipe 
 
 48-inch 
 Pipe 
 
 Pattern size, inches 
 
 Weight, pounds 
 
 Pattern size, inches 
 
 Weight, pounds 
 
 Pattern size, inches 
 
 Weight, pounds 
 
 
 
 
 
 52% 6 " 
 
 12,779 
 
 64% 
 
 15,882 
 
 525/^'" 
 12,987 
 6413/16 
 16,136 
 
 521/16' 
 13,195 
 
 em 
 16,390 
 
 523/4'" 
 13,443 
 64IM6 
 16,644 
 
 521% 6 
 13,611 
 
 60-inch 
 Pipe 
 
 Pattern size, inches 
 
 Weight, pounds. .... 
 
 65 
 16,898 
 
 
 
 
 Thickness, inches 
 
 25/^2 
 
 2H6 
 
 2^2 
 
 2Vi 
 
 2^62 
 
 40-inch 
 
 Pipe 
 42-inch 
 
 Pipe 
 ^'-inch 
 
 Pipe 
 60-inch 
 
 Pipe 
 
 Pattern size, inches 
 
 Weight, pounds 
 
 Pattern size, inches 
 
 Weight, pounds 
 
 Pattern size, inches 
 
 Weight, pounds 
 
 Pattern size, inches 
 
 Weight, pounds . ' 
 
 
 
 
 
 651/6' 
 17,152 
 
 65^'" 
 17,407 
 
 653/6" 
 17,662 
 
 e'sii" 
 17,917 
 
 65M6'" 
 
 18,172 
 
 
 
 
CHAPTER XV 
 MECHANICAL ANALYSIS 
 
 While chemical analysis is absolutely necessary for the determination 
 of the constituents of iron and the fuels, and is of greatest importance to 
 the foundryman as a guide in their purchase, chemists cannot, however, 
 as yet predict with certainty the physical properties which will result 
 from the mixture of irons possessing identical composition. 
 
 Test bars have shown, that of two irons, precisely the same in their 
 chemical constituents, one may exceed the other in tensile strength by 
 as much as 50 per cent. No satisfactory explanation of the discrepancy 
 has been made. Various suggestions, attributing the cause to the ores, 
 changes of temperature in the furnace, to difference in cooling, etc., are 
 offered, but the problem is still unsolved. 
 
 Whatever may be the cause of these differences, the foundryman needs 
 some means of quickly detecting and correcting them. He should 
 have prompt information as to shrinkage, softness and strength of his 
 castings. 
 
 During 1885, Mr. Keep made the important discovery that the shrink- 
 age of test bars varied inversely as the siUcon content, and that by 
 measurement of shrinkage the silicon is practically determined. 
 
 His investigations resulted in pointing out the intimate relations which 
 exist between shrinkage and the other properties of cast iron, both 
 chemical and physical. Mr. Keep's conclusions as to the importance of 
 mechanical analysis are summarized as follows: 
 
 The physical properties of the casting are not wholly dependent upon 
 its chemical composition. 
 
 Mechanical analysis measures the physical properties of the iron, 
 which are, shrinkage, strength, deflection, set and depth of chill. The 
 measure of these properties shows the combined influence of each element 
 in the chemical composition, and in addition thereto, it shows the in- 
 fluence of fuel and every varying condition attending melting. 
 
 These influences, particularly that of sulphur, are counteracted by the 
 use of silicon. 
 
 The measurement of shrinkage tells whether more or less silicon is 
 needed to bring the quality of the casting to an accepted standard of 
 excellence. 
 
 371 
 
372 Mechanical Analysis 
 
 Instead of calculating the chemical composition and predicting the 
 physical properties, mechanical analysis ascertains the physical proper- 
 ties first, and determines from the shrinkage whether more or less silicon 
 is required to produce castings of a given standard. Measurement of 
 shrinkage is made quickly at a nominal cost and alone gives all necessary 
 information. 
 
 It teUs the founder exactly what physical properties his castings have 
 and exactly what to do to bring each of those properties to standard. 
 By this method a founder can determine whether a low-priced iron is 
 suitable for his use. 
 
 Having fixed upon a standard, he can ascertain during the heat 
 whether the mixture is of the desired quality, and if necessary can increase 
 or decrease the silicon, according as the shrinkage should be reduced or 
 increased. 
 
 Mechanical analysis answers all the requirements of the ordinary 
 founder. Its simphcity renders the employment of an expert unneces- 
 sary. 
 
 Pig iron and coke, having been purchased upon guaranteed analysis, 
 an occasional analysis of the castings is only required. 
 
 In a report to The American Society of Mechanical Engineers, Mr. 
 Keep presents a Shrinkage Chart and Strength Table, which are given 
 below with his directions for using them. 
 
 Shrinkage Chart 
 
 W. J. Keep 
 
 While the tensile tests show an increase of strength with an increase 
 of phosphorus, yet the transverse tests seem to show that phosphorus 
 reduces strength. This is also general shop experience. 
 
 Sulphur. — There is not in these tests enough imiformity between 
 the percentage of sulphur and the strength to show any decided influence, 
 but the indication is that sulphur decreases strength. In some cases 
 sulphur might add to strength by causing the grain to be closer. 
 
 Manganese. — The percentage is too nearly the same in these series 
 to show any influence on strength. 
 
 By comparing strengths and chemical composition of the irons nearest 
 ahke, with all chemical elements nearly alike, and no scrap, but with 
 quite different strengths, it is very evident that strength is dependent 
 upon something outside of the ordinary chemical composition. 
 
 Slow cooHng decreases strength by making the grain of a casting 
 coarse and more open. The larger the casting the weaker it become? 
 per square inch of section. The weakness is not caused by a decrease 
 in combined carbon because a complete analysis of each size of test bar 
 
Shrinkage Chart 
 
 373 
 
 (Transactions, American Society of Mechanical Engineers, Vol. XVI, 
 p. hoc) shows the same combined carbon in all sizes of many series, 
 but in all cases the strength per unit of section decreased as the size 
 increased. 
 
 Strength of any size of test bar cannot be calculated by any mathe- 
 matical formula from the measured strength of another size, because the 
 grain changes by slow cooling. 
 
 1.00 1.25 1.50 1.75 2.00 2.25 2.50 2.75 3.00 3.25 3.50 
 
 425 
 400 
 375 
 350 
 325 
 300 
 275 
 250 
 225 
 200 
 175 
 
 3400 
 3200 
 3000 
 2800 
 2600 
 2400 
 2200 
 
 - 
 
 
 
 
 
 
 
 
 
 ^ 
 
 
 
 
 
 
 
 ^ 
 
 
 
 
 
 
 
 ^ 
 
 M 
 
 
 
 
 
 
 
 
 y 
 
 y" 
 
 
 
 
 
 
 
 J 
 
 
 
 
 
 
 
 
 
 
 / 
 
 
 
 
 
 
 
 
 
 
 
 
 ^^ 
 
 -^ 
 
 
 
 
 
 
 
 ■^ 
 
 
 
 
 2x 
 
 1" 
 
 
 
 
 
 2000 
 
 - 
 
 / 
 
 ^^' 
 
 
 
 
 • 
 
 1800 
 
 — 
 
 
 ^ 
 
 
 2 
 
 
 
 
 
 
 
 1600 
 
 
 
 
 
 . 3 
 
 ~> — — 
 
 
 
 
 
 ' 
 
 1400 
 
 
 
 
 
 
 -~^ 
 
 ^S_ 
 
 ■ 
 
 
 
 -- 
 
 
 
 
 
 
 
 
 . 
 
 
 ~^ 
 
 1.00 1.25 1.50 1.75 2.00 2,25 250 2.75 3,00 3.25 3.50, 
 Percent Silicon. 
 
 Fig. 104. 
 
 Tensile Strength Chart. — Fig. 105 shows this chart. The dotted line 
 
 estimated. 
 
 " Table for Obtaining the Strength of any Size of Test Bar from the 
 Measured Strength of the Standard Test Bar. — Table on p. 375 is cal- 
 culated for a standard i-inch square test bar. Measure the shrinkage 
 per foot of the standard test bar, then on the shrinkage chart. Fig. 105, 
 find this shrinkage on the left-hand margin and follow horizontally 
 until you intersect the line of the measured test bar. Follow the 
 vertical line at the intersection to the top of the chart, and you find 
 the percentage of silicon that is expected to produce the shrinkage. 
 Find this same percentage at the top of Table i , and follow down to the 
 size of test bar that you wish the strengths of. If you wish the actual 
 
374 
 
 Mechanical Analysis 
 
 strength use the lower figures as multiplier of the measured strength of 
 the standard i-inch bar. If you wish the strength of a section i inch 
 square by 12 inches long of the required test bar use the upper number 
 to multiply by." 
 
 "If you have the strength of any size of test bar other than a i-inch 
 bar and know the silicon percentage, divide such strength by the lower 
 
 'I. I.Z5 1.50 ir75 2.00 2Z5 ?.50 2.75 3.00 3.25 350 
 Percent. 
 
 Fig. 105. 
 
 number for the bar, or if you have the strength of a section of the re- 
 quired test bar i inch square by 12 inches long, divide by the upper 
 number, and the result in either case is the strength of the standard 
 I-inch bar." 
 
 "To find the Strength of any Casting. — Divide the cubic contents of 
 the casting by the square inches of cooling surface, and the quotient is 
 the cooling ratio. If the casting has a large flat surface the edges may 
 be neglected; for example, a casting i inch thick and 24 inches square. 
 
Keep's Strength Table 
 
 375 
 
 M I> t> 
 
 8 8 8 -2 8 ^8 
 
 lO O 
 00 t- 
 lO w 
 
 00 t~ 
 
 P> S 
 
 8 8 
 
 ft 8 
 
 §;§ 
 
 ro O 
 00 CTi 
 (^ (N 
 00 00 
 
 
 ;^^ 
 
 ^^ eg ^ 
 
 00 00 J> CI 
 
 <0 (O 
 
 00 00 l~- CO 
 
 <0 Q fO O 
 
 1-- o o> o 
 o o <o lO 
 
 R2 
 
 00 to 
 
 o> o c?> o 
 
 to M O 
 
 lO o 
 
 i~0 o 
 (M ro 
 
 M l> ■'t 
 
 t^ o 
 
 to ^ 
 
 CO lO 
 
 J> ^ 
 
 PO O to o 
 
 00 3> 00 •* 
 
 00 a> 00 to 
 
 8 §S 88 
 
 S R 
 
 13 ^ 
 
 
 :s 
 
376 
 
 Mechanical Analysis 
 
 A strip one inch wide and 24 inches long would have 24 cubic inches 
 contents and 48 square inches of cooling surface. 24 ^ 48 = 0.5 ratio. 
 Find this ratio at the top of the chart, Fig. 105, and follow down to the 
 
 Iron follow-board with yokes and brass 
 pasterns for test bars Yi in. square X 
 12 in. long. 
 
 Fig. 106. 
 
 Iron Flask. 
 
 diagonal and we find that a 2-inch square test bar represents the strength 
 of the casting." 
 
 "With the shrinkage of a standard i-inch test bar, cast at the same 
 time as the casting, find on the shrinkage chart the percentage of silicon 
 
 in the casting. Then in the Table 
 
 Taper steel scale which measures 
 shrinkage. 
 Fig. 107. 
 
 find the upper multiplier for a 2 -inch 
 test bar. This multipHed by the 
 measured strength of the standard 
 test bar gives the strength of a sec- 
 tion of the casting i inch square 
 and 12 inches long." 
 
 Mechanical analysis covers tests 
 for shrinkage, strength and hard- 
 
 Figs. 106 and 107 show a device 
 designed by Mr. Keep for determin- 
 ing shrinkage. 
 
 Determinations for strength are 
 generally made by taking the trans- 
 verse strength and deflection. 
 
 The Riehle Machine as shown in 
 Fig. 108 is in common use for this 
 purpose. 
 
 This illustration represents faith- 
 fully the general appearance of this 
 machine. The specimen is shown in position. The weighing-beams 
 and levers are all carefully sealed to the standard of the United States 
 Government, and guaranteed to be accurate and reliable. 
 
 Fig. 108. 
 
Constituents of Cast Iron 377 
 
 Operation 
 
 The weighing-beam must be balanced before the specimen is arranged 
 for testing. The wheel shown must be moved from left to right, and, 
 as the beam rises, the poise must be moved out to restore the equipoise. 
 If more strain is required to break the specimen than can be weighed by 
 the poise, move the poise back to zero and place the loose weight on the 
 weight dish shown at the extreme left (small end) of weighing-beam, and 
 move the poise out as before, until the test is completed. The calcula- 
 tions are made so that the beam registers the center load. 
 
 Dimensions 
 
 Extreme length 3 ft. 2 in. 
 
 Extreme height . 3 ft. i in. 
 
 Extreme width i ft. 4 in. 
 
 Weight 200 lbs. 
 
 Shipping weight . 230 lbs. 
 
 Adaptation 
 Transverse specimens 12 in. long 
 
 Hardness 
 
 This property may be measured by embedding steel balls in the casting 
 to be tested, by Turner's Scleroscope (see cut, page 114, Turner's Lec- 
 tures on " Founding "); or by Keep's Machine (see cut, page 187, " Cast 
 Iron "). The latter method is the more simple and gives accurate results. 
 A small high speed drill may be used for this piupose, but it must be so 
 arranged that the load on the spindle will be constant. 
 
 Standard Methods for Determining the Constituents 
 of Cast Iron 
 
 As reported by the Committee of the American Foundrymen's Association, Phila- 
 delphia Convention, May 21-24, IQO?- 
 
 Determination of Silicon 
 
 Weigh one gram of sample, add 30 c.c. nitric acid (1.13 sp. gr.); 
 then 5 c.c. sulphuric acid (cone). Evaporate on hot plate imtil all 
 fumes are driven off. Take up in water and boil until all ferrous sul- 
 phate is dissolved. Filter on an ashless filter, with or without suction 
 pump, using a cone. Wash once with hot water, once with hydrochloric 
 acid, and three or four times with hot water. Ignite, weigh and evapo- 
 
378 Chemical Analysis 
 
 rate with a few drops of sulphuric acid and 4 or 5 c.c. of hydrofluoric acid. 
 Ignite slowly and weigh. Multiply the difference in weight by 0.4702, 
 which equals the per cent of siHcon. 
 
 Determination 0} Sulphur 
 
 Dissolve slowly a three-gram sample of driUings in concentrated nitric 
 acid in a platinum dish covered with an inverted watch glass. After 
 the iron is completely dissolved, add two grams of potassium nitrate, 
 evaporate to dryness and ignite over an alcohol lamp at red heat. Add 
 50 c.c. of a one per cent solution of sodium carbonate, boil for a few 
 minutes, filter, using a little paper pulp in the filter if desired, and wash 
 with a hot one per cent sodium carbonate solution. Acidify the filtrate 
 with hydrochloric acid, evaporate to dryness, take up with 50 c.c. of 
 water and 2 c.c. of concentrated hydrochloric acid, filter, wash and after 
 diluting the filtrate to about 100 c.c. cool and precipitate with barium 
 chloride. Filter, wash well with hot water, ignite and weigh as barium 
 sulphate, which contains 13.733 per cent of sulphur. 
 
 Determination of Phosphorus 
 
 Dissolve 2 grams sample in 50 c.c. nitric acid (sp. gr., 1.13), add 10 c.c. 
 hydrochloric acid and evaporate to dryness. In case the sample contains 
 a fairly high percentage of phosphorus it is better to use half the above 
 quantities. Bake imtil free from acid, redissolving in 25 to 30 c.c. of 
 concentrated hydrochloric acid; dilute to about 60 c.c, filter and wash. 
 Evaporate to about 25 c.c, add 20 c.c. concentrated nitric acid, evapo- 
 rate imtil a film begins to form, add 30 c.c. of nitric acid (sp. gr., 1.20) 
 and again evaporate until a film begins to form. Dilute to about i5(» c.c 
 with hot water and allow it to cool. When the solution is between 70 
 degrees and 80 degrees C. add 50 c.c. of molybdate solution. Agitate 
 the solution a few minutes, then filter on a tarred Gooch crucible having 
 a paper disc at the bottom. Wash three times with a 3 per cent nitric 
 acid solution and twice with alcohol. Dry at 100 degrees to 105 degrees 
 C. to constant weight. The weight multiplied by 0.0163 equals the per 
 cent of phosphorus in a i-gram sample. 
 
 To make the molybdate solution add 100 grams molybdic acid to 
 250 c.c. water, and to this add 150 c.c. ammonia, then stir until all is 
 dissolved and add 65 c.c. nitric acid (1.42 sp. gr.). Make another solu- 
 tion by adding 400 c.c. concentrated nitric acid to iioo c.c water, and 
 when the solutions are cool, pour the first slowly into the second 
 with constant stirring and add a couple of drops of ammonium 
 phosphate. 
 
Determination of Total Carbon 379 
 
 Determination of Manganese 
 
 Dissolve one and one-tenth grams of drillings in 25 c.c. nitric acid 
 (1.13 sp. gr.), filter into an Erlenmeyer flask and wash with 30 c.c, of the 
 same acid. Then cool and add about one-half gram of bismuthate until 
 a permanent pink color forms. Heat until the color has disappeared, 
 with or without the precipitation of manganese dioxide, and then add 
 either sulphurous acid or a solution of ferrous sulphate until the solution 
 is clear. Heat until all nitrous oxide fumes have been driven off, cool 
 to about fifteen degrees C; add an excess of sodium bismuthate — about 
 one gram — and agitate for two or three minutes. Add 50 c.c. water 
 containing 30 c.c. nitric acid to the litre, filter on an asbestos filter into 
 an Erlenmeyer flask, and wash with fifty to one hundred c.c. of the nitric 
 acid solution. Run in an excess of ferrous sulphate and titrate back with 
 potassium permanganate solution of equal strength. Each c.c. of N-io 
 ferrous sulphate used is equal to o.io per cent of manganese. 
 
 Determination of Total Carbon 
 
 This determination requires considerable apparatus; so in view of 
 putting as many obstacles out of the way of its general adoption in cases 
 of dispute, your committee has left optional several points which were 
 felt to bring no chance of error into the method. 
 
 The train shall consist of a pre-heating furnace, containing copper 
 oxide (Option No. i) followed by caustic potash (1.20 sp. gr.), then 
 calcium chloride, following which shall be the combustion furnace in 
 which either a porcelain or platinum tube may be used (Option No. 2), 
 The tube shall contain four or five inches of copper oxide between plugs 
 of platinum gauze, the plug to the rear of the tube to be at about the 
 point where the tube extends from the furnace. A roll of silver foil about 
 two inches long shall be placed in the tube after the last plug of platinum 
 gauze. The train after the combustion tube shaU be anhydrous cupric 
 sulphate, anhydrous cuprous chloride, calcium chloride, and the absorp- 
 tion bulb of potassium hydrate (sp. gr., 1.27) with prolong filled with 
 calcium chloride. A calcium chloride tube attached to the aspirator 
 bottle shall be connected to the prolong. 
 
 In this method a single potash bulb shall be used. A second bulb is 
 sometimes used for a coimterpoise being more liable to introduce error 
 than correct error in weight of the bulb in use, due to change of tempera- 
 ture or moisture in the atmosphere. 
 
 The operation shall be as follows: To i gram of weU-mixed drilhngs 
 add 100 c.c. of potassium copper chloride solution and 7.5 c.c. of hydro- 
 chloric acid (cone). As soon as dissolved, as shown by the disappearance 
 
380 Chemical Analysis 
 
 of all copper, filter on previously washed and ignited asbestos. Wash 
 thoroughly the beaker in which the solution was made with 20 ex. of 
 dilute hydrochloric acid [i to i], pour this on the filter and wash the carbon 
 out of the beaker by means of a wash bottle containing dilute hydro- 
 chloric acid [i to i] and then wash with warm water out of the 
 filter. Dry the carbon at a temperature between 95 and 100 de- 
 grees C. 
 
 Before using the apparatus a blank shall be run and if the bulb does 
 not gain in weight more than 0.5 milligram, put the dried filter into the 
 igm'tion tube and heat the pre-heating furnace and the part of the com- 
 bustion furnace containing the copper oxide. After this is heated start 
 the aspiration of oxygen or air at the rate of three bubbles per second, to 
 show in the potash bulb. Continue slowly heating the combustion tube 
 by turning on two burners at a time, and continue the combustion for 
 30 minutes if air is used; 20 minutes if oxygen is used. (The Shimer 
 crucible is to be heated with a blast lamp for the same length of 
 time.) 
 
 When the ignition is finished turn o2 the gas supply gradually so as 
 to allow the combustion tube to cool off slowly and then shut off the 
 oxygen supply and aspirate with air for 10 minutes. Detach the potash 
 bulb and prolong, close the ends with rubber caps and allow it to stand 
 for 5 minutes, then weigh. The increase in weight multiplied by 0.27273 
 equals the percentage of carbon. 
 
 The potassium copper chloride shall be made by dissolving one pound 
 of the salt in one litre of water and filtering through an asbestos 
 filter. 
 
 Option No. I. — While a pre-heater is greatly to be desired, as only 
 a small percentage of laboratories at present use them, it was decided 
 not to make the use of one essential to this method; subtraction of the 
 weight of the blank to a great extent eliminating any error which might 
 arise from not using a pre-heater. 
 
 Option No. 2. — The Shimer and similar crucibles are largely used as 
 combustion furnaces and for this reason it was decided to make optional 
 the use of either the tube furnace or one of the standard crucibles. In 
 case the crucible is used it shall be followed by a copper tube He inch 
 inside diameter and ten inches long, with its ends cooled by water jackets. 
 In the center of the tube shall be placed a disk of platinum gauze, and 
 for three or four inches in the side towards the crucible shall be silver foil 
 and for the same distance on the other side shall be copper oxide. The 
 ends shall be plugged with glass wool, and the tube heated with a fish 
 tail burner before the aspiration of the air is started. 
 
Graphite 381 
 
 Graphite 
 Dissolve one-gram sample in 35 c.c. nitric acid [1.13 sp. gr.], filter on 
 asbestos, wash with hot water, then with potassium hydrate [i.i sp. gr.] 
 and finally with hot water. The graphite is then ignited as specified in 
 the determination of total carbon. 
 
CHAPTER XVI 
 MALLEABLE CAST IRON 
 
 The process of rendering iron castings malleable was discovered by- 
 Reaumur in 1722 and is essentially the same as that pursued at the 
 present day. 
 
 McWilliams and Longmuir divide malleable castings into two classes. 
 
 1. Black Heart 
 
 Black heart has a silvery outside and black inside, with a silky 
 lustre. This is made of a hard white iron, containing from 3 to 4 per 
 cent carbon, as hard carbide of iron. 
 
 By the process of annealing, to be described later, the carbide of iron 
 is decomposed into free carbon (annealing carbon) and iron; leaving a 
 soft malleable iron, which contains nearly all of the initial carbon but 
 in the free state finely divided and intermixed with the iron. 
 
 Black heart is mostly made in America. The process is conducted 
 much more rapidly than that of the ordinary (or Reaumur process), but 
 requires more skill and scientific information. The iron used must be 
 low in silicon and sulphur but need not necessarily be a white iron. 
 
 The analysis should approximate to, silicon, i per cent to 0.5 per cent; 
 sulphur, .05 per cent as a maximum; phosphorus, .1 per cent maximum; 
 manganese, .5 per cent maximum and carbon 3 per cent. 
 
 The principle involved is that of taking white iron castings of suitable 
 composition, heating them to high temperature and converting them to 
 the malleable condition by precipitating the carbon in a fine state of 
 division, as annealing carbon. High temperature shortens the process, 
 but it has been found more desirable to use a lower temperature and 
 longer anneal, as the desired change is more readily secured. 
 
 The method of molding is the same as for gray iron, with same allow- 
 ance for shrinkage. The amount of feeder required varies from 12.5 
 to 25 per cent of the weight of casting. Skill is required to make solid 
 castings with minimum amount of metal. 
 
 After cleaning in the usual manner the castings are packed in cast iron 
 boxes of varying sizes to suit their character, with iron scale or sand, 
 bone dust or fire clay; the boxes are covered with lids and luted, then 
 
 382 
 
Black Heart 
 
 383 
 
 stacked in the annealing oven (to be described later). The temperature 
 of the oven is gradually raised to about 1 100° C, maintained at that point 
 for two days and then allowed to drop slowly until sufficiently cool to 
 permit removal of the boxes. 
 
 The composition of the castings after annealing is only altered in the 
 carbon, the total amount being somewhat less but practically all present 
 in the free state. The composition of castings made by one of the 
 largest English makers is as follows: 
 
 Si 0.5; S 0.04; P. 0.07; Mn 0.4; graphitic carbon 2.5; combined 
 carbon 0.05. A test piece i/^-inch square bent 180° — cold; tensile 
 strength 40,000 pounds per square inch, elongation 6 per cent in 2 inches, 
 reduction of area 9 per cent. 
 
 Black heart is more reliable for light than for heavy work. To avoid 
 the introduction of sulphur, the pig iron is usually melted in an air 
 furnace. 
 
 Messrs. Charpy & Grenet's experiments on irons of the following 
 compositions are given herewith. 
 
 No. 
 
 Silicon 
 
 Sulphur 
 
 Phosphorus 
 
 Manganese 
 
 Carbon 
 
 I 
 
 .70 
 
 .01 
 
 trace 
 
 .03 
 
 3.60 
 
 2 
 
 .27 
 
 .02 
 
 .02 
 
 trace 
 
 3.40 
 
 3 •• 
 
 .80 
 
 .02 
 
 .03 
 
 trace 
 
 3.2s 
 
 4 
 
 1.25 
 
 .01 
 
 .01 
 
 .12 
 
 3.20 
 
 ^ 
 
 2.10 
 
 .02 
 
 .01 
 
 .12 
 
 3.30 
 
 These irons were poured into cold water and contained no appreciable 
 amount of graphite, excepting the last which had 20 per cent. Samples 
 of these were subjected to various reheatings and to ascertain as nearly 
 as practicable the condition at any one temperature, the samples were 
 quenched at that temperature and then analyzed. 
 
 1. Heated at 1100° C. or any low temperature for long periods gave 
 no graphitic carbon; but at 1150° C. the separation of graphitic carbon 
 was produced. 
 
 2. Heated for four hours each at 700°, 800°, 900° and 1000° C. showed 
 no free carbon; but it appeared in heating to 1100° C. 
 
 3. Showed traces at 800° C. 
 
 4. 5. Showed traces at 650° C. 
 
 In the case of No, 5, after heating at 650° C. for 6 hours, the content 
 of graphitic carbon had increased from o.io to 2.83 per cent. 
 
 The separation of graphite, once commenced, continues at tempera- 
 tures inferior to those at which the action begins. 
 
 Thus: A sample of No. i, heated at 1170° C. and quenched, contained 
 
384 
 
 Malleable Cast Iron 
 
 only 0.50 graphitic carbon and 2.6 combined carbon, while another 
 sample of the same cast iron, heated at the same time to 1170° C, cooled 
 slowly to 700° C. and then quenched contained 1.87 graphitic carbon 
 and 0.43 combined carbon. 
 
 Again a fragment of No. 3, heated to 1170° C. and quenched, contained 
 1.42 graphitic carbon and 1.69 combined carbon, while another fragment 
 heated to 1170° C. cooled slowly to 700° C. and then quenched contained 
 2.56 graphitic carbon and 0.38 combined carbon. 
 
 At a constant temperature the separation of the graphite is effected 
 progressively, at a rate that is the more gradual, the lower the tempera- 
 ture or the less the silicon content. 
 
 The authors show that these cast irons, with regard to the critical 
 points, have the usual carbon change point, about 700° C, but that there 
 is another well-marked arrest in heating at 1140°, 1165°, 1137° and 
 1165° C, for numbers i, 2, 3, 4 and 5, respectively; and similarly in 
 cooling at 1120°, 1130°, 1137° and 1145° C. 
 
 In an experiment made by W. H. Hatfield, with six bars, all containing: 
 
 Si i.o; S 0.04; P 0.04; Mn 0.22; graphitic carbon 2.83; combined 
 carbon 0.08, all white irons as cast; variously heat-treated so as to give 
 the same composition to analysis, but to have the free carbon in all 
 states of division from fine in No. i to coarse in No. 6. 
 
 Bars I inch square by 18 inches long were tested transversely on knife 
 edges 12 inches apart and gave 
 
 No. 
 
 Inches 
 deflection 
 
 No. 
 
 Inches 
 deflection 
 
 I 
 
 
 5 
 
 6 
 
 
 2 
 
 3 
 
 before fracture; the gradually decreasing deflections given being due 
 entirely to the increasing coarseness of the free carbon. 
 
 Another set of four test bars, containing 0.45, 0.90, i.ia-i.88 per cent 
 sihcon but otherwise similar in composition to the above; heat-treated 
 so that all should have the same type of free or annealing carbon, gave 
 95°, 98°, 94° and 89°, respectively, when subjected to the ordinary 
 bending test. 
 
 The microstructure of these bars consisted of ferrite or silicon ferrite 
 speckled with annealing carbon, which if kept of suitable structure affects 
 the malleability little more than does the slag in the case of wrought 
 
Ordinary or Reaumur Malleable Cast Iron 
 
 385 
 
 Pearlite, when present, after heat-treating white irons, greatly in- 
 creases the tenacity, one sample having a tenacity of 32,6 tons per square 
 inch, with an elongation of 6 per cent on 2 inches, and a bending angle 
 of 90°, when treated so as to leave 0.35 per cent of carbon in the com- 
 bined form and present as pearlite in the structure. 
 
 Another sample of the same general composition, but treated to leave 
 only 0.06 per cent as combined carbon had a tenacity of 21.2 tons per 
 square inch, elongation 11 per cent on two inches and a bending angle 
 of 180° unbroken. 
 
 2. Ordinary or Reaumur Malleable Cast Iron 
 
 In this class of castings the carbon is completely eliminated, leaving 
 a soft material similar in analysis to wrought iron. 
 
 It is stated that irons containing as much as 0.5 sulphur may be used 
 in this class of castings. The irons employed are mottled or white, 
 analyzing as follows: Si 0.5 to 0.9; S 0.25 to 0.35; P 0.05 to 0.08; Mn 
 0.1 to 0.2, total carbon 3^ per cent 
 
 It may be melted in the crucible, in the cupola, or in the air fiu-nace. 
 The cupola is more in general use in England than the air furnace. 
 
 The table below shows approximately the influence of remelting by 
 the several processes. 
 
 Original pig 
 iron 
 
 Crucible 
 
 Cupola 
 
 Reverb. 
 
 Siemens 
 
 C 3.S 
 
 Si 8s 
 
 S 25 
 
 Mn 20 
 
 P 05 
 
 3.4 
 .82 
 .30 
 .10 
 • OS 
 
 3.4 
 .75 
 .31 
 .10 
 .054 
 
 3.2 
 .65 
 .27 
 .10 
 .052 
 
 3.2 
 .70 
 .26 
 .10 
 .05 
 
 Whichever furnace is used it is necessary to have the metal fluid 
 enough to fill the most intricate parts of the molds to be poured in any 
 one batch. Molding operations are the same as for green sand, except 
 that provision must be made for the narrow range of fluidity and the 
 high contraction of white iron. 
 
 Allowance for shrinkage is }i inch to the foot. The castings after 
 proper cleaning are packed in cast-iron boxes of suitable sizes, with red 
 hematite ore broken up finely. New ore is not used alone but one 
 part new is mixed thoroughly with four parts that have been used 
 before; the castings are carefully packed in this mixture so that no 
 two are in contact. 
 
 The oxygen from the ore oxidizes the carbon in the castings, gradually 
 
386 
 
 Malleable Cast Iron 
 
 eliminating it. The ore, previous to use, is red oxide of iron (Fe203), 
 but after the annealing process is found to be black oxide corresponding 
 to the formula Fe304. 
 
 After stacking the boxes in the anneaHng oven, the temperature is 
 gradually raised during 48 to 72 hours; maintained at the annealing 
 temperature from 12 to 24 hours, then allowed from 48 to 72 hours to 
 cool. 
 
 The length of time during which the high temperature is maintained 
 varies with the thickness of the castings. For thick work the high 
 temperature may have to be continued for a period increasing with the 
 thickness of the, castings up to 96 hours. 
 
 Typical Temperature Curve for Annealing Oven 
 
 1000 
 
 500 
 
 O'C 
 
 
 1 2 
 
 3 4 5 6 
 Fig. 109. 
 
 Some makers anneal at as low a temperature as 850° C. (see P. Long, 
 "Metallurgy, Iron and Steel," page 130). Within reasonable hmits, 
 chemical composition of the castings in this process has little bearing 
 on the result provided they are white iron as cast. 
 
 The silicon may run from 0.3 to 0.9; sulphur 0.05 to 0.5; phosphorus 
 should be under o.i; manganese causes trouble if over 0.5. 
 
 Castings made by this process give a tensile strength of 18 to 22 tons; 
 an elongation of 2V-i. to 6 per cent on 2 inches and a reduction of area of 
 5 to 8 per cent, with a cold bend on i^-inch square, of 45° to 90°. 
 
 Mr. P. Longmuir obtained the following results from a commercial 
 casting: Tensile strength, 27 tons; elongation, 5.7 per cent on 2 inches; 
 reduction of area 10 per cent; it analyzed Si 0.65; S 0.3; P 0.04; 
 Mn 0.15. 
 
 In the process of annealing the carbon only is affected, being con- 
 siderably reduced in amount; what remains is partly free and partly 
 . combined. An annealed sample containing 0.6 per cent free carbon and 
 0.4 combined is considered good. 
 
 Mr. Percy Longmuir places the average silicon for good malleable 
 castings at 0.6, sulphur 0.3, phosphorus 0.05, and combined carbon 3 
 to 3.5 per cent. 
 
Ordinary or Reaamiir Malleable Cast Iron 387 
 
 Analyses Before and After A.nnealing 
 
 Constituents 
 
 Iron as 
 
 cast 
 
 After pro- 
 longed an- 
 nealing in 
 iron ore 
 
 Total carbon 
 
 3.43 
 .45 
 .06 
 .31 
 .53 
 
 10 
 
 Silicon 
 
 45 
 
 Sulphur 
 
 06 
 
 Phosphorus 
 
 32 
 
 Manganese 
 
 53 
 
 
 
 Interesting experiments were made by Mr. W. H. Hatfield of Sheffield, 
 and results published in ''The Foundry," Oct., 1909, by Mr. G. B. 
 Waterhouse. 
 
 "Three converted bars of identical composition analyzing: 
 
 Constituents 
 
 Per cent 
 
 Constituents 
 
 Per cent 
 
 Total carbon 
 
 Combined carbon 
 
 1.64 
 
 1.64 
 
 .03 
 
 Manganese 
 
 Sulphur 
 
 Phosphorus 
 
 trace 
 01 
 
 Silicon 
 
 .01 
 
 One was packed in charcoal, another in pure quartz sand, the third 
 in a red hematite ore mixture, consisting of two parts old and one part 
 new. The pots were placed close together in the annealing oven and 
 slowly raised to about 800° C. This required about three days. They 
 were held at this temperature for 24 hoxirs, then raised to 900° C, held 
 there for two days, then cooled slowly. Upon removal and breaking 
 the following results appeared. 
 
 No. I, from charcoal, broke short and gave a coarsely crystalline 
 structure showing imder the microscope absolutely no free carbon. 
 
 Its carbon was 1.63 per cent, the other elements remaining unchanged. 
 
 No. 2, from sand, Was fairly tough but broke without bending. 
 Fracture crystalline and steely. Its carbon was 0.74 per cent and again 
 no free carbon was found. 
 
 No. 3, from the ore mixture, bent considerably before breaking 
 and was fairly ductile. Its carbon was 0.15 per cent and again no 
 free carbon could be found, the structure being of ferrite crystals. 
 The experiments appearing to prove conclusively the possibihty of 
 carbon being removed without previous formation of free or temper 
 carbon. 
 
388 
 
 Malleable Cast Iron 
 
 For the second series of experiments, an ordinary white iron was 
 taken containing: 
 
 Constituents 
 
 Per cent 
 
 Constituents 
 
 Per cent 
 
 
 3.5 
 
 none 
 .50 
 
 Manganese 
 
 Sulphur 
 
 Phosphorus 
 
 Trace 
 
 
 .35 
 
 
 
 
 
 The packing was the ore mixture previously referred to. 
 
 Samples were heat-treated and sections were given a careful micro- 
 scopical examination, with the following results: 
 
 Decarburization began 54 hours after commencement of heating and 
 at 770° C, showing a thin skin of ferrite; the remaining portion of the 
 casting retained the typical structine of white iron. 40 hours later, 
 during which time the temperature gradually raised to 980° C, the de- 
 carburized skin increased in thickness to Yis inch. 
 
 Fourteen hoiurs later, at a temperature of 970° C, the interior had 
 broken down and free or temper carbon was apparent. During the 
 next interval' of 60 hours, at 950° C. very little change occurred. The 
 center showed pearlite, with a little cementite and containing temper 
 carbon, merging gradually into the skin of ferrite. 
 
 During the following 72 hours, the temperature was dropped to 
 140° C, resulting in the production of a really good sample of Enghsh 
 malleable cast iron of the following analysis: 
 
 Constituents 
 
 Per cent 
 
 Constituents 
 
 Per cent 
 
 Combined carbon 
 
 .65 
 1. 10 
 
 Sulphur 
 
 ■ 35 
 
 Temper carbon 
 
 Phosphorus . ... 
 
 ■ 05 
 
 
 1 
 
 
 The author's conclusion is, that carbon is eHminated while still in 
 combination with the iron. 
 
 It (the elimination) begins to take place at the comparatively low 
 temperature of 750° C, and increases in activity with the temperature 
 imtil such a temperature is reached that free or temper carbon is pre- 
 cipitated. 
 
 Previous to this change the interior consists of white iron, with the 
 original quantity of combined carbon. 
 
 As the operation proceeds the temper carbon is gradually taken back 
 into combination to replace that removed by the oxidizing influences. 
 
American Practice 389 
 
 American Practice 
 
 The mixtures of iron vary as the castings are thick or thin. The iron 
 is melted either in the cupola, the air furnace or the open hearth furnace. 
 The latter produces the best castings, but can only be used advanta- 
 geously where the output is large enough to permit of running the fur- 
 nace continuously. 
 
 The air furnace is most frequently used. 
 
 The castings may or may not be packed in an oxidizing material. 
 Sand or fire clay are frequently used. 
 
 Dr. Moldenke, who is recognized as an authority on malleable cast 
 iron, states: "That it is absolutely necessary to have the hard castings 
 free from graphite." He advises the following: 
 
 Contents: Per Cent 
 
 Carbon 3 -3.5 
 
 Silicon, heavy work, not over 0.45 
 
 Sihcon, ordinary work, not over o . 65 
 
 SiHcon, agricultural work, not over o. 80-1 . 25 
 
 Sulphur, not over o . 05 
 
 Phosphorus, not over o. 225 
 
 Manganese, not over o. 40 
 
 "In anneaKng, the temperature of the furnace should be run up to 
 ' heat' in the shortest safe time possible; the limit is the danger of injury 
 to furnace. Then the dampers should be closed and the temperature 
 evenly maintained for 48 hoiurs. The fiu"nace should then be gradually 
 cooled to a black heat before dumping. 36 hovirs are usually required 
 to bring the oven up to heat. 
 
 The entire process occupies about seven days. The annealing tem- 
 perature is 1350° F. and this must obtain at the coldest part of the fur- 
 nace, usually the lower part of the middle of the front row of pots. 
 
 A difference of 200° F. in temperature is often found at different 
 parts of the furnace. 
 
 Cupola iron requires an annealing temperature 200" F. higher than 
 that frorri an air furnace. 
 
 The fuel ratio of an air furnace runs from i to 2 to i to 4. 
 
 Loss in sihcon about 35 points. 
 
 Temperatures should be carefuUy watched and measured with a 
 Le Chateher pyrometer." 
 
 The Doctor has much to say about the danger of injury to the melted 
 iron in the bath, from oxidation. His practice was to have three tapping 
 spouts at different levels, so that for an 18-ton furnace, three taps of 
 6 tons each may be made at intervals, tapping at the upper hole first 
 and then in order from upper to bottom hole. 
 
390 Malleable Cast Iron 
 
 Mr. H. E. Diller, in the Journal of The American Foundrymen's 
 Association, Vol. XI, Dec, 1902, says: 
 
 The hard casting should have its carbon practically all in the com- 
 bined state, while the annealing process should convert this to the so- 
 called temper, or annealing carbon. 
 
 In the manufacture of malleable castings the special make of iron 
 called 'Malleable Bessemer' or 'Malleable Coke Iron' is the principal 
 material used. The charcoal irons, while unequalled for value, are con- 
 fined to the regions where they can compete with the cheaper coke 
 irons. 
 
 The composition required is as follows: 
 
 Per cent 
 
 Silicon o . 75 to 1 . 50 
 
 Sulphur, below 0.04, if possible 
 
 Phosphorus, under ....0.20 
 
 With the pig iron, hard sprues (unannealed scrap), steel and also malle- 
 able scrap are charged. The latter two materials are very good to add 
 to the mixture, as they raise the strength of the casting very consider- 
 ably. • 
 
 Too much must not be added, as it would reduce the carbon to a 
 point where fluidity and life in the melted metal is sacrificed. 
 
 The most serious objection to cupola iron is its poor behavior under 
 bending test, the deflection being very slight. Test bars from this 
 class of iron seldom run above 40,000 pounds per square inch in tensile 
 strength, while with furnace iron, there is no difficulty in getting a few 
 thousand pounds more. 
 
 The metal may be tapped from the furnaces into hand ladles; or it 
 may be caught in crane ladles, carried to the distributing point and there 
 emptied into the hand ladles. 
 
 When tapped into hand ladles, time is a serious item, for the begin- 
 ning and the end of the heat will be two different things. The latter 
 iron will be inferior as it was subjected to the oxidizing effect of 
 the flame much longer than the first part. This difficulty is some- 
 what remedied by pouring the light work first, the heavier pieces 
 coming later, when the silicon has been lowered too much for good light 
 castings. 
 
 The gating should be done to avoid the shrinkage effects as much 
 as may be. The little tricks that can be applied make a surprising 
 difference in the molding loss. Some malleable works seldom lose 
 more than 10 per cent, while in others 20 per cent and over is the 
 rule. 
 
 'After the castings have been tumbled they go to the annealing room, 
 
American Practice 
 
 391 
 
 where they are packed in mill cinder or iron ore, in cast-iron boxes. 
 These are carefully luted up and heated in suitably constructed ovens, 
 for five or six days. 
 
 It usually takes from 36 hours to 48 hours to get the oven up to heat, 
 the temperature ranging from 1600° to 1800° F. in the oven, the boxes 
 having a somewhat lower temperature at the coldest point. 
 
 When the fires are extinguished, the dampers are closed tight, all 
 air excluded, and the oven allowed to cool very gradually; often only 
 400"^ F. the first day. 
 
 After the castings come from the anneahng oven, they are again 
 tumbled to remove the burnt scale; then chipped and ground for ship- 
 ment. 
 
 A well-annealed casting should not have much over 0.06 to 0.12 
 per cent combined carbon remaining in it. There is a material difference 
 between the strength of an over-annealed casting and a normal one. 
 
 Fig. 1 10. — Typical American Air Furnace. 
 
 Two bars were taken from each of five heats. One from each set 
 was given the usual anneal and the others reannealed. The average 
 tensile strength of those annealed as usual, was 50,520 pounds per 
 square inch, and the average elongation 6% per cent in six inches. 
 
 The reannealed set had an average tensile strength of 43,510 pounds 
 per square inch; the average elongation was 6h per cent in six inches. 
 Over anneahng had therefore cost the metal some 7000 pounds of its 
 strength. 
 
 'Malleable' can be made up to 60,000 pounds per square inch, though 
 this is not advisable as the shock resisting qualities are sacrificed. 
 
 Prof. Ledebur determined by experiment that the higher the silicon 
 the lower the annealing temperature required, and the higher the tem- 
 perature and silicon the quicker the change. He used five samples: 
 
 1 with 0.07 silicon. Could not be annealed. 
 
 2 with 0.27 silicon. Required temperature almost at melting point. 
 
 3 with 0.80 siHcon. Began to anneal at 1675° F. 
 
 4 with 1.25 sihcon. Began to anneal at 1200° F. 
 
 5 with 2.10 silicon. Began to anneal at 1200° F. 
 
392 
 
 Malleable Cast Iron 
 
 Specifications for Malleable Castings of J. I. Case Co. 
 
 Tensile strength per sq. in., 35,000 to 50,000. 
 
 Elongation, 1.5 in 4 in. 
 
 Transverse test for O bar .8 inch diameter on supports 12 inches 
 apart, must show 1750 pounds to 2,400 pounds breaking strength and 
 deflection of not less than 0.31 inch. 
 
 Drop Test. — A bar .8 inch diameter on supports 12 inches apart must 
 not break under less than 1650 inch pounds, the drop being 22 poimds 
 and the first drop through 3 inches, second 4 inches and so on imtil 
 rupture occurs. 
 
 Tortional test should closely approximate the tensile strength. 
 
 Bending Test. — Pieces from Me to %& inch thick and from i to 
 3 inches wide, should bend over on themselves, around a circle equal 
 
 Fig. III. — Annealing-Oven equipped for Gas. 
 
 in diameter to twice the thickness of the piece and bend back again 
 without break. 
 
 The anneal is specified at not less than 72 hours for light and 120 hours 
 for heavy work. 
 
 Comparison of Tests made in 1885 ivith those made in igo8 
 1885 By Prof. Ricketts 
 
 %-inch D bar, tensile strength, 30,970 to 44,290 per square inch. 
 Elongation, 1.8 inches in 5 inches. 
 
 Bars I by .2,2,, tensile strength, 32,750 to 36,990 per square inch. 
 Round bars, i/i inch diameter, tensile strength, 36,200 to 44,680 per 
 
 square inch. 
 Round bars, % inch diameter, tensile strength, 26,430 to 34,600 per 
 
 square inch. 
 Compression, 108,900 to 160,950 pounds per square inch. 
 
American Practice 393 
 
 igo8 
 
 Bars H-inch D, tensile strength, 52,000 to 59,000 per square inch. 
 Larger sections, tensile strength, 42,000 to 47,000 per square inch. 
 Dr. Moldenke states that the tensile strength should run from 40,000 
 
 to 44,000. 
 The Iron Trade Review gives the production of malleable castings in 
 
 1903 for the United States and Canada as 750,000 tons. 
 Combined output of the rest of the world 50,000 tons. 
 
CHAPTER XVII 
 
 STEEL CASTINGS IN THE FOUNDRY 
 
 There is a great demand on the part of foundrymen for an appliance 
 to successfully melt steel in smaU quantities; permitting small steel 
 castings, or castings for which the demand is immediate, to be made in 
 the gray iron foundry. Many efforts have been made to realize this 
 desire, but so far have met with indifferent success. There are several 
 appHances offered to manufactiirers, some employing the Bessemer 
 converter, others the electric furnace in connection with the cupola. 
 
 Men especially skilled are required to manipulate steel furnaces. The 
 processes of mixing and melting the metal and annealing castings differ' 
 so radically from those of the gray iron foimdry, that in the present 
 undeveloped state of steel founding on a small scale, steps on the part 
 of the foundryman in that direction should be taken with extreme 
 caution. 
 
 Mr. Percy Longmuir defines ordinary steel "as iron containing from 
 O.I to 2 per cent of carbon in the combined form, which has been sub- 
 mitted to complete fusion and poured into an ingot, or mould, for the 
 production of a malleable or forgeable metal." 
 
 "Mild steel contains about 0.2 per cent carbon; the element increasing 
 as the harder varieties are approached, being highest of all in the tool 
 steels." 
 
 "The mechanical effect of this carbon is shown in the following table." 
 
 Material 
 
 Carbon 
 
 Silicon 
 
 Sulphur 
 
 Phos- 
 phorus 
 
 Tenacity 
 
 in tons 
 
 per square 
 
 inch 
 
 Extension 
 per cent 
 on two 
 inches 
 
 Contrac- 
 tion 
 per cent 
 of area 
 
 Mild steel.... 
 Tool steel 
 
 .10 
 1. 00 
 
 .03 
 .03 
 
 .02 
 .02 
 
 .02 
 .02 
 
 20.00 
 60.00 
 
 50.0 
 5.0 
 
 70.0 
 10. 
 
 "Within limits, an increase of carbon is accompanied by an increase in 
 tenacity and a decrease in ductility, each increment of carbon showing 
 distinctly these increases." 
 
 "The following classification embraces the most famiUar tempers of 
 Bessemer, Siemens and crucible steel." 
 
 394 
 
Steel Castings in the Foundry 
 
 395 
 
 Class of steel 
 
 
 Content 
 
 of carbon 
 
 .20 
 
 Purpose 
 
 
 
 Ship and boiler plates, sheets, etc. 
 
 
 .25 
 
 Axle steel. 
 
 Bessemer steel 
 
 ■•i 
 
 .03 
 
 Tire steel. 
 
 
 
 .03 
 
 Rail steel. 
 
 
 ..1 
 
 .50 
 
 Spring steel. 
 
 
 .20 
 
 Boiler plate. 
 
 Siemens or open hearth . . 
 
 .65 
 
 Spring steel. 
 
 
 I 
 
 1.30 
 
 Tool steel. 
 
 
 r 
 
 .90 
 
 Chisel steel. 
 
 
 ! 
 
 1. 10 
 
 Large files, drills and similar tool steels. 
 
 Crucible steel 
 
 .J 
 
 1.20 
 1.40 
 
 Turning tool steels. 
 
 
 Saw file steels. 
 
 
 
 1.50 
 
 Razor steels. 
 
 A steel containing o.io per cent carbon is unaffected in hardness by 
 quenching, while one containing i per cent carbon becomes so hard under 
 same conditions that it will scratch glass. 
 
 Manganese is present in all commercial steels, varying from traces up 
 to I per cent. It promotes soundness and neutralizes the effect of 
 sulphur. 
 
 Sihcon tends to the production of sound metal; while it is present in 
 insignificant quantity in forging steel, in casting steels it may exist to the 
 extent of 0.3 per cent. 
 
 Phosphorus produces an exceedingly brittle, cold short metal. Pure 
 steels contain 0.02 to 0.03 per cent. 
 
 Usual specifications limit the phosphorus content to 0.06; at o.i the 
 danger limit is reached. 
 
 Steels containing appreciable amounts of sulphur are red short. In 
 high quahty of steels the sulphur content runs about o.oi per cent. 
 Ordinary specifications place the limit at 0.04 per cent. 
 
 The variations in the carbon content to suit various requirements are 
 shown in the following table : 
 
 Content of 
 
 carbon in 
 
 steel 
 
 Purpose for which the steel, in the form of a hardened or 
 
 tempered tool, is suitable 
 
 .50 
 
 Springs. 
 
 .60 
 
 Stamping dies. 
 
 .65 
 
 Clock springs. • 
 
 .75 
 
 Hammers, shear blades, axes, mint dies. 
 
 .80 
 
 Boiler punches, screw dies, cold sets. 
 
 .90 
 
 Edge tools, slate saws. 
 
 .95 
 
 Circular saws, pins. 
 
 I. CO 
 
 Cold chisels, cross-cut saws. 
 
 1. 10 
 
 Drills, large files, hand saws, mill picks. 
 
 1.20 
 
 Granite and marble saws, mill chisels. 
 
 1.30 
 
 Harder files, cutters, spindles, turning tools. 
 
 1.40 
 
 Saw files. 
 
 1.50 
 
 Turning tools for chilled rolls, razors and surgical instruments. 
 
396 
 
 Steel Castings in the Foundry 
 
 The following table is taken from Prof. J. O. Arnold's "Influence 
 of Carbon on Iron." 
 
 Mechanical Properties "Normal Steels" 
 
 Carbon 
 
 Elastic limit, 
 
 tons per 
 square inch 
 
 Maximum 
 stress, tons 
 per square 
 inch 
 
 Elongation 
 
 Reduction 
 of area 
 
 .08 
 .21 
 .38 
 .59 
 ■89 
 1.20 
 1-47 
 
 12.19 
 17.08 
 17.95 
 19.82 
 24.80 
 35.72 
 32.27 
 
 21.39 
 25.39 
 29.94 
 42.82 
 52.40 
 61.64 
 55.71 
 
 46.6 
 42.1 
 34.5 
 19.9 
 I3-0 
 8.0 
 2.8 
 
 74 
 67 
 56 
 22 
 15 
 7 
 3 
 
 8 
 8 
 3 
 7 
 4 
 8 
 3 
 
 "Normal steels" represent the rolled bars heated to 1000° C. and 
 cooled in air. 
 
 " Comparing this table with the foregoing statements, it appears that 
 as pearlite replaces ferrite, the maximum stress increases, continmng 
 to do so until a structure consisting of pearlite and very thin meshes of 
 cementite is reached. Further increase in carbon resulting in greater 
 dispersal of free cementite is associated with a decrease in maximum 
 stress"." 
 
 Bessemer Process 
 
 The Bessemer process consists in blowing a large volume of compressed 
 air through a bath of molten pig iron; the oxygen of the air combining 
 with carbon, sihcon and manganese to form oxides. That combined 
 with carbon passes off as gas while with sihcon and manganese slags are 
 formed. 
 
 On removal of carbon, silicon and manganese, assmning that sulphur 
 and phosphorus are low, a product resembling wrought iron is obtained. 
 Meantime during the process of oxidation, there is a rise in temperature 
 sufficient to maintain mild steel in a fluid condition. The oxidation of 
 silicon has the greatest effect in producing the rise in temperature. The 
 irons must be low in sulphur and phosphorus, as these elements are not 
 removed. An average content of 2.5 per cent silicon in the pig iron gives 
 the best results. Higher than this, the heats are Hable to require scrap- 
 ping; while with a lower content of sihcon there is danger of "cold 
 blows." The melted metal is taken directly from the cupola, led by 
 runners to the converter. 
 
The Baby Converter 
 
 397 
 
 The Baby Converter (Robert) 
 
 This consists of a steel shell mounted on trunnions, so that it may be 
 properly rotated. It is flattened on the back and lined with silica brick 
 or ganister. On the flattened side the tuyeres are introduced horizontally. 
 
 The surface of the metal lies approximately at the bottom of the 
 tuyeres so that the blast may impinge upon it. The blast is from 3 to 
 4 pounds per square inch and means are provided for regulating it. The 
 tuyeres being inclined radially, a rotary motion is imparted to the molten 
 metal by the blast. 
 
 In some cases the surface of the metal may be above the tuyere level, 
 but seldom exceeds that by more than three or four inches. The high 
 tuyere level permits some of the air to escape and burn on the surface 
 of the bath; carbon monoxide is formed in the bath by the oxidation of 
 the carbon. 
 
 The combustion of carbon monoxide gives rise to considerable heat, 
 which is absorbed by the bath. To this reaction is due the higher tem- 
 perature of the side blow converter. 
 
 The Tropenas converter has a double row of tuyeres which are hori- 
 zontal when the converter is vertical. They are not radially inclined 
 as in the Robert. The surface of the metal is at the bottom edge of the 
 lower row of tuyeres; the blast is always on the surface of the metal. 
 
 When blowing the converter is slightly inchned, causing the direction 
 of the tuyeres to slope towards the surface of the metal. During the 
 early stage of the blow the lower tuyeres only are used; but on the 
 appearance of the carbon flame the upper row is opened. The carbon 
 monoxide, partly consumed by air from the lower tuyeres, is supplied 
 with sufi&cient oxygen for complete combustion by that from the upper 
 row, generating additional heat. 
 
 Recarbonization is effected in the converter or in the ladles according 
 to the character of the composition required. 
 
 The chemical changes taking place in a two ton Tropenas converter 
 are given as follows : 
 
 Constituents 
 
 Cupola 
 metal 
 
 After 5 
 minutes 
 blowing 
 
 After 12 
 minutes 
 blowing 
 
 After 14 
 minutes 
 blowing 
 
 After 18 
 minutes 
 blowing 
 
 End of 
 blow 
 
 Fin- 
 ished 
 metal 
 
 Graphite 
 
 Combined car- 
 bon 
 
 Silicon 
 
 Sulphur 
 
 Phosphorus 
 
 Manganese 
 
 3.180 
 
 .350 
 2.310 
 .037 
 .054 
 .610 
 
 2.920 
 
 .340 
 1.620 
 .037 
 .053 
 .600 
 
 2.900 
 .466 
 .035 
 .054 
 .101 
 
 2.300 
 .382 
 .036 
 .054 
 .040 
 
 .860 
 .084 
 .038 
 .051 
 .040 
 
 .100 
 
 .074 
 .038 
 .050 
 .042 
 
 .240 
 .326 
 .037 
 .0S8 
 1.080 
 
398 Steel Castings in the Foundry 
 
 Theoretically the feeder on a steel casting should sink due to shrinkage. 
 If, however, instead of sinking, a rise is shown, this is clear evidence of 
 internal unsoundness or sponginess. To prevent this result one of the 
 first essentials lies in having the steel thoroughly dead melted or "killed" 
 before casting. A properly "killed" steel pours quietly and settles 
 down gently in the mould. "Wild metal " acts in the opposite way and 
 in some cases is represented by an over-oxidized metal. 
 
 A distinction must be drawn between a "pipe" and a blow hole. 
 
 The former is due entirely to contraction or shrinkage in passing from 
 the Hqmd to the solid state and must be obviated by feeding. 
 
 "Blow-holes" are entirely different from "pipes" and are formed by 
 the hberation of gases absorbed during the melting process. 
 
 In considering the character of these gases, oxygen naturally arises 
 first, owing to the strong affinity between iron and oxygen. There is 
 every reason to suppose, however, that the oxygen absorbed when the 
 iron is molten, remains stable at low temperatures -as an oxide, and in 
 the absence of a deoxidizing agent this ferrous oxide is intermingled with 
 the iron. Oxygenated steel is "dry" under the hammer and this con- 
 dition is not necessarily due to blow-holes, but to "red-short" metal. 
 Further, if free oxygen were present in quantity in the gas contained in 
 a blow-hole, its skin would show an oxide film. 
 
 The majority of blow^-holes have bright surfaces; comparatively few 
 show colored tints, ranging from a straw to a blue, due to oxidation. 
 These colored blow-holes owe their oxidized film, not to free oxygen 
 hberated by the iron, but to air mechanically trapped during casting. 
 Analyses of the gases seldom show more than traces of oxygen. Mr. E. 
 Munker reports sixty-seven analyses of gases evolved by molten pig 
 iron; the highest content of oxygen in the series is found at 0.8 per cent. 
 Average analyses of gases in blow-holes give results of the following 
 order: Per cent 
 
 Hydrogen 75 
 
 Nitrogen . 23 
 
 Carbon monoxide . 2 
 
 The actual amount of these gases absorbed depends to some extoit 
 on the temperature and composition of .the bath. While fluid the gases 
 are retained; but with a fall in temperature after casting they are evolved. 
 Those set free by a fall in temperature bubble through the pasty mass, the 
 trapped bubbles representing blow-holes in the casting. As the tem- 
 perature continues to fall less movement is offered and the gases cannot 
 force passages through the stiffening metal. Hence more bubbles are 
 trapped. Finally a stage is reached at which the mass becomes rigid 
 and the further formation of blow-holes becomes impossible. 
 
The Baby Converter 
 
 399 
 
 The author's conclusions from the investigations of Wahlberg are: 
 
 "i. If no internal movement is possible in the solidifying steel, the 
 gas cannot disengage itself and so leads to the formation of blow-holes." 
 
 "2. The presence of sihcon and manganese lead to the retention of 
 the gases until sohdification is complete, hence preventing the formation 
 of blow-holes." 
 
 Methods of prevention include: 
 
 "i. Liquid compression. 
 
 "2. Additions to the steel of sihcon, manganese or aluminum. Each 
 of these elements acts powerfully on the oxygen or the oxides of iron, 
 combining with the oxygen to form slag." 
 
 " Aluminum will remove carbonic oxide. There is, however, no reason 
 to suppose that it will remove either hydrogen or nitrogen." 
 
 "There are grounds for the belief that silicon, manganese and alum- 
 inum increase the solvent power of the steel for hydrogen and nitrogen 
 and that these gases remain dissolved." 
 
 BrineU found that to produce an ingot of perfect density in the absence 
 of sihcon, 1.66 per cent of manganese is necessary. In the absence of 
 manganese 0.32 per cent sihcon is required; and with no manganese or 
 sihcon 0.0184 per cent of aluminum is sufficient to produce a perfectly 
 sound ingot. Or expressed in another way he states that aluminum is 
 90 times as effective as manganese and 17.3 times as much so as sihcon, 
 in removal of gases. 
 
 Metalhc borides are suggested by Weber for removal of oxygen; these 
 in conjunction with ferrotitanium tend to removal of nitrogen. 
 
 The casting temperature exercises a great influence upon the properties 
 of the metal. These are found to rise and fall with the temperature 
 above and below the casting heat, as shown by the following table: 
 
 Analyses 
 
 Maximum 
 
 stress, 
 
 tons per 
 
 square 
 
 inch 
 
 Elonga- 
 tion, 
 per cent 
 
 in 
 2 inches 
 
 Reduc- 
 tion of 
 
 No. 
 
 Carbon 
 
 Si 
 
 Mn 
 
 s 
 
 P 
 
 per cent 
 
 80 A.... 
 
 81 A.... 
 
 82 A.... 
 
 83 A.... 
 
 .29 
 .29 
 .29 
 .29 
 
 .07 
 .07 
 .07 
 .07 
 
 .16 
 .16 
 .16 
 .16 
 
 .07 
 .07 
 .07 
 .07 
 
 .c6 
 .06 
 .06 
 .06 
 
 24.2 
 27.2 
 27.0 
 25.5 
 
 95 
 
 24.0 
 12.5 
 8.0 
 
 18.0 
 32.3 
 17-5 
 12.0 
 
 These steels were poured from one large ladle at intervals of a few 
 minutes. They are exactly of the same analysis; the bars were annealed 
 together, each bar receiving exactly the same treatment, and apart from 
 variation of casting temperatures, the conditions were the same for all. 
 These results have been repeated many times. When the steel is poured 
 at an excessive temperature, similar ones are always obtained. 
 
400 
 
 Steel Castings in the Foundry 
 
 Annealing 
 
 The following is extracted from McWiUiams and Longmuir's " Gen- 
 eral Foundry Practice." 
 
 Steel castings are usually annealed in the reverberatory gas furnace. 
 The anneaKng recommended by Prof. Arnold for general work is to heat 
 the castings up to about 950° C. keeping them at that temperature for 
 about 70 hours, then luting the furnace and allowing them to cool slowly 
 for 100 hours. 
 
 The Clinch- Jones annealing furnace is highly spoken of, the controlling 
 idea being that while the castings are heated in a muffle, by keen flames 
 outside the walls of the muffle, virgin gas from the producer is allowed 
 to come into the muffle and combine with all the oxygen that may enter, 
 thus preventing it from getting to the castings to scale them by oxidizing 
 at their surfaces. A cut of this oven is shown on page 266 (McW. &L.). 
 
 The micrographs (McW. & L.) show the structural changes produced 
 by annealing. It should be remarked that the unannealed bar, Fig. 112, 
 (McW. & L.) %-inch diameter when bent over a ^^-inch radius broke at 
 43°. After annealing, same bar bent double without fracture. 
 
 after annealing 
 Fig. 112. 
 
 f ^H 
 
 EKIF^^''' ^ 
 
 r ^^^V 
 
 *■P^-~--<^.j^ 
 
 ^^^ 
 
 
 i^^S^ 
 
 ^^B^^p^R 
 
 ^^. 
 
 ^^m 
 
 faS^Kj 
 
 pj^Mff^X 
 
 nH^IHBl 
 
 ^^^Sbt^^^W '^s^ 
 
 ^r^BBl 
 
 ^BKrS^^Sir^^ 
 
 m v^OB 
 
 BSOf^^^ 
 
 3ii^— 4^ 
 
 Fig. 113. 
 
 Fig. 113 (McW. & L.) shows the structure of a portion of a large 
 open hearth casting, having originally the same structure as the unan- 
 nealed part of Fig. 112 after insufficient annealing. When thoroughly 
 annealed the structure was as shown in Fig. 114. 
 
 A test bar i inch square as shown in Fig. 113 broke at 40°; while one 
 
Tropenas Process 401 
 
 as per Fig. 114 bent at 101° without fracture, showing tensile strength of 
 33 tons per square inch; elongation 30 per cent; reduction of area 41 
 per cent. The composition of the casting was C.C. 0.24, Si 0.15, 
 Mn 0.8, P 0.04, S 0.05. 
 
 Fig. 114. 
 
 Other micrographs of most interesting character are shown on pages 
 293 to 297 and 338 to 354 (McW. & L.). 
 
 The process of annealing must be varied to suit different compositions 
 and purposes for which the steel is provided. 
 
 Tropenas Process 
 
 This process was patented by Alex. Tropenas of Paris in 1891; the 
 first converter, 800 pounds capacity, was erected at the works of Edgar 
 Allen & Co., Ltd., ShefiQeld, Eng., and introduced into the United States 
 in 1898. 
 
 It produces hotter steel than any other process. The steel may be 
 carried for considerable distances in hand ladles or shanks and poured 
 into small castings. 
 
 The Tropenas process consists in melting a calculated mixture in the 
 cupola, transferring the metal to a special type of converter and its 
 conversion to steel therein. The reactions are identical with those of 
 the Bessemer and open hearth furnaces; the difference lies in the manner 
 of producing these reactions. The converter is designed to conserve 
 and increase the heat as much as possible and by preventing evolution 
 in the bath, to keep out any gases not necessary for or caused by the 
 
402 
 
 Steel Castings in the Foundry 
 
 decarburization, mechanical disturbance, gyration or ebullition of the 
 bath is reduced to a minimum. 
 
 The converter is in general similar to the Bessemer converter, the 
 particular difference being in the location and construction of the 
 tuyeres. 
 
 Figs. 215 and 216, pages 307 and 308 McW. & L. give fair illustra- 
 tions of the device. The operation consists in melting the iron in the 
 cupola precisely as for gray iron castings, except that enough for the 
 charge must be gathered at the first tapping. The melted iron is then 
 transferred to the converter and skimmed clear of slag. The converter 
 is so adjusted that the level of the metal reaches exactly to the lower edge 
 
 Fig. 115. 
 
 Fig. 116. 
 
 of the bottom tuyeres, so that the blast will strike exactly upon the 
 surface of the metal. The longitudinal axis of the converter should 
 make an angle of from 5° to 8° with the vertical. This is a matter of 
 importance and extreme care must be taken to obtain the correct position 
 before applying the blast. The upper tuyeres are closed and the blast 
 turned on with about 3 pounds pressure. 
 
 If the composition of the iron is correct and it has been melted hot, 
 sparks and smoke will be emitted from the converter for about four 
 minutes, then flame appears which gradually increases in volume and 
 brilliancy. After about ten minutes, what is known as "the boil" 
 appears. In a few minutes this dies down considerably, and the blow 
 remains quiescent for a time. Then the flame increases again, attains 
 the maximum brilliancy and finally dies down for the last time. 
 
• Chemistry of the Process 403 
 
 This is the end of the blow, the carbon, silicon and manganese having 
 been reduced to the lowest limits. 
 
 The converter is now turned down, the blast shut off and a weighed 
 amount of ferrosilicon, ferromanganese or silicon speigel added to 
 recarbonize the steel to the desired point. The steel is now ready for 
 casting. On account of its great fluidity and thin slag it may be poured 
 over the hp of an ordinary ladle, instead of from one with a bottom pour. 
 
 Claims made for this process. 
 
 1. The form of the bottom of the converter gives a greater depth in 
 proportion to the surface area and cubic contents than any other pneu- 
 matic process, preventing the disturbance of the bath when blowing. 
 
 2. The symmetrical position of the tuyeres with respect to the center 
 tuyere prevents any gyrating or churning of the bath. This is directly 
 opposed to all other processes. 
 
 3. The special position of the bottom tuyeres during blowing, so that 
 they are never below the surface of the bath, reduces the power necessary 
 for blowing; as only enough air Is introduced to make the combustion 
 and not to support or agitate the bath. 
 
 4. The oxidation of the metalloids takes place at the surface only, the 
 reaction being transmitted from molecule to molecule without any 
 mechanical disturbance. 
 
 5. The addition of a second row of tuyeres completely burns the CO 
 and H produced by the partial combustion of carbon and the decomposi- 
 tion of moisture introduced with the blast and this increases the tem- 
 perature of the bath by radiation. 
 
 6. Very pure steel is obtained, as the slag and the iron are not mixed 
 together. 
 
 7. There is a minimum of waste on account of the bath being kept 
 comparatively quiet. 
 
 8. Less final addition is required on account of the purity of the steel 
 and its freedom from oxides. 
 
 Chemistry of the Process 
 
 No fuel is needed in the converter. The increase in temperature after 
 the melted metal is introduced is occasioned by the combustion of the 
 metalloids during their removal. 
 
 These elements are carbon, siUcon and manganese. The oxidation 
 of the siUcon furnishes by far the greatest part of the useful heat. Prof. 
 Ledebur has calculated that the rise in temperature of the bath due to 
 the combustion of i per cent of each of the constituents is as follows: 
 SiHcon 300° C; phosphorus 183° C; manganese 69° C; iron 44° C; 
 carbon 6° C. 
 
404 Steel Castings in the Foundry * 
 
 It is necessary that the composition of the bath before blowing should 
 be that which has been found to give the best results. 
 
 Sulphur and phosphorus are as unaffected here as in any other acid- 
 hned f lurnace and the content of those elements in the finished steel will 
 depend on how much the stock melted contained. 
 
 The cupola mixture generally consists of low phosphorus pig iron and 
 steel scrap, composed of runners, risers and waste from previous heats. 
 As much as 50 per cent scrap may be carried successfully. The mixture 
 must be made in such proportions that the analysis after melting will be: 
 
 Per cent 
 
 Silicon 1 . 90-2 . 25 
 
 Manganese o. 60-1 . 00 
 
 Carbon, about 3 • 00 
 
 The result of low silicon is to make the blows colder; that of high 
 silicon to make the blows unduly long and to increase the wear on the 
 lining. 
 
 Manganese should be kept w^ithin the limits specified. Low man- 
 ganese tends to make the slag thick. High manganese makes the blow 
 sloppy and corrodes the lining. 
 
 During the first period of the blow, the silicon chiefly is oxidized and 
 the carbon changed from graphitic to combined. The manganese is the 
 most active element in the middle of the blow, being most rapidly 
 eliminated at the boil. The last period brings the carbon flame, and the 
 indications are so plain that it is feasible to stop the blow before all the 
 carbon is burned out, thereby reducing the amount of carburiser needed. 
 In addition to these elements a certain amount of iron is unavoidably 
 oxidized and the total loss of all elements included is about 12 per cent. 
 
 Converter Linings 
 
 The converter is generally lined with an acid or silica lining. Success- 
 ful experiments have been made with a basic lining (dolomite), but it has 
 not been developed commercially. Special shaped blocks to fit the 
 converter or the regular standard shapes may be used. 
 
 The material must be of the highest grade sihca stock, burnt at the 
 highest possible kiln temperature. It usually contains from 95 to 97 
 per cent Si02, and is practically free from lime and magnesia. 
 
 Another method in frequent use is to run ground ganister around a 
 collapsible form. This probably is the cheapest method. Before making 
 the first blow, the converter is made white hot by a coke or oil fire. 
 
 Mr. J. S. Whitehouse of Columbus, Ohio, in a paper read before the 
 American Foundrymen's Association, states that the claims which were 
 
Converter Linings 405 
 
 made for the side blow converter, when first introduced into America 
 were, to say the least, absurd. Many failures were made by employ- 
 ing inexperienced workmen, who had only limited instructions from 
 experts sent out with the apparatus and the results were frequently 
 disastrous. 
 
 A year's experience, at least, under proper instruction is required before 
 a man can become a competent blower. He must be able to tell the 
 temperature of the metal soon after the flame starts and to judge the 
 siUcon by the first period. He must tell when the blow is finished from 
 the slag as well as by the flame. He must know how to keep the lining 
 in the best shape to get all the heat possible from the process, and the 
 hundred little kinks of the trade, which, as a rule, the expert will never 
 impart, but are obtained only from experience. 
 
 A man with the above qualifications will blow with a loss of less than 
 17 per cent — about 15 per cent. 
 
 With proper blowing the main loss comes from the silicon in the charge, 
 usually 2 per cent, which is oxidized together with iron and manganese 
 to form the slag. 
 
 Mr. Whitehouse learned to blow with 2 per cent silicon, but for the 
 past few years has been blowing iron, analyzing from 0.90 to 1.25 per 
 cent silicon from the cupola, and often has been obliged to use scrap 
 while blowing. 
 
 There is an advantage in the increased amount of scrap which can be 
 carried, as it cuts down the cupola loss by increasing the amount of 
 carbon in the charge. For example: He charges 50 per cent pig carrying 
 about 3.75 per cent carbon and 50 per cent scrap having 0.25 per cent 
 carbon. Tests from such iron from the cupola give 3.25 to 3.50 per cent 
 carbon, showing a gain of 1.25 to 1.50 per cent carbon, taken from the 
 coke, instead of purchased in the pig iron. 50 per cent scrap can be 
 melted in the cupola, using only i2i/i per cent coke, but the blower must 
 have a complete knowledge of cupola practice. Most blowers use too 
 much volume and too high pressure of blast to get the best results. With 
 low silicon the volume and pressure of blast must be low. No two blows 
 will act alike and require different treatment, which can be determined 
 by the flame, but which he is unable to describe. 
 
 It is as necessar}^ for the blower to regulate the air valve to get proper 
 combustion as it is for the melter to adjust air and gas valves. With 
 ordinary care the steel produced in a converter is very uniform in carbon 
 and silicon; more so, he thinks, than in the open hearth. The greatest 
 variation seems to be in manganese. The temperature of the metal 
 and the condition of the slag cause more variation in the converter than 
 in the acid open hearth. It is possible to run several weeks without 
 
4o6 
 
 Steel Castings in the Foundry 
 
 taking an analysis and find at the end of the run very little variation in 
 the elements. 
 
 While this is possible with the open hearth, it is not practiced on 
 account of the risk. It is, however, frequently done in converter practice. 
 The method of making the molds is identical with that followed in the 
 open-hearth practice. 
 
 Fig. 117. — Arrangement of the Cupola and Converter. The Metal is 
 Handled by a Fovir-ton Pneumatic Jib Crane. 
 
 An ordinary converter shop, with one two-ton converter is capable of 
 producing between 100 and 150 tons of good castings per month, blowing 
 three times a week. He concludes with saying that the management 
 must be good and the salaries paid the officers as reasonable as possible, 
 otherwise the shop is fore-doomed to failure, regardless of the quaUty of 
 the product. 
 
 At the Cincinnati Meeting of the American Foundrymen's Associa- 
 tion, Mr. Whitehouse, in reply to various inquiries, made the following 
 statements : 
 
Converter Linings 
 
 407 
 
 When the flames show that the blow is getting very hot, scrap is 
 thrown in at the top of the converter until it cools down. The scrap is 
 as small as can be conveniently handled and is not preheated. 
 
 The blast pressure averages from 2.25 to 2.50 pounds. 
 
 Fig. 118. — Pouring the Iron into the Converter before the Blow. 
 
 Sometimes, after the sihcon is reduced and during the blow, steel scrap 
 is thrown into the converter. 
 
 The carbon can be varied by the final additions. 
 
 It is usual and customary to blow the heat down till the flame drops; 
 the carbon is then about o.io per cent. The carbon is then raised by the 
 addition of melted pig iron or pulverized coke. The carbon can be 
 raised as much as desired. If more than 0.40 or 0.50 per cent carbon is 
 
4o8 
 
 Steel Castings in the Foundry 
 
 required, the blow is stopped before completion. It is customary to 
 blow down to .09 or o.io per cent carbon, then to recarbonize with ferro- 
 manganese, melted pig iron and spiegeleisen. I usually use coke. If 
 ferromanganese is melted in a small cupola, as has been done in the East, 
 the loss is very heavy. The most economical practice is to throw the 
 ferromanganese into the converter at the end of the blow. The usual 
 custom is to add ferromanganese and then pig iron. 
 
 "My practice is never to reline entirely. At the end of the heat day, 
 the converter is cooled off, patched up, dried out and is then ready for 
 _ the next day. Where the converter is 
 
 used until it is cut out, the Uning re- 
 moved and then renewed, there is a great 
 loss of iron." 
 
 The practice is to blow just at the sur- 
 face, with the blast impinging slightly on 
 the metal. During the blow the tuyeres 
 are submerged, and if the pressure is sud- 
 denly stopped for any cause the iron. wiU 
 run into the wind box. The converter is 
 so placed that the blast will strike the 
 surface of the metal at an angle of 175** 
 to 171°. He does not use a second row 
 of tuyeres. Upon starting to use the 
 converter, there was an upper row of 
 tuyeres, but they were subsequently dis- 
 carded. The lower tuyeres furnish all 
 the blast required. 
 
 Formerly he used bull ladles in pour- 
 ing small castings and experienced no 
 trouble. At the present time, the entire 
 heat, sometimes consisting of castings 
 weighing less than thirty pounds, is poured with a thousand-pound 
 ladle. 
 
 The following extract is from the Foundry, Jan., 19 10, describing the 
 equipment of the recently erected steel foundry of the Vancouver En- 
 gineering Works, Ltd., Vancouver, B.C. 
 
 The cupola is the Standard Whiting type, having a rated capacity of 
 six to seven tons per hour. 
 
 Iron is tapped from the cupola into a six-thousand-pound ladle, carried 
 by a pneumatic crane. Two taps are made to obtain a full charge for 
 the converter. 
 The composition of the iron is as follows: Si. 1.80 to 2.00; S. 0.04; 
 
 Fig. 119. — View of One End of 
 the Foundry, Showing the Con- 
 verter Discharging Steel into a 
 Ladle. 
 
Standard Specifications for Steel Castings 
 
 409 
 
 Phos. 0.04; Mn. 0.60 to 1.50. The cupola charge is so proportioned as to 
 give about one per cent manganese. Steel scrap is available as desired. 
 
 The converter, of two-tons capacity, 
 is of the standard Whiting type (Tro- 
 penas) and is lined with ganister, sand 
 and fireclay. This lining, if cared for, 
 will give from 180 to 200 blows. The 
 air pressure of blast to converter ranges 
 from three to five pounds per square 
 inch, regulated by valve on operator's 
 platform. 
 
 The blowing operation requires from 
 15 'to 20 minutes, varying with the 
 percentage of metalloids in the iron. 
 The temperatiure of the bath depends 
 upon the rapidity of the blow. 
 
 Fig. 
 
 120. — The Converter in 
 Operation. 
 
 Reduction in the weight of metal is about 18 per cent. 
 The steel comes from the converter at 1700° C, insuring sufficient 
 fluidity to give sharp, sound castings of light section. 
 
 Standard Specifications for Steel Castings Adopted 
 BY American Association for Testing Materials 
 Process of Manufacture 
 
 1. Steel for castings may be made by the open hearth, crucible or 
 Bessemer process. Castings to be annealed or unannealed a& specified. 
 
 Chemical Properties 
 
 2. Ordinary castings, those in which no physical requirements are 
 specified, shall contain not over 0.40 per cent carbon, nor over 0.08 per 
 cent of phosphorus. 
 
 3. Castings which are subject to physical test shall contain not over 
 0.05 per cent of phosphorus, nor over 0.05 per cent of sulphur. 
 
 Physical Properties 
 
 4. Tested castings shall be of three classes, hard, medium and soft. 
 The minimum physical qualities required in each class shall be as foUows: 
 
 Properties 
 
 Hard 
 castings 
 
 Medium 
 castings 
 
 Soft 
 castings 
 
 Tensile strength, pounds per inch 
 
 Yield point, pounds per inch 
 
 Elongation per cent in 2 inches 
 
 85,000 
 
 38,250 
 
 15 
 
 20 
 
 70,000 
 
 31.500 
 
 18 
 
 25 
 
 60,000 
 
 27,000 
 
 22 
 
 
 
4IO 
 
 Steel Castings in the Foundry 
 
 
 5. A test to destruction may be substituted for tensile test in the case 
 of small or unimportant castings, by selecting three castings from a lot. 
 This test shall show the material to be ductile, free from injurious defects, 
 and suitable for the purposes intended. 
 
 A lot shall consist of all castings from the same melt, or blow annealed 
 in the same furnace charge, 
 
 6. Large castings are to be suspended and hammered all over. No 
 cracks, flaws, defects, nor weakness shall appear after such treatment. 
 
 7. A specimen one inch by one-half inch (i " X v/') shall bend cold 
 around a diameter of one inch (i") without fracture on outside of bent 
 portion, through an angle of 120° for the "soft," and 90° for "medium" 
 castings. 
 
 Test Pieces and Methods of Testing 
 
 8. The standard turned test specimen, one-half inch {W) diameter 
 and two inch (2") gauged length, shall be used to determine the physical 
 properties specified in paragraph No. 4. It is shown in the following 
 sketch. 
 
 9. The number of standard 
 test specimens shall depend 
 upon the character and im- ' 
 portance of the castings. A 
 test piece shall be cut cold from 
 a coupon to be molded and cast 
 on some portion of one or more 
 castings from each blow or melt, or from the sink heads (in case heads 
 of sufl&cient size are used). The coupon, or sink head, must receive 
 the same treatment as the casting, or castings, before the specimen is 
 cut out and before the coupon, or sink head, is removed from the 
 casting. 
 
 10. One specimen for bending test, one inch by one-half inch (i" X 
 W) shall be cut cold from the coupon, or sink head, of the casting, or 
 castings, as specified in paragraph No. 9. The bending test may be 
 made by pressure or by blows. 
 
 11. The yield point specified in paragraph No. 4 shall be determined 
 by careful observation of the drop of the beam, or halt in the gauge of 
 the testing machine. 
 
 12. Tiu-nings from the tensile specimen, drillings from the bending 
 specimen or drillings from the small test ingot, if preferred by the in- 
 spector, shall be used to determine whether or not the steel is within 
 the limits, in phosphorus and sulphur, specified in paragraphs Nos. 2 
 and 3. 
 
 41 
 
 ■11 
 
 2i"- 
 
 -Mi"k- 
 
 
 Fig. 
 
Open-Hearth Methods for Steel Castings 411 
 
 Finish 
 
 13. Castings shall be true to pattern, free from blemishes, flaws or 
 • shrinkage cracks. Bearing surfaces shall be solid, and no porosity shall 
 
 be allowed in positions where the resistance and value of the casting 
 for the purpose intended will be seriously affected thereby. 
 
 Inspection 
 
 14. The inspector, representing the purchaser, shall have all reasonable 
 facilities afforded him by the manufacturer to satisfy himself that the 
 finished material is furnished in accordance with these specifications. 
 
 All tests and inspections shall be made at the place of manufacture, 
 prior to shipment. 
 
 The following paper, by Mr. W. M. Carr, on the manufacture of steel 
 castings in small quantities by the open-hearth process is given herewith 
 in full. 
 
 Open-Hearth Methods for Steel Castings 
 
 With Remarks on the Small Open-Hearth Furnace 
 By W. M. Caer, New York City 
 
 It is a fact that the open-hearth process for the manufacture of steel 
 is gradually gaining ground, as can be proved by statistics. The reason 
 for its supplanting other methods is mainly one of quality. Further, the 
 basic open-hearth process permits a mixture of pig iron and miscellaneous 
 steel scrap of a lower grade and cheaper price than raw material necessary 
 to other processes. 
 
 With the foregoing facts in mind the author presents this article for 
 the consideration of prospective investors in the manufacture of steel 
 castings in small, moderate and large tonnages; to be more explicit, 
 small tonnages are capacities of melting units in one-half, one and two 
 tons per heat. Moderate tonnages are capacities of furnaces of two to 
 five tons per heat, and large tonnages are capacities from ten to twenty- 
 five tons per heat. There are thus offered possible outputs to meet 
 almost any requirements. 
 
 In presenting the claims, it is with the recognition of the following 
 advantages : 
 
 1. The small capacity furnaces cost less to install than any other 
 steel making devices excepting only crucible melting furnaces. 
 
 2. The economy in operation of open-hearth furnaces in any capacity 
 over that of any other steel-making process. 
 
 3. The certainty of results, the greater degree of control in operation 
 and the reduction of the personal equation to the lowest possible expres- 
 sion. 
 
412 
 
 Steel Castings in the Foundry 
 
 It is generally known to the foundrymen that the largest production 
 of steel castings comes through open-hearth furnaces of capacities of 
 j&ve to twenty-five tons per heat. Such practice is established and 
 requires constant demand to be profitable, and investment of consider- 
 able capital varying with the size of the plant. It has been thought that 
 capacities of less than five tons per heat are not possible by open-hearth 
 methods, and engineers generally have dissuaded those who wish to 
 
 Fig. 122. 
 
 engage in the manufacture of steel castings either for their own con- 
 sumption or the trade from using open-hearth methods, since up till 
 quite recently the tendency has been rather to increase the capacity of 
 the open hearth, supposedly for economical reasons rather than to build 
 small units with less capacities. 
 
 The author, however, has had the opportunity to demonstrate the 
 possibilities of the miniature open hearth and has found from actual 
 practice that it is economical, and comparing operation costs with stand- 
 
Open-Hearth Methods for Steel Castings 413 
 
 ard capacity furnaces, bears equally well in economy. This fact is 
 somewhat of an innovation, but nevertheless true, and it can be said 
 that the operating cost of the miniature open hearth is less than that 
 of any type of steel-producing unit or process, making steel in equal 
 quantity. 
 
 To assist those who may not be famihar with an open-hearth furnace 
 and its operation, a study of the diagram herewith, (Fig. 122) given may 
 be instructive. The upper part of the furnace is represented in sectional 
 elevation. The structure is built of refractory bricks and boiuid se- 
 curely with structural steel beams and plates at certain points not 
 shown in the diagram. The lower part of the furnace, usually below 
 the charging floor level or carried below the shop level, consists of the 
 chambers, connecting flues leading to a reversing valve and thence to a 
 regenerator stack. Referring again to the main body of the furnace it 
 will be noticed that the hearth, which is practically a shallow dish lined 
 with "siKca" sand is fused into one sohd mass at a high temperature at 
 the time of what is known as "making bottom." This is the laboratory 
 where the raw material is melted and refined to steel of any desired 
 composition. In outhne the practice is as follows and refers to the opera- 
 tion of a miniature open hearth fired with fuel-oil being recommended 
 in preference to producer gas in capacities of less than five tons per 
 heat. 
 
 After the furnace has been brought up to a working temperature — 
 white heat — a mixture of acid pig iron and low phosphorus steel scrap 
 usually in the proportions, one-third pig and two-thirds scrap, is charged 
 into the furnace, adding the pig iron first, and when that becomes 
 molten, following with the scrap. The whole mass subsequently becomes 
 liquid by means of the oil flame passing above it. At this stage the 
 temperature of the furnace has been lessened through the addition of 
 the cold stock, but it will still be at a temperature above that required 
 to melt pig-iron. But in order to elevate the temperature above that 
 required to melt steel and have it in condition to pour, the advantage 
 of the principle of regeneration is available. This consists in returning 
 to the furnace waste heat which in other types of furnaces escapes to the 
 stack. Without a system of regeneration it is not possible to reach a 
 proper steel casting temperature ; that is to say, a reverberatory furnace 
 without regeneration gives a temperature, (where the combustion of the 
 fuel is supported by cold air) , less than that required to properly liquefjj 
 steel, but with the principle of regeneration applied to such a furnace, 
 high temperatures are readily reached. 
 
 To imderstand this principle we will foUow the course of the flame of 
 the burning oil as indicated by the arrows in the diagram. Begirming 
 
414 Steel Castings in the Foundry 
 
 at the right hand end oil is deHvered to the burner which is shown 
 surrounded with a water cooled casing to protect the burner fittings. 
 The oil is deHvered either by gravity or pump pressure, but before 
 reaching the end of the burner it is atomized or vaporized by air under 
 pressure. This air is designated as primary air and performs httle or 
 no part in supporting combustion of the oil vapor, and the quantity of 
 air delivered in excess above the amount necessary to promote combus- 
 tion of the oil is known as secondary air. The secondary air enters the 
 reversing valve shown at the stack connection, passes through the right 
 hand regenerator, enters the uptakes below the water cooled burner 
 casing, performs its function and passes along the roof of the furnace, in 
 part, and the remainder, mixed with the products of combustion with 
 the strata of flame plajang above the bath, enters the downtake at the 
 left hand end of the furnace and in its passage to the stack gives up 
 the major portion of its heat to a large quantity of brick work piled 
 within the chamber. When the waste gases have passed through the 
 reversing valve and entered the stack they have just about enough heat 
 to induce the necessary draft. Now, after an interval of twenty to 
 thirty minutes the right hand burner may be shut ofl", but not withdrawn 
 from the furnace; the reversing valve is thrown and the oil and primary 
 air turned on at the left hand end of the furnace. The secondary air 
 will then be diverted by the reversing valve to flow through the left hand 
 regenerator or checker chamber, and passing through innumerable pas- 
 sages in that set of checkers absorbs a large quantity of heat radiating 
 from the glowing bricks which became heated in the first instance by the 
 outgoing gases during a previous cycle of operation. This radiated heat 
 regenerating the secondary air will be added to the temperatiure gener- 
 ated by the burning fuel and the products of combustion will accordingly 
 have an increased quantity of heat to impart to the checker work at 
 the outgoing or right hand end. In other words, whatever temperature 
 may be carried in by the secondary air will be equivalent to an increase 
 in efficiency of the burning fuel. Successive reversals of the fuel, pri- 
 mary and secondary air produce constantly increasing increments in 
 flame temperatures below the melting points of the refractory brick 
 works. 
 
 We have seen what can be accomplished by storing up and restoring 
 to the furnace waste heat from the products of combustion, producing 
 4he effect of a higher possible temperature than in any type of melting 
 furnace. In addition to this effect another one is quite active and that 
 is reflection of heat from the walls and roof of the furnace upon the surface 
 of the bath of metal. This latter effect, known as radio-activity, is more 
 pronounced in a narrow melting chamber than in a wider one and conse- 
 
Open-Hearth Methods for Steel Castings 415 
 
 quently the result will be two factors, one a decreasing fuel consumption 
 and the other the possibihty of superheating steel in a miniature open- 
 hearth. This fact has not been recognized heretofore because most open- 
 hearth furnaces are fired with producer gas, and since that fuel requires 
 pecuKar furnace construction to get the best results in burning it, it has 
 not been found possible to make use of such fuel in a comparatively short 
 furnace hearth and therefore all furnaces designed to use that fuel must 
 have a comparatively long hearth tending mainly in the direction of 
 increased capacities rather than decreased. On the other hand, the length 
 of the hearth is not restricted where oil can be substituted for producer 
 gas and therefore it has been found possible to operate an open-hearth 
 furnace as small as 350 pounds capacity per -heat. Thus a new field is 
 opened to make steel by the open-hearth process. 
 
 Referring again to the operating method, we saw where the bath of 
 metal was molten and at a moderate temperature. This temperature 
 was due to the fact that the metal was highly carburized, since the 
 presence of carbon lowers the melting point of iron. We saw how it was 
 possible to gradually increase the temperature of the fiu-nace by the 
 regeneration of the secondary air, and with that constant elevation of 
 temperature, dormant chemical actions will be set up. The first effect 
 will be an oxidization of the siHcon occurring mostly on the surface of 
 the metal by the oxidizing action of the flame. The product would be 
 sihca, which combines with whatever oxide of iron might be present in 
 the bath of metal. The combination would form a slag of comparatively 
 Ught weight that would rise to the surface and cover the bath. The slag 
 is shown in the diagram by the heavy black Hne. This layer of slag 
 prevents the metal below from direct contact with the flame. After the 
 removal of the silicon the next action will be the removal of the carbon. 
 This action is a gas-forming one and wiU cause a bubbling or boil through- 
 out the bath. The action can be augmented from time to time by the 
 addition of iron oxide in the form of iron ore. As the decarburization 
 progresses test plugs are taken from time to time, the operator judging 
 the amount of carbon in the bath by their fracture and malleability. 
 When the carbon has decreased to a predetermined point, the boil may 
 be stopped or killed by deoxidizing agents such as ferrosilicon and ferro- 
 manganese in properly weighed amounts. The metal can then be trans- 
 ferred to molds. This method as outhned refers to the acid process. 
 In it the elements sulphur and phosphorus are not removed. The basic 
 process consists of a hearth hning made of magnesite. Such a hning 
 permits an addition of hmestone to form a slag which will absorb the two 
 elements and make a purer steel, chemically speaking, than the acid 
 process, and at the same time allow the use of cheaper and irregular 
 
4i6 Steel Castings in the Foundry 
 
 raw materials against the acid process with strictly limited chemical 
 composition concerning the two elements mentioned. 
 
 With open-hearth furnaces designed to use producer gas and which 
 rarely go below five tons capacity it is not possible to adapt them to 
 intermittent operation. Even in the smaller producer-gas fired furnaces 
 the roof span is considerable, resulting in heavy stresses on the side walls. 
 These stresses will vary as the furnace is heated and cooled, and if such 
 alternations are frequent there is danger of collapse of the furnace. It 
 becomes necessary then to maintain them continuously at a steady tem- 
 perature. Unless there should be demand for regular tonnage the fuel 
 consumption during idle periods would be a constant expense. 
 
 In miniature open-hearth furnaces, owing to the comparatively narrow 
 hearth chamber, the roof span is of course lessened and therefore v/hat- 
 ever expansion or contraction therein following heatings and coolings, 
 wiU result in comparatively slight stresses, and these results decrease in 
 effect with the lessened capacity furnaces, and they therefore lend 
 themselves to intermittent operation with greater ease and lessened 
 liabihty of repairs. The miniature open hearth is most satisfactory in 
 the roUing type with the body cylindrical, so that the stresses even 
 though slight will be evenly distributed, whereas in a rectangular -form 
 the roof will always rest and thrust upon the inside walls. In fact the 
 miniature open hearth is not recommended to be built in the stationary 
 type. 
 
 In conclusion the miniature open hearth is not costly to install, is 
 comparatively simple to operate, gives results equal to standard open- 
 hearth practice, makes hotter steel than the regular open hearth and . 
 can show costs equally as low per poimd of molten metal in the ladle. 
 
Comparative Cost of Steel made by Different Processes 417 
 
 Comparative Cost of Steel made by DiSerent 
 Processes 
 
 From paper presented to the American Foundrymen's Association 
 by Mr. Bradley Stoughton. 
 
 Table I. — Acid Open Hearth 
 
 Raw materials 
 
 Pig iron 
 
 Heads, gates, etc 
 
 Foreign scrap 
 
 Defective castings* (account bad metal) 
 Ferro-alloys 
 
 Total metal 
 
 Operating costs 
 
 Cost of steel in ladle 
 
 Per 2000 pounds of steel in ladle 
 
 Price 
 
 of raw 
 materials 
 per 2000 
 pounds 
 
 $14.00 
 14.00 
 14.50 
 50.00 
 40.60 
 
 Weight 
 used, 
 pounds 
 
 300 
 660 
 1080 
 20 
 29 
 2089 
 
 Per cent 
 used 
 
 Cost 
 
 $2. 10 
 
 4.62 
 
 7.83 
 
 .50 
 
 ^ 
 
 $15.64 
 
 5.5ot 
 
 $21.14 
 
 Cost 
 
 $15.64 
 8.85 t 
 $24.49 
 
 Cost of Steel in Castings 
 
 
 
 
 Cost of steel in ladle -^ 65 per cent J = 
 Less credit for heads, etc., as_scrap = . 
 
 
 
 
 $32.52 
 4.62 
 
 $27.90 
 
 $37.68 
 
 
 
 
 4.62 
 
 
 
 
 $33.06 
 
 
 
 
 
 
 * The price given for defective castings is over and above their value as scrap 
 See the text following for further discussion of this charge. 
 
 t The charge of S5.50 for operating costs is the figure for a 2S-ton furnace and large 
 tonnage; that of $8.85 is for a small furnace and small production. 
 
 t Of the steel in the ladle, 65 per cent goes into castings, 33 per cent goes into heads, 
 gates, etc. and 2 per cent is lost in spattering, etc. 
 
4i8 
 
 Steel Castings in the Foundry 
 Table II. — Basic Open Hearth 
 
 Raw materials 
 
 Pig iron 
 
 Heads, gates, etc. . . . 
 
 Foreign scrap 
 
 Defective castings*. . 
 Ferro-alloys 
 
 Total metal 
 
 Operating costs . . 
 Cost of steel in ladle. 
 
 Per 2000 pounds of steel in ladle 
 
 Price 
 
 of raw- 
 materials 
 per 2000 
 pounds 
 
 $12.75 
 14.00 
 II. 15 
 SO. 00 
 40.60 
 
 Weight 
 used, 
 pounds 
 
 Per cent 
 used 
 
 Cost 
 
 1040 
 
 52 
 
 $6.63 
 
 660 
 
 33 
 
 4.62 
 
 350 
 
 17 ^i 
 
 1.9s 
 
 40 
 
 2 
 
 1. 00 
 
 33 
 
 1I/2 
 
 .67 
 
 2123 
 
 106 
 
 $14.87 
 6. lot 
 $20.97 
 
 Cost 
 
 $14.87 
 9 -55 ! 
 
 $24.42 
 
 Cost of Steel in Castings 
 
 Cost of steel in laddie H- 65 per 
 cent J — 
 
 
 
 
 $32.26 
 4.62 
 
 $27.64 
 
 $37.57 
 4 62 
 
 Less credit for heads, etc. as scrap = . 
 
 
 
 
 Net cost of steel in castings . ... 
 
 
 
 
 $32.95 
 
 
 
 
 
 
 * See footnote under Hearth, Table I. 
 t See footnote under Table I. 
 
 t Of the steel in the ladle, 65 per cent goes into castings, 33 per cent goes into heads, 
 gates, etc., 2 per cent is lost in spattering in pouring. 
 
Acid Open Hearth and Basic Open Hearth 
 
 419 
 
 Acm Open Hearth and Basic Open Hearth 
 [When Together in One Plant] 
 
 Raw materials 
 
 Acid open hearth per 
 
 2000 pounds of steel 
 
 in ladle 
 
 Basic open hearth per 
 2000 pounds of steel 
 in ladle 
 
 Price of 
 
 raw materials 
 
 per 2000 
 
 pounds 
 
 M 
 
 
 8 
 
 
 
 h 
 
 1 
 
 
 $14.00 
 
 14.00 
 14.50 
 50.00 
 40.60 
 
 300 
 
 1320 
 
 420 
 
 20 
 
 29 
 
 15 
 
 66 
 21 
 
 I 
 I 
 
 104 
 
 $2.10 
 
 9.24 
 
 3.05 
 
 .50 
 
 ■ 59 
 
 $12.75 
 II. 15 
 
 so. 00 
 40.60 
 
 1040 
 
 lOIO 
 
 40 
 
 33 
 2123 
 
 52 
 
 '151/2 
 2 
 11/2 
 
 $6.63 
 
 Heads, gates, etc., from 
 
 
 5.63 
 
 
 Ferroalloys 
 
 .67 
 
 Total metal 
 
 
 2089 
 
 $15.48 
 
 5.50 
 
 $20.98 
 
 
 71 
 
 $13.93 
 
 6.10 
 
 $20.03 
 
 Operating costs 
 
 Cost of steel in ladle 
 
 
 Cost of Steel 
 
 in Castings 
 
 
 Cost of Steel in Castings 
 
 Cost of steel in ladle -h 65 pe 
 
 
 
 $32.28 
 
 4.62 
 
 $27.66 
 
 
 
 
 
 $30.81 
 
 
 
 
 4.62 
 
 
 
 
 $26 . 19 
 
 
 
 
 
420 
 
 Steel Castings in the Foundry 
 Table IV. — Converter 
 
 
 Per 
 
 2000 pounds of steel in ladle 
 
 Raw materials 
 
 Price 
 
 of raw 
 
 materials 
 
 per 2000 
 
 pounds 
 
 Weight 
 used, 
 pounds 
 
 Percent 
 used 
 
 Cost 
 
 Cost 
 
 Pig iron 
 
 $14.00 
 17.40 
 14.00 
 80.00* 
 40.60 
 
 300 
 
 1280 
 
 660 
 
 20 
 
 35 
 
 229s 
 
 15 
 64 
 33 
 
 It 
 
 2 
 
 115 
 
 $2.10 
 II. 14 
 4.62 
 .8ot 
 .71 
 
 $19.37 
 3. sot 
 
 $22.87 
 
 
 Pig iron 
 
 
 Heads, gates, etc. 
 
 
 Defective castings (account bad metal) 
 Ferroalloys . . 
 
 
 Total metal 
 
 $19-37 
 
 
 
 Cost of steel in ladle 
 
 
 $24.87 
 
 
 
 
 Cost of Steel in Castings 
 
 
 
 
 
 $35.18 
 4.62 
 
 $30.56 
 
 $38.26 
 
 
 
 
 
 4.62 
 
 Net cost of steel in castings . . . . 
 
 
 
 
 $33.64 
 
 
 
 
 
 • See footnote under Table I. 
 
 t The percentage of defective castings in converter practice will actually be less 
 than this, so that the cost is a little higher than justice to average converter practice 
 demands. In the absence of average figiures, we have charged it the same as acid 
 open hearth, with this correction. 
 
 t Operating cost, $3-5o, is for one 2-ton converter making 150 tons per week. The 
 $5-50 per ton is a 2-ton converter with small production. 
 
Converter, with Large Waste 421 
 
 Table V. — Converter, with Large Waste 
 
 
 Per 2000 pounds of steel in ladle 
 
 
 Raw materials 
 
 Price 
 of raw- 
 materials 
 per 2000 
 pounds 
 
 Weight 
 used, 
 pounds 
 
 Per cent 
 used 
 
 Cost 
 
 Cost 
 
 Pig iron .... 
 
 $14.00 
 17.40 
 14.00 
 80.00 
 40.60 
 
 300 
 1360 
 
 660 
 
 20 
 
 _^ 
 
 2378 
 
 IS 
 
 68 
 
 33 
 
 I 
 
 2 
 
 119 
 
 $2.10 
 
 11.83 
 
 4.62 
 
 .80 
 
 .77 
 
 $20.12 
 
 3.50 
 
 $23.62 
 
 
 Pig iron 
 
 
 Heads, gates, etc. 
 
 
 Defective castings account bad metal. 
 
 
 Total metal 
 
 $20.12 
 
 
 
 5.50 
 
 Cost of steel in ladle 
 
 
 $25.62 
 
 
 
 
 Cost of Steel in Castings 
 
 Cost of steel in ladle -^ 65 per cent . 
 
 Less credit for heads, etc., as scrap. 
 
 Net cost of steel in castings 
 
 $36.34 
 4.62 
 
 $31.72 
 
 $39-42 
 4.62 
 
 $34.80 
 
422 Steel Castings in the Foundry 
 
 Table VI. — Acm Open Hearth [Making Small Castings] 
 
 Raw materials 
 
 Pig iron 
 
 Heads, gates, etc 
 
 Foreign scrap 
 
 Defective castings account bad metal, 
 Ferroalloys 
 
 Total metal 
 
 Operating costs 
 
 Cost of steel in ladle 
 
 Per 2000 pounds of steel in ladle 
 
 Price 
 of raw- 
 materials 
 per 20CX) 
 pounds 
 
 S14.00 
 14.00 
 14.50 
 50.00 
 40.60 
 
 Weight 
 
 used, 
 
 pounds 
 
 300 
 
 660 
 
 120 
 29 
 
 Per cent 
 used 
 
 Cost 
 
 $2.10 
 4.62 
 7. II 
 300 
 
 ^ 
 
 $17-42 
 
 5.50 
 
 $22.92 
 
 Cost 
 
 $17-42 
 
 8.85 
 
 $26.27 
 
 Cost of steel in castings 
 
 Cost of steel in ladle -f- 65 per cent*. 
 
 Less credit for heads, etc., as scrap. . 
 
 Net cost of steel in castings 
 
 $35.26 
 
 4.62 
 
 $30.64 
 
 S40.41 
 4.62 
 
 $35.79 
 
 * Of the steel in the ladle, 65 per cent goes into castings, 33 per cent goes into heads, 
 gates, etc., 2 per cent is lost in spattering during pouring. In making small castings, 
 the loss in pouring from a bottom-poured ladle would be much larger than this, and 
 the cost of steel in castings would be increased $1 to $3 per ton, but data is lacking 
 for exact estimates. 
 
Crucible Castings 
 
 423 
 
 Table VIL — 
 
 Basic Open Hearth [Making Small Castings] 
 
 
 Per 
 
 2000 pounds of steel in 
 ladle 
 
 Per 2000 pounds of 
 steel in ladle 
 
 Raw materials 
 
 Price of 
 
 raw materials 
 
 per 2000 
 
 pounds 
 
 13 
 
 li 
 
 
 S 
 
 1 
 
 
 
 
 
 
 
 5 
 
 
 $12.75 
 14.00 
 II. IS 
 50.00 
 40.60 
 
 1040 
 660 
 190 
 200 
 
 33 
 
 52 
 33 
 
 10 
 
 1I/2 
 
 $6.63 
 
 4.62 
 
 1.06 
 
 5.00 
 
 .67 
 
 $17.98 
 9-55 
 
 1040 
 
 660 
 350 
 300 
 
 33 
 
 52 
 
 33 
 
 17I/2 
 15 
 
 1 1/2 
 
 $6.63 
 
 4.62 
 
 1.95 
 
 7.50 
 
 .67 
 
 
 Heads, gates, etc. . . . 
 
 Foreign scrap 
 
 Defective castings . . . 
 
 
 
 
 Total metal 
 
 Operating costs . . 
 
 2123 
 
 106 
 
 $17.98 
 6.10 
 
 2124 
 
 106 
 
 $19.93 
 6.10 
 
 $19.93 
 9.55 
 
 Cost of steel in ladle.. 
 
 
 $24.08 
 
 $27.53 
 
 $26.03 
 
 $29.48 
 
 Cost of Steel in Castings 
 
 Cost of steel in ladle -j- 65 per cent . 
 
 Less credit for heads, etc., as scrap 
 
 Net cost of steel in castings 
 
 $37.05 
 4.62 
 
 $32.43 
 
 $42.35 
 4.62 
 
 $37.73 
 
 $40.05 
 4.62 
 
 $35.43 
 
 $45.85 
 4.62 
 
 $40.73 
 
 Table VIII. — Crucible Castings 
 
 
 
 
 Per 2000 pounds steel in ladle 
 
 Raw materials 
 
 Price of 
 
 raw materials 
 
 per 2000 
 
 pounds 
 
 to OQ 
 
 It 
 
 
 1 
 
 
 
 1. 
 
 ^ p. 
 
 1 
 
 
 1 
 
 
 
 
 $25.50 
 14.50 
 14.00 
 
 125.00 
 40.60 
 
 1360 
 
 "660' 
 10 
 12 
 
 68 
 
 33 
 
 V2 
 
 102 
 
 $17.34 
 
 ■■4;62 
 .63 
 
 .24 
 
 $22.83 
 35.00 
 
 $57.83 
 
 1330 
 
 660 
 
 10 
 
 12 
 
 33 
 
 lOOl/i 
 
 
 Foreign steel scrap — 
 
 Heads, gates, etc '. 
 
 Defective castings 
 
 Ferroalloys 
 
 $9.64 
 
 4.62 
 
 .63 
 
 .24 
 
 Total metal 
 
 Operating costs . . . 
 Cost of steel in ladle.. 
 
 2042 
 
 2012 
 
 $15.13 
 35.00 
 
 $50.13 
 
 Cost of Steel in Castings 
 
 Cost of steel in ladle -f- 66 per cent* $87.62 
 
 Less credit for heads, etc. , as scrap 4 . 62 
 
 Net cost of steel in castings $83 .00 
 
 $75.95 
 4.62 
 
 $71-33 
 
 * Of the steel in the ladle, 66 per cent goes into castings, 33 per cent goes into heads, 
 gates, etc. and i per cent is lost in poiiring. 
 
424 
 
 Steel Castings in the Foundry 
 Table IX. — Electric Furnace 
 
 Raw materials 
 
 Steel scrap 
 
 Heads, gates, etc.. 
 Defective castings. 
 
 Ferroalloys 
 
 Total metal... 
 
 Per 2O0O pounds of steel in ladle 
 
 Price 
 
 of raw 
 
 materials 
 
 per 2000 
 
 poimds 
 
 $9.50 
 14.00 
 125.00 
 40.60 
 
 Weight 
 
 used, 
 
 pounds 
 
 1330 
 
 660 
 
 10 
 
 12 
 
 2012 
 
 Per cent 
 used 
 
 661/i 
 33 
 
 looH 
 
 Cost 
 
 Cost of netting steel 
 
 In ladle 
 
 Electric power at i cent per kilowatt hour 
 " " " 2 cents '* " " 
 
 " " 3 " *' " 
 
 • 4 " " " 
 
 • 5 ' 
 
 $39.03 
 52.89 
 66.76 
 80.62 
 94.49 
 
CHAPTER XVIII 
 FOUNDRY FUELS (Cupola) 
 
 The fuels available for melting iron in the cupola are anthracite coal 
 and coke. 
 
 Anthracite Coal 
 
 Lehigh lump is the best coal for the purpose. It produces a hot iron 
 and melts it rapidly. On account of the cost as compared with coke, it 
 is now Uttle used in districts removed from the anthracite region. 
 
 A mixture of anthracite and coke, particularly for the bed, gives most 
 excellent results, especially for prolonged heats. 
 
 Coke 
 
 When bituminous coal is exposed to a red heat for a prolonged period 
 with total or partial exclusion of air, the volatile matter is driven off and 
 the residuum is coke, containing more or less impurities. The coal used 
 is of the coking variety and to produce good foundry coke should be low 
 in sulphur and ash. Seventy-two hour Bee Hive Coke is most generally 
 used by foundrymen. This has a hard, cellular, columnar structure, 
 with a gray, silvery surface. The smooth, glistening appearance iound 
 in much of it is due to quenching in the furnace. (Weight about 25 
 pounds to cubic foot.) There will be found in each carload of coke 
 "black-tops" and "black-butts"; the appearance of the former is due 
 to deposits of carbon from the imperfect combustion of the gases at the 
 top of the furnace. They in no way affect the value of the fuel. Black 
 butts, however, come from incomplete burning and contain unconverted 
 coal. These should be accepted only in limited quantities. 
 
 The following are analyses from different sections: 
 
 Localities 
 
 Fixed 
 carbon 
 
 Volatile 
 matter 
 
 Moisture 
 
 Ash 
 
 Sulphur 
 
 
 89. 58 
 92.58 
 80. SI 
 92.38 
 87.29 
 
 .46 
 
 .49 
 
 1. 10 
 
 .03 
 .20 
 .45 
 
 9. II 
 6.05 
 
 16.34 
 7.21 
 
 10.54 
 
 .81 
 
 
 .68 
 
 Chattanooga. ". 
 
 New River. 
 
 1.59 
 .56 
 
 Birmingham 
 
 1. 19 
 
 
 
 425 
 
426 Foundry Fuels 
 
 Specific gravity averages 1.272. Coke will absorb from 10 to 30 per 
 cent of its weight in moisture, depending on exposiu-e. After exposure 
 to a hard storm the increase in weight may easily be 15 per cent. 
 
 Less pressure of air, more volume and larger tuyere area are required 
 when melting with coke than with anthracite coal. 
 
 The following specifications for coke from the J. I. Case Co. are given 
 by Mr. Scott. 
 
 Gk)od clean 72-hour coke, massive and free from granulation, dust and 
 cinder. Per cent 
 
 Moisture not over i . 50 
 
 Volatile matter not over 3 . 50 
 
 Fixed carbon not under 86 . 00 
 
 Sulphur not over 0.75 
 
 Ash not over 11 . 50 
 
 Coke which has over 0.85 sulphur, 0.05 phosphorus, less than 85 
 fixed carbon or less than 5.00 ash will be rejected. 
 I Good foundry coke should be high in carbon, low in sulphur, have 
 good columnar structure, and there should not be a large percentage of 
 small pieces in a carload. The product should be uniform. 
 
 By-Product Coke 
 
 Certain chemical works, in the distillation of bituminous coal for 
 ammonia, manufacture coke as a by-product. This, when especially 
 prepared for foundry purposes, gives excellent results. It is darker, 
 harder and more irregular in form than beehive coke. It is high in 
 carbon and low in sulphur, makes a very hot fire and will melt more 
 iron than an equal weight of beehive. The short description of the 
 process of making this coke by Mr. W. J. Keep is given herewith. 
 
 "The retort oven is a closed chamber from 15 to 24 inches in width, 
 5 to 8 feet in height and from 25 to 45 feet long. From 25 to 50 of these 
 ovens are placed in a battery. 
 
 "The coal is charged through three or more openings in the top and 
 levelled off to within a foot of the roof, after which the oven is carefully 
 closed and sealed, in order to exclude the air. The oven is heated by a 
 portion of the gas driven off in the process of coking. This is not burned 
 in the oven itself, but in flues constructed in their walls. The heat is 
 conducted through the walls of these combustion flues to the charges of 
 coal and distillation thereof is started immediately. 
 
 "The gas which is driven off is conducted through an apparatus in 
 which the tar and ammonia are recovered; after which a portion of the 
 gas is returned to be burned in the oven flues, and the balance disposed 
 of as local conditions determine. 
 
Effect of Atmospheric Moisture upon Coke 427 
 
 "Distillation proceeds from the side walls toward the middle of the 
 oven and the gas is probably driven toward the center of the oven, where 
 it rises, forming a cleavage plane the whole length of the oven. When 
 the process is completed, which takes place in from 20 to 36 hours, 
 depending upon the width of the oven and the temperature maintained, 
 the whole charge is pushed out by a steam or electric ram and is immedi- 
 ately quenched. The oven is at once closed and, without any loss of 
 heat from the oven itself, is again charged with coal. 
 
 "On account of the cleavage plane through the center of the charge, 
 no piece of coke can be longer than half the width of the oven." 
 
 "Owing to the complete exclusion of air, there is no combustion in the 
 oven; and as the temperature of the oven, when the coal is charged, is 
 very high, there is a considerable decomposition of volatile matter with 
 consequent deposition of carbon upon the coking charge. As a result 
 the yield of coke is a little higher than the theoretical yield, as cal- 
 culated from the analysis of the coal. Quenching the coke outside the 
 ovens mars its appearance somewhat, destroying its bright, silvery 
 lustre, but probably results in carrying off an appreciable quantity of 
 sulphur." 
 
 " Coke made from the same coal will have a slightly higher percentage 
 of fixed carbon and a slightly lower percentage of ash than if made in a 
 retort oven." 
 
 " The quality of retort oven coke depends upon the skill of the operator, 
 upon the method of preparing the coal and more than all, upon the 
 quality of the coal used. 
 
 He further says that after having satisfied himself that it was good 
 coke, "in spite of its very bad appearance," by the use of several car- 
 loads, "from that time to this we have never had a pound of other 
 coke. All through 1902 the coke was so uniform and satisfactory that 
 we melted 9 pounds of iron with i pound of coke." 
 
 EfEect of Atmospheric Moisture upon Coke 
 
 Under normal conditions, at a temperature of 70° F., 1000 cubic feet 
 of air, equal in weight to about 75 pounds, contains i pound of moisture. 
 Each pound of moisture requires the use of o.io additional pounds of 
 coke. Therefore, every additional i.o per cent to the moisture of the 
 atmosphere requires 0.03 additional pounds of coke to melt one ton of 
 iron. 
 
 From 20 to 40 per cent of the sulphur in the coke is taken up by the 
 iron in melting. This may be largely reduced by the liberal use of 
 limestone. 
 
428 Foundry Fuels 
 
 Specifications for Foundry Coke Suggested by 
 Dr. Richard Moldenke 
 
 Coke bought under these specifications should be massive, in large 
 pieces and as free as possible from black ends and cinders. 
 
 Sampling 
 
 Each carload or its equivalent shall be considered as a unit, and 
 sampled by taking from the exposed surface at least one piece for each 
 ton, so as to fairly represent the shipment. These samples, properly 
 broken down and ground to the fineness of coarse sawdust, well mixed 
 and dried before analysis, shall be used as a basis for the payment of the 
 shipment. In case of disagreement between buyer and seller an indepen- 
 dent chemist, mutually agreed upon, shall be employed to sample and 
 analyze the coke, the cost to be botne by the party at fault. 
 
 Base Analysis 
 
 The following analysis, representing an average grade of foundry coke 
 capable of being made in any of the districts supplying foundries, shall 
 be considered the base, premiums and penalties to be calculated thereon 
 as determined by the analysis on an agreed base price: 
 
 Volatile matter i . 00 Ash 12 . 00 
 
 Fixed carbon 85 . 50 Sulphur i . 10 
 
 Penalties and Bonuses 
 
 Moisture. — Payment shall be made on shipments on the basis of 
 "dry coke." The weight received shall, therefore, be corrected by 
 deducting the water contained. (Note. — Coke producers should add 
 sufficient coke to their tonnage shipments to make up for the water 
 included, as shown by their own determinations.) 
 
 Volatile Matter. — For every 0.50 or fraction thereof, above the i.oo 
 allowed, deduct . . cents from the price. Over 2.50 rejects the shipment 
 at the option of the purchaser. 
 
 Fixed Carbon. — For every i.oo or fraction thereof, above 85.50 add, 
 and for every i.oo or fraction thereof below 85.50, deduct . . cents. 
 Below 78.50 rejects the shipment at the option of the purchaser. 
 
 Ash. — For every 0.50 or fraction thereof below 12.00, add, and for 
 every 0.50 or fraction thereof above 12.00 deduct . . cents from the price. 
 Above 15.00 rejects the shipment at the option of the purchaser. 
 
 Sidphur. — For every o.io or fraction thereof below i.io add, and for 
 every o.io or fraction thereof above, deduct . . cents from the price. 
 Above 1.30 rejects the shipment at the option of the purchaser. 
 
Fluxes 429 
 
 Shatter Test 
 
 On arrival of the shipment the coke shall be subjected to a shatter 
 test, as described below. The percentage of fine coke thus determined, 
 above 5 per cent of the coke, shall be deducted from the amount of coke 
 to be paid for (after allowing for the water) , and paid at fine coke prices 
 previously agreed upon. Above 25 per cent fine coke rejects the ship- 
 ment at the option of the purchaser. Fine coke shall be coke that passes 
 through a wire screen with square holes 2 inches in the clear. 
 
 The apparatus for making the shatter test should be a box capable 
 of holding at least 100 pounds coke, supported with the bottom 6 feet 
 above a cast-iron plate. The doors on the bottom of the box shall be 
 so hinged and latched that they will swing freely away when opened and 
 win not impede the fall of the coke. Boards shall be put around the 
 cast iron plate so that no coke may be lost. 
 
 A sample of approximately 50 pounds is taken at random from the 
 car, using a iH inch tine fork, and placed in the box without attempt to 
 arrange it therein. The entire material shall be dropped four times upon 
 the cast iron plate, the small material and the dust being returned with 
 the large coke each time. 
 
 After the fourth drop the material is screened as above given, the 
 screen to be in horizontal position, shaken once only, and no attempt 
 made to put the small pieces through specially. The coke remaining 
 shall be weighed and the percentage of the fine coke determined. 
 
 If the sum of the weights indicates a loss of over i per cent the test shall 
 be rejected and a new one made. 
 
 Rejection by reason of failure to pass the shatter test shall not take 
 place until at least two check tests have been made. 
 
 Fluxes 
 
 The object of a flux is to render fusible the ash from the fuel, sand 
 and rust from the iron, and dirt of any sort, found in the cupola, into 
 slag and to put it in condition for easy removal. 
 
 Slag always forms to a greater or less extent where iron is melted, 
 but unless a flux is present, it will not be sufficient in volume to give 
 clean iron. Limestone and fluor spar are the most corrimon fluxes in 
 use. There are many compounds furnished for the purpose, but a 
 limestone containing 90 per cent or more carbonate of lime, or oyster 
 shells, furnish as good fluxing material as can be procured. 
 
 The following is copied from a paper by Mr. N. W. Shed, presented 
 to the Cleveland meeting of the American Foundrymen's Association 
 at June, 1906. 
 
430 Foundry Fuels 
 
 "The value of fluxes in the cupola is not generally appreciated by 
 foundrymen. Hundreds of cupolas are not slagged at all and the 
 cinder dumps show an immense amount of iron actually wasted. Not 
 only is iron lost by the large amount combined with the cinders, but the 
 more or less variable cinder encloses small masses and shots of iron 
 which cannot be separated. It is a fact that the cinder dumps of many 
 foundries contain more iron than many workable deposits of iron ore, 
 and if these accumulations could be obtained by the Geiman blast fur- 
 naces they would be quickly utilized. 
 
 Another value of fluxes is their cleansing action on the cupola. 
 A weU slagged cupola has no hanging masses of iron and cinder which 
 require laborious chipping out. The time and labor saved in conse- 
 quence is an item that is well worth considering. In the running of 
 heavy tonnage from a single cupola, fluxes are indispensable. It would 
 be well nigh impossible to run large heats in the same cupolas without 
 using a good flux. 
 
 The value of fluxes being generally admitted, the question arises, 
 what flux is best to use and how much? 
 
 There are two available fluxes for the cupola. These are limestone 
 and fluor spar. 
 
 Fluor spar is much advertised as a flux and the promoters claim that 
 it gives marvellous properties to the iron. The glowing advertisements 
 have evidently deceived the U. S. Geological Survey, for the reports 
 of the Survey speak of its great use and value in foundry practice. " 
 
 The practical test of fluor spar, made by the writer showed it to be 
 an inferior flux. It did not remove sulphur and the properties of the 
 iron were not improved in the least by its use. There is no doubt of 
 the value of fluor spar in certain branches of metallurgy, but the writer 
 has failed to find a single supporter of its value in the foundry. 
 
 Limestone is far cheaper than fluor spar and far better as a flux. 
 It makes little difference what form the limestone has so long as it is 
 pure. It may be marble, soft limestone, hard limestone, oyster shells, 
 or mussel shells, but it must be good. A limestone containing over 
 3 per cent sihca is poor stuff, and one containing any considerable 
 amount of clay should be rejected. There should be at least 51 per cieht 
 of lime present. The sulphur should be below i to 2 per cent. The 
 phosphorus is unimportant. A magnesian limestone would do as well 
 as an ordinary limestone for the cupola. 
 
 The amount of limestone to be used is variable, depending: 
 
 First: on the amount of silica in the coke ash. 
 
 Second: on the amount of siUca or sand adhering to the pig or scrap. 
 
 Third: on the amount of silica to be carried by the slag. 
 
Fluxes 431 
 
 The amount of limestone required to flux the coke ash can be 
 figured according to the ordinary method of calculating blast furnace 
 charges. 
 
 The amount of sand on the pig and scrap is so variable that it is 
 difficult to know just the additional amount of limestone to add. 
 
 The most practical and easily fusible slag has been found to be a 
 monosilicate, which means having equal amoimts of silica and alkaline 
 bases. Having these variables in mind, we find it a good rule to figure 
 the hmestone on the weight of the coke, using 25 per cent hmestone. 
 
 For example, if the charge of coke on the bed is 4000 pounds, we 
 use 1000 pounds of limestone. If the next charge of coke is 1000 pounds, 
 we would use 250 pounds of limestone. This amount of limestone will 
 flux any ordinary coke ash with the average amount of sand on pig 
 and scrap. If we know the amount of sand on the pig to be excessive 
 we figure 30 per cent limestone on the weight of the coke. 
 
 With a low coke ash, machine pig and clean scrap, the limestone 
 may be reduced to 20 per cent and make a good cinder. Many foundry- 
 men are afraid to use limestone, fearing some injury to the iron. This 
 is a superstition for lime has no effect on the iron. 
 
 There is usually a slight reduction in the amount of sulphur, but 
 owing to the great amount of iron present, the iron absorbs a large 
 amount of sulphur from the coke. 
 
 If more than 30 per cent is required to make a good cinder and clear 
 the cupola it is evident that either the coke is very high in ash, or else 
 the limestone is high in silica. In the latter case a large amount of 
 lime is used in fluxing its own silica. 
 
 On account of the frequent variations in the stock, it is a good plan 
 to have coke, limestone and cinder analyzed occasionally. 
 
 The cinder usually tells about the condition of the furnace. A light 
 brown indicates a small amount of iron and the iron unoxidized. A 
 black cinder indicates a large amount of iron and some oxidation. A 
 shiny metallic lustre shows an excess of oxide of iron due to over-blow- 
 ing or lack of coke. Practically all the lime cinders from a cupola are 
 glossy in appearance, while the cinders with no lime are usually dull 
 and earthy. Occasionally a cinder is found full of bubbles, the color 
 is usually black and shots of iron are found through the frothy slag. 
 This is called foaming cinder, and is made when the last few charges 
 are at the bottom of the cupola. This cinder often rises to the charging 
 door and flows out over the floor. The iron cast at this time is hard 
 and is low in manganese, silica and carbon. 
 
 With foaming slag a dense smoke of reddish brown color pours out 
 of the stack. 
 
432 
 
 Foundry Fuels 
 
 Analysis of the foaming slag shows the iron to be in an oxidized 
 condition and in large amount. Sometimes the iron will run 30 per 
 cent in frothy cinder, sometimes only 12 per cent. The oxidized cinder 
 and the red smoke show that iron is being rapidly burned in the cupola, 
 and the action going on is very much like the action in a Bessemer con- 
 verter when it is tilted back a little and blown to gain heat by burning 
 the iron. The cinder is oxidized and the red smoke is produced in the 
 same way. In both cases the iron is burnt to oxide, which is quickly 
 taken up by the slag. The oxide in the slag acts upon the carbon in 
 the iron forming a large amount of carbonic oxide, which rises through 
 the cinder blowing it to a frothy condition. 
 
 There are two ways of avoiding this troublesome condition. If 
 possible, reduce the blast. If the blast cannot be reduced, add more 
 coke. The presence of a good body of coke will stop the burning of the 
 iron, and frothing does not take place. In some cases the loss of sili- 
 con is very serious, and to insure good castings it is necessary to add 
 crushed silicon metal and ferro-manganese to the stream of iron as it 
 runs from the spout. 
 
 Analysis of cupola slags where no flux is used show from 14 to 28 per 
 cent ferrous oxide. These slags contain 2 to 4 per cent of shot iron 
 mingled with the cinder. This proves that some of the iron must be 
 lost in order to flux the coke ash and sand. If we use limestone as a 
 flux the amount of iron in the cinder is rarely over 3 per cent, showing 
 that the lime fluxes the ash and sand leaving the iron for the ladle. 
 And the question is simply whether we will use iron as a flux at ^18.00 
 per ton or limestone at ^1.50 per ton. 
 
 Another point in favor of the limestone is the clean cupola men- 
 tioned in the first part of this paper. 
 
 Following will be found an analysis of cupola cinder using lime." 
 
 Comparison of Analyses of Slags, Made With and Without 
 Lime 
 
 Constituents 
 
 Using 
 lime 
 
 Without 
 lime 
 
 CaO 
 
 34.60 
 
 4.10 
 
 11.02 
 
 48.20 
 
 1.40 
 
 .20 
 
 99-52 
 
 6.60 
 21.76 
 11.80 
 58.44 
 
 1.30 
 .10 
 
 FeO 
 
 AI2O0 .. 
 
 SiOs 
 
 MnO 
 
 S 
 
 Total 
 
 100.00 
 
 
Slags 433 
 
 The following analyses are extracted from " The Foundry," Dec, 
 1909- 
 
 Analysis of Slag from a Cupola Melting Car Wheel Iron, in the South 
 
 Per cent Per cent 
 
 Silica 48 . 77 Oxide of iron 13.18 
 
 Aluminum 10 . 90 Metallic iron 9 . 23 
 
 Lime 13 • 79 Manganese . 4 . 84 
 
 Magnesia 6.05 Sulphur 0.81 
 
 Analysis of Slag from a Cupola Melting Gray Iron, No Fluor spar 
 Being Used 
 
 Per cent Per cent 
 
 Silica 42 . 84 Magnesia 13 • 28 
 
 Alumina Manganese 2 . 34 
 
 Oxide of iron 21.32 Manganese oxide 3 . 01 
 
 Lime 21.16 
 
 Analysis of Slag from a Cupola Melting Gray Iron, Fluor spar 
 Being Used 
 
 Per cent Per cent 
 
 Silica 39 • 50 Magnesia n . 05 
 
 Alumina Manganese 2 . 24 
 
 Oxide of iron 22.82 Manganese oxide 2.89 
 
 Lime 24.50 
 
 Analysis of Slag from a Cupola Melting Malleable Iron 
 
 Per cent Per cent 
 
 Silica. . . . : 41 • 72 Magnesia 15 .06 
 
 Oxide of iron Manganese 3 . 20 
 
 Alumina 22 . 24 Metallic iron S . 82 
 
 Lime 17-84 Manganese oxide 4.12 
 
 Analysis of Slag from a Cupola Melting Car Wheel Iron, in the North 
 
 Per cent Per cent 
 
 Silica 44.00 Magnesia 7.27 
 
 Oxide of iron 13 • 16 Metallic iron 9.21 
 
 Alumina 9.76 Manganese 5 . 70 
 
 Lime iS-99 Sulphur 0.78 
 
 Cupola Slag from a Western Foundry 
 
 Per cent Per cent 
 
 Silica 37 -16 Oxide of iron 13-73 
 
 Alumina 9 . 16 Metallic iron 9 . 61 
 
 Lime 8-98 Manganese oxide. ... 2 . 77 
 
 Magnesia 8.44 Sulphur 0.36 
 
434 
 
 Foundry Fuels 
 
 Sufi&cient flux must be used to obtain a fluid slag to carry off the 
 silica from the iron and ashes and to reduce the oxidation as much as 
 possible. 
 
 With low blast pressure the slag must be thin, to run off readily. 
 
 When slag wool is freely produced, the indication is that the slagging 
 is satisfactory. 
 
 A good slag contains approximately 40 per cent of silica and from 28 
 to 30 per cent lime. If the slag is thin, the metaUic iron will fall through 
 it readily and an increase of lime tends to decrease the oxide of iron. 
 
 Rusty scrap produces a dark-colored slag caused by the oxide of 
 iron. 
 
 A large body of slag is favorable to desulphurization, as the amount 
 of sulphur which can be taken up by the slag is limited. At high temper- 
 atures sulphur tends to combine with the slag and under these conditions 
 it has not its greatest afi&nity for iron. 
 
 Fire Brick and Fire Clay 
 A good brick has a light yellow color, a coarse and open structure, 
 uniform throughout. It should be burned to the limit of contractility. 
 The clay from which it is made should contain as little iron, lime, potash 
 and soda as possible. 
 
 Analyses op Fire Clays Used por Making Fire Brick 
 
 Clay loses its plasticity at a temperature above 100° C, and it cannot again 
 be restored. 
 
 Localities 
 
 J 
 
 CO 
 
 C3 
 g 
 
 < 
 
 "o 
 
 4) C 
 
 0" 
 
 s 
 
 
 1 
 
 1 
 
 Stourbridge, Eng. 
 
 17.34 
 12.74 
 11.70 
 5. 34 
 5.4s 
 
 45.25 
 50.45 
 49 -20 
 59-95 
 70.70 
 55.62 
 56.12 
 
 28.77 
 35.90 
 27.80 
 33.85 
 21.70 
 38.55 
 37.48 
 
 7.72 
 1.50 
 
 4.17 
 4.43 
 
 .47 . 
 .13 
 .40 
 2.05 
 .40 
 .24 
 .36 
 
 20 
 10 
 55 
 37 
 24 
 29 
 
 • 95 
 .99 
 
 
 Mt. Savage, Md. 
 
 
 Mineral Point, Ohio 
 
 
 Port Washington, Ohio 
 
 
 Springfield, Pa. 
 
 24 
 
 Springfield, Pa. 
 
 
 .23 
 
 
 
 
 Pure silicate of alumina melts at 1830° C. 
 
 Fire bricks should stand continuous exposure to high temperatures 
 of the furnace without decomposition or softening; should stand up 
 under considerable pressure without distortion or fracture; should be 
 unaffected by sudden and considerable variations of temperature; should 
 not be affected by contact with heated fuel. 
 
Fire Sand 
 
 435 
 
 Fire brick should be regular in shape and uniform in character. The 
 size of the ordinary straight fire brick is 9 by 4y2 by 2y2 inches, and the 
 weight is 7 pounds. 
 
 Cupola brick are usually 4 inches thick and 6 inches wide radially. 
 
 Slabs and blocks are made in sizes up to 12 by 48 by 6 inches. 
 
 Silica Brick 
 Silica brick are used for resisting very high temperatures. They are 
 composed mostly of silica in combination with alkaline matter. 
 They are somewhat fragile and need careful handling. 
 
 Analysis of Silica Brick 
 
 Silica 
 
 Alumina 
 
 Ferric 
 oxide 
 
 Lime 
 
 Magnesia 
 
 Potash 
 
 97.5 
 90.0 
 
 1-4 
 3.0 
 
 .55 
 .80 
 
 .15 
 .20 
 
 .10 
 .10 
 
 
 .6 
 
 Canister 
 Canister is made from an argillaceous sandstone, is a close-grained 
 dark-colored rock containing no mica. There is present sufiicient clay 
 to cause the particles to become adherent under ramming, after the rock 
 has been ground. The rock is ground to a coarse powder and some- 
 times if the binding properties are insufficient a little milk of lime is 
 added during the grinding process. The composition of ganister will 
 fall in the limits as given below. 
 
 Constituents 
 
 Per cent 
 
 From 
 
 To 
 
 Silica 
 
 87.00 
 4.00 
 
 95.00 
 
 5.00 
 
 1.50 
 
 .75 
 
 1. 00 
 
 Alumina 
 
 Ferric oxide 
 
 Lime and Magnesia 
 
 .25 
 
 Alkalies 
 
 
 
 Fire Sand 
 
 An exceedingly refractory sand containing sometimes as much as 
 97 per cent silica. It is used in the setting of silica brick and in making 
 the hearths of furnaces. 
 
 Pure silica melts at 1830° C. 
 
436 Foundry Fuels 
 
 Magnesite 
 
 Magnesite contains a small percentage of lime and ferrous silicates 
 with serpentine. The ferrous silicates are separated out; thereupon 
 calcining, magnesia is obtained. The calcined material is then mixed 
 with from 15 to 30 per cent of the raw material, and from 10 to 15 per 
 cent water, then moulded into briclis, dried and burned in the ordinary 
 manner. 
 
 Bauxite 
 
 This is a hydrated aluminous ferric oxide, containing usually about 
 60 per cent of alumina, i to 3 per cent of silica, 20 per cent ferrous oxide 
 and from 15 to 20 per cent water. It is very refractory and, notwith- 
 standing the large amount of ferrous oxide contained, is practically 
 infusible. 
 
 Calcined bauxite is mixed with from 6 to 8 per cent of clay, or other 
 binding material and plumbago, then molded into bricks. 
 
 When heated the plumbago reduces the iron of the bauxite, producing 
 a most refractory substance. 
 
 Such bricks are far more durable than the best fire bricks. They resist 
 the action of the basic slags, as well as that of intense heat. 
 
 They become extremely hard after exposure to continued heat. 
 
CHAPTER XIX 
 THE CUPOLA 
 
 The cupola is used in ordinary foundry practice in preference to the 
 air furnace, not only on account of its simplicity, but because it melts 
 more rapidly and economically. There are many forms manufactured. 
 All of them are good, but it is doubtful if any furnishes better results 
 than have been obtained from the ordinary old-fashioned cupola so 
 commonly in use, such as is shown in the sketch below. 
 
 For the advantages of the various styles offered for sale, the reader is 
 referred to the manufacturers' catalogues. 
 
 The cupola is essentially a vertical hollow cylinder, lined with refrac- 
 tory material, having the top open and the bottom closed, with pro- 
 vision for admission of the charges of fuel and iron part way up on the 
 side, also for admission of air below the charges and for drawing off 
 the melted metal at the bottom. 
 
 The cupola is divided into five zoiies. 
 
 First: The Crucible, extending from sand bottom to the tuyeres. 
 
 Second: The Tuyere Zone, extending kom the crucible to melting 
 zone. 
 
 Third: The Melting Zone, reaching from the tuyere zone to a point 
 about 20 inches above the tuyeres. 
 
 Fourth: The Charging Zone, extending from melting zone to charging 
 door. 
 
 Fifth: Stack, from charging door to top of furnace. 
 
 The Lining 
 
 The lining is usually made of two thicknesses of arch brick placed 
 on end with the flat sides in radial planes. Several standard rectangular 
 brick are placed in each ring or course to facihtate the removal of the 
 rings when necessary. Angle iron rings are riveted to the shell at 
 intervals of about six feet, to support the upper sections, when a lower 
 one is removed for repairs. 
 
 The outer lining is kept about Yi inch away from the shell to pro- 
 vide for expansion, and the interval is filled in loosely with sand and 
 broken brick. 
 
 437 
 
438 
 
 The Cupola 
 
 The distance from the sand bottom to the charging door should be 
 about 31/i to 4 times the inside diameter of the lining. For cupolas 
 
 Fig. 123. 
 
 under 48 inches, one door is, sufficient; for larger sizes two are more 
 convenient. The doors may be hung on hinges or slide on a circular 
 track above the openings. It is not necessary that they should be lined. 
 
Tuyeres 
 
 439 
 
 At the level of the charging door the lining should be covered with a 
 cast-iron ring to protect it during the charging. 
 
 The bricks are laid with very close joints in mortar composed of 
 fire clay and sand. The interior lining is daubed with a mixture of one- 
 half fire clay and three-fourths sharp sand for a thickness of three- 
 fourths inch. Any joints are well filled. A handful of salt to a pail of 
 daubing will cause the interior of the shell to be glazed over and will 
 reduce the amount of chipping required. Washing the daubing with 
 strong brine and fire clay serves the same purpose. 
 
 Tuyeres 
 
 The tuyeres may be circular or rectangular in section with the bottoms 
 inclining slightly toward the interior of the shell so that the drippings 
 may not run into the wind box. Castings for tuyeres should not be 
 over ^i inch thick. 
 
 The area of the tuyeres is made from lo to 25 per cent that of the 
 inside fining at the tuyeres; 20 per cent gives good results. As a matter 
 of fact the tuyeres cannot be made too large. A continuous tuyere 
 having an opening about 2 inches in height and extending all around the 
 lining is frequently used. 
 
 An excellent plan is to have an air chamber 
 all around the outer lining and inside of the 
 shell in the vicinity of the tuyeres; at the 
 level of the bottom of the tuyeres place a 
 cast-iron ring, in sections, on top of the 
 double lining. On this, at intervals of from 
 7 to 10 inches, so as to divide the circum- 
 ference of the interior of the lining into equal 
 parts, place hollow iron blocks 2 inches wide, 
 3 inches high and 7 inches long. On top of the 
 blocks place another segmental ring, which ^^' ^^^" 
 
 shoiild be kept 3 or more inches away from the interior of the shell. 
 Upon this ring the upper courses of the lining are built. This forms 
 a nearly continuous tuyere, broken only by the iron blocks. 
 
 This construction involves a contraction of the fining at the tuyeres 
 of about 8 inches. The bottom of the tuyeres should be from 10 to 
 20 inches above the sand bottom, depending upon the quantity of 
 melted iron to be collected before tapping. Where the iron is allowed 
 to run continuously from the spout, as in stove and other foundries 
 doing fight work, the tuyeres may be even lower than 10 inches. 
 
 Frequently an additional row of tuyeres, having about one-eighth of the 
 main row in area, is placed just below the melting zone. These upper 
 
440 The Cupola 
 
 tuyeres should be arranged so that the admission of air through them 
 may be regulated. The object is to supply the necessary air to convert 
 whatever carbonic oxide is formed in. the tuyere zone into carbonic acid 
 at the melting zone. The heat developed at these upper tuyeres is such 
 that the Uning near them is often badly cut, therefore, care must be 
 exercised as to the admission of air at this point. 
 
 A row of adjustable tuyeres about lo inches above the melting zone 
 is most effective in producing the combustion vvithin the charges of 
 carbonic oxide, forced above that zone, effecting thereby not only a 
 saving of fuel, but the suppression of flame at the charging doors. The 
 admission of air above the melting zone must be carefully regulated so 
 that only enough will enter to burn the carbonic oxide. 
 
 The "Castings" for September, 1908, illustrates a cupola designed 
 by Mr. J. C. Knoeppel, which presents an admirable arrangement of 
 tuyeres and provides for the object above outlined. 
 
 Two or more of the lower tuyeres, should have slight depressions 
 in the bottoms, to permit the slag or iron, should either reach that 
 level, to run out upon sheet lead plates placed in the wind box in 
 the line of these depressions. By the melting of these plates, and 
 the discharge through the resulting holes, warning is given to the 
 cupola tender, and the accumulation of slag or iron in the wind box 
 avoided. 
 
 Unless the blast is much higher than good management permits, it 
 will not penetrate the fuel in the cupola for more than 30 inches radially, 
 Therefore, where the inside diameter of the cupola is over 6c inches, 
 it should be contracted at the tuyeres to 60 inches or less diameter; 
 or in place of this a center blast may be used. Large cupolas are fre- 
 quently made oval in section with the same object in view. 
 
 In the wind box directly opposite each tuyere there should be a small 
 door 5 inches in diameter, fastened with a thumb screw, for access to 
 the tuyeres, to remove any stoppages in front of them; each door should 
 be provided with a peek hole i>i inches in diameter covered with mica. 
 
 The Breast 
 
 The breast is made by taking a mixture of one-half fire clay and one- 
 half molding sand, thoroughly mixed and just moist enough to be 
 kneaded. A quantity of this is placed around a bar 13.4 inches in diam- 
 eter and made into cylindrical shape, 4 or 5 inches in diameter and about 
 6 inches long. This is placed in the opening for the breast, and the bar, 
 while held in a nearly horizontal position, forced down until its bottom 
 is on a line with the sand bottom, and % inch above the upper side of 
 
Sand Bottom 441 
 
 lining to trough. The inner end of the clay cylinder should be flush 
 with the inside of the cupola hning. 
 
 Ram hard around this cylinder with molding sand and fill opening 
 for breast completely. Care must be taken that this clay cyhnder is 
 well secured in place. Remove the forming bar and enlarge the hole 
 toward inside of cupola, leaving only about 3 inches in length of the 
 original diameter from the front. 
 
 The slag hole is made up in same way, but should be only one and a 
 half inches long. A core about 2H inches in diameter may be inserted 
 for the slag hole, and this dug out, when tapping for slag, until opening 
 is sufficiently large, say about i inch diameter. 
 
 It sometimes happens that the breast gives way during the heat. 
 In such an event, the blast is shut off and the cupola drained of iron and 
 slag. The defective part of the breast is removed, and replaced with 
 stopping clay, which is hammered with the side of a bar, well against 
 the surrounding portion of the breast. The remaining hole is then filled 
 with clay, carefully packed so as not to be driven to the interior of the 
 cupola. Through this clay a tap hole is made by gently inserting the 
 tapping bar and enlarging the hole after the ball of clay has been pene- 
 trated. In from fifteen to twenty minutes the clay will have been 
 baked hard. The blast can then be turned on and melting resumed. 
 This operation must be conducted with great care, as the operator is 
 in danger of being severely burned. 
 
 Swab the lining from the bottom to 2 feet above the tuyeres with 
 clay wash and salt, and black wash the tapping hole formed as above 
 described. 
 
 Sand Bottom 
 
 The sand bottom is made from gangway sand passed through a No. 4 
 riddle. This bottom should be about 8 inches thick. It must be well 
 rammed, especially next to the lining, where it should join with a liberal 
 fillet. It must not be too wet. Care must be taken not to ram the 
 bottom so hard that the iron will not lie on it quietly. The bottom 
 should slope in all directions towards the tapping hole, the slope being 
 one inch in four feet, and it should reach the tapping hole exactly on a 
 level with its lower surface. 
 
 Black wash the bottom, build a light wood fire and dry out the lining 
 thoroughly. The bottom doors should have a dozen or more %-inch 
 holes drilled through them to allow any moisture in the bottom to 
 escape. The doors are held in place by an iron post under the center, 
 which can readily be knocked out to drop the bottom. The breast 
 should be made up before the bottom. 
 
442 The Cupola 
 
 Zones of Cupola 
 
 The crucible zone extends from the sand bottom to the tuyeres. 
 The object of this zone is to hold the melted iron and slag. If the tap 
 hole is kept open continuously, this zone may not be over 4 to 6 inches 
 in depth from sand bottom to bottom of tuyeres. If it is to hold a 
 large quantity of melted iron, the tuyeres must be correspondingly 
 high. Metal can be melted at a higher temperature with low tuyeres, 
 (collecting it in a ladle), than by holding it in 'the cupola. 
 
 Tuyere Zone 
 
 This is where the blast enters in contact with the fuel. Here com- 
 bustion begins. This zone is confined to the area of the tuyeres. The 
 combined area of the tuyeres should be about one-fifth that of a section of 
 the cupola at this point, and should also largely exceed that of the outlet 
 of the blower. It is important to keep the tuyeres as low as the condi- 
 tions of the foundry, as to amount of melted iron to be collected at one 
 tap, will permit. With low tuyeres the iron is hotter, there is less oxida- 
 tion and the fuel required on the bed is less. 
 
 Melting Zone 
 
 The melting zone is the space immediately above the tuyeres. It 
 extends upward from 20 to 30 inches, depending upon the pressure and 
 volume of the blast, increasing in height with increased pressure. No 
 iron is melted above or below it. The melting occurs through the upper 
 4 to 6 inches of that zone. 
 
 Charging Zone 
 
 This zone is that part containing the charges of iron and coke, and 
 extends from the melting zone to charging door. 
 
 The stack is the continuation of the cupola from charging door through 
 the roof. Contracting the stack above the charging door has no influ- 
 ence upon the efficiency of the cupola. 
 
 The spouts should be lined with fire brick. Above the fire brick 
 bottom at center of trough, there should be iVi inches of moulding 
 sand. From the center the sand should slope rapidly each way to 
 sides. The sand lining of trough at' center should be % inch below 
 the tap hole. After lining, trough should be black washed and dried. 
 Stopping material is made of one-half fire clay and one-half moulding 
 sand. 
 
 It is the common practice to leave the top hole open until iron begins 
 
Chemical Reactions in Cup)ola 443 
 
 to run freely, in order to prevent freezing at the hole. This causes 
 the oxidizing of considerable metal, and is unnecessary. The following 
 method may be pursued. Just before the blast goes on, close up the 
 inner end of the tap hole with a ball of greasy waste, then ram the 
 remainder of the hole full of moulding sand. This is easily removed 
 with the tapping bar, and does away with all the annoyance of escaping 
 blast and sparks. 
 
 Chemical Reactions in the Ordinary Cupola with 
 Single Row of Tuyeres 
 
 When the air blast comes in contact with the burning coke, its oxygen 
 unites with the carbon of the coke to form carbonic acid (CO2), as the 
 result of complete combustion. As the temperature above the tuyeres 
 increases to that necessary for melting iron, part of the CO2 seizes upon 
 the incandescent coke, takes up another equivalent of carbon and is 
 converted into carbonic oxide (CO). If the supply of air is in excess 
 of that required, the CO, being combustible gas, takes up another 
 equivalent of oxygen and is burned to CO2. 
 
 Again some of the CO2, parting with an equivalent of oxygen to the 
 iron for such oxidation as occurs, or by the acquisition of another equiva- 
 lent of carbon from the coke; or by both, is reconverted into CO. These 
 reactions take place at or near the melting zone. 
 
 After passing that zone, no more air is supplied, and the products of 
 combustion, consisting of CO and CO2 pass up the stack without further 
 change until reaching the charging door. Here air is admitted, the 
 CO is supplied with oxygen and is burned to CO2. 
 
 If the air supplied at the tuyeres is insufi&cient for complete combus- 
 tion, the evolution of CO is increased and the efficiency of the furnace 
 reduced. On the other hand, an excessive supply of air is objectionable, 
 as a reducing flame (that from CO) is desirable to prevent oxidation 
 of the metal. 
 
 For the complete combustion of one pound of carbon, there is required 
 12 pounds, or about 150 cubic feet of air, developing 14,500 B.t.u.; but 
 the combustion of one pound of carbon to CO requires only one-half the 
 air, and the resulting heat is 4500 B.t.u.; hence for whatever portion of 
 the fuel is burned to CO, there is a loss of over two-thirds its heat- 
 producing value. 
 
 For the purpose of saving this waste heat, an upper row of tuyeres, 
 just below the melting zone, is employed; and to utilize the heat which 
 escapes above the melting zone, tuyeres have been introduced with 
 good results, at from 5 to 10 inches above that zone. By the use of 
 
444 
 
 The Cupola 
 
 the latter tuyeres the heat developed is absorbed by the charges in the 
 stack, and the flames at charging door are suppressed. Where such 
 tuyeres are used, they must be provided with means for easily regulating 
 the admission of air. 
 
 The following table taken from West's Moulders' Text Book gives 
 the quantity of air required for the combustion of one pound each of 
 coke and coal. 
 
 Combustibles, 
 I pound weight 
 
 Weight of oxy- 
 gen consumed 
 per pound of 
 combustible, 
 pounds 
 
 Quantity of air con- 
 sumed per pound 
 of combustible 
 
 Total heat of ' 
 combustion 
 of I pound of 
 
 Pounds 
 
 Cubic feet 
 at 62° F. 
 
 combustible, 
 units of heat 
 
 Coke, desiccated 
 
 Coal, average 
 
 2.51 
 2.46 
 
 10.9 
 10.7 
 
 143 
 141 
 
 13,550 
 14,133 
 
 
 
 By reason of the contact of the molten iron with the fuel, changes in- 
 atmospheric conditions, the amount of air used, and other conditions, 
 the same mixtiu-e may produce different kinds of castings at different 
 times; and there may also be variations in the same heat. 
 
 Chemical Reactions in the Cupola 
 
 The complete combustion of one pound of carbon to CO2 requires: 
 2.66 pounds of oxygen 
 or 12.05 pounds of air 
 
 and develops 14,500 B.t.u. 
 
 The burning of one pound of carbon to CO requires: 
 1.33 pounds of oxygen 
 or 6.00 pounds of air 
 
 and develops 4500 B.t.u, 
 
 Therefore one pound of coke, having 86 per cent fixed carbon requires 
 for complete combustion 
 
 2.66 X 0.86 = 2.29 pounds oxygen 
 or 12.00 X 0.86 = 10.32 pounds air 
 
 and develops 14,500 X 0.86 = 12,470 B.t.u. 
 
 The 10.32 pounds of air less 2.29 pounds oxygen leave 8.03 nitro- 
 gen. 
 
Wind Box 445 
 
 Taking the specific heat of oxygen at 0.218, carbon at 0.217, nitrogen 
 at 0.244. The temperature resulting from the complete combustion of 
 one pound of coke to CO2 is 
 
 12,470 ^ o p 
 
 0.217 X 0.86 + 0.218 X 2.28 + 0.244 X 8.03 ^' 
 That resulting from the combustion of one pound of coke to CO is 
 
 3870 . ^ O p 
 
 0.217 X 0.86 + 0.218 X 1.15 + 0.244 X 4.015 
 
 Hence for every pound of coke burned to CO, instead of CO2, there is 
 a loss of 8600 B.t.u., and a reduction of the resulting temperature of 
 1983° F. Taking the specific heat of cast iron at the average of temper- 
 atures between 2120° and 2650° F. as 0.169, and the latent heat of fusion 
 as 88 B.t.u., and assuming the temperature of the escaping gases at 
 1330°, then the heat wasted is (i330°-7o°) X (0.217 X o-86 + 0.218 
 X 2.28 + 0.244 X 8.03) equals 3330 B.t.u.; . and the heat available for 
 melting iron is 12,470 — 3330 = 9140 B.t.u. for each pound of coke 
 having 86 per cent fixed carbon. 
 
 For I pound of iron melted at 2650° F. (or 2580° F. above atmosphere) 
 the number of heat units required is 2580 X 0.17 = 439 to which must 
 be added the latent heat of fusion giving 439 + 88 = 527 B.t.u. 
 
 Therefore, - — = 17.^4 pounds of iron, which should be melted by 
 ' 527 ' ""^ ^ • 
 
 one pound of coke, if all the carbon was converted into CO2 and the gases 
 escaped at 1330° F.; also neglecting the heat lost in the slag and by 
 radiation. 
 
 Wind Box 
 
 The area of cross section of the wind box should be three or four times 
 that of the combined area of the tuyeres, in order that there may be 
 sufficient air reservoir to permit a steady pressiu"e. There should be 
 two or more doors in the box for ready access in cleaning out when 
 necessary; and also for admission of air when the wood fire is started. 
 As before stated, there should be small doors opposite each tuyere. 
 
 The blast pipe ought, if the situation will permit, to enter the box on 
 a tangent, and box should be continuous. If it is necessary to divide 
 it into two boxes, on account of the tapping or slag holes, there must, 
 then, of course, be a blast pipe for each box and they should enter the 
 boxes vertically. 
 
 The bottom of the box should be provided with at least two small 
 openings opposite the alarm tuyeres, which are covered with sheet lead. 
 These should be so placed that slag or iron running through them will 
 be at once seen by the tapper. 
 
446 
 
 The Cupola 
 
 The manufacturing of cupolas for the trade has become an important 
 industry, and although the designs of the various makers differ largely 
 in details, the essential features in all are the same. 
 
 Perhaps the names best known to the foundry industry are: CoUiau, 
 Calumet, Newten, Whiting. 
 
 All of these give good results. For special information reference 
 should be made to the manufacturers' catalogues. 
 
 The melting capacities based on 30,000 cubic feet of air per ton of 
 iron are given in the following table. 
 
 Builders' Rating 
 
 Diameter 
 
 inside of 
 
 lining, 
 
 inches 
 
 
 Colliau 
 
 Calumet 
 
 Newten 
 
 24 
 30 
 36 
 42 
 48 
 54 
 60 
 66 
 72 
 78 
 84 
 
 Melting capacity, ^ 
 tons per hour 
 
 I- 1K2 
 3- 4 
 4-6 
 6- 8 
 8-10 
 
 lO-II 
 
 12-14 
 
 15-16 
 
 17-20 
 
 . 25-27 
 
 1- 2 
 
 2- 3 
 4- 5 
 6-7 
 8-9 
 
 lo-ii 
 
 12-14 . 
 
 15-17 
 
 18-20 
 
 21-24 
 
 24-27 
 
 IH- 2l/^ 
 
 3-5 
 4.-6 
 
 8 -9 
 
 9 -II 
 
 11 -12 
 
 12 -14 
 14 -18 
 18 -20 
 20 -24 
 
 
 
 A wind gauge should be attached to the wind box at a convenient place. The 
 charging platform should not be more than 24 inches below the bottom of charging 
 door for sizes up to the 48 inch; for the larger sizes not over 6 to 8 inches. 
 
 The Blast 
 
 The air for the blast is supplied by centrifugal blowers of the Sturte- 
 vant tj^e, or by Positive Pressure Blowers of the Root type. Both are 
 efficient, and it does not appear that either has any special advantage 
 not possessed by the other. 
 
 For successful melting a large volume of air at low pressure is required. 
 From 8 to 10 ounces pressure will usually be found sufficient; in no case 
 should it be allowed to exceed 14 ounces. 
 
 As a rule 30,000 cubic feet of air per ton of iron are allowed. This is 
 somewhat too small, especially if the air contains much moisture; 
 35,000 cubic feet per ton is better practice. 
 
 With blast at low pressure and with high temperature in the furnace, 
 iron may gain in carbon during the process of melting. The reverse 
 may occur, however, under contrary conditions. Oxidation increases 
 with the intensity of the blast. 
 
The Blast 
 
 447 
 
 The castings produced by low blast pressure are softer and stronger, 
 the loss by oxidation is less, there is less slag, less expenditure of power 
 and less injury to the lining of the cupola. 
 
 Coke requires less pressure and more volume of air, as well as greater 
 tuyere area than coal. 
 
 Low pressure, large volume, large tuyere area and good fluxing tend to 
 prevent choking at the tuyeres. However, too much air must be avoided 
 as it reduces the temperature of the furnace and may produce dull iron. 
 
 The main blast pipe should be as short, and the tuyeres as few as 
 possible. Its diameter should be greater than the outlet of the blower. 
 For each turn allow three feet in length of pipe. The minimum radius 
 of the turn should not be less than the diameter of the pipe. It should 
 be provided with a wind gate, and, where a pressure blower is used, an 
 escape valve, both under control of the melter. The wind gate should 
 be kept closed until after the blower is started to prevent gas from 
 collecting in the blast pipe. For the same reason, the blower should, if 
 possible, be located lower than the wind box. 
 
 At the commencement, the blast should be low, and gradually in- 
 creased to the maximum as the heat progresses, then dropped toward 
 its close. 
 
 The friction of air in pipes varies inversely as their diameters, directly 
 as the squares of the velocities, and as the lengths. The table below 
 shows the loss in pressure and the loss in horse power by friction of air 
 in pipes loo feet long; corresponding losses for other lengths can readily 
 be calculated therefrom. 
 
 Loss IN Pressure in Ounces and Horse Power in Friction 
 OF Air in Pipes ioo Feet Long 
 
 Diam- 
 eter of 
 
 Tons of 
 
 Cubic 
 
 Velocity 
 
 Diam- 
 
 Diam- 
 
 T,o,ss of 
 
 Horse 
 
 cupola 
 
 iron 
 
 feet of 
 
 of air 
 in feet 
 
 eter of 
 blast 
 
 eter of 
 
 pressure 
 
 power 
 
 inside of 
 
 melted 
 
 air per 
 
 outlet of 
 
 in ounces 
 
 lost in 
 
 lining, 
 inches 
 
 per hour 
 
 minute 
 
 per 
 minute 
 
 pipe, 
 inches 
 
 blower 
 
 per square 
 inch 
 
 friction 
 
 24 
 
 1.5 
 
 875 
 
 1600 
 
 10 
 
 8 
 
 .313 
 
 .099 
 
 30 
 
 3.0 
 
 i,7So 
 
 2200 
 
 12 
 
 9 
 
 .448 
 
 
 211 
 
 36 
 
 4.5 
 
 2,600 
 
 2400 
 
 14 
 
 II 
 
 .457 
 
 
 320 
 
 42 
 
 6.0 
 
 3.500 
 
 2500 
 
 16 
 
 12 
 
 .434 
 
 
 40s 
 
 48 
 
 8.0 
 
 4,700 
 
 2600 
 
 18 
 
 14 
 
 .417 
 
 
 523 
 
 54 
 
 10. 
 
 5,800 
 
 2700 
 
 20 
 
 15 
 
 .406 
 
 
 653 
 
 60 
 
 12.5 
 
 7,300 
 
 2300 
 
 22 
 
 18 
 
 .246 
 
 
 485 
 
 66 
 
 15.0 
 
 8,750 
 
 2400 
 
 24 
 
 20 
 
 .246 
 
 
 594 
 
 72 
 
 18.0 
 
 10,500 
 
 2500 
 
 26 
 
 22 
 
 .231 
 
 
 582 
 
 78 
 
 22.0 
 
 12,800 
 
 2500 
 
 28 
 
 23 
 
 .202 
 
 
 507 
 
 84 
 
 25.0 
 
 14,560 
 
 2600 
 
 30 
 
 24 
 
 .190 
 
 
 498 
 
 Computed from catalogue of B. P. Sturtevant & Co., and from Foundry Data 
 Sheet No. 5. 
 
448 
 
 The Cupola 
 
 The following tables give the capacities of centrifugal and pressure 
 blowers. As these are based on 36,000 cubic feet of air per ton of iron, 
 the selection of sizes somewhat larger than those given in the tables is 
 desirable, as the allowance of air is too small. 
 
 The Sturtevant Steel Pressure Blower Applied to Cupolas 
 
 No. of 
 blower 
 
 Diam- 
 eter of 
 inside of 
 cupola 
 lining 
 
 Melting 
 capacity 
 per hour 
 
 in 
 pounds 
 
 No. of 
 
 square 
 
 inches of 
 
 blast 
 
 Cubic 
 feet of 
 air per 
 minute 
 
 Speed 
 
 Pressure 
 in ounces 
 of blast 
 
 Horse 
 
 power 
 
 required 
 
 I 
 
 22 
 
 1,200 
 
 4.0 
 
 324 
 
 413s 
 
 5 
 
 0.5 
 
 2 
 
 26 
 
 1,900 
 
 5.7 
 
 507 
 
 3756 
 
 6 
 
 i.o 
 
 3 
 
 30 
 
 2,880 
 
 8.0 
 
 768 
 
 3250 
 
 7 
 
 1.8 
 
 4 
 
 35 
 
 4,130 
 
 10.7 
 
 1 102 
 
 3100 
 
 8 
 
 3.0 
 
 5 
 
 40 
 
 6,178 
 
 14.2 
 
 1646 
 
 2900 
 
 19 
 
 5.5 
 
 6 
 
 46 
 
 8,900 
 
 18.7 
 
 2375 
 
 2820 
 
 12 
 
 9-7 
 
 7 
 
 S3 
 
 12,500 
 
 24.3 
 
 3353 
 
 2600 
 
 14 
 
 16.0 
 
 8 
 
 60 
 
 16,560 
 
 32 
 
 4416 
 
 2270 
 
 14 
 
 22.0 
 
 9 
 
 72 
 
 23,800 
 
 43.0 
 
 6364 
 
 2100 
 
 16 
 
 35. 
 
 10 
 
 84 
 
 33,300 
 
 60.0 
 
 8880 
 
 1815 
 
 16 
 
 48.0 
 
 The Sturtevant Steel Pressure Blower Applied To Cupolas 
 
 (Power saved by reducing the speed and pressure of blast.) 
 
 Speed 
 
 Pressure, 
 
 Horse 
 
 Speed 
 
 Pressure, 
 
 Horse 
 
 ounces 
 
 power 
 
 ounces 
 
 power 
 
 3445 
 
 5 
 
 .8 
 
 3100 
 
 4 
 
 .6 
 
 3000 
 
 6 
 
 1.5 
 
 2750 
 
 5 
 
 I.I 
 
 2900 
 
 7 
 
 2.5 
 
 2700 
 
 6 
 
 2.0 
 
 2560 
 
 8 
 
 4.0 
 
 2390 
 
 7 
 
 3.3 
 
 2550 
 
 10 
 
 7-4 
 
 2260 
 
 8 
 
 5.3 
 
 2380 
 
 12 
 
 12.7 
 
 2150 
 
 10 
 
 9.4 
 
 2100 
 
 12 
 
 16.7 
 
 1900 
 
 10 
 
 12.7 
 
 i960 
 
 14 
 
 28.4 
 
 1800 
 
 12 
 
 22.5 
 
 1700 
 
 14 
 
 39-6 
 
 1566 
 
 12 
 
 31.7 
 
 
 
 
 
 
 
 Kent, page S19. 
 
Pressure and Rotary Blowers 
 
 449 
 
 Buffalo Steel Pressure Blowers Speeds and Capacities as 
 Applied to Cupolas 
 
 Square 
 inches 
 in blast 
 
 
 Diam- 
 eter 
 
 
 Speed, 
 
 Melting 
 
 Cubic 
 feet of 
 
 No. of 
 blower 
 
 inside of 
 cupola, 
 inches 
 
 in 
 ounces 
 
 No. of 
 
 revs. 
 
 per min. 
 
 capacity, 
 pounds 
 per hour 
 
 air 
 reqmred 
 per min. 
 
 4 
 
 20 
 
 8 
 
 4793 
 
 1,545 
 
 412 
 
 5 
 
 25 
 
 8 
 
 391 1 
 
 2,321 
 
 619 
 
 6 
 
 3o 
 
 8 
 
 3456 
 
 3,093 
 
 825 
 
 7 
 
 35 
 
 8 
 
 3092 
 
 4,218 
 
 1 125 
 
 8 
 
 40 
 
 8 
 
 2702 
 
 5.425 
 
 1444 
 
 9 
 
 45 
 
 10 
 
 2617 
 
 7,818 
 
 2085 
 
 ID 
 
 55 
 
 10 
 
 2139 
 
 11,29s 
 
 3012 
 
 II 
 
 73 
 
 12 
 
 1639 
 
 21,978 
 
 5861 
 
 12 
 
 88 
 
 12 
 
 1639 
 
 32,395 
 
 8626 
 
 Horse 
 
 power 
 
 required 
 
 i.o 
 1.2 
 
 2.0s 
 3-1 
 3.9 
 7.1 
 10.2 
 23.9 
 36.2 
 
 
 Speed, 
 
 Melting 
 
 Cubic feet 
 
 
 Pressure in 
 
 no. of revs. 
 
 capacity in 
 
 of air re- 
 
 Horse power 
 
 ounces 
 
 per mm. 
 
 pounds per 
 hour 
 
 quired per 
 minute 
 
 required 
 
 9 
 
 5095 
 
 1,647 
 
 438 
 
 1.3 
 
 10 
 
 4509 
 
 2,600 
 
 694 
 
 2.2 
 
 10 
 
 3974 
 
 3,671 
 
 926 
 
 3.1 
 
 10 
 
 3476 
 
 4,777 
 
 1274 
 
 4.2s 
 
 10 
 
 3034 
 
 6,082 
 
 1622 
 
 5.52 
 
 12 
 
 2916 
 
 8,598 
 
 2293 
 
 936 
 
 12 
 
 2353 
 
 12,378 
 
 3301 
 
 12.0 
 
 14 
 
 1777 
 
 23,838 
 
 6357 
 
 30.3 
 
 14 
 
 1777 
 
 35,190 
 
 6384 
 
 43.7 
 
 Kent, page 950. 
 
 The Root Positive Rotary Blowers 
 
 Size 
 
 number 
 
 Cubic feet 
 per revo- 
 lution 
 
 Revolutions 
 
 per minute for 
 
 cupola melting 
 
 iron 
 
 Size of cupola, 
 
 inches inside 
 
 lining 
 
 Will melt iron 
 per hour, tons 
 
 Horse 
 
 power 
 required 
 
 2 
 3 
 
 4 
 S 
 6 
 
 7 
 
 5 
 8 
 13 
 23 
 
 42 
 65 
 
 275-325 
 200-300 
 185-275 
 170-250 
 150-200 
 137-175 
 
 24-30 
 30-36 
 36-42 
 42-50 
 50-60 
 72 or %5 
 
 2l/^-3 
 
 3-4^^ 
 42/^-7 
 8-12 
 I2l/i-l6% 
 
 17^-22% 
 
 8 
 
 17% 
 
 27 
 
 40 
 
 Kent, page 526 
 
450 
 
 The Cupola 
 
 Diameter of Blast Pipes for Pressure Blowers for Cupolas 
 
 B. F. Sturtevant ^ Co. 
 The following table has been constructed on this basis, namely, allow- 
 ing a loss of pressure of one-half ounce in the process of transmission 
 through any length of pipe of any size as a standard; the increased fric- 
 tion due to lengthening the pipe has been compensated for by an 
 enlargement of the pipe, sufi&cient to keep the ioss still at y? ounce. 
 
 The Blast 
 
 Blower No. i 
 
 Blower No. 6 
 
 Cubic 
 feet of 
 
 Lengths of blast pipe in feet 
 
 Cubic 
 
 feet of 
 
 air 
 
 Lengths of blast pipe in feet 
 
 air 
 
 
 
 
 
 
 
 
 
 
 
 trans- 
 
 50 
 
 100 
 
 ISO 
 
 200 
 
 300 
 
 trans- 
 
 50 
 
 100 
 
 150 
 
 200 
 
 300 
 
 initted 
 
 
 
 
 
 
 mitted 
 
 per 
 minute 
 
 
 
 
 
 
 per 
 minute 
 
 Diameter in inches 
 
 Diameter in inches 
 
 360 
 
 5% 
 
 6H 
 
 6% 
 
 71/4 
 
 7% 
 
 1,872 
 
 10^^ 
 
 I2H 
 
 I31/4 
 
 13% 
 
 IS 
 
 515 
 
 63^ 
 
 7\i 
 
 7% 
 
 -8H 
 
 8/8 
 
 2.679 
 
 12H 
 
 14 
 
 15% 
 
 16 
 
 I7H 
 
 635 
 
 63/4 
 
 7% 
 
 m 
 
 9 
 
 9% 
 
 3,302 
 
 131/4 
 
 15/8 
 
 16/2 
 
 iiYi 
 
 18% 
 
 740 
 
 7H 
 
 m 
 
 9 
 
 91/2 
 
 loH 
 
 3.848 
 
 14!/^ 
 
 16H 
 
 I71/2 
 
 18}.^ 
 
 20% 
 
 Blower No. 2 
 
 Blower No. 7 
 
 504 
 
 614 
 
 1% 
 
 1% 
 
 8I/4 
 
 8/8 
 
 2.592 
 
 12 
 
 133/4 
 
 IS 
 
 15% 
 
 17% 
 
 721 
 
 714 
 
 Wi 
 
 9 
 
 9K2 
 
 iQi/i 
 
 3,708 
 
 13% 
 
 15% 
 
 17H 
 
 I8H 
 
 I9H 
 
 889 
 
 7% 
 
 9 
 
 934 
 
 10^^ 
 
 II 
 
 4,572 
 
 15H 
 
 n% 
 
 18% 
 
 19% 
 
 2I5% 
 
 1036 
 
 8^8 
 
 9>i 
 
 io% 
 
 II 
 
 II3/4 
 
 5,238 
 
 16 
 
 18 H 
 
 20 
 
 211/4 
 
 23 
 
 Blower No. 3 
 
 Blower No. 8 
 
 720 
 
 7^- 
 
 m 
 
 9 
 
 m 
 
 loM 
 
 3,312 
 
 13H 
 
 15% 
 
 16/2 
 
 17!/^ 
 
 18% 
 
 1030 
 
 %% 
 
 q\i 
 
 I03/8 
 
 II 
 
 Il2/ 
 
 4,738 
 
 15H 
 
 17% 
 
 I9i'i 
 
 20% 
 
 21% 
 
 1270 
 
 Q^ 
 
 1034 
 
 iiH 
 
 11% 
 
 123/4 
 
 5,842 
 
 16^^ 
 
 19^/^ 
 
 203/4 
 
 22 
 
 23% 
 
 1480 
 
 9% 
 
 II 
 
 12 
 
 125,^ 
 
 I3H 
 
 6.808 
 
 17^/^ 
 
 20/4 
 
 22% 
 
 2m 
 
 2S% 
 
 Blower No. 4 
 
 Blower No. 9 
 
 1008 
 
 m 
 
 m 
 
 loH 
 
 I07/^ 
 
 XT% 
 
 4,320 
 
 uH 
 
 17 
 
 18% 
 
 19% 
 
 21% 
 
 1442 
 
 9H 
 
 loH 
 
 11% 
 
 12/2 
 
 13% 
 
 6.180 
 
 17 
 
 19}^ 
 
 21/4 
 
 22l/i 
 
 2A% 
 
 1778 
 
 I034 
 
 iiVs 
 
 12% 
 
 13^/^ 
 
 uH 
 
 7.620 
 
 l83/i 
 
 21% 
 
 23% 
 
 24% 
 
 26% 
 
 2072 
 
 II 
 
 125/8 
 
 133/4 
 
 14!/^ 
 
 151/2 
 
 8,880 
 
 19^/2 
 
 22/2 
 
 24i^ 
 
 26 
 
 28% 
 
 Blower No. 5 
 
 Blower No. 10 
 
 1440 
 
 qH 
 
 10% 
 
 iili 
 
 12H 
 
 I33/i 
 
 5,760 
 
 im 
 
 19 
 
 20% 
 
 21% 
 
 23% 
 
 2060 
 
 II 
 
 125^ 
 
 1334 
 
 I4i/i 
 
 iSi/i 
 
 8,240 
 
 1^% 
 
 21% 
 
 233/4 
 
 25% 
 
 27H 
 
 2540 
 
 11% 
 
 iM 
 
 14% 
 
 155/^ 
 
 16% 
 
 10.160 
 
 205/i 
 
 233/4 
 
 25% 
 
 21% 
 
 29H 
 
 2960 
 
 12% 
 
 I4H 
 
 15% 
 
 l65/^ 
 
 18 
 
 11,840 
 
 22H 
 
 2554 
 
 27^ 
 
 29% 
 
 31H 
 
 Kent, page 520. 
 
Dimensions, Etc., of Cupolas 
 
 451 
 
 The quantities of air in the left-hand column of each division indicate 
 the capacity of the given blower when working under pressures of 4, 
 8, 12 and 16 ounces. Thus a No, 6 blower will force 2678 cubic feet of 
 air at 8 ounces pressure through 50 feet of 121-4-inch pipe with a loss of 
 \i ounce pressure. If it is desired to force the air 300 feet without an 
 increased loss by friction, the pipe must be enlarged to 17H inches 
 diameter. 
 
 The table below gives the important dimensions, distribution of 
 charges and melting capacities of cupolas from 24 inches to 84 inches 
 diameter inside of lining. The table is based upon the consumption 
 of 3 5, 000 cubic feet of air per ton of iron and represents the best aver- 
 age practice. 
 
 Higher fuel ratios are frequently realized and the foundrymen must 
 vary the fuel and air supply as the conditions indicate. It is imwise, 
 however, to strive for high fuel ratio at the risk of a dull heat. The 
 loss on castings from one melt may far outweigh the saving on coke, 
 as between the ratios of 10 to^i and 9 to i, for many heats. Coke is 
 one of the cheapest articles about the foundry; while hot, clean iron is 
 an item of the highest importance. 
 
 In general the cupola should furnish 20 pounds of melted iron per 
 minute per square foot of area of the melting zone. 
 
 Dimensions, Etc., of Cupolas 
 
 
 
 Height 
 
 
 
 
 
 
 
 Diameter 
 
 of cupola 
 
 inside of 
 
 lining, 
 
 inches 
 
 Height 
 from bot- 
 tom-plate 
 to charg- 
 ing door, 
 feet 
 
 from 
 
 sand bot- 
 tom to 
 
 underside 
 of tu- 
 yeres, 
 inches 
 
 Area of 
 tuyeres, 
 sq. in. 
 
 Pounds 
 of coke 
 on bed, 
 Jpounds 
 
 First 
 charge 
 of iron, 
 pounds 
 
 Suc- 
 ceeding 
 charges 
 of coke, 
 pounds 
 
 Suc- 
 ceeding 
 charges 
 of iron, 
 pounds 
 
 Pres- 
 sure of 
 
 blast, 
 ounces 
 
 24 
 
 9.0 
 
 8-10 
 
 90 
 
 225 
 
 320 
 
 40 
 
 320 
 
 5- 7 
 
 30 
 
 10. 
 
 8-10 
 
 142 
 
 370 
 
 560 
 
 62 
 
 560 
 
 6-8 
 
 36 
 
 10.6 
 
 8-12 
 
 204 
 
 460 
 
 850 
 
 85 
 
 850 
 
 6- 8 
 
 42 
 
 10.6 
 
 10-12 
 
 277 
 
 530 
 
 1200 
 
 no 
 
 1200 
 
 6- 8 
 
 48 
 
 12.0 
 
 10-12 
 
 362 
 
 820 , 
 
 1500 
 
 140 
 
 1500 
 
 8-10 
 
 54 
 
 13.0 
 
 10-15 
 
 458 
 
 1 100 
 
 1900 
 
 180 
 
 1900 
 
 8-10 
 
 60 
 
 15.0 
 
 10-18 
 
 S65 
 
 1400 
 
 2500 
 
 225 
 
 2500 
 
 10-12 
 
 66 
 
 16.0 
 
 10-18 
 
 684 
 
 1900 
 
 3000 
 
 275 
 
 3000 
 
 10-12 
 
 72 
 
 18.0 
 
 IQ-20 
 
 814 
 
 2400 
 
 4000 
 
 320 
 
 4000 
 
 12-14 
 
 78 
 
 19.0 
 
 10-20 
 
 955 
 
 3000 
 
 5000 
 
 400 
 
 5000 
 
 12-14 
 
 84 
 
 19.0 
 
 ic-22 
 
 1 108 
 
 3600 
 
 6000 
 
 500 
 
 6000 
 
 14-16 
 
452 The Cupola 
 
 Dimensions, Etc., oe Cupolas. — (Continued) 
 
 Volume 
 
 Diameter 
 of blast 
 
 Size of 
 Root 
 
 Num- 
 ber of 
 
 Horse 
 
 Size of 
 
 Sturte- 
 
 vant 
 
 Num- 
 ber of 
 revolu- 
 
 Horse 
 power 
 
 Melting 
 capac- 
 
 of air per 
 
 pipe not 
 
 blower 
 
 revolu- 
 
 power 
 
 blower 
 
 tions 
 
 re- 
 
 ity per 
 
 minute, 
 cu. ft. 
 
 over 100 
 
 feet long, 
 
 inches 
 
 required, 
 no. 
 
 tions per 
 
 minute, 
 
 revs. 
 
 required 
 H.P. 
 
 re- 
 quired, 
 no. 
 
 per 
 
 minute, 
 
 revs. 
 
 quired, 
 H.P. 
 
 hour, 
 pounds 
 
 875 
 
 10 
 
 I 
 
 300 
 
 2 
 
 3 
 
 3500 
 
 2 
 
 3,000 
 
 1. 750 
 
 12 
 
 2 
 
 300 
 
 5 
 
 5 
 
 2900 
 
 5-5 
 
 6,000 
 
 2,600 
 
 14 
 
 4 
 
 175 
 
 8 
 
 6 
 
 2800 
 
 10 
 
 9,000 
 
 3.500 
 
 16 
 
 4 
 
 230 
 
 12 
 
 7 
 
 2600 
 
 15 
 
 12,000 
 
 4.700 
 
 18 
 
 5 
 
 200 
 
 20 
 
 8 
 
 2300 
 
 22 
 
 16,000 
 
 5.800 
 
 20 
 
 5i/i 
 
 190 
 
 25 
 
 8 
 
 2500 
 
 25 
 
 20,000 
 
 7,300 
 
 22 
 
 6 
 
 180 
 
 33 
 
 9 
 
 2200 
 
 35 
 
 25,000 
 
 8,700 
 
 24 
 
 6H 
 
 170 
 
 45 
 
 10 
 
 1800 
 
 45 
 
 30,000 
 
 10,500 
 
 26 
 
 7 
 
 150 
 
 55 
 
 10 
 
 2000 
 
 55 
 
 36,000 
 
 12,800 
 
 28 
 
 7'A 
 
 150 
 
 70 
 
 2-8 
 
 2500 
 
 60 
 
 44,000 
 
 14,500 
 
 30 
 
 7H 
 
 170 
 
 80 
 
 2-9 
 
 2200 
 
 70 
 
 50,000 
 
 Charging and Melting 
 
 In preparing the cupola for melting, a bed of shavings is spread evenly- 
 over the bottom; on this a layer of kindling wood; then enough cord 
 wood cut in short lengths to come well above the tuyeres. The doors 
 in the wind box or, two or more of those covering the tuyeres, should be 
 left open to admit air to the fire. The wood should be covered with coke 
 for a depth of from 12 to 15 inches. Where wood is scarce or expensive, 
 the coke may be lighted directly with a kerosene oil blow torch. To use 
 the torch place two strips of boards 3" X i" on edge from the tap 
 hole to center of cupola. Then place other strips of same size crosswise 
 of the bottom forming a shallow trough about 6 inches wide in the shape 
 of a T. Large pieces of coke are placed over the trough to form a 
 cover, and on top of this coke is spread uniformly for a depth of about 
 15 inches. The torch is then applied at the tap hole. 
 
 After the fire is lighted and the top of the coke bed becomes red, 
 enough coke is added to bring the top of the bed 20 inches above the 
 tuyeres when the wood has burned out. 
 
 The necessary amount of coke for bottom is determined by gauging 
 from the charging door. The proper depth of bed is a matter of great 
 importance. Too much is as bad as too little. With too much coke, 
 the melting will be slow and dull; with too little the iron after commence- 
 ment of heat becomes dull, the cupola is bunged up and the bottom 
 may have to be dropped. 
 
The Charging Floor 453 
 
 There should be sufficient coke to locate the top of the melting zone 
 about 20 inches above the tuyeres, and the subsequent charges of coke 
 should be just enough to maintain this position. 
 
 With proper depth of bed, the molten iron will appear at the spout in 
 from 8 to 10 minutes after the commencement of the blast. The first 
 and subsequent charges of iron should be of the same weight, and these 
 should be small. 
 
 The amount of coke between each charge of the iron and the preceding 
 one should be 10 per cent of the iron. In many foundries the coke 
 between the charges is made less than this, but 10 per cent is good 
 practice. It is not the best policy to run the risk of making a poor heat 
 by cutting down the coke. The charges should be continued as indi- 
 cated until the cupola is filled to the charging door. 
 
 In charging care must be taken to distribute both iron and coke uni- 
 formly. 
 
 The pig iron (broken) should be charged first, beginning at the lining 
 and proceeding toward the center, pigs should be placed sidewise to the 
 lining. Next comes the scrap; if there are large pieces, they should be 
 placed in the center of the cupola with the pig surrounding them. 
 
 The iron must be kept well around the lining and care exercised to 
 avoid cavities. If the scrap is fine, it must not be charged so closely as 
 to impede the blast. After the iron comes the coke, which must be 
 evenly distributed throughout. After the second or third charge, lime- 
 stone, broken into pieces about i}^ cube, is added. From 25 to 40 
 pounds of limestone per ton of iron is used according to the character 
 of pig and scrap as to sand and rust, and to that of coke as to ash. 
 
 The top of the bed should not be permitted to drop more than 6 or 
 8 inches during the heat. This determines the weight of iron for each 
 charge as well as that of the coke, the latter having a depth of 6 or 8 
 inches. The weights of all the materials going into the cupola should be 
 kept separately. The melter should be furnished each day with a charging 
 schedule giving the composition and the weight of each charge. 
 
 The fire should be started about two hours before the blast is put on, 
 to allow the charges in the stack to become well heated. The openings 
 in the wind box are closed immediately after starting the blast. 
 
 The egg-shaped section at the melting zone, which the cupola gradually 
 assumes by use, should be maintained. 
 
 The Charging Floor 
 
 The charging floor should be large enough, if circumstances permit, to 
 accommodate all the materials for the heat. Each charge of pig iron 
 and scrap, after weighing, should be piled by itself and in the order in 
 
454 
 
 The Cupola 
 
 which it is to be used. The proper amount of coke for each charge is 
 placed in cans or baskets. In larger works where the material is brought 
 
 to the platform on charging cars, the 
 cars are arranged so as to reach the 
 cupola in proper order. 
 
 The cuts show two different meth- 
 ods of charging at large foundries. 
 At one the charging is done by hand 
 and at the other by machine. 
 
 While the material is handled more 
 rapidly and at less expense by the 
 latter method, it is doubtful if the 
 saving effected compensates for irregular melting and lack of uniformity 
 in product, which is likely to result from unequal distribution of the 
 charges. 
 
 125 
 
 Charging Floor. 
 
 Fig. 126. — Cupola Charging Machine 
 in Normal Position. 
 
 Fig. 127. — Cupola Charging Machine 
 in Charging Position. 
 
 Melting Losses 
 
 Melting losses in a well-managed cupola should not exceed 4 per cent 
 for the annual average. Instances are known where the losses for long 
 periods were not over 2 per cent. The following records are taken from 
 the report of the secretary of the American Foundrymen's Association, 
 and cover the results from 41 cupolas. The percentage of castings 
 made and the returns are calculated from the quantities given and added 
 to each table. 
 
Light Jobbing 
 Table I. — General Jobbing 
 
 455- 
 
 Numbers 
 
 Usual tonnage 
 
 Time melting 
 
 Blast pressure 
 
 Fan or blower 
 
 Pig iron 
 
 Per cent southern 
 
 Fuel used , lbs 
 
 Scrap bought 
 
 Pig iron used 
 
 Scrap used 
 
 Castings made 
 
 Scrap made 
 
 Per cent melting lost 
 
 Per cent melt in returns . . . . 
 Per cent in good castings . . . 
 
 I hr. 15 m, 
 8 oz. 
 Fan 
 Coke 
 None 
 Coke 
 Mach. 
 10,400 
 9,600 
 i6,49S 
 1,352 
 10.7 
 66 
 82.4 
 
 3 
 
 hr. 
 
 Fan 
 Coke 
 
 Coke 
 Med. mach 
 3200 
 3200 
 5504 
 620 
 4-3 
 97 
 86 
 
 3 
 
 4 
 
 3 
 
 3 
 
 ihr. 15 m. 
 
 2hrs. 
 
 
 80Z. 
 
 Fan 
 
 Blower 
 
 Coke 
 
 Coke 
 
 None 
 
 None 
 
 Coke 
 
 Coke 
 
 Mach. 
 
 Stove 
 
 2657 
 
 268s 
 
 2886 
 
 3885 
 
 3916 
 
 4057 
 
 872 
 
 1873 
 
 13.6 
 
 9-7 
 
 IS. 7 
 
 28. 5 
 
 70.6 
 
 61.7 
 
 80Z. 
 Fan 
 
 Mach. 
 20,000 
 20,000 
 3S.200 
 2,200 
 6.5 
 6.5 
 
 Average melting loss 7-6 per cent 
 
 Average of melt in returns 8.8 per cent 
 
 Average of melt in good castings 83.0 per cent 
 
 Table II. — Light Jobbing 
 
 Numbers 
 
 Usual tonnage 
 
 Time of melting 
 
 Blast pressure, oz 
 
 Fan or blower 
 
 Pig iron 
 
 Per cent southern 
 
 Fuel used 
 
 Scrap bought 
 
 Pig iron used, lbs 
 
 Scrap used, lbs 
 
 Castings made 
 
 Scrap made 
 
 Per cent melting loss 
 
 Per cent melt in returns. . 
 Per cent in good castings . 
 
 72 
 
 3 hrs. 30 m, 
 
 13 
 
 Blower 
 
 Coke 
 
 None 
 
 Coke 
 
 102,000 
 
 42,000 
 108,300 
 27,500 
 5.7 
 19. 1 
 75-2 
 
 I hr. 30 m. 
 6.5 
 Fan 
 Coke 
 None 
 Coke & coal 
 Stove 
 4.500 
 7,500 
 10,300 
 1,200 
 4.2 
 10 
 85.8 
 
 16 
 2 hrs. 30 m. 
 
 Fan 
 
 Coke 
 
 None 
 
 Coke 
 
 Lt. mach. 
 
 19,200 
 
 12,800 
 
 21,000 
 
 9,100 
 
 6 
 
 28.4 
 65.6 
 
 2.5 
 Ihr. 
 
 Fan 
 Coke 
 None 
 Coke 
 Med. mach. 
 3200 
 1800 
 4000 
 800 
 4 
 16 
 80 
 
 Average melting loss 25.5 per cent 
 
 Average of melt in returns 20.8 per cent 
 
 Average of melt in good' castings 73-6 per cent 
 
456 
 
 The Cupola 
 Table III. — Light Machineey 
 
 Numbers . 
 
 Usual tonnage 
 
 Time of melting 
 
 Blast presstire, oz 
 
 Fan or blower 
 
 Pig iron 
 
 Per cent southern 
 
 Fuel used 
 
 Scrap bought 
 
 Pig iron used, lbs 
 
 Scrap iron used, lbs. 
 
 Castings made 
 
 Scrap made 
 
 Per cent melting loss 
 
 Per cent melt in returns 
 
 Per cent melt in good castings . 
 
 lo 
 I hr. lo m. 
 
 6 
 
 2 hrs. 
 
 Fan 
 Coke 
 
 Coke & coal 
 None 
 i6,ooo 
 4,ooo 
 13.220 
 4,500 
 6.5? 
 22.6 
 66.1 
 
 Fan 
 Coke & ch. coal 
 
 Coke 
 Med. mach. 
 6,000 
 6,000 
 10,000 
 900 
 9.2 
 7.5 
 83.3 
 
 35 
 
 I hr. 30 m. 
 7 
 Blower 
 Coke 
 None 
 Coke 
 Lt. mach. 
 3900 
 2750 
 3738 
 2762 
 2.3 
 41-5 
 56.20 
 
 
 13 
 
 14 
 
 IS 
 
 
 
 5 
 
 I hr. 30 m. 
 
 5 
 
 Fan 
 
 Coke 
 
 50 
 
 Coke & coal 
 
 Med. mach. 
 
 4500 
 
 4280 
 
 7640 
 
 800 
 
 3.9 
 
 9-1 
 
 87 
 
 15 
 
 2hr. 
 
 7 
 
 Blower 
 
 Coke 
 
 35 
 
 Coke 
 Lt. mach. 
 14,000 
 16,000 
 20,500 
 6,000 
 II. 6 
 20 
 68.3 
 
 
 
 6 hrs. 40 m. 
 
 
 Fan or blower . 
 
 Fan 
 
 
 Coke 
 
 
 
 Fuel used 
 
 Coke 
 
 
 
 Pig iron used, lbs. 
 
 56,000 
 24,000 
 
 Scrap iron used, lbs. 
 
 
 Scrap made 
 
 16,000 
 
 Per cent melting loss 
 
 5 
 
 Per cent melt in returns 
 
 2,000 
 
 Per cent melt in good castings 
 
 75 
 
 There is an error in this record. The loss should be 11.3 if the statement as to 
 castings and scrap are correct. 
 
 Average melting loss 7.33 per cent 
 
 Average of melt in returns 19. 55 per cent 
 
 Average of melt in good castings 73.0 per cent 
 
Stove Plate 
 Table IV. — Heavy Machinery 
 
 457 
 
 Numbers ... ... 
 
 i6 
 
 17 
 
 18 
 
 19 
 
 
 
 Usual tonnage 
 
 13 
 2 hrs. 
 
 6 
 
 Blower 
 
 Coke 
 
 5o 
 Coke 
 Mach. 
 14,720 
 11,130 
 18,845 
 4,870 
 8.4 
 18.8 
 72.9 
 
 15 
 
 2 hrs. 
 
 10 
 
 Blower 
 
 Coke 
 
 70 
 
 Coke 
 
 H'vy mach. 
 
 20,000 
 
 10,000 
 
 21,300 
 
 7,200 
 
 5 
 
 24 
 
 71 
 
 21 
 4 hrs. 
 
 9 
 Blower 
 Coke & coal 
 17 
 Coke 
 Mach. 
 25,740 
 16,270 
 37,760 
 7,560 
 4 
 18 
 78 
 
 15 
 
 Time of melt 
 
 2 hrs. 
 
 Blast pressure, oz. 
 
 14 
 
 Fan or blower 
 
 Blower 
 
 Pig iron 
 
 Per cent southern 
 
 Coke 
 20 
 
 Fuel used 
 
 Coke 
 
 Scrap bought 
 
 
 Pig iron used, lbs. 
 
 15,500 
 
 Scrap used lbs. 
 
 11,500 
 
 
 
 
 
 
 7-4 
 
 Per cent melt in returns 
 
 Per cent melt in good castings . 
 
 22.2 
 70.4 
 
 Average melting loss 5-8 per cent 
 
 Average of melt in returns 20 . 6 per cent 
 
 Average of melt in good castings 73 . 6 per cent 
 
 Table V. — Stove Plate 
 
 Numbers . 
 
 Usual tonnage 
 
 Time of melt 
 
 Blast pressure, oz 
 
 Fan or blower 
 
 Pig iron 
 
 Per cent southern 
 
 Fuel used 
 
 Scrap bought 
 
 Pig iron used, lbs 
 
 Scrap used, lbs 
 
 Castings made 
 
 Scrap made 
 
 Per cent melting loss 
 
 Per cent melt in returns 
 
 Per cent melt in» good castings . 
 
 2 hrs. 15 min. 
 14 
 Blower 
 Coke 
 100 
 Coke and coal 
 Stove 
 20,000 
 20,000 
 24,000 
 14,200 
 4-5 
 35.5 
 60 
 
 15 
 
 I hr. 30 min. 
 
 II 
 
 Coke 
 
 50 
 Coke 
 Stove 
 18,000 
 12,000 
 20,192 
 9,000 
 2.7 
 
 30 
 
 67.3 
 
 13 
 
 Blower 
 
 Coke 
 
 25 
 
 Coke and coal 
 
 11,863 
 7,906 
 
 11.750 
 7,624 
 
 38.5 
 59-4 
 
 Average melting loss 3.3 per cent 
 
 Average of melt in returns 34- 3 per cent 
 
 Average of melt in good castings 62 . 3 per cent 
 
45^ 
 
 The Cupola 
 Table VI. — Sanitary Ware 
 
 
 23 
 
 24- 
 
 25 
 
 26 
 
 
 
 
 12 
 
 2 hrs. 
 
 5 
 
 Fan 
 
 Coke 
 
 None 
 
 Coal and coke 
 
 Medium 
 
 ii,8oo 
 
 I2,200 
 
 17,228 
 
 6,048 
 
 3 
 
 25.4 
 71.7 
 
 32 
 
 3 hr. IS m. 
 
 14 
 
 Blower 
 
 Coke 
 
 38 
 3 h. IS m. 
 
 14 
 Blower 
 Coke 
 
 60 
 Coke 
 None 
 56,000 
 20,000 
 51,614 
 18,386 
 7.9 
 24.1 
 67.9 
 
 16 
 
 Time of heat 
 
 Blast pressure, oz. 
 
 2 h. 30 m. 
 SO 
 Fan 
 
 
 
 Coke 
 
 
 
 
 Coke 
 
 
 
 
 
 51,000 
 12,000 
 46,660 
 12,234 
 6.5 
 
 19.4 
 
 74 
 
 9.875 
 22,625 
 
 Scrap used, lbs 
 
 Castings made 
 
 23,276 
 
 Scrap made 
 
 8,055 
 
 Per cent melting loss 
 
 Per cent melt in retioms 
 
 Per cent in melt good castings 
 
 3.6 
 
 24.7 
 71.6 
 
 Numbers 
 
 27 
 
 28 
 
 29 
 
 30 
 
 
 
 Usual tonnage 
 
 . 25 
 
 3 h. 45 m. 
 
 14 
 
 Blower 
 
 Coke 
 
 26 
 3 h. 45 m. 
 
 40 
 3 h. 45 m. 
 5 
 Fan 
 Coke 
 None 
 Coal and coke 
 Medium 
 35,560 
 47.210 
 S9.400 
 21,960 
 1.7 
 26.5 
 71.7 
 
 23 
 
 Time of heat 
 
 3I1. 
 
 
 
 Fan or blower , 
 
 Pig iron 
 
 Blower 
 Coke 
 
 Blower 
 Coke 
 
 Per cent southern 
 
 
 
 Coke 
 
 None 
 
 31,470 
 
 17.960 
 
 35.956 
 
 11,270 
 
 4.1 
 
 22.9 
 
 73 
 
 Coke 
 
 Coke 
 
 Scrap bought 
 
 None 
 
 
 33,000 
 19.850 
 37,250 
 11,300 
 8.1 
 
 21.3 
 
 70 
 
 29,000 
 
 
 17.500 
 
 
 33.385 
 
 
 11,500 
 
 Per cent melting loss 
 
 Per cent melt in returns 
 
 Per cent melt in good castings 
 
 3.5 
 24.7 
 71.8 
 
 Average melting loss . 
 
 Average of melt in returns 
 
 Average of melt in good castings. 
 
 4 . 84 per cent 
 23.60 per cent 
 71.50 per cent 
 
Railroad Castings 
 Table VII. — Agricultural 
 
 459 
 
 Numbers 
 
 31 
 
 32 
 
 33 
 
 34 
 
 35 
 
 
 
 Usual tonnage .... 
 
 80 
 
 4 h. 20 m. 
 
 15 
 
 Blower 
 
 Coke 
 
 50 
 
 Coke 
 
 Ag. No. I 
 
 80,000 
 
 80,000 
 
 108,800 
 
 42,700 
 
 5.3 
 
 26.7 
 
 67.5 
 
 45 
 
 3 h. 15 m. 
 
 12 
 
 Blower 
 
 Coke 
 
 ' Coke ' 
 
 Ag. No. I 
 
 45,000 
 
 45, 000 
 
 61,200 
 
 24,300 
 
 5.2 
 
 27 
 
 67.7 
 
 41 
 
 3 h. 30 m. 
 
 13 
 
 Blower 
 
 Coke 
 
 50 
 
 Coke 
 
 Med. Mach. 
 
 45,700 
 
 35,800. 
 
 62,960 
 
 15,600 
 
 3.6 
 
 19.2 
 
 77.2 
 
 9 
 2 hrs. 
 
 12 
 
 Blower 
 
 Coke 
 
 50 
 
 Coke & coal 
 
 Stove 
 
 7,071 
 
 10,674 
 
 11.845 
 
 5,200 
 
 4 
 
 29.3 
 
 67 
 
 9-5 
 I h. 20 m 
 
 Time of heat 
 
 Blast pressure, oz 
 
 Fan or blower . 
 
 9 
 
 Blower 
 
 Pig iron 
 
 Coke 
 
 Per cent southern 
 
 Fuel used 
 
 None 
 Coke & coal 
 
 Scrap bought 
 
 Pig iron used, lbs 
 
 Scrap used, lbs. . 
 
 Stove 
 7,500 
 11,600 
 
 
 
 Per cent melting loss . . . 
 
 Per cent melt in returns 
 
 Per cent melt in good 
 
 castings 
 
 5.3 
 
 55.7 
 
 39 
 
 Average loss in melt 4. 77 per cent 
 
 Average of melt in returns •. 26. 73 per cent 
 
 Average of melt in good castings 68 . 4 per cent 
 
 Table VIIL — Railroad Castings 
 
 Numbers . 
 
 38 
 
 Usual tonnage 
 
 Time of heat 
 
 Blast pressure, oz 
 
 Fan or blower 
 
 Pig iron 
 
 Per cent southern 
 
 Fuel used • 
 
 Scrap bought 
 
 Pig iron used 
 
 Scrap used 
 
 Castings made 
 
 Scrap made 
 
 Per cent melting loss 
 
 Per cent of melt in returns . . . . 
 Per cent melt in good castings . 
 
 47 
 5 hrs. 20 m. 
 
 16 
 Blower 
 Coke 
 None 
 Coke 
 None 
 66,500 
 28,500 
 60,400 
 28,900 
 6.1 
 
 30.3 
 
 63.5 
 
 32 
 
 6.5 
 
 3 hrs. 45 m. 
 
 2 hrs. 
 
 4 
 
 9 
 
 Fan 
 
 
 Ch., coal and coke 
 
 Coke 
 
 60 
 
 None 
 
 Coke and coal 
 
 Coke 
 
 None 
 
 
 25,000 
 
 6,76s 
 
 39.000 
 
 6,235 
 
 54,000 
 
 10,000 
 
 7,500 
 
 2,38s 
 
 3.9 
 
 4-7 
 
 II. 7 
 
 18.3 
 
 84.3 
 
 76.9 
 
 Note. — No. 37 is an average of 27 heats. No. 38 is an average of 25 heats. 
 
 Average melting loss 5 . 64 per cent 
 
 Average of melt in returns 22 . 43 per cent 
 
 Average of melt in good castings 72.22 per cent 
 
460 
 
 The Cupola 
 Table IX. — Floor Plates, Grate Bars, etc. 
 
 
 39 
 
 40 
 
 
 Usual tonnage 
 
 30 
 
 3 hrs. 40 m. 
 16 
 Blower 
 Coke 
 None 
 Coke 
 Med. mach. 
 20,000 
 40,000 
 47,400 
 8,200 
 7.3 
 13-7 
 79 
 
 3 
 
 Time of heat 
 
 I hr. 
 
 Blast pressure, oz 
 
 
 Fan or blower 
 
 Fan 
 
 Pig iron 
 
 Coke 
 
 Per cent southern 
 
 
 Fuel used 
 
 Coke and coal 
 
 Scrap bought 
 
 Light mach. 
 
 Pig iron used, lbs 
 
 None 
 
 Scrap used, lbs 
 
 6,000 
 
 Castings made ... . 
 
 5,100 
 
 
 525 
 
 
 6.2 
 
 
 8.8 
 
 
 85 
 
 
 
 Average melting loss 
 
 Average of melt in returns 
 
 Average of melt in good castings . 
 
 7 . 23 per cent 
 
 8 . 88 per cent 
 85 per cent 
 
 Table X. — 
 
 Car Wheels 
 
 
 Number 
 
 41 
 
 Number 
 
 41 
 
 
 
 
 Usual tonnage 
 
 200 
 
 7 hrs. 
 
 10 
 Blower 
 
 Scrap bought 
 
 Wheel 
 
 Time of heat 
 
 Per cent melting loss 
 
 2.1 
 
 
 Per cent melt in returns 
 
 Per cent melt in good castings. 
 
 
 Fan or blower 
 
 
 From the above tables, the following table showing the average results 
 for each class of work is compiled. 
 
 Table XI 
 
 Percentage 
 
 1^ 
 
 St 
 
 
 3't 
 
 
 0. 
 
 I 
 
 o5 
 
 si 
 
 CO 
 
 
 
 < 
 
 13 
 
 It 
 
 
 Number of records. 
 Per cent melt in 
 
 4 
 
 83.9 
 8.2 
 
 7-7 
 
 4 
 
 73.6 
 20.8 
 
 55 
 
 6 
 
 73.01 
 
 19 SS 
 7.33 
 
 4 
 
 73.6 
 
 20.6 
 5.8 
 
 3 
 
 62.3 
 
 34.3 
 3.3 
 
 8 
 71. 5 
 
 23.6 
 4.84 
 
 5 
 68.5 
 
 26.7 
 
 4.77 
 
 3 
 
 72.3 
 
 22.43 
 5.24 
 
 2 
 
 79-5 
 
 13.2 
 7.2 
 
 rt 
 !§ 
 
 Per cent melt in 
 
 
 
 Per cent melt lost . 
 
 
 Note. No. 12 was omitted in obtaining these averages. Evidently there was 
 something wrong about this heat as shown by the excessive returns. 
 
Melting Ratio 461 
 
 The figures in the preceding table are to be taken as approximations. 
 The loss may be reduced in practice by careful management. 
 
 When the weight of the coke on the bed, and the weights of the iron 
 and coke in each charge are known, to determine the necessary amount 
 of iron which must be melted to produce a desired melting ratio: 
 
 Let X = the total iron; 
 Y = the total coke; 
 A = weight of coke on bed; 
 B = weight of coke in each charge; 
 C = weight of iron in each charge; 
 D = the desired melting ratio. 
 
 (i) Then f = D, F = ^ total coke (2) 
 
 (3) and -f; = the number of charges. 
 The total coke is found in equation (4) 
 
 (4) Y = {.^-i^B+A. 
 
 From equations (2) and (4) X = -~ — =-ir-^ 
 
 C — DB 
 
 (5) 
 
 Having found the total amount of iron, the total coke and number of 
 charges are found from (2) and (3). 
 
 By applying these formulas to a 54-inch cupola as given in table on 
 pp. 451-2 the required weight of iron to be melted to produce a melting 
 ratio of 9 to I may be found. 
 
 Melting Ratio 
 
 Weight of coke on bed ^ = 1100 pounds 
 
 Weight of coke to each charge B = 180 pounds 
 
 Weight of iron to each charge C = 1900 pounds 
 
 Required melting ratio Z) = 9 to i pounds 
 
 From equation (5) 
 
 1900 X 9 (iioo — 180) . ^ 
 
 ^ ^ 1900 - 9 X 180 = 56,185, 
 
 Y = — = 6243 pounds. 
 
 And the nimiber of charges 
 
 56,185 
 
 ^-^-^ = 29.57. 
 1900 ^^' 
 
 Coke may be charged from dumps, as it can be uniformly spread. 
 
462 The Cupola 
 
 The cupola should be kept full to the charging door until all the iron 
 is in. Later the sweepings from the charging platform may be thrown 
 on. The platform should, if possible, be large enough to accommodate 
 the materials for the entire melt. Each charge of pig and scrap should 
 be weighed and piled by itself; the coke kept in convenient charging 
 buckets, and the broken limestone in a bin from which it may be charged 
 by measure, above the coke. 
 
 Appliances about Cupola 
 
 The conditions will indicate the necessity for elevator and charging 
 cars. In every foundry yard there should be a cinder mill and scrap 
 breaker. In many foundries the cinders are frequently ground in the 
 tumbling barrel. It is purely a matter of convenience; but locating 
 the cinder mill in the yard promotes cleanliness, especially when broken 
 fire brick are ground. 
 
 The cinder mill is made up of cast-iron staves from 8 to 10 inches wide 
 and of convenient length, placed about polygonal heads; the latter 
 mounted on trunnions, and the whole rotated slowly by any suitable 
 means. The staves are so placed that there is not over an eighth of an 
 inch opening at the joints, in order that the shot iron may not escape. 
 Magnetic and hydraulic separators are frequently used to recover the 
 shot, and they effect large savings. 
 
 The scrap breaker is located conveniently to the cars, or placed 
 where heavy scrap is received. It consists of a derrick and ball with 
 hoisting apparatus. The height of the derrick should be from 30 to 
 40 feet and the ball should weigh 2500 to 3000 pounds, both depending 
 
 on the probable dimensions of the 
 largest scrap. 
 
 The sketch below shows a simple 
 and effective device for tripping the 
 ball. 
 
 Ladles 
 
 Hand ladles, and shank ladles 
 
 holding 200 pounds or less, are best 
 
 ' y-v % made of sheet steel, as they are 
 
 f \ \ much lighter and are easily repaired. 
 
 A // These, as well as larger sizes, to be 
 
 handled by cranes, are furnished by 
 Fig. 128. , . / , ■, 
 
 the foundry supply nouses. 
 
 It is usually best to tap into a fore ladle. This is kept under the 
 
 spout, and has sufficient capacity to hold one entire charge. From it 
 
 © 
 
The Bod Stick 463 
 
 the smaller ladles are filled. By making large tappings, the various 
 grades of iron in the cupola become thoroughly mixed in the fore ladle. 
 The iron in the ladle is kept hot by covering the surface with charcoal 
 or slacked lime. 
 
 In English practice the Fore Hearth is largely used instead of the fore 
 ladle, but its use has not met with favor in the United States. An illus- 
 tration of this arrangement is shown on page 248 of McWilliams and 
 Longmuir's General Foundry Practice. 
 
 Lining of Ladles 
 
 The ladles are lined with a mixture of one-half fire clay and one-half 
 sharp sand. With small ladles the lining is from % inch to iH inches 
 thick on the bottom and gradually tapers to 14 to % inch thick at the 
 top. 
 
 Large ladles have first a lining of fire brick, then the clay daubing. 
 
 After the linings are completed they must be thoroughly baked either 
 by placing the ladles in an oven or by building wood fires in them. It 
 is customary to reline the small ladles after each heat. The larger ones, 
 if completely drained of iron, may, by chipping out and patching, be 
 made to last over many heats. The skulls from ladles are rattled with 
 the cinders. Shanks for ladles holding 100 pounds and upwards are 
 commonly made with single and double ends. The better practice is 
 to make both ends double, the helper's end having a swivel joint. With 
 this type of shank the helper can use both hands in carrying and two 
 men can handle a 200-pound ladle easily. The iron bottoms of the 
 larger ladles should have 10 or 12-%-inch holes through them to permit 
 the escape of moisture. 
 
 Tapping Bar 
 
 The tapping bar is usually made of i-inch gas pipe, having a long 
 tapered point (24 inches in length) welded to it at one end. Frequently 
 the tapper stands along one side of the spout, and opens the tap hole 
 with a single-handed bar. He carefully picks away the center of the 
 bod, until a hole is made through it, then enlarges the hole to ¥s inch, or 
 an inch, according to the stream desired. 
 
 The Bod Stick 
 
 The bod stick is an iron bar about i inch in diameter, having at one 
 end a flat disc 2H inches in diameter. To this disc is attached the 
 clay bod, used in stopping up the tap hole. In stopping the stream 
 of iron, the bod, placed above the stream at the tap hole, is forced down- 
 
464 The Cupola 
 
 Table Showing Capacities of Ladles with Bottom Diameters 
 
 Depth 
 
 Diameter of ladle at bottom, inches 
 
 20 
 
 22 
 
 24 
 
 26 
 
 28 
 
 30 
 
 32 
 
 34 
 
 36 
 
 Ins. 
 2 
 
 4 ■ 
 6 
 8 
 10 
 12 
 14 
 16 
 18 
 20 
 22 
 24 
 26 
 
 30 
 32 
 34 
 36 
 38 
 - 40 
 42 
 44 
 46 
 
 157 
 318 
 483 
 652 
 825 
 1002 
 1 183 
 1368 
 1557 
 1749 
 1946 
 2149 
 
 191 
 334 
 585 
 788 
 997 
 1210 
 1427 
 1648 
 1873 
 2102 
 2337 
 2576 
 2821 
 
 227 
 
 459 
 
 696 
 
 938 
 
 1 185 
 
 1436 
 
 1693 
 
 1954 
 
 2221 
 
 2492 
 
 2769 
 
 3050 
 
 3337 
 
 3630 
 
 267 
 538 
 815 
 1096 
 1383 
 1676 
 1973 
 2276 
 2585 
 2900 
 3221 
 3548 
 3880 
 4218 
 4560 
 
 309 
 624 
 945 
 1272 
 1604 
 1942 
 2286 
 2606 
 2992 
 3353 
 3720 
 4093 
 4472 
 4807 
 5248 
 5645 
 
 356 
 717 
 1084 
 1457 
 1836 
 
 2221 
 2612 
 3009 
 3412 
 3821 
 4237 
 4660 
 5089 
 5525 
 5968 
 6417 
 6871 
 7329 
 
 403 
 812 
 1228 
 1651 
 2080 
 2516 
 3142 
 3408 
 3863 
 4325 
 
 4793 
 5268 
 5750 
 6238 
 6734 
 7237 
 7747 
 8261 
 8781 
 
 455 
 917 
 1,385 
 1,860 
 2,342 
 2,830 
 3,326 
 3,829 
 4,339 
 4,855 
 5.378 
 5,911 
 6,451 
 6.998 
 7.552 
 8,114 
 9,682 
 9,258 
 9,840 
 10.42S 
 
 510 
 1,026 
 1,550 
 2,08s 
 2,62s 
 3.172 
 3.726 
 4,288 
 4.856 
 5.432 
 6,016 
 6,608 
 7.208 
 7.816 
 8,432 
 9,054 
 9,694 
 10,332 
 10,978 
 11,630 
 12,288 
 
 48 
 
 For steel add 5% 
 
 50 
 
 52 
 
 54 
 56 
 58 
 60 
 62 
 64 
 66 
 68 
 
 
 
 
 
 
 
 
 
 
 
 
 wards into the hole squeezing off the stream. Many severe burns have 
 been caused by stopping directly against the stream. 
 
 The spout is sometimes made with a side opening to carry off slag 
 running on the stream of iron. This opening is made about the middle 
 of the spout, and the trough in that vicinity is somewhat increased in 
 width. About 2 inches below the side opening a fire brick is placed 
 across the trough, leaving room below it for the iron to pass, but 
 being low enough to skim off the slag, which runs out of the side at 
 the opening. A swinging spout is occasionally used. This is hung 
 on a pivot below the spout proper, and in a transverse direction. 
 
Capacities of Ladles 465 
 
 Varying from 20 to 54 Inches, Slope of Sides iVz to i Foot 
 
 
 
 
 Diameter of ladle at bottom, inches 
 
 
 
 Depth 
 
 
 
 
 
 
 
 
 
 
 38 
 
 40 
 
 42 
 
 44 
 
 46 
 
 48 
 
 50 
 
 52 
 
 54 
 
 Ins. 
 
 
 
 
 
 
 
 
 
 
 2 
 
 568 
 
 630 
 
 694 
 
 762 
 
 832 
 
 906 
 
 984 
 
 1,064 
 
 1,146 
 
 4 
 
 1,144 
 
 1,268 
 
 1,396 
 
 1,600 
 
 1,672 
 
 1,820 
 
 1,978 
 
 2,138 
 
 2,302 
 
 6 
 
 1,728 
 
 1,914 
 
 2,106 
 
 2,310 
 
 2,522 
 
 2,774 
 
 2,982 
 
 3,222 
 
 3,469 
 
 8 
 
 2,330 
 
 2,568 
 
 2,824 
 
 3,096 
 
 3,380 
 
 3.678 
 
 3,996 
 
 4,316 
 
 4,829 
 
 10 
 
 2,930 
 
 3,330 
 
 3,552 
 
 3,892 
 
 4,248 
 
 4,622 
 
 5.019 
 
 5,420 
 
 6,063 
 
 12 
 
 3,538 
 
 3,900 
 
 4,288 
 
 4,696 
 
 5,124 
 
 5,576 
 
 6,052 
 
 6,334 
 
 7,308 
 
 14 
 
 4,154 
 
 - 4,578 
 
 5,032 
 
 5,510 
 
 6,012 
 
 6,540 
 
 7.095 
 
 7,659 
 
 8,564 
 
 16 
 
 4,776 
 
 5,264 
 
 5,784 
 
 6,332 
 
 6,910 
 
 7,514 
 
 8,149 
 
 8,784 
 
 9,831 
 
 18 
 
 5,406 
 
 5,958 
 
 6,546 
 
 7,154 
 
 7,816 
 
 8,498 
 
 9.213 
 
 9.930 
 
 10,711 
 
 20 
 
 6,044 
 
 6.660 
 
 7,316 
 
 7,994 
 
 8,730 
 
 9.492 
 
 10,287 
 
 11,086 
 
 11,936 
 
 22 
 
 6,690 
 
 7,370 
 
 8,094 
 
 8,844 
 
 9,6S4 
 
 10,496 
 
 11,371 
 
 12,253 
 
 13,212 
 
 24 
 
 7,344 
 
 8,088 
 
 8,880 
 
 9,702 
 
 10,588 
 
 11,510 
 
 12,465 
 
 13.422 
 
 14,479 
 
 26 
 
 8,C5o6 
 
 8,816 
 
 9,676 
 
 10,570 
 
 11,532 
 
 12,533 
 
 13.569 
 
 14.623 
 
 15,757 
 
 28 
 
 8,676 
 
 9,552 
 
 10,480 
 
 11,446 
 
 12,486 
 
 13.566 
 
 14,683 
 
 15,826 
 
 17,046 
 
 30 
 
 9.354 
 
 10,296 
 
 11,294 
 
 12,334 
 
 13.450 
 
 I4,6c9 
 
 15,808 
 
 17,038 
 
 18,346 
 
 32 
 
 10,040 
 
 11,048 
 
 12,116 
 
 13,232 
 
 14,424 
 
 15,663 
 
 16,943 
 
 18,261 
 
 19.657 
 
 34 
 
 10,734 
 
 11,810 
 
 13,943 
 
 14,140 
 
 15,408 
 
 16,727 
 
 18,089 
 
 19.495 
 
 20,979 
 
 36 
 
 11.436 
 
 13,580 
 
 .13,788 
 
 15,059 
 
 16,402 
 
 17,801 
 
 19,249 
 
 20,740 
 
 22,312 
 
 38 
 
 12,146 
 
 13,358 
 
 14,618 
 
 15,988 
 
 17,406 
 
 18,885 
 
 20,412 
 
 21,996 
 
 23,657 
 
 40 
 
 12,864 
 
 14,144 
 
 15.496 
 
 16,927 
 
 18,420 
 
 19.998 
 
 21,591 ' 
 
 23,263 
 
 25,014 
 
 42 
 
 13,590 
 
 14,940 
 
 16,364 
 
 17,876 
 
 19,443 
 
 21,083 
 
 22,782 
 
 24,541 
 
 27,070 
 
 44 
 
 14,322 
 
 15,712 
 
 17,240 
 
 18,83s 
 
 20,476 
 
 22,197 
 
 23,98s 
 
 25,830 
 
 27,761 
 
 45 
 
 
 16,550 
 
 18,122 
 19,014 
 
 19,802 
 20,776 
 22,198 
 
 21,519 
 22,573 
 23,637 
 
 23,322 
 
 24,557 
 25,703 
 
 25,197 
 26,420 
 27,654 
 
 27.130 
 28,441 
 29,763 
 
 29,152 
 
 48 
 
 For steel add 5% 
 
 30,55s 
 
 50 
 
 
 
 31,920 
 
 52 
 
 
 
 
 
 24,711 
 
 26,859 
 
 28,899 
 
 31,096 
 
 33,397 
 
 54 
 
 
 
 
 
 
 28,032 
 
 30,155 
 
 32,441 
 
 34,336 
 
 56 
 
 
 
 
 
 
 29,223 
 
 31,422 
 
 33,798 
 
 36,287 
 
 58 
 
 
 
 
 
 
 30,256 
 
 32,690 
 
 35,166 
 
 37,750 
 
 60 
 
 
 
 
 
 
 
 33,979 
 
 36,545 
 
 39.225 
 
 62 
 
 
 
 
 
 
 
 35,279 
 
 37,941 
 39,343 
 42,312 
 
 40.712 
 
 64 
 66 
 
 The foundry 
 
 42,211 
 43.729 
 
 68 
 
 
 
 
 
 
 
 46,011 
 
 While the stream is running it can be tipped so as to let the iron 
 run into a ladle at either side. In rapid melting this obviates stop- 
 ping up when ladles are changed. 
 
 Applying Metalloids in Ladle 
 
 Where metalloids are added to the iron, if the amount to be used is 
 sprinkled into the stream as it flows through the spout, a more intimate 
 mixture is obtained than results from placing the material in the ladle 
 and drawing the iron on to it. 
 
466 
 
 The Cupola 
 
 Cranes 
 
 The equipment of cranes as to size, style and motive power is indi- 
 cated entirely by the character and volume of production. Ample and 
 convenient hoisting facilities are absolutely essential. A mistake is 
 seldom made in providing cranes of too great capacity. 
 
 Most of the modem foundries are fitted with electric traveling cranes, 
 which not only have access to the cupola, but sweep over the moulding 
 floors. In addition to the electric crane, post and wall cranes are 
 supplied for special requirements. There should be a small jib crane 
 attached to the cupola for handling the fore ladle. 
 
 The manufacture of cranes has become a specialty, and the reader is 
 referred to manufacturers' catalogues for special information. 
 
 Spill Bed 
 
 In many foundries the excess iron, and iron on the bench floor, is 
 frequently dumped into holes in the sand heaps or floors. This is a 
 slovenly practice and greatly injures the sand. 
 
 A very convenient and simple spill bed is shown in Fig. 129. This 
 is so made that the iron is collected in pieces weighing from 60 pounds to 
 80 pounds, of convenient size to be handled in charging. 
 
 A small bed of same character serves an excellent purpose when placed 
 near the snap floors. 
 
 Dumping Spill Bed 
 
 Fig. 129. 
 
Gagger Mould 
 Gagger Mould 
 
 467 
 
 Fig. 
 
 130. 
 
 By a little care all the excess iron may be put through beds as above 
 and sent to the cupola in good shape for melting. 
 
 The usual practice is to allow the bottom to remain where it drops 
 until the next morning, simply wetting it thoroughly. 
 
 Below is shown a sketch of a large rake. If the bottom is dropped 
 on this and the mass pulled out from under the cupola (by means of a 
 
 Fig. 131. 
 
 chain passing through a snatch block to the crane) and then wetted 
 down, it will be found in much better shape for picking over in the 
 morning. 
 
 The pieces of unconsumed coke should be picked out and used in 
 core ovens, or as part of the last charge of coke, in the cupola. Little 
 savings of this kind, although small of themselves, amount to an impor- 
 tant item in the course of the year, particularly if the operations are 
 extensive. 
 
CHAPTER XX 
 MOULDING SAND 
 
 Moulding sand contains from 75 to 85 per cent silica, with varying 
 proportions of alumina, magnesia, lime and iron. 
 The essential properties are: 
 
 Cohesion, Refractoriness, 
 
 Permeability, Durability, 
 
 Porosity, Texture. 
 
 Cohesion or Bonding Power 
 
 Moulding sand must possess sufficient cohesion, not only to remain 
 in position after ramming, but to resist the pressure of the molten 
 metal, and its abraiding action while being poured. 
 
 Pure sand has no cohesive strength, but clay (double silicate of 
 almnina) has, and as moist sands cohere more strongly than dry, 
 the bonding power must depend on the amount of clayey matter and 
 water contained. The moisture must not be in excess, otherwise the 
 sand will pack too densely. 
 
 Permeability and Porosity 
 
 Permeability is the property which sand possesses of allowing liquids 
 or gases to filter through it, and depends on the size of the pores. 
 By porosity is meant the volume of pore space. 
 These properties are not the same. A sand may contain a few large 
 openings through which the liquids or gases may readily escape and yet 
 have a small pore space. On the other hand, the total pore space may 
 be large, but by reason of the small size of the pores, permeability by 
 either liquids or gases might be difficult. 
 The permeability of sand may be influenced: 
 By the tightness of packing; 
 By the size of the grains; 
 By the fluxing elements in the sand. 
 By tamping or packing, the space occupied by a given weight of 
 sand may be reduced, as the grains are forced into their closest arrange- 
 ment producing the minimum pore space. Fine-grained sands have 
 larger pore space than coarse-grained. 
 
 468 
 
Texture 469 
 
 If silt or clay are present, and segregated, the sand will pack more 
 closely than if the grains are cemented together in the form of com- 
 poimd grains. In the latter case the permeability and porosity would 
 be larger than if the grains were separate. 
 
 The decreased permeability under increased tamping explains why 
 some good sands behave badly. Permeability of sand is also influenced 
 by the amount of water present. The relation between permeability 
 and fluxing impurities is shown in the process of casting. If the clayey 
 particles filling the interstices of the sand fuse when heated by the metal, 
 their coalescence in melting will close up the pores to some extent. For 
 this reason, in part, a high percentage of fluxing impurities is undesirable. 
 
 The proper permeability of a moulding sand is a matter of vital 
 importance. A pathway must be opened for the escape of the gases 
 to avoid blowing. The finer the sand the lower its permeability. 
 
 Refractoriness 
 
 A moulding sand must be sufficiently refractory to prevent complete 
 fusion in contact with molten metal. Highly siliceous sands are, there- 
 fore, the more desirable. At the same time a high percentage of silica is 
 gained at the expense of alumina and a consequent loss of bonding power. 
 Generally silica should not exceed 85 per cent. Silica is refractory, does 
 not shrink when heated, but has no cohesive nor bonding power. 
 
 Alumina, a most important component, is present in moulding sands 
 in amounts varying from 4 to 12 per cent. It is refractory, has great 
 bonding power, but shrinks greatly when heated. Too high a percentage 
 of alumina makes the sand impermeable. 
 
 Durability 
 
 Sands begin to lose some of their desirable qualities after one or 
 more heats and become dead or rotten. The injury to the sand arises 
 from its dehydration, or loss of combined water by the heat of the molten 
 metal, whereby its bonding power is destroyed. The water of com- 
 bination cannot be restored. 
 
 The amount of sand burned is a layer of varying thickness next to 
 the casting. 
 
 Texture 
 
 By texture is meant the percentage of grains of different sizes. This 
 is determined by passing the sand through a series of sieves of decreas- 
 ing mesh and noting the percentage remaining on each sieve. Mr. W. 
 G. Scott pursues the following method: 
 
 "Ten grams of sand are placed on the loo-mesh sieve, together with 
 ten jie steel balls, and shaken with a circular motion for one minute. 
 
470 
 
 Moulding Sand 
 
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Texture 
 
 471 
 
 The sand passing through is weighed and credited to the 100- mesh sieve. 
 That which remains, together with the balls, is emptied on the 80-mesh 
 sieve and the operation repeated. In like manner sieves of varying 
 size up to 20 mesh are used. The preceding table shows the texture or 
 sand from different localities. " 
 
 Lime is a fluxing element. If present as a carbonate, it loses its 
 carbonic acid under heat, and in excessive amount the gas causes the 
 mould to flake or crumble. Caustic lime fluxes and forms slag on sur- 
 face of castings. 
 
 Magnesia is also a flux, and to a modified extent has the effect of hme. 
 
 Iron, as a carbonate or an oxide, if present in the mould near the 
 casting, is converted into ferrous oxide, which is a flux. 
 
 Combined water is present in all sands containing clay, carbonate of 
 lime or gypsum. It is driven off at a low red heat and increases the 
 porosity of the sand. 
 
 Moulding sands are not always used alone. One or more grades are 
 frequently mixed together. Blending is extensively practiced at the 
 pit as well as at the foundry. In addition to blending to increase cer- 
 tain physical properties, foreign substances, such as ground coal, graph- 
 ite, molasses, flour, beer, linseed oil or cinders are used, either to increase 
 the bonding power or permeability of the material. A sand deficient 
 in its natural condition" may be greatly improved by "doctoring." 
 The sand from any one deposit does not always run uniformly, and with- 
 out previous careful examination of the shipments, unfavorable results 
 may appear in the foundry. 
 
 The following table, taken from "The Iron Age," gives the analysis 
 of eight different samples. 
 
 Constituents 
 
 Silica 
 
 Alumina 
 
 Ferric oxide . . . . 
 
 Lime 
 
 Magnesia 
 
 Potash 
 
 Soda 
 
 Water 
 
 Organic matter. 
 
 92.08 
 5. 41 
 2.49 
 
 91.90 
 
 5.68 
 
 2.17 
 
 .41 
 
 92.91 
 
 5.85 
 1.24 
 
 90.62 
 6.66 
 2.70 
 
 81.50 
 9.88 
 3.14 
 
 1.04 
 .65 
 
 84 
 
 82.90 
 21 
 90 
 62 
 
 85 
 
 79.81 
 
 10.00 
 
 4.44 
 
 .70 
 
 2.89 
 
 Sands which contain the largest percentage of silica, sufficient alimiina 
 to impart cohesiveness and plasticity, with from i to 3 per cent of 
 magnesia are the best for facing. Such sand should be entirely free 
 from lime. 
 
472 
 
 Moulding Sand 
 
 Specifications of W: G. Scott, Racine, Wis. 
 
 "Moulding sand for iron work generally contains from 75 to 85 per 
 
 cent of silica; 5 to 13 per cent of alumina; less than 2.5 per cent lime 
 
 and magnesia; not over 0,75 per cent soda and potash and generally 
 
 less than 5 per cent oxide of iron; not more than 4 per cent of water. " 
 
 Sand for Brass 
 
 Sand for brass may contain a much higher percentage of iron and 
 lime without detriment. 
 
 All moulding sands contain more or less organic matter. Carbonate 
 of lime must not exceed 1.5 per cent for iron sands, nor 234 per cent for 
 brass. Iron oxide must not exceed 5.5 per cent for iron nor 7 per cent 
 for brass sand; organic matter not to exceed i per cent. Any sand 
 showing an excess of 13 per cent alumina will be rejected. 
 
 Analysis 
 
 Constituents 
 
 SUica... 
 
 Alumina 
 
 Iron oxide 
 
 Lime... 
 
 Lime carbonate . 
 
 Soda 
 
 Potash; 
 
 Manganese 
 
 Combined water. 
 Organic matter . . . 
 Specific gravity . . 
 Fineness 
 
 For light 
 iron work 
 
 82.21 
 948 
 4.2s 
 
 2.64 
 
 .28 
 
 2.652 
 
 85.18 
 
 For 
 medium 
 iron work 
 
 85.85 
 
 8.27 
 
 2.32 
 
 .50 
 
 .29 
 
 .81 
 
 .10 
 
 .03 
 
 Trace 
 
 1.68 
 
 .15 
 
 2.654 
 
 66.01 
 
 For heavy 
 iron work 
 
 6.30 
 
 2.00 
 
 .78 
 
 .50 
 
 .25 
 1.73 
 
 .04 
 
 2.63 
 
 46.86 
 
 For light 
 brass 
 
 78.86 
 
 7.89 
 
 S.45 
 
 • SO 
 
 1.46 
 
 1. 18 
 
 .13 
 
 .09 
 
 Trace 
 
 3.80 
 
 .64 
 
 2.64 
 
 94.88 
 
 Any of these sands would answer very well so far as their chemical 
 composition is concerned, for any class of work; but it is absolutely 
 necessary that they should possess the proper degree of fineness. 
 
 The finer sands are less siliceous and as a rule carrj' higher percentages 
 of almnina and fluxes than coarser grades, as shown by the following 
 table. 
 
 Size 
 
 60 
 
 80 
 
 TOO 
 
 100 
 
 Silica 
 
 95.92 
 
 1.29 
 
 .56 
 
 .10 
 
 2.13 
 
 97.87 
 
 94.35 
 
 1.47 
 
 .56 
 
 .04 
 
 3.58 
 
 96.42 
 
 94.66 
 
 1.47 
 
 .40 
 
 .34 
 
 3.13 
 
 96.87 
 
 91.06 
 
 
 4.57 
 
 Ferric oxide 
 
 .80 
 
 Lime 
 
 72 
 
 Alkalies 
 
 2 8s 
 
 Total 
 
 97.15 
 
 
Testing Moulding Sand 473 
 
 The greater the average fineness, the lower the permeability. 
 
 Prof. Ries, from whose paper the above notes are extracted, concludes 
 that the chemical analysis of moulding sands are not of as much impor- 
 tance as their physical properties. 
 
 To test the "temper" and strength of sand, the moulder squeezes 
 a handful into a ball. If it takes the impression of his hand readily 
 and leaves the hand clean, it is considered sufficiently damp. Its 
 strength or binding power is tested by lifting the lump from one end, 
 or by carefully breaking it apart; or he may squeeze a ball of sand about 
 a little stick or nail and see if it can be lifted by the stick. He then 
 blows through it to test its porosity. Such crude tests are in constant 
 use and, conducted by experienced moulders, serve the purpose. 
 
 A. E. Outerbridge instituted a series of experiments to determine 
 these characteristics more definitely. The following is extracted from a 
 paper read before A.S.M.E., at their New York meeting in 1907. 
 
 "A number of test bars of green sand 6" X i" X 1" were made 
 imder uniform conditions of pressure, dampness and quality of material 
 used in forming the ordinary mould. These little test bars were placed 
 upon a smooth metal plate with sharp square edges. The bars were 
 then pushed over the edge of the plate until they broke, when the amount 
 of the overhang was measured. It was soon found that there was a 
 great difference in the length of the overhang, which was regarded as 
 a quantitative measure of the toughness of the sand. These differences 
 were not even noticeable in the crude ball test. 
 
 Samples taken from different parts of a small sand heap that had been 
 uniformly dampened, or tempered, varied greatly in this respect, owing 
 no doubt to the irregular distribution of the alumina or clay binder; 
 and the correctness of this inference was subsequently confirmed by 
 simple analytical tests. After a sufficient number of these test bars 
 had been made and broken to prove the reliability of the method, further 
 tests were devised to ascertain whether the usual methods of riddling 
 and mixing the sand for the moulder's use affected its quality either by 
 increasing or decreasing its toughness, as shown by the amount of over- 
 hang of similar test bars of green sand. It was proved that the more 
 thoroughly the sand was worked, the greater the overhang, due, as al- 
 ready stated to the more uniform distribution of the binder. 
 
 "The ideal moulding sand is a material in which the individual grains 
 of silex, constituting approximately 90 per cent of the mass, are com- 
 pletely covered with an overcoat of alumina or clay and the more 
 uniform the grains are in size and shape, the better is the sand with 
 respect to porosity in relation to the average size of the grain. 
 
 "It was found on passing a sample of sand a number of times through 
 
474 
 
 Moulding Sand 
 
 a handriddle, and making test bars from the sample after each riddling, 
 that the overhang was increased measurably. Thus, a sample of sand, 
 which, after tempering and mixing by hand with a shovel, showed an 
 overhang of less than two inches of the test bar, increased to nearly 
 three inches after a dozen riddlings. It would not be practicable to 
 treat large masses of sand in this manner, nevertheless, the informa- 
 tion thus obtained was quite valuable and led to important practical 
 results. 
 
 "Another novel observation was concurrently made, viz., that the 
 increased toughness and porosity noticed in these tests might be partly 
 due to "aeration" or to the separation of the grains of sand when 
 falling from the sieve to the floor. In order to discover the truth or 
 falsity of this view, a quantity of sand was shaken in a box with a closed 
 lid for several minutes and test bars were made before and after shaking. 
 The correctness of the theory was quickly shown, for the shaking with- 
 out sieving proved to be more effective than the sieving without shaking. 
 Tests for porosity were also made, but these were not very satisfactory 
 owing possibly to lack of suitable means of controlling and measuring 
 the compressed air." 
 
 Using one of Wm. Seller's & Co. 's centrifugal sand mixers, the develop- 
 ment of which was largely due to Mr. Outerbridge's experiments, a series 
 of tests were made with facing sand prepared as follows: 
 
 Strong Sand 
 
 Parts 
 
 Strong Lumberton sand (new) 14 
 
 Gravel (new) 7 
 
 Flour sand (old) . 6 
 
 Coal dust 2 
 
 Fig. 132. — Green Sand Test Bars made from One Sample of Sand. 
 
 "Fig. 132 is from a photograph showing eleven bars 6" X 1" X i", 
 made from strong sand under uniform conditions of quantity, temper 
 (dampness) and pressure. 
 
Testing Moulding Sand 475 
 
 "The bar labeled o was pressed from a sample of the sand after 
 having been dampened and turned over several times, with a shovel, 
 and only partly mixed. The object of such preliminary mixing is 
 simply to prevent the coal dust from flying out of the centrifugal ma- 
 chine on subsequent treatment. 
 
 "The other bars were made from the same pile of strong sand, after 
 passing through the centrifugal machine from one to ten times. These 
 bars were laid side by side upon the smooth metal plate, resting upon a 
 table, and were slowly pushed over the edge of the plate until they 
 broke." 
 
 The following table gives the measurements of the overhang of each 
 bar as nearly as the somewhat irregular shape of the break permitted. 
 
 Inches 
 
 214 
 
 • ■■■ 3 
 
 •• 3H 
 
 3^ 
 
 3H 
 
 ■ ■••• 3^ 
 
 3H 
 
 3% 
 
 3^ 
 
 3% 
 
 • 3% 
 
 No. length of overhang 
 
 No. I 
 
 
 No. 2 
 
 
 No. 3 " 
 
 
 No. 4 " 
 
 
 No. 5 " 
 
 
 No. 6 " 
 
 
 No. 7 
 
 
 No. 8 
 
 
 No. 9 " 
 
 
 No. 10 " 
 
 
 "It will be observed that the first treatment increased the overhang 
 % inch, the subsequent treatments increased the overhang in some 
 cases H inch, and in some cases not measurably. The first treatment 
 was, therefore, the most effective, and for practicable purposes one 
 treatment is often sufficient to insure good mixing of the materials and 
 thorough disintegration of any lumps. 
 
 "The strain tending to break the sand beam is increased by the 
 additional weight of the increasing length of the overhanging portion, 
 and also by the increased moment of its center gravity. It is readily 
 seen, therefore, that an increase in length of the overhang of % inch 
 on the first treatment in the centrifugal machine means an increased 
 tenacity of 75 per cent. In like manner an increase in overhang of 
 50 per cent means an increase in strength of sand of 225 per cent. 
 
 The illustration. Fig. 133, shows the fractured surfaces of the same 
 bars. 
 
 "Bar No. o shows the heterogeneous components of the partly mixed 
 sand, while the other fractures show increasing uniformity due to more 
 thorough mixing, and disintegration of lumps up to No. 3, after which 
 no further increase in uniformity is observable to the eye. 
 
476 
 
 Moulding Sand 
 
 Fig. 133. — End View of the 
 Test Bars in Fig. 132. 
 
 The illustrations convey a very fair impression of the actual appearance 
 of the bars. The appearance of the fractured surfaces coincides with 
 the tests for overhang, and shows that a single treatment in this machine 
 
 is in many cases sufficient, and two 
 treatments are all that are usually 
 needed with any sand mixtures. 
 
 In mixing core sand containing flour, 
 the effectiveness of this method is still 
 more strikingly evident, owing to the 
 almost total disappearance of the white 
 flour, due to its thorough commingUng 
 with the sand and coal in one treat- 
 ment. 
 
 The centrifugal machine is especially 
 efficient in mixing sharp sand with lin- 
 seed oil for cores. When so used it is 
 run at a lower speed than when used for 
 tempering and mixing moulding sand. 
 Two treatments are sufficient to insure 
 thorough mixing of sharp sand and oil for cores. 
 
 There are many other devices for tempering and mixing sand mechan- 
 ically, such as, shakers, revolving reels, etc., which are effective. 
 
 The amoimt of cohesive matter, or binder, in moulding sand should be 
 limited to that which will permit good ramming, without destroying its 
 porosity, so that the gases will escape readily, without allowing the iron 
 to penetrate. 
 
 The sand in a mould next to the casting is burned and loses much or 
 all of its cohesion. This is due to driving off the water of combination 
 in the alumina which cannot be restored. The thickness of the layer 
 of burned sand depends upon the size of the casting and temperature of 
 same. 
 
 It is impossible to separate all of this burned sand after the removal 
 of the castings. Much of it gets mixed in the sand heaps, which must 
 be strengthened from time to time with new sand . 
 
 Aside from the loss of combined water and increase in iron content, 
 chemical analysis shows little difference in the composition of new and 
 burned sand. This is shown in the table on page 437, made by analyz- 
 ing the same sand before and after using. 
 
 In general, moulding sand must possess the following requirements. 
 It must be sufficiently porous to allow the free passage of air and 
 the gases generated in casting. 
 
 It must resist high temperature without fusing. 
 
Moulding Sand Requirements 
 
 477 
 
 It must permit of easy removal from the cold castings. 
 
 When rammed into shape it must, be firm and sufi&ciently compact 
 to resist the pressure of the liquid metal. 
 
 It must be strong enough to resist the abraiding action of the stream 
 of metal entering the mould. 
 
 Constituents 
 
 New 
 
 Burned 
 
 Silica 
 
 83.49 
 
 7-25 
 
 4.71 
 
 .36 
 
 .35 
 
 1.30 
 
 .41 
 
 .30 
 
 1.66 
 
 82.32 
 
 7.80 
 
 3.98 
 
 .54 
 
 .41 
 
 1.64 
 
 .81 
 
 .22 
 
 .19 
 
 2.38 
 
 100.28 
 60.80 
 
 
 
 
 
 Potash 
 
 Soda 
 
 Titanic oxide 
 
 Water 
 
 Ferrous oxide 
 
 Total 
 
 99.86 
 64.50 
 
 
 
 For Dry Sand Moulding 
 
 Any sand which, when rammed, will permit of drying into a compact, 
 coherent but porous mass, will answer the purpose of a dry sand mix- 
 ture. Many green sands dry into friable masses. 
 
 Such sands must be mixed with some substance to give them strength. 
 For such purpose, flour, stale beer, molasses-water, or clay-wash may 
 be used. When flour is used, it is mixed in the proportion of one to 
 twenty or thirty, depending upon the character' of the sand. 
 
 With some sands the flour may be dispensed with and the sand 
 strengthened sufficiently with molasses- water or clay wash. In dry 
 sand moulds, only one or two inches of the sand next the pattern are of 
 the prepared mixture. The remainder of the flask is filled with ordinary 
 heap sand. This should be as open as possible to permit the ready 
 escape of the gases. The facing should likewise be as open as can be 
 safely worked. The amount of moisture should be about the same as is 
 used in green sand. Dry sand facings must be thoroughly well mixed. 
 
 Mr. West gives the following mixtures for dry sand facings. 
 
 For Large Spur Gears p^j.^g 
 
 Lake sand 12 
 
 Strong loam sand 12 
 
 Moulding sand 4 
 
 Coke, amount i-io 
 
 Flour iH 
 
 Wet with water. 
 
47^ Moulding Sand 
 
 Or Part 
 
 Moulding sand i 
 
 Jersey sand i 
 
 Fire sand i 
 
 Sea coal i-io 
 
 Wet with thin clay wash. 
 
 For Close Facing 
 
 Moulding sand 6 
 
 Lake or bank sand iJ^ 
 
 Flour i-so 
 
 Wet with clay wash. 
 
 This mixture may be used for blacking, using flour 1-40. 
 
 For Cylinders - 
 
 Fair loam 4 
 
 Lake sand i 
 
 Sea coal or coal dust 1-14 
 
 Wet with clay wash. 
 
 General Work _ ^ 
 
 Part 
 
 Moulding sand i 
 
 Bank sand i 
 
 Flour 1-30 
 
 Sea coal 1-20 
 
 Wet with clay wash. 
 
 Parts 
 
 Strong loam sand 6 
 
 Lake sand 6 
 
 Old dry sand 2 
 
 Flour 1-40 
 
 Sea coal 1-14 
 
 Wet with water. 
 
 For Rolls 
 
 Parts 
 
 Dry sand 2 
 
 Lake sand i 
 
 Sea coal 1-12 
 
 Flour 1-18 
 
 Wet with clay wash. 
 
 For Renewing Old Dry Sand for Body of Moulds p 
 
 Old sand 16 
 
 Lake sand 8 
 
 New loam 4 
 
 Wet with water. 
 
 Or 
 
Core Sand 
 
 479 
 
 Dry Sand Moulds 
 
 Old dry sand becomes very close. It should be passed through a 
 No. 8 riddle to remove the dust and very fine particles. The coarse 
 material mixed with new sand works well. 
 
 Skin Drying 
 
 Instead of making dry sand moulds which are baked in the oven, moulds 
 are more frequently "skin dried." Skin dried moulds are essentially 
 the same as "dry sand" except that the drying does not extend to as 
 great depths and the facing is not as strong. 
 
 For skin dried moulds mix with ordinary heap sand about i to 30 flour. 
 After the mould is finished sprinkle with molasses water. The mould is 
 dried either with the kerosene blow torch, or fire of wood, coke or char- 
 coal, built in iron baskets which are placed in the mould. Often the 
 mould is covered with sheet iron and fires are built on top of the iron. 
 In drying copes, they are suspended and fires built under them." 
 
 Before drying, the moulds are brushed with black wash, made of plum- 
 bago and water, to which a little molasses water or clay wash is added. 
 Sometimes moulds are black washed after drying. 
 
 Core Sand 
 
 Core sand should be high in silica and low in alumina. A sand con- 
 taining much alumina does not permit the ready escape of gases after 
 baking. 
 
 Analyses of Core Sands 
 
 (W. G. Scott) 
 
 Constituents 
 
 Good 
 
 quality 
 
 core sand 
 
 Fair 
 quality- 
 core sand 
 
 Silica 
 
 94.30 
 
 1.95 
 
 .33 
 
 1.63 
 
 69.31 
 4.76 
 1.58 
 3.50 
 8.19 
 7.77 
 .12 
 2.95 
 1.82 
 
 Alumina 
 
 Iron oxide . . ... 
 
 Lime carbonate 
 
 Lime sulphate. 
 
 Magnesia 
 
 Alkalies 
 
 .54 
 
 .05 
 
 1.05 
 
 .15 
 
 Combined water 
 
 Organic matter 
 
 "Since the greater portion of a core is to be entirely surrounded by 
 metal, the sand of which it is composed encounters conditions much 
 
480 Moulding Sand 
 
 more severe than those met with by facing sands. Three conditions 
 must be noted. 
 
 First. — The core is subjected to much handling. 
 
 Second. — The gases generated in casting must find egress through 
 the core and not through the metal. 
 
 Third. — The core has finally to be removed from the casting. 
 
 "All cores, before entering the mould, are dried, and in this condition 
 must be hard enough to permit handling, and porous enough to admit 
 the free escape of gases. Yet the sand must not be burned or converted 
 into a compact mass by the heat; if so, it will be extremely difficult to 
 remove from the casting. 
 
 "A sand high in siUca should yield the best results. To such a sand 
 the necessary bond must be added. An ideal core sand is one in which 
 the silica is given bond by the addition of an organic substance, which 
 produces a firm core, capable of withstanding high temperatures and 
 resisting the penetrating action of fluid metal. Such a core is friable 
 in the cold casting, and is, therefore, easily removed. 
 
 "If bond is given to silica by clayey matter alone, then the metal 
 bakes the cores hard, and renders their removal difficult. 
 
 "A hard surface imparted to the sand by ramming is fatal, as fluid 
 metal will not lie on it, but a hard surface resulting from the binder 
 does not necessarily represent an impervious one, and fluid metal will 
 usually lie quietly on it. Heat tends to loosen a sand made hard in 
 this way, instead of fusing it. 
 
 Core Mixtures 
 
 "There should be just enough bonding material in a core mixture to 
 coat each individual grain of sand, without filling the interstices between 
 the grains, and the value of the core depends greatly upon the thorough- 
 ness with which the mixture is incorporated. Too much attention 
 cannot be given to this feature. As a rule mechanical mixers give the 
 best results. The binders in common use are 
 
 Flour, 
 
 Linseed oil, 
 
 Glue, 
 
 Rosin, 
 
 Molasses, 
 
 Rosin oil. 
 
 In addition to these there are many commercial binders of more or 
 less value, all of them designed to offer a binder cheaper than those 
 above mentioned. 
 
 Cores made with flour, glue or molasses soften quickly when exposed 
 to dampness. Therefore they must be kept in a dry place, or used soon 
 after they are made. The moulds in which they are placed should be 
 
Dry Binders 481 
 
 poured shortly after the cores are set. If allowed to stand for a period 
 of 24 hours, the cores should be taken out and dried. 
 
 Cores made with glue are very friable when hot and must be handled 
 with great care. Less gas is given off by them than by those made 
 with any other binder. Glue cores leave a smoother hole and do not 
 require to be blackened as do flour cores. 
 
 Flour is mixed with sand in proportions varying from i to 18, to i to 
 30, depending upon the strain which the core is to resist. The weaker 
 the mixture, the more readily the gas escapes. 
 
 Glue is first soaked in warm water and then boiled untU entirely dis- 
 solved. Glue water should consist of 2 pounds of glue to 3 gallons of 
 water. This mixture is sufficient to treat 100 pounds sand. 
 
 Rosin must be first pulverized; it is then mixed with sand in propor- 
 tions of I to 20, or I- to 30, as required. 
 
 Rosin oil is used i to 18, or i to 24 as the requirements of the case 
 indicate. 
 
 Molasses, mixed i to 20 water is used more for spraying cores to give 
 a hard surface, than for entire mixtures. 
 
 Linseed oil with sharp sand, mixed about i to 30 furnishes the best core 
 of all binders. It is strong, porous and is easily removed from the 
 casting. For light, delicate cores, such as gas engine and automobile 
 work it is unequaled. 
 
 Large percentages of old cores, gangway sand and moulding sand may 
 be used in the core mixtures. 
 
 Core sand should be quite damp for use, but not so wet as to adhere 
 to the core box. Wet sands require much less binder than dry. 
 
 A saving may be made in the use of flour by boiling it thoroughly 
 and then using the paste (very thin) to wet the sand. As already 
 mentioned, the more thoroughly the binder is incorporated with the 
 sand, the better will be the cores. 
 
 Mr. A. M. Loudon made an extensive series of experiments to deter- 
 mine the comparative values of various core binders, and published the 
 results in a most interesting paper presented to the American Foundry- 
 men's Association at the Cleveland meeting 1906. From it the follow- 
 ing extensive extracts are made. 
 
 Dry Binders 
 
 Test No. I. — Flour sand core mixture. _ 
 
 Parts 
 
 New moulding sand 2 
 
 New fire sand i 
 
 Flour I to 12 and i to 18 
 
 Wet down with thick clay wash. 
 
482 Moulding Sand 
 
 Cores from this mixture are usually very strong. If not thoroughly 
 dried or if slightly burned or scorched, cause great trouble by blowing 
 or scabbing. Cores were removed from castings with difficulty. Be- 
 came damp in mould quickly, especially small cores. 
 
 Test No. 2. — Syracuse dry core compound mixture. 
 
 Old flour sand H 
 
 New moulding H 
 
 Sharp or beach H 
 
 One part binder to 35 parts sand thoroughly tempered with water. 
 Cores made from this mixture dried quickly, were clean and sharp and 
 left good surface on castings. Resisted dampness well. 
 
 Mr. Loudon states that the dampness test for each mixture was to 
 dip a core partly in water, allowing it to stand after removal from the 
 water for two or three days to air dry only. Iron was then cast in an 
 open mould around the end which had been immersed. 
 
 Test No. 2. — Included the water test as did all the other tests for 
 dry and oil binders, the conditions being the same for all. 
 
 The binder used in Test No. 2 stood the water test in a manner en- 
 tirely satisfactory. The hot iron came in contact with the core without 
 any distiubance. 
 
 This binder in Mr. Loudon's judgment is best suited to large plain 
 work, or small round and square cores. 
 
 Test No. 3. — Dextrin or British gum mixture. 
 
 Per cent 
 
 Old flour sand 50 
 
 New moulding sand - . . 25 
 
 Beach or sharp sand 25 
 
 I part binder to 150 parts sand, tempered with water. 
 
 This mixture was valuable for large cores, strong, with sharp edges 
 and easily dried. 
 
 If the cores are burned in the oven, wash with some of the binder 
 dissolved in water, and dry in oven for ten minutes. They are thus 
 completely restored. For small intricate cores the following mixture 
 was used. 
 
 Per cent 
 
 Old sand 33 
 
 New moulding sand , 33 
 
 Sharp sand 33 
 
 I part dextrin to 100 parts sand. 
 
 A core from this mixture was treated by the water test, and allowed 
 to stand for two days. It resisted the action of melted iron better than 
 cores from many mixtures, when fresh from the oven. 
 
Dry Binders 483 
 
 Test No. 4. — Wago core-compound mixture. 
 
 Per cent 
 
 Old sand 33 
 
 New moulding sand 33 
 
 Sharp sand 33 
 
 I part Wago to 30 parts sand. 
 
 Made a good core; did not gum the box, and gave off very little 
 smoke. 
 A second mixture made from Wago: 
 
 Per cent 
 
 New moulding sand 50 
 
 Sharp sand 50 
 
 I part Wago to 35 parts sand. 
 
 Unusually strong, true and sharp, but not as easily removed from 
 casting as the first mixture with Wago. 
 
 One of these cores was dipped in water and left for two days to air 
 dry. The melted iron was perfectly quiet when poured around it. 
 
 Test No. 5. — Cleveland core-compound mixture. 
 
 Per cent 
 
 Old sand ^^ 
 
 Sharp sand 33 
 
 New moulding sand 33 
 
 I part binder to 30 parts sand tempered with warer. 
 
 Strong core, easily removed from casting, very satisfactory for general 
 use. 
 
 A mixture i part binder to 40 sand was tried, but cores were too soft. 
 Cores from the i to 30 mixture when submitted to the water test gave 
 excellent results. 
 
 Test No. 6. — Peerless core-compound mixture. 
 
 Per cent 
 
 Old sand 33 
 
 Sharp sand S3 
 
 New moulding 33 
 
 I part binder to 30 parts sand. 
 
 The mixture as above given was unsatisfactory, therefore, the follow- 
 ing mixture was tried. 
 
 I part binder to 20 parts sand. 
 
 This was satisfactory, being strong and true to box, but harder to 
 remove from castings than most of those previously tested. It gave 
 good results when submitted to the water test. The iron showed no 
 signs of blowing. 
 
484 Moulding Sand 
 
 Tests Nos. 7, 8, 9 were made from samples of flour submitted. Sand 
 mixed in same proportions as before. 
 
 Thus, the first sample of flour was mixed with 15 sand, 
 the second sample of flour was mixed with 18 sand, 
 the third sample of flour was mixed with 20 sand. 
 
 These were made as comparative tests of the different samples of 
 flour. 
 
 1. Made the strongest core, but was the most difi&cult to remove from 
 the casting. 
 
 2. Good for general work. 
 
 3. Was too soft. 
 
 A mixture of i to 18 from 3 to 9 was good, better than Nos. 2 to 8 in 
 same proportion. Each of the above mixtures was subjected to water 
 test and failed. When withdrawn from the water and held in hori- 
 zontal position, they broke at the line of submersion. Nos. 2 and 3 were 
 not as good in this respect as No, i. 
 
 The cores from the peerless compound and most of the others resisted 
 the water so that it could be wiped off with a rag without injuring the 
 cores. 
 
 Test No. 10. — Paxton dry compound mixture. 
 
 Per cent 
 
 Sharp sand ^^ 
 
 New moulding sand 33 
 
 Old sand 33 
 
 I part compound to 30 parts sand, made a very soft core. 
 
 When mixed i to 20 it made a very strong core. 
 
 One of these when subjected to the water test went to pieces, while 
 the last mixture made a strong open core. It is readily affected by 
 moisture. 
 
 Liquid Core Binders 
 
 Test No. II. — Holland linseed mixture. 
 
 Parts 
 
 Sharp sand 30 
 
 Oil I 
 
 Made a strong core for small and medium shapes, but required vent- 
 ing. A core from this mixture immersed in water for half an hour was 
 returned to the oven and dried. It was then as good as any which had 
 not been immersed. 
 
 Test No. 12. — Syracuse core oil mixture. 
 
 Parts 
 
 Sharp sand 35 
 
 Oil I 
 
Moulding Sand Mixtures 485 
 
 Tempered with water and well mixed. These cores were excellent; 
 without vents were not satisfactory. 
 
 A core from this mixture was immersed for 15 hours, taken out and 
 dried in the oven for 15 minutes. Molten iron when cast about it 
 showed no disturbance. 
 
 Tests Nos. 13, 14, 15. — Sterling oil samples from each of above were 
 mixed at same time. 
 
 Mixture p^^^ 
 
 Sand ic 
 
 Oil ;:.:::; i 
 
 Nos. I and 2 of these samples showed too much oil. No. 3 was about 
 right. 
 
 Another mixture was then made. 
 
 Parts 
 Sand 4^ 
 
 Oil :::::::; i 
 
 Nos. I and 2 dried out quickly and made good strong cores, but when 
 subjected to the water test the moisture acted quickly upon them, 
 more so than on the other sand and oil mixtures. The cores were 
 strong and were easily cleaned from the castings, but moulds which were 
 left over night, and poured the next day blew very badly. 
 
 Test No. 16. — Gluten or Esso mixture. p^^. ^^^^ 
 
 New sand 33 
 
 Sharp sand 33 
 
 Old sand ^^^ 
 
 Gluten I part to 30 parts sand 
 
 Cores were so hard that the iron would not lay to them. 
 
 One part gluten to 50 parts sand, — cores were good, sharp and 
 strong. Iron somewhat disturbed. The gluten was mixed with water 
 and the sand tempered with water. 
 
 One part gluten to 70 parts sand. 
 
 These cores were soft and did not stand the fire as well as the others. 
 When subjected to water as before 
 
 I to 30 stood very well, 
 
 I to 50 became soft, 
 
 I to 70 melted like sugar, 
 
 showing that for a free core, one not inclined to blow, i to 70 took 
 
 moisture very quickly. 
 
 Test No. 17. — Glue melted in hot water mixture. p^^. ^^^^ 
 
 New moulding sand 25 
 
 Sharp sand 25 
 
 Old sand 50 
 
 I pound of glue to 100 pounds of sand for small cores. 
 I pound of glue to 150 pounds of sand for large cores. 
 
486 Moulding Sand 
 
 Lump or granulated glue, the cheaper the better. 
 
 The glue water was made by dissolving two pounds of glue in three 
 gallons of water. 
 
 Cores from the first of the glue mixture when submitted to the water 
 test absorbed water but held their shape. After redrying were as good 
 as when first made. Should such cores be burned in the oven, washing 
 them with a mixture of plumbago and glue water restores them. 
 
 Mr. Loudon highly recommends the first of the above glue mixtures, 
 using it for cores without vents for small port cores. 
 
 Cores made from it can safely be used for all purposes, taking care to 
 have them thoroughly dried. 
 
 Cores for large beds have remained in the mould three and four days 
 without causing trouble. 
 
 Test No. i8. — Glucose melted with hot water mixture. „ 
 
 Per cent 
 
 Sharp sand 33 
 
 New moulding sand 33 
 
 Old sand 33 
 
 I pound of glucose to 100 pounds of sand. 
 
 Cores of every description were first class, easily dried, easily cleaned 
 from casting, emitting no smoke. They acted like green sand cores, 
 dried and gave good results in every respect. 
 
 Parting Sand 
 
 The particles of burned sand, having been deprived of combined mois- 
 ture will not cohere. Such sand, taken from the cleaning room, is used 
 to separate the parts of the moulds and is also dusted on patterns to 
 prevent the moulding sand from adhering to them. 
 
 A most excellent parting sand for intricate work is made by saturat- 
 ing very fine burned sand with kerosene or crude oil, and setting fire to 
 the mixture. 
 
 Lycopodium is also used for parting in particular work, but the high 
 price subjects it to adulteration. 
 
 Facings 
 
 When molten iron comes in contact with a sand mould it tends to 
 penetrate the pores of the sand and to fuse the particles in immediate 
 contact, leaving a rough surface or scale, varying in thickness from Mi 
 to H of an inch, depending on the weight of the casting. 
 
 Facing sands containing large percentages of carbonaceous material 
 are used to prevent this difficulty and to leave smooth surfaces on the 
 castings. The carbon of the facing is decomposed by the heat, and the 
 
Facings 487 
 
 gases generated prevent the hot iron from attacking the sand. Facing 
 sand which is composed of ground coal (sea coal), and sand in the pro- 
 portions of from I coal to 8 sand, and i coal to 20 sand, depending upon 
 the character of the work, is placed next to the pattern in a layer from 
 y2 to i>2 inches in thickness. Back of this and completely filling the 
 flask is the heap, or floor sand. By the continued use of facing the 
 floor sand becomes black with it. 
 The term facing includes 
 
 Sea coal, Coal dust, 
 
 Plumbago, Charcoal. 
 
 Talc (or soapstone). 
 
 It must adhere to the surface of the mould and cause the casting to 
 peel when shaken out. 
 
 Sea coal is a ground bituminous gas coal, free from sulphur and slate. 
 It is mixed mechanically with new moulding sand in the proportion 
 of I to 10, usually, and used generally on all work. For the purpose of 
 obtaining smoother and brighter surfaces than result from the use of 
 sea coal alone as a facing, the moulds are finished with plumbago or some 
 mixture of which plumbago is the base. Plumbago is the best of all 
 materials for this purpose. 
 
 Soapstone is used largely in connection with plumbago as an adulter- 
 ant, as also are coke dust and the dust of anthracite coal. 
 
 The facing is applied to the mould either by hand, with a camel's hair 
 brush, or it is mixed with molasses water and applied by a spray or with 
 a brush. The latter method is usually used on dry sand moulds. 
 
 Mr. W. G. Scott gives the analysis of Yougheogheny gas coal, from 
 which the best "sea coal" facing is made as follows: 
 
 Per cent 
 
 Moisture i .00 Sulphur o. 33 
 
 Volatile matter 35 • 00 Ash 5 . 60 
 
 Fixed carbon 58.07 Specific gravity i . 28 
 
 Cannel coal is also used as facing and analyzes as follows: 
 
 Moisture 3 . 30 Sulphur o. 20 
 
 Volatile matter 48 . 50 Ash 6 . 00 
 
 Fixed carbon 42 .00 Specific gravity i . 229 
 
 "Sulphur and ash are the two constituents of sea coal to be guarded 
 against. If sulphur exceeds 0.75 the coal is inferior, and if sulphur is 
 in excess of 1.5, the coal is unsuitable for facing. 
 
 "Facing containing over 11 per cent ash ought not to be used. 
 
 "Slack and culm are often ground and used as adulterants, but are 
 readily detected by the amount of ash present. 
 
488 Moulding Stand 
 
 Graphite Facing 
 
 "Pure graphite contains about 99 per cent carbon, but this degree 
 of purity is not found in the natural product. A high grade natural 
 graphite contains 75 per cent carbon; inferior grades contain from 15 
 to 65 per cent. 
 
 "As the regulation method of determining carbon in facings is to 
 burn off a weighed amount of sample and call the loss carbon, an un- 
 scrupulous dealer may add coke or anthracite dust sufficient to raise 
 the carbon content to any desired point. 
 
 "Adulterations of this sort may be determined in several v/ays. 
 
 "If several small beakers are filled with water and pure graphite, 
 coke dust, anthracite dust, soft coal dust or charcoal are carefully 
 sprinkled on the surface of the water, each in a separate glass, none of 
 the powder will settle except the coke dust and some charcoals. This 
 test eliminates coke dust and non-greasy charcoals. By shaking in a 
 test tube H gram of the sample with 15 c.c. of acetone and allowing 
 the mixture to stand 10 or 15 minutes, it will be seen that the pure 
 graphite settles clear, leaving the liquid colorless. Coke imparts a 
 gray to the solution and remains in suspension a long time; anthracite 
 coal imparts a faint brown color and settles more rapidly; soft coal 
 dust imparts a deep brown color. 
 
 "The above tests are qualitative only. Equal parts of glacial acetic 
 acid and sulphuric ether answer as well as acetone for this test." 
 
 The following analyses from Scott of graphite, coke dust, coal and 
 charcoal give a general idea as to the character of the diflFerent forms 
 of carbon. 
 
 Chemically Pure Graphite 
 
 Per cent Per cent 
 
 Moisture 0.02 Sulphur o . 00 
 
 Volatile matter 0.09 Ash o. 10 
 
 Fixed carbon 99-79 
 
 Commercially Pure Graphite 
 
 Per cent Per cent 
 
 Moisture o. 15 Sulphur trace 
 
 Volatile matter o. 79 Ash 4 . 46 
 
 Fixed carbon 94 . 60 Specific gravity 2 . 293 
 
 Stove-plate Graphite Facing 
 
 Per cent Per cent 
 
 Moisture o. 75 Sulphur. o. 20 
 
 Volatile matter 5 . 29 Ash 37-66 
 
 Fixed carbon 56 . 10 Specific gravity 2 .363 
 
Facings 
 
 4S9 
 
 The Composition of Ash in Above Sample 
 
 Per cent 
 
 .Silica 25.60 
 
 Alumina 5.25 
 
 Iron oxide 4 . 94 
 
 Lime 
 
 Magnesia o . 80 
 
 Per cent 
 1.07 
 
 Cheap "Green Sand'^ Facing 
 
 Moisture o. 45 
 
 Volatile matter 5 . 75 
 
 Fixed carbon 41 -49 
 
 Sulphur 0.62 
 
 Ash 51-69 
 
 Specific gravity 2 .489 
 
 Per cent 
 
 Of which the ash analyzed. 
 
 Silica 32.13 
 
 Alumina 2.77 
 
 Iron oxide 6 . 78 
 
 Lime i . 64 
 
 Magnesia 8.32 
 
 This sample was said to contain 25 per cent soapstone. 
 The following analyses are given for comparison. 
 Coke Dust 
 
 Per cent 
 
 Moisture 0.19 
 
 Volatile matter ...... i . 40 
 
 Fixed carbon 86 . 8q 
 
 Per cent 
 
 Sulphur o . 98 
 
 Ash. 10.54 
 
 Specific gravity i .886 
 
 Anthracite Coal Dust 
 
 Constituents 
 
 Selected 
 
 lump, 
 per cent 
 
 Screenings, 
 per cent 
 
 Moisture 
 
 .05 
 
 4.40 
 
 92.00 
 
 .57 
 
 2.98 
 
 1.565 
 
 3. SO 
 8.99 
 
 68.70 
 .86 
 
 17.95 
 1.590 
 
 Volatile matter 
 
 Fixed carbon 
 
 Sulphur 
 
 Ash . 
 
 Specific gravity ... 
 
 
 Analysis of Soft Coal 
 
 Constituents 
 
 Selected 
 
 lump, 
 per cent 
 
 Screenings, 
 per cent 
 
 Moisture 
 
 1.39 
 
 33.82 
 
 58.68 
 
 .96 
 
 5.15 
 
 1. 321 
 
 4.44 
 32.79 
 37.61 
 
 3.10 
 22.06 
 
 1.486 
 
 Volatile matter 
 
 
 
 Ash 
 
 
 
490 
 
 Moulding Sand 
 Analysis of Wood Charcoal 
 
 Constituents 
 
 Common 
 variety, 
 per cent 
 
 Medicinal, 
 per cent 
 
 Moisture 
 
 3.83 
 26.57 
 66.63 
 None 
 2.97 
 1.362 
 
 3.66 
 33.15 
 
 58.52 
 None 
 4.67 
 1. 412 
 
 Volatile matter 
 
 
 Sulphur 
 
 Ash 
 
 Specific gravity 
 
 
 Analysis of Soapstone and Talc 
 
 Constituents 
 
 Vermont 
 
 soapstone, 
 
 per cent 
 
 French 
 
 talc, 
 per cent 
 
 Silica 
 
 51.20 
 8.45 
 5.22 
 1. 17 
 
 26.79 
 7.17 
 
 61.8s 
 
 • 25 
 
 2.61 
 
 Trace 
 
 34.52 
 
 .77 
 
 
 
 
 
 Water 
 
 
 Mr. Scott gives the following as a test for the presence of anthracite 
 coal in graphite. 
 
 "Treat 0.5 gram of sample with 50 c.c. of strong nitric acid, boiling 
 about 10 minutes. Then add 0.5 grams of pulverized potassium chlo- 
 rate and boil until most of the chlorine is off. Dilute with 30 c.c. of 
 cold water and filter, reserving the filtrate for examination. 
 
 The filtrate from pure graphite treated in this manner should be 
 clear and colorless unless iron is present, in which case it may be some- 
 what yellow in color. 
 
 The filtrate from any kind of coal and charcoal will have a distinct 
 amber brown color, the soft coals giving a deeper color than the hard 
 coals or charcoal. 
 
 To confirm the test add 30 c.c. of stannous chloride solution and 
 note the change in color. The graphite filtrate will be reduced to a 
 colorless liquid if iron is present, or remain unchanged if free from 
 iron; whereas the filtrate from the coal having an amber color will be 
 much deeper in color and in some cases nearly black. The only caution 
 to be observed in this test is sufi5cient boiling to remove all of the hydro- 
 carbon coloring matter in the coal. 
 
 The determination of magnesia is the only method to be rehed upon 
 for detecting the addition of soapstone to graphite. Mixed with graph- 
 
Facings 401 
 
 ite or anthracite dust, it answers very well for certain classes of work. 
 
 Facing made entirely of anthracite or mixed with a low grade of 
 natural graphite is termed Mineral Facing and is represented by one 
 or more letters X to designate the fineness. Such facings may be added 
 to wet blacking; or mixed with graphite, may be used on heavy work. 
 
 All facings should be kept in a dry place as they readily absorb mois- 
 ture. A high grade of plumbago makes the most suitable facing for 
 producing bright clean castings. A good plumbago must not only 
 have the proper chemical analysis, be of such refractory nature as to 
 withstand the hot iron from cutting into the mould, but must also be of 
 such a nature as will not retard the flow of the molten metal." 
 
CHAPTER XXI 
 
 THE CORE ROOM AND APPURTENANCES 
 
 The important relation which the core room bears to the foundry- 
 product demands the most careful consideration as to location, con- 
 struction and equipment. Unfortunately for the core maker, such con- 
 siderations have been neglected in many foundries. Whatever could, 
 has been made to serve so long as the imperative demands were 
 satisfied. Good castings cannot be made without good cores. Their 
 production requires the same attention and forethought as the making 
 of good moulds. 
 
 Constant intercornmunication between the moulding floors and core 
 room, the handling of sand, fuel and ashes, etc., point to a location 
 affording the greatest accessibility to the moulding floors and to the 
 storage for sand and fuel. 
 
 The core room should be well lighted and ventilated. The space 
 allotted should be ample, not only for the convenience of the workmen 
 but for storage of supplies, movable equipment, core plates, etc., so that 
 the place may be kept neat and orderly. The arrangement of the 
 work benches, machinery, cranes, racks, etc., must be governed by 
 circumstances. 
 
 The oven is the important feature in the core room. Where the cores 
 are not very large and the demand for them not very great, some form 
 of portable oven may answer the purpose. Many varieties are made, 
 adapted to small and medium work. The convenience offered by them 
 in placing and removing cores before and after baking, the small floor 
 space occupied and the small fuel consumption commend them for 
 light work. Most large foundries have one or more of these ovens. 
 Where great quantities of small cores are required, some form of con- 
 tinuous oven is frequently used. An oven with a revolving reel is very 
 desirable for medium-sized work. 
 
 The sketch below is taken from West's "American Foundry Practice," 
 page 133. 
 
 "The oven is round, with an upright cast-iron shaft, having five 
 flanges on which to bolt plates or arms XX, the shape of which is 
 shown at B. This oven is built with an 8-inch brick wall to form the 
 outside and a cast-iron plate for the top, on which plate is a box D, to 
 
 492 
 
The Core Room and Appurtenances 
 
 493 
 
 which a cap can be bolted to hold the top of the shaft, the bottom of 
 which rests in a cast iron seat. 
 
 "The fireplace should be outside of the circle, as shown, so that the 
 cores will not get the direct heat from the fire. In building the walls, 
 hinges HH, should be built in for hanging the oven door. 
 
 Fig. 134. 
 
 "This door should be made in two pieces, so as to open to the right 
 and left, and should be the full height of oven, to provide for putting 
 cores on the top shelves. 
 
 "The chimney should have a top flue, as well as a bottom one, as 
 shown at PP and dampers in both, so as to throw the heat down or 
 up, as required. 
 
 "When starting a fire, both dampers should be open, and when the 
 cores to be dried are on the top shelf, the bottom damper may be closed, 
 and vice versa. 
 
 "This style of oven is very handy for drying cores that can be lifted 
 by hand, and will hold and dry more cores with less fuel than any oven 
 I know of. Should you want to dry a single core quick, put jt on the 
 top shelf and turn it round to the fire. 
 
 "This oven can be filled with cores and they can be taken out again 
 without going farther than the door, which alone is of great value to 
 the core maker. 
 
 "The size of this oven was about 8 feet in diameter and 7 feet high." 
 The oven was heated with a cast-iron fire basket. 
 
 On page 135 of same book is shown a sketch for a small oven of which 
 Mr. West speaks very highly. The advisability of building such an 
 oven is somewhat doubtful, however, in view of the great variety of 
 portable ovens on the market which can be purchased at a reasonable 
 price. 
 
494 
 
 The Core Room and Appurtenances 
 
 For large cores the dimensions of the oven are governed entirely by 
 the requirements of the foundry. 
 
 Unless the drying of large moulds is comtemplated, it is not advisable 
 to make an oven more than 12 feet wide by 20 feet long. Where greater 
 capacity is required, it is better to duplicate it, on account of the greater 
 loss of fuel in large ovens, which are not stored to their full limits. 
 
 
 Fig. 135. — Core Oven. 
 
 Among the sketches of large ovens shown by Mr. West, that on page 
 227, "Moulders' Text Book," presents a most excellent design. An en- 
 larged sketch is given above. The dimensions may of course be varied 
 to suit the requirements. 
 
 Mr. West in describing ovens of this design says: "They surpass 
 any I know of for properly drying moulds or cores. Although we use 
 
The Core Room and Appurtenances 495 
 
 slack or soft coal for the fires, a mould or core will when dry, be almost 
 as clean as when first put into the oven. Another important feature 
 is that the ovens will dry rapidly and still not burn a mould or core. " 
 
 Three ovens are fired from one pit, the draft flues being at the 
 extreme ends of the oven and the channel for heat to travel being di- 
 verted from side to side. There is but a small chance for heat to escape 
 entering through the joints and thickness of the boiler plate up into the 
 oven, before it can enter the flue at F, H and K. The arrow-like lines 
 represent the heat passing from the fires to the flue. The partitions X 
 divert the direction of the heat and also support the covering plates 
 and carriage tracks. 
 
 The covering plates, 2, 3, 4, 5, 6 and 7 are boiler iron M inch thick, 
 cut into sections the width of the flue partitions. 
 
 The plates on the outside of the track are free at any time to be 
 lifted in order to clean out the soot. Where the fire enters the first 
 flue or partition,'' the boiler plates are left out, and in their place a cast- 
 iron plate ¥2 inch thick, having prickers 2 inches long (on underside) 
 and daubed up with fire clay is used. 
 
 This is to prevent the direct flame from buckling and burning out the 
 plates. 
 
 There are no holes whatever in any of the plates, the heat passing 
 through them and their joints, which of course are not air tight, heat 
 up the oven. 
 
 Were there holes in the plates, they would seriously injure the draught 
 of the under flues, and also let much of the smoke into the ovens, thereby 
 destroying essential points to be overcome in using slack for firing. 
 
 To be able to fire with slack or soft coal, and stiH keep moulds and 
 cores free from soot is something that wifl be appreciated by all moulders 
 and core makers that work around ovens. Not only does soot make 
 everything look dirty, but it is more or less productive of rough castings. 
 
 "Another arrangement which I doubt being found in any other 
 foundry oven is that for preventing smoke. Upon each side of the fire- 
 places, about on a level with the fire, are %-\nch. openings, seen at E 
 in elevation. In. the rear of these openings the brick is left open about 
 4" X 6", running the entire length of the fireplace. This opening gives 
 a reservoir in which the air becomes heated before being drawn into 
 the fireplace. This is, I believe, claimed to be beneficial in assisting 
 'smoke burning' or combustion." 
 
 The grate surface for the fire contains an area equal to about 32''X 38". 
 
 "The fireplaces are all faced with one thickness of fire bricks, and the 
 tops of fireplaces are arched over with fire bricks. Under the large 
 oven are two fireplaces. The one nearest core oven is used for heating 
 
496 The Core Room and Appurtenances 
 
 the same, and is so constructed with damper arrangement, that should 
 an extra heat be required in the large oven, both of the fires can be turned 
 on to it. 
 
 "As shown at D in elevation of oven, each one has a small manhole 
 door, whereby the flue leading to the chimney K can be readily cleaned. 
 
 "The tops of the ovens are covered with a series of arches. 
 
 "Upon the tops of these ovens we store and keep shop tools, etc. The 
 way the tops are formed, tons of weight can be laid upon them and do 
 no harm; and the combined area of the tops makes a splendid store- 
 room for systematically keeping foundry tools. " 
 
 "Altogether the ovens are a success, and a credit to their designer, 
 the late Mr. Hallo way. " 
 
 Note. — Only one ol the ovens is shown in the sketch. The other two 
 are in all respects the same as the one shown. 
 
 Another excellent design for a large oven is shown on page 129, West's 
 "American Foundry Practice." A description of one good oven is all 
 that can be permitted here. 
 
 The essential requirements for an oven are good draught and means 
 for regulating it. Where the fire is made directly in the oven, as is 
 frequently the case, there should be openings into the chimney at the 
 top and bottom, with dampers for changing the direction and regulating 
 the draught. There should also be a damper on top of the chimney 
 so as to retain the heat when the fire is not urged. Aside from coal and 
 coke, crude oil and natural gas are used for heating. 
 
 The temperature of the ovens should range from 450° to 900° F. and 
 must be varied somewhat according to the core sand mixtures. 
 
 Flour sand requires a higher temperature than rosin or oil. The 
 workmen soon learn the part of the oven in which the drying is most 
 rapid and place the cores where they will dry quickly or slowly as re- 
 quired. 
 
 A pyrometer is a most valuable attachment and will often prevent 
 the destruction of cores by overheating. 
 
 The doors to these ovens are usually made in one piece of sheet iron 
 and are provided with counter weights, so as to permit of being raised 
 or lowered easily. In some cases they are made of overlapping, plain or 
 corrugated strips, which are wound upon rollers. 
 
 Core Oven Carriages 
 
 These are mounted on wheels having anti-friction bearings. The 
 top of the carriage extends over on each side as far as convenient. The 
 carriages have usually three or more decks as required. The whole 
 
Wire Cutter 497 
 
 is made up of bars and angles properly trussed, and left as open as 
 possible, for the passage of hot air to the cores. 
 
 The track should be evenly laid, so that there may be no jarring as 
 the car passes over it. 
 
 Mixing Machines 
 
 Machines for this purpose are of greatest value to the core room. 
 The worth of a binder and that of a core depends largely upon the 
 thorough incorporation of the components of the core. Each individual 
 grain of sand should receive a coating of the binding material, but the 
 latter should not be present in such quantity as to fill up the pores of 
 the sand. To accomplish this result requires long-continued manipu- 
 lation. The best results are obtained by a mechanical mixer, driven by 
 power or by hand, as the conditions permit. A machine of this sort is 
 indispensable in a well-appointed core room. There are many different 
 kinds on the market. The centrifugal machine is, perhaps, the most 
 desirable. 
 
 Sand Conveyors 
 
 Many of the large foundries are provided with sand elevators and 
 conveyors, whereby the sand after mixing is carried to the bench of 
 each core maker and delivered through spouts. The necessity for 
 appliances of this sort will be indicated by the extent and character of 
 the work, simply bearing in mind that the core maker should have the 
 sand delivered to him. 
 
 Rod Straighteners 
 
 Core wires and rods by use become crystallized, and bent in all manner 
 of shapes; so that it is not unusual to find about core rooms, large 
 heaps of material of this kind, which are picked over by the core maker 
 in search of what he requires. In this condition it is practically worth- 
 less; therefore the expense for wire and rods is not inconsiderable. By 
 annealing they may be softened, and if then passed through a straight- 
 ener are rendered serviceable. Both hand and power machines for 
 this purpose are made. 
 
 Wire Cutter 
 
 A machine' for this purpose is very useful where there are many small 
 cores of a kind to be made. Otherwise the common hand cutter serves 
 the purpose. 
 
498 
 
 The Core Room and Appurtenances 
 
 Sand Driers 
 
 A sand drier is frequently very desirable. A simple one can be made 
 by taking a sheet-iron cylinder from, 15 to 20 inches in diameter, 
 and say 5 feet long. Surround this by an inverted sheet-iron frustum 
 of a cone, having a diameter at the base such that the space between 
 it and the cylinder may contain any desired amount of sand. Near the 
 intersection of the cone and cylinder there should be two or more small 
 shding doors. Mount the cylinder on a grate for coke; provide a 
 cover for the top for checking the fire. This costs little and will dry 
 sand very rapidly. The cut below shows a drier in frequent use. 
 
 The Champion Sand Dryer 
 
 Capacity, 20 tons daily. 
 
 Requires less fuel and has greater capacity than any of the dryers 
 now in use, and being made of cast iron throughout, will outlast any 
 made partially of sheet iron. 
 
 The parts, being made interchangeable, can be 
 replaced at any time. 
 
 Set the dryer upon a solid foundation, and first 
 placing casting No. i. in position, follow up with 
 the other casting as numbered. 
 No. I, Ash pan and base. 
 " 2. Flat rings, with slides. 
 " 3. Wide ring of outside casing. 
 " 4. Fire box. 
 
 " 5. Rings with which to form casing. 
 " 6. Center pipe. 
 " 7. Outside pipes. 
 " 8. Plates to secure top of pipes. 
 No. 9. Cover for pipes and seat for stove pipe. 
 " 10. Flaring ring. 
 " II. Slide, 
 " 12. Door. 
 Nos. 13 and 14. Grates. 
 
 Fire lightly, being careful not to get the dryer too hot. Never leave 
 the dryer full of sand with a fire in it; and do not attempt to use it for 
 heating purposes, as it radiates no heat outside the casing. 
 
 Fig. 136. 
 
 Core Plates and Driers 
 
 A great variety of core plates, varying in sizes, is required. These 
 plates are usually rectangular and for sizes less than 12 X 20 are li inch 
 
Cranes and Hoists 499 
 
 thick. Larger plates are thicker. Each must be smooth and true on 
 one side; on the opposite side are cast stiffening strips. Larger plates 
 are of sizes and shapes required. For work of extreme accuracy, the 
 plates should be planed on one side. The exposure of these plates to 
 frequent heating and cooling finally warps them to such an extent that 
 they become unserviceable. There should- be racks for the storage of 
 these plates so that any size desired may be quickly found. 
 
 Irregular shaped cores which cannot be turned out on fiat plates, or 
 which must be supported in drying, require iron shapes made to conform 
 to one of the surfaces of the core. The shapes are in reality portions 
 of the core boxes. The cores are baked on them, thereby retaining the 
 original form when dried. 
 
 The expense for driers is often great, therefore they should be handled 
 carefully, and put away with the core boxes to which they belong. 
 
 Core Machines 
 
 Where great numbers of small cores of uniform cross section, round, 
 square, oval, polygonal or rectangular are used, a core machine is 
 of the greatest value. One of these machines will make 200 or 300 
 linear feet of small core in an hour. The cores are pushed out of a 
 former as sausage from a sausage machine, on to metal drying trays. 
 The cores are cut up into lengths as required and pointed to fit the 
 prints. 
 
 There are several different machines of this kind made, but the 
 differences are not important. 
 
 Machines 
 
 Moulding machines are used in making cores for plain work, where the 
 demand for the product warrants. 
 
 Machmes for making straw rope. These are little used except in 
 pipe foundries. It occasionally happens in a jobbing foundry that a 
 rope body for a core is required. In such a case the rope is made by 
 hand. Straw rope is furnished by supply houses at low cost. 
 
 Cranes and Hoists 
 
 The requirements and location of these implements are regulated by 
 the character of, and demand for, the work. Where the work is large 
 there should be a traveling crane covering the track and the "big floor. " 
 Circumstances will dictate in such cases. 
 
500 The Core Room and Appurtenances 
 
 Other appliances are screw clamps, spike claws, glue heaters, clay 
 tubs, horses, etc. In view of the great number of implements 
 needed about a core room, the necessity for adequate room, that the 
 place may be kept neatly, orderly, and as cleanly as possible, wiU be 
 apparent; and as the production of good castings depends upon the 
 character of the cores, as well as upon that of the moulds, the neglect 
 to provide proper facilities for the core maker is inexcusable. 
 
CHAPTER XXII 
 THE MOULDING ROOM 
 
 Too much attention cannot be given, in selecting a location for a 
 foundry, to the character of the ground; good drainage is a primary 
 requisite. Gravelly subsoil is altogether desirable. If the natural 
 features of the situation do not permit proper drainage, the surface 
 should be raised by proper filling so that the floor may be at least one 
 foot above the ground exterior to the foundry. Much damage often 
 results from the flooding of the floor during severe storms. 
 
 Pits of greater or less depth have frequently 'to be made in the floor 
 for heavy castings, and if the ground is not well drained great expense 
 may be involved in keeping the pits dry. 
 
 In preparing the moulding floor the surface soil should be removed 
 and replaced with coarse sandy loam. After this is leveled it should 
 be covered with from 2 to 3 inches of moulding sand, rammed and 
 leveled. 
 
 Provide gangways of liberal width, one leading from the cupola and 
 others perpendicular to it. The number and location of the gangways 
 and the subdivisions of the floor are dependent on the character of the 
 business. 
 
 The main gangways, particularly the one leading out of the foundry, 
 should be supplied with railroad tracks of standard gauge, connected 
 to the switching; system. 
 
 Where it will best serve the purpose, ample space should be set aside 
 for the Foundry Office and Pattern Loft. In the selection of this 
 space regard should be had for access to the pattern storage. If at 
 one end of the shop, it may be overhead. 
 
 The proper fighting of a foundry is a matter of the greatest impor- 
 tance. The windows should be large and close together, and all light 
 possible admitted through the roof. The monitor roof is generally 
 adopted, but the saw tooth or weaving shed roof serves well. What- 
 ever style is adopted, it should carry provisior for good ventilation. 
 No investment can make larger returns than that expended in procuring 
 a well lighted foundry floor. 
 
 Lavatories and closets are located where most convenient. 
 
 501 
 
S02 
 
 The Moulding Room 
 
 Cranes 
 
 Unless the shop is small, or all the work light, a traveling crane is 
 indispensable. The capacity and span of the ciane is governed by the 
 conditions. Electric cranes are most commonly used and are probably 
 the best for the purpose. The necessity for wall and post cranes will 
 be indicated by the requirements of the business. Liberality in supply- 
 ing cranes of lifting power in excess of the probable needs is never mis- 
 placed. Occasions arise in every foundry which tax the cranes to their 
 utmost capacity. Wire cables, instead of chains, for cranes are alto- 
 gether preferable. Warning is always given of weakness in a cable, 
 whereas a link in a chain may break at any moment. 
 
 Abundant head room is a matter of great importance. Too fre- 
 quently the inability to raise a heavy weight a few inches higher than 
 the head room permits, occasions the greatest annoyance. 
 
 . Hooks and Slings 
 
 For the strength and dimensions of hooks, see Table, page 172. 
 
 For chains, see Table, page 
 
 173- 
 
 Chains and hooks should be 
 frequently annealed. They 
 are liable to give way at any 
 time and seldom give warning 
 of weakness. There is an 
 endless variety of chains and 
 hooks devised by the ingen- 
 uity of the moulder to meet 
 exigencies which continually 
 arise. Fig. 137 furnishes ex- 
 amples of those in ordinary 
 use. 
 
 Hooks and Chains 
 
 Figs. I, 2, 3, 4 and 5 show 
 JI.S heavy hooks for the crane. 
 
 No. I is the type of heavy 
 hook for crane block. 
 
 No. 2 is an imattached 
 hook which is often found 
 very convenient. 
 
 Nos. 3, 3, 3 show different forms of change hooks. They are used in 
 shifting a load from one crane to another. 
 
Lifting Beams 
 
 503 
 
 Nos. 4 and 5 "S. & C." hooks, made very heavy, are in frequent 
 demand in connection with heavy lifting. 
 
 No. 6 is the form of hook usually attached to slings for lifting iron 
 They are made with flat or chisel points from iH to 3 inches 
 
 flasks 
 wide. 
 
 No, 
 No, 
 
 7 is the ordinary chain hook. 
 
 8 is a claw hook for shortening hitches and adjusting chain 
 lengths. 
 
 No. 9 represents beam slings for hoisting copes, rolling flasks, etc. 
 The hooks should be flat and thin, 
 so as to engage easily in the long 
 Hnks A, A. There should be two 
 or more of these long links in each 
 chain, spaced at equal distances. 
 Several pairs of these slings about 
 every foundry where the lifting is 
 by cranes are most convenient. 
 
 No. 10 shows a most serviceable 
 sling. It is usually fitted with grab 
 hooks like No. 6. 
 
 No. II is a rigid beam sling used 
 on flasks with trunnions. There 
 should be two or more pairs of 
 this type of sling. Another form 
 of trunnion sling is made of a large 
 strap ring to which is attached a 
 short chain with hook or ring for 
 engaging the crane chains. 
 
 No. 12 is the ordinary turn- 
 buckle, an invaluable implement; 
 of which there should be several pairs of varying strength. 
 
 Fig. 138. 
 
 Lifting Beams 
 
 No. 13 shows a light forged beam, or spreader. This is most con- 
 venient especially for light work. 
 
 The usual lifting beam is made of cast iron with notches for slings. 
 While such a beam is very serviceable, it is too heavy to handle for 
 moderate weights and unsafe for heavy loads. 
 
 No. 14 shows a beam made of oak reinforced with iron straps. 
 Such a beam is light and may be used for moderately heavy 
 loads. 
 
504 
 
 The Moulding. Room 
 
 Fig. 139 
 
 No. 15 for heavy loads. 
 The beam should be made 
 of steel I beams, or chan- 
 nels, and to carry any load 
 to the full capacity of the 
 crane. 
 
 Where very large and 
 heavy copes are to be lifted, 
 the beam is frequently made 
 in the form of a cross, so 
 that attachment can be made 
 in four or more places, dis- 
 tributing the strain on the 
 cope as desired. 
 
 The following table gives 
 the dimensions of I beams 
 and loads they may safely 
 carry. The table is calcu- 
 lated for an extreme fibre 
 stress of 12,000 pounds per 
 square inch. 
 
 Safe Loads for Lifting Beams 
 
 
 
 
 
 
 
 Safe load for 
 
 
 Depth of 
 
 Weight 
 
 Area of 
 
 
 Width of 
 
 extreme fibre 
 
 between 
 slings 
 
 I 
 beam. 
 
 per 
 foot, 
 
 section, 
 square 
 
 Thickness 
 of web 
 
 flange, 
 inches 
 
 stress of 
 12,000 poimds 
 
 inches 
 
 pounds 
 
 inches 
 
 
 
 per square 
 
 
 
 
 
 
 
 inch, pounds 
 
 8 
 
 6 
 
 16 
 
 4-7 
 
 .26 
 
 3.63 
 
 4,772 
 
 10 
 
 6 
 
 16 
 
 4.7 
 
 .26 
 
 3.63 
 
 3.818 
 
 8 
 
 8 
 
 22 
 
 6.5 
 
 .27 
 
 4.5 
 
 8,982 
 
 10 
 
 8 
 
 22 
 
 6.5 
 
 .27 
 
 4.5 
 
 7,185 
 
 10 
 
 10 
 
 33 
 
 9.7 
 
 .37 
 
 5.0 
 
 12,900 
 
 12 
 
 10 
 
 33 
 
 9.7 
 
 .37 
 
 5.0 
 
 10,750 
 
 10 
 
 12 
 
 40 
 
 II. 7 
 
 .39 
 
 5. 50 
 
 18,753 
 
 12 
 
 12 
 
 40 
 
 II. 7 
 
 .39 
 
 5. SO 
 
 15,627 
 
 14 
 
 IS 
 
 80 
 
 23. 5 
 
 .77 
 
 6.41 
 
 29,937 
 
 16 
 
 15 
 
 80 
 
 23. 5 
 
 .77 
 
 6.41 
 
 26,200 
 
 16 
 
 20 
 
 80 
 
 23.5 
 
 .60 
 
 7.00 
 
 36.225 
 
 18 
 
 20 
 
 80 
 
 23.5 
 
 .60 
 
 7.00 
 
 32,200 
 
 18 
 
 24 
 
 80 
 
 23. 5 
 
 .SO 
 
 6.95 
 
 38,136 
 
 20 
 
 24 
 
 80 
 
 23.5 
 
 .50 
 
 6.95 
 
 34,323 
 
Binder Bars 
 
 505 
 
 No. 16 shows a cross with detachable arms. This is frequently used 
 for large copes or rings, where the points of attachment must be dis- 
 tributed equally. It does not answer for very great weights. Crosses 
 with shorter arms cast in one piece are often of great service. 
 
 The foundry supplies itself with such appliances as occasion requires. 
 
 a a a 
 a a a 
 
 J 
 
 'vnaai 
 
 Fig. 140. 
 
 Binder Bars 
 
 Binder bars are usually made of cast iron, except for very heavy work, 
 when steel beams are used. The binders are ordinarily made in open 
 sand with the ends slotted for bolts. For heavy work holes are made 
 in the ends instead of slots. 
 
 
 
 - Upper Rib for Heavy Bars 
 
 
 
 
 
 _-— — — —- . 
 
 V 
 
 1 1 
 
 ' — r- 
 
 
 
 
 1 
 
 
 ^ 
 
 
 
 
 <^ 
 
 
 
 
 
 
 
 Fig. 141. 
 
 The binders are held by bolts to similar bars under the bottom board 
 of flask, or are fastened to anchors in the floor. For safe loads on steel 
 I beams employed as binders, multiply the loads given in the table 
 on page 504. 
 
 Binder bars for supporting sides of flasks are of same character as 
 those for holding down copes, except that they are shorter and not as 
 heavy. 
 
5o6 
 
 The Moulding Room 
 
 Clamps 
 
 There are many types of clamps on the market. Adjustable, steel 
 and malleable iron, but it is extremely doubtful if anything has been 
 found to take the place of the common, old fashioned, cast-iron clamp 
 and wooden wedge. 
 
 A large assortment of the sizes in ordinary use should be kept on 
 hand. Where very long ones are required D wrought iron bars are 
 bent to shape. It is the better practice, however, to use binders in 
 place of exceedingly long clamps. 
 
 ^ 
 
 1^ CFD 
 
 Fig. 142. 
 
 Fig. 143. 
 
 Iron flasks are frequently held together by short clamps on the flanges. 
 
 Flasks 
 
 The wood flask has been used for ages and has served its purpose 
 most admirably. Wood, however, is becoming so expensive that the 
 iron or steel flask is rapidly superseding it. 
 
 Cast-iron flasks are so durable and so easily made, that an assortment 
 covering the ordinary range of work is almost indispensable. 
 
 The ordinary wooden flask is nothing more than a plain box. For 
 light work it is made of 2-inch plank, of width and other dimensions to 
 
 suit the requirements. 
 
 Fig. 144 shows the ordinary wood 
 flask for light work; the ends are 
 gained into the sides y2 inch and 
 spiked. The upper part is called 
 the cope and the bottom the nowel 
 or drag. The depth of these parts 
 depends entirely on the pattern. 
 
 It is essential that the joint at 
 "A" should be a plane surface, 
 or as the workmen say, "out of 
 wmd." 
 
 ^^^•^44. Each flask is provided with a 
 
 bottom board B. This is made of boards one inch thick, nailed to 
 battens. 
 The limit for copes made with no support for the sand except that of 
 
 Co^^. 
 
 - Nowe/ drT>m0=:~ } \ 
 
 r77///;/^/WJ}////////////W/ zm7m 
 
Flasks 
 
 507 
 
 the wood sides is about 20 X 20 depending largely upon the character 
 of the moulding sand. 
 
 For larger flask-bars, boards iH inch thick are placed crosswise 
 of the cope and about 6 or 8 inches apart. The cope is also strengthened 
 by rods at the end ^ running from side to side. The rods should have 
 large washers under the nuts. There should be one or more rods at 
 each end depending upon the depth of the cope. The lower edges of 
 the bars are chamfered to sharp edges, and the edges are kept from 
 ¥i to I inch away from the pattern, the bars having been cut to con- 
 form to the general shape of the pattern. Where the distance between 
 the edges of the bars and the surface of the pattern is more than U inch, 
 nails are driven slantwise into the bars so that their heads may come 
 within three-quarters inch of pattern. 
 
 The cope is coated with thick clay wash before placing it in position 
 to receive the sand. The ordinary mediimi-sized wood cope is gener- 
 ally made as shown in sketch below. 
 
 M^ 
 
 x^ 
 
 < 
 
 ^W 
 
 1 : — ,. -^r-3-^ 
 
 > 
 
 -^- 
 
 Fig. 145. 
 
 The short bars A, A are used where the copes are over 24 inches 
 wide. 
 
 The following table showing the thickness of plank desirable for 
 flasks of different dimensions is copied from the Transactions of the 
 American Foundrymen's Association. The table is based on a depth 
 of 6 inches for copes and drags. For each additional depth of 6 inches, 
 the thickness should be increased 25 per cent. 
 
5o8 
 
 The Moulding Room 
 
 Square flasks, 
 
 Sides. 
 
 Bars, 
 
 inches 
 
 inches 
 
 inches 
 
 24 and under 
 
 ii/^ 
 
 I 
 
 24-36 
 
 2 
 
 1 1/4 
 
 36-48 
 
 2l/i 
 
 1 1/2 
 
 48-60 
 
 3 
 
 i^^ 
 
 Rectangular flasks 
 
 18x48 
 
 2 
 
 I 
 
 18x60 
 
 2 
 
 I 
 
 18X72 
 
 2V^ 
 
 I 
 
 18x84 
 
 2M 
 
 I 
 
 24X48 
 
 2 
 
 iH 
 
 24X60 
 
 2 
 
 iH 
 
 24X72 
 
 2\(l 
 
 iH 
 
 24X84 
 
 2V2 
 
 iH 
 
 36X48 
 
 2I/2 
 
 114 
 
 36X60 
 
 2V% 
 
 i}^ . 
 
 36X72 
 
 2V1 
 
 iV^ 
 
 36X84 
 
 2^/1 
 
 iH 
 
 48X48 
 
 3 
 
 ii/i 
 
 48X60 
 
 3 
 
 ii/^ 
 
 48X72 
 
 3 
 
 ii-i 
 
 48X84 
 
 3 
 
 ii/i 
 
 Bars should not be over 8 inches apart, center to center. 
 
 Square flasks, from 24 to 36 inches square should have one row of 
 short cross bars running through center of flask, connecting the long 
 bars that extend from side to side. 
 
 Sizes from 36 to 48 inches square should have at least one cast-iron 
 bar, preferably two, and should also have one row of short cross bars. 
 
 Sizes from 48 to 60 inches square should have two iron bars and two 
 rows of short cross bars. 
 
 With rectangular flasks, the statement that connecting bars are not 
 needed until the flasks are 36 inches wide does not accord with the 
 usual practice. Ordinarily connecting bars are used in flasks over 
 18 inches wide. 
 
 Rectangular flasks over 60 inches wide should have one cast bar 
 crosswise in the center. Flasks over 48 inches wide should have two 
 rows of cross bars and two cast bars at equal distances from the end of 
 the flask. 
 
 AU copes should have a H-inch bolt running from side to side at each 
 end, and where the cope is longer than three feet it should have a bolt 
 in the center. Where copes are over 6 feet long, the bolts should be 
 
Flasks 
 
 509 
 
 spaced every two feet apart. All bolts should have large washers at 
 
 each end. 
 Drags should also have bolts at each end, but as conditions often. 
 
 prevent their use in the center, 
 
 long-nosed clamps placed cross- 
 wise every 18 to 24 inches and se- 
 curely wedged are recommended. 
 The form of flask shown above 
 
 is that most commonly used 
 
 when they are made of wood. 
 
 It is a short-lived affair, being 
 
 quickly knocked and racked out 
 
 of shape, and soon goes to the 
 
 cupola for kindling wood. Such 
 
 flasks may be greatly strength- 
 ened and their durability in- 
 creased by bolting cast-iron angles 
 
 in the corners or even reinforcing (CJ 
 
 the corners with blocks of wood, 
 
 well spiked to sides and ends. 
 
 Without greatly increasing the 
 
 cost a far better flask is made 
 
 by making the ends of cast iron. 
 
 Such flasks are in common use 
 
 for making cylinders or other 
 
 castings, requiring large circular cores as per following sketch. 
 
 Flasks of similar construction 
 are often used for cylinders as 
 large as 20 inches diameter of 
 bore. The sides of the flask 
 must be made of plank from 3 
 to 4 inches thick depending on 
 the size. For rectangular flasks 
 made of wood and iron, the con- 
 struction shown below, offered 
 by Mr. P. R. Ramp, is excellent. 
 
 __ The suggestion to core the 
 
 •^J-* trunnion, as at yl, is also valu- 
 
 FiG. 147. able, as it greatly reduces the 
 
 chance of unsoundness at that point. 
 Flasks that are heavy enough to require trunnions should have iron 
 
 ends. The trunnions may be cast on the ends or on trunnion plates, 
 
 which are bolted to the ends. 
 
 Fig. 146. 
 
Sio 
 
 The Moulding Room 
 
 Iron Flasks 
 
 Although the first cost is somewhat greater, iron flasks soon pay for 
 themselves by durability. They are stronger, more rigid and reduce 
 the liabihty to swells and rim-outs. 
 
 The copes and drags of small iron flasks are usually made each in 
 one piece. At the joints for flasks with straight sides, flanges extend 
 all the way around the inside. 
 
 The handles may be of wrought iron cast in place, or, of cast iron, for 
 sizes requiring two men to lift the cope. 
 
 Some are made with sides turned 
 up edgewise like troughs, so that the 
 greatest length and breadth will be 
 at the middle of the section. 
 
 These are more expensive to mould 
 and present no advantages over 
 the flask with flat sides as shown 
 in fig. 148. 
 
 Fig. 148. 
 
 Fig. 149. 
 
 An assortment of small flasks of this description, ranging from 12 X 14 
 to 16 X 18 is of great value to any foundry. 
 
 Iron flasks of medium and large sizes are best made in sections and 
 bolted together. 
 
 Flasks of this style are made and fitted up very quickly. A few 
 patterns answer for a large assortment. With proper stop-offs, the ends 
 and sides can be lengthened or shortened as desired. 
 
 Where the copes are too large to be lifted off by hand, bosses are 
 cast on the end. These are drilled to receive a yoke and the cope may 
 then be lifted by crane and turned. 
 
 If the flask is heavier than can be safely lifted with such a yoke, 
 trunnions may be made on the ends and heavier lifting gear employed. 
 
 The requirements for heavy flasks are so varied that it is impossible 
 to specify any general type. 
 
 By making them in standard sections as much as possible, having 
 
Iron Flasks 
 
 511 
 
 the parts interchangeable, a rectangular flask of almost any required 
 dimensions may be constructed. By so doing the number of flasks is 
 greatly reduced. 
 
 O QO 0|P 0|5| O 
 
 O I O O 
 
 o,ix, p o o| o o 13 ,jif> 
 
 )'xr'o o 
 
 o 
 ) o o 
 
 Section A-B 
 
 ^ 
 
 V 2 y^ 
 
 
 )~ 1™ 
 
 
 ^ — ' 
 
 a, 1 
 
 l<^ 
 
 ^ 6 M 
 
 Fig. 150. 
 
 Care must be taken to number and store the parts systematically so 
 that they may be readily accessible. 
 
 It is seldom that a large flask will need to be less than 6 feet by 8 feet, 
 and 12 inches deep. Starting with the end pieces 6 feet X i foot, and 
 having four distance pieces, each i, 2, 3 and 4 feet long, ends can be 
 assembled 6, 8, 10, 12, 14, 16 and 18 feet long; by duplicating the parts, 
 the depth of cope or drag can be made any number of even feet. 
 
 Where the depth of cope or drag is over one foot, it is desirable to 
 break joints in lapping the sections. 
 
 It is better to have the trunnion plates loose, so that they may be 
 bolted to any of the 4 or 6 feet lengths. 
 
 ^ 
 
 ^ 
 
 
 
 \m.t 
 
 Jo o C 
 3 O C 
 
 Fig. 151. 
 
 The top and bottom edges must be planed and the holes in ends and 
 sides drilled to templets. 
 
 Flanges top and bottom must be from 3^^ to 4 inches wide, and the 
 4 and 6 feet sections drilled at the center of flanges for pins. The 
 
512 
 
 The Moulding Room 
 
 planed surface need only be H inch wide; the flanges should drop away 
 from edges from H to Vie inch. 
 
 The web of sections should be ^/i inch thick and the 
 flanges iH inches. 
 
 The Hfting is in most cases done by attaching to 
 the flanges, but where the weight is too great to be 
 safely borne by these flanges, heavy wrought-iron 
 loops are bolted to the sections, for points of attach- 
 ment. 
 
 On page 98, "American Foundry Practice," Mr. 
 West shows an admirable form of extension flask for 
 moderate sizes. 
 
 "The handles W, W, are of wrought iron cast into 
 the flask. They are placed on a slant so as to be in line with the chains 
 when lifting. Guides X, X should be cast on for driving stakes along 
 the side. The plate Y forms the end of flask. Should it be desired to 
 make the flask longer, distance pieces may be bolted in between the 
 flask proper and the plate Y. 
 
 Fig. 152. 
 
 
 ^ 1 i 
 
 i 
 
 \\\ 
 
 
 
 .^-^^ S-^ 
 
 
 vf-^ri) 
 
 
 
 
 r 1 
 
 i. 
 
 
 1 1 
 
 
 1 
 
 
 
 I i 
 
 y 
 
 1 
 
 € 
 
 
 1 1 
 
 1 
 
 1 
 
 
 Q 
 
 I 
 
 
 im 
 
 D 
 
 ol loM 
 
 1 j il Y 
 1 'OU 
 
 
 |o 
 
 Fig. 153. 
 
 "To accomplish the same purpose, the whole flask may be c^st in one 
 piece, and the bottom edge of Y cut out H of an inch so there may 
 be no bearing on the joints. When a longer flask is wanted a section 
 may be bolted to it. This is not as desirable as the form shown in 
 sketch." 
 
 Flasks of this style are commonly used as copes to cover bedded work. 
 
Iron Flasks 
 
 513 
 
 Where the conditions do not warrant the extension flask as above 
 described special flasks are more or less in demand. 
 
 30 
 :; 
 Jo 
 
 000 
 
 
 000 
 
 000 
 
 
 000 
 
 000 
 
 
 000 
 
 000 
 
 
 000 
 
 or 
 
 oL 
 
 Jo 
 
 -.00 
 
 -!o 
 
 000 
 
 
 000 
 
 000 
 
 
 000 
 
 000 
 
 
 000 
 
 000 
 
 
 000 
 
 oC 
 
 p 
 ol- 
 
 Jo 
 
 T 
 
 Jo 
 
 1 
 
 
 1 
 
 000 
 
 
 000 
 
 000 
 
 
 000 
 
 000 
 
 
 
 000 
 
 io or 
 
 00^ 
 
 j oL 
 
 Fig. 154. 
 
 The above sketch represents an ordinary heavy flask (cope) say 
 6' X 12' X 3'. 
 
 In making large door frames, where the interior of the flask is not 
 used, or for similar work, it is customary to have the flask follow the 
 outline of the pattern and leave the interior vacant as shown in sketch 
 below. 
 
 
 ; ] 
 
 1 
 
 
 
 -^1 
 
 
 
 
 - rJ 
 
 ~^i 
 
 !> i 
 
 
 
 
 1 ( 1 
 
 i' ^ 
 
 
 
 
 I r 1 
 
 ! ^ 
 
 ll 
 
 
 
 
 r 1 
 
 iU 
 
 1 — r 
 
 I J 
 
 r-l 
 
 Fig. 155. 
 
 Flasks are made in all sorts of irregular shapes both in plan and eleva- 
 tion, as necessitated by the patterns. The bottom plates of heavy 
 flasks are made of cast iron. These are fastened to the bottom flange 
 of the drag by short heavy clamps. Thus. 
 
 Circular flasks are in common use. They 
 serve as copes to wheels cast in the floor 
 and for other purposes. For large wheels 
 which are swept up, instead of sweeping out 
 the face in a pit, large rings are used for the 
 cheek. The arms and hub are made with ^^^' ^5^" 
 
 cores and interior of wheel swept up and not disturbed subsequently. 
 
514 
 
 The Moulding Room 
 
 The cheek is rammed up against segments, and when lifted gives free 
 access to all parts for finishing. 
 
 Fig. 157, 
 
 For wheels 16 to 18 feet in diameter the cheeks are cormnonly made 
 in six segments, which are bolted together. 
 
 Fig. 158, 
 
 Flasks made of sheet steel pressed to shape are light and convenient. 
 
 They are, however, much 
 more expensive. They are 
 not as durable as cast-iron 
 flasks, and when worn out 
 are of no value; whereas 
 with the cast flasks, noth- 
 ing is lost but the labor. 
 The cuts following from a 
 manufacturer's catalogue 
 show standard types of 
 Ught and heavy flasks. 
 
 I 
 
 
 • 
 
 
 
 » 
 
 Fig. 159. 
 
Sterling Steel Flasks 
 
 515 
 
 Sterling Steel Flasks 
 
 The scarcity and increased cost of good flask lumber is making it 
 necessary for foundrymen to consider other flasks than wooden ones. 
 
 The line of steel flasks shown herewith combine strength, durability, 
 lightness and efficiency. They will give splendid service. They have 
 in many instances entirely supplanted wooden flasks, to the advantage 
 of the user in every instance. 
 
 Style "A" Square Ribbed Tight Flask 
 
 Sheet Steel with Malleable Trimmings 
 
 Stock Sizes 
 
 Height cope and drag, 23-^2, 3, 3H, 4, 4H 
 and 5 inches. 
 
 Length cope and drag, 12, 14, 16 and 18 
 inches. 
 
 Width cope and drag, 12, 14 and 16 
 inches. 
 
 Weight less than one-half as much as cast 
 flasks and practically indestructible. 
 
 A complete small square-ribbed steel flask for general work in all 
 foundries, made in above standard sizes, from which innumerable 
 combinations can be made. 
 
 Can be made in special sizes when it is required and a sufficient num- 
 ber ordered to warrant the extra work in manufacturing. 
 
 Fig. 160. 
 
 Style "B" Round Ribbed Tight Flask 
 
 Sheet Steel with Malleable Trimmings 
 
 Stock Sizes 
 
 Height cope or drag, 2)'^, 3, 3H, 4, 4^, 
 and 5 inches. 
 
 Diameter, 12, 14, 16, and 18 inches. 
 From the above dimensions many com- 
 binations can be made. 
 
 The illustration gives a clear idea of 
 round-ribbed steel flask for general cir- 
 cular work, when the snap flask is not 
 desirable. 
 
 Weighs less than half as much as a cast flask, and is unbreakable. 
 
 Fig. 161. 
 
5i6 
 
 The Moulding Room 
 
 Style "C" Square Con\'ex Tight Flask 
 Sheet Steel with Malleable Trimmings 
 Stock Sizes 
 
 Height cope or drag, 2^^, 3, 3^, 4, 4^ 
 and 5 inches. 
 
 Length cope or drag, 12, 14, 16 and 
 18 inches. 
 
 Width cope or drag, 12, 14 and 16 
 inches. 
 
 Fig. 162. Made in the above stock sizes, which 
 
 admit of comitless combinations of sizes. 
 
 This flask is particularly adapted to brass, bronze, or any special 
 metal foundry work. It is a new departure, having convex sides and ends 
 for holding the sand. It does nice work, and while not half as heavy 
 as the cast flask, is much more durable. 
 
 Style "F" Channel Iron Floor Flask 
 
 Fig. 163.. 
 Stock Sizes 
 
 Size, 
 inches 
 
 Depth, 
 inches 
 
 Cope, 
 inches 
 
 Drag, 
 inches 
 
 Price 
 
 20x24 
 20x28 
 24x30 
 24x36 
 30X36 
 30X42 
 
 10 
 10 
 12 
 12 
 14 
 .4 
 
 5 
 
 I 
 
 6 
 7 
 7 
 
 S 
 S 
 6 
 6 
 
 7 
 7 
 
 
 
 
 
 
 
 
Snap Flasks 
 
 S17 
 
 This is a decided departure in flask manufacture. It is constructed 
 of structural channel steel with flanges to the outside, having a smooth 
 wall on the inside. The interior is provided with staples arranged at 
 intervals to permit of inserting corrugated swivel gaggers for sand 
 supports. 
 
 This type of flask does away with the flask maker entirely, as each 
 moulder arranges his gaggers or sand supports to suit the necessity. 
 
 An equipment of these flasks is an excellent investment, 
 
 1. They cut out the use of expensive material (lumber). 
 
 2. They practically do away with the flask maker. 
 
 3. They eliminate expense of handling flasks. 
 
 4. They will remain in foundry and save storage. 
 
 5. And the most important feature to be considered is the increased 
 output, better castings', less scrap, all of which will appeal directly to 
 the proprietor. 
 
 These floor flasks are furnished with a complete equipment of corru- 
 gated swivel gaggers for sand supports which the moulder arranges 
 easily to suit requirements. 
 
 Snap Flasks 
 
 Snap flasks are used by bench molders for light work. They must 
 be easily and quickly handled, although snaps are sometimes made so 
 large as to require two men. The flask is removed from the mould, hence 
 one flask serves for an entire floor. 
 
 They are usually made of cherry or mahogany; the hinges should 
 lock and unlock quickly and be rigid when locked. The corners are 
 Strengthened with iron corner bands, and the cope is faced on top with 
 
5i8 
 
 The Moulding Room 
 
 iron. For special work the joint may be made to conform with the 
 parting. Rectangular snap flasks 3 feet long by 14 to 16 inches wide 
 are not uncommon. For some classes of work round snaps are required. 
 
 In the hands of a rapid, skillful moulder the snap flask is an indispen- 
 sable implement for a foundry having large quantities of small work. 
 
 Pieces weighing as much as 100 pounds may be made in the snap 
 flask. 
 
 The cuts herewith illustrate the construction of the different kinds 
 of snaps referred to. 
 
 Snap flasks of standard dimensions from i2Xi2toi2X2o can be 
 purchased of most of the foundry supply houses. 
 
 Where many moulds are to be made from one pattern, a match board, 
 on which the patterns are placed, and upon which the parting is made, 
 is practically a necessity. If these matches are not to be preserved, 
 and are only to be used for a moderate number of moulds, they are made 
 of moulding sand and fine sharp sand, half and half, stiffened with molasses 
 water, or linseed oil, and dried; but if a permanent match board is desired, 
 a mixture composed of one-half new moulding sand, one-half parting 
 sand, >4o litharge, mixed with linseed oil and tKoroughly dried will serve 
 admirably. The match should be varnished with shellac and kept with 
 the pattern. Such a match board is shown in Fig. 165.. 
 
 Fig. 165. 
 
 Fig. 166. 
 
 The moulds made in snap flasks must be covered with weights before 
 they are poured. The weight should be about iH inches thick and 
 should cover the cope entirely. 
 
 Where the contents of the flask are quite heavy, or where the patterns 
 approach the sides of the flask closely, the moulds require to be sup- 
 ported by boxes, as well as to be weighted. For this purpose wood 
 boxes of i-inch lumber are made so that the interior shaU have the 
 same dimensions as the interior of the whole flask (cope and drag); 
 this is shoved down over the mould and supports it against lateral 
 pressure. Care must be taken that the boxes are not so small as to 
 shave the mould nor so large as not to support it; they should just fit all 
 around. 
 
 These boxes are sometimes made of cast iron. Very serviceable ones 
 made of sheet iron can be purchased at moderate prices. 
 
Pins, Plates and Hinges 
 
 519 
 
 Galvanized Iron Slip Boxes 
 Straight Taper 
 
 Fig. 167. 
 
 The above are undoubtedly the best slip boxes on the market. They 
 are more durable than wood or cast-iron boxes, are lighter and will not 
 break by falling. They are made either straight or tapered, of No, 23 
 iron with a No. 9 wire in top and bottom and creased. 
 
 In ordering, state whether straight or tapered and give the exact 
 size of inside of flasks. 
 
 These boxes are for light handling and will not stand careless run-outs, 
 as the hot iron will warp them. They are very rigid, however, and with 
 the ordinary one-inch margin outside of pattern there will be no run- 
 outs. 
 
 When ordering taper jackets, give taper or degree per foot on side, or 
 make sketch giving size of top and bottom, also depth of drag. 
 
 Pins, Plates and Hinges 
 
 In order that the cope of a flask, when lifted from the drag after 
 ramming, may be returned exactly to its original position, so that the 
 two parts of the mould may match perfectly, guides must be provided 
 which will insure correct closing. 
 
 These are frequently made of 
 wood, and if kept in good shape, 
 serve the purpose admirably. 
 Wooden guides are especially 
 advantageous for long lifts. 
 
 Fig. 168 shows a wood guide, 
 of which there should be at 
 least three on the flask. The 
 moulder must exercise care when 
 preparing to ram up a flask, to 
 see that the guides and pins are securely nailed, that there is no lateral 
 play and that the cope may be lifted and returned to its place with- 
 out sticking at the pins. 
 
 Guides of this kind, while chiefly in use on wood, are sometimes 
 employed on large iron flasks. In the latter case wooden blocks are 
 
 Fig. 168. 
 
520 
 
 The Moulding Room 
 
 securely fastened in the pockets between flanges, and the guides nailed 
 to the blocks. 
 
 The usual guide for the ordinary wood flask is a common cast-iron 
 plate and pin. 
 
 These are continually getting loose and 
 furnish no end of trouble to the moulder 
 
 Fig. 170. 
 
 as well as causing many castings to be scrapped. It is the most worth- 
 less appliance of its kind. 
 A very good iron guide may be made as per sketch. (Fig. 170.) 
 
 m 
 
 (S);^, 
 
 ^ 
 
 HEAVY HIMOE 
 Fig. 171. 
 
 Such a guide may be fastened 
 rri to the flask with very little 
 more work, and the flanges give 
 good support. An excellent 
 pin and guide is made tri- 
 angular in shape. 
 
 Cast-iron flasks either have 
 
 lugs to receive the pins and 
 
 holes, or where the flanges are 
 
 wide, pin holes are put in 
 
 - — * them. 
 
 Fig. 172. -Light Hinges. pj^^ ^^^ .^^^ ^^^^^ ^^^^^^ 
 
 be accurately turned, the sizes should be standard, and those of each 
 
 -^ m 
 
Pins, Plates and Hinges 
 
 521 
 
 size interchangeable. An assortment of such pins should always be 
 kept on hand. 
 
 Fig. 173. — Ball and Socket Hinge. 
 
 E 
 
 i2!h 
 
 
 
 Fig. 174. — Heavy Hinge. 
 
 Standard Iron Flask Pin No. 2 
 For Iron Flasks 
 
 Fig. 175. 
 
 This is a nicely turned pin, with thread chased and hexagon nut, 
 designed especially for cast-iron flasks. 
 
522 
 
 The Moulding Room 
 Sweeps 
 
 Fig. 176. 
 
 The above sketch shows the ordinary sweep used for making large 
 pulleys, fly wheels, etc. A large class of work, circular in horizontal 
 section, can be made with the sweep, thereby saving largely in the 
 expense for patterns. 
 
 To obtain accurate work by the use of the sweep, the stepping A 
 must be firmly placed, so that the axis of the spindle B shall be vertical. 
 The upper support D must be held rigidly, either by braces to wall of 
 foundry or otherwise as most convenient. The box D may be made 
 with a flange surrounding it from which three or four rods lead away 
 to any suitable anchorages. These rods are provided with tumbuckles 
 so that the spindle may be held rigidly in a vertical position. 
 
 E is an adjustable collar fastened in position by a set screw. 
 
 C is an iron arm carrying the wood strikes. The bearings by which 
 this arm is supported should be farther apart than the width of the 
 arm, so as to avoid any sagging of the latter. 
 
 If these bearings are split in a direction parallel to the spindle and 
 drawn up with clamp screws, lost motion can be taken up at any time. 
 Any play in the supports for the arm, or neglect to maintain the spindle 
 in a vertical position, will result in a distorted casting. Sweeps are 
 
Anchors, Gaggers and Soldiers 
 
 523 
 
 often constructed with elaborate mechanical attachments for making 
 gears, spiral wheels, spiral cones, etc. 
 
 Sometimes the steppings are placed permanently on concrete piers, 
 where there are many wheels, etc., to be made. 
 
 The strikes are cut in any desired shape and are used for inside or 
 outside sweeping. Swept moulds are usually skin dried. 
 
 Anchors » Gaggers and Soldiers 
 
 These devices are used for sup- 
 porting the sand where the ordinary 
 bars are insufficient or inapplicable. 
 
 Fig. 177 shows an anchor used 
 for making pulleys. It consists 
 of six cast-iron segmental plates 
 about Vi inch thick, which are 
 so placed between the arms of 
 the puUey as to leave a space for 
 sand, % inch wide, all around them. 
 The upper sides of the plates are 
 on the parting line of the arms. 
 
 The plates are held together by 
 wrought iron loops, passing over 
 the arms, and cast in place. All 
 the plates are poured at once,' and 
 in open sand. 
 
 Instead of wrought-iron loops, 
 
 WFf] 
 
 Fig. 177. 
 
 these connections may be made by 
 cast-iron loops, furnishing a much stiffer anchor. 
 On the under side of each plate are cast one or. 
 more long conical projections, which serve as 
 guides by which to replace the anchor. Each 
 plate is provided with an eye bolt long enough to 
 reach to the joint of flask. 
 
 The interior parting is made on center line of 
 arms, sand is rammed on top of the anchor and 
 another parting made flush with the rim upon 
 which the cope is rammed. 
 
 After the cope is removed, the sand covering 
 the arms is lifted out by hooking to the eye bolts 
 in anchor. 
 
 Fig. 178 shows an anchor for lifting out a 
 
524 The Moulding Room 
 
 Where the anchor cannot rest on the bottom, but must permit iron 
 to nm under it, it is bolted to the cope and Hfted out with it. 
 
 The necessities of the situation indicate the size and shape of anchors. 
 Frequently, the pocket is such that the anchor must be broken to remove 
 it from the casting. It is well to keep down the weight of the anchors 
 as much as possible, relieving the cope to that extent. 
 
 Very many cores, as well as moulds, require to be supported in this 
 manner. * 
 
 Gaggers 
 
 In the use of gaggers it should be borne in mind, that they are heavier 
 than the sand; it is simply due to the cohesion of the sand, holding 
 them up to the sides of the flask or bars, that they are of assistance in 
 supporting the cope. The gagger is of use just in proportion to the 
 length that is surroimded with packed sand. All that part which pro- 
 jects above the cope is a detriment. They are first immersed in thick 
 clay wash, and placed flat up against the bars or sides of flask, having 
 about % inch sand under them. They are made in the gagger mould, 
 already described, which is kept near the cupola. Costing practically 
 nothing, they may be used freely. A good supply should always be 
 kept on hand. 
 
 Many shops use gaggers made of Vi inch square bar iron bent to 
 shape. They are not as serviceable, however, as they do not offer as 
 good a surface to which the sand can adhere, and are more expensive. 
 
 Soldiers 
 
 Soldiers are simply pieces of wood about one inch square, cut from 
 boards, with clay washed and placed around the mould instead of gag- 
 gers, where the latter cannot be used; or to assist the gaggers in deep 
 lifts. The sand adheres to soldiers better than to gaggers. 
 
 The free use of either gaggers or soldiers is to be encouraged, as it 
 is better to place too many of them in a mould than to have a drop. At 
 the same time care must be exercised to have the ends well protected 
 by sand, so that the hot iron will not come in contact with them, as 
 there will surely be a "blow" in that event. 
 
 Sprues, Risers ajid Gates 
 
 The following tables, giving the equivalent areas of round gates, also 
 of square and rectangular gates as compared with round ones, are taken 
 from West's "Moulder's Text Book," pp. 245 and 246. 
 
Table of Equivalent Areas of Gates 
 
 525 
 
 Table 
 
 or 
 
 Equivalent Areas of 
 
 Round Gates 
 
 
 One iH inch 
 
 is equal 
 
 in area to two 
 
 I 
 
 He, three ^, 
 
 or four %-inch gate 
 
 " 13/4 
 
 
 
 
 " 
 
 iH 
 
 
 I * 
 
 J^ 
 
 " 2 
 
 
 
 
 <( 
 
 l7l6 
 
 
 I Me 
 
 I 
 
 " 2H 
 
 
 
 
 a 
 
 iH 
 
 
 iMe 
 
 iH 
 
 " 2H 
 
 
 
 
 11 
 
 iM 
 
 
 iMe 
 
 iH 
 
 " 2% 
 
 
 
 
 (I 
 
 I^Me 
 
 
 iH 
 
 1% 
 
 " 3 
 
 
 
 
 u 
 
 2^^ 
 
 
 1% 
 
 iH 
 
 " 3H 
 
 
 
 
 u 
 
 2M6 
 
 
 I^i 
 
 i5i 
 
 " 3H 
 
 
 
 
 (I 
 
 2^^ 
 
 
 2 ' 
 
 iH 
 
 " 3^'^ 
 
 
 
 
 " 
 
 2IH6 
 
 
 2?^6 ' 
 
 i^/i 
 
 " 4 
 
 
 
 
 (i 
 
 2IM6 
 
 
 2M6 
 
 2 
 
 « 4H 
 
 
 
 
 a 
 
 3 
 
 
 2V16 
 
 2H 
 
 " 4H 
 
 
 
 
 a 
 
 3M« 
 
 
 2H 
 
 2M 
 
 " 4H 
 
 
 
 
 a 
 
 3?^ 
 
 
 2% 
 
 23/i 
 
 " 5 
 
 
 
 
 " 
 
 3?i6 
 
 
 2% 
 
 2^ 
 
 Note. " The fractional parts of an inch as seen by the table are not carried out any 
 further than Me, for the reason that the subject does not call for any closer figures. 
 Therefore, the figures given will be understood as being ' nearly ' equal in area. 
 As given, the sizes can be readily discerned, and are also applicable to measurements 
 by the shop pocket rules commonly used." 
 
 Table of Eqltvalent Areas in Square and Rectangular 
 Gates to That of Round Gates 
 
 (See note above) 
 
 Round 
 
 Square 
 gates 
 
 Rectangtilar 
 
 Rectangular 
 
 Rectangular 
 
 Rectangular 
 
 gates. 
 
 gates 
 
 gates 
 
 gates 
 
 gates 
 
 inches 
 
 I inch thick 
 
 iH inch thick 
 
 2 inches thick 
 
 21-^ ins. thick 
 
 I 
 
 -'A 
 
 
 
 
 
 t^ 
 
 iMe 
 
 
 
 
 
 m 
 
 l9/i6 
 
 IX 23/^ 
 
 
 
 
 2 
 
 m 
 
 IX 3% 
 
 ii^X 2H6 
 
 
 
 2H 
 
 2 
 
 23/6 
 2M6 
 
 IX 4 
 IX 5 
 IX 6 
 
 ii/iX 2IM6 
 iHX 3^6 
 l}iX 4 
 
 
 
 2H 
 
 
 
 2% 
 
 2X3 
 
 
 3 
 
 211/16 
 
 IX 7M6 
 
 li/X 4% 
 
 2X39i6 
 
 
 3Vi 
 
 2jt 
 
 IX SMe 
 
 li^X S/2 
 
 2X4^6 
 
 2^X3M6 
 
 3H 
 
 3H 
 
 IX 9H 
 
 li/iX 6^6 
 
 2X4^i 
 
 2^X3% 
 
 3% 
 
 35/6 
 
 iXiiHe 
 
 li/^X 7% 
 
 2XS^/i 
 
 2HX4H6 
 
 4 
 
 391 6 
 
 IXI2?16 
 
 iHX &% 
 
 2X61/ 
 
 2HX5 
 
 m 
 
 33/4 
 
 1X14^6 
 
 iHX 9H 
 
 2X7^/^ 
 
 2HXSH 
 
 AVi 
 
 4 
 
 1X151^6 
 
 iI^XiqS^ 
 
 2X8 
 
 2HX6% 
 
 m 
 
 4^6 
 
 1X17% 
 
 ii/^Xili^e 
 
 2X87/i 
 
 2HX7% 
 
 5 
 
 4^6 
 
 1X19H 
 
 1HX13H6 
 
 2x913/6 
 
 2Vixm 
 
 "The term 'equivalent' used does not imply that two or more small gates having 
 a combined area equal to one large gate, all having like 'head pressure,' will deliver 
 the same amount of metal per second." 
 
526 
 
 The Moulding Room 
 
 "The flow of metal is retarded by friction in proportion to the surface 
 area with which it comes in contact. Now although four 2V^-inch round 
 gates are of equal area to one 5 -inch roimd gate, we find the frictional 
 resistance to the flow of a like 'head pressure' through four aJ^-inch 
 round gates to be double that generated in one 5-inch round gate, 
 simply because the combined circumferences of four 2H-inch round gates 
 are 31.416 inches, whereas the circumference of one 5-inch round gate is 
 15.708 inches. As gates are generally combined under varying compli- 
 cated conditions, the tables as given can be better practically used than 
 where they are lumbered with the question of frictional resistance. " 
 Risers are generally double the diameter of the pouring sprue. The 
 function of the' riser is twofold. It 
 serves to catch and carry away any 
 dirt entering the mould from the pour- 
 ing sprue and also to furnish a supply 
 of Uquid metal to provide for shrink- 
 age. Risers are placed either in con- 
 nection with the gate, or on some part 
 of the mould whence the deficiency 
 from shrinkage can be most readily 
 supplied. When located on the gate 
 the latter is usually so cut as to impart 
 a whirling motion to the metal ascend- 
 ing the riser. The metal enters the 
 riser near the bottom and flows to the mould through a channel opened 
 above the entrance. 
 
 In the sketch A represents the pouring sprue, B is the riser, C the 
 gate from sprue to riser which is cut tangential to B. D is the gate 
 from riser to casting. The gates should be somewhat smaller in area 
 than the pouring sprue so that the pouring basin E may always be kept 
 full. 
 
 Top Pouring Gates 
 
 The advantage of this form of gate 
 for large castings is that the dirt is 
 kept at the top of the poUring basin, 
 allowing the clean iron to flow into 
 the mould from beneath. 
 
 The first dash of iron may carry 
 some dirt, but the greater portion 
 of it will flow with the stream over 
 the gates; the runner being quickly 
 filled, no dirt can enter subsequently if kept full. See West's "Moulder's 
 Text Books," page 129. 
 
 Fig. 179. 
 
 Fig. 180. 
 
Horn Gates 
 
 527 
 
 Whirl Gates 
 
 The object of the whirl gate is to impart a rotary motion to the iron 
 in the basin and riser B, B. 
 
 By centrifugal force the metal is kept in contact with the exterior 
 of the riser, and the dirt is carried up in the middle of it. 
 
 Fig. 181. 
 
 The riser B should be larger than the pouring sprue A , and A should 
 be larger than C, in order that the pouring basin may be kept full. 
 
 It is best to have patterns made for whirl gates; they can be used in 
 either cope or drag. 
 
 The "Cross" Skim Gate 
 
 This as shown in Fig. 182 is an excellent device and is largely 
 used. 
 
 A is the gate leading from pouring sprue to 
 basin B, C is a, core in which is the gate D, 
 leading to casting. The iron enters B, tangen- 
 tially, a whirhng motion is imparted to it carry- 
 ing the dirt to the riser, 
 while the clean iron flows 
 out through D. 
 
 Another form of same gate is made as shown 
 in fig. 183. 
 
 It diflfers from the first form simply in having 
 a flat core E placed acrpss the gate D, instead 
 
 CP<J^ 
 
 Fig. 182. 
 
 Fig. 183. 
 of forming a part of it 
 
 Horn Gates 
 
 These are principally used for bottom 
 pouring, leading from the parting of 
 flask to the casting below. 
 
 They are made smaller at the point 
 joining the casting to permit of easy 
 removal and to choke the stream of metal. 
 
 Fig. 184. 
 
The Moulding Room 
 
 Pouring basins have frequently skimming 
 cores placed between the basin and the down 
 sprue to hold the dirt in basin. A pattern is 
 usually made for them. 
 
 Strainers and Spindles 
 
 Fig. 185. Thin perforated plates from He to %2 inch 
 
 thick, and wide enough to cover the entrance to pouring gate are fre- 
 quently placed in the runner 
 basin over the gate. When the 
 iron strikes the strainer it is held 
 back until the latter is melted 
 allowing the basin to fill partly, 
 raising the dirt to the surface 
 and furnishing clean iron to the 
 gate 
 purpose 
 
 Fig. 186. Spindle gate 
 Spindle gates consisting of many small gates serve the same 
 
 Weights 
 
 For medium castings, weighting the copes will be found more con- 
 venient than the use of binding bars. There should be about every 
 foundry a large assortment of weights depending on the class of work. 
 Weights to be handled by the crane will be found more convenient, if 
 made square in cross section and of whatever length desired. Holes 
 are cast in the ends into which bars are inserted for Hfting. Weights 
 made in this way are more readily piled than if provided with eye bolts. 
 
 Chaplets 
 
 Chaplets are properly anchors, and should come under that heading. 
 They are used mostly for securing cores in place in moulds. Except for 
 special requirements the foundryman can procure chaplets from the 
 supply houses far cheaper than he can make them. Cuts and sizes of 
 the various chaplets in use are given below. 
 
 The Peerless Perforated Chaplet 
 
 Fig. 187, 
 
Liquid Pressure on Moulds 529 
 
 Manufacturers of all classes of castings requiring small cores will 
 readily observe the advantage in using a chaplet, such as is illustrated 
 above. 
 
 Made from perforated tin-plated sheet metal, insuring perfect ven- 
 tilation of the chaplet, eliminating all possibilities of blow holes, air 
 pockets, chills, etc., forming a perfect union with the molten metal, 
 thereby insuring an absolute pressure tight joint; something not ob- 
 tained with any other chaplet on thin work. Through its use, not only 
 are time and labor of the workman saved in adjusting the cores to the 
 matrix of the mould, particularly on water backs or fronts, radiators, gas 
 burners, pipe fittings, gas and gasoline engine work, and similar castings, 
 but it also greatly lessens the hability of flaws, defects and consequent 
 losses in castings, such as commonly result from the ordinary chaplets 
 or anchors now in use. 
 
 Liquid Pressure on Moulds 
 
 The pressure of the liquid metal at any point of the mould is deter- 
 mined by multiplying the distance in inches from that point to the top 
 of the metal in pouring basin by .26 pounds. The product is the pressure 
 in pounds per square inch. 
 
 To overcome this pressure laterally, reliance is placed on the rigidity 
 of the flask, supported, if necessary, in deep castings by binding bars. 
 
 The binding bars are of same character as those already described for 
 holding down copes. They are tied across top and bottom of flask by 
 rods, or otherwise. 
 
 The static pressure on the cope is ascertained by multiplying the area 
 of the casting in square inches, at the joint of the flask by the height 
 in inches from the joint of the flask to level of iron in pouring basin 
 and by .26 pounds. 
 
 In addition to this there is the pressure due to resistance in overcoming 
 the velocity of the rising iron, which pressure is measured by one-half 
 the product of the weight of the rising iron by the square of the velocity. 
 WTiile this pressure may be acciurately calculated with sufficient data, 
 it is usually difficult to get them, and the results are, therefore, only 
 approximate. 
 
 However, when the mould is nearly full, the pouring is slackened as 
 much as possible without letting the dirt into the sprue, thereby reduc- 
 ing the head and velocity, and greatly lessening the shock as the iron 
 reaches the cope. 
 
 The formulae given for determining holding down weights for copes 
 are empirical. The moulder will not be led astray by calculating the 
 lifting area of the mould in square inches, multiplying this by the head 
 
53d 
 
 The Moulding Room 
 
 measured to pouring basin, in inches, and this product by .26 pounds- 
 Add 20 per cent to the result, this will make ample provision for the 
 lift due to the blow of the rising iron. 
 
 The Peerless Perforated Chaplet 
 
 The following list will give an idea of the approximate number of the 
 various sized chaplets required to make a pound. 
 
 Length 
 
 Breadth 
 
 Thickness 
 
 No. to the 
 pound 
 
 % 
 
 H 
 
 % 
 
 1600 
 
 Vi 
 
 % 
 
 H 
 
 1400 
 
 Vz 
 
 Yi 
 
 H 
 
 1200 
 
 Vi 
 
 Vi 
 
 3/16 
 
 IIOO 
 
 % 
 
 % 
 
 3/16 
 
 600 
 
 I 
 
 I 
 
 M 
 
 300 
 
 % 
 
 % 
 
 H 
 
 250 
 
 
 
 H 
 
 130 
 
 
 
 % 
 
 100 
 
 iH 
 
 iVi 
 
 Vi 
 
 80 
 
 
 
 Yi 
 
 90 
 
 iH 
 
 IH 
 
 3/4 
 
 80 
 
 
 
 3/4 
 
 45 
 
 2H 
 
 
 I 
 
 35 
 
 
 
 I 
 
 40 
 
 m 
 
 1 1/4 
 
 I 
 
 30 
 
 Over two thousand different shapes, sizes and styles of these chaplets 
 are made. Many hundred standard sizes and shapes are kept in stock. 
 
 The prices depend upon the sizes and number required to make a 
 pound. 
 
 The Peerless Perforated Chaplet. — {Continued) 
 
 (Net prices per pound.) 
 
 No. to the 
 
 1 
 Price per 
 
 No. to the 
 
 Price per 
 
 pound 
 
 pound 
 
 pound 
 
 pound 
 
 20- 40 
 
 $0.35 
 
 200- 2SO 
 
 S0.8S 
 
 40- 50 
 
 .35 
 
 250- 300 
 
 .90 
 
 50- 60 
 
 .40 
 
 300- 3SO 
 
 95 
 
 60- 70 
 
 .45 
 
 350- 400 
 
 1. 00 
 
 70- 80 
 
 .50 
 
 400- 500 
 
 1.05 
 
 3o- 90 
 
 .55 
 
 500- 600 
 
 1. 10 
 
 90-100 
 
 .60 
 
 600- 700 
 
 I. IS 
 
 ioa-125 
 
 .65 
 
 700- 800 
 
 1.20 
 
 125-IS0 
 
 .70 
 
 800- 900 
 
 1.25 
 
 150-175 
 
 .75 
 
 900-1000 
 
 1.30 
 
 175-200 
 
 .80 
 
 lOOO-IIOO 
 
 1. 35 
 
ChapletS 
 
 531 
 
 Double Head Chaplet Stems 
 
 Plain or Tinned 
 inch round iron, H to i H inches long (measur- 
 
 Made of 
 ing from face to shoulder). 
 
 Price per hundred, from ^A to iH inches . 
 Price per hundred, from iH to 2^4 inches. 
 
 $4.00 
 5.00 
 
 ^^p 
 
 Fig. 188. 
 
 Fig. 189. 
 
 Double Head Chaplets with Forged Heads 
 
 Plain or Tinned 
 
 Made of %-inch round iron, from H to 2H inches long, 
 with head above %-inch diameter. 
 
 Price per hundred, from H to iH inches. . $5.00 
 Price per hundred, from iJ^^ to 2H inches. 6.00 
 
 With Square or Round Plates Fitted 
 
 Plain or Tinned 
 
 Fig. 190. 
 
 Square plates always furnished unless otherwise ordered. 
 Stems made of He inch round iron from ¥& to iH inches long. 
 
 Price per hundred, % to ^A inch with plates any size $4.00 
 
 Price per hundred, H to i inch with plates any size 4 -50 
 
 Price per hundred, i>i to iH inch with plates any size. . . 5 .00 
 
 Stems made from M-inch round iron from H to 2H inches long. 
 
 Price per hundred, H to i inch with plate any size $6.00 
 
 Price per hundred, i to iH inches with plate any size. . , " 
 Price per hundred, i^^ to 2 inches with plate any size.. . . " 
 Price per hundred, 2 to 2H inches with plate any size "' 
 
532 
 
 The Moulding Room 
 
 Price List of Double Head Chaplet Stems 
 
 (Plain or tinned with square plates fitted, heavy stem and plate.) 
 
 Diameter 
 of stem 
 
 Length 
 
 I 
 
 m 
 2 
 
 214 
 
 3K2 
 3% 
 4 
 
 4K 
 
 4K2 
 
 I 
 
 m 
 2 
 
 2H 
 2l/^ 
 2% 
 
 3 
 
 3H 
 3!/^ 
 3% 
 4 
 
 4}4 
 
 4^/4 
 5 
 
 Per 100 
 
 $8.00 
 8.00 
 9.00 
 10.00 
 11.00 
 12.00 
 1300 
 14.00 
 15.00 
 16.00 
 17.00 
 18.00 
 19.00 
 20.00 
 21.00 
 22.00 
 23.00 
 24.00 
 9.00 
 9.00 
 10.00 
 11.00 
 12.00 
 1300 
 14.00 
 15.00 
 16.00 
 17.00 
 18.00 
 19.00 
 20.00 
 21.00 
 22.00 
 23.00 
 24.00 
 25.00 
 
 Diameter 
 of stem 
 
 Length 
 
 Per 100 
 
 ^ 
 
 $10.00 
 
 I 
 
 10.00 
 
 iVi 
 
 11.00 
 
 1]^ 
 
 12.00 
 
 m 
 
 1300 
 
 2 
 
 14.00 
 
 2K 
 
 15.00 
 
 2H 
 
 16.00 
 
 2% 
 
 17.00 
 
 3 
 
 18.00 
 
 M 
 
 19.00 
 
 3H 
 
 20.00 
 
 3% 
 
 21.00 
 
 4 
 
 22.00 
 
 4H 
 
 23.00 
 
 4H 
 
 24.00 
 
 4% 
 
 25.00 
 
 5 
 
 26.00 
 
 li 
 
 11.00 
 
 I 
 
 11.00 
 
 iH 
 
 12.00 
 
 i>i 
 
 1300 
 
 1% 
 
 14.00 
 
 2 
 
 1500 
 
 2M 
 
 16.00 
 
 2\i 
 
 17.00 
 
 2% 
 
 18.00 
 
 3 
 
 19.00 
 
 3M 
 
 20.00 
 
 3>^ 
 
 21.00 
 
 3% 
 
 22.00 
 
 4 
 
 23.00 
 
 AM 
 
 24.00 
 
 AM 
 
 25.00 
 
 A% 
 
 26.00 
 
 5 
 
 27.00 
 
Wrought-Iron Chaplet Stems 
 
 533 
 
 Wrought-Iron Chaplet Stems with Square or 
 Round Plates Fitted 
 
 Plain or Tinned 
 
 Fig. 191. 
 
 Square plates always furnished unless otherwise specified. 
 Price per Hundred 
 
 Diameter of plates . . 
 Thickness of plates . 
 Diameter of stem. . . 
 
 iVi ins. 
 
 ij^ ins. 
 
 1% ins. 
 
 2 ins. 
 
 21-^ ins. 
 
 He in. 
 
 %4 in. 
 
 \i ins. 
 
 1 Mi in. 
 
 Me in. 
 
 Hin.- 
 
 Me in. 
 
 % in. 
 
 H2 in. 
 
 5/8 in. 
 
 $3.10 
 
 $5.10 
 
 • $6.70 
 
 $11.30 
 
 $20.00 
 
 3. IS 
 
 5. IS 
 
 6.80 
 
 II. 4S 
 
 20.2s 
 
 3.20 
 
 S.20 
 
 6.90 
 
 11.60 
 
 20.50 
 
 3.25 
 
 5.25 
 
 7.00 
 
 II. 7S 
 
 20.7s 
 
 3.30 
 
 5.30 
 
 7.10 
 
 11.90 
 
 21.00 
 
 3.35 
 
 S.3S 
 
 7.20 
 
 12. OS 
 
 21.25 
 
 3.40 
 
 5.40 
 
 7.30 
 
 12.20 
 
 21.50 
 
 3.45 
 
 S.4S 
 
 7.40 
 
 12. 3S 
 
 21.75 
 
 3.50 
 
 5. SO 
 
 7. SO 
 
 12.50 
 
 22.00 
 
 3.55 
 
 S.55 
 
 7.60 
 
 12.65 
 
 22.25 
 
 3.60 
 
 5. 60 
 
 7.70 
 
 12.80 
 
 22.50 
 
 3.70 
 
 S.70 
 
 7.90 
 
 13.10 
 
 23.00 
 
 3.80 
 
 5.80 
 
 8.10 
 
 13.40 
 
 23.50 
 
 3.90 
 
 S.90 
 
 8.30 
 
 13.70 
 
 24.00 
 
 4.00 
 \ 
 
 6.00 
 
 8. so 
 
 14.00 
 
 24.50 
 
 1 - 
 
 • SO 
 
 .60 
 
 .75 
 
 .90 
 
 3 ins. 
 Yi in. 
 
 Vi in. 
 
 Length, inches 
 3 
 
 zY^ 
 
 4 
 
 aM 
 
 5 
 
 SH 
 
 6 
 
 m 
 
 7 
 
 7^ 
 
 8 
 
 9 
 
 10 
 
 11 
 
 12 
 
 Net prices for curv- 
 ing plates to suit 
 diameter of core 
 
 $31.25 
 31.62 
 32.00 
 32.37 
 32.75 
 33.12 
 33.50 
 33.87 
 34-25 
 34.62 
 35. 00 
 35.75 
 36.50 
 37.25 
 38.00 
 
 1. 25 
 
534 
 
 The Moulding Room 
 
 Wrought-Iron Chaplet Stems 
 
 Plain or Tinned 
 
 \sfYmv 
 
 Fig. 192. 
 Price per Hundred 
 
 Length, 
 measuring from 
 
 Diameter 
 
 face to stem, 
 inches 
 
 H 
 
 5/16 
 
 % 
 
 1/^ 
 
 % 
 
 % 
 
 3 
 
 $2.40 
 
 2.45 
 2. so 
 2.55 
 2.60 
 2.65 
 2.70 
 2.7s 
 2.80 
 2.85 
 2.90 
 2.95 
 300 
 3 OS 
 3.10 
 
 $3 fi=: 
 
 S4.50 
 4.60 
 4.70 
 4.80 
 4.90 
 5.00 
 5.10 
 5.20 
 5.30 
 5.40 
 5.50 
 5.70 
 5. 90 
 6.10 
 6.30 
 
 % 8.2=; 
 
 $13.00 
 13.25 
 13.50 
 13.75 
 14.00 
 14.25 
 14.50 
 14.75 
 1500 
 15.25 
 15.50 
 16.00 
 16.50 
 17.00 
 17.50 
 
 $19.20 
 
 31^ 
 
 3 
 3 
 3 
 3 
 3 
 3 
 4 
 4 
 4 
 4 
 4 
 4 
 4 
 
 70 
 75 
 80 
 85 
 90 
 95 
 00 
 05 
 10 
 20 
 
 25 
 
 30 
 
 35 
 
 8 
 8 
 8 
 8 
 9 
 9 
 9 
 9 
 9 
 9 
 10 
 10 
 10 
 
 40 
 55 
 70 
 85 
 00 
 15 
 30 
 45 
 60 
 85 
 20 
 55 
 90 
 2=; 
 
 19.60 
 
 4 • • 
 
 20.00 
 
 aH . 
 
 20.35 
 
 5 
 
 20.85 
 
 S^i 
 
 21.20 
 
 6 
 
 21.60 
 
 6H 
 
 21.95 
 
 7 
 
 22.30 
 
 71^ 
 
 22.65 
 
 8 
 
 23.00 
 
 9 
 
 23.75 
 
 10 
 
 24.50 
 
 II 
 
 25.25 
 
 12 
 
 
 
 
 
 
 Gray Iron Chaplets 
 
 Fig. 193. 
 
 Length, inches. . . H % Vi % H % i 
 
 Per hundred ... . $0.72 $0.78 $0.84 $0.90 $1.00 $1.10 $1.20 
 
 Length, inches. . . xM iH iH i^^ iH 2 
 
 Per hundred $1.40 $1.60 $1.70 $1.80 $2.20 $3.00 
 
 Double Head Water Back Chaplets 
 
 Made of ^ie-inch round iron, from H to 2H inches long, 
 with heads about % inch in diameter. 
 
 Price per hundred, from H to iH inches. ... $5.00 
 Price per hundred, from iVz to 2>^ inches. . . 6.00 
 
 Fig. 194. 
 
Radiator Chaplets 
 
 535 
 
 Wrought-Iron Chaplets with Forged Heads 
 
 Plain or Tinned 
 
 Fig. 195. , 
 Price per Hundred 
 
 Diameter of head. . . 
 
 1/^,1 He 
 and 1^6 
 
 i}i 
 
 iH 
 
 m 
 
 iH 
 
 2 
 
 Diameter of stem. . . 
 
 and Vi 
 
 Vie 
 
 H 
 
 V2 
 
 H 
 
 H 
 
 Length, inches 
 3 
 
 ?2.40 
 
 2.45 
 2.50 
 2.55 
 2.60 
 2.6s 
 2.70 
 2.75 
 2.80 
 2.85 
 2.90 
 2.95 
 3.00 
 3.0s 
 3.10 
 
 .40 
 
 $3.6^ 
 
 $4.50 
 4.60 
 4.70 
 4.80 
 4.90 
 
 5-00 
 5.10 
 5.20 
 5.30 
 S.40 
 5.50 
 5.70 
 5.90 
 6.X0 
 6.30 
 
 .75 
 
 $ 8.25 
 8.40 
 8.55 
 8.70 
 
 8.8s 
 9.00 
 915 
 930 
 9-45 
 9.60 
 9.85 
 10.20 
 10.55 
 10.90 
 11.25 
 
 1. 00 
 
 $13.00 
 13.2s 
 13.50 
 13.75 
 14.00 
 14.2s 
 14.50 
 14.75 
 
 IS. 00 
 
 15.25 
 15.50 
 16.00 
 16.50 
 17.00 
 17.50 
 
 1.25 
 
 $19.20 
 19.60 
 
 3H 
 
 3 
 3 
 3 
 3 
 3 
 3 
 
 70 
 75 
 80 
 85 
 90 
 95 
 00 
 05 
 10 
 20 
 25 
 30 
 35 
 40 
 
 60 
 
 
 4^ ••• 
 
 20.35 
 20.85 
 21 20 
 
 SH 
 
 6 
 
 
 6}^.. 
 
 21.95 
 22.30 
 22.65 
 23.00 
 23.75 
 24.50 
 25.25 
 26 00 
 
 7 
 
 7H 
 
 8 
 
 9 
 
 
 II 
 
 12 
 
 Net price for point- 
 ing 
 
 1.50 
 
 
 
 
 
 Single Head Water Back Chaplets 
 
 Head H inch, stem Vis inch, length to order. For price /%__» 
 list see Wrought-iron Chaplets with Forged Heads. x^T™'^ 
 
 Fig. 196. 
 
 Radiator Chaplets 
 
 I "^ Head % X %, stem and length to order. 
 
 LIT' 
 
 Special chaplets and plates made to order. 
 Fig. 197. 
 
536 
 
 The Moulding Room 
 
 Round and Square Head Chaplets 
 
 Stems made of Me-inch round iron, from 5^ to iH inches 
 long. 
 
 Plates Vi inch round and % inch square, Me, %, H, %, H, H 
 Fig. 198. ^^^ ^ '^^^^ ^ong. 
 
 Price per hundred, all sizes $3 .00 
 
 Tinned Clout Nails 
 
 ^■. 
 
 Fig. 199. 
 
 An indispensable article in the foundry. Do not rust like the ordinary 
 black cut nail. Shipped in 100-pound kegs. All lengths from Vs inch to 
 2 inches, inclusive. 
 
 List Prices 
 
 Inches 
 
 1 
 
 Per pound 
 
 3-8 
 
 $0.70 
 
 31/^-8 
 
 .60 
 
 1-2 
 
 .50 
 
 4^/^-8 
 
 .45 
 
 5-8 
 
 .43 
 
 5H-8 
 
 .41 
 
 3-4 
 
 .40 
 
 6H-8 
 
 ■ 39 
 
 7-8 
 
 .38 
 
 I and longer 
 
 .36 
 
 Pressed Tin Shell Chaplets 
 
 For certain classes of work these chaplets are inval- 
 uable. They form perfect union with the cast metal. 
 
 Sizes H inch to H inch inclusive are made in both 
 two and three prongs, ^He inch to i inch inclusive 
 are three prong only. 
 
 Fig. 200- 
 
Sprue Cutters 
 Price List 
 
 537 
 
 Size, 
 
 Two prong, 
 
 Three prong, 
 
 Inches 
 
 per thousand 
 
 per thousand 
 
 M 
 
 $300 
 
 $3.50 
 
 M 
 
 300 
 
 3. so 
 
 Me 
 
 3.20 
 
 3.70 
 
 % 
 
 3.50 
 
 4.00 
 
 Me 
 
 3.50 
 
 4.00 
 
 1/^ . 
 
 4.00 
 
 4.50 
 
 9i6 
 
 4.00 
 
 4- SO 
 
 % 
 
 4. SO 
 
 S.oo 
 
 iHe 
 
 
 S.oo 
 
 % 
 
 
 S-Oo 
 
 1^6 
 
 
 S-oo 
 
 % 
 
 
 S.25 
 5.25 
 
 1^6 
 
 
 I 
 
 
 S.2S 
 
 
 Steel Sprue Cutters 
 
 <S> % 
 
 u u 
 
 Fig. 201. 
 
 These sprue cutters are all 6 inches in length. 
 They are made of steel and in four sizes, viz. : 
 
 No. I. — H inch at bottom, % inch at top. 
 
 No. 2. — % inch at bottom, i inch at top. 
 
 No. 3. — Vi inch at bottom, iM inches at top. 
 
 No. 4. — % inch at bottom, iH inches at top. 
 
 Price 50 cents each 
 
 Brass Sprue Cutter 
 
 Fig. 202. 54-inch diameter, 10 inches long. . .$4.80 per dozen 
 
CHAPTER XXIII 
 MOULDING MACHINES 
 
 The moulding machine has become of such importance that no f oimdry 
 can afford to be without it. The reduction of cost in the production 
 of the classes of work for which it is adapted and the superiority of the 
 product as compared with hand work render the machine absolutely- 
 indispensable to the successful conduct of a foundry engaged in com- 
 petitive work. 
 
 While the moulding machine is in some respects invaluable, it must 
 not be supposed that its value can be realized without the exercise of a 
 high order of intelligence. 
 
 To produce accurate work by machine requires the utmost care and 
 accuracy in fitting up patterns and flasks. Apphances which may be 
 used successfully in hand moulding would entail disastrous results in 
 machine moulding. Again, no particular machine is adapted to all 
 kinds of work. It has a certain range for a certain character of pro- 
 duction. Without those limits its use is not warranted. 
 
 There are many kinds of machines, operated in various ways; by 
 compressed air, hydraulic pressure, mechanical pressure, gravity and 
 impact. 
 
 It is not the purpose of this book to discuss the merits of the different 
 machines. The various types have been in service long enough to 
 indicate the particular class of work to which each is best adapted. 
 One type of machine is best suited for light, small work; another to 
 stove-plate; another to car castings, etc. 
 
 In choice of machines the foundryman should profit by the experi- 
 ence of those who have preceded him in this field, and must be especially 
 cautious in not attempting to extend the range of any one type beyond 
 that for which it is particularly fitted. 
 
 There are machines which simply perform the operation of ramming; 
 others which only draw the pattern, the ramming having been done 
 by hand; while others perform both operations. In many instances 
 the character of the work determines the function of the machine. 
 
 It is doubtful, however, if hand ramming for deep pockets, etc., can 
 be dispensed with by use of the machine. In fact, except in cases where 
 the plainest character of work is produced, it is a mistake to believe 
 
 538 
 
Moulding Machines 539 
 
 that the moulding machine does not reqmre the services of an experienced 
 moulder. 
 
 Mr. S. H. Stupakoff, in his comprehensive paper on the moulding 
 machine, referring to the object of the machine as one to save labor, to 
 increase the output, to decrease cost of production, to produce uniform 
 and better castings, etc., says: 
 
 "It is obvious that it would require a complicated mechanism to per- 
 form successively and successfully all the necessary operations to make 
 a complete mould, even if it were only the mould of a simple pattern. 
 In consequence the general equipment of a foundry which accom- 
 plishes this object must be necessarily quite an elaborate and expensive 
 matter. The majority of designs of moulding machines run in this 
 direction, whereas in most cases it would have been better if the energy 
 expended had been directed to their simplification. 
 
 "Such tendencies lead to complications which are altogether unsuited 
 for foundry practice; they meet with little favor and machines built 
 upon these principles are of short Hfe." 
 
 "Only the simpler moulding machines have a chance of meeting with 
 more or less success, even if they perform but a few operations, provid- 
 ing they perform these well." 
 
 "The first step in the evolution of the moulding machine was a device 
 for withdrawing patterns from the sand. The next was to employ 
 stripping plates, then an attempt to ram the mould by machinery." 
 
 In these three operations He the basic principles of all moulding ma- 
 chines: all subsequent improvements and additions have been matters 
 of detail; but to these improvements and to superior workmanship is due 
 the real success of the modern moulding machine. 
 
 In the chart (p. 549), given by Mr. Stupakoff, moulding machines 
 are divided into two classes — hand and power machines. The chart 
 gives the variations of each class. 
 
 The selection and arrangement of machines, etc., is a matter governed 
 entirely by the specific circumstances. Only hand machines are portable. 
 They effect a great saving in the cost of carrying sand, but their use 
 is Hmited by their size and weight. Mr. Stupakoff discusses the advan- 
 tages and use of pattern plates as follows: 
 
 "At first sight it may appear that the construction and manipulation 
 of pattern plates has but little connection with moulding machines, but 
 I hope that I will succeed in showing in the course of this work, that 
 they are not only intimately connected with each other, but that they 
 are in fact the principal parts of all moulding machines. The lack of 
 intimate knowledge of how to make use of them to the best advantage, 
 the want of proper means to effect this purpose and the wretchedly 
 
540 Moulding Machines 
 
 little effort which is made to catch the right spirit of their nature, is 
 generally the reason why a moulding machine becomes an elephant on 
 the hands of the moulder and an eyesore to its owner." 
 
 The recommendations given by Mr. Stupakoff for the adoption of 
 plate moulding by hand apply equally well to machine moulding. 
 
 1. Plated patterns give the best service when used continuously. 
 
 2. Castings which are to be produced in quantities are perferably 
 moulded with plated patterns. 
 
 3. Standard patterns are preferably plated for economic production 
 in the foundry. 
 
 4. Plated patterns should be made .of metal to give good service." 
 
 5. When plated patterns are used good flasks only will insure good 
 castings. 
 
 6. Accurate workmanship is one of the main requisites in plated 
 patterns. 
 
 7. The use of wood patterns on plates is not excluded. 
 
 8. All patterns when placed on plates should be provided with 
 plenty of draft. 
 
 9. Plated metal patterns are preferably made hollow. 
 10. Rapping is destructive of plates and patterns." 
 
 The chapter on jigs is regarded of such importance that it is given 
 here in full. 
 
 The Moulding Machine 
 
 By S. H. Stupakoff, Pittsburgh, Pa. 
 
 Journal of the American Foundrymen's Association, Vol. XI, June, 1902, Part i. 
 
 Jigs 
 
 The deduction arrived at in the foregoing chapter might make it 
 appear that plated patterns are not Ukely to find extensive use in 
 jobbing foundries, whereas this is really not altogether the case. There 
 is no doubt that plate moulding as now practiced, or rather as ordi- 
 narily applied, is practically excluded from jobbing shops. But, if a 
 plate is used in connection with a suitable jig, specially prepared for the 
 purpose, objections are not only overcome, but the application and use 
 of plates offer excellent advantages, even in such cases where only a 
 small number of castings of the same pattern are required at one time. 
 At best, the economic use of plated patterns is limited by the shape and 
 size of the castings. The fundamental principle involved in their 
 construction and application must be fully understood by the user, 
 if satisfactory results are expected. 
 
Jigs 
 
 541 
 
 Irrespective of its relation to the moulding machine, it would seem that 
 this subject — on its own merits — is of such importance, that it should 
 be investigated by all foundrymen. It should specially interest the ma- 
 jority of our members. I have therefore somewhat enlarged the scope 
 of this treatise on the moulding machine by including a detailed study 
 of the construction and modus operandi of this particular contrivance. 
 
 To begin with, it should be understood that all plates are provided 
 with guide-pin holes, which are accurately fitted to corresponding guide 
 pins forming part of the flasks. Unless special flasks are used in con- 
 nection with such plates the customary flask pins should not be con- 
 foimded with these guide pins, as they will never answer the purpose. 
 In order that misconceptions in this respect may be avoided, this term 
 will be adhered to in what follows, and strict distinction will be made 
 between flask pins and guide pins wher- 
 ever they may be mentioned in the 
 course of this work. 
 
 The guide-pin holes, G and G', Fig. 
 205, are preferably arranged on opposite 
 ends of the plate, in even multiples of an 
 inch, and equidistant from its center and 
 on a line dividing the plate into two 
 equal rectangles. There are exceptional 
 cases, in which three or four guide pins 
 must be used. The most serious objec- ^°^- 
 
 tion against this arrangement is the greater difficulty experienced in 
 locating the patterns correctly. 
 
 Accuracy in preparing the plates becomes of the utmost importance, 
 as the magnitude of all errors occurring in the original laying out is 
 doubled by each subsequent operation. The guide-pin holes should be 
 drilled and reamed out at right angles to the surface of the plate, and it is 
 advisable to provide them with hardened and ground steel bushings. 
 All guide pins should be of uniform diameter irrespective of 
 the size of the plate. A pair of test pins should be kept on 
 hand, which snugly fit the guide-pin holes; one-half of one of 
 their ends should have been cut down to about H inch in 
 length, leaving as remainder exactly one-half of the cylindrical 
 portion (Fig. 204). If these test pins are inserted into their 
 respective holes and a straight edge is placed against their 
 P flattened faces, it will serve for locating the base or the cen- 
 
 ter line of the plate, for marking off and laying out the dowel 
 pin holes, arranging the patterns and checking off all work relating 
 to it. 
 
542 
 
 Moulding Machines 
 
 The exact location of the center of the plate, and likewise the center of 
 the flask, is found by dividing the base line from center to center gnjde- 
 pin hole into two equal parts. Let us drill a hole C in this place (Fig. 
 205), and let this hole serve as the starting point for future operations. 
 Now we will assume that we have procured a tri-square with a row of 
 holes drilled in each of its legs; these holes are spaced equally — say 
 
 Fig. 205. 
 
 I inch apart — care being taken that each row stands exactly in a 
 straight line, and that both rows include an exact angle of 90 degrees. 
 We place this square in such a manner on our plate that the hole in its 
 apex corresponds with the center hole C of our plate, and insert a good 
 fitting dowel pin through both. Thus we are able to shift the square 
 over the whole surface of the plate by turning it around the center pin. 
 Next we bring one leg of the square over the base line of the plate and 
 insert a second dowel pin (which may be shouldered if necessary) through 
 G into the corresponding hole of our square. Secured in this manner 
 the square should be absolutely rigid and should not shake to right or 
 left on the surface of the plate. We now drill one hole each into the 
 plate through the guides H and 7 of the square, then we remove the pin 
 from G, turn the square around the center pin over 90 degrees, so that 
 one of its legs points upward and the other one to the left, insert a dowel 
 through the hole in the leg pointing upward into the top hole I' of the 
 plate, and drill the hole H^; finally we turn it again over 90 degrees, 
 secure it in the same manner as before, and drill the hole P. Fig. 205 
 
Jigs 543 
 
 Illustrates the square in the first position as located on the plate; the 
 holes H^ and P, which are drilled subsequently, are shown in faint lines. 
 In the future, we shall, call these holes "pilot holes," in order to dis- 
 tmguish them from others in the same plate. These four pilot holes 
 include an exact rectangle or square, and each opposite pair is located 
 at uniform distances from the center of plate and flask. It will be under- 
 stood that it is not absolutely necessary to employ the square for drilUng 
 the pilot holes. For instance, after one plate has been prepared in this 
 manner, this plate can serve as a jig for drilling any number of additional 
 plates in the same manner by a single setting. Such an original or 
 master plate is especially serviceable, if all holes are provided with good 
 steel bushings. The pilot holes in connection with the center hole will 
 serve us hereafter as guides for locating pattern dowels. 
 
 Our object in view is to use this plate as a base for any and all suit- 
 able patterns, and as an illustration we will arrange it for the reception 
 of patterns of a globe valve and a bib cock. We wiU assume that the 
 patterns are aU in good shape and properly parted. However, they 
 shall originally not have been intended for use with either moulding ma- 
 chine or drawplate. Our plate and flasks are of a suitable size, but the 
 job is in a hurry — as all jobs are — and we must get out quite a num- 
 ber of these castings to-day. What are we going to do about it? Take 
 my advice and make it in the old fashioned way, unless you are pro- 
 vided with a suitable jig plate and an inexpensive, but a good small 
 driU press, which was never used by your blacksmiths or yard laborers, 
 but was expressly reserved for this purpose only, was always under the 
 care of a mechanic who understood how to handle it, and who took pride 
 in keeping it in good shape. 
 
 This jig plate (Fig. 205) should be provided with a number of holes, 
 two rows of which, at least, are drilled exactly in the same manner as 
 those in the above-mentioned square; the balance is laid out prefer- 
 ably, but not necessarily so, in straight and paraUel hues, all equidistant 
 from each other. Its dimensions should be sufficient to cover one 
 corner, or one-fourth of your pattern plate. 
 
 If these things are part of your equipment you will have easy sailing, 
 and you wiU be better fitted to tackle the job than your competitor. 
 
 Place this jig in such a manner in one corner of your draw plate that 
 the hole (Fig. 205) corresponds with the hole C in its center; hold both 
 together with dowel pins inserted into the pilot holes, and drill the holes 
 through the jig into your plate, which are required for securing the 
 patterns in the predetermined places. To avoid mistakes be sure that 
 the hole in that particular corner of the jig, which corresponds to the 
 one described as located in the apex of the square is distinctly marked 
 
544 
 
 Moulding Machines 
 
 on both sides of the jig plate — in our figure marked — and note 
 carefully which holes in the jig were used for drilling the dowel holes 
 into the pattern plate. Thereafter turn the jig upside down on the 
 pattern plate, insert the dowel pins again through the same holes and 
 01 into C and /', and the third one through OH into H^, and then, as 
 before, drill through the same guide holes of the jig the corresponding 
 
 dowel holes into the second quarter 
 of the pattern plate. Repeat the 
 same process at the lower half of the 
 plate, being always careful that C and 
 remain together and your plate is 
 ready to receive the patterns. 
 
 That there may be no doubt as to 
 the method of operation, I suggest 
 that you will refer to the two plates 
 which are attached hereto, one of 
 which (Fig. 206) is made on transpar- 
 ent — so-called "onion skin" paper. 
 The cut on the latter represents the jig. In faint lines thereon is shown 
 the outline of the position of patterns, which corresponds to the arrange- 
 ment of the same on the pattern plate (Fig. 207). Horizontal and vertical 
 
 Fig. 206. 
 
 Fig. 207, 
 
 lines, which are provided with identification marks, cross all the holes 
 in the jig plate. The holes which are to be used in this special case as 
 guides for drilling the necessary dowel pin or screw holes in the pattern 
 plate are indicated by circles drawn in heavy. Thus, the holes // X 
 and 8* are used for securing the globe valve body pattern, II + and 
 
Jigs 545 
 
 /// 1 1 for the body of the bib cock, and so forth. By placing the onion 
 skin in such a manner over the drawing of the pattern plate, that its 
 hole corresponds with the center hole C of the latter, and 01 and OH 
 respectively with /' and H', it will be noticed that the outlines repre- 
 senting the patterns cover each other in both cuts. The jig placed in 
 this position over the pattern plate, and secured to it by the pilot pins 
 at 0, 01 and OH is used in this manner for drilling all dark lined holes 
 in the right-hand upper corner of the draw plate. This being done, the 
 pilot pins are withdrawn and the jig plate is reversed and turned into 
 the upper left-hand corner of the pattern plate, just as if it were hinged 
 at the line 01; the pilot pins are replaced into the same holes of the jig 
 as before and in this position they will secure it to the pattern plate by 
 entering its pilot holes C, I' and H"^. It will be observed that in this 
 position also, and equally well, the outlines of the patterns in both cuts 
 fall exactly together. The jig is used in this position as before, the same 
 guide holes which were used in the first position in the upper right hand 
 corner serve again as guides for drilling the second quarter of the pattern 
 plate. Identically the same process is then repeated at the lower left 
 hand and lower right-hand corners of the plate, by first turning the jig 
 plate around the imaginary hinge center OH, and then around 01. 
 
 In order to prepare the patterns to suit the above conditions, we pro- 
 ceed exactly in the same manner, by securing one-half of each separately, 
 and always the one which has the dowel holes, at the previously deter- 
 mined place on the jig plate and drilling clear through them the holes 
 which coincide with those drilled previously into the pattern plate. 
 The second halves of these patterns are then placed in position against 
 the first (drilled) halves; they are prevented from moving sideways by 
 their original dowel pins, and they may be held together by suitable 
 clamps. These clamps are preferably made of a universal type which 
 adapts them for use with all kinds of patterns, their lower portion being 
 constructed in the shape of a frame which rests on the table of the drill 
 press without rocking and which is adapted for fastening the patterns 
 in such a manner that their parting faces stand parallel to the drill 
 table. The half of the pattern which has been drilled first with the aid 
 of the. jig occupies the upper position in this clamp or drill frame, and 
 the holes in this one will now serve as guides for the drill to drill the 
 holes in the second half which stands directly underneath. Finally, 
 have the original dowel pins of the patterns removed and fasten all 
 parts separately in place on the pattern plate by either dowels or screws, 
 or both, whichever may be preferable and most convenient in your 
 particular case. 
 
 If I may call your attention again to the drawings, you will observe 
 
546 Moulding Machines 
 
 that we have prepared the pattern plate in this manner with four com- 
 plete sets of patterns; yet we have used only two. The castings result- 
 ing from the use of these plates should be perfect as to match. The 
 amount of labor required to withdraw the patterns from the sand is 
 reduced to a minimum; additional time is saved by the use of a station- 
 ary gate or runner on the plate, and double the quantity of castings can 
 be produced in this manner with the same number of patterns and in 
 the same number of flasks. All this can be accomplished by making 
 an effort of no longer duration than it took to describe. 
 
 If you have followed the above description carefully, you may have 
 noticed that it is not necessary to have an individual plate prepared for 
 each set of patterns. Yet I thought it better to describe this method 
 of preparing pattern plates, and patterns for plate moulding in detail, 
 than to leave room for any doubt or error. You can easily see that much 
 of the time which it apparently took to get the plate and patterns ready 
 for the moulder, can be saved by providing the entire surface of the plate 
 with dowel holes before putting it into use. This should be done with 
 the aid of the jig and in identically the same manner as has been suffi- 
 ciently explained in the foregoing. Thus, only new patterns have to 
 be prepared for the purpose, and all others, which once have been fitted, 
 are easily replaced and secured to their correct positions on the plate, 
 providing their dowel holes were promptly provided with specific nimi- 
 bers, letters or identification marks. The additional holes, in the plate 
 will not impair its working qualities, but they could be easily closed 
 up with bees- wax if objectionable. Finally, it is well to note that 
 each plate can be used in connection with all patterns within its range, 
 and that it can be kept in continuous service, while the patterns may be 
 changed at will, and as often as desirable. 
 
 While the above description may appear somewhat too extended, I 
 assure you that a serious mistake would have been made had the sub- 
 ject been slighted merely for the sake of brevity. At the same time I will 
 say in justification of my apparent digression, that my original subject 
 has not been sidetracked. At first sight, it may appear, that the con- 
 struction and the manipulation of pattern plates has but little connection 
 with moulding machines, but I hope that I will succeed in showing in 
 the course of this work, that they are not only intimately connected with 
 each other, but that they are in fact the principal parts of all moulding 
 machines. The lack of intimate knowledge of how to make use of them 
 to the best advantage, the want of proper means to effect this purpose 
 and the wretchedly little effort which is made to catch the right spirit of 
 their nature is generally the reason why a moulding machine becomes an 
 elephant on the hands of a moulder and an eyesore to its owner. 
 
Flasks 547 
 
 Flasks 
 
 Good flasks are especially important in machine or plate moulding. 
 To insure good results from moulding machines the flasks must be prac- 
 tically perfect. They must be constructed to insure firm holding of 
 the moulding sand; must be stiff, light and durable. 
 
 "The pins must be accurately fitted. The flasks, if made in sets, 
 must be absolutely interchangeable. The pins should be square with 
 the flask surface, must not bind and still must not fit too loosely. 
 
 Copes and drags when assembled, must not rock or shake sideways. 
 
 Wooden flasks, such as are used in most foundries, are not likely to 
 give good results in moulding machine practice. However, if carefully 
 and substantially made, there is no reason why their application in 
 machine moulding shoiild be absolutely condemned. ' 
 
 Iron flasks are always preferable, especially since they do not shrink, 
 warp or get out of joint. " 
 
 Pressed steel flasks are still more desirable. 
 
 If wooden flasks are used the}^ should be faced with an iron ring, 
 this ring serving not only to maintain alignment, but also as a base for 
 securing flask pins. Taper steel pins secured to lugs by nuts give best 
 satisfaction. The holes in lugs on drags may be reamed tapering and 
 the lower ends of pins turned to fit, and tapped lightly into place. After 
 the flask is closed and clamped these pms may be 
 removed, thus making a few pins serve for any 
 number of flasks. When not in use they should 
 be removed from the flasks and properly taken 
 care of. The pins are sometimes cut away so as 
 
 to give them a triangular cross section, so that sand adhering to them 
 may not interfere with readily inserting them in the holes. 
 
 By continued use the pins and sockets are so worn as to be unservice- 
 able. The pins, of course, are replaced by new ones, but the sockets 
 must be bushed by sleel thimbles. The old holes are drilled out to 
 standard size, so that the thimbles may be interchangeable. It is 
 advisable to have the pin holes bushed when the flasks are made, so as 
 to avoid subsequent annoyance. 
 
 "The makers of moulding machines are undoubtedly very well aware 
 of all the requirements which are covered by the observance of these 
 little details. They wiU appreciate their importance and must admit 
 that they are essential to make their machines a success. Yet to my 
 knowledge these facts have never been mentioned. Is this information 
 kept from the foundry man purposely, that he may not be scared from 
 the purchase of machines? If he should be told all this he might in the 
 first place think of the expense, and next that bis moulders cannot get 
 
548 Moulding Machines 
 
 used to refinement of this kind, which by the way is not a very creditable 
 opinion. But if he buys one or more of the machines oSered, he cannot 
 help finding all this out before long, to his own chagrin. He may tjirow 
 the machines away, or persist in the use of them and pay dearly for his 
 experience. All this vexation could have been prevented in the first 
 place and at a reasonable cost, had he been furnished in connection with 
 the machine, with jigs, sample flasks, pins, etc., and above all. with the 
 necessary information to which he was entitled." Many failures to 
 introduce and maintain labor-saving devices can be traced to the lack 
 of intelligent instructions sent with them. 
 
 Mr. Stupakoff further discusses in detail the different kinds of ma- 
 chines remarking: "It is a grievous mistake to think that a moulding 
 machine of any description will replace a skilled moulder. There is no 
 less ingenuity required to produce good castings on a machine than to 
 make them by hand. 
 
 "A moulder is aided by his experience and by his good judgment, A 
 machine hand (customarily selected from unskilled labor) has nothing 
 to offer but his muscle and good will. These qualities . . . are but 
 poor substitutes for the dexterity of an expert. Therefore, imder 
 ordinary circumstances the chances are but slight to obtain good cast- 
 ings and good results by mechanical means which are imperfectly under- 
 stood and subject to reckless abuse by hands which are unquestionably 
 green in the business. 
 
 Owners of moulding machines should not expect marvels from an 
 inert piece of mechanism, but it is safe to say they will seldom fail in 
 their calculations if they are satisfied with a reasonable increased pro- 
 duction, provided they are willing to pay the best possible attention to 
 their manipulation." 
 
 Messrs. McWilliams and Longmuir in discussing the advantages of 
 moulding machines conclude their remarks as follows: 
 
 "With ordinary small work, such as is usually included in boxes up 
 to 14 inches by 16 inches, the greatest time consumers are (i) ramming, 
 (2) jointing , and (3) setting cores. Jointing is largely obviated with 
 a good odd-side, and altogether so with a plate. Ramming by the aid 
 of a press reduces the time occupied to that required for the pulling 
 forward of a lever. 
 
 Obviously, then, the greatest time consumers, with one exception, 
 may be very considerably reduced by the simple and inexpensive aid 
 offered by plate moulding and the hand press. " 
 
 The exception referred to is that of setting cores, which holds good 
 with all forms of mechanical moulding. Pattern drawing does not take 
 up so much time as is usually supposed. With machines, jointing and 
 
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 (549) 
 
550 Moulding Machines 
 
 pattern drawing are eliminated and in certain cases, the initial outlay 
 is comparatively small. 
 
 On standard, but changing work, our best results in machine prac- 
 tice have been obtained from the hand press supplemented, in case of 
 deep patterns, such as flanged valve bodies, etc., by the hand rammed 
 pattern drawing machine. Accessories in either case are not costly; 
 the output is high and the quality good. Our best results on standard 
 work, in which one plate could be run for at least 300 moulds, have been 
 obtained from a pneumatic vibrator machine. 
 
 If the same plate could be run over a period of four or five days 
 without changing, then production costs fall very considerably. . . . 
 
 Whatever may be said to the contrary, stripping plate machines 
 involve costly accessories, but this outlay is warranted if the patterns 
 are of a sufficiently standard character. These machines are especially 
 good on intricate patterns, such as small spur wheels or others having 
 little or no taper on the sides. While hand machines of any type 
 represent a low first cost, the cost of subsequent accessories must not be 
 forgotten. 
 
 Power machines represent a higher initial and maintenance cost, 
 but if they can be maintained in constant operation, they give a low 
 production cost. Finally, the chief drawback to the further develop- 
 ment of machine moulding of any type occurs in core making and core 
 setting. 
 
 An improvement in the mechanical production of irregular cores will 
 result in a very considerable advance in machine practice." 
 
 The following remark is quoted from page 131, same book: 
 
 "As a rule we have found that while the initial cost of the machine 
 is not considered, the after cost of the accessories is cut down to the 
 narrowest possible margin. This is short sighted for if mechanical aids 
 are adopted, there must be no half measures, or failure will inevitably 
 follow. It cannot be too strongly urged that the cost of a machine 
 represents only the beginning of expenditure." 
 
CHAPTER XXIV 
 
 CONTINUOUS MELTING 
 
 There are some large shops where the processes of melting and mould- 
 ing are carried on continuously. In some instances the moulds are made 
 in one department, taken on trucks to the neighborhood of cupola, 
 where they are filled; then to the dumping floor where the flasks are 
 knocked out, and sent along on same truck to moulding floor. The 
 manner of conducting this operation at the Westinghouse Foundry is 
 described by Mr. Sheath, and is given in substance further on. In 
 other shops, where work of the character of iron bedsteads is produced, 
 the operation is also continuous, but the pouring is done in the ordinary 
 way. 
 
 The management of the cupola is practically the same as in the ordi- 
 nary foundry, except that the melter must have means for controUing 
 the blast, so that he may increase or decrease the supply of air as the 
 demand for melted iron may be greater or less. The cupola is run con- 
 tinuously from 7 A.M. to 6 p.m. with an interval of one hour at noon. 
 
 In respect to the cupola Mr. Sheath's advice is: "See that the coke 
 bed is burning evenly all around, then charge just as you would for an 
 ordinary run, allowing an extra amount of coke for the dinner hour. 
 After running about an hour open the slag hole and keep it open, except 
 during the dinner hour. Use about 40 to 50 pounds of Hmestone to the 
 ton of molten metal — better use too much than too little. Have the 
 cupola shell large enough, as it is easy to put in an extra Hning for smaller 
 heats." 
 
 "The Westinghouse Company have in their foundry at Wilmerding, 
 Pa., three cupolas, one 60 inches, two 70 inches, inside lining. When 
 running full, i.e., night and day, we melt 280 tons, running each cupola 
 about ten hours. We have operated one cupola from Friday night at 
 6 o'clock, until Saturday noon the following day, closing down at 
 II P.M. for one-half hour for lunch, and again at 6.30 in the morning for 
 three-quarters of an hour for breakfast. This is rather hard on the 
 lining so we do not make a practice of it. We have tried a great many 
 experiments with cupolas, but as yet have been unable to find any that 
 will give better results than the double row of tuyeres. It is not neces- 
 sary to keep the upper ones open all the time. Our blast pressure is 
 
 551 
 
552 Continuous Melting 
 
 about II ounces in the cupola bustle. When running full we melt ten 
 to eleven pounds of iron to one pound of coke. . . . 
 
 All charges are the same from beginning to the end of the heat. 
 
 As the iron must come very soft and uniform we do not charge more 
 than 4000 pounds at one time. 
 
 In the discussion of his paper at the Cincinnati meeting of the Amer- 
 ican Foundrymen's" Association, May, 1910, Mr. Sheath gave much 
 interesting information, which is summarized briefly. 
 
 Blast pressure, 11 ounces. 
 
 Little metal is held in cupola, consequently tuyeres are very low. 
 
 We are ready to tap almost after the whistle blows in the morning. 
 
 The melting is fast or slow as the moulds appear for pouring. 
 
 More coke is used for a small heat and slow melting, than with a 
 large heat and rapid melting." 
 
 The sand is conveyed to the moulding machines by overhead recipro- 
 cating conveyors. Mr. Sheath's description of the pouring table is 
 as follows: 
 
 "I might describe how we handle what we call our No. 2 table for 
 No. 2 work. On that table there are castings, a great many of them 
 measuring only a few inches. Notwithstanding the small size of the 
 castings, we were running. 5 2 tons ojff that table alone on a lo-hours rim, 
 showing what a great amount of metal can be used up under the con- 
 tinuous process in pouring small castings. We move the table at the 
 rate of 20 feet per minute. A drag is put on. There are cores in it. 
 As it passes up the core setters set the^ cores. Then the cope is put 
 on. It then goes around to the casters in front of the cupola, which is 
 connected with an endless control system. The casters have a ladle 
 which can be raised or lowered by hand. They step on the table and 
 travel with it, pouring anywhere from two moulds to a half dozen or a 
 dozen, and by the time they are poured oE, they are off at that end, and 
 they can ride back to the cupola. " 
 
 They do that all day long. The table is not supposed to stop, 
 but just goes right straight ahead. It moves at the rate of about 21 feet 
 a minute, which allows them to core up, cast, cover down and all. The 
 core-setters walk with the platform and become veiy expert. 
 
 In some moulds we put in eight cores and two or three anchors 
 at the same time, and it would take more than one man to do the 
 coring. 
 
 Sometimes one man will core it, sometimes it takes two. The 
 casters move right along with the table, take their ladle, and travel with 
 it, the same as if they were on the floor. 
 
 One man handles a ladle that holds from 60 to 70 pounds. 
 
Continuous Melting 4 553 
 
 The sand does not ball up, because we do not carry it very far 
 with the conveyor. In the iron foundry from the time we make the 
 mould and pour, until the mould is shaken out, that same sand is back 
 again in twenty minutes. The sand is not touched by the men in any 
 way. It simply goes down through the conveyor. The sand drops 
 through the grating and is wet there and then taken overhead to the 
 machine. 
 
 The lowest we have ever run was 40 to 50 tons. We have run as 
 low as 5 tons an hour. This takes a little more lining up. 
 
 The economy comes in the room occupied by the moulds and the 
 handling of the sand. The sand that we pour into, is back to the ma- 
 chine again in twenty minutes. We get the sand, the flasks and every- 
 thing back empty every twenty minutes. There is a very httle jarring 
 about the platform. We have rebuilt one after running it nineteen 
 years. 
 
 There is very little shake to it if it is working right. We use both 
 the hydraulic and pneumatic moulding machines. ... 
 
 The cutting of the cupola lining as compared with ordinary practice 
 varies in proportion to the length of time in blast. We do not have 
 any trouble from slag. At 12 o'clock all the metal Is tapped out. We 
 tap for slag twenty minutes before twelve and run it all out. The 
 blast is shut off and metal run out before twelve. All the openings are 
 stopped up. Very little iron comes down after the blast is stopped. 
 
 The cupola is drained before starting to work again and the blast 
 put on at full pressure so as to heat up quickly. Perhaps 300 pounds 
 metal is pigged before operations are resumed. 
 
 The smallest output any one day was 50 tons. I do not consider 
 that the continuous process would pay if the production was as low as 
 20 or 30 tons per day. If there were no moulding machines the process 
 would be economical upon a basis of two tons per hour." 
 
 When asked as to injury from jarring, Mr. Sheath replied: 
 
 "We make some moulds that have thirteen pockets hanging down in 
 our smooth moulds; but there are much larger moulds which we have not 
 put on the table at all, because our green sand cores are just held by a 
 few fingers, and we would not risk putting them on. But we make 
 lots of moulds that have quite deep pockets hanging down, and there is 
 very little jarring to it. The table has a slow movement which ehmi- 
 Dates jarring. 
 
 The displacing of the sand in the mould gives very little trouble. 
 
 Xhe continuous system is adapted only for heats where the metal 
 is of same character throughout. If two grades of metal are used they 
 should be melted in separate cupolas. 
 
554 I Continuous Melting 
 
 The moulds may be made by machine or on the floor, and the table 
 used for pouring anything placed on it. 
 
 Our conveyor makes a complete revolution in twenty minutes. We 
 find in our hne of work that the moulds and castings will be cold enough 
 by the time they travel to the shaking out end. 
 
 The flasks are all iron and when shaken out are immediately put 
 back on the table and carried to the moulding machine. They are 
 carried entirely by the conveyor. 
 
 Our castings are not heavy. The sand is hot when it is shaken out, 
 but when it is wet and elevated and shaken back and forward in the 
 reciprocating conveyor, by the time it gets to the machine and iron 
 patterns it is all right. We have to keep the patterns warm to prevent 
 the sand from sticking to them. 
 
 Cores placed in hot sand will draw dampness. This feature was 
 provided for. Our heaviest work is with flasks containing two castings 
 which together weigh 45 pounds. Other flasks contain from thirty- 
 two to forty castings, weighing a few ounces each. 
 
 I am familiajr with a foundry where the cupola is 36 inches inside the 
 lining. It is run from 7 a.m. to 5.30 p.m., continuously. The product 
 is 60 tons per day. The sand is conveyed from the shaking out stand to 
 the machines. Casting is continuous. 
 
 I am imable to say how small an output could be economically pro- 
 duced by this system. My experience is on a production from 50 to 
 280 tons. With us the casters do nothing but cast, the machine men 
 do nothing but mould and the shakers-out do nothing but shake out. 
 
 We have had no trouble with freezing at the tap hole during the 
 noon shut down." 
 
 As regards melting losses, Mr. Sheath was uncertain whether there 
 were records or not. His opinion was that it runs from three to four 
 per cent. The gates and sprues are returned to the cupola without 
 cleaning. 
 
 "The pouring is done by a man moving with the table. The table 
 is large enough for a man to stay on it with the mould. There is an 
 overhead traveler, which travels with him as he is pouring. As soon 
 as he has poured off and is at the end of his trolley line, he steps off the 
 table and comes right back to the cupola. The coring is done by men 
 standing and dropping in the cores as the moulds pass, or maybe taking 
 a couple of steps, depending on the number of cores. The table does 
 not stop from 7.15 a.m. until 12 m. miless for some special cause." 
 
 Mr. G. K. Hooper, in the discussion on Mr. Sheath's paper, remarked 
 in response to the inquiry as to the minimum production for which the 
 continuous process can be economically employed: 
 
Multiple Moulds 555 
 
 "That it was not so much a question of tonnage as of the number 
 of moulds to be poured. " The handUng of a smaller tonnage than that 
 mentioned by Mr. Sheath, if distributed over a large number of moulds 
 would unquestionably be productive of great economy if performed 
 mechanically and continuously. The mould is the unit which must be 
 employed in determining whether the continuous system can be applied 
 to any particular production." 
 
 Mr. Hooper also states that 20 minutes are not necessary for the 
 manipulation and cooling of the sand. He had experience with a 
 plant where the sand was returned in six minutes. 
 
 His further experience is that the foundry losses are less than are met 
 with in the same class of work made on the floor. 
 
 Belts are more desirable than conveyors for moving sand. Rubber 
 belts are better suited for the purpose than canvas. Flat belts are 
 better than those which are troughed, and wide belts moving slowly 
 are better than narrow ones at high speed. 
 
 A drag or scraper conveyor is the best for distributing sand to the 
 hoppers over the moulding machines. It is preferably made of wooden 
 troughs and flights. 
 
 Nettings, riddles, sieves, bolts and nuts are best made of phosphor 
 bronze. 
 
 It is possible to handle all the sand required by productions up to 
 100 tons of castings per day, or more, with two men; even though as 
 much as 100 tons of sand per hour may be passing through the system. 
 
 He has subjected moulds to very rough treatment to determine the 
 liability of injury from jarring and confirms Mr. Sheath's statement 
 that no trouble arises from this cause. 
 
 Mr. Hooper commends a system wherein the moulds are carried by an 
 overhead trolley and allowed to swing freely except at the point where 
 the pouring was done. Less power is required, less wear entailed, and 
 the expense is less. 
 
 The continuous system is in no sense experimental. Its worth is demon- 
 strated by use through many years in many large shops. ... By means of 
 mechanical handhng systems in the foundry, the efficiency of the workman 
 is increased from 10 to 50 per cent. The average wage can often be re- 
 duced somewhat; the foundry loss is decreased; the floor space reduced; 
 in fact by such appliances only can the full capacity of moulding machin- 
 ery be realized. 
 
 Multiple Moulds 
 
 When several moulds are stacked one on top of another and poured 
 from a common sprue connecting to each mould, the . process is styled 
 multiple moulding. 
 
SS6 
 
 Continuous Melting 
 
 The top and bottom sections are like the cope and drag of the ordinary 
 mould; each intermediate section forms the drag for that immediately 
 above and the cope for the one directly below. 
 
 A number of these sections, perhaps eight or even nine, are piled on 
 top of each other and the pouring gate extends from the top cope to the 
 
 209. — Rathbone Multiple Moulding Machine. 
 
 bottom drag. The special advantages of the system result from the 
 reduction of floor space, the amount of sand used; the nimiber of flasks 
 required, and the labor of pouring ofl". 
 
 Mr. E. H. Mumford, in a paper presented to the American Foundry- 
 men's Association, stated: "That the reduction in the amount of sand 
 used and in the number of flasks is 37 per cent; and in floor space 
 88 per cent below that required for ordinary floor moulding. " 
 
Multiple Moulds 
 
 557 
 
 The pouring may be done with a crane ladle; therefore, one of the 
 great difi&culties encountered in pouring off machine floors is ehminated. 
 The great weight of sand, together with good clamping overcomes the 
 tendency of straining. 
 
 Fig. 2IO. 
 
 Fig. 211. 
 
 Fig. 212. 
 
 Fig. 213. 
 
 Fig. 214. 
 
 Fig. 215. 
 
 As originally practiced this method of moulding covered the piling of 
 ordmary moulds, one above the other, and pouring from a cormnon gate. 
 The advantages were confined to reduced floor space and reduction of 
 pouring difficulties. Subsequently each intermediate section was 
 made to serve as a cope and drag; but the process was confined to pat- 
 
558 
 
 Continuous Melting 
 
 tems having plane bases, the drag having simply a flat surface. This 
 limitation arose from the difl&culty encountered in obtaining good 
 moulds by pressing the patterns into the sand to form the drag. Later 
 it was foimd that by bringing the drag up suddenly against the presser 
 head, the sand was made by its inertia to take the impression of the 
 pattern equally as well as when pressed from above. The scope of the 
 process was immediately enlarged and although the method is not as yet 
 extensively employed there seems to be a reasonable probabihty that 
 it may be extended to cover the range of moderately small work now 
 made by mechanical processes. 
 
 The cut above (Fig. 209) shows a machine of this character designed 
 for making chilled plow points. 
 
 The moulds in position for clamping, and samples of castings made 
 are shown in cuts above (Fig. 210-215). 
 
 Permanent Moulds 
 
 Moulds of more or less permanency made in loam, and moulds for chilled 
 work, such as car wheels, etc., have long been in use, but moulds of a 
 permanent character have only recently been used for extended lines 
 of castings which are not chilled. 
 
 The management of the cupola, melting and pouring are very much 
 the same as pursued in the continuous process already described. 
 
 The moulds are either mounted on frames near the cupola or are placed 
 on revolving tables. 
 
 The iron from which the moulds are made must be soft enough for 
 machiDing; it must be strong and of suitable composition to stand 
 repeated heating without warping; it must also have a close structure 
 to withstand the abraiding action of hot metal. The moulds are very 
 heavy so that the mass of iron may carry away the heat rapidly from 
 the casting and at the same time not permit its temperature to rise 
 above 300° or 400° F. Keeping the temperature within these limits 
 reduces the frequency with which the mould may be used. The moulds 
 are machined at the joints and preferably hinged; the outside of. the 
 lower half of mould is also machined on the bottom. 
 
 Mr. Richard H. Probert of Louisville, Ky., in a paper read at the 
 Cincinnati meeting of the American Foundrymen's Association gave 
 the following analysis for moulds which had given good results: 
 
 Si 
 
 s 
 
 Phos. 
 
 Mn 
 
 C. C. 
 
 G. C. 
 
 2.02 
 
 .07 
 
 .89 
 
 .29 
 
 .84 
 
 2.76 
 
Permanent Moulds 559 
 
 He also states that he had used moulds made from high carbon steels 
 for castings having sharp thin projections. In constant use these moulds 
 become roughened, but are not burnt or eaten away, as with cast-iron 
 moulds. 
 
 He likewise suggests that pressure applied to the moulds immediately- 
 after pouring would result in castings presenting sharp clean lines of 
 great density and strength. 
 
 Mr. Edgar A. Custer of Tacony, Pa., presented at the same meeting 
 a most interesting paper on the same subject and also submitted many 
 sample castings, made by this process. Without giving definite informa- 
 tion as to sizes of moulds with respect to patterns, he impressed the 
 necessity for great mass in them. For instance, a mould for a 2-inch soil 
 pipe T, weighs 500 pounds; one for a 3-inch trap 1700 pounds. In a 
 mould for 4-inch soil pipe weighing 65 pounds, there were 6500 pounds 
 iron. Castings were made in this mould every seven minutes without 
 raising its temperature over 300° F. 
 
 He found that it is imnecessary to coat the moulds, but that their 
 temperature must be sufficiently high to prevent the condensation of 
 moisture before casting. If the castings are removed from the moulds 
 immediately upon setting, there is little trouble about sticking after 
 60 to 100 castings have been made. The moulds improve by continued 
 use, but how long they will last is unknown. He has now in use a mould 
 in which 6000 castings have been made and it shows no signs of deterio- 
 ration. The life of a mould depends not so much on the number of cast- 
 ings made in it as upon the number of times it has been allowed to 
 become entirely cold and then reheated. Continuous pouring, when 
 correctly timed so as to preserve a generally even temperature, has but 
 very slight tendency to crack the mould. If the castings are rem.oved 
 from the mould as soon as they have set sufficiently to handle, there is 
 with proper mixture no appearance of chill when cold. This was shown 
 by a number of samples which had been machined. The iron was soft, 
 and was readily filed on the parts not machined. 
 
 Cores are made of cast iron, and if straight, or curved in circular 
 shape, can easily be removed from the castings, if taken out quickly 
 while the casting is at a bright red. It is altogether probable that the 
 time to remove the castings is at any period after setting and prior to 
 the third expansion, and that the core should be removed during the 
 third expansion. See Keep's "Cast Iron," Chapter \TII. The iron 
 must be melted very hot. Mr. Custer's view is that the percentage 
 of silicon may range between 1.75 and 3 per cent. The mixture in use 
 by bim is as follows: 
 
56o 
 
 Continuous Melting 
 
 Si 
 
 Phos. 
 
 s 
 
 Mn 
 
 G. C. 
 
 C. C. 
 
 2.24 
 
 1. 12 
 
 .01 
 
 .38 
 
 3.02 
 
 1.54 
 
 Mr. Custer summarizes as follows: 
 
 "Any casting that can be poured in a sand mould can be poured in an 
 iron mould. If the iron is hot enough to run in green sand mould it will 
 surely run in an iron mould. 
 
 Iron that is suitable for radiator fittings, or brake shoes, or any 
 other class of duphcate work that -is made in sand, will be suitable for 
 the use of permanent moulds. The same experience that shows the- 
 f oundryman what is best for sand moulding can be applied in permanent 
 mould work. 
 
 It is true that a somewhat wider range of iron can be used in per- 
 manent moulds for the same class of work than is the case in sand mould- 
 ing, but any change from the general practice in selecting irons for any 
 particular class of work must be made with a great deal of care. It is of 
 course a subject that demands close and incessant study, and every 
 manufacturer who wishes to use permanent moulds must give the same 
 care and thought to this method that he has given to those previously 
 employed. " 
 
 Interesting information was brought out in the discussion of -Mr. 
 Custer's paper which is summarized below. 
 
 Temperature of moulds is not allowed to exceed 300° F.; the pouring 
 is proportioned at intervals so as not to exceed that temperature. 
 
 It takes 25 seconds to make a 4-inch soil pipe T. No sand used in 
 the core. The core for this mould was shown, which had been in con- 
 stant use for thirteen months. 
 
 The mould for a 2-inch T weighed 500 pounds, the T itself weighs 
 8^i poimds. 
 
 The core with which the T was made was shown. It had been in use 
 seven months during which period 3500 castings were made. 
 
 A casting can be made from it every forty-five seconds throughout 
 the day. 
 
 No precaution is taken against shrinkage. Chilling quickly to point 
 of set makes castings homogeneous, reducing shrinkage strains to a min- 
 imum. A trap weighing 42 pounds made on a sand core was shown. 
 One is made every seven minutes. The mould weighs 1900 pounds. 
 The casting is taken out within four seconds after pouring. 
 
 No special care is taken to keep the moulds from dampness. They 
 are simply wiped out carefully before using. The core, upon which a 
 
Centrifugal Castings 561 
 
 four-inch pipe, 5 feet 3 inches long was made, was shown. The pipe 
 was H inch thick and weighed 65 pounds. The core had Me inch taper 
 in the whole length. 
 
 The pouring table revolves once in jVz minutes. There are on it 
 35 pipe moulds, and a casting is produced every fifteen seconds. 
 
 In a ten-hour run at this rate of production, the temperature of the 
 moulds never exceeds 250° F. The operations are automatic. With a 
 2-inch pipe, the casting can be taken from the mould within three seconds; 
 it must not be allowed to remain in mould over six seconds. With a 
 six-inch pipe, the time of removal is from five to sixteen seconds. 
 
 One man operates the table, pouring and removing the pipe, cleaning 
 out the moulds, and setting the cores. The iron is white hot as it comes 
 from the cupola. No attention is paid to coating the moulds; they are 
 wiped out from time to time with a greasy rag if any dirt is present. 
 The heaviest castings made are 6-inch pipes weighing no pounds each. 
 
 Gates are made larger than in green sand practice. 
 
 Mr. Custer did not consider the phosphorus content of importance. 
 He prefers iron 0.5 to i.o per cent phosphorus on account of fluidity. 
 
 Chilling occurs so quickly that there is no segregation. The tensile 
 strength of castings made in iron moulds is about 30 per cent greater than 
 that of same character made in sand. 
 
 Brake shoes are left in the mould seven seconds. It takes about a 
 minute to make a brake shoe. The castings do not warp. 
 
 Six-inch pipes can be laid on the pile within 20 seconds after casting. 
 
 The silicon content should not be lower than 1.75 per cent, sulphiu: 
 should be below 0.05 per cent, total carbon high as possible not below 
 2.65. 
 
 Has used 70 per cent scrap with pig carrying 3 per cent silicon. 
 
 Centrifugal Castings 
 
 In 1809, Anthony Eckhardt of Soho, England, was granted a patent 
 for making castings in rotating moulds, procuring in this manner either 
 hollow or solid castings. Nothing favorable seems to have resulted 
 from the scheme. 
 
 In 1848, Mr. Lovegrove attempted to make pipes in this manner. 
 Subsequently a Mr. Shanks patented the same method in England. 
 Sir Henry Bessemer endeavored to remove the gases from steel castings 
 by a similar process. 
 
 About the same time a Mr. Needham endeavored to apply the method 
 to making car wheels. So far as can be learned nothing of practical 
 value resulted from these efforts. It is said that car wheels are now 
 made in Germany in this way using a high carbon steel for the rim and 
 
562 Continuous Melting 
 
 soft material for the center. The mould is made to revolve about 120 
 times per minute while pouring. The principle is used by dentists success- 
 fully, and there seems to be no good reason why it could not be applied 
 to some classes of iron castings where difiSculty is encountered in running 
 delicate parts, or to obtain increased density at the periphery. 
 
 Castings under Pressure 
 
 Attempts have been made to submit the liquid iron to pneumatic 
 or hydraulic pressure in order to eliminate porosity or shrinkage cavi- 
 ties. So far these have been entirely experimental; the successful 
 application of the idea would remove all doubt as to shrinkage in rims 
 of fly wheels or in similar castings, where undiscoverable defects may 
 exist. 
 
 Direct Casting 
 
 Making castings directly from the furnace has been practiced more 
 or less since the discovery of reducing iron from the ores. But by 
 reason of the presence of impurities and gases, which are to a greater 
 or less extent eliminated in the process of refining in the cupola, the pro- 
 duction of castings by the direct process has never been followed to 
 any extent. In fact, except for quantities of large coarse castings, or 
 an occasional piece required at the furnace, it may be said that the 
 process has been entirely disregarded. The presence of kish in large 
 quantity has been the greatest obstacle to contend with. The use of a 
 receiver with reheating provision, in connection with manganese would 
 seem to indicate a solution of this difficulty, especially for pipes and 
 other coarse castings, where the physical characteristics are not matters 
 of vital importance. 
 
 In view of the advancement in modem metallurgy, it is more than 
 probable that commercial competition will turn manufacturers of prod- 
 ucts for which such iron is suitable to further efforts in this direction. 
 
 Carpenter Shop and Tool Room 
 
 In every foundry the services of a carpenter and machinist are more 
 or less in demand. In the larger works it is found most convenient to 
 devote separate space to each. 
 
 The carpenter shop should be given sufficient room for construction 
 and repair of wood flasks, bottom boards, etc., and with its equipment 
 of benches, trestle, etc., should be provided with a cut-off saw. 
 
 The tool room should have a drill press and smaU lathe. Unless there 
 is a laboratory connected with the works, the testing machines are con- 
 veniently located in the tool room. 
 
Tumblers 
 
 563 
 
 The Cleaning Room 
 
 The cleaning room should be adjacent to the moulding room, but 
 separated from it by a wall or partition to exclude the dust and dirt 
 from the foundry. 
 
 Where the work is heavy there should be proper facihties in the way 
 of tracks and cranes. The necessary equipment comprises tumbling 
 barrels, brushes, chipping (either hand or pneumatic) and grinding 
 apparatus. 
 
 The sand blast is also of the greatest value. 
 
 Tumblers 
 
 The shape, size and number of tumblers depend entirely upon the 
 character and volume of the work. Tumblers are made to revolve 
 about inclined or horizontal axes. Those having inclined axes are used 
 for very light castings, brass, forgings, etc. They are seldom found in 
 the ordinary foundry. The barrel may be tilted for loading or dis- 
 charging. The following cut shows the general character of this type. 
 They vary in size as re- _ 
 
 quired. 
 
 Fig. 216 shows the No. 
 2 machine mounted with 
 28-inch cast-iron barrel in 
 partially lowered position 
 preparatory to dumping. 
 
 This machine is designed 
 along the same lines as the 
 No. I tumbler excepting that 
 it is much heavier and the 
 crank shaft is back geared 2 
 to I, making the raising and 
 lowering of the barrel when 
 heavily loaded quick and 
 
 Fig. 216. 
 
 easy. It is driven by tight and loose pulleys 16 inches in diameter by 
 3M-inch face, and will take barrels from 22 to 36 inches diameter, of 
 wood, cast iron, steel, wrought brass and cast brass. The tumbling 
 process may be wet or dry as desired, and the design of the machine 
 is such that the barrel may be located at any required angle while in 
 motion, to suit quantity of work being operated upon, and lowered to 
 empty by means of the crank, ratchet and pawl. It has a belt shifter 
 not shown in cut. 
 
564 
 
 Continuous Melting 
 
 Floor space, with barrel, 42 by 60 inches. 
 
 Weight, without barrel, 600 pounds. 
 
 Speed of tight and loose pulleys, 147 to 168 rev. per min. 
 
 Speed of barrel, 35 to 40 rev. per min. 
 
 The ordinary horizontal tumbler is from 30 to 36 inches in diameter 
 and from 4 to 6 feet long. It may revolve on trunnions or on friction 
 rollers. 
 
 The barrel is made up of cast-iron staves securely bolted to the heads, 
 and with closely fitting joints. The peripheral speed should be about 
 90 feet per minute. They are used singly, in pairs, or in batteries. 
 The castings, large and small, are packed as closely as possible in the 
 barrels, together with a quantity of shot, sprues or stars. Any im- 
 occupied space is filled by pieces of wood. If any of the castings are 
 dehcate they are tumbled by themselves, so as to avoid breakage. It is 
 not uncommon to tumble castings weighing 600 to 800 pounds; they 
 must be packed very closely, however. The length of time that castings 
 must be rattled to clean them depends entirely upon the intricacy of 
 the shapes. While ten minutes may answer for some, others may 
 require 30 minutes or even an hour. 
 
 The injury to castings from grinding away sharp corners or angular 
 projections arises from the improper packing or too long continued 
 tumbling. Since the dust comes from the tmnblers in great volume, 
 as an act of humanity, they should either be enclosed, or provided with 
 exhaust fans. The dust may be carried to a water seal, or discharged 
 outside the shop. 
 
 The cuts following show several varieties of tumblers manufactured. 
 Usually each shop makes its own tumblers, so that the patterns may be 
 at hand for repairs. 
 
 Fig. 217. 
 
Reliable Steel Square Tumbling Mills 
 
 565 
 
 "The Falls" Friction-driven 
 Tumbling Mill 
 
 This ipill was designed by an 
 expert foundryman. It is of the 
 very best workmanship through- 
 out, and is guaranteed to give 
 splendid satisfaction. 
 
 Made in six sizes as follows: 
 
 No 
 
 Diameter, 
 
 Length, 
 
 
 inches 
 
 inches 
 
 I 
 
 26 
 
 48 
 
 2 
 
 32 
 
 54 
 
 3 
 
 38 
 
 60 
 
 4 
 
 42 
 
 54 
 
 5 
 
 48 
 
 72 
 
 6 
 
 54 
 
 78 
 
 Reliable Steel Square Tumbling Mills 
 
 Particularly Suited for Light Castings 
 
 Fig. 219. 
 
 This is a strong mill with double heads. Each side is strengthened 
 by a T bar run and riveted the full length and doubly bolted to each 
 head. Edges are enclosed by an angle securely riveted and countersunk 
 from end to end. Door opening is strongly reinforced. 
 
566 Continuous Melting 
 
 Friction-driven Exhaust Tumbling Mills 
 
 Fig. 220. 
 
 These mills are especially adapted to be run in gangs from one shaft 
 and one driving pulley. They can be stopped or started independently 
 or may be removed with contents from the driving frame by crane and 
 conveyed to any part of the foundry. Mills may be equipped at small 
 extra cost with reversing device, permitting rotation in either direction, 
 miUs still remaining portable and interchangeable. 
 
 They combine strength with simphcity. 
 
 Mr. Outerbridge discovered that the strength of castings was increased 
 by tumbhng. Following up this discovery Mr. Keep determined that 
 the increase of strength by tumbling ceased after two hours treatment, 
 that the increase in strength was due to smoothing and pressing the 
 surface, closing any incipient cracks and openings. 
 
 Chipping 
 
 Much of the chipping must be done by hand. The pneumatic hammer 
 has, however, superseded the hand chisel to a great extent. There are 
 few foundries not equipped with this device. 
 
 Grinding 
 
 To finish castings properly, the fins and gate spots should be groimd. 
 In addition to the ordinary emery wheel, the portable wheel driven by a 
 flexible shaft is employed advantageously. 
 
 The Sand Bliast 
 
 This appliance is of the greates-t importance. More surface can be 
 cleaned with it in a given time than by any other means except the 
 rattler. The use of the other appliances above mentioned is not dis- 
 placed by it, however, as there are many recesses about castings which 
 are protected from the blast, and which must be cleaned by hand. 
 
 The importance of properly cleaning castings should not be over- 
 looked. No matter how well made or how good in respect of material, 
 if they are sent from the cleaner in a slovenly condition, their commercial 
 value is greatly impaired. 
 
Pickling 567 
 
 Pickling 
 
 Formerly pickling castings was largely employed, but of recent years, 
 by reason of the improved facings used, the practice is not so much 
 followed. Nevertheless there are places about castings from which the 
 sand is not properly removed by the ordinary processes, and again 
 some machine shops prefer pickled castings, as the cutting edges of 
 their tools are not injured so quickly, by reason of the entire removal 
 of the sand. This process is also followed where the castings are to be 
 galvanized or tinned, as it leaves clean metallic surfaces. 
 
 For pickling, either sulphuric or hydrofluoric acid is used, the former 
 more commonly. The acid solution must be weak; one part of ordinary 
 vitriol to four or six parts of water attacks the iron rapidly, whereas the 
 undiluted acid has no effect. 
 
 In diluting the acid, care must be taken to pour the acid into the 
 water, and not the water into the acid. Dilute sulphuric acid dissolves 
 the iron in contact, thereby loosening the sand. The action is more 
 rapid with warm than with hot solution. 
 
 This solution, when applied to castings, will loosen the sand scale in 
 from one to twelve hours, depending upon the thickness of the scale. 
 The acid solution is kept in a lead-hned wood vat. The vat should 
 be about two feet deep, the other dimensions varying \vith the amount 
 of castings to be treated. At the bottom of the vat is a wooden grating 
 fastened together by wood dowels. The grating is held down by lead 
 weights. It must be high enough above the boittom of the vat for the 
 sand to drop through. Upon this grating the castings rest as they are 
 immersed. 
 
 After remaining in the bath the requisite length of time, they are 
 removed and thoroughly washed with hot water. The acid must be 
 completely removed or they will rust. It is a good plan to dip them in 
 a strong solution of lye or soda before washing. 
 
 Another practice is to place a lead-lined platform so that one edge 
 may overhang one end of the vat; the platform inclining a couple of 
 inches toward the vat, and having the remaining edges raised two inches, 
 so that all the drainage may be into the vat. Upon this platform is 
 placed a wood grating, and the castings on the grating. The pickle is 
 then dipped from vat with an iron bucket and poured over the castings. 
 
 They are washed thoroughly with the pickle, so that there may be 
 no sand surface which has not been saturated. It may be necessary 
 to repeat the operation more than once. When the sand scale begins 
 to loosen, the castings are removed and washed as before. The washing 
 may be done with a hose while the castings are on the bed, but in such 
 
568 Continuous Melting 
 
 case provision must be made to carry off the water in a trough so that 
 it may not enter the vat. 
 
 The strength of the solution must be kept up by addition of fresh 
 acid from time to time. 
 
 Hydrofluoric Acid 
 
 Where this acid is used for pickling, the solution should be one part 
 of 48 per cent acid to 30 parts of water. Hydrofluoric acid dissolves 
 the sand instead of acting on the iron. The treatment of the castings 
 is the same as with the vitriol, but the sand must be removed from below 
 the grating, otherwise the acid will be rapidly neutraUzed. 
 
 The workmen should be cautioned in handling either of these acids 
 as they cause severe bums, if they come in contact with the flesh. 
 Where acid is spilled on the flesh or clothing, wash the parts freely with 
 water and then with dilute ammonia. Raw hnseed oil applied to bm-ns 
 produces a soothing effect. 
 
 Hydrofluoric acid leaves the surface of the castings bright and clean, 
 and is, therefore, best for electroplating. 
 
CHAPTER XXV 
 
 Method of Ascertaining the Weight of Castings from the 
 Weight of Patterns 
 
 
 Weight when cast in 
 
 Pattern weighing 
 one pound 
 
 Cast 
 
 iron, 
 
 pounds 
 
 Yellow 
 brass, 
 pounds 
 
 Gun 
 
 metal, 
 pounds 
 
 Zinc, 
 pounds 
 
 Alumi- 
 num, 
 pounds 
 
 Copper, 
 pounds 
 
 
 8.8 
 8.5 
 16.1 
 10.7 
 12.0 
 8.5 
 9.2 
 9.4 
 10.9 
 14-7 
 I3-I 
 16.4 
 
 9.9 
 9-5 
 18.0 
 12.0 
 13. 5 
 95 
 10.3 
 10. 5 
 12.2 
 16.5 
 14.7 
 18.4 
 
 10.3 
 
 10. 
 18.9 
 12.6 
 
 14. 1 
 10. 
 10.8 
 II. 
 12.8 
 17.3 
 IS. 4 
 19-3 
 
 8.5 
 8.2 
 15-6 
 10.4 
 II. 6 
 8.2 
 8.9 
 9.1 
 10.6 
 14.3 
 12.7 
 15.9 
 
 
 10.5 
 
 Beech 
 
 3 
 5 
 3 
 
 4 
 3 
 3 
 3 
 3 
 5 
 4 
 5 
 
 I 
 8 
 9 
 3 
 I 
 2 
 4 
 9 
 3 
 7 
 9 
 
 Cedar 
 
 19.2 
 12 8 
 
 Cherry 
 
 Linden 
 
 14.3 
 10 I 
 
 Mahogany 
 
 Maple 
 
 
 Oak 
 
 
 Pear... 
 
 
 
 17. 5 
 
 15. 6 
 19-5 
 
 Pine, yellow 
 
 Whitewood 
 
 
 Allowance should be made for any metal in the pattern. 
 
 Specific Gravity and Average Weight per Cubic Foot of 
 Pattepjst Lumber 
 
 Wood 
 
 Specific 
 gravity 
 
 Average 
 weight per 
 cubic foot, 
 
 pounds 
 
 Beech 
 
 TX 
 
 46 
 
 Cedar 
 
 
 62 
 66 
 60 
 81 
 68 
 77 
 74 
 45 
 61 
 75 
 
 39 
 41 
 
 Cherry 
 
 Linden 
 
 37 
 
 
 Maple 
 
 
 Oak, white 
 
 48 
 
 Oak, red 
 
 46 
 
 
 28 
 
 
 38 
 
 Walnut 
 
 38 
 
 
 
 
 
 569 
 
570 
 
 Determination of Weight of Castings 
 
 Weight of Castings Determined from Weight of Patterns 
 
 (By F. G. Walker.) 
 
 
 Will weigh when cast in 
 
 A pattern weighing 
 one pound made of 
 
 Cast 
 
 iron, 
 
 pounds 
 
 Zinc, 
 pounds 
 
 Copper , 
 pounds 
 
 Yellow 
 brass, 
 pounds 
 
 Gun 
 metal, 
 pounds 
 
 Alumi- 
 num, 
 pounds 
 
 Lead, 
 pounds 
 
 Mahogany, Nassau 
 
 Mahogany, Honduras. 
 Mahogany, Spanish. . . . 
 
 10.7 
 12.9 
 
 8.5 
 12.5 
 16.7 
 14. 1 
 
 9.0 
 
 10.4 
 12.7 
 
 8.2 
 12. 1 
 16. 1 
 13.6 
 
 8.6 
 
 12 
 15 
 10 
 14 
 19 
 16 
 10 
 
 8 
 3 
 
 I 
 9 
 8 
 7 
 
 4 
 
 12.2 
 14.6 
 9.7 
 14.2 
 19.0 
 16.0 
 10.4 
 
 12.5 
 iS.o 
 9.9 
 14.6 
 19. 5 
 16. s 
 10.9 
 
 SO 
 
 
 Pine, white 
 
 
 
 
 Oak 
 
 
 Weight of a Superficial Foot of Cast Iron 
 
 Thick- 
 ness, 
 inches 
 
 Weight, 
 pounds 
 
 Thick- 
 ness, 
 inches 
 
 Weight, 
 pounds 
 
 Thick- 
 ness, 
 inches 
 
 Weight, 
 pounds 
 
 Thick- 
 ness, 
 inches 
 
 Weight, 
 pounds 
 
 
 9.37 
 14.06 
 18.7s 
 23.43 
 
 I 
 
 m 
 
 28.12 
 32.81 
 37.50 
 42.18^ 
 
 1 3/8 
 1I/2 
 
 46.87 
 SI. 56 
 S6.2S 
 60.93 
 
 1% 
 2 
 
 65.62 
 70.31 
 75.00 
 
 Formulas for Finding the Weight of Iron Castings 
 
 To find the weight of square 
 or rectangular castings, multi- 
 ply the length by the breadth, 
 by the thickness, by 0.26: 
 W = LBT X 0.26. 
 
 Fig. 221. 
 
 To find the weight of 
 solid cylinders, the weight 
 equals the outside diameter 
 squared, multiplied by the 
 length, multiplied by 0.204: 
 
 W 
 
 9M\ 
 
 
 ^^ 
 
 
 -D— >| 
 
 [<_ L 
 
 Fig. 222. 
 D.204. 
 
 - -H 
 
Determination of Weight of Castings 
 
 571 
 
 W = weight of casting in pounds; 
 L = length of casting in inches; 
 T = thickness of casting in inches; 
 B = breadth of casting in inches; 
 D = outside or large diameter in inches. 
 
 To find the weight of hol- 
 low cylinders, multiply the 
 small or inside" diameter plus 
 the thickness, by the length, 
 by the thickness, by 0.817: 
 
 W={d + T)TLXo.Si7. 
 
 Fig. 
 
 223. 
 
 DdL X 0.204. 
 W = weight of casting in pounds; 
 L = length of casting in inches; 
 T = thickness of casting in inches; 
 D = large diameter in inches; 
 d = small diameter in inches. 
 
 To find the weight of a hollow hemisphere, 
 multiply the thickness by the small radius 
 plus the thickness divided by 2, squared, by 
 1.652: 
 
 / T\2 
 
 T X 1.652. 
 
 To find the weight 
 of a sohd ellipse, mul- 
 tiply the large diam- 
 eter by the small di- 
 ameter, by the length, 
 by 0.204: 
 
 To find tl^e weight of a solid sphere, mul- 
 tiply the diameter cubed by 0.1365: 
 
 W = D^X 0.1365. 
 
 Fig. 226. 
 
 W = weight of casting in pounds; 
 
 R = outside or large radius in inches;" 
 r =■ inside or small radius in inches; 
 
 T = thickness in inches; 
 
 P — outside or large diameter in inches. 
 
572 
 
 Determination of Weight of Castings 
 
 Formulas for Finding the Weight of a Hollow Iron Sphere 
 and a Body of Rammed Sand 
 
 To find the weight of a hollow sphere mul- 
 tiply the outside diameter cubed, minus the 
 inside diameter cubed, by 10.365: 
 
 W = {D^ 
 
 Fig. 227. 
 
 W = weight of casting in pounds; 
 
 D = outside or large diameter in inches; 
 
 d = inside or small diameter in inches. 
 
 0.1365. 
 
 To find the weight of a body of rammed 
 sand, multiply the length by the breadth, by 
 the height in feet, by 87: 
 
 W = LBHX2>T. 
 
 W = weight of body of sand in poimds; 
 
 L = length of body of sand in feet; 
 
 B = breadth of body of sand in feet; 
 H = height of body of sand in feet. 
 
 jMniiii 
 
 Q!sil!!iMii.LLiLiLlICu3 
 
 Fig. 228. 
 
 Formulas for Finding the Weight of Iron Castings 
 
 l<-s--H" P 
 
 L— -.— — 
 
 Fig. 229. 
 
 To find the weight of a flywheel, 11 feet in 
 diameter, having elliptical arms. The first 
 operation is to find the weight of the hub; 
 second, the rim; and third, the arms. The 
 sum of these gives the weight of the wheel. 
 
 To find the weight of the hub: 
 
 W= (d+T)TLXo.Si7. 
 
 To find the weight of the rim, the same 
 formula as above is used. 
 
 To find the weight of one arm : 
 
 W = DdL X 0.24. 
 
 To find the weight 
 of a triangular casting, 
 multiply the length by 
 the breadth, by the 
 thickness, by 0.13: 
 
 W = LBT X 0.13. 
 
Determination of Weight of Castings 573 
 
 Multiply by six to find the weight of the six arms. 
 
 W = weight of casting in pounds; 
 D = outside or large diameter in inches; 
 d = inside or small diameter in inches; 
 L = length in inches; 
 T = thickness in inches; 
 B = breadth in inches. 
 
 To find the weight of a spherical segment of one base, multiply the 
 square of the height by the difference between the radius of the sphere 
 and one-third of the height, by 0.818; or, to the 
 radius of the base squared, multiplied by the 
 height by 0.409, add the height cubed multiplied 
 by 0.136: 
 
 W 
 
 -(-!) 
 
 X 0.81^ 
 
 or 
 
 W = r^H X 0.409 -\-H^X 0.136. 
 W = weight of casting in pounds; 
 R = radius of sphere in inches; 
 H = height of segment in inches; 
 r = radius of base in inches. 
 
 Fig. 231. 
 
 To 
 radius 
 
 find the weight of a spherical segment of two bases, from the 
 of the sphere multiplied by the difference between the squares of 
 the distances from the bases to the poles by 
 0.818, subtract the difference between the cubes 
 of the distances from the bases to the pole, 
 multiplied by 0.273, or: 
 
 To the sum of the squares of the radii of the 
 bases, multiplied by the height by 0.409, add 
 the height cubed, multiplied by 0.136: 
 
 W = R{A^- B^) X 0.818 - (43 _ 53) X 0.273, 
 
 ^ 
 
 Z7^ 
 
 Fig. 232. 
 
 TF = H (r2 + ^2) X 0.409 + i73 X 0.136. 
 W = weight of casting in pounds; 
 R = radius of sphere in inches; 
 
 r = radius of large base of segment in inches ; 
 
 5 = radius of small base of segment in inches; 
 A = distance from large base to pole in inches; 
 B = distance from small base to polo in inches; 
 H = height of segment in inches. 
 
574 
 
 Determination of Weight of Castings 
 
 . To find the weight of a ring made by cutting a cylindrical hole through 
 the center of a sphere, multiply the chord cubed by 0.136: 
 
 W = ax 0.136. 
 
 The chord is equal to the square root of the 
 result obtained by subtracting the square of 
 the diameter of the hole from the square of 
 the diameter of the sphere: 
 
 233- 
 
 C = VZ)2 _ dK 
 
 W = weight of casting in pounds; 
 D = diameter of sphere in inches; 
 d = diameter of hole in inches. 
 
 To find the weight of a ring of circular cross section, multiply 
 the radius of the cross section squared by the radius of the circle 
 passing through the center of the cross section, 
 by 5.140: 
 
 W = rmx 5.140. 
 
 W = weight of casting in pounds; 
 r = radius of cross section in inches; 
 R = radius of circle passing through cen- 
 ter of cross section in inches. ^^^- 234. 
 
 To find the. weight of a frustrum of a hexagonal pyramid, multiply 
 the sum of the side of the large base squared, the side of the small base 
 
 squared and the product 
 of the two sides, by the 
 length, by 0.226, or mul- 
 tiply the sum of the dis- 
 tance across the flats of 
 the large base squared, 
 the distance across the 
 
 k"- 
 
 Fig. 235. 
 
 flats of the small base squared and the product of these two distances, 
 by the length, by 0.075. 
 
 W = {S^ + s'' -{- Ss) L X 0.226, or W = (F^ +P + Ff) L X 0.075- 
 
 To find the weight of 
 a straight fillet, multiply 
 the radius squared by the 
 length, by 0.0559. 
 
 W = R^LX 0.0559. 
 
 Fig. 236. 
 
Weight Required on Copes 
 
 575 
 
 W = weight of casting in pounds; 
 L = length of casting in inches; 
 S = side of large base in inches; 
 5 = side of small base in inches; 
 F = distance across the flats of large base in inches; 
 / = distance across the flats of small base in inches; 
 R = radius of fillet in inches. 
 
 1 
 
 1 1 
 
 Ci_^ 
 
 " u ,.^ 
 
 Formulas for Finding the Weight Required on a Cope to 
 Resist the Pressure of Molten Metal; and the Pres- 
 sure Exerted on the Mould 
 
 To find the weight required on a cope to resist the pressure of molten 
 iron, multiply the cope area of the casting in 
 square inches by the height of the riser top 
 above the casting in inches, by 0.21: 
 
 W = AH X 0.21. "'' ' ''"'"" " 
 
 Fig. 237. 
 
 W = weight to be placed on a flask in pounds; 
 
 A = cope area of casting in square inches; 
 
 H = height of riser top above casting in inches. 
 
 To find the pressure exerted on a mold by molten iron multiply the 
 height in inches from the point of pressure to 
 the top of the riser by 0.26: 
 
 P = HX 0.26. 
 .•..;.•;:••. :■^•:y.•:■.•^•v^.•L^^v.:•; P = pressure in poimds per square 
 
 Fig. 238. inch; 
 
 H = height from point of pressure to the top of the riser in 
 inches. 
 
 To find the weight of an inside circular fillet, 
 multiply the difference between the diameter of 
 the cyhnder made by the side of the fillet and 
 the product of the radius and 0.446, by the 
 radius squared, by 0.176, or, from the diameter 
 of the cyhnder made by the side of the fillet, 
 multipUed by the radius squared, by 0.176, sub- 
 tract the radius cubed multiplied by 0.0784. 
 
 W = (D - 0.446 R) R' X 0.176, 
 or W = DR^ X 0.176 - R^ X 0.0784. 
 
 Fig. 239. 
 
576 
 
 Determination of Weight of Castings 
 
 To find the weight of an outside circular fillet, multiply the sum of 
 the diameter of the cylinder made by the side of the fillet and the product 
 of the radius and 0.446, by the radius squared, 
 by 0.176, or to the diameter of the cylinder 
 made by the side of the fillet multiplied by the 
 radius squared, by 0.176, add the radius cubed 
 multipHed by 0.0784: 
 
 TF = (D + 0.446 R) R" X 0.176, 
 or 
 
 W = DJR? X 0.176 + i?3 X 0.0784. 
 
 W = weight of casting in pounds; 
 R = radius of fillet in inches; 
 D == diameter of cylinder made or generated by 
 the side of fillet in inches. 
 
CHAPTER XXVI 
 
 WATER SUPPLY, LIGHTING, HEATING AND 
 VENTILATION 
 
 Water Supply 
 
 Provision for water supply to the foundry is a matter of the first 
 importance. If water cannot be obtained from the pubUc mains, facil- 
 ities for pimiping and distributing must be provided. The system 
 must be so arranged, either by elevated tanks or otherwise, as to furnish 
 water under a pressure of from 25 to 30 pounds. While the supply 
 must be abundant, the natural tendency to its wasteful use must be 
 suppressed. 
 
 Fig. 241. — Water Box and Hose Connection. 
 
 Conveniently located near the cupola for quenching the dump, should 
 be a hydrant with hose attached, ready for immediate use. Pipes should 
 be so run about the foundry that taps may be conveniently distributed 
 for wetting down the floors and sprinkling the sand heaps; each floor 
 must have easy access to the sprinkling hose. Ample provision should 
 be made for drinking; basins near the drinking fountains, in which to 
 bathe their arms and faces, add greatly to the comfort of the workmen. 
 
 The illustrations herewith, taken from the Iron Age, show provisions 
 
 577 
 
578 Watey: Supply, Lighting, Heating and Ventilation 
 
 made for this purpose and for lavatories, etc., in a large Cleveland 
 foundry 
 
 Running water should be suppHed at the closets. In many foundries 
 of recent construction, wash basins, shower baths and lockers are pro- 
 vided, enabling the men to wash and change their clothes before leaving 
 the works. The free use of water implies, of course, a system of sewer- 
 age. Care must be taken to avoid puddles or wet spots about the floors. 
 The matter of water supply for fire protection is entirely independent 
 of that for foundry purposes, and should be provided for separately. 
 
 Fig. 242. — Porcelain Washbowls and Steel Lockers in Lavatory. 
 
 Lighting 
 
 Next to water supply in importance is the matter of lighting. Many 
 foundries are deficient in this respect and suffer either in the character 
 or quantity of product from improper lighting. Daylight is invaluable, 
 and should be utilized to the fullest extent. In the construction of 
 foundry buildings, the windows should be tall and as close together as 
 the character of the structure will permit; they should not extend 
 lower than four feet from the floor. A modem construction showing 
 the sides of the building made almost entirely of glass is shown in the 
 engraving below. 
 
 Windows in the moniter should be swiveled and arranged to open easily 
 for ventilation. Skylights are to be avoided if possible, as they cause 
 no end of annoyance. The weaving-shed roof gives excellent results, 
 and is frequently used in foundry construction. The glazing should be 
 of a character to prevent the direct admission of sunlight. Ground 
 glass, wire glass or glass with horizontal ribs afford a mellow light, 
 relieving the eyes from the glare of direct sunlight. 
 
Heating and Ventilating 
 
 579 
 
 Artificial light for the early morning and late evening hours, during 
 the season of short days, is best aflforded by some adaptation of the 
 electric lamp. Tungsten lamps in groups of four, distributed at inter- 
 vals of about 40 feet are largely used. Such lamps are provided with 
 reflectors to direct the rays downwards and diffuse them. The lamps 
 must be placed so as to clear the crane ways, and should be elevated 
 about 20 feet from the floor. The Cooper-He we tt mercury lamps, 
 placed about 50 feet apart and covered with reflectors, are very satis- 
 factory. The flaming arc lamps, similarly placed, furnish the greatest 
 illumination for a given expenditure of current. 
 
 
 , Fig. 243- 
 
 A recent type of kerosene burner, the Kauffman, having a mantel 
 somewhat similar to the Wellsbach, is said to furnish a given candle 
 power at less cost than any tamp known. 
 
 With any system of lighting, care must be taken to keep the lamps 
 clean and in good order, otherwise their efficiency is soon greatly im- 
 paired. Where electric hghts are used, the generators should be inde- 
 pendent of those which furnish current to the motors. Power for fans, 
 elevators, cranes, sand mixers, etc., is most conveniently supplied by 
 electricity. Each machine should have an independent motor. Elec- 
 tric trucks, operated by storage batteries, and magnetic hoists, for 
 service in the foundry and yard are almost indispensable. In fact 
 the introduction of electricity has so simplified foundry operations 
 that its use is imperative. 
 
 Heating and Ventilating 
 
 Heating and ventilating the foundry are subjects which formerly 
 received little attention. A few stoves or open fires in iron rings, placed 
 where they would be least in the way, constituted the usual equipment; 
 foundries fitted with steam heating or hot-air systems were exceptional, 
 
580 Water Supply, Lighting, Heating and Ventilation 
 
 Gradually foundrymen have learned to appreciate the advantages of a 
 comfortable •working temperature and good ventilation, as shown by 
 increased output. A cold shop and chiUed or partly frozen sand heaps 
 may easily reduce the value of a morning's work from 20 to 25 per cent. 
 As foundry operations require active physical exertion, the temperature 
 of the shop should not exceed 50° to 55° F. At 7 o'clock in the morning 
 the building should be warm throughout. "For this purpose direct and 
 vacuum steam heating systems are used with good results. Both are 
 open to objections. The warm air is not evenly distributed; much of 
 it is sent to the upper part of the building, where it does no good. With 
 either system several hours are required in extremely cold weather to 
 produce a comfortable temperature in the morning. Cold air enters 
 through the windows and doors, causing drafts and an uneven distribu- 
 tion of heat. 
 
 More satisfactory results are furnished by the fan and hot-blast system. 
 This consists of a sheet-iron chamber, in which are placed the requisite 
 number of coils heated either by direct or exhaust steam, if the latter 
 is available, an exhaust fan and the distributing pipes. The fan draws 
 the air over the coils and from the chamber and forces it about the build- 
 ing through large ducts, from which branch pipes are taken at proper 
 intervals; through these branches the warm air is discharged at the 
 desired spots within the shop. This system is largely used and possesses 
 advantages over those having direct radiation. 
 
 The amount of heat absorbed by air flowing over pipes increases 
 rapidly with the velocity of the air. When the velocity of the air current 
 flo\ving over the pipes in the heating chamber is about 1500 feet per 
 minute (the usual velocity) the area of the heating surface required to 
 accomplish a given heating effect is only about one-fifth that for direct 
 radiation. With the fan and hot-blast system the building is filled 
 with air under slight pressure, termed a plenum, which prevents cold air 
 from entering; warm air flows out through all leaks. The warm air 
 is discharged from the pipes near the floor, and uniformly distributed 
 through the lower part of the building. By reason of such distribution 
 and the great volume of air discharged, the shop may be quickly warmed 
 in the morning. If the fan is driven by an independent engine, the 
 exhaust steam is sent directly to the coils, thereby making the expendi- 
 ture for power nominal. Where live steam is not available for an engine 
 the fan may be driven by a motor. With the motor-driven fan, the 
 watchman can start the apparatus during exceedingly cold nights, and 
 thereby prevent the sand heaps from freezing. The ducts are usually 
 circular in section, made of galvanized iron and supported by the chords 
 of the building so as to clear the crane'way. 
 
Heating and Ventilating 
 
 581 
 
 The sketch below shows the usual arrangement for fans and ducts. 
 In shops of moderate size, where but one fan is required, the ducts, ©f 
 course, must nm all around the building. 
 
 Fig. 244.— Typical Arrangement of Heating and Ventilating System for 
 Foundry with Unobstructed Craneway. 
 
 From the ducts, discharge pipes are dropped at intervals of from 30 to 
 40 feet. These usually terminate about 8 feet above the floor hne, and 
 leave the ducts at an angle of about 45°, inclined in the direction of the 
 
582 Water Supply, Lighting, Heating and Ventilation 
 
 air currents. Where the discharges are dropped as above stated, the 
 open ends should incline about 20° from the vertical; they should 
 alternately face the walls and the center bay. Six square inches of dis- 
 charge opening are ordinarily allowed for every 1000 cubic feet of space, 
 and the aggregate area of the openings should be 25 per cent greater 
 than the area of the ducts. From these data the size of the ducts may 
 be calculated for any building of known dimensions. 
 
 Underground ducts with vertical discharge pipes are desirable, as 
 they offer no obstruction to foundry operations, but they are quite 
 expensive; the overhead ducts seem best to meet all requirements. 
 
 Where steam or hot air is used for heating, the matter of ventilation 
 requires no provision, except for that period of the day occupied in 
 melting, as the leakages are sufficient to supply an abundance of fresh 
 air. During the heat, vapor and gases rise in great volumes; to permit 
 them to escape or to permit fresh air to enter, the swiveled windows in 
 the monitor are opened. 
 
 Where steam heat is employed, discomfort is occasionally experienced 
 during cold or stormy weather, as the gases fall as soon as they begin 
 to cool, and the vapor is condensed by the incoming air. With the hot- 
 blast system this difficulty does not occur, since the plenum is sufficient 
 to drive out the gases and vapor through the open windows. Mr. W. 
 H. Carrier of the Buffalo Forge Company, Buffalo, N. Y., has discussed 
 the subject of Foundry Heating and Ventilating so fully in a paper pre- 
 sented at a meeting of the American Foundrymen's Association, that 
 advantage is taken of the opportimity presented through the courtesy 
 of the Buffalo Forge Company to make extensive extracts therefrom: 
 "The proper distribution of heat in the foundry is comparatively difficult. 
 In general the problem is that of a large open space, affording little 
 opportunity for efficient placing of direct radiation. On account of 
 the monitor type of building usually employed, there is relatively a 
 great height. The hot air rises up into the lantern and passes out through 
 the ventilators, if fans are not provided to deliver it near the floor. The 
 heated column of air in the building serves to draw cold air from with- 
 out at every opening. This inward leakage of cold air, not only de- 
 mands a great amount of heat, but makes a thorough distribution of 
 heat at the floor line most essential for comfort and economy of opera- 
 tion. A slight plenum, or outward leakage, of air at the doors and 
 openings, caused by the delivery and proper distribution of sufficient 
 heated air into the building is the only solution of the difficulty. Ample 
 ventilation is at times most necessary. The lantern t3^e of build- 
 ing is best adapted to quickly ventilate, since the ventilators simply 
 have to be opened to permit the hotter and lighter gases and vapors 
 
Heating and Ventilating 583 
 
 to pass out. External air must enter the building to replace that 
 escaping through the ventilators. Cold air entering the doors and 
 openings tends to cool and condense the rising vapors. It is there- 
 fore essential that a system be installed which will deliver warmed 
 fresh air during the pouring periods, when ventilation is of first im- 
 portance. 
 
 Rapid heating of the building in the morning means that the best 
 efficiency from the men will be obtained over the entire working period. 
 A system which is elastic, and which may be rapidly varied to suit the 
 requirements is to be favored. Coke or gas fired salamanders are appar- 
 ently the most economical means of heating, as all the heat goes directly 
 into the building. The atmosphere in a tightly closed building heated 
 by this method becomes intolerable, and if sufficient ventilation is 
 provided to make conditions healthful, the amount of heat required is 
 greater than with other systems. The grade of fuel used is also con- 
 siderably more expensive than that used in other systems of heating, 
 to say nothing of the care of a large number of separate fires scattered 
 about the building. 
 
 In heating with direct radiation, steam is usually employed, although 
 hot-water systems with forced circulation have been successfully oper- 
 ated. Unless there is a large amount of hot water available, it is not 
 an economical system to employ, on" account of the greatly increased 
 amount of radiating surface required at the lower temperature. In 
 steam heating, the high pressure, the low pressure or the vacuum system 
 of distribution may be used; the selection of the particular system 
 depends on load conditions. Where high-pressure steam is available, 
 and there is no exhaust steam, it should of course, be used. If, however, 
 there is no high pressure or exhaust steam available from the power 
 plant, then an independent low-pressure boiler should be installed, fur- 
 nishing steam at from 5 pounds to 10 pounds pressure. For low-pressure 
 work cast-iron boilers may be used; no boiler feed pumps are required. 
 The boiler should be placed at a level low enough for the condensation 
 to drain back by gravity. If this is impracticable, then a centrifugal 
 pump may be employed to return the condensed water to the boiler. 
 A vacuum system should always be used when exhaust steam from the 
 power plant is available. In a vacuum system of distribution, the 
 back pressure should not exceed i pound, as otherwise the losses will 
 outweigh the gain. The fan system is undoubtedly the best for foundry 
 heating and ventilating, and it is particularly adapted to the severe 
 requirements of foundries, and other buildings of this construction, 
 where there are large open spaces to be heated. The principal advantages 
 of the fan system over direct radiation are: 
 
584 Water Supply, Lighting, Heating and Ventilation 
 
 1. The thorough distribution of heat secured by discharging the air 
 under pressure through suitable outlets, with sufl&cient velocity to 
 carry the heat to the points where it is most needed without causing 
 perceptible draughts. 
 
 2. No heat is wasted as in direct radiation, where a large part is sent 
 directly through the walls, with slight effect upon the temperature of 
 the building. The fan system affords means of supplying heat directly 
 to the interior of the building. 
 
 3. No heat is wasted by heating unoccupied spaces, as along the roof 
 and in the monitor. Tests of the fan system installed in foundries have, 
 in certain instances, shown lower temperatures in the monitors than at 
 5 feet above the floor hne. 
 
 4. Fan systems heat up very much more rapidly in the morning, 
 when it is desirable to bring up the temperature in as short time as 
 possible. 
 
 5. It gives a rapid warm air change, which effectually removes 
 smoke, steam and dust during pouring time; an effect possible only 
 with a fan system. During such periods, when ventilation is required, 
 the fresh and return air dampers should be adjusted to take all the air 
 from out of doors. During the remainder of the day, however, the 
 greater part of the air should be returned from the building to the 
 apparatus, so that the heat required for ventilation may be the least 
 possible. Precaution should always be taken to see that this feature 
 is provided for. 
 
 6. Fan systems cost less to install properly, since the apparatus is 
 centrally located, and it is not necessary to pipe the steam to all parts 
 of the building as in direct radiation. 
 
 7. The cost of maintenance is less, since the radiating surface of a 
 direct system along the walls is frequently damaged, while in the cen- 
 trally-located fan apparatus, it is thoroughly protected. 
 
 As in direct radiation, steam or hot water can be used in the fan 
 system heater coils; but as the cool air is drawn over these coils by 
 the fan, a great deal more heat is obtained from the same amount of 
 heating surface. This permits the square feet of radiation to be re- 
 duced about two-thirds. The fan is often driven by a direct-connected 
 steam engine, the exhaust from which is used in the heater coils. This 
 is an exceedingly economical method, as practically all of the heat of 
 the steam is utilized. 
 
 A new type of fan heating system, which is giving the highest degree 
 of satisfaction, has been developed by the Buffalo Forge Company; this 
 is the direct air furnace system. Instead of burning 'fuel under boilers , 
 generating steam, transferring steam from boilers to heater coils through 
 
Heating and Ventilating 585 
 
 a long run of pipe, and finally giving up heat to air from the heater 
 coils, this system transfers the heat of the burning fuel directly to the 
 air for distribution. An efficiency of 85 to 90 per cent has actually 
 been attained, as against the usual efficiency of 50 to 60 per cent derived 
 from steam service. The Buffalo Forge Company has made many 
 installations using gas for fuel, and recently erected one in which pow- 
 dered coal was used. Fuel oil can also be employed. The construc- 
 tion of the furnace is similar to that for a water tube boiler. The hot 
 gasses pass through the tubes, a fan draws the circulating air around 
 the tubes, by which it is heated, and then distributes it through the 
 building. Fig. 244 shows one of these furnaces recently installed in an 
 important factory in the West. The main hot air ducts from the fan 
 are usually made of galvanized iron, and are carried in the roof trusses. 
 When these ducts are placed at a height not exceeding 20 feet, the air 
 may be delivered directly into the building through short outlets. The 
 design of these outlets is of particular importance to the success of the 
 system. The velocity must be properly proportioned to the height, 
 to the size of the outlet and to the horizontal distance which the air 
 is to be blown. The greater the distance and height above the floor, 
 and the smaller the outlets, the higher the velocity must be to obtain 
 the proper distribution. On the other hand, if the velocity is exces- 
 sive for these conditions, objectionable draughts will be produced. 
 
 In some cases the main pipe has to be placed too far above the floor 
 to permit good distribution of heat at the floor line with short outlets. 
 In such cases it is usual to provide drop pipes from the main at the 
 columns or along the side walls. Where the drop pipes are placed at 
 the colunms, each pipe is usually provided with two branches; one 
 blowing toward the base of the windows at the side walls, the other 
 blowing toward the center of the building. Where the drop pipes are 
 extended downward at the side walls, it is usual to provide three outlets 
 to each pipe, two blowing sidewise along the walls, and the third out- 
 ward toward the center of the building. 
 
 In wide buildings it is customary to run two lines of pipes along the 
 columns on each side; while in narrower buildings it is possible to 
 obtain an entirely satisfactory distribution of heat with one line of 
 main pipe, having outlets so proportioned as to blow across the building 
 to the further side. A very neat, though more expensive system of 
 distribution is with underground main ducts, with galvanized iron 
 vertical risers, arranged along the columns or side walls; or in some 
 instances, as in particularly wide buildings, at both places. The system 
 of outlets in this case will be practically the same as where drop pipes 
 are used. Fans may be either motor or engine driven. When an 
 
5S6 Water Supply, Lighting, Heating and Ventilation 
 
 abundance of exhaust steam is available for use in the heater coils, the 
 motor-driven fan will be found the more economical and satisfactory. It 
 is preferred by many on account of the simplicity of operation and the 
 shght care and attention required. With small fans it is good practice 
 to direct-connect the motor to the fan; but with the larger apparatus 
 the speed of operation is so low as to make it advisable to belt-drive the 
 fan, by reason of the high cost of slow speed motors. Engine -driven 
 fans are advisable when moderately high pressure steam is available. 
 The steam can be used to drive the fan and the exhaust is available for 
 the heater coils. This method is exceedingly economical, since prac- 
 tically all of the heat is utihzed. 
 
 The power used to drive the fan is almost negligible, as the engine is 
 really little more than a pressure reducing valve. The speed of operation 
 with engine drive is also much more flexible, allowing a wider range of 
 speed, as may be necessitated by varying weather conditions. Direct 
 radiation and the fan system of heating cost practically the same to 
 install, the fan system as a rule being somewhat cheaper. Of course, 
 with the fan system, the power necessary to drive the fan is additional, 
 and it might seem that the operating expense would be somewhat more 
 than with direct radiation ; but the more equable distribution of heat by 
 the fan system cuts down the losses and reduces the radiating surface 
 materially. The operating expenses of the two systems, however, vary 
 little in the long run. " 
 
CHAPTER XXVII 
 FOUNDRY ACCOUNTS 
 
 Any system of foundry accounting must be subject to variation in 
 details to meet the requirements of different classes of work. 
 
 A system suitable for a foundry producing pipe, car wheels or other 
 standard work must be modified in some of its details to adapt it to 
 the requirements of a jobbing foundry. The value of an accounting 
 system, aside from determining the cost of production, Ues in r-educing 
 the expenses and in pointing out by comparative analysis the direction 
 in which reductions can be made. 
 
 Cost keeping is too often neglected. Many foundrymen establishing 
 prices, etc., by those of competitors, have absolutely no knowledge of 
 actual costs. There are few branches of business in which the indirect 
 expenses, those apart from the cost of material and labor, exceed those 
 of the foundry. Only by constant comparison, by tracing increase or 
 decrease from one period to another, and continually following lines 
 indicating improved results, can the expenses be made to approach the 
 minimum. 
 
 An effective cost system must not only furnish accurate results, but 
 must furnish them promptly, so as to permit ready and periodical com- 
 parison. 
 
 Prompt information as to any means of increasing production or of 
 decreasing losses or costs greatly enhances its value. The system must 
 not be so elaborate as to render it impractical, but simplicity must not 
 be accompanied with neglect. One that is not accurately or system- 
 atically followed is worse than useless. Any effective system requires a 
 large amount of clerical work, but the results are profitable in the high- 
 est degree. 
 
 The one given below has been in satisfactory use by a large manu- 
 facturing establishment, making castings for its own consimaption. 
 
 An order emanates from the management, going to the drawing room. 
 There it is given a shop order number. A form bearing this number is 
 filled out, showing the patterns required, the drawing number, pattern 
 number and number of castings wanted from each pattern, date of 
 delivery from the foundry and any changes to be made. This form, 
 No. I, passes to the Requisition Clerk, who makes a requisition in quad- 
 
 587 
 
588 
 
 Foundry Accounts 
 
 ruple, form No. 2, on the foundry. This form is about six by nine inches; 
 and as many sets of blanks, all bearing the same shop order number, are 
 used as are required. These forms are in shape for indexing with 
 guide cards. Three of each set of these forms after completion are 
 sent to the foundry, and the fourth is filed in the office. 
 
 Of the three sets sent to the foundry, one is marked "Foundry Requisi- 
 tion," one "Pattern Shop" and the third "Core Room." 
 
 The foundry clerk fills in date of receipt, date for delivery of patterns 
 and cores and the casting date; then, having marked on them the 
 deUveries required, he transmits to the Pattern Shop and Core Room 
 their respective requisitions. The Pattern Shop and Core Room fore- 
 men each stamp them with date of receipt. 
 
 Form 2. 
 
 FOUNDRY REQUISITION 
 
 Williams & Jones 
 
 Shop Order, 5486. Date, 3/9/10. Castings wanted, 4/4/10. 
 
 For 25 9x12 C. Crank, S. Valve Throttling Engines. 
 
 Name of part 
 
 Drawing 
 number 
 
 Pattern 
 number 
 
 No. of 
 pieces 
 wanted 
 
 Alterations 
 
 Cylinder 
 
 7984 
 
 8092 
 8093 
 8140 
 8098 
 
 8099 
 7642 
 7990 
 7991 
 
 46,854 
 
 46,855 
 46,856 
 46,857 
 46,859 
 
 46,860 
 46,861 
 46,862 
 46,863 
 
 25 
 
 25 
 
 25 
 
 25 
 25 
 
 25 
 
 100 
 
 25 
 
 8 
 
 Increase thickness of 
 
 Front head 
 
 flange at exhaust out- 
 let Vs inch. 
 
 Back head 
 
 
 St'f'ng box gland 
 
 Steam chest cover 
 
 Steam chest glands 
 
 Cylinder lagging 
 
 Piston 
 
 Add He inch to each end 
 of cover. 
 
 
 
 
 
 Requisition received in foundry, 3/ 10/10. 
 Requisition received in pattern shop. 
 Requisition received in core room. 
 
 Order to be completed, 3/31/10.* 
 Floor date, 3/22/10. 
 Patterns wanted, 3/21/10. 
 Cores wanted, four sets, 3/22/10. 
 Four sets each day thereafter. 
 
 
 
 
 
 Record of Castings Made 
 
 
 
 
 
 Date 
 
 Good 
 
 Bad 
 
 Date 
 
 Good 
 
 Bad 
 
 Date 
 
 Good 
 
 Bad 
 
 Date 
 
 Good 
 
 Bad 
 
 3/22 
 
 3 
 
 I 
 
 3/29 
 
 2 
 
 
 
 
 
 
 
 
 3/23 
 
 4 
 
 
 
 
 
 
 
 
 
 
 
 3/24 
 
 4 
 
 
 
 
 
 
 
 
 
 
 
 3/25 
 
 4 
 
 
 
 
 
 
 
 
 
 
 
 3/26 
 
 4 
 
 
 
 
 
 
 
 
 
 
 
 3/28 
 
 4 
 
 
 
 
 
 
 
 
 
 
 
Pattern Card 
 
 589 
 
 In filling out the floor or casting date, the date of delivery, etc., the 
 foundry clerk knows that only four cyUnders can be made at each heat. 
 He therefore fixes the date for completion at 3/31/ 10; this allows four 
 days to provide for any contingencies. The Foundry Requisition is 
 then filed under its floor date." 
 
 At the end of each week the index cards up to that date are with- 
 drawn from the front and passed to rear of card box. There are enough 
 cards in the box to cover six months or a year as desired. 
 
 Any unfilled orders at the end of the week are advanced to the first 
 date of the coming week, so that the current orders are aU at the front 
 of the box. Each day the foreman and clerk spend time to select 
 orders and make out a program for the next heat. 
 
 As the orders are completed, each requisition with its supplementary 
 orders is filed away for reference. 
 
 The Foundry Pattern Loft is divided into two parts, one for uncom- 
 pleted orders (Live End), and the other for completed orders (Dead 
 End). 
 
 The patterns are delivered by Pattern shop at the Live End. 
 
 A man from Pattern Storage has a book in which he takes receipts 
 for patterns delivered. He also receipts for patterns which he removes 
 from Dead End. 
 
 Precisely the same system is pursued with core boxes. The Pattern 
 Shop delivers and removes the boxes, taking and giving receipts. 
 
 Attached to each pattern is a tag, on which all the data above the 
 heavy line is made out in Pattern Shop : all below is filled out in Foundry. 
 
 PATTERN CARD 
 
 o 
 
 
 Moulder's Tag. 
 
 Foundry Tag. 
 
 F 
 
 Date issued, 3/21/10. 
 
 : Date issued, 3/21/10 ' 
 
 
 
 Shop order, 5486. 
 
 Shop order, 5486. 
 
 r 
 
 Name of piece, 9X12 cylinder. 
 
 Name of piece, 9x12 cyUnder. 
 
 m 
 
 Pattern No. 46,854- 
 
 Pattern No. 46,854. 
 
 3 
 
 No. wanted 25. Date 3/31. 
 
 No. wanted 25, date, 3/31. 
 
 
 Name of moulder, John Hayes. 
 
 Name of moulder, John Hayes. 
 
 
 Date in sand, 3/22/10. 
 
 Date in sand, 3/22/10. 
 
 
 Tally //// //// //// //// //// 
 
 Moulder's time. 
 
 
 Moulder must return this tag 
 
 John Hayes - ¥ ¥ ¥ ¥ ¥ 
 
 
 with pattern. 
 
 John Hayes - V- ¥ ¥ 
 Wm. Moran - ¥ ¥ ¥ ¥ ¥ 
 Wm. Moran — %' ¥ ¥ 
 
 The tag is perforated across the middle. When the pattern is issued 
 to the moulder, the clerk tears off and retains the foundry tag on which 
 
590 
 
 Foundry Accounts 
 
 the time is entered and then filed away. The moulder's tag is de- 
 stroyed when pattern is removed to storage. 
 
 The foreman of core room enters time of core makers on core room 
 requisition. It will be noticed that the clerk has not only entered on 
 the Foundry tag the time of John Hayes, but also that of Wm. Moran, 
 helper. 
 
 There must be a case in which are kept cards showing records of pig 
 iron, scrap, coke, sand, sea coal, fire clay and any other material re- 
 ceived in car lots. 
 
 PIG IRON CARD 
 
 Car, N. P. R.R., 438,827 
 Wt., G. T., 24.23. 
 
 Pig Iron 
 From Jones, Smith & Company 
 Brand No. 2, S. 
 A nalysis 
 
 Received, 2/10/10. 
 Price. $16.50 Did. 
 
 Silicon 
 2.38 
 
 Sulphur 
 .032 
 
 Phosphorus 
 .43 
 
 Manganese 
 • 54 
 
 Net weight, 54,282. 
 Expended, 54,660. 
 Overrun, 378. 
 
 o I 00 
 
 o 6 o o lo o Q ! 
 o, q o_ o^ 00.0 : 
 
 IN 00" o" o" PJ rO ai 00 
 
 00 M 1-1 1-1 
 
 •^ :;;;:;; ' 
 
 \r, 
 
 -T) 
 
 ^ s ■ 
 
 g) a ::::::: § 
 JS » ^ 
 
 . . ^-- "-- ~\ ~\ ^-- ^^ ^-^ X 
 
 +j-(_>(NC»lNCqM(NN O 
 
 On back of this card the withdrawals and corresponding dates are 
 entered and balance cast up on face. 
 
 The cards for sand, fire clay, etc., are the same as for coke, without 
 the analysis. It is advisable, however, to have these supplies analyzed 
 occasionally. 
 
Pig Iron 
 COKE CARD 
 
 591 
 
 COICE 
 
 
 Form 5. 
 
 
 Car No. 7482, N. Y. C. 
 
 Received, 2/7/10. 
 
 Ovens, Hamilton by-product. 
 
 Weight, 32,600. 
 
 $4.85 Deld. 
 
 
 Analysis 
 
 
 
 Per cent 
 
 Fixed carbon 
 
 8s 
 
 Sulphur 
 
 8 
 
 Ash : 
 
 II 
 
 Moisture 
 
 T 
 
 1 
 
 As a matter of convenience to the foreman in making up the mixture, 
 it is desirable to enter the pig iron in a special book, as per diagram 
 below as well as to keep the cards. 
 
 PIG IRON 
 
 Form 6. 
 
 Sample Page of Pig Iron Book. 
 
 Date 
 
 re- 
 ceived 
 
 Car 
 
 No. 
 
 Brand 
 
 Net 
 weight 
 
 Ex- 
 pended 
 
 12/9/09 
 
 132,568 
 
 No. 2S 
 
 78,594 
 
 12/20 
 
 12/9/09 
 
 35.689 
 
 No. 2S 
 
 76,432 
 
 12/27 
 
 12/1S/09 
 
 46,351 
 
 No. 2 N 
 
 69,496 
 
 1/14/10 
 
 1/7/10 
 
 25,135 
 
 No. 3N 
 
 58,439 
 
 2/8/10 
 
 2/10/10 
 
 439.827 
 
 N0-2S 
 
 54,282 
 
 3/2/10 
 
 Analysis 
 
 I* Si 3.2s S .03 P .89 Mn .82 
 
 2* Si 3.09 S .032 P .85 Mn .76 
 
 1 Si 2.84 S .038 P .76 Mn .68 
 
 2 Si 2.80 S .040 P .74 Mn .66 
 
 1 Si 2.19 S .027 P .29 Mn .75 
 
 2 Si 2.10 S .026 P .27 Mn .74 
 
 1 Si 1.67 S .024 P .26 Mn .69 
 
 2 Si 1.65 S .023 P .24 Mn .67 
 
 .52 
 
 1 Si 2.38 S .032 P .43 Mn .54 
 
 2 Si 2.2s S .036 P .48 Mn 
 
 * No. I is the furnace analysis; No. 2, that of the foundry chemist. 
 
 The Heat Book is given on page 592. In this book the foreman enters 
 for the coming heat the irons which are to be used and the mixture. 
 The remainder of the account may be filled out later by the clerk after 
 returns are made. This book is of the greatest importance as it enables 
 
592 
 
 Foundry Accounts 
 
 the foreman to repeat at once any mixture used at any time, or for any 
 particular purpose. 
 
 The sheet shown is for the heat of 2/22/ from which 4 cyUnders are 
 to be poured and a special charge (the first) containing 10 per cent steel 
 scrap is made. The cylinders weigh about 500 pounds each, and as 
 there are crank disc and other castings requiring strong iron, the entire 
 first charge will contain steel. 
 
 The charges are 4000 pounds each, and the mixture is uniform through- 
 out the heat, except for first and last charges. Turning to the Pig Iron 
 Book, the foreman selects such iron as will furnish the desired mixture 
 for cylinders, also those for the remaining charges and enters them on 
 the heat book. A memorandum is given the boss of the yard gang, 
 showing the car numbers and the amount of iron from each car for each 
 charge. 
 
 The number of charges for the ordinary mixture is left blank until 
 later in the day, when the total amount to be melted is ascertained. 
 
 The weighman has a pad of forms upon which he prepares a slip for 
 each charge giving the car number, weight of iron from each car, weight 
 of coke and lime. 
 
 Each charge of iron is piled by itself on cupola platform in regular 
 order. The coke with limestone is sent up in cars as the charging of 
 cupola proceeds. 
 
 SAMPLE SHEET FROM HEAT BOOK 
 
 Williams & Jones Foundry 
 
 Form 7. 
 
 
 
 
 
 
 
 
 Heat of 3/22/10. 
 
 
 
 Weight 
 
 
 
 
 
 
 
 
 
 Pig iron 
 
 Car 
 No. 
 
 per 
 charge. 
 
 No. of 
 charges 
 
 
 Analysis 
 
 
 
 Remarks 
 
 
 
 pounds 
 
 
 
 
 
 
 
 
 
 Silvery 
 
 8.296 
 
 200' 
 
 
 Si 4.20 S 
 
 .03 
 
 P 
 
 .72 
 
 Mn 
 
 .68 
 
 
 No. 2 Sou . 
 
 439,827 
 
 400 
 
 
 Si 2.25 S 
 
 .036 
 
 P 
 
 .48 
 
 Mn 
 
 • 52 
 
 
 No. 2 Sou. . 
 
 46,351 
 
 400 
 
 
 Si 2.10 S 
 
 .026 
 
 P 
 
 .27 
 
 Mn 
 
 .74 
 
 First 
 
 No. 2 Nor.. 
 
 328,503 
 
 800 • 
 
 I 
 
 Si 2.29 S 
 
 .023 
 
 P 
 
 .24 
 
 Mn 
 
 .67 
 
 charge 
 
 No. 2 Nor.. 
 
 
 
 
 
 
 
 
 
 
 
 Scrap 
 
 
 1800 
 
 
 Si 2.10 S 
 
 .084 
 
 P 
 
 .63 
 
 Mn 
 
 .63 
 
 
 Steel scrap . 
 
 
 400. 
 
 
 
 
 
 
 
 
 
 No. 2 Sou. . 
 
 27,935 
 
 800^ 
 
 
 Si 3.75 S 
 
 .017 
 
 P 
 
 .86 
 
 Mn 
 
 .36 
 
 
 No. 2 Nor.. 
 
 328,503 
 
 600 
 
 
 Si 2.29 S 
 
 .023 
 
 P 
 
 .24 
 
 Mn 
 
 .67 
 
 20 
 
 No. 2 Nor.. 
 
 45,541 
 
 200 
 
 20 
 
 Si 1.92 S 
 
 .024 
 
 P 
 
 .28 
 
 Mn 
 
 .63 
 
 charges 
 
 Scrap 
 
 
 2400 
 
 
 Si 2.10 S 
 
 .084 
 
 P 
 
 .68 
 
 Mn 
 
 .63 
 
 Last 
 
 Clean-up . . . 
 
 
 1050 
 
 I 
 
 
 
 
 
 
 
 charge 
 
Sample Sheet From Heat Book 
 
 593 
 
 Amount Charged 
 
 Pig iron. 
 
 
 
 33.800 
 
 Scrap. 
 
 
 
 49,800 
 
 Steel scrap. 
 
 
 
 400 
 
 Clean-up. 
 
 
 
 1,050 
 
 Total. 
 
 
 
 85,050 
 
 Coke. 
 
 10,950. 
 
 Returned 320. 
 
 10,630 
 
 Fhix. 
 
 
 
 1,600 
 
 Production 
 
 Good castings. 
 
 
 66,466 
 
 Bad castings. 
 
 
 2,708 
 
 Gates and sprues. 
 
 
 6,106 
 
 Over iron. 
 
 
 5. 143 
 
 Shot. 
 
 
 650 
 
 Clean-up. 
 
 
 1,670 
 
 Total accounted for. 
 
 
 82,743 
 
 Lost in melt. 
 
 
 2,307 
 
 Per cent melt in good castings. 
 
 
 78.2 
 
 Per cent castings good. 
 
 
 96.1 
 
 Per cent castings bad. 
 
 
 3.9 
 
 Per cent melt in returns. 
 
 
 19.0 
 
 Per cent loss in melt. 
 
 
 2.7 
 
 Iron melted per pound coke. 
 
 
 8 lbs. to I 
 
 Mixtures 
 
 1st charge special. 
 Regular charges. 
 
 5% car 8296. 
 20% car 328,503. 
 20% car 27,935. 
 60% scrap. 
 
 10% car 439,827. 
 
 10% steel. 
 
 15% car 328,503. 
 
 10% car 46,351. 
 45% scrap. 
 5% car 45,541. 
 
 Analysis 
 
 Computed. 
 
 1st charge. 
 
 Si 1.66 
 
 S 
 
 .075 
 
 p 
 
 .42 
 
 Mn 
 
 .46 
 
 Have 
 
 analyses 
 
 Computed. 
 
 Regular. 
 
 Si 2.21 
 
 S 
 
 .088 
 
 p 
 
 .63 
 
 Mn 
 
 .47 
 
 made 
 
 as re- 
 
 Actual. 
 
 1st charge. 
 
 Si 1.64 
 
 s 
 
 .080 
 
 p 
 
 .43 
 
 Mn 
 
 .45 
 
 quired 
 
 
 Actual. 
 
 Regular. 
 
 Si 2.23 
 
 s 
 
 .092 
 
 p 
 
 .65 
 
 Mn 
 
 • 44 
 
 
 
594 
 
 Foundry Accounts 
 
 Cost of Labor 
 
 
 Productive 
 
 Non- 
 productive 
 
 Totals 
 
 Gen. 
 
 Av. 
 
 
 Hours 
 
 Cost 
 
 Hours 
 
 Cost 
 
 Hours 
 
 Cost 
 
 Cost 
 per 
 hour 
 
 Foundry 
 
 Core room 
 
 Cleaning room 
 
 I 133- 6 
 II3-6 
 
 $274.90 
 34.08 
 
 180 
 36 
 234 
 
 S28.80 
 
 5.76 
 
 39-84 
 
 1697.2 
 
 $383.38 
 
 22.60 
 
 Total 
 
 1247.2 
 
 $308.98 
 
 450 
 
 $74.20 
 
 Helpers are 
 included in 
 foundry as 
 productive. 
 
 Blast on, i :5o p.m. 
 First tap, 2:15 p.m. 
 Test bar special. 
 Test bar regular. 
 
 Pressure, 9 ounces. 
 Bottom dropped, 4:45 p.m. 
 Transverse, 2800. 
 Transverse, 2200. 
 
 First iron, 2 p. 
 
 The melter and boss of the yard gang are each furnished with a copy 
 of charging schedule. After the charges are all up, the weighman turns 
 in to foundry office, slips for the bottom coke, and one for each charge 
 giving complete weights of everything entering the cupola. 
 
 Form 9. 
 
 Charging Schedule 
 
 Date, 3/22/10. 
 
 Charges 
 
 1st charge . 
 
 20 charges . 
 
 Last charge . 
 
 Materials 
 
 Bottom coke 
 
 Steel scrap 
 
 Car 8296 
 
 Car 439.827 
 
 Car 46,351 
 
 Car 328,503 
 
 Scrap (selected) 
 
 Coke 
 
 Car 27,935 
 
 Car 328,503 
 
 Car 45.541 
 
 Scrap .' . . . 
 
 Returned coke 
 
 Clean-up 
 
 Use 80 pounds limestone from third to 
 nineteenth charge inclusive. 
 
 Weights 
 
 2850 
 400 
 200 
 400 
 400 
 800 
 
 1800 
 
 400 
 800 
 600 
 200 
 2400 
 
 100 
 1050 
 
Weigh Slips 
 
 595 
 
 Form lo. 
 Charge No. i. 
 
 Weigh Ticket 
 
 Date 
 
 3/22/10. 
 
 Coke bottom 
 
 
 
 2850 
 400 
 200 
 400 
 400 
 . 800 
 1800 
 
 Steel scrap , 
 
 
 
 Car 8296 
 
 
 
 Car 439,827 
 
 
 
 
 
 
 Car 328,503 
 
 
 
 Scrap 
 
 
 
 
 
 
 Limestone. 
 
 Form 10. 
 Charge No. 2. 
 
 Weigh Ticket 
 
 Date, 3/23/10. 
 
 Coke. . . 
 
 
 400 
 
 Car 27 935 
 
 
 800 
 
 Car 328,503 
 
 
 600 
 
 Car 45,541 . . ' 
 
 
 200 
 
 Scrap 
 
 
 2400 1 
 
 
 Limestone. 
 
 On the day following the heat, after recovering the iron from the 
 gangways, cinders, etc., the yard foreman turns the weight into the 
 office. 
 
 Form II. 
 3/23/10. 
 
 Returns 
 
 FROM 
 
 Foundry 
 
 Heat of 3/22/10. 
 
 
 
 
 
 650 
 
 
 
 
 
 
 Shot 
 
 
 
 
 650 
 
 Clean-up 
 
 
 
 
 1670 
 
 Returned coke 
 
 
 
 
 ^20 
 
 " 
 
 The bad castings on above slip are those thrown out in the foundry, 
 to which are subsequently added those rejected in the cleaning room. 
 
596 Foundry Accounts 
 
 From the moulder's tags, turned in on the 22nd, and from information 
 obtained from the floor concerning work on tags which have not been 
 turned in, the clerk prepares in part, duphcate cleaning room reports. 
 He enters the shop order numbers, pattern numbers, names of parts 
 and nmnber of parts made. This report then goes to foreman of clean- 
 ing room, who completes it, sending one copy to the foundry ofl&ce and 
 the other to the work's office. 
 
 The form is given on page 597. As many sheets as are necessary are 
 used for each heat. 
 
 The Time Book, Weigh Tickets, Foundry Returns and Cleaning Room 
 Report furnish all the data, except analysis and test, for completion 
 of entry in heat book for 3 22 10. Information as to the last two items 
 is obtained from time to time as required. The heat report is made out 
 in duplicate; original sent to Works Office and duplicate filed in Foundry. 
 This is followed by a weekly summary. At the end of each month an 
 inventory is taken of all supplies; and their cost, per himdred poimds 
 good castings, is determined for the month passed. This cost is used in 
 making out foundry reports for the succeeding month. 
 
 All supplies except the btilky materials, such as sand, fire clay, etc. 
 are kept in store room and are issued upon requisition from foremen 
 or clerk, upon blanks as per sketch. 
 
 Requisition on Dale, 3/21/10. 
 
 Store Keeper, Issue to 
 
 Jno. Sullivan, 
 5 Pounds Silver Lead. 
 
 Wm. Wilson, Foreman. 
 
 These requisitions, together with tallies of sand, fire clay, etc., are 
 turned into office by store keeper at end of month. 
 
 Careful scrutiny and comparison of these monthly statements and 
 expenditures result in marked savings. They promote among the 
 departments a strife for the lowest record. The reduction in the amount 
 of core supplies, nails, rods and sand is especially noticeable. 
 
 As regards iron flasks and other castings made for the foundry, if 
 they are for permanent equipment, they are so charged. If on the 
 other hand they are for temporary ser\dce, they are charged to foundry 
 at cost of labor, plus the difference between the cost of good castings 
 and scrap. 
 
 Monthly comparisons, or more frequent if desired, are made with 
 statements from the works office. Comparisons are likewise made at 
 the end of the fiscal year. 
 
Cleaning Room Report 
 
 597 
 
 TO T) 
 
 rONTfON'^NO 
 
 00 O^ O* ro M ro 00 ^ 
 
 S.6 
 
 rOM-*fON-*CN|VOH 
 
 fJN-^fVjeqrtCStOW 
 
 
 o aj w ij w ^ :=; 
 
 ,<^ 
 
 &; &h" o 0^ ►^ p^ 
 
 M i-i w O O O 
 M (M <N (N (N N 
 
 
 P! N <N <N CS CM 
 
 .S a Ti<s ^ ,^ ,^ "1 o o 
 
 OfeCQOTCOWOPnP^ 
 
 ^ O 
 CM 
 
 
 
 00 
 
 =0. 
 
 00 
 
 
 
 *- 
 "§ 
 
 «5 
 
 to 
 
 1 
 
 lO 
 
 1 
 
 § 
 s 
 
 s 
 s 
 
 s 
 
 ^ 
 
 lO 
 
 1 
 
 
598 
 
 Foundry Accounts 
 
 Form 14. 
 
 FOUNDRY 
 
 Williams & 
 Heat of 
 
 Grade 
 
 No. I 
 
 
 No. 2 
 
 
 No. 3 
 
 
 No. 4 
 
 
 
 Car No. 
 
 Silvery 
 
 8296 
 
 Weight 
 200 
 
 Car No. 
 Sou. 
 
 439,827 
 46,351 
 27,935 
 
 Weight 
 
 No. 2 N.^ 
 
 400 
 
 400 
 
 16,000 
 
 Car No. 
 
 328,503 
 45,541 
 
 Weight 
 
 12,800 
 4,000 
 
 Car No. 
 
 Weight 
 
 Weight... 
 Cost 
 
 
 200 
 $1.49 
 
 
 16,800 
 S123.73 
 
 
 16,800 
 $127.51 
 
 
 
 
 
 
 
 
 
 
 _^ 
 
 
 
 "rtij 
 
 -S.r- 
 
 
 Returns not 
 including 
 
 bad 
 castings 
 
 ■S^ 
 
 •0 
 
 '1.1 
 
 '^0 
 
 
 H 
 
 Cost 
 
 Iron 
 
 goo 
 
 casti 
 
 
 
 J6 
 
 8° 
 
 |1^ 
 
 Weight... 
 
 85.050 
 
 66,466 
 
 2708 
 
 13,569 
 
 2307 
 
 82,743 
 
 78.2 
 
 96.1 
 
 Cost 
 
 $634.66 
 
 $520.73 
 
 
 
 
 
 
 
 Costs 
 
 
 
 
 
 
 
 to 
 
 w 
 
 >. to 
 
 
 
 
 
 
 w M 
 
 h OT M 
 
 W M 
 
 H m M 
 
 
 c 
 
 1 
 
 
 > 
 
 ^1 
 
 3 
 e2 
 
 ill 
 
 
 
 III 
 
 '-'00 
 
 otal found 
 
 cost per 
 100 pound 
 ood castin 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 M 
 
 '^'' M 
 
 M 
 
 H M 
 
 Hours 
 
 1133-6 
 
 113. 6 
 
 450 
 
 1697.2 
 
 2.55 
 
 
 
 
 Cost 
 
 $274.98 
 
 $34.08 
 
 $74.40 
 
 $383.38 
 
 $0.5765 
 
 $0,0396 
 
 $0,783 
 
 $1,399 
 
Foundry Reports 
 
 599 
 
 REPORTS 
 
 Jones Co. 
 3/22/10. 
 
 
 
 
 
 
 
 
 CO a 
 
 
 
 
 to 
 
 
 
 
 ^.13 
 
 iH-o 
 
 
 — 0. 
 
 11 
 
 ^1= p. 
 
 1 
 
 .2" 
 
 
 
 
 
 
 IP 
 
 ^§1 
 
 
 
 
 
 
 
 
 
 400 
 
 49,800 
 
 loso 
 
 85,050 
 
 10,630 
 
 1600 
 
 8-1 
 
 
 
 $3.00 
 
 $348.60 
 
 $4.20 
 
 S608.53 
 
 $25.53 
 
 So. 60 
 
 
 $0,746 
 
 
 
 3.9 
 
 ga 
 
 
 Total cost of melt . . 
 Cr. 
 
 Returns 16,275 pounds 
 .70 
 
 Cost of iron in good 
 casting 
 
 $634.66 
 113.93 
 
 III 
 
 520.73 
 
 
 $0,783 
 
6oo 
 
 Foundry Accounts 
 WEEKLY FOUNDRY REPORT 
 
 Williams & Jones Foundry 
 
 Form IS 
 
 • 
 
 
 
 
 
 
 
 Heats of 3/23-2S and 28/10. 
 
 Date 
 
 
 
 
 of 
 
 
 Consumption 
 
 Product 
 
 heat 
 
 
 
 
 u 
 
 "a 
 
 "2 
 
 6-- 
 
 0. 
 
 2 
 
 t. 
 
 
 
 1 
 
 3 
 
 -si 
 
 
 1^1 
 
 || 
 
 1 
 
 1 
 
 ^•S 
 
 ^•S 
 
 c^ 
 
 !/3 
 
 H 
 
 
 
 fe 
 
 0^ 
 
 
 M| 
 
 -^^ 
 (4-^^ 
 
 h 
 
 23 
 
 36,500 
 
 5,800 
 
 32,980 
 
 5.000 
 
 80,360 
 
 11,250 
 
 1250 
 
 57,859 
 
 2703 
 
 16,172 
 
 3626 
 
 80,360 
 
 25 
 
 27,720 
 
 3.600 
 
 23,880 
 
 5.000 
 
 60,200 
 
 9.540 
 
 900 
 
 43,344 
 
 1340 
 
 13,244 
 
 2272 
 
 60,200 
 
 28 
 
 27,520 
 
 7,800 
 
 26,800 
 
 
 62,200 
 
 9.930 
 
 950 
 
 45.406 
 
 1900 
 
 12,406 
 
 2488 
 
 62,200 
 
 Totals.. 
 
 91.740 
 
 17,280 
 
 83.740 
 
 10,000 
 
 202,760 
 
 30,720 
 
 3100 
 
 146,609 
 
 5943 
 
 41,822 
 
 8386 
 
 202,760 
 
 Summary 
 
 Total iron melted 
 
 Total coke used 
 
 Total flux used 
 
 Total cost melt 
 
 Credit 
 
 Returns (including bad castings) 7oj^ per 100 pounds 
 
 Total loss 
 
 Total good castings 
 
 Total bad castings 
 
 Total productive labor 
 
 Total non-productive labor 
 
 Total labor 
 
 Total cost of supplies 
 
 Total foundry cost of good castings . 
 
 Per cent of melt in good castings 
 
 Per cent of melt in bad castings 
 
 Per cent of melt in bad return (including bad cast- 
 ings) 
 
 Per cent of melt in loss 
 
 Per cent of castings good 
 
 Per cent of castings bad 
 
 Average cost of labor per hour 
 
 Cost of iron per 100 pounds 
 
 Cost of iron melted per 100 pounds 
 
 Cost of iron in good castings oer 100 pounds 
 
 Cost of labor, good castings per 100 pounds 
 
 Cost of supplies, good castings per 100 pounds 
 
 Total foundry cost, good castings per 100 pounds . 
 Iron melted per pound of coke 
 
 Pounds 
 
 20,7260 
 
 30,720 
 
 3,100 
 
 47,765 
 
 8,386 
 
 146,609 
 
 5.943 
 
 Hours 
 2,482 
 1,490 
 3.972 
 
 6.6 lbs. 
 
 $1476.09 
 
 74.50 
 
 1. 17 
 
 1551.76 
 
 33460 
 
 615.72 
 246.29 
 
 Per cent 
 72.3 
 2.93 
 
 23.5 
 4-1 
 
 96.1 
 
 3.9 
 
 Cents 
 
 21.7 
 0.728 
 0.76s 
 
 1217.16 
 
 826.01 
 
 58.05 
 
 2137.22 
 
 0.830 
 0.588 
 0.0396 
 1.4576 
 
Monthly Expenditure of Supplies 
 
 6oi 
 
 Form i6. 
 
 MONTHLY EXPENDITURE OF SUPPLIES 
 
 Williams & Jones Foundry 
 
 February, 1910. 
 
 Materials 
 
 Quantity 
 
 OS 
 
 o ^ 
 
 Anchors 
 
 Belting 
 
 Belt lacing 
 
 Bellows 
 
 Beeswax 
 
 Bolts 
 
 Brick, red 
 
 Brick, fire 
 
 Brick, block 
 
 Brooms 
 
 Barrows, wheel 
 
 Barrows, pig iron 
 
 Brushes, soft 
 
 Brushes, hard 
 
 Brushes, core 
 
 Brushes, casting 
 
 Brushes, camel's hair. . . 
 
 Brushes, paint . '. 
 
 Brushes, white wash. . . 
 
 Brushes, wheel 
 
 Blocks, chain 
 
 Candles 
 
 Cable wire 
 
 Carbons , 
 
 Castings 
 
 Cans, blow 
 
 Chisels, cold 
 
 Chaplets 
 
 Charcoal 
 
 Chain 
 
 Chain links 
 
 Chalk 
 
 Chalk, line 
 
 Clay 
 
 Clay, fire 
 
 Clamps 
 
 Clamps, spike 
 
 Clamps, screw 
 
 Core, compound dry. . . 
 Core, compound liquid 
 
 Core vent, metallic 
 
 Coke forks 
 
 Coke baskets 
 
6o2 Foundry Accounts 
 
 Monthly Expenditure of Supplies (Continued) 
 
 Materials 
 
 Quantity 
 
 3s 
 
 
 3 O 
 
 Coke scoops 
 
 Crow bars 
 
 Crucibles 
 
 Cloth wire ...;... 
 
 Cups, tin 
 
 Cutter's emery. . . 
 Facing mineral... 
 
 Flour 
 
 Fuel 
 
 Gauges, wind 
 
 Gauges, air 
 
 Globes, electric . . . 
 Globes, lantern. . . 
 
 Glue 
 
 Glutrin 
 
 Grease 
 
 Hammers 
 
 Handles, hammer 
 Handles, sledge... 
 
 Hose, air 
 
 Hose, water 
 
 Hose, couplings . . 
 
 Hose, nozzles 
 
 Iron bar 
 
 Iron, sheet 
 
 Irons, draw 
 
 Irons, flasks 
 
 Jackscrew 
 
 Jack-bolts 
 
 Levels, spirit 
 
 Lead, bar 
 
 Lead, sheet 
 
 Lead, pipe 
 
 Lead, red 
 
 Lead, white 
 
 Lead, silver 
 
 Lime 
 
 Lumber 
 
 Litharge 
 
 Lycopodium 
 
 Mallets 
 
 Mauls 
 
Monthly Expenditure of Supplies 
 Monthly Expenditure of Supplies (Continued) 
 
 603 
 
 Materials 
 
 Manganese, ferro 
 
 Mercury 
 
 Molasses 
 
 Nails 
 
 Nuts 
 
 Oil, core 
 
 Oil, coal 
 
 Oil, belt 
 
 Oil, lard...." 
 
 Oil, linseed 
 
 Oil, hard 
 
 Oil, black 
 
 Oil, machine .... 
 
 Oil, rosin 
 
 Oil, cans 
 
 Pails, iron 
 
 Pails, wood 
 
 Pencils, lead. . . . 
 
 Pipe, iron 
 
 Pipe, fittings 
 
 Picks, cupola 
 
 Pliers 
 
 Pliers, cutting... 
 Pots, sprinkling. 
 
 Paper, sand 
 
 Paper, toilet 
 
 Paper, emery 
 
 Paper, wrapping. 
 
 Rammers 
 
 Rammers, bench 
 
 Riddles 
 
 Riddles, brass 
 
 Rivets, copper... 
 
 Rivets, iron 
 
 Rosin 
 
 Rope 
 
 Saws, hand 
 
 Saws, hack 
 
 Screws 
 
 xScrews, drivers . . . 
 
 Stationary 
 
 Scrapers - 
 
 Silicon, ferro 
 
 Straps, lifting. . . , 
 Stars, tumbler. . . 
 Sand, moulding , 
 
 Quantity 
 
 OS 
 
 
 ■-BB 
 
6o4 Foundry Accounts 
 
 Monthly Expenditure of Supplies (Continued) 
 
 Materials 
 
 Quantity 
 
 2S 
 o o 
 
 ^2 
 
 •S6 
 
 a o 
 
 o ^ 
 
 H 
 
 Sand, lake 
 
 Sand, bank 
 
 Sand, fire 
 
 Shovels, moulders' 
 Shovels, laborers' . , 
 Sprayers, blacking. 
 
 Sponges 
 
 Smooth-on 
 
 Swabs , 
 
 Sledges 
 
 Stone, emery 
 
 Salt 
 
 Sulphur 
 
 Sea coal 
 
 Talc 
 
 Tacks 
 
 Torches, blow 
 
 Twine 
 
 Straw 
 
 Vitriol 
 
 Wire, iron 
 
 Wire, copper 
 
 Wire, wax vent 
 
 Wire, cable 
 
 Washers 
 
 Wheels, emery 
 
 Wheels, sheave 
 
 Wheels, barrow 
 
 Wrenches, open 
 
 Wrenches, monkey. 
 Wrenches, pipe 
 
 Total $284.56 
 
 Good castings for month 7X8.57- 
 
 Cost of supplies for 100 good castings for February, 1910 $0.0396 
 
 Use this price for the month of March, 1910. 
 
Monthly Comparisons of Foundry Accounts 
 
 605 
 
 O ^ 
 
 SI 
 
 g g 
 
 o g 
 
 S § 
 
 <! 2 
 
 i i 
 
 S I 
 
 § s 
 
 fO t- o 
 
 M t~ 00 
 «0 00 t^ 
 
 
 ioOOOnOI>0 >/5 
 
 
 
 
 s 
 
 ^ 
 
 S 
 
 ^^ 8 
 
 ^ 
 
 t~ 1/5 rfoo '^ 
 
 
 ro 
 
 " 
 
 O cd 
 O 
 
 2 S^ 6 
 
 COCO 
 
 a g -^ SI'S § 
 
 ■S -g ^* 2 S' PQ CC 
 
 f' C3 <u . . . . 
 
 ;3 in ;h (4 Ih 
 
 w x* O, 0000 
 
 ^ 3 O, XI 43 J3 XJ 
 
 S o 
 
 M I- 
 
 S3 
 
 O 
 
 2 -a 
 
 
 
 
 
 OOco 
 
 ' Jj +i rQ 
 
 «-• "2 u. X! 
 
 en O. 
 
 o c 
 
 a> C bo O 
 
 C! o c a 
 
 a-Sl o 
 
 G e! y +, 
 
 1 it 8 
 
 rt (U (U o 
 
 PQ0:!P^ H 
 
6o6 
 
 Foundry Accounts 
 
 
 g 
 
 O . 
 
 >< 
 
 O ^ 
 
 2 i 
 8 I 
 
 H 
 
 s ^ 
 
 l^aox 
 
 ro VO !-<' I> O 
 t^ IT) (£) VO 1/2 
 
 ut sscrj 
 
 t^co ino rCOoO O t~' 
 N M(0 CON lOOOOO 
 
 t~<0 N 00 
 
 : IN r- 00 
 ci m" in r<5 ci ci cT r<5 N ci 
 
 sSupsBO p-eq 
 Suipnpui 
 
 OH"^t^cyiM(NTr 
 
 s3uiq.ffeD 
 pBg 
 
 pobo 
 
 xtiM 
 
 95100 
 
 \e%oj^ 
 
 ^o^s 
 
 dBJog 
 
 iiojx 3ijj 
 
 uoji Sid 
 
 AjBniqa^ 
 
 M 
 
 „ 
 
 
 
 IN 
 
 
 
 
 
 m 
 
 o Q 
 
 M 
 
 
 
 
 ^ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 W) 
 
 00 
 
 
 t> 
 
 in o> 
 
 l~ 
 
 M 
 
 M 
 
 M 
 
 !N 
 
 " 
 
 IN 
 
 '^ 
 
 
 N 
 
 IN 
 
 M M 
 
 S 
 
 O^OlHOOooallNO)■*^0 
 lO00wt-iTtI>OiO-*0 
 
 OOOOOOOO 
 M -^rOM ir> ir, in pTi I. 
 
 l-IOOO>Ot^(NI>0^ 
 
 m" m" ai o" oo" o" i> oi <N m" cf> cri 
 
 H IN <0 VO 
 
 VO lO lO 
 
 R-g 8 
 
 <0 r^ Tf 
 
 * 00 00 t^ O^ 00 00 
 
 _ °. '^ °°. "^ °° °0 °0 
 X) di'^ o" M (M oo" 1/5 l-^ (nT ro to" 
 <NIN(Nro<MrOMM<NrOINP) 
 
 OOOOOiJJOOOOOO 
 I>-1^0^0000 OCSINt>OlNIN 
 
 " r<5 oo" oo" ro o" lO di VO vo" l> »> 
 "*■'""■-" M IN W m Ol tM 
 
 ro IN <N (N (N 
 
 fOiOOOONiOt-OJrO>000 iS 
 MHMMIHWNIN 5 
 
 H 
 
Monthly Comparison of Foundry Accounts 
 
 607 
 
 
 w 00 f- 
 00 ITi O 
 
 tS lO •^ 00 
 
 01 <o 
 
 ro O^ w o^ t^ t^ t^ 
 (^ (^ O ro M O 6 
 
 0\ N 
 <0 cs 
 
 00 OOvOO SvOO^lO 
 oi cfi o" oThh Cf> lO li? 
 
6o8 
 
 Foundry Accounts 
 
 
 <S IT) 
 
 ^^^!5 
 
 8 
 
 g 
 
 vo ro i> oo 
 
 € 
 
 ^ 
 
 
 cs 
 
 
 O O <0 00 PO 
 
 Hf 8 
 
 '"§8 
 
 M fO 0> lO 
 ro PO rO l~- 
 
 i£> O 00 
 
 
 O O 
 03 to 
 
 
 |8 
 
 C C S G C fl r ^ 
 
 2 82 § o o fe^ 
 
 .S .H ^, -*-■ -(J p< 
 
 IN 'q- u. _^ V ^ Cu 
 
 H H^l 
 
 ^ g.a-" 
 
 S^-o 
 
 W O v^ M 
 
 
 CQ CO Jft 
 
 ••^ s 
 
 ^•1^^^' 
 
 " c 
 
 bor, B 
 bor, P 
 
 itchin 
 rdlab 
 rtage. 
 jected 
 aries i 
 
 SS^>^C 
 
 fSc^ 
 
 :2:28 
 
 ?^S ^^„^ 
 
 > o 
 OH 
 
 o o o 
 
 c^ ir> PO 
 
 00 O 1/5 
 
 C to 
 
 o 2 
 
 ■*^ bO CO 
 S fi o 
 
 ii|g| 
 I 111 § 
 
 d V Oi > p 
 
 ° S 
 
 ., O Vi; 
 
 «8 8 
 
 +j p. ^ 
 
 C« ,n C 
 
 2 "S <H 
 
 211 
 ill 
 
 ^ 8 P 
 
 HOi 
 
Annual Comparison of Foundry Accounts 
 
 I 
 
 o a 
 
 O " 
 
 <! " 
 
 S^ 
 
 Q 
 O 
 
 o 
 
 O H i 
 
 M z i 
 
 § I 
 
 A, H 
 
 o 1^ 
 o g 
 
 ID 
 
 
 
 § 
 
 F^ox 
 
 ux ssoq 
 
 sSut;sbo p-eq 
 Suxp'npui "iou 
 
 
 sSux:^SB^ 
 pooQ 
 
 00 rf O H 
 
 J, <yi ■<* O ' 
 
 O Tf t^ lO M O ro 
 >* 00 N IH 0-. U^ Oi 
 N (M W W N PO ^ 
 
 ^ M lO OO 
 
 • 00VO<O ICO lorovo 
 
 (NO^OOlOt^lOtONt^ 
 
 Tf 1/1 Tf 
 
 O '^ "fl- 
 
 XHM 
 
 3JIOO 
 
 O O 00 N 
 
 r<3iO^r0P0<N (TJN M f^i«< 
 
 
 UOJt 
 
 t^ 0> ro ro 
 
 O •* l> W 
 
 ^oqs 
 
 d-BJOg 
 
 uoit Sid 
 
 o <o N <o *o ■* 
 
 o^ o o M 00 vo 
 
 (N 0> 00 lO O CS 
 
 "£ H ro M H M 
 
 t~ to lo a> 
 
 5 r<5 00 
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 P>^^S 
 
 R'gi^S'S'^ 
 
 S 
 
 
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 r<5<£> (N lO t- 0> 
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 u, M M M M N 
 
 1 
 
 _^ M W Ol 
 
 ro PO ro ro 
 
 uojx Sxd 
 
 t- i/:i CT» (N vo iri \r> 
 liO N O O^ O C> 00 
 
 
 
 ^ 
 
 
 609 
 
6io 
 
 Foundry Accounts 
 
 1 8 
 
 O CO 
 fa 
 
 I 
 
 % 
 
 r*5 M M 
 
 1/5 loo <r) 
 00 ■* t^ o 
 
 00 00 ro O 
 
 w C^ "* ro 
 
 tj lO I> ro 
 
 hH o" ■* ''f 
 
 pq o> lo Tf 
 
 w M "3- o »0 ^ 
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 to D 
 
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 —J M to "* 
 
 rr-l cfi w w 
 
 o " g g 
 
 M O ^ T^ "J '-' i^ 
 
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Transmission of Orders 
 
 6ii 
 
 Chart Showing Direction or Transmission of Shop and 
 Foundry Orders, Together With That of Return 
 Reports 
 
 1 j Superintendent 
 
 Drawing Room 
 
 Works Office 
 
 Cleanincj Yard 
 Room 
 
 Cupola Moulding 
 
 Floor 
 
 
 
 Core 
 Room 
 
 Fig. 245. 
 
 The chart above shows the direction of transmission of orders from 
 the superintendent to the foundry office, and thence, with supplementary 
 orders, to the dehvery of the completed product at the cleaning room; 
 as also that of return reports to foundry office, works office, and superin- 
 tendent. Full lines indicate the course of orders outward; dotted lines 
 that of the return reports. 
 
 From Superintendent . 
 
 From Drawing Room . 
 
 From Foundry. 
 
 From Foundry Office. 
 
 (i) to 
 
 (2) to 
 
 (4) to 
 
 (4) to 
 
 Works Office . . . 
 Drawing Room. 
 
 Foundry 
 
 Works Office . . . 
 Pattern Shop . . 
 Pattern Shop . . 
 Core Room. . . . 
 
 Floor 
 
 Cupola 
 
 Yard 
 
 Cleaning Room . 
 
 (3) 
 
 (2) 
 
 (4) 
 
 (3) 
 
 (5) 
 
 (5) 
 
 (6) 
 
 (7) 
 
 ■ (8) 
 
 . (9) 
 
 (10) 
 
6 12 Foundry Accounts 
 
 From Pattern Shop (5) to | IZtL^''/. ! i : ! '(^ 
 
 From Core Room (6) to Moulding Floor (7) 
 
 From Cupola (8) to Moulding Floor .... (7) 
 
 From Moulding Floor (7) to Cleaning Room. ... (10) 
 
 Return Reports 
 
 From Moulding Floor. ... (y)^ 
 
 From Core Room (6) > r:, •, ^^c / x 
 
 FromCupola ..: (8) ^^ Foundry Office (4) 
 
 From Cleaning Room. . . .(io)J 
 
 From Foundry Office (4) to {'^^S"^^^':.::: S 
 
 From Works Office (3) to Superintendent (i) 
 
 The system of accounting as above described has been followed for 
 some years by one of the western foundries, with excellent results. It 
 involves considerable clerical work, but one clerk can handle it. 
 
 Some modifications are required to adapt it to a jobbing foundry. 
 These are indicated at once and are readily made. 
 
 As showing different methods of foundry accounting, each having its 
 advantages and disadvantages, papers presented on the subject to the 
 American Foundrymen's Association by Mr. B. A. FrankHn and Mr. J. 
 P. Golden are given. . . One can be developed from the lot which will 
 meet any requirement. 
 
 AMERICAN FOUNDRYMEN'S ASSOCIATION 
 
 Foundry Costs 
 By B. a. Franklin, Boston, Mass. 
 "... Form I illustrates the first method of foundry cost showing: 
 The operations are divided into the elements of^ 
 
 Section A 
 
 Melting, 
 
 Moulding 
 
 Metal. 2. Fuel. 
 
 3. Melting Expense. 
 
 Section B 
 
 4. Moulding Labor. 
 5. Moulding Expense — Floor and Bench separately 
 
 Section C 
 
 6. Cleaning Labor. 10. Pickling. 
 
 7. Cleaning Expense. 11. Pickling Expense. 
 
 8. Tumbling Labor. 12. Sand Blasting Labor. 
 
 9. TumbUng Expense. 13. Sand Blasting Expense. 
 
Foundry Costs 613 
 
 Section D 
 14. Core Labor. 15. Core Expense. 
 
 Section E 
 16. General Expense. 
 
 "In discussing this system no attempt is made to discuss the method 
 of getting the information because such methods are simple and easily 
 worked out." 
 
 "The Basic Costs are illustrated in Form i, which shows the weekly 
 operation of the foundry as a whole, and Form 2 represents the cost of 
 an actual casting. Form 3 represents the monthly foundry showing 
 of profit and loss, ofifering means of proof of the foundry cost and show- 
 ing the net result. " 
 
 ". . . As nearly as possible foundry shop economy demands, and 
 foundry work permits a daily clean-up, though, of course, some oper- 
 ations happen one day after the beginning." 
 
 "A foundry cost might then be a daily record sheet. ' Weekly records, 
 however, are sufi&cient generally, and the one presented is on this 
 basis. " 
 
 Form i 
 
 ^'Section A. Deals with metal." 
 
 "Here is shown, separately for each different mixture, of which one 
 foundry might generally employ two or three, the weights and value 
 of iron charged. These weights may readily be proved by checking 
 as each car or lot of scrap is used up. In the case of scrap made in the 
 foundry or 'own scrap' no value is put on -this since it' is put into the 
 heat in an iron foundry, on the basis that scrap made on each heat will 
 be approximately the same per cent, and what is made one day is gathered 
 up and used the next day. The exception to this is in the case of 'bad 
 castings,' charged at scrap value, and, as seen later, accounted for in 
 casting cost." 
 
 "In a Steel Foundry it would be necessary to change all scrap at 
 scrap value and credit same to particular castings. " 
 
 "The 'metal-used' value is shown and the pounds melted, 'but the 
 'metal cost' is obtained by dividing, not by pounds melted, but by 
 poimds of 'castings made' — i.e., good and bad castings. The bad 
 castings are to be charged to the particular order as will be seen later. 
 We thus arrive at a weekly metal cost for each mixture. " 
 
 "Likewise for purposes 'of general guidance, there is shown weekly 
 the 'per cent, of good castings to melt,' the 'per cent of bad castings 
 
6i4 Foundry Accounts 
 
 to castings made,' and the per cent of metal disappearance or 'per cent 
 of loss.' " 
 
 "Now for management guidance toward general shop economy, 
 these figures present standards and bases for striving for lower costs — 
 viz., to make the percentage of good castings to the melt as high as 
 possible, to make the percentage of bad castings to castings made as 
 low as possible, and the record will quickly show that the cost fluctuates 
 with these conditions." 
 
 "And it will be found that melting and handling of metal and fuel 
 can be done on piece work to bring best economy in metal-cost." 
 
 "A definite and valuable point to note is that in addition to the 
 weekly figure of cost per pound, there is carried along the average or 
 
 'period cost per pound.' This is the figure to be used in cost work. 
 
 J) 
 
 "... The weekly figures are constantly compared with the period 
 figures showing whether the weekly result is better or worse than the 
 average, and an observation of the detail shows why. ..." 
 
 " In each section it will be noted that the costs are brought down to a 
 few vital units or percentages, and when these vary, they are significant 
 of a gain or loss in economy of production, the reason for which can be 
 readily observed by casting the eye up the details and observing the 
 comparison of them." 
 
 "... Section B. Moulding. — Here are two elements to be con- 
 sidered — productive labor and expense. The expense is shown in 
 relation to productive labor. It may be shown in relation to hours if 
 desired, but in each class of moulding labor there is generally no great 
 fluctuation of rate per hour. ..." 
 
 "The productive labor and expense should be kept separately as to 
 class of moulding, as floor, bench, machine, etc., since the expense varies 
 considerably with the class." 
 
 "... A little thought and experiment would seem to show that on 
 the whole the expenses approximately vary according to time spent in 
 productive labor rather than by the pound. " 
 
 "In the matter of productive labor it is to be understood that 
 money paid for moulding each job, whether day work or piece work, 
 is to be known and used in figuring definite casting, as shown in 
 Form 2." 
 
 "It is in this productive labor cost that the first element of variation 
 in casting costs is to be found, the expense percentage being the same or 
 taken as the same, except in the matter of certain direct charges or 
 expenses to be discussed later. " 
 
Foundry Costs 615 
 
 "Section C. Cleaning Castings. — In the matter of cleaning castings 
 there must be some division. Tiunbling, pickling, and sand blasting 
 are taken separately as shown below. This leaves for consideration 
 here the cleaning of castings by other than these three methods and 
 applies mainly to large castings. ..." 
 
 " . . . In Tumbling the labor can best be put on piece work and will 
 generally be done by the pound, and expenses will be shown by the 
 pound. ..." 
 
 ''In Sand Blasting and Pickling the expenses are shown in relation to 
 productive labor, and the work can be put on piece work. ..." 
 
 "Section D. Core Room. — Here the labor can in the main be put 
 on f>iece work and the expenses shown in detail. ..." 
 
 "Section E. . . . General Expenses. — This is shown in relation to 
 productive labor, the items of productive labor being those of Moulding, 
 Core Making and Cleaning operations. 
 
 "... Thus we arrive at certain weekly and period basic figures of 
 cost in the main elements in the foundry of 
 
 Metal. Core Making. 
 
 Moulding. General Expenses. 
 
 Cleaning. 
 
 "The items of metal and expense are easily provable with the books 
 monthly, .and the labor with the pay roll weekly, so that we get a proved 
 weekly picture of the foundry situation as compared with average or 
 period, and we get it in such detail as will show the reasons of all varia- 
 tions of operation. ..." 
 
 "Consideration of Casting Cost. The first element to consider is 
 that of direct charges. In many jobs, but by no means all of them, 
 are certain charges which it seems desirable should be charged directly 
 to the particular order. They need in most foundry work be very small 
 in number. These charges must essentially be gathered and held until 
 the job is shipped and cost ready to work out. " 
 
 Form 2 
 
 "Form 2 illustrates this final casting cost." 
 
 "In all castings finished in a given period, the varying elements of 
 unit cost would be purely the productive labor items of moulding and 
 cleaning and direct charges, the metal, fuel, melting, moulding, cleaning 
 and general expense charges being taken from the period figures on the 
 weekly cost sheet." 
 
 "Therefore, in working out the cost of a finished casting, it is essential 
 to know of it as a particular job; the weight — and the shipping slip 
 
6i6 Foundry Accounts 
 
 gives that; the moulding and core making labor and the cleaning labor, 
 whefe average rates per pound are not used. " 
 
 "... Direct charges are added and also loss on bad castings. A 
 record of bad castings is necessary and simple." 
 
 "On bad castings the loss would depend on how far the work had 
 progressed when discovered as bad, and what work on them had been 
 paid for. The metal, of course, would be credited at scrap value." 
 
 "By this method then it will be observed that with very small clerical 
 labor, the practical foundryman or manager gets a weekly, or daily, 
 if he so designs, view of his foundry costs and their fluctuations which 
 form a definite and correct basis for accurate estimate, and he can very 
 quickly get a particular job or casting cost by having the money spent 
 on moulding and cleaning, etc., gathered." 
 
 "The Cost System settled, the bookkeeping should be made to parallel 
 the cost system, in which case the monthly showing would be made to 
 show as per Form 3." 
 
 "Thus is obtained a complete monthly analysis. In most foundries 
 one clerk and almost invariably two, can operate the system as far as 
 costs are concerned." 
 
Cost of Metal 
 
 617 
 
 Metal — Section A. No. i. Form i 
 
 Mixture No. i 
 
 Pig Grade i 
 
 Pig Grade 2 
 
 Pig Grade 3 
 
 Pig Grade 4 
 
 Pig Grade 5 
 
 Bought scrap 
 
 "Own scrap chillers 
 
 Own scrap floor scrap 
 
 Own scrap bad castings 
 
 Own scrap gates 
 
 Weekly totals metal used 
 
 Period totals metal used 
 
 Weekly total pounds castings 
 
 made 
 
 Period total pounds castings 
 
 made 
 
 Good castings made 
 
 Period castings made 
 
 Per cent good castings to melt 
 Period per cent castings made 
 
 Bad castings 
 
 Per cent bad castings to 
 
 castings made 
 
 Shop scrap 
 
 Per cent shop scrap . 
 
 Total pounds (weekly) 
 
 Total pounds (period) . 
 
 Pounds lost 
 
 Period pounds lost 
 
 Per cent lost 
 
 Period per cent lost 
 
 Weekly metal cost per 100 
 
 pounds 
 
 Period metal cost per 100 
 
 pounds 
 
 Oct. 9 
 
 Pounds 
 
 34,240 
 
 32,270 
 
 5,680 
 
 36,310 
 
 31,500 
 
 15.900 
 
 1,275 
 
 7,300 
 
 10,000 
 
 36,100 
 
 210,575 
 
 149,280 
 
 140,125 
 66.5 
 9,155 
 
 6.1 
 51,8c 
 
 210,08 
 
 9,495' 
 
 4.5 
 
 Amount 
 
 252 . 22 
 234-10 
 38.67 
 259.35 
 249 . 61 
 106.47 
 o 
 
 Oct. 16 
 
 Pounds 
 
 33,950 
 
 33,290 
 
 14,270 
 
 32,070 
 
 32,720 
 
 17,000 
 
 1,420 
 
 9,000 
 
 9,000 
 
 34,800 
 
 217,520 
 
 428,095 
 
 150,441 
 
 299,721 
 139.867 
 279,992 
 64 .3 
 
 10,574 
 
 7 
 54,400 
 
 204,841 
 
 12,679 
 22,174 
 5.8 
 
 .84 
 
 Amount 
 
 253.87 
 249.68 
 97. IS 
 232.65 
 259.28 
 113.84 
 
 63.00 
 o 
 1269.47 
 2479.89 
 
 Oct. 23 
 
 Pounds 
 
 25,620 
 
 25,440 
 6,010 
 
 30,150 
 
 25,' 
 
 11,900 
 1,135 
 7,700 
 
 10,000 
 
 26,500 
 169,535 
 597,630 
 
 116,^ 
 
 416,172 
 109,069 
 389,061 
 
 64.3 
 
 65.1 
 7,382 
 
 6.3 
 
 43,700 
 
 160,151 
 
 9,384 
 31.558 
 5.5 
 5.3 
 
 .85 
 
 .83 
 
 Amount 
 
 191.58 
 187.39 
 40.92 
 218,72 
 198.74 
 79.68 
 o 
 o 
 
 70.00 
 o 
 
 987.03 
 
 3466.92 
 
6i8 
 
 Foundry Accounts 
 
 Metal — Section A — No. 2. Form i 
 
 Fuel and melting expense 
 
 Labor (cupola men) 
 
 Labor (handling coke and 
 coal) 
 
 Labor (miscellaneous) 
 
 Labor (handling iron) 
 
 Coke 
 
 Coal 
 
 Wood. 
 
 Fire brick. 
 
 Fire clay 
 
 Oyster shells 
 
 Mica sand 
 
 Chg. from other depts. 
 
 Analysis of iron 
 
 Relining cupola and repairs. . 
 
 Tumbling cupola bottom 
 
 Crane labor 
 
 Elevator labor 
 
 Blower labor 
 
 Handling oyster shells. 
 
 Bituminous facing. 
 
 Interest on investment 
 
 Heat, light and power 
 
 Taxes, insurance and depre- 
 ciation 
 
 Weekly expense 
 
 Period expense 
 
 Weekly pounds castings made 
 
 Period pounds castings made. 
 
 Weekly cost per loo pounds . . 
 
 Period cost per loo pounds. . . 
 
 Weekly pounds melted to 
 pounds fuel 
 
 Period pounds melted to 
 pounds fuel 
 
 Oct. 9 
 
 Pounds 
 
 149,280 
 
 Amount 
 
 45-65 
 1.80 
 
 5.73 
 
 53.50 
 
 1.82 
 
 3.20 
 1.64 
 2.63 
 
 30.00 
 2.00 
 2.90 
 
 10-95 
 
 8.66 
 
 .53 
 
 10.20 
 6.15 
 
 12.42 
 199.78 
 
 8.7 
 
 Oct. 16 
 
 Pounds 
 
 150,441 
 299,721 
 
 Amount 
 
 18.51 
 55.97 
 
 .90 
 2.00 
 2.63 
 
 30.00 
 
 10.75 
 
 8.52 
 
 .80 
 
 10.20 
 6.15 
 
 12.42 
 203.55 
 403.33 
 
 • 135 
 .135 
 
 8.4 
 8.5 
 
 Oct. 23 
 
 Pounds 
 
 116,451 
 416,172 
 
 Amount 
 
 9 
 
 .22 
 
 44 
 
 08 
 
 8 
 
 25 
 
 I 
 
 53 
 
 2 
 
 63 
 
 9.30 
 6.93 
 
 .44 
 
 10.20 
 
 6.15 
 
 12.42 
 174.85 
 578.18 
 
 • IS 
 
 .139 
 
 8.3 
 
 8.5 
 
Moulding Expense 
 
 619 
 
 Moulding — Section B. Form i 
 
 
 Oct. 9 
 
 Oct. 16 
 
 Oct. 23 
 
 
 Pounds 
 
 Amount 
 
 Pounds 
 
 Amount 
 
 Pounds 
 
 Amount 
 
 Bench Moulding 
 
 
 884.80 
 
 10.00 
 
 6.58 
 2.42 
 7.50 
 2.60 
 
 23.16 
 
 46.37 
 
 6.30 
 
 .47 
 
 2.30 
 
 30.58 
 
 41.94 
 192.22 
 
 21.8 
 
 
 858.80 
 1743.60 
 
 10.00 
 
 6.88 
 2.80 
 
 10.48 
 23.54 
 
 50.83 
 6.88 
 
 .40 
 
 1.65 
 30.58 
 
 41.94 
 185.98 
 387.20 
 
 21.7 
 21. 1 
 
 
 715.40 
 2459.00 
 
 5.00 
 
 1. 15 
 
 1.09 
 
 1.60 
 
 8.19 
 
 37-77 
 
 6 10 
 
 Period productive labor 
 
 Moulding Expense on 
 Productive Labor 
 
 Non-pruductive labor 
 
 Flasks, snap boards and 
 
 matches 
 
 Miscellaneous supplies 
 
 Ladles 
 
 Shovels and screens 
 
 Rammers. 
 
 Charges from other depts — 
 Making bottom boards for 
 . moulding machines 
 
 Sand 
 
 Handling sand 
 
 Handling weights and bands. 
 
 Reclaiming sand 
 
 Parting sand. 
 
 Interest on investment 
 
 Heat, light and power. 
 Taxes, insurance and depre- 
 ciation 
 
 .62 
 
 30.58 
 
 41.94 
 134 04 
 
 Weekly expense 
 
 
 
 Per cent moulding expense to 
 
 18.7 
 
 Period per cent moulding 
 expense to prod, labor 
 
 20.8 
 
620 
 
 Foundry Accounts 
 
 Cleaning and Tumbling — Section C. Form i 
 
 Productive labor 
 
 Number of pounds cleaned 
 and tumbled 
 
 Period pounds cleaned and 
 tumbled 
 
 Cost per 100 pounds (if day- 
 work) 
 
 Period cost per lOO pounds 
 (if day work) 
 
 Cleaning and Tumbling 
 Expense 
 
 Supplies. 
 
 Overseeing 
 
 Non-productive labor 
 
 Charges from other depts. . . 
 
 Tumblers 
 
 Stars for tumbling 
 
 Interest on investment 
 
 Heat, light and power 
 
 Taxes, insurance and depre- 
 ciation 
 
 Weekly gross expense 
 
 Stars used in No. 3. 
 
 Weekly expense 
 
 Period expense 
 
 Weekly expense cost per loc lbs 
 
 Period expense cost per 100 
 pounds 
 
 Weekly total cleaning and 
 tumbling cost 
 
 Period total cleaning and 
 tumbling cost 
 
 Oct. 9 
 
 Pounds 
 
 134,462 
 
 Amount 
 
 74.62 
 
 .056 
 
 S.44 
 55.44 
 
 8.40 
 71.73 
 
 71.73 
 .053 
 
 .109 
 
 Oct. 16 
 
 Pounds 
 
 139,089 
 273,551 
 
 Amount 
 
 70.92 
 
 .053 
 .054 
 
 .40 
 
 .40 
 
 .65 
 
 4.00 
 
 S.44 
 55.44 
 
 8.40 
 74.73 
 
 74.73 
 146.46 
 .053 
 
 .053 
 
 .106 
 
 .107 
 
 Oct. 23 
 
 Pounds 
 
 105,203 
 378,754 
 
 Amount 
 
 .054 
 • 053 
 
 1.93 
 
 .75 
 
 2.02 
 
 10.00 
 
 S.44 
 
 55.44 
 
 8.40 
 73.98 
 
 73.98 
 
 220.44 
 
 .07 
 
 .058 
 
 .124 
 
 III 
 
Pickling Expense 
 
 621 
 
 Pickling — Section C — No. 2. Form i 
 
 Weekly prod, labor 
 
 Period prod, labor 
 
 Weekly pounds pickled 
 
 Period pounds pickled 
 
 Weekly cost per loo. pounds 
 
 (if day work) 
 
 Period cost per loo pounds 
 
 (if day work) 
 
 Pickling Expense 
 
 Non-productive labor 
 
 Oil of vitriol 
 
 Hydrofluoric acid. 
 
 Acid spigots. 
 
 Charges from other depts. . . , 
 
 Interest on investment 
 
 Heat, light and power 
 
 Taxes, insurance and depre- 
 ciation 
 
 Total weekly expense 
 
 Total period expense 
 
 Per cent dept. expense to 
 prod, labor 
 
 Period per cent dept. expense 
 to prod, labor 
 
 Oct. 9 
 
 Pounds 
 
 62,818 
 
 Amount 
 
 20.70 
 
 1-75 
 2.06 
 23.92 
 
 3.40 
 3.08 
 
 2.53 
 36.74 
 
 177. 5 
 
 Oct. 16 
 
 Pounds 
 
 65,600 
 128,418 
 
 Amount 
 
 19.82 
 40.52 
 
 .030 
 .032 
 
 15.28 
 
 1.88 
 3.40 
 3.08 
 
 2.53 
 26.92 
 63.66 
 
 I3S.8 . 
 
 ISS.8 
 
 Oct. 23 
 
 Pounds 
 
 36,220 
 164,638 
 
 Amount 
 
 13.10 
 53.62 
 
 .036 
 .034 
 
 1. 10 
 
 lo.si 
 
 1.48 
 3.40 
 3.08 
 
 2.53 
 22.10 
 85.76 
 
 168.7 
 160 
 
622 Foundry Accounts 
 
 Sand Blasting — Section C — No. 3. Form i 
 
 Weekly prod, labor 
 
 Period prod, labor 
 
 Weekly pounds sand blasted 
 Period pounds sand blasted . 
 Weekly cost per loo pounds 
 
 (if day work) 
 
 Period cost per loo pounds 
 
 (if day work) 
 
 Sand Blasting Expense 
 
 Non-productive labor 
 
 Supplies 
 
 Sand 
 
 Charges from other depts . . . 
 
 Interest on investment 
 
 Heat, light and power 
 
 Taxes, insurance and depre- 
 ciation 
 
 Total weekly expense 
 
 Total period expense 
 
 Per cent dept. expense to 
 prod, labor 
 
 Period per cent dept. expense 
 to prod, labor 
 
 Prod. labor 
 
 Oct. 9 
 
 Pounds Amount 
 
 .043 
 
 • 75 
 1. 10 
 
 6.80 
 IS. 40 
 
 1.38 
 25.43 
 
 581.9 
 
 Oct. 16 
 
 Pounds Amount 
 
 11,800 
 22,000 
 
 6.06 
 10.43 
 
 .051 
 .048 
 
 .61 
 
 6.80 
 15.40 
 
 1.38 
 25.29 
 
 SO. 72 
 
 417.4 
 
 486.3 
 486.3 
 
 Oct, 23 
 
 Pounds Amount 
 
 8,100 
 30,100 
 
 4.61 
 15.04 
 
 .057 
 .05 
 
 .41 
 
 1. 10 
 
 6.80 
 15.40 
 
 1.38 
 25.09 
 75.81 
 
 544.2 
 
 S04.2 
 504.2 
 
Core-Making Expense 
 Core Department — Section D. Form i 
 
 623 
 
 
 Oct. 9 
 
 Oct. 16 
 
 Oct. 23 
 
 
 Pounds 
 
 Amount 
 
 Pounds 
 
 Amount 
 
 Pounds 
 
 Amount 
 
 Productive labor 
 
 
 233.55 
 
 24.00 
 12.65 
 19.14 
 12.10 
 17. II 
 21.80 
 2.92 
 6.44 
 
 5.54 
 
 13.67 
 1.43 
 
 21.61 
 158.41 
 
 67.8 
 
 
 220.65 
 454.20 
 
 24.00 
 12.63 
 18.08 
 11.78 
 15.16 
 18.32 
 2.45 
 5.58 
 
 3.00 
 
 13.67 
 1.43 
 
 21.61 
 
 147.71 
 306.12 
 
 66.9 
 
 67.4 
 67.4 
 
 
 16S.6S 
 619.85 
 
 24.00 
 7.87 
 
 13.89 
 9.62 
 
 13.37 
 
 25.89 
 1.56 
 1.73 
 
 1. 55 
 
 13.67 
 1.43 
 
 Period productive labor 
 
 Core Making Expense 
 
 Tending ovens 
 
 Inspecting cores 
 
 Storing cores 
 
 General labor 
 
 Sand 
 
 Coke ... . 
 
 Coal 
 
 Rosin. 
 
 Miscellaneous supplies 
 
 Flour. 
 
 Interest on investment 
 
 Heat, light and power 
 
 Taxes, insurance and depre- 
 
 Weekly core making expense. 
 
 Period core making expense. . 
 
 Weekly per cent expense to 
 
 prod, labor 
 
 136.19 
 
 442.31 
 
 82 '' 
 
 Period per cent expense to 
 prod. labor .... 
 
 71.3 
 71.3 
 
 
 
624 
 
 Foundry Accounts 
 
 General Expense — Section E. Form i 
 
 Executive 
 
 Foreman 
 
 9396— 2— B. 
 
 Non-productive labor 
 
 Clerical 
 
 Supplies 
 
 Charged from other Depts. 
 
 Scrap 
 
 Gas 
 
 Inspecting 
 
 Injured employee 
 
 Tending pattern safe 
 
 Brooms 
 
 Interest on investment 
 
 Heat, light and power 
 
 Taxes, insurance and depre- 
 ciation 
 
 Weekly general expense 
 
 Period general expense 
 
 Weekly prod, labor 
 
 Period prod, labor. 
 
 Per cent expense to prod, 
 labor 
 
 Period per cent expense to 
 prod, labor 
 
 Oct. 9 
 
 Pounds Amount 
 
 27.00 
 48.00 
 
 12.74 
 49.00 
 .87 
 IS. 55 
 45.38 
 1. 00 
 63.20 
 
 11.47 
 
 11.56 
 
 22.59 
 
 310.45 
 618.81 
 
 984.49 
 
 62.9 
 
 Oct. 16 
 
 Pounds Amount 
 
 27.00 
 48.00 
 
 25.08 
 
 49- 00 
 1.43 
 
 26.00 
 3.57 
 1. 00 
 
 64.59 
 
 9.60 
 11.56 
 
 22.59 
 
 310.45 
 599.87 
 1218.68 
 955.60 
 1940.09 
 
 62.8 
 
 Oct. 23 
 
 Pounds Amount 
 
 27.00 
 48.00 
 
 16.67 
 49.00 
 
 1. 8s 
 27.75 
 13.98 
 
 1. 00 
 42.6s 
 
 5. 00 
 
 7.20 
 
 • 75 
 
 11.56 
 
 22.59 
 
 310.45 
 585.45 
 
 1804.13 
 790.25 
 
 2730.34 
 
 73.9 
 65.8 
 
 Individual Job of Casting Cost. Form 2 
 
 Date, Oct. 12 
 150 Blocks — J. & 8. Co. — 850 pounds 
 
 Amount 
 
 Unit cost 
 
 Value 
 
 Metal 
 
 Melting expense 
 
 Moulding 
 
 Motilding expense 
 
 Cores 
 
 Cores, expense 
 
 Cleaning and tumbling. 
 
 850 
 
 Cleaning and tumbling expense. 
 
 Sand blasting. 
 
 Sand blasting expense. 
 
 Pickling 
 
 Pickling expense 
 
 General expense 
 
 Spoiled work 
 
 Total 
 
 Cost per pound 
 
 .83 per 100 
 . 139 per 100 
 
 20.8% 
 
 71.3% 
 
 .053 per 100 
 
 pounds 
 
 . 058 per 100 
 
 pounds 
 
 .034 
 
 160% 
 65.8% 
 
 7-05 
 
 1. 18 
 
 3.00 
 
 .62 
 
 • SO 
 .36 
 
 • 45 
 .49 
 
 .29 
 
 2.13 
 
 .42 3 spoiled 
 16.95 
 • 0199 
 
 Note. — In this case no selling expense is added, as it might be in many cases. 
 
A Successful Foundry Cost System 625 
 
 Monthly Showing. Form 3 
 Quick Assets. 
 Cash. 
 Accounts Receivable. 
 
 Permanent Assets. 
 Real Estate. 
 Building. 
 Machinery. 
 
 Raw Material on Hand. 
 
 Pig Iron, (Credit amount used each week as per costs and charge 
 
 to Mfg. Acct.) 
 Scrap. 
 
 Manufacturing Acct. (See analysis below.) 
 
 Expenses undivided (meaning expense supplies not used). 
 Quick Liabilities. 
 
 Accoimts Payable. 
 Permanent Liabilities. 
 
 Capital. 
 
 Depreciation. 
 
 Surplus. 
 
 Details of Mfg. Acct. 
 
 Dr. 
 Inventory at start of castings in process. 
 
 Metal 1 
 
 Labor ? each month. 
 
 Expense ) 
 
 Cr. 
 
 Sales. 
 
 Inventory of castings in process ist of each 
 month. 
 
 Balance Profit or Loss monthly. 
 
 A SUCCESSFUL FOUNDRY COST SYSTEM 
 
 By J. P. Golden, Columbus, Ga. 
 "... The system consists of, first: a Daily Cupola Report, the 
 printed form having column for charge, number of poimds coke and 
 brand, pounds pig iron and brand, and per cent silicon and sulphur, 
 scrap, foreign and returns, and total charge also hues for weekly totals 
 for use in weekly report. Ratio of coke to iron. Time blast started. 
 Time bottom dropped. Average blast pressure. Per cent sulphur in 
 heat. Per cent silicon in heat. Remarks. With each sheet signed by 
 foreman. 
 
626 Foundry Accounts 
 
 "Second: The Daily Foundry Report, which is made up by the 
 Riunbhng Room foreman. This report consists of a sheet, with columns 
 for name of moulder, hoiur or piece rate, niunber of moulds, number of 
 castings, time of helper, pattern description with columns for weights 
 of the various classes of work, as pulleys, sheaves, hangers, hanger 
 boxes, pillow blocks, couplings, cane mills, factories, miscellaneous, 
 etc. Also colmnn for number of pieces lost, total weight of each kind 
 of piece lost, and a cause column for same, showing if it did not run, if 
 it was crushed, blowed, or whatever cause of defect. There is a line 
 at bottom of sheet for weekly totals to be used in weekly report. The 
 daily foundry report furnishes a ready means of comparison of each 
 moulder's record, with his own, or with other moulders as to quantity of 
 good castings, castings lost, weight and cost of same. This report also 
 shows the amount of good and bad castings for each day, in each class, 
 with the weekly total for each. 
 
 '^ Third: There is a book for defective and other castings returned 
 from shop and customers, in which is the following rule: 
 
 'AH castings returned by machine shop and customers, before 
 being made over, must be entered in this book, giving cause for 
 making over. Castings returned to foundry from shop or cus- 
 tomers, through no fault of foundry, must not be deducted from 
 net foundry castings, and should be considered as foreign scrap. 
 If fault of foundry, they are charged back to foundry and are con- 
 sidered as foundry return scrap.' 
 
 This book has columns for showing date returned, by whom, descrip- 
 tion, cause and weight. Without this book, there could be returned 
 defective castings, which were the foundry's fault and made over with- 
 out the superintendent's knowledge. With the "to be made over" 
 casting book, all castings returned are specified therein. If the fault 
 of the machine shop, it is so stated. If returned from customers, this 
 is noted with date, description, cause and weight. No casting is made 
 over without being recorded in this book. This book, being always open 
 to superintendent and foreman, saves inquiries and explanations. . . . 
 
 ^^ Fourth: The Weekly Foundry Report Sheet. This sheet is made 
 up from the daily foundry report, and cupola sheets and the book (to 
 be made over castings). On this sheet, provision is made for record 
 of bad castings returned from foundry, shop or customer, by classes, 
 as well as the good castings made. The total of good castings minus 
 defective castings gives net good castings for week. The average per 
 cent of all castings lost is given, with the per cent loss in each class, with 
 the total pounds pig and foreign scrap charged in cupola, and the net 
 
A Successful Foundry Cost System 627 
 
 good castings deducted therefrom, we find the per cent lost in remelt, 
 cupola droppings, gangways, etc. The weekly foundry report also has 
 a record of total melt taken from daily cupola sheet, which with net 
 good castings deducted gives per cent, bad castings, gates, etc., of total 
 melt, including foreign scrap, returns and pig. In a division headed 
 cupola charge is given the number of pounds pig iron, foreign scrap and 
 coke, with current price of each and total cost per week. To these 
 amounts are added the total wages, giving a total of material and wages 
 for week, which divided by the net good castings gives the cost per 
 100 pounds, net castings, including pig iron, scrap, coke, wages. 
 
 "The weekly report also has separate divisions for non-producers, 
 rumbling department, moulding department, core shop, day and night 
 cleaning gangs, in which the wages of each class of men in each division 
 are given separately, by total, and the wage cost per hundred pounds. 
 . . . The weekly report also embodies the grand total wages cost per 
 100 pounds, and this is the most important item, for both foreman and 
 superintendent, for this item is one which the foreman can control to 
 the greatest extent, and which speaks the loudest in favor of the system. " 
 
 "... In connection with the weekly report is a detailed report of 
 the pounds of good castings, to whom sold or charged, and price for each 
 lot, and from this sheet is prepared, on the back of the weekly report, 
 a statement giving the estimated profit or loss for week." 
 
 "And lastly, there is a ready reference sheet (headed Comparison of 
 Per cents, Wages Cost per 100 Pounds in Different Departments of 
 Foundry from Weekly Foundry Report) giving the comparison by 
 weeks and the average comparison at the end of each year of the fol- 
 lowing items after date. Net good castings for week, castings killed, 
 in machine shop with columns for the per cent loss of each of the several 
 classes of castings, each class in a separate column, gives a ready means 
 of comparison in that class for all of its weeks. 
 
 "There are also columns for the cost per week per 100 pounds, net 
 castings including pig iron, scrap, coke and wages, the wage cost per 
 100 pounds, in the non-producers, rumbling and moulding departments, 
 also the core shop, day and night cleaning gangs with a column for 
 grand total wage cost per 100 pounds. 
 
 "Both the superintendent and foreman have access to the several 
 reports giving each the means of knowing the actual conditions in all 
 departments of the foundry at all times. ' 
 
 "This system gives the foreman the means of remedying a small or 
 defective output by the knowledge of the cause producing it, and to 
 place each moulder upon the class of work to which he is best fitted to 
 increase the general output." 
 
628 
 
 Foundry Accounts 
 
 £3 i 
 o a 
 
 S i 
 
 J 
 
 
 ^q3pA\ 
 
 ^SOX S903ld 
 
 jaquin^ 
 
 snoauBi 
 
 
 
 Ajo^objI 
 
 snuiuini 
 
 
 sjiTm au-B3 
 
 s3uTt<Jno3 
 
 sj[ooiq 1 
 
 saxoq 1 
 jsSuBji 1 
 
 sjaSuBjj 
 
 saABaqs 
 
 sAannj 
 
 
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 1 
 
 1 
 
 
 dpH 
 
 
 s3uit(.SB0 
 JO jaquinfyi 
 
 
 spinoui 
 JO jgquin]^ 
 
 
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 i 
 
 2; 
 
 
Castings To Be Made Over 
 
 629 
 
 "... The system furnishes a basis for closer estimates than formerly 
 upon work a little out of the usual run, by knowing exactly what prices 
 can be accepted for the regular work. The foundry foreman in this 
 case is allowed nominal control of the foundry, hiring and discharging 
 his men, fixing their wages, and increases in pay for his men are by his 
 recommendations subject to approval of superintendent. ..." 
 
 SAMPLE SHEET FROM ''CASTINGS RETURNED FROM 
 SHOP AND CUSTOMERS, TO BE MADE OVER." 
 
 Note: All castings returned by machine shop and customers, before 
 being made over, must be entered in this book, stating cause for being 
 made over. 
 
 Castings returned to foundry from shop or customers, through no 
 fault of foundry, must not be deducted from net foundry castings, but 
 should be considered as foreign scrap; but if fault of foundry, they 
 should be charged back to foundry, and considered as foundry return 
 scrap. 
 
 All castings returned by shop or customers, in excess of number 
 ordered, will be charged to foundry the same as defective castings, and 
 placed in foundry return scrap, unless otherwise ordered by superin- 
 tendent. 
 
 Sample of Entry 
 
 Date 
 returned 
 
 By whom 
 returned 
 
 Description 
 
 Cause 
 
 Whose fault 
 
 Weight, 
 pounds 
 
 April 26, 1909 
 
 Our Mach. shop 
 
 I S. B. pulley 
 36x8-2^6 
 in. bore 
 
 Bored too 
 large 
 
 Mach. shop 
 
 240 
 
 April 29, 1909 
 
 Our Mach. shop 
 
 I split pulley 
 24X6-2fi6 
 in. bore 
 
 Broke lug 
 in split- 
 ting 
 
 Mach. shop 
 
 120 
 
 May 3, 1909 
 
 Customer 
 
 12 gear castings 
 P. 2 
 
 Cored too 
 large 
 
 Foundry 
 
 14 
 
 May 5, 1909 
 
 Foundry 
 
 I D. B. pulley 
 36X8-215^6 
 in. bore 
 
 Blow hole 
 in face 
 
 Foundry 
 
 260 
 
630 Foundry Accounts 
 
 WEEKLY FOUNDRY 
 
 GoLDENs' Foundry and Machine Co., Columbus, Ga. 
 
 For Week Ending Friday, 19 
 
 Bad castings returned from foundry. 
 
 Total pounds good castings made. 
 
 Defective castings returned from shop and customers 
 
 Net good castings for week. Total amount ( ) 
 
 Total pounds pig and foreign scrap charged in cupola. 
 Net good castings for week. 
 
 Per cent lost in re melt, cupola droppings, gangways, etc. 
 
 Per cent bad castings, gates, etc., of total melt. 
 Including foreign scrap, rettirns and pig. 
 
 Average per cent of cast- 
 ings lost. 
 
 Remainder. 
 
 Total melt. 
 
 Net good castings. 
 
 
 
 Proportionate Wage Cost Per Hundred 
 
 No. 
 
 Non-producers 
 
 Wages 
 
 
 
 Foundry foreman. 
 Foundry assistant. 
 Pulley man. 
 Crane man. 
 
 
 $ 
 
 - 
 
 
 Clerk. 
 
 Cupola tender. 
 Cupola helpers. 
 Carpenters. 
 Watchman. 
 
 
 Total $ 
 
 Wages cost perj 
 • hundred pounds > $ 
 net castings. ) 
 
 No. 
 
 Rumbling Departmeni 
 
 Wages 
 
 
 
 Foreman. 
 Assistant. 
 Men. 
 
 
 1 ] 
 
 J 
 Total $ 
 
 Wages cost per 
 hundred pounds 
 net castings, 
 chipped, cleaned, 
 and ready to ship. 
 
 Grand Total Wo 
 
 ge Cost 
 
 Note. — Castings returned to foundry from our shop and customers, through no 
 fault of foundry, must not be deducted from net foundry castings, and should be 
 
Weekly Foundry Report 
 
 631 
 
 REPORT 
 
 
 1 
 & 
 
 1 
 
 1- 
 
 SI 
 
 ii 
 
 
 3 
 
 a 
 a 
 
 Ph 
 
 '31 
 ■g,S 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 Cupola Charge 
 
 Pounds pig iron @ per hundred $ -j Cost per hundred ■ 
 Pounds foreign scrap @ per hundred 1 pounds net castings 
 Pounds coke @ per hundred j including pig iron, j 
 Total wages $ J scrap, coke, wages. J 
 Total $ 
 Material cost per hundred pounds net castings made as per sheet. $ 
 Total cost per hundred pounds net castings made as per sheet. $ 
 
 $ 
 
 Pounds in Different Departments 
 
 No. 
 
 Moulding Department 
 
 Wages 
 
 Moulders (white). 
 Helpers (white). 
 Helpers (black). 
 
 Total $ 
 
 Wages cost per ] 
 hundred pounds | $ 
 net castings. 
 
 No. 
 
 Core Shop 
 
 Wages 
 
 Foreman. 
 Core makers. 
 Help. 
 
 Total $ 
 
 Wages cost per ^ 
 hundred pounds > $ 
 net castings. ) 
 
 No. 
 
 Night Cleaning Gang 
 
 Wages 
 
 Headman. 
 Men. 
 
 Total $ 
 
 ^ Wages cost per l 
 > hundred pounds [ $ 
 ) net castings. ) 
 
 No. 
 
 Day Cleaning Gang 
 
 Wages 
 
 Headman. 
 Men. 
 
 per Hundred Pounds $ 
 
 $ 
 Total $ 
 
 Wages cost per ' 
 hundred pounds [ S 
 net castings. 
 
 put in foreign scrap pile. Weekly foundry report, made up from daily foundry re- 
 port and cupola sheet. 
 Pounds castings " killed " in machine shop. 
 
 Ik 
 
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 H 
 
 r rt 
 o o 
 
 H PM 
 
 § I 
 
 t3 
 
 w 
 
 f4 
 
 
 
 o 
 
 !^ 
 
 £ 
 
 spunod 001 J9d 
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 19 . 
 
 Goldens' 
 
 Foundry & 
 
 Machine Co. 
 
 Week 
 
 ending 
 
 
CHAPTER XXVIII 
 PIG IRON DIRECTORY 
 
 The Classification and Directory of Pig Iron Brands given herewith 
 are taken from Professor Porter's Report. 
 
 "Pig Iron is classified as: 
 First. — Cold, Warm or Hot Blast. 
 Second. — Coke, Anthracite or Charcoal. 
 Third. — Sand or Machine. 
 Fourth. — Basic, Bessemer, Malleable, Foundry or Forge. 
 
 "It is only necessary to define the fourth classification as the others 
 are self-explanatory. " 
 
 "Basic iron means primarily one with low silicon. The standard for 
 this grade having silicon under i per cent and sulphur under 0.05 per 
 cent." 
 
 " Bessemer iron means primarily phosphorus under i per cent. Stand- 
 ard Bessemer contains from i to 1.25 per cent silicon with sulphur 
 under 0.05, but the grade is essentially based on low phosphorus. Irons 
 with extra low phosphorus and variable siHcon are sometimes designated 
 as low phosphorus irons." 
 
 "Foundry and Forge Irons embrace practically everything in the way 
 of ordinary iron, these grades being subdivided on the basis of siHcon 
 and sulphur content." 
 
 "The following subclassification of Foundry and Forge iron has been 
 agreed upon by the blast furnace interests of the districts indicated: 
 
 Classification and Grades of Foundry Iron 
 
 Southern Points 
 
 No. I foundry 
 
 No. 2 foundry 
 
 No. 3 foundry 
 
 No. 4 foundry 
 
 Gray forge 
 
 No. I soft 
 
 No. 2 soft 
 
 Silicon, per cent 
 
 Sulphur, per cent 
 
 2.75-3.25 
 
 .05 and under 
 
 2.25-2.75 
 
 .05 " 
 
 1.75-2.25 
 
 .06 " 
 
 1.25-2.00 
 
 .07 " 
 
 I. 25-1. 75 
 
 .08 " 
 
 3 . 00 and over 
 
 .05 " 
 
 2.5(^3.25 
 
 .05 " 
 
 633 
 
634 Pig Iron Directory 
 
 Classification and Grades of Foundry Iron (Continued) 
 
 Eastern Points 
 
 No.iX 
 
 No. 2X 
 
 No. 2 plain 
 
 No. 3 foundry 
 
 No. 2 mill 
 
 Gray forge 
 
 Mottled and White by Fracture, Cen- 
 tral West and Lake Points 
 
 No. I foundry 
 
 No. 2 foundry 
 
 No. 3 foundry 
 
 Gray forge 
 
 Buffalo Grading 
 
 Scotch 
 
 No. I foundry 
 
 No. 2 foundry 
 
 No. 2 plain 
 
 No. 3 foundry 
 
 Gray forge 
 
 Silicon, per cent 
 
 2.75 and up 
 
 2.25-2.75 
 
 1.75-2.25 
 
 I .25-1. 75 
 
 1 . 25 and under 
 
 1.50 " 
 
 2.25-2.75 
 1.75-2.25 
 1 . 75 and under 
 
 3 . GO and over 
 2.50-3.00 
 2.00-2.50 
 1.50-2.00 
 1.50 (under) 
 
 Sulphur, per cent 
 
 030 and under 
 045 " 
 050 " 
 065 " 
 065 " 
 065 and up 
 
 . 05 and under 
 
 .05 " 
 
 .05 " 
 
 . 05 and over 
 
 . 05 and under 
 
 .05 " 
 
 .05 " 
 
 .05 " 
 
 .05 " 
 
 . 05 and (over) 
 
 Note. — If sulphur is in excess of maximum, it is graded as lower 
 grade, regardless of silicon. 
 
 "Charcoal is not as a rule graded according to the above table but is 
 sold by fracture, by analysis, by chill tests, or by some special system 
 of grading according to the custom of the maker and demand of the 
 purchaser. " 
 
 " It will be noted that so far as Foundry iron is concerned the grading 
 system is based exclusively on silicon and sulphur. One reason for 
 this is that the phosphorus and manganese are fixed by the composition 
 of the ores used, whereas the silicon and sulphur can be varied at will 
 by shght changes in the method of operating the furnace. Since in 
 many, perhaps, the majority of, cases a blast furnace will be limited 
 to a very few ores as a source of supply, it follows that it will be limited 
 also in the range of phosphorus and manganese in the iron it produces. 
 For this reason, a given brand of iron will usually run fairly constant 
 as regards phosphorus and manganese, although its silicon and sulphur 
 can be varied at the wish of the management. However, this condition, 
 while common, is not imiversal, for some concerns possess a variety of 
 ores and can by mixing them produce iron of any composition desired. 
 
Coke and Anthracite Irons 635 
 
 "In using this directory please bear in mind that it is not infallible. 
 Much of the data has been difficult to get, a few concerns refusing abso- 
 lutely to furnish information. Again, in some cases time brings changes 
 in ownership and character of ore supply, etc., and of course, these 
 things will affect the character of the product. In spite of these defic- 
 iencies, however, it is believed that the following tables represent the 
 most accurate information along these lines available at the present 
 time and that they will be found of considerable value." 
 
 "Finally, it must be emphasized that the use of the data is not to tell 
 the foundryman the exact analysis of any carload of any brand, but 
 rather to help him locate those brands which have, or can be made to 
 have a composition suitable for his work." 
 
 "In these tables the percentage of sulphur is not usually given. It 
 should be understood that all furnaces strive for, and usually obtain, 
 low sulphur in their iron. Practically all foundry grades are sold on the 
 understanding that the sulphur is under 0.05 per cent and hence no 
 useful purpose is served in giving the sulphur range except in a very 
 few cases where it normally runs unusually low." 
 
 Coke and Anthracite Irons 
 
 Adrian. — Adrian fee., D.uBois, Pa. (A-drian fee. Co.) 
 
 Hot blast coke, sand cast, foundry iron, from Lake Superior ores. 
 Sil. 1.0-4.0% Mang. 0.4-1.2% Phos. 0.4-0.9% 
 
 Alice. — Alice fee., Birmingham, Ala. (Tenn. Coal, Iron & Ry. Co.) 
 Hot blast, coke, sand or chill cast iron, from Ala. red and brown ores. 
 Fdry. Sil. 1.0-4.0% Mang. 0.1-0.4% * Phos. 0.71-0% 
 
 Basic Under 1% 0.1-0.4 Under 1% 
 
 Alice. — AHce fee., Sharpsville, Pa. (The Youngstown Sheet & Tube 
 Co.) 
 
 Hot blast, coke iron, from Lake Superior ores. 
 
 Usually make Bessemer only for use in their own steel works. 
 
 Alleghany. — Alleghany fee., Iron Gate, Va. (Oriskany Ore & Iron Co.) 
 Hot blast, coke, sand cast, foundry iron, from local brown ores. 
 Sil. 1.0-4.0% Mang. 0.7-1.5% Phos. 0.2-0.6% 
 
 Allegheny. — McKeefrey fee., Leetonia, O. (McKeefrey & Co.) 
 
 Hot blast, coke, sand cast, foundry iron, from Lake Superior ores. 
 Sil. 0.7-2.0% Mang. 0.4-0.8% Phos. 0.4-0.7% 
 
 * Sometimes higher. 
 
636 Pig Iron Directory 
 
 Andover. — Andover fee., Phillipsburg, N. J. (Andover Iron Co.) 
 
 Hot blast, coke, sand cast, foundry iron, from local magnetic ore, 
 
 Lake Superior ore, iron nodules and roll scale. 
 Sil. 1.5-4.0% Mang. 0.6-1.5% Phos. 0.6-0.9% 
 
 A. R. Mills. — (2 stacks), Allentown, Pa. (Allentown Rolling Mills Co.) 
 Hot blast, anthracite and coke iron, from local hematites and N. J. 
 and N. Y. magnetites. 
 Ashland. — Ashland fees. (2 stacks), Ashland, Ky. (,Ashland Iron & 
 Min. Co.) 
 Hot blast, raw coal and coke, sand cast iron, from local brown and 
 
 Lake Superior ores. 
 High Sil. Fdry. Sil. 5.0-12.0% Mang. 0.5-0.8% Phos. 0.5-0.9% 
 Bess. Ferro Sil. 9.0-14.0% 0.5-0.8% under 1.0% 
 
 Aurora. — Aurora fee., Columbia, Pa. (Susquehanna Iron Co.) 
 
 Hot blast, anthracite and coke, forge and foundry iron, from native 
 
 and Lake Superior ores. 
 Not in operation, March, 1910. 
 Battelle. — Battelle fee., Battelle, Ala. (Lookout Mt. Iron Co.) 
 
 Hot blast, coke, sand cast, foundry iron, from local red hematite. 
 Not in operation March, 1910. 
 Bay View. — Bay view fees. (2 stacks), Milwaukee, Wise. (lUinois 
 Steel Co.) 
 Hot blast, coke, sand cast iron, from Lake Superior ores. 
 Mall. Bes. Sil. 1.0-3.0% Phos. under 0.20% Mang. 0.50-1.0% 
 Fdry. 1.0-3.0% over 0.50% 0.50-1.0 
 
 Belfont. — Belfont fee., Ironton, O. (Belfont Iron Works Co.) 
 
 Hot blast, coke, fdry iron, sand cast, from Lake Superior and native 
 
 ores. 
 Sil. 1.50-2.50% Phos. 0.40-0.70% Mang. 0.50-0.90% 
 
 Bellefonte. — Bellefonte fee., Bellefonte, Pa. (Bellefonte Furnace Co.) 
 Hot blast, coke, sand cast, foundry iron, from native and Lake 
 
 Superior ores. 
 Sil. 1.75-4-0% Phos. 0.5-0.7% Mang. 0.5-0.7% 
 
 Belmont. — Belmont fee., Wheeling, W. Va. (Wheeling Iron & Steel 
 Co.) 
 Hot blast, coke, sand cast, from Lake Superior ores. 
 Make only iron for their own steel plant. 
 
 Bessemer.— Bessemer fees. (5 stacks), Bessemer, Ala. (Term. C. I. 
 & Ry. Co.) 
 Same as De Bardeleben, which see. 
 
Coke and Anthracite Irons 637 
 
 Bessie. — Bessie fee., New Straitsville, O. (Bessie Ferro Silicon Co.) 
 Hot blast, coke and raw coal, sand cast, ferro silicon, from Lake 
 
 Superior low phos. ore. 
 Sil. 8.0-14.0% Phos. under 0.10% Mang. under 1.0% 
 
 Big Stone Gap. — Union fee. No. i, Big Stone Gap, Va. (Union Iron 
 and Steel Co.) 
 Hot blast, coke, sand cast, fdry iron, from local fossil brown ores. 
 Sil. usually high Phos. 0.40-0.80% Mang. 0.40-1.0% 
 
 Bird. — Bird fee., Culbertson, O. (The Bird Iron Co.) 
 
 Hot blast, coke, sand cast, fdry iron, from Lake Superior and native 
 
 ores. 
 Not in operation March, 19 10. 
 
 Boyd. — Ashland fees. (2 stacks), Ashland, Ky. (Ashland I. & Miu. 
 Co., Inc.) 
 Hot blast, raw coal and coke, sand cast, fdry iron, from Bath Co. 
 I & Lake Superior ores. 
 Sil. 1.50-3.0% Phos. 0.40-0.90% Mang. 0.50-0.80% 
 
 Brier Hill. — Grace fee., No. 2, Youngstown, O. (The Brier Hill I. & 
 C. Co.) 
 Hot blast, coke basic and Bessemer iron, from Lake Superior ores. 
 
 Bristol. — Bristol fee., Bristol, Tenn. (Va. Iron, Coal & Coke Co.) 
 • Hot blast, coke, from local brown ores. 
 Fdry. Sil. 2.0-2.75% Phos. abt. 0.50% 
 
 Basic (chill cast) low abt. 0.60% 
 
 • Mang. abt. 0.75% 
 1.0-1.50% 
 
 Brooke. — Brooke fees. (2 stacks), Birdsboro, Pa. (E. & G. Brooke Co.) 
 Hot blast, anthracite and coke, from Lake Superior, Newfoundland 
 and magnetic ores. 
 
 Buckeye. — Columbus fees. (2 stacks), Columbus, G. (The Columbus 
 L&S. Co.). 
 Hot blast, coke, chill mold iron, from Lake Superior ores. 
 Fdry Sil. 1.0-3.0% Phos. 0.40-0.60% Mang. 0.60-0.80%* 
 
 Mai. Bes. 0.50-2.50 under 0.20 0.60-1.0. f 
 
 Basic under i.o under 0.20 0.80-1.0 
 
 Stand. Bes. 1.0-2.0 under o.io 
 
 * Sometimes iigher. t Higher or lower if desired. 
 
6sS Pig Iron Directory 
 
 Buena Vista. — Buena Vista fee., Buena Vista, Va. (Oriskany Ore & 
 Iron Co.) 
 
 Hot blast, coke, chill, and sand cast iron, from Oriskany brown 
 
 hematite. 
 
 Fdry. Sil. 1.0-4.0% Phos. 0.2-1.0% Mang. 0.6-1.5% 
 
 Basic under i.o 0.2-0.5 0.6-1.5% 
 
 Spec, car wheel i. 0-1.50 0.2-0.5 0.6-1.5 
 
 Buffalo. — BuQalo Union fee. (3 stacks), Buffalo, N. Y. (The Buffalo 
 U. F. Co.) 
 Hot blast, coke, sand east iron, from Lake Superior ores. 
 Fdry. Sil. 1.50-3-25% Phos. 0.40-0.70% Mang. 0.50-1.0% 
 
 Mai. 0.75-2.0 0.10-0.20 0.40—1.0 
 
 Burden. — Burden fee., Troy, N. Y. (The Burden Iron Co.) 
 
 Hot blast, mixed anthracite coal and coke, occasionally coke alone. 
 Magnetic concentrates from northern New York. 
 Out of operation March, 19 10. 
 
 Carbon. — Carbon fee., Perry ville, Pa. (Carbon Iron & Steel Co.) 
 
 Hot blast, anthracite coal and coke foundry iron, magnetic from 
 
 N. J. & Lake Champlain, Lake Superior, and foreign ores. 
 Sil. 1.50-3.00% Phos. 0.40-0.90% Mang. 0.40-0.90% 
 
 Carondelet. — Missouri fee., So. St. Louis, Mo. (St. Louis Blast Fee. 
 Co.) 
 
 Hot blast, coke, Missouri red and brown hematite. 
 
 Analysis refused. 
 Chateaugay. — Standish fee., Standish, N. Y. (Northern Iron Co.) 
 
 Hot blast, coke, sand east, foundry iron, from local magnetic ores. 
 
 Sil. 1.0-3.0% Phos. 0.02-0.035% Mang. 0.15-0.50% 
 
 Chattanooga. — Chattanooga fee., Chattanooga, Tenn. (The Southern 
 
 I. & S. Co.) 
 Hot blast, coke, sand cast, foundry iron, from Alabama red and 
 
 Georgia brown hematite. 
 Sil. 1.50-3.50% Phos. 1.0-1.5% Mang. 0.6-1.0%* 
 
 Cherry Valley. — Cherry Valley fee., Leetonia, O. (United I. & S. Co.) 
 Hot blast, coke, sand east, foundry iron, from Lake Superior ores. 
 Sil. as desired Phos. 0.20-0.60% Mang. 0.60-0.80% 
 
 Chickies. — Chickies fees. (2 stacks), Chickies, Pa. (Standard Iron 
 Min. & Furnace Co.) 
 Hot blast, anthracite and coke, sand east, foimdry iron, from mag- 
 netites. 
 
 * Sometimes higher. 
 
Coke and Anthracite Irons 639 
 
 Citico. — Citico fee., Chattanooga, Tenn. (Citico Furnace Co.) 
 
 Hot blast, coke, sand cast, soft foundry, from red and brown hema- 
 tites from Tennessee and Georgia. 
 Sil. 2.0-3.0% Phos. abt. 1.25% Mang. abt. 0.60% 
 
 Claire. — Claire fee., Sharpsville, Pa. (Claire Furnace Co.) 
 
 Hot blast, coke, Bessemer iron only, from Lake Superior ores. 
 
 Cleveland. — Cleveland fees. (2 stacks), Cleveland, O. (Cleveland Fur- 
 nace Co.) 
 Hot blast, coke, from Lake Superior ores. 
 Analysis refused. 
 
 Clifton. — Clifton fees. (2 stacks). Iron ton, Alabama. (Alabama Con- 
 sol. C. & I. Co.) 
 Hot blast, coke, sand east, foundry iron, from local brown hematite. 
 Sil. 1.0-6.0% Phos. 0.35-0.70% Mang. 1.0-2.0% 
 
 Climax. — Hubbard fees. (2 stacks), Hubbard, O. (The Andrews & 
 
 Hitchcock I. Co.) 
 Hot blast, coke, sand cast, strong foundry iron, from Lake Superior 
 
 ores. 
 Sil. 1.35-1-75% Phos. 0.30-0.40% Mang. 0.50-0.80% 
 
 Clinton. — Clinton fees., Pittsburgh, Pa. (Clinton I. & S. Co.) 
 
 Hot blast, coke, sand east, foundry iron, from Lake Superior 
 
 ores. 
 Sil. up to 3.0% Phos. 0.20-0.75% Mang. 0.50-1.0% 
 
 Colonial. — Colonial fees. (2 alt. stacks), Riddlesburg, Fa. (Colonial 
 Iron Co.) 
 Hot blast, coke, sand cast, foundry iron, from Lake Superior and 
 
 native ores. 
 Sil. up to 4.0% Phos. 0.40-0.60% Mang. 0.50-0.80% 
 
 Covington. — Covington fee., Covington, Va. (Low Moor Iron Co. of 
 Va.) 
 Hot blast, coke, sand cast iron, from native brown hematite. 
 Fdry. Sil. 1.5-3.0% Phos. 0.90-1.2% Mang. 0.70-1.0% 
 
 High Sil. silvery 4.0-8.0 0.90-1.2 0.70-1.0 
 
 Cranberry. — Cranberry fee., Johnson City, Tenn. (The Cranberry 
 
 Fee. Co ) 
 Hot blast, coke, sand cast, low phos. iron, from local magnetic 
 
 ore. 
 Sil. 1.0-3.5% Phos. under 0.035% Mang. 0.4-0.6% 
 
640 Pig Iron Directory 
 
 'Crane. — Crane fees. (3 stacks), Catasauqua, Pa. (Empire S. & I. Co.) 
 Hot blast, anthracite and coke, sand cast iron, from N. J. magnetic, 
 
 Pa. hematite, Lake Superior and foreign ores. 
 Fdry. Sil. 0.75-3.50% Phos. 0.60-0.90% Mang. 0,50-2.0% 
 
 Basic mider i.o under i.o 0.50-0.80 
 
 Low phos. 1.0-3.0 under 0.03 0.50-3.0 
 
 Crozer. — Crozer fees. (2 stacks), Roanoke, Va. (Va. Iron, Coal & 
 
 Coke Co.) 
 Hot blast, coke, sand cast iron, from Va. limonite, moimtain and 
 
 specular ores. 
 Fdry. Sil. 2.10-2.75% Phos. 0.60-0.80% Mang. 0.60-0.90% 
 
 Basic abt 0.70 abt. 0.70 abt. 1.25 
 
 Cumberland. — Cumberland fee., Cumberland Fee. P. O., Tenn. (War- 
 ner Iron Co.) 
 Hot blast, coke, sand east foundry, from local brown and red hema- 
 tites. 
 Sil. 2.0-4.5% Phos. abt. 2.0% Mang. abt. 0.30% 
 
 Dayton. — Dayton fees. (2 stacks), Dayton, Tenn. (The Dayton C. & 
 I. Co. Ltd.) 
 Hot blast, coke, sand east, foundry iron, from Tenn. fossil and 
 Georgia hematite. 
 De Bardeleben. — Bessemer fees. (5 stacks), Bessemer, Tenn. (Tenn. 
 C. I. & Ry. Co.) 
 Hot blast, coke, sand and chill east iron, from local red and brown 
 
 hem. 
 Fdry. & Mill Sil. up to 3.25% Phos. 0.70-1.0% Mang. 0.10-0.40 
 Basic up to 1.0 up to 1.0 0.10-0.40 
 
 Detroit. — Detroit fee., Detroit, Mich. (Detroit Furnace Co.) 
 
 Hot blast, coke, sand cast, foundry iron, from Lake Superior ores. 
 Dora. — Dora fee., Pulaski City, Va. (Va. Iron, Coal & Coke Co.) 
 
 Hot blast, coke, sand east foundry iron, from native limonite and 
 mountain ores. 
 
 Sil. 1.50-3.00% Phos. 0.40-0.80% Mang. 0.50-0.90% 
 Dover. — Dover fee., Canal Dover, O. (The Pa. Iron & Steel Co.) 
 
 Hot blast, coke, sand cast, foundry iron, from Lake Superior ores. 
 Dunbar. — Dunbar fees. (2 stacks), Dunbar, Pa. (Dunbar Furnace Co.) 
 Hot blast, coke, sand or machine cast iron, from Lake Superior 
 
 specular and soft ores. 
 Fdry. Sil. 1.5-3.0% Phos. 0.30-0.60% Mang. 0.30-0.60% 
 
 Malleable 1.0-2.0 under 0.20 0.30-0.80 
 
Coke and Anthracite Irons 641 
 
 Durham. — Durham fee., Riegelsville, Pa. (Durham Iron Co.) 
 
 Hot blast, anthracite and coke, sand cast iron, from Lake Superior, 
 local hematite and New Jersey magnetite. 
 
 Eliza. — Pittsburgh fees. (5 stacks), Pittsburgh, Pa. (Jones & Laughlin 
 St. Co.) 
 Hot blast, coke, Bessemer and basic, machine east iroij, from Lake 
 Superior ores. 
 
 Ella. — Ella fee., West Middlesex, Pa. (Piekands, Mather & Co.) 
 
 Hot blast, coke, foundry and malleable iron, from Lake Superior 
 
 ores. 
 On account of the large assortment of ores available, this furnace 
 
 can make practically any desired composition. 
 
 Embreeville. — Embreeville fee., Embreeville, Tenn. (Embree Iron Co.) 
 Hot blast, coke, foundry iron, from local brown hematite. 
 
 Empire. — Reading, Pa. (Empire Steel & Iron Co.) 
 
 Hot blast, anthracite and coke, foundry iron, from Lake Superior, 
 
 Porman and magnetic ores. 
 Sil. 2.0-3.0% Phos. 1,25-2.50% Mang. 0.50-1.0% 
 
 Emporium. — Emporium fee.. Emporium, Pa. (Emporium Iron Co.) 
 Hot blast, coke, foundry iron, from brown hematite. 
 Sil. as desired Phos. abt. 0.80% Mang. abt. 0.60% 
 
 Ensley. — ^Ensley fees. (6 stacks), Ensley, Alabama. (Tenn. C. I. & 
 
 Ry. Co.) 
 
 Hofblast, coke, machine cast iron, from red and brown hematite. 
 Basic Sil. up to 1.0% Phos. 0.70-1.0% Mang. 0.10-0.40%* 
 
 Fdry. & Mill up to 2.50 0.70-1,0 0.10-0.40* 
 
 Essex. — Northern fee.. Port Henry, N. Y. (Northern Iron Co.) 
 Hot blast, coke, foundry iron, from local magnetic ores. 
 Sil. 1.0-2.50% Phos. 0.40-0.90% Mang. 0.10-0.40% 
 
 Etowah. — Etowah fees. (2 stacks), Gadsden, Ala. (Ala. Consol.) 
 
 Hot blast, coke, foundry iron, from local red and brown hematite. 
 Sil. 1.0-06% Phos. 0.70-1,20% Mang. 0.40-0.80% 
 
 Eureka. — Same as Oxmoor, which see. 
 
 Everett. — Earlston fee., Earleston, Pa. (Jos. E. Thropp.) 
 
 Hot blast, coke, foundry iron, from Lake Superior and local brown 
 
 ores. 
 Sil. 1.50-3-50% Phos. 0.40-0.70% Mang. 0,50-0,90% 
 
 * Sometimes higher. 
 
642 Pig Iron Directory 
 
 Fannie. — Fannie fee., West Middlesex, Pa. (.United Iron & Steel 
 Co.) 
 Hot blast, coke, foundry iron, from Lake Superior ores. 
 Sil. as desired Phos. 0.20-0.60% Mang. 0.60-0.80% 
 
 Federal. — Federal fees. (2 stacks), S. Chicago, 111. (Federal Furnace 
 Co.) 
 Hot blast, coke, mal. and foundry iron, from Lake Superior ore. 
 Sil. as desired. Phos. as desired. Mang. as desired. 
 
 Florence. — Philadelphia fee., Florence, Ala. (Sloss-Sheffield S. & I. 
 Co.) 
 Hot blast, coke, sand cast, foundry iron, from Ala. brown hematite. 
 Sil. as desired.. Phos. 0.80-1.25% Mang. 0.40-0.80% 
 
 Fort Pitt. — Cherry Valley fee., Leetonia, O. (United I. & S. Co.) 
 Hot blast, coke, spec, car wheel iron, from Lake Superior ore. 
 Sil. as desired. Phos. 0.20-0.80% Mang. 0.60-0.80% 
 
 Franklin. — Franklin fee., Franklin Springs, N. Y. (Franklin Iron 
 
 Mfg. Co.) 
 Hot blast, coke, foundry iron, from fossil, red hematite from CHn- 
 
 ton, N. Y. 
 Not in operation March, 1910. 
 Sil. 2.25-3.0% Phos. 1.25-1.50% Mang. 0.25-0.40% 
 
 Gem. — Same as Shenandoah, which see. 
 
 Genesee. — Genesee fee., Charlotte, N. Y. (Genesee Furnace Co.) 
 Hot blast, coke, from Lake Superior ore. 
 Not in operation March, 1910. 
 
 Girard. — Mattie fee., Girard, O. (Girard Iron Co.) 
 
 Hot blast, coke, foundry iron, from Lake Superior ore. 
 
 Sil. 1.50-3.0% Phos. 0.40-0.70% Mang. 0.50-0.80% 
 
 Globe. — Globe fee., Jackson, O. (Globe Iron Co.) 
 
 Hot blast, raw coal and coke, sand cast, high silicon silvery iron, 
 
 from native ores. 
 Sil. 4.0%-! 2.0% Phos. 0.40-0.80% Mang. 0.40-0.80% 
 
 Grafton. — McKeefrey fee., Leetonia, O. (McKeefrey & Co.) 
 Hot blast, coke, foundry iron, from Lake Superior ores. 
 Sil. 2.0-2.50% Phos. 0.40-0.70% Mang. 0.40-0.80% 
 
 Graham. — Graham fee., Graham, Va. (Va. Iron, Coal & Coke Co.) 
 Hot blast, coke, foundry and basic iron, from Lake Superior and 
 native brown hematite. 
 
Coke and Anthracite Irons 643 
 
 Hamilton. — Hamilton fee., Hanging Rock, O. (The Hanging Rock 
 Iron Co.) 
 Hot blast, coke, sand cast iron, from native block and limestone 
 
 and Lake Superior ores. 
 Fdry. Sil. as desired. Phos. 0.3-0.4% Mang. 0.5-0.7% 
 
 Mall. as desired. under 0.20 
 
 Hector. — Chnton fee., Pittsburgh, Pa. (CKnton Iron & St. Co.) 
 Hot blast, coke, foundry iron, from Lake Superior ores. 
 Sil. up to 3.50% Phos. 0.50-0.75% Mang. up to 1.0% 
 
 Helen. — Helen fee., Clarksville, Tenn. (Red River Furnace Co.) 
 
 Hot blast, coke, sand cast soft, fluid foundry iron, from local brown 
 
 hematite. 
 Sil. 2.0-3.0% Phos. abt. 1.25% Mang. 0.40-0.60% 
 
 Henry Clay. — Henry Clay fees. (2 stacks), Reading, Pa. (Empire 
 Steel & Iron Co.) 
 Hot blast, anthracite coal and coke, foundry and forge iron, from 
 
 local hematite and magnetite. 
 Fdry. Sil. 1.50-4.50% Phos. 2.50-3.50% 
 
 Hillman. — Grand River fees. (2 stacks). Grand Rivers, Ky. (Hillman 
 Land & Iron Co.) 
 Hot blast, coke, foundry and forge sand east iron, from local brown 
 
 hematite. 
 Not in operation March, 19 10. 
 
 Hubbard. — Hubbard fees. (2 stacks), Hubbard, O. (The Andrews & 
 Hitchcock Iron Co.) 
 
 Hot blast, coke, malleable iron, from Lake Superior ore. 
 
 Sil. 1.0-2.0% Phos. under 0.20% Mang. under 0.80% 
 
 Hubbard Scotch. — Hubbard fees. (2 stacks), Hubbard, O. (The 
 Andrews & Hitchcock Iron Co.) 
 
 Hot blast, coke, soft foundry iron, from Lake Superior ores. 
 
 Sil. up to 3.00% Phos. 0.50-0.65% Mang. about 0.60% 
 
 Hudson. — Secausus fee., Secausus, N. J. (Hudson Iron Co.) 
 
 Hot blast, anthracite coal and coke, foundry iron, from N. Y. mag- 
 netite, N. J. limonite and Lake Superior ores. 
 
 Sil. up to 3-4% Phos. 0.60-0.95% Mang. up to 0.50% 
 
 Imperial. — Shelby fee.. No. i, Shelby, Ala. (Shelby Iron Co.) 
 
 Hot blast, coke, iron from local brown hematite. 
 
 Not in operation March, 1910. 
 Inland. — Inland fee., Indiana Harbor, Ind. (^Inland Steel Co.) 
 
 Hot blast, coke, basic iron, from Lake Superior ores. 
 
644 Pig Iron Directory 
 
 Ironaton. — Clifton fees. (2 stacks), Ironaton, Ala. (Alabama Consol. 
 C. &. I. Co.) 
 
 Hot blast, coke, foundry iron, sand cast, from local brown ore. 
 
 Sil. 1.0-6.0% Phos. 0.70-0.90% Mang. 0.70-1.0% 
 
 Iroquois. — Iroquois fees. (2 stacks), S. Chicago, 111. (Iroquois Iron 
 Co.) 
 
 Hot blast, coke, foundry iron, from Lake Superior ores. 
 
 Sil. 1.35-2-50% Phos. 0.3-0.4%* Mang. 0.40.-0.70% 
 
 Ivanhoe. — Ivanhoe fee., Ivanhoe, Va. (Carter Iron Co.) 
 
 Hot blast, coke, sand cast, foundry iron, from local and Lake 
 Superior ores. 
 
 Sil. % as desired. Phos. abt. 0.40% Mang. abt. 0.70% 
 
 Jenifer. — Jenifer fee., Jenifer, Ala. (Jenifer Iron & Coal Co.) 
 
 Hot blast, coke, sand cast, foundry iron from local brown hematite. 
 
 Not in operation March, 1910. 
 Jisco. — Jisco fee., Jackson, O. (Jackson Iron & Steel Co.) 
 
 Hot blast, coke and raw coal, high siHcon iron, from native and Lake 
 Superior ores. 
 
 Sil. 4.0-14.0% Phos. up to 0.9% Mang. up to 0.9% 
 
 Josephine. — Josephine fee., Josephine, Pa. (Josephine Furnace & 
 Coke Co.) 
 
 Hot blast, coke, sand cast iron, from Lake Superior ores. 
 
 Fdry. Sil. up to 4.0% Phos. 0.50-0.80% Mang. under 0.90% 
 
 Bessemer 1.25-2.0 0.085-0.10 under 0.90 
 
 Juniata. — Marshall fee., Newport, Pa. (Juniata Fee. & Fdry, Co.) 
 
 Hot blast, anthracite coal and coke, sand cast, foundry iron, from 
 local hematite and Lake Superior ores. 
 
 Sil. up to 2.0% Phos. under 1.0% Mang. under 1.0% 
 
 Lackawanna. — (12 stacks). (Lackawanna Steel Co.) 
 
 Lackawanna fees. (7 stacks), Lackawanna, N. Y. 
 
 Bird Coleman fees. (2 stacks), Cornwall, Pa. 
 
 Colebrook fees. (2 stacks), Lebanon, Pa. 
 
 N. Cornwall fee., Cornwall, Pa. 
 
 Hot blast, coke, Bes. and basic iron, from Lake Superior and Corn- 
 wall ores. 
 
 Lady Ensley. — Lady Ensley fee., Sheffield, Ala. (Sloss-Sheffield S. & 
 I. Co.) 
 Hot blast, coke, sand cast, foundry iron, from local brown hematite. 
 Sil. as desired. Phos. 1.0-1.50% Mang. 0.50-0.80% 
 
 * Sometimes higher. 
 
Coke axid Anthracite Irons 645 
 
 La Follette. — Lsi Follette fee., La Follette, Tenn. (La FoUette C, I. 
 
 & Ry. Co.) 
 Hot blast, coke, sand cast, foundry iron, from local fossil, red and 
 
 brown hematite. 
 Sil. up to 4.0% Phos. 1.0-1.25% Mang. 0.50-0.75% 
 
 L. C. R. — Lebanon, O. (Lebanon Reduction Co.) 
 Coke and charcoal, low phos. pig. 
 Operated for experimental purposes only. 
 
 Lebanon Valley. — Lebanon fee., Lebanon, Pa. (Lebanon Valley Fee. 
 Co.) 
 
 Hot blast, anthracite coal and coke, sand cast, foundry iron, prin- 
 cipally Cornwall ore. 
 
 Sil. as desired. Phos. 0.3-0.4% Mang. p.3-0.4% 
 
 Lees port. — Leesport fee., Leesport, Pa. (Leesport Furnace Co.) 
 
 Hot blast, anthracite coal and coke, sand cast, foundry iron, from 
 
 local hematite and magnetite. 
 Sil. as desired. Phos. 0.2-0,3% Mang. abt. 1.00% 
 
 Lehigh. — Lehigh fee., Allentown, Pa. (Lehigh Iron & Steel Co.) 
 
 Hot blast, anthracite and coke, siand cast, foundry and mill iron, 
 
 from Lake Superior, local hematite and New Jersey magnetite. 
 Not in operation March, 1910. 
 
 Lone Star. — Sam Lanham fee.. Rusk, Texas. (State of Texas.) 
 Hot blast, coke, from local brown hematite. 
 Not in operation March, 1910. 
 
 Longdale. — Longdale fee., Longdale, Va. (The Longdale Iron Co.) 
 Hot blast, coke, chill cast iron, from local brown hematite. 
 "Basic" Sil. under 1.0% Phos. [0.90-1.0% Mang. 1.0-1.5% 
 "Off Basic Sil." 1.0-1.75 0.90-1.0 1.0-1.50 
 
 "Off Basic Sul." * 0.25-0.75 0.90-1.0 1.0-1.50 
 
 Lowmoor. — Lowmoor fees. (2 alt. stacks), Lowmoor, Va. (Lowmoor 
 I. Co. of Va.) 
 Hot blast, coke, sand east iron, from local brown hematite. 
 Fdry. Sil. 1.50-3.0% Phos. 0.80-1.0% Mang. 0.90-1.2% 
 
 High Sil. silvery 4.0-8.0 0.80-1.0 0.90-1.2 
 
 Macungie. — Macungie fee., Macungie, Pa. (Empire Steel & Iron Co.) 
 Hot blast, anthracite and coke, sand cast, foundry iron, from local 
 
 hematites, Lake Superior and foreign ores. 
 Sil. 0.75-3.50% Phos. 0.60-0.90% Mang. 0.50-2.0% 
 
 * Sulphur over .05 per cent. 
 
646 Pig Iron Directory 
 
 Malleable. — Iroquois fees. (2 stacks), S. Chicago, III. (Iroquois Iron Co.) 
 Hot blast, coke, sand cast, foundry iron, from Lake Superior ores. 
 Sil. 1.25-2.50% Phos. under 0.2% Mang. 0.40-0.70% 
 
 Mannie. — Aliens Creek fees. (2 stacks), Mannie, Tenn. (Bon Air C. 
 & I. Co.) 
 
 Hot blast, coke, sand cast, foundry iron, from local brown hematite. 
 
 Sil. up to 8.0% Phos. abt. 2.0% Mang. 0.40-0.65% 
 
 Marshall. — Marshall fee., Newport, Pa. (Juniata Fee. & Fdry Co.) 
 
 Hot blast, anthracite and coke, sand east, foundry iron, from local 
 hematite and Lake Superior ores. 
 
 Sil. up to 3.0% Phos. under 1.0% Mang. under 1.0% 
 
 Martin's Ferry. — Martin's Ferry fee., Martin's Ferry, W. Va. « (Wheel- 
 ing Iron & Steel Co.) 
 
 Hot blast, coke, Bessemer only, from Lake Superior ores. 
 Ma,x Meadows. — Max Meadows fee.. Max Meadow^s, Va. (Va. Iron, 
 Coal & Coke Co.) 
 
 Hot blast, coke, sand cast iron, from Va. limonite and mountain ores. 
 
 Fdry. Sil. 1.75-2.75% Phos. 0.40-0.70% Mang. 1.0-2.0% 
 
 Basic under i.o under i.o Mang. abt. 1.50 
 
 Miami. — Hamilton, O. (Hamilton Iron & Steel Co.) 
 
 Hot blast, coke, iron, from Lake Superior ores. 
 
 Fdry. Sil. 1.0-3.50% Phos. 0.40-0.70% Mang. 0.50-0.80% 
 
 Mall. 0.75-2.0 imdero.2o 0.60-1.0 
 
 Basic imder 1.0 under 0.20 as desired 
 
 Missouri. — Missouri fee., S. St. Louis, Mo. (St. Louis Blast Furnace 
 Co.) 
 
 Hot blast, coke, basic iron, from Mo. red and brown hematites. 
 
 Analysis refused. 
 Musconetcong. — Musconetcong fee.. Stanhope, N. J. (Musconetcong 
 Iron Works.) 
 
 Hot blast, anthracite and coke, foundry iron, from New Jersey 
 magnetic. Lake Superior, Cuban and other foreign ores. 
 
 Sil. 2.50-3.50% Phos. 0.60-0.70% Mang. 0.60-0.70% 
 
 Napier. — Napier fee., Napier, Tenn. (Napier Iron Works.) 
 
 Hot blast, coke, foundry iron, from local brown hematite. 
 
 Sil. 2.0-2.75% Phos. 0.75-1.50% Mang. 0.40-0.80% 
 
 Nellie. — Ironton, O. (The Ironton Iron Co.) 
 
 Hot blast, coke, from Lake Superior ores. 
 
 Fdry. Sil. 1.25-3.0% Phos. 0.40-0.60% Mang. 0.50-0.80% 
 
 Mall. Bes. 1.0-2.0 under 0.20 0.50-0.90 
 
Coke and Anthracite Irons 647 
 
 Nellie. — Alice & Blanche fees. (alt. stacks), Ironton, O. (The Mar- 
 ting I. & S. Co.) 
 Hot blast, coke, sand cast iron, from Lake Superior and Kentucky 
 
 ores. 
 Fdry. Sil. 1.0-3.0% Phos. 0.40-0.60% Mang. 0.50-1.0% 
 
 Mall. 0.50-3.0 under 0.20 0.50-1.0 
 
 Niagara. — Niagara fee., N. Tonawanda, N. Y. (Tonawanda Iron & 
 Steel Co.) 
 Hot blast, coke, foundry iron, from Lake Superior hematite. 
 Analysis refused. 
 Nittany. — Same as Bellefonte, which see. 
 Norton. — Ashland, Ky. (Norton Iron Works.) 
 
 Hot blast, coke, mall, and Bess, iron, from Lake Superior ores. 
 Norway. — Colonial fees. (2 alt. stacks), Riddlesburg, Pa. (Colonial 
 Iron Co.) 
 Hot blast, coke, foundry iron, from Lake Superior and native ores. 
 Sil. up to 4.0% Phos. 0.60-0.90% Mang. 0.70-1.0% 
 
 Oxford. — Oxford fee., Oxford, N. J. (Empire Steel & Iron Co.) 
 
 Hot blast, anthracite and coke, basic iron, from local magnetic and 
 
 special ores. 
 Sil. under 1.0% Phos. under 1.0% Mang. 0.75-1.25% 
 
 Oxmoor. — Oxmoor fees. (2 stacks), Oxmoor, Ala. (Tenn. Coal, I. & 
 Ry. Co.) 
 Hot blast, coke, foundry and forge, sand cast, from red and brown 
 
 hematite. 
 Sil. up to 3.50% Phos. 0.70-1.0% Mang. 0.10-0.40%* 
 
 Perry. — Carbon fee., Perryville, Pa. (Carbon Iron & Steel Co.) 
 
 Hot blast, anthracite and coke, Bess, iron, from Lake Superior, 
 foreign, Lake Champlain and New Jersey ores. 
 Paxton. — Paxton fees. (2 stacks), Harrisburg, Pa. (Central I. & S. 
 Co.) 
 Hot blast, anthracite and coke, various ores. 
 
 Peerless. — Iroquois fees. (2 stacks), S. Chicago, 111. (Iroquois Iron 
 Co.) 
 Hot blast, coke, foundry iron, from Lake Superior ores. 
 Sil. 3.0-3.5% Phos. 0.30-0.40% Mang. 0.40-0.70% 
 
 Pencost. — Bessie fee., New Straitsville, O. (Bessie Ferro-Silicon Co.) 
 Hot blast, coke, ferro-sihcon, from Lake Superior ores. 
 Sil. 5.0-12.0% Phos. 0.30-0.70% Mang. under 1.0% 
 
 * Sometimes higher. 
 
648 Pig Iron Directory 
 
 Pequest. — Pequest fee., Buttzville, N. J. (Pequest Co.) 
 
 Hot blast, anthracite and coke, foundry iron, from N. J. magnetic 
 
 and manganiferous ores. 
 Out of blast March, 1910. 
 
 Perry. — Perry fee., Erie, Pa. (Perry Iron Co.) 
 
 Hot blast, coke, sand cast iron, from Lake Superior ores. 
 Fdry. Sil. 1.75-3.0% Phos. 0.40-0.70% Mang. 0.40-0.80% 
 
 Fdry. 1.00-2.00 1. 15-0.30 0.40-0.80 
 
 Special '2.00-3.50 1.00-1.50 0.40-0.80 
 
 Pioneer. — Pioneer fees. (3 stacks) , Thomas, Ala. (Republic Iron &S t. Co.) 
 Hot blast, coke, foundry iron, from red and brown hematite. 
 Sil. up to 3.5o%o* Phos. 0.75-0.95% Mang. 0.40-0.80% 
 Poughkeepsie. — Poughkeepsie fees. (2 stacks), Poughkeepsie, N. Y. 
 (Poughkeepsie Iron Co.) 
 Hot blast, anthracite and coke, from Lake Superior, local brown 
 
 hematite and Port Henry magnetite ores. 
 Not in operation March, 19 10. 
 
 Poughkeepsie. — Poughkeepsie fees. (2 stacks), Poughkeepsie, N. Y. 
 (Poughkeepsie Iron Co.) 
 Not in operation March, 1910. (See Poughkeepsie.) 
 
 Princess. — Princess fee.. Glen Wilton, Va. (Princess Furnace Co.) 
 Hot blast, coke, foundry iron, from local limonite. 
 Sil. up to 3.0 or 4.0% Phos. 0.60-0.80% Mang. up to 1.0% 
 
 Pulaski. — Pulaski fee., Pulaski, City, Va. (Pulaski Iron Co.) 
 Hot blast, coke, foxmdry iron, from local brown ores. 
 Sil. 2.0-3.50% Phos. 0.50-0.80% Mang. 0.40-0.70% 
 
 Punxy. — Punxy fee., Punxsutawney, Pa. (Punxsutawney Iron Co.) 
 Hot blast, coke, foundry iron, from Lake Superior hematite. 
 Sil. 1.0-4.0% Phos. 0.40-0.60% Mang. 0.45-1.60% 
 
 Radford. — Radford Crane fee., Radford, Va. (Va. Iron, Coal & Coke Co.) 
 Hot blast, coke, foundry iron, from Va. limonite and mountain ores. 
 Sil. 1.5-2.75% Phos. abt. 1.00% Mang. abt. 1.25% 
 
 Rebecca. — Rebecca fees. (2 stacks), Kittanning, Pa. (Kittanning I. 
 & S. Mfg. Co.) 
 Hot blast, coke, chill east iron, from Lake Superior ores. 
 Fdry. Sil. up to 3.0% Phos. 0.40-0.80% Mang. imder 1.0% 
 
 Basic under i.o under 0.50 under i.o 
 
 Mall. 1. 0-1.50 under 0.20 under 1.0 
 
 * Sometimes up to 8.00 per cent. 
 
Coke and Athracite Irons 649 
 
 Red River. — Helen fee., Clarksville, Tenn. (Red River Furnace Co.) 
 Hot blast, coke, from local brown hematite. 
 Fdry. Sil. 2.0- 3.0% Phos. abt. 0.80% Mang. abt. 0.65% 
 Scotch 3.5- 5.5 abt. 0.80 abt. 0.60 
 
 High Silicon 8.0-12.0 abt. 0.80 abt. 0.40 
 
 Rising Fawn. — Rising Fawn fee., Rising Fawn, Ga. (Southern I. 
 & S. Co.) 
 
 Hot blast, coke, iron from red and brown hematites. 
 Not in operation March, 1910. 
 
 Roanoke. — West End fee., Roanoke, Va. (West End Furnace Co.) 
 Hot blast, coke, foundry iron, from Va. brown hematite. 
 
 Sil. as desired. Phos. 0.75-1.0% Mang. 0.50-1.0% 
 
 Robesonia. — Robesonia fee., Robesonia, Pa. (Robesonia Iron Co. 
 Ltd.) 
 Hot blast, anthracite and coke, foundry iron, from Cornwall ore. 
 Sil. 2.0-3.50% Phos. under 0.04% Mang. abt. 0.10% 
 
 Rockdale. — Rockdale fee., Rockdale, Tenn. (Rockdale Iron Co.) 
 Hot blast, coke, iron from Tenn. brown hematite. 
 Fdry. Sil. 2.0 -2.75% Phos. abt. 1.40% Mang. abt. 0.25% 
 
 Ferro Phos. 0.07-0.75 17.0-22.0 0.15-0.25 
 
 Rockhill. — Rockhill fees., (2 alt. stacks), Rockhill P. O., Pa. (Rockhill 
 Fee. Co.) 
 Hot blast, coke, iron from fossil and Lake Superior ores. 
 Not in operation March, 19 10. 
 
 Rockwood. — Rockwood fees. (2 stacks), Rockwood, Tenn. (Roane 
 Iron Co.) 
 Hot blast, coke, foundry iron, from red fossil ore. 
 Sil. 1.75-2.75% Phos. abt. 1.40% Mang. abt. 0.50% 
 
 Sampson Strong. — Upson fee., Cleveland, O. (Upson Net Co.) 
 Hot blast, coke, foundry iron, from Lake Superior ore. 
 Sil. 1.5-1.8% Phos. 0.40-0.60% Mang. 0.60-1.0% 
 
 Sarah. — Sarah fee., Ironton, O. (The Kelley Nail & Iron Co.) 
 Hot blast, coke, Bessemer iron, from Lake Superior ore. 
 
 Saxton. — Saxton fees. (2 stacks), Saxton, Pa. (Jos. E. Thropp.) 
 
 Hot blast, coke, foundry iron, from Lake Superior and local brown 
 
 ores. 
 Sil. 1.5-3-5% Plios- 0.40-0.90% Mang. 0.50-0.90% 
 
 Scottdale. — Seottdale fee., Scottdale, Pa. (.Scottdale Furnace Co.) 
 Hot blast, coke, foundry iron, from Lake Superior ore. 
 
650 Pig Iron Directory 
 
 Senega. — McKeefrey fee., Leetonia, O. (McKeefrey & Co.) 
 Hot blast, coke, foundry iron, from Lake Superior ores . 
 Sil. 1.0-2.0% Phos. under 0.20% Mang. 0.40-0.80% 
 
 Sharpsville. — Sharpsville fee., Sharps ville, Pa. (Sharpsville, Fee. Co.) 
 Hot blast, coke, mostly Bess, iron, from Lake Superior and New 
 York magn. ores. 
 
 Sheffield. — Shemeld f-ces. (3 stacks), Sheffield, Ala. (Sheffield C. & 
 
 I. Co.) 
 Hot blast coke, foundry iron, from Alabama and Tennessee brown 
 
 hematites. 
 Sil. as desired. Phos. abt. i.o;% Mang. abt. 0.50% 
 
 Sheffield. —B.a,ttie Ensley fee., Sheffield, Ala. (Sloss-Sheffield S. & I. 
 Co.) 
 Hot blast, coke, foundry iron, from local brown hematite. 
 Sil. as desired. Phos. abt. 1.20% Mang. abt. 0.50% 
 
 Shenandoah. — Gem fee., Shenandoah, Va. (Oriskany Ore & Iron Co.) 
 Hot blast, coke, foundry iron, from local brown hem. and Lake 
 
 Superior ores. 
 Sil. as desired. Phos. 0.40-0.80% Mang. 0.60-1.0% 
 
 Shenango. — Shenango fees. (5 stacks), Sharpsville, Pa. (Shenango 
 Fee. Co.) 
 Hot blast, coke, basic, chill east iron, from Lake Superior ores. 
 Sil. under 1.0% Phos. under 0.05% Mang. 0.70-1.30% 
 
 Sheridan. — Sheridan fee., Sheridan, Pa. (Berkshire Iron Works.) 
 Hot blast, anthracite and coke, foundry iron, sand cast, from Corn- 
 wall local hematite. 
 Sil. 1.0-4.0% Phos. 0.40-0.90% Mang. up to 0.75% 
 
 Silver Creek. — Rome fee., Rome, Ga. (Silver Creek Furnace Co.) 
 Hot blast, coke, sand cast, foundry iron, from red and browm hema- 
 tite, local. 
 Sil. up to 5.0% Phos. under 1.0% Mang. up to 2.0% 
 
 Silver Spring. — Paxton fees. (2 stacks), Harrisburg, Pa. (Central 
 I. & S. Co.) 
 Hot blast, anthracite and coke, foundry iron, from various ores. 
 
 Sloss. — Sloss fees. (4 stacks), Birmingham, Ala. (Sloss-Sheffield S. 
 
 & I. Co.) 
 Hot blast, coke, foundry iron, from red fossil, hard and soft and 
 
 brown hematites. 
 Sil. as desired. Phos. abt. 0.75% Ma^ng. abt. 0.40% 
 
Coke and Anthracite Irons 651 
 
 Soho. — Soho fee., Pittsburg, Pa. (Jones & Laughlin Steel Co.) 
 Hot blast, coke, basic and Bes. iron, from Lake Superior ores. 
 
 South Pittsburgh. — So. Pittsburgh fees. (3 stacks). So. Pittsburgh, Tenn. 
 (Tenn. Coal, Iron & R.R. Co.) 
 Hot blast, coke, mill and foundry, sand east iron, from local hard 
 
 red hematite, and brown hematite from Georgia. 
 Sil. up to 3.50%* . Phos. 1.00-1.50% Mang. 0.50-1.50% 
 
 Spritig Valley. — Spring Valley fee.. Spring Valley, Wise. (Spring 
 Valley Iron & Ore Co.) 
 Hot blast, coke or sometimes charcoal, sand cast iron, from brown 
 
 hematite ore. 
 Mall. Sil. 0.80-1.50% Phos. under 0.20% Mang. 1.0-1.5% 
 
 Fdry. 1.5-3.00 under 0.20 1.0-1.50 
 
 Standard. — Standard fee., Goodrich, Tenn. (Standard Iron Co.) 
 Hot blast, coke, foundry iron, from local brown hematite. 
 Sil. 1.75-4.50% Phos. abt. 0.95% Mang. abt. 0.40% 
 
 Star. — Star fee., Jackson, O. (Star Furnace Co.) 
 
 Hot blast, raw coal and coke, sand cast, Jackson Co. softener, from 
 
 native limonite and block ores. 
 Sil. 5.00-12,00% Phos. 0.43-0.80% Mang. abt. 0.70% 
 
 Star &" Crescent. — Rusk fee., Cherokee Co., Pa. (Frank A. Daniels.) 
 Hot blast, coke, foundry iron, from local brown hematite and black 
 
 ores. 
 Not in operation March, 1910. 
 
 Sterling Scotch. — Iroquois fees. (2 stacks). So. Chicago, 111. (Iroquois 
 I. Co.) 
 
 Hot blast, coke, foundry iron, from Lake Superior ores. 
 
 Sil. 2.50-3.0% Phos. 0.30-0.40% Mang. 0.40-0.70% • 
 
 Stewart. — Stewart fee., Sharon, Pa. (Stewart Iron Co., Ltd.) 
 
 Hot blast, coke, sand cast iron, from Lake Superior ores. 
 
 Bess. Sil. 1.0-2.50% Phos. 0.09-0.10% Mang. 0.60-0.80% 
 
 Low Phos. 1.0-2.50 under 0.04 0.20-0.40 
 
 Struthers. — Aurora fee., Struthers, O. (The Struthers Fee. Co.) 
 
 Hot blast, coke, sand east iron, from Lake Superior ores. 
 
 Basic Sil. under 1.00% Phos. under 0.25% Mang. 0.60-1.2% 
 
 Mall. 1. 00-1.50 imdero.2o abt. i.o 
 
 Susquehanna. — (2 stacks) , Buffalo, N.Y. (Buffalo & Susquehanna I. Co.) 
 
 Hot blast, coke, from Lake Superior ores. 
 
 Analysis refused. 
 
 * Sometimes higher. 
 
Basic up to i.oo 
 
 up to I.O 
 
 Bess. I.O-2.0 
 
 up to O.IO 
 
 Low Phos. 1.0-2.50 
 
 up to 0.035 
 
 Spec. High Mang. i. 0-1.50 
 
 up to 0.80 
 
 652 Pig Iron Directory 
 
 Swede. — Swede fees. (2 stacks), Swedeland, Pa. (Richard Heckscher 
 & Sons Co.) 
 Hot blast, coke, sand cast iron, from Lake Superior and high grade 
 foreign ores. 
 Fdry. Sil. up to 3.25% Phos. up to 0.80% Mang. up to 0.80% 
 
 up to 1.25 
 up to 2.0 
 up to 4.50 
 over 1.50 
 
 Sydney. — Mayville fees. (2 stacks), Mayville, Wise. (Northwestern 
 
 Iron Co.) 
 Hot blast, coke, foundry iron, from Lake Superior and local 
 
 ores. 
 Sil. 1.40-2.50% Phos. 0.60-0.80% Mang. 0.50-1.0% 
 
 Talladega. — Talladega fee., Talladega, Ala. (Northern Ala. C, I., & 
 R.R. Co.) 
 Hot blast, coke, foundry iron, from native brown ore. 
 Not in operation March, 1910. 
 
 Temple. — Temple fee., Reading, Pa. (Temple Iron Co.) 
 
 Hot blast, anthracite and coke, foundry iron, from Lake Superior, 
 
 local hematite, N. J. magnetic and foreign ores. 
 Sil. 1.75-3.50% . Phos. 0.60-0.80% Mang. 0.40-0.80% 
 
 The Mary. — Mary fee., Lowellville, O. (The Ohio Iron & Steel Co.) 
 Hot blast, coke, Bessemer only, from Lake Superior ores. 
 
 Thomas. — Thomas fee., Milwaukee, Wise. (Thomas Furnace Co.) 
 Hot blast, coke, sand cast iron, from Lake Superior ores. 
 Mai. Bess. Sil. 1.00-2.00% Phos. 0.10-0.20% Mang. 0.40-1.25% 
 Fdry. as desired. 0.15-0.60 0.50-1.25 
 
 Thomas. — (9 stacks.) (The Thomas Iron Co.) 
 
 Hokendauqua fees. (4 stacks), Hokendauqua, Pa. 
 Keystone fee. (i stack). Island Park, Pa. 
 Lock Ridge fees. (2 stacks), Alburtis, Pa. 
 Saucon fees. (2 stacks), Hellertown, Pa. 
 
 Hot blast, anthracite and coke, sand and chill cast iron, from local 
 brown hematite, N. J. magnetic and foreign ores. 
 Fdry. Sil. as desired. Phos. 0.60-0.90% Mang. abt. 0.50% 
 
 Basic under 1.0% under i.o variable 
 
Coke and Anthracite Irons 653 
 
 Toledo. — Toledo fees. (2 stacks), Toledo, O. (Toledo Furnace Co.) 
 Hot blast, coke, sand cast iron, from Lake Superior ores. 
 Mai. Sil. 1.00-2.00% Phos. under 0.20% Mang. 0.60-1.25% 
 
 Basic under I. o under 0.20 0.60-1.25 
 
 Fdry. 1.25-2.25 0.50-0.60 0.60-1.25 
 
 Scotch 2.25-3.00 0.50-0.60 0.60-1.25 
 
 Tonawanda Scotch. — Niagara fees. (2 stacks), N. Tonawanda, N. Y. 
 (Tonawanda Iron & Steel Co.) 
 Hot blastj coke, foundry iron, from Lake Superior hematite. 
 Analysis refused. 
 
 Top Mill. — Top fee., Wheeling, W. Va. (WheeHng Iron & Steel Co.) 
 Hot blast, coke, Bess, iron, from Lake Superior ores. 
 
 Topton. — Topton fee., Topton, Pa. (Empire Steel & Iron Co.) 
 
 ^ Hot blast, anthracite and coke, foundry iron, from Lake Superior, 
 native hematite and magnetite ores. 
 Sil. 0.75-3.50% Phos. 0.60-0.90% Mang. 0.50-2.00% 
 
 Trussville. — Trussville fee., Trussville, Ala. (Southern I. & S. Co.) 
 Hot blast, coke, sand east, foundry iron from Alabama red and 
 
 Georgia brown hematites. 
 Sil. up to 3.50% Phos. 0.90-1.20% Mang. 0.50-1.50% 
 
 Tuscaloosa. — Central fee., Holt, Ala. (Central Iron & Coal Co.) 
 
 Hot blast, coke, sand east, foundry iron from red and brown hema- 
 tites. 
 Sil. 1.25-2.75% Phos. 0.80-1.0% Mang. .0.50-0.90% 
 
 Tuscarawas. — Dover fee.. Canal Dover, O. (The Penn. I & C. Co.) 
 Hot blast, coke, foundry iron, from Lake Superior ores. 
 
 Union. — Buffalo Union fees. (3 stacks), Buffalo, N. Y. (Buffalo 
 Union Furnace Co.) 
 Hot blast, coke, foundry scotch iron, from Lake Superior ores. 
 Sil. 1.75-2.50% Phos. 1.20-1.50% Mang. 0.50-1.0% 
 
 Upson Scotch. — Upson fee., Cleveland, O. (Upson Nut Co.) 
 Hot blast, coke, foundry iron, from Lake Superior ores. 
 Sil. 2.0-3.0% Phos. 0.40-0.60% Mang. 0.60-0.90% 
 
 Vatiderhilt. — Vanderbilt fees. (2 stacks), Birmingham, Ala. (Birm- 
 ingham C. & I. Co.) 
 Hot blast, coke, foundry iron, from local hematites. 
 Sil. up to 4.00% Phos. under 1.00% Mang. 0.40-1.00% 
 
654 Pig Iron Directory 
 
 Vesta. — Vesta fee., Watts, Pa. (Susquehanna Iron Co.) 
 
 Hot blast, anthracite and coke, foundry iron, from local hematites 
 
 and magnetites. 
 Not in operation March, 19 lo. 
 
 Victoria. — Victoria fee., Goshen, Va. (The Goshen Iron Co.) 
 
 Hot blast, coke, foundry and forge iron, from brown hematite from 
 
 Rich Patch mines. 
 Sil. as desired. Phos. 0.40-0.80% Mang. 1.0-1.50% 
 
 Viking. — Same as Carbon, which see. 
 
 Warner. — Cumberland fee., Dickson Co., Tenn. (Warner Iron Co.) 
 Hot blast, coke, foundry iron, from local red and brown hematite. 
 Sil. 2.0-2.75% Phos. abt. 1.60% Mang. abt. 0.40% 
 
 Warwick. — Warwick fees. (3 stacks), Pottstown, Pa. (Warwick I. & 
 S. Co.) 
 Hot blast, coke, machine cast foundry iron, from Lake Superior, 
 
 N. Y., New Jersey, and foreign ores. 
 Sil. 1.0-3.0% Phos. 0.40-0.80% Mang. 0.40-0.80% 
 
 Watts. — Watts fees. (2 stacks), Middlesborough, Ky. (Va. Coal & 
 Coke Co.) 
 Hot blast, coke, foundry iron, from native ores. 
 Sil. 1.50-2.75% Phos. abt. 0.45% Mang. abt. 0.20% 
 
 Wellston. — Wtnston fees. (2 stacks), Wellston, O. (Wellston S. & 
 I. Co.) 
 Hot blast, coke, sand cast iron, from Lake Superior ores. 
 Str. fdry. Sil.- 1.50-1.75% Phos. 0.18-0.20% Mang. 0.60-0.90% 
 Mall. 0.60-2.00 under 0.20 0.40-1.00 
 
 Wharton. — Wharton fees. (3 stacks), Wharton, N. J. (Joseph Whar- 
 ton.) 
 Hot blast, coke, occasionally some anthracite, from N. J. mag., N. Y. 
 and Lake Superior hematites. 
 
 Wickwire. — Wickwire fee., Buffalo, N. Y. (Wickwire Steel Co.) 
 Hot blast, coke, basic iron, from Lake Superior ores. 
 
 Williamson. — Williamson fee., Birmingham, Ala. (Williamson Iron 
 Co.) 
 Hot blast, coke, iron from red fossil, and brown hematite. 
 Woodstock. — Woodstock fees. (2 stacks), Anniston, Ala. (Woodstock 
 I. Wks., Inc.) 
 Hot blast, coke, foundry iron, from local brown hematite. 
 Sil. 1.50-5.00% Phos. abt. 1.15% Mang. 0.80-1.25% 
 
Charcoal Irons 655 
 
 Woodward. — Woodward fee., Woodward, Ala. (Woodward Iron Co.) 
 Hot blast, coke, foundry iron, from local red fossil ores. 
 Sil. 1.0-3.0% Phos. abt. 0.80% Mang. abt. 0.30% 
 
 Zenith. — Zenith fee., W. Duluth, Minn. (Zenith Furnace Co.) 
 Hot blast, coke, iron, from Lake Superior ores. 
 Bess. Sil. 1.00-2.00% Phos. 0.08-0.10% Mang. under 1.0% 
 
 Mall. 1.00-2.00 under 0.2 0.80-1.20 
 
 Fdry. 1.50-5.00 under 0.20 over 0.60 
 
 Zug. — Detroit, Mich. (Detroit Iron & Steel Co.) 
 
 Hot blast, coke, foundry iron, from Lake Superior ores. 
 
 Charcoal Irons 
 
 Aetna. — Aetna, Ala. (J. J. Gray.) 
 
 Hot or cold blast, charcoal, car wheel iron, from local brown hema- 
 tite. 
 Not in operation March, 19 10. 
 
 Alamo. — Quinn fee., Gadsden, Ala. (Quinn Furnace Co.) 
 
 Hot blast, charcoal, foundry iron, from local red and brown hema- 
 tite. 
 Not in operation March, 19 10. 
 
 Anchor. — Oak Hill, O. (Jefferson Iron Co.) 
 
 Warm blast, ehafcoal, strong foundry iron, from native limestone 
 
 and block ores. 
 Sil. abt. 2.26% Phos. abt. 0.87% . Mang. abt. 0.51% 
 
 Antrim. — Antrim fee., Mancelona, Mich. (Superior Charcoal Iron Co.) 
 Hot blast, charcoal, foundry iron, from Lake Superior ores. 
 Sil. up to 2.62% Phos. 0.15-0.22% Mang. 0.30-0.70% 
 
 Berkshire. — Cheshire fee., Cheshire, Mass. (Berkshire Iron Works.) 
 Warm blast, charcoal, foundry iron, from local red and brown hema- 
 tite. 
 
 Berlin. — Glen Iron fee.. Glen Iron, Pa. (John T. Church.) 
 Cold blast, charcoal, iron from local fossil, and hematite. 
 • Sil. 1.0-1.5% Phos. 0.50-0.65% Mang. 0.40-0.60% 
 
 Bloom. — Bloom Switch, O. (The Clare Iron Co.) 
 
 Hot blast, charcoal, foundry iron, from local hematite. 
 Not in operation March, 1910. 
 
656 Pig Iron Directory 
 
 Blue Ridge. — Tallapoosa fee., Tallapoosa, Tenn. (Southern Car Wheel 
 Iron Co.) 
 Cold and warm blast, charcoal, iron from brown hematite. 
 
 Phos. 0.18-1.50% Mang. up to 2.0% 
 
 Buckhorn. — Olive fee., Lawrence Co., 0. (McGugin Iron & Coal 
 Co.) 
 Hot or cold blast, charcoal iron, from native limestone ore. 
 Not in operation March, 19 10. 
 
 Cadillac. — Cadillac fee., Cadillac, Mich. (Mitehell-Diggins Iron Co.) 
 Hot blast, charcoal iron, from Lake Superior ores. 
 Sil. up to 2.50% Phos. 0.16-0.20% Mang. up to 1.0% 
 
 Center. — Superior P. O., O. (The Superior Portland Cement Co.) 
 Charcoal iron, from native limestone. 
 Not in operation March, 1910. 
 
 Champion. — Manistique, Mich. (Superior Charcoal Iron Co.) 
 Warm blast, charcoal, foundry iron from Lake Superior ores. 
 Sil. up to 2.62% Phos. 0.15-0.22% Mang. 0.30-0.70% 
 
 Cherokee. — Cherokee fee., Cedartown, Ga. (Alabama & Georgia Iron 
 
 Co.) 
 Hot blast, charcoal, sand cast, strong foundry iron, from brown 
 
 hematite. 
 Sil. up to 2.50% Phos. 0.35-0.70% Mang. 0.30-1.60% 
 
 Chocolay. — Chocolay fee., Chocolay, Mich. (Lake Superior Iron & 
 Chemical Co.) 
 Warm blast, charcoal iron, from Lake Superior ores. 
 Fdry. Sil. up to 2.0% and over Phos. 0.17-0.22% 
 
 .Car Wheel 0.05-2.0 and over 0.17-0.22 
 
 Mall. 0.17-0.22 
 
 Mang. up to 0.65% and over 
 
 0.30-0.65 and over 
 0.30-0.65 and over 
 
 Copacke. — Copacke Iron Works, N. Y, (Copaeke Iron Works.) 
 Cold and warm blast, charcoal iron, from N. Y, ores. 
 Not in operation March, 19 10. 
 
 Dover. — Bear Spring fee., Stewart Co., Tenn. (Dover Iron Co.) 
 Cold blast, charcoal, foundry iron, from local brown hematite. 
 Sil. 0.40-2.0% Phos. abt. 0.40% Mang. abt. 0.25% 
 
Charcoal Irons 657 
 
 Elk Rapids. — Elk Rapids, Mich. (Superior Charcoal Iron Co.) 
 
 Hot blast, charcoal, pig for car wheels and mall., from Lake Superior 
 
 ores. 
 Sil. up to 2.62% Phos. 0.15-0.22% Mang. 0.36-0.70% 
 
 Excelsior. — Carp fee., Marquette, Mich. (Superior Charcoal Iron Co.) 
 Warm blast, charcoal iron, from Lake Superior ores. 
 Sil. up to 2.62% Phos. 0.15-0.22% Mang. 0.20-0.70% 
 
 Gertrude. — Maysville fees. (2 stacks), Maysville, Wise. (Northwest 
 Iron Co.) 
 Hot blast, charcoal, foimdry iron, from Lake Superior and local 
 
 ores. 
 Sil. 2.50% and over Phos. 0.60-0.80% Mang. 0.50-1.00% 
 
 Glen Iron. — Glen Iron fee.. Glen Iron, Pa. (John T. Chmrch.) 
 Cold blast, charcoal iron, from local fossil and hematite. 
 Sil. up to 1.00% Phos. 0.70-1.25% Mang. 0.60-1.50% 
 
 Hecla. — Hecla fee., Milesburg, Pa. (The McCoy-Linn Iron Co.) 
 Cold blast, charcoal, foundry iron, from Nittany Valley hematite. 
 Sil. 0.65-1.25% Phos. abt. 0.30% Mang. 0.15-0.25% 
 
 Hecla. — Hecla fee., Ironton, O. (Hecla Iron & Mining Co.) 
 Cold or warm blast, charcoal, foundry iron, from local ore. 
 
 Hematite. — Center fee.. Center, Ky. (White, Dixon & Co.) 
 Cold blast, charcpal, foundry iron, from local hematite. 
 Sil. 0.50-1.40% Phos. 0.25-0.39% Mang. 0.20-0.25% 
 
 Hinkle. — Ashland fee., Ashland, Wise. (Lake Superior Iron & Chem- 
 ical Co.) 
 Warm blast, charcoal iron, from Lake Superior ores. 
 Sil. up to 3.00% Phos. 0.10-0.18% Mang. to 0.70% and over 
 
 Jefferson. — Jefferson fee., Jefferson, Tex. (Jefferson Iron Co.) 
 Hot blast, charcoal iron, from local brown hematite. 
 Not in operation March, 1910. 
 
 Liberty 1^12. — Liberty fee., Shenandoah Va. (Shenandoah I. & C. 
 Co., Va.) 
 Warm blast, charcoal iron, from brown hematite. 
 
 Marquette. — Pioneer fee., Marquette, Mich. (Superior Charcoal Iron 
 Co.) 
 Hot blast, charcoal, foundry iron, from Lake Superior ore. 
 Sil. up to 2.62% Phos. 0.15-0.22% Mang. 0.30-0.70% 
 
658 Pig Iron Directory 
 
 Michigan. — Newberry fee., Newberry, Mich. (Superior Charcoal Iron 
 Co.) 
 Warm blast, charcoal iron, from Lake Superior ores. 
 Sil. up to 2.62% Phos. 0.15-0.22% Mang. 0.30-0.70 
 
 Muirkirk. — Muirkirk fee., Muirkirk, Md. (Charles E. Coffin.) 
 Warm blast, charcoal iron, from local carbonate ores. 
 Sil. 0.70-2.50% Phos. 0.25-0.30% Mang. 0.80-2.50% 
 
 Olive. — Olive fee., Lawrence Co., O. (The McGugin I. & C. Co.) 
 Hot or cold blast, charcoal iron from native limestone ores. 
 
 Pine Lake. — Boyne City fee., Boyne City, Mich. (Superior Charcoal 
 Iron Co.) 
 Hot blast, charcoal iron, from Lake Superior ores. 
 Sil. up to 2.62% Phos. 0.15-0.22% Mang. 0.30-0.70% 
 
 Pioneer. — Pioneer fee., Gladstone, Mich. (Superior Charcoal Iron Co.) 
 Warm blast, charcoal iron, from Lake Superior ores. 
 Sil. up to 2.62% Phos. 0.15-0.22% Mang. 0.30-0.70% 
 
 Reed Island. — Reed Island fee.. Reed Island, Va. (Va. Iron, C. & C. Co.) 
 Cold blast, charcoal iron, from local limonite. 
 
 Richmond. — Richmond fee., Berkshire Co., Mass. (Richmond Iron 
 Works.) 
 Warm blast, charcoal iron, from local brown hematite. 
 Sil. up to 2.00% Phos. 0.28-0.35% Mang. up to 0.44% 
 
 Rock Run. — Rock Run fee., Rock Run, Ala. (The Bass Foundry & 
 
 Machine Co.) 
 Warm blast, charcoal iron for chill rolls, ear wheels, strong eastings, 
 
 from local brown hematite. 
 Sil. 0.30-2.25% Phos. 0.30-0.50% Mang. 0.40-1.00% 
 
 Rome. — Rome fee., Rome, Ga. (Silver Creek Furnace Co.) 
 
 Warm blast, charcoal iron, from local red and brown hematites. 
 Sil. 1.75-2.25% Phos. 0.35-0.60% Mang. 0.50-0.80% 
 
 Round Mountain. — Round Mt. fee,. Round Mt., Ala. (Round Moun- 
 tain Iron & Wood Ale. Co.) 
 Cold blast, charcoal iron, from local red hematite. 
 Not in operation March, 1910. 
 Salisbury. — Canaan fees.. East Canaan, Conn. (2 stacks). (Bamum 
 Richardson Co.) 
 Warm blast, charcoal iron, from Salisbury brown hematite, sand 
 
 cast. 
 Sil. 1.32-1.92% Phos. abt. 0.30% Mang. 0.50-1.0% 
 
Charcoal Irons 659 
 
 Salisbury Chatham. — Chatham fee., Chatham, N. Y. (Union Iron & 
 St. Co.) 
 Charcoal iron. 
 
 Shelby. — Shelby fee., Shelby, Ala. (Shelby Iron Co.) 
 
 Warm blast, charcoal iron, from local brown hematite. 
 
 Sil. 0.15-2.25% Phos. 0.30-0.50% Mang. 0.50-0.80% 
 
 Sligo. — Sligo fee., Sligo, Mo. (Sligo Furnace Co.) 
 
 Hot blast, charcoal iron, from local blue specular and red ore. 
 
 Spring Lake. — Fruitport fee., Fruitport, Mich. (Spring Lake Iron 
 Co.) 
 Hot blast, sand cast, charcoal iron, from Lake Superior ores. 
 Sil. up to 2.50% Phos. 0.16-0.20% Mang. up to 1.0% 
 
 Spring Valley. — See under Coke Irons. 
 
 Tassie Bell. — Tassie Bell fee.. Rusk, Tex. (New Birm. Devel. Co.) 
 Hot blast, charcoal iron, from local brown hematites. 
 Not in operation March, 1910. 
 
 White Rock. — Smyth Co., Va. (Lobdell Car Wheel Co.) 
 
 Warm and cold blast, charcoal iron, from local brown hematite. 
 All used by the Company. 
 
 Wyebrooke. — Isabella fee., Wyebrooke, Pa. (W. M. Potts.) 
 
 Cold blast, charcoal iron, from local magnetic and hematites and 
 
 foreign and Lake Superior ores. 
 Not in operation March, 1910. 
 
AUTHORITIES 
 
 BOLAND, S. 
 
 Buchanan, J. S. 
 Buchanan, Robert. 
 Byron, T. H. 
 
 " Castings. " 
 Carpenter, H. A. 
 Carr, W. N. 
 Christopher, J. E. 
 Chrystie, J. 
 Cheney, F. R. 
 Colby, A. L. 
 Cook & Hailstone. 
 Cook, E. S. 
 Crobaugh, F. L. 
 Custer, E. A. 
 Cunningham, R. P. 
 
 De Clercy, Jules. 
 Dickinson, W. E. 
 DiLLER, H. E. 
 
 Fay, a. E. 
 Field, H. E. 
 Firmstone, F. 
 Franklin, B. A. 
 "The Foundry." 
 
 Gilmore, E. B. 
 Golden, E. B. 
 
 Hall, J. L. 
 Hatfield, W. 
 Hawkins, D. S. 
 Hiones, a. H. 
 Holmes, J. A. 
 
 Hooper, G. K. 
 Howe, Prof. H. M. 
 Hyndman, N. p. 
 
 "Iron Age." 
 
 "Iron Trade Review." 
 
 Jewett, L. C. 
 Johnson, F. 
 Johnson, J. E., Jr. 
 
 Kane, W. H, 
 Keep, W. J. 
 Kent, Wm. 
 Kirk, E. 
 Knoppell, C. E. 
 
 Lane, H. M. 
 Ledebur, Prof. A. 
 Long, A. T. 
 
 LONGMUIR, P. 
 
 Loudon, A. M. 
 
 Marshall, S. P. 
 May, W. J. 
 
 McWilliams & Longmuir. 
 McGahey, C. R. 
 "Mechanics." 
 Moldenke, Dr. R. 
 mumford, e. h. 
 Murphy, Jos. A. 
 
 Nagle, a. F. 
 
 Outerbridge, a. E. 
 
 660 
 
Authorities 
 
 66i 
 
 Palmer, R. H. 
 Pierce, E. H. 
 Porter, Prof. J. J. 
 Probert, R. H. 
 Putnam, E. H. 
 
 Rankine, Prof. W. J. M. 
 RiES, Prof-. H. 
 Raup, p. R. 
 Recketts, Prof. P. C. 
 Robertson, J. S. 
 Rogers, S. M. 
 RoTT, Prof. Carl 
 Rossi, A. G. 
 
 Sadlier, J. G. 
 Saunders, W. M. 
 Sameur, Prof. A. 
 Scott, W. G. 
 Shed, N. W. 
 
 SiSSONS, C. W. 
 Stahlund, Eissen. 
 Stickle, F. W. 
 Stupakoff, S. H. 
 Stead, J. E. 
 Sleeth, S. D. 
 Stoughton, Prof. B. 
 
 Trautwine, J. C. 
 Turner, Prof. T. 
 Taylor, E. M. 
 
 West, Thos. D. 
 Whitehouse, J. S. 
 Whitney, A. W. 
 Williams, A. D. 
 
 W ANGLER, J. 
 
 WuEST, Prof. F. 
 Wylie, C. 
 
INDEX 
 
 Abbreviations and signs, v. 
 
 Acceleration of falling bodies, 191-93. 
 
 Accounts, See Foundry accounts. 
 
 Acid open hearth, 417, 419, 422. 
 
 Acid-resisting-castings, mixture for, 
 276. 
 
 Addition in algebra, 8. 
 
 Agricultural castings, average of five 
 meltings, 459. 
 
 Agricultural machinery, mixtures for, 
 276. 
 
 Air, weight of, for combustion, 204; 
 properties of , 215-18; required for 
 combustion of one pound each 
 of coke and coal, 444; loss in 
 pressure and horse power from 
 friction in pipes, 447. 
 
 Air, compressed, horse power required 
 for, 217-18. 
 
 Air cylinders, mixture for, 276 
 
 Air furnace, American, 391. 
 
 Algebra, 7-15. 
 
 Alligation, 5. 
 
 Alloys, 222-27. 
 
 Alviminvun, properties of, 266; in- 
 fluence of, in cast iron, 266-67. 
 
 Aluminum bronze, 226. 
 
 American Foundrymen's Association, 
 See Foundrymen's Association. 
 
 American Steel & Wire Co., gauge of 
 sizes, 146. 
 
 Ammonia cyUnders, mixture for, 276. 
 
 Analysis, mixing iron by, 274-89. 
 
 Anchors, gaggers and soldiers, 523-24. 
 
 Angle, problems of the, 17-18. 
 
 Angles, approximate measurement of, 
 115-16. 
 
 Annealing boxes, mixtures for, 277. 
 
 Anneahng-oven equipped for gas. 392. 
 
 Annealing steel castings with micro- 
 graphs, 400-1. 
 
 Anthracite coal, 425. 
 
 Antimony, alloys containing, 227. 
 
 Apothecaries' or wine measure, 38. 
 Apothecaries' weight, table of, 36. 
 Appliances about cupola, 462-67. 
 Arithmetic, 1-7. 
 Arnold, Prof. J. O., on carbon in steels, 
 
 241, 347; mechanical properties 
 
 of normal steels, 396. 
 Atmosphere, pressure of, at various 
 
 readings of barometer, 216. 
 Authorities, 660-61. 
 Automobile castings, mixtures for, 277. 
 Avoirdupois weight, table of, 36. 
 
 B.t.u. = British thermal unit, 207. 
 
 Babbitt metal, 227. 
 
 Baby (Robert) converter, the, 397. 
 
 Balls for ball mills, mixture for, 277. 
 
 Band and hoop iron weights, 121- 
 22. 
 
 Barometric readings, pressure of at- 
 mosphere at various, 216; corre- 
 sponding with different altitudes, 
 217. 
 
 Bars of wrought iron, weight and 
 areas of square and round, 136- 
 39- 
 
 Basic open hearth, 418, 419, 423. 
 
 Bauxite, fire bricks of, 436. 
 
 Beams, transverse strength of, for- 
 mulas for, 188-90. 
 
 Bearing-metal alloys, 226. 
 
 Bed-plates, mixture for, 277. 
 
 Belt velocity, tables oi, 229-30. 
 
 Belting, formulas for, 227-28. 
 
 Benjamin, Charles H., strength of 
 materials, 213-14. 
 
 Bessemer process, the, 396. 
 
 Binder bars, 505. 
 
 Binders, See Agricultural machinery. 
 
 Birmingham gauge for sheet metals 
 except steel and iron, 120. 
 
 Black heart malleable cast iron, 382- 
 85. 
 
 663 
 
664 
 
 Index 
 
 Blast, the, in the cupola, 446-47 ; loss 
 
 of air pressure from friction in 
 
 pipes, 447. 
 Blast pipes for pressure blowers, 
 
 tables of, 450. 
 Blow-holes, trouble with, 316; in 
 
 steel, 398. 
 Blowers, pressure, for cupolas, tables 
 
 of, 448-49. 
 Board and timber measure, 44. 
 Board measure, table of, 91-92. 
 Bod stick, the, 463-64. 
 Boiler castings, mixture for, 277. 
 Boiling points at gea level, 204; at at- 
 mospheric pressure, 210. 
 Bolt end's and lag screws, 158. 
 Bolt heads and nuts, weights of, 159. 
 Bolts and nuts, U. S. standard, 150-51. 
 Bolts, machine, weight of, per 100, 
 
 155-56; list prices, 157. 
 Borings and turnings, melting, 293; 
 
 per cent of, 322. 
 Box strapping, 236. 
 Brake shoes, mixture for, 287. 
 Brass, fillets of, areas and weights of, 
 
 145- 
 Brass foundries, alloys in use in, 223. 
 Brass, moulding sand for, 472. 
 Brass, sheet and bar, weight of, 144. 
 Brass tubes, seamless drawn, 167-69. 
 Brass wire and plates, weight of, 143. 
 Breaking loads, formula for, 301; 
 
 ratio of tensile strength to, 10 to i, 
 
 302. 
 Breast of cupola, 440-41. 
 Buffalo steel pressure Blowers, 449. 
 
 Cables, See Chains and cables. - 
 Cables, transmission or standing, 
 
 179- 
 
 Calorie, French thermal unit, 207. 
 
 Cap screws, 161. 
 
 Car castings, mixtures for, 278. 
 
 Car wheel iron test bars, moduli of 
 rupture of, 300. 
 
 Car wheels, qualities of iron for, 275; 
 mixtures for, 278; specifications 
 for, 3SO-5S- 
 
 Carbon and iron, forms of combi- 
 nation of, 313. 
 
 Carbon, combined, See Cementite. 
 
 Carbon content in steel, 395. 
 
 Carbon, properties of, 252-53; in- 
 fluence of, as constituent of cast 
 iron, 253-54; loss or gain of, in 
 remelting, 254-56. 
 
 Carbon, total, per cent, 308, 310; in 
 micrographs, 311; ways of re- 
 ducing, 315—16; for elasticity, 
 323; reduced for hardness, 328; 
 high to decrease shrinkage, 332; 
 high aids fluidity, 335; for re- 
 sistance to heat, 337-38; for 
 high permeability, 340; for re- 
 sistance to corrosion, 341; de- 
 termination of, 379-80. 
 
 Carpenter shop and tool room, 562. 
 
 Carr, W. M., open-hearth methods 
 for steel castings, 411-16. 
 
 Carrier, W. H., on foundry heating 
 and ventilating, 582-86. 
 
 Cast iron, constituents of, standard 
 methods for determining, 377-80: 
 Silicon, 377-78; sulphur, 378; 
 phosphorus, 378; manganese, 
 379; total carbon, 379-80; graph- 
 ite, 381. 
 
 Cast iron, effect of structure of, upon 
 its physical properties, 306-14; 
 microscopic evidence, 308-12; 
 Prof. Porter on, 312-14. 
 
 Cast iron, fillets of, areas and weights 
 of, 145. 
 
 Cast iron, influence of chemical con- 
 stituents of, 252-72: Carbon, 252- 
 56; silicon, 256-60; sulphur, 
 260-63; phosphorus, 263-64; 
 manganese, 265-66; aluminum, 
 266-67, nickel, 267; titanium, 
 267-68; vanadium, 268-70; ther- 
 mit, 270; oxygen, 270-71; ni- 
 trogen, 271—72. 
 
 Cast iron, mechanical analysis of, 
 see Mechanical analysis. 
 
 Cast iron, weight of a superficial foot 
 of, 570. 
 
 Casting, direct, 562. 
 
 Casting properties of iron, 343-45- 
 
 Castings,, mixtures for various classes 
 of, 273-74; (alphabetical) 276-87; 
 amounts of different irons to be 
 used found by percentage, 287-89. 
 
 Castings, qualities of iron necessary 
 for different grades of, 275. 
 
Index 
 
 665 
 
 Castings, shrinkage of, per foot, 234. 
 
 Castings under pressure, 562. 
 
 Castings, weight of, determined from 
 weight of patterns, 569-70; for- 
 mulas for finding, 570-76. 
 
 Cement mortar, tensile strength of, 
 215. 
 
 Cementite (combined carbon), 241; 
 in micrographs, 308-1 1 ; physical 
 characteristics of, 313; per cent 
 combined carbon, 315, 319-20, 
 323; causes hardness, 324-29; 
 for fusibility, 332-34; low for 
 fluidity, 335; for resistance to 
 heat low, 337-38; low for per- 
 meability, 340; in micrographs, 
 346-49- 
 
 Center of gravity, 195-97. 
 
 Centigrade to Fahrenheit, equiva- 
 lent temperatures, 211-12. 
 
 Centismal years, 43. 
 
 Centrifugal castings, 561-62. 
 
 Centrifugal force, 215. 
 
 Chain end link and narrow shackle, 
 174. 
 
 Chain hooks, proportions for, 172. 
 
 Chains and cables, U. S..Navy stand- 
 ard, 173. 
 
 Chaplets, 528-36; peerless perforated, 
 530; double head, 531-32; 
 wrought-iron, 533-35- 
 
 Charcoal iron, 250. 
 
 Charcoal pig irons, directory of, 655-59. 
 
 Charging cupolas, 452-54. 
 
 Charging floor, the, 453-54- 
 
 Charpy & Grenet's experiments on 
 irons, 383. 
 
 Chemical analyses of cast iron, 315-49 : 
 Strength, 315-22; elastic prop- 
 erties, 322-29; shrinkage, 329- 
 32; fusibility, 332-34; fluidity, 
 334-35; resistance to heat, 335- 
 38; electrical properties, 338-40; 
 resistance to corrosion, 340-42; 
 resistance to wear, 342; coeffi- 
 cient of friction, 342-43; casting 
 properties, 343-45; micro-struc- 
 ture, 345-49- 
 
 Chemical analyses of test bars, 308- 
 12; micrographs, 308-11; forms 
 of combination of iron and car- 
 bon, 313. 
 
 Chemical constituents of cast iron, 
 influence of the (W.- G. Scott), 
 252. 
 
 Chemical reactions in the cupola, 443- 
 
 Chilled castings, mixtures for, 274, 
 275, 278. 
 
 Chilled iron defined, 326-28. 
 
 Chilled roll (furnace) iron test bars, 
 moduli of rupture of, 299. 
 
 Chills, mixture for, 278. 
 
 Chipping and grinding, 566. 
 
 Chords for spacing circle, 89-90. 
 
 Chords of arcs from one to ninety de- 
 grees, 88. 
 
 Circle, length of chord for spacing, 
 89-90. 
 
 Circle, problems of the, 15, 18-20; 
 ratio of circumference to di- 
 ameter, 28; area of, 28. 
 
 Circles, areas and circumferences of, 
 for diameters from -^q to 100, by 
 tenths, 70-79; rules to compute 
 larger, 79. 
 
 Circles, areas and circumferences of, 
 for diameters in units and eighths, 
 64-69. 
 
 Circular arcs, table of, 80-82. 
 
 Circular arcs, table of lengths of, to 
 radius i, 82-84. 
 
 Circular measure, 43. 
 
 Circular segments, table of areas of, 
 84-87. 
 
 Cisterns and tanks, number of bar- 
 rels in, loo-i. 
 
 Clamps, 506. 
 
 Clarke, D. K., formula for extreme 
 fibre stress, 304; volume, den- 
 sity and pressure of air at vari- 
 ous temperatures, 216. 
 
 Cleaning room, the, 563-68; tumblers, 
 563-66; chipping, grinding, the 
 sand blast, 566; pickHng, 567; 
 hydrofluoric acid, 568. 
 
 Clout nails, tinned, 536. 
 
 Coach screws, gimlet points, 159. 
 
 Coke and anthracite pig irons, direc- 
 tory of, 635-55. 
 
 Coke, 425-29: Analyses of various 
 kinds of, 425-26; by-product 
 coke, 426-27; effect of atmos- 
 pheric moisture upon, 427; 
 
666 
 
 Index 
 
 specifications for, by R. Mol- 
 denke, 428-29 ; number of pounds 
 of iron melted by one pound of, 
 
 444-45- 
 Colby, A. L., influence of the mould 
 
 upon pig iron, 249. 
 Coleman, J. J., heat-conducting power 
 
 of covering materials, 210. 
 Collars and couplings, mixture for, 278. 
 Combining equivalents, 204. 
 Conductivity of metals, 206, 209. 
 Cone, the, 32-33- 
 Contraction or shrinkage, 329-32. 
 Converter linings, 404-5; practice, 
 
 405-9- 
 
 Converter steel, cost of, 420, 421. 
 
 Converters, the Baby (Robert) and 
 Tropenas, 397. 
 
 Cook, E. S , on different results from 
 two irons of same chemical com- 
 position, 330-32. 
 
 Cook, F. J., and G. Hailstone, micro- 
 scopic evidence why similar irons 
 have different relative strengths, 
 306-12, 317-19- 
 
 Cooling, influence of rate of, 318. . 
 
 Cope, formula to find weight re- 
 quired on a, to resist pressure of 
 molten metal, 575. 
 
 Copper and tin, alloys of, 222. 
 
 Copper and zinc, alloys of, 223. 
 
 Copper-nickel alloys, 224. 
 
 Copper, round bolt, weight of, per 
 foot, 144. 
 
 Copper, tin and zinc, useful alloys of, 
 225. 
 
 Copper tubes, seamless drawn, 167-69. 
 
 Copper wire and plates, weight of, 143. 
 
 Core machines, 499. 
 
 Core mixtures, 480-86. 
 
 Core ovens, 492-95. 
 
 Core plates and driers, 498-99. 
 
 Core room and appurtenances, 492- 
 500: The oven, 492-96; core 
 oven carriages, 496; mixing ma- 
 chines, sand conveyors, rod 
 straighteners, wire cutter, 497; 
 sand driers, 498; core plates and 
 driers, 498-99; core machines, 
 mould-machines, cranes and 
 hoists, 499-500. 
 
 Core sand with analysis, 479-80. 
 
 Corrosion, resistance to, 340-42. 
 
 Corrugated iron roofing, weight of, 
 141. 
 
 Cosine, 107. 
 
 Cotters, steel spring, 164. 
 
 Cotton machinery, mixture for, 278. 
 
 Covering materials, heat-conducting 
 power of, 210. 
 
 Cranes and hoists for core room, 499- 
 500. 
 
 Cranes for cupola service, 466. 
 
 Cranes for moulding room, 502. 
 
 Crucible castings, 423. 
 
 Crusher jaws, mixture for, 278. 
 
 Cube of a whole number ending with 
 ciphers, to find, 56. 
 
 Cube root, 4-5. 
 
 Cube root of large number not in 
 table, to find, 62-63. 
 
 Cube roots of numbers from 1000 to 
 10,000, 57-61. 
 
 Cubes and cube roots of numbers 
 from .01 to 1000, tables of, 46-56. 
 
 Cupola, construction of the, 437-52: 
 Five zones, 437, 442-43; the 
 lining, 437-39; tuyeres, 439-40; 
 the breast, 440-41; sand bottom, 
 441; chemical reactions in ordi- 
 nary, 443-45; wind box, 445; 
 builders' rating, 446; blowers for 
 the blast, 446-49; diameter of 
 blast pipes, 450-51; dimensions, 
 etc., of, 451-52. 
 
 Cupola appliances, 462-67: Ladles, 
 462-65; tapping bar, 463; bod 
 stick, 464-65-; cranes, 466; spill 
 bed, 466; gagger mould, 467; 
 rake, 467. 
 
 Cupola charging and melting, 452-61: 
 The charging floor, 453-54; 
 tables of meltings and losses, 455- 
 61; melting ratio, 461. 
 
 Cupola makers, best known, 446. 
 
 Custer, Edgar A., on permanent 
 moulds, 559-61. 
 
 Cutting tools, mixture for, 278. 
 
 Cylinder, the, 32. 
 
 Cylinder iron test bars, moduli of 
 rupture of, 300. 
 
 Cylinders or pipes, contents of, 102-3. 
 
 Cylinders, locomotive, mixtures for, 
 273, 282; specifications for, 355. 
 
Index 
 
 667 
 
 Cylinders, marine and stationary, 
 mixtures for, 273; see also Cylin- 
 ders, 279. 
 
 Cylinders, solid and hollow iron, for- 
 mulas for finding weigiit of, 570- 
 71. 
 
 Decimal equivalents of parts of one 
 
 inch, 6. 
 Deflections, table of, 183-85. 
 Delta metal, 225. 
 Diamond polishing wheels, mixture 
 
 for, 279. 
 Dies for drop hammers, mixture for, 
 
 279- 
 Diller, H. E., tests of use of steel scrap 
 
 in mixtures of cast iron, 290-91; 
 
 on malleable cast iron, 390-91. 
 Division in algebra, 10. 
 Dry measure, British Imperial, see 
 
 Liquid and dry measures, British 
 
 Imperial, 39-40. 
 Dry measure, table of U. S., 39; 
 
 weights of, 39. 
 Dynamo and motor frames, mixtures 
 
 for, 279. 
 Dynamo frame iron test bars, moduli 
 
 of rupture of, 299. 
 
 Earth, measurements of, and on the, 
 238-39- 
 
 Eccentric straps, 279. 
 
 Elastic properties, 322-23. 
 
 Elasticity, modulus of, 181; table of 
 moduli, 182-83. 
 
 Electric furnace steel, cost of, 424. 
 
 Electrical and mechanical units, equiv- 
 alent values of, 220-21. 
 
 Electrical castings, mixture for, 279. 
 
 Electrical properties, 338-40. 
 
 Elimination, 12-13. 
 
 Ellipse, construction of an, 21-22; 
 circumference and area of an, 
 _ 29. 
 
 Ellipse, solid iron, formula to find 
 weight of a, 571. 
 
 Engine castings, mixtures for, 279. 
 
 Equations, quadratic, 14-15. 
 
 Equations, simple, 11-14; solution 
 of, 12. 
 
 Expansion, lineal, for solids, 205. 
 
 Eye bolts, table for, 175. 
 
 Facings, 486-87 ; graphite facing and 
 analyses, 488-91. 
 
 Factors, useful, 44-45. 
 
 Fahrenheit to Centigrade, equivalent 
 temperatures, 211— 12. 
 
 Falling bodies, acceleration of, for- 
 mulas and table, 191-92. 
 
 Fans and blowers, 280. 
 
 Farm implements, mixture for, 280. 
 
 Fe-C-Si, influence of, on cast iron, 
 315, 320.^ 
 
 Ferrite, pure iron, 241, 347. 
 
 Field, H. E., on carbon and silicon in 
 pig iron, 253. 
 
 Fillet, cast iron straight, formula to 
 find weight of a, 574; of a cir- 
 cular, 575-76. 
 
 Fillets of steel, cast iron and brass, 
 areas and weights of, by E. J. 
 Lees, 145. 
 
 Fire brick, 236. 
 
 Fire brick and fire clay, 434-36; 
 analyses, 434-35; ganister, 435; 
 fine sand, 435; magnesite, 436; 
 bauxite, 436. 
 
 Fire clays, analysis of, 237. 
 
 Fire pots, mixture for, 280. 
 
 Flanged fittings, cast iron, 232. 
 
 Flasks, 506-18: Wooden cope and 
 drag, 506-9; iron, 510-14; ster- 
 ling steel, 515-17; snap, 517-18; 
 slip boxes, 519; in machine 
 moulding, 547-50- 
 
 Flat rolled iron, see Iron, flat rolled. 
 
 Flat rolled steel, see Steel, flat rolled. 
 
 Floor plates, grate bars, etc., average 
 of two meltings, 460. 
 
 Fluidity, factors governing, 334-35- 
 
 Fluxes, 429-34: Limestone and fluor 
 spar, 430-31; analyses of slags, 
 432-33. 
 
 Flywheel, cast iron, formulas to find 
 weight of a, 572-73. 
 
 Foot, inches to decimals of a, 6. 
 
 Foot pound, the unit of work, 45. 
 
 Forces, parallelogram and parallelopi- 
 pedon of, 192. 
 
 Foundry accounts, 587-632: Foundry 
 requisition, 588-89; pattern card, 
 589-90; pig iron card, and book, 
 59o> 591; coke card, 591; heat 
 book, 592-96; cleaning room re- 
 
668 
 
 Index 
 
 port, 597; foundry reports, 598- 
 600; monthly expenditure of 
 supplies, 601-4; monthly com- 
 parison of accounts, 605-7; ^.n- 
 nual comparison, 608-10; chart 
 of transmission of orders, 611-12; 
 foundry costs (B. A. FrankHn), 
 612-25; successful foundry cost 
 system (J. P. Golden), 625-32. 
 
 Foundry cost system, a successful 
 (J. P. Golden), 625-32. 
 
 Foundry costs (B. A. Franklin), 612- 
 25; outline of scheme, 612-13. 
 
 Foundry pig iron, see Pig iron. 
 
 Foundrymen's Association, American, 
 standard specifications for found- 
 ry pig iron, 246-48; table of 
 mixtures for various castings, 
 275-76; report of committee on 
 test bars, 294-306. 
 
 Fractions, products of, expressed in 
 decimals, 7. 
 
 Fracture, of pig iron, index of com- 
 position, 273. 
 
 Franklin, B. A., foundry costs, 612- 
 25; outline of scheme, 612-13. 
 
 Frick, Louis H., dimensions of stand- 
 ard wrot pipe, 167. 
 
 Friction clutches, mixture for, 280. 
 
 Friction, coefficient of, 215, 342-43. 
 
 Frustrum of a cone, 33; center of 
 gravity of a, 196. 
 
 Frustrum of a hexagonal pyramid of 
 cast iron, formula to find weight 
 of, 574- 
 
 Frustrum of a pyramid, 30-31. 
 
 Fuels, foundry, 425-29: Anthracite 
 coal, 425; coke, 425-29. 
 
 Furnace castings, mixture for, 280. 
 
 Furnace temperatures, 206. 
 
 Fusibility, or melting point, 332-34. 
 
 Gagger mould, 467. 
 
 Gaggers, 524. 
 
 Galvanized sheet iron, weight of, 141. 
 
 Ganister, composition of, 435. 
 
 Gas engine cylinders, mixture for,. 280. 
 
 Gases, specific gravity of, 197. 
 
 Gates, tables of areas of, 524-25; top 
 
 pouring, 526; whirl, 527; "cross" 
 
 skim, 527; horn, 527. 
 Gears, mixtures for, 280-81. 
 
 Geometry, plane, problems in, 15-24. 
 
 German silver, 224. 
 
 Golden, J. P., a successful foundry 
 cost system, 625-32. 
 
 Grain structure of cast iron, 329. 
 
 Graphite, shown in micrographs, 308- 
 II, 346-48; physical character- 
 istics of, 313; per cent of, 315-17, 
 330-31; size of flakes in relation 
 to strength, 317-19; per cent of, 
 for fusibility, 333-34; for resist- 
 ance to heat, 337-38; low, for 
 friction, 342. 
 
 Graphite facing, with analyses, 488-91. 
 
 Grate bars, mixture for, 281. 
 
 Gray iron castings, specifications for, 
 296-97. 
 
 Grinding machinery, mixture for, 281. 
 
 Grinding wheel speeds, table of, 231. 
 
 Guldin's theorems, 34. 
 
 Gun carriages, mixture for, 281. 
 
 Gun iron, mixture for, 281. 
 
 Gun iron test bars, moduli of rupture 
 of, 300. 
 
 Gyration, radius of, 197. 
 
 Hailstone, G., see Cook, F. J. 
 
 Hangers for shafting, mixture for, 
 281. 
 
 Hardness, control of, 324-28. 
 
 Hardware, light, mixture for, 281. 
 
 Hatfield, W. H., experiment on de- 
 flection with six bars, 384; in 
 breaking bars, 387-88. 
 
 Heat, measurement of, 206-10; radi- 
 ation of, 208; resistance to, 335- 
 38. _ 
 
 Heat unit defined, 45. 
 
 Heat-resisting iron, mixture for, 281. 
 
 Heating and ventilating, 579-86. 
 
 Height corresponding to acquired 
 velocity, 193. 
 
 Hemisphere, hollow iron, formula for 
 finding weight of a, 571. 
 
 Hexagon, relations of inscribed, to 
 circle, 20. 
 
 Hoisting rope, pliable wire, 179. 
 
 Hollow ware, qualities of iron for, 
 275; mixture for, 282. 
 
 Hooks, slings and chains, 502-3. 
 
 Hooper, G. K., on continuous melt- 
 ing, 554-55- 
 
Index 
 
 669 
 
 Horse power defined, 45; required to 
 
 compress air, 217—18. 
 Housings for rolling' mills, mixture 
 
 for, 282. 
 Hydraulic cylinders, mixtures for, 
 
 282. 
 Hydraulic pressures, formulas for 
 
 dimensions of cast iron pipe to 
 
 withstand, 232-33. 
 Hydrofluoric acid used for pickling, 
 
 568. 
 Hyperbola, the, 23-24. 
 
 Inch, -one, decimal equivalents of 
 
 parts of, 6. 
 Inches to decimals of a foot, 6. 
 Inclined plane, 194. 
 Information, useful, 234-39. 
 Ingot mould iron test bars, moduli of 
 
 rupture of, 299. 
 Ingot moulds and stools, mixture for, 
 
 282. 
 Iron and carbon, forms of combi- 
 nation of, 313. 
 Iron, band and hoop, weights per 
 
 lineal foot, 121-22. 
 Iron, burnt, of no use except for sash 
 
 weights, 293. 
 Iron castings, formulas for finding 
 
 weight of, 570^75- 
 Iron, flat, weight of, per foot, 45. 
 Iron, flat plates, weight of, per square 
 
 foot, 45. 
 Iron, flat rolled, weights of, per lineal 
 
 foot, 123-28; a:reas of, 129. 
 Iron, mixing, by fracture, 273-74; by 
 analysis, 274-89; mixtures for 
 various classes of castings (al- 
 phabetical), 276-87. 
 Iron ores, varieties of, 240. 
 Iron, physical properties of, 241. 
 Iron, pig, see, Pig iron. 
 Iron roofing, corrugated, weight of, 
 
 141. 
 Iron, round, weight of, per foot, 45. 
 Iron, sheet, gauges used by U. S. 
 mills in rolling, 120; weight per 
 foot, 141. 
 Iron, temperatures of, corresponding 
 
 to various colors, 239. 
 Iron wire, gauges and weights of, 146; 
 list prices of, 147. 
 
 Iron, wrought, weight and areas of 
 square and round bars, 136-39. 
 
 Jigs, by S. H. Stupakoff, 540-46. 
 Jobbing castings, general, average of 
 
 five meltings, 455. 
 Jobbing castings, light, average of four 
 
 meltings, 455. 
 Joule's equivalent, 207. 
 
 Keep, W. J., on pig iron cast in iron 
 moulds and in sand, 249-50; in- 
 fluence of silicon on cast iron, 
 259-60; injurious influence of 
 sulphur, 263; effect of manga- 
 nese, 266; on recovery of shot 
 iron, 292; shrinkage of test bars, 
 371-72; shrinkage chart, 372-74; 
 strength table, 375; process of 
 making coke, 426. 
 
 Kent, William, altitudes correspond- 
 ing to barometric readings, 217; 
 head in feet of water corre- 
 sponding to pressure, 219; pres- 
 sure for different heads, 219. 
 
 Kettles to stand red heat, mixture 
 for, 274. 
 
 Ladles and table of capacities, 462-65. 
 
 Lag screws, 158. 
 
 Land measure, table of, 37. 
 
 Le Chatelier, M., on furnace tem- 
 peratures, 206. 
 
 Lead pipes, sizes and weights of, 171. 
 
 Ledebur, Prof. A., influence of silicon 
 on annealing temperature, 391. 
 
 Lees, Ernest J., areas and weights of 
 fillets of steel, cast iron and brass, 
 145- 
 
 Lever, the, 194. 
 
 Lifting beams, 503-5; table of safe 
 loads for, 504. 
 
 Lighting, importance, 578-79. 
 
 Lime mortar, tensile strength of, 215. 
 
 Liquid and dry measures, British Im- 
 perial, weights of, 39-40. 
 
 Liquid measure, table of U. S., 38; 
 weights of volumes of distilled 
 water, 39-40. 
 
 Liquid pressure on moulds, 529-30. 
 
 Locks and hinges, see Hardware, light. 
 
 Locomotive castings, mixtures for, 282, 
 
670 
 
 Index 
 
 Locomotive cylinders, mixtures for, 
 273, 282; specifications for, 355. 
 
 Long measure, table of, 36; miscel- 
 laneous, 37. 
 
 Longmuir, Percy, on the sulphur con- 
 tent of cast iron, 261-62; micro- 
 structure of cast iron, 345-49; 
 on sihcon in malleable castings, 
 386; on steels, 394. 
 
 Loudon, A. M., comparative values 
 of core binders, 481-86. 
 
 Lumber, weight of, per 1000 feet 
 board measure, 93. 
 
 McGahey, C. B., tests of use of steel 
 scrap in mixtures of cast iron, 291. 
 
 Machine-cast pig iron, see Pig iron, 
 248-50. 
 
 Machinery castings, heavy, average 
 of four meltings, 457. 
 
 Machinery castings, light, average of 
 six meltings, 456. 
 
 Machinery castings, qualities of iron 
 for, 275; mixtures for, 283. 
 
 Machinery iron test bars, moduli of 
 rupture of, 299, 300. 
 
 McWilliams & Longmuir on malleable 
 castings, 382; on annealing, 400- 
 i; on moulding machines, 548. 
 
 Magnesite, bricks of, 436. 
 
 Malleable cast iron, 382-93: Black 
 heart, 382-85; experiments on 
 varying compositions of, 383-84; 
 ordinary or Reaumur, 385-88; 
 mixtures in American practice, 
 389-91; specifications and tests, 
 391-93- 
 
 Manganese, per cent, 308, 310, 315; 
 high, 322; for elasticity, 323; as 
 hardening agent, 324-25; in 
 chilled iron, 328, 337; effect on 
 grain structure, 329; increases 
 shrinkage, 332; little effect on 
 melting point, 334; for heat re- 
 sistance, 337; low for permeabil- 
 ity, 340; for acid resistance, 341; 
 for resistance to wear, 342; skin 
 effects, 344; in micrographs, 346- 
 48; determination of, 379. 
 
 Manganese, properties of, 265; in- 
 fluence of, as constituent of cast 
 iron, 265-66, 272. 
 
 Mann, W. I., lengths of chords for 
 spacing circle whose diameter is 
 i» 90- 
 
 Martensite "beta" form of iron, 313. 
 
 Mayer, Dr. A. M., on radiation of 
 heat, 208. 
 
 Measures, miscellaneous, 39; and 
 weights, 44. 
 
 Measures of work, power and duty, 
 45- 
 
 Measures, see Weights and measures; 
 also name of measure, as Dry 
 measure. Liquid measure, etc. 
 
 Mechanical analysis of cast iron, 371- 
 77; Keep's shrinkage chart, 372- 
 74; strength table, 375. 
 
 Mechanical equivalent of heat, 207. 
 
 Melting, continuous, 551-55. 
 
 Melting losses in cupolas, tables of, 
 454-61. 
 
 Melting ratio, 461. 
 
 Mensuration, 26-34. 
 
 Metalloids, influence of the more im- 
 portant, on combined carbon, 
 272; method of adding, to the 
 iron, 465. 
 
 Metals, conductivity of, 206, 209; 
 weights per cubic inch of, 239. 
 
 Metals, sheet, Birmingham gauge for, 
 except steel and iron, 120; 
 weights of, per square foot, 142. 
 
 Metric measures and weights in U. S. 
 standard, 40-43. 
 
 Micrographs of graphite, 308-11. 
 
 Micro-structure of cast iron by P. 
 Longmuir, 345-49- 
 
 Mixing machines in core room, 497. 
 
 Modulus of elasticity, 181-83. 
 
 Modulus of rupture, 185-86; for- 
 mula for, 304; in pounds per 
 square inch, 298-303. 
 
 Moldenke, Dr. R., effects of titanium 
 and vanadium in cast iron, 2 68-70; 
 on fusibility of cast iron, 332-33.; 
 contents of malleable cast iron, 
 389; specifications for foundry 
 coke, 428-29. 
 
 Molten iron, formulas to find pres- 
 sure of, 575. 
 
 Moment of inertia, 187; of rotating 
 body, 197. 
 
 Moments, location of, 180. 
 
Index 
 
 671 
 
 Monomial, 10. 
 
 Mortar, lime and cement, tensile 
 strength of, 215. 
 
 Motor frames, see Dynamo. 
 
 Mould, pressure on, by molten metal, 
 formula to find, 575. 
 
 Moulding, dry sand, mixtures for 
 (West), 477-78. 
 
 Moulding machines, 538-50: Jigs by 
 S. H. Stupakoff, 540-46; flasks, 
 547-50; diagram of moulding 
 operations, 549. 
 
 Moulding operations, diagram of 
 (Stupakoff), 549. 
 
 Moulding room and fixtures, 501-37: 
 Cranes, 502; hooks, slings and 
 chains, 502-3; lifting beams, 
 503-5; binder bars, 505; clamps, 
 506; flasks, 506-19; pins, plates 
 and hinges, 519-21; sweeps, 522- 
 23; anchors, gaggers, and sol- 
 diers, 523—24; sprues, risers and 
 gates, 524-27; tables of areas of 
 gates, 525; strainers and spindles, 
 528; weights, 528; chaplets, 528- 
 37; liquid pressure on moulds, 
 529-30; sprue cutters, 537. 
 
 Moulding sand, 468-91: Cohesion, 
 468; permeability and porosity, 
 468-69; refractoriness, 469; du- 
 rability, 469; texture, 469, 471; 
 grades of various, 470; analysis, 
 471 ; sand for brass, with analysis, 
 472; test bars of green sand, 
 473-76; for dry sand moulding, 
 477-79; skin drying, 479; core 
 sand, and analyses, 479-80; 
 core mixtures, 480-86; parting 
 sand, 486; facings, 486-87; 
 graphite facing, 488; analyses, 
 488-91. 
 
 Moulds, multiple, 555-58; perma- 
 nent, 558-61; mixtures for per- 
 manent, 283. 
 
 Multiphcation in algebra, 8-10. 
 
 Nagle, F. A., on erratic results of in- 
 vestigation of test bars, 298, 301- 
 _ 3- 
 
 Nails, common wire, 148. 
 
 Nails, force required to pull, from 
 various woods, 238. 
 
 Nickel, properties of, 267; effect of, 
 in cast iron, 267; imparts most 
 valuable properties to steel, 267. 
 
 Niter pots, see Acid-resisting. 
 
 Nitrogen, properties of, 271; effect 
 of, on cast iron and steel, 271. 
 
 Nonconductivity of materials, 209-10. 
 
 Novelty iron test bars, moduli of rup- 
 ture of, 300. 
 
 Nuts and bolt heads, weights of, 159. 
 
 Nuts and washers, number of, to the 
 pound, 152. 
 
 Open-hearth methods for steel castings 
 by W. M. Carr, 411-16. 
 
 Ordway, Prof., on non-conductivity, 
 209. 
 
 Ornamental work, mixture for, 283. 
 
 Outerbridge, A. E., tests of moulding 
 sands, 473-75- 
 
 Oxygen, effect of dissolved oxide on 
 cast iron, 315, 318, 319, 320. 
 
 Oxygen, properties of, 270; causes 
 foundryman much trouble, 270- 
 71; effective deoxidizers, 271. 
 
 Parabola, the, 22-23. 
 
 Parallelogram, area of, 26. 
 
 Parenthesis, in algebra, 10, 
 
 Parting sand, 486. 
 
 Pattern lumber, specific gravity and 
 weight per cubic foot of, 569. 
 
 Pattern plates, preparation of, 540-46. 
 
 Patterns for test bars of cast iron, 297. 
 
 Pearlite, a mixture of fernite and 
 cementite, 241, 347. 
 
 Pentagon, to construct a, 20. 
 
 Percentage, 5-7. 
 
 Permeability and porosity of moulding 
 sand, 468-69. 
 
 Permeabihty, importance of, 339-40. 
 
 Phosphorus, properties of, 263; in- 
 fluence of, as constituent of cast 
 iron, 264, 272; per cent, 308, 320- 
 21; in micrographs, 309-11; low, 
 for strong castings, 321; and for 
 elasticity, 323; slight hardenmg 
 effect, 324; slight influence on 
 chill, 328; decreases shrinkage, 
 332; increases fusibihty, 332-33, 
 336; keep high for fluidity, 334- 
 35; low for wear resistance, 342; 
 
672 
 
 Index 
 
 presence in micrographs, 346-49; 
 determination of, 378. 
 
 Physical constants, tables of, 202-3. 
 
 Piano plates, mixture for, 283. 
 
 PickUng, 567-68. 
 
 Pig iron, physical properties of, 241- 
 42; grading, 242-43; foundry, 
 244-48; machine-cast, 248-50; 
 charcoal iron, 250; grading scrap 
 iron, 250-51; fracture of, index 
 of composition, 273. 
 
 Pig iron directory, 633-59: Coke and 
 anthracite irons, 635-55; char- 
 coal irons, 655-59- 
 
 Pillow blocks, mixture for, 284. 
 
 Pins, plates and hinges, 519-21. 
 
 Pipe and pipe fittings, mixtures for, 
 284. 
 
 Pipe, cast-iron, specifications for, 356- 
 63; tables of dimensions, 358 
 of thicknesses and weights, 359 
 volume and weight, 364-65 
 pattern, size and weight, 366-70. 
 
 Pipes, contents of, 102-3. 
 
 Piston rings, mixture for, 284. 
 
 Plane figure, irregular, area of any, 27- 
 28. 
 
 Plane figures, properties of, 24-26. 
 
 Plane surfaces, mensuration of, 26-29. 
 
 Plow points, chilled, mixture for, 284. 
 
 Polygon, area of a, 27. 
 
 Polyhedra, 31-32. 
 
 Polynomials, lo-ii. 
 
 Porter, Prof. J. J., effects of sulphur 
 on cast iron, 262-63; of phos- 
 phorus, 264; influence of the 
 metalloids on combined carbon, 
 272; report on mixtures for 
 various classes of castings (al- 
 phabetical), 276-87; on proper- 
 ties and mixtures of cast iron, 
 312-14; pig iron classification 
 and directory, 633-59. 
 
 Pouring temperature, influence of, 
 318. 
 
 Powers of quantities, 9-10. 
 
 Prince, W. F., process for melting 
 borings, 293. 
 
 Printing presses, see Machinery cast- 
 ing. 
 
 Prism, the, 30. 
 
 Prismoid, the, 31. 
 
 Probert, Richard H., analysis of iron 
 for permanent moulds, 558-59. 
 
 Propeller wheels, mixture for, 284. 
 
 Proportion, 1-2. 
 
 Pulleys, circumferential speed of, 229- 
 30; rules for speeds and diameters 
 of, 231; mixtures for, 274, 284- 
 85. 
 
 Pumps, hand, mixture for, 285. 
 
 Pyramid, the, 30-31. 
 
 Quadratic equations, solution of, 14- 
 
 15- 
 
 Quadrilateral, area of any, 27. 
 
 Quantities, in algebra, 7-10: addition 
 of like and unlike, 8; multi- 
 phcation of simple and com- 
 pound, 9. 
 
 Radiation of heat, 208. 
 Radiators, mixture for, 285. 
 Railroad castings, mixture for, 285; 
 
 average of three meltings, 459. 
 Rake, cupola, 467. 
 Ratio, 1-2. 
 Reaumur malleable cast iron, 385-88: 
 
 Remelting, 385-86; annealing, 
 
 386; analyses, 387-88. 
 Retorts, See Heat resisting castings. 
 Richards, horsepower required for air 
 
 compression and delivery, 217-18. 
 Ries, Prof. H., analyses of moulding 
 
 sands, 472-73. 
 Rings, cast iron, formulas to find 
 
 weight of, 574. 
 Rivets, iron, round head, 166. 
 Rolling mill rolls, mixture for, 274. 
 Rolls, chilled, mixtures for, 274, 275, 
 
 285. 
 Roofing, corrugated iron, weight of, 
 
 141. 
 Roofing, tin and other, 169-70. 
 Root Positive Rotary Blowers, 449. 
 Roots of numbers, 3-5. 
 Rossi, G. A., on effect of titanium in 
 
 cast iron, 268. 
 Rupture, modulus of, 185-86; for- 
 mula for, 304. 
 
 Sand blast, the, 566. 
 
 Sand bottom of cupola, 441. 
 
 Sand conveyors and driers, 497, 498. 
 
Index 
 
 673 
 
 Sand, rammed, to find weight of, 572. 
 
 Sand roll iron test bars, moduli of 
 rupture of, 299. 
 
 Sanitary ware, qualities of iron for, 
 27s; average of eight meltings, 
 ■4S8. 
 
 Sash weight, mixture for, 274, 275. 
 
 Sash weight iron test bars, moduli of 
 rupture of, 299. 
 
 Scales, mixture for, 2S5. 
 
 Scott, W. G., influence of the chemi- 
 cal constituents of cast iron, 252. 
 
 Scott, W. G., specifications for coke, 
 426; for moulding sand, 472; 
 analyses of core sands, 479-89; an- 
 alysis of Yougheogheney gas coal, 
 487; analyses of graphite, coke 
 dust, coal and charcoal, 488-91. 
 
 Scott, W. G., specifications for graded 
 pig irons, 243. 
 
 Scrap iron, grading, 250-51. 
 
 Secant, the, 108. 
 
 Set screws, steel, list price per 100, 169. 
 
 Shafting, See Steel shafting. 
 
 Sheath, Mr., on continuous melting, 
 
 55 1-54- 
 Sheet brass and all metals except steel 
 and iron, Birmingham gauge for, 
 120. 
 
 Sheet iron. See Iron, sheet. 
 
 Sheet metals, weights of, per square 
 foot, 142. 
 
 Shot iron, recovering and melting, 
 291-93. 
 
 Shrinkage chart, by W. J. Keep, 372- 
 374- • 
 
 Shrinkage of castings per foot, 234. 
 
 Shrinkage or contraction, 329-32. 
 
 Signs and abbreviations, v. 
 
 Silica brick, analysis of, 435. 
 
 Silicon, per cent, 308, 310; should be 
 low, 315, 321; for elasticity, 323; 
 for hardness, 325; for chill, 327; 
 decreases shrinkage, 332; little 
 effect on fusibility, 334; aids 
 fl.uidity, 334; favors growth by 
 repeated heating, 337; increases 
 permeability, 340; increases acid 
 resistance, 341; decreases resist- 
 ance to wear, 342; unrecognizable 
 in micrographs, 346; determina- 
 tion of, 377-78. 
 
 Silicon, properties of, 256; influence of 
 
 as a constituent of cast iron, 256- 
 
 60, 272. 
 Sines, natural, tangents and secants, 
 
 107-8; tables of, 1 10-14. 
 Skin drying moulds, 479. 
 Slag car castings, mixture for, 285. 
 Slags, comparison of analyses of, 432- 
 
 33- 
 Smoke stacks, locomotive. See Loco- 
 motive castings. 
 Soil pipe and fittings, mixture for, 
 
 286. 
 Soldiers, 524. 
 
 Solids, and their mensuration, 30-34. 
 Solids, center of gravity of, 196-97; 
 
 lineal expansion for, 205. 
 Specific gravity of various substances, 
 
 197-201. 
 Specifications for steel castings, stand- 
 ard, 409-11. 
 Speeds, grinding wheel, 231. 
 Speeds, surface, rules for obtaining, 
 
 232. 
 Sphere, the, 33-34- 
 Sphere, hollow iron, formula forjfind- 
 
 ing weight of a, 572; of a solid 
 
 iron, 571. 
 Spheres, table of surface and volumes 
 
 of, 93-98. 
 Spherical segments, cast iron, for- 
 mulas to find weight of, 573. 
 Spill bed, 466. 
 Sprocket wheels for ordinary link 
 
 chains, 176-78. 
 Sprue cutters, steel, 537. 
 Square measure, tables of, 37-38. 
 Square of a whole number ending with 
 
 ciphers, to find, 56. 
 Square root, 3-4. 
 Square root of large number not in 
 
 table, to find, 62. 
 Square roots of numbers from 1000 to 
 
 10,000, 57-61. 
 Squares and square roots of numbers, 
 
 of from .01 to 1000, tables of, 
 
 46-56. 
 Stead, J. E., on relations of iron and 
 
 phosphorus, 348. 
 Steam chests. See Locomotive and 
 
 Machinery castings. 
 Steam cylinders, mixtures for, 286. 
 
674 
 
 Index 
 
 Steel castings in the foundry, 394-416: 
 Content of carbon in varieties, 
 394~95J mechanical properties 
 "Normal steels," 396; Bessemer 
 process, 396; Baby converter 
 (Robert), 397; gases in, 398; 
 chemical changes in Tropenas 
 converter, 397-99; annealing, 
 with micrographs, 400-1 ; Trope- 
 nas process, 401-3; chemistry of 
 the process, 403-4; converter 
 linings, 404-5 ; converter practice, 
 406-9; standard specifications, 
 409-11; open-hearth methods by 
 W. M. Carr, 411-16. 
 
 Steel, comparative cost of, made by 
 different processes (B.Stoughton), 
 417-24: Acid open hearth, 417, 
 419, 422; basic open hearth, 418, 
 419, 423; converter, 420, 421; 
 crucible castings, 423; electric 
 furnace, 424. 
 
 Steel, fillets of, areas and weights of, 
 
 I4S- 
 
 Steel, flat rolled, weights of, per lineal 
 foot, 130-35- 
 
 Steel scrap, use of, in mixtures of 
 cast iron, 290-91; points to be 
 watched in melting, 316-17; 
 closes the grain, 319; per cent of, 
 322. 
 
 Steel shafting, cold rolled, weights and 
 areas of, 140. 
 
 Steels, mechanical properties of "nor- 
 mal, " 396. 
 
 Steels, unsaturated and supersatu- 
 rated, 241. 
 
 Stoughton, Bradley, tables of com- 
 parative cost of steel made by 
 different processes, 417-21. 
 
 Stove plate, qualities of iron for, 275; 
 mixture for, 286; average of 
 three meltings, 457. 
 
 Stove-plate iron test bars, moduli of 
 rupture of, 300. 
 
 Straight line, problems of the, 15-17. 
 
 Strainers and spindles, 528. 
 
 Straw rope for core bodies, 499. 
 
 Strength of beams, transverse, for- 
 mulas for, 188-90. 
 
 Strength of cast iron, nine factors 
 which influence, 315-22. 
 
 Strength of materials, 185-86, 213-14. 
 
 Strength table by W. J. Keep, 375. 
 
 Strengths, transverse, table of, 1S5-86. 
 
 Stupakoff, S. H. Chapter on jigs, 
 540-46. 
 
 Sturtevant Steel Pressure Blower, 448. 
 
 Subtraction in algebra, 8. 
 
 Sulphur, properties of, 260; deleteri- 
 ous influence of, in cast iron, 261- 
 63, 272; per cent, 308, 315, 321; 
 low for elasticity, 323; harden- 
 ing effect of, 325; increases com- 
 bined carbon, 327-28; effect on 
 shrinkage, 332; on melting point, 
 334. 336; low for heat resistance, 
 337; and for corrosion resistance, 
 339-42; increases resistance to 
 wear, 342; causes dirty castings, 
 343; in micro-structure, 346-48; 
 determination of, 378. 
 
 Sulphuric acid, use of, in pickling, 
 567-68. 
 
 Sweeps, 522-23. 
 
 Tacks, length and number of, to 
 pound, 148. 
 
 Tangent, 107. 
 
 Tanks, rectangular, capacity of, in 
 U. S. gallons, 99-100; number of 
 barrels in, loo-i. 
 
 Tapers per foot and corresponding 
 angles, table of, 1 17-18. 
 
 Tapping bar,. 463. 
 
 Taylor and White, temperatures cor- 
 responding to various colors of 
 heated iron, 239. 
 
 Temperatures, equivalent. Centigrade 
 to Fahrenheit, 211-12. 
 
 Temperatures, furnace, 206. 
 
 Tensile Strength, ratio of, to breaking 
 loads, 10 to I, 302; D. K. 
 Clarke's formula for, 304. 
 
 Tensile test, size of bar for, 295-97. 
 
 Test bars, report on by committee of 
 American Foundrymen's Asso- 
 ciation, 294-306: Character of 
 the heats, 294; making of cou- 
 pons, 295; specifications for gray 
 iron castings, i296-97; patterns 
 for, 297; moduli of rupture, 298- 
 300; erratic results, 298, 301-2; 
 comparison of, 302-3; casting 
 
Index 
 
 67s 
 
 defects, 304; circular, 304-6; 
 microscopical evidence why simi- 
 lar irons have different relative 
 strengths, 306-12; Prof. Porter 
 on the physical properties of cast 
 iron, 312-14. 
 
 Thermit, use of, in the foundry, 270. 
 
 Thermometer scales, comparison of, 
 213. 
 
 Threads, U. S. standard, 149. 
 
 Thumb screws, 165. 
 
 Tin and copper, alloys of, 222. 
 
 Tin, copper and zinc, alloys of, 224-25. 
 
 Tin, roofing, 169-70. 
 
 Tin, sheet, sizes and weight of, 142. 
 
 Titanium, properties of, 267; effect 
 of, in cast iron, 267-68. 
 
 Tobin bronze, 225. 
 
 Tons, gross, in pounds, 235. 
 
 Transverse strength, See Strength. 
 
 Transverse test, size of bar for, 295- 
 98; See Test bars. 
 
 Trapezium, area of a, 27. 
 
 Trapezoid, area of a, 27. 
 
 Triangle, area of a, 26. 
 
 Triangle, right-angled, solution of, 
 109. 
 
 Triangles, obUque-angled, solution of, 
 109. 
 
 Tropenas converter, chemical changes 
 in a, 397. 
 
 Tropenas process of steel making, 
 401-3; chemistry of the process, 
 
 405-4- 
 
 Troy weight, table of, 36. 
 
 Tubes, brass and copper, seamless, 
 167-69. 
 
 Tumblers and tumbUng mills, 563-66. 
 
 Turn-buckles, drop-forged, 162-63. 
 
 Turner, Prof.- T., on varieties of pig 
 iron, 253; percentages of com- 
 bined carbon, 256; on the use 
 of silicon, 257-59; phosphorus 
 in cast iron, 264. 
 
 Tuyeres, construction of, in cupola, 
 439-40. 
 
 Two-foot rule, measurement of angles 
 with, 1 1 5-1 6. 
 
 Unit of heat, 207. 
 
 Units, electrical and mechanical, 
 equivalent values of, 220-21. 
 
 Valves, mixtures for, 286. 
 
 Vanadium, properties of, 268; Mol- 
 denke's experiments on action of, 
 on cast iron, 269-70. 
 
 Ventilating, See Heating and venti- 
 lating. 
 
 Walker, F. G., shrinkage of castings 
 per foot, 234; weight of castings 
 determined from weight of pat- 
 terns, table, 570. 
 
 Washer, lock, 153; positive lock, 
 154- 
 
 Washers, wrought steel plate, 153. 
 
 Water, distilled, weights of volumes 
 of, 39-40. 
 
 Water heaters, mixtures for, 286. 
 
 Water, pressure of, 219. 
 
 Water supply, 577-78. 
 
 Watts in terms of horse power, 45, 
 
 Wear, resistance to, 342. 
 
 Weaving machinery, See Machinery 
 castings. 
 
 Wedge, the, 31, 195. 
 
 Weight of castings determined from 
 weight of patterns, 569-70; for- 
 mulas for finding, 570-76. 
 
 Weights, 528. 
 
 Weights and measures, 35-^45; tables 
 of various, 46—106. 
 
 Wells, contents of linings of, 104-6. 
 
 West, Thomas D., on power of cast 
 iron to stretch, 332. 
 
 Wheel and axle, 194. 
 
 Wheels, mixtures for, 287. 
 
 Whitehouse, J. S., on side blow con- 
 verters, 404-8. 
 
 Willson, E. M., table of tapers per 
 foot and corresponding angles, 
 1 1 7-1 8. 
 
 Wind box of the cupola, 445-46. 
 
 Window glass, panes of, in a box, 
 236. 
 
 Wine measure, table of, 38. 
 
 Wire, brass. See Brass. 
 
 Wire, copper. See Copper. 
 
 Wire, coppered Bessemer spring, 
 147. 
 
 Wire, coppered market, 147. 
 
 Wire gauges, different standards for, 
 119-20. 
 
676 Index 
 
 Wire, iron, gauges and weights of, 146; Wrought Iron, See Iron, wrought. 
 
 list prices of, 147. 
 
 Wood working machinery. See Ma- Zinc and copper, alloys of, 223. 
 
 chinery castings. Zinc, copper and tin, alloys of, 224-25. 
 
 Wrot pipe, dimensions of standard, Zones in cupola, 437, 442—43. 
 
 167-69. 
 
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