Glass "H 14* Book. lCl^. Copyright^ . l^o<# COPYRIGHT DEPOSIT. WORKS OF PROF. R. C. CARPENTER PUBLISHED BY JOHN WILEY & SONS. Heating and Ventilating of Buildings. 8vo, xv + 5^2 pages, 277 figures, cloth, $4.00. Experimental Engineering. For Engineers and for Students in Engineering Laboratories. 8vo, xix + 843 pages, 335 figures, cloth, $6.00. EXPERIMENTAL ENGINEERING AND MANUAL FOR TESTING. FOR ENGINEERS AND FOR STUDENTS IIV ENGINEERING LA BORA TORIES. BY ROLLA C. CARPENTER, M.S., C.E., M.M.E., PROFESSOR OF EXPERIMENTAL ENGINEERING, SIBLEY COLLEGE, CORNELL UNIVERSITY. SIXTH REVISED AND ENLARGED EDITION. FIRST THOUSAND. NEW YORK : JOHN WILEY & SONS. London: CHAPMAN & HALL, Limited* 1906. V*> » LIBRARY of 0ON6RESS TwoGooles Received MAY 10 1906 ' COPY B. Copyright, 1892, 1906, BY ROLLA C. CARPENTER. £ x* P ?v ROBERT DKUMMOND, ELECTROTYPER AND PRINTER, NEW YORK. i PREFACE TO THE SIXTH EDITION. The first edition of the present work, entitled " Notes to Mechanical Laboratory Practice," was published in 1890; a second edition was published in 1891, and soon exhausted by an unexpected demand from engineering schools and the profession. The two early editions were prepared especially for the use of students in the Laboratory of Experimental Engineering, Sibley College, Cornell University, for the purpose of facilitating in- vestigation of engineering subjects, and of providing a systematic course of instruction in experimental work. The book was rewritten and much enlarged in 1892, and the title changed to Experimental Engineering. Four revised editions, containing a total of nearly ten thousand volumes, have been published since that time, in which various errors in the previous editions have been eliminated and additions made as required by the advance in the engineering art. The present, or sixth, edition is a complete revision of the entire book, with a new index and more than 100 pages of additional matter, including chapters on the testing of the Steam-turbine, the Air-compressor, and the Refrigerating-machine. It also contains much new matter relating to the testing of the Gas-engine. Respecting the field of the book, attention is called to the well-known and universally acknowledged fact that nearly all the recent progress in the engineering art is due to experimental investigation and research. Without such research the coefficients which are employed in making practical application of theoretical laws would not have been known, and engineering constructions iv PREFACE TO THE SIXTH EDITION. and machines which are now designed with confidence to pro- duce definite results, in advance of actual trial, would not have been possible. Experimental research and test are also valuable in discriminating between correct and false theories, since it is true that any reliable theory will be verified by experiment, whereas no theory can be correct which does not accord with experimental results. On the other hand, experimental results may lead to erroneous conclusions if the fundamental rational theory which applies is unknown, and it is for this reason important to understand the fundamental theory, if any exist, in advance of the experimental work. The fact should be noted and appreciated that without theory all engineering knowledge would be reduced to a mere inventory of the results of observations. It is attempted in the work on Experimental Engineering to point out the relation between the fundamental theory and the experimental results where such a theory exists, and for other cases to point out general methods of drawing conclusions from the observations and data obtained in performing the experiments. The principal object of the present edition is to supply a text- book for laboratory use, but it is also believed that the volume will not be without value as a reference-book to the consulting and practising engineer, since it contains in a single volume the prin- cipal standard methods which have been from time to time adopted by various engineering societies for the testing of materials, engines, and machinery, and an extensive series of tables useful in com- puting results. It also contains a description of the apparatus required in testing, directions for taking data and deducing results in engineering experiments, as applied in nearly every branch of the art. The book is, however, intended chiefly for use in engineering laboratories, and presents information which the experience of the author has shown to be necessary to carry out experiments intelligently and without great loss of time on the part of students. For this purpose it gives a brief statement of the theoretical prin- PREFACE TO THE SIXTH EDITION. V ciples involved in connection with each experiment, with references to complete demonstrations, short descriptions of the various classes of engineering apparatus or machinery, a full statement of methods of testing and of preparing reports. For a few cases where references cannot readily be given, demonstrations of the fundamental principles are given in full. An attempt has been made, by dividing the book into several chapters of moderate length, by making the paragraphs short, and by placing the paragraph-numbers at the top of the page, to make references to the book easy to those who care to consult it. References which will, it is believed, be found ample for all purposes of the student or engineer are given, where needed, to more complete treatises on the various subjects discussed. The importance of an engineering laboratory is now so fully recognized in colleges of engineering that it is hardly necessary to refer to the advantages which it confers. If devoted to educa- tional purposes, it should afford students the opportunity of obtaining practical knowledge of the application and limitation of theoretical principles by personal investigation, under such direction as will insure systematic methods of observation, accurate use of apparatus, and the proper methods of drawing conclu- sions and of making reports. If of an advanced character, it should also provide facilities for systematic research by skilled observers, for. the purpose, among other things, of discovering laws or coefficients of value to the engineering profession. This work deals principally with the educational methods, the use of apparatus, and the preparation required for making a skilled observer. In an engineering laboratory for the education of students, a systematic schedule of experiments parallel to the course of instruction in theoretical principles is recommended. While such a laboratory course cannot be laid down here as applicable to all courses of instruction in engineering, the following schedule of studies is presented for consideration as one which has been successfully adopted in the instruction of large classes in Sibley VI PREFACE TO THE SIXTH EDITION. College. The order of the experiments was largely determined by the previous training of the men, and by the attempt to make a limited amount of apparatus do maximum duty. The schedule is presented more as an illustration of one that has been practically tested, and for which the work on Experimental Engineering is adapted, than as a model for other institutions to follow. COURSE OF EXPERIMENTS, SIBLEY COLLEGE ENGINEERING LABORATORY. Junior Year. First Term. Strength of Materials — Tensile and Transverse; Calibration — Indicator- springs and Steam-gauges; Weirs and Water-meters; Mercurial Thermom- eters; Pyrometers; Transmission-dynamometers; Slide-rule; Calculating- machines; Planimeters; Calorimeter and Indicator-practice. Second Term. Strength of Materials — Compression and Torsion; Lubricants — Viscosity; Flash-test; Coefficient of Friction; Steam-engine — Valve-setting; Flue -gas Analysis; Temperature — Pyrometers, Air- thermometers; Calibration — Indi- cator-springs; Efficiency-tests — Steam-boiler; Steam-pump; Steam-engine; Hydraulic Ram. Senior Year. First Term. Strength of Materials — Brick; Stone; Cement; Efficiency -tests — Hot-air Engine (2 tests) ; Gas-engine (3 tests) ; Injector; Centrifugal Pump; Hydrau- lic Motor; Belting; Steam Boiler; Compound Engine; Oil-engine (2 tests); DeLaval Steam Turbine; Parsons Steam Turbine. Second Term. Strength of Materials — Springs; Tension test on Emery -machine ; Efficiency -tests — Air-compressor; Triple -expansion Engine; University Elec- tric-lighting Plant; Doble Water-wheel; Pelton Wheel; Refrigeration; Com- pound and Triple-expansion Engine by Hirn's Method; Special Research; Thesis Work. The work required of each student per week is substantially as follows: one laboratory exercise three hours in length, one PREFACE TO THE SIXTH EDITION. Vll recitation one hour in length, and the computation of the data and the preparation of a report, including data, results, and all necessary curves. The report is required to be full and com- plete, and is expected to train the young man in methods of writing English and of reporting in his own language what he has learned respecting the subject under investigation in the laboratory and in the references, as well as to teach him method? of observing and recording the data and of computing the results of the test. For the purpose of performing the experiments the students are divided into groups of three, and the experiments are usually arranged as to require three observers or multiples thereof. The computation of results is made by all the members of the group, but each man is required to write an individual report of the test. The credit given is the same as for a recitation course requiring three hours per week. The student's work is performed under the personal direction of a competent instructor, who has charge usually of twelve to fourteen men, who gives such detailed instruc- tion as is required, and reads, corrects, and grades all reports. The student is required, whenever practicable or possible, to operate his own machine or apparatus during the test, in order to obtain practical skill in the handling and operation of appara- tus, machines, and prime movers, which is believed to meet an important requirement of an engineering laboratory. He is not expected to do the shop work required for construction of the apparatus, or that required for the preparation of the experi- ment, as the time at his command is not sufficient for such work; and besides, instruction in shop work is given in a different department in Sibley College. The full list of subjects treated in the book is given in the table of contents which immediately follows the preface. Some of the more important divisions of the work are as follows • Experimental Methods of Investigation. Reduction of Experimental Data Analytically and Graphically. Apparatus for Reduction of Experimental Data, including use of Slide-rule, Planimeter, etc. Vlll PREFACE TO THE SIXTH EDITION. Strength 01 Materials, including General Formulae, Description of Testing machines, and Methods of Testing. Cement-testing Machines and Methods of Testing. Machines and Methods for Testing Lubricants and Friction. Dynamometers and Machines for the Measurement of Power. Hydraulics, Hydraulic Machinery, and Methods of Testing. Measurement of Pressure and Temperature. Measurement of Moisture in Steam by Calorimeters. Fuel-calorimeters and Flue-gas Analysis. Tne Steam-engine and Methods of Testing. The Steam-boiler and Methods of Testing. The Steam-turbine and Methods of Testing. Gas and Hot-air Engines and Methods of Testing. The Injector and Methods of Testing. Methods of Testing Locomotives. Methods of Testing Pumping-engines. Air-compressors and Methods of Testing. Refrigerating-machines and Methods of Testing. The author has been assisted in the preparation of the various editions of the book by his colleagues and assistants in Sibley College, and is indebted to them for many suggestions and a great deal of valuable information. Ample credit is given authori- ties from whom information has been obtained in the body of the book in connection with the matter under discussion. In the early editions of the work the writer was under special obligation to the late Dr. R. H. Thurston and to Professor C. W. Scribner; for the later editions to Assistant Professor H. Diederichs, and C. Hirshfeldt, and to Mr. R. L. Shipman, Mr. W. M. Sawdon, and Mr. G. B. Upton. TABLE OF CONTENTS. INTRODUCTION. ARTICLE PAGE i. Objects of Engineering Experiment i 2. Relation of Theory to Experiment 2 3. The Method of Investigation * 2 4. Classification of Experiments 3 5. Efficiency-tests 3 CHAPTER I. REDUCTION OF EXPERIMENTAL DATA. 6. Classification of Errors 5 7. Probability of Errors 6 8. Errors of Simple Observations 7 10. Combination of Errors 9 12. Deduction of Empirical Formulae 10 15. Rules and Formulas for Approximate Calculation 15 16. Rejection of Doubtful Observations 17 17. Errors to be Neglected 18 18. Accuracy of Numerical Calculations 19 19. Graphical Representation of Experiments 20 21. Autographic Diagrams 21 22. Construction of Diagrams 22 CHAPTER II. APPARATUS FOR REDUCTION OF EXPERIMENTAL DATA. 2^. The Slide-rule 24 25. The Vernier 29 26. The Polar Planimeter 30 30. The Suspended Planimeter 41 31. The Coffin Planimeter 41 tx x TABLE OF CONTENTS. ARTICLE PAGE 34. The Roller Planimeter 45 36. Care and Adjustment of Planimeters 50 37. Directions for Use of Planimeters 51 38. Calibration of Planimeters 52 39. Errors of Planimeters 55 40. The Vernier Caliper 57 41. The Micrometer 58 42. The Micrometer Caliper 59 43. The Cathetometer 62 44. Computation Machines 64 CHAPTER III. STRENGTH OF MATERIALS — GENERAL FORMULAE. 45. Definitions 67 46. Strain-diagrams 69 47. Viscosity 70 48. Notation 72 49. Tension 72 51. Compression 73 52. Transverse 76 54. Shearing and Torsion 81 55. Modulus of Rigidity 83 58. Combination of Two Stresses 84 60. Thermodynamic Relations 86 CHAPTER IV. STRENGTH OF MATERIALS — TESTING-MACHINES. 6l. 65. 66. 68. 70. 73- 75- 76. 77- General Description of Machines 88 Shackles or Holders 98 Emery Testing-machine 100 Riehle Bros.' Testing-machine 107 Olsen Testing-machine no Thurston's Torsion Machines 114 Riehle's and Olsen's Torsion Machines 118 Impact Testing-machine 119 Cement-testing Machines 119 Testing-machine Accessories 124 TABLE OF CONTENTS. xi ARTICLE PAGE 78 to 86. Extensometers 124 87. Deflectometer 135 CHAPTER V. METHODS OF TESTING MATERIALS OF CONSTRUCTION. 88. Form of Test-pieces . 136 93. Elongation — Fracture. 143 94. Strain-diagrams 144 95. Tension Tests 145 99. Compression Tests 154 100. Transverse Tests 155 102. Elastic Curve 159 103. Torsion Test 160 105. Impact Test 163 107. Special Tests of Materials 165 109. Method of Testing Bridge Materials 168 1 10. Admiralty Tests 172 in. Lloyd's Tests for Steel used in Ship-building 173 112. Tests for Cast-iron Water-pipe 174 114. Testing Stones 175 115. " Bricks 178 116. ' ' Paving Material 179 117. ' * Hydraulic Cements 181 122 127 128 129 130 *3i 136 143 144 147 151 152 CHAPTER VI. FRICTION— TESTING OF LUBRICANTS. Friction — Definitions — Useful Formulae 196 Friction of Teeth 199 " " Cords or Belts . 199 " Fluids 200 ' ' ' ' Lubricated Surfaces 201 Testing of Lubricants — Density 201 ' ' " " Viscosity 2C9 ' ' " Gumming 210 " " " Flash-test 210 Testing of Lubricants — Cold Test 213 Oil-testing Machines— Rankine's 215 Thurston's 217 Xll TABLE OF CONTENTS. ARTICLE p AGE 155. Coefficient of Friction 222 157. Riehle's Oil-testing Machine 224 158. Durability Test of Lubricants . . 226 159. Ashcroft's Oil-testing Machine 227 160. Boult's " " 227 162. Experiment with Limited Feed 231 163. Forms for Report of Lubricant Test 233 CHAPTER VII. MEASUREMENT OF POWER — BELT-TESTING. 165. Absorption Dynamometer. The Prony Erake 235 173. " " " Alden Brake 241 178. Practical Directions for Use of Brake 244 179. Pump-brakes 245 180. Fan-brakes 245 181. Traction Dynamometers 246 182. Transmission Dynamometers — Morin 247 186. 187. 188. 189. 192. 194. 195- Steelyard 250 Pillow-block 252 Lewis 252 Differential 255 Emerson 259 Van Winkle. 261 Belt 263 197. Belt-testing Machine, with Directions 264 CHAPTER VIII. MEASUREMENTS OF LIQUIDS AND GASES. 200. Theory of the Flow of Water 270 201. Flow of Water over Weirs — Formulae 272 203. " " " through Nozzles — Formulae 275 205. " ' ' " under Pressure — Formulae 276 206. ' { * ' " in Circular Pipes 277 207. " " " through a Diaphragm — Formulae 279 209. Method of Measuring the Flow of Water by Weirs 281 213. " " " " " " " " Meters 283 217. " " tl " " il " "Nozzles 287 219. " " " " " " " "Diaphragms 288 220. " " " " " li " "inStreams 289 222. " " " " " " " " Pitot'sTube 292 TABLE OF CONTENTS. xni ARTICLE PAGE 225. Flow of Compressible Fluids through an Orifice. 295 229. " " " " in a Pipe 299 230. " " Steam , , 300 232. Gas-meters 304 2^. Anemometer 306 CHAPTER IX. HYDRAULIC MACHINERY. 235. Classification 308 239. Water-pressure Engines. ........ 1 309 241. Overshot Water-wheels 311 242. Breast-wheels 313 243. Undershot Wheels 313 244. Impulse -wheels. . . . 314 245. Turbine 315 248. Reaction -wheels 317 249. The Hydraulic Ram 321 250. Methods of Testing Water-motors 322 253. Pumps 327 256. Test of Pumps 330 258. Form for Data and Report of Pump-test 332 CHAPTER X. DEFINITIONS OF THERMODYNAMIC TERMS. 259. Books of Reference 325 260. Units of Pressure 336 261. Heat and Temperature 337 264. Properties of Steam 340 267. Steam-tables 344 CHAPTER XL MEASUREMENT OF PRESSURE. 268. Manometers 345 271. Mercury Columns 349 273. Draught-gauges 351 Xiv TABLE OF CONTENTS. ARTICLE PAGE 277. Steam-gauges 357 281. Apparatus for Testing Gauges 363 CHAPTER XII. MEASUREMENT OF TEMPERATURE. 285. Mercurial Thermometers 369 288. Air-thermometers 37! 295. Calibration of Thermometers 380 296. Metallic Pyrometers 380 298. Air and Calorimetric Pyrometers 381 299. Determination of Specific Heat 382 302. Electric Pyrometers 385 303. Optical Pyrometers , . . 386 CHAPTER XIII. METHODS OF MEASURING MOISTURE IN STEAM. 305. Definitions 390 307. General Methods 391 314. Errors in Calorimeters 396 315. Sampling the Steam 399 317. Water Equivalent of Calorimeter .".... 401 318. Barrel Calorimeter 402 321. Hoadley Calorimeter 407 323. Barrus Continuous Calorimeter 411 326. ' ' Superheating " 416 328. Throttling Calorimeter.^ 418 336. Separator " 430 341. Chemical " 440 CHAPTER XIV. HEATING VALUE OF COALS — FLUE -GAS ANALYSIS. 343. Combustion — Definition and Table 443 344. Heat of Combustion 444 345. Determination of Heat by Welter's Law 446 346. Temperature produced by Combustion 448 TABLE OF CONTENTS. 347. Composition of Fuels 450 348. Fuel-calorimeters — Principle 451 352. " Favre and Silbermann's 453 353- Thompson's 455 354- Berthkr. 456 355. ' ' Berthelot Bomb 459 35 6 - Carpenter 463 357. Value of Fuel by Boiler-trial 472 358. Analysis of the Products of Combustion 473 360. Reagents for Flue -gas Analysis 475 363. Elliot's Flue-gas Apparatus 479 364. Wilson's " " 481 365. Orsat's " " 481 366. Hemple's " " 483 367. Deductions from Flue-gas Analysis 486 CHAPTER XV. METHOD OF TESTING STEAM-BOILERS. 369. Objects of Eoiler-testing 492 371. Efficiency of a Eoiler 493 375. Standard Method of Testing Steam-boilers 495 377. Concise Directions for Testing Boilers 513 CHAPTER XVI. THE STEAM-ENGINE INDICATOR. 378. Uses of the Indicator 515 380. Early Forms 517 381. Richards 518 382. Thompson 519 383. Tabor 520 384. Crosby 521 385. Indicators with External Springs 523 387. Optical Indicators 525 390. Reducing-motions 529 393. Calibration 535 397. Method of Attaching to the Cylinder 543 398. Directions for Use 545 XVI TABLE OF CONTENTS. CHAPTER XVII. THE INDICATOR-DIAGRAM. ARTICLE PAGE 400. Definitions 547 401. Measurement of Diagrams 551 403. Form of Diagram 553 4C6. Weight of Steam from the Diagram 557 407. Clearance from the Diagram 560 408. Cylinder-condensation and Re-evaporation 561 409. Discussion of Diagrams 562 410. Diagrams from Compound Engines 565 411. Crank -shaft and Steam-chest Diagrams 567 CHAPTER XVIII. METHODS OP TESTING THE STEAM-ENGINE. 412. Engine Standards 569 414. Measurement of Speed 571 417. Surface Condenser 576 418. Calibration of Apparatus 578 419. Preparations for Testing 581 421. Quantities to be Observed 583 422. Preliminary Indicator-practice 584 423. Valve-setting 586 424. Friction-test 589 425. Efficiency-test 589 426. Hirn's Analysis 590 430. " " of Compound Engines , 603 CHAPTER XIX. PUMPING-ENGINES AND LOCOMOTIVES. 433. Standard Method of Testing Pumping-engines 614 434. ' ' ' ' " " Locomotives 634 435. Experimental Engines. 656 TABLE OF CONTENTS. xvn CHAPTER XX. EXPERIMENTAL DETERMINATION OF INERTIA. ARTICLE PAGE 436. General Effects of Inertia 660 437. The Williams Inertia-indicator. . . . 661 438. ' ' Inertia -diagram e 664 CHAPTER XXI. THE INJECTOR AND PULSOMETER. 439. Description of the Injector. 670 440. Theory 672 442. Limits of 676 443-5. Directions for Testing 679 446-7. The Pulsometer 683 CHAPTER XXII. THE STEAM-TURBINE. 448. General Principles < 686 449. Impulse Type (De Laval) 687 450. Reaction Type (Parsons). 689 451. Combined Type (Curtis) 690 452. Testing 691 CHAPTER XXIII. HOT-AIR AND GAS ENGINES. 454. General Principles 692 455. Ericsson Hot-air Engine 692 456. Rider Hot-air Engine. 693 457. Theory 695 458. Method of Testing 095 460. The Gas-engine 701 461. Oil-engines 709 462. Theoretical Formulae. 711 463. Cycle of Operation 713 TABLE OF CONTENTS. ARTICLE PAGE 464. Method of Testing 7I4 465. Data and Results of Test 7x7 CHAPTER XXIV. AIR-COMPRESSORS. 466. Types of Compressors 720 467. Piston Air-compressor 720 468. Rotary Blowers 723 469. Centrifugal Fans 724 470. Measurement of Pressure and Velocity 725 471. Clearance, Effect of 728 472. Loss of Work Due to Rise of Temperature 728 473. Centrifugal Fan, Theory of 729 474. Test of Air-compressor Data Sheets 730 475. * ' ' ' Centrifugal Elower 733 CHAPTER XXV. MECHANICAL REFRIGERATION. 476. Systems of Mechanical Refrigeration 734 477. Relation of. Work to Heat Transfer 735 478. Working Fluids, Properties of 736 479. Efficiency of the Refrigerating -machine 738 480. Heat Losses 740 481. The Air-refrigerating Machine 741 482. The Ammonia Refrigerating -machine 742 483. Relations of Pressure and Volume 744 484. Absorption System of Refrigeration 747 Logs and Data Sheets 749 CHAPTER XXVI. PRACTICAL TABLES. TABLE I. U. S. Standard and Metric Measures 754 II. Numerical Constants -. 756 III. Logarithms of Numbers 769 IV. Logarithmic Functions of Angles 771 TABLE OF CONTENTS, xix TABLE PAGE V. Natural Functions of Ang.es 777 VI. Coefficients of Strength of Materials 781 VII. Strength of Metals at Different Temperatures 782 VIII. Important Properties of Familiar Substances 783 IX. Coefficient of Friction 784 X. Hyperbolic Naperian Logarithms 784 XL Moisture Absorbed by Air 785 XII. Relative Humidity of the Air 785 XIII. Table for Reducing Beaume's Scale-reading to Specific Gravity 786 XIV. Composition of Fuels of U. S 787 XV. Buel's Steam-tables 788 XVI. Entropy of Water and Steam 794 XVII. Discharge of Steam: Napier Formula 795 XVIII. Water in Steam by Throttling Calorimeter 795 Diagram for Determining Per Cent of Moisture in Steam 796 XIX. Factors of Evaporation 797 XX. Dimensions of Wrought-iron Pipe 798 XXI. Density and Weight of Water per Cubic Foot 799 XXII. Horse -power per Pound Mean Pressure. . 800 XXIII. Water Rate Computation Table for Engines 801 XXIV. Weirs with End Contraction 803 XXV. Weirs without End Contraction 803 XXVI. Horse-power of Shafting 804 XXVII. " " Belting 804 Sample-sheet of Cross-section Paper 805 IMPORTANT TABLES IN BODY OF BOOK. Moments of Inertia 78 Units of Pressure Compared 336 Thermometric Scales 337 Melting-points and Specific Heats of Metals 383 Maximum Temperature of Combustion. . 450 Average Composition of Fuels 451 Properties of Saturated Ammonia 738 INTRODUCTION. I. Objects of Engineering Experiments. — The object of experimental work in an engineering course of study may be stated under the following heads : firstly, to afford a practical illustration of the principles advanced in the class-room ; sec- ondly, to become familiar with the methods of testing; thirdly, to ascertain the constants and coefficients needed in engineer- ing practice ; fourthly, to obtain experience in the use of vari- ous types of engines and machines , fifthly, to ascertain the efficiency of these various engines or machines ; sixthly, to de- duce general laws of action of mechanical forces or resistances, from the effects or results as shown in the various tests made. The especial object for which the experiment is performed should be clearly perceived in the outset, and such a method of testing should be adopted as will give the required informa- tion. This experimental work differs from that in the physical laboratory in its subject-matter and in its application, but the methods of investigation are to a great extent similar. In per- forming engineering experiments one will be occupied princi- pally in finding coefficients relating to strength of materials or efficiency of machines ; these, from the very nature of the ma- terial investigated, cannot have a constant value which will be exactly repeated in each experiment, even provided no error be made. The object will then be to find average values of these coefficients, to obtain the variation in each specific test 2 EXPERIMENTAL ENGINEERING. [§ 3- from these average values, and, if possible, to find the law and cause of such variation. The results are usually a series of single observations on a variable quantity, and not a series of observations on a con- stant quantity; so that the method of finding the probable error, by the method of least squares, is not often applicable. This method of reducing and correcting observations is, how- ever, of such value when it is applicable, that it should be familiar to engineers, and should be applied whenever practi- cable. The fact that single observations are all that often can be secured renders it necessary in this work to take more than ordinary precautions that such observations be made correctly and with accurate instruments. 2. Relation of Theory to Experiment. — It will be found in general better to understand the theoretical laws, as given in text-books, relating to the material or machine under inves- tigation, before the test is commenced ; but in many cases this is not possible, and the experiment must precede a study of the theory. It requires much skill and experience in order to deduce general laws from special investigations, and there is always reason to doubt the validity of conclusions obtained from such investigations if any circumstances are contradictory, or if any cases remain unexamined. On the other hand, theoretical deductions or laws must be rejected as erroneous if they indicate results which are con- iradictory to those obtained by experiments subject to condi- tions applicable in both cases. 3. The Method of Investigation is to be considered as consisting of three steps : firstly, to standardize or calibrate the apparatus or instruments used in the test ; secondly, to make the test in such a way as to obtain the desired information ; thirdly, to write a report of the test, which is to include a full description of the methods of calibration and of the results, which in many cases should be expressed graphically. The methods of standardizing or calibrating will in gen- eral consist of a comparison with standard apparatus, under §5-] INTRODUCTION. ' 3 conditions as nearly as possible the same as those in actual prac- tice. These methods later will be given in detail. The manner of performing the test will depend entirely on the experiment. The report should be written in books or on paper of a pre- scribed form, and should describe clearly: (i) Object of the experiment; (2) Deduction of formulas and method of perform- ing the experiment; (3) Description of apparatus used, with methods of calibrating; (4) Log* of results, which must include all the figures taken in the various observations of the calibra- tion as well as in the experiment. These results should be arranged, whenever possible, in tabular form; (5) Results of the experiment; these should be expressed numerically and graphically, as explained later; (6) Conclusions deduced from the experiment, and comparison of the results with those given by theory or other experiments. 4. Classification of Experiments. — The method of per- forming an experiment must depend largely on the special object of the test, which should in every case be clearly comprehended. The following subjects are considered in this treatise, under various heads: (1) The calibration of apparatus; (2) Tests of the strength of materials; (3) Measurements of liquids and gases; (4) Tests of friction and lubrication; (5) Emciency- tests, which relate to (a) belting and machinery of transmission, (b) water-wheels, pumps, and hydraulic motors, (c) hot-air and gas engines, (d) air-compressors and compressed-air machinery, (e) steam-engines, boilers, injectors, and direct-acting pumps. 5. Efficiency-tests. — Tests may be made for various ob- jects, the most important being probably that of determining the efficiency, capacity, or strength. The efficiency of a machine is the ratio of the useful work delivered by the machine to the wfyole work supplied or to the whole energy received. The limit to the efficiency of a machine is unity, which denotes the efficiency of a perfect machine. The whole work performed in driving a machine is evidently equal to the useful work, plus the work lost in friction, dissi- pated in heat, etc. The lost work of a machine often consists 4 EXPERIMENTAL ENGINEERING. [§ 5- of a constant part, and in addition a part bearing some definite proportion to the useful work; in some cases all the lost work is constant. Efficiency -tests are made to determine the ratio of useful work performed to total energy received, and require the deter- mination of, first, the work or energy received by the machine; second, the useful work delivered by the machine. The friction and other lost work is the difference between the total energy supplied and the useful work delivered. In case the efficiency of the various parts of the machine is computed separately, the efficiency of the whole machine is equal to the product of the efficiencies of the various component parts which transmit energy from the driving-point to the working-point. The work done or energy transmitted is usually expressed in foot-pounds per minute of time, or in horse-power, which is equivalent to 33,000 foot-pounds per minute, or 550 foot-pounds per second of time. EXPERIMENTAL ENGINEERING, REDUCTION OF EXPERIMENTAL DATA. METHOD OF LEAST SQUARES— NUMERICAL CALCULATIONS- GRAPHICAL REPRESENTATION OF EXPERIMEN1 >. CHAPTER I. APPLICATION OF THE METHOD OF LEAST SQUARES. In the following articles the application of this method to reducing observations and producing equations from experi- mental data is quite* fully set forth. The theory of the Method of Least Squares is not given, but it can be fully studied in the work by Chauvenet published by Lippincott & Co., or in the work by Merriman published by John Wiley & Sons. 6. Classification of Errors. — The errors to which all ob- servations are subject are of two classes: systematic and acci- dental. Systematic errors are those which affect the same quanti- ties in the same way, and may be further classified as instru- mental and personal. The instrumental errors are due to imperfection of the instruments employed, and are detected by comparison with standard instruments or by special methods of calibration. Personal errors are due to a peculiar habit of the observer tending to make his readings preponderate in a certain direction, and are to be ascertained by comparison of 5 6 EXPERIMENTAL ENGINEERING. [§ 7« observations: first, with those taken automatically; second, with those taken by a large number of observers equally skilled ; third, with those taken by an observer whose personal" error is known. Systematic errors should be investigated first of all, and their effects eliminated. A ccidental errors are those whose presence cannot be fore- seen nor prevented; they may be due to a multiplicity of causes, but it is found, if the number of observations be sufficiently great, that their occurrence can be predicted by the law of probability, and the probable value of these errors can be com- puted by the METHOD OF LEAST SQUARES. Before making application of the " Method of Least Squares," determine the value of the systematic errors, elimi- nate them, and apply the method of least squares to the de- termination of accidental errors. 7. Probability of Errors. — The following* propositions are regarded as axioms, and are the fundamental theorems on which the Method of Least Squares is based : 1st. Small errors will be more frequent than large ones. 2d. Errors of excess and deficiency (that is, results greater or less than the true value) are equally probable and will be equally numerous. 3d. Large errors, beyond a certain magnitude, do not occur. That is, the probability of a very large error is zero. From these it is seen that the probability of an error is a function of the magnitude of the error. Thus let x represent any error and y its probability, then By combination of the principles relating to the probability of any event Gauss determined that y = ce~** t ....... (i) in which c and h are constants, and e the base of the Napierian system of logarithms. § 9-] APPLICATION OF METHOD OF LEAST SQUARES. 7 8. Errors of Simple Observations. — It can be shown by calculation that the most probable value of a series of obser- vations made on the same quantity is the arithmetical mean, and if the observations were infinite in number the mean value would be the true value. The residual is the difference between any observation and the mean of all the Observations. The mean error of a single observation is the square root of the sum of the squares of the residuals, divided by one less than the number of observations. The probable error is 0.6745 time the mean error. The error of the result is that of a single observation divided by the square root of their number. Thus let 11 represent the number of observations, 5 the sum of the squares of the residuals; let e, e x , e if etc., represent the residual, which is the difference between any observation and the mean value ' let 2 denote the sum of the quantities indi- cated by the symbol directly following. Then we shall have Mean error of a single observation ± \/ . Probable error of a single observation ± 0.6745 a / , Mean error of the result ± a / -7 r. . (4) y n(n — 1) w (2) (3) y n(n- Probable error of the result ± 0.6745 a / . _ -r. (5) In every case 5 = -2V*. 9. Example. — The following example illustrates the method of correcting observations made on a single quantity : A great number of measurements have been made to determine the relation of the British standard yard to the 8 EXPERIMENTAL ENGINEERING. B* meter. The British standard of length is the distance, on a bar of Bailey's bronze, between two lines drawn on plugs at the bottom of wells sunk to half the depth of the bar. The marks are one inch from each end. The measure is standard at J2° Fah., and is known as the Imperial Standard Yard. The meter is the distance between the ends of a bar of platinum, the bar being at o° Centigrade, and is known as the Metre des Archives. The following are some of these determinations. That made by Clarke in 1866 is most generally recognized as of the greatest weight. COMPARISON OF BRITISH AND FRENCH MEASURES. Name of Observer. Date. Observed length of meter in inches. Difference from the mean. Residual = e. Square of the Residuals. * 2 . Kater 1821 1832 1866 1884 1885 39.37079 39-38I03 39.370432 39-370I5 39-36985 — O.OOI460 + 8780 — 1818 — 2IOO — O.OO2400 0.000002 13 16 O.OOOO770884 O.OOOOO33124 O.OOOOO44100 O.OOOOO57600 Clarke Mean value 39.372250 O.OOOO907024 2e* = S = 0.0000907024, n = 5, n{n — 1) = 20. Mean error of a single observation 00476. Probable error of single observation = ± 0.003 17. Mean error of mean value = ± \ / -7- — -x = 0.00213, Probable error of mean value = ± 0.00142. §11.] APPLICATION OF METHOD OF LEAST SQUARES. 9 That is, considering the observations of equal weight, it would be an even chance whether the error of a single obser- vation were greater or less than 0.00317 inch, and the error of the mean greater or less than 0.00142. 10. Combination of Errors. — When several quantities are involved it is often necessary to consider how the errors made upon the different quantities will affect the result. Since the error is a small quantity with reference to the re- sult, we can get sufficient accuracy with approximate formulae. Thus let X equal the calculated or observed result, F the error made in the result ; let x equal one of the observed quantities, and f its error. Then will F = ff x • ....... (6) in which -7— is the partial derivative of the result with respect to the quantity supposed to vary. In case of two quantities in which the errors are F, F f , etc., the probable error of the result = ± VF 2 + F n (7) II. As an example, discuss the effect of errors in counting the number of revolutions, and in measurement of the mean effec- tive pressure, acting on the piston, with regard to the power furnished by a steam-engine. Denote the number of revolu- tions by n, the mean pressure by p, the length of stroke in feet by /, and the area of piston in square inches by a ; the work in foot-pounds done on one side of the piston by W. Then W — plan, F = lanf y F dW , _, -j. = —j— = lan y b =.plaf\ J d P F' dW ■ 7 = ~dn =? la ' IO EXPERIMENTAL ENGINEERING. [§ 12. The error/ in the mean pressure is itself a complicated one, since p is measured from an indicator-diagram and depends on accuracy of the indicator-springs, accuracy of the indicator- motion, and the correct measurement of the indicator-diagram. These errors vary with different conditions. Suppose, however, the whole error to be that of measurement of the indicator- diagram. This is usually measured with a polar planimeter, of which the minimum error of measurement may be taken as 0.02 square inch ; with an indicator-diagram three inches in length this corresponds to an error of 0.0067 of an inch in ordi- nate. In a similar manner the error in the number of revolu- tions depends on the method of counting: with a hand-counter the best results by an expert probably would involve an error of one tenth of a second ; with an attached chronograph the error would be less, and would probably depend on the accu- racy with which the results could be read from the chronograph- diagram. The ordinary errors are fully three times those given here. Take as a numerical example, a = 100 square inches, 1 = 2 feet, n = 300, / = 50 pounds, /= 0.335, /' = 0.5. F = 20,100, F = 5,000, W = 3,000,000. Probable error = ± VF' Z + F* = 20,712 ft.-lbs., which in this case is 0.0069 of the work done. 12. Deduction of Empirical Formulae. — Observations are frequently made to determine general laws which govern phenomena, and in such cases it is important to determine what formula will express with least error the relation between the observed quantities. These results are empirical so long as they express the re- lation between the observed quantities only; but in many cases they are applicable to all phenomena of the same class, in which case they express engineering or physical laws. In all these cases it is important that the form of the equa- tion be known, as will appear from the examples to be given later. The form of the equation is often known from the § 1 3-] APPLICATION OF METHOD OF LEAST SQUARES. II general physical laws applying to similar cases, or it may be determined by an inspection of the curve obtained by a graphical representation of the experiment. A very large class of phenomena may be represented by the equation y = a + Bx + Cx 1 + Dx 3 + etc (8) In case the graphical representation of the curve indicates a parabolic form, or one in which the curve approaches parallel- ism with the axis of X, the empirical formula will probably be of the form y = A + £x* + Cx* + Dx*-\-etc. ... (9) In case the observations show that, with increasing values of x, ;/ passes through repeating cycles, as in the case of a pendulum, or the backward and forward motion of an engine, the charac- teristic curve would be a sinuous line with repeated changes in the direction of 'curvature from convex to concave^ The equation would be of the form y^A + B.sin l —x + £ 2 cos ^—x + C x sin ^-2X m mm + C a cos - — -2x + etc. . . . (10) m Still another form which is occasionally used is y = A -f- B sin mx -f- C sin 2 mx -\- etc. . . (1 1) 13. General Methods. — A method of deducing the em- pirical formula is illustrated by the following general case : In a series of observations or experiments let us suppose that the errors (residuals) committed are denoted by e, £' ', e" 9 12 EXPERIMENTAL ENGINEERING. |_§ J 3* etc., and suppose that by means of the observations we have deduced the general equations of conditions as follows: e = h -f- ax -\- by -\- cz, e' =h' \-a'x + b f y + c'z, I e" = h" + a"x + b"y + c"z, \ e »> - h"' + a'"x + *"> + *"'*, | etc. etc. etc. J Let it be required to find such values of x, y, z, etc., that the values of the residuals e, e\ e" y e'" , etc., shall be the least pos- sible, with reference to all the observations. If we square both members of each equation in the above group and add them together, member to member, we shall have f _|_ e " _[- e ' n + e" n + etc. = x\a 2 + a /2 + a"* + etc.) + 2x\{ah + a'h' + a"h" + etc.)+ a{py +cz + etc.) + a\b'y + c'z + etc.) + etc. \ + h 2 + h' 2 + etc. This equation may be arranged with reference to x as follows : u = e * + ^' 2 + ?" 2 + etc. = Px 2 + 20* + ^ + etc. ; in which the various coefficients of the different powers of x are denoted by the symbols P, Q, R, etc. Now in order that these various errors may be a minimum, ^ 2 _j_ e n _|_ e "* _j_ etc. = u must be a minimum, in which case its partial derivative, taken with respect to each variable in succession, should be separately equal to zero. Hence or, substituting the values of P and Q, x(a 2 + a' 2 + etc.) + aA + ah' + etc. -\- a (ty + cz + etc.) + a '(£> + ^ + etc.) + etc. = O. Similar equations are to be formed for each variable. § 1 4.] APPLICATION OF METHOD OF LEAST SQUARES. 1 3 From the form of these equations we deduce the principle that in order to find an equation of condition- for the minimum error with respect to one of the unknown quantities, as x for example, we have simply to multiply the second member of each of the equations of condition by the coefficient of the unknown quantity in that equation, take the sum of the products, and place the result equal to zero. Proceed in this manner for each of the unknown quantities, and there will result as many equations as there are unknown quantities, from which the required values of the unknown quantities may be found by the ordinary methods of solving equations. 14. Example. — As an illustration, suppose that we require the equation of condition which shall express the relation be- tween the number of revolutions and the pressure expressed in inches of water, of a pressure-blower delivering air into a closed pipe. Let m represent the reading of the water-column, and n the corresponding number of revolutions. Suppose that the observations give for m = 24 inches, n = 297 revolutions • " m = 32 " n — 340 " " m = 33 " » = 355 " m = 35 " n = 376 " Average values for m = 31 inches, n = 342 revolutions. Arranging the results in the following form, we have : Water-column. Revolutions. Observations. Residuals. Observations. Residuals. 24 32 33 35 -7 + 2 + 4 297 340 355 376 -45 — 2 + 13 + 34 Assume that the equation of condition is of the form A+Bx+Cx 2 =y. 14 EXPERIMENTAL ENGINEERING. [§1 + To find those values of A, B, and C which will most nearly satisfy the equation, as shown in the experiment: Taking the values of x, as the residual or difference between the mean and any observation in height of water-column, and the value of y as the corresponding residual in number of revolutions, we have the following equations of condition : A - 7 B + 4 gC= -45, j A + £+ C=- 2, I A + 2B+ 4 C= + i 3 , J * A+4B+i6C=+ 34 .) Multiplying each equation by the coefficient of A in that equation, we have A -yB + 4gC= -45, A+ B + C= - 2, A + 2B+ 4 C= + i 3 , A + 4 B+i6C= + 3 4 . Equations of minimum condi- tion of error with respect to A. 4 A -\-0B-\-j0C = O. III. Sum of equations in group II. Multiplying each equation in group I by the coefficient of B in that equation, we have -7^+49^-343^= 315 ~ A + B + C=- 2 2A+ 4 B+ SC= 26 4^ + 16^ + 6 4 C= 136 Equations of minimum IV. condition of error with respect to B. oA -f- yoB — 270C = 475 Sum of equations in group IV. Multiplying each equation in group I by the coefficient of C in that equation, we have 49^ — 343^ + 2401 C — — 2205 A+ B+ C=- 2 4^+ SB+ i6C= 52 \6A-\- 64^?+ 2566^= 544 Equations of minimum V. condition of error with respect to C. JoA — 26SB + 2674C = — 161 1 Sum of equations in group V. § 1 5-] APPLICATION OF METHOD OF LEAST SQUARES. 1 5 The sums of these various equations of minimum condition are the same in number as the unknown quantities, and by com- bining them the various values of A, B, C, etc., can be deter- mined. We have, in the following case : 4A + oB + yoC = o \ oA + 70B — 270C = 475 v VI. 70^ — 268^ + 2674(7 = — 1611) Solving the above, A = 1.608 ; B = 7.140 ; C = — 0.0919. Substituting in the original equation of condition, y — 1.608 -j- 7.140^ — 0.0919^. To reduce this form to an equation expressing the probable relation of the number of revolutions to the height of the water- column, we must substitute for y its value, n — 342 ; and for x its value, m — 31. In this case we shall have m — 342 = 1.608 + 7.i4(w — 31) — 0.09 I9(w — 3i) a ; which reduced gives the following equation as the most proba- ble value in accordance with the observations : n = 34.952 -\- 13.02/^ — 0.0919*0"; which is the empirical equation sought. 15. Rules and Formulae for Approximate Calculation.— When in a mathematical expression some numbers occur which are very small with respect to certain other numbers, and which are therefore reckoned as corrections, they may often be ex pressed with sufficient accuracy by an approximate formula, which will largely reduce the labor of computation. i6 EXPERIMENTAL ENGINEERING. [§15. On the principle that the higher powers of very small quan- tities may be neglected with reference to the numbers them- selves, we can form a series by expansion by the binomial formula, or by division, in which, if we neglect the higher powers of the smaller quantities, the resulting formulae become much more simple, and are usually of sufficient accuracy. Thus, for instance, let d equal a very small fraction ; then the expression (a + S) m = a m + ma m - 1 d + VI- (m — 1) etc., will become a m + ma m ~ 1 S, if the higher powers of d be neglected. If d is equal to 10 1 00 part of a, the error which results from omitting the remaining terms of the series becomes very small, as in this case the value of d 2 = 100 ^ 000 fl. 000000' The following table of approximate formulae presents several cases which can often be applied with the effect of materially reducing the work of computation, without any sensible effect on the accuracy: (1 + d) m = 1 + mS t (I + d) 2 = 1 + 2d, i/T+d = i+id, (1 + d) 3 =i+3*, = 1 - d, i + d 1 1 4/T+d = I — 2d, = !■-**, (I- - 6) m = I — md ; (I- - d) 2 = I — 2d; Vi — d = r-R; (I- -d) 3 = 1-3*; I I — d = 1 + *; I = I+2d; Vi — s = !+£*; (I + -5- 9 X 4> etc.,— until all the factors have been used, checking them off as they are used, to guard against skipping any or using one twice. §24.] APPARATUS. 2J To multiply, move the runner; to divide, move the slide: in either case see that the runner points to a graduation on the slide corresponding to the factor. The result at the end or at any stage of the process is given by the runner on the station- ary scale. Or, to be more exact, the significant figures of the result are given, for in no case does the slide-rule show where to place the decimal point. If the decimal point cannot be located by inspection of the factors, make a rough cancel- lation. Involution and evolution are readily mastered by simple practice. Slide-rules working on the same prin- ciple are frequently made with circular or cylindrical scales, which in the Thacher and Fuller instruments are of great length. Thacher's calculating instrument consists of a cylinder 4 inches in diameter and 18 inches long, working within a frame- work of triangular bars. Both the cylinders and bars are grad- Fig. 2. — Thacher's Calculating Instrument. uated with a double set of logarithmic scales, and results in multiplication or division can be obtained from one setting of the instrument, hence it is especially convenient when a series of numbers are to be multiplied by a common factor. The scales in this instrument are about 50 feet in length, and results can be read usually to five places. The instrument is similar to the straight slide-rule previously described, the scale on the triangular bars corresponding to the stationary scale, that on the cylinder to the sliding scale, and a triangular index / to the sliding pointer or runner. The method of using is essentially similar to that of the plain slide-rule ; 28 EXPERIMENTAL ENGINEERING. [§24- thus, to solve an example of the form a/b, put the runner / on the triangular scale at the number corresponding to a, bring the number corresponding to b on the cylindrical scale to register with a on the triangular scale ; the respective numbers on the trianglar scale and cylinder will in this position all be in the ratio of a to b, and the quotient will be read by noting that number on the triangular scale which registers with I on the cylindrical scale. The product of this quotient by any other number will be obtained by reading the number on the trian- gular scale registering with the required multiplier on the cylin- drical scale. Fuller's slide-rule consists of a cylinder C which can be moved up or down and turned around a sleeve which is attached to the handle H. A single logarithmic scale, 42 feet in length, Fig. -The Fuller Slide-rule. is graduated around the cylinder spirally, and the readings are obtained by means of two pointers or indices, one of which, A, is attached to the handle, and the other, B, to an axis which slides in the sleeve. This instrument is not well adapted for multiplying or dividing a series of numbers by a constant, since the cylinder must be moved for every result. The instrument is, however, very convenient for ordinary mathematical com- putations, and the results may be read accurately to four deci- mal places. The method of using the instrument is as follows : Call the pointer^, fixed to the handle, the fixed pointer, the other BB\ which may be moved independently as the movable index. To use the instrument, as for example in performing the oper- ation indicated by {a X b) ~- c, set the fixed pointer A to the first number in the numerator, then bring the movable index § 25-] APPARATUS. 29 B to the first figure in the denominator; then move the cy- linder C until the second figure in the numerator appears under the movable index, finally read the answer on the cylinder C underneath the fixed pointer A. In general, to divide with this instrument move the index B; to multiply, move the cylinder C\ read results under the fixed pointer A. The movable index BB' has two marks, one at the middle, the other near the end of the pointer, either of which may be used for reading, as convenient, their distance apart corresponding to the entire length of the scale on the cylinder C. 25. The Vernier. — The vernier is used to obtain finer sub- divisions than is possible by directly dividing the main scale, which in this discussion we will term the limb. The vernier is a scale which may be moved with reference to the main scale or limb, or, vice versa, the vernier is fixed and the limb made to move past it. The vernier has usually one more subdivision for the same distance than the limb, but it may have one less. The theory of the vernier is readily perceived by the following discussion. Let d equal the value of the least subdivision of the limb; let 11 equal the number of subdivisions of the vernier which are equal to n — 1 on the limb. Then the value of one subdivision on the vernier is d[ \ 71 The difference in length of one subdivision on the limb and one on the vernier is j-j[ n 11 1 n which evidently will equal the least reading of the vernier, and indicates the distance to be moved to bring the first line of the vernier to coincide with one on the limb. In case there is one more subdivision on the limb than on the vernier for the same distance, the interval between the graduations on the vernier is greater than on the limb, and the vernier must be 30 EXPERIMENTAL ENGINEERING. [§ 2& behind its zero-point with reference to its motion, and hence is termed retrograde. The formula for this case, using the same notation as before, gives d\ ) —d=— for the least reading. The following method will enable one to readily read any vernier: i. Find the value of the least subdivision of the limb. 2. Find the number of divisions of the vernier which corre- sponds to a number one less or one greater than that on the limb: the quotient obtained by dividing the least subdivision of the limb by this number is the value of the least reading of the vernier. The following rules for reading should be care- fully observed : Firstly. Read the last subdivision of the limb passed over by the zero of the vernier on the scale of the limb as the reading of the limb. Secondly. Look along the vernier until a line is found which coincides with some line on the limb. Read the number of this line from the scale of the vernier. This number multiplied by the least reading of the vernier is the reading of the vernier. Thirdly. The sum of these readings is the one sought. Thus, in Fig. 5, page 31, (1) the reading of the limb rs 4.70 at a\ (2) that of the vernier is 0.03 ; (3) the sum is 4.73. 26. The Polar Planimeter. — The planimeter is an instru- ment for evaluating the areas of irregular figures, and in some one of its numerous forms is extensively used for finding the areas of indicator and dynamometer diagrams. The principal instrument now in use for this purpose was invented by Amsler and exhibited at the Paris Exposition in 1867. This form is now generally known as Amsler's Polar Planimeter; as most of the other instruments are modifications of this one, it is important that it be thoroughly understood. The general appearance of the instrument is shown in Fig. 4, from which it is seen that it consists of two simple arms PK and FK t pivoted together at the point K. The arm /^during use is free to rotate around the point P, and is held in place by a weight. The arm KF carries at one end a tracing-point, which is passed around the borders of the area to be integrated 26.] APPARA TUS. 31 It also carries a wheel, whose axis is in the same vertical plane with the arm KF, and which may be located indifferently be- tween AT and F, or in KF produced. It is usually located in KF, produced as at D. The rim of this wheel is in contact with the paper, and any motion of the arm, except in the direction of its axis, will cause it to revolve. A graduated scale with a vernier denotes the amount of lineal travel of its circumference. This wheel is termed the record-wheel. Fig. 4. — Amsler's Polar Planimeter. The detailed construction of the record-wheel, and the ar- rangement of the counter G, showing the number of revolutions, Fig. 5.— The Record-wheel. Amsler's Polar Planimeter. is shown in Fig. 5. The wheel D is subdivided into a given number of parts, usually 100 ; the value of one of these parts is to be obtained by dividing the circumference of the rim of the wheel which is in contact with the paper by the number of. 3 2 EXPERIMENTAL ENGINEERING. [§ 27 . divisions. This result will give the value of the least division on the limb; this is subdivided by an attached vernier, in this par- ticular case to tenths of the reading of the limb, so that the least reading of the vernier is one thousandth of that of one revolution. 27. Theory of the Instrument. (See Fig. 9.) — The Zero- circle. — If the two arms be clamped so that the plane of the record- wheel intersects the centre P, and be revolved around P, the graduated circle will be continually travelling in the direction of its axis, and will evidently not revolve. A circle generated under such a condition around P as a centre is termed the zero- circle. If the instrument be undamped and the tracing-point be moved around an area in the direction of the hands of a watch outside the zero-circle, the registering wheel will give a positive record • while if it be moved in the same direction around an area inside the zero-circle, it will give a negative record. This fact makes it necessary, in evaluating areas that are very large and have to be measured by swinging the instrument completely around P as a centre, to know the area of this zero-circle, which must be added to the determination given by the instrument, since for such cases that circumference is the initial point for measurement. Geometrical and Analytical Demonstration. — If a straight line mn move in a plane, it will generate an area. This area may be considered positive or negative according to the direction of motion of the line. In Fig. 6, let the paths of the ends m and n of the line be the perimeters of the areas A and B respectively; then it is at once apparent that the net area generated is A + C — C—B or A— B. The immediate corollary to this is that if the area B be reduced in width to zero, i.e., become aline along which n travels back and forth, the area swept over will be A, around which m is carried. Analyzing a differential motion of the line from mn to m'n' (Fig. 8), it may be broken up into three parts: a movement per- pendicular to the line, giving area Idp; a movement in the direc- tion of the length of the line, giving no area; and a movement of rotation about one end, giving as area \PdQ. The total differ- ential of area is then dA=ldp + %l 2 dd. I is always a constant §27-] APPARATUS. 33 during the operation of a planimeter, so that A= j dA=lj dp + wfdd. The common use of a planimeter is that typified in Fig. 7, where the tracing-point is carried around the area to be meas- ured, while the other end of the tracing-arm is guided back and forth along some line. The guide-line is usually either a straight line or an arc of a circle. When the tracing-point has returned to its initial position the net angle turned through by the tracing- arm, or j ddj is zero. Hence A =lj dp x simply. But j dp is the net distance the arm has moved perpendicular to itself. Call this R, and there results the equation of the planimeter A=l-R. Fig. 6. Fig. 7. If the polar planimeter is so used as to bring in the zero-circle, the case is that of Fig. 6, each end of the line describing an area. The tracing-arm sweeps over the difference between the area described by T (Fig. 9) and the circle made by G about P as centre. This difference-area is not, however, recorded by the planimeter because the / dd is now 2tz instead of zero, T making a complete revolution about G. The linear turning of the edge of the recording- wheel is I dp — 27m, where n is the distance from guided point G to the plane of the wheel. The effect on the reading is the same as if the radius PG were increased. The 34 EXPERIMENTAL ENGINEERING. [§ 2J zero- circle is traced by T when the plane of W passes through P. Then jdp = 27tn, and the wheel records zero. In practice the area described by the tracing-point is found by adding to the area of the zero- circle the area recorded by the wheel, taking account of the algebraic sign of the latter. Fig. 8. Fig. 9. The following demonstration is of German origin and, although less general in its nature, is retained for the reason that it is more satisfactory to some minds than the one given above. Movement of the Record-wheel. (Fig. 10.) — From the preced- ing discussion it is seen that the record- wheel does not register, so long as its plane is radial, or so long as angle ED'F" = 90 . The amount of rotation due to variation in the angle EJD between the arms is, if an area be completely circum- scribed, equal in opposite directions, and hence does not affect the result, so that it is necessary to discuss merely the case of motion around the pole E, with the angle EJD fixed. Thus, for instance, suppose angle EJD to remain constant, and the tracing-point to swing through the infinitesimal angle F"EF, designated by dd, the record-wheel would move near the path DD' more or less irregularly, but subtending an equal angle DED' '. The component of this motion which constitutes the record is OD f , designated by dR, which is the projection of §27.] APPARATUS. 35 this path on a perpendicular to JF. Since DED' is infinitesi- mal, and dd = tan dd, we have DD' = Z>£tftf ; also dR = OD' = DD' cos ED'D ; but ED'D = isZ>c9 from similar triangles. Hence dR = ED cos EDOdd. Denote the length of arm EJ by m, the length of arm JF from pivot to tracing-point by /, the distance /X> from pivot to record- wheel by n, the angle EJD by B. Let fall a perpendicular from E on FD, or FD produced at 0. Then we have EDcosEDO = <9Z> =JO-JD = mcosB — n. Hence dR = (m cos B — n)dd (i) Second, the infinitesimal area FtF"t' , lying adjacent to the zero-circle. — Let EF = r, let ZjF" = r', the radius of the zero-circle. Let dA = the area sought. Let dd = FEt. Then area /?£/ = £rW0, and area F"£/' = \r n dd. Then dA^FEt-F f, Et f = ^-^)de. . . . (2> From the oblique triangle Zj/F, r* = »2 3 + /* + 2mlcosB • (3) 36 EXPERIMENTAL ENGINEERING. [§ 27. From the right triangle ED ' F n ', r ri zzztn' + S -\-2nl. ....'.... (4) Substituting the values of r % and r' 2 in equation (2), we have dA = /(mcosB — n)dd. ...... (5) By comparing equation (5), the differential equation for the area, with equation (1), the corresponding equation for the Fig. 10. — Polar Planimeter. record, we see that dA = ldR\ , . . . . . . (6) or by integration between limits o and R, since / is a constant, A=IR (7) This shows that the area is equal, to the length of arm from pivot to the tracing-point, multipliea by the space registered § 28.] APPARA TUS. 37 on the circumference of the record-wheel, and is independent of the other dimensions of the instrument. That this is true for areas not adjacent to the zero-circle, or for areas partly inside and out, can readily be proved by subtracting the areas between the zero-circle and the given area, or by a similar process. Hence the demonstration is general. The Amsler instrument is usually constructed so that the arm / is adjustable in length, and consequently it may be made available for any scale or for various units. Gradua- tions are engraved on the arm which show the length required to give a record in a given scale or for given units. The area of tJie zero-circle is usually engraved on the top of the arm /. In case it is not given, it may be found by evaluating the areas of two circles of known area, each greater than the area of the zero-circle nr'*. Let the areas of such circles be respectively C and C' t and the corresponding read- ings of the record-wheel R and R\ in proper units. Then we have C = nr' 2 + R and C = nr n + R\ from which 27tr'* = C-\-C -(R+R f ) (8) Having found r' 2 , we can compute n, since r'* = m* + / 2 + 2nl t and m and / can both be obtained from measurement. 28. Forms of Polar Planimeters. — Polar planimeters are made in two forms: I. With the pivot/, Fig. io, fixed. 2. With pivot J movable, so that the arm / between pivot and tracing- point may be varied in length. Since the area is in each case equal to the length of this arm, multiplied by the lineal space R moved through by the record-wheel, we have in the first case, since / is not adjustable, the result always in the same unit, as square inches or square centimeters. In this case it is 38 EXPERIMENTAL ENGINEERING. [§ 2& customary to fix the circumference of the record-wheel and compute the arm / so as to give the desired units. For example, the circumference of the record-wheel is. assumed as equal to 100 divisions, each one-fortieth of an inch, thus giving us a distance of 2.5 inches traversed in one revolu- tion. The diameter corresponding to this circumference is 0.796 inch, which is equal to 2.025 centimeters. The distance from pivot to tracing-point can be taken any convenient dis- tance : thus, if the diameter of the record-wheel is as above, and the length of the arm be taken as 4 inches, the area described by a single revolution of the register-wheel will be 2.5 X 4 = 10.0 square inches. Since there were 100 divisions in the wheel, the value of one of these would be in this case 0.1 square inch. This would be subdivided by the attached vernier into ten parts, giving as the least reading one one-hundredth of a square inch. By mak- ing the arm larger and the wheel smaller, readings giving the same units could be obtained. The formula expressing this reduction is as: follows : Let d equal the value of one division on the record-wheel ; let / equal the length of the arm from pivot to tracing-point ; let A equal the area, which must evidently be either 1, 10, or 100 in order that the value of the readings in lineal measures on the record- wheel shall correspond with the results in square measures. Then by equation (7) we shall have, supposing 100 divisions, IOO dl— A; (8) /= i^ fe> If A = iO square inches and d = ^ inch, 2-5 § 29.I APPARA TUS. ' 39 If A = 10 square inches and d = -fo inch, /-=-* The length of the arm from centre to the pivot has no effect on the result unless the instrument makes a complete revolu- tion around the fixed point E, in which case the area of the zero-circle must be considered. It is evident, however, that this arm must be taken sufficiently long to permit free motion of the tracing-point around the area to be evaluated. The second class of instruments, shown in Fig. 2, are arranged so that the pivot can be moved to any desired posi- tion on the tracing-arm KF, or, in other words, the length can be changed to give readings in various units. The effect of such a change will be readily understood from the preceding discussion. 29. The Mean Ordinate by the Polar Planimeter.— If we let/ equal the length of the mean ordinate, and let L equal the length of the diagram, then the area A = Lp, but the area A = IR [eq, (7)]. Therefore Lp — IR, from which l+L=p-±R (10) In an instrument in which / is adjustable, it may be made the length of the area to be evaluated. Now if / be made equal L, p = R. That is, if the adjustable arm be made equal to the length of the diagram^ the mean ordinate is equal to the reading of the record-wheel, to a scale to be determined. The method of making the adjustable arm the length of the diagram is facilitated by placing a point U on the back of the planimeter at a convenient distance back of the tracing- point F and mounting a similar point Fat the same distance back of the pivot C\ then in all cases the distance UVyriM be equal to the length of the adjustable arm /. The instrument is readily set by loosening the set-screw 5 and sliding the frame 4Q EXPERIMENTAL ENGINEERING. L§ 29. carrying the pivot and record-wheel until the points c^Fare at the respective ends of the diagram to be traced, as shown in Fig. 11. In the absence of the points U and V the length of the diagram can be obtained by a pair of dividers, and the distance of the pivot C from the tracing-point F made equal to ihe length of the diagram. In this position, if the tracing-point be carried around the diagram, the reading will be the mean ordinate of the diagram Fig. -Method of Setting the Planimeter for Finding the Mean Ordinate. expressed in the same units as the subdivisions of the record- wheel ; thus if the subdivisions of this wheel are fortieths of one inch, the result will be the length of the mean ordinate in fortieths. This distance, which we term the scale of the record- wheel, is not the distance between the marks on the graduated scale, but is the corresponding distance on the edge of the wheel which comes 'in contact with the paper. The scale of the record-wheel evidently corresponds to a linear distance, and it should be obtained by measurement or computation. It is evidently equal to the number of divisions in the circumference divided by nd, in which d is the diameter, or it can be obtained by measuring a rectangular diagram with a length equal to /, and a mean ordinate equal to one inch, in which case the reading of the record-wheel will give the num- ber of divisions per inch. A diameter of 0.795 inch, which corresponds to a radius of one centimeter, with a hundred sub- 32-] APPARA TUS. 41 divisions of the circumference, corresponds almost exactly to a scale of forty subdivisions to the inch, and is the dimension usually adopted on foreign-made instruments. 30. The Suspended Planimeter. — In the Amsler sus- pended planimeter as shown in Fig. 12, pure rolling motion without slipping is assumed to take place. The motion of the record-wheel, not clearly shown in the figure, is produced by the rotation of the cylinder c in contact with the spherical Suspended Planimeter. segment R. The rotation of the segment is due to angular motion around the pole O, that of the cylinder c to its posi- tion with reference to the axis of the segment. This position depends on the angle that the tracing arm, ks f makes with the radial arm, BB. The area in each case being, as with the polar planimeter, equal to the product of the length of tracing arm from pivot to tracing point multiplied by a constant factor. 31. The Coffin Planimeter and Averaging Instrument. — This instrument is shown in Fig. 13, from which it is seen that it consists of an arm supporting a record-wheel whose axis is parallel to the line joining the extremities of the arm. This instrument was invented by the late John Coffin, of Johnstown, in 1874. The record-wheel travels over a special surface ; one end of the arm travels in a slide, the other end passes around the diagram. 32. Theory of the Coffin Instrument. — This planimeter may be considered a special form of the Amsler, in which the point P, see Fig. 14, page 43, moves in a right line instead of 42 EXPERIMENTAL ENGINEERING. [§32- swinging in an arc of a circle, and the angle CPT, correspond- ing to B in eq. (1), is a fixed right angle. The differential equation for area therefore is dA=lndd, (il) Fig. 13.— The Coffin Averaging Instrument. and the differential equation of the register becomes dR — ndd s2) Hence, as in equation (7), A = IR (13) §32-] APPARA TUS. 43 That is, the area is equal to the space registered by the record- wheel multiplied by the length of the planimeter arm. This instrument may be made to give a line equivalent to the mean ordinate (M. ) by placing the diagram so that Fig. 14. — Coffin Averaging Instrument. one edge is in line with the guide for the arm ; starting at the farthest portion of the diagram, run the tracing-point around in the usual manner to the point of starting, after which run the tracing-point perpendicular to the base along a special guide provided for that purpose until the record-wheel reads as at the beginning. This latter distance is the mean ordinate. 44 EXPERIMENTAL ENGINEERING. [§ 33* To prove, take as in Art. 29 the M. O. = /, the length of diagram = Z, the perpendicular distance = S. Then A = pL=/R. ......... (14) Let C be the angle, EPT, that the arm makes with the guide, Fig. 8. In moving over a vertical line this angle will remain constant, and the record will be R = 5 sin C. . • . . . . . o (15) For the position at the end of the diagram sin C '= L -f- /; therefore R=SL+L Substituting this in equation (14), pL = IR = ISL + 1 = SL. Hence p = 5 (15^), which was to be proved. . From the above discussion it is evident that areas will be measured accurately in all positions, but that to get the M. O. the base of the diagram must be placed perpendicular to the guide, and with one end in line of the guide pro- duced. It is also to be noticed that the record-wheel may be placed in any position with reference to the arm, but that it must have its axis parallel to it, and that it registers only the perpen- dicular distance moved by the arm. 33. The Willis Planim eter. — This planimeter is of the same general type as the Amsler Polar, but in place of the record - wheel for recording-arm it employs a disk or sharp-edged wheel free to slide on an axis perpendicular to the tracing-arm. The distance moved perpendicular to this arm is read on the graduated § 34-] APPARATUS. 4$ edge of a triangular scale which is supported in an ingenious man- ner, as shown in the accompanying figure. The planimeter-anri can be adjusted as in the Amsler Planimeter so as to read the M. E. P. direct. An adjustable pin, E, is employed for the purpose of setting off the length of the diagram. The mathematical demonstration is exactly as for the Amsler Planimeter, but in this case it is evident that the perpendicular distance which is registered on the scale is independent of the Fig. 14a. — The Willis Planimeter. circumference of the wheel. The only conditions of accuracy- are, that the axis of the scale shall be at right angles to the arm of the planimeter, and that its graduations shall be equal to the area to be measured divided by the length of trie- arm. 34. The Roller-planimeter. — This is the most accurate^ of the instruments for integrating plane areas, and is capable of measuring the area of a surface of indefinite length and of lim- ited breadth. This instrument was designed by Herr Corradi of Zurich, and is manufactured in this country by Fauth & Com- pany of Washington, D. C. A view of the instrument is shown in Fig. 15. The features of this instrument are: firstly, the unit of the vernier is so small that surfaces of quite diminutive size may be determined with accuracy; secondly, the space that can be encompassed bv one fixing of the instrument is very large; thirdly- the 4 6 EXPERIMENTAL ENGINEERING. [§34- results need not be affected by the surface of the paper on which the diagram is drawn ; and, fourthly, the arrangement of its working parts admit of being kept in good order a long time. The frame B is supported by the shaft of the two rollers R X R X , the surfaces of which are fluted. To the frame B are fitted the disk A, and the axis of the tracing-arm F. The whole apparatus is moved in a straight line to any desired length upon the two rollers resting on the paper, while the tracing- point travels around the diagram to be integrated. Upon the shaft that forms the axis of the two rollers R X R X a minutely FlG. 15. — R.OLLER-PLANIMETER* divided mitre-wheel R, is fixed, which gears into a pinion R 2 . This pinion, being fixed upon the same spindle as the disk^4, causes the disk to revolve, and thereby induces the roll- ing motion of the entire apparatus. The measuring-roller E, resting upon the disk A, travels thereon to and fro, in sympathy with the motion of the tracing- arm F, this measuring-roller being actuated by another arm fixed at right angles to the tracing-arm and moving freely between pivots. The axis of the measuring-roller is parallel to the tracing-arm F. The top end of the spindle upon which §35-] APPARATUS. 47 the disk A is fixed pivots on a radial steel bar CC X , fixed upon the frame B. 35. Theory. — The following theory of the roller-plan im- eter is partly translated from an article by F. H. Reitz, in the Zeitschrift fur Vermessungs-Wesen, 1884. According to the general theory of planimeters furnished with measuring-rollers, it is immaterial what line the free end of the tracing-arm travels over ; nevertheless there is some practical advantage in the construction of the apparatus to be obtained from causing that end to travel as nearly as possible in a straight line. Still it is obvious that a slight deviation from the straight line would not involve any inaccuracy in the result. Seeing that the fulcrum of the tracing-arm keeps travelling in a straight line, it appears advisable, in evolving the theory of the apparatus, to assume a rectangular system of co-ordinates, and fix upon the line along which that fulcrum travels as the axis of abscissae. The passage of the tracing-point around the perimeter of a diagram maybe looked upon as being made up of two motions — one parallel to the axis of abscissae and the other at right angles to that axis. Inasmuch as the latter of these two motions, in the direction of the axis of ordinates, is after all but an alternate motion of the tracing-point which takes place in an equal ratio until the tracing-point has returned to its starting-point, no one point of the circumference of the measur- ing-roller is continuously moved forward in consequence of this motion. Therefore it is only necessary to take the differential motion of the tracing-point in the direction of the axis of abscissae into consideration. In Fig. 16 the same letters of reference denote identical parts or organs as in Fig. 15 and the position of the parts in the two figures correspond exactly, the letter D denoting the distance between the fulcrum of the tracing-arm and the axis of the disk A. The amount of motion of a point on the record- wheel E, while the tracing-point travels to the extent of dx> must be determined. If the construction of the planimeter is 48 EXPERIMENTAL ENGINEERING. [§35- correct, this quantity must be the product of a constant derived from the instrument, multiplied by the differential expression for the surface. This latter quantity with reference to rectan- gular co-ordinates is ydx. It is readily seen that as the tracing-point moves an amount equal to dx, a point in the circumference of the rollers R X R X must be shifted the same amount, since the axes of these rollers are parallel to the ordinate y. Any point in the pitch-line of the mitre-wheel R % must move an amount equal to ~^dx. Fig. 16. Suppose that while the tracing-point moves a distance dx % the disk A moves a distance ab, Fig. 10, since this disk is turned foy the mitre-wheel whose pitch-circle is R % , and ad is the dis- tance from record-wheel to the axis of this wheel, we must have R a ad (16) §35-] APPARA TUS. 49 Because of the position of the axis of the record-wheel E> the motion of the disk A to the extent of ab produces a shifting of a point in the circumference of E equal to cb, while the record-wheel slips a distance ac. The distance cb is the reading of the record-wheel and is the quantity required. We have dab = 90 , cag — 90 ; hence caf = a y and fab = fi, and cab = «-)-/?. So that since acb — 90 , cb = ab sin (a -f- /3) = ab (sin a cos fi -J- cos a sin /?). , (17) But it is seen that sin a = jf. Hence cos a = = \A - w' . „ af sin t* m S S" X m X X" AX m AX AX" Gm € e" Um u U" M m M M" 8 8" w m W W" /« J J" Safe Limit. P' * r a s* X' AX' e' U' M' 8' W f Tension. Compression. Shearing, Modulus of Elasticity Et E c E s Area sq. inches F Length, " / Factor of safety n Ordinary moment of inertia / Polar moment of inertia Ip Maximum fibre-distance .e 49. Formulae for Tensile Strength. (Church's Mechanics, pp. 207-221.) — Since in tension the stress is uniformly distrib- uted, we have P=FT; (2) P=r> (3) X € = (4) The modulus of elasticity by definition equals the load per square inch divided by the strain per inch of length, within the elastic limit. Hence p P__P}__ pl X - X - FX " * ° * * 7 K. — iL — t- _ £1 _ (5) § 5I-] STRENGTH OF MATERIALS— GENERAL FORMULAE. 73 Resilience U = mean force X total space = \P"X" = \P"e"l = \T"e"FL But Fl equals the volume V. .\ U= : kT"e"V=\P"e"L . . . . (6) 50. Modulus of Elasticity from Sound emitted by a Wire. — Let / equal the length of the wire, d equal its specific gravity, n equal the number of vibrations per second, v equal the velocity in feet per second. Determine the number of vibrations by comparing the sound emitted, caused by rubbing longitudinally, with that made by the vibration of a tuning-fork. In this manner de- termine the note emitted. The number of vibrations per second can be found by consulting any text-book devoted to acoustics. We shall have finally v = 2nl) also 'Eg W§ from which This result usually gives a larger value by one or two per cent than that obtained by tension-tests, owing to the viscosity of the body. 51. Formulae for Compression-tests. — The compression- tests are of value in determining the safe dimensions of mate- rial subject in use to a crushing or compressive stress. Nearly 7 A EXPERIMENTAL ENGINEERING. [§ 5 1. all bearings in machinery, a portion of the framework, the connecting-rod of an engine, during some portion of a revo- lution, are illustrations of common occurrence, of members strained by compression. Columns and piers of buildings, masonry-walls, are familiar illustrations in structures. The subject is naturally divided into two heads, the strength of short specimens and the strength of long specimens, since the strain is manifestly different in each case. Short Pieces, or those in which the length is not more than four diameters, yield by crushing, and the force acts uniformly over each square inch of area, so that formulae similar to those used in tension apply. (For notation see article 48, page 62.) We have (8) (9) (10) Resilience U. = iP"X" = iP"e"/=iC"e"F/. . . (n) The compression-strain is accompanied with a shearing- strain acting at right angles to the specimen equal to P sin a cos a, being a maximum when a = 45 . Hence, brittle materials tend to fly to pieces at that angle, leaving two pyra- mids with facing points. Long Pieces, in which the length equals ten or twenty diam- eters, yield by bending on the side of least resistance. Rankine's formula is most used for this case (Church's Mechanics, page 374). Breaking-load for flat ends, P i= FC+(i+P F ).. . c . . . (12) p P, — FC: fi — -^.. . * e — -r • --. / p pi PI n < — e - A - FX' * e e • § 51.] STRENGTH OF MATERIALS— GENERAL FORMULAE. 75 Breaking-load for round-ended or two-pin column, I2aj Breaking-load for one round end and one square end orpin and square end, >, = FC+{i+%pQ. ....... (12 9 /£ *) Value of Coefficients as given by Rankine. Coefficients. Cast-iron. Wrought-iron. Timber. € in pounds per sq. inch 80000 I -T- 6400 36000 I -7- 36000 7200 I -T- 3000 Notation in above Formulas, F = area in square inches. /= length in inches. K = radius of gyration. K 2 — I -1- F. See page 7% for values of /. In case the modulus of elasticity is required, Enter's for- mula should be used ; in this p: r = eitz 1 -f. i m for round-ended columns, in which l" = / — - K 9 In' (13) For a column with flat ends, P i " = 4 El7r> + l">; l" = l-Ti. . . .(13a) For a column with one pin or round end and the other end square, />" = \EIn* -j- 1"\ /" = /-*.. . . . (13$) Euler's formula has only been approximately verified by experiment. 76 EXPERIMENTAL ENGINEERING. [§ 52. 52. Transverse Stress. — Theory. — In case of transverse stress the force, or a component of the force, is applied at right angles to the principal dimensions of the material. The material is generally in the form of a beam, and the strains produced make the beam assume a concave form with refer- ence to the direction of the force applied. The result of this is a compression of the fibres nearest the force, and a corre- sponding elongation of those farthest away. The fibres of the beam not strained or deformed by any longitudinal force lie in what is called the neutral axis. The curve which the neutral axis assumes due to the forces acting is termed the elastic curve. The weight carried tends to rupture the beam at right angles to the neutral axis ; this stress is equal to the resultant force acting at any point, and is termed the transverse shear. In addition to this there is a shearing-force tending to move the fibres of the beam with reference to each other in a longitudi- nal direction, which is termed parallel shear; this force is a small one compared with the other forces, and for that reason is difficult to measure experimentally. Formula. — In this case the external load is applied with an arm, and tends to produce rotation ; the result is termed the Moment of Flexure or Bending-moment, which is denoted by M. The internal moment of resistance is equal to pT -r- e, in which p equals the intensity of. strain on the outermost fibre of the piece, I equals the moment of inertia, e equals the distance of the outermost fibre to the neutral axis. Since these moments must be equal, we have M = pf-r-e, . (14) which formula may be used for strength. We also have EI+p = M, (15). which may be used for flexural stiffness (Church's Mechanics, page 250), in (approximately). d*y page 250), in which p = radius of curvature = 1 -=- ~t-\ §52.] STRENGTH OF MATERIALS— GENERAL FORMULAE. 77 Hence ±EI % = M ' < 16 ) which is the differential equation of the elastic curve. To find the external moment M, consider the beam as a lever, subject to action of forces, only on one side of the free section. If we consider A as the amount carried by any abut- ment, or the resistance acting at one end, x the distance to the free section, W the weight of any load or loads between the abutment and the free section, and x' the distance of the point of centre of gravity of these loads to the free section, then by the principles of moments we have the general equation M=Ax- Wx'. ...... (17) In problems relating to the elastic curve assume the general differential equation Find the numerical value of M expressed in terms of one dimension of the beam as variable. Thus, as above, M = Ax — Wx. Select the origin of co-ordinates in such a position that the constants of integration can be determined. Then dy integrate. The first integration will give the value of — - or the tangent of the elastic curve ; the second integration will give j, the ordinate to the elastic curve. The parallel shear is maximum in the neutral axis, and de- creases either way proportionally to the ordinates of a parabola. The value of the parallel shear per unit of section in the neutral axis is area above neu- \ ( the distance of its ] tral axis (or VxK centre of gravity >; (18) below) ) I from that axis, j 78 EXPERIMENTAL ENGINEERING. [§52. in which I is equal to the moment of inertia, J the total trans- verse shear, and b a the thickness of beam in the neutral axis. In the ordinary cases of shearing-forces, such as act on rivets or pins, the intensity is uniform ; this case is considered later. The following tables of moments of inertia, of transverse loads, and of external moments will be useful in working up the results of the experiments. TABLE NO. I. Moments of Inertia. Rectangle, width b, depth h Hollow rectangle, symmetrical Triangle, width = b, height = h.. . Circle of radius r. . Ring of concentric circles Rhombus h — vertical diagonal. . . Square with side (b) vertical Wat 45° Ordinary Moment. /. tV^ 3 A** 3f2 b i h* Polar Moment. AW + A') A** Max. Fibre Dist. r \b \b^2 TABLE NO. II. Formulas for Transverse Loads. Deflection = d. Maximum fibre-strain /. ....... Safe load.. Coefficient R' Relative strength, equal length Relative stiffness, equal load.. . " " safe load. . . . Modulus elasticity Max. shear Cantilevers. With one End Load P -. Wt. of Beam neglected. EI Pie -h 1 R'l -r- le Pie -hi PI* -H 3 dl Pa.t support With Uni- form Load. lV=wl. \WP-h El Wle -4- 2/ ■*R'l -hie Wle -s- 2/ WP -h 8dl W at support Beams with Two Supports. Load P, in Middle. Wt. of Beam neglected. &PP h- EI Pie -4- 4/ 4 R'l -h le Pie h- 4/ Uniform Load. W=wl. PI* -h 4 8*7 \P at supp't &WP + E1 Wle -h 8/ BR'I * le Wle -h 8/ 8 4* V 5^/3-4-384^/ $Wa.t supp't § 5 2 -J STRENGTH OF MATERIALS— GENERAL FORMULAE. 79 a o o >-. o «= x . •2 3 Js s II- H Ho -f- 1 ' & H» H ^ ^ ^ H I Hi M T^H ■H l e e fe|' i ^h * hi .IN g | H H I I ^ >* w S :.S M a; ! z a <*< o g .o 3.-'° «,2 »t 3 ^ & & « h» ~ ~ x So ° •** £ § Jo < ^ •a a> .22 5 S^- lis C »* CO (75 > 6 g || "3 m P^ i 0(33 80 EXPERIMENTAL ENGINEERING. [§ 53« 53. Moment of Inertia by Experiment. — If the body can be suspended on a knife-edge so that it can be oscillated back- ward and forward like a pendulum, its moment of inertia can be found as follows : First, balance the body on a knife-edge, and find experimentally the position of its centre of gravity; denote the distance of the centre of gravity from the centre of suspen- sion by 5. Weigh the body, and compute its mass M; denote its weight by W. Suspend the body on the knife-edge, and set it swinging through a very small arc ; find the time of a single vibration, by allowing it to swing for a long time and divid- ing by the number of vibrations. Let / equal the time in seconds of a single vibration or beat ; let K equal radius of gyration, so that MK a equals moment of inertia. Then, by mechanics, or, by reduction, 7l 2 *'=¥• 09) In this equation K is reckoned from the point of suspension, and the moment of inertia is the moment around the point of suspension. The moment of inertia about a parallel axis through the centre of gravity, may be denoted by MK C \ and we shall have mk; + ms 2 = mk*\ See Weisbach, Vol. I., page 662. § 55-] STRENGTH OF MATERIALS— GENERAL FORMULAE. 8 1 from which and MKf = M(K 2 - S 2 ). 54. Shearing-strain. — This strain acts in a transverse direction, without an arm, and thus tends to produce a square break ; it acts uniformly over the whole section, so that P=SF; S = P+F. (20) The strain produces on the molecules of the material an angular distortion, which is usually expressed in n measure, or the linear length of the degree of distortion to a radius unity, and is denoted by S. Let p s be the stress per square inch. E s =p s + d. . (21) E s is termed the modulus of rigidity. The coefficient of shearing-strength S can be obtained by direct experiments, by using the specimen in the form of pins or rivets holding links together, the links being fitted to go in the machine like tensile specimens, and tensile force applied ; if the specimen is a plate, its resistance to shearing-strain can be found by forcing a punch through, as in compression- strains. The angular distortion cannot be measured directly, but may be determined by tests in torsion, as described. 55. Torsion. — The strain produced by torsion is essentially a shearing-strain on the elements of the specimen. The effect of torsion is to arrange the outer fibres of the specimen into the form of helices, as can readily be seen by examining a test- piece broken by torsion stress ; each one of these fibres makes an angle with its original position or axis of the piece, equal to its angular distortion, or 6, which is expressed in n measure. This has the effect also of moving any particle in the surface of 82 EXPERIMENTAL ENGINEERING. [§ 55. the specimen, through an angle lying in a plane perpendicular to the axis and with its vertex in the axis. This last angle is called a. Letting / equal the length of the specimen, e equal its radius, we have, neglecting functions of small angles, ea — lS, (22) from d = ea-*r L (22a) But since E s =p s -f- #, E s —p s l-^-ea\ (22b) from which E s , the modulus of rigidity, may be computed. Since the external moment of forces is equal to the internal moment of resistance, if we let P equal the external load, a its lever-arm, and I P the polar moment of inertia, we will have P* = (pJ p )~e, (23) from which p s = Pae-T-f p . ...... (24) For a circular rod of radius r 1 , Ia = — — , also e = y. 2 Let the external moment Pa. = M t . Then § 57.] STRENGTH OF MATERIALS— GENERAL FORMULAE. 83 The torsional resilience, or work done, will equal the aver- age load multiplied by the space, or U^iPjLCt. ......... (25) 56. Modulus of Rigidity of a Wire by swinging under Torsion. — The transverse modulus of elasticity, or the modu- lus of rigidity, can be determined by hanging a heavy weight on the wire, and swinging it around a vertical axis passing through its point of suspension. Let /equal its length in feet, r its radius in feet, I P the polar moment of inertia of the swing- ing weight, t the time in seconds of an oscillation. Let E s be the modulus of rigidity. Then E < = 7^ ^ 57. Relation of E s and E t . — Let the distortion in direc- tion of the stress equal e, the angular lateral distortion = 6, the lineal lateral distortion = m ; then f S\ 1 — m tan [45 1 = — — — = 1 — m — e, nearly. But since d is small, tan (45 ° J = 1 — 6, nearly. Hence, by substituting, S = m + e. Now E t = t and E, = il; e o 84 EXPERIMENTAL ENGINEERING. [§ 58. Hence E s € € E t 26 2(m + e) In cast-iron, by experiment, Prof. Bauschinger found for cast-iron m = .236; hence for this case E s = 0.407 E t . 58. Combination of Two Stresses. Intensity of combined Shearing* and normal Stress. — Let q be the intensity of the shearing-stress, which acts on the transverse section and on a parallel section, and let/ be the intensity of the normal stress on the transverse section ; it is required to find a third plane such that the stress on it is wholly normal, and to find r the intensity of that stress ; let this plane make an angle 6 with the transverse section. Then, from equilibrium of forces, (r — p) cos 6 = q sin 0, and r sin = q cos 6. Hence tan 26 = 2q -7- p (27) r = ip± *y + i/v- • • • (28) 58a. Twisting combined with Longitudinal Stress. — In a circular rod of radius r x , a total longitudinal force P\\\ the direction of the axis gives a longitudinal normal stress p 1 = P-r- area =P -r- 7tr?. A twisting-couple M applied to the same rod gives a shearing- stress whose greatest intensity q, = 2M t +- nr*. * Encyc. Britannica, art. " Strength of Materials." § 59-] STRENGTH OF MATERIALS— GENERAL FORMULA?. 85 The two together give rise to a pair of principal stresses, as above, P , /(2MV . 7^ , . ^^iVW+K (29) 59. Twisting combined with Bending. — This important practical case is realized in a crank-shaft. Let P be the force applied to the crank-shaft ; let R be the radius of the crank-shaft ; let B equal the outboard bearing, or the distance between the plane of revolution of the centre of the crank-pin and the bearing. If we neglect the shearing-force, there are two forces acting: a twisting-force M x — PR, and ben ding-moment M^ = PB. The stresses per unit of area on the outer fibre would be p t = 4M 3 -r- nr? (in which r t is the radius of the crank-shaft) from formulae for transverse strength, and p s = 2M X -5- nr* from for- mula for torsion. Combining these as in equation (27), we find for the prin- cipal stress r = 2(M 2 ± VM? + M?) ~ nr!. By substituting values of M x and M % , r=2PiB±VB* + R')+nr!. • • . . (30) The greatest shearing-stress equals p s = 2P\ / B 2 +R*-r-nr!. (31) The axes of principal stresses are inclined so that tan 26 = M x -5- M % = R ~ B. . . . . . . (32) 86 EXPERIMENTAL ENGINEERING. [§ 60. 6o. Thermodynamic Relations.* — Thermodynamic theory shows that heat is absorbed when a solid is strained by opposing and is given out when it is strained by yield- ing to any elastic force of its own, the strength of which would diminish if the temperature were raised. As, for example, a spiral spring suddenly drawn out will become lower in temperature, but when suddenly allowed to draw in will rise in temperature. With an india-rubber band the reverse condition is true, which indicates that the effect of heat is to contract instead of to expand the rubber. From this theory the rise in temperature can be calculated for a- given strain. Thus let / equal the absolute temperature of the body; the elevation of temperature produced by sudden specific stress/ ; let e equal the corresponding strain ; /Joule's equivalent ; k the specific heat of the body under constant stress ; 6 its density. Then •=% <33> in which both *and/ are infinitesimal, or very small quantities. Rubber differs from other material in the relation of strain to stress and consequently in the direction of curvature of the strain diagram. While most materials show a great in- crease in strain after passing the elastic limit, rubber on the contrary shows a decrease. *See paper by Wm. Thomson in Philosophical Magazine 1877, also vol, III, page 814, ninth edition Encyc. Britannica. CHAPTER IV. STRENGTH OF MATERIALS-TESTING MACHINES. 61. Testing-machines and Methods of Testing. — The testing-machines consist essentially of, fin,t, a device for weigh- ing or registering the power applied to rupture material; second, head and clamps for holding the specimen ; third, suit- able machinery for applying the power to strain the specimen ; and fourth, a frame to hold the various parts together, which must be of sufficient strength to resist the stress caused by rupture of the specimen. Machines, are built for applying K-a-iE Fig. 29.— Old Form. Fig. 30.— Thurston, Polmeyer. tensile, compressive, transverse, and torsional stresses ; they vary greatly in character and form ; some are adapted for applying more than one kind of stress, while others are limited to a single specific purpose. Ir> ^11 machines the weighing device should be accurate and sufficiently sensitive to detect any essential variation in the stress, and every laboratory should be provided with means for calibrating testing-machines from time to time ; the weighing system is usually independent of the system for applying power, although in certain early machines a single lever mounted on a fulcrum was used, as shown in Figs. 29 and 30, and in which the power system and weighing system were com- bined, the power applied being measured by multiplying the weight by the ratio of the lever-arms b/a. § 6 1.] STRENGTH OF MA TE RIALS— TESTING-MACHINES. The power system, when independent of the weighing sys- tem, usually consists of a hydraulic press, as shown in Fig. 31, or a train of gears, as shown in Fig. 32. The principal advantage of having the power system independent from the weighing system is due to the fact that under such conditions the stretching of the specimen, which almost invariably takes place, does not affect the accuracy of weighing. The shackles or clamps for holding the specimen vary with the strain to be applied. The clamps for tension-tests usually consist of truncated wedges which are inserted in rectangular Fig. 31. — Hydraulic Press. Fig. 32.— Form of Gearing. openings in the heads of the testing-machines, and between which the specimen is placed. The interior face of the wedges is for flat specimens, plane or slightly convex and serrated, but for round or square specimens is provided with a triangle or V-shaped groove into which the head of the specimen is placed. When the strain is applied to the specimen the wedges are drawn close together, exerting a pressure on the specimen somewhat in proportion to the strain and often injurious to its strength. In many instances shackles with internal cut threads are used, into which specimens provided with a corresponding external thread are screwed ; this latter construction is much preferable to the former, though adding much to the expense of preparing the specimen. It is very important that the shackles should hold the specimens nrmly and accurately in 90 EXPERIMENTAL ENGINEERING. [§6i. the axis of the machine and should not exert a crushing strain which is injurious to the material. General Character of Testing-machines. Testing-machines are classified as vertical or horizontal, depending upon the position of the specimen ; this, however is not an important structural difference, although certain classes of machines are better adapted for the one method of testing than the other. Machines may also be classified as tensive, compressive, or transverse machines, depending upon whether they are better suited to apply one class of stresses than the other, but as the method of testing is generally dependent simply upon the method of supporting the specimen, this classification is of little importance structurally. Machines can Fig. 33.— Wicksteed, Martens, Michaelis, Buckton. perhaps be best classified by the form and character of weigh- ing mechanism, it being generally understood that power may be applied through the medium of gears or by a hydraulic press, as desired, and with any class of machine. Under this classification we have: First, the simple lever machines, forms of which have been shown in Figs. 29 and 30, in which the power for breaking was obtained from the weighing mechanism. Fig. 33 shows a single-lever machine much used at the present time in Eng- land, in which the power is applied to the specimen at B, and the amount of stress is determined by the position of the jockey weight w, and the amount of weight on the poise R. § 6 1 .] S TRENG TH OF MA TERIA L S— TES TING -MA CHINES. 9 1 *§> A single-lever machine in which the lever is of the second order is shown in Fig. 34. The specimen is placed between the fulcrum and the weigh- ing mechanism. The latter consists of a hydraulic cy- linder with diaphragm and attached gauge, and is in- teresting as being the proto- type of the Emery testing- machine. Second, differential-lever machines, one kind of which is shown in Fig. 35 . This consists of a single lever with poise, to which the draw-head is connected by links placed at unequal Fig. 34.— Thomasset. Fig. 35.— Riehle:. distances from the fulcrum. A machine of this form was manufactured at one time by Riehle Brothers.* Third, compound-lever machines. These have been much used in America for the last twenty years, and are manufactured by Riehle Brothers, Olsen, and Fairbanks. In these machines power is usually applied by gearing; at least, such a construc- tion is generally preferred in this country. The diagram, * The forces acting in this machine can be represented by the following equation: Rd -f- we — f + S (af-bg). 9 2 EXPERIMENTAL ENGINEERING. [§6i. Fig. 36, shows the arrangement of levers adopted in the Fair- banks machine. Power is applied at F, specimen is placed at s 9 and the stress is transmitted by the various levers P, E t and c ^0=, ff//////J\$22^ Fig. 36. — Fairbanks Machine. to the weighing-scale. The various fulcrums marked r rest on a fixed support. Fig. 37 shows arrangement of levers adopted in the Olsen and Riehle machines, power being applied to the lower draw-head B, and the stress transmitted through the speci- men by means of the various levers to the weighing-scale w. In this diagram P denotes the position of fixed fulcrums. By placing the specimen between the lower draw-head B and the platform EE, it may be broken by compression B C, iftE=3 TTTti =CF 1 'I A IUp 1TF Fig. 37. — Olskn and RiehlIs. By providing suitable support resting on the platform EE a transverse stress can be applied. Fourth, direct-acting hydraulic machines. Fig. 38 shows a simple form of a hydraulic machine, in which power is applied by liquid pressure to move the piston R, the speci- men being located at s for tension and at a'b f for compression. Machines of this kind have been built of the very largest capacity, as for instance that designed by Kellogg at Athens, Pa., has a capacity of 1,250,000 pounds, and at the Phoenix § 6 1 . ] S TRENG TH OF MA TERIA LS— TES TING-MA CHINES. 9 3 Iron Works has a capacity of 2, 000,000 pounds, while one built by Professor Johnson at St. Louis has a capacity of about 750,000 pounds. In all these machines the stress is measured by multiplying the readings of the gauge by a con- stant depending upon the area of the cylinder, the effect of E D — r -» • Fig. 38. — Kellogg, Johnson. friction being eliminated by keeping the piston rotating, or in other cases neglecting it or determining its amount and cor- recting the results accordingly. Such machines are not adapted for accurate testing, but are suited for testing of a character which permits considerable variation from the correct results. A modified form of the simple hydraulic machine was made by Werder in 1852, having a capacity of 100 tons, the principle of its construction being shown in Fig. 39. In this machine the line of action of the stress is in RF, while that Fig. 39.— The Werder, 1852. of the resistance is in the line Ad which is to one side of RF, These forces are balanced by adjusting the weights on the scale-beam, thus providing means of weighing the force applied to the specimen. Fig. 40 is a sketch of the working parts of the Maillard machine, in which the weighing apparatus consists of a fluid which is put under pressure by means of a diaphragm against 94 EXPERIMEN TA L ENGINEERING. [§ 61. which the stress applied to the specimen reacts. This force is measured on a hydraulic gauge similar in many respects to the weighing apparatus of the Emery testing-machine. Fig. 40. — Maillard. Fifth, the Emery machine. The general principle of the Emery testing-machine is shown in Fig. 41. Fewer is applied by means of the double-acting hydraulic press R so as to break the specimen either in tension or compression, as desired. The specimen is placed at s, and the stress trans- mitted is received, if in tension, first by the draw-head BB, thence transmitted to the draw-head B' B\ thence in turn to Fig. 41. — Emery. the fluid in the hydraulic support v through a frictionless dia- phragm, from which the fluid pressure is transmitted to the vessel with the smaller diaphragm d, the pressure of which is balanced and weighed on the weighing-scale w. If the specimen is in compression the force is transmitted by the draw-head BB to the bottom of the hydraulic support v, thus crowding the hydraulic support and its contents against the diaphragm, which in turn causes a liquid pressure which is measured on the weighing-scale as before. The springs which § 6 1 . ] S TRENG TH OF MA TEE I A LS-TES TING- MA CHINES. 9 $ receive the pressure of the liquid are adjusted by screws rr, connected to the frame, and of sufficient strength to resist the greatest stress applied in compression. In order that the levers of a testing-machine may transmit the force to the weighing poise with as little loss as possible, and in such a manner that a large force can be balanced by a small weight, a knife-edge bearing is in nearly every case pro- vided for each lever. The knife-edge as usually constructed is a piece of hardened steel with a sharp edge which is inserted rigidly in the weighing-lever and rests upon a hardened steel plate fastened to the fulcrum, although in some cases the positions of knife-edge and plate are reversed. The knife-edge should be as sharp as it can be made without crumbling or cut- ting the contact-plate, and it should be kept clean and free from dirt or rust in order to keep the friction at the lowest possible point. In practice the knife-edge is made from 30 to 1 10 degrees, depending upon the load. Machines of the type shown in Fig. 37 have been constructed in which the friction and other losses as shown by trial did not exceed 100 pounds in 100,000. The fulcrums for supporting the levers in the Emery test- ing-machine are thin plates of steel rigidly connected to both the lever and its support, as shown in Figs. 41, 51, and 52. A flexure of the fulcrum-plates is produced by an angular motion of the levers ; but as this motion in practice is small,, and as the fulcrums are very thin, the loss of force is inappre- ciable and all friction is eliminated. The plate fulcrums also possess the advantage of holding the levers so that end motion is impossible, and thus preventing any error in weighing due to change of lever-arm. The peculiar form of the plate ful- crums is such as to be unaffected by dirt ; furthermore in practice a higher degree of accuracy in weighing has been ob- tained than is possible with knife-edge levers. The principal characteristics of the Emery machine are, first, the hydraulic supports, which are vessels filled with a liquid and having a flexible side or diaphragm, which transmits the pressure to a similar support in contact with the weighing apparatus. The 9 6 EXPERIMENTAL ENGINEERING. [§62. detailed construction of an hydraulic support as used in a ver- tical machine is shown in Fig. 50, its method of operation in Fig. 41. Second, the peculiar steel-plate fulcrums, which have been described. These together with excellent work- manship throughout have served to make the Emery testing- machine an instrument of precision with a greater range of capacity and an accuracy far superior to that of any other machine. Fig. 42 gives a perspective view of the Emery machine with the working parts marked the same as in the diagram. Emery Horizontal Machine. In this figure M is the pump for operating the hydrjulic press, hh' the connecting piping, TT screws forming a part of the frame and used for adjusting the position of the press for different lengths of specimens, c which are connected to the specimen and carry two hard ebonite rollers, d, d, which turn on accurately centred spindles. The spindles are prolonged, and support mirrors, g, g, which rotate in the plane of the figure as the spindles rotate. A clip, aa, is fastened to each side of the test-piece at the opposite extremity, and is connected by spring-pieces, 26 EXPERIMEN TA L ENGINEERING. l%7^ with the rollers. The spring-pieces are slightly roughened by file, and turn the rollers by frictional contact, so that the least extension of the test-piece causes a rotation of the mirror through an angle. If a scale be placed at s, s f and telescopes at e, e, the reflection of the scale will be seen in the mirror in looking through the telescope, and any extension of the test- piece will cause a variation in the reading of the scale as seen in the mirror. The apparatus is equivalent to a lever apparatus having for a small arm the radius of the roller^, and for a long arm the double distance of the scale from the mirror. With this instrument it is evidently possible to obtain very accurate measurements, but on the other hand the instru- ment is very cumbrous and difficult to use. The mean of the two readings with the Bauschinger instrument is the true extension of the piece. Professor Unwin obviates the use of two mirrors and two telescopes by attaching clips to the centre of the specimen and having the single mirror revolve in a plane at right angles with the plane passing through the clips and the axis of the specimen. Strolimeyer s Roller Extensometer was designed in 1886. and is a double- roller extensometer similar in principle to Buzby's and Johnson's. The appa- ratus consists of a roller carrying a needle which is centred with respect to a graduated scale. The roller moves between side-bars extending to clips which are fastened to each end of the specimen. The tension between these side-bars can be regulated by a spring with a screw adjustment. The objections to this form of extensometer are due, first, to slipping of side-bars on the roller, and second, to the difficulty in making the roller per- fectly round. Regarding the various forms of extensometers, the writer Fig. 69. — The Strohmeyer Extensometer. §8i.] TESTING-MACHINE ACCESSORIES. 12' would say that his experience has covered the use of nearly every form mentioned, and none have proved to be superior in accuracy to that with the double micrometer-screw, and few can be applied so readily. 79. Wedge-scale. — The wedge-shaped scale, Fig. 67, which could be crowded between two fixed points on the test-piece, was one of the earliest devices to be used. In using the scale two projecting points were attached to the speci- men, and as these points separated, the' scale could be inserted farther, and the distance measured. 80. The Paine Extensometer. — This instrument, shown in Fig. 70, operates on the principle of the bell-crank lever, the long arm moving a vernier over a scale at right angles to the axis of the specimen. It reads by the scale to thousandths of an inch, and by means of the vernier to one ten-thou- sandth of an inch. Points on the instru- ment are fitted to indentations in one side of the test-piece, and the instrument is held in place by spring clips. It is of historical importance, having been invented by Col- onel W. H. Paine, and used in the tests of material for the Brooklyn Bridge, and also on the cables of the Niagara Suspension Bridge when, a few years since, the question of its strength was under investigation. 81. Buzby Hair-line Extensometer. — This is an extensometer in which the strain is utilized to rotate a small friction-roller connected with a graduated disk as shown in Fig. 71. A projecting pin placed in the axis of the graduated disk is held between two parallel bars, each of which is connected FlG - 7°. to the specimen. The strain is magnified an amount propor- 128 EXPERIMENTAL ENGINEERING. [§ tional to the ratio of diameters of the disk and pin. The amount of strain is read by noting the number of subdivisions of the disk passing the hair-line. To prevent error of parallax in reading, a small mirror is placed back of the graduations, and readings are to be taken when the graduations, the cross- hair, and its reflection are in line. In the late styles of this Fig. 71. — Buzby Hair-line Extensometer. Y\c. 72.— The RiehlIs Extensometer. instrument the disk is made of aluminium, with open spokes, to reduce its weight. To operate this instrument it is only necessary to clamp it to the specimen, to adjust the mirror and cross-hair, and then to revolve the disk by hand until the zero-line corre- sponds with the cross-hair and its reflection. Stress is then applied to the specimen, and readings taken as desired in the manner described. The Riehle' Extensometer. — The Riehle extensometer is a combination of compound levers which are attached to both sides of the specimen, and arranged so that one side carries a scale and the other a vernier. It is only mechanical in opera- tion, and can be used on specimens varying in length from 6 to 8 inches. It is adjusted to the specimen by the clamp screws in the usual manner, and the ends of the graduations are then brought together at zero at both sides at the same time. Pressure is then applied to the specimen and the §82.] TES TING-MA CHINE A CCESSORIES, 129 readings taken in the same manner as any scale and vernier, the scale being graduated to thousandths and the vernier to ten thousandths. Johnson s Extensometer. — Johnson's extensometer, shown in Fig. 73, is a modification of the Strohmeyer, the elongation being de- noted by the motion of a needle over a graduated scale. The elongation for each side is shown separately, and the alge- braic sum of the two readings gives the total elongation. 82. Thurston's Extensometer This extensometer was designed by Prof. R. H. Thurston and Mr. Wm. Kent, and was the first to employ two microm- eter-screws, at # equal distances from the axis of the specimen. These were con- nected to a battery and an electric bell in such a manner that the contact of the micrometer-screws was indicated by sound of the bell. The method of using this instrument is essentially the same as that of the Henning and Marshall instrument, to be described later. With instruments of this nature a slight bending in the specimen will be corrected by taking the average of the two readings. The accuracy of such extensometers depends on — 1. The accuracy of the micrometer-screws. 2. The screws to be compensating must be two in number, in the same plane, and at equal distances from the axis of the specimen. 3. The framework and clamping device must hold the mi- crometers rigidly in place, and yet not interfere with the ap- plication of stress. 83. The Henning Extensometer. — This instrument, which was designed by G. C. Henning and C. A. Marshall, is shown in Fig. 74- It is constructed on the same general principles as the Fig. 73.— Johnson's Exten- someter. no EXPERIMENTAL ENGINEERING^ [§83- Thurston Extensometer, but the clamps which are attached to the specimen are heavier, and are made so that they are held firmly in position by springs up to the instant of rupture. This extensometer is furnished with links connecting the two parts together. The links are used to hold the heads exactly eight inches apart, and are unhooked from the upper head Fig. 74.— The Henning Micrometer. before stress is applied to the specimen. The micrometer is connected to an electric bell in the same manner as the Thurston extensometer. Henning 's Mirror Extensometer \* — In 1896 Gus. C. Henning designed a mirror extensometer differing in several particulars from that of Bauschinger. The instrument is intended for accurate measurements of the extension or compression on both sides of the test-piece within the elastic limit, and is said to fulfil the following conditions: (a) It is applicable for measures of extension or compression, (b) Readings in either direction, negative or positive, can be taken without interrup- tion or adjustment. (•;) The instrument is free from changes of shape during the test, (d) There is neither slip nor play of the working parts. * See Transactions American Society Mechanical Engineers, vol. xviii. §84-] TEST1NGMA CHINE A CCESSORIES. 131 The instrument consists of two parts; the first is a telescope provided with levelling-screws, mounted on a horizontal and vertical axis and furnished with supports tor two linear scales, which may be arranged so that the reflection will show in mirrors attached to the specimen. The second part consists of a frame which can be fastened to the test-specimen near one end by opposite-pointed screws, and which is connected to spindles carrying the mirrors by spring side-bars. A portion of each mirror-spindle is double knife-edged, and when adjusted Fig. 75. — The Marshall Extensometer Fig. 76. — Jenning's Extensometei is brought in contact on one side with the test-piece, and on the other with the spring side-bar. The elongation of the test-piece causes an angular motion of the mirror, which in turn causes a multiplied motion of the reflection of the scale as seen from the telescope. The mirrors are so arranged that the reflections from both scales can be seen continually and without adjustment of the telescope, and the apparatus as a whole has fewer parts and is more readily adjusted than the Bauschinger. It is limited to a total elongation of about 0.04 inch and hence is accurate only for measurements within the elastic limit. 84. The Marshall Extensometer. — This extensometer, shown in Fig. 75> is the latest design of the late Mr. C. A. Marshall. Its principal difference from the Thurston exten- 132 EXPERIMENTAL ENGINEERING. [§85. Fig. 77- someter is in the convenient form of clamps, which are well shown in the cut, and in the spring apparatus for steadying the lower part. The micrometer-screw used with this instrument has a motion of only one inch. When the motion exceeds the range of the micrometer-screws, the movable bars BP, B'P r are changed in position, and a new series of readings taken with the micrometer- screw. To facilitate the change of posi- tion of these bars, and allow the microme- ter-screw to return to zero at each change, the arrangement shown in Fig. 77 is adopted, which consists of a nut to which is attached a slotted taper-screw, on which screws a second nut, which serves to clamp the lower nut to the bar ; by turning the lower nut when clamped, the desired adjustment can be made. The following are the directions for use : Run wire (Fig. j6) from one terminal of battery to lower clamp at A, from B and B' to binding-post C on the electric bell, from the other binding-post marked D to switch E, and from there back to the other terminal of battery. To measure strain, screw up micrometer-screws at P and P' until each of them makes connection and bell rings; then take the readings on both sides. 85. Boston Micrometer Extensometer. — This instru- ment consists, as shown in Fig. 78, of the graduated microm- eter-screw, reading in thousandths up to one inch, and having pointed extension-pieces attached, for gauging the distance between the small projections on the collars fastened to the specimen at the proper distance. These collars are made partly self-adjusting by the springs which help to centralize them. They are then clamped in place by means of the pointed set-screws on the sides, and measurements are made between the projections on opposite sides of the specimen and com- pared, to denote any changes in shape or variations in the two sides. 86.] TESTING-MA CHINE A CCESSORIES. 13. The Brown and Sharpe micrometer can readily be used with similar collars,thus forming an exten- someter ; .the accuracy of this form is considerably less than those in which the micrometers are fixed, but it will, however, be found with careful handling to give good results. Of the various extensometers de- scribed, the Paine, Buzby, Marshall, and Riehle are manufactured by Riehle Bros., Philadelphia ; the Thurston, by Olsen of Philadelphia ; the others, by the respective de- signers. 86. Combined Extensometer and Autographic Apparatus. — An extensometer designed by the author, and quite extensively used in the tests of materials in Sibley College, is shown in Fig. 80 in ele- vation and in Fig. 81 in plan. In this extensometer micrometers of the kind shown in Fig. 22, Article 42, p. 60, with the addition of an exten- sion-rod for holding, are used. This rod sets into a socket A, which holds the micrometer in position. Read- ings are taken on the thimble B, as explained on p. 52. Connections are made with bell and battery at m, n, and m\ n', so that contact of the micrometer- screws is indicated by sound. The construction of the clamp- ing device is fully shown in the plan view, Fig. 81. The principal peculiarity of this extensometer consists in the addition of four pulleys, C lt C 2 , C % and C A , which are arranged so that a cord ab can be fastened at C 3 and passed down and around the pulley C lf thence over the guide-pulley W, Fig. 81, to pulley £T 2 , thence over the pulley C K , and thence to a paper Fig. 7 8. 134 EXPERIMENTAL ENGINEERING. [§86. drum. It is at once evident that any extension of the speci- men SS' will draw in the free end of the cord at twice the rate of the extension ; moreover, any slight swinging or rock- ing of the extensometer head will produce compensating effects on the length of the cord. By connecting the free end of the cord to a drum, the drum will be revolved by the stretch Fig. 80. Fig. 8i. of the specimen. As this work may be done against a fixed pull, there may be a uniform tension on the cord so that the motion of the drum would be uniform and proportional to the stretch. A pencil is moved along the axis of the drum pro- portional to the motion of the poise. An autographic device constructed in this way has given excellent diagrams, and in addition has served as an extensom- eter for accurate measurements of strain within the elastic limits. Wire has been used to connect extensometer to drum in place of the cord with success. A suggested improvement is § 87-1 TESTING-MACHINE ACCESSORIES. I 35 to rotate the drum by the motion of the poise, and to move the pencil by the stretch of the material, using two pencils, one of which is to move at a rate equal to fifty times the strain, the other at a rate equal to five times the strain ; thus producing two diagrams — one on a large scale, for use in deter- mining the strains during the elastic limit; the other on a small scale, for the complete test. 87. Deflectometer for Transverse Testing. — Instru- ments for measuring the deflection of a specimen subjected to transverse stress are termed deflectometers. The deflectometer usually used by the author consists of a light metal-frame of the same length as the test-piece, and arched or raised sufficiently in the centre to hold a micrometer of the form used in the extensometer described in Article 86, above the point to which measurements are to be taken. In using the deflectometer it is supported on the same bearings as the test-piece, and measurements made to a point on the specimen or to a point on the testing-machine which moves downward as the specimen is deflected. This instrument eliminates any error of settlement in the supports. A steel wire is sometimes stretched by the side of the specimen, and marks made on the specimen showing its original position with reference to the wire. The deflection at any point would be the distance from the mark on the specimen to the corre- sponding point on the wire. The cathetometer, see Article 43, page 63, is very useful in determining the deflection in long specimens. The deflection is often measured from a fixed point to the bottom of the specimen, thus neglecting any error due to the settlement of the supports. One of the most use- ful instruments of this kind is made by Riehle Bros., and is shown, together with the method of attachment, in Fig. 82. Fig. CHAPTER V. METHODS OF TESTING MATERIALS OF CONSTRUCTION. Standard Methods. — The importance of standard methods of testing material can hardly be overestimated if it is desired to produce results directly comparable with those obtained by other experimenters, since it is found that the re- sults obtained in testing the strength of materials are affected by methods of testing and by the size and shape of the test- specimen. To secure uniform practice, standard methods for testing various materials have been adopted by several of the engineering societies of Germany and of the United States, as well as by associations of the different manufacturers. The general and special standard methods adopted by these asso- ciations form the basis of methods described in this chapter. 88. Form of Test-pieces. — The form of test-pieces is found to have an important bearing on the strength, and for this reason engineers have adopted certain standard forms to be used. The form recommended by the Committee on Standard Tests and Methods of Testing, of the American Society of Mechanical Engineers is as follows:* " Specimens for scientific or standard tests are to be pre- pared with the greatest care and accuracy, and turned accord- ing to the following dimensions as nearly as possible. The tension test-pieces are to have different diameters according to the original thickness of the material, and to be, when ex- pressed in English measures, exactly 0.4, 0.6, 0.8, and 1.0 inch in diameter; but for all these different diameters the angle, but * See Vol. XL of Transactions. 136 §88.] TESTING MATERIALS OE CONSTRUCTION. 17 not the length, of the neck is to remain constant. This neck is a cone, not a fillet connecting the shoulders and body. The length of the gauged or measured part to be 8 inches, of the cylindrical part 8.8 inches. The length of the coned neck to be 2i times the diameter, increasing in diameter from the cylindrical part to \\ times the cylindrical part. The shoul- ders to have a length equal to the diameter, and to be con- nected with a round fillet to a head, which has a diameter equal to twice that of the cylinder, and a length at least ij the diameter. Fig. 83 shows the form of the test-piece recommended for tension ; the numbers above the figure give dimensions in S-25-4-20-4* 50— "^ 2 20 millimetres-—*- 4" 5 <> *< \r-i- ) r\— f— • * z± 20>|*-25-* Millet 0.1 R. ! U.fr»+-- — 2 4 1 *"""" ' 8.8-inches 4« 2 » <0.8+--l— »J Fig. 83.— Standard Test-piece in Tension. millimeters, those below in inches. For flat test-pieces the shape as shown in Fig. 84 is recommended : such specimens -*f-i2*fc i— . n -^12*- \J- |*W 8.8- rv Fig. 84.— Test-piece for Flat Specimens. are to be cut from larger pieces ; the fillets are to be accurately milled, and the shoulders made ample to receive and hold the full grip of the shackles or wedges. The length for rough bars is to remain the same as for fin ished test-pieces, but the length of specimen from the gauge- mark to the nearest holder is to be not less than the diameter 138 EXPERIMENTAL ENGINEERING. [§89. of the test-piece if round, or one and a half times the greatest side if flat. For commercial testing the standard form cannot always be adhered to, and no form is recommended.* It is recommended in all cases that the specimens be held by true bearing on the end shoulders, as gripping or holding devices in common use produce undesirable effects on the cylindrical portion of the specimen. The forms of test-specimens which have been heretofore used are somewhat different from the standards recommended. These forms are shown in Fig. 85, No. 1 to No. 5, and are as follows : No. i. Square or flat bar. at rolled. J 6 To 20- No. 2. Round bar, as roiled. No. 3. Standard shape for flats of ,;'.,;■ squares. Edges must < B 2a ^ be smooth and true. Fil- lets, one half inch radius. "i. g ^, Specimens not over three BETWEEN FILLETS inches wide. 1 61 20 ^ No. 4. Standard shape for rounds. - gtt -,. ft. 11 No: 5. Government shape for marine-boiler plates only. Not in general use, as it gives too high a test. Fig. 85.— /orms of Specimen for Tensile Strains formerly used. $9. Test-pieces of Special Materials. — Wood. — Wood is a difficult material to test in tension, as the specimen is likely to be crushed by the shackles or holders. The author has had fairly good success with specimens, made with a very large bearing-surface in the shackles, of the form shown in Fig. 84, * A discussion of the effect of varying proportion of test-pieces is given in Thurston's ■• Text-book of Materials," pages 356-7- §8 9 -] TESTING MATERIALS OF CONSTRUCTION, '39 page 137 for flat specimens, but with the breadth of the shoul- ders or bearing-surfaces increased an amount equal to one half the diameter of the specimen over that shown in Fig. 84. Cast-iron. K — Cast-iron specimens of the usual or standard forms are very likely to be broken by oblique strains in tension tests much before the true breaking-point has been reached. To insure perfectly axial strains Riehle Bros, propose a form of specimen shown in Fig. 86, A, B, and C, cast with an enlarged Fig. 86.— Proposed Form for Cast-iron Specimens. head, the projecting portion of which, as shown in C, has a knife-edge shape. The specimen is carried in holders o«" shackles, A and B, which rest on knife-edges extending at right angles to those of the specimen. This permits free play of the specimen in either direction, and renders oblique strains nearly impossible. Chain, — In the case of chain, large links are welcjed at the ends, as shown in Fig. 87 ; these are passed through the heads of the testing-machine and held by pins. v 1 -^ liyi^riiiTfeni' ^tj Fig. 87.— Chain Test-piece. 4o EXPERIMENTAL ENGINEERING. L§89- Hemp Rope. — A similar method is used in testing hemp rope, the specimen being prepared as shown in Fig. 88. Fig. -3.o?e Test-piece. Special hollow conical shackles have also been used for hold- ing the rope with success. Wire Rope. — Wire-rope specimens may be prepared as shown in Fig. 89, or they may be prepared by pouring a mass Fig. 89.— Wire-rope Test-piece. of melted Babbitt metal around each end and moulding into a conical form, taking care that the rope is in the exact centre of the metal. Cement. — Cement test-pieces for tension are made in moulds and permitted to harden for some time before being tested. It is found that the strength is affected by the form 6f the speci- Fig. 90. — Old C E. Standard Specimen for Cement. men, by the amount of water used, and by the method of mix- ing the cement. To get results which may safely be compared, it is necessary to have the test-specimens or briquettes of exactly the same form, and pulled apart in shackles or holders 5 89.] TESTING MATERIALS OF CONSTRUCTION. I 4 I which exert no side strain whatever, and the strain applied uni- formly and without any jerky motion. Various standard forms of briquettes have been employed; the one most used in America prior to 1904 is shown full size in Fig. 90. That recently adopted is shown half size in Fig. 94. Fig. 91. — Cement Moulds and Briquettes. The form of the mould for making the briquettes, and the holders or shackles generally used, are shown in Figs. 91 to 93. J DETAILS FOR GANG MOULD Fig. 92. FORM OF CLIP DETAILS FOR BRIQUETTE Fig. 93. Fig. 94. Standard Clip and Briquette adopted by the American Society for Testing Materials, 1904. The gang-mould, as shown in Fig. 92, consisting of several moulds united in one construction, is preferred when numerous briquettes are to be made. 142 EXPERIMENTAL ENGINEERING. [§ 90. Standard revised specifications for testing cement were adopted by the American Society of Civil Engineers and approved by the American Society of Testing Materials, 1904. The form of briquette adopted is shown in Fig. 94, which differs from the earlier form principally in the use of rounded instead of sharp corners, as noted by comparing Figs. 90 and 94. 90. Compression-test Specimens — Test-pieces. — Test- pieces are in all cases to be prepared with the greatest care, to make sure that the end surfaces are true parallel planes normal to the axis of the specimen. 1. Short Specimens. — The standard test specimens are to be cylinders two inches in length and one inch in diameter, when ultimate resistance alone is to be determined. 2. Long Specimens. — For all other purposes, especially when the elastic resistances are to be ascertained, specimens one inch in diameter and ten or twenty inches long (see No. 2, Fig. 85) are to be used. Standard length on which strain is to be meas- ured is to be eight inches, as in the tension-tests. Greatest care must be taken in all cases to insure square ends and that the force be applied axially. The specimens are to be marked and the compression meas- ured as explained for tension- test pieces, page 126. 91. Transverse-test Specimens. — For standard trans- verse tests, bars one inch square and forty inches long are to be used, the bearing blocks or supports to be exactly thirty-six inches apart, centre to centre. For standard or scientific tests of cast-iron, such bars are to be cut out of a casting at least two inches square or two and a quarter inches in diameter, so as to remove all chilling effect. For routine tests, bars cast one inch square may be used, but all possible precautions must be taken to prevent surface-chilling and porosity. Test-bars of wood are to be forty inches in length, and three inches square in section. 92. Torsion-test Specimens. — For standard tests, cylin- drical specimens with cylindrical concentric shoulders are to be used; the two are connected by large fillets. The specimen §93*1 TESTING MATERIALS OF CONSTRUCTION. 1 43 is to be held in the chuck or heads of the machine by three keys, inserted in key-ways \ inch deep, cut in the shoulder. 93. Elongation — Fracture. — The character of the fracture often affords important information regarding the material. The structure of the fractured surface should be described as coarse or fine, either fibrous, granular, or crystalline. Its form, whether plane, convex, or concave, cup-shaped above or below, should in each case be stated. Its location should be accu- 19 18 17 16 15 14 13 Fig 95. *ately given, from marks on the specimen one half inch or less apart. The reduction of diameter which accompanies fracture should be accurately measured. Accompanying the report should be a sketch of the fractured specimen. Fracture occurs usually as the result of a gradual yielding of the particles of the specimen. The strain, so long as the .stress is less than the maximum load, is distributed nearly uni- formly over the specimen, but after that point is passed the dis- tortion becomes nearly local ; a rapid elongation with a corre- sponding reduction in section is manifest as affecting a small portion of the specimen only. This action in materials with sensible ductility takes place some little time before rupture; in very rigid materials it cannot be perceived at all. This peculiar change in form is spoken of as " necking." The drawing Fig. 95 shows the appearance of a test speci- men in which the " necking " is well developed. Rupture occurs at b— b, a point in the neck which may be near one end of the specimen. In order to measure the elongation of the specimen fairly, a correction should be applied, so that the reduced elongation shall be the same as though the stretch either side of the point 144 EXPERIMENTAL ENGINEERING. [§ 94* of rupture were equal. This can only be done by dividing up the original specimen into equal spaces, each of which is marked so that it can be identified after rupture. Supposing that twenty spaces represent the full length be- tween gauge-marks : then if the rupture be nearest the mark o, Fig. 95, three spaces from the nearest gauge-mark, the total length to compare with the original length is o to 3 on the right, plus o to 10 on the left, plus the distance 3 to 10 on the left. These spaces are to be measured, and the sum taken as the total length after rupture. The stretch is the difference between this and the original length ; the per cent of stretch, or elongation, is the stretch divided by the original length. This method is stated in a general form as follows : Divide the standard length into m equal parts, and repre- sent the number of these parts in the short portion after rupture hy s. Note two points in the long portion, A and B, at s and ^m divisions respectively from the break. Lay the parts to- gether, and measure from the gauge-mark in the short por- tion to point A. This distance increased by double the measured distance from A to B gives the total length after rupture. Subtract the original length to obtain the total elon- gation: thus the elongation of the standard m parts will be obtained as though the fracture were located at the middle division. 94. Strain-diagrams. — The results of measurements of the strain should be represented graphically by a curve termed a strain-diagram. Strain-diagrams are drawn (see Art. 46, page 70) by taking the loads per square inch (/>) as ordinates, and the relative stretch or strain (e) to a suitable scale as abscissae. The curve so formed will be a straight line from the origin to the elastic limit, and the tangent of the angle that it makes with the axis of X {p -f- e = E) will be proportional to the modulus of elas- ticity. The area included between the axis of X and that por- tion of the curve preceding the elastic limit will represent the Elastic Resilience or work done by the resistance of the material to that point. §95*] TESTING MATERIALS OF CONSTRUCTION. I45 Autographic Strain-diagrams are drawn automatically on a revolving drum. In most machines the drum is revolved by the stretch of the material and a pencil is moved parallel to its main axis and proportional to the motion of the weigh- ing poise, although in some devices for drawing autographic diagrams the drum is actuated by the poise motion, the pencil by the stretch. The Olsen autographic apparatus is described in Article 71, Figs. 56 to 60, page 11 1. This apparatus is very perfect in all its details, and produces a diagram similar to that shown in Fig. 96. The ordinates on this diagram are proportional to the load, the abscissae to the strain. The lines are straight and nearly vertical until the yield-point ; then for a time the strain rapidly increases, with little increase of stress as shown by the line of stress ; this is followed by an increase of both stress and strain, until the point of maximum loading is reached. After passing the elastic limit the strain increases very rapidly, the stress but little. The autographic attachment is a valuable addition to a testing-machine, especially if its use does not interfere with the measurement by micrometers ; but if the scale of the dia- gram does not exceed five or ten times that of the actual strain, it is of value only in showing the general character of the strain, and is not to be considered of value in obtaining coefficients or moduli within the elastic limit. TENSION TESTS. 95. Objects of Tension Tests. — Tension tests are con- sidered valuable as affording information of the qualities of material, and a certain tensile strength is required of nearly all materials used, even though in practice they may be sub- jected to different kinds of strain. The breaking-strength is frequently specified within limits, and is to be accompanied with a certain amount of ductility. Directions for Tension Tests. — Examine the test-piece care. §950 TESTING MATERIALS OF CONSTRUCTION. 14/ fully for any flaw, defect, irregularity, or abnormal appearance, and see that it is of correct form and carefully prepared. In- dentations from a hammer often seriously affect the results. In wood specimens, abrasions, slight nicks at the corners, or bruises on the surface will invariably be the cause of failure. Next, carefully measure the dimensions, record total length, gauge-length (or length on which measurements of strains are made), also form and dimensions of shoulders. Divide the specimen between the gauge-marks into inches and half inches, which may be marked with a special tool, or by rubbing chalk on the specimens and marking each division with a steel scratch. Fig. 97. — Laying-off Gauge. A special gauge as shown in Fig. 97 is convenient for this pur- pose. These marks serve as reference points in measuring the elongation after rupture, and this elongation should be meas- ured, not from the centre of the specimen, but from the point of rupture either way, as explained in Art. 93, page 143. See that the testing-machine is level and balanced before each test ; insert the specimen in a truly axial position in the machine by measuring carefully its position in two directions, and by applying a level. Calculate from the known coefficients of the material the probable load at elastic limit. Take one tenth of this as the increment of load. The Committee on Standard Tests, American Society of Mechanical Engineers, recommend that the increment be one half or one third that of the probable load at the elastic limit, thus giving larger strains but fewer observations. Apply one increment of load to the specimen before measurements of elongation are made, since by loading specimens up to 1000 or 2000 pounds per square inch the effect of initial errors, such as occur generally at the com- mencement of each test, are lessened. The auxiliary apparatus 148 EXPERIMENTAL ENGINEERING. [§0. adjusts itself somewhat during this period of loading, and the specimen assumes a true position should any slight irregularity exist. 96. Attachment of Extensometer. — Attach the auxiliary apparatus for measuring stretch, or obtaining autographic dia- grams. The method of attaching extensometers will depend on the special form used (see Articles 80 to 86), but this act should always be carefully performed, and the specimen exactly centred in the extensometer, and the gauge-points arranged 8 inches apart. The following directions for applying and using the Henning extensometer will serve to show the method to be used in all cases. The Henning extensometer (see Article 83, Fig. 74, page 130) is attached and used as follows: Before attaching the in- strument, adjust the knife-edges in the clamps by means of the two milled nuts so that they are equally distant from the frame and not so far apart as the diameter of the test-piece. Then, since the springs acting on the knife-edges are of equal strength, the instrument will adjust itself in the plane of the screws symmetrically with respect to the test-piece. Advance or withdraw the set-screws until their points are equally distant from the frame and far enough apart to admit the test- piece. Separate the upper portion of the instrument, put it around the test-piece (already inserted in the machine) near the upper shoulder, with the smaller part to the right, force together and fasten securely. Advance the set-screws simultaneously until their points indent the test-piece. Separate the lower portion, put it around the test-piece with the vertical scales to the front, force together and secure. Hang the links on the proper bear- ings on both portions of the instrument. Then advance the set-screws as above. Throw the links out, take readings of the micrometers, apply the first increment of load, and proceed with the test as directed. To read the micrometers make the electrical connections ; advance one micrometer until the bell rings announcing contact, back off barely enough to stop ring, ing, and advance the other until the bell rings. Back off as § 9 8 -] TESTING MATERIALS OF CONSTRUCTION. 1 49 before, and read both micrometers. The vertical scale and the micrometer head are graduated so that readings to i-o-$nF inch can be obtained directly. 97. Tension Test. — The test is made by applying the stress continuously and uniformly without intermission until the instant of rupture, only stopping at intervals long enough to make the desired observations of stretch and change of shape. The stress should at no time be decreased and re- applied in a standard test, but should be maintained continu- ously. The auxiliary apparatus for measuring strain must be removed before rupture takes place, except it is of a character not likely to be injured. It should usually be taken off very soon after the elastic limit is passed ; although for ductile material it may be left in place for a longer time after the elastic limit has been passed than for hard and brittle materials. The material is then to be loaded until fracture takes place, keeping the beam floating, after which the distortion for each part is to be measured by comparison with the reference divi- sions on the test-piece, measured from the point of rupture as previously explained. It is to be noted that measurements within the elastic limit are of especial importance, since materials in use are not to be strained beyond that point. 98. Report. — Remove the fractured piece from the machine ; make measurements of shape, external and fractured surface ; give time required in making the test.* When fracture is cup- shaped, state the position of cup — whether in upper or lower piece. In recording the results of tests, loads at elastic limit, at yield-point, maximum, and instant of rupture are all to be noted. The load at elastic limit is to be that stress which produces a change in the rate of stretch. The load at yield-point is to be that stress under which the rate of stretch suddenly increases rapidly. * See Report of Committee on Standard Tests, Vol. XL, Am. Society Mech. Engrs. 150 EXPERIMENTAL ENGINEERING. [§ 98. The maximum load is to be the highest load carried by the test-piece. The load at instant of rupture is not the maximum load carried, but a lesser load carried by the specimen at the instant of rupture. In giving results of tests it is not necessary to give the load per unit section of reduced area, as such figure is of no value; (1) because it is not always possible to obtain the load at in- stant of rupture ; (2) because it is generally impossible to obtain a correct measurement of the area of section after rupture; (3) lastly, because the amount of reduction of area is principally dependent upon local and accidental conditions at the point of rupture. The modulus or coefficient of elasticity is to be deduced from measurements of strain observed between fixed increments of load per unit section ; between 2000 pounds per square inch and 12,000 pounds per square inch; or between 1000 pounds per square inch and 11,000 pounds per square inch. With this precaution several sources of error are avoided, and it becomes possible to compare results on the same basis. In the report describe the testing-machine and method of testing, form and dimensions of specimen, character and posi- tion of rupture. Calculate coefficients of elasticity, maximum strength, breaking-strength, strength at elastic limit, and resili- ence, and submit a complete log of test. Also, draw a strain- diagram on cross-section paper ; make a sketch of surface of rupture. The curve of stress and strain is to be drawn as follows : Plot a curve of stress and strain up to a point beyond the elastic limit, using for ordinates values of /, on the scale I div. == 2000 lbs. per sq. in., and for abscissae values of e, on the scale 1 div. = 0.0001"; compute E and/. Then plot the complete curve of stress and strain to the point of rupture, using scales of I div. = 10,000 lbs. per sq. in., and 1 div. = 0.01 inch for ordinates and abscissae, respectively. A blank form for the log is shown below, which is to be filled out and filed. On this log is to be entered, value of the §98.] TESTING MATERIALS OF CONSTRUCTION. 151 modulus of elasticity, load at elastic limit, character of rupture, area of least section, and measurements between each mark made on the specimen. The following form is used by the author for both tension and compression tests : Test of by. Kind of Test Material from Machine used Time of Testing min. Date 189 Tempt degrees F. No. Load. Micrometer- readings. Extension. Actual. P Per sq. in. P I II Mean. Actual. k Difference. Per in. e Modulus Elasticity. E Original length in. Diameter in. Area sq. in. Final " in. Diameter in. Area. " Form of section Fracture: position ; character.. Moduli: resilience ; breaking-strength Load per sq. inch: elastic limit max breaking Equivalent elongation for 8 inches inches per cent. Elongation Reduction area per cent. Local elongation each half-inch, from top, 1st ; 2d ; 3d ; 4th ; 5th ; 6th ; 7th ; 8th ; 9th ; 10th ; nth ; 12th ...; 13th ; 14th ; 15th ; 16th The following form, from Vol. XL Trans. American Society Mech. Engineers, is excellent for reporting the principal results of a series of tests. Attention is called to the full descriptions accompanying the report. 152 EXPERIMENTAL ENGINEERING. L§98. V) W 5 S. 5 V cu U * ^ o IT 2 « 5 ** ■^•2 <2^ 2 £ 5 "5 ■3a ^ S C 8 CO 3 O u BO 3 O u CD *J 5« C73 1 u V S W c o ■a .O J g «« rt '35 "3 5 5*0 J3 ^1 5-a &3 3 1) 3 S-. •r u5 u ^ >nU E 1 73 CO 4J M "co • S3 3 -a cu CO o 2 u £ COMPRESSION-TESTS. 99. Methods of Testing by Compression. 1. Short Pieces : Method of Testing. — In case of short pieces, measure- ments of strain cannot be made on the test-piece itself, but must be made between points on the heads of the testing- machine. It is necessary to ascertain and make a correction for the error due to the yielding of the parts of the testing- machine. This is done as follows: Lower the moving-head until the steel compression-plate presses on the steel block in the lower platform with a force of about 500 pounds. Attach the micrometers to the special frame, which is supported by the upper platform, and read to a point on the movable head. With load at 500 pounds, read both micrometers. Apply loads by increments of 1000 pounds up to three fourths the limit of the machine, taking corresponding readings. Plot a curve of loads and deflections with ordinates 1 long division = 1000 pounds, and abscissae I long division = 0.001 inch. From this curve obtain corrections for the deflections caused by the loads used in the compression-test. In making the test calcu- late the increment of load as explained for tensile strain, Arti- cle 98. Conduct the experiment in the same manner as for tension, except that the stress is applied to compress instead of to stretch the specimen. If the material tested is hard or brittle, as in cast-iron, care should be taken to protect the person from the pieces which sometimes fly at rupture. Report and draw curve as for tension-tests, and in addition show why brittle material breaks in planes, making angles of about 45 with the axis of the piece ; compare the results obtained for wrought-iron in compression with those obtained in tension. 2. Long Pieces : Method of Testing. — In this case the exten- someters used for tension-tests can be connected directly to the specimen, and the measurements taken in substantially the same May, except that the heads of the extensometer will approach instead of recede from each other ; this makes it § IOO.] TESTING MATERIALS OE CONSTRUCTION. 15$ necessary to run the screws back each time after taking a meas- urement a distance greater than the compression caused by the increment of load. In case large specimens are tested horizontally, initial flexion is to be avoided by counterweight- ing the mass of the test-piece. Calculate the increment of load as one tenth the breaking- load given by Rankine's formula, Article 51, page 74. Apply the first increment and take initial reading of micrometers; continue this until after the elastic limit has been passed, after which remove the extensometer, and apply load until rupture takes place. Protect yourself from injury by flying pieces. Compute the breaking coefficient C by Rankine's formula, and compare with the usual results. Compute the modulus of elasticity by Euler's formula: (1) P," = £1^ + /'" (Church," Mechanics of Materials," p. 366). (2) E = t"*P " -T- jtV. /"=■/- \". (3) £ = (/- VJP' ~ ?t*L Also by the method used in testing short specimens. In the above approximate formula the notation is the same as in Article 48, page 72. Note in the report, load at elastic limit, yield-point, and ultimate resistance, as well as increase of section at various points, and total compression calculated as explained for tension. Submit a strain-diagram, and follow the same general direc- tions as prescribed in the report for tensile strain, Article 98. TRANSVERSE TESTS. 100. Object. — This test is especially valuable for full-sized pieces tested with the load they will be required to carry in actual practice. The deflections of such pieces, with loads at centre or in various other positions, afford means of computing the coeffi- cients of elasticity and the form of the elastic curve. Method of Testing. — Arrange the machines for such tests 156 EXPERIMENTAL ENGINEERING. [§ IOO. by putting in the supporting abutments, and by arranging the head for such tests, or else by using the special transverse testing-machine. In this experiment the test-piece is usually a prismatic beam, 3 feet long (see Article 91, page 142), and it is supported at both ends, the stress being applied at the centre. The same data are required to be observed as in the preceding experiment, viz., loads and deflections, or stresses and corre- sponding strains. Sharp edges on all bearing-pieces are to be avoided, and the use of rolling bearings which move accurately with the angular deflections of the ends of the bars are recommended ; otherwise the distance between fixed supports measured along the axis of the specimen is continually changing. Place the test-bar upon the supports, and adjust the latter 36 inches apart between centres, and so that the load will be applied exactly at the middle. Obtain the necessary dimen- sions, and calculate the probable strength at elastic limit and at rupture by means of the formula/ = Wle -^ 4L (See Arti- cle 52, page 78.) Adjust the specimen in the machine in a horizontal plane, and apply the stress at the centre normal to the axis of the specimen, and in a plane passing through the three points of resistance. Measure the deflections at the centre from a fixed plane or base, allowing for the settling of the supports, or by the special deflectometer (see Article 87, page 1 3 5), from which compute the coefficient of resilience and the modulus of elasticity. Balance the scale-beam with the test-bar in position and the deflectometer lying on the platform. Set the poise for one increment of load and apply stress until the beam tips. Place the poise at zero, and balance by gradually removing the load. Place the deflectometer in position on the supports, and with the micrometer at zero make contact and record zeio-reading and zero-load. Apply the load in uniform increments equal to about one fifth the calculated load for the elastic limit, stopping only § IOI.] TESTING MATERIALS OF CONSTRUCTION. 157 long enough to measure the deflections. Wrought-iron is to be strained only until it has a sensible permanent set, but cast- iron and wood are to be tested to rupture. Wood specimens generally rupture on one side only : in that case turn over and make complete test as in the first instance. IOI. Form of Report. — In the report describe the ma- chine, method of making test, form of cross-section, peculi- arities of the section, and make a sketch showing position and form of rupture. Submit a complete log of the test, together with drawing of the elastic curve, to be filed for permanent record. The following is a form for data and results of a transverse test : DATA OF TRANSVERSE TEST OF, Form of cross-section .... Length between supports ins. On Testing-machine. Time hrs mins. Date Observers: Load W. Deflection. Remarks. No. Reading. Net. REPORT OF TRANSVERSE TEST. Material , Form 1 Composition Specific Gravity Load A pplied \ estinn machine Time hrs min. pate ,189 Observers:^ Wt. per cu. ft ?bs. i 5 8 EXPERIMENTAL ENGINEERING. [§ 101. Dimensions. Symbol | i c o '& •c E a Length Diameter Breadth in. in. in. / D b h e I Height in. in. Load. Actual. Reduced per sq. in. in Outer Fibre. Elastic limit Deflection. I 3 ' Modulus of elasticity £ Modulus of resilience ft. lbs. "o Remarks: JS o V M The following forms are used by Prof. Lanza in the labora- tory of the Institute of Technology for log and report of trans verse test : LOG. Date No Specimen Span Wt. of beam Position of load Tested by Wt. of yoke, etc.... e Loads. Micrometer-readings. Mean. Differences. Remarks. i 2 I 2 Modulus of elasticity Modulus of rupture (including weight of beam). Maximum intensity of longitudinal shear § 102.] TESTING MATERIALS OF CONSTRUCTION. 159 REPOR' Date.. No Specimen Span, Dimensions, Weight of beam, . . . , Weight of yoke, etc., . . . Deflection, Modulus of elasticity, . . . Modulus of rupture (including weight of beam), Maximum intensity of longitudinal shear, . . (Signed) 102. Elastic Curve. — The object of this experiment is to determine the coefficient and moduli of the material, by loads less than that required at the elastic limit. The required general formulae are to be found in Art. 52, page 77- A table of deflections corresponding to various centre loads is to be found on page 79. The beam is to be supported at both ends on rounded supports or on rollers. The loads consist of weights of known amount that can be suspended at various points. Apparatus needed. — Cathetometer or other suitable instru- ment for measuring deflection. Directions. — Obtain dimensions of beam, compute moment of inertia of cross-section ; note material of beam, and com- pute probable deflection and corresponding load at elastic limit. Carefully divide the length of the beam into equal parts, and mark these divisions on the centre-line of the beam. With no load on the beam, take cathetometer-readings of each point, then apply successive increment of loads, each equal to one fifth the £ robable load at the elastic limit, and take correspond- ing readings of the cathetometer. From readings, obtain the deflections for each point, and plot the elastic curve. Compute the deflections for the corresponding points from the formula, using tabulated values of E, and plot the correspond- ing theoretical curve. Make deductions concerning the rela- tion of the two curves. 160 EXPERIMENTAL ENGINEERING. [} IO3 The above experiment is to be performed with the load at center, and again with the load at a point one fourth or one third the length of the beam. Similar experiments may be performed on beams fixed at one end, or fixed at one end and supported at the other. TORSION-TEST. 103. Object. — The object of this experiment is to find the strength of the material to resist twisting forces, to find its general properties, and its moduli of rigidity and shearing, strength. Thurston's Machine. — The special directions apply only to Thurston's torsion-machine (see Article 73, Figs. 61 and 62, page 114). In the use of the machine the constants are first ob- tained, the test-piece inserted between the jaws of the machine, stress applied, and the autographic strain-diagram obtained. This diagram is on a iarge scale, and gives quite accurate measures of the stresses or loads. The diagram is, however, drawn by attachment to the working parts of the frame, and consequently any yielding of the frame or slipping of the jaws appears on the diagram as a strain or yield of the specimen. The angular deformation a, as obtained from the diagram, is likely to be too great, especially within the elastic limit. This error should be determined in each test by attach- ing index arms at each end of the specimen, and corrections made to the results obtained from the diagram. The characteristic form of diagram given by the torsion- machine is shown in Fig. 98, in which the results of tests of several materials is shown. In the above diagrams* the ordi- nates are moments of torsion (Pa), the abscissae are develop- ments of the angle of torsion (a). The value of one inch of ordinate is to be found by measuring the ordinate correspond- ing to a known moment of torsion, and the abscissa corre- * See " Mechanics of Materials," page 240, by I. P. Church. Published by Wiley & Son, N. Y. I04-] TESTING MATERIALS OF CONSTRUCTION. :6i sponding to one degree of torsion is to be calculated from the known radius of the drum. Knowing these constants, numerical values can readily be obtained, and the coefficients of the strength of the material can be computed. During the test, relax the strain occasionally : if within the elastic limit, the diagram will be retraced ; but if beyond that limit, a new path is taken, called an " elasticity " line by Thurston, which is in general parallel to the first part of the line, and shows the amount of angular recovery BC y and the per- manent angular set OB. 104. Methods of Testing by Torsion with Thurston's Autographic Testing-machine. (See Articles 55 and 73.) Method. — Determine first the maximum moment of the pendulum. This may be done by swinging the pendulum so that its centre-line is horizontal, supporting it on platform- scales and taking the weight and the distance of the point ot support from the centre of suspension of the pendulum. The product of these two quantities is the maximum moment of the pendulum. Make three determinations, using different lever-arms, and take the mean for the true moment of the pendulum. A correction for the friction of the journal of the pendulum must be made. When hanging vertically, measure with a spring-balance, inserted in the eye near the bob, the force necessary to start the pendulum. Add this moment to that obtained above, and the result is the total maximum moment of the pendulum. From this the value of the mo ment for any angular position may be calculated. 1 62 EXPERIMENTAL ENGINEERING. [§104 u .S c d "So ^ ffi ^ \j $ Js £ § k 6 * «-» t/> Sf H <* c/3 s W 5? H < in a o* 2 00 3 r, •c m • >» • cd • s i £ to ^ 1 « § U5T3 TO 8 ^ O ^ bo c ftj 31^ to "3 cq rt.S ^ fdhJ * a :§ la ^ .5 S *a sa ■as * rt 3 q £"3 ^ 2 2 £ t- CO N e» r* o o " m « co o S> « cm n 2o o w 10 m u \o « 9 Si o to .13 •a" M to CJ 4-1 c u 3 J3 V cd •0 B > c .3 s CO £ to 0. O c T3 M V C 3 O 3 c cd .3 3 to C c -5 CO CU 4-> Cu c .5 c T3 c 3 O a a, to 2 a cd c *« CJ C ) r^ 13 « J (O (Ti to *n c 6 .0 M C cu a M CU 3 c cd 3 •a s > V w a . - 3 £ 3 a cu ■8 T * C c cd ■d G .2 s CO cd V , ^- to c CO CJ «•*, cd *3 e CJ cd c V. c CJ CO S CO T) u re I *o bo c c 3 O (0 Id 3 *3 cd c a. CO cu 3 II u c CJ Vl V c . « rf a, cd r^ •a c cu cu O 3 (/J 3 3 O VI 2 2 0* J3 M c cd •4-> c 3 to cd cu to *8 00 uj s a C co a m 3 *— ^ a te * — ' « *3 s cd I V •3 J3 c DO O c J3 a I a M .2 to 3 "t •3 ° c H-4 <• ^ I 105.] TESTING MATERIALS OF CONSTRUCTION. 1 6 Note the variation of the pencil-point between the vertical and the horizontal positions of the pendulum. This distance laid down on the F-axis of the record-sheet corresponds to the maximum moment obtained above, whence calculate the value of one inch of ordinate. Calculate the length corre- sponding to one degree on the surface of the paper drum, parallel to the ^T-axis. This will be the unit to be used in calculating the angle of torsion. Fix the paper on the drum and draw the datum-line or X-axis. Insert the test-piece be- tween the centres and screw in the centre until the neck of the test-piece is about midway between the jaws. Wedge the test- piece between the jaws as firmly as possible by hand, and then tap the wedges slightly with a copper hammer. Fasten an index-arm to each end of the specimen in such a manner that twisting or slipping of the specimen can be observed by ref- erence to the centre of the pendulum on one end, and to a fixed point on the drum on the opposite end. Throw the worm into gear and turn the handle slowly and steadily until rupture occurs, only relaxing the stress once or twice during the test. Take the record of all the test-pieces on the same sheet with the same origin of co-ordinates. Correct each diagram for amount of slipping of test-piece or yielding of frame by reference to index-arms carried by the test specimen. The record of torsion-tests, page 162, is a numerical example, obtained from diagrams similar to those shown in Fig. 98. IMPACT TESTS. 105. Directions for Testing Cast-iron by Impact with Heisler's Impact Testing-machine. (See Article 76, p. 1 19.; Method. — Take a transverse test-bar of cast-iron and place it in the machine, cope side out, so that the blow will be struck in the middle of its length. Arrange the autographic device so that it will register the deflection of the bar. Place the tripping device or "dog" for a fall of two inches Catch the bob at this point, and trip at every notch above 1 64 EXPERIMENTAL ENGINEERING. [§ I0& successively until the bar breaks. Note the maximum height of fall. Report on the experiment the behavior of the test- bar and character of its fracture, and the number of impacts and the force in inch-pounds of the last blow. Compute the resilience of the test-piece. Try a similar bar at same ultimate fall, and observe the number of blows required to break it. Draw conclusions. Write complete report, and give moduli and coefficients. 106. Drop-tests. — The following method of making drop- tests has been recommended by the Committee on Standard Methods of Testing appointed by the American Society of Mechanical Engineers, and is substantially the same as adopted by the German Engineers at Munich in 1888 : Drop-tests are to be made on a standard drop », which is to embody the following essential points : a. Each drop-test apparatus must be standardized. b. The ball {falling mass) shall weigh 1000 or 1500 pounds; the smaller is, however, preferable. c. The ball may be made of cast-iron, cast or wrought steel ; the shape is to be such that its centre of gravity be as low as possible. d. The striking-block is to be made of forged steel, and is to be secured to the ball by dovetail and wedges in a rigid manner, and so that the striking-face is placed strictly sym- metrical about and normal to its vertical axis passing through the centre of gravity. Special permanent marks are to indi- cate the correctness of the face in these respects. Special marks should be made to indicate the centre of the anvil-block. e. The length of guides on the ball should be more than twice the width between the guides, which are to be made of metal ; i.e., rails so placed that the ball has but a minimum amount of play between them. Graphite is recommended as lubricant. f. The detachment or shears must not cause the ball to oscillate between the guides, and must be readily and freely controllable, with the point of suspension truly above the ^ § 10/.] TESTING MATERIALS OF CONSTRUCTION. 1 65 centre of gravity of the ball ; and a short movable link, chain, or rope is to be fixed between the ball and shears or detach- ment. g. When a constant height of drop is used, an automatic detaching device is recommended. h. The bearings for the test-piece are to be rigidly attached to the scaffold or frame, and they should be, wherever possible, in one piece with it. i. The weight of frame, bearings, and anvil-block should be at least ten times that of the ball. k. The foundation should be inelastic, and consist of masonry, the magnitude of which is to be determined by the locality and subsoil. /. The surface struck should always be accurately level ; therefore proper shoes or bearing-blocks are to be provided for testing rails, axles, tires, springs, etc., etc., to insure a proper level upper surface ; these blocks are to be as light as possible. The exact shape of these bearing-blocks is to be given on each test report. m. The gallows or frame should be truly vertical and the guides accurately parallel. n. The height of fall of ball should be 20 feet clear, be- tween striking and struck surfaces. 0. Drops which by friction of ball on guides absorb two per cent of the work due to impact are to be discarded. p. For large tests a ball weighing 2000 pounds is to be used. q. A sliding-scale is to be attached to the frame, and in such a manner that the zero-mark can always be placed on a level with the top of the test-piece. SPECIAL TESTS OF MATERIALS. 107. The following comparative tests are often useful : 1. The Welding-test. — This is to be done with a hammer weighing eight to ten pounds, with a given number of blows. 1 66 EXPERIMENTAL ENGINEERING. [§ IO7. The weld is to be a simple scarf weld, made in a coke or gas flame without fluxes. Each bar to be tested to be treated in the same way, using in each case two or three samples of iron ; one sample to be tested on the tension-machine, the other to be nicked to the depth of the weld and then bent or broken, to show the character of the welded surfaces. 2. The Bending-test. — This affords a ready means of find- ing the ductility of metals. The test-piece is to be bent about a stud having a diameter twice that of the specimen. The piece is to be bent with a lever, and no pounding is permitted. If the plate holding the stud is graduated, the angular deflec- tion at time of permanent set may be read at once. A modi- fication of the bending-test is often used to determine the property of toughness, by bending the specimen, first hot and then cold, until it is doubled over on itself. 3. The Hardening-test is used in connection with the other tests to determine the qualities of the specimen ; the mate- rial, one specimen of which, having been previously welded, is carefully heated to a red heat, and plunged in water having a temperature of 32-40 degrees. This specimen is tested by torsion and bending, the same as the unhardened specimen. 4. The Forging-test. — The material is brought to a red heat and hammered until cracks begin to show, the relative amount of flattening indicating the red-shortness of the ma- terial. Useful principally with rivet-rods. 5. Punching-tests. — Find the least material that will stand between the edge and the hole punched, by measurement. 6. Abrasion-tests. — Find the amount of wear from a given amount of work. 7. Hammer-test. — This is made with a light hammer, and the character of the material is determined by the sound emitted. Is useful in locating defects in finished products* but of little value on test specimens. Fatigue of Metals, or the effect of repeated stresses, is a matter of great practical importance, and was investigated very extensively by Wohler. These results are discussed in full in a work by Weyrauch. It is well established that the 'S .§ 108.] TESTING MATERIALS OF CONSTRUCTION. 1 67 breaking-point is lowered by a large number of applications of stress. The proportional loads for wrought-iron, according to Wohler, being as follows : Breaking-load applied once, 4 ; tension alternating with no stress, 2 ; tension alternating with compression, 1. Rest of materials or removal of stress in some instances seems to restore both strength and elasticity. Viscosity or the fluidity of metals under certain conditions is also well established. The effect of temperature on the strength of metals has now been thoroughly investigated. The investigations at the Watertown Arsenal show that steel and wrought-iron bars in- crease slightly in tensile strength as the temperature increases to 6oo° F., and then decrease in proportion to increase of temperature, so that the breaking coefficients at 1600 F. lie between 10,000 and 20,000 pounds. See U. S. Report, Test of Metals, 1888. 108. Tests required for Different Material.* — In general the material is to be tested in such a manner as to develop the same strains that will be called forth in the peculiar use to which it is devoted. The table, page 148, shows the tests that are prescribed for materials for various uses, by the Committee on Standard Tests and Methods of Testing of the American Society of Mechanical Engineers. Pipes and Pipe-fittings. — These should be subject to an internal hydraulic pressure. Car-wheels, — Car-wheels are usually subjected to the drop- test. The following method is employed by the Pennsylvania Railroad Company for testing cast-iron wheels : For each fifty wheels which have been shipped, or are ready to ship, one wheel is taken at random by the railroad company's inspector, either at the railroad company's shops or at the wheel-manufacturer's, as the case may be, and subjected to the following test: The wheel is placed flange downward on an anvil-block weighing 1700 pounds, set on rubble masonry two feet down, and having three supports not more than five * For detailed information see Proceedings Am. Soc. Testing Materials. 1 68 EXPERIMENTAL ENGINEERING. TABLE SHOWING TESTS REQUIRED. Required Test denoted by x. L§ 109. Material used for C '35 c w B rf u H c* .0 '33 H a a a bib c is bio •5 c u cc be a "c u •a u X c '5b u c '55 re < i '■a a Railroad rails X X X X X X X X X X .... X X " car-axles . . . " " tires Shafting X X X X X X X X Building — wrought-iron .... " low steel. X X X X X X " high steel Boiler — wrought-iron " plates. X X X X X X X X X X X X X X " shape-iron X " rivet-rods " low steels Ship materials " plates X X X X X X X X X X* :. X Wire A X X X X X X Copper and soft metals Woods. X X * Repeat in both directions— also by winding. t Longitudinal. inches wide for the wheel to rest upon. This arrangement being effected, the wheel is struck centrally on the hub by a weight of 140 pounds, falling from a height of twelve feet. Should the wheel break in two or more pieces before nine blows or less, the fifty wheels represented by it are rejected. If the wheel stands eight blows without breaking in two or more pieces, the fifty wheels are accepted. 109. Methods of Testing Bridge-materials. — The follow- ing directions are abstracted from the standard specifications adopted by bridge-builders.* Wrought-iron. 1. Appearance. — All wrought-iron must be tough, ductile, fibrous, and of uniform quality for each class ; * See Handbook published by Carnegie, Phipps & Co., Pittsburg. § IO9.] TESTING MATERIALS OF CONSTRUCTION. 169 straight, smooth, free from cinder pockets or injurious flaws, buckles, blisters, or cracks. When rolls are working at maxi- mum thickness, poorer finish will be accepted. 2. Manufacture. — No special process of manufacture re- quired. 3. Standard Test-piece. — The tensile strength, limit of elas- ticity and ductility shall be determined from a standard test- piece, not less than one quarter-inch in thickness, cut from a full-sized bar, and planed or turned parallel ; if the cross-sec- tion is reduced, the tangent between shoulders shall be at least twelve times its shortest dimensions, and the minimum area of cross-section shall not be less than one fourth square inch in area and not more than one square inch. Whenever practicable, two opposite sides of the piece are to be left as they come from the rolls. A full-sized bar if less than the re- quired dimensions may be used as its own test-piece. The ductility, or per cent of strain, is obtained by measuring the elongation after breaking from the point of rupture both ways, on an original length, ten times the least cross-section, or at least five inches long. In this length must occur the curve of reduction of area. 4. Strength. — The strength of the specimens to be a func- tion of the size, and to be determined by the formulae in the following table : STRENGTH OF IRON REQUIRED FOR BRIDGE-BUILDING. Character of the Iron. Tension-iron, pins and bolts, and ) plate-iron less than 8 inches wide, f Plate-iron 8 to 24 inches wide 24 to 36 " " 36 to 48 " " Shaped iron not specified above : " less than £ inch thick " over ■£ inch thick Formulae for Ulti- mate Strength. Pounds per sq. in. T joooA 52000 — 48000 46000 50000 — yoooA Strength at Elastic Limit. Per cent of Breaking. 5° 54-2 5i-5 50 Elongation at Rupture. Per cent. 20 12 IO 5 170 EXPERIMENTAL ENGINEERING. [§ IO9. In above formulae A represents area in square inches, B circumference in inches. 5. Hot-bending. — All plates and angles must stand at a working heat a sharp bend at right angles without sign of fracture. 6. Rivet-iron. — Rivet-iron must be tough and soft, and capable of bending cold until the sides are in close contact. 7. Cold-bending. — All tension-iron pins, bolts, and plate less than 8 inches wide, must bend cold 180 , to a curve whose inner radius equals the thickness, without sign of fracture. 8. Specimens of full thickness, from plate-iron or from flanges or webs of shaped iron, must bend cold through 90 to a curve whose inner radius is \\ times its thickness. 9. Number of Test-pieces. — Four standard test-pieces to be tested free of cost on each contract, with one additional for each 50,000 pounds of iron, and as many more as the con- tractor will pay for at $5 each. If any test-piece gives results more than 4 per cent below the requirements, the particular bar from which it was taken may be rejected, but the results shall be included in the average. If any test-piece have a manifest flaw, its test shall not be considered. Two test-bars out of ten falling more than 4 per cent below the requirements shall be a cause for rejecting the whole lot from which they were taken as a sample. A variation of more than 2\ per cent of weight will also be a cause for rejection. Steel. — The requirements as for manufacture, finish, num- ber of test-pieces and method of testing as for iron. 1. Test-pieces. — Round test-pieces are to be obtained from three separate ingots of each cast, not less than three quarters of an inch in diameter and of a length not less than eight inches between the jaws of the testing-machine. These bars are to be truly rounded, finished at a uniform heat, and ar- ranged to cool uniformly, and from these test-pieces alone the quality of the material shall be determined. 2. Strength. — All the above-described bars are to have a tensile strength, not less than 4000 pounds of that specified, an § I09-] TESTING MATERIALS OF CONSTRUCTION. \J \ elastic limit not less than one half the tensile strength of the test-bar, a percentage of elongation not less than 1,200,000, divided by the tensile strength in pounds per square inch ; and a percentage of reduction of area not less than 2,400,000 di- vided by the tensile strength in pounds per square inch. The elongation should be measured after breaking on a specimen, with length at least ten times the least diameter of the cross- section, in which length must occur the entire curve of reduc- tion from stretch. Directions for testing and rejecting specimens same as for iron. 3. Rivet-steel. — The required strength is 60,000 pounds tensile strength, with elastic limit, elongation, and fracture as in clause 2. To be rejected if under 56,000 pounds, and to stand the same bending-test as rivet-iron. Cast-iron. — All castings, except where chilled iron is specified, shall be tough gray iron, free from cold-shuts or blow-holes, true to pattern and of workmanlike finish. Sample pieces I inch square, cast from the same heat of metal in sand- moulds, shall sustain on a clear space of 4 feet 6 inches a cen- tral load of 500 pounds. Workmanship. — Workmanship must be first-class ; fin- ished surfaces protected by white-lead and tallow ; rivet- holes accurately spaced, and truly opposite before the rivets are driven. Rivets must completely fill the holes, and be of a height not less than 0.6 diameter of the rivet. Eye-bars and Pin-holes. — Pin-holes must be accurately bored, and within -^ inch of position shown on drawing; its diameter not to exceed that of the pin by 0.02 inch if under 3J- inches, or by 0.03 inch if over 3-^ inches. Eye-bars must be straight, with holes in centre-line and in centre of head, and no welds in the body of the bar. All chord eye-bars from the same panel must permit pins to be easily inserted when placed in a pile. Tests of Eye-bars. — Tests are to be made on full-size I7 2 EXPERIMENTAL ENGINEERING. \% I IO. specimens, rolled at the same time as those required for the structure. The lot to which the sample test-bars belong shall be ac- cepted when — a. Not more than one third the bars tested, break in the eye. b. Or if more than one third break in the eye, the ten- sile strength is within 5 per cent required by the formula, iqoqA T= 52000 — — 75 — — 500 (width of bar) ; all in inches. Steel bars must show a strength within 4000 pounds of that required in clause 13. A variation in thickness of heads will be allowed, not ex- ceeding -g^ inch small, or ^ inch large, from the specifications. Annealing. — If a steel piece is partially heated during the progress of the work, the whole piece must be subsequently annealed. All bends in steel must be made cold, or the piece must be subsequently annealed. 1 10. Admiralty Tests. Tests for Iron Plate. Hot, to bend without fracture from 90 to 125 . Cold, to bend without fracture to the following angles : I -inch plate., .lengthwise io° to 15 , crosswise 5 f- " " ... " 20°t0 25°, " 5 to 10° • i- " " ... " 30° to 35 , " io° to 15 J- " "... " 55°to7o°, " 20 to 30* Tests for Plate Steel.* I. Strength. — Strips cut lengthwise or crosswise of the plate to have an ultimate tensile strength of not less than 26 and not exceeding 30 tons per square inch of section, with an elongation of 20 per cent in a length of 8 inches. * See " Manual of the Steam-engine," Vol. II., page 488, by R. H. Thurston. § III.] TESTING MATERIALS OF CONSTRUCTION. 1 73 2. Temper. — Strips cut lengthwise of the plate if inches wide, heated uniformly to a low cherry-red and cooled in water of 82 F., must stand bending in a press to a curve of which the inner radius is one and a half times the thickness of the plates tested. 3. The strips are to be cut in a planing-machine, and have sharp edges removed. 4. The ductility of every plate is to be tested by the appli- cation of the shearing or bending tests on the contractor's premises and at his expense. The plates are to be bent cold with the hammer. 5. All plates to be free from lamination and injurious surface defects. 6. One plate out of every fifty or fraction thereof to be taken for testing by tensile and tempering test from every invoice. 7. The pieces cut out for testing are to be of parallel width from end to end, or for at least 8 inches in length. A latitude or variation in thickness will be permitted of 10 per cent for plates less than one half-inch thick, and of 5 per cent for plates over that thickness. Tests for Angle, Bulb, or Bar Steel. 1, 2. Strength and Temper. — The requirements the same as for plate steel. 3. Number of Tests. — Cross ends to be cut off, and one piece for each fifty or fraction thereof to be tested in each invoice. in. Lloyd's Tests for Steel used in Ship-building.* I. Strength. — Strips cut lengthwise or crosswise of the plate, and also angle and bulb steel, to have an ultimate tensile strength of not less than 27 and not exceeding 31 tons per square inch of section, with an elongation corresponding to 20 per cent on a length of 8 inches before fracture. 2. Temper. — Tempering test the same as the Admiralty *See Thurston's " Steam-engine," Vol. II. 174 EXPERIMENTAL ENGINEERING. [§ II 3. test, except that inner radius of bend is three times the thickness. Rivets to be same size as required for iron. 112. Standard Specifications for Cast-iron Water-pipe, Adopted by the American Water-works Association, Phila- delphia, 1 891. (Abstract from Transactions.) 1. Length. — Each pipe shall be of the kind known as "socket and spigot," and shall be 12 feet long from bottom of the socket to the end of the pipe. 2-7. Metal. — The metal shall be best quality neutral pig- iron, with no admixture of cinder, cast in dry-sand moulds, placed vertically, numbered and marked with name of maker and date of making. The shell to be smooth and round, with- out imperfections, and of uniform thickness. 8-10. Test-bars. — Test-bars to be 26 inches long, 2 inches wide, and I inch thick, and to be tested for transverse strength. These bars shall stand, when carried flatwise on supports 24 inches apart, a centre load of 1900 lbs., and show a deflection of not less than 0.25 inch before breaking. Test-bars are to be cast when required by the inspector, and to bd as nearly as possible the specified dimensions. 12-16. All pipes to be thoroughly cooled when taken from the pit, afterward thoroughly cleaned without the use of acid, then heated to 300 F., and plunged into coal-pitch varnish. When removed, the coating to fume freely and set hard within an hour* 17. Testing. — The pipes to be tested after the varnish hard* ens with hydrostatic pressure of 300 lbs. per square inch for all sizes below 12 inches diameter, and 250 lbs. for all above that diameter, and simultaneously to be struck with a 3-lb. hammer. 18-20. Templates to be furnished by the maker ; the weight of pipe to vary not over 3 per cent from the standard ; all tests to be made at expense of maker. 113. Tests of Stone, Brick, Cements. — These materials are principally used in walls of buildings and for foundations. For this use they are subjected principally to compression § U4-] TESTING MATERIALS OF CONSTRUCTION. 17 5 or crushing stresses. The important properties are strength and durability. Stone is usually tested for compressive and transverse strength, brick for compressive strength, and cement and mortar for tension. 114. Testing Stones. — The specimens for compressive strength are cubes of various sizes, depending principally on the capacity of the testing-machine. These cubes are to be nicely made with the opposite sides perfectly parallel to pro- vide a uniform bearing-surface. It is found that the larger the blocks the greater the strength per unit of area.* To test Stone for Compressive Strength. — Have the specimen dry and dressed, and ground to a cube — inches on each edge, and with the opposite faces parallel planes. This is important, as imperfect or wedge-shaped faces concentrate the stress on a small area. In testing, use a layer of wet plaster-of- Paris between the specimen and the faces of the machine, to distribute the stress. To test Stone for Transverse Strength. — In this case the specimen is dressed into the form of a prism 8 inches long and 2 by 2 inches in section. It is supported on bearings 6 inches apart, and a centre load applied. The strength is computed as explained under head of Transverse Testing, page 78. Durability of stone is tested accurately only by actual trial. Some idea can be formed by noticing the effect of the weather on the exposed rocks in the quarry from which the specimen came. In the method of standard tests adopted in Munich in 1887 the following additional tests are recommended: I. Trial method with (a) a jumper or drill, (b) by rotary boring. The amount of work done by the drill to be deter- mined by the momentum of drop, its velocity of rotation, and the shape or cutting angle of the drill or cutting tool. These qualities are to be determined by comparison with a standard * See Unwin, "Testing of Materials. 1 76 EXPERIMENTAL ENGINEERING. [§ II4, drill working under definite conditions. 2. Examine the stone for resistance to shearing as well as to boring. Report the results of the boring test on the following form : STANDARD REPORT BLANK FOR BORING TEST. 1. Description of stone in its geological and mineralogical relations. 2. Miner's classification (hard, very hard, or extremely hard). 3. Texture \\. e., coarse-grained, fine-grained, parallel, normal to or inclined to axis of drill-hole). 4. Specific gravity of the stone. 5. Diameter of hole drilled. 6. Diameter of hole and core when boring. 7. Straight or curve edged drills. 8. Angle of edge of drills. 0. Number of blows per revolution of drill. 10. Effective weight of drill. 11. Mean effective drop of drill. 12. Number of blows required to drill the depth of hole. 13. Number and form of teeth of borer. 14. Statement of pressure on and velocity of bore, while boring. 15. Actual or total depth of bore-hole. 16. Calculated or indicated work done during boring stated in meter-kilo- grams per c. m. of hole bored. (When using a hollow borer the annulus ot stone cut away is alone to be considered.) 3. Find when possible the position in the quarry originally occupied by the specimen tested. 4. Find out the intended use of the stone, and determine the character of tests largely from that. 5. Dry the stone until no further loss of weight occurs at a temperature of 30 C. (86° F.), and test in a dry condition. Make the tests for strength as described, using as large specimens as possible. Also, test by compression rectangular blocks. Test also for tension and bending. 6. Obtain the specific gravity, after drying at a temperature of 86° F. 7. Examine the specimen for resistance to frost by using samples of uniform size, 7 cm. (2.76 inches) on each edge. 8. The frost-test consists of : a. The determination of the compressive strength of satti* rated stones, and its comparison with that of dried pieces. § 1 1 4-] TESTING MATERIALS OF CONSTRUCTION. I 77 b. The determination of compressive strength of the dried stone after having been frozen and thawed out twenty-five times, and its comparison with that of dried pieces not so treated. c. The determination of . the loss of weight of the stone after the twenty-fifth frost and thaw. Special attention must be had to the loss of those particles which are detached by the mechanical action, and also those lost by solution in a definite quantity of water. d. The examination of the frozen stone by use of a magni- fying-glass, to determine particularly whether fissures or scal- ing occurred. 9. For the frost-test are to be used : Six pieces for compression-tests in dry condition, three normal and three parallel to the bed of the stone, provided these tests have not already been made, in which it is permis- sible, on account of the law of proportions, to use cubical test- blocks larger than 7 cm. (2.76 inches). Six test-pieces in saturated condition — not frozen, how- ever ; three tested normal to and three parallel to bed. Six test-pieces for tests when frozen, three of which are to be tested normal to and three parallel to bed of stone. 10. When making the freezing-test the following details are to be observed : a. During the absorption of water the cubes are at first to be immersed but 2 cm. (0.77 inch) deep, and are to be lowered little by little until finally submerged. b. For immersion, distilled water is to be used at a tem- perature of from 1 5 C. (59 F.) to 20 C. (68° F.). c. The saturated blocks are to be subjected to temperatures of from — io° to — 15 C. (14 to 5 F.). This can be done in a vessel surrounded with melting ice and salt. d. The blocks are to be subjected to the influence of such cold for four hours, and they are to be thus treated when completely saturated. e. The blocks are to be thawed out in a given quantity of distilled water at from 59 F. to 64 F. I7 8 EXPERIMENTAL ENGINEERING. IS 1 * 5- II. An investigation of zveathering qualities — stability un- der influences of atmospheric changes — can be neglected when the frost-test has been made. However, the effects in this re- spect, in nature, are to be carefully observed and compared with previous experience in the use of similar material. Observe — a. The effect of the sun in producing cracks and ruptures in stones. b. The effect of the air, and whether carbonic-acid gas is given off. c. The effect of rain and moisture. d. The effect of temperature. 115. Bricks or Artificial Building-stone.— Brick are tested for strength, principally by compression. 1. They should be ground to a form with opposite parallel faces, and are tested between layers of thin paper; or, without grinding, between thin layers of plaster-of-Paris, as explained for stone. The variation in size of specimen, and whether the brick is tested on end, side-ways, or flat-ways, will make a great differ- ence in the results. The test, to be of any value, must state the method of testing. Whole bricks are stronger per unit of area than portions of bricks, and should be used when practi- cable. 2. It is also recommended that brick be tested for compres- sion in the shape of two half-bricks superimposed, united by a thin layer of Portland cement, and covered on top and bottom with a thin layer of such paste to secure even bearing- surfaces.* 3. The transverse test for brick is believed to be a valuable index to its building properties. Support the brick on knife- edges 6 inches apart, and apply the load at the centre. Com- pute the modulus of rupture : K ~~2 bd" *See Vol. XI. (Standard Method of Testing), Transactions of American Society Mechanical Engineers, regarding Articles 114-118. § 1 1 6.] TESTING MATERIALS OF CONSTRUCTION. \Jg in which W equals the centre-load, / the length, b the breadth, d the depth, all in inches. 4. Dry as for stone, and determine the specific gravity. 5. Test hard-burned and soft-burned from the same kiln. 6. Determine the porosity of the brick as follows : Thoroughly dry ten pieces on an iron plate ; weigh these pieces ; then submerge in water to one half the depth for twenty-four hours ; then completely submerge for twenty-four hours, dry superficially, and weigh. Determine porosity from the weight of water absorbed, which should be expressed as per cent of volume. Express absorption as per cent of weight. 7. Determine resistance against frost, as previously ex- plained for stones, using five specimens, and repeating the operation of freezing and thawing twenty-five times for each specimen. Observe the effect with a magnifying-glass. After freezing, test for compression, and compare the results with that obtained with a dry brick. 8. To test brick for soluble salts, obtain samples from an underburned brick and grind these to dust. Sift through a sieve 4900 meshes per square cm. (31,360 per square inch). The dust sifted out is lixiviated in 250 c.c. of distilled water, boiled for about one hour, filtered, and washed. The amount of soluble salts is then determined by boiling down the solu- tion and bringing the residue to a red heat for a short time. The amount is determined by weight and expressed in per- centage ; its composition is determined by a chemical analysis. 9. Determinations of the presence of carbonate of lime, mica, or pyrites are to be made by chemical analysis. 116. Tests of Paving Material, Stones, and Ballast, Natural and Artificial. — In this case the following observa- tions and tests should be made : 1. Information in regard to petrographic and geologic classification, the origin of the samples, etc., etc. ; also : 2. Statement in regard to utilization of same. 3. Specific gravity of the samples is to be determined. 4. All materials used in the construction of roads, provided they are not to be used under cover or in localities without l8o EXPERIMENTAL ENGINEERING. [§ 1 16. frost, are to be tested for their frost-resisting qualities by similar test to those prescribed for natural stone. 5. Stones or brick used for paving are tested most satisfac- torily in a manner representing their mode of utilization by de- termining the wearing qualities by an abrasion-test described by Prof. I. 0. Baker as follows :* The abrasion-tests are made by putting the bricks and a number of pieces of iron into a re- volving horizontal cylinder. The cylinder used by Prof. Baker was a foundry-rattler 45 inches long, 26 inches in diameter, and revolved at rate of 24 revolutions per minute. The iron used consisted of 546 pieces of " foundry-shot," weighing about J- pound each, thus making a total weight of 83J pounds. In making the test, the " brick " is inserted in the rattler, which is put in motion and the loss determined by weighing at the end of each run. Three runs are made, each one half- hour in length ; the comparisons are all made from the loss during the third run, expressed in percentages. Granite and various stones treated in the same way afford a valuable basis for comparison. The uniformity of wearing qualities of brick for parts more or less distant from the exterior surface is determined by re- peating the trial on the same piece, and not merely testing one, but a greater number of pieces. It is, moreover, necessary to test samples of the best, the poorest, and the medium qualities of bricks in any one kiln. 6. Obtain the transverse strength as explained. 7. Obtain the per cent of water absorbed after the bricks have been thoroughly dried at 30 C. (83 F.), as explained Arts. 91-95. 8. Test materials for ballast in a similar manner. 9. In some cases it may be desirable to test stones as to the capacity for receiving a polish. 10. Examinations of asphalts can only be made in an exhaustive manner by the construction of trial roads. An See Clay-worker t August and September 1891. § 1 1 70 TESTING MATERIALS OF CONSTRUCTION. l8l opinion coinciding with the results of such trial may be formed by- (a) Determination of the quantity and quality of the bitu- men contained therein (whether the bitumen be artificial or natural). {b) By physical and chemical determination of the residue, (c) By determination of the specific density of test-pieces of the material used by a needle of a circular sectional area of I sq. mm., carrying a weight of 300 grams. (See Art. 1 18, p. 163.) (d) By the determination of the wear of such test-pieces by abrasion or grinding trials. (e) By the determination of the resistance to frost of these test-pieces. (See Art. 119, page 163.) 117. Hydraulic Cements and Mortars — Definitions.— The standard scientific methods of testing cements depend prin- cipally upon researches conducted in the German laboratories. The standard method as here given is that recommended by the Committee on Standard Methods of Testing at Munich in 1888. The following definitions will serve to distinguish the dif- ferent classes of hydraulic bond materials : 1. Common limes are produced by roasting or burning lime- stones containing more or less clay or silicic acid, and which when moistened with water become wholly or partly pulverized and slaked. According to local circumstances, these are sold in shape of lumps or in a hydrated condition in the shape of a fine flour. 2. Water-limes and Roman cements are products obtained by burning clayey lime marls below the temperature of decrepita- tion, and which do not disintegrate upon being moistened, but must be powdered by mechanical means. 3. Portland cements are products obtained by burning clayey marls or artificial mixtures of materials containing clay and lime at decrepitation temperature, and are then reduced to the fine- ness of flour, and which contain for one part of hydraulic material at least 1.7 parts of calcareous earth. To regulate 1 82 EXPERIMENTAL ENGINEERING, [§ 1 1 8. properties technically important, an admixture of 2 per cent of foreign matter is admissible. 4. Hydraulic fluxes are natural or artificial materials which in general do not harden of themselves, but do so in presence of caustic lime, and then in the same way as a hydraulic ma= terial ; i.e., puzzuolana, santorine earth, trass produced from a proper kind of volcanic tufa, blast-furnace slag, burnt clay, 5. Puzzuolana cements are products obtained by most care fully mixing hydrates of lime, pulverized, with hydraulic fluxes in the condition of dust. 6. Mixed cements are products obtained by most carefully mixing existing cements with proper fluxes. Such bond ma- terials are to be particularly stated as " Mixed Cements," zt the same time naming the base and the flux used. Mortar is made by mixing three or four parts of sharp sand with one part of quick-lime or cement, and adding water until of tfie proper consistency. Mortar made from quick-lime will neither set nor stay hard underwater; that made from hydraulic- or water-lime, if allowed to set in the air, will not be softened by water; while that made from cement will harden under water. 118. Method of Testing Cements. — The principal prop- erties which are necessary to know are : (1) its fineness; (2) time of setting ; (3) its tensile strength ; (4) its soundness or freedom from cracks after setting ; (5) its heaviness or specific gravity ; (6) its crushing strength ; (7) its toughness or power to resist defi- nite blows. The following standard method of testing cements was adopted by a committee ot the American Society of Civil Engineers and of the American Society of Testing Materials in 1903 and 1904. Selection 0) Sample— -The sample shall be a fair average of the contents of the package; it shall be passed through a sieve having 20 meshes per lineal inch before testing to remove lumps. In obtaining a sample from barrels or bags, an auger or sampling- iron reaching to the centre should be used. A chemical analysis, if required, should be made in accord- § II 8.] TESTING MATERIALS OF CONSTRUCTION. 183 ance with the directions in the Journal of the Society of Chemical Industry, published Jan. 15, 1902. Specific Gravity. — This is most conveniently made with Le Chatelier's apparatus, which consists of a flask (D) 7 Fig. 99, of 'Pig. 99. — Le Chatelier's Specific-gravity Apparatus. 120 cu. cm. (7.32 cubic inches) capacity, the neck of which is about 20 cm. (7.87 inches) long; in the middle of this neck is a bulb (C), above and below which are two marks (F and E); the volume between these marks is 20 cu. cm. (1.22 cubic inches). The neck has a diameter of about 9 mm. (0.35 in.), and is gradu- ated into tenths of cubic centimeters above the mark F. Ben- zine (62 ° Baume naphtha), or kerosene free from water, should be used in making the determination. The specific gravity can be determined in two ways: (1) The flask is filled with either of these liquids to the lower mark (E), and 64 gr. (2.25 ounces) of powder, previously dried at ioo° C. (2 1 2 F.) and cooled to the temperature of the liquid, is grad- ually introduced through the funnel (B) [the stem of which ex- tends into the flask to the top of the bulb (C)], until the upper mark (F) is reached. The difference in weight between the cement remaining and the original quantity (64 gr.) is the weight which has displaced 20 cu. cm. 1 84 EXPERIMENTAL ENGINEERING. [§ I 1 8. (2) The whole quantity of the powder is introduced, and the level of the liquid rises to some division of the graduated neck. This reading plus 20 cu. cm. is the volume displaced by 64 gr. of the powder. The specific gravity is then obtained from the formula : _ . Weight of cement Specific gravity = ^ — \ : : . J Displaced volume The flask during the operation is kept immersed in water in a jar, A, in order to avoid variations in the temperature of the liquid. Different trials should agree within 1 per cent. The apparatus is conveniently cleaned by inverting the flask over a glass jar, then shaking it vertically until the liquid starts to flow freely. Repeat this operation several times. Fineness. — The fineness is determined by the use of circular sieves, about 20 cm. (7.87 inches) in diameter, 6 cm. (236 inches) high, and provided with a pan 5 cm. (1.97 inches deep, and a cover. The wire cloth should be woven (not twilled) from brass wire having the following diameters: No. 100, 0.0045 inch; No. 200, 0.0024 inch. This cloth should be mounted on the frames without distor- tion; the mesh should be regular in spacing and be within the following limits: No. 100, 96 to 100 meshes to the linear inch; No. 200, 188 to 200 " " " " 50 to 100 gr. dried at a temperature of 212 F. prior to sieving should be used for the test, the sieves having previously been dried. The coarsely screened sample is weighed and placed on the No. 200 sieve, which is moved forward and backward, at the same time striking the side gently with the palm of the other hand, at the rate of about 200 strokes per minute. The opera- tion is continued until not more than one tenth of one per cent passes through per minute. The work is expedited by placing § 1 1 8.] TESTING MATERIALS OF CONSTRUCTION, 1 85 in the sieve a small quantity of large shot, or, better, some flat pieces of brass or copper about the size of a cent. The residue is weighed, then placed on a No. 100 sieve and the operation repeated. The results should be reported to the nearest tenth of one per cent. Normal Consistency. — The use of a proper percentage of water in mixing the cement or mortar is exceedingly important. No method is entirely satisfactory, but the following, which con- sists in the determination of the depth of penetration of a wire of a known diameter carrying a specified weight, is recommended The apparatus recommended is the Vicat needle shown in Fig. 100, which is also used for determining the time of setting. This consists of a frame, K, bearing a movable rod, L, with a cap, D, at one end, and at the other the cylinder, G, 1 cm. (0.39 inches) in diameter, the cap, rod, and cylinder weighing 300 gr. (10.58 oz.). The rod, which can be held in any desired position by a screw, F, carries an indicator, which moves over a graduated scale attached to the frame, K. The paste is held by a conical hard- rubber ring, 7, 7 cm. (2.76 inches) in diameter at the base, 4 cm. (1.57 inches) high, resting on a glass plate, /, about 10 cm. (3.94 inches) square. In making the determination, the same quantity of cement as will be subsequently used for each batch in making the briquettes (but not less than 500 grams) is kneaded into a paste and quickly formed into a ball with the hands, completing the operation by tossing it six times from one hand to the other, maintained 6 inches apart ; the ball is then pressed into the rubber ring, through the larger opening, smoothed off, and placed (on its large end) on a glass plate and the smaller end smoothed off with a trowel; the paste, confined in the ring, resting on the plate, is placed under the rod bearing the cylinder, which is brought in contact with the surface and quickly released. The paste is of normal consistency when the cylinder pene- trates to a point in the mass 10 mm. (0.39 inch) below the top of the ring. Great care must be taken to fill the ring exactly to the top. 1 86 EXPERIMENTAL ENGINEERING. [§n8. The trial pastes are made with varying percentages of water until the correct consistency is obtained. The Committee has recommended, as normal, a paste the consistency of which is rather wet, because it believes that varia- tions in the amount of compression to which the briquette is subjected in moulding are likely to be less with such a paste. ML W sl ' iff I, Jw Fig. ioo. — Vicat Needle. Time of Setting. — The object of this test is to determine the time which elapses until the paste ceases to be fluid and plastic, called the initial set, and also the time required for it to acquire a certain degree of hardness, called the final set. For this purpose the Vicat needle, which has already been described, should be used. In making the test, a paste of normal consistency is moulded and placed under the rod (X), Fig. ioo; this rod when bearing the cap (D) weighs 300 gr. (10.58 oz.). The needle (H), at the lower end, is 1 mm. (0.039 inch) in § H9-] TESTING MATERIALS OF CONSTRUCTION. 1 8/ diameter. Then the needle is carefully brought in contact with the surface of the paste and quickly released. The setting is said to have commenced when the needle ceases to pass a point 5 mm. (0.20 inch) above the upper surface of the glass plate, and is said to have terminated the moment the needle does not sink visibly into the mass. The test-pieces should be stored in moist air during the test. This is accomplished by placing them in a rack over water con- tained in a pan and covered with a damp cloth, the cloth to be kept away from them by means of a wire screen, or preferably they may be stored in a moist box or closet. The determination of the time of setting is only approxi- mate, since it is materially affected by the temperature of the mixing water, the percentage of the water used, and the amount of moulding the paste receives. Standard Sand. — The committee recommend at present the use of a natural sand from Ottawa, 111., screened to pass a sieve having 20 meshes per lineal inch and retained on a sieve having 30 meshes per lineal inch; the wires to have diameters of 0.0165 and 0.0112 inch respectively. This sand will be furnished by the Sandusky Portland Cement Co., Sandusky, Ohio, at a mod- erate price. This sand gives in testing considerably more strength than the crushed quartz of the same size formerly employed for this purpose. Form of Briquette. — The form of briquette recommended is shown in Fig. 94. It is substantially like that formerly used except that the corners are rounded. Moulds. — The moulds should be made of brass, bronze, or some equally non-corrodible material, and gang moulds of the form shown in Fig. 92 are recommended. They should be wiped with an oily cloth before using. 119. Mixing. — All proportion^ should be stated by weight; the quantity of water to be used should be stated as a percentage of the dry material. The metric system is recommended be- cause of the convenient relation of the gram and the cubic centi- meter. The temperature of the room and the mixing water 1 88 EXPERIMENTAL ENGINEERING. [§ 1 1 9. should be as near 21 C. (70 F.) as it is practicable to main- tain it. The sand and cement should be thoroughly mixed dry. The mixing should be done on some non-absorbing surface, preferably plate glass. If the mixing must be done on an absorbing surface, it should be thoroughly dampened prior to use. The quantity of material to be mixed at one time depends on the number of test-pieces to be made; about 1000 gr. (35.28 oz.) makes a con- venient quantity to mix, especially by hand methods. The material is weighed, dampened, and roughly mixed with a trowel, after which the operation is completed by vigorously kneading with the hand for \\ minutes. Moulding. — Having worked the mortar to the proper con- sistency it is at once placed in the mould by hand, being pressed in firmly with the fingers and smoothed off with a trowel without ramming, but in such a manner as to exert a moderate pressure. The mould should be turned over and the operation repeated. The briquettes should be weighed prior to immersion, and those which vary in weight more than 3 per cent from the average should be rejected. Storage of the Test-pieces. — During the first twenty-four hours after moulding, the test-pieces should be kept in moist air to prevent them from drying out. A moist closet or chamber is so easily devised that the use of the damp cloth should be abandoned if possible. Covering the test-pieces with a damp cloth is ob- jectionable, as commonly used, because the cloth may dry out unequally, and, in consequence, the test- pieces are not all main- tained under the same condition. Where a moist closet is not available, a cloth may be used and kept uniformly wet by im- mersing the ends in water. It should be kept from direct con- tact with the test-pieces by means of a wire screen or some similar arrangement. A moist closet consists of a soapstone or slate box, or a metal- lined wooden box — the metal lining being covered with felt and this felt kept wet. The bottom of the box is so constructed as to hold water, and the sides are provided with cleats for holding § I 1 9-] TESTING MATERIALS OF CONSTRUCTION. 189 glass shelves on which to place the briquettes. Care should be taken to keep the air in the closet uniformly moist. After twenty-four hours in moist air the test-pieces for longer periods of time should be immersed in water maintained as near 21 C. (70 F.) as practicable; they may be stored in tanks or pans, which should be of non-corrodible material. Tensile Strength. — The tests may be made on any standard machine. A solid metal clip, as shown in Fig. 93, is recommended. This clip is to be used without cushioning at the points of con- tact with the test specimen. The bearing at each point of con- tact should be J inch wide, and the distance between the centre of contact on the same clip should be ij inches. Test-pieces should be broken as soon as they are removed from the water, the load being applied uniformly at the rate of about 600 pounds per minute. The average tests of the briquettes of each sample should be taken as the strength, ex- cluding any results which are manifestly faulty. Constancy 0) Volume. — The object is to develop those quali- ties which tend to destroy the strength and durability of a cement. As it is highly essential to determine such qualities at once, tests of this character are for the most part made in a very short time, and are known, therefore, as accelerated tests. Failure is re- vealed by cracking, checking, swelling, or disintegration, or all of these phenomena. A cement which remains perfectly sound is said to be of constant volume. Tests for constancy of volume are divided into two classes; (1) normal tests, or those made in either air or water main- tained at about 21 C. (70 F.), and (2) accelerated tests, or those made in air, steam, or water at a temperature of 45 C, (11 5 F.) and upward. The test-pieces should be allowed to re- main twenty-four hours in moist air before immersion in water or steam, or preservation in air. For these tests, pats, about 7 J cm. (2.95 inches) in diameter, 1} cm. (0.49 inch) thick at the centre, and tapering to a thin edge, should be made, upon a clean glass plate [about 10 cm. (3.94 inches) square], from cement paste of normal consistency. 190 EXPERIMENTAL ENGINEERING. [§ 120. Normal Test. — A pat is immersed in water maintained as near 21 C. (70 F.) as possible for 28 days, and observed at intervals. A similar pat is maintained in air at ordinary tem- perature and observed at intervals. Accelerated Test. — A pat is exposed in any convenient way in an atmosphere of steam, above boiling water, in a loosely closed vessel for three hours. To pass these tests satisfactorily, the pats should remain firm and hard, and show no signs of cracking, distortion, or disintegration. Should the pat leave the plate, distortion may be detected best with a straight-edge applied to the surface which was in contact with the plate. In the present state of our knowledge it cannot be said that cement should necessarily be condemned simply for failure to pass the accelerated tests, nor can it be considered entirely satisfactory if it has passed these tests. 120. Specifications for Cement. — The following specifica- tions were adopted by the committee of the American Society for Testing Materials, Nov. 14, 1904: General Conditions. — 1. All cement shall be inspected. 2. Cement may be inspected either at the place of manufacture or on the work. 3. In order to allow ample time for inspecting and testing, the cement should be stored in a suitable weather-tight building having the floor properly blocked or raised from the ground. 4. The cement shall be stored in such a manner as to permit easy access for proper inspection and identification of each shipment. 5. Every facility shall be provided by the contractor and a period of at least twelve days allowed for the inspection and necessary tests. 6. Cement shall be delivered in suitable packages with the brand and name of manufacturer plainly marked thereon. 7. A bag of cement shall contain 94 pounds of cement net. Each barrel of Portland cement shall contain 4 bags, and each barrel of natural cement shall contain 3 bags of the above net weight. 8. Cement failing to meet the seven-day requirements may be held await- ing the results of the twenty-eight-day tests before rejection. 9. All tests shall be made in accordance with the methods proposed by the Committee on Uniform Tests of Cement of the' American Society of § 120.] TESTING MATERIALS OF CONSTRUCTION. 191 Civil Engineers, presented to the Society January 21, 1903, and amended January 20, 1904, with all subsequent amendments thereto. 10. The acceptance or rejection shall be based on the following require- ments: 11. Natural Cement. — Definition. — This term shall be applied to the finely pulverized product resulting from the calcination of an argillaceous limestone at a temperature only sufficient to drive off the carbonic acid gas. 12. Specific Gravity. — The specific gravity of the cement thoroughly dried at ioo° C. shall be not less that 2.8. 13. Fineness.— It shall leave by weight a residue of not more than 10% on the No. 100 sieve, and 30% on the No. 200. 14. Time of Setting. — It shall develop initial set in not less than ten minutes, and hard set in not less than thirty minutes nor more than three hours. 15. Tensile Strength. — The minimum requirements for tensile strength for briquettes one inch square in cross-section shall be within the following limits, and shall show no retrogression in strength within the periods specified:* NEAT CEMENT. Age Strength. 24 hours in moist air 50-100 lbs. 7 days (1 day in moist air, 6 days in water) 100-200 " 28 days (1 day in moist air, 27 days in water) 200-300 " ONE PART CEMENT, THREE PARTS STANDARD SAND. 7 days (1 day in moist air, 6 days in water) 25-75 " 28 days (1 day in moist air, 27 days in water) 75~i5o " 16. Constancy of Volume. — Pats of neat cement about three inches in diameter, one-half inch thick at centre, tapering to a thin edge, shall be kept in moist air for a period of twenty-fours hours. (a) A pat is then kept in air at normal temperature. (b) Another is kept in water maintained as near 70° F. as practicable. 17. These pats are observed at intervals for at least 28 days, and, to satisfactorily pass the tests, should remain firm and hard and show no signs of distortion, checking, cracking, or disintegrating. 18. Portland Cement. — Definition. — This term is applied to the finely pulverized product resulting from the calcination to incipient fusion of an intimate mixture of properly proportioned argillaceous and calcareous mate- * For example, the minimum requirement for the twenty-four-hour neat-cement test should be some specified value within the limits of 50 and 100 pounds, and so on for each period stated. 192 EXPERIMENTAL ENGINEERING. [§ 120 rials, and to which no addition greater than 3% has been made subsequent to calcination. 19. Specific Gravity. — The specific gravity of the cement, thoroughly dried at ioo° C, shall be not less than 3.10. 20. Fineness. — It shall leave by weight a residue of not more than 8% on the No. 100 sieve, and not more than 25% on the No. 200. 21. Time of Setting. — It shall develop initial set in not less than thirty minutes, but must develop hard set in not less than one hour nor more than ten hours. 22. Tensile Strength. — The minimum requirements for tensile strength for briquettes one inch square in section shall be within the following limits, and shall show no retrogression in strength within the periods specified:* NEAT CEMENT. Age. Strength. 24 hours in moist air 150-200 lbs. 7 days (1 day in moist air, 6 days in water) 450-550 " 28 days (1 day in moist air, 27 days in water) 550-650 " ONE PART CEMENT, THREE PARTS SAND. 7 days (1 day in moist air, 6 days in water) 150-200 28 days (1 day in moist air, 27 days in water).. ...... 200-300 a 23. Constancy of Volume. — Pats of neat cement about three inches in diameter, one-half inch thick at the centre, and tapering to a thin edge, shall be kept in moist air for a period of twenty-four hours. (a) A pat is then kept in air at normal temperature and observed at intervals for at least 28 days. (b) Another pat is kept in water maintained as near 70 F. as practicable, and observed at intervals for at least 28 days. (c) A third pat is exposed in any convenient way in an atmosphere of steam, above boiling water, in a loosely closed vessel for five hours. 24. These pats, to satisfactorily pass the requirements, shall remain firm and hard and show no signs of distortion, checking, cracking, or dis- integrating. 25. Sulphuric Acid and Magnesia. — The cement shall not contain more than 1.75% of anhydrous sulphuric acid (S0 3 ), nor more than 4% of mag- nesia (MgO). * For example, the minimum requirement for the twenty-four-hour neat-cement test should be some specified value within the limits of 150 and 200 pounds, and so on for each period stated. § 120.] TESTING MATERIALS OF CONSTRUCTION. I93 The following observations are taken with respect to each briquette : Brand of cement Temperature of air at mixing* Temperature of water at mixing Percentage of sand " " water " " cement.. Date of mixing . . Time of mixing In the log of the tests the following are the headings for the columns : No. ; Time of Testing ; Weight of Water ; Ten sile Strength ; and Remarks. Prof. Lanza of Boston requires a report of the following form: CEMENT TEST. Date of test, Date of mixing, No. of days set, Manner of setting (in air or in water), Kind of cement, I3rand ...•••■o.. Cement. Sand Mixture (by wt.), % Breaking-strength per sq. in. (tension), . ♦ Crushing- load (2-in. cube), ...... Signed Water, ............. Lime. •* % The cement-testing laboratory of Berlin, which has perhaps the best reputation for this line of work, makes observations as shown on the following schedule, which gives the results of eleven tests, as given in a paper by P. M. Bruner, before the Engineers' Club of St. Louis: 1 94 EXPERIMEN TA L ENGINEERING. 120, >n O N CO vo \o O >rtio«MiHHNwcn-4- 6 be u £■§35 £ OtsOh •axjrj a3d m 3 ! 3 M •puBjg ro ro ro ro *vOM s-t t^co mOOvomnvoOmoo rovo ON O CO m « CO LOCO CO OCO O lllNNOflOO mmovS ro io CJ\roON Nm o tM\fl o ro o> ro r>. m a r^\© m On ro ox friction, whose tangent is the coefficient of friction. The angle of repose ox friction, ,„ Square of reaction of bearing. Weight on journal (squared) . . Moment of friction Work of friction per minute. . . iV 2 vm M U W* - F* = W\\ - sin 2 0) = W* cos 2 (p. N* + F* = N\i +/ 2 ) = F\i +/*) _3 bfl .5 Fr = Wr sin =/Wr -4- |/i +/». War sin

= 27tnr/IV-r- |/i-r-/ 2 . "c3 c 1- 3 >> t> u Cm Weight on journal (general). . . Intensity of pressure at 6=90° Weight, perfect fit of journal. . Pressure per square inch Maximum pressure per sq. inch Total pressure on bearing .... Total force of friction Work of friction w p' w p pnt P F ip M U /» + « / plr cos QdQ. p -T- cos 0. p'lr / cos 2 BdQ = 1.57/^. •J-y#r 0.64 IV cos 6 -T- Ir. 0.64 W -f- /y. 0.64 w/ cosQdQ = i.2TlV. fP'W= 1.27/W. I.2J/W (space). P'/r = i.vjfWr. Ma = 1.27/ Wr = 2.^71 fnrW. Moment of friction Work of friction per minute . . Maximum pressure per sq. inch Total pressure P' P' F M U W-t-2/r. p'litr -\itW ' = 1.57 JF. P'f =t.StfW. P'fr= i.si/Wr. Ma = \.e>7afWr— 2it/Wrn. ^0 Total force of friction Moment of friction 3 2 Work of friction per minute. . . 125. Friction of Journals in V or Triangular Bearings. — Force of friction F= P cos sin -f- cos <*, in which /> equals the force transmitted through the shaft. When cos = 1, F — P sin -f- cos a, 126. Friction of Pivots on Flat Rotating Surfaces.— Intensity of pressure = / ; total pressure = P. Moment of § 128.] FRICTION— TESTING OF LUBRICANTS. 1 99 friction, M — \fPr. Work of friction, U = ^nnfPr. For a conical pivot, M = ^fPr -r- sin a. a = \ angle of cone. For Friction on a Flat Collar. — Moment of friction, M = IfP^-r'^ir'-r"); r= radius of collar ; r'= radius of shaft on which it is fitted. 127. Friction of Teeth— Rolling Friction. — Work lost in a unit of time, U=nFPs, in which s equals the sliding or slip- ping ; n, number of teeth ; other terms as before. For in volute teeth, in which C 1 = length of arc of approach, C % that of arc of recess, the obliquity of action, r, and r 3 respective pitch-radii, we have for involute teeth U = nfPs 6= nfP(C? + C*)(^ + l ~) + 2 cos ft 1 ' a' This is nearly accurate for any teeth. (-See article " Me- chanics," Encyc. Britannica.) 128. Friction of Cords and Belts— Sliding Friction.— Let T x be the tension on driving side of belt, T 2 on the loose side, Tthe tension at any part of the arc of contact; let 6 be the length of the arc of contact divided by the radius, i.e., ex- pressed in circular measure ; let c equal the ratio of the arc of contact to the entire circumference; let d equal the number of degrees in the arc of contact, e the base of the Napierian logarithms = 2.71828, m the modulus of the common loga- rithms = 0.434295 ; let F equal the force of friction. _ nr d nd e '-78~o7 = T8o' -W _ d '-3S-2? W a = = 360& (c) it The tension at any point, dT, is equal to the resistance TfdO. Hence dT = Tfdd, ....... (d) or 200 EXPERIMENTAL ENGINEERING. [§ 1 29. This integrated between limits T 1 and 7!, gives T 1 T fd = log e -^ = — (common) log ^ ; . • . ■ . (*) hence rp fndm ■* 2 From the nature of the stress, F=T t -.T. fe) -~? = the number corresponding to the logarithm, which is ■* 2 1 /•/, fndm equal fdm y or — — , or 2itfcm. Substituting numerical values, fdm = 0.434/0, ^-^ == 0.00758/5/, and 27r/cm = 2^2SS/c. From equations (/), common log f ~J = 0434/9 = 2.7288/fc. By solving equations (/) and (g), T > = F B=i W T .= F TT=? « 129. Friction of Fluids (1) is independent of pressure ; (2) proportional to area of surface ; (3) proportional to square of velocity for moderate and high speeds and to velocity for low speeds ; (4) is independent of the nature of the surfaces ; (5) is proportional to the density of the fluid, and is related to viscosity. The resistance to relative motion in case of fluid friction. R=/AV 2 = zghfA =fkwA ; § 131.] FRICTION— TESTING OF LUBRICANTS, 201 the work of friction, 17= Rs = RVt =/A VH = fAhwVt. In the above formulae R = resistance of friction, A = area of surface, F= velocity of slipping, h = head corresponding to velocity, w = weight, f t«he resistance per unit of area of surface,/ 7 = coefficient of liquid friction, f = -^— . Viscosity and density of fluids do not affect to any appreci- able extent the retardation by friction in the rate of flow, but have some influence upon the total expenditures of energy. Molecular or internal friction also exists. 130. Lubricated Surfaces. — Lubricated surfaces are no doubt to be considered as solid surfaces, wholly or partially separated by a fluid, and the friction will vary, with different conditions, from that of liquid friction to that of sliding fric- tion between solids. Dr. Thurston * gives the following laws, applicable to perfect lubrication only: 1. The coefficient of friction is inversely as the intensity of the pressure, and the resistance is independent of the pressure. 2. The coefficient varies with the square of the speed. 3. The resistance varies directly as the area of journal and bearing. 4. The friction is reduced as temperature rises, and as the viscosity of the lubricant is thus decreased. Perfect lubrication is not possible, and consequently the laws governing the actual cases are likely to be very different from the above. The coefficient of friction in any practical case is likely to be made up of the sum of two components, solid and fluid friction. TESTING OF LUBRICANTS. 131. Determinations required. — The following determina- tions are required in a complete test of lubricants : 1. The composition, and detection of adulteration. 2. The measurement of density. * See Friction and Lost Work, by Thurston. 202 EXPERIMENTAL ENGINEERING. £§ 133, 3. The determination of viscosity. 4. The detection of tendency to gum. 5. The determination of temperatures of decomposition, vaporization, ignition, and solidification. 6. The detection of acids. 7. The measure of the coefficient of friction. 8. The determination of durability and heat-removing power. 9. The determination of its condition as to grit and foreign matter. 132. Adulteration of Oils. — Adulteration can be detected only by a chemical analysis.* Animal oils may be distinguished from vegetable oils by the fact that chlorine turns animal oil brown and vegetable oil white. 133. Density of Oils. — The density or specific gravity is usually obtained with a hydrometer (see Fig. 10 1) adapted for this special purpose, and termed an oleometer. The distance that it sinks in a vessel of oil of known temperature is measured by the graduation on the stem ; from this the specific gravity of the oil may be found. The density is usually expressed in Beaume's hy- drometer-scale, which can be reduced to correspond- ing specific gravities as compared with water by a table given in the Appendix. Beaume's hydrometer is graduated in degrees to accord with the density of a solution of common salt in water ; thus, for liquids heavier than water the zero of the scale is obtained by immersing in pure water; the five-degree mark by immersing in a five-per-cent solution ; the ten-degree mark in a ten- Fig. 101. p er _ cen t solution ; etc. For liquids lighter than Hydrombter. r ......... water the zero-mark is obtained by immersing in a ten-per-cent solution of brine ; the ten-degree mark by im- mersing in pure water. After obtaining the length of a degree the stem is graduated by measurement. — - * See Friction and Lost Work, by R. H. Thurston. § J 35-] FRICTION— TESTING OF LUBRICANTS. 203 The density may be found by obtaining the loss of weight of the same body in oil and in distilled water. The ratio of loss of weights will be the density compared with water. It may also be obtained by weighing a given volume on a pair of chemical scales. The density of animal oils varies from .62 to .89; sperm-oil at 39 F. has a density of .8813 to .8815 ; rape-seed oil has a density of .9168; lard-oil (winter) has a density of .9175 ; cotton-seed oil a density of .9224 to .9231 for ordinary, and of .9128 for white winter; linseed-oil, raw, has a density of .9299; castor-oil, pure cold-pressed, a density of .9667. 134. Method of finding Density. — A. With Hydrometer Thermometer, and Hydrometer Cylinder. Method. — 1. Clean the cylinder thoroughly, using benzine fill first with distilled water. Set the whole in a water-jacket, and bring the temperature to 6o° F. Obtain the reading of the hydrometer in the distilled water and determine its error. 2. Clean out the cylinder, dry it thoroughly, and fill with the oil to be tested ; heat in a water-jacket to a temperature of 60 ° F., and obtain reading of hydrometer ; also obtain reading, at temperatures of 40 , 8o°, ioo°, 125 , and 150 , and plot a curve showing relation of temperature and corrected hydrome- ter-reading. Reduce hydrometer-readings to corresponding specific gravities, by table given in Appendix. B. Weigh on a chemical balance the same volume of dis- tilled water at 6o° F., and of the oil at the same temperature; and compute the specific gravity. C. Weigh the same metallic body by suspending from the bottom of a scale-pan of a balance : 1. In air; 2. In water ; 3. In the oil at the required temperature. Carefully clean the body with benzine after immersing in the oil. The ratio of the loss of weight in oil to that in water will be the density. *35- Viscosity. — Viscosity of oil is closely related but not proportional to its density. It is also closely related, and in many cases it is inversely proportional, to its lubricating prop- 204 EXPERIMENTAL ENGINEERING. [§ 136. erties. The relation of the viscosities at ordinary temperatures is not the same as for higher temperatures, and tests for vis- cosity should be made with the temperatures the same as those in use. The less the viscosity, consistent with the pressure to be used, the less the friction. The viscosity test is considered of great value in determin- ing the lubricating qualities of oils, and it is quite probable that by means of it alone we could determine the lubricating qualities to such an extent that a poor oil would not be accepted nor a good oil rejected. It is, however, in the present method of performing it, to be considered rather as giving comparative than absolute results. There are several methods of determining the viscosity It is usual to take the viscosity as inversely proportional to its ,. flow through a standard nozzle while maintained at a constant or constantly diminishing head and constant temperature, a comparison to be made with water or with some well-known oil, as sperm, lard, or rape-seed, under the same conditions of pressure and temperature. 136. Viscosimeter. — A pi- pette surrounded by a water- jacket, in which the water can be heated by an auxiliary lamp and maintained at any desired temperature, is generally used as a viscosimeter. Fig. 72 shows the usual arrangement for this test. E is the heater fig. io a .-ViscosiTY of Oils. for the jacket-water, BB the jacket, A the pipette, C a thermometer for determining the temperature of the jacket-water. The oil is usually allowed to run partially out from the pipette, in which case the head diminishes. Time for the whole run is noted with a stop-watch. § 1 390 FRICTION— TESTING OF LUBRICANTS. 205 In the oil-tests made by the Pennsylvania R. R. Co. the pipette is of special form, holding 100 c.c. between two marks, — one drawn on the stem, the other some distance from the end of the discharge-nozzle. 137. Tagliabue's Viscosimeter. — In Tagliabue's viscosim- eter, shown in Figs. 103 and 104, the oil is supplied in a basin C, and trickles down- ward through a metal coil, being dis- charged at the faucet on the side into a vessel holding 50 c.c. The oil is main- tained at any desired temperature by heating the water in the vessel B sur- rounding the coil ; cold water is supplied from the vessel A, as required to main- tain a uniform temperature. The tem- perature of the oil is taken by the ther- mometer D. 138. Gibbs' Viscosimeter. — In the practical use of viscosimeters it is found that the time of flow of 100 c.c. of the same oil, even at the same temperature, ,. 1 Fig. 103.— Tagliabue's Visco- is not always the same, — which is probably simeter. due to the change in friction of the oil adhering to the sides of the pipette. To render the conditions which produce flow more constant, Mr. George Gibbs of Chicago surrounds the viscosimeter, which is of the pipette form, with a jacket of hot oil. A circulation of the jacket-oil is maintained by a force-pump. The oil to be tested is discharged under a constant head, which is insured by air-pressure applied by a pneumatic trough. The tempera- ture of the discharged oil is measured near the point of dis- charge. 139. Perkins' Viscosimeter. — The Perkins Viscosimeter consists of a cylindrical vessel of glass, surrounded by a water or oil bath, and fitted with a piston and rod of glass. The edges of this piston are rounded, so as not to be caught by a slight angularity of motion. The diameter is one-thousandth of an 206 EXPERIMENTAL ENGINEERING. L§ ML inch less than that of the cylinder. In practice the cylinder is filled nearly full of the oil to be tested, and the piston inserted. Fig. 104. — Tagliabue's Viscosimeter. The time required for the piston to sink a certain distance into the oil is taken as the measure of the viscosity.* 140. Stillman's Viscosimeter. — Prof. Thomas B. Stillman of Stevens Institute uses a conical vessel of copper, 6f inches in length and if inches greatest diameter, surrounded by a water-bath, and connected to a small branch tube of glass, #hich is graduated in cubic centimeters ; the time taken for 25 c.c. to flow through a bottom orifice -f x of an inch in diam- eter is taken as the measure of the viscosity, during which time the head changes from 6 to 5 inches. Prof. Stillman makes all comparisons with water, which is the most convenient and uniform standard. The temperature of the oil is taken at about the centre of the viscosimeter. 141. Viscosimeter with Constant Head A form of viscosimeter which possesses the advantage of having a con- stant head for flow of oil regardless of the quantity in the instrument, as made by Tinius Olsen & Co. of Philadelphia, * See paper by Prof. Denton, Vol. IX., Transactions of Am. Society of Mechanical Engineers. I4i.] FRICTION— TESTING OF LUBRICANTS. 207 is shown in the next figure. It is simple in form and can be very readily cleaned. It is provided with a jacket, and oils may be tested at any temperature. This instrument is now the principal standard used in the Sibley College Laboratories. Description. — A is a cup similar in construction to that of the kerosene reservoir of a* students' lamp, with a capacity of about 125 c.c, and is sur- rounded with a jacket D, in which may be placed insulating materials to main- tain a constant temperature while the oil is flowing; C is a thermometer-cup, to the bottom of which is secured a small cap containing the orifice F ; N is a channel connecting chamber con- taining A with C; B is one of four small tubes which admit air to the in- terior of the cup A and thus maintain atmospheric pressure on oil in it; this action secures a constant level of the surface of the oil in the cup C and the surrounding space, at the height of the lower opening in the tube B. H is a valve to retain oil in A while placing it into D. M and N are brackets serving as guides for valve- stem K. The mechanism L, G, G is a device for opening and closing the orifice F readily, and is held in a closed position by spring catch L. The instrument is supported by three legs about eight inches in length. Operation.— Withdraw cup A, fill it in an inverted posi- tion with the oil, hold valve H on its seat while reinserting the cup into its former place as seen in figure, in which latter operation the valve H is raised and the oil allowed to flow out of A until chambers N and C are filled a little above Fig. 105. — Viscosimeter 208 EXPERIMENTAL ENGINEERING. [§ 1 4 1. lower opening of tube B. A beaker graduated in c.c.'s, of capacity of about no c.c, is placed under F; L is released and G allowed to drop, permitting oil to flow through F freely into the beaker. When oil in C falls below the bottom of tube B, air is admitted to the top of the oil in A and oil flows out until it rises a little above tube B again, when flow out of A is stopped until the level falls below B again. This action continues throughout entire run, intermittently but so rapidly that a constant head is maintained at F. In C a thermometer is suspended so that its bulb is immersed in the oil, by which means the temperature of oil can be observed immediately before flowing out of orifice F y which is essential in ascertaining the viscosity of the oil. The oil may be heated in the viscosimeter by applying a Bunsen burner, but it is usually more conveniently heated in a separate vessel until it has attained the proper temperature. Method of Conducting a Test. — Since water is taken as the standard of comparison, the amount of flow for 100 c.c. is first determined. Clean apparatus thoroughly, then fill A with water, allow 100 c.c. to flow and note time; similarly make four or five runs so as to get a fair average. Wipe apparatus again thoroughly dry and proceed in a similar manner, using oil at different temperatures. The jacket should be heated a little with every movement of tem- peratures. The oil should be heated in a separate vessel and then poured into A. The ratio of time of flow of a quantity of oil to time of flow of an equal quantity of water measures the relative viscosity of the given sample of oil to that of water at the given temperature. For comparing the results obtained with this instrument, the time of flow of 100 c.c. only need be known, since all the instruments are standardized. A simple form of viscosimeter has been used with success by the author, consisting of a copper cup in form of a frustum of a cone, having dimensions as follows: bottom diameter I.25 inches, top diameter 1.95 inches, depth 6 inches. The § I43-] FRICTION— TESTING OF LUBRICANTS. 209 flow takes place through a sharp-edged orifice in the centre of the bottom ^ inch in diameter. The whole height is 6£ inches. The instrument when made of copper requires a glass oil-gauge, showing the height of the oil in the viscosi- meter. This should be connected to the viscosimeter 3 inches from the bottom. The time for the flow of 100 c.c. is taken as the measure of the viscosity, during which time the head changes from 6 to about 3.5 inches, the area of exposed surface diminishes at almost exactly the rate of decrease of velocity of flow, so that the fall of level is very nearly constant. The comparative number of vibrations of a pendulum swinging freely in the air, and when immersed in an oil dur- ing a given time, is also said to afford a valuable means of determining the viscosity. 142. Viscosity Determinations of Oil, by Prof. Thomas B. Stillman. Fluid. Water Prime lard-oil No. 1 '* " Gelatine-oil Rosin-oil, ist run " " 2d run Sperm-oil Castor-oil Cotton-seed oil — winter... " " " summer. Rape-seed oil Olive-oil Time of Flow in Seconds of 25 c.c. through Orifice as explained. 20 C. 68° F. 15 55 70 240 70 33 39 5i 57 7i 63 so°c. IOO° C. 122° F. 212° F. 29 19 30 18 8O 19 23 15 22 16 24 17 26 27 27 18 26 20 24 18 16 16 360 15 14 15 16 15 15 16 16 Viscosity compared with water at 20° C (68° F.). I.O 3-6 4.6 16.O 4.6 2.2 2.6 3-4 3.8 4.2 4-7 143. Method of measuring Viscosity. — Apparatus. Stop- watch and viscosimeter. Fill the jacket of the viscosimeter with water and arrange for the maintenance of the same at any desired temperature. This is most conveniently done by cir« culation from a water-bath. Fill the viscosimeter with the oil 210 EXPERIMENTAL ENGINEERING. [§ 144- to a point above the upper or initial mark. Allow the oil to run out, noting accurately with the stop-watch the exact time required to discharge a given amount. Make determinations at 6o°, ioo°, and 150 F., two for each temperature. Clean the apparatus thoroughly at the beginning and end of the test, using benzine or alkali to remove any traces of oil. 143. Gumming or Drying. — Gumming or drying is a con- version of the oil into a resin by a process of oxidation, and occurs after exposure of the oils to the air. In linseed and the drying oils it occurs very rapidly, and in the mineral oils very slowly. Methods of Testing. — Nasmyttis Apparatus. — An iron plate six feet long, four inches wide, one end elevated one inch. Six or less different oils are started by means of brass tubes at the same instant from the upper end : the time taken until the oil reaches the bottom of the plane is a measure of its gum- ming property. Bailey s Apparatus consists of an inclined plane, made of a glass plate, arranged so that it may be heated by boiling water. A scale and thermometer is attached to the plane. Its use is the same as the Nasmyth apparatus. This effect may also be tested in the Standard Oil-testing Machine by applying fresh oil, making a run, and noting the friction ; then exposing the axis to the effect of the air for a time, and noting the increase of friction. In all cases a com- parison must be made with some standard oil. 144. The Flash-test. — The effect of heat is in nearly every case to increase the fluidity of oils and to lessen the vis- cosity ; the temperature at which oils ignite, flash, boil, or congeal is often of importance. The Flash-test determines the temperature at which oils discharge by distillation vapors which may be ignited. The test is made in two ways. Firstly. With the open cup. — In this case the oil to be tested k placed in an open cup of watch-glass form, which rests on a sand-bath. The cup is so arranged that a thermometer can be kept in it. Heat is applied to the sand-bath, and as the oil §144-] FRICTION— TESTING OF LUBRICANTS. 211 becomes heated a lighted taper or match is passed at intervals of a few seconds over the surface of the oil, and at a distance of about one half-inch from it. At the instant of flashing the temperature of the water-bath is noted, which is the tempera- ture of the " flash-point." Fig. 1 06 shows Tagliabue's form of the open cup, in which heat is applied by a spirit-lamp to a water or sand bath sur- rounding the cup containing the oil. The method of applying the match is found to a have great influence on the temperature of the flash-point, and should be distinctly stated in each case. When the vapor is heavier than CtNlRAL BUREAU OF ENO' Fig. 106.— Open Cup. Fig. 107.— Closed Cup for Flashing-point. air, a lower flash-point will be shown by holding n?,ar one edge of the cup. Secondly. With the closed oil-cup. — Fig. 107 is a view of Tag- liabue's closed cup for obtaining the flash-point ; in this instru- ment the oil is heated by a sand-bath above a lamp. The thermometer gives the temperature of the oil, and the match 212 EXPERIMENTAL ENGINEERING. [§ 1 46. applied from time to time at the orifice d, which in the inter- vals can be covered with a valve, determines the flash-point. The open cup is generally preferred to the closed one as giving more uniform determinations, and it is also more con- venient and less likely to explode than the closed one. Method of Testing. — Put some dry sand or water in the outer cup and some of the oil to be tested in the small cup. Light the lamp and heat the oil gently — at the rate of about 50 F. in a quarter of an hour. At intervals of half a minute after a temperature of ioo° F. is. attained, pass a lighted match or taper slowly over the oil at a distance of one half inch at the surface. The reading of the thermometer taken immediately before the vapor ignites is the temperature of the flash-point. With the closed cup the method is essentially the same. The lighted taper is applied to the tube leading from the oil vessel, the valve being opened only long enough for this pur- pose. 145. Method of Determining the Burning-point. — The burning-point is determined by heating the oil to such a tem- perature, that when the match is applied as for the flash-test the whole of the oil will take fire. The reading of the ther- mometer just before the match is applied is the burning-point. With Open Cup. — Apparatus: Open cup of watch-glass form ; thermometer suspended so that bulb is immersed in cup ; outer vessel filled with sand or water, on which the open vessel rests; lamp to heat the outer vessel. Method. — The burning-point is found in the same manner as the flash-point, with the open cup, the test being continued until the oil takes fire when the match is applied. The last reading of the thermometer before combustion commences is the burning-point. 146. Evaporation. — Mineral oil will lose weight by evapo- ration, which may be ascertained by placing a given weight in a watch-glass and exposing to the heat of a water-bath for a given time, as twelve hours. The loss denotes the existence of volatile vapors, and should not exceed 5 per cent in good oil. Other oils often gain weight by absorption of oxygen. § I47-] FRICTION— TESTING OF LUBRICANTS. 213 147. Cold Tests. — Cold tests are made to determine the behavior of oils and greases at low temperatures. The method of test is to expose the sample while in a wide-mouthed bottle or test-tube to the action of a freezing mixture, which surrounds the oil to be tested. Freezing mixtures may be made with ice and common salt, with ice alone, or with 15 parts of Glauber's salts, above which is a mixture of 5 parts muriatic acid and 5 parts of cold water. The temperature is read from a thermometer immersed in the oil. The melting- point is to be found by first freezing, then melting. Tagliabue has a special apparatus for the cold test of oils shown in section in Fig. 108. The oil is placed in the glass y^?y Fig. 108.— Tagliabue's Cold-test Apparatus. vessel, which is surrounded with a freezing mixture. The glass containing the oil can be rocked backward and forward, to insure more thorough freezing. A thermometer is inserted into the oil and another in the surrounding air-chamber ; the oil is frozen, then permitted to melt, and the temperature taken. 214 EXPERIMENTAL ENGINEERING. [§ 1 50. In making this test considerable difficulty may be experi- enced in determining the melting-point, since many of the oils do not suddenly freeze and thaw like water, but gradually soften, until they will finally run, and during this whole change the temperature will continue to rise. This is no doubt due to a mixture of various constituents, with different melting- points. In such a case it is recommended that an arbitrary chill-point be assumed at the temperature that is indicated by a thermometer inserted in the oil, when it has attained suffi* cient fluidity to run slowly from an inverted test-tube. The temperature at the beginning and end of the process of melting is to be observed. 148. Method of Finding the Chill-point. — Apparatus. — Test-tube thermometer, and dish containing freezing mixture. Method. — Pour the sample to be tested in the test-tube, in which insert the thermometer ; surround this with the freezing mixture, which may be composed of small particles of ice mixed with salt, with provision for draining off the water. Allow the sample to congeal, remove the test-tube from the freezing mixture, and while holding it in the hand stir it gently with the thermometer. The temperature indicated when the oil is melted is the chill-point. In case the operation of melting is accompanied with a dis, tinct rise of temperature, note the temperature at the begin- ning and also at the end of the process of melting. In report describe apparatus used and the methods of test- ing. 149. Oleography. — An attempt has been made to deter- mine the properties of oil by cohesion-figures, by allowing drops of oil to fall on the surface of water, noting the time re- quired to produce certain characteristic figures, also by noting the peculiar form of these figures. Electrical Conductivity is different for the different oils, and this has been proposed as a test for adulteration. 150. Acid Tests. — Tests for acidity may be made by ob- serving the effects on blue litmus-paper ; or better by the fol- lowing method described by Dr. C. B. Dudley : Have ready (1) § 151.] FRICTION— TESTING OF L UBRICANTS. 2 I 5 a quantity of 95 per cent alcohol, to which a few grains of car- bonate of soda have been added, thoroughly shaken and al- lowed to settle ; (2) a small amount of turmeric solution ; (3) caustic-potash solution of such strength that 31 \ cubic centi- meters exactly neutralize 5 c.C. of a solution of sulphuric acid and water, containing 40 milligrams H 2 S0 4 per c.c. Now weigh or measure into any suitable closed vessel — a four-ounce sample bottle, for example — 8.9 grams of the oil to be tested. To this add about two ounces No. 1, then add a few drops No. 2, and shake thoroughly. The color becomes yellow. Then add from a burette graduated to c.c, solution No. 3 un- til the color changes to red, and remains so after shaking. The acid is in proportion to the amount of solution (3) re- quired. The best oils will require only from 4 to 30 c.c. to be neutralized and become red. COEFFICIENT OF FRICTION OF LUBRICANTS. 151. Oil-testing Machines. — Measurements of the coefficients of friction are made on oil-testing machines, of which various forms have been built. These machines are all species o. dynamometers, which provide (1) means of measuring the total work received and that delivered, the difference being the work of friction ; or (2) means of measuring the work of friction directly. Machines of the latter class are the ones commonly employed for this especial purpose. Rankine's Oil-testing Machine. — Rankine describes two forms of apparatus for testing the lubricating properties of oil and grease. I. Statical Apparatus. — This consists of a short cylindrical axle, supported on two bearings and driven by pulleys at each end. In the middle of the axle a plumber-block was rigidly connected to a mass of heavy material, forming a pendulum. The lubricant to be tested was inserted in the plumber-block attached to the pendulum, and the coefficient of friction determined by its deviation from a vertical. In this machine the axle was provided with reversing-gears, so that it 2l6 . EXPERIMENTAL ENGINEERING. [§ 1 5 1. could be driven first in one direction and then in the opposite. With this class of machine, if r equal the radius of the journal, R the effective arm of the pendulum, P the total force acting on the journal, the angle with the vertical, we shall have the product of the force W into the arm R sin equal to the moment of resistance Fr. That is, Fr = WR sin 0, from which / - p - p r ~ • II. Dynamic or Kinetic Apparatus. — In this case a loose fly-wheel of the required weight is used instead of the pendu- lum. The bearings of journals and of fly-wheel are lubricated; then the machine is set in motion at a speed greater than the normal. The driving-power is then disengaged, and the fly- disk rotates on the stationary axis until it comes to rest. The coefficient of friction is obtained by measuring the retardation in a given time. Thus, let W equal the weight of the fly- wheel, k its radius of gyration, so that Wk? ~ g equals its moment of inertia. Let n equal number of revolutions at beginning, and n' at end of period /. Then the retardation in angular velocity per second is 2n(n — n') -s- t ; the moment producing retardation, If we neglect the resistance of the air, this must equal the moment of friction fWr. Equating these values, J gfr § 152.] FRICTION— TESTING OF LUBRICANTS. 217 In case the moment of inertia and radius of gyration are un- known, they may be found as in Article 53, page 80. 152. Thurston's Standard Oil-testing Machine. — This machine permits variation in speed and in pressure on the journal ; it also affords means of supplying oil at any time, of reading the pressure on the journal, and the friction on grad- uated scales attached to the instrument. ^W*^.NC*».W>t Fig. 109 —Section of Thurston's Oil-testing Machine. Fig. iio. — Perspective View of Thurston's Oil-testing Machine. This machine, as shown in the above cuts, Figs. 109 and 1 10, consists of a cone of pulleys, C, for various speeds carried be- tween two bearings, B, B' , and connected to an overhanging axis, F\ on this overhanging part is a pendulum, H> with plumber-block in which the axis is free to turn ; the pendulum is supported by brasses which are adjustable and which may be set to exert any given pressure by means of an adjusting screw, !£', acting on a coiled spring within the pendulum. The pressure so exerted can be read directly by the scale M y attached to the pendulum ; a thermometer, Q, in the upper brass gives the temperature of the bearings. The deviation 21 8 EXPERIMENTAL ENGINEERING. ]% I 53. of the pendulum is measured by a graduated arc, PP\ fastened to the frame of the machine. The graduations of the pendu- lum scale M show on one side the total pressure on the jour- nal P, and on the other the pressure per square inch, p ; those on the fixed scale, PP', show the total friction, F; this divided by the total pressure, P, gives/, the coefficient of friction. From the construction of the machine, it is at once per- ceived that the pressure on the journal is made up of equal pressures due to action of the spring on upper and lower brasses, and of the pressure due to the weight of the pendu- lum, which acts only on the upper brass. This latter weight is often very small, in which case it can be neglected without sensible error. 153. Thurston's Railroad Lubricant-tester. — The Thurston machine is made in two sizes ; the larger one, having axles and bearings of the same dimensions as those used in standard-car construction, is termed the " Railroad Lubricant Testing-machine." A form of this machine is shown in the following cut, arranged for testing with a limited supply of lubricant. (See Fig. ill.) Explanation of symbols : T, thermometer, giving temperature of bearings. R, S, rubber tubes for circulation of water through the bearings. N, burette, furnishing supply of oil. M, siphon, controlling supply of oil. P, candle-wicking, for feeding the oil. H, copper rod, for receiving oil from G. The Railroad Testing-machine, which is shown in section in Fig. 1 1 2, differs from the Standard Oil-testing Machine princi- pally in the construction of the pendulum. This is made by screwing a wrought-iron pipe,/, which is shown by solid black shading in Fig. 1 12, into the head K, which embraces the jour- nal and holds the bearings a a in their place. In this pipe a loose piece, b, is fitted, which bears against the under journal- bearing, a'. Into the lower end of the pipe /a piece, cc, is screwed, which has a hole drilled in the centre, through which § I 53-] FRICTION— TESTING OF LUBRICANTS. 2 19 a rod, f, passes, the upper end of which is screwed into a cap, d\ between this cap and the piece cc a spiral spring is placed. The upper end of the rod bears against the piece b } which in turn bears against the bearing a' . The piece b has a key, /, arhich passes through it and the pipe /. This key bears Fig. hi.— Thurston's Railroad-Lubricant Testing-machine. against a nut, 0, screwed on the pipe. By turning the nut the stress on the journal produced by screwing the rod /"can be thrown on the key /, and the bearing relieved of pressure, without changing the tension on the spring. A counterbalance above the pendulum is used when accurate readings are de- 220 EXPEKIMEN TA L ENGINEERING. [§154. sired. The " brasses " are cast hollow, and when necessary a stream of water can be passed through to take up the heat, and maintain them at an even temperature. The graduations on the machine show on the fixed scale. Fig. 112.— Section of Railroad Lubricant Testing-machine. as in the standard machine, the total friction ; and on the pendulum, the total pressures (1) on the upper brasses, (2) on the lower brasses, and (3) the sum of these pressures. 154. Theory of the Thurston Oil-testing Machines. — The mathematical formulae applying to these machines are as I follows : Let P equal the total pressure on the journal ; / the pressure per square inch on projected area of journal ; T the tension of the spring; W the weight of the pendulum; r the radius of the journal ; R the effective arm of the pendulum ; §154-] FRICTION— TESTING OF LUBRICANTS. 22 1 6 the angle of deviation of the pendulum from a vertical line ; F the total force of friction ; / the coefficient of friction ; / the length of bearing-surface of each brass. Since in this machine both brasses are loaded, the pro- jected area of the journal bearing-surface is 2(2r)/ == 4/?*. We shall evidently have P=2T+ W, (1) P 2T+ W *=? &=-&—' < 2 > By definition /= F + P. Since the moment of friction is equal to the external mo- ment of forces acting, Fr = Pfr=f(2T+W)r= WR sin 6. . . . (3) From which 1 F WR sin f=~P = — yp — • (4) In the machines WR sin h- r is shown on the fixed scale^ and the graduations will evidently vary with sin 0, since WR -s- r is constant. P, the total pressure, is shown on the scale attached to the pendulum. In the standard machine the weight of the pendulum is neglected, and P = 2 T; but in the Railroad Oil-testing Machine the weight must be considered, and P= 2T -\- W, as in equa- tion (1). Constants of the Machine. — As the constants of the machine are likely to change with use, they should be deter- mined before every important test, and the final results cor- rected accordingly. 222 EXPERIMENTAL ENGINEERING. [§ *5S 1. To determine the constant WR, swing the pendulum to a horizontal position, as determined by a spirit-level ; support it in this position by a pointed strut resting on a pair of scales. From the weight, corrected for weight of strut, get the value of WR ; this should be repeated several times, and the average of these products obtained. 2. Obtain the weight of the pendulum by a number of care- ful weighings. 3. Measure the length and radius of the journal ; compute the projected bearing-surface 2{2lr). WR 4. Compute the constant , which should equal twice the reading of the arc showing the coefficient of friction when the pendulum is at an angle of 30 , since sine of 30 equal J. The following are special directions for obtaining the co- efficient of friction with the Thurston machine. 155. Directions for obtaining Coefficient of Friction with* Thurston's Oil-testing Machines. — Cleaning. — In the testing of oils great care must be taken to prevent the mixing of different samples, and in changing from one oil to another the machine must be thoroughly cleaned by the use of alkali or benzine. In the test for coefficient of friction the loads, velocity, and temperature are kept constant for each run ; the oil-supply is sufficient to keep temperature constant, the journals being generally flooded. The load is changed for each run. The following are the special directions for the test of Coefficient of Friction, as followed in the Sibley College Engi- neering Laboratory. Apparatus. — Thurston's Standard Lubricant Testing-ma- chine; thermometer; attached speed-counter. (See Art. 151, page 217.) Method. — Remove and thoroughly clean the brasses and the steel sleeve or journal by the use of benzine. Put the sleeve on the mandrel ; place the brasses in the head of the pendulum and see that the pressure spring is set for zero and pressure as indicated by the pointer on the scale. Slide the § 1 55-] FRICTION— TESTING OF LUBRICANTS. 22$ pendulum carefully over the sleeve, put on the washer, and secure it with the nut. See that the feeding apparatus is in running order. Belt up the machine for the high speed and throw on the power, at the same time supplying the oil at a rate calculated to maintain a free supply. By deflecting the pendulum and using a wrench on the nut at the bottom in- crease the pressure on the brasses gradually until the pointer indicates 50 lbs. per square inch. Determine the constants of the machine as explained irr Article 1 54, page 222; measure the projected area of journal bearing-surface, and the weight and moment of the pendulum. Ascertain the error, if any, in the graduation of the machine,, and correct the results obtained accordingly. Make a run at this pressure, and also foi pressures of 100, 150, and 200 lbs.; but do not in general permit the maximum pressure in pounds per square inch to exceed 44,800 ~ (v -f- 20}. Begin by noting the time and the reading of the revolution- counter ; take readings, at intervals of one minute, of the arc and the temperature until both are constant. . At the end of the run read the revolution-counter and note the time. The velocity, v, in rubbing surface in feet per minute should be computed from the number of revolutions and circumfer- ence of the journal. Make a second series of runs, with constant pressure and variable speed. In report of the test state clearly the objects, describe apparatus used and method of testing. Tabulate data, and make record of tests on the forms given. Draw a series of curves on the same sheet, showing results of the various tests as follows : 1. With total friction as abscissae, and pressure per square inch as ordinates ; for constant speed. 2. With coefficient of friction as abscissae, and pressure per square inch as ordinates ; for constant speed. 3. With coefficient of friction as abscissae, and velocity o£ rubbing in feet per minute as ordinates ; pressure constant. 224 EXPERIMENTAL ENGINEERING. [§ 157- 156. Instructions for Use of Thurston's R. R. Lubricant- tester. (See Article 152, page 218.) — Follow same directions for coefficient of friction-test as given for the standard machine, applying the pressure as explained in Article 155, page 222. Water or oil of any desired temperature can be forced through the hollow boxes by connecting as shown in Fig. 80, page 191, and the temperature of the bearings thus maintained at any desired point. With this arrangement the machine may be used for testing cylinder-stocks, as explained in directions for using Boult's machine (see Article 161, page 231). The con- cise directions are : 1. Clean the machine. 2. Obtain the constants of the machine ; do not trust to the graduations. 3. Make run under required conditions, which may be with ^ach rate of speed. a. With flooded bearings, temperature variable. b. With flooded bearings, temperature regulated by forcing oil or water through hollow brasses. c. Feed limited, temperature variable or temperature regulated. In all cases the object will be to ascertain the coefficient of friction. 157. Riehle's Oil-testing Machine. — This machine con- sists of an axis revolving in two brass boxes, which maybe clamped more or less tightly together. The machine as shown in Fig. 113 has two scale-beams, — the lower one for the purpose of weighing the pressure put upon the journal by the hand- screw on the opposite side of the machine, the upper one for measuring the tendency of the journal to rotate. The upper scale-beam shows the total friction, or coefficient of friction, as the graduations may be arranged. A thermometer gives the temperature of the journal ; a counter the number of revolu- tions. Let P equal the total pressure applied to the bearings. Let B equal the projected area of the journal-bearings,/ equal § 1 57.] FRICTION— TESTING OF LUBRICANTS. 225 the pressure per square inch ; F equal the total friction ; / equal Fig. 113.— RiEHLfi's Oil-testing Machine. the coefficient of friction; n equal the arm of the bearing a the arm of the total pressure. Then do we have /-; /= *r. and Bfn = aP 9 226 EXPERIMENTAL ENGINEERING. [§ 1 58. If / be maintained constant, and a -=- n be made the value of the unit of graduation on the scale-beam f= graduation. 158. Durability of Lubricants.— In this case the amount of oil supplied is limited, and it is to be used for as long a time as it will continue to cover and lubricate the journal and pre- vent abrasion. To give satisfactory results, this requires a limited supply or a perfectly constant rate of feed, an even dis- tribution of the oil, and the restoration of any oil that is not used to destruction ; these difficulties are serious, and present methods do not give uniform results.* The method at present used is to consider the endurance or durability proportional to the time in which a limited amount, as one fourth c.c. will con- tinue to cover and lubricate the journal without assuming a pasty or gummy condition, and without giving a high coefficient of friction. The average of a number of runs is taken as the correct determination. In this test care must be taken not to injure the journal, and it must be put in good condition at the end of the run. The time or number of revolutions required to raise the temperature to a fixed point — for instance, 160 F. — is in some instances considered proportional to the durability. The Ashcroft (see Article 159, page 227) and the Boult (see Article 160, page 228) machines are especially designed for de- termining the durability of oils — from the former by noting the rise in temperature, from the latter by noting the change in the coefficient of friction. The difficulty of properly making this test no doubt lies in the loss of a very slight amount of oil from the journals, which is sufficient, however, to make the results very uncertain. *See paper by Professor Denton, Vol. XL, p. 1013, Transactions of Anr: can Society of Mechanical Engineers. §IOO.] FRICTION— TESTING OF LUBRICANTS. 227 159. Ashcroft's Oil-testing Machine. — This machine (Fig I i4)consists of an axle revolving in two brass boxes ; the pressure on the axle is regulated by the heavy overhanging counterpoise shown in the engraving. The tendency to rotate is resisted by a lever which is connected to the attached gauge. The gauge is graduated to show coefficient of friction. Fig. 114.— Ashcroft's Oil-testing Machine. The temperature is taken by an attached thermometer, and the number of revolutions by a counter, as shown in the figure. In this macnine the weights and levers are constant, the variables being the temperature and coefficient of friction. It is used exclusively with a limited supply of oil, the value of the oil being supposed to vary with the total number of revolutions required to raise the temperature to a given degree —for instance, to 160 F. 160. Boult's Lubricant-testing Machine. -^This machine, designed by W. S. Boult of Liverpool, is a modification of 228 EXPERIMENTAL ENGINEERING. LI 1(50. the Thurston oil-tester, yet it differs in several essential feat- ures. A general view of the machine is shown in Fig 115, and a section of its boxes and the surrounding bush in Fig. 1 16, Fig. 115.— Boult's Lubricant-tester. The machine is designed to accomplish the following pur- poses: I. Maintaining the testing journal at any desired tem- perature. 2. Complete retention on the rubbing surfaces of the oil under test. 3. Application of suitable pressure to the rubbing surfaces. 4. Measurement of the friction between the rubbing surfaces. § i6o.] FRICTION— TESTING OF LUBRICANTS. 229 To secure the complete retention of the oil, a complete bush with internal flanges is used instead of the brasses employed in other oil-testing machines. On the inside of the bush is an ex- panding journal, DD, Fig. 1 16, the parts of which are pressed outward against the surrounding bush by the springs E } or they may be drawn together by the set-screws B i?, compressing the springs is. A limited amount of oil is fed from a pipette or graduated cylinder on the journal, with the bush removed. This oil, it is claimed, will be maintained on the outer surface of the journal and on the interior surface of the metallic bush, so that it may be used to destruction. The bush is hollow, and can be filled with water, oil, or melting ice and brine. The oil to be tested can be FlG ii6 ^ ECTION OF BouLT , s LuBRICANTe maintained at any desired tern- tester. perature by a burner, F, which heats the liquid CC in the sur- rounding bush. The temperature of the journal can be read by a thermometer whose bulb is inserted in the liquid CC. The friction tends to rotate the bush ; this tendency is re- sisted by a lever connected by a chain to an axis carrying a weighted pendulum, G, Fig. 115. The motion of the pendulum is communicated by gearing to a hand, passing over a dial graduated to show the total fric- tion on the rubbing surfaces. The formulae for use of the instrument would be as follows : Let / equal coefficient of friction ; G the weight of the bob on the pendulum, R its lever arm ; a the angle made by the pendulum with the vertical; a the length of the connecting lever; c the radius of the axis to which the pendulum is 2 30 EXPERIMENTAL ENGINEERING. |_§ 1 6 1, attached ; r the radius of the journal ; A the projected area of the journal ; Pthe total pressure on the journal. Then -.— Gsina =/AP, re J from which aGR sin a sin a /= rc AP ~ = ~~F~> ( constant -) In this instrument the total pressure P is usually constant and equal to 68 lbs., so that the graduations on the dial must be proportional to sin a. If the graduations are correct, the coefficient is found by dividing the readings of the dial by P (68 lbs.). The work of friction is the product of the total space travelled into the total friction, and this space in the Boult instrument is two thirds of a foot for each revolution, or two thirds of the number of revolutions. The instrument cannot be used with a constant feed of oil, nor can the pressures be varied except by changing the springs E. 161. Directions for Durability Test of Oils with Boult's Oil-testing Machine. — To fill cylindrical oil-bath, take out the small thumb-screw in cylindrical bath and insert a bent funnel. Pour in oil— any sort of heavy oil maybe used — until it overflows from the hole in which funnel is inserted, and re- place thumb-screw. I. See that the friction surfaces are perfectly clean. These can be examined by tightening the set-screws in order to de- press the spring. This will enable the cylindrical bath to be lifted away. After seeing that the surfaces are perfectly clean, pour on a measured quantity of the lubricant to be tested, and reset the cylinder-bath in position. Slacken set-screws so as to allow the spring to have full pressure. The set-screws should not be removed entirely when slackening. § 1 62. J FRICTION— TESTING OF LUBRICANTS. 23 I • 2. Light the Bunsen burner. 3. The thermometer indicates the temperature to which the lubricant has to be subjected in the steam-cylinder, being graduated in degrees Fahrenheit, and their equivalent in pounds pressure. Thus, if the working steam-pressure is 60 lbs., the thermometer shows that the heat of steam at that pressure is 307 Fahr.; whilst at lOO lbs. pressure its temperature is 358 Fahr., etc. Run the tester, say, until there is a rise of 50 per cent ; in some cases it is preferable to run the tester until there is a rise of 100 per cent of the friction first indicated. There does not appear to be any advantage in going beyond this, as the oil is then practically unfit for further use, and there is danger of roughening the friction surfaces. 4. When it is considered desirable to ascertain the distance travelled by the friction surfaces during a test, read off the counting-indicator before and after the test, and subtract the lesser from the greater total, and the difference will represent the number of revolutions made during the test. As the fric- tion surfaces travel two thirds of a foot during each revolution, the number of feet travelled is arrived at by simply deducting from the number of revolutions made, one third thereof. The value of the oil is proportional to the number of feet travelled by the rubbing surfaces. The speed at which the tester should be run should be about five to six hundred revolutions per minute. For quick- speed engine-oil the speed may be increased to about a thou- sand per minute. 162. Experiment with Limited Feed.— The object of this experiment is to ascertain the variation in the coefficient of friction due to a change in the rate of feed. The experiment is to be made with the feeding apparatus arranged so that the supply can be regulated. Different runs are made with different rates of feed, and the variation in the coefficient of friction determined. Fig. 1 1 1, p. 219, repre- sents the Thurston R. R. Lubricant-tester as arranged for the experiment, with a Constantly diminishing rate of feed, by Pro- fessor G. W. Bissel. In this case oil is obtained by the siphon 32 EXPERIMENTAL ENGINEERING. IS 162. M from the burette N, and conveyed by the candle-wicking P to a copper rod H inserted in the bearings. The rate of flow will depend upon the height of the oil in the burette N above the end of the siphon-tube M, and as the head gradually di- minishes from loss of oil, the rate of flow will decrease. The quantity of oil used is to be determined by gradua- tions on the burette. The increase in coefficient of friction due to the constantly diminishing rate of feed is shown in Fig. 86, the coefficients of friction being shown by the dotted lines, corresponding to a given rate of feed and a given time in minutes. .002 Coefficient ofJFriction Fig .006 The experiment with head and feed maintained constant during each run would represent very closely the usual condi- tions of supplying lubricants. In this case, provided there was no loss of oil from the journals, the experiment might show — 1. The laws of friction for ordinary lubrication. 2. The most economical rate of feed for a given lubricant. § 1630 FRICTION— TESTING OF LUBRICANTS. 233 3. The value of the lubricants on the joint basis of amount consumed and coefficient of friction. A few tables showing coefficients of friction which has been obtained in various trials are given in the Appendix for refer- ence. 163. Forms for Report. — The following are the forms used in Sibley College for data and results of lubricant test: REPORT OF LUBRICANT TEST. Name of Lubricant Mark...* Lab. No Date Source Observer. . Investigation No. of test Pressure on journal, lbs. per sq. inch... Total pressure on journal, lbs Amount of oil used on journal, m. g Average coefficient of friction , Minimum coefficient of friction. , No. of revolutions No. of feet travelled by rubbing surface, Elevation of temperature Time. Min- utes. Total Revolu- tions. Temper- ature. Read- ing on Arc. Coeffi- cient of Friction. Time. Min- utes. Total Revolu- tions. Temper- ature. Read- ing on Arc. Coeffi- cient of Friction. VISCOSITY AND RESULTS OF OIL TEST. Kind of oil Date.. 189.... Received from... Color. Ash % Specific gravity ° B. Tar % " " waterioo. Chill-pt • F. Flashing pt ° F. Loss at ° F. for 3 hrs % Burning-pt ° F. Acid 2 34 EXPERIMENTAL ENGINEERING, VISCOSITY TEST. [§ 163. No. Time of Flow of 100 c.c. in Seconds. Temperature Degrees F. Lubricating Value Lard-oil 100. Sample. Lard-oil. Water. I 2 a A C RESULTS OF FRICTION TEST. Date. 189 . Highest reading Lowest reading Average reading Drops per min Time of run, min. . . . Speed: Rev. per min Miles per hour.. . . Pressure: Total lbs Per sq. in., lbs. Coefficient of friction. Temp. Arc II. Temp. Arc III. Temp. Arc Average. TEST FOR RESINS. Flow on plane inclined degrees. Kind of plane Tempt, room. Time in hrs., Sample , Lard-oil , Water. CHAPTER VII* MEASUREMENT OF POWER— DYNAMOMETERS— BELT- TESTING MACHINES. 164, Classes. — Dynamometers are instruments for measur- ing power. They are of two classes : 1. Absorption; 2. Trans- mission. In the first class the work received is transformed by friction into heat and dissipated ; in the second class the dynamometer absorbs only so much force as is necessary to overcome its own friction, the remainder being transmitted. 165. Absorption Dynamometer.— The Prony Brake.* — The Prony brake is the most common form of absorption dy- namometer. This brake is so constructed as to absorb the work done by the machine in friction, this friction being pro- duced by some kind of a surface connected to a stationary part, and which rubs on the revolving surface of the wheel with which it is used. The brake usually consists of a por- tion which can be clamped on to a wheel (see Fig. n 8, page 2 39), with more or less pressure, and an arm or its equivalent. The part exerting pressure on the wheel is termed the brake- strap ; the perpendicular distance from the line of action of the weight, G, to the centre of the wheel is termed the arm of the brake. The brake is prevented from turning by a definite load which we term G, applied at a distance equal to the length of the arm (a) from centre of motion. The work of resistance would then evidently be equal to the product of the weight of resistance, G, into the distance it would pass through *See Engine and Boiler Trials, by R. H. Thurston, page 157; Mechanics of Materials, by I. P. Church, page 269; Du Bois' Weisbach's Mechanics of En- gineering, page 13. 235 236 • EXPERIMENTAL ENGINEERING. [§ 1 67, if free to move. If n be the number of revolutions per minute, the horse-power shown by the brake would evidently be 2nGan -r- 33000. ....... (1) Brakes are made with various rubbing surfaces, and with various devices to maintain a constant resistance. 166. Stresses on the Brake-strap. — Formula. — The strains on the brake-strap are essentially the same as those on a belt, as given in Article 128, page 199. That is, if T x represent the greatest tension, T 2 the least tension, c the percentage that the arc of contact bears to the ■whole circumference, N the normal pressure, F the resistance of the brake, f coefficient of friction, T t -T n = Fi N = F+f; T —L = iqwWc— Number whose log is 2.7288/*: = B T ' = B^ (3) 167. Designing a Brake.* — The actual process of designing a brake is as follows : There is given the power to be absorbed, number of revolutions, diameter and face of the brake-wheel. In case a special brake-wheel is to be designed, the area of bearing surface is to be taken so that the number obtained by multiplying the width w of the brake in inches by the velocity of the periphery v of the wheel in feet per minute, divided by *See " Engine and Boiler Trials," by R. H. Thurston, pages 260 to 282; also, " Friction and Lubrication." §167.] MEASUREMENT OF POWER. 237 the horse-power H> shall not exceed 500 to 1000.* Call this result K. Then „, WV K= w . 400 to 500 is considered a good average value of K. The value of the coefficient of friction f should be taken as the lowest value for the surfaces in contact (see table of co- efficient of friction in Appendix). This coefficient is about 0.2 for wood or leather on metal, and about 0.15 for metal on metal.. Let H be the work to be transmitted in horse-power, ;z the number of revolutions of the brake-wheel, D its diamete*-- then the resistance F of the brake must be p __ 33000^ f The arc of contact is known or assumed, and may be expressed as convenient (see Article 128) in circular measure 0, degrees a, or in percentage of the whole circumference c. Example. — Assume the arc of contact as 189 degrees (c =0.5), the diameter of brake-wheel 4 feet, coefficient or friction (/*=o.i5), face of brake-wheel 10 inches, revolutions 90, horse-power 70. Find the safe dimensions of the brake- strap and working parts of the brake. Then, from page 236, B = icf^m = jo ** 6 . That is, B equals the number whose logarithm is 0.2046 ; or, B = 1.602. *See also " Engine and Boiler Trials," by R. H. Thurston, pp. 272 and 270^ 238 EXPERIMENTAL ENGINEERING. [§ 1 67. Thus if the brake-wheel is 4 feet diameter revolving at 90 revolutions per minute : from equation (4) (33000^(70) = (*)(4)( 9 o) 2 °43P°«nas. Taking B as above, and substituting in equations (2) and (3). we have - 20 « fig) = 5436; A% .602 3395, ^=52*3 = 13620. .15 From the value of T, , the maximum tension, we compute the required area of the brake-straps, using 10,000 pounds as the safe-working strain. Section of brake-straps = 5436 -r- 10000 = 0.55 square inch. The assumed width of brake-wheel is 10 inches ; this gives for the value of K, by equation page 237. K = (10) (1 132) -T- 70 = 162 ; a low value. If it is proposed in this brake to use 3 straps, each 2 inches wide, the thickness will then be 0.55 -r- 6 = 0.091 inch. To determine a convenient length of the brake-arm, con- sider equation (1) for work deliyered in horse-power. H = 2nGan -7- 33000. § 169.] MEASUREMENT OF PQWER. 239 By dividing both terms by 27t, H '= Gan ~ 5252; £_5252 H an 168. Brake Horse-power. — The following table will often be convenient for determining the delivered horse-power from a brake. HORSE-POWER PER 100 REVOLUTIONS FROM A BRAKE. Length of Brake-arm, Factor to multiply Ratio of scale-read- feet. scale-reading to give ing to horse- power, horse-power, H-r~ G. G^-H. I O.OI9 52.52 2 .038 26.26 3 .057 17.51 4 .076 13-13 5 .090 IO.5O 5.252 .IOO IO.OO 6 .114 8.75 7 .133 7-50 8 .1*2 6.56 9 .172 5.83 10.504 .200 5.00 169. Different Forms of Prony Brakes. — Various forms of brakes are made. Fig. 118 shows a very simple form of TC Fig. 118. — Prony Brake. Prony brake, in which the rubbing surfaces are made by two wooden beams clamped together by the bolts C C. Weight is applied to the arm E at the point G ; the stops D D prevent a great range of motion of the arm ; the projection F is used to hang on sufficient counterbalance to prevent the brake from 240 EXPERIMENTAL ENGINEERING. [§ I7a revolving by its own arm-weight when the screws C C are very- loose. The net load acting on the brake-arm is the difference between the weight at G and that at F, reduced to an equiva- lent weight acting at G. Brakes are usually constructed by fastening blocks of wood, on the inside of flexible bands of iron, so as to encircle a wheel. The inside of the blocks should be fitted to the wheel, and the spaces between the blocks should be at least equal to one third the area of the block. The iron bands are connected to the brake-arm in such a manner that the tension on the wheel can readily be changed. The form of such a brake is shown in Fig. 119 attached to a portable engine. Fig. 119*— Brake applied to Portable Engine. 170. Strap-brakes. — Brakes are sometimes made by taking one or more turns of a rope or strap around a wheel, as shown Fig. 120.— Strap-brake. in Fig. 120. In this case weights must be hung on both sides, and since the arm of action is equal, the resultant force § I73-] MEASUREMENT OF POWER. 24 1 acting is the difference between the two weights : that is, in the figure the resultant force \s A — B ; the equivalent space passed through is the distance travelled by any point of the circumference of the wheel in a given time. The work done is the product of these quantities. 171. Self-regulating Brakes. — Brakes with automatic regulating devices are often made ; in this case the direction of motion of the wheel must be such as to lift the brake-arm. If the tension is too great the brake-arm rises a short distance, and this motion is made to operate a regulating device of some sort, lessening the tension on the brake- ^ wheel ; if the tension is not great enough, ^=jjk k b l the brake-beam falls, producing the oppo- ^fipf£\ j | f site effect. V\V ! I i 172. Brake with oblique Arm. — A v%N \ very simple form of self -regulating brake \'^?M = is shown in Fig. 121: in this case the \ pJ, ;E arm is maintained at an angle with the ^••'' A horizontal. If the friction becomes too JL great, the weight G rises, and the arm of w the brake swings from A to E. thus in- ™ - „ , ^ <=» ' Fig. 121.— Self-regulating creasing the lever-arm from BC to LC; if Brake. the friction diminishes, the lever-arm is correspondingly dimin- ished, thus tending to maintain the brake in equilibrium. 173. Alden Brake. — The Alden brake (see Figs. 122 to 12 5) is an absorption dynamometer in which the rubbing surfaces are separated by a film of oil, and the heat is absorbed by water under pressure, which produces the friction. It is con- structed by fastening a disk of cast-iron, A, Fig. 122, to the power-shaft ; this disk revolves between two sheets of thin copper E E joined at their outer edges, from which it is sepa- rated by a bath of oil. Outside the copper sheets on either side is a chamber which is connected with the water-supply at G. The water is received at G and discharged at H, thus main- taining a moderate temperature. Any pressure in the chamber causes the copper disks to press against the revolving plate, pro= ducing friction which tends to turn the copper disks. As these 242 EXPERIMENTAL ENGINEERING. [§ 174. are rigidly connected to the outside cast-iron casing and brake, arm P, the turning effect can be balanced and measured the same as in the ordinary Prony brake. The pressure of water is automatically regulated by a valve V, Fig. 125, which is par- ZETS s fsl Fig. 124. — Section. Fig. 123. — Alden's Brake Fig. 122. — Section. Fig. 125.— Valve. tially closed if the brake-arm rises above the horizontal, and is partially opened if it falls below ; this brake with a constant head gives exceedingly close regulation. 174. Hydraulic Friction-brake. — The author has designed a hydraulic friction-brake that can be applied to the surface of an ordinary brake-wheel. The brake consists of a tube of copper with an oval or rectangular cross-section, which very nearly encircles the brake-wheel, and has both ends closed. The greatest dimension in its cross-section is equal to the width of the brake-wheel, and its least dimension is one half to three fourths of an inch. One end of the tube is connected with the water-supply, the other to the discharge, which can be throttled as required. Outside is a band of iron completely encircling the tube and the brake-wheel, and held rigidly to- gether by means of bolts. To this band is fastened the brake- arm, and also one end of the copper tube. When water-pres- § 176.] MEASUREMENT OF POWER. 243 sure is applied to the tube, it tends to assume a round cross- section, the shorter diameter increasing and the greater diameter diminishing. As these changes cannot take plact because of the outer band of iron, pressure is exerted on the surface of the brake-wheel, and motion of the brake-wheel tends to revolve the tube and band of iron. This is resisted by the weight on the arm of the brake. The water-pressure is regulated automatically by a slight motion of the brake-arm, which closes or opens the supply-valve as is required. The arm may be permitted to act downward on a pair of scales, by interposing a spring of the requisite stiffness between it and the platform of the scales. To prevent wear of the copper tube thin sheets of iron may be interposed. A lubricant is applied by means of lubricators fixed near the ends of the tube. 175. Removal of the Heat generated by the Brake. — Various devices have been adopted to secure the removal of the heat. One method is to cast the outer rim of the brake- wheel hollow, and connect this by a tube with a cavity in the centre of the axis, so that water can be received at one end of the axis and discharged at the other. Another way is to leave a deep internal flange on the brake-wheel, and in using the brake, to supply water by means of a crooked pipe on one side and to scoop it out by a pipe with a funnel-shaped mouth bent to meet the current of water near the opposite side of the wheel. Water is sometimes run on to the surface through a hose, but aside from the inconvenience due to flying water, if anv of the rubbing surfaces are of wood it is likely to make sudden and irregular variations in the coefficient of friction that are difficult to control. 176. Applying Load. — In applying the load, care must be taken that its direction is tangent to the circle that would be described by the brake-arm were it free to move. In other words, the virtual brake-arm must be considered as perpendic- ular to this force. If a vertical load or weight is applied, the brake-arm must be horizontal, and equal in length to the dis- tance from this vertical line to the centre of the motion. 244 EXPERIMENTAL ENGINEERING. [§ 1 78. It will be found in general safer and more satisfactory to have the motion of the brake-wheel such as to produce a downward force, which may be measured by a pair of scales, rather than the reverse, which requires a weight to be sus- pended on the brake-arm. There should be a knife-edge between the brake-arm and the load ; in case of downward motion, the support upon the scales, should be made the proper length to hold the brake-arm horizontal. 177. Constants of Brake. — All brakes with unbalanced arms have a tendency to turn, due to weight of the arm. This amount must be ascertained and added to or taken from the scale or load readings as required by the rotation, in order to give the correct load. To ascertain this amount, the brake may be balanced on a knife-edge, with a bearing point directly over the centre of the wheel, and the correction to the weight obtained by readings on the scale. It is obtained more accu- rately by making the brake loose enough to move easily on the wheel ; then apply a spring-balance at the end of the arm ; first pull the arm upward through an arc of about 3 either side of -its central position, moving it very slowly and gradually: the reading will be the weight plus the friction. Then let it back through the same arc very slowly and gradually, and the read- ing will be the weight less the friction. The sum of these two results will be twice the correction for the brake-arm. Repeat this three times for an average result. In case the friction is greater than the weight this second result will be negative, but the method will remain the same. The weight of the brake, as generally mounted, is carried on the main bearings of the wheel, from which the power is obtained, and virtually increases its weight. This may in some instances increase perceptibly the friction of the journals of the wheel, but is generally an imperceptible amount. This weight can be reduced when desired, by a counterbalance con- nected to the brake by means of guide-pulleys. 178. Directions for Using the Prony Brake.— i. See that the brake-wheel is rigidly fastened to the main shaft. 2. Provide ample means of lubrication. § l8o.j MEASUREMENT OF POWER. 245 3. If the brake-wheel has an internal rim, provide means for supplying and removing water from this rim. 4. Find the equivalent weight of brake-arm to be taken from or added to the load, depending on the direction of motion of the wheel. 5. In applying the load, tighten the brake-strap very I slowly, and give time for the friction to become constant >e« ; fore noting readings of the result. 6. Note the time, number of revolutions, length of brake- arm, corresponding load, and calculate the results. 179. Pump Brakes. — A rotary pump which delivers water through an orifice that can be throttled or enlarged at will, has been used with success for absorbing power. If the casing of the pump is mounted so as to be free to revolve, it can be held stationary by a weighted arm, and the absorbed power measured, as in the case of the Prony brake. If the casing of the pump is stationary, the work done can be measured by the weight of water discharged multiplied by the height due to the greatest velocity of its particles multiplied by a coefficient to be determined by trial.* A special form of the pump-brake, with casing mounted so that it is free to revolve, has been used with success on the Owens College experimental engine by Osborne Reynolds. In this case the brake is practically an inverted turbine, the wheel delivering water to the guides so as to produce the maximum resistance. The water forced through the guides at one point is discharged so as to oppose the motion Df the wheel at anothe; point. 180. Fan-brakes^— A fan or wheel with vanes revolved in water, oil, or air will absorb work, and in many instances forms a valuable absorption-dynamometer. The resistance to be obtained from a fan-brake is expressed by the formula f IT Rl=lKDA—> • ^ * See Rankine, Machinery and Mill-work, page 404. \ Ibid., page 406. 246 EXPERIMENTAL ENGINEERING, in which ^/equals the moment of resistance, V the velocity in feet per second of the centre of vane, A the area of the vane in square feet. / equals the distance from centre of vane to axis in feet, D the weight per cubic foot, of fluid in which the vane moves, K a coefficient, found by experiment by Pon- celet to have the value iST =1.254+ l _ s , n which s is the distance in feet from the centre of the entire vane to the centre of :hat half nearest the axis. vVhen set at an angle i with the direction of motion the value for Rl must be multi- 2 sin 2 i plied by — ; — r-7-. . r 1 + sin 1 181. Traction-dynamome- ters. — Dynamometers for sim- ple traction or pulling are usually constructed as in Fig. 126. Stress is applied at the two ends of the spring, which rotates a hand in proportion to the force exerted. en ( I , il / > / Q O 55 T tu « III u o° Q a K O O 111 W ti\\ <$> INC 2. O ! 1 H ydxL J -RE M (S-~- PS | ~^-~- ""'--iJJ II ; 1 _ a 6 l \ i wl Fig. 146. — Dynamometer for Traction. § 183.] MEASUREMENT OF POWER. 2.47 Recording Traction-dynamometers. — These are constructed in various forms. Fig. 127 shows a simple form of a recording traction-dynamometer, designed by C. M. Giddings. Paper is placed on the reel A, which is operated by clock-work; a pencil is connected at K to the band, and this draws a diagram, as shown in Fig. 128, the ordinates of which represent pounds Tbsr Fig. 128.— Diagram from Traction-dynamometer. of pull, the abscissae the time. The drum may be arranged to be operated by a wheel in contact with the ground : then the abscissa will be proportional to the space, and the area of the diagram will represent work done. 182. General Types of Transmission-dynamometers.* — Transmission-dynamometers are of different types, the ob- ject in each case being to measure the power which is received without absorbing any greater portion than is neces- sary to move the dynamometer. They all consist of a set of pulleys or gear-wheels, so arranged that they may be placed between the prime movers and machinery to be driven, while the power that is transmitted is generally measured by the flexure of springs or by the tendency to rotate a set of gears, which may be resisted by a lever. 183. Morin's Rotation-dynamometer. — In Morin's dy- namometer, which is shown in Fig. 129, the power is trans- mitted through springs, FG, which are thereby flexed an amount proportional to the power. The flexure of the springs is recorded on paper by a pencil z fastened to the rim of the * See Thurston's Engine and Boiler Trials, page 264 ; also Weisbach'9 Mechanics, Vol. II., pages 39-73 ; also Rankine's Steam-engine, page 42. 248 EXPERIMENTAL ENGINEERING. L§ i»a wheel. A second pencil is stationary with reference to the frame carrying the paper. The paper is made to pass under the pencil by means of clock-work driven by the shafting, which can be engaged or disengaged at any instant by operating the lever R. The springs are fastened at one end rigidly to the main axle, which is in communication with the prime mover, and at the other end to the rim of the pulley, which otherwise is free to turn on the main shaft. The power is taken from this last pulley, and this force acts to bend the Fig. 129. — Morin Rotation-dynamometers. springs as already described. In the figure A is a loose pulley B is fixed to the shaft The autographic recording apparatus of the Morin dyna- mometer consists essentially of a drum, which is rotated by means of a worm-gear, UK > cut on a sleeve, which is concentric with the main axis. This sleeve slides longitudinally on the axis, and may be engaged with or disengaged from the frame at any instant by means of a lever. When this sleeve is engaged with the frame and made stationary the recording apparatus is put in motion by the concentric motion of the gearing, SV, with respect to the axis. The pencil attached to the spring will at this instant trace a diagram on the paper whose ordi- § 184.] MEASUREMENT OE POWER. 249 nates are proportional to the force transmitted. The rate of rotation of the drums carrying the paper, with respect to the main axis, is determined in the same manner as though the gears were at rest — by finding the ratios of the radii of the respective wheels. Thus the amount of paper which passes off from one drum on to the other can be proportioned to the space passed through, so that the area of the diagram may be proportional to the work transmitted. To find the value of the ordinates in pounds the dyna- mometer must be calibrated ; this may be done by a dead pull of a given weight against the springs, thus obtaining the deflections for a given force ; or, better, conneGt a Prony brake directly to the rim of the fixed pulley B, and make a series of runs with different loads on the brake, and find the correspond, ing values of the ordinates of the card. 184. Calibration of the Morin Dynamometer. — Appara- tus. — Speed-indicator, dynamometer-paper, and Prony brake. 1. Fasten paper on the receiving drum, wind off enough to pass over the recording drum, and fasten the end securely to the winding drum. See that the gears for the autographic apparatus are in perfect order, and that both pencils give legible lines. Adjust the pencil fixed to the frame of the clock-work, so that it will draw the same line as the movable pencil, when no load is applied. 2. With the apparatus out of gear apply the power. Take a card with no load. This card will be the friction work of the dynamometer. 3. Apply power and load, take cards at intervals: these cards will represent the total work done. This, less the fric- tion work, will be the power transmitted. The line traced by the pencil affixed to the frame of the clock-work must in all cases be considered the zero-line, or line of no work. 4. To calibrate the dynamometer, attach a Prony brake to the same shaft and absorb the work transmitted. This trans- mitted work must equal that shown by the Prony brake. Find constants of brake as explained Article 177, page 211. 5. Draw a calibration-curve, with pounds on a brake-arm, 250 EXPERIMENTAL ENGINEERING. [§ 186. reduced to an equivalent amount acting at a distance equal to the radius of the driving-pulley of the dynamometer, as abscissae, and with ordinate of the diagram as ordinate. Work up the equation of this curve. 6. In report of calibration make record of time, number of revolutions brake-arm, equivalent brake-load for arm equal to radius of dynamometer-pulley, length of ordinate, scale of ordinate. Describe the apparatus. 7. In using it, insert it between the prime mover and re. sistance to be measured. Determine the power transmitted from the calibration. 185. Form of Report— The following form is useful in calibrating this dynamometer : CALIBRATION OF MORIN DYNAMOMETER. Kind of brake used • Length of brake-arm Weight of brake-arm lbs. Zero-reading of scales. . . . Radius of driving-pulley ft. Observers ..ft. .lbs. Date. 189. No. Resolutions per Minute. Up. Down, Mean Effective Brake-load lbs. Equivalent Load on Driving- pulley, lbs. Ordinate, Inches. Up. Down. Mean Brake H. P. Remarks: Equation of Curve, ...... K- , 186. Steelyard-dynamometer. — In this dynamornetei the pressure of the axle of a revolving shaft is determined by shifting the weight G on the graduated scale-beam AC. The power is applied at P, putting in motion the train of gear-wheels, and is delivered at Q. Denote the applied force by P, the delivered force by Q, 1 86.] MEASUREMENT OF POWER. 25 the radius KM by a, KE by r, LF by r x , NL by b % the force delivered at E by R t that at F by R t . We shall have Rr = Pa, also Rf^Qb. But R(ED) = R % {FD)\ and since is/> = F27, R = R t . The resultant force Z == R -f- tf, = 2R. .:R = iZ-, P=iZr + a; Q = \Zr x ±*. If we know the number of revolutions, the space passed through by each force can be readily calculated, and the work found by taking the product of the force into the space passed through. JL c Fig. 130. — Hachette's Steelyard-dynamometer. Consideration of Friction.— The friction of the axle and gear-teeth will increase the force R and decrease the force R r Let pi be the experimental coefficient expressing this friction. Then P=i(i+»)Zr + a; Q^Hi-^Zr^t; Par, — Qbr M = Par, + Qbr 252 EXPERIMENTAL ENGINEERING. [§ 188 Fig. 131.— Pillow-block Dyna MOMETER. 187. Pillow-block Dynamometer. — The pillow-block dy. namometer operates on the same principle as the steelyard dynamometer, but no intermediate wheel is used. This dynamometer, shown in Fig. 131, consists of the fixed shaft L, which is rotated by the power Q applied at N. The power rotates the gear-wheel EL, which communicates motion to the wheel KE on the same shaft with the wheel KM. This shaft is sup ported on a pair of weighing-scales so that the downward force Z acting on the bearing can be weighed. Let P equal the force delivered, let a equal the angle this force makes with the horizontal, let KM equal a and KE equal r , G equal the weight of shaft and wheel. The weight on the pillow-block at K must be Z = G + P sin a +^P = G + p(sin a + ^\ From which Z-G P = sin a -\ r When the belt is horizontal. tf«0 and P = {Z-G)-. 188. The Lewis Dynamometer.* — This transmission-dy namometer is a modified form of the pillow-block dyna- mometer, arranged in such a manner that the friction of the gearing or journals will not affect the reading on the weighing- scales. This dynamometer is shown in Fig. 1 32 , and also in Fig. 139, Article 195, page 265. The dynamometer consists of two *See Vol. VII., page 276, Trans. Am. Society Mechanical Engineers. 88.] MEASUREMENT OF POWER. 253 ^ear-wheels A and C, whose pitch-circles are tangent at B; the gear-wheel A is carried by the fixed frame T, the wheel C is carried on the lever BD : the lever BD is connected to the flxed frame T by a thin steel fulcrum, as used in the Emery Testing-machines (Article 67, page 105). The point D, the centre of wheel C, and the fulcrum are in the same right line. The fulcrum B permits vertical motion only of the point D. The point D rests on a pillar, which in turn is supported by a pair of scales. The shaft leading from the wheel C is fur- nished with a universal joint (see Fig. 139), so that its weight does not affect that on the journal C. In Fig. 132, A is the Fig. 132.— The Lewis Dynamometer. driving and C the driven wheel, the force to be measured being received on a pulley on the shaft a } transmitted through the dynamometer, and delivered from a pulley on the shaft c. From this construction it follows, that no matter how great the friction on the journals of the shaft c, there will be no pressure at the point D except what results from torsio» of the shaft c. This will be readily seen by considering: 1. That any downward force acting at B will be resisted by the fixed frame T, and will not increase the pressure at D. 2. A downward force acting on the lever between B and D will produce a pressure proportional to its distance from B. 3. If the driven wheel C were firmly clamped to its frame, no force acting at B would change the pressure at D ; and since 254 EXPERIMENTAL ENGINEERING. |J l88 - journal-friction would have the effect of partially clamping the wheel to the journal c, it would have no effect on the scale- reading at D. Denote the transmitted torsional force by Z\ the radius of the driven pulley by r ; the length of lever BD by a ; the scale- reading at D by W. Then from equality of moments r The effective lever-arm BD is to be obtained experimen- tally as follows : Disconnect the universal joint, shown in Fig. 108, so as to leave the wheel C, free to turn ; block the driving- pulley A ; fasten a horizontal arm, ef (dotted lines, Fig. 101), to the shaft c, parallel to the line DB and carrying a weight G ; balance the scales in this position, then move the weight out on the lever, until the reading of the scales is increased an amount equal to the weight moved. The distance moved by the weight will equal length of the lever DB. Thus let ef, shown in dotted lines, represent the lever clamped to the axis c ; let e represent the first position of the weight G, and /the second position; let J^and W represent the corresponding scale-readings, after balancing scales without G on the lever, ef. Then we have Hence W - U DB 1 W+G=W' = G { ^-. c _ W' - W __ c (f B-eB) __ c ef DB " DB ~'DB' Then will DB = ef. § 189.] MEASUREMENT OF POWER. 255 189. The Differential Dynamometer. — This is often called the Bachelder, Francis, or Webber dynamometer ; was invented by Samuel White, of England, in 1780, and brought to this country by Mr. Bachelder in 1836. The dynamometer portion consists of four bevel-gears, shown in plan in Fig, 133. Power is applied to the pulley M, which carries the bevel- x Fig. 133.— The Differential Dynamometer. wheel EE X ; the resistance is overcome by the pulley N, which carries the bevel- wheel FF X . Both wheels run loosely upon the fixed shaft XX X , and are connected by the wheels island E X F X . By the action of the force P and the resistance Q, the pressure of the wheels EE X and FF X is downward at E and F, and upward at E 1 and F x , tending to swing the lever GG X around the axis XX X , one half as fast as the pulley M. The weight which holds the lever-arm stationary, multiplied by the space it would pass through if free to move, is the measure of the work of the force P. A dashpot is usually attached to the lever GG X at G x , to lessen vibrations and act as a counterbal- ance. Let Z equal the vertical force acting at B and B x ; R, the vertical pressure between the teeth at each point of con^ tact ; b, the distance of B and B x from the centre C; a, the distance, AC, to the weight. . Then we have evidently 2Z = ^R, or Z=2R\ also Ga = 2Zb = 4Rfr. 256 EXPERIMENTAL ENGINEERING. [§ I90* If a! is the radius of the driving-pulley M, and r the radius of each bevel-gear, r> / r> r> 2Rr G r a Pa' = 2Rr, or P— — r = — - -„ a' 2 b a! If friction is considered, P=(i+M) G r a ~2 ~b a'' The mechanical work received is equal to P multiplied by the space passed through in the given time. This instrument has been improved by Mr. S. Webber, as shown in Fig. 134. Fig. 134. — The Webber Dynamometer. These dynamometers are used in substantially the same way as the Morin dynamometers. 190. Calibration of the Differential Dynamometer. — 1. See that it is well oiled, in good condition, its axis horizon- tal, and also that the weighing arm is horizontal for no load. 2. Observe constants of the apparatus ; obtain weight of small poise* of large poise; of amount to balance beam W e . Measure the arm of each, and calculate the foot-pounds per 100 revolutions corresponding to weights and graduations. § I90.] MEASUREMENT OF POWER. 2$? 3. Make a preliminary run without load, and note the reading of the poise required to balance the arm. This will determine the friction of the dynamometer without load. Determine the length of the arm, and the value of each sub- division in foot-pounds. 4. Attach a strap-brake (see Art. 169, p. 239) to the delivery pulley of the dynamometer, and absorb all the force trans- mitted. Make a series of ten runs, each ten minutes in length, and during each of which the load on the Prony brake-arm is kept as constant as possible, but which is increased by equal increments, in the different runs. Take observations each minute during the run. 5. The difference between the work absorbed by the brake and that shown by the dynamometer should be carefully de- termined. It is the error of the dynamometer. 6. Note whether this error is a constant quantity, or is a percentage of the work delivered. 7. In your report, describe the apparatus, give the results of the calibration, and draw a curve, using brake foot-pounds as ordinates, and dynamometer foot-pounds as abscissae. 8. To use the dynamometer insert it between the prime mover and the machinery to be run. Special Directions for Calibrating the Webber Differential Dynamometer, Apparatus required : I. Ten small tension-weights. 2. Spring-balance or plat« form-scales. 3. Measuring-scale. 4. Calipers. 5. Stop-watch. Measurements : a. Weight of small tension-weights, b. " " fixed poise-weights. c. " " dynamometer-arm. d. ° " sliding poise. e. Length of dynamometer-arm to fixed poise. /. Length of dynamometer-arm to sliding poise. g. Diameter of brake-pulley. k. Thickness of brake-strap. 2 5 8 EXPERIMENTAL ENGINEERING. [§ 191 I. Friction-run. — Remove brake. Find time, in seconds, of 1000 revolutions (10 rings of bell). Balance dynamometer, arm ; the reading is the " zero-reading" by the beam, and must be corrected to get the true friction-reading. II. Test-runs. — Put on brake ; hang one weight on its slack side. Time, 1000 revs. Read simultaneously dynamom- eter-arm and platform scales. Repeat the same with succes- sive weights added. III. To Weigh Dynamometer-arm. — Run by hand, first for- ward and then backward, weighing in each case the turning effect, with the platform-scale applied at the knife-edge of the dynamometer-arm, and sliding-poise set at the zero-mark. 191. Form of Report.— The following blank is used in the exercises with the differential dynamometer in Sibley College: MECHANICAL LABORATORY, SIBLEY COLLEGE, CORNELL UNI- VERSITY. Calibration of Differential Dynamometer. Kind of Brake used Length of Brake-arm ft. Weight of Brake-arm lbs. Zero-reading of Brake-scales lbs. Date.* .189. . Observers 09 § 1- « O ,<" •- G II fi fl a! en rt V CO a u M 2 PQ £ T\ T* Ti-T* w d w c w^-w. »"4 wt-w D.H.P. I 2 3 4 5 6 7 8 9 IO § I93J MEASUREMENT OF POWER. CONSTANTS OF MACHINE. 259 Moment Arm ft. Data for Beam. Sliding Poise, Weight.... lbs. Loads at Knife-edge. Weight, lbs. Value, ft.- lbs. per 100 Revs. Moment Arm, Feet. Value, ft.. lbs. per 100 Revs. First Notch Last Notch Dvnamometer-beam ...= JV e Increase per Notch. W*= Zero-reading b y Beam. . ..ft.-lbs. Wq-\- W e =Friction-reading= . . .ft.-lbs. 192. Emerson's Power-scale. — One of the most complete transmission-dynamometers is shown in Fig. 135, with attached numbers showing the dimensions of the various sizes manu- factured. In this instrument the wheel C is keyed or fastened to the shaft ; the wheel B is connected with the wheel C near its outer circumference by projecting studs; the amount of pressure on these studs is conveyed by bent levers to a collar* which in turn is connected with weighing-levers. Small weights are read off from the scale D, and larger ones by the weights in the scale-pan N. A dash-pot is used to prevent sudden fluctuations of the weighing-lever. 193. Form of Report. — The following forms for report and log of tests on Webber Dynamometer and Emerson's Power-scale are used by the Massachusetts Institute of Tech- nology. REPORT. Test on •••• , No. Date. No. of test.... Ft.-lbs. per .seconds WEBBER DYNAMOMETER. I !.....:. I EMERSON POWER-SCALE. No. of test Duration of test Revolutions per minute. Load 26o EXPERIMENTAL ENGINEERING. [§ x 93. Emerson's Power-scales. § I94-] MEASUREMENT OF POWER. 26l BRAKE. I 1 2 <2 T-l . . T 2 Coefficient of friction No. of test H. P. by dynamometer. H. P. by power-scale.. H. P. by brake... 2-3 Signed.. . LOG. Test on No. Date. Webber Dynamomete r. Emerson Power-scale. Brake. u5 u c O c c 4- V a 3 CJ c •3 u a a .2 3 3.2 T3 a c 3 O U tn bO a •3 Pi 3 i 1-. 4) a CO 3 _o 3 O > V Pi < TestN umber 1 —. Tes mber I 2 3 1-3 2-3 H. P. by dynamometer H. P. by power-scale H. P. by brake ]••• Constants and Remarks. 194. The Van V/inkle Power-meter. — The Van Winkle Power-meter is shown in Fig. 136, complete, and with its parts 262 EX PERI MEN TA L ENGINEERING. [§ 194. separated, in Fig. 137. It consists of a sleeve with attached plate, B, that can be fastened rigidly to the shaft; and a plate ; A, which is revolved by the force communicated through Fig. 136.— Tan Winkle Power-meter. the springs ss. The angular position of the plated with refer- ence to B will vary with the force transmitted. This angular motion is utilized to operate levers, and move a loose sleeve I which may be clamped to the hub of L by the screw T. As this device moves only one one-hundredth as fast as the main shafts, the amount of 5 slip can be easily read. The pulley F and the brake M are mounted on a carriage, which can be drawn back by the screw N. The pulley E is mounted in a frame, supported on knife- edges below, R. The shaft H is fitted with a universal joint, to eliminate the effect of transverse strains on the dynamom- eter. Weighing-scales are placed at Ay £, and C, respectively, that at A is termed the dynamometer-scales ; that at B, the brake- scales that at C, the tension-scales. The reading on the tension- scales C, multiplied by the horizontal arm K, divided by the height d of the pulley E upon the knife-edge, gives the total tension on the belts T x -f- T 2 . The reading on brake-scales B, divided by the arm b of the brake, and multiplied by the radius D of the pulley F, gives the difference of tensions T 1 —T 2 . The brake-scale reading, multiplied by the brake-arm b y and by 2nn, n being the number of revolutions, gives tru delivered work in foot-pounds. The dynamometer scale-read- ing A y multiplied by the equivalent dynamometer-arm a and by 27T/Z, gives the work received in foot-pounds. The dyna- mometer-arm a is to be found as described in Article 1881 page 253. 198. Directions for Belt-test I. Before starting: (a) Get speed-indicator and log-blanks. (b) Oil all bearings and loose pulley under main belt. £ iq8.] measurement of power. 267 (c) Balance scales A and C, and note their "zero- readings." 2. With test-belt off : (d) Take friction-reading on scales A for driving-shaft, counting its revolutions. {e) Weigh brake-arm (see note below) to get zero- reading of scale B and then remove brake from brake-pulley. 3. With brake off : (/) Put on test-belt (while loose), first moving brake- shaft frame by unscrewing hand-wheel next the floor. Tighten belt to read while at rest 75 lbs. net, on scales C. (g) Take friction-reading again on scales A. Count revolutions of driving-shaft and read " per cent of slip," from which the speed of brake-shaft can be calculated. 4. Run I. (Ji) For tension of belt : Set scales C to read 50 lbs. net with belt at rest, by screwing up hand-wheel next the floor r which should not be changed during the run. Take reading of scales C for each load added on brake-scales B. (t) For power given out by belt : Set scales B to read 5 lbs. " net " or effective " load," and balance by tightening brake while running. Feed a light stream of water into rim of brake-pulley. Count its revolution*. (k) For power put into .belt : Read scales A and take speed of driving-shaft. (/) For slip of belt : Read graduated " slip-disk,'* which has 100 equal divisions. When vernier is set, it turns with the disk, and shows one per cent of slip when falling back one division during one turn of the slip-disk. (m) Thus continue to increase brake-load by $ lbs. of increments on scales B. Each time keep it carefully balanced, and take simultaneous readings on scales A, scales B, scales C 9 slip-disk, and revolution-counter. 5. Runs II., III., and IV. (n) For run II., set tension-scales to read 75 lbs. net with belt at rest, and proceed as in run I. Increase this initial tension-reading by 25 lbs. each, for runs III. and IV. 268 EXPERIMENTAL ENGINEERING. L§ '99- 6. Measurement of machine-constants : (p) Get length in feet of (i) brake-arm, (2) dynamom- eter-arm, (3) arms of bell-crank acting on tension-scales, and (4) circumferences of test-belt pulleys, — latter with steel tape. Calculate diameters. (p) If the pulleys differ in diameter, the reading on slip-disk, obtained while running " light " (see (g), above), will be the " zero" of all the slip-readings. N.B. Shut off water at brake-pulley when it stops. Note. — To weigh brake-arm : Loosen brake and oil face of pulley. Balance arm on scales while turning pulley first back- ward and again forward. The mean of the two readings will be the weight required. 199. Form of Log and Reports as used in Sibley Col- lege. Test of Belting by 189. . Description of Belt, Material Made by Length feet. Width inches. Thickness inches. Condition : = 6 £ g-g. O u *3 c B> £Q Pi n c i d 53 •j $ a j c u Scale-readings, lbs. i + + 3 *3 H h P c u .2 > "Jo'C gQ H V H Sh , O CO •Si Pi. O O Q Q £G~ < Rectangular; Usual form . . . h O b .63 to .58 Icbh \/^fh Francis h O b .622 %ch ^2gh{b — 0.\nh) Submerged.. . h ti b %cb\/2g(?$-h'*) r h h' b .62 cb{h-h')\/g(h+h'} Triangular: \ h O b' .617 •hcb'h \f2gh__ I h O 2.h tan a .617 ■fecbh? tan a \/2gh Ang. at b. 6o° h O i.i547^ .617 2.\-]c$ Ang. at b. 90 h O ih .617 ftbh* V^gh Trapezoidal: Cippoletti's. . . h O * + \h 0.629 %cbh ^2gh § 204- j MEASUREMENT OF LIQUIDS AND GASES. 27$ When still water cannot be found above the weir, and we have a velocity of approach that can be measured and is equal %>' — V2gh\ we can compute h\ Then Q=$.l$cb\_{k + k'f-k'*l* .... (16) In above formula Q = discharge in cubic feet per second, b the length of sill at bottom of notch. 203. Efflux of Water through Nozzles, or Conical Con- verging Orifices. — In this case, if we denote least area in square feet by F, in which c" is the coefficient of contraction, c f that of velocity, and c that of discharge, Qz=c'c' , FV~2~gk = cFV2gh (17) In this case the head is to be measured by a pressure-gauge attached close to the nozzle. The value of c is a maximum when the sides of the nozzle make an angle of 13 24/, attaining a value of 0.946. When the angle of the nozzle is 3 io', c = 0.895, and when 49 , c = 0.895. (See Church's Mechanics, page 692 ; " Hydromechanics," Encyc. Brit., page 475.) 204. Efflux of Water through Venturi Tubes or Bell- mouthed Orifices. — A conically divergent orifice, with rounded entrance to conform to the shape of the contracted vein, is now termed, from the first experimenter, Venturis tube. The dimensions of such a tube, as given in Encyc. Britannica, Vol. XII., page 463, are as follows, in terms of the small diameter (d). Large diameter (D) at opening equals 1.25*/; length equals .625^, or .$D. The sides are in section a circular arc, struck with a radius of 1.625^, from a centre in the line of (a) produced. * Rankine's Steam-engine. Hamilton Smith writes formula Q = 5.35^0*+ iKA 276 EXPERIMENTAL ENGINEERING. [§ 205. The formula of discharge is Q = c f FV^~k, ....... (18) in which F is the least area, h the head to be measured by a pressure-gauge attached to the pipe before the area of cross- section is reduced, c' the coefficient of velocity. The coeffi- cient of contraction in this case is equal to one. Weisbach gives the value of c' as .959, .975, and .994 for heads respec* tively 2 feet, 40 feet, and 160 to 1000 feet. Prof. Church, in his Mechanics, page 694, describes an ex- periment on a conically divergent tube 3 inches long, .8 inch diameter at least section. Coefficient of discharge with heads from 2 to 4 feet varied from .901 to .914. 205. Flow of Water under Pressure. — The pressure ex- erted by flowing water in pipes is very different from that due to still water under the same head. The pressure follows more or less closely the law enunciated in the theorem of Bernouilli, which may be stated in a general form as follows : " The exter- nal and internal work do7ie on a mass is equal to the change of kinetic energy produced ;" that is, the total energy of a flowing stream remains constant except for losses due to friction. In the flow of water through a pipe with varying cross- section the velocity of flow will be very nearly inversely as the area of cross-section. Since the energy or product of pressure and velocity is nearly constant by Bernoulli's theorem, as the velocity increases the pressure must diminish, and we shall find least pressure at the points where the cross-sections are least. From some experiments made by the author, the same law of varying pressure with varying cross-section applies in a less degree to the flow of steam through a pipe.* The formula expressing Bernouilli's theorem, neglecting friction, is & . P . — A \- z = constant; — *See "Hydromechanics," Encyc. Britannica, page 468. § 2o6.] MEASUREMENT OF LIQUIDS AND GASES. 2JJ in which v 1 -f- 2g is the velocity-head, / is the pressure per square foot, y the weight per cubic foot ; so that / -f- y is the pressure-head, and z the potential head, or vertical distance from any horizontal reference line. 206. Flow of Water in Circular Pipes.* — In this case there is a loss of head, h', due to friction. Denote the sine of the angle of inclination by t, diameter by d, length by L, loss of head by k/, all in feet coefficient of loss of head by £ ,,-^_ From experiments of Darcy, (19) C = 0.005 ( 1 + — %] for clean pipes; C = 0.0 1 ( 1 -| %) for incrusted pipes ; C = o.a\i + Y^j in general ; -y/i %#i (20) Q = jfv. (21) Loss of Head at Elbows. — In this case the loss is principally due to contraction. Weisbach gives the following formula? : *' = c£ • • (22) See " Hydromechanics, " Encyc. Britannica. 2J 8 EXPERIMENTAL ENGINEERING. If equal the exterior angle, [§ 206. C. = 0.9457 sin 3 — + 2.047 sin 4 -|. . . . (23) From this are deduced the following values 20° O.O46 40° O.I39 6o° 0.364 8o° 0.740 90° 0.984 IOO° 1.26 110° 1.556 120° I. 861 130° 2.158 For pipes neatly bent the value of Q e is much less. By equating k/ and hj in equations (19) and (22), a length of pipe can be found which will produce a loss of head equiva- lent to that produced by any given elbow. We shall have this additional length : Z = 4C* (24) On substituting the values of C e as above, and £ as equal to 0.006, this additional length will be found not to vary much trom 40 diameters for each 90 elbow, and 7 diameters for each 45 elbow. Loss of Head on entering a Pipe. — This loss is very small when a special bell-mouthed entrance is used, but is great in other cases. The loss of head in entering a straight tube is expressed by the formula ' = C zg (25) § 20%] MEASUREMENT OF LIQUIDS AND GASES. 279 Weisbach found Q c = 0.505. By making h p ' of equation (19) equal to n a \ and reducing, we find the additional length, L, of straight pip^ producing the same loss of head. L = 4C* Assuming C lias an average value of 0.006, and Q e as above, L = 2od. Loss of Head by abrupt Contraction of Pipe.- Weisbach found -In this case / = 0.316^, which would correspond to an additional length of pipe equal to about 13 diameters. When the mouth of the contracted pipe is reduced by an aperture smaller than the pipe, Weis- bach found the following values of C c . In the table, F 1 is area of orifice, F 2 that of pipe into which the flow takes place. Ei + F 2 C C • • O.I O.OI6 23I.7 gsod 0.2 0.614 50.99 2I2d 0.3 0.612 I9.78 S2d O.4 0.6IO 9.6l2 40-(f }■ ■<*> Substituting numerical values for the ratio of p^ to />, , we have &= 108.7^^0.16957; (33) * See article " Hydromechanics," Encyc. Britannica, Vol. XII, page 48] § 227.] MEASUREMENT OF LIQUIDS AND GASES. 297 To express this in terms of the volume discharged from the reservoir Q l , in which p x is reservoir pressure and p 2 pressure of discharge, we have a = (£)'&. Substituting numerical values for free flow, a = (o.s2 7 y- m Q, = 0.6339a-, ft=io8.7^(J)y^{i-(^ 29 }. . . (34) Substituting values of p t -f-/,, Q, = 68.8^ V^ri^T, (35) 227. Velocity of Flow of Air through an Orifice. — The velocity of flow is obtained by substituting numerical values in the preceding equations. We have, denoting by T x the abso- lute temperature in the reservoir as the greatest velocity of flow of air, £=183.6 7x1-0.8305). (36) Solving equation (36), we have the following theoretical results : Temperature of Air in Reservoir. 1 Velocity of Flow in Feet Degrees Fahr. Absolute. per Sec. 32 492.6 991 70 530.6 1030 IOO 560.6 IO58 I50 610.6 1 105 200 660.6 II48 300 760.6 1233 400 860.6 1312 500 960.6 1386 298 EXPERIMENTAL ENGINEERING. [§ 228. 228. The Weight of Air discharged. — This is to be com- puted by multiplying the volume of discharge by the specific weight. Thus the weight of air is P G. = l -^ pounds per cubic foot, when /, and T x are, respectively, pressure and absolute tem- perature in the reservoir. Hence the weight of air dis- charged is W y [ = Q 1 G 1 =ioS. 7 cF 1 G 1 [p^T i (i-(jJ' 2 \ . ( 37 ) Weisbach has found the following values of c, the coefficient of discharge : Conoidal mouth-piece of the form of the con- tracted vein, with effective pressures of 0.23 to 1.1 atmospheres 0.97 to 0.99 Circular sharp-edged orifices 0.563 to 0.788 Short cylindrical mouth-pieces 0.81 to 0.84 The same rounded at the inner end 0.92 to 0.93 Conical converging mouth-pieces „ . .... 0.90 to 0.99 In the general formula for the flow of air, the weight de- livered becomes a maximum when A / 2 \ y-x A V + " " This equals 0.527 for air and 0.58 for dry steam. This has been verified by experiment, and tends to prove that the press- ure of the orifice of discharge is independent of the back- pressure. In the flow of air from a higher to a lower pressure § 229.] MEASUREMENT OF LIQUIDS AND GASES. 299 through a small tube or orifice, the pressure in the orifice may be less than the back-pressure. 229. Flow of Air in Pipes. — When air flows through a long pipe, a great part of the work is expended in overcoming fric- tional resistances. This friction generates heat, which is largely used in increasing the pressure in the pipes, the only loss being from radiation, which is small. The expansion then is isothermal, the heat generated by friction exactly neutralizing the heat due to work. For pipes of circular section, when d is the diameter, /the length, p Q the greater and ■ p x the less pressure, T the absolute temperature, C the coefficient of discharge, c p (= 53.15 foot-lbs.) the specific heat, we have the initial velocity - = W^l <3*> This may be reduced to «.= (i.i 3 i9-a 7 26^)y/^. It has been found from recent experiments that fair values of the coefficient are as follows : * C = 0.005(1+^ in ordinary pipes for velocities of 100 feet per second ; C = 0.002 8 (l + 4) for pipes as smooth as those at the St. Gothard Tunnel. __ — ■ — * See " Hydromechanics," Encyc. Britannica, Vol. XII, p. 491. 300 EXPERIMENTAL ENGINEERING. [§ 230. Weight of air flowing per second in circular pipes in pounds is given by the equation =o.6nj/jg(A s -A')}- Approximately, ^=(0.6916/. -o.4438/i)(^)*. • • • (39) 230. Flow of Steam through an Orifice. — Velocity. — In this case, as in Article 226, the expansion is supposed to be adiabatic. Denote by A the reciprocal of the mechanical equivalent of one B. T. U. corresponding to the quantity 778 ; by x x the quality or percentage of dry vapor in the reservoir, corre- sponding to the pressure per sq. foot /, , and by x^ the quality in the tube, corresponding to pressure/, ; by r x the latent heat per pound in reservoir, r 2 the same in the tube ; T x and 7!, the respective absolute temperatures, 6 X and 3 the respective entropies of the liquids, c the specific heat of the liquid, q x and q^ the sensible heat of the liquid in reservoir and tube ; the reciprocal of the weight of a cubic foot of the liquid by cr. Then At? = X f x _ x%r% J r a x -q, + A cr(p i - / 3 ). . (40) x, can be determined from the relation expressed in the equation ^ + 0, = ^+0, (4I) § 230.] MEASUREMENT OF LIQUIDS AND GASES. 301 If no tables are at hand for 0, , its approximate value can be deduced, since T t e x - # 2 = c log, T 1 8 (42) So that ---■= -5F" + * log, =-. Eliminating x^ in equations (40) and (41), Av 2 _x l r 1 IF" (r a -r s )- T^-^+C^-^ + ^fo-A). (43) The following table, condensed from Peabody's steam tables, gives the value of the entropy of the liquid : TABLE OF ENTROPY OF THE LIQUID. Absolute Entropy Absolute Entropy Steam- of the Steam- of the pressuret Liquid, pressure, Liquid, P P I O.1329 65 0.4337 IO O.2842 70 O.4402 15 0.3I43 75 O.4464 20 O.3363 80 O.4522 25 0.3539 85 0.4579 . 30 O.3685 90 O.4633 35 O.38H 95 O.4686 40 O.3921 100 0.4733 45 O.4020 105 O.4780 50 O.4109 no O.4826 55 O.419I 115 O.4869 60 O.4267 120 0.4911 In the above equations^ has a numerical value of I -r- 778, a is nearly equal to 0.016, g to 32. 16. * See Thermodynamics, by Peabody, page 138. 302 EXPERIMENTAL ENGINEERING. [_§ 2 3 2 - It has been shown that in the flow of saturated steam p will not fall below 0.58 of p lt because at that point there is the maximum weight of discharge. In the actual trials this seems to be nearer 0.61 than 0.58. If we assume p a equal to 0.6/ , , the velocity will be found to be nearly constant, and to vary but little from 1400 feet per second. 231. Weight of Steam discharged through an Orifice. — This was determined experimentally by R. D. Napier, and expressed by the formula 70' in which W= weight discharged in pounds per second, F — area of orifice in square inches, and/, is the absolute pressure of the steam, pounds per square inch, which is equal to or greater than if that of the atmosphere. This formula has been verified by experiments made in the Laboratories of Sibley College and also at the Massachusetts Institute of Technology, and is found to vary but little from the actual results. 232. Measurement of the Flow of Gas. — Gas-meters. — In the measurement of gas the product of absolute pressure, p, by volume, v, divided by absolute temperature, T, is a con- stant quantity. Thus pv p x v x Y == ~7\' If p and T can be kept constant, the quantity discharged will vary as the volume ; \i p and T are known, the quantity dis- charged can be computed. Gas-meters are instruments for measuring the volume of gas passing them. They are constructed on various plans and are known as Wet or Dry, depending on whether water is used. The volume is usually measured in cubic feet. Meter-prover. — This is the name given to a sort of gasometer arranged as shown in Fig. 147. It consists of an open vessel. § 232.J MEASUREMENT OF LIQUIDS AND GASES. 303 BE, partly filled with water, into which a vessel, AF, of some- what smaller diameter is inverted. The weight of the vessel AF is counterbalanced by a weight W which descends into a vessel of water CK at such a rate as to keep the sum of the displace- ments of the two vessels constant, in which case the pressure Fig. on the confined gas in the vessel AF will remain constant. The gas flows out through the pipe T, its pressure being taken by a manometer at m, its temperature by a thermometer at t. Fig. 148 shows a form of meter-prover made by the Ameri- can Meter Co., in which the counterweight lifts an additional weight moving over an involute wheel, so calculated that the pressure on the outflowing gas remains constant. These instru- ments are used principally to calibrate meters ; they give very accurate results, but are not suited for continuous measure- ments. Wet-meter. — The wet-meter works on the same principle as the meter-prover, but is arranged with a series of chambers 304 EXPERIMENTAL ENGINEERING. [§ 232. which are alternately filled and emptied with gas. These chambers are usually arranged like an Archimedean screw, as shown in section in Fig. 149. Fig. 148.— Meter-prover. Gas is admitted just above the surface of the water, and raises the partition of the chamber, bringing it above the water and filling it. The outlet-pipe is submerged until the chamber is filled. It is connected with the case of the meter, as shown in the figure. The gas is completely expelled as the cylinder revolves. § 232. J MEASUREMENT OF LIQUIDS AND GASES. 305 The wet-meter is a very accurate measure of the gas pass- ing, provided the water-level be maintained at the constant standard height. Any change of the water-level changes the size of the chambers accordingly. The motion of the cylinder actuates the recording mechanism. Fig 149.— The Wet-meter. The Dry Gas-meter. — The dry gas-meter possesses the ad- vantage of not being affected by frost, nor of increasing the amount of moisture in the gas. The dry-meter is made in vari- ous forms, and generally consists of two chambers separated from each other by partitions. Each chamber is divided into two parts by a flexible partition which moves backwards and forwards, and actuates the recording mechanism as the gas flows in or out. This motion is regulated by valves somewhat similar to those of a steam-engine. The gas-meter is calibrated by comparing with . a meter-pro ver as already described. These meters are not supposed to be instruments of great accuracy. 306 EXPERIMENTAL ENGINEERING. L§ 233. 233. Anemometers.— Instruments that are used to measure the velocity of gases directly are termed anemometers. They consist of flat or hemispherical vanes mounted like arms of a light wheel so as to revolve easily. The motion of the wheel actuates a recording mechanism. Robinson's Anemometer, which consists of hemispherical cups revolving around a vertical axis, is much used for meteorological observations. A form shown in Fig. 150 with flat vanes, and with the Fig. 150. — Biram's Portable Anemometer. dial arranged in the centre as shown, or on top of the case in various positions, is much used as a portable instrument. The dial mechanism of the anemometer can be started or stopped by a trip arranged convenient to the operator ; in some instances the dial mechanism is operated by an electric current similar to that described in connection with the tachometer, Article 221, page 262. It is also made self-recording, by attach- ing clock-work carrying an endless paper strip which is moved under a pencil operated by the anemometer mechanism. § 234-J MEASUREMENT OF LIQUIDS AND GASES. 307 234. Calibration of Anemometers. — Anemometers are calibrated by moving them at a constant velocity through still air and noting the readings on the dials for various positions. This is usually done by mounting the anemometer rigidly on a long horizontal arm which can be rotated about a vertical axis at a constant speed. The distance moved by the anemometer in a given time is computed from the known distance to the axis and the number of revolutions per minute ; from these data the velocity is computed. In performing this experiment care must be taken that the axis of the anemometer is at right angles to the rotating arm. Readings should be taken at various speeds, since the correc- tion is seldom either a constant quantity or one directly de- pendent on the velocity. The Anemometer can also be calibrated by computing the heating effect due to the condensation of a given amount of steam. The method of calibration would be as follows: pass the air through a tube or box containing a coil of steam-pipe sufficient to warm the air sensibly, say 20 or 30 degrees. Measure the quality of the entering steam and the amount of condensation, and from that compute number of heat-units taken up by the air. Guard against all loss of heat by the air; then this last quantity becomes evidently equal to the increase in temperature of the air multiplied by its specific heat, multiplied by its weight. From this computation the weight of the air can be computed. Knowing the weight of air and its temperature, compute the volume flowing in a given time, divide this result by the area of the cross-section, and obtain the velocity. This method is likely to give more satisfactory results than that of swinging the dynamometer in the air. Also see Chapter XXIV, Art. 490. CHAPTER IX. HYDRAULIC MACHINERY. 235. General Classification. — Hydraulic machinery may be divided into the two classes, hydraulic motors and pumps. In the first class a quantity of water descending from a higher to a lower level, or from a higher to a lower pressure, drives a machine which receives energy from the water. In the latter class a machine driven by some external source of energy is employed in lifting water from a lower to a higher level. The student is advised to consult the following authorities on the subject : Rankine's Steam-engine ; article " Hydromechanics," En- cyc. Britannica ; Weisbach's Mechanics, Vol. II. (Hydraulics); " Systematic Turbine-testing," by Prof. Thurston, Vol. VIII. Transactions Mechanical Engineers ; " Notes on Hydraulic Motors," by Prof. T. P. Church. 236. Hydraulic Motors — Classification. — The following classes of hydraulic motors are usually recognized : I. Water-bucket Engines, in which water poured into sus- pended buckets causes them to descend vertically, so as to lift loads and overcome resistances. II. Water-pressure Engines, in which water by its pressure drives a piston backward and forward. III. Vertical Water-wheels, in which the water acts by weight and impulse to rotate them on a horizontal axis. IV. Turbines, in which the water acts by pressure and im- pulse to rotate them around a vertical axis. V. Rams and Jet-pumps, in which the impulse of one mass of fluid is used to drive another. 308 §239-] H YDFA ULIC MA CHINER V. 3 09 237. Energy of Falling Water. — Hydraulic motors are driven either by the weight, pressure, or impulse of moving water. Neglecting the losses due to friction or other causes, the energy of falling water is the same whether it act by (I.) weight, (II.) by pressure, or (III.) by impulse. This is proved as follows : Let h equal the head or total height of fall, Q the discharge in cubic feet per second, G the weight per cubic foot,/ the pressure in pounds per square foot, v the velocity in feet per second, P the pressure in pounds per square inch. Since the work done is equal to the product of the force acting into the space moved through, we have for the work done per second in the several cases (I.) GQh, (II.) (pQ), (III.) GQ— ; but since p = Gh and h = — , we have by substitution GQk=pQ=GQ~ = i44PQ^ .... (I.) 238. Parts of an Hydraulic Power- system. — The hydrau- lic power-system in general requires — 1. A supply-channel or tube leading the water from the highest accessible level. 2. A discharge-pipe or tail-race conveying the water away from the motor. 3. Gates or valves in the supply-channel, and a waste-chan- nel or weir to convey surplus water away from the motor. 4. The motor, which may belong to any of the classes de- scribed in Article 236, and suitable machinery for transmitting the energy received from the motor to a place where it can be usefully applied. 239. Water-pressure Engines.* — Water-pressure engines are well adapted for use where a slow motion is required and a great pressure is accessible. * See Weisbach's Hydraulics, Vol. II, p. 558. 3io EXPERIMENTAL ENGINEERING. [§ 2 4 0. These engines resemble in many respects a steam-engine, water being the motive force instead of steam. They consist of a cylinder (Fig. 151) in which a piston T is worked alter- Fig. 15T.— Water-pressure Engine. nately forward and backward, water being admitted alternately at the two ends of the cylinder by the moving slide-valve 6". While water is passing into one end of the cylinder through the passages D> E, C, it is being discharged through the pipe E t G t H, which is proportioned so as to afford a free exit to the water. Near the end of the stroke of the piston the slide- valve S closes both admission-ports, and the pressure in the cylinder C x is increased by the diminution of volume caused by the motion of the piston. When the pressure in the cham- ber C x exceeds that in the supply-pipe the valve W x opens, and the water passes into the supply. Simultaneously the valve Fis opened by suction, and water passes into the cham- ber C from the discharge-pipe. The effect of this action is to gradually arrest the motion of the piston at the end of the stroke by reducing the pressure on one side and increasing the resistance on the other. When the piston reaches the end of the stroke the slide-valve is reversed in position and a new stroke is commenced. 240. Vertical Water-wheels. — There are four classes of vertical water-wheels : I. Overshot, in which the water is received on the top of §241.] HYDRA ULIC MA CHINE R Y. 3" the wheel and discharged at the bottom, the water acting prin- cipally by weight. 2. Breast, in which the water is received on the side of the wheel and held in place by a guide or breast, the water acting both by impact and weight. 3. Undershot, in which the water acts only on the under side of the wheel, the water acting principally by impact. 4. Impact, in which the water is delivered to the wheel by a nozzle, acting generally on the top or bottom, and by im- pulse only. 241. Overshot Water-wheels. — The overshot water-wheel shown in section in Fig. 152 is well adapted to falls between 10 and 70 feet and to a water- supply of from 3 to 25 cubic feet per minute. On the outside of the wheel is built a series of buckets, which should be of such a form as to receive the water near the top at D without spilling or splashing, to retain the water until near the bottom, and to empty completely at the bot- tom. The number of buckets must be such that there shall be no spilling by overflow at the top. The head of water above the wheel must be sufficient to give the falling water greater velocity than the periphery. The peripheral velocity in practice is from 5 to 10 feet per second, that of the falling water from 9 to 12 feet per second, corresponding to a height of from 16 to 27 inches above the wheel. These wheels are not adapted to run in back water, and have the greatest efficiency for a given head when revolving just free from the discharged water. The principal formulae relating to the overshot-wheel are as follows : Fig. 152. — Section of Overshot Water- wheel. 3 I2 EXPERIMENTAL ENGINEERING. [§ 2 4 I. Let d equal the depth of the buckets, b the width of the wheel, r the radius of the wheel, n the number of revolutions per second, v the peripheral velocity in feet per second, Q the water-supply in cubic feet per second, Q x the capacity of that part of the wheel that passes in one second, m the ratio of the water actually carried to the capacity of the buckets — m being usually about one fourth — .AT the number of buckets. Fig. 153.— Section of Breast-wheel. Then, supposing the wheel to be set just free of the back water, h = 2r -\- (i-J- to 2) all in feet ; 27ZT N = —j- = , usually, or ; bv Q 1 = —{2rd— d*) = bdv, nearly; Q — mQ, —rnbdv ; v = 2nnr. § 243-] HYDRA ULIC MA CHINE R Y. 3 I 3 The efficiency is the ratio of the work delivered to the en- ergy received from the falling water. The efficiency of the best wheels of this class reaches 75 per cent. 242. Breast-wheels. — The form of breast-wheel is shown in Fig. 153. The water is received at a height slightly above or below the centre C of the wheel, and is prevented from falling away from the wheel by the curved breast ABB; the water acts on the radial or .slightly curved buckets, thus tending to revolve the wheel partly by weight and partly by impulse. The flow of water is regulated by a gate at 5. The formulae applying to breast-wheels are essentially the same as those for overshot-wheels. The efficiency of the best wheels of this class varies from 58 to 62 per cent. 243. Undershot-wheels. — The undershot-wheel differs from the breast-wheel in receiving the water at or near the bottom ; the water flows in a guide under the wheel, which guide in some cases extends some dis- tance up the sides. The usual form of such wheels is shown in Fig. 154; the buckets or floats are often radial, sometimes, however, of con- cave or bent form. If we let c equal the velocity of water as it strikes the wheel, v the peripheral velocity of the wheel, Q the quantity of water in cubic feet FlG - 154.— Undershot-wheel. per second, G the weight per cubic foot, k 2 the portion of the head corresponding to the elevation of the entering water as it strikes the wheel over that of the discharge, P the force de- livered at the circumference of the wheel ; then will the effi- ciency rf be obtained by the following formulae :* Pv Tf=z &[£=&+$ * See Weisbach's Hydraulics, page 291. 314 EXPERIMENTAL ENGINEERING. [§244 From experiments of Morin it was found that when v -r- c was less than 0.63, the efficiency 7 was 0.41. When v -7- c was between 0.63 and 0.8, rf was 0.33. The efficiency obtained from the best form of these wheels is O.55. Poncelefs Wheel. — When the floats of the undershot wheel are curved in such a manner that the entering jet of water is allowed to flow along the concave sides and press against them without causing shock, a greater effect is obtained than when the water strikes more or less perpendicularly against plane floats. Such wheels are called, after their inventor, Poncelet wheels. The efficiency of such wheels in some instances has reached 68 per cent. 244. Impulse-wheels. — In this class of wheels several jets of water impinge on the buckets of the wheel as they are successively brought into position by the rotation. This class is very efficient for high heads and a small supply of water. The efficiency to be obtained by the action of a jet of water on a moving bucket is fully discussed in Vol. II., Church's " Mechanics of Engineering," page 808. Denote by c velocity of the jet, v the peripheral velocity of the vane, ex the angle of total deviation relatively to the vane of the stream leaving the vane from its original direction, G the weight per cubic foot of water, F the area of the stream, Q the volume of flow per unit of time over the vane. The work done per unit of time, OC L = Pv = —-(c — v)v[i — cos a], o This is maximum when v — \c. In case a hemispherical vane is used, a will equal 180 , and 1 — cos a = 2. For that case, a == 180 and v = \c> we have L=Z QG t_ g ' *' In case the absolute velocity of the particles leaving the vane equal zero, an efficiency equal to unity would be possible. § 245-] HYDRA ULIC MA CHINE R Y 315 One or more jets of water are used as necessary to produce the maximum power. Fig. 155 shows the Pelton wheel, provided with four jets. The bucket of this wheel shown at B is of double hemispherical form with a sharp midriff, separating the two parts, which splits the jet and turns each part through an angle of 180 . The efficiency of is wheel has in some instances ex- ceeded 80 per cent. Fig. 155. — The Pelton Impulse-wheel with Four Jets. There is a large number of motors in this class, some of which are adapted for high heads and large powers. The Doble wheel is provided with a needle regulating- valve controlled by the governor. The Cascade has buckets arranged on each side of the wheel, the edge of the wheel serving to divide the jet. Most of the small hydraulic motors are of impulse type. 245. Turbines. — The turbine-wheels receive water con- stantly and uniformly, and usually in each bucket simultane- ously. The buckets are usually curved, and the water is guided into the buckets by fixed plates. The name was originally applied in France to any wheel rotating in a horizontal plane, but the wheels are now frequently erected so as to revolve in vertical planes. The turbine was invented by Fourneyron in 1823, the original wheel being constructed to receive water near 3l6 EXPERIMENTAL ENGINEERING. [§246. the axis, and to deliver it by flow outward at the circumfer- ence. Turbines are now built for water flowing parallel to the axis, and also inward from the circumference toward the centre ; they are also constructed double and compound. In some of the turbines the wheel-passages or buckets are com pletely filled with water, in others the passages are only partly filled. The following classes are usually recognized : I. Impulse Turbines. II. Reaction Turbines. In both these classes the flow may be axial outward, in- ward, or mixed, and the turbine may be in each case simple, double, or compound. In the Impulse turbines the whole available energy of the water is converted into kinetic energy before it acts on the mov- ing part of the turbine. In these wheels the passages are never entirely filled with water. To insure this condition they must be placed a little above the tail-water and discharge into free air. In the Reaction turbines a part only of the available energy of the water is converted into kinetic energy before it acts on the turbine. In this class of wheels the pressure is greater at the inlet than at the outlet end of the wheel-passages. The wheel-passages are entirely filled with water, and the wheel may be, and is generally, placed below the water-level in the tail-race. 246. Theory of the Turbine. * — The water flowing through a turbine enters at the admission-surface and leaves at the dis- charge-surface of the wheel, with its angular momentum rela- tive to the wheel changed. It must exert a couple —M, tend- ing to rotate the wheel, and equal and opposite to the couple M which the wheel exerts on the water. Let Q cubic feet enter and leave the wheel per second, c x , c 2 be the tangential com- ponents of the velocity of the water at the receiving and dis- charging surfaces of the wheel, r 1 , r 2 the radii of these surfaces. Then -if=^(v.— vj (1) g_ * See " Hydromechanics, " Encyc. Britannica. § 246. J H YDRA ULIC MA CHINER Y. 3 I 7 If a is the angular velocity of the wheel, the work done on the wheel is GO T = Ma = — — (c x r i — c^r^a foot-pounds per second. (2) The total head of the water h t is reduced by friction and resistances h p in the channels leading to the wheel, so that the effective head h which should be used in calculating the efficiency is h — h t — h p (3) In case the construction of the turbine requires that it set above tail-race d feet, the velocity of water in the turbine should be calculated for a head of h— d, but the efficiency for a head of h feet. The work of the turbine is partially absorbed in friction. Let T equal the total work, T d the useful work, and T t the work used in friction. Then T=T d +T t (4) The gross efficiency '=A" • • ; « The hydraulic efficiency n= m (6 > The hydraulic efficiency is of principal importance in the theory of turbines. Substituting this value of T in equation (2), far, — cs^a . 1- g k ' (7 > which is the fundamental equation in the theory of turbines. 318 EXPERIMENTAL ENGINEERING. [§247. For greatest efficiency the velocity of the water leaving should be o, in which case c t = o and C T SY V = ^- ....... (8) But r t a is the lineal velocity of the wheel at the inlet surface ; if we call this V x , V= C 4r (9) The efficiency of the best turbines is 0.80 to 0.90. Speed of the Wheel. — The best speed of the wheel depends on frictional losses which have been neglected in the preced- ing formulae. The best values are the ones obtained by ex- periment. Let V equal the peripheral velocity at outlet, V { at inlet, r and r t the corresponding radii of outlet and inlet surfaces. Then we shall have as best speeds* for axial-flow turbine V — V t = 0.6 V2gk to 0.66 V2gh ; radial outward-flow turbine V t = 0.56 \2gh; V = FJ r n r n radial inward-flow turbine V t = 0.66 V2gh ; V = V t - . 247. Forms of Turbines. — Fourneyron s Turbine. — This is an outward-flow turbine, with a horizontal section as shown in Fig. 156. C is the axis of the wheel, which is protected irom the water by vertical concentric tubes shown in section. On the same level with the wheel and supported by these tubes is a fixed cylinder, with a bottom but no top, contain- ing the curved guides F F. The wheel AA is supplied with curved buckets bd, b x d x , so arranged as to absorb most of the energy of the water; the water enters the wheel at -the inner edges of the buckets and is discharged at the outer circum- * " Hydromechanics " Encyc. Britannica. § 2 4 8.] HYDRAULIC MACHINERY. 319 ference. Gates for regulating the supply of water are shown in section between the ends of the guides and the wheel. Fig. 156.— Outward-flow Turbine. 248. Reaction - wheels. — The simple reaction-wheel is shown in Fig. 157, from which it is seen to consist of a vertical cylinder, CB, which receives the water, and two cylindric arms, G and F\ on opposite sides of each arm is a circular orifice through which the water is discharged. The effect of this arrangement is to reduce the pressure on the sides toward the ori- fices, thus producing an unbalanced pressure which tends to make the wheel revolve. If we denote by h the available fall measured from the level of the water in the vertical pipe to the B|j||j§|j centre of the orifices, r the radius of Bl rotation measured from the axis to the FlG - 157.-THE Reaction-wheel. centre of each orifice, v the velocity of discharge, a the angular velocity of the machine, F the area of the orifices, — when at rest the velocity would equal ¥2gh, but when in motion the water in the arms moves with a velocity ar, which corresponds to an increased head due to centrifugal force of arV -+- 2g. 320 EXPERIMENTAL ENGINEERING. [§ 2 4 8. Hence the velocity of discharge through the orifices is v = V2gh + tfV 2 ; /he quantity discharged FV2gk + a i r\ Since the orifices move with a velocity ar, the velocity with reference to a fixed point is v — ar. If G be the weight per cubic foot, the momentum or mass times the velocity is — (v — ar) g This mass moves with an angular velocity a and arm r, hence the work done per second in rotating the wheel is CO (v — ar)ar foot-pounds. The work expended by the water-fall is GQk. Hence the efficiency p = (v — ar\ar gh This increases as ar increases, or the maximum efficiency is reached when the velocity is infinite. The friction considera- bly reduces these results, and experiment indicates the greatest efficiency when ar = V2gk. In which case, by substitution, we should have rf = 0.828. The best efficiency realized in prac- tice with these wheels is about 0.60. The Scottish turbine, shown in Pip - , 1 16 in section, is a reaction-wheel with Fig, 158.— Scottish Turbine, three discharge-jets, the water being supplied from a tube filled with water under pressure beneath the wheel. $ 2 49-] HYDRAULIC MACHINERY. 321 249. The Hydraulic Ram. — The hydraulic ram is a ma- chine so arranged that a quantity of water falling a height k forces a smaller quantity through a greater height h\ 2 - > Fig. T59.— Hydraulic Ram. The essential parts of the hydraulic ram are: I. The air- chamber C, connected with the discharge-pipe eD, and pro- vided with a clack or check-valve 0, opening into the chamber C from the pipe ss. 2. The waste-valve, Bd, is a weighted clack or check- valve, opening inward and connected to a stem df\ on the stem is a nut or cotter at f to regulate the length of stroke, i.e., amount of opening of the waste-valve. 3. The supply-pipe ss, that leads to a reservoir from which the supply is derived, should be of considerable length. If it is very short when laid in a straight line, bends must be made to secure additional length, and also to present some resistance to the backward wave-motion ; its length must not be less than five times the supply-head. The working parts of the ram are the check-valve o and the waste-valve dB ; these parts move in opposite directions, and alternately. The action of the ram is explained as follows : 322 EXPERIMENTAL ENGINEERING. [§ 250. Water is supplied the ram by the pipe ss ; the waste-valve dB being open, the water escapes with a velocity due to the height h. The water escaping at <^ suddenly closes the waste- valve. The acquired momentum of the moving column of water in the pipe ss is sufficient to raise the valve and dis- charge a portion of its weight to a height k '. As soon as the pressure is reduced the valve closes, the waste-valve dB opens and the water again flows down the pipe ss. These motions are produced with regularity, and the water acquires a backward and forward wave-motion in the pipe ss. A small air-chamber at/, with a small check-valve opening inward at c to supply the chamber with air, are found to add to its efficiency. The wave-motion has been utilized to operate a piston back- ward and forward beyond the waste-valve, the piston being utilized as a pump in raising water from a different supply. Formnlce. — Let h equal the height of the reservoir above the discharge-valve of the ram, h' the height to which the water is raised above reservoir, Q the total water supplied to the ram per second, q the amount raised to the height h! , G the weight per cubic foot. Then the useful work equals Gqh' ; the work which the water is capable of doing equals Gh(Q — q). The efficiency qh' V = (Q - q)Jl Rankine (see Steam-engine, page 212) gives the following formulae for obtaining the dimensions of a ram : Let L equal length of supply-pipe, D the diameter of supply-pipe in feet ; other symbols as above. Then 2h' D = V1.63Q, L = h + ti + -p Volume of air-chamber C equals volume of feed-pipe. 250. Methods of Testing Water-motors. — The methods of testing hydraulic motors require in all cases the measure- § 250.] HYDRA ULIC MA CHINER Y. 323 ment (1) of volume or weight of the water discharged, (2) of the net head, or pressure acting on the motor, or (3) the velocity of discharge. From these measurements may be com- puted the energy received by the motor, by the formulas already given. 1. Measurement of the Water may be made in the case of small motors by receiving the discharge in tanks standing on scales ; two tanks will be required, one of which is filling while the other is emptying. Temperature observations must be taken, and from the known weight and temperature the volume (<2) may be computed, if required. The tanks may be previ- ously calibrated by filling to a known point, and be so con- nected that any excess will pass into the tank recently emptied, in which case a method similar to the above may be used with- out scales. The measurement will usually have to be made by discharg- ing over weirs (see page 2 74) or through nozzles or Venturi tubes; this will be especially true for large motors. With water-pressure engines an approximate measurement may be made by the piston-displacement, corrected for slip. A discussion of the effect of slip is to be found on page 302. 2. Measurement of the Head (h) may be made, in the first place, by taking a series of levels from standing water in the tank or dam above, to the level of the water in the tail-race. This measurement must be corrected for loss of head by fric- tion in the pipes, or by flowing over obstructions, etc., this at best can be made only in an approximate manner. To secure the full effects of the head, some turbine-wheels are set with draught or suction tubes leading from the wheel to the water- level in the tail-race ; this will not affect the method of measur- ing the head. The head acting on the wheel is measured most accurately by a calibrated pressure-gauge, placed in the supply- pipe near the motor. The reading of this gauge if merely at- tached to the supply-pipe in the usual manner, would be that due to the pressure-head only, and would be less than the true head acting on the pipe. By inserting a tube well into the current, and bent so as to face the current, thus forming a Pitot 324 EXPERIMENTAL ENGINEERING. [§ 2 5l» tube (Article 222, page 292), the pressure will be increased the amount due to the velocity-head, and the gauge if attached to this tube will give the pressure corresponding to the actual head. To the head so obtained must be added the distance from the centre of the gauge to the level of the water in the tail-race. In case the draught-tube is used, a vacuum gauge or mercury manometer can be attached, and the suction-head calculated from the gauge-reading may be compared with the measured distance. In case two gauges are used, the vertical distance between them must be measured, and considered a portion of the head. To obtain the head corresponding to a given pressure, in pounds per square inch, multiply the gauge-reading by the height, in feet, of water corresponding to one pound of pressure. One pound of pressure per* square inch corresponds to 2.308, 2.309, 2.31, 2.312, 2.315, 2.319, and 2.32 feet of head of water at the temperatures of 40 , 50 , 6o°, yo°, 8o°, 90 , and ioo° F., respectively. The head of one inch of mercury corresponds to 1.13 feet of water a_ ;\r>° F. Knowing che quantity or weight of discharge and the head, the energy received may be computed by any one of the four forms in equation (1), Article 237, p. 309. 3. The velocity of discharge can seldom be measured directly \ it can be computed from measures of the pressure or net head,, since the velocity V = V2gh. It is rarely of importance. In case the motor is supplied with water through a nozzle, its least area may be determined by measurement ; then the quantity discharged may be computed as the product of ve- locity, least area, and coefficient. (See Article 204, p. 275.) 251. Special Tests. — Backus or Pelton Motors. — Apparatus needed. — Pressure-gauges, two receiving tanks on scales or small w r eirs, Prony brake, pipes to remove water, thermometer. Testing Directions. — Measure nozzle ; note its position and the angle at which jet will strike buckets ; attach pressure- gauge, and arrange to measure discharged water ; attach Prony brake. Vary the head of water by throttling the supply ; if §251.] H YDRA ULIC MA CHINER V. 325 heads are required greater than will be given by the water-works pressure, they must be supplied by pumping with a steam- pump. Take four runs of one half-hour each, with heads varying by one fourth, the greatest to be attained. Obtain corrections to head for position of gauge. Make running start. Take observations once in five minutes of water dis- charged, temperature, gauge-readings, weight on Prony brake- arm, and number of revolutions. In report, describe motor, with dimensions, method of test- ing; compute energy received in foot-pounds per minute and in horse-power ; compute work done in the same units ; compute efficiency of each run, also for varying velocity of perimeter. Make a plot on cross-section papef, with work delivered in foot-pounds per minute as abscissae, and heads as ordinates. Compare theoretical with actual efficiency. Turbine Water-wheels. — Large weirs must be arranged with which the discharged water can be measured. A Prony brake is to be arranged to absorb the power from the wheel, or a large transmitting dynamometer may be provided to receive the power developed by the wheel. Measurements to be made as explained in Article 250. Water-pressure Engines are to be tested essentially as described for the hydraulic ram. When used to operate a pump, indicator-diagrams are to be taken from both engine and pump ends, as explained in the chapter on steam-engine testing. From these can be computed the energy received by the pistons of the water-engine and that delivered from the piston of the pump. The quantity of water received will have to be meas- ured independently. Hydraulic Ram. — Apparattis ' as before, with additional pressure-gauge for discharge-pipe, means of measuring the water delivered and the water wasted. Testing. — Measure head of water acting on the ram and of that delivered as explained. Make runs of one half-hour each, with varying heads of supply and delivery. Take ob- servations once in five minutes of gauge on supply-pipe, on 326 EXPERIMEN TA L ENGINEERING. [§ 252. delivery-pipe, of weir-readings or weights of water wasted, and of water delivered. Compute the energy received and work done expressed in foot-pounds per minute, and also the effi- ciency for each run. In Report. — Describe the ram, method of testing, and draw a curve, with heads as ordinates and foot-pounds of work as abscissae. 252. Forms for Tests of Hydraulic Motors. — The fol- lowing form for log and results has been used by the author : Efficiency test of Water-wheel. Type Rapacity At \ Date B n Length of Brake-arm. . . ... .ft. ; Weir zero Diam. Temp. Water °F. Q = DATA. £ = D. H. P . WXH X 33,ooo. Head on Wheel. Lbs. Ft Water used. Cu. ft. per sec. Lbs. per min. eta. D.H.P. 2 c - V O l-i a o P.t! Form and dimensions of Buckets Number of Buckets Form of Delivery-tube Diameter The following form for test of the Swain turbine is used at the Massachusetts Institute of Technology : § 2530 No. HYDRAULIC MACHINERY. TEST ON SWAIN TURBINE. Date 327 188.. Time. Read- ing of Coun- ter. Revolu- tions per.... Minutes. Load on Brake. Height of Water in Tank. Height of Water Wheel- pit. Read- ing of Hook- gauge. f Hook- "If I gauge 1 1 Read-f I ing- J Tem- pera- ture in Wheel- pit. Total Diameter of wheel ft. Radius of brake ft. Crest of weir above floor of pit ft. Width of weir and pit ft. Correction for hook-gauge ft. Observed depth on weir (corrected). .ft. Total head acting on wheel ft. Weight of 1 cubic foot water at ° Fahr lbs. Revolutions of wheel per minute Quantity of water passing weir (uncorrected) cu. ft. " " " (corrected) cu. ft. Available work ft.-lbs. per sec. Work at brake ft.-lbs. per sec. Efficie ,per cent. lency .... , H orse-power of wheel , Velocity due to head acting on wheel ft. per sec Velocity of outside of wheel ft. per sec Signed 253. Classification of Pumps. — The different classes of pumps correspond almost exactly to the different classes of water-motors, with the mechanical principles of operation reversed. 328 EXPERIMENTAL ENGINEERING. [§ 2 34. Ordinary reciprocating pumps correspond to water-engines; chain- and bucket-pumps, to water-wheels in which the water acts principally by weight. Scoop-wheels are similar to under- shot water-wheels, and centrifugal pumps to turbines. The various classes of pumps are as follows : A. Reciprocating, divided according to the method of con- struction into lift, force, combined lift and force, double-acting, and diaphragm. B. Rotary, divided into: (1) inferential, in which the water is urged forward by the velocity of the working parts of the pump, as in the centrifugal pump ; (2) positive, in which all the water that passes the pump is lifted or forced by the work- ing parts of the pump to a higher level ; the working parts of these pumps are usually gears or cams meshing together. These pumps are often spoken of as rotary, in distinction from centrifugal. Pumps are also classified by the power used to drive them. Thus, pumps driven directly by attached engines are termed steam pumping-engi?tes or steam-pumps; those driven from run- ning machinery by belts or gears are termed power-pumps; those operated by hand, hand-pumps. 254. Duty and Capacity. — The term duty is applied to the work done by steam-pumps. This term originally signified the number of pounds of water lifted one foot by the consumption of one bushel (94 pounds) of coal ; more recently it has been the water lifted one foot by the consumption of 100 pounds of coal. It has, in recent tests, been customary to assume that each pound of coal evaporates ten pounds of water, from and at 212 , under atmospheric pressure. As each pound of water evaporated under such conditions requires 965.7 British thermal units,* and each B. T. U. is equivalent to 778 foot-pounds of work, a definite amount of work is done by 100 pounds of coal, equivalent to 965,700 B. T. U., or to 751,314,600 foot-pounds. The duty of a power-pump, expressed in the same manner, * A British thermal unit, symbol B. T. U., is the heat absorbed in raising one pound of water one degree Fahr. in temperature. §255-] H YDRA ULIC MA CHINER Y. 3 2 9 k the number of foot-pounds of water raised by 751,314,600 foot-pounds of energy expended on the pump and accessories. A committee appointed by the American Society of Me* chanical Engineers (see Vol. XL of Transactions American Society Mechanical Engineers, p. 668) recommend that in a standard method of conducting duty trials, 1,000,000 thermal units, or 778,000,000 foot-pounds, be taken as the basis from which the duty is computed. This is equivalent to the evapo- ration of 10.35 pounds of water per pound of coal, from and at 212 , and is likely to be adopted in future trials, in which case the duty becomes the number of foot-pounds of water delivered for 1,000,000 British thermal units of energy supplied the plant. The capacity of a pump is usually expressed as the number of gallons of water that can be raised against a specified head in 24 hours of time; a gallon being considered as equivalent to 8.3389 pounds at a temperature of 39. 2°. 255. Measurement of Useful Work. — The useful work done by a pump is the product of the number of pounds of water delivered into the head through which it is raised. The head is the total vertical distance in feet from the sur- face of the water-supply to the discharge, increased by friction. It is measured most accurately by pressure-gauge connected to a Pitot's tube (p. 292) with its nozzle facing the current inserted in the discharge pipe, near the pump, and by a vacuum gauge or manometer connected to the suction pipe. The head in feet is equal to the distance between these gauges plus the total readings of the gauges, reduced to equivalent heads of water (see p. 324). The water delivered may be measured by discharging over a weir, or through a nozzle or tapering pipe called a Venturi tube. (See Article 204, p. 275.) The discharge through a Venturi tube may be taken as 98 per cent of the theoretical discharge, that through a straight conical nozzle as 97.7 per cent.* * See papers before Am. Soc. Civil Engineers, by Clemens Herschel, Not, 1887 and Jan. 1888, and by J, R. Freeman, Nov. 1889. 33° EXPERIMENTAL ENGINEERING. [§ 25^. Delivery measured from Piston-displacement. — Slip. — The water delivered in the case of piston-pumps is often computed by multiplying the total piston-displacement during the test by I, minus the slip. The total piston-displacement is equal to the product of area of piston by length of strokes, by total number of single strokes. In piston-pumps the length of stroke is often variable, in which case especial means must be adopted to find the average length. The slip is the percentage that the actual delivery is less than the total piston-displace- ment ; it can only be determined accurately by comparing the volume actually discharged with the total displacement. The slip is caused by air in suction-pipe, leakage past piston, leak- age past valves in either suction- or discharge-pipe, and imper- fect port-openings. The principal cause probably comes from leakage past the piston, and this leakage can often be deter- mined by removing the cylinder-head, blocking the piston, subjecting it to the water-pressure for at least one hour, and measuring all the water that leaks past it. This test should be repeated for various positions in the stroke. The valve leakage can often be determined by a similar test. No air should be admitted to the suction-pipe. A table of percentage of slip is given in Hill's Manual, published by the Harris-Corliss Engine Co., from which it is seen that the slip for large pumps is about two per cent, and that it varies from one to five per cent. 256. Efficiency-tests of Pumps. — An -efficiency-test will require in each case measurements of, firstly, the energy 01 work supplied the pump ; secondly, the useful work ; thirdly the lost work. The difference in methods of testing the various classes of pumps, as described in Article 253, simply extends to the meas- urement of the power supplied the pump. The steam-pump, or steam pumping-engine, is to be con sidered as a combination of the steam-engine with a pump. The power received by the pump is that delivered by the engine, and is determined by a steam-engine test. The method of testing steam pumping-engines, and standard method §257] H YDRA UL1 C MA CHTNER Y. 3 3 I of making duty-trials, as adopted by the American Society of Mechanical Engineers, will be given under special applications of the method of testing engines. The power-pump receives its energy from machinery in operation ; the energy received may be measured by a stand- ardized transmitting-dynamometer (see Chapter VII.), or, in the case of a rotary or centrifugal pump, by mounting in a frame having a free angular motion, which is unaffected by the tension on the driving-belt. The resistance to rotation is ob- tained by a known weight on a known arm, and the power supplied in foot-pounds is the product of the circumference that might be described by the arm as radius, number of revolutions, and the weight. Such a framework is termed a cradle-dy namometer. 257. Special Efficiency-tests— Power-pumps. — Efficiency- test of Centrifugal Pumps — Directions. Apparatus needed. — Pressure-gauge for delivery, manometer for suction, transmission-dynamometer, thermometer, weir for discharge. Directions. — Connect suction-pipe to supply-tank, and ar- range discharge with throttle-valve to deliver water over a weir. Connect delivery-gauge to an elongated air-chamber, which in turn is connected with the delivery-pipe, provided with a water gauge-glass opposite the pressure-gauge, and means of changing water-level and air-level.* Connect manom- eter or vacuum-gauge to suction-pipe ; obtain vertical distance between these gauges. Arrange a standardized transmission- dynamometer to receive the power, and drive the pump. During the test maintain the water in the air-chamber at height of centre of the gauge. Testing. — Set the machinery in operation ; arrange the throttie-vaive to give an approximate head of 50 feet. After uniform conditions are assumed, start the run ; take readings once in five minutes of hook-gauge at weir, of temperature of water, of discharge-gauge, of sucticn-guage, of dynamometer- *See Test of Steam Pumpingengines. 332 EXPERIMENTAL ENGINEERING. [§2 5 8. or power-scale. Continue the run for one hour with uniform pressure on discharge-gauge. Make a second run with an approximate head of 75 feet, and a third run with an approximate head of 100 feet. Report. — In report, calculate efficiency, duty, and capacity for each head ; draw a curve of each test, using power in foot- pounds as ordinates, and total water delivered as abscissae. Describe the pump and method of testing. Efficiency-test — Rotary Pump — Directions. — Apparatus and connections as for centrifugal pump, the power transmitted being measured either by a transmission-dynamometer, or by a balanced cradle-dynamometer ; the water may be measured by a weir, or it may be delivered into two weighing tanks, one of which is filling, the other emptying, and the water weighed. Directions for the test are as in the preceding. 258. Form for Log and Report of Pump-tests. — The following form for data and report is used at the Massachusetts Institute of Technology for log and data of test on Webber centrifugal pump and on rotary power-pump : No. TEST ON WEBBER CENTRIFUGAL PUMP. Date v a Water. Heads. Emerson Power-scale. •a V Pi V be 3 rt bo ii X c v . <~ c — £S p s qj — Total . . Av Diameter discharge-pipe ins. Transverse area discharge-pipe , sq. ft. Distance between gauges. ■. ft § 258.] HYDRA ULIC MA CHINE R V. 333 Crest of weif above bottom of channel f: Width of weir ft. Revolutions of pump per minute Water pumped in lbs. Duration of test mins. o ( Depth of water on weir. , ft. > ( Temperature at weir (corrected) ° C ° F. ' Suction-gauge (corrected) ins. ft. Discharge-gauge (corrected) lbs ft. Actual suction ft. Actual head ft. Scale-reading .-.„ » lbs. Revolutions per minute v ( Scale-reading lbs. {2 ( Revolutions per minute Water pumped in minutes lbs. Capacity in gallons per minute Total work by power-scale (pumping) H. P. Tare H. P. Work given to pump » H. P. Work delivered by pump H. P. Efficiency per cent. Duty (ft. -lbs. per 1,000,000 B. T. U.) Signed. , •2 ( No. LOG OF TEST ON ROTARY PUMP. Date Time. Power-scale. Gauges. Orifices. No. of Gong. Pumping. Tare. Suction, inches mercury Deliv- ery, lbs. per sq. in. Head, in feet. Temper- ature. Counter Revolu- tions. Weight. C. R. W. Av Cor . 334 EXPERIMENTAL ENGINEERING. L§ 2 5 8 RESULTS OF TEST ON ROTARY PUMP. No Date Duration of test , min. Power-scale, pumping, revolutions per minute " weight ... „ . .lbs. " tare, revolutions per minute c , t , " " weight c lbs. Suction-head by gauge inches mercury. ft. H 2 Discharge-head by gauge lbs. per sq. in " Head on orifices " Temperature ° C. * F. Revolutions of pump per minute Area of discharge at gauge sq. ft. Vertical distance between gauges ft. Diameter of orifices, a.. . ., b. . . ., c. . .., d e. ...,/...., g. . . ., h...., i. . . . Coefficients, a. . . ., o...., c. . . ., d. . . ., e. ...,/...., g. . . ., h...., i. . . . Constant for power-scale ft. Power-pumping, by scale H . P. Tare , ,....H. P. Power given to pump H. P. Velocity-head of discharge ft. Total head = press, heads -f- vel. head + vert. dist. bet. gauges ft. Water pumped lbs. per sec. Work done by pump H. P Efficiency of pump per cent. Capacity of pump in gallons per minute Duty of pump (ft. -lbs. per 1,000,000 B. T. U.) Signed. Part II. METHODS OF TESTING THE STEAM-ENGINE. CHAPTER X. DEFINITIONS OF THERMODYNAMIC TERMS. 259. General Remarks. — The methods of testing the steam-engine which are given here presume an accurate knowledge of the principles of action of the engine, an ac- quaintance with the details of its mechanism, and a knowledge of the thermodynamic principles which relate to the transfor- mation of heat-energy into work. In connection with the methods of testing, the student is advised to read one or more of the following books : Manual of the Steam-engine, by R. H. Thurston. 2 vols. N. Y., J. Wiley & Sons. Manual of Steam-boilers. Ibid. Engine and Boiler Trials. Ibid. Etude Experimental Calorimetrique de la Machine a Vapeur, par V. Dwelshauvers-Dery. Paris, Gauthier-Villars et Fils, Steam-engine, by D. K. Clark. 2 vols. N. Y., Blackie & Co. Steam-engine, by C. V. Holmes. 1 vol. London, Longmans, Green & Co. Steam-engine, by J. M. Rankine. 1 vol. London, Chas, Griffin & Co. Steam-making, by C. A. Smith. 1 vol. Chicago, American. Engineer. Steam-using. Ibid. 335 ;36 EXPERIMENTAL ENGINEERING. [§ 26o. Steam-engine, by James H. Cotterill. London, E. & F. N. Spon. Thermodynamics, by C. H. Peabody. N. Y., J.Wiley & Sons. Thermodynamics, by De Volson Wood. N. Y., J. Wiley & Sons. Thermodynamics, by R. Clausius. N. Y., Macmillan. Steam-tables, by C. H. Peabody. N. Y., J. Wiley & Sons. Handy Tables, by R. H. Thurston. N. Y., J. Wiley & Sons. 260. Relations of Units of Pressure. — The term pressure, as employed in engineering, refers to the force tending to com- press a body, and is expressed as follows : (1) In pounds per square inch ; (2) In pounds per square foot ; (3) In inches of mercury ; (4) In feet or inches of water. The value of these different units of pressure are as follows: TABLE SHOWING RELATION BETWEEN PRESSURE EXPRESSED IN POUNDS, AND THAT EXPRESSED IN INCHES OF MERCURY, OR FEET OF WATER. 70 Fah. Pressure in Pressure in pounds per sq. pounds per sq. inch. foot. Inches of mer- cury. Feet of water. Inches of water. I 144 2.0378 2.307 27.68 2 288 4.0756 4.614 55.36 3 432 6.II34 6.921 83.04 4 576 8.0512 9.23 IIO.72 5 720 IO.1890 it. 54 138.40 6 864 12.2268 13.85 166.08 7 IOO8 14.2646 16.15 103.76 8 1152 16.3024 18.46 221.44 9 1296 18.3402 20.76 249.12 10 1440 20.3781 23.07 276.80 The barometer pressure is that of the atmosphere in inches of mercury reckoned from a vacuum. At the sea-level, latitude of Paris, the normal reading of the barometer is 29.92 inches, corresponding to a pressure of 14.7 pounds per square inch. Gauge or Manometer pressure is reckoned from the atmos- pheric pressure. Absolute pressure is measured from a vacuum, and is equal to the sum of gauge-pressure and barometer readings expressed § 26 1.] DEFINITIONS OF THERMODYNAMIC TERMS. 337 in the same units. Absolute pressure is always meant unless otherwise specified. Pressure below the atmosphere is usually reckoned in inches of mercury from the atmospheric pressure, so that 29.92 inches would correspond to a perfect vacuum at sea-level, latitude 49 . 261. Heat and Temperature. — The term heat is used sometimes as referring to a familiar sensation, and again as applying to a certain form of energy which is capable of pro- ducing the sensation. In this treatise it is used in the latter sense only. Temperature is essentially different from heat, and is merely one of its qualities ; it is difficult to define, but two bodies are of equal temperature when there is no tendency to the trans- fer of heat from one to the other. Temperature is measured by the expansion of some substance in an instrument termed a thermometer. Two points, that of melting ice and of steam from water boiling at atmospheric pressure, are fixed tempera- tures on all scales of thermometry. The expansion between these points is divided into various parts according to the scale adopted, and each part is termed a degree. The following thermometric scales are in use in different portions of the world : Fixed Points, Temperature of Water. Fahrenheit. Centigrade. Rdaumur. Degrees between freezing and boil- \ 180 32 I 1 4 "5" IOO O t I 1 80 Temperature at freezing point Comparative length 1 degree < < << << t( it << O t f I Degrees of temperature taken on one scale can easily be reduced to any other; thus, let t f be the temperature of a body on the Fahrenheit scale, t c on the Centigrade scale, and t r on the Reamur scale. We shall have, from the preceding table, */-=K + 32°; t. = W f -32 ); 338 EXPERIMEN TA L ENGINEERING. [§ 262. The Fahrenheit thermometer is used principally by English- speaking people, and unless otherwise mentioned is the one us^d in this treatise. The Thermometric Substances principally used are mercury,, alcohol, and air, from the expansion of which the temperature is obtained. Absolute Zero. — This quantity is fixed by reasoning as the point where gaseous elasticity or expansion would be zero. This is 492 , more exactly 491. 8°, of the Fahrenheit scale or 2 73° +* °f tne Centigrade scale below the freezing-point of water, so that in the Fahrenheit scale the absolute tempera- ture is 460 + the reading of the thermometer, and on the Centigrade scale 273°-)- the reading of the thermometer. Absolute Temperature, on any scale, is temperature reckoned from absolute zero. 262. Specific Heat. — Specific heat is the ratio of that re- quired to raise a pound one degree in temperature compared with that required to raise one pound of water from 6o° to 61 ° Fahr. Specific heat of water is not quite constant, but varies as follows : f Centigrade. Fahrenheit. Specific Heat. Centigrade. Fahrenheit. Specific Heat. o° 32° I.0072 30° . 86° O.9954 5° 41° I . 0044 35 °o 95° O.9982 io° 50° I. OO16 40 104° I . OOOO 15° 59° I . 0000 45° 113° I.008 20° 68° O.9984 155° • 3"° I.046 25° 77° O.9948 200° 39 2 ° I.046 Specific heat of saturated steam at atmospheric pressure was found by Regnault to equal 0.478. Investigations made at Sibley College show that the specific heat of superheated steam increases with the pressure and temperature. The heat contained in different bodies of the same tempera- * Encyc Brit., Vol. XI. p. 573. f See Peabody's Steam-tables. § 264.] DEFINITIONS OF THERMODYNAMIC TERMS. 339 ture, or in the same body in its liquid and gaseous condition, is quite different and cannot be measured by the thermometer. Thus in equal weights of water and iron at the same tempera- ture, the heat in the water is several times that in the iron. This is known because in cooling a degree in temperature, water will heat a much greater weight of some other substance. 263. Mechanical Equivalent of Heat. — The experiments made by Rumford and Joule established the fact that heat- energy could be transformed into work, or vice versa. The re- sults of Joule's latest determination gave the mechanical work equivalent to the heating of one pound of water one degree Fahr. in temperature as 774 foot-pounds, while the later and more refined determinations of Rowland, reduced to 45 of latitude and to the sea-level, make the mechanical work equivalent to the raising the temperature of one pound of water from 62 to 63 Fahr. to be 778 foot-pounds. The heating of one pound of water one degree, from 39 to 40 Fahr., is termed a British thermal unit, B. T. U., and this is equivalent in me- chanical work to 778 foot-pounds. This number is represented by J and its reciprocal by A throughout this work. The heat needed for raising one kilogram of water one de- gree Centigrade is termed a calorie, and this is equivalent to 426.9 foot-pounds. In some treatises a British thermal unit is the heat required to raise one pound of water from 62 to 63 Fahr., which differs little from that defined above. 264. Relations of Pressure and Temperature of Steam, — There is a definite relation between the temperature and pressure of steam in its normal or saturated condition. This relation was very carefully investigated 1836-42 by M. V. Reg- nault in Paris by a series of careful experiments made on a large scale. These experiments form the basis of our experimental knowledge of the properties of steam. The properties of steam are also shown by the thermody- namic laws, and are given in tables of Rankine, Clausius, M. V. Dwelshauvers-Dery, Peabody, and Buel. The following empirical formula, deduced from Regnault's 34° EXPERIMENTAL ENGINEERING. [§ 265. experiments, gives the relation between the temperature and pressure of steam at a latitude of 45 : For steam* from 32 to 21 2° Fahr. pressure in pounds per square inch, \og/> = a-ba T +cB T , in which a = 3.025908, log b = 0.61 174, log c = 8.13204 — 10, log a = 9.998181015 — 10, log B = 0.0038134, T=t — 32 . For steam from 212 to 428 Fahr., lo g p = a 1 -b 1 a 1 T + c 1 B/ t in which a x = 3.743976, log b x — 04120021, log c 1 = 7.74168 — 10, log ^=9.998561831 — 10, \ogB 1 — 0.0042454, T= t — 212 . 265. Properties of Steam. — Definitions. — Steam occurs in two different conditions: 1, saturated ; 2, superheated. 1. Dry and Saturated Steam, or, as frequently called, dry steam, is the vapor of water at point of precipitation, and may- be considered the normal condition of steam. Saturated steam of any pressure is at the lowest tempera- ture and possesses the least specific volume and the greatest density consistent with that pressure. The slightest decrease in total heat results in partial condensation, forming what is termed moist or wet steam, in distinction from dry steam. Thus saturated steam may be either wet or dry. The percentage of dry steam in a mass of wet steam is termed its quality. 2. Superheated steam has properties similar in every respect to those of a perfect gas. Its temperature is higher, its specific volume greater and its density less than saturated steam of the same pressure. Steam-tables give the properties of dry saturated steam only and usually arranged with absolute pressure as the argument or given quantity. The important properties are as follows : (a) Total Heat (symbol, A). — This is the amount of heat required to convert one pound of water from 32 into saturated * Steam-tables, by Prof. Cecil H. Peabody. §265.] DEFINITIONS OF THERMODYNAMIC TERMS. 34 1 steam at a pressure P. If t is the temperature of the steam, the total heat, A, is calculated by an empirical formula based on the experiments of Regnault. Expressed in English units, X = 1081.4 + 0.305*. (b) Heat of the Liquid (q) is the number of thermal units used in heating one pound of water from 32 Fahr. to the tem- perature required to generate steam. According to Regnault, q == t -f- 0.00002 f -f- o. 0000003 *' for Centigrade units. And according to Rankine for English units when t x is the initial and t the final temperature, q — t — t x + 0.000000103 [(* - 39 - 1 ) 3 — (A — 39°-i) 3 ]- (c) Internal Latent Heat (p). — This is the work done, measured in thermal units, in separating the molecules of the steam beyond the range of mutual attraction. It is calculated from the formula p = 1061 — 0.791/. (d) External Latent Heat (APu). — This is the work, ex- pressed in heat-units, of expanding the steam against an external pressure which is equal to that of the steam generated. Thus, let u = s — the height on the side of the pressure. Then Fig. 161. U-shaped Ma NOMETER. from which f + *=A + *i> Pi-P = h-K The U-shaped tube, in construction similar to Hoadleys draught- gauge, Art. 275, can be used with two liquids of dif- ferent densities, using the heavier liquid on the side of the lighter pressure. Let d x denote the density of the lighter liquid, and d that of the heavier; h v and //, the corresponding § 27O.J MEASUREMENT OF PRESSURE. 2)47 heights of the columns. We shall have as before, taking all measurements from the lower surface of the heavier liquid, p l + fid = p + k 1 d 1 , from which p x — p = h x d x — hd. This instrument is much more delicate and is better suited for measuring small differences of pressure than when a single liquid is used ; the reason for which will be readily seen if we consider an example. Suppose that water be used as the heavier liquid, of which the specific gravity is I, and that crude olive-oil be used as the lighter liquid, of which the specific gravity is 0.916. Suppose that all pressures are meas- ured in equivalent height of a water column expressed in inches, and that h = 6 inches,/, — p = \ inch ; then h x , which is the difference of level of the water in the two branches, will be \ -f- 6.(0.916) = 6.0 inches, whereas it would have been but one-half inch had there been only water, or 0.545 if the liquid had been olive-oil. By making the density of the liquids more and more nearly equal the instrument will become more and more delicate. A dilute mixture of water and alcohol of which the density must be determined (see Article 275, page 354), for the heavier, and of crude olive-oil for the lighter, gives excel- lent results. If the instrument can be so manipulated that p^-p=_h(d x -d\ and the calculation becomes very simple, as in that case the reading would have to be multiplied only by the differences oi the densities of the two liquids. 270. Cistern-manometer.— In the case of a manometer oi the form of Fig. 162 or Fig. 163, the cistern or vessel into 348 EXPERIMENTAL ENGINEERING. [§ 270. which the tube is connected has a large that of the tube. Pressure is applied to the top of the liquid in the cistern, the surface of which will be depressed a small amount, and the liquid in the tube will be raised an amount sufficient to balance this pressure. The pressure corresponds to the vertical distance from the surface of the liquid in the tube to that in the cistern. As the liquid is not usually in sight in the cistern, a correction is neces- sary to the readings in order to find the correct height corresponding to a given pressure. This correction is calculated as follows : Let A equal the area of sur- face of the liquid in the cistern, a the area of the manometer-tube, H the fall of liquid in the cistern, h the correspond- ing rise of liquid in the tube, b the height required for one pound of pressure (see Article 260, page 336), p the number of pounds of pressure. We have then area relative to H P\ 162. — Cistern-manom- eter. and since the tube is supplied by liquid from the cistern, HA = ha. Eliminating H in the two equations, Apb If p = one pound, h = k = A+a Ab A+a' § 2 7 2.] MEASUREMENT OF PRESSURE. 349 which is the length the graduation should be made to allow for fall of mercury in the cistern and give a value equal to one pound of pressure. To make this correction uniformly ap- plicable the area of cross-section of both tube and cistern should remain uniform. 271. Mercury Columns. — Mercury col- umns, as used in the laboratories, are usually made on the principle of the cistern-manom- eter. The tube is very long and made of glass or steel carefully bored out to a uniform diameter. If the tube is of glass, the height of mercury can be readily perceived and read ; if of steel, the height of the mercury is usually obtained by a float, which in some instances is connected to a needle which moves around a graduated dial. In some of these instruments electric con- nections are broken whenever the mercury passes a certain point, and an automatic register of the reading is made. Fig. 163 shows the usual form of the mercury col- umn, in which the pressure is applied in the upper part of the cistern, so as to come directly on the top of the mercury. In the case of a glass column the graduations are usually made on an attached scale, and are corrected as explained in Article 270 for the fall of mercury in the cistern. 272. Corrections to the Mercury Col- umn. — The mercury column is usually the standard by which all pressure-gauges are compared, and its accuracy should be thoroughly established in every particular. The requirements for an accurate mer- cury column are : I IOO- F I 90 as fh ii ;..:i m Fig. 163. — Mercury Column. 350 EXPERIMENTAL ENGINEERING. L§ 272. 1. Uniform bore in cistern and tube. 2. Accurate graduations, spaced as explained in Article 270. As it is impossible to make the graduations perfectly accurate, the error in this scale should be carefully determined, and the readings corrected accordingly. The corrections to the readings are: 1. For expansion of the mercury and tube due to increase of temperature. The method of correcting for expansion of the mercury and the material enclosing it would be as follows : Let A equal the coefficient of lineal expansion of the mer- cury, and 3A. that of the cubical expansion per degree Fahr. ; let S equal the coefficient of lineal expansion of the metal of the cistern, and S' that of the metal of the tube. Let H' equal the depression in the cistern, h' the corresponding elevation in the tube corresponding to a pressure of one pound, and a difference of level of b ' . Let b equal the difference of level corresponding to a pressure of one pound at a temperature of 6o° Fahr. Then, as before, ti A'V a' +~A' A(i+2S)b(i+ 3 \) a(i +2d') + A(i +2$)' 2. Correction for the capillary action of the tube. This force depresses the mercury in the tube a distance which decreases rapidly as the diameter increases. The amount of this depression is given in Loomis's Meteor- ology as follows : Diameter of Tube. Inch. Depression. Inch. Diameter of Tube. Inch. Depression. Inch. O.05 O. IO O.I5 0.20 O.25 O.30 0-35 O.295 0. 141 O.087 O.058 O.041 O.029 0.02I O.40 0.45 O.50 O.60 O.70 O.80 O.OI5 O.OI2 0.008 0.004 O.OO23 0.0012 §^73-] MEASUREMENT OF PRESSURE. 35 I 3. There might also be considered a very slight correction due to the fact that the force of gravity in different latitudes varies somewhat. Since the weight of a given mass of mercury is equal to the product of the mass into the force of gravity, it will vary directly as the force of gravity, or, in other words, the assumed weight of mercury may not be exactly correct. This correction is a refinement not necessary in usual tests. 4. Difference of barometer-readings at top and bottom of the tube might make some difference. While it is well to give all these corrections their true weight, yet a false impression should not be incurred concerning their importance. It is hardly probable that the corrections for change in temperature, or corrections for the difference in the force of gravity from that at the sea-level on the equator, would in any event make a sensible difference in the readings. 273. Direct-reading Draught-gauges. — The ascending force which causes smoke or heated air to rise in a chimney is called the draught. The pressure in such a case is below that of the atmosphere, and is usually measured in inches of water. Draught-gauges are U-shaped manometers adapted to measure pressures less than that of the atmosphere. See Figs. 160 and 161. To use this manometer, water is poured into the tube until it stands at the point marked o, Fig. 161; one side is then connected by a pipe to the flue or chimney of which the draught is to be measured. The difference of level of the water, as shown by the manometer-tubes, is the draught ex- pressed in inches of water. An inch of water at a temperature of 70 Fahr. corresponds to 0.036 pound. Allerts Dr aught- gauge. — A very complete draught-gauge of the U-shaped manometer type, with attached thermometer and a movable scale the zero of which can be set to correspond to the lower water surface, is shown in Fig. 164 as designed by J. M. Allen of the Hartford Boiler Insurance Co. A draught-gauge designed by the author is shown in Fig. 164a, which is arranged so that one scale will give difference in elevation of the liquid in the two columns. This is accomplished 352 EXPERIMENTAL ENGINEERING. [§ 274. by setting the collar F to the lower meniscus of the liquid by the screw E\ then by setting the collar H to the meniscus of the liquid in the other column by means of the micrometer- screw R, the height of the column may be read on the attached scale and the Fig. 164. — Draught-gauge. Fig. 164a. — Draught-gauge- micrometer- screw R. The reflection from the two edges of the meniscus enables the scales to be set with great accuracy. The inches and tenths of inches are read on the attached scale, the hundredths of inches by the graduations of the micrometer- screw R. 274. Draught-gauges with Diagonal and Level Scales. — Peclel's Draught- gauge. — A draught-gauge with diagonal scale is shown in Fig. 165. It consists of a bottle, A, with a mouth- piece near the bottom into which a tube, EB, is inserted with any convenient inclination. The upper end of the tube is bent up- ward, as at BK, and connected with a rubber tube, KC, leading to the chimney. The tube is fastened to a convenient support, 275-] MEASUREMENT OF PRESSURE, 353 and a level, D y is attached. To use the instrument, first level it, note reading of scale, then attach it to the chimney, and take the reading, which will be, if the inclination is one to five, Fig 165. — Draught-gauge A SsJ Fig 166.— Higgins's Draught- gauge. five times the difference of level in the bottle and tube. The scale should be graduated to show differences of level in the bottle, and thus give the pressure directly in inches of water. Higgins's Draught-gauge. — Another form of this class of draught-gauges is shown in Fig. 166, as designed by Mr. C. P. Higgins of Philadelphia. The gauge is filled with water above the level of the horizontal tube, in such a manner as to leave a bubble of air about one- half inch long near one end of the hori- zontal tube when the water is level in the side tubes. The inside diameter of the vertical tubes being the same, say one-half inch, and that of the horizontal tube one eighth of an inch, a draught equivalent to one inch in water, or which will cause the water-level in the vertical tubes to vary one inch, will cause the bubble in the tube to move eight inches in the horizontal tube. In general the air-bubble moves a distance inversely proportional to the area of the tubes, and hence it can be read more accurately than in case of the ordinary draught-gauge. 275. Hoadley's Draught-gauge. — This gauge was used in the trials of a warm-blast apparatus described in Vol. VI. Tran- sactions American Society Mechanical Engineers, page 725. It consists of two glass tubes, as shown in Fig. 167, about 30 inches long, and about 0.4 inch inside diameter and 0.7 inch outside, joined at each end by means of stuffing-boxes to suitable brass tube connections, by which they are secured to a 354 EXPERIMEN TA L ENGINEERING. L§ 275. backing of wood. The glass tubes can be put in communica- tion with each other at top and bottom by opening a cock in each of the brass connections. Directly over each tube is a brass drum-shaped vessel 4.25 inches in diameter and with heads formed of plate-glass. These drums are connected to the tubes, and also provided with stop-cocks and nipples to which rubber tubes can be attached. Two sliding-scales are arranged along the tubes, one to measure the de- pression, the other the elevation, of the surface of a liquid filling the lower halves of the tubes. In the use of the instrument two liquids of different densities were used, a mixture of water and alcohol with specific gravity about 0.93 being used for the heavier liquid, and crude olive-oil with a specific gravity of 0.916 for the lighter. In using the instrument the heavier liquid was first put into the tubes, care being exercised to avoid wetting the top attachments ; then the top connection between the tubes was opened and the olive-oil poured in. In using the instru- ment one branch was connected to the chimney, the other being opened to the air, the bottom connection opened and the top connection closed. The liquid would rise in the tube with the lighter pressure a distance inversely pro- portional to the respective areas of exposed surface of the tube and drum. The bottom connection was then closed, the connection to the flue removed, and the top connection opened ; the surface of the olive-oil would then become level in the two tubes, that of the water remaining at different heights. It was then attached to the flue and these operations repeated, until the heavier liquid would no longer flow to the side of the lighter pressure; in that case we should have the condition of equilibrium between two liquids of different den- sities, Article 269, page 347, in which the lengths of columns Fig. 167. — HoAn- ley's Dkaughi- GAUGE. § 276.] MEASUREMENT OE PRESSURE. 355 of the two liquids are equal. Hence, noting that p is here the greater, the difference of pressure in inches of water is p-p 1 = h(d 1 -d), in which d\ and d are the respective specific gravities of the liquids used. 276. Multiplying Draught-gauges. — Fig. i6Sa shows a draught-gauge designed by Prof. Wm. Kent, the dimensions of which are marked on the figure, although they are not material for its operation. The gauge consists of a cup, B, which is partly filled with water, and an inverted cup, A, suspended above the cup B by a spring, C, with the lower and open end submerged in the water of the cup B. The tube, E, extends through the side of the cup B, with its upper end projecting above the surface of the water in the cup B, and is extended by suitable connection to the flue. Fig. 168&. By this connection the pressure in the inverted cup, A, is re- duced to that in the flue where the pressure is to be measured, putting a greater load on the spring, C, which causes it to elongate. The amount of elongation will be proportional to the reduction in pressure and can be determined by the use of a suitable scale, the values of which are found by calibration. It is evident that the distance through which the cup A will move is dependent upon the area of its cross-section and the strength and length of the spring, C, and the immersion in the water. 3$6 EXPERIMENTAL ENGINEERING. [§ 276. Peclet in his work, "Traite de la Chaleur," published in 1878, describes a similar gauge. In Vol. XI of the Transactions of the Am. Soc. Mech. En- gineers Prof. J. B. Welb describes a draught-gauge of similar principle, but in which the change in pressure is weighed on a pair of balances. A U-shaped gauge as shown in Fig. i6Sb, in which two liquids of different density are employed, has been frequently used to measure small pressures. In the gauge shown, each arm of the U tube is enlarged near its upper end for a short distance. Sup- posing the liquids employed to be water and kerosene oil, water is first put into the U tube in one of the arms, as, for instance, the arm B; kerosene oil is put in the arm A, the surface of both liquids being in the enlarged parts C and D. If the side con- taining the lighter liquid is connected to the flue, the surface in the enlarged portion B will move in proportion to the pressure. If a be the point of junction of the heavier and lighter liquids, this motion will be as much greater than the surface D as the area is smaller; if, for instance, the area at a be one fourth that at D, the motion will be four times as great. The motion of the surface A could be determined by calculation, but it can be much more accurately and more easily determined by a calibra- tion, which consists of a comparison with a direct- reading draught- gauge used to measure the same pressure. A form of pressure-gauge has been made in which the pres- sure has been transmitted to the measuring manometer by a piston having faces or sides of unequal areas connected. In this case the total pressure acting on each face of the piston will be in equilibrium ; consequently the pressure per square inch on each face will vary inversely as the areas of the two faces of the piston. The objection to the instrument is the resistance due to friction of the piston, which can in large measure be elimi- nated by keeping it in rotation during its use. In place of a piston two diaphragms of unequal area with a connecting solid part have in some cases been employed for the purpose of eliminat- ing friction. § 277-] MEASUREMENT OF PRESSURE. 357 277. Steam-gauges. — The steam-gauges in general use are of two classes, known respectively as the Bourdon and Dia- phragm Gauges. The Bourdon Gauge. — In the Bourdon gauge the pressure is exerted on the interior of a tube, oval in cross-section, bent to fit the interior of a circular case ; the application of pressure tends to make the cross-section round and thus to straighten the tube. This motion communicated by means of racks and gears rotates an arbor carrying a needle or hand. The various forms of levers used for transmitting the motion of the tube to the needle are well shown in the accom- Fig. 169. — Crosby Bourdon Gauge. panying figures, 169 to 173. The levers are in general adjust- able in length so that the rate of motion of the needle with respect to the bent tube can be increased or diminished at will. Thus in Fig. 169, and also in Fig. 170, the lever carrying the sector is slotted where it is pivoted to the frame ; by loosen- ing a set-screw the pivot can be changed in position, thus alter- ing the ratio of motion of hand and spring in different parts of the dial. Fig. 170 shows a gauge with a steel tube or diaphragm for use with ammoniacal vapors which attack brass. 353 EXPERIMENTAL ENGINEERING. [§ *77- FlG. 170. — SCHAEFFER & BuDENBERG AMMONIA-GAUGE. Fig. 171. — Bourdon Gauge. In nearly all these gauges lost motions of the parts are to some extent taken up by a light hair-spring wound around the needle-pivot. § 2 7 8.] MEASUREMENT OF PRESSURE, 359 278. The Diaphragm Pressure-gauge. — In the dia- phragm-gauge the pressure is resisted by a corrugated plate, which may be placed in a horizontal plane, as in Fig. 172, or in a vertical plane, as in Fig. 173. The motion given the plate is transmitted to the hand in ways similar to those just explained. Fig. 172. — Diaphragm-gauge. In Fig. 172 the pressure is exerted on the corrugated dia- phragm below the gauge, and the motion is transmitted to the hand by the rods and gears shown in the engraving. The construction shown in Fig. 173, in which the diaphragm is vertical, is as follows : the lever is in two parts which are pivoted at the centre; one end is fixed to the frame, the other connected to the sector. The centre pivot is pressed outward by the action of the diaphragm, drawing the free end downward and rotating the sector, which in turn moves the needle. In gauges of usual construction of either class, when there is no pressure on the gauge, the needle rests against a stop, which is placed somewhat in advance of the zero-mark, so that 360 EXPERIMENTAL ENGINEERING [§ 2/9. minute pressures are not indicated by the gauge. In the use of the instrument the needle sometimes gets k>ose on the pivot, or turned to the wrong position with reference to the gradua- tions ; in such a case the needle is to be removed entirely, and set when the gauge is subjected to a known pressure. These Diaphragm-gauge. gauges are also affected by heat. Hence, when set up for use a bent tube, termed a siphon, or a vessel which will always contain water, should be interposed between the gauge and the steam. 279. Vacuum-gauges. — Vacuum-gauges are constructed in the same method as the Bourdon or diaphragm gauges; the removal of pressure from the interior of the bent tube or dia- phragm causes a motion which is utilized to move the needle. These are graduated to show pressure below that of the at- mosphere corresponding to inches of mercury, zero being at atmospheric pressure, and 29.92 a perfect vacuum. The differ- ence between the reading by such a gauge and that of the § 280.J MEASUREMENT OF PRESSURE. 361 barometer would be the absolute pressure in inches of mer- cury. Fig. 174.— Edson*s Speed and Pressure Recording Gauge and Alarm. The principal makers of steam-gauges in this country are the Crosby Steam Gauge and Valve Co., Boston ; American Steam Gauge Co., Boston; Ashcroft Steam Gauge Co., New York; Schaeffer & Budenberg, New York ; Utica Gauge Co., Utica, N.Y. 280. Recording- gauges. — Recording-gauges are arranged so that the pressure moves a pencil parallel to the axis of a revolving drum which is moved at a uniform rate by clock- work. The Edson recording-gauge is shown in Fig. 174. In this gauge the steam-pressure acts on a diaphragm which oper- 362 EXPERIMENTAL ENGINEERING. [§ 2*50. furnished ates a series of levers giving motion to a needle moving over a graduated arc showing pressure in pounds ; also to a pencil- arm moving parallel to the axis of a revolving drum. This instrument has an attachment, which is when required, to record fluctuations in the speed, and consists of a pul- ley on a vertical axis below the instru- ment that is put in motion by a belt to the engine-shaft. On the small pulley-shaft are two governor-balls which change their vertical position with variation in the speed, giving a corresponding movement up or down to a pencil near the lower part of the drum. A diagram is drawn on which uniform speed would be shown by a straight line. Fig. 175 shows Schaeffer & Buden- berg's recording-gauge. This con- sists of a pressure-gauge below the recording mechanism. The drum B is operated by clock-work, the piston- rod C, which carries the pencil, being moved by the pressure. The pencil- movement is much like that on the t, . . . .... Fig 175* — Recording Pressure- Kichards steam-engine indicator. gauge. Fig. 176 shows a portion of a diagram made by a recording- gauge. The drum is operated by an eight-day clock, and ar- Fig. 176.— -Diagram from Pressure-recording Gauge. § 28 1.] MEASUREMENT OF PRESSURE. 363 ranged to rotate once in twenty-four hours. In the diagram the ordinates show pressure, and the abscissae time in hours and fractions of an hour. 281. Apparatus for Testing Gauges. — Apparatus for testing gauges consists of a pump or other means of obtaining pressure, and some method of attaching the gauge to be tested, and the standard with which it is to be compared. The form of pump usually employed for producing the pressure is shown in Fig. 177. The gauge is attached at £, the standard at E x ; the hand-wheel D is run back, and water is supplied by filling the cup between the gauges and opening the cock; after the cylin- der C is filled the cock below the cup is closed ; if the hand- wheel D is turned, an equal pressure will be put on the standard and on the gauge. The standards used for testing may be manometers or cab- brated gauges, or apparatus for lifting known weights by the pressure acting on a known area. Of these various standards, the mercury column, as described in Article 271, page 349, is to be given the preference, since the only errors of any prac- tical importance are those due to graduation. The readings given by the mercury column are on a larger scale than those given by any other instrument, and no corrections for friction are required. The other standards, of which the short mer- cury columns have been described (see Article 264), will be found to give excellent results in practice, since the graduations on the gauges to be tested are usually so close together that the friction of the moving parts of the apparatus is inap- preciable. Apparatus for Testing Gauges with Standard Weights, There are two forms of this apparatus on the market, in one of which the pressure is received on a round piston, and in the other on a surface exactly one square inch in area. The friction in both cases is practically inappreciable ; the errors in areas can be determined by comparison with a standard mer- cury column. The Crosby Steam-gauge Testing Apparatus. — This is shown in Fig. 178, from which it is seen to consist of a small cylinder 3^4 EXPERIMENTAL ENGINEERING. [§ 23 JU Wig. 177.— Test-pump for Gauges. §28l.J MEASUREMENT OF PRESSURE. 365 in which works a nicely fitted piston ; this cylinder connects with a U-shaped tube ending in a pipe tapped and fitted for Fig. 178.— Crosby Steam-gauge Testing Apparatus. attaching a gauge. The tube is filled with glycerine, in which case a known weight added to the piston produces an equal pressure on the gauge, less the friction of the piston in the tube. This is almost entirely overcome by giving the weight and piston a slight rotary motion. The Square-inch Gauge. — This apparatus consists of a tube the end of which has an area of one square inch enclosed with sharp edges. This is connected to the test-pumps in place of the standard (see Fig. 177, page 364); a given weight is sus- pended from the centre of a smooth plate which rests on the square inch orifice. The gauge to be tested is connected at E, and the pressure applied until the plate is lifted and water escapes from the orifice. 366 EXPERIMENTAL ENGINEERING. [§ 282- 282. Calibration and Correction of Pressure-gauges. — The correctness of gauges is determined in each case by com- parison with apparatus known to be correct, the apparatus being subject to a fluid pressure of the same intensity. The calibration may be done by comparison with any of the stand- ards described. Calibration of Gauges with the Mercury Column. First, with Steam-pressure. — In this case attach the gauge with a siphon connection to a steam-drum, making the center of the gauge the height of the zero of the column. This drum is to be connected at one end to the mercury column, and the steam-pressure is to be applied to it so that it can be regulated by throttling the admission or discharge. Admit steam- pressure to the gauge and the mercury column ; adjust the pressure to a given reading by throttling the valves. Starting at five pounds of pressure on the gauge, note the correspond- ing reading of the mercury column, temperature of the mer- cury and of the room. Increase the pressure and take readings once in five pounds. In no instance allow the pressure to exceed that at the time of making the reading. In case the pressure is made too great at any time, run it some distance below the required amount and make a new trial, it being necessary to keep the mercury column and gauge hand moving continually upward or downward. Repeat the same operation in the reverse direction, commencing with the highest pressures ; the average reading of the mercury column, corrected for error as explained in Article 272, page 350, and reduced to pounds of pressure, is the correct pressure with which the gauge-reading is to be compared. Second, with Water-pressure. — In this case a hand force- pump (see Article 281) must be used after the limits of pressure • of the water-main have been reached. Proceed as follows: Run out the piston of the pump attached to the mercury -column to the end of its travel ; close drip-cock and open the ■ connectiag-valve. Attach the gauge to be tested with its centre opposite the zero of the column. Open the cock. § 28 3 .] MEASUREMENT OF PRESSURE. 367 Draw water from the mains until the gauge indicates 5 lbs. pressure. Shut off the water and adjust the pressure exactly at 5 lbs. by using the displaces Note the height of the mer- cury in the tube. Increase the pressure to 10 lbs. and take readings. Carry the pressure as far as desired by increments of 5 lbs. Use the pump alone when water-pressure fails. From the maximum pressure attained descend by increments of 5 lbs., taking readings as before. Tabulate data and plot a curve, using gauge-readings as ordinates and actual pressures as abscissae. By inspection of the curve determine the fault in the gauge and give directions for correcting it. In these tests it may not be possible to set the centre of the gauge as low as the zero of the column. In that case the reading on the mercury column should be greater than that at the centre of the gauge by a pressure due to the length of a column of water equal to the elevation of the' centre of the gauge above the zero of the -mercury column. This is a con- stant amount ; it should be obtained and the read- ings of the column corrected accordingly. The method of calibrating gauges with other standards is to be essentially the same, except as to the manipulation of the apparatus. Further di- rections do not seem necessary. Correction of Gauges. — If an error appears as a result of calibration, it may generally be corrected ; if the error is a constant one, the hand may be removed with a needle-lifter, and moved an amount corresponding to the error, or in some gauges the dial may be rotated. If the error is a gradually increasing or diminishing one, it can be corrected by changing the length of the lever-arm between the spring and the gearing by means of adjustable sleeves or the equivalent. It is to be noted that the pin to stop the motion of the hand is not placed at zero, but in high-pressure gauges is usually set at u-shS-eJma- three to five pounds pressure. 283. Calibration of Vacuum-gauges. — This is best done by a comparison with a U-shaped mercury manometer, as shown 368 EXPERIMENTAL ENGINEERING. [§284. in Fig. 179, of which each branch of the tube should exceed 30 inches in length. Before calibrating, the manometer is filled with mercury to one half the length of the tubes, and is attached near the gauge to be tested to the receiver of an air-pump. In case a condensing engine is used, both the gauge and the standard may be connected to the condenser. A comparison of the readings of the vacuum-gauge with the difference of level of mercury in the two tubes will determine the error of the gauge. 284. Forms for Calibration of Gauges. CALIBRATION OF STEAM-GAUGE BY COMPARISON WITH THE MERCURY COLUMN. Maker and No. of Gauge. Date. 189 Observers, No. Gauge, lbs. Mercury Column. Gauge, lbs. Inches. Pounds. Up. Down. Mean. Error, lbs. Temperature of Room .... deg. Fahr. Centre of Gauge above o of column . . ft. Correction to column reading .... lbs. CALIBRATION OF STEAM-GAUGE BY COMPARISON WITH THE SQUARE-INCH GAUGE, OR WITH CROSBY'S GAUGE- TESTING APPARATUS. Maker and No. of Gauge Date 189 . Observers ■\ No. Load in lbs. on Valve. Gauge. Error. Remarks. CHAPTER XII. MEASUREMENT OF TEMPERATURE. 285. Mercurial Thermometers. — Measurements of tem- perature are determined by the expansion of some ther- mometric substance, mercury, alcohol, or air being commonly employed. The mercurial thermometer is commonly used ; this con- sists of a bulb of thin glass connected with a capillary glass tube ; on the best thermometers the graduations are cut on the tube, and an enamelled strip is placed back of them to facil- itate the reading. When the mercury is inserted, every trace of air must be removed in order to insure perfect working. There are certain defects in mercurial thermometers due to perma- nent change of volume of the glass bulb, with use and time, that results in a change of the zero-point. This defect is so serious as to render the mercurial thermometer useless for very minute subdivisions of a degree. In a good thermometer the bore of the tube must be perfectly uniform, which fact can be tested by separating a thread of mercury and sliding it from point to point along the tube, and noting by careful measure- ment whether the thread is of the same length in all portions of the tube : if the readings are the same, the bore is uniform or graduated by trial. In most thermometers the graduations are made with a dividing engine ; in some thermometers the prin- cipal graduations are obtained by the thread of mercury, as described ; in the latter case change in diameter of bore would be compensated. To determine the accuracy of temperature 369 37° EXPERIMENTAL ENGINEERING. [§ 286. measurements thermometers used should be frequently tested for freezing-point and boiling-point. The accuracy of inter- mediate points shouid be determined by comparison with a standard mercurial or air thermometer. The mercurial-weight thermometer which was employed by Regnault, but is now very little used, consists .of a glass vessel with a large bulb and capillary tube, open at the top ; it is filled with mercury when at the temperature of the freezing-point ; it is then heated to the temperature of boiling water, and the amount of mercury that runs out is carefully weighed, and de- termines the value of the thermometric scale. The temperature of any enclosure is then found by placing in it the thermome- ter, previously filled when at freezing-point and weighing the amount that escapes ; from this the temperature can be cal- culated by simple proportion. The expansion of mercury is not perfectly uniform for all temperatures, so that mercurial thermometers are never per- fect for extreme ranges of temperature. 286. Rules for the Care of Mercurial Thermometers. — The following rules for handling and using mercurial thermome ters, if carefully observed, will reduce accidents to a minimum : 1. Keep the thermometer in its case when not in use. 2. Avoid all jars ; exercise especial care in placing in ther- mometer-cups. 3. Do not expose the thermometer to steam heat unless the graduations extend to or beyond 350 F. 4. In measuring heat given off by working-apparatus, or in continuous calorimeters, do not put the thermometers in place until the apparatus is started, and take them out before it is stopped. Be especially careful that no thermometer is over- heated. 5. In general do not use thermometers in apparatus not fully understood or which is not in good working condition. 6. Never carry a thermometer wrong end up. 7. See that the thermometer-cups are filled with cylinder- oil or mercury. If cylinder-oil is used, keep water out of the cups or an explosion will follow. §288.] MEASUREMENT OF TEMPERATURE. 37 1 8. After a thermometer is placed in a cup, keep it from contact with the metal by the use of waste. 287. Alcohol-thermometers. — Other liquids, as alcohol -or spirits of wine, are better suited for low temperatures than mercury, but on account of the tension of their vapors are not suited for high temperatures, and are probably subject to the same objections in a less degree as mercurial thermometers. 288. Air-thermometers. — Air-thermometers,in which either air or hydrogen may be used, are not open to the objections which hold with the mercurial thermometer, as the expansion for uniform increments of heat is under all conditions the same. There are two plans of these thermometers : I. Increase of volume of air at constant presssure. II. Increase of pressure at constant volume. The latter plan was found to give better results by Reg- nault, and constitutes the principle of the " Normal Air-ther- mometer." The air-thermometer in construction is a U-shaped tube, one branch enlarged into a bulb for the air, the other open for the mercury. Adjacent to the tube for the mercury is a gradu- ated scale which can be read by a vernier to small divisions of an inch ; a single mark is placed in the air branch, at a dis- tance of eight or ten inches from its top. This mark serves to define the limit of volume used. There are various forms of instrument in use ; the one adopted at Sibley College was designed by Mr. G. B. Preston and is shown in Fig. 180. The air-bulb, C, is approximately if inches by 6 inches ; the bulb is joined by a capillary tube, F, straight or bent into any convenient form as may be required* In order that the bulb may be conveniently located for heat- ing, this capillary tube is joined to a tube of glass about -^inch bore, the end of which is bent at right angles ground true, and joined by a short piece of rubber tubing to a glass tee at B. The tee has a branch provided with a cock, and connection for rubber tubing. The opposite side of this tee is joined in a similar way to a tube, BE, of the same bore, which is given a length sufficient to measure the required temperatures. A mark 372 EXPERIMENTAL ENGINEERING. [§28& a is made on the glass near F, at the junction of the capillary tube with the larger one for the mercury, and serves to deter- mine the limit of volume of air used. The bottle, A\ is filled with mercury, and connected by a rubber tube to the cock B. By opening the cock and elevating the bottle, mercury will v^ / y/y^ /// /// //y//^///^////////////// ( < y//y///yyy^yyy/y/yyy^yy^y^^^ Fig. i8o.-— Preston Air-thermometer. pass into the tubes : when it reaches the height of the mark a f the connecting cock B is closed, and the amount that the col- umn BE extends above the level of this mark, or fails of reaching this level, is read on the scale. Hoadley Air-thermometer. — The Hoadley air-thermome- ter, as described in the Transactions of the American Society of Mechanical Engineers, Vol. VI., page 282, is shown in Fig. 181, with all the dimensions marked. It differs from the preceding one in having no means provided for introducing or removing mercury to maintain the volume of air constant. The tube con- nected to the air-bulb, instead of being capillary, is about -ig- inch diameter. The instrument consists of a U-tube about § 288.] MEASUREMENT OF TEMPERATURE. 373 § inch external diameter, -^ bore, having a short leg about 39 inches long, and the other leg longer by 12 inches or more, the latter sur- mounted by a bulb blown out of the tube if inches in diameter, 6f inches in extreme length. The branches of the U-tube are 2 inches apart and vertical ; these are separate tubes, each one bent to a right angle by a curve of short radius, ground square and true at the ends and united by a short coupling of rubber tubing, ea, firmly bound on each branch with wire. After it is filled with dry air according to the directions in Article 290, page 376, it is fastened on a piece of board by annealed wire staples, and paper scales affixed as shown in the figure. The difference in height of .the £ two columns of mercury is taken as the read- I ing of the thermometer, and no correction is % made for slight variations in the volume of I air, as shown by variation in the position of the 1 height of the mercury column in the branch < BC. The error caused in this way is very small | and amounts to only 0.0030 inch per inch of \ height. This is equivalent to an error of about ■§ five degrees in a range of temperature of 600 § degrees F. J The Jolly Air-thermometer . — An exceedingly J simple form of the air-thermometer, and one also [ very accurate, consists of the air-bulb C, and a I capillary stem attached to three or four feet | of rubber tubing, which replaces the U-tube js in Fig. 180; in the other end of the rubber tubing is inserted a piece of glass tube 8 to 12 inches long and about -^ inch bore ; on this glass tube, and also on the capillary tube, is etched a single mark ; the rubber tube is filled with mercury, which extends up the glass tube p IG# on the other branch. A fixed scale, similar to DE £J X «• x 1 * I 1 n> F 1" 2* D G 'di. C c '-16 -M -14 -13 -12 -11 -10 -8 -8 -C -5 -4 -3 —2 c r 1 hi I ~c 3 3 5 ~J 3 3 3 n-jj 12J 13 j1 14J 15-1 10-J 17 ' !$]QB£ ' H -0 e t8i.— The Hoad- AlR-THERMOM- 374 EXPERIMENTAL ENGINEERING. [§ 28 9 . in Fig. 181, is located near the instrument. To use the instru- ment the tube is manipulated until the air is brought to its limit of volume, then the other end of the tube is held oppo- site the scale, and the reading corresponding to the height of. the mercury is taken. This is repeated for several tempera- tures, and, if the constant of the instrument is known, gives the data for computing the temperature. 289. Formulae for the Air-thermometer of Constant Vol- ume. — The pressure exerted by the confined air, added to the weight of mercury, in the branch Bfr, Fig. 180, will equal the weight of mercury in the other branch plus the weight of the atmosphere. Thus let p equal the pressure expressed in inches of mercury of the confined air, v its volume, tn the height of the mercury in the branch of the tube on the side of the air- bulb, m! the height in the other branch, b the pressure of the atmosphere expressed in inches of mercury, T the absolute temperature, t the thermometer-reading, h the height of mer- cury in the tube BE above the mark a, no mercury being above the point a in the tube BF. Let a equal constant ratio of T to pv. Then we have, since the pressures in both branches of the tube are equal, p -j- m z=£ m! -\- b\. ...... (1) p = m' — m -f- h. Since m* — m = k, . (2) P = h + t. (3) From physics, pv T -=, = constant (4) £289.] MEASUREMENT OF TEMPERATURE. S7 5 and if v be made constant,/ will vary as T; also T= 4 6o f /; ,. (5) p = Z(constant) = (460 + t)a ; .... (6) hence { A 6o + t)a = b + k (7) Let the same symbols with primes denote other values of the corresponding quantities. Then (460 + t')a = b' + k r (8) By comparing equations (7) and (8), 460 -f- 1 _ b + h 4 6o + f ~ V + ti W From which, by solving, T+T (46 ° + ^J ~ 46 ° (l °) f = To apply the formula, take readings of the instrument at 32 F., or some known temperature, and ascertain the con- stants of the instrument. Thus suppose the air-bulb to be packed in ice and the temperature reduced to 32 F. In this case t = 32 ; b and h are to be observed and recorded. 37 '6 EXPE RIM EN TA L ENGINEERING. If / = 32° in equation (10), [§ 290. t' = ^r h ib' + h')- A ^ (II) which is an equation to determine any temperature. If b and h are constant, 492 ~ {b -\- h) is constant and equals K. t = K(b / + /i / )-46o; (12) which is the practical equation for use in determining tem- peratures. If the height of the mercury in the column EB, Fig. 180, is less than that in FB, h will be negative, and is to be so con- sidered in the preceding formulae. In the use of the air-thermometer the mercury must be maintained constantly at the point a in the branch FB; this will require the addition of mercury to the U-tube as the press- ure increases, which -is readily done by raising the bottle A and opening the connecting-cock B. By a reverse process mercury may be removed as the pressure decreases. 290. Construction of the Air-thermometer. — The bulb of the air-thermometer must be filled with perfectly dry air, as any vapor of water will vitiate the results. To accomplish this, the bulb is provided with a small open- ing opposite the capillary tube, which is fused after the dry air is introduced. To effect the introduction of dry air, all the mercury is drawn into the bottle A, Fig. 180; the end of the tube E is connected to a U-tube about 6 inches long in its branches and about J inch internal diameter, filled with dry lumps of chloride of calcium and surrounded by crushed ice; the opening in the end of the air-chamber is connected by a rubber tube to an aspirator (a small injector supplied with water would act well as an aspirator), and air is drawn through §292.] MEASUREMENT OF TEMPERATURE. 377 for three or four hours: at the end of this time the bulb and tube should be filled with dry air. While the current of air is still flowing, the cock B is opened and mercury allowed to pass into the tubes until it rises to the point a in the tube BF; the opening in the air-chamber is then hermetically sealed with a blow-pipe, and the connections to the chloride-of-calcium tube removed. This operation fills the bulb with air at atmospheric pressure. By closing the cock B before the mercury has risen to the point a the pressure will.be increased ; by closing it after it has passed the point a it will be diminished. Packing the bulb C in ice, or heating it, will also increase or diminish the pressure as required. 291. Corrections to Determinations by the Air-thermom- eter. — The corrections to the air- thermometer are all very small, and affect the results but little if considered. They are : 1. Capillarity, or adhesion of the mercury to the glass. In general the mercury in the two tubes j5.Fand BE (Fig. 180) is moving in opposite directions, and the effect of adhesion is neutralized. For error in other cases see table on page 351. 2. Expansion of the glass. This is a small amount, and may usually be neglected. The coefficient of surface expan- sion of glass is 0.00001 per degree F. ; it is entirely neutralized if the column of mercury is not reduced in area at the point of meeting the air from the bulb. 3. Expansion of the mercury should in every case be taken into account by reducing all observations to 32 F., the coeffi- cient of expansion being 0.0001 per degree F. Reduce all ob- servations before applying formulae. 4. Errors in the fixed scale should be determined and observations reduced before applying formulas. 292. Practical Uses of the Air-thermometer. — The air- thermometer may be used as a standard with which to compare mercurial thermometers ; in this case the bulb of the air-ther- mometer is surrounded with a non-conducting chamber (Fig. 180), in which the thermometer to be compared is inserted. For low temperatures water may be circulated through this chamber, and simultaneous readings taken ; for higher tern- 37 8 EXPERIMENTAL ENGINEERING. [§293. peratures steam may be used. Time must in each case be given to permit the fluid in the air-thermometer to arrive at the true temperature. In comparison with mercurial thermometers, an exact agreement may be found at freezing and boiling points ; but at other places a slight disagreement may be expected, which will increase rapidly for high temperatures. The air-thermometer may also be used to measure tempera tures directly. When the bulb is connected with a long capil- lary stem it may be introduced into flues, and temperatures below the melting-point of glass measured. The melting point will vary from 600 to 800 degrees F. By using porcelain bulbs extremely high temperatures can be measured. 293. Directions for Use of the Air-thermometer. First. To obtain the Constants of the Instruments. — Enclose the air-bulb with crushed ice, arranged so that the water will drain off. Note the reading of the mercury column of the air- thermometer h and of the barometer b ; by means of the at- tached thermometers reduce these readings for a temperature of the mercury corresponding to 32 F. Correct for errors of graduation. Divide 492 by the sum of these corrected readings for the constant of the air-thermometer. Call this constant K. Second. To Measure any Temperature t'. — Note the corre- sponding reading of the mercury column k ', and that of a barometer b' in the same room. The reading of the mercury column plus that of the barometer will correspond to b' -\-h r in the formula t' = ^Ab' + h') - 460 = K(b' + h') - 460. Third. To Compare a Mercurial Thermometer. — Make simul- taneous readings of the thermometer when hanging in the chamber with the air-bulb, and the height of the mercury column. Perform reduction, and plot a calibration curve for each io° of graduation. Fourth. For general use of the air-thermometer, arrange § 294-] MEASUREMENT OE TEMPERATURE. 379 the bulb so that it can be inserted into the medium whose temperature is to be measured, with the U-shaped tubes in an accessible position for reading. Obtain the temperature as explained above (see Second). 294. Form for Reducing Air-thermometer Determina- tions. TEMPERATURE DETERMINATIONS WITH AIR-THERMOMETER. By 189... Determination of Constant. Symbol. I. II. III. IV. Temperature of air-bulb Reduced to 32° b Thermometer. Reduced to 32 . h A Determination of Temperature. t' = K(b' + h') -460. Barometer. Air-thermometer. Z>'+ k' Sum. t' Tem- pera- ture. Mercury Thermometer. No. Read- ing. Ther. b' re- duced. Read- ing. Ther. h' re- duced. Read- ing. Error. I 2 3 4 5 6 7 8 9 10 12 1 3 8o EXPERIMENTAL ENGINEERING. [§ 2 9 6. 295. Determination of Boiling and Freezing Points. First. To test for Boiling-point.- — Suspend the thermometer so that it will be entirely surrounded in the vapor of boiling water at atmospheric pressure but will not be in contact with the water. Note the reading. From the barometer-reading calculate the boiling-point for the same time. The dif- ference will be the error in position of the boiling-point. The engraving (Fig. 182) shows an in- strument for determining the boiling- point. The bulb of the thermometer is exposed to steam at atmospheric pressure, which passes up to the top of the instru- ment around the tube, and down on the outside, discharging into the air, or it may be returned directly to the cup, thus ob- viating the need of supplying water. In the form shown, the parts telescope into each other for convenience in carrying, which is entirely unnecessary for labora- tory uses. Secondly. To test for Freezing-point. — Surround the bulb of the thermometer by a mixture of water and ice, or water and snow ; drain off most of the water. The difference between the reading obtained and the zero as marked on the thermometer (32 for Fahr. scale) is the error in location of freezing-point. 296. Metallic Pyrometers are instruments used for meas- uring high temperatures. The ordinary instruments sold under this name are made of two metals which have different rates of expansion, copper and iron generally being used. The differ- ence in the rate of expansion is employed by means of levers and gears to rotate a needle over a dial graduated to degrees. In using the metallic pyrometer no reading should be taken until it has had sufficient time to arrive at :he temperature of Fig. 182. — Apparatus to Test boiling-point. § 298.J MEASUREMENT OF TEMPERATURE. 38 1 the medium in which it is enclosed ; when one tube alone is heated, the needle may be stationary on the dial, or even have a retrograde motion. The metallic pyrometer is usually calibrated by immersing in a pipe filled with steam under pressure and comparing the temperature with that given by a calibrated mercurial ther- mometer. The scale so obtained is assumed to be uniform throughout the range of the pyrometer and beyond the limits of the calibration. Comparison might be made with an air- thermometer. The extreme range of such pyrometers is about 1200 Fahr., but they are probably of little value for tempera- tures exceeding 1000 Fahr. Wedgewood's Pyrometer is based on the permanent contrac- tion of clay cylinders due to heating. This contraction is determined by measurement in a metal groove with plane sides inclined towards each other. This pyrometer does not give uniform results. 297. Air-pyrometer. — The air-thermometer with a bulb of porcelain, or platinum or other refractory material, affords an, accurate method of measuring high temperatures. Mr. Hoadley* states that the ordinary air-thermometer made of hard glass can be used to determine temperatures of 8oo° Fahr. With porcelain bulb it has been used to measure tem- peratures of 1900 Fahr. 298. Calorimetric Pyrometers. — Pyrometers of this class determine the temperature by heating a metal or other refrac- tory substance to the heat of the medium whose temperature is to be measured. Suddenly dropping the heated body into a large mass of water, the heat given off by the body is equal to that gained by the water ; from this operation and the known specific heat of the substance the temperature is computed. Thus, let K equal the specific heat of the body, M its weight ; let W equal the weight of water, t its temperature before, and t' after, the body has been immersed ; let T equal the tempera- ture of the heated body, t' its final temperature. Then KM{T-f)= W{t' -t). * See Vol. VI., Transactions American Society Mechanical Engineers. 382 EXPERIMENTAL ENGINEERING. [§ 300. From which W In connection with pyrometrical work, the specific heat of the substance used often has to be determined. 299. Determination of Specific Heat. — The specific heat of a body is determined by heating it to a known temperature ; for instance, after heating it in steam of atmospheric pressure until it has attained a known temperature T, its weight M having been accurately determined, it is dropped suddenly without loss of heat into a vessel containing ^pounds of water at a temperature of 6o° Fahr. Let K be the specific heat of the body, and t' the resulting temperature. The vessel must be so made that there is no loss of heat, and that the water can be thoroughly agitated so that an accurate measure of the temperature t' can be taken ; also the effect of the vessel in cooling the body must be determined and considered a part of the weight W. Then will the loss of heat of the body be equal to that gained by the water. K{T- t')M= W{t' - 6o°). From which ~ m {T—ty The specific heat of most bodies is not quite constant but is found to increase with higher temperatures. 300. Values of Specific Heat and Melting-point— The metals required for pyrometrical purposes are those with a high melting-point and a uniform and known specific heat. The obvious losses of heat in (1) conveying the heated body to the calorimeter, and (2) radiation of heat from the calorim- eter, may be considerable, and should be ascertained by radia- tion tests and the proper correction made. Nearly all metals are oxydized, or acted on by the furnace-gases, long before the melting-point is reached; so that, in general, whatever metal is used, it must be protected by a fire-clay or graphite crucible. Platinum, copper and iron are usually employed. The following table gives determinations of melting-points and specific heats: S300.J MEASUREMENT OF TEMPERATURE. 3*3 TABLE OF MELTING-POINTS AND SPECIFIC HEATS OF METALS. Metal. Melting-point. Specific Heat. Low Temperatures. Degrees Fahr. Degrees Centigrade. 2900 3400 2550 1870 700 630 493 426 - 38 239 2000 415 325 264 228 425 . O.034 0.II8 O.IIO O.14 O.94 O.170 O.094 0.O93 O.030 O.030 O.O47 O.030 0.200 Steel Wrought- iron. ... Copper Porcelain Zinc Bismuth Tin Mercury Antimony The mean specific heat of Platinum* has been the subject of careful investigation. It was found to vary from 0.03350 at ioo° C. to 0.0377 at 1 ioo° C. by Poullet, the experiment being made with a platinum reservoir air-thermometer. The following were the determinations : Platinum. Copper. Range of Temperature. Mean Specific Range of Temperature. Mean Specific Degree Centigrade. Heat. Degree Centigrade. Heat. O to IOO O.03350 15 to TOO O.O9331 O " 200 .03392 16 " 172 O.09483 O " 300 .03434 17 " 247 O.09680 O " 400 .03476 O " 500 •03518 O " 600 .03560 O " 700 .03602 O " 800 . 03644 O " 90c .03686 O " IOOO .03728 " IIOO .03770 * See Encyclopaedia Britannica, art. Pyrometer. 384 EXPERIMENTAL ENGINEERING. L§ 301.. For zvr ought-iron the true specific heat at a temperature t on the Centigrade scale is given as follows by Weinbold : C t = 0.105907 + 0.00006538/ + o. 000000066477 f. Porcelain or Fire-clay having a specific heat from 0.17 to o.2 r although not a metal, is well adapted for pyrometrical purposes. 301. HoacUey Calorimetric Pyrometer. — The Hoadley pyrometer is described in Vol. VI., p. 712, Transactions of the American Society of Mechanical Engineers. It consisted of a vessel, Fig. 183, made of several concentric vessels of copper, with water in the inner one, eider-down in the inter- mediate spaces, and a cover of the same nature. Also a sub- Fig. 183. — Hoadley Pyrometer. stance to be heated consisting of balls of platinum, or wrought- hon and copper covered with platinum. These balls were heated in a crucible, conveyed to the calorimeter and suddenly dropped in. The calorimeter was provided with an agitator made of hard rubber, with a hole in the centre for a thermome- ter. The balls used as heat-carriers weighed about three quar- ters of a pound each ; the vessel held about twelve pounds of water. This apparatus is now at Cornell University. § 3Q3-] MEASUREMENT OF TEMPERATURE. 385 The balls were heated in crucibles and conveyed to the calorimeter in a fire-clay jar as shown in Fig. 142. The cover Fig. 183. — Platinum Balls and Crucible. of this jar was quickly removed and the balls dropped into the water in the calorimeter. 302. Electric Pyrometers. — The fact that electric currents are excited by differences of temperature in different parts of a metallic circuit is made use of for measuring large as well as small differences of temperature. The electromotive force of a circuit at different tempera- tures is given by Professor Tait* as E = A(t l -t,)[T-U.t l + t,)l in which E = electromotive force ; T, a constant temperature, such that no current is produced if temperatures on either side are equal, and which depends on the metal : for copper and iron it is about 284 C. A is a constant depending on the metals ; t 1 = the higher temperature, t 2 the lower. 303. Siemens's Pyrometer. — This instrument is based on the well-known principle of increase of resistance with rise of temperature. The formula given by Siemens for the resistance of metals is R=aVT+/3T+y; * See article Pyrometer, Encyc. Britannica. 3&6 EXPERIMENTAL ENGINEERING. [§ 304. in which R equals the resistance to be measured, a, 0, and y are coefficients, and T equals the absolute temperature. The resistance is ascertained by a volt-meter, and the co- efficients a, fi, and y are determined by special calibration. The heated substance is a platinum wire wound around a clay cylinder and protected by a covering of fine clay; this is in- serted into the furnace or medium whose temperature is required. The current is passed alternately in different direc- tions, and the resistance is measured by the gas accumulating in a volt-meter at either pole. The instrument is very sensitive to slight changes of tem- perature, and is well suited for accurate measurements of moderate temperatures. In the measurement of high tem- peratures considerable difficulty was experienced because of change in the coefficients due to the extreme heat. Callendar's platinum thermometer is an electrical pyrometer of the resistance type arranged so that one portion is maintained at constant temperature by being kept in a vessel of water contain- ing melting ice, while the other part is subjected to the tempera- ture to be measured. The difference in resistance of these two parts affords a basis for determining the temperature. This apparatus is exceedingly accurate and capable of measuring very small subdivisions of a degree. Professor Brown of McGill University has devised a form of the Callendar instrument in which the difference of temperature is determined by equalizing the resistance through two circuits until they are the same, which fact is indicated by the use of a telephone which transmits no sound at that instant. 304. Optical Pyrometers. — From the fact that the color of an incandescent body varies with the wave length and this again with the temperature, it is possible to determine the temperature of such bodies by theii appearance. For ihis purpose a number of optical pyrometers have been devised. The Mesure and Nouel's pyrometric telescope meas- ures the temperatures by taking advantage of the rotation of the plane of polarization of light passing through a quartz plate cut § 304-] MEASUREMENT OF TEMPERATURE. 387 perpendicular to its axis. The angle of rotation is directly pro- portional to the thickness of the quartz, and approximately in- versely proportional to the square of the wave length. Light from an incandescent object, passing through the slightly ground diffusing-glass G (Fig. 185), enters a polarizing Fig. 185. — Mesure and Nouel Pyrometric Telescope. nicol P, and, traversing the quartz plate Q, strikes the analyzer A, and is seen through the eye piece OL. In the use of the instrument the analyzer is turned until the object appears to have a lemon-yellow color. The position of '-■ Fine =f3 f JIilli_Ammeter Fig. 186. — The Morse Thermo-gauge. the analyzer is indicated by the graduated circle C, the reading of which may be referred to a temperature scale. Because of the variations due to personal errors of different observers the uncertainties of observations are likely to amount to fully ioo° C. The instrument is very convenient for use and is approximately accurate. 388 EXPERIMEN TA L ENGINEERING. [§ 304. The Morse thermo-gauge is shown in Fig. 186. It employs an incandescent lamp with a rheostat arranged so that the current flowing through it and its consequent brightness may be regu- lated. The amount of current flowing through is shown by a milli-voltmeter connected in circuit, the reading of which can be referred to a scale for the determination of temperature. The lamp is adjusted from an experimental scale for its degree of brightness at different ages. In using this instrument the incandescent lamp is located between the eye and the object whose temperature is to be meas- ured, and the current is regulated until the lamp is invisible. This instrument is designed for use in hardening steel and has an extensive use in that industry. General Remarks regarding Pyrometers. — An ex- tended series of experiments with the different pyrometers described has led the author to believe that the calorimetric forms, as described in Articles 298 and 301, despite their in- convenience and the losses from radiation which attend their use, give, if we except the air-pyrometer, more uniform and re- liable results than the others. The electrical pyrometers are subject to the same inaccuracy as the calorimetric pyrometers, due to complex changes in the electrical resistances of the thermometric substance, so that the results are quite uncer- tain for high temperatures. The electrical pyrometers also need for their successful use a command of electrical energy and the possession of a set of electrical measuring instruments. While these pyrometers may give reliable results with skilled electricians, they are of little practical use to the engineer. The calorimetric pyrom- eters are cheap, portable, and easy to use, and with careful handling give uniform and fairly reliable results. The best substance for use in these instruments as a heat-conveyer is, in the opinion of the author, a porcelain or fire-clay ball about 2 inches in diameter. The metals, not even excepting platinum, are readily attacked by the furnace-gases, and when i 304.] MEASUREMENT OF TEMPERATURE. 389 employed need to be protected in a crucible of refractory material. If used by heating directly in the furnace, wrought- iron is perhaps as good as any of the metals. It may be oxi- dized and fall in pieces" but since the oxide has about the same specific heat as the original metal, determinations may be made with the residue without any great error. The porcelain or fire-clay balls seem to be unaffected by the furnace-gases, and do not radiate heat as rapidly as the metals, so that were the specific heat as accurately determined they would be superior in every way to the metallic balls. The determination of the specific heat of burned fire-clay as made by Mr. D. J. Jenkins at Sibley College was 0.1702 at temperature of boiling water. By comparison with results obtained with a metal whose specific heat was known, the specific heat at 1000 C. (1832 F.) is calculated as about 0.20. The latter quantity is subject to correction. The air -py- rometer with a porcelain or plat- inum bulb can be used convenient- ly, and the cor- responding tem- peraturesso read- ily and easily deduced from the determinations that it is worthy a much more ex- tended use. The bulb may be made in any de- sired form and Element op Le Chatelier's Pyrometer. a long capillary stem can be led from the bulb to the meas- uring tubes a long distance without sensible error, so that it may be adapted to a variety of uses. Le Chatelier's Electrical Pyrometer. CHAPTER XIII. METHODS OF DETERMINING THE AMOUNT OF MOISTURE IN STEAM. / 305. Quality of Steam. — Degree of Superheat, — Steam may be dry and saturated, wet or superheated, as described in Article 265, page 340. The term quality is used to express the relative condition of the steam as compared with dry and saturated steam of the same pressure. It is in any case the total heat in a pound of the sample steam, less the heat of the liquid, divided by the total latent heat of evaporation of one pound of dry steam at the same pressure, see page 343. For moist or wet steam, which is to be considered as made up of a mixture of water and dry steam, the quality would equal the percentage by weight of dry steam in the mixture. For superheated steam the quality would exceed unity, and is to be considered as that weight of dry and saturated steam, the heat in which is equivalent to that in one pound of the superheated steam, neglecting in both cases the heat of the liquid. In case of superheated steam, its temperature is higher than that of dry and saturated steam at the same pressure ; this excess of temperature is termed degree of superheat. 306. Importance of Quality Determinations. — The im- portance of correctly determining the quality of steam is great, because the percentage of water carried over in the steam in the form of vapor or drops of water may be large, and this water is an inert quantity so far as its power of doing work is concerned, even if not a positive detriment to the engine. Any tests for the efficiency of engine or boiler not accompanied with determinations of the amount of water carried over in the 390 § 309-] THE AMOUNT OF MOISTURE IN STEAM. 391 steam would be defective in essential particulars, and might tead to erroneous or even absurd results. 307. Methods of Determining the Quality. — The methods of measuring the amount of moisture contained in steam may be considered under three heads: first, Calorimetry proper ; in which the method is based on some process of comparing the heat actually existing in a pound of the sample with that known to exist in a pound of dry and saturated steam at the same pressure. Secondly, Mechanical Separation of the water from the steam, involving the processes of separation and of weighing. Thirdly, a Chemical Method, in which case a soluble salt is introduced into the water of the boiler. This salt is not absorbed by dry steam, and if it is found in the steam it indi- cates the presence of water. The quality is equal to the ratio of salt in the steam to that in an equal weight of water drawn from the boiler. All methods for determining the quality of steam are included under the head of calorimetry , and instruments for determining the quality are termed calorimeters. 308. Classification of Calorimeters. — The following clas- sification of different forms of calorimeter is convenient and comprehensive: [Jet. Calorimeters ' Condensing Superheating. Surface Barrel or Tank. Continuous. Barrus — Continuous. Hoadley Calorimeter. Kent — Tank Calorimeter. External — Barrus Superheating. Internal — Peabody Throttling. L Directly determining moisture \ c^m^ah 309. Error in Calorimetric Processes. — The calorimetric processes proper depend on the method of measuring the heat actually existing in a pound of the sample steam at a known pressure. This measurement is then compared with the re- sults given in a steam-table for dry and saturated steam, and the quality is computed as will be explained later. 392 EXPERIMEN TA L ENGINEERING. [§3io. In nearly every calorimetric process the heat of the sample is determined by condensing the steam at atmospheric press- ure, or at least measuring the heat when its conditions of pressure and temperature are different from its original state. This process involves no error. The following is a statement of an investigation concerning it made by Sir William Thomson:* " If steam have to rush through a long fine tube or through a fine aperture within a calorimetric apparatus, its pressure will be diminished before it is condensed ; and there will, therefore, in two parts of the calorimeter be saturated steam at different temperatures; yet on account of the heat developed by the fluid friction, which would be precisely the equivalent of the mechanical effect of the expansion wasted in the rushing, the heat measured by the calorimeter would be precisely the same as if the condensation took place at a press- ure not appreciably lower than that of the entering steam." 310. Use of Steam-tables. — In reducing calorimetric ex- periments steam-tables will be required. The explanation of the terms used will be found in Article 265, page 340, and tables will be found in the Appendix of the book. Students will please notice, that the pressures referred to in the steam-tables are absolute, not gauge pressures, and that gauge pressures are to be reduced to absolute pressures, by adding the barometer-reading reduced to pounds per square inch, before using the tables. The following symbols will be employed to represent the different properties of steam : TABLE OF SYMBOLS. Properties of Steam. Symbol. Properties of Steam. Symbol. Pressure, pounds per sq. in. Pressure, pounds per sq. foot Temperature, degrees Fahr. Temperature absolute P P t T q or S p or I APuor E r or L Total heat B. T. U Weight of cu. ft. of steam lbs. Vol. of 1 lb. steam, cubic ft. Vol. of 1 lb. water, cubic ft . Change in volume v — o~ . . . Quality of steam Xor H 8 or W v or C cr u External latent heat Total latent heat Per cent of moisture Degree of superheat I — X D * Mathematical Papers, XLVIIL, p. 194. § 3 I2 THE AMOUNT OF MOISTURE IN STEAM. 393 The quantities q, p, APu, r, and A are given in B. T. U. per pound of saturated steam reckoned from 32 Fahr. 311. General Formula for the Heat in One Pound of Steam. — The heat existing in one pound of steam with any quality x can be expressed by the formula xp-\-q — h. (1) The heat, however, which is required to raise water from 32 F. and convert it into steam at a given temperature will include the external latent heat, and will be expressed by the formula xr-\-q = h'. . . . . . . . (2) The heat that may be given out by condensation or change of pressure is expressed in equation (2) ; that which exists in the steam without change of pressure or external work, by equation (1). Since in all calorimetric processes the steam is condensed, or at least the pressure changed, equation (2) is to be employed to represent the available heat. If the pressure of the steam is known, r and q can be found from the steam-tables. If the heat h in B. T. U. above 32 can be found for the sample steam, all the quantities in the above equation with the exception of x are known, and we shall find x = — — *. ....... (3) In case x is greater than unity, the steam is superheated, and the degree of superheat "-^ «> when 0.48 equals the specific heat of steam, c p . 312. Methods of Determining the Heat in a given Sample of Steam. — There are two methods of determining the heat h in a given sample of steam. 394 EXPERIMENTAL ENGINEERING. [§ 312. I. Condensing the Steam at Atmospheric Pressure. — In this case the weight of the steam is obtained by weighing the con- densing water before and after condensation has taken place and determining the corresponding temperatures. Thus let the weight of condensing water be represented by W, that of the condensed steam by w; the temperature of the condensing water cold by t 1 , the condensing water warm by / 2 ; the original temperature of the steam by t } that of the condensed steam by t % . Suppose that the calorimeter absorb heat to the same extent as k pounds of water; then the heat added by con- densing one pound of steam is equal to ^«.-<.> » The original heat above 32 from equation (2), page 363, is xr-\-q. Since in equation (5) the temperature is reck- oned above zero, it will be more convenient to use, instead of xr-\- q-\- 32, xr -\- t, which is very nearly identical. Since the heat lost in condensing one pound of steam is equal to that gained by the water, we shall evidently have from which W+k{t-t) (t-t t ) x = w r r (6) If the temperature of condensed steam equal that of the warm condensing water, t % = t 2 , which is the usual condition of condensation. 2. Superheating the Steam. — If the pressure and tempera- ture of superheated steam is known, the degree of superheat D can be found by deducting the normal temperature, as given in the steam-table for that pressure, from the observed tem- perature. The total heat in a pound of the superheated steam § S l 3-] THE AMOUNT OF MOISTURE IN STEAM. 395 is equal to that in a pound of saturated steam, as given by the steam-tables, plus the product of the degree of superheat into the specific heat c P of the steam ; that is, H = X + c p D. The superheating may be done by extraneous means, as in the Barrus superheating calorimeter, or by throttling, as in the throttling calorimeter. In the latter the heat required for superheating is obtained by reducing the pressure, which, being accompanied by a corresponding reduction of boiling point, liberates heat sufficient to evaporate a small percentage of moisture only. In the case of the superheating calorimeter, the heat re- quired to evaporate the moisture and superheat the steam is measured by the loss of temperature n in an equal weight of superheated steam, so that c p n = r(i — x) -f- c p D ; «-* = *fe^ (7) In the case of the throttling calorimeter there is no change in the total amount of heat, but there is a change of pressure, so that the quantities in the first member of (8) correspond to the original pressures of steam before throttling, and those in the second member to the calorimeter pressures after throttling, and xr + g=*K + c& x= X <-4 + c > D . . . (8) 313. Condensing Calorimeters. — Condensing calorimeters are of two general classes : 1. The jet of steam is received by the condensing water, and the condensed steam intermingles directly with the condensing water. 2. The jet of steam is condensed in a coil or pipe arranged as in a surface condenser. 39 6 EXPERIMENTAL ENGINEERING. [§ 314. and the condensed steam is maintained separate from the con- densing water. The principle of action of both classes of condensing calo- rimeter is essentially the same, and is expressed by equation (6): w+ H*,-ti C-'O w r / r In the first class t s = / 3 , and x _ W +k(t- tl ) (t-t,) ( W Both forms of condensing calorimeter can be made to act con- tinuously or at intervals, and there are several distinct types of each. The most common type of condensing calorimeter is one in which the condensing water is received in a barrel or tank, and hence is termed a barrel calorimeter. The special forms will be described later. 314. Effect of Errors in Calorimeter Determinations. First. Condensing Calorimeters. — To determine the effect of error, suppose in each case the quantity under discussion to be a variable and differentiate the equation W £(/,-0-(/-« jr = — We have Ax -T- A W — (/, — O -f- wr ; Ax -T- Aw = — ( W~- w 2 ) (t % — *,) -J- r : Ax + At, =£(JP-*-«0 + i]-i-r; Ax h- At^ = W -f- wr. § 3I4-] THE AMOUNT OF MOISTURE IN STEAM. 397 Since Ar — — At, nearly, for ordinary pressures of steam, and further is a function of the pressure, we have approximately Ap = Ap =z — Ar ; Ax+Ap = [^(^-0 -t-r + t^r\ The weight of condensing water usually held by the barrel- calorimeters is from 300 to 400 lbs., while the weight of the steam condensed varies from 16 to 20 lbs., and the correspond- ing temperatures have a range of 50 to yo° F. For these cases it will be found that the percentage of error in quality, sup- posing other data correct, is approximately the same as the percentage of error in the weights. The error in thermometer- determination has nearly the same effect, whether made before or after the steam has been condensed. For the amounts usu- ally employed the error of one fifth of one degree in tempera ture has about the same effect as one half of one per cent error in weight ; that is, it makes an error of about the same amount in the quality of steam. The following shows in tabular form the effect of errors with condensing calorimeters in which the ordinary weights of water and of steam are used : TABULATION OF ERRORS. Error Error Error •Sc' U V Error in Error in in in in u Condensing Water. Condensed Steam. Temperature, Temperature, Steam- Cdo S Cold Water. Warm Water. pressure. c • "3 >« Lbs. Per ct. Lbs. Per ct. Degs. Per ct. Degs. Per ct. Lbs. Perc. 3 — Total wt. = 360 lbs. Total wt. = 20 lbs. Temp. =50° F. Temp. =no° F. Pr. = 88 lbs. 3-€ 1.0 0.2 1.0 o-53 1.2 0.65 0.60 7.0 8.0 1 2 1.8 o-5 0.1 05 0.27 0.6 0.30 0.30 3-5 4.0 0.6 1.5 0.40 0.08 0.4 0.18 o-S 0.25 2-5 3-o 3-5 05 ©■3 0.08 0.016 0.08 0.045 O.I 0.05 0.50 0.6 07 O.I Total wt. = 300 lbs. Total wt. = 20 lbs. 0.25 1-5 0.5 O.I O-S 0.2 2.2 *; s 39 8 EXPERIMENTAL ENGINEERING. [§ 3 1 4. In the table, the errors in the various observations ex- pressed in the same horizontal line have the same effect on the result. From the table it is seen, for the given weights, that an error of 3.6 pounds in condensing water, of 0.2 pound in com densed steam, of 0.53 F. in temperature of cold water, of 0.65 F. in warm water, or of 7 pounds in steam-pressure will sever- ally make an error in the result of 1.2 per cent. Expressed in percentages, an error of 1 per cent in weight or 1.2 and 0.6 per cent in thermometer-readings makes an error in the quality of 1.2 per cent. The conditions for determination of moisture within one half of one per cent require — 1. Scales that weigh accurately to half of one per cent of the quantity to be weighed. 2. Thermometers that give accurate determinations to about one fifth of one degree F. 3. An accurate pressure-gauge. 4. Correct observations of the resulting quantities. 5. Determination of loss caused by calorimeter. Secondly. Superheating Calorimeters. — The Barrus Super- heating Calorimeter. — In this, if t 3 — t is the gain of tempera- ture of the sample steam, and / 2 — t^ is the loss of temperature in the superheated steam, we have, neglecting radiation, 1 — x — o.48[/ a — t x — (t s — 1)~\ -f- r. In the Throttling Calorimeter, where the steam is super- heated by expanding, we have by equation (7), making c p = 0.48, \ + 0.4SD — q x = . In either form of superheating calorimeter the effect of an error of one degree in temperature is to make an error in x of 0.06 of one per cent, while an error of 9 in temperature will affect the value of x but 0.5 per cent. The boiling-point § 3150 THE AMOUNT OF MOISTURE IN STEAM. 399 should be correctly determined, however, especially if the amount of superheating is small. An error in gauge-reading has about, one half the effect on the quality of the steam as in the other class of calorimeters. 315. Method of Obtaining a Sample of Steam. — It is usually arranged so as to pass only a very small percentage of the total steam through the calorimeter, and it is important that this sample shall fairly represent the entire quantity of steam. From experiments made by the author, it is quite cer- tain that the quality varies greatly in different portions of the same pipe, and that it differs more in horizontal than in verti- cal pipes. Steam drawn from the surface of the pipe is likely to contain more than the average amount of moisture ; that from the centre of the pipe to contain less. The better method for obtaining a sample of steam is to cut a long threaded nipple into which a series of holes may be drilled, and screw this well into the pipe. Half-inch pipe is gen- erally used for calorimeter connections, and it may be screwed into the main pipe one half or three quarters of the distance to the centre, with the end left open and without side-perfora- tions, as shown in Fig. 187, or screwed three fourths the ^ PiBO fflllMMM^^H »*• Fig. 187. Collecting-nipples. Fig. 188. distance across the pipe, a series of holes drilled through the sides, and the end left open or stopped, as shown in Fig. 144. A lock-nut on the nipple, which can be screwed against the pipe when the nipple is in place, will serve to make a tight joint The best form of nipple is not definitely determined, although many experiments have been made for this purpose; a form extending nearly across the pipe and provided with a 400 EXPERIMENTAL ENGINEERING. [§3l6. slit or with numerous holes is probably preferable. When the current of steam is ascending in a vertical pipe, the water seems to be more uniformly mixed than when descending in a vertical pipe or when moving in a horizontal one. There , however, considerable variation tor this condition; is especially if the steam contains more than 3 per cent of water., 316. Method of Inserting Thermometers. — In the use of calorimeters it is frequently necessary to insert thermometers Fig. 189. — Steam-thermometer. Fig 190.— Thermometer-cup. into the steam in order to correctly measure the temperature. For this purpose thermometers can be had mounted in a brass case, as shown in Fig. 189, which will screw into a threaded opening in the main pipe. The author prefers to use instead a thermometer-cup of the form shown in Fig. 190, which is screwed into a tapped open- § 3 1 ?-] THE AMOUNT OF MOISTURE IN STEAM. 401 ing in the pipe. Cylinder-oil or mercury is then poured into the cup, and a thermometer with graduations cut on the glass inserted. The thermometer-cups are usually made of a solid brass casting, the outside being turned down to the proper di- mensions and threaded to fit a f-inch pipe-fitting. The inside hole is drilled \ inch in diameter, and the walls are left T V inch thick. The total length varies from 4J to 6 inches — depending on the place where it must be used. In either case it is essen- tial that the thermometer be inserted deep into the current of steam or water, and that no air-pocket forms around the bulb of the thermometer. The thermometer should be nearly ver- tical, and as much of the stem as possible should be protected from radiating influence. If the thermometer is to be inserted into steam of very little pressure, the stem of the thermometer can be crowded into a hole cut in a rubber cork which fits the opening in the pipe. In case the thermometer cannot be inserted in the pipe it is sometimes bound on the outside, being well protected from radiation by hair- felting; but this practice cannot be recom- mended, as the reading is often much less than is shown by a thermometer inserted in the current of flowing steam. In the use of thermometers, breakages will be lessened by carefully observing the directions as given in Article 286, p. 370. 317. Determination of the Water-equivalent of the Calorimeter. — The calorimeters exert some effect on the heating of the liquid contained in them, since the inner sub- stance of the calorimeter must also be heated. This effect is best expressed by considering the calorimeter as equivalent to a certain number of pounds of water producing the same result. This number is termed the water- equivalent of the calorimeter. The water-equivalent, k, can be found in three ways : 1. By computing from the known weight and specific heat of the materials composing the calorimeter. Thus let c be the specific heat, W c the weight; then k = cW c . 402 EXPERIMENTAL ENGINEERING. [§3 l8 « 2. By drawing into the calorimeter, when it is cooled down to a low temperature, a weighed quantity of water of higher temperature and observing the resulting temperature. Thus let W equal the weight of water, t x the first and / 2 the final temperatures, and k the water-equivalent sought. Since the heat before and after this operation is the same, (w+ky, = Wt x From which 3. By condensing steam drawn from a quiescent boiler, and thus known to be dry and saturated, with a weighed quantity of water of known temperature in the calorimeter ; the tempera- ture, pressure, and weight of the steam being known. The con- ditions are the same as for equation (6), page 394, all the quantities being known excepting k. By solving equation (6), k = — ^ ■ — — W. .... (10) For the barrel and jet condensing calorimeters generally, t % = / 2 , and we have k _ w{rx + t — / 3 ) W. The cooling effect of superheating calorimeters is generally expressed in degrees of temperature in the reading of one of the thermometers. SPECIAL FORMS OF CALORIMETERS. 318. Barrel or Tank Calorimeter. — The barrel calorim- eter belongs to that class of condensing calorimeters in which a jet of steam intermingles directly with the water of conden- sation. It is made in various ways ; in some instances the § 3!8.] THE AMOUNT OF MOISTURE IN STEAM. 403 walls are made double and packed with a non-condensing substance, as down or hair-felting, to prevent radiation, and the instrument is provided with an agitator consisting of paddles fastened to a vertical axis that can be revolved and the water thoroughly mixed ; but it usually consists of an ordi- nary wooden tank or barrel resting on a pair of scales, as shown in Fig. 191. Fig. 191. — The Barrel Calorimeter. A sample of steam is drawn from the main steam-pipe by connections, as explained in Article 315, page 369, and con- veyed by hose, or partly by iron pipe and partly by hose, to the calorimeter. In the use of the instrument, water is first admitted to the barrel and the weight accurately determined. The pipe is then heated by permitting steam to blow through it into the air ; steam is then shut off, the end of the pipe is submerged in the water of the calorimeter, and steam turned on until the temperature of the condensing water is about 1 io° F. The pipe is then removed, the water vigorously stirred, the temperature and the final weight taken. If the effect of the calorimeter, k, expressed as additional weight of water, is known, the quality can be computed as in equation (6), page 394. ,=^±i*to_&=^. . . . (6) wr 7 J 404 EXPERIMENTAL ENGINEERING. L§ 3 J ^ A tee screwed crosswise of the pipe, as shown in Fig. 189, forms an efficient agitator, provided the temperature be taken immediately after the steam is turned off. The pipe may remain in the calorimeter during the final weighing if supported externally, and if air be admitted so that it will not keep full of water ; in such a case, however, it should also be in the barrel during the first weighing, or else the final weight must be corrected for displacement of water by the pipe. The effect of displacement is readily determined by weighing with and without the pipe in the water of the calo- rimeter. The determination of the water-equivalent of the barrel calorimeter will be found very difficult in practice, and it is usually customary to heat the barrel previous to using it, and then neglect any effect of the calorimeter. This nearly elimi- nates the effect of the calorimeter. The accuracy of this instrument, as shown in Article 314, page 397, depends prin- cipally on the accuracy with which the temperature and the weight of the condensed steam are obtained. The conditions for obtaining the temperature of the water accurately are seldom favorable, as it is nearly impossible to secure a uniform mixture of the hot and cold water; the result is that deter- minations made with this instrument on the same quality of steam often vary 3 to 6 per cent. From an extended use in comparison with more accurate calorimeters, the author would place the average error resulting from the use of the barrel calorimeter at from 2 to 4 per cent. Example. — Temperature of condensing water, cold, ^,is 52°.8 F.; warm, / 2 , I09°.6 F. Steam-pressure by gauge, 79.7; absolute, 94.4. Entering steam, normal temperature, from steam-table, t, 323°.5 F. Latent heat, r y 888.2 B. T. U. Weight of condensing water cold, W, 360 pounds ; warm, W-\-w t 379.1 pounds, wet steam, w, 19.1 pounds. Calorim- eter-equivalent eliminated by heating. The quality ^60 (1096- 52.8) _ 323.5 - 1 09.6 = 19. 1" 888.2 888.2 yi> ' 4 ' § 320.] THE AMOUNT OF MOISTURE IN STEAM. 405 319. Directions for Use of the Barrel Calorimeter. — Apparatus. — Thermometer reading to \ degree F., range 32 to 212 ; scales reading to -^ of a pound ; barrel provided with means of filling with water and emptying ; proper steam con- nections ; steam-gauge or thermometer in main steam-pipe. 1. Calibrate all apparatus. 2. Fill barrel with 360 pounds of water, and heat to 130 degrees by steam ; waste this and make no determinations for moisture. This is to warm up the barrel. 3. Empty the barrel, take its weight, add quickly 360 pounds of water, and take its temperature. 4. Remove steam-pipe from barrel ; blow steam through it to warm and dry it ; hang on bracket so as not to be in contact with barrel ; turn on steam, and leave it on until temperature of resulting water rises to no° F. Turn off steam; open air- cock at steam-pipe as explained. 5. Take the final weights with pipe in barrel, in same po- sition as in previous weighings ; also take weights with the pipe removed : calculate from this the displacement due to pipe, and correct for same. Alternative for fourth and fifth operations. — Supply steam through a hose, which is removed as soon as water rises to a temperature of no° F. Weigh with the hose removed from the barrel. Stir the water while taking temperatures. 6. Take five determinations, and compute results as ex- plained. Fill out and file blank containing data and results. 7. Compute the value of the water-equivalent, k, in pounds by comparing the different sets of observations. 320. The Continuous-jet Condensing Calorimeter.— A calorimeter may be made by condensing the jet of steam in a stream of water passing through a small injector or an equiva- lent instrument. The method is well shown in Fig. 193. A tank of cold water, B, placed upon the scales R, is connected to the small injector by the pipe C; the injector is supplied with steam by the pipe S, the pressure of which is taken by the gauge P; the temperature of the cold water is taken at e, that of the warm water at g. Water is discharged into the 406 EXPERIMENTAL ENGINEERING. [§ 320. weighing-tank A, The amount taken from the tank B is the weight of cold water W; the difference in the respective weights of the water in tanks A and B is the weight of the steam w. The quality is computed exactly as for the barrel calorim- eter. In case an injector is used, as shown in Fig. 192, the tank B is not needed : water can be raised by suction from the tank A through the pipe d. The original weight of A will be that Fig. 19a.— The Injector Calorimeter. of the cold water ; the final weight will be that of steam added to the cold water. In case an injector is not convenient, and the water is sup- plied under a small head, a very satisfactory substitute can be made of pipe-fittings, as shown in Fig. 193. In this case, steam of known pressure and temperature is supplied by the pipe A cold water is received at S', and the warm water is discharged at vS. The temperature of the entering water is taken by a thermometer in the thermometer-cup T\ that of the discharge by a thermometer at T. The steam is condensed in front of the nozzle C. This class of instruments present much better opportunities of measuring the temperatures accurately than the barrel calorimeter, and the results are somewhat more reliable. § 32i.] THE AMOUNT OF MOISTURE IN STEAM. 407 In the use of continuous calorimeters of any class, the in- strument should be put in operation before the thermometers are put in place or any observations taken. The poise on the weighing-scale can be set somewhat in advance of its bal- ancing position, and when sufficient water has been pumped out the scale-beam will rise ; this may be taken as the signal Fig. 193.— Jet Continuous Calorimeter. for saving the water which has been previously wasted, and of commencing the run. The water-equivalent of the calorimeter, k, will be small, and due principally to radiation. It can be found by passing hot water through the calorimeter and noting the loss in tern* perature. 321. The Hoadley Calorimeter. — This instrument be^ longs to the class of non-continuous surface calorimeters. The 408 EXPERIMENTAL ENGINEERING. [§ 321. instrument is described in Transactions of the American So- ciety of Mechanical Engineers, Vol. VI., page 716, and consisted of a condensing coil for the steam, situated in the bottom of a tank-calorimeter, very carefully made to prevent radiation- losses. The dimensions were 17 inches diameter by 32 inches deep, with a capacity of about 200 pounds of water. The Fig. 194. — Hoadley's Calorimeter. calorimeter was made of three concentric vessels of galvanized iron, the spaces being filled with hair-felt and eider-down. The condenser consisted of a drum through which passed a large number of half-inch copper tubes, the steam being on the outside, the water on the inside, of these tubes ; the agitator consisting of a propeller-wheel attached to an axis that could be rotated by turning the external crank K t effectu- ally stirring the water. The thermometer for measuring the temperature was inserted in the axis of the agitator at T. § 322,] THE AMOUNT OF MOISTURE IN STEAM. 409 In the hands of Mr. Hoadley the instrument gave accurate determinations. In practice the instrument was arranged as in Fig. 195; the calorimeter E was placed on the scales F, and supplied by cold water from the elevated barrel A. The temperature of the entering water was taken at C. Steam was admitted to the condensing-coil until the temperature of the condensing water reached, say, 1 io° F. The weights before and after k°) (sj- Fig. 195. — Hoadley's Calorimeter Arranged for Use. adding steam were taken by the scales F; the temperature ot the warm condensing water was taken by a thermometer, G t inserted in the axis of the agitator. The water-equivalent was determined as explained in Article 317, page 401, and the quality computed by equation (6), page 394. The rate of cooling was determined, and an equivalent amount added as a correction for any loss of heat by radiation. 322» The Kent Calorimeter. — This instrument differs from the Hoadley instrument principally in the arrangement of the condensing coil. This when filled with steam could be removed from the calorimeter, so as to enable the weight ot 4io EXPERIMEN TA L ENGINEERING. [§ 323- steam to be taken on a smaller and more delicate pair of scales than those required for the condensing water, thus giving more accurate determinations of the weight of the steam con- densed. 323. The Barrus Continuous Calorimeter. — This calo- rimeter is shown in Fig. 196 in section and in Fig. 197 in per- spective. It consists of a steam-pipe, a/, surrounded by a Condensed Steam Fig. 196.— Barrus Continuous Calorimeter. tub or bucket, O, into which cold water flows; the condensing water is received as it enters the bucket in a small brass tube, k, surrounding the pipe a, and is conveyed over and under baffle-plates, m, so as to be thoroughly mixed with the water in the vessel, and is finally discharged at c. Thermometers are placed at /and at g to take the temperature of the water as it § 3 2 3-] THE AMOUNT OF MOISTURE IN STEAM. 4 II enters and leaves, and finally the condensing water is caught from the overflow and weighed. The condensed steam falls below the calorimeter ; by means of the water-gauge glass at " Fig 197 — The Baruus Continuous and Superheating Calorimeters. it may be seen and kept at a constant height. The temperature of the condensed steam while it is still under pressure is shown by a thermometer at h. In order to use the calorimeter it is necessary to weigh the condensed steam ; this cannot be done without further cooling, as it would be converted into steam were the pressure removed. For this purpose it is passed through a coil of pipe immersed in a bucket filled with water, 412 EXPERIMENTAL ENGINEERING. [§ 324. shown at 5 in Fig. 197. The water used in the cooling bucket 5 has no effect on tne quality of the steam and is not con- sidered in the results ; it is allowed to waste, but the condensed steam is caught at W, Fig. 197, and weighed. The quality of steam is computed by omitting k in for- mula (6), page 394. Hence w r r ' w is the weight of condensed steam after correction for radia- tion-loss as explained in Article 324 ; w being equal to w' — u. 324. Directions for Using the Barrus Continuous Calo- rimeter. — Apparatus needed. — Thermometers ; pail for receiv- ing condensed steam ; tank and scales for the condensing water. Directions. — I. Fill the thermometer-cups with cylinder- oil. (Do not put thermometers in place until apparatus is working.) 2. Turn on condensing water and steam ; regulate the flow of condensing water so as to keep the bucket O nearly full, and the temperature of the discharge-water as much above tem- perature of the room as injection is below : this should be about no° F. Regulate the flow of condensed steam so as to keep the water in the glass e at a constant level. Turn water on to the cooling coil in the bucket S, and reduce the con- densed steam to a temperature of about 120 . 3. After the apparatus is working under uniform condi- tions, put the thermometers in the cups for temperature of injection and discharge water, and having previously weighed the vessels, at a given signal, note time and commence to catch the condensed steam and the condensing water. Con- tinue the run until about 360 or 40c pounds of condensing water has run into the receiving tank. Without disturbing the condition of the apparatus, commence simultaneously to waste the discharge from both pipes. Find the weights of § 324.] THE AMOUNT OF MOISTURE IN STEAM. 4 1 3, condensed steam (w') and condensing water (W) ; note time of ending run. 4. Make three more runs similar to the first. 5. To find the radiation-correction of the instrument: Empty the bucket of condensing water, and surround the condensing tube a with hair-felting ; make a run of the same length, and with steam of same pressure as in the previous runs. The weight of steam conden-sed will be the radiation- loss, which we call u, and is to be deducted from the weight of condensed steam obtained in the previous runs of the same length. Find the condensation per hour. 6. Work up quality of steam by the formula b^v- '.)-(' -'.)]-*- Make report as described for other calorimeters. Example. — The following is the result of a trial with the Barrus continuous calorimeter: Temperature of injection-water, /, = 37°. 5 Fahr. ; temperature of discharge-water, / 2 = 83°.8 Fahr. ; temperature of condensed steam, t % = 304.9 Fahr. ; steam-pressure by gauge, 72.4 lbs. ; temperature of entering steam, t = 31 7°. 9 ; length of test, 40 minutes ; weight of cool- ing water, W = 573.5 lbs. ; weight of condensed steam, w' = 29.89 lbs. ; radiation-loss u = 0.13 lb. Neglecting value of u, x = 573.5 (83-8 - 37.5) _ (3I7-9-3Q4-9) 29.89 891 891 19.21 X 46.3 — 13.0 876.4 ~ 8oTi = I9T - 98 ' 4 * x — 98.4 if not corrected for radiation-loss. If corrected, *= (^46.3-130)^891 = 98.9. 414 EXPERIMENTAL ENGINEERING. [§ 325. 325. Forms for Use with Condensing Calorimeters. MECHANICAL LABORATORY, SIBLEY COLLEGE, CORNELL UNIVERSITY. Priming Test with Condensing Calorimeter. Made 07. Tsst cf . , , . Kind of calorimeter 189.. Steam. N. Y. I. II. III. IV. V Duration of run , minutes Symbols. P V W-i- V Scale-readings, tare, lbs Tare and cold water, lbs Quantities : w w h ?2 h t W -7- w X I — X D Temperatures, deg. Fahr. : Condensing water, cold Condensing water, warm Steam at pressure P Degree of super-heat Correction due to displacement of water by hose lbs. Calorimeter-equivalent lbs. How found Temp, r^ cm deg. Fahr. Barometer-reading inches. W 1 Quality x = j — (/a — ti Degree of super-heat D = (x — i)r -5- 0.48. § 325-] THE AMOUNT OF MOISTURE IN STEAM. CALORIMETER TEST. Date No 415 No. of a u c u s Condensing Water. Condensed Water. Temperature of Condensing Water. h «j -v. 3 en 5 .... " " " Thermal units in water corresponding to absolute pressure of steam.. . .B.T.U. Heat acquired by condensing water " Heat given up by condensed steam in cooling to temperature of ther- mometer in same. , " Weight of water condensed by radiation lbs Heat given up by each pound of steam in condensing... B.T.U. Latent heat of one pound of steam at average absolute pressure " Per cent of • , Signed 416 EXPERIMENTAL ENGINEERING. [§ 326, STEAM TO BE TESTED"- 326. Barrus Superheating Calorimeters. — In the Barrus Superheating Calorimeter, Fig. 198, the steam-pipe leading from the main is bifurcated, one branch, E y passing over the flames of a large Bunsen burner, the other passing up- ward, and finally downward, when it is jacketed by the enlargement of the ■STEAM FOR SUPERHEATER DCIH temp first branch. The branches discharge separately, each through equal orifices, about one-eighth inch in diameter. This instrument is shown in Fig. 198 in elevation, and on the left-hand side of Fig, 197 in perspective. The steam in one branch is superheated at G\ that in its normal condition is received at H, and is discharged at N. The superheated steam forms a jacket from I to K outside the sample to be tested, and is discharged at the orifice M. The temperature of the jacket steam is taken at A and at B ; that of the normal steam is measured at C, as it is discharged ; it is found as it enters from its pressure taken at H, by reference to the steam-table. The theory of this calorimeter is as follows: —Barrus Super- heating Calorimeter. § 326.] THE AMOUNT OF MOISTURE IN STEAM. 417 1. An equal weight of steam flows through each branch of the pipe. 2. The steam, superheated by the gas-flame, is used as a jacket for the other branch, and parts with as much heat, ex- cept for radiation, as the other gains. 3. This amount may be measured provided the steam dis- charged from the central tube is superheated. To measure this gain or loss of heat, thermometers are placed to take the temperature of steam as it enters and leaves the jacket, and on the central pipe near the same places. Formula. — Let (1 — x) be the amount of water to be evap- orated ; in so doing it will take up from the jacket-steam r(i — x) heat-units. Let t be the normal temperature of the steam at the gauge pressure ; let T x be the temperature of the superheated jacket-steam at entering, and T 9 as it leaves ; let T 3 be the temperature of the superheated steam discharged from the sample pipe, and let radiation-loss in degrees F. be /. If the specific heat of steam be 0.48, since gain and loss of heat are equal, we have 0.48(7; - 7, - /) = r(i - x) + 0.48(7-3 - t). .-. i-* = o.48[r,- T,-/-(T 3 -l)-] + r; from which x may be found. To find /, the radiation-loss in degrees, shut off steam in the branch leading to the centre steam-pipe, and find reading of thermometers T x and 71, . After a run of same length as in test, take ■/= T x — T % . Directions for using Barrus Superheating Calorimeter. — Ap- paratus needed. — Three thermometers reading 400° F. each, and pressure-gauge, superheating lamps, etc. First. Calibrate instruments, and ascertain by a run of twenty minutes that equal amounts of steam are discharged from each orifice. This may be done by condensing the steam. Second. Put cylinder-oil in oil-cups ; attach gauge. 41 S EXPERIMENTAL ENGINEERING. [§ 328. Third. Put in working order ; after thermometer at end of sample-steam-pipe shows superheat, commence the run. Fourth. Take readings once in two minutes for twenty minutes. Fifth. Obtain radiation-loss / as explained. Sixth. Work up results as explained, and make report as in previous cases. 327. Form for Determination with Barrus Superheat- ing Calorimeter. No. BARRUS SUPERHEATING CALORIMETER. Date Time. Temp. Jacket-steam Entering. Temp. Jacket steam at Exit. Temp. Sample Steam at Exil. Steam- pressure by- Gauge. Barometer. Total Average . . Corrected. Duration of test min. Barometer in. ; lbs. per sq. in. Sample steam, gauge pressure lbs. per sq. in. " " absolute " lbs. per sq. in. '* " temperature at absolute pressure C; F. "outlet C; F. Superheated steam, temperature at inlet C. ; F. " * 4 " "outlet C; F. Latent heat of steam at absolute pressure B. T. U. Specific heat of superheated steam B. T. U, Correction for condensation " " radiation „ Per cent of moisture in steam 328. The Throttling Calorimeter. — This instrument was designed in 1888 by Prof. C. H. Peabody of Boston, and rep- § 328.] THE AMOUNT OF MOISTURE IN STEAM. 419 resents a greater advance than any previously made in practical calorimetry. The equations for its use and limitations of the same were given by Prof. Peabody in Vol. IX., Transactions Am. Society Mechanical Engineers. As designed originally, it consisted of a small vessel four inches in diameter by six to eight inches long, and connected to the steam-supply with a pipe Containing a valve, &, used to throttle the steam supplied the calorimeter. Fig. 199 shows the original form of the calorimeter, which is arranged so that any de- sired pressure less than that in the main steam-pipe can be maintained in the calorimeter A. The press- ure in the calorimeter is shown by a steam-gauge at g, and the tem- perature 'by a thermometer at D\ the main steam-pipe is provided with a drip at f, to drain the pipe before making calorimetric tests. In using the calorimeter, any desired pressure can be main- tained in the vessel A by regulating the opening of the ad- mission and exhaust valves. The effect of this operation will be to admit the heat due to high-pressure steam into a vessel filled with steam of lower pressure. The excess of heat is utilized firstly in evaporating moisture in the original steam ; secondly, if there is sufficient heat remaining, in raising the temperature in the vessel A above that due to its pressure, thus superheating the steam. Unless the steam in the chamber A is superheated, no deter- minations can be made with the instrument. The equation for its use is obtained as follows : the heat in one pound of high- pressure steam before reaching the calorimeter is expressed as in formula (2), Article 311, page 393, by xr -f- q. After reaching the calorimeter the heat is that due to the press- Fig. 199.— Peabody's Throttling Calorimeter. 420 EXPERIMENTAL ENGINEERING. [§ 32S. ure in the calorimeter added to that due to the superheat, or A, -|-o.48( T t — 7^). Since these quantities are equal, xr + g = \, + o.48(T l -T c ); from which x = lK-q + o.4&{T t - T c )1 + r 00 in which r equals latent heat, and q heat of liquid due to pressure in main pipe as given in the steam-table. X c = total heat in one pound of dry steam at calorimeter pressure ; T x = reading of thermometer in calorimeter, and T c = normal temperature of steam in calorimeter due to calo- rimeter pressure. Care must be taken that both X c and q are given in the same units. Example, — Suppose that the gauge pressure on the main steam-pipe is 80 pounds, that on the calorimeter 8 pounds atmospheric pressure 14 pounds, as reduced from the barom- eter-reading, and that the thermometer in the calorimeter reads 274°.2 F. Required the quality of the steam. In this case we obtain the following quantities from the steam-table : Entering steam. In calorimeter. . p Absolute Pressure. T Temperature Deg. F. q Heat of Liquid, B. T. U. X Total Heat, B. T. U. 94 22 323-1 233-1 293.2 202.0 "53-o r Latent Heat. B. T. U. 887.3 951.O From which * = [1 153 - 293-2 + 0.48(274.2 - 233.1)] -r- 887.3 ; ^ = 99.1. Per cent of moisture, 100 — x — 0.9. § 3 2 9-J THE AMOUNT OF MOISTURE IN STEAM. 42 L 329. Recent Forms of Throttling Calorimeters These instruments differ from Peabody's principally in size and form. They all work in the same general manner and detailed descriptions are hardly necessary. Fig. 900.— Heisler's Throttling Calorimeter. Heisler's throttling calorimeter is shown in Fig. 200, with attached manometer for measuring the pressure in the calorimeter chamber, it is of small size and keeps the current of steam intimately in contact with the thermometer. Carpenter's throttling calorimeter, shown in Fig. 201, is pro- vided with an attached nozzle for spraying the sample of steam over the themometer-bulb. The instrument may be used with or without a thermometer-cup, but in every case the thermometer must be deeply immersed in the steam. This instrument is made by SchafTer and Budenberg, New York. 422 EXPERIMENTAL ENGINEERING, [§330 TO MANOMETTB Fig. 201.— Carpenter's Calorimeter. Throttling Calorimeter of Pipe-fittings. — A very sat- isfactory calorimeter can be made of pipe-fittings, as shown : B Fig. 202.— Throttling Calorimeter of Pipe-fittings. in Fig. 202. Connection is made to the main steam-pipe, as explained already elsewhere. The calorimeter is made THE AMOUNT OF MOISTURE IN STEAM. 423 §330 of f inch fittings arranged as shown ; the steam-pipe W is of |-inch pipe, and the throttling orifice is made by screwing on a cap, in which is drilled a hole -J or T V inch in diameter. A thermometer-cup, Fig. 190, page 400, is screwed into the top, and an air-cock inserted opposite the supply of steam. A manometer, B, for measuring the pressure is attached by a piece of rubber tubing as shown. The exhaust steam is dis= charged at E. The back-pressure on the calorimeter can be increased any desired amount by a valve on the exhaust-pipe ; when no valve is used the pressure is so nearly atmospheric that a manometer is seldom required. Method of finding Normal Temperature in the Calor- imeter. — It is essential to know the normal temperature within the calorimeter; this will vary with the pressure on the calorimeter, which pressure is equal to the barometer-reading plus the manometer-reading. The following table gives the normal temperature corre- TABLE OF BOILING-POINTS. Normal Total Pressure Normal Total Pressure Temperature. on Calorimeter. Temperature. on Calorimeter. Degrees F. Inches Hg. Degrees F. Inches Hg. 209.5 28.466 • 7 •744 .6 •523 .8 .803 •7 .580 •9 .863 .8 .037 212.0 .922 •9 .095 .1 .982 210.0 .752 .2 30.041 .1 .8lO •3 .101 .2 .867 • 4 .I6l •3 .925 •5 .221 •4 •983 .6 .281 •5 29.O4I •7 •341 .6 .099 .8 .401 •7 .157 •9 .462 .8 .215 213.0 .522 , -9 .274 .8 31.004 211. •332 214.0 .107 .1 •391 215.0 .692 .2 •449 216.0 32.277 •3 .508 217.0 .862 •4 .567 218.0 33-447 •5 ' .626 219.0 34.032 .6 .685 220.0 .617 Difference i° F =- 0.585 inch. Difference 1 inch = l .709. 424 EXPERIMENTAL ENGINEERING. [§332 sponding to various absolute pressures nearly atmospheric, ex- pressed in inches of mercury: In the use of the instrument the total pressure in the calorimeter is to be taken as the sum of the barometer-reading and the attached manometer. The degree of superheat of the steam in the calorimeter is the difference between the tempera- ture as shown by the pressure and that shown by the inserted thermometer. Graphical Solution for Throttling-Calorimeter Deter- minations. — In the practical use of this instrument it is customary to exhaust at atmospheric pressure, so that the normal temperature in the calorimeter is the boiling-point at atmospheric pressure, and X c is 1 146.6; in which case formula (11) becomes 1 146.6 + 0.48(7; — 212) ■— q x = ' r 1 146.6 — q , 0.48(7, — 212) If in this form we suppose the steam-pressure constant, and the degree of superheat and quality of steam alone to vary, r and q will both be constant, and we shall have the equation 1 146.6 — q . of a right line, in which is the distance above the origin that the line cuts the axis of ordinates, and 0.48 -=- r is the tangent of the angle that the line makes with the axis of abscissae. Drawing lines corresponding to the different gauge or absolute pressures, a chart may be formed from which the values of x may be obtained without calculation. Using degrees of superheat in the calorimeter as abscissae and absolute steam-pressure as ordinates, and drawing lines corresponding to various percentages of moisture, we have a diagram shown in Fig. 203, from which the results of observa- tions made with the throttling calorimeter may be taken at once without further calculation. 'fti -M _ fl §'- »l: ^i## :; #t|ttf H E iP"-i "Wffr : ^TFT 1 1 j [ |/| 1 1 j j - f i *■+- 1 TTT f ! Tt/l 1 j 1 7TT1 1 1 1 ; Hi!' 1/T -Ue : a | j 1 1 cgE "Til" r" / - f-4444 m 11 Ml "1 nti" lljlll -||| -H-hiFTp /""Tntl 7TT |JJB:S| i 1 i Fi il i J--rT^- jtrtTttp] ±Jl||Hx): | [ r j , l 11 y ■*jj §1 §g 5e T^Trr \y'\ 9J-H-H- ill si 1 -\v_: Ififfi IT 1/ -U-H- :: +141°^ - - Lj 1 h 1 ^ I/Im rfiT WJ\ j 1 j 1 = 4r : 1 ' ! TKjTTj I i'l | i If 1 V\ 1 j H-^ MJ-JJ+-/-- 1 1T IT !"'" ' /ill ' / I | i 4+ H -j+r -- TTTTTM 1 ' /[ lh { ' IpM 111 !>ffi I'll _LV/ 1 1 1 1 1 /WW TiliU'r+^ij i p i : P-LLj- jc -i-j-t- — i *1 j 1 j ' j -fffi 4ffl : i ^~T- S3 1 I ||Jm 4M II ttw- 11 j \y ffrflf wfcpff jljlljl 1 1 i/i i "tttttt"""^! iM' :: W 1 riir ■tA in- = R" ^ -j-j f- -Fl 4-T- -1 Wr ^ ffl^ frftt 4 S Ttft JT " T ^ Tl 175^ TNT "I 7 ITT iffi'TII TRT 1:1 llll ffiiiiiiBiB :|jl|J|; M ;: :T:H:ROf^L±N:G: iC:K.£f r "m — n~tj lillllllil/; 11 !'! ffff Irj j I; ; " t : "| 1 i l»r T — rril | ' 1 ' : 1 ] 1 1 i JlRtMEfTERt: Wr j 1 1 1 1 1 | ' 1 "--- + -J-4--""- |;;;:;S:ffi ffl ....J- tH-H- ~S±Ea d^-rIe --T-I-+H -'it Eh. E-S4G- 4w- ©WheWc:: r-h e"act- 1 n- -t-4 mm I'RE'SStlF'-'- +^ Sl:|:±:::::|:::::::: H-EfG-A-bO R 1- \fl-E-T E-R Fig. 203.— Diagram giving Results from Throttling Calorimeter without Computation. 426 EXPERIMENTAL ENGINEERING. [§333 Use of the Diagram. — To find the percentage of moisture in the steam from the diagram, pass in a horizontal direction along the base-line until you arrive at the number corresponding to the degree of superheat in the calorimeter; then pass in a ver- tical direction until you reach the required absolute pressure of steam. The position with reference to the curved lines shows at once the percentage of moisture, and can be read easily to one tenth of one per cent. Thus, for example, sup. pose that we have the following readings : Barometer, 29.8 inches; attached manometer, 1.5 inches — making a total press- ure in the calorimeter of 31.3 inches, corresponding to a tem- perature of 2I4°.27 Fahr. Steam-gauge, 80 pounds; absolute pressure, 94.7 pounds; thermometer-reading in calorimeter, 254 Fahr. From which the degree of superheat is found to be 254 -2i4°.27=r39 .73. Following the directions as given, the percentage of moist- ure is seen from the diagram to be 1.66 per cent. The quality would be 1.00 — 1.66 = 98.34 per cent. While the diagram is especially computed for determinations when the pressure in the calorimeter is atmospheric or but slightly above, it will be found to give quite accurate results when the calorimeter is under pressure, by considering that the ordinates represent the difference of pressures on the steam and in the calorimeter. Thus, in the example, Article 328, page 390, the steam-pressure was 80 pounds, calorimeter-pressure 8 pounds ; degree of super- heat 274.2 — 233.I = 41. 1 ; resulting quality by calculation 99.1, indicating 0.9 per cent of moisture. Using difference of press- ure 80 — 8 = 72 as ordinate, and 41. 1 as abscissa, we find from the chart that the percentage of moisture is 0.92 ; from which x — 99.08. The results for the throttling calorimeter may be com- puted from the temperatures instead of the pressure of the original sample of steam as compared with the temperature in the calorimeter when at atmospheric pressure. Carpenter's calorimeter, Fig. 201, is especially adapted for such determina- tions, since it provides an easy method of calibrating the thermometer when in position. This is especially important since thermometers will ordinarily read two or three degrees low when there is a portion of the stem exposed. § 333-] THE AMOUNT OF MOISTURE IN STEAM. 427 For using the instrument in this manner, the boiling- point in the calorimeter is first determined by opening both the supply and discharge valves C and D and showering the instrument and connections with water until the steam in the calorimeter is' moist, in which case the reading of the ther- mometer will be that due to the boiling-point. Second, close the discharge-valve with the supply- valve open and obtain full boiler pressure in the calorimeter; when the thermometer has become stationary note the temperature: this will be the boiling-temperature for the given pressure as read by the given thermometer. Third, open the discharge-valve of the instrument, and after the mercury has become stationary note the reading of the thermometer. Deduct from this latter reading the reading first taken and we shall have the degree of superheat in the calorimeter. From these two numbers the quality may be computed by reference to steam tables as explained, but it is more easily done by reference to the following diagram, in which the temperature of the steam is the ordinate and is that given when the discharge-valve is closed, and the temperature in the calorimeter is the abscissa, on the supposition that the boiling-temperature at calorimeter pressure is 212 degrees. If the boiling-temperature is more or less than this amount, a corresponding correction must be made to the result. As an illustration, suppose that the boiling-temperature in the calorimeter is 2 1 1 or one degree low, that the actual temperature in the calorimeter when both valves are open is 265, and that the temperature of the steam obtained with the discharge-valve closed is 320. To find the quality we look in the line over 266 and opposite 330, and read the results by the diagonal lines, the quality as shown on the diagram being 98.8 (see Fig. 204). Limits of the Throttling Calorimeter. — To deter- mine the amount of moisture that can be evaporated by throttling, make T x = T c in formula (11) ; then x = (A,— -q) ~-r (12) The amount of moisture that can be determined by the TEMPERATURE IN CALORIMETER 220 230 £40 250 260 270 £80 290 300 310 320 330 340 •fer ~'^y ! - -; i=v:-|.:^i i.vfeoo^-276=^soEt' r m-^r= w=\^m - TEMPERATURE IN CALORIMETER Fig. 204.— Diagram for Computing Results with Throttling Calorimeter. §3551 THE AMOUNT OF MOISTURE IN STEAM. 429 throttling calorimeter in expanding from the given pressure to atmospheric, as computed by substituting in formula (12), is as follows : LIMITS OF THE THROTTLING CALORIMETER. Pressure, pounds per square in. Maximum per cent of prim- ing. Quality of the steam, per cent. Absolute. Gauge. 300 250 200 175 I50 125 100 75 50 285.3 235-3 185.3 160.3 135.3 no. 3 85.3 . 60.3 35-3 07. 7 7-0 6.1 5.3 5.2 4.6 4.0 3-2 2-3 9 2 -3 93-o 93-9 94.2 94.8 95-4 96.0 96.8 97-7 By reducing the pressure below the atmosphere, the limits of the instrument may be somewhat increased. Directions for Use of Throttling Calorimeter. — Apparatus. — Steam-thermometer; pressure-gauge; manometer for measuring pressure in calorimeter in inches of mercury. 1. Attach the calorimeter to a perforated pipe extending well into the main steam-pipe to secure a fair sample of steam. Calibrate all the apparatus. 2. Fill thermometer-cup with cylinder-oil, having first care- fully removed any moisture from the cup. Place thermometer in the cup, and after it has reached its maximum commence to take observations. 3. Read steam-pressure, attached manometer, and tempera- ture at frequent intervals. 4. Compute the quality of the steam for each observation. Forms for Throttling-Calorimeter Determinations. Priming tests of. Made by 189. . . . at ., N. Y., with Throttling Calorimeter. Steam used during run Ibs^ Barometer-reading , . .inches. 430 EXPERIMENTAL ENGINEERING, [§336 1 2 3 4 5 6 7 8 9 3 v> 1 m t x tc P o.&it-t') Kc r Kc — q 1 — X X D Time 1 Steam-pressure, main 00 Manometer reading calo- -f Observed temperature Heat at steam-pressure P. Normal temperature in < 11 Absolute pressure in a 1 % s. Total heat, pressure m... Latent heat for pressure P v- 3 uality egrees s Ac— y + o.48(/,— tc) Per cent of entrained water a a AVERAGE RESULTS OF CALORIMETER TEST. Date Duration of test. > min. Barometer in. ; . . lbs. per sq. in. Boiler-pressure by gauge " " absolute " " Calorimeter-pressure by gauge " •' absolute " " Calorimeter-temperature *. C; F. Per cent of moisture in steam Signed 336. The Separating- Calorimeter. — The separating calorimeter is an instrument which removes all water from the sample of steam by some process of mechanical separa- tion, and provides a method of determining the amount of water so removed and also the weight of the sample. This process is dependent upon the greater density of water as compared with that of steam. Thus, for instance, steam at 100 lbs. absolute pressure is more than 260 times lighter than water at the same temperature, and if the sample of steam when moving with considerable velocity can be made to change its direction of motion abruptly, the water will be deposited by the action of inertia. § 33 6 -] THE AMOUNT OF MOISTURE IN STEAM. 431 The accuracy of this instrument depends on the possibility of completely separating the water from the steam by mechanical methods. To determine this a series of tests were conducted for the author by Messrs. Brill and Meeker with steam of varying degrees of quality. The range in moisture was from 33 to 1 per cent, yet in every case the throttling calorimeter attached to the exhaust gave dry steam within limits of error of observation. The following were the results of this examination. SEPARATING CALORIMETER. Examination of Exhaust Observations on Entering Steam. Steam from Calorimeter by Throttling- Calorimeter. T P w w X t X No. of Obser- vations Calori- meter. Duration Run, Gauge Pressure, Pounds Separated Water in Run. Pounds Condensed Steam in Run. Quality Steam, Temp, in Calori- Quality Steam in minutes. pounds. per cent. meter. Exhaust. i\ 25 81.5 I-I5 4.45 79.46 281 99-95 6 25 78.2 O.15 5.20 97.2 281.3 IOO.OO 6 i\ 25 80.8 0.525 4.25 89.005 286.5 IOO.OO 6 25 79-5 O.150 4-75 96.94 281.8 99-95 6 i\ 25 78.5 O.300 5.000 94-34 2S2.8 100.00 6 25 77.6 .150 5-45 97-32 282.3 100.00 6 i\ 24 79-5 1.8 4-55 71.65 280.I 99.94 6 24 78.5 1.4 4.90 77-77 279-5 99.9 6 i\ 20 83.5 1. 15 4.1 77.67 286.5 100.00 5 20 81.6 1.70 4-75 73-64 282.7 99.98 5 20 74.8 0.65 3-95 85.87 . 283.7 100.05 5 20 82.0 0.85 3-95 82.29 286.8 100.05 5 20 • 82.6 o.35 4-15 92.22 285.6 100. 5 20 81.5 0.20 3-95 95-15 285.2 100.05 5 1! 20 81.4 2.20 4 • 325 66.28 283.1 100. 5 20 80.3 0.30 4-55 93.81 282.8 100. 5 i\ 20 82.0 0.20 4-65 95-8 282.8 99.98 5 20 81. 1 0.20 4.40 95-7 284.0 100. 5 Averaj r e of 18 trials, invr )lving 98 observati oris 99.998 This experiment indicates that the complete separation of moisture from steam is possible by mechanial means. Any radiation in the instrument will increase tne apparent moisture in the steam, and must also receive consideration, especially if it be sufficient in amount to sensibly affect the results. 432 EXPERIMEN TA L ENGINE ERING. [§ 337- 337. Description of Various Forms. — The earliest form of separating calorimeter used in experimental work, in the Sibley College laboratory, consisted of a vessel with an interior G n Fig. 205. — The Separator Calorimeter. oozzle, extending below the outlet and so arranged that the eurrent of steam would abruptly change direction and deposit the moisture into the bottom portion of the vessel. The dry steam was allowed to escape near the top. Fig. 205 shows § 337-] THE AMOUNT OF MOISTURE IN STEAM. 433 a form, used in the early experiments, which was constructed of pipe-fittings. This instrument, even when covered with hair felt, gave off sufficient amount of heat to sensibly affect the results, and a correction for radiation was essential. The amount of radia- tion was determined by using two instruments of the same kind and size, arranged so that the discharge from one was the supply to the other. The second instrument receives perfectly dry steam from the first, the water deposited is due to the radiation loss, which, being the same in both instruments, provides a method of determining its amount. In figuring the percentage of moisture, the amount thrown down by radiation in the second instrument is to be deducted from the total amount caught in the first calorimeter. In later forms of the instrument the amount of radiating surface has been made so small as to render the correction for radiation, in all ordinary cases, negligible, by constructing the instrument in such a manner as to be jacketed by steam of the same pressure and temperature as in the sample. The form of this instrument is shown in Fig. 207, in which the steam is supplied through the pipe D, the moisture being received in the interior vessel E, the discharge steam passing out of the chamber E at the top, into the jacket F, and thence out of the instrument through a small opening at L; the opening at L being made sufficiently small to maintain the pressure in the jacket the same as that in the sample. The discharged steam is then condensed in a can, J. This can is provided with a small top in which is set a gauge-glass with attached scale, graduated so as to read to pounds and tenths of pounds of water. A gauge-glass N attached to the calorimeter is provided with index, inn, arranged to move over a graduated scale, S, which shows the weight of water in the vessel E in pounds and hundredths. In using this instrument the condensing can J is filled with water to the zero-point of the scale. The amount of condensed steam is 434 EXPERIMENTAL ENGINEERING. [§ 337- read on the scale of the can, J\ the amount of water in the sample of steam for the same time is read on the scale 5. The percentage of moisture, in case radiation is neglected, is the quotient of the reading of the calorimeter scale 5 divided by the sum of the readings on both scales. The latest form of the instrument is shown complete with all accessories in Fig. 206, and is a great improvement over the earlier forms in points of portability and convenience. It differs principally from the form last described in the con- struction of the steam-separating device, which has been increased in efficiency and in the substitution of a gauge attached to the outer jacket, which registers the total flow of steam through the instrument in ten minutes of time. The flow of steam through a given orifice is proportional to the absolute steam-pressure, by Napier's law* which has been proved correct for pressures above 25 pounds absolute; and hence it is possible to calibrate by trial a pressure-gauge in such a manner that the graduations will show the flow of steam in a given time. The only error which is produced in this graduation is that due to changes in barometric pressure, which is never sufficient to sensibly affect the results obtained in the use of the instrument. Should any doubt arise, the accuracy of the readings of the gauge are easily verified by condensing the discharged steam for a given period of time. This should be done occasionally to test the gaduations. The instrument may be described as follows: It consists of two vessels, one being interior to the other; the outer vessel surrounds the interior one so as to leave a space which answers for a steam-jacket. The interior vessel is provided with a water-gauge glass 10 and a graduated scale 12. The sample of steam whose quality is to be determined is supplied through the pipe 6 into the upper portion of the interior vessel. The water in the steam is thrown downward into * See Transactions American Society Mechanical Engineers, Vol. XL, 1887, paper by Prof. C. H. Peabody. § 337-] THE AMOUNT OF MOISTURE IN STEAM. 435 the cup 14, together with more or less of the steam; the course of the steam and water is then changed through an angle of nearly 180 degrees, which causes the entire amount of water to be thrown outward through the meshes in the cup into the space 3, which con- stitutes the inner chamber. The cup serves to prevent the current of steam from taking up any moisture which has already been thrown out by the force of inertia. The meshes or fins project upward into the inside of the cup, so that any water intercepted will drip into the chamber 3. The steam then passes upward, and enters the top of the out- side chamber. It is discharged from the bottom of the outside chamber through an orifice 8 of known area, which is much smaller than any section of the passages through the calorimeter, so that the steam in the outer chamber suffers no sensible reduction in pressure. The pressure in the outer chamber, being the same as in the interior, has the same temperature, and consequently no loss by radia- tion can take place from the interior chamber except that which takes place from the exposed surface of the gauge- glass and fittings. The pressure in the outer chamber, and also the flow of steam in a given time, is shown by suitably engraved scales on the attached gauge. The scale for show- ing the flow of steam is the outer one on the gauge, and is graduated by trial, and gives the discharge of steam in pounds in ten minutes of time. The readings on the scale 12 show the weight of water in the interior vessel 3, and should be taken at the beginning and end of the interval. The total size of the instrument is about 12 X 2J inches, and its weight about 8 pounds. Fig. 206. — Improved Sepa- rating Calorimeter. 436 EXPERIMENTAL ENGINEERING. [§338* FlG. 207. — Separating Calorimeter with Condensing Can. 338. Formula for Use of the Separating Calorimeter, — Let w equal the weight of dry steam discharged at the exhaust-orifice, W the water drawn from the separator, R the water thrown down during the run by radiation. Then the quality of the steam is w + R x = W+w' the amount of moisture w I — ■ X R W + w § 339-] THE AMOUNT OF MOISTURE IN STEAM. 437 To reduce the radiation loss as much as possible the in- strument should be thoroughly covered with hair felt to the thickness of 1/2 to 3/4 inch. In this case the total loss by radiation will be about 0.4 B. T. U.* per square foot per hour for each degree difference of temperature between the steam and the surrounding air. This will amount to about 220 B. T. U. per square foot per hour, or about 1/5 of a pound of steam under usual conditions of pressure and temperature. In the instrument described the actual exposed surface amounts to about 1/12 sq. ft., so that the condensation loss may be considered as from 1/50 to 1/60 of a pound of steam per hour. The total flow of steam through the instrument usually varies from 40 to 60 lbs. of steam per hour, so that if the instrument is covered, the radiation loss would be less than 1/20 of one per cent. If the instrument be not covered, the loss would be about five times this amount, or under usual conditions about 1/5 of one per cent. The radiation loss can in every case be determined by using steam of known quality as determined by the throttling calorimeter, or better still by arranging two separating calori- meters of exactly the same size in series so that the steam exhausted from the first is used as a supply to the second in a manner already explained. The Limits of the Instrument. — The instrument will give correct determinations with any amount of moisture that the sample of steam may contain. With steam containing a very small amount of moisture, the radiation loss will have more effect than with steam containing a great amount. When the fact is considered, however, that a sample of steam cannot probably be obtained but what differs more than 1/2 per cent from the average, the futility of making this correction becomes at once apparent. 339. General Method of Using. — The general method of using is given only for the latest instrument described, which *See numerous experiments, Carpenter's Heating and Ventilation > 3 a min. lbs. P lbs. •w lbs. W lbs. JV-\-w lbs. R lbs. 1 -X per ct. X per ct. I 2 3 4 5 6 7 8 9 10 440 EXPERIMENTAL ENGINEERING. [§ 34 1. Diameter of orifice in. Area of orifice sq. in. Symbol A. Barometer-reading in. Formula of instrument, i — x — {W — R) + ( W + w). Napier's Rule, Flow of Steam, pounds per second = ^ PA. Method of determining R , Results Method of determining W 341. The Chemical Calorimeter. — This instrument de- pends on the fact that certain soluble salts will not be absorbed by dry steam, but will be carried over by water, so that if the salt appears in the steam its presence indicates water. Various salts have been used, but common salt, chloride of sodium, gives as good results as any. The proportion that the salt in a given weight of con- densed steam bears to that in a given weight of water drawn from the boiler, is the percentage of moisture in the steam. The method of analysis is a volumetric one, and is as follows : Add three or four ounces of common salt to the water in the boiler ; after it is dissolved, draw from the boiler a small amount of water and condense an equal weight of steam, which are to be kept in separate vessels. Add to each of them a few drops of neutral chromate of potash, but in each case an equal quantity, which amount may be measured by a pipette ; the same amount should also be added to a vessel containing an equal weight of distilled water, in order to obtain a standard or zero-point foi the scale used in the analysis. By means of a graduated pipette a triturated solution of nitrate of silver is permitted to flow, a single drop at a time, into each of the three solutions. The effect is to cause the formation of the chloride of silver, and until that formation completely takes place the resulting liquid will be whitish or milky; but because of the presence of the bichromate, the in- stant the chloride has all been precipitated the liquid turns red. The amount of nitrate of silver required is measured by the graduated pipette, and gives the information regarding the salt present. § 34 2 -] THE AMOUNT OF MOISTURE IN STEAM. 44I The detailed directions for the test are as follows : Take in each case 100 cubic centimeters of liquid contain- ing a few drops of neutral chromate of potassium, and drop from a triturated solution holding 10.8 grams of silver to the liter ; the following data were obtained in a test : AMOUNT OF NITRATE OF SILVER REQUIRED TO TURN 100 c. c. RED. of Condensed steam .... Water from the boiler Distilled water First Trial. O.I c. c. 13.6 c. c. 0.05 c. c. Second Trial. 0.05 c. c. 14.0 c. c. 0.05 c. c. Third Trial. O.I c. c. 13.35 C. C. 0.05 c. c. Letting the results with these three samples be denoted by a, b, and c respectively, and the amount of moisture by 1 — x, we have x = b-c This gives the following results : First Trial. Second Trial. Third Trial. Amount moisture 0.1 — 0.05 0.05 — 0.05 = 14.0 — 0.05 0.1 — 0.05 13.6 - .05 i3'35 -0.D5 Average = 0.0025. This method is evidently applicable only in determining the amount of moisture in the steam as it leaves the boiler, and will give no information regarding the additional moisture that may be added to the steam by condensation. Instead of common salt, sulphate of soda is sometimes used, and the percentage of moisture determined by the percentage of sulphuric acid present in the steam as compared with that in water from the boiler. 342. Comparative Value of Calorimeters. — These instru- ments, arranged in order of accuracy, are no doubt as follows: 442 EXPERIMENTAL ENGINEERING. [§ 342. throttling ; separating ; Barrus superheating ; Hoadley ; con- tinuous condensing ; chemical ; and lastly the barrel. The ease with which the throttling and separating instru- ments can be used, their small bulk, and great accuracy, render them of chief practical importance. The throttling calorimeter can be used only for steam with a small amount of moisture, as explained in Article 333 ; but the separating instrument is not limited by the amount of moisture entrained in the steam. It is not, however, as well adapted for superheated steam, nor can the results be deter- mined as quickly as with the throttling instrument ; when carefully handled the accuracy is, however, substantially the same. CHAPTER XIV. DETERMINATION OF THE HEATING VALUE OF FUELS— FLUE-GAS ANALYSIS. 343. Combustion, — Combustion or burning is a rapid chemical combination. The only kind of combustion which is used to produce heat for engineering purposes is the combina- tion of fuel of different kinds with oxygen. In the ordinary sense the word combustible implies a capacity of combining rapidly with oxygen so as to produce heat. The chief elemen- tary constituents of ordinary fuel are carbon and hydrogen. Sulphur is another combustible constituent of ordinary fuel, but its quantity and its heat-producing power are so small that it is of no appreciable value. The chemical elements are those which have not been de- composed ; these unite with each other in various definite proportions, which may be represented by certain numbers termed chemical equivalents or atomic weights. These for gaseous bodies are very nearly proportional to their densities at the same pressure and temperature. The atomic weight of a chemical compound equals the sum of the atomic weights of all the elements entering into the com- bination. Air is not a chemical compound, but a mechanical mixture of nitrogen and oxygen. The following table gives the properties of the principal elementary and compound substances that enter into the com- position of ordinary fuels : 444 EXPERIMENTAL ENGINEERING. [§ 344- Substance. Oxygen Nitrogen Hydrogen Carbon Phosphorus Sulphur Silicon Air...., Water Ammonia Carbonic oxide Carbonic acid Olefiant gas Marsh gas Sulphurous acid Sulphuretted hydrogen Bisulphuret of carbon. Symbol. O N H C P S Si 77N 4- 23O H 2 NH 3 CO co 2 CH 2 CH 4 so 2 SH 2 S 2 C Chemical Equivalent by Weight. 16 M I 12 31 32 14 IOO 18 17 28 44 14 16 64 34 76 Chemical Equivalent by Volume. IOO 2 2 2 2 2 2 2 2 2 Properties of Elements by Volume. 79N + 2lO H + O H + N O + o 2 + H 2 + H 4 + 3 + H 2 + S 2 344. Calorific Power or Heat of Combustion. — The calorific value of a fuel is expressed in British thermal units or in calories, according as Fahrenheit or Centigrade therm o- metric scales are used. The calorific value may be deter- mined by direct experiment, or it may be computed from a chemical analysis as follows : The carbon is credited with its full heating power, due to its complete oxidation as determined by a calorimeter ex- periment. The hydrogen is credited with its full heating power, after deducting sufficient to form water with the oxygen present in the compound ; since when hydrogen and oxygen exist in a compound in the proper proportion to form water, the combination of these constituents has no effect on the total heat of combustion. The calorimetric value, determined experimentally, of one pound of hydrogen is 62,032 B. T. U. ; that of one pound of carbon, 14,500 B. T. U. Hence the combustion of one pound of hydrogen is equivalent to that of 4.28 pounds of carbon. A formula for the total heat, h, of combustion in B. T. U. § 344-] THE HEATING VALUE OF FUELS. 445 for each pound of the compound containing hydrogen and carbon would be ^=i 4 ,5oo[c + 4 .28(h --)].. . . , (i) For theoretical evaporative power, in pounds of water from and at 212 F., £ = ^=H.6[C + 4. 2 8(H -§)].. . , ( 2 ) The number of pounds of air required to supply the oxygen necessary for the combustion of one pound of fuel to C0 2 can be computed from the formula ^ I2 [c + 3 (h-1t)] ; . • ,3) and the corresponding volume in cubic feet can be found by mul- tiplying by the specific volume of one pound at JO degrees Fr. In which case the volume in cubic feet is «=i 49 [c + 3(h-°)] (4) In the above formulae, C, H, and O represent the number of pounds respectively of carbon, hydrogen, and oxygen in the product of combustion. When in the combustion of hydro-carbon fuels in an ordi- nary furnace hydrogen is consumed, the water formed passes off in the state of vapor, hence the latent heat of evaporation is not available. One pound of hydrogen burns to 9 pounds of water, the latent heat of which at 21 2° is 966 units; hence we must deduct 966 X 9 = 8694 units from the tabular value 44^ EXPERIMENTAL ENGINEERING. [§ 345- of the heat due to the combustion of hydrogen. This leaves 53,338 units available. Therefore the actual value in terms of carbon is H = 3.67C, instead of 4.28C as stated in (1), and the heat of combustion actually available is -&=i 4 ,5oo[c + 3.67(h--°)] (5) The following table gives the heat of combustion of the principal combustible substances : TOTAL HEAT OF COMBUSTION WITH OXYGEN. Substance. Hydrogen gas Carbon burned to CO Carbon burned to CO2. Olefiant gas. . , Liquid hydro-carbon, Sulphur to S0 2 Silicon to Si0 2 Phosphorus to P 2 5 Marsh gas, C 2 H 4 Crude petroleum Oil of turpentine Wax Ether .... Tallow Alcohol . . Methyl alcohol (wood-spirit). Bisulphide of carbon, CS 2 . . . Carbonic oxide u O « •-Dh p <5 .n u e •+-. 1) o o &U "■a S ■a u 1- c u efl 3 '5^ £ 36 6 12 15-43 4-5 10.2 . 6-5 16.2 15-0 5-7 6 CQ* Eg -Oh 62,032 4,400 14,450 21,344 19,000 21,700 3,740 14,000 10,250 26,400 18,600 19,200 18,800 16, ion 16,000 12,700 9,200 5,750 IO, IOO U U " O o u 2 62.6 4-50 14.67 22.1 20 ) 22 5 ) 4.09 14.24 10.45 26.68 18.53 19-73 19.04 16.41 16.37 13.06 9-65 6.18 10.4 Product of Combustion. H 2 CO co 2 C0 2 and H 2 S0 2 Si0 2 p 2 o 5 CO a and H a O <■ n «( {( CO a and S0 2 CO a 345. Determination of the Heating Value by the Oxygen required. — It was observed by Welter* that those * Chemical Technology, Vol. I., p. 336 : Graves and Thorp. §345-] THE HEATING VALUE OF FUELS. 447 constituents of a compound which require an equal amount of oxygen for combustion evolve also equal quantities of heat ; from which he concluded that since the oxygen required for the combustion of a body is in the same relation as the quan- tity of heat evolved, it might fairly be made the measure of the heating power. When, therefore, oxygen is consumed by the burning of carbon, wood, hydrogen, etc., the heat which is evolved must increase with the quantity that is consumed ; or the same amount of heat is generated by a certain given weight of oxygen, whether that quantity be employed in con- verting carbon into carbonic acid, or hydrogen into water. The oxygen required is 2§ for one part of carbon ; 8 for one part of hydrogen. One part by weight of carbon will raise the temperature of 80.5 parts of water from freezing to boiling. One part by weight of hydrogen will raise 234 parts of water from freezing to boiling. One part by weight of oxygen in burning carbon will heat 80.5 — 5- = 29. 1 parts of water. One part by weight of oxygen in burning hydrogen will heat -2-|A — 29.3 parts of water from the freezing to the boiling point. In round numbers, therefore, the heating effect of oxygen may be assumed as sufficient to raise 29.2 parts of water from the freezing to the boiling point. This is equivalent to 2920 Centigrade heat-units, or to 5230 B. T. U. Calorific Value. — The calorific value of the fuel would therefore be the product of this number by the number of parts of oxygen required. Thus let a equal the number of parts of oxygen required for each combustible ; then the heat produced by the combustion is h = 2920a: in Centigrade units ; h = 5230a in B. T. U. Thus, for example, in the combustion of carbon to CO,, 448 EXPERIMENTAL ENGINEERING. |_§ 346, 2| parts by weight of oxygen are required for ea w *i one of carbon ; hence for this case a = 2§ , and h— 5230 X 2| = 14,100. In the combustion of hydrogen to water 8 parts by weight of oxygen are required, and in this case a = 8 ; hence h = 5230 X 8 = 41,840. This is about two thirds of the actual value of the calorific power of hydrogen, but does not differ much from the heat available in ordinary combustion. In case of a compound body, let a fuel contain a, b, c, and d parts by weight of different combustible ingredients ; and let «, a x , a 9 , a z be the parts by weight of oxygen required by each. Then h = 2g2o(aa 4- ba x -f- ca 2 -f- da 3 ) in Centigrade units ; . = $2$o{aa -f" & a i + ca i + d a *) m Fahrenheit units. 346. Temperature produced by Combustion. — In the determination of the calorific value of a fuel two principal factors are involved, namely, the calorific power, or the total amount of heat to be obtained from the perfect combustion of its constituents, and the calorific intensity, or the temperature attained by the gaseous products of combustion. The calorific power will be the same regardless of the method of combustion ; that is, a unit of carbon or of hydrogen will give the same heat whether burned with the oxygen of the air or of a metallic oxide. The calorific intensity or temperature, however, will be greater as the volume of gases heated is less. Thus carbon burned to C0 2 will produce a much higher temperature when burned in oxygen gas than when in the air, since in the latter case it must heat an additional quantity of nitrogen equal to rather more than three times the weight of the oxygen. §346.] THE HEATING VALUE OF FUELS. 449 The maximum temperature cannot be either computed or determined experimentally with complete accuracy, partly be- cause the total combustion of a quantity of fuel in a given time at one operation is practically impossible, but more par- ticularly from the fact that dissociation of gaseous compounds produced in burning takes place at temperatures far below those indicated as possible by calculation. The maximum temperature is calculated as follows : The value of one pound of carbon is 8080 Centigrade heat- units, or 14,500 B. T. U. The heat absorbed by any body is equal to the product of its weight, w, specific heat, s, and rise of temperature, t. Hence wst = 8080, or t — 8080 -r- ws, in Centigrade degrees, and t = 14,550 -r- ws, in Fahrenheit degrees. In the case of combustion of carbon to CO a in oxygen gas, the oxygen required for each part of carbon is 2f parts ; the specific heat of C0 2 is 0.216. Hence the maximum temperature 8080 = 10,187° C, 3.67 X 0.216 or 3.67 X 0.216 ° ' In case it is burned in air an additional weight of 8.88 pounds of nitrogen, with a specific heat of 0.24, must be raised to the temperature of combustion. Hence the maxi- mum rise of temperature will be 8080 3.67 X 0.216 + 8.888 X 0.24 = 2731 C ° r 486o ° R The maximum temperature to be attained by combustion of the following substances, as calculated by R. Bunsen, is : 450 EXPERIMENTAL ENGINEERING. [§ 347- Combustible. In Oxygen. In Air. Carbon 9873° c. 7067 9187 7851 8061 17,803° F. 12,752 16,568 14,103 14,542 2458° c 3042 5413 5329 3259 4456° F. 5507 9775 9624 5898 Carbonic oxide, If the air supplied to the fuel be in excess of that required for perfect combustion, the temperature will be less. When the excess of air is 50 per cent, the maximum tem- perature from combustion of carbon is 351 5 F. ; when the excess is 100 per cent, the maximum temperature is 2710 F. The specific heats under constant pressure of the gases usu- ally occurring in connection with combustion are Carbonic-acid gas 0.2 17 Steam °475 Nitrogen 0.245 Air O.238 Ashes (probably) O.200 Oxygen . 0.241 Carbonic oxide , 0.288 Hydrogen 0.235 347. Composition of Fuels. — The fuels in ordinary use contain, in addition to the combustible compounds, more or less mineral or earthy matter that remains as ash after the combustion has taken place ; there is also frequently water in the hygroscopic state. The presence of these incombustible substances and the fact that perfect combustion can rarely be secured tend to make the actual heating effect less than that indicated by the theory. The percentage of ash as given in various boiler trials shows a wide variation, as follows: American coals 5 to 22 percent English coals 2.9 to 27.7 " Prussian coals 1.5 to 1 1.6 " Saxon coals 7.4 to 63.4 " 348.] r FHE HEATING VALUE OF FUELS. 45* The following table gives the composition of the principal fuels and the weight of air required to produce perfect com- bustion: AVERAGE COMPOSITION OF FUELS. Fuel. Charcoal from wood. " from peat. . . Coke, good Coal, anthracite dry bituminous. coking cannel dry, long-flaming... lignite Peat, dry Wood, dry " air-dried, 20% H 2 0. Mineral oil Carbon. C 0-93 O.80 O.94 O.915 O.87 O.85 0.75 O.84 O.77 O.70 O.58 O.51 39- 6 O.85 Hydrogen. H O.035 O.05 O.05 O.05 0.06 O.05 0.05 O.06 O.057 4.8 O.15 Oxygen. O O.026 O.04 O.06 0.05 0.08 O.15 O.20 O.31 42,0 34-8 Ash. 0.03 to 0.05 0.04 to 0.22 5 to 15 O.OI O.OI Pounds of Air required for one of Fuel. II. 16 9.6 11. 3 12.13 12.06 11-73 10.58 11.88 10.32 9-30 7.68 6.00 6.00 15./ 348. Principle of Fuel-calorimeters. — The caloric value of a fuel is determined by its perfect combustion under such conditions that the heat evolved can be absorbed and measured. It is essential in such cases that (1) the combustion be perfect, and that (2) the heat evolved be absorbed and measured. The combustion may take place in atmospheric air, in oxy- gen gas, or in combination with a chemical that supplies the oxygen required. It is essential in all cases that the supply of oxygen be adequate for perfect combustion. The heat evolved by combustion is determined by the rise in temperature of a given weight of water in a calorimeter of which the cooling effect, K, has been carefully determined, and in which the escaping gases are reduced to the temperature of the room. Let w equal the weight of fuel, R the heat evolved in heat-units by the combustion of one part, PFthe number of parts by weight of water heated from a temperature t' to t. Then if the escaping gases be reduced in temperature to that of the room, wE = (K+ W){t - t'), 452 EXPERIMENTAL ENGINEERING. 1§35I< from which B {K+W)(t-f) m w 340. Method of Obtaining Sample of the Fuel.— The calorimetric determination is made only on a very small portion of the fuel, and care should be exercised to have the se- lected sample fairly represent the fuel to be tested. To select a sample of coal for calorimetric examination several lots of ten pounds each should be chosen from different por- tions of the coal to be tested. These should be put in one pile, thoroughly mixed, and from the mixture several lots of one pound each taken. These latter quantities are to be pulver- ized, thoroughly mixed into one pile, and from this the required sample selected. It is recommended that the sample be sub- jected to a considerable pressure by placing it in a cylinder and compressing it by means of a piston moved by hydraulic pressure or by a screw : this is of especial importance if the fuel is to be burned in oxygen gas, since small particles are likely to form an explosive mixture ; and further, soot and tarry masses, which under the most favorable circumstances might be burned, will be found in the residue. 350. Heat-equivalent of the Calorimeter. — The effect of the calorimeter is most conveniently expressed as equivalent to a given weight of water; this is obtained, as for calorimeters used in determining the quality of steam (see Article 317, page 401), either by finding the sum of the products of the weights and specific heats of the various constituents of the calorimeter, or by comparing the results obtained with those which should have been found by the combustion of some fuel whose calo- rific power is known — as for instance pure carbon in oxygen gas — or again by its cooling effect on steam of known pressure 3,nd weight, or on warm water as explained on page 372. 351. Method of Determining Perfect Combustion. — Ths quality of the combustion is only to be determined by an analysis of the resulting gases and of the products of combus- tion. In case of perfect combustion all carbon is reduced tc § 35 2 -J THE HEATING VALUE OF FUELS. 453 C0 2 , all available hydrogen to water, sulphur to sulphuric acid; and further, the sum of the weights of all the products of com- bustion should, after deducting the air and oxygen obtained from the atmosphere, equal the original weight of the coal. The method adopted by Favre and Silbermann * of ascer. taining the weight of the substances consumed by calculation from the weight of the products of combustion was as follows : Carbonic acid was absorbed by caustic potash, carbonic oxide was first oxidized to carbonic acid by heated oxide of copper and then absorbed by caustic potash ; water vapor was absorbed by sulphuric acid. This system showed that it was necessary to analyze the products of combustion in order to detect im= perfect action. Thus in the case of substances containing car- bon, CO was always present to a variable extent with C0 2 , and corrections were necessary in order to determine the total heat due to the complete combination with oxygen. The conclusion arrived at by these experimenters was that in gen- eral there was an equality in the heat disengaged or absorbed in the respective acts of chemical combination or of decom- position of the same elements ; that is, the heat evolved during the combination of two simple elements is equal to the heat absorbed at the time of the chemical separation, and the quan- tity of heat evolved is the measure of the sum of the chemical and mechanical work accomplished in the reaction. 352. Favre and Silbermann's Fuel-calorimeter. — This apparatus, as shown in Fig. 208, consisted of a combustion- chamber, A, formed of thin copper, gilt internally, and fitted with a cover through which solid combustibles could be intro- duced into the cage C. The cover was traversed by a tube, E, connected bv means of a suitable pipe to a reservoir of the gas to be used in combustion, and by a second tube, D, the lower end of which was closed with alum and glass, transparent but adiathermic substances which permitted a view of the process of combustion without any loss of heat. For convenience of observation a small inclined mirror was placed above the peep-tube D. *See Conversion of Heat into Work : Anderson. 454 EXPERIMENTAL ENGINEERING. [§352. The products of combustion were carried off by a pipe, F y the lower portion of which constituted a thin copper coil, and the upper part was connected to the apparatus in which the non-condensible products were collected and examined. The whole of this portion of the calorimeter was plunged into a thin copper vessel, G, silvered internally and filled with water, which ■1 ESSE! -8-^-inch- TTTTT Fig. 208. — Favre and Silbermann's Fuel-calorimeter. was kept thoroughly mixed by means of agitators, H. The second vessel stood on wooden blocks inside a third .one, /, the sides and bottoms of which were covered with swan-skins with the down on, and the whole was immersed in a fourth vessel,/, filled with water kept at the average temperature of the laboratory. Thermometers, K, K, of great delicacy were § 353-] THE HEATING VALUE OF FUELS. 455 used to measure the increase of temperature in the water sur- rounding the combustion-chamber. The quantity of heat developed by the combustion of a known weight of fuel was determined by the increase of temperature of the water con- tained in the vessel G. For finding the calorific value of gases only, the cage C was removed and a compound jet, NO, sub- stituted for the single gas-pipe, ignition being produced by an electric spark or by some spongy platinum fixed at the end of the jet. 353. Thompson's Calorimeter. — Thompson's Calorimeter* is often employed for determination of the heating values of fuels. It consists of a glass jar graduated to contain 1934 grams of water; in this are inserted (1) a thermometer to indi- cate elevation of temperature, and (2) a cylindrical combustion- chamber with a capacity of about 200 grams of water. This chamber is capped at the top, and a small tube furnished with a valve is screwed into it, to hold the fuel. The combustible to be examined, 2 grams, is mixed as intimately as possible with 22 grams of a very dry mixture of 3 parts of potassic chlorate and 1 part of potassic nitrate, and introduced into the combus- tion-tube ; a nitrate-of-lead fuse is added and lighted. This tube is introduced into the combustion-chamber, the cap screwed on, and the whole placed without delay in the water of the calorimeter. The combustion takes place directly in the water, and the gases disengaged rise to the surface. The water is proportioned to the fuel as 966 is to 1, so that the rise in temperature in degrees F. is proportional to the evaporative power. The oxygen required for the combustion is supplied by the chemicals added. The water-equivalent of the calorim- eter as above described is about ten per cent. When com- bustion has ceased, the rise in temperature of the water is observed ; to this one tenth is added for the water value of the calorimeter. The corrected number gives the number of grams of water which a gram of the combustible can evaporate. *See Chemical Technology, Vol. I. 45 6 EXPERIMENTAL ENGINEERING. [§ 355- 354. The Berthier Calorimeter.* — This calorimeter is based on the reduction of oxide of lead by the carbon and hydrogen of the coal, the amount of lead reduced affording a measure of the oxygen expended, whence the heating power may be calculated by Welter's law, Article 345. One part of pure carbon being capable of reducing 34-J times its weight in lead. The operation is performed by mixing intimately the weighed sample (10 grams) with a large excess of pure litharge (400 grains). The mixture, placed in a crucible sufficiently capacious to contain three times its bulk, and rendered im- pervious to the gases of the furnace by a coating of fire-clay or by a glaze, is covered with an equal quantity of pure litharge (protoxide of lead). The crucible, being closed with a lid and placed on a support in the furnace, is slowly heated to redness, and when the gases which cause the mixture to swell considerably have escaped, it is covered with fuel and strongly heated for about ten minutes, in order to collect the globules of lead in a single button. The oxygen from the litharge com- bines with and burns the combustible ingredients of the fuel, leaving for every equivalent of oxygen consumed an equiva- lent of reduced metallic lead. The heating power is calculated as follows : 1 part of pure car- bon requires 2.666 parts of oxygen by weight, which taken from litharge leaves 34.5 parts of metallic lead. The same weight of carbon is sufficient to heat 80 parts of water from 32 to 212 . Hence every unit of lead reduced by any kind of fuel corre- 80 sponds by Welter's law with = 2.23 parts of water raised from the freezing to the boiling point. 355. The Berthelot Calorimeter. — This calorimeter, as modified by Hempel, consists of a very strong vessel with a capacity of about 250 c.c, into which the fuel is placed after being compressed into a solid form ; the combustion is per- Chemical Technology, Vol. I., page 337. § 356-] THE HEATING VALUE OF FUELS. 457 formed in an atmosphere of oxygen gas under a pressure of 10 to 12 atmospheres.* The fuel is ignited by an electric spark, and the heat gen- erated is known by measuring the rise in temperature in the sur- rounding water, as in the Favre and Silbermann calorimeter. The oxygen gas is generated in. a tube about one inch in diameter connected to the calorimeter by an intervening tube about \ inch in diameter. To this latter tube is attached a pressure-gauge to indicate the pressure, and a safety-gauge to prevent damage from explosion or excessive pressure. A stop-cock is also inserted close to the calorimeter. For gen- erating the oxygen the tube is filled with 40 grams of a mix- ture of equal parts of manganese dioxide and potassium chlorate. It is then heated by the full flame of a Bunsen burner applied first at the end nearest the calorimeter and gradually moved to the farther end. To use the instrument, the fuel, connected to platinum wires for electrical ignition, is introduced and suspended in the calorimeter, the top of which is firmly screwed on and the valve closed. Oxygen gas is then generated until the pressure reaches 90 pounds, and exhausted into the air to remove other gases from the calorimeter. The escape-valve from the calo- rimeter is closed and oxygen gas generated until the pressure- gauge shows 150 to 175 pounds pressure per square inch ; then the connecting stop-valve is closed and the electric current ap- plied. After the heat of combustion has been absorbed the determination is made as with the Favre and Silbermann calo- rimeter. 355. The Bomb Calorimeter. — This instrument was designed by the French chemist M. Berthelot, and consists of a strong steel vessel provided with a tightly fitting cover into which the coal is placed for combustion. For the pur- pose of combustion an excess of oxygen gas is supplied under a pressure of from 20 to 30 atmospheres. The fuel is sup- ported by a cage of platinum connected to the cover. The fuel is fired by an electric current passing through connecting * See Hempel's Gas Analysis, translated by Dennis. 4^8 EXPERIMENTA L ENGINEERING. [§355. wires and generated by a battery of ten bichromate cells. To prevent the oxidation of the instrument, the bomb built by Berthelot was lined with platinum. The heat given off during the process of combustion was absorbed by water in a vessel surrounding the bomb. During the process of com- bustion this water was kept in motion by a stirrer, and the heat given off determined by its rise in temperature. Various modifications of coal-calorimeters employing the principle of Berthelot's instrument have been made and are in extensive use. The form built by Mahler, Fig. 212, is perhaps the best known, which differs from that of Berthelot only in the form of the stirring apparatus and in the lining of the bomb, which is of porcelain enamel, instead of platinum. The German chemist Hempel has also designed a bomb calorimeter in which the bomb is made of steel, the interior of which is protected by an oxidized surface which has been found to give practical results. The oxygen for use in the calorimeters can be obtained from the decomposition of water by electrical means, or it may Fig. 209. — Parts of Thompson's Calorimeter in Action. be made by heating a crucible filled with equal parts of man- ganese dioxide and potassium chlorate- Some chlorine will usually pass over, which may be removed by passing through §3550 THE HEATING VALUE OF FUELS. 459 a close roll of brass wire-gauze. The oxygen may be received into a small gasometer and compressed by the action of a pump to the required density. Oxygen is also now- manufactured as a commercial article and can be purchased in cylinders holding 4 or 5 cubic feet and under a pressure of 20 atmospheres in nearly all the large cities. Thus it may be purchased in New York of Eimer & Amend. In the Hempel calorimeter, as shown in Fig. 210, the crucible for making the oxygen is attached directly to the Fig. 2io.~Hempel's Calorimeter with Enlarged Charging-plug. calorimeter by means of connecting pipes. In this case the calorimeter is charged before connecting the crucible. The crucible is filled with a mixture of equal parts dioxide of manganese and chlorate of potash, and the oxygen is driven off by the application of heat with the Bunsen burner; the heat being first applied at the end of the crucible nearest the calorimeter. A pressure-gauge B is connected to the pipe, and when the required pressure is reached the burner is removed, a connecting stop-cock b closed, and the connections to the 460 EXPERIMENTAL ENGINEERING. [§ 355. crucible removed. To prevent danger from accidents during the generation of the oxygen, the crucible and gauge should be enclosed in a large wooden vessel. The value of the fuel burned is determined from the rise in temperature of the water; account being taken of the weight of water and also the weights and specific heats of all parts of the calorimeter. Usually during combustion some nitric acid is formed which is deposited on the walls of "the calorimeter. The heat liberated in the formation of nitric acid should be taken into account, but as this is seldom greater than \ of one per cent, it is usually less than the unavoidable Fig. 211.— Charging Calorimeter with Oxygen. errors of observation. To avoid the numerous corrections and the tedious calculations which result therefrom, the chemist Hempel adopted the plan of standardizing his instru- ments by burning definite amounts of pure carbon, the value of which he took as known from the best investigations by Berthelot. To obtain pure carbon with which to standardize the instrument, he pulverized and carbonized crystallized sugar several times in succession, driving off at a high heat all volatile matter. This process of calibration gave a series of factors, which multiplied by thermometer-readings reduced the results to heat-units. The following example from 462 EXPERIMENTAL ENGINEERING. VI 355. " Traite Pratique de Calorimetre Chimique," by M, Berthe- lot, illustrates the process of reduction necessary in using the bomb calorimeter. The weight of each part of the calorimeter is carefully ascertained and multiplied by the specific heat of the material composing the part. The sum of these various products gives the water equivalent of the calorimeter which is given later. DETERMINATION OF THE HEAT IN PURE CARBON. Dried at a temperature of from 120 to 130 degrees C. until it had attained a constant weight and permitted to cool in a closed vessel and in the presence of concentrated sulphuric acid. (Observations of time and temperature,) Preliminary Observations Before Combustion. Observations During Combustion. Observations After Combustion. min., 17.360 deg. C. 1 " 17.360 " 2 " 17.360 "' 3 " 17-360 4 " 17.360 " 5 6 7 8 min., 18.500 deg. C. " 18.782 18.820 11 18.818 9 10 11 12 13 14 min., 18.810 deg. C. " '18.802 " 18.795 " 18.785 " 18.775 " 18.770 Initial cooling per minute, zero degrees; final cooling per minute, 0.008 deg. C. Total correction for cooling, 0.046 deg. C. Variation of temperature, not corrected, 18.818 — 17.360 = 1.438 deg. C. Corrected — 1.484 deg. C. Value in water of the calorimeter and contents = 2398. 4gr. Weight of nitric acid formed = 0.0173 gr. (Each gram is equal to 227 calories.) Each gram of iron burned is equal to 1650 calories. Total heat observed =3558.5 calories. Disengaged by the combustion of the " iron-ware 22.4 cal. Disengaged by the formation of nitric acid 3.9 cal. Heat obtained from the combustion of the 26.3 carbon = 3532.9 calories. 3532.2 Heat for one gram 0.4342 8136.6 § 35 6 -] rHE HEATING VALUE OF FUELS. 463 The latest determinations of Berthelot give the absolute heating power of amorphous carbon as 8137.4 calories = I4629.5 B. T. U. In the use of the calorimeter, the coal is to be first powdered and then reduced by pressure to a cylindrical cake or lump which is fired by the heat from an electric current. Corrections to the result are to be made for the heat disengaged by the oxidization of the iron and by the formation of nitric acid and by the vapor of water remaining in the atmosphere of the bomb. All these correc- tions are very small and may be avoided by using the process of calibration employed by Hempel. As noticed in the example above cited, the rise in tem- perature of the surrounding water is very small, and in order to obtain accurate results this water must be thoroughly agitated to produce a uniform temperature; the thermometer used must be capable of reading very small increments of a degree and must be read by a strong reading-glass or attached vernier. The accurate determination of small increments of temperature is nearly impossible with the apparatus to be found in an engineering laboratory. To overcome this diffi- culty, the author has designed a form of calorimeter in which the increase in temperature is determined by the expansion of the entire amount of water in the vessel surrounding the calorimeter. The value of the scale is determined by calibra- tion. Two forms of this instrument are manufactured by Schaeffer and Budenberg, Brooklyn, N. Y. In one form the combustion is performed in a steel bomb lined with enamel in many respects similar to the Mahler calorimeter. In the other the combustion is performed in a current of oxygen gas under low pressure, and the heat of combustion is absorbed by water in the surrounding vessel, the products of combus- tion passing through a coil and being finally discharged into the atmospheric air. 356. Fuel-calorimeter in which Heat is Measured by Expansion of Water. — The general appearance of the instru- ment is shown in Fig. 212; a sectional view of the interior 464 EXPERIMENTAL ENGINEERING. [§35^ part is shown in Fig. 214, from which it is seen that, ir principle, the instrument is a large thermometer, in the bulb of which combustion takes place, the heat being absorbed by the liquid which is within the bulb. The rise in temperature is denoted by the height to which a column of liquid rises in the attached glass tube. In construction, Fig. 214, the instrument consists of a chamber, No. 15, which has a removable bottom, shown in section in Fig. 213, and in perspective in Fig. 214. The chamber is supplied with oxygen for combustion through tube 23, 24, 2$, the products of combustion being discharged through a spiral lube, 29, 28, 30. Surrounding the combustion-chamber is a larger closed chamber, 1, Fig. 214, filled with water, and connecting with an open glass tube, 9 and 10. Above the water-chamber I is a diaphragm, 12, which can be changed in position by screw 14 so as to adjust the zero level in the open glass tube at any desired point. A glass for observing the process of combustion is inserted at 33, in top of the combustion- chamber, and also at 34, in top of the water-chamber, and at 36, in top of outer case. This instrument readily slips into an outside case, which is nickel-plated and polished on the inside, so as to reduce radiation as much as possible. The instrument is supported on strips of felting, 5 and 6, Fig. 214. A funnel for filling is provided at 37, which can also be used for emptying if desired. The plug which stops up the bottom of the combustion- chamber carries a dish, 22, in which the fuel for combustion is placed; also two wires passing through tubes of vulcanized fibre, which are adjustable in a vertical direction, and con- nected with a thin platinum wire at the ends. These wires are connected to an electric current, and used for firing the fuel. On the top part of the plug is placed a silver mirror, 38, to deflect any radiant heat. Through the centre of this plug passes a tube, 25, through which the oxygen passes to §356.J THE HEATING VALUE OF FUELS. 465 supply combustion. The plug is made with alternate layers of rubber and asbestos fibre, the outside only being of metal, which, being in contact with the wall of the water-chamber, can transfer little or no heat to the outside. The discharge-gases pass through a long coil of copper Fig. 213.— Fuel-calorimeter. Fig. 214.— Enlarged Section. pipe, and are discharged through a very fine orifice in a cap at 30. The instrument has been so designed that the combustion can take place in oxygen gas having considerable pressure, and in the form of a bomb; but in practice we have found that very reliable results have been obtained with pressures 466 EXPERIMENTAL ENGINEERING. [§ 35& of 2 to 5 pounds per square inch in an instrument of the form described, and this has been commonly used in investigations at Sibley College. For the purpose of making determinations of fuel, oxygen gas has been made and stored in a gasometer holding about 15 cubic feet, from which it was drawn as required. Method of Using the Calorimeter. — 1. Select an accurate sample by a system of quartering, which shall commence with a very great amount, if possible, and finally terminate with a very small fraction of a pound. 2. Reduce to powder by grinding, in a mortar or a mill, sufficient coal for several samples. A coffee-mill answers excellently for this purpose. 3. Introduce the sample into a small asbestos cup, drive out moisture by warming it over a Bunsen burner or alcohol lamp. Weigh accurately on a fine chemical balance-scale. 4. Introduce the sample into the calorimeter: (a) start the oxygen gas flowing; {b) fire the charge, which should be done by pressing on a key; (c) at instant coal is lighted, throw off the current and note the reading of the scale and time. During combustion keep the discharge orifice open, occasionally trying it with a small wire. 5. Watch the combustion, which will usually require about ten minutes for each gram of coal, and when completed note the scale reading and the time. The difference between first and second reading is the actual scale reading. 6. To correct for radiation note the amount, the water in the column has fallen for the same time as required for com- bustion ; add this to the actual reading to get the corrected scale reading. 7. Divide the value as shown on the diagram by the weight in pounds of the sample burned. The result will be the value in B. T. U. of one pound of coal. 8. Remove the dish in which the combustion took place; weigh it carefully with and without contents. If the com- bustion has been perfect, the difference of these weights gives § 3 5 6-] THE HEATING VALUE OF FUELS. 467 the ash. Wipe the combustion-chamber dry for another determination. 9. To prepare for another determination, remove the calorimeter from the outside case and immerse in cold water, care being taken to prevent any water entering oxygen-tubes or combustion-chamber. This method is preferable to emptying the calorimeter and adding fresh water each time, since the air, which is always present in water, will affect the results and is a diffi- cult element to remove. The operation of cooling takes but a few minutes and is easily performed. In order that the instrument may give accurate values, it is necessary that all air be removed from the water, and that the oxygen be supplied at a constant pressure. The pressure with which the instrument was calibrated is given with the calibration curve, and if any other pressure is used a new cali- bration should be made. Do not attempt to use the calorimeter in a room whose temperature is above 80 degrees Fahr., as the calorimeter should always be warmer than the air of the room. In case oxygen is purchased in a condensed form, it can be reduced to any desired amount by passing it into a small gasometer before reading the calorimeter. The gasometer may be made by simply inverting one pail into another which is partly filled with water. By weighting the top pail any pressure required can be produced. If oxygen is made for especial use, it can be received in a gasometer, made as described, but with sufficient capacity for several tests. Oxygen can be made by heating a mixture of about equal parts of dioxide of manganese and chlorate of potash placed in a closed retort. In lighting the platinum wire we use 16 Mesco dry batteries connected in four series. A single cell of a storage battery, the current of which is ordinarily used for incandes- cent lighting, may be used with success. 468 EXPERIMENTAL ENGINEERING. [§ 356. EXAMPLE SHOWING HOW TO DETERMINE THE CALORIFIC POWER OF COAL. Weight of crucible 1 .269 grams. il " and coal. ... ._ 3-0!7 " " " and ash 1*567 " 'combustibles I-450 " ^ ash 297 << " coal 1.747 " 1.747 reduced to pounds = 1.747 X .002205 = .003852 lbs. First scale-reading, 3.90 inches, time 2 o'clock, 55 minutes. Second " 14.70 " " 3 " 20 Third " 14.30 " " 3 " 45 " Actual scale reading 3.90 — 14.70 = 10.80 inches. For radiation 14.30—14.70= .40 " Corrected scale-reading 1 1.2 " On the diagram 1 1.2 corresponds to 46.25 B. T. U.'s in sample. As 46.25 B. T. U. are .00385 lbs., one pound will be: 46.25 -7- .00385 = 12,000 heat-units. All calorimeters are calibrated before shipment, but to enable purchasers to make a new calibration in case a new glass tube should have to be inserted we give the following instructions: 1. Make a pure coke, reduce some soft coal to powder, fill a porcelain or clay crucible 2/3 full, cover it air-tight, glow it with a blast-lamp or in a forge-fire for one hour. If cold, grind it in a mortar to a very fine powder. Repeat this operation. 2. Remove gland and hexagon plug-screw from top of calorimeter and fill it with water. Close the plug-screw and connect the glass-tube opening by some rubber hose or glass tube with a smaller vessel filled with water. Boil the water in the calorimeter body ; this may be done by a Bunsen burner, protecting the calorimeter by a thin sheet of asbestos. Place § 35 6 -] THE HEATING VALUE OF FUELS. 469 the instrument in such a position that the glass-tube opening may be its highest point and so enable all air and steam to pass through the connection to the smaller vessel. Also keep the water in the smaller vessel boiling until the calorimeter has fully cooled off. Remove rubber connection, fill the glass tube with boiled water and screw it tight. Take care not to allow it to pass so far into the calorimeter that air will be trapped. Put about two inches kerosene oil on top of water-column to prevent air from coming in contact with the water. Should it be found that the water in column stands too high after the calorimeter has taken the temperature of the room, loosen the plug and allow water to leak out slowly until the scale- reading is about two inches, then close it securely. 3. If the instrument is ready for calibration, follow in- structions given under method of using the calorimeter. The difference of weight between the weight of crucible and carbon (coke) and the weight of crucible and ash is the weight of pure carbon burned. Dividing 14540 by the weight of burned carbon, we obtain the number of heat-units in the sample. By drawing the oblique line on the chart, take the num- ber of corrected scale-reading as ordinates, and the number of B. T. U.'s in sample as abscissae, make a point on crossing and draw a line to zero. EXAMPLE OF CALIBRATION. Weight of crucible and coke in grams 3.002 " ash " " I.064 " burned pure carbon 1.935 I.935 grams reduced to pound = .00426 lbs. 1.935 X. 002205 = .00426 lbs. 14540 X .00426 = 61.86 B. T. U. in sample. First scale-reading, 3.33 inches, time 11 o'clock, 15 minutes. Second " 16.85 " " II " 40 " Third " 16. " " 12 " 10 " << (I 470 EXPERIMENTAL ENGINEERING. [§ 356. Actual reading 16.85 — 3-35 = I3-5Q inches. For radiation 16.00—16.85= -$5 " Corrected scale-reading 14. 35 « « " DIRECTIONS FOR PROXIMATE ANALYSIS.* — COAL AND COKE." The sample should be finely pulverized in a mortar, and then thoroughly mixed. Moisture. — Place the weighed sample (about 1 gram) in a porcelain crucible, and dry in an air-bath for one hour, at a temperature between 105 and no degrees C. Weigh as soon as cool. Loss is moisture. Volatile Matter. — Weigh about \\ grams of the undried pulverized coal, place it in a platinum crucible and cover tightly. Heat it for 3| minutes over Bunsen burner (bright red heat), and then immediately, without cooling, for 3I- minutes over blast-lamp (white heat). Cool and weigh. Loss, less the moisture, is volatile matter. Fixed Carbon. — If a coke be formed in the preceding opera- tion, make a note of its properties, color, firmness, etc., then place the crucible, with cover removed, in an inclined posi- tion, and heat over Bunsen burner until all carbon is burned., .i.e., to constant weight. The combustion may be hastened by stirring the charge from time to time with a platinum wire. Difference between this and last weight is the fixed carbon. Ash. — Difference between last weight and weight of cruci- ble is the ash. Total Sulphur in Coal and Coke. — Prepare a fusing mixture by thoroughly mixing two parts calcined magnesia with one part anhydrous sodium carbonate. Determine the sulphur in the mixture. Thoroughly mix I gram of the finely pulverized coal with if grams of fusing mixture. Heat over an alcohol lamp, in an open platinum or porcelain crucible, so inclined that only *See " Crooke's Select Methods," 2d Edition, pp. 595-607. g 356.] THE HEATING VALUE OF FUELS. 47 1 its lower half may be brought to a red heat. The crucible should not be over ^ or f full, and the heat should be gentle at first, to avoid loss upon the consequent sudden escape of volatile matter, if present in large amount. Raise the heat gradually (it must not at any time be high enough to fuse the mixture), and stir the contents of the crucible every five minutes with a platinum wire. The oxidation of the carbon is complete when ash becomes yellowish or light gray (about one hour). Cool crucible, add 1 gram pulverized NH 4 N0 3 to the ash, mix thoroughly by stirring with a glass rod, and heat to redness for five to ten minutes, the crucible being covered with its lid. Cool, digest the mass in water, transfer the crucible con- tents to a beaker, rinse out the crucible with dilute warm HC1, dilute solution in beaker to about 150 c.c, acidulate with HC1, and heat almost to boiling for five minutes. Filter and precipitate the sulphuric acid in filtrate by BaCl 2 in usual manner. Phosphorus. — If present, it will be found in the ash. Ignite about 10 grams of the coal in a large platinum crucible, and determine the phosphorus in the ash in the usual manner. (See Fresenius, p. 741.) Sulphur and phosphorus are not usually of importance, un- less the coal is destined for certain uses where these ingredients would be harmful; the determination requires much more time than that of all other processes in the proximate analysis. The operation recommended for a mechanical laboratory would differ principally from that described, first, in the use of larger samples; and second, in the use of porcelain instead of platinum crucibles. In the determination of the volatile matter the conclusion of the operation may be known by change of color in the flame. During the operation the flame would be yellow or yellowish so long as any volatile matter remained : it would then die down, and when the carbon commenced to burn would be decidedly blue. The operation to be always stopped 472 EXPERIMENTAL ENGINEERING. [§ 357- soon after the blue flame appears. The crucible recom- mended is made of Royal Meissen porcelain, and provided with cover. It has a capacity of half an ounce, and costs seventeen cents. During the operation the cover is fitted snugly in place, and the gases escape around the edge, and are kept burning. The percentage of ash is determined by weighing the residue which remains after combustion in the calorimeter. The burning of the fixed carbon requires a long time when performed in the air, but in the calorimeter the operation is performed very quickly and very accurately, so that the total time required to determine the proximate composition and also the heat-values of a sample of coal need not exceed twenty or thirty minutes, for a person familiar with the operations. 357. Value of Coal determined by a Boiler-trial. — The calorific value of a coal is sometimes determined by the amount of water evaporated into dry steam under the con- ditions of use in a steam-boiler. This method is fully ex- plained in the latter part of the present work in the chapter on the methods of testing steam-boilers. The calorific values obtained in actual boiler-trials are much less than those ob- tained in the calorimeters, because of loss of heat by radiation into the air and by discharge of hot gases into the chim- ney. The results obtained by such a trial by Prof. W. R. Johnson at the Navy Yard, Washington, in 1843, with a small cylindrical boiler, were as follows : Area of Fire- grate, Sq. Ft. Coal per Hour. Water evaporated per Hour. Water evaporated from 212 F. per lb. of Coal. Coal. Total. Per Sq. Ft. of Grate. Total. Per Sq. Ft. of Grate. Anthracite (7 samples). . . Bituminous coals, free burning (11 samples). . . Bituminous coking coals, Virginian (10 samples).. I4.3O I4.I4 14.15 94.94 99.16 105.02 6.64 7.OI 7.42 12.37 13-73 I2.l6 O.87 O.97 O.86 9-63 9.68 8.48* 14.20 99-71 7.02 12-75 O.90 9.26 § 35 8 -] THE HEATING VALUE OF FUELS. 473 358. Object of Analysis of the Products of Combustion. — The products resulting from the combustion of ordinary fuel contain principally a mixture of air, C0 2 , and some combus- tible gases, as CO and H. To determine whether or not the combustion is perfect, it is necessary to know the percentage that the combustible gases escaping bear to the total products of combustion. It is also important to know whether the air supplied is sufficient for the purposes of combustion, and also whether it is in excess of the amount actually required. As •shown in Article 346, page 448, the presence of an excess of air over that required has the effect of lowering the tempera- ture of the furnace ; steam would have the same effect even in a greater degree, as can readily be shown by calculation. From a careful examination of the products of combustion we should be able to ascertain its character and make the necessary corrections for such losses as may be due to imper- fect combustion. The methods to be employed must be such as any en- gineer can fully comprehend, and the apparatus portable and convenient. The degree of accuracy sought need not be such as would be required in a chemical laboratory where every convenience for accurate work is to be found. Indeed, considering the approximations to be made in its ap- plication, it is very doubtful if determinations nearer than one per cent in volume are required, or even of any value. Such determinations are obtained readily with simple instruments, and serve to show the. approximate condition of the gaseous products of combustion. The student is referred to " Hand- book of Technical Gas Analysis," by Clemens Winkler (London, John Van Voorst), and to "Methods of Gas Analysis," by Dr. W. Hempel, translated by L. M. Dennis (Macmillan & Co.); also to a paper on tests of a hot-blast apparatus by J. C. Hoad- ley, Vol. VI. Transactions of the American Society of Mechani- cal Engineers. In a thorough examination of the value of fuel, the ashes should also be analyzed, since if they contain any combustible, 474 EXPERIMENTAL ENGINEERING. [§ 359. or partly burned combustible, the heating value must be de- termined, and proper allowance made for the same. 359. General Methods of Flue-gas Analysis. — The gases to be sought for are C0 2 , CO, O, and H. Unless the temperature is very high, CO is found only in very small quantities, and rarely exceeds one per cent. Prof. L. M. Dennis, of Cornell University, makes the statement that Dr. W. Hempel, of Dresden, whose principal work has been the analysis of gases, states that rarely ever is more than a trace of carbonic oxide (CO) to be found in the products resulting from ordinary combustion. Considering the difficulty of ab- sorbing CO, and the consequent errors that are likely to arise, it may be in general better to neglect it. The hydrogen, H, present is also a very small quantity, unless the temperature is abnormally low, and can be neglected without sensible error. The analysis may be of two kinds, gravimetrical and volumetric. The former is seldom used, but will be found described in an article by J. C. Hoadley, Transactions of the American Society of Mechanical Engineers, Vol. VI., page 786. In this case the various gases are passed through solid absorbents, and the several constituents successively absorbed and weighed. The method of analysis usually adopted is a volumetric one, and consists of the following steps, which wiL be described in detail later on. A. The sample is first collected and then introduced into a measuring-tube ; 100 c.c. of the gas is retained, the remainder wasted. B. The constituents of the gas are then absorbed by suc- cessive operations, in the following order : carbonic acid (C0 2 ), free oxygen (O), carbonic oxide (CO), and hydrogen (H). The absorption is accomplished by causing the gas to flow over the reagent in the liquid or solid form, which is introduced into the gas or remains permanently in a separate treating- tube. It is then made to flow back to the measuring-tube and the loss of volume measured. The loss is due to absorp- tion, the various absorbents used being as follows : §360.] THE HEATING VALUE OF FUELS. 475 ¥ ok carbonic acid, CO,, either potassium hydroxide (caustic potash KOH), or barium hydroxide. For oxygen, O, either (1) a strong alkaline solution of pyrogallic acid, (2) chromous chloride, (3) phosphorus, (4) metallic copper. For carbon monoxide, CO, either an ammoniacal or a hydro- chloric-acid solution of cuprous chloride. For hydrogen, H, an explosion or rapid combustion in the presence of oxygen, or absorption by metallic potassium, sodium, or palladium. The reagent usually employed as an absorbent is the one first mentioned in each case. 360. Preparation of the Reagents.— Absorbents of Oxy- gen. — 1. Potassium pyrogallate. This is prepared by mixing together, either directly in the absorption pipette or in the apparatus, 5 grams of pyrogallic acid dissolved in 15 c.c. of water, and 120 grams of caustic potash (KOH) dissolved in 80 c.c. of water. Caustic potash purified with alcohol should not be used for analysis. The absorption of the gas should not be carried on at a temperature under 15 C. (55 Fahr.) ; it may be completed with certainty in three minutes by shaking the gas in contact with the solution. 2. Chromous chloride will absorb oxygen alone in a mixture of oxygen and hydrogen sulphide ; it is prepared with difficulty, and not much used. 3. Phosphorus is one of the most convenient absorbents: it is to be kept in the solid form under water and in the dark; the gas is to be passed over the reagent, displacing the water, and kept in contact with it for about three minutes. The end of the absorption is shown by a disappearance of a light glow, which characterizes the process of absorption. The phosphorus will remain in serviceable condition for a long time. 4. Copper, at a red heat or in the form of little rolls of wire- gauze immersed in a solution of ammonia and ammonium car- bonate, is a very active absorbent for oxygen. Absorbents of Carbonic Acid (CO,). — i. Caustic potash. This solution may be used in varying strengths, depending on the method of gas analysis. With the Elliot apparatus, a solu- 47^ EXPERIMENTAL ENGINEERING. [§ 360. tiou of 3 to 5 per cent of KOH in distilled water is sufficiently strong, the gas being kept in contact with it for several min- utes. When a separate treating-tube is used for each reagent, a solution of one part of commercial caustic potash to two parts of water is employed. The absorption is accomplished very quickly in the latter case, and often bypassing the gas but once through the treating-tube. The process is more quickly and thoroughly performed by introducing into the treating- tubes as many rolls of fine iron-wire gauze as it will hold. 2. Barium hydroxide in solution is the best absorbent in case the quantity of C0 2 is very small ; in this case titration with oxalic acid will be required. Absorbents of Carbon Monoxide (CO). — i. (a) Hydrochlo- ric-acid solution of cuprous chloride is prepared by dissolving 10.3 grams of copper oxide in 100 to 200 c.c. of concentrated hydro- chloric acid, and then allowing the solution to stand in a flask of suitable size, filled as full as possible with copper wire, until the cupric chloride is reduced to cuprous chloride, and the solution is completely colorless. (i>) Winkler directs that 86 grams of copper scale be mixed with 17 grams of copper powder, prepared by reducing copper oxide with hydrogen, and that this mixture be brought slowly and with shaking into 1086 grams of hydrochloric acid of 1. 1 24 specific gravity. A spiral of copper wire is then placed in the solution, and the bottle closed with a soft rubber stopper. It is dark at first, then becomes colorless, but in contact with the air becomes brown. The absorbing power is 4 c.c. of CO. The ammoniacial solution is to be used in case hydrogen is to be absorbed by palladium. This is prepared from the colorless solution (a) as follows : Pour the clear hydrochloric acid solution into a large beaker-glass containing i-J to 2 litres of waiter, to precipitate the cuprous chloride. After the pre- cipitate has settled, pour off the dilute acid as completely as of possible, then wash the cuprous chloride with 100 to 150 c.c. distilled water, and add ammonia to the solution until the liquid takes a pale-blue color. The solutions of cupric chloride de- compose readily, and in general should be used when fresh, or si 361.] THE HEATING VALUE OF FUELS. All preserved under a layer of petroleum. The treating-tube con- taining the reagent is frequently supplied with spirals of small copper wire which tend to preserve and increase the absorb- ing capacity of this reagent. 361. Method of obtaining a Sample of the Gas. — In order to take a sample of the gas for analysis from any place, such as a furnace, flue, or chimney, an aspirating-tube is intro- duced into the flue : this consists of a tube open at both ends, the outside end being provided with a stop-cock and connected with the collecting apparatus by an india-rubber tube. There mm -■ 'M Mm Fig. 215.— Hoadley's Flue-gas Sampler. is probably a great diversity in the composition of gases from various parts of the flue. For obtaining an average sample, J. C. Hoadley employed a mixing-box B* provided with a large number of J-inch pipes, ending in various parts of the cross-section of the flue A. An elevation of the mixing-box is shown at B' . From the mix- ing-box four tubes CC lead downward from various parts to a mixing-chamber D, from which a pipe E leads to the collecting apparatus. Two of these mixing-boxes were used, one placed in the flue a short distance above the other, and an agreement of the samples obtained from each was regarded as proof of the substantial accuracy of the sample. * Trans. Am. Soc. M. E., Vol. VI. 4/8 EXPERIMENTAL ENGINEERING. [§ 36 1. It is hardly probable that a tube furnished with various branches or a long slit will give a fair sample, since the velocity of gases in the aspirating-tube is such that most of the gas will be collected at the openings nearest the collecting appa- ratus ; the author has often employed a branch-tube with holes opening in different portions of the chimney. The material for the aspirating-tube is preferably porcelain or glass, but iron has no especial absorptive action on the gases usually to be found in the flue, and may be used with satisfaction. A long length of rubber tubing may, however, sensibly affect the results. The gas should be collected as closely as possible to the furnace, since it is liable to be diluted to a considerable extent by infiltration of air through the brick-work beyond the furnace. In order to induce the gas to flow outward and into the collecting apparatus, pressure in the collecting vessel, termed an aspirator, must be reduced below that in the flue. This is accomplished by using for an aspirator two large bottles con- nected together by rubber tubing near the bottom, or better still, two galvanized iron tanks, about 6 inches diameter and 2 feet high, connected near the bottom by a rubber tube, in which is a stop-cock; one of the bottles or tanks has a closed top and a connection for rubber tubing provided with stop- cock at the top ; the other bottle or tank is open to the atmos- phere. To use the aspirator, the vessel with the closed top is filled with water by elevating the other vessel ; it is then con- nected to the aspirating-tube, the open vessel being held so high that it will remain nearly empty. After the connection is made, and the stop-cocks opened, the empty vessel is brought below the level of the full one, and the water passing from the one connected to the aspirating-tube lessens the pres- sure to such an extent that it will be filled with gas. This process should be repeated several times in order to in- sure the thorough removal of all air from the aspirating- tubes. The liquid used for this purpose is generally water, which is an absorbent to a considerable extent of the gases § 3 6 3-J THE HEATING VALUE OF FUELS. 479 contained in the flues. To lessen its absorbent power, the water used should be shaken intimately with the gas in order to saturate it before the sample for analysis is taken. When mercury is used as the liquid this precaution is not necessary. A small instrument, on the principle of an injector, in which a small stream of water or mercury is constantly delivered, is an efficient aspirator, and is extremely convenient for continu- ous analysis. 362. General Forms of Apparatus employed for Volu- metric Gas Analysis. — The apparatus employed for volumetric gas analysis consists of a measuring-tube, in which the volume of gas can be drawn and accurately measured at a given press- ure, and a treating tube into which the gases are introduced and then brought in contact with the various reagents already described. The apparatus employed may be divided into two classes: (1) those in which there is but one treating-tube, the different reagents being successively introduced into the same tube ; (2) those in which there are as many treating-tubes as there are reagents to be employed, the reagents being used in a concentrated form, and the gases brought into contact with the required reagent by passing them into the special treating tube. In either case the steps are, as explained in Article 358: {a) Obtain 100 c.c. by measurement; (b) to absorb the C0 2 , bring the gas in contact with KOH, and measure the reduction of volume so caused ; this is equivalent to the percentage of C0 2 ; (c) bring the gas in contact with pyrogallic acid and KOH, and absorb the free oxygen. Measure the reduction of volume so caused ; this is equivalent to the percentage of free oxygen ; (d) determine the other constituents in a similar manner. In performing these various operations it is essential that the tubes be kept clean and that the reagents be kept entirely separate from each other. This is accomplished by washing or causing some water to pass up and down the tubes or pipettes several times after each operation. 363. Elliot's Apparatus. — This is one of the most simple outfits for gas analysis, and consists of a treating-tube AB and 480 EXPERIMENTAL ENGINEERING. [§ 363. Fig. 216.— Elliot's Apparatus. a measuring-tube A'B', Fig. 216, connected by a capillary tube at the top, in which is a stop-cock, G. The tubes shown in Fig. 163 are set in a frame-work having an upper and a lower shelf, on which the bottles L and K can be placed. In using the apparatus, it is first washed, which is done by filling the bottles with water, opening the stop-cocks F and G, and alternately raising and lowering the bottles K and L. The bottles are then filled with clean distilled water, raised to the positions shown, and the stop-cocks G and F closed. The gas is then introduced by connecting the discharge from the aspirator to the stem of the three-way- cock F, and turning it so that its hollow stem is in connection with the interior of the tube AB ; lowering the bottle L, the water will flow out from the tube AB and the gas will flow in. When the tube AB is full of gas the cock F is closed, the aspirator is disconnected, and the gas is measured. The gas must be measured at atmos- pheric pressure. That may be done by holding the bottle in such a position that the surface of the water in the bottle shall be of the same height as that in the tube. A distinct meniscus will be formed by the surface of the water in the tube ; the reading must in each case be made to the bottom of the meniscus. To measure the gas, which will be considerably in excess of that needed, the cock G is opened, the bottle ^de- pressed, the bottle L elevated ; the gas will then pass over into the measuring-tube A'B' ; the bottle K is then held so that the surface of the water shall be at the same level as in the measuring- tube, and the bottle L manipulated until exactly 100 c. c. are in the measuring-tube ; then the cock G is closed, the cock F opened, the bottle L raised, and the remaining gas wasted, causing a little water to flow out each time to clean the con- necting tubes. The measuring-tube A'B' is surrounded with a jacket of water to maintain the gas at the uniform temperature of the room. After measuring the sample it is then run over into the treating-tube AB, and the reagent introduced through 365-j THE HEATING VALUE OF FUELS. 481 the funnel above F by letting it drip very slowly into the tube AB. After there is no farther absorption in the tube AB, the cock F is closed and the gas again passed over to the measur- ing-tube^^, and its loss of volume measured. This operation is repeated until all the reagents have been used ; in each case, when the gas is run back from the measuring-tube, pass over a little water to wash out the connections ; exercise great care that in manipulating the cocks K or G no gas be allowed to escape or air to enter. 364. Wilson's Apparatus .*— This apparatus is illustrated in Fig. 217. It is used in essentially the same manner as the Elliot apparatus, mercury being used as the displacing liquid in place of water. It consists of a treating-tube d, a measuring- tube a, connected at the top by a capillary tube f. The measuring- tube ends in a vessel filled with mercury, and in this case the press- ure on the tubes can be regulated by lowering and raising the single bottle filled with mercury, and the gas can be manipulated as in the Elliot apparatus, using one bottle instead of two. Reagents are in- troduced into the funnel e y and come in contact with the gas in the treating-tube d. The collecting-tube used with this apparatus is shown at B, and consists of a vessel filled with mer- cury. One side is connected to the aspirator -tube ; some of the mercury is allowed to run out through a cock, and the space is filled by the gas. Sufficient mercury is retained to form a seal. 365. Fisher's Modification of Orsat's Apparatus. — This * Thurston's Engine and Boiler Trials, p. 107. Fig. 217. — Apparatus for Gas Analysis. 482 EXPERIMENTAL ENGINEERING. [§ 365. apparatus, shown in Fig. 218, belongs to the class in which each reagent is introduced in a concentrated form into a special treating-tube. The apparatus consists of a measuring-tube surrounded by a water-jacket, into which the gas can be intro- duced substantially as explained for the Elliot apparatus. Each Fig. 218.— Orsat's Gas-analysis Apparatus. reagent is introduced in a concentrated form into a pair of burettes connected at the bottom by a U-shaped tube. In making an analysis the gas is first drawn into the measuring-tube and 100 c.c. retained ; the cock in the tube leading to one of the treating-tubes is then opened, the bottle raised, and the gas driven over into the treating-tube. This §366.] THE HEATING VALUE OF FUELS. 483 operation is facilitated by connecting a soft rubber bag to the opposite side of the treating-tube, by means of which alternate pressure and suction can be applied, and the reagent protected from the atmosphere. After the absorption is com- plete, which will take from one to three minutes in each tube, the gas is returned to the measuring-tube by lowering the bottle and exerting pressure on the attached rubber bag. The rubbei bag is not shown in Fig. 218, and is not required, pro- vided the treating-tube is completely filled with the reagent on the side toward the measuring-tube. The treating-tubes are filled in order from the measuring- tube with the following reagents: (1) with 33 per cent solution of KOH ; (2) with a solution of pyrogallic acid and KOH, or with sticks of phosphorus (see Article 360) ; (3) with a hydrochloric-acid or an ammoniacal solution of cuprous chloride in contact with copper wire (see Article 359). In the first treating-tube is absorbed C0 2 , in*the second O, ard in the third CO. A modification of the Orsat apparatus has a fourth tube in wnich hydrogen can be exploded ; the reduction in volume, due to the explosion, gives the amount of hydrogen present. An apparatus for flue-gas analysis has been designed by the author in which the treating-tubes are arranged as in the Orsat, but they are of such a form as to permit the use of solid reagents for absorbing oxygen, and are much less liable to rupture. It is used exactly as described for the Orsat, but is much more convenient and is somewhat more accurate. 366. Hempel's Apparatus for Gas Analysis.* — This ap- paratus, shown in Figs. 219 to 224, is especially designed for the accurate analysis of the constituents of various gases ; for laboratory use it presents many advantages over the other apparatus described. The apparatus consists of the following parts : I. The measuring burette, shown in Fig. 220, which is constructed and used as follows : It is furnished with an iron *See Hempel's Gas Analysis, by L. M. Dennis. Catalogue of Eimer & Amend, New York. 4^4 EXPERIMENTAL ENGINEERING. [§ 366. base, which is connected by a rubber tube to an open tube a (see Fig. 219) with a similar base. The stop-cock d is opened, the tube a elevated, and water or mercury, whichever may be Fig. 219. Fig. used, flows from a over to b. Gas is introduced as follows: The measuring-tube b is filled with liquid, the cocks d and c closed, and connection made at e to the vessel containing the gas to be measured ; the cocks d and c are then opened, the § 366.] THE HEATING VALUE OF FUELS. 4 3 5 tube a lowered ; the liquid will then flow from the measuring- tube b to a, and the gas will fill the measuring-tube. To meas- ure the volume of gas, hold the tube a as shown in Fig. 219, so that the water-level shall be the same in both tubes^ thus bringing the gas under atmospheric pressure. Read the vol- FlG. 221. Fig. 222. Figs. 223-224. — Hempel's Absorption Burettes. ume directly by the graduation corresponding to the lower edge of the meniscus. The absorption-pipettes are different in form from those used in the Orsat apparatus, and are connected only as required to the measuring-burette, but are used in essentially the same way. Several forms of these are employed as shown in Figs. 221 to 224. The forms shown in Fig. 222 and Fig. 224 are 486 EXPERIMENTAL ENGINEERING. [§ 367 ordinarily used for reagents in solution. In such a case the measuring-tube is connected at e, Fig. 222, the reagent occupy- ing the bulbs a and b. The top of the measuring-burette e, Fig. 219, is connected to the absorption-pipette, and the gas moved alternately forward and backward as required by raising or lowering the tube a. In case reagents in the solid form are to be used, the absorption-pipette is made of the form shown in Fig. 223, in case regents which decompose very easily are used a pipette of the form shown in Fig. 221 is employed. The general methods employed are the same as those pre- viously described. 367. Deductions and Computations from Flue-gas Analysis. — The determinations give the percentage of volume of C0 2 , O, and CO existing in the products of combustion. Of these constituents the carbon is derived entirely from the fuel and the oxygen in great part from the atmosphere. Every part of oxygen drawn in from the atmosphere brings with it nitrogen, which passes through the furnace unchanged. The nitrogen is calculated as follows : The proportion of nitrogen to oxygen existing in the atmosphere is 79 to 21 by volume; call this ratio S\ denote the percentage of volume of the gases existing in the sample as follows : C0 2 by K', oxygen by 0\ CO by U'j nitrogen by N'. Then we shall have K'+0'+ U'+N'= 100 per cent, . . . (1) from which N f = 100 - {K' + a + uy .... (2) If the oxygen were all derived from the atmosphere, both the amount of nitrogen N' and of carbonic oxide U' could be computed, since in such a case the volume occupied by the free oxygen before combining would equal K'+O' + W. Hence the nitrogen N" = S{K' + 0' + i[/'y . .... . . (3) § 367.] THE HEATING VALUE OF FUELS. 487 Substituting this latter value in equation (1), K* + a + u f + s(K r + a+W) = 100, from which U'={i*>-{K'+0')(i+S)\+[i + S). . (4) Since there is to be found from 2 to 5 per cent of oxygen in the fuel, equation (4) will generally give negative values for the CO, and should not be used. The composition of the flue-gases is an index of the com- pleteness of the combustion. The flue-gases should contain only nitrogen, oxygen, steam, and carbon dioxide, if the com- bustion is perfect. Since the amount of CO and of hydrogen compounds are always small, the excess of air can be com- puted very nearly from the amount of C0 3 . Thus, were the products of combustion free oxygen, nitrogen, and carbon dioxide, only, the volume of oxygen and carbon dioxide would replace that of oxygen in the air, or would equal about 20.8 per cent. On account of slight losses, it is more nearly 20 in actual cases. The percentage of excess of air would then be 20 less the per cent of carbon dioxide divided by the percentage of carbon dioxide, 20 - k ' / X y=~v- (5) Siegert gives an approximate formula for the percentage of heat lost, T — t V x = 0.65 rn = in centigrade units, (6) in which T= temperature of the flue; t = temperature of air entering furnace, C0„ = percentage of C0 2 . The principal object of the flue-gas analysis may be con- sidered as accomplished when the percentage of uncombined 488 EXPERIMENTAL ENGINEERING. [§ 3^7- oxygen and of C0 2 is determined, since in every case the amount of the ether gases present will be very small. From these we can find the ratio of the total oxygen supplied to that used. This ratio, which is called the dilution coefficient X, shows the volume of air supplied to that required to furnish the oxygen for the combustion. It may be computed by comparing the total volume of gases with that required to unite with the combined oxygen, from which = N'-so' " I 1 + ~K r r nearly * • * (7) The analysis and the computations considered relate to volumes of the various gases. They may be reduced to pro- portional weights by multiplying the volume of each gas by its molecular weight and dividing by the total weights. Knowing the proportional weights for each gas and the total carbon consumed, the total air passing through the furnace can be computed. Thus for the perfect combusrion of a pound of carbon will be required 2.67 pounds of oxygen, for which will be required 11.7 pounds of air. If the ratio of air used to that required be X, then the weight of air per pound of fuel equal 11. yX. One pound of air at 32 Fahr. occupies 12.5 cubic feet. Knowing which, the volume of air per pound of coal can be computed as equal 12.5 X 11.7X— 146.2X The maximum temperature T m , that can possibly be attained in the furnace, is to be calculated as in Article 346, page 449. r _ 14500 m ~ (3.67X0.216) + (8.88X0.24) + (X- i)(i2.6)(o.238> 14500 5000 . . 1 = 2.91+ 2.8 4 (X - 1) = -JT a PP ro *' matel y- • • (8) § 368.] THE HEATING VALUE OF FUELS, 489 Having the maximum temperature of the furnace and the temperature of the escaping gases, the efficiency, ■£, of the boiler and grate may be calculated by the formula E= - ~ , (9) in which TJ is the excess of temperature of the furnace and T f the excess of temperature of the escaping gases above that of the entering air. This hypothesis would be strictly true were there no loss of heat and were the weight of entering and discharge gases the same. The error in the calculation is not usually a serious one. Rankine, in his work on the steam-engine, pages 287 and 288, gives formulae for computing velocity of flow in flues, the head required to produce a given reading of the draught- gauge, and the required height of chimney. These formulae are developed from the experimental work of Peclet, and while they do not agree well with modern practice, still give interesting results for comparison. The practical application is shown in the following example of an analysis made at Cornell University, the coal burned being that obtained after deducting ashes and clinkers. 368. Form for Data and Computations in Flue-gas Analysis. — Test made Nov. 3, 1890. Determinations made by F. Land, H. B. Clarke, and O. G. Heilman. Location of plant, Ithaca, N. Y. Owners, Cornell University. Area of grate, so, ft 181 Area of chimney, so. ft. (symbol A) 12.5 Height of chimney, in feet (symbol H') 100 Length of heated flue (symbol /), feet ....,.« 130 Inside perimeter of chimney, feet 14 Ntimbet of boilers . . . , 3 Size of boilers : one of 61 H. P., two of 250 H. P. Kind of boilers : Water-tube, made by Babcock & Wilcox. Character of draught, forced by steam-blowers. 49Q EXPERIMENTAL ENGINEERING. [§368. CO 0"> w r^ C* w <" -I + + 1 CO n + Ste 1 ^ + ^^•^vg^ b b ^ ^ ^ -a bo c v S c 1 I ■« s? V v bjo V 73 ^0 > 0} - = ■c txo of u 1 £ C bO s- = 3 3 «j c fe 73 o ttJ X) CN a o s o Cfi tf * 72 C c sw CO o o ♦J ) bfi CU c c 3 >- V a rt oj 3 CT >H >-i a! 3 73 73 o O O sO 3 o S CO CU s II o Co co P c 73 1 S e'S. CHAPTER XV. METHODS OF TESTING STEAM-BOILERS. 369. Object of Testing Steam-boilers. — The object of the test must be clearly perceived in the outset ; it may be to determine the efficiency of a given boiler under given condi- tions; the comparative value of various fuels, or of different boilers working under the same conditions ; or the quantity of coal consumed and water used in providing steam for a given engine. The results of the test are usually expressed in pounds of water evaporated for one pound of the fuel used. The conditions of temperature and pressure between which boilers work vary within wide limits, the amount of heat ab- sorbed per pound of steam produced is not constant, and a standard of reference is necessary. Thus to convert a pound of steam from feed-water at a temperature of 70 degrees Fahr. »nto steam at 70 pounds absolute pressure per square inch will require, per pound of steam, (1 174.3 — 70 -(- 32) = 1 136.3 B. T. U. ; but to convert a pound of water at a temperature of 212 into steam at atmospheric pressure will require only 967 B. T. U. To compare the work done with a standard con- dition it is customary to express the, results of the test as equivalent to the evaporation per pound of fuel from water at 212 Fahr. to steam at atmospheric pressure, or, in other words, " from and at 212 ." The fuel also varies greatly in its evaporative power, as shown in the preceding chapter, and, moreover, a certain propor- tion is likely to drop through the grates unconsumed, so that 492 § 37 1 -] METHODS OF TESTING STEAM-BOILERS. 493 it is customary to reduce the results still further, and to find the evaporation per pound of the combustible part. 370. Definitions. — The following terms are frequently used : Actual evaporation. This is the evaporation per pound of fuel or of combustible under the actual conditions of the test, uncorrected for temperature of feed-water and for moisture. Equivalent evaporation from and at 21 2° is the amount of water that would have been evaporated had the temperature of feed-water been 21 2°, the steam dry and at atmospheric pressure. If x represent the quality of steam, e the factor of evaporation, the equivalent evaporation is equal to the actual multiplied by xe. Factor of evaporation is the ratio that the total heat, A, in one pound of steam at the given pressure and reckoned from the temperature, /, of feed-water, bears to the latent heat of evaporation at 212°, r. That is, X-t + 32 A table of the factors of evaporation is given in the Appendix. The ash is the actual incombustible part of the coal ; it is the residue which falls through the grates, less any combustible particles. The combustible is the fuel less the residue which falls through the grates ; it is the weight of that portion actually burned. In the absence of any determinations whatever, the combustible is frequently assumed as f of that of the coal. The quality of the steam is the percentage by weight of dry saturated steam in a mixture of steam and water. It is to be found by a throttling or separating calorimeter attached very near the boiler (see Articles 334 to 338). 371. The Efficiency of a Boiler.— The efficiency is the ratio of the heat utilized to that supplied. The heat supplied is measured by the coal consumed, multiplied by the heat value per pound. 494 EXPERIMENTAL ENGINEERING. [§ 37 2 There are in use two methods of denning and calculating the efficiency of a boiler. They are: ^,-c . r ^i i_ -i Heat absorbed per lb. combustible 1. Efficiency of the boiler = .— : 1- • Heating value of I lb. combustible 2. Efficiency of the boiler and grate _ Heat absorbed per lb. coal Heating value of I lb. coal The first of these is sometimes called the efficiency based on combustible, and the second the efficiency based on coal. The first is recommended as a standard of comparison for all tests, and this is the one which is understood to be referred to when the word " efficiency" alone, is used without qualifica- tion. The second, however, should be included in a report of a test, together with the first, whenever the object of the test is to determine the efficiency of the boiler and furnace together with the grate (or mechanical stoker), or to com- pare different furnaces, grates, fuels, or methods of firing. In calculating the efficiency where the coal contains an ap- preciable amount of surface moisture, allowance is to be made for the heat lost in evaporating this moisture by adding to the heat absorbed by the boiler the heat of evaporation thus lost. 372. The Heat-balance. — An approximate ''heat-bal- ance, or statement of the distribution of the heating value of the coal among the several items of heat utilized and heat lost should be included in the report of a test when analyses of the fuel and of the chimney-gases have been made. This should show both in B.T.U. and in per-cent the total heat received, that absorbed by the boiler, discharged in the flue with the products of combustion, that lost in evaporating moisture in the combustible, that due to incomplete combus- tion of carbon or hydrogen, and that not accounted for. 373. Horse-power of a Boiler. — The horse-power of a boiler is a conventional definition of capacity, since the boiler of itself does no work. As the weight of steam required for different engines varies within wide limits, an arbitrary rating was adopted by the judges of the Centennial Exhibition in I 375-] METHODS OF TESTING STEAM-BOILERS. 495 1876 as a standard nominal horse-power for boilers. This standard, which is now generally used, fixed one horse-power as equivalent to 30 pounds of water evaporated into dry steam per hour from feed-water at ioo° Fakr., and under a pressure of seventy pounds per square inch above the atmosphere. This is equal to an evaporation of 34.488 pounds from and at 21 2° F. The " unit of evaporation " being 966.7 B. T. U., the commer- cial horse-power is 34.488 X 966.7 ==' 33,391 B. T. U. 374. Graphical Log. — The results of a boiler-test can be represented graphically by considering intervals of time as proportional to the abscissae, and ordinates as proportional to the various pressures and temperatures measured, as shown in Fig. 225, from Thurston's Engine and Boiler Trials. Indicated Horse Power .(9216.1) 1.3010.50 11.10 11.30 11.60 12.10 12.30 12.50 1.10 1.30 1.50 2.10 2.30 2.50 3.10 3.30 3.50 4.10 .4.30 4.50 Fig. 225. 375. Method of Making a Boiler-test— A standard method of making a boiler-test was adopted by the American Society of Mechanical Engineers in 1884; this was revised in 1899. The first report is published in the Transactions, Vol. VI, the latter in Vol. XXI, with discussion on the same as appendices. 49 6 EXPERIMENTAL ENGINEERING. [§ 375 EULES FOE CONDUCTING BOILEE TEIALS. CODE OF 1899. I. Determine at the outset the specific object of the proposed trial, whether it be to ascertain the capacity of the boiler, its efficiency as a steam generator, its efficiency and its defects under usual working conditions, the economy of some particular kind of fuel, or the effect of changes of design, proportion, or opera- tion ; and prepare for the trial accordingly. (Appendix II.) II. Examine the boiler, both outside and inside ; ascertain the dimensions of grates, heating surfaces, and all important parts ; and make a full record, describing the same, and illustrating special features by sketches. The area of heating surface is to be computed from the surfaces of shells, tubes, furnaces, and fire- boxes in contact with the fire or hot gases. The outside diam- eter of water-tubes and the inside diameter of fire-tubes are to be used in the computation. All surfaces below the mean water level which have water on one side and products of com- bustion on the other are to be considered as water-heating surface, and all surfaces above the mean water level which have steam on one side and products of combustion on the other are to be considered as superheating surface. IIL Notice the general condition of the boiler and its equipment, and record such facts in relation thereto as bear upon the objects in view. If the object of the trial is to ascertain the maximum economy or capacity of the boiler as a steam generator, the boiler and all its appurtenances should be put in first-class condition. Clean the heating surface inside and outside, remove clinkers from the grates and from the sides of the furnace. Eemove all dust, soot, and ashes from the chambers, smoke connections, and flues. Close air leaks in the masonry and poorly fitted clean- ing doors. See that the damper will open wide and close tight. Test for air leaks by firing a few shovels of smoky fuel and im- mediately closing the damper, observing the escape of smoke through the crevices, or by passing the flame of a candle over cracks in the brickwork. IV. Determine the character of the coal to be used. For tests of the efficiency or capacity of the boiler for comparison with other boilers the coal should, if possible, be of some kind which is commercially regarded as a standard. For New England § 375-] TESTING STEAM-BOILERS. 497 and that portion of the country east of the Allegheny Moun- tains, good anthracite egg coal, containing not over 10 per cent, of ash, and semi-bituminous Clearfield (Pa.), Cumberland (Md.), and Pocahontas (Va.) coals are thus regarded. West of the Allegheny Mountains, Pocahontas (Va.) and New Kiver (W. Va.) semi-bituminous, and Toughiogheny or Pittsburg bituminous coals are recognized as standards.* There is no special grade of coal mined in the Western States which is widely recognized as of superior quality or considered as a standard coal for boiler testing. Big Muddy lump, an Illinois coal mined in Jackson County, 111., is suggested as being of sufficiently high grade to answer these requirements in districts where it is more conveniently obtainable than the other coals mentioned above. For tests made to determine the performance of a boiler with a particular kind of coal, such as may be specified in a contract for the sale of a boiler, the coal used should not be higher in ash and in moisture than that specified, since increase in ash and moisture above a stated amount is apt to cause a falling off of both capacity and economy in greater proportion than the proportion of such increase. V. Establish the correctness of all apparatus used in the test for weighing and measuring. These are : 1. Scales for weighing coal, ashes, and water. 2. Tanks, or water meters for measuring water. Water me- ters, as a rule, should only be used as a check on other measure- ments. For accurate work, the water should be weighed or measured in a tank. (See Chapter VII.) 3. Thermometers and pyrometers for taking temperatures of air, steam, feed-water, waste gases, etc. (Chapter XII.) 4. Pressure-gauges, draught-gauges, etc. (Chapter XI, pages 345 to 369.) The kind and location of the various pieces of testing appara- tus must be left to the judgment of the person conducting the test ; always keeping in mind the main object, i.e., to obtain authentic data. VI. See that the boiler is thoroughly heated before the trial to its usual working temperature. If the boiler is new and of a * These coals are selected because they are about the only coals which possess the essentials of excellence of quality, adaptability to various kinds of furnaces, grates, boilers, and methods of firing, and wide distribution and general accessi- bility in the markets. See various appendices in Vol. XXI, Transactions A. S. M. E. 49 8 EXPERIMENTAL ENGINEERING. [§ 375- form provided with a brick setting, it should be in regular use at least a week before the trial, so as to dry and heat the walls. If it has been laid off and become cold, it should be worked before the trial until the walls are well heated. VII. The hoiler and connections should be proved to be free from leaks before beginning a test, and all water connections, includ- ing blow and extra feed pipes, should be disconnected, stopped with blank flanges, or bled through special openings beyond the valves, except the particular pipe through which water is to be fed to the boiler during the trial. During the test the blow-off and feed pipes should remain exposed to view. If an injector is used, it should receive steam directly through a felted pipe from the boiler being tested.* If the water is metered after it passes the injector, its tem- perature should be taken at the point where it leaves the injector. If the quantity is determined before it goes to the injector the temperature should be determined on the suction side of the injector, and if no change of temperature occurs other than that due to the injector, the temperature thus determined is properly that of the feed-water. When the temperature changes between the injector and the boiler, as by the use of a heater or by radi- ation, the temperature at which the water enters and leaves the injector and that at which it enters the boiler should all be taken. In that case the weight to be used is that of the water leaving the injector, computed from the heat units if not directly measured, and the temperature, that of the water entering the boiler. Let w = weight of water entering the injector. x = " " steam " h 1 — heat units per pound of water entering injector. \ = " " " " " steam it A 3 = " " " " " water leaving iC Then, w + x = weight of water leaving injector. h 3 — h } x = W j 1 — - T L - K — K * In feeding a boiler undergoing test with an injector taking steam from another boiler, or from the main steam pipe from several boilers, the evaporative results may be modified by a difference in the quality of the steam from such source compared with that supplied by the boiler being tested, and in some cases the connection to the injector may act as a drip for the main steam pipe. If it is known that the steam from the main pipe is of the same pressure and quality as that furnished by the boiler undergoing the test, the steam may be taken from such main pipe. § 375-] TESTING STEAM-BOILERS. 499 See that the steam main is so arranged that water of con- densation cannot run back into the boiler. VIII. Duration of the Test. — For tests made to ascertain either the maximum economy or the maximum capacity of a boiler, irre- spective of the particular class of service for which it is regularly used, the duration should be at least 10 hours of continuous run- ning. If the rate of combustion exceeds 25 pounds of coal per square foot of grate surface per hour, it may be stopped when a to- tal of 250 pounds of coal has been burned per square foot of grate. In cases where the service requires continuous running for th,e whole 24 hours of the day, with shifts of firemen a number of times during that period, it is well to continue the test for at least 24 hours. When it is desired to ascertain the performance under the working conditions of practical running, whether the boiler be regularly in use 24 hours a day or only a certain number of hours out of each 24, the fires being banked the balance of the time, the duration should not be less than 24 hours. IX. Starting and Stopping a Test. — The conditions of the boiler and furnace in all respects should be, as nearly as possible, the same at the end as at the beginning of the test. The steam pressure should be the same ; the water level the same ; the fire upon the grates should be the same in quantity and condition ; and the walls, flues, etc., should be of the same temperature. Two methods of obtaining the desired equality of conditions of the fire may be used, viz. : those which were called in the Code of 1885 " the standard method " and " the alternate method," the latter being employed where it is inconvenient to make use of the standard method.* X. Standard Method of Starting and Stopping a Test. — Steam being raised to the working pressure, remove rapidly all the fire from the grate, close the damper, clean the ash pit, and as quickly as possible start a new fire with weighed wood and coal, noting the time and the water level t while * The Committee concludes that it is best to retain the designations "stand- ard" and " alternate," since they have become widely known and established in the minds of engineers and in the reprints of the Code of 1885. Many engineers prefer the " alternate" to the "standard " method on account of its being less liable to error due to cooling of the boiler at the beginning and end of a test. f The gauge-glass should not be blown out within an hour before the water level is taken at the beginning and end of a test, otherwise an error in the read- ing of the water level may be caused by a change in the temperature and density of the water in the pipe leading from the bottom of the glass into the boiler. 500 EXPERIMENTAL ENGINEERING. [§ 375. the water is in a quiescent state, just before lighting the fire. At the end of the test remove the whole fire, which has been burned low, clean the grates and ash pit, and note the water level when the water is in a quiescent state, and record the time of hauling the fire. The water level should be as nearly as possible the same as at the beginning of the test. If it is not the same, a correction should be made by computation, and not by operating the puiLp after the test is completed. XI. Alternate Method of Starting and Stepping a Test. — The boiler being thoroughly heated by a preliminary run, the fires are to be burned low and well cleaned. Note the amount of coal left on the grate as nearly as it can be estimated ; note the pressure of steam and the water level. Note the time, and record it as the starting time. Fresh coal which has been weighed should now be fired. The ash pits should be thor- oughly cleaned at once after starting. Before the end of the test the fires should be burned low, just as before the start, and the fires cleaned in such a manner as to leave a bed of coal on the grates of the same depth, and in the same condition, as at the start. When this stage is reached, note the time and record it as the stopping time. The water level and steam pressures should previously be brought as nearly as possible to the same point as at the start. If the water level is not the same as at the start, a correction should be made by computation, and not by operating the pump after the test is completed. XII. Uniformity of Conditions. — In all trials made to ascertain maximum economy or capacity, the conditions should be main- tained uniformly constant. Arrangements should be made to dispose of the steam so that the rate of evaporation may be kept the same from beginning to end. This may be accom- plished in a single boiler by carrying the steam through a waste steam pipe, the discharge from which can be regulated as desired. In a battery of boilers, in which only one is tested, the draft may be regulated on the remaining boilers, leaving the test boiler to work under a constant rate of production. Uniformity of conditions should prevail as to the pressure of steam, the height of water, the rate of evaporation, the thickness of fire, the times of firing and quantity of coal fired at one time, and as to the intervals between the times of cleaning the fires. § 375-1 TESTING STEAM-BOILERS. 5 01 The method of firing to be carried on in such tests should be dictated by the expert or person in responsible charge of the test, and the method adopted should be adhered to by the fire- man throughout the test. XIII. Keeping the Records. — Take note of every event con* n?,cted with the progress of the trial, however unimportant it may appear. Record the time of every occurrence and the time of taking every weight and every observation. The coal should be weighed and delivered to the fireman in equal proportions, each sufficient for not more than one hour's run, and a fresh portion should not be delivered until the pre- vious one has all been fired. The time required to consume each portion should be noted, the time being recorded at the instant of firing the last of each portion. It is desirable that at the same time the amount of water fed into the boiler should be accurately noted and recorded, including the height of the water in the boiler, and the average pressure of steam and tem- perature of feed during the time. By thus recording the amount of water evaporated by successive portions of coal, the test may be divided into several periods if desired, and the de- gree of uniformity of combustion, evaporation, and economy analyzed for each period. In addition to these records of the coal and the feed water, half hourly observations should be made of the temperature of the feed water, of the flue gases, of the external air in the boiler-room, of the temperature of the fur- nace when a furnace pyrometer is used, also of the pressure of steam, and of the readings of the instruments for determining the moisture in the steam. A log should be kept on properly prepared blanks containing columns for record of the various observations. When the " standard method " of starting and stopping the test is used, the hourly rate of combustion and of evaporation and the horse-power should be computed from the records taken during the time when the fires are in active condition. This time is somewhat less than the actual time which elapses be- tween the beginning and end of the run. The loss of time due to kindling the fire at the beginning and burning it out at the and makes this course necessary. XIV. Quality of Steam. — The percentage of moisture in the steam should be determined by the use of either a throttling or 502 • EXPERIMENTAL ENGINEERING. \% 37$.. a separating steam calorimeter. The sampling nozzle should be placed in the vertical steam pipe rising from the boiler. It should be made of J-inch pipe, and should extend across the diameter of the steam pipe to within half an inch of the oppo- site side, being closed at the end and perforated with not less than twenty |-inch holes equally distributed along and around its cylindrical surface, but none of these holes should be nearer than \ inch to the inner side of the steam pipe. The calorim eter and the pipe leading to it should be well covered with felting. Whenever the indications of the throttling or separat- ing calorimeter show that the percentage of moisture is irregu- lar, or occasionally in excess of three per cent., the results should be checked by a steam separator placed in the steam pipe as close to the boiler as convenient, with a calorimeter in the steam pipe just beyond the outlet from the separator. The drip from the separator should be caught and weighed, and the percent- age of moisture computed therefrom added to that shown by the calorimeter. (See Chapter XIII, page 438.) ) Superheating should be determined by means of a thermome- ter placed in a mercury well inserted in the steam pipe. The degree of superheating should be taken as the difference be- tween the reading of the thermometer for superheated steam and the readings of the same thermometer for saturated steam at the same pressure as determined by a special experiment, and not by reference to steam tables. For calculations relating to quality of steam and corrections for quality of steam, see Chapter XIII, pages 393 and 435. XV. Sampling the Coal and Determining its Moisture. — As each barrow load or fresh portion of coal is taken from the coal pile, a representative shovelful is selected from it and placed in a barrel or box in a cool place and kept until the end of the trial. The samples are then mixed and broken into pieces not exceeding one inch in diameter, and reduced by the process of repeated quartering and crushing until a final sample weighing about iiYe pounds is obtained, and the size of the larger pieces is such that they will pass through a sieve with J-inch meshes. From this sample two one-quart, air-tight glass preserving jars, or other air-tight vessels which will prevent the escape of moist- ure from the sample, are to be promptly filled, and these sam- ples are to be kept for subsequent determinations of moisture and of heating value and for chemical analyses. During the § 375-] TESTING STEAM-BOILERS. 5°3 process of quartering, when the sample has been reduced to about 100 pounds, a quarter to a half of it may be taken for an approximate determination of moisture. This may be made by placing it in a shallow iron pan, not over three inches deep, carefully weighing it, and setting the pan in the hottest place that can be found on the brickwork of the boiler setting or flues, keeping it there for at least 12 hours, and then weighing it. The determination of moisture thus made is believed to be ap- proximately accurate for anthracite and semi-bituminous coals, and also for Pittsburg or Youghiogheny coal ; but it cannot be relied upon for coals mined west of Pittsburg, or for other coals containing inherent moisture. For these latter coals it is impor- tant that a more accurate method be adopted. The method recommended by the Committee for all accurate tests, whatever the character of the coal, is described as follows : Take one of the samples contained in the glass jars, and subject it to a thorough air-drying, by spreading it in a thin layer and exposing it for several hours to the atmosphere of a warm room, weighing it before and after, thereby determining the quan- tity of surface moisture it contains. Then crush the whole of it by running it through an ordinary coffee mill adjusted so as to pro- duce somewhat coarse grains (less than T Vinch), thoroughly mix the crushed sample, select from it a portion of from 10 to 50 grams, weigh it in a balance which will easily show a variation as small as 1 part in 1,000, and dry it in an air or sand bath at a temperature between 240 and 280 degrees Fahr. for one hour. Weigh it and record the loss, then heat and weigh it again repeatedly, at intervals of an hour or less, until the minimum weight has been reached and the weight begins to increase by oxidation of a portion of the coal. The difference between the original and the minimum weight is taken as the moisture in the air-dried coal. This moisture test should preferably be made on duplicate samples, and the results should agree within 0.3 to 0.4 of one per cent., the mean of the two determinations being taken as the correct result. The sum of the percentage of moisture thus found and the percentage of surface moisture previously determined is the total moisture. XVI. Treatment of Ashes and Refuse. — The ashes and refuse are to be weighed in a dry state. If it is found desirable to* show the principal characteristics of the ash, a sample should be subjected to a proximate analysis and the actual amount- 504 EXPERIMEN TA L ENG I NEE RING E§ 375- of incombustible material determined. For elaborate trials a complete analysis of the ash. and refuse should be made. XVII. Calorific Tests and Analysis of Coal.— The quality of the fuel should be determined either by heat test or by analysis, or by both. The rational method of determining the total heat of combus- tion is to burn the sample of coal in an atmosphere of oxygen gas, the coal to be sampled as directed in Article XV. of this code. (See Chapter XIV.) The chemical analysis of the coal should be made only by an expert chemist. The total heat of combustion computed from the results of the ultimate analysis may be obtained by the use of Dulong's formula (with constants modified by recent determinations), viz. : 14,600 C + 62,000 (*-D + 4000 s, in which C, H, 0, and S refer to the proportions of carbon, hy- drogen, oxygen, and sulphur respectively, as determined by the ultimate analysis.* It is desirable that a proximate analysis should be made, thereby determining the relative proportions of volatile matter and fixed carbon. These proportions furnish an indication of the leading characteristics of the fuel, and serve to fix the class to which it belongs. (Page 470.) As an additional indication of the characteristics of the fuel, the specific gravity should be determined. XVIII. Analysis of Flue Gases. — The analysis of the flue gases is an especially valuable method of determining the relative value of different methods of firing, or of different kinds of fur- naces. In making these analyses great care should be taken to procure average samples — since the composition is apt to vary at different points of the flue pages 475 to 492). The com- position is also apt to vary from minute to minute, and for this reason the drawings of gas should last a considerable period of time. Where complete determinations are desired, the analyses should be intrusted to an expert chemist. For approximate determinations the Orsat t or the Hempel J apparatus may be used by the engineer. (See pages 481 and 483.) * Favre and Silberraan give 14,544 B.T.U. per pound carbon ; Berthelot 14,64V B.T.U. Favre and Silberman give 62,032 B.T.U. per pound hydrogen ; Thomseu 61,816 B.T.U. + See R. S. Hale's paper on " Flue Gas Analysis," Transactions, vol xviil., p. 901. X See Hempel's " Methods of Gas Analysis " (Macmillan & Co.). § 375-] TESTING STEAM-BOILERS. 505 For the continuous indication of the amount of carbonic acid present in the flue gases, an instrument may be employed which shows the weight of the sample of gas passing through it. XIX. Smoke Observations. — It is desirable to have a uni- form system of determining and recording the quantity of smoke produced where bituminous coal is used. The system com- monly employed is to express the degree of smokiness by means of percentages dependent upon the judgment of the observer. The Committee does not place much value upon a percentage method, because it depends so largely upon the personal ele- ment, but if this method is used, it is desirable that, so far as possible, a definition be given in explicit terms as to the basis and method employed in arriving at the percentage. The actual measurement of a sample of soot and smoke by some form of meter is to be preferred. (See Appendices XXXIV. and XXXV.) XX. Miscellaneous. — In tests for purposes of scientific re- search, in which the determination of all the variables entering into the test is desired, certain observations should be made which are in general unnecessary for ordinary tests. These are the measurement of the air supply, the determination of its contained moisture, the determination of the amount of heat lost by radiation, of the amount of infiltration of air through the setting, and (by condensation of all the steam made by the boiler) of the total heat imparted to the water. As these determinations are rarely undertaken, it is not deemed advisable to give directions for making them. XXI. Calculations of Efficiency. — Two methods of defining and calculating the efficiency of a boiler are recommended. They are : 1 -n«? • <3- O IN in d O ci O c5 T3 u SB E G cw Q erf «< a £ c O O CT> vO O Tt O CJ CO K in m r>. T O O J3 ■* ^ O CO S ■"• O O OJ* O" ^ •2 O £ in "13 vO B 2 6 6 d "a. CO TD rt < £ § CO P4 to' CO \n "a. CO O H -*-+ in O 6 6 00 CO CO d O CJ /!-» Q c c 8 1/ w CO 13 £ u erf * 10 ■> m 10 in CN CO in < C • O* d M ' d 'a, CO < ^ § .5PW u 2 fe >< T • co s 1) coU t- c C c E in cn h d CO 6 CO IN CO CO d .d <*■ I *^ CO g> CO > 1 2 ClH (—1 CO oco pa • C c E co in IN vO X! in 0. to CO c c g fi° < > " O d CN Jis c 3 b a . 43 > coCJ c c ; 5 1 vO r^ co 2o ! jj XT, a> CO rf O erf U c PC > °. d d in CN O '5. CO vO c u «J ai c« c en O V .5 10* .52 • *Su ; ! > O £ c V £ 1. 1/ c i CO T3 C ; 3 c c l/i 'a. CO G C w 'a 6" s -a a. VI S G >- O c S cu > - G 6 "u c V a* C .s < 1 ! T < . a 3 <■ 3 * • "a; : £ S Q < S Q '"u 6 O c •w ca ~ be a 1 §39°-] THE STEAM-ENGINE INDICATOR. 529 The Bachelder indicator (see Fig. 238) is made with a flat spring, and to a certain extent the tension is regulated by changing its fulcrum. 5. The Paper-drum, to which the card is attached, consists of a brass cylinder attached to a spindle which is connected to the drum-spring, the action of which has been described. The drum can be removed readily, and the tension on the spring changed at pleasure. Two clips or fingers serve to hold the paper in position. 6. The Cord used, although not a part of the indicator, must be selected with great care; it must be of a character not to be stretched by the forces acting on the indicator. Steel wire is sometimes used for this purpose. Any variation in length of the connecting cord affects the abscissa in the diagram. 7. The Reducing-motioits, also not a part of the indicator, must give an exact reproduction, on a smaller scale, of the motion of the piston ; otherwise the length of the indicator- diagram will either not be accurately reduced, or the events will not be properly timed. 389. The table opposite gives the actual dimensions of the principal indicators described, as obtained by careful measure- ment of those owned by Sibley College. 390. Reducing-motions for Indicators. — The maximum motion of the indicator-drum is usually less than four inches ; consequently it can seldom be connected directly to the cross- head of the engine, but must be connected to some apparatus which has a motion less in amplitude but corresponding exactly in all its phases to that of the cross-head. This apparatus is termed a reducing-motion. Since the horizontal components of the indicator-diagram and consequently its area and form depend upon the motion of the piston, it is evident that the accuracy of the diagram depends upon the accuracy of the reducing-motion. Various combinations of levers and pulleys have been used * for reducing-motions, a few of which will be See Thurston's Engine and Boiler Trials. 530 EXPERIMENTAL ENGINEERING. [§ 390. described. Several simple forms of reducing-motion are given here as suggestions, but it is expected that the student will devise other motions if required, and ascertain the amount of error, if any, in the motion used. FlG. 242. — The Simple Pendulum Reducing-motion. The cheaper and more easily arranged reducing-motion* consist usually of some form of swinging lever or pendulum (see Fig. 242) pivoted at one point, and connected at its lower end to the cross-head by a lever. The indicator-cord is attached to the swinging lever at some point having the proper motion. These motions never give an exact reproduc- §390.] THE STEAM-ENGINE INDICATOR. 531 tion of the motion of the piston ; but if the pendulum and cross-head are simultaneously at the centre of the stroke, the error is very small. Fig. 243.— The Brumbo Pulley. A form of the pendulum-motion, called the Brumbo pulley \ is frequently used as shown in Fig. 243. The pendulum is some- times modified, so that its lower end is pivoted directly to a Fig. 244 —The Pantograph. point in the cross-head, its upper half moving vertically in a swinging tube. The cord is attached to an arc on this tube as in Fig. 242. 532 EXPERIMENTAL ENGINEERING. L§ 391. The pantograph, or lazy-tongs, as shown in Fig. 244 with plan of method of attachment shown in Fig. 245, is a perfect reducing motion, but because of its numerous joints it is not adapted to high-speed engines. Fig. 245.— Method of Attaching the Pantograph. A form of pantograph with four joints only, shown in Fig. 246, is much better adapted to high-speed engines than the one with more numerous joints shown above. Fig. 246.— Method of Using the Pantograph. Reducing-wheels. — Reducing wheels, which consist of a large and a small pulley (see Fig. 247) attached to the same axis, are extensively used by engineers. The method of attach- ing this reducing-motion to an engine is shown in Fig. 248. 391. The Indicator-cord.— The indicator-cord should be as nearly as possible inextensible, since any stretch of the cord causes a corresponding error in the motion of the indicator- arum. As it is nearly impossible to secure a cord that will not § 391-1 THE STEAM-ENGINE INDICATOR. 533 stretch, it should be made as short as possible, and a fine wire of steel or iron or of hard-drawn brass should be used if practicable. Fig. 247.— Schaeffer and Budenberg Reducing-motiok. Fig. 248.— Webster and Perks Reducing-motion. The indicator-cord supplied by makers of indicators is a braided hard cotton cord, stretching but little under the required stress. 5 34 EXPERIMENTAL ENGINEERING. [§ 392. If a "rig" is to be permanently erected, it is recommended that the motion be taken from a sliding bar attached to the cross- head and extending to or beyond the indicators. The angle of the cord with the path of motion of the cross-head should be as nearly constant as possible, since any variation in this angle will cause a distortion in the motion of the drum. In Figs. 243, 246, and 248 will -be seen devices to over- come the effect of angularity of the indicator-cord. The indicator-cord is usually hooked and unhooked into a loop in a cord fastened to the reducing-motion. A very con-, venient form for such a loop, and one that can readily be ad- justed, is shown in Fig. 249. The indicator-cord is usually Fig. 249.— The Loop. provided with a hook fastened as shown in Fig. 182, which is hooked when diagrams are needed into the loop attached to the reducing-motion. The author would strongly urge that the indicator-cord be arranged so as to avoid the necessity of frequent hooking and unhooking, thus throwing severe and unnecessary strains on the indicator-drum and cord : this can be done by connecting a point on the cord near the indicator with a spiral spring fastened to a fixed point in the line of the cord produced. This spring should be strong enough to keep the slack out of the cord. When it is desired to stop the motion, the drum-cord is pulled toward the reducing-motion to the extent of its travel, and held or tied until another diagram is needed. Some of the indicator-drums are provided with ratchets or detents that serve the same purpose. When several indicators are in use and simultaneous diagrams are required, a detent-motion worked by an electric current will prove very satisfactory. In case of compound engines when numerous indicators are re- quired these suggestions become of even greater importance. 392. Standardization of the Indicator. — The accuracy of §393-] THE STEAM-ENGINE INDICATOR. 535 the indicator-diagram depends upon the following features, all of which should be the subject of careful examination : (1) Uniformity of the indicator-spring. (2) Accuracy of the drum-motion. (3) Parallelism of the piston-movement to the cylinder. (4) Parallelism of the pencil-movement to the axis of the drum. (5) Friction of the piston and pencil-movements. (6) Lost motion. The calibration of these parts should be made as nearly as possible under the conditions of actual use and as described in the following articles. 393. Calibration of the Indicator-spring.— The accuracy of the indicator-spring is only to be determined by comparison with standardized apparatus. This may be done as follows : Firstly : with the open mercury column. This can be done with steam only, as the leakage of water past the loosely-fitting piston would render it impossible to maintain the pressure. Insert the spring; see that the indicator is oiled and in good condition. Attach the indicator as previously explained for the calibration of steam-gauges, page 366 ; put paper on the drum; turn on steam-pressure until the instrument is warm; turn off the steam, and pressing the pencil lightly against the paper, turn the drum by hand, thus drawing the atmospheric line. Apply pressure by increments equal to one fifth that marked on the spring, keeping the motion continually upward, stopping only long enough to draw the line for the required pressure. Take ten increments first up then down ; the average position of any line will give the ordinate corresponding to that pressure ; the difference between any two lines (see Fig. 250) will be twice the friction of indicator-piston at that point. Second : with the standard scales. This method was devised by Professor M. E. Cooley, of Ann Arbor. In this case the indicator is supported on a bracket above the platform of the scales. Force is applied to the indicator-piston by means of a rod which can be raised or lowered by turning a hand-wheel; this rod terminates above in a cap nicely fitted to the under 53^ EXPERIMENTAL ENGINEERING. [§ 393- side of the piston, and below it rests on a pedestal standing on the platform of the scales. Any force applied to compress the spring is registered on the scale-beam. The reading of the scale-beam is that force acting on one-half square inch, as the piston is usually one-half square inch in area ; this is to be multi- plied by 2 to correspond with the reading given by the indica- tor-spring. The indicator can be heated by wrapping rubber tubing around the cylinder and passing steam through the tube. y TTp / Down. feu 55 b'yj 45 40 S3 SO 25 20 Jb 10 b Tip. 1) * Down. Fig 250. — iNDiCATOk-spRiNG Calibration. FORM FOR CALIBRATION OF INDICATOR-SPRING. By comparison with Make of indicator Mark and No. of spring Date. Observers No. Gauge. Actual Pressure. Ordinates. • Actual Pressure. Inches Lbs. Inches. Pounds. Up. Down. Mean. Error. Per cent. § 3941 THE STEAM-ENGINE INDICATOR. 537 The indicator-springs should be calibrated as nearly as possi- ble under the conditions of actual use. The springs are elon- gated by increase in temperature and weakened because of that fact, so that the calibration of the spring cold will give results which differ by approximately 3 per cent, from the calibration when the spring is at a temperature approximating 212 , as has been proved by extended experiments.* Various forms of apparatus have been devised for the testing of indicator-springs both cold and hot. A simple device is shown Fig. 251.— Indicator-spring Testing Device. in Fig. 251 consisting of a cylinder, A, supported on a bracket above a pair of scales and fitted with a piston having an area of cross-section exactly the same as the indicator-piston. A rod from this piston extends downward on to a platform scale, as shown in the figure. The indicator is connected by suitable * Experiments, Marks and Barraclough, Vol. XV, Transactions A. S. M. E. 538 EXPERIMEN TA L ENGINEERING. [§ 395- piping to the upper end of the cylinder. The steam for the pur- pose of calibration is adjusted in pressure by a valve, E, before it enters the drum, B. The pressure in the steam in the drum is shown on the attached gauge. This steam-pressure exerts an upward pressure on the indicator-piston and a downward pressure on the piston in the cylinder, A, which latter, cor- rected for dead weight, is measured on the weighing-scales shown. A modification of this apparatus is shown in Fig. 252, which consists of a vessel, A, into which steam can be admitted p%= Fig. 252.— Indicatob.-spring Testing Apparatus. at any desired pressure. The pressure in the vessel acts on the piston, K, which is J square inch in area and may be measured by the attached scale-beam. The same pressure reacts on the indicator-piston. By taking simultaneous read- ings of the pressure on the piston, K, and on the indicator- piston, the calibration may be performed substantially as described. This apparatus has proved satisfactory after an extensive use. It can be purchased of Schaeffer & Budenberg of Brooklyn, N. Y. § 395-] THE STEAM-ENGINE INDICATOR. 539 394. Test for Parallelism of the Pencil-movement to the Axis of the Drum. — This is tested by removing the spring from the indicator, rotating the drum, and drawing an atmos- pheric line ; then hold the drum stationary in various positions and press the piston of the indicator upward throughout its full stroke, while the pencil is in contact with the paper. The lines thus drawn should be parallel to each other and perpen- dicular to the atmospheric line. Parallelism of the piston-movement to the cylinder axis is shown when the increments for equal pressure are the same in all positions of the diagram. It is important that the piston is not cramped or pushed over by the spring, in any part of its stroke. Friction of the piston and pencil-movement can be determined in the calibration of the indicator-spring as explained. When the spring is removed from the indicator, the parts should work easily and freely but without lost motion. 395. Accuracy of the Drum-motion. — The accuracy of the drum-motion depends on the form of the drum-spring, the mass moved, the length of the diagram, and the elasticity of the connecting cord. Indicator-drums would revolve in a harmonic motion if the inertia of the mass could be neglected. The speed of ro- tation is greatest near the half-stroke of the piston ; therefore, if the drum-spring tension can be adjusted so as to exactly counterbalance the effect of the inertia of the moving parts, the theoretical harmonic motion will be nearly realized. In most indicator drum-springs the tension increases directly in proportion to the extension. Since the speed of the drum is greatest at half stroke, at this point the drum will run ahead of its theoretic motion if the spring tension is not suffi- cient to counteract the effect of the inertia of the moving parts. Therefore if the tension of the drum-spring is adjusted to exactly balance the effect of inertia at half-stroke, the card should be as nearlyas possible theoretically correct. To ob- tain the value of this tension, use is made of the formulae for the harmonic motion of a body as follows. Let 540 EXPERIMEN TA L ENGINEERING. [§ 395- t = time of \ length of card = \ of a revolution ; s = i length of card ; t — Va ; (see Church's Mechanics.) P — pM — T, where T is the tension in the spring at £ the length of the card. M = — sa\ W a = — == mass of rotating parts ; a = /. t = yws 4 W s T ~Ms The foot, pound, second system is used in the formulae, The results are shown in the following table. TABLE FOR TENSION ON INDICATOR DRUM OF i.o lb. WEIGHT. Revolutions Pounds of Revolutions Pounds of per Force to pull per Force to pull Minute. Drum 1.75 in. Minute. Drum 1.75 in. 50 O IO 225 2.5 75 O.25 250 3.15 100 O.50 275 3.8 125 0.8 300 4-55 150 I- 15 350 6.15 175 1-55 375 7.0 200 2.0 400 8.0 The total error introduced by inertia can be determined as follows : Attaching the indicator to an engine, permit it to run sufficiently long to harden the cord and the knots, then stop the engine, turn it over by hand and find the length of the diagram with the speed so small as to eliminate the inertia ; leaving the cords connected, run the engine at full speed : any § 395-] THE STEAM-ENGINE INDICATOR. 54 1 inertia etitct will be shown by an increase in the length of the diagram. This increase in length may be partly due to stretch in the indicator-cord caused by inertia of the rotating parts, as even with the best tension on the springs, determined as ex- plained, it may be sensibly lessened by the use of wire. A simple arrangement, consisting of a pin and connecting-rod leading to the face-plate of a lathe, the tool-rest being utilized as a guide, may be used instead of an engine for obtaining complete determination of this error. The amount of error caused by over-travel of the drum has been found by experi- ment to be from 0.5 to 1.5 per cent at 250 revolutions, with the best tension on the drum spring. Uniform Tension on the Indicator-cord. — It is often impor- tant to determine whether the drum-spring maintains a uniform tension on the cord, or whether it alternately exerts a greater Fig. 253. — Brown Drum-spring Testing-device or less stress; this may be determined by the instrument shown in Fig. 253. The testing instrument consists of a wooden plate, A, on one end of which is fastened the brass frame, BB y carrying the slide, C, with its cross-head, D. The head of the spring, R, is screwed to the cross-head, while the other end is connected with the bent lever, G, carrying the pencil The connecting-rod, E, which moves the slide, C, receives its motion from a crank not shown in the figure. The swinging leaf upholds the paper on which the diagram is to be ' taken. The indicator to be tested is clamped to the plate as shown, and the drum-cord connected with the free end of the spring. The crank is made to move at the speed at which it is desired to test the drum-spring. The paper is then pressed up to the pencil and the diagram taken. If the tension 542 EXPERIMENTAL ENGINEERING. 1% 39^- on the cord is constant, the lines which represent the forward and return strokes will be parallel to the motion of the slide; but, if the stress is not constant, the pencil will rise and fall as the stress is greater or less. The line drawn when the cord has been detached from the indicator (Fig. 254) is the line of no stress. In the diagram, horizontal distance represents the position of the drum, and vertical distance represents strain on the cord. The perfect diagram would be two lines near together and parallel to the line of no stress, and would repre- sent a constant stress, and consequently a constant stretch of the cord, from which no error would result. When the length of the cord and the amount it will stretch under varying stresses is known, the errors in the diagram due to stretch of cord caused by irregular stresses applied by the drum-spring can be calculated. Indicator. 250 revolutions A Indicator. 250 revolutions Indicator. 400 revolutions Indicator. 400 revolutions D Fig. 254.— Diagrams showing Variation in Drum-spring Stress. 396. To Adjust and Calibrate a Drum-spring. 1. Find the weight of the moving parts, and compute the theoretic stress on the indicator-cord. (See Article 395.) 2. Attach to the face-plate of a lathe in such a manner that the speed can be varied within wide limits. 3. Draw diagrams at various rates of speed, various lengths of stroke, and various tensions on the drum-spring. 4. Find the en or in the diagram for each condition. Plot the results, and deduce from the curve shown the best length of diagram and best tension for each speed. § 397-] THE STEAM-ENGINE INDICATOR. 543 5. Repeat the same operations with the Brown spring test- ing-device, and compare the results. 397. Method of Attaching the Indicator to the Cylinder. — Holes for the indicator are drilled in the clearance-spaces at the ends of the cylinders, in such a position that they are not even partially choked by any motion of the piston. These holes are fitted for connection to half-inch pipe : they are located preferably in horizontal cylinders at the top of the cylinder ; but if the clearance-spaces are not sufficiently great they may be drilled in the heads of the cylinder, and connec- tions to the indicators made by elbows. The holes for the in- Fig. 255.— Section of Crosby Three-way Cock. Fig. 256. — Elevation of Crosby Three-way Cock. dicator-cocks are usually put in the cylinders by the makers of the engine, but in case they have to be drilled great care must be exercised that no drill-chips get into the cylinder. This may be entirely prevented by blocking the piston and admitting twenty or thirty pounds of steam-pressure to the cylinder. The connections for the indicator are to be made as short and direct as possible. Usually the indicator-cock can be screwed directly into the holes in the cylinder, and an indicator attached at each end. In case a single indicator is used to take dia- grams from both ends of the cylinder, half-inch piping with as easy bends as possible is carried to a three-way cock, as in Fig. 544 EXPERIMENTAL ENGINEERING. [§ 398. 194, to which the indicator is attached. The cock is located as nearly as possible equidistant from the two ends of the cylinder. The form of the three-way cock is shown in Figs. 199 and 200. and the method of connecting in Fig. 194. In connecting an indicator-cock, use a wrench very care- fully ; but on no account use lead in the connections, as it is likely to get in the indicator and prevent the free motion of the piston. 398. Directions for Taking Indicator-diagrams. Firstly, provide a perfect reducing-motion, and make ar- rangements so that the indicator-drum can be stopped or started at full speed of the engine. (See Article 391.) Secondly, clean and oil the indicator, and attach it to the engine as previously explained. Insert proper spring ; oil piston with cylinder-oil. Thirdly, put proper tension on the drum-spring (see Article 395) ; see that the pencil-point is sharp and will draw a fine- line. Fourthly, connect the indicator-cord to the reducing-motion; turn the engine over and adjust the cord so that the indicator- drum has the proper movement and does not hit the stops. Fifthly, put the paper on the drum ; turn on steam, allow it to blow through the relief-hole in the side of the cock ; then admit steam to the indicator-cylinder, close the indicator-cock, start the drum in motion, and draw the atmospheric line with engine and drum in motion ; open the cock, press the pencil lightly and take the diagram ; close the cock and draw a second atmospheric line. Do not try to obtain a heavy diagram, as all pressure on the card increases the indicator friction and causes more or less error. Take as light a card as can be seen ; brass point and metallic paper are to be used when especially fine diagrams are required. When the load is varying, and the average horse-power is required, it is better to allow the pencil to remain during a number of revolutions, and to take the mean effective pressure from the several diagrams drawn. § 399-] THE STEAM-ENGINE INDICATOR. 545 Remove card after diagram has been taken, and on the back of card make note of the following particulars, as far as conveniently obtainable : No Time Date. Diagram from M Engine Diameter of cylinder Length of stroke Revolutions per minute , Pressure of steam, in lbs., in boiler. Position of throttle-valve Vacuum per gauge, in inches Temperature of hot-well Scale of spring , Inside diameter of feed-pipe " " " exhaust-pipe Valves Built by. Pressure . Barometer reads ..Throttle.. Regulator Remarks Sixthly, after a sufficient number of diagrams has been taken, remove the piston, spring, etc., from the indicator while it is still upon the cylinder ; allow the steam to blow for a moment through the indicator-cylinder, and then turn attention to the piston, spring, and all movable parts, which must be thoroughly wiped, oiled, and cleaned. Particular attention should be paid to the springs, as their accuracy will be impaired if they are al- lowed to rust ; and great care should be exercised that no gritty substance be introduced to cut the cylinder or scratch the piston. Be careful never to bend the steel bars or rods. 399. Care of the Indicator. — The steam-engine indicator is a delicate instrument, and its accuracy is liable to be im- paired by rough usage. It must be handled with care, kept clean and bright ; its journals must be kept oiled with suitable oil. It must be kept in adjustment. In general, all screws can be turned by hand sufficiently tight,' and no wrench should be used to connect or disconnect it. Never use lead on the con- nections. Before using it, take it apart, clean and oil it. Try each part separately. See if it works smoothly ; if so, put it together without the spring. Lift the pencil-lever, and let it 546 EXPERIMENTAL ENGINEERING. [§399- fall ; if perfectly free, insert the spring as explained, and see that there is no lost motion ; oil the piston with cylinder-oil, and all the bearings with nut- or best sperm-oil. Give it steam, but do not attempt to take a card until it blows dry steam through the relief. If the oil from the engine gums the indicator, always take it off and clean it. After using it remove the spring, dry it and all parts of the indicator, then wipe off with oily waste. Fasten the indicator in its box, in which it will go, as a rule, only one way, but it requires no pounding to get it properly in place ; carefully close the box to protect it from dust. CHAPTER XVII. THE INDICATOR-DIAGRAM. 400. Definitions. — The indicator-diagram is the diagram taken by the indicator, as explained in Article 378, page 515. In the diagram the ordinates correspond to the pressures per square inch acting on the piston, the abscissae to the travel Fig. 257.— Diagram from an Improved Greene Engine. Cylinder, 16 Inches in Diameter, 36 Inches Stroke. Boiler-pressure, ioo lbs. 80 Revolutions per minute. Scale, 50. of the piston. During a complete revolution of an engine occur four phases of valve- motion which are shown on the indi- cator-diagram, viz. : admission, CDE, when the valve is open and the steam is passing into the cylinder ; expansion, EF t when steam is neither admitted nor released and acts by its 547 54 8 EXPERIMENTAL ENGINEERING. [§ 40a expansive force to move the piston ; exhaust, FGH, when the admission-port is closed and the exhaust opened so that steam is escaping from the cylinder; and compression, HC y when all the ports are closed and the steam remaining in the cylinder acts to bring the piston to rest. The Atmospheric Line, AB, is a line drawn by the pencil of the indicator when the connections with the engine are closed and both sides of the piston are open to the atmosphere. This line represents on the diagram the pressure of the atmosphere,, or zero gauge-pressure. The Vacuum Line, OK, is a reference-line drawn a distance corresponding to the barometer-pressure (usually about 14.7 pounds) by scale below the atmospheric line. It represents a perfect vacuum, or absence of all pressure. The Clearance Line, OY, is a reference-line drawn at a dis- tance from the end of the diagram equal to the same per cent of its length as the clearance or volume not swept through by the piston is of the piston-displacement. The distance between the clearance line and the end of the diagram represents the volume of the clearance of the ports and passages at the end of the cylinder. The Line of Boiler -pressure, JK, is drawn parallel to the atmospheric line, and at a distance from it by scale equal to the boiler-pressure shown by the gauge. The difference in pounds between it and DE shows the loss of pressure due to the steam-pipe and the ports and passages in the engine. The Admission Line, CD, shows the rise of pressure due to the admission of steam to the cylinder by opening the steam- valve. If the steam is admitted quickly when the engine is about on the dead-centre, this line will be nearly vertical. The Point of Admission, C, indicates the pressure when the admission of steam begins at the opening of the valve. The Steam Line, DE, is drawn when the steam- valve is open and steam is being admitted to the cylinder. The Point of Cut-off, E, is the point where the admission of steam is stopped by the closing of the valve. It is difficult to determine the exact point at which the cut-off takes place* :§ 4°°-J THE INDICATOR DIAGRAM. 549 It is usually located where the outline of the diagram changes its curvature from convex to concave. It is most accurately determined by extending the expansion line and steam line so that they meet at a point. The Expansion Curve, EF, shows the fall in pressure as the steam in the cylinder expands doing work. The Point of Release, F, shows when the exhaust-valve opens. The Exhaust Line, FG, represents the change in pressure that takes place when the exhaust-valve opens. The Back pressure Line, GH, shows the pressure against which the piston acts during its return stroke. On diagrams taken from non-condensing engines it is either coincident with or above the atmospheric line, as in Fig. 201. On cards taken from condensing engines it is found below the atmospheric line, and at a distance greater or less according to the vacuum obtained in the cylinder. The Point of Exhaust Closure, H, is the point where the exhaust-valve closes. It canno^ be located very definitely, as the first slight change in pressure is due to the gradual closing of the valve. The Point of Compression, H, is where the exhaust-valve closes and the compression begins. The Compression Curve, HC, shows the rise in pressure due to the compression of the steam remaining in the cylinder after the exhaust-valve has closed. The Lnitial Pressure is the pressure acting on the piston at the beginning of the stroke. The Terminal Pressure is the pressure above the line of perfect vacuum that would exist at the end of the stroke if the steam had not been already released. It is found by con- tinuing the expansion curve to the end of the diagram, as in Fig. 201. This pressure is always measured from the line of perfect vacuum, hence it is the absolute terminal pressure. Admission Pressure is the pressure acting on the piston at end of compression, and is usually less than initial pressure. 550 EXPERIMENTAL ENGINEERING. [§ 4OCX Compression Pressure is the pressure acting on the piston at beginning of compression ; this is also the least back pressure. Cut-off Pressure is the pressure acting on the piston at beginning of expansion. Release Pressure is the pressure acting on the piston at end of expansion. Mean Forward Pressure is the average height of that part of the diagram traced on the forward stroke. Mean Back Pressure is the average height of that part traced on the return stroke. Mean Effective Pressure (M. E. P.) is the difference between mean forward and mean back pressure during a forward and return stroke. It is the length of the mean ordinate inter- cepted between the top and bottom lines of the diagram mul- tiplied by the scale of the diagram. It is obtained without regard to atmospheric or vacuum lines. Ratio of Expansion is the ratio of the volume of steam in the cylinder at end of the stroke, compared with that at cut- off. In computations for this quantity the volume of clear- ance must be taken into account. Ratio of expansion is denoted by r. For hyperbolic expansion,/ being pressure in pounds per square foot at cut-off, and v the corresponding total volume, the work done per stroke and per square foot of area = pv{\ -f- Hy log r). The volume may be expressed as proportional to linear feet, with an additional length equal to the per cent of clear- ance, since the area of the cylinder is constant. The product of pressure per square foot into total volume is a constant quantity for hyperbolic expansion. The ratio of expansion is the reciprocal of the cut-off measured from the clearance line. This cut-off is distinguished from that shown directly on the card by designating it as the absolute cut-off. Initial Expansion is the fall of pressure during admission, due to an imperfect supply of steam. Wire -drawing is the fall of pressure between the boiler and cylinder; it is usually indicated by initial expansion. § 4 oi.j THE INDICA TOR-DIA GRAM. 551 401. Measurement of Diagrams. — The diagrams taken are on a small scale, they are often irregular, and the boundary lines are frequently obscure, so that the measurement must be made with great care. The diagrams may be taken from each end of the cylinder on a separate card, as shown in Fig. 257; or by the use of the three-way cock (see Article 398), in which case the two dia- grams will be drawn on the same card as shown in Fig. 258. In the latter case each diagram is to be considered separately; that is, the area of each diagram, as CDEBFC and GHIJKG, is to Fig. 258. be determined as though on a separate card. The object of diagram-measurements is principally to obtain the mean effect- ive pressure (M. E. P.). Two methods are practised. First, the method of ordinates. In this case the atmos- pheric line AB is divided into ten equal spaces, and ordinates are erected from the centre of each space. The sum of the length of these various ordinates divided by the number gives the mean ordinate. This multiplied by the scale of the dia- gram gives the mean effective pressure. The sum of the ordinates is expeditiously obtained by successively transferring the length of each ordinate to a strip of paper and measuring its length. Secondly, with the planimeter. The planimeter gives the mean ordinate much more accurately and quickly than the 552 EXPERIMENTAL ENGINEERING. [§ 4°2, method of ordinates. The various planimeters are fully described, pages 32 to 55. With any planimeter the area of the diagram can be ob- tained, in which case the mean ordinate is to be found by dividing by the length of the diagram. Several of the pla- nimeters give the value of the mean ordinate, or M. E. P., directly. In some instances the indicator-diagram has a loop, as in Fig. 2 59, caused by expanding below the back-pressure line; in this case the ordinates to the loop are negative and should be Fig. 259. subtracted from the lengths of the ordinates above. In case of measurement by the planimeter, if the tracing-point be made to follow the expansion-line in the order it was drawn by the indicator-pencil, the part within the loop will be circum- scribed by a reverse motion, and will be deducted automatically by the instrument, so that the reading of the planimeter will be the result sought. 402. Indicated Horse-power. — Indicated horse-power is the horse-power computed from the indicator-diagram, being obtained by the product of M. E. P. (/), length of stroke in feet (/), area*of piston in square inches (a), and number of revolu- tions (n), as represented in the formula plan ~ 33,000. In this computation the area on the crank side of the piston is to be corrected for area of piston-rod, and the two ends of the cylin- ders computed as separate engines. Further, in this computa- tion, it will not in general answer to multiply the average M.E.P. of a number of cards by the length of stroke and by the §403-] . THE INDICATOR-DIAGRAM. 553 average of the number of revolutions, but each card must be subjected to a separate computation and the results averaged. This can be readily done for each engine by computing a table made up of the products of the average value of n by length of stroke and area of piston, and for different values of M. E. P. from 1 to 10. Take from this table the values corresponding to the given M. E. P., increase or diminish this as required by the per cent of change of speed from the average. A very convenient table for this purpose, entitled " Horse-power per Pound, Mean Pressure," is given in the Appendix to this work, arranged with reference to diameter of cylinder in inches and piston-speed in feet per minute. 403. Form of the Indicator-diagram. — The form of the indicator-diagram has been carefully worked out for the ideal case by Rankine and Cotterell.* In the ideal case the steam works in a non-conducting cylinder, and all loss of heat is due to transformation into work, the expansion in such a case being adiabatic. In the actual case the problem is much more com- plicated, since a large portion of the heat is utilized in heating the cylinder, and is returned to the steam at or near the time of exhaust; doing little work. It is found, however, in the best engines working with quick-acting valve-gear, that the steam and back-pressure lines are straight and parallel to the atmos- pheric line, and that the expansion and compression lines are very nearly hyperbolae, asymptotic to the clearance line and to the vacuum line. If we denote by p the pressure measured from the vacuum line, and by v the volume corresponding to a distance meas- ured from the clearance line, so that pv shall be the co-ordinates of any point, we shall have as characteristic of the hyperbola pv = constant. This is the same as Mariotte's law for the expansion of non- condensible gases, since, according to that law, the pressure varies inversely as the volume. * Steam-engine, by James H. Cotterell. 5 54 EXPERIMENTAL ENGINEERING. [§404. Rankine found by examination of a great many actual cases that the expression pv* = constant agrees very nearly with the ideal case of adiabatic expansion. The variation from the ideal expansion line in any given case may be considerable, and the hyperbola drawn from the same origin is considered as good a reference-line as any that can be used, and the student should become familiar with the best methods of constructing it. 404. Methods of Drawing an Hyperbola. — The methods of drawing an hyperbola, the clearance and vacuum lines being given, are as follows : First Method. (See Fig. 260.) — CB, the clearance line, and CD, the vacuum line, being given, draw a line parallel to the Fig. 260. — Method of Drawing an Hyperbola. atmospheric line through B ; find by producing the steam and expansion lines the point of cut-off, c. Draw a series of radiating lines from the point C to the points E, F, G, H, and A, taken at random, and a line cb intersecting these lines, drawn from c parallel to BC. From the points of the inter- section of cb with these radiating lines draw horizontal lines to meet vertical lines drawn from the points E, F, G, H, and § 405-] THE INDICATOR-DIAGRAM. 555 A ; the intersections of these lines at e, f, g, /i, and a are points in the hyperbola passing through the point c. If it is desired to produce the hyperbola from a upward, the same method is used, but the line AB is drawn through the point " gas, 71 = 1.408; Isothermal " " n = 1.0. These three expansion curvesf are represented in Fig. 262 ; the pressures from o to 90 pounds per square inch are repre- sented by the ordinates, and the volumes in cubic feet corre- sponding to one pound in weight are represented by abscissae. * Rankine's Steam-engine, page 385. f See Thurston's Engine and Boiler Trials, page 251. § 4o6.] THE INDICATOR-DIAGRAM. 557 In the figure the curve A to G is the hyperbola, A to / the saturation curve, and A to L the adiabatic curve. ON is the axis of the hyperbola, of which OB and OH are asymptotes. It is to be noticed that the saturation curve corresponds to a uniform quality of steam, the adiabatic curve to a condition in which the moisture is increasing, and the hyperbolic curve 1800 1700 1600 1500 1400 1300 1200 1100 1000 900 800 700 600 500 400 Fig. 262.— The Three Expansion Curves. 300 300 to a condition in which the moisture is decreasing, the latter agreeing more closely with the actual condition. 406. Weight of Steam from the Indicator-diagram. — The diagram shows by direct measurement the pressure and volume at any point in the stroke of the piston ; the weight per cubic foot for any given pressure may be taken directly from a steam-table. The method, then, of finding the weight of steam for any point in the stroke is to find the volume in cubic feet, including the clearance and piston displacement to the given point, which must be taken at cut-off or later, and multiply this by the weight per cubic foot corresponding to the pressure at the given point as measured on the diagram. This will give the weight of steam in the cylinder accounted for by the indicator-diagram, per stroke. In an engine work- ing with compression, the weight of steam at terminal pressure 558 EXPERIMENTAL ENGINEERING. [§ 4°6- filling the clearance-space is not exhausted ; this weight, com- puted for a volume equal to clearance -and with weight per cubic foot corresponding to compression pressure, should be subtracted from the above. This may be reduced to pounds of steam per I. H. P. per hour, by multiplying by the number of strokes required to develop one horse-power per hour of time. The method of computing would then be : Find the weight per cubic foot, from a steam-table corresponding to the abso- lute pressure, at the given point, multiply this by the corre- sponding volume in cubic feet, including clearance, and this by the number of strokes per hour. Correct this for the steam imprisoned in the clearance-space. Divide this by the horse- power developed, and we shall have the consumption in pounds of dry steam per I. H. P. as shown by the diagram. Thus let. A '— area of piston in square feet ; a= " " " " " inches; N —~ number of strokes per hour; n= " " " " minute; w = weight of cubic foot of steam at the given pressure ; / = total length of stroke in feet ; 4 = length of stroke in feet- to point under consideration ; c = per cent of clearance; I' = 4 + cl\ b = corresponding per cent ; w' = weight of cubic foot of steam at compression pressure. Then the consumption of dry steam in pounds per hour per horse-power (indicated). „ NAl„ , N 6ol na(bw — cw') is,7$o[l>iv—cw''] 33>ooo The above equation corrects for the steam caught in the clearance spaces during compression. As an example: Compute the steam consumption as shown in Fig. 257 at point of cut-off E and at terminal pressure. §406.] THE INDICATOR-DTAGRAM. 559 The absolute pressure shown by the diagram is 97 pounds at cut-off and 37 at end of the stroke. Neglect steam in clear- ance. The length of stroke total is 3 feet, at cut-off is J foot. Clearance is 3.2 per cent. M. E. P. (p) is 50 pounds. Steam-consumption at Cut-off. — From steam-table w=o.22o8. 5= 13.750 (02 5 2 08)(a75 +°^^i6.. 7 lb S . per LH.P.per hour. St earn- consumption at End of Stroke. — From steam-table w = 0.0896. S=I 3 i7S0 ^^(3±o^9) = 2537lbsperIHpperhour This, it should be noticed, is not the actual weight of steam used per horse-power by the engine, but is that part which cor- responds to the amount of dry steam remaining in the cylinder at the points under consideration. The amount is usually less when computed at cut-off than at the end of the stroke, since some of the steam which was condensed when the steam first entered the cylinder is restored by evaporation during the latter portion of the period of expansion. The equations and examples as given above apply only to a simple engine. They may be applied to a compound or triple- expansion engine by considering that all the work is done in the low-pressure cylinder as represented on a combined diagram. In such a case, p of the formula would equal the equivalent M. E. P. for the combined diagram. That is, p'/r + p"=p, in which r is the ratio of the areas of the cylinders, p' the M. E. P. of the high-, and p" that of the low-pressure cylinder. If we consider the steam- consumption only for the end of the stroke, l a of equation (1) becomes equal to /, and the equation reduces to the following form : w St = i3>75°j( 1 +c) (2) 560 EXPERIMENTAL ENGINEERING. [§ 407. Neglecting the clearance, 4=13,750-; ........ (3) in which / = the M. E. P. of the diagram, and w the weight per cubic foot corresponding to the terminal pressure. For- mula (3) has been tabulated as follows : Thompson's tables, given in the Appendix, give values of 13,7502^, and the tabular values must be divided by the M. E. P. to give the steam-consumption per I. H. P. per hour. Tabor's tables give values of , and the tabular values P must be multiplied by the weight of a pound of steam corre- sponding to the terminal pressure, to give the steam-consump- tion. Williams's tables, published in the Crosby catalogue, give values of — — — , and the results in each case have to be multi- 42543 plied by 32. ^2w to give the steam-consumption. A graphical correction is made in all cases for compression by drawing a horizontal line through the terminal pressure to compression line of diagram, and multiplying the result given in the table by the ratio of the portion of this line intercepted between terminal point and compression, to the whole stroke. 407. Clearance Determined by the Diagram. — The clearance is usually to be determined by actual measurement of the volume of the spaces not swept through by the piston, and comparing this result with the volume of piston-displace- ment, the ratio being the clearance. Since the expansion and compression lines of the diagram are nearly hyperbolae, the clearance line can be drawn by a method nearly the reverse of that used in constructing an hyperbola (Article 404). In this case proceed as follows: Lay off the vacuum line CD (Fig. 207) parallel to the atmospheric line FT, and at a distance corresponding to the atmospheric pressure. The position of the clearance line can be determined by two methods, corresponding to those used in drawing the hyperbola. First § 4o8.] THE INDICATOR-DIAGRAM. 5 6l method: Take two points, a and b in the expansion curve and c and d in the compression line, and draw horizontal and vertical lines through these points, forming rectangles aa'bb' and cc'dd- '. Draw the diagonal of either rectangle, as a'b' , to meet the vacuum line CD: the point of intersection C will be _^L \ ? V^-o Fig 263. — Methods of Finding the Clearance. a point in the clearance line CB, and the clearance will equal CN -T- FT. Second method: Draw a straight line through either curve, as mn through the compression curve or ef through the expansion curve, and extend it in both direc- tions. On the line m'n' lay off tin! equal to mm\ or on the line e'f lay off ee' equal to ff ; then will either of the points e' or n' be in the clearance line and the line drawn perpendicular to the vacuum line through either of these points is the clear- ance line. In an engine working with much compression the clearance will be given more accurately from the compression curve than from the expansion curve, since it is more nearly an hyperbola. 408. Re-evaporation and Cylinder Condensation. — By considering the hyperbolic curve as a standard, an idea can be obtained of the restoration by re-evaporation and the loss by 562 EXPERIMENTAL ENGINEERING. is 409. cylinder condensation. Thus in Fig. 264, suppose that a is the point of cut-off at boiler-pressure, construct an hyperbola as explained ; in the example considered it is seen to lie above the expansion line for a short distance after cut-off, then to cross the line at b, and remain below it nearly to the end of the stroke. The amount by which the expansion line rises above the hyperbola may be considered as due to re-evaporation. The area of the diagram lying above would represent the work added by heat returned to the steam from the cylinder. The methods for determining the cylinder condensation are * b' d' Fig. 264. — Work Restored by Re-evaporation. similar to this process, except that the hyperbola is usually drawn upward from the point corresponding to the terminal pressure, to meet a horizontal line drawn to represent the boiler- pressure, as follows : This construction is shown by the dotted lines in the diagrams in Fig. 265. The area of the figure enclosed by the dotted lines, compared with that of the diagram, is the ratio that the ideal diagram bears to the real ; the difference is the loss by cylinder condensation. The student should understand that both these methods are approximations which may vary much from the truth. 409. Discussion of Diagrams. — Diagrams are often taken §409-] THE INDICATOR-DIAGRAM. 5 6 3 where some portion of the engine is out of adjustment, or the indicator or reducing motion is not in perfect order. It is often i. Steam 80 lbs. 91 per cent of ideal. 40.0 Horse Power 60 lbs.Boiler Press. 90 per cent of ideal. /y r- 62.4 Horse Power ^ 1 53 per cent of Ideal. 65 lbs.Boiler Press. r\ 54 per cent of ideal. . 15 Horse Power Fio 265.— Loss by Cylinder-condensation. possible in such cases to determine the defect from the dia- gram, and to suggest the proper remedy. A few examples are submitted. Such examples could be multiplied indefinitely, and skill and experience will, in general, be required to prop- Bottom - of cylinder Steam "side. Vacuum side- Fig. 266. — Unsymmetrical Valve-setting. eriy interpret them. Thus Fig. 266 is an illustration of a dia- gram taken when the valves were set unsymmetrically. Curves or waves in the expansion or compression lines indicate inertia- 564 EXPERIMEN TA L ENGINEERING. [§409. effects in the drum-motion, which is sometimes sufficient to make the compression line concave when it should be convex, as shown in the lower diagram of Fig. 267. Vertical curves are due in large measure to vibrations in the pencil-lever and indicator-spring ; they are usually excessive with a light spring and high speed. In the case of an automatic engine running under variable loads, each revolution will show a different dia- gram, as shown in Fig. 267. ^a Fig. 267. — Variation i.f Load. Different Forms of Admission-lines. — The form of the ad- mission-line is changed* according to the relative time of valve- opening and position of piston in its stroke. The normal form is shown at A. In B C D and E the valve opens late, and after the piston has started on its return stroke t In F and G the exhaust-valve closes late, so that live steam escapes. H and / are familiar examples of extreme compres- sion, produced on high-speed automatic engines working with a light load. J shows a sharp corner above the compression * Power, September 1891. § 4io.] THE IND1 CA TOR-DIA GRA M. 565 line, and in general indicates too much lead. In case the valve opens too early, the admission-line leans as at K. 410. Diagrams from Compound and Triple-expansion Engines. — The diagram from any cylinder of a compound or triple-expansion engine is not likely to differ in any noticeable Fig. 268.— Typical Admission-lines. particular from those taken from a simple engine as already described. They are usually taken with different springs for the different cylinders, but may have very nearly or exactly the same lengths. The diagrams from a compound engine may be reduced to an equivalent diagram, taken from a single cylinder by the fol- lowing method : Lay off a vertical line OB, and a horizontal line PQ. Let PQ be the vacuum line, and BC the line of 566 EXPERIMENTAL ENGINEERING. [§4IO. highest steam-pressure acting in the small cylinder. Lay off ON proportional to the volume of the small cylinder, and OP proportional to the volume of the large cylinder. Let FA be the line of back pressure of the large cylinder, AD that of the small cylinder : then BCD A is the diagram from the small cylinder, EKFA that from the large cylinder. To combine them into one diagram, draw a line KGJf par- allel to POQ, intersecting both diagrams, and lay off upon it HL = KG ; and GL — GH-\- KG represents the total volume K^ E B C G H/ D < — ' ^^ M F A f D ( d r \ Q Fig. 269. in both cylinders when the pressure is OG, and L is a point in the expansion line the same as though the action took place in the large cylinder only. In the same way other points may be found, and the line CDLM drawn. This diagram may be discussed as if it represented the steam acting in the large cylinder only. Fig. 270 is a combined diagram from a triple-expansion engine,* in which the cylinders have the ratio of I : 2.25 : 2.42, and the total ratio of expansion is 8. The length of each dia- gram is made proportional to the total volume of the cylinder from which it was taken ; the diagrams are all drawn to the same scale of pressures, and each is located at a distance from a vertical line proportional to the volume of its clearance. From the point of cut-off corresponding to boiler-pressure an hyperbola is drawn as has been explained, and the area sur- rounding the diagrams is shaded. The work done in the three cylinders can be computed from the diagram as though done in one only. * See Thurston's Engine and Boiler Trials, page 202. 55 4"-] THE INDICATOR-DIAGRAM. 567 411. Crank-shaft and Steam-chest Diagrams.— Dia- grams may be taken with the motion of the indicator-drum proportional to any moving part of the engine, as for instance the crank-shaft. Fig. 270. — Combined Diagram from Triple-expansion Engine. In such a case, shown by Fig. 271 the ordinates will be as before proportional to the pressures per square inch acting on the piston, but the abscissae will correspond to distances moved Fig. 271,— Shaft-diagram. through by the crank-pin. In Fig. 271, A to B is the exhaust, from B to C compression, D to E steam line, E to A expan- sion. Diagrams may also be taken with the indicator mounted on the valve-chest ; in this case the indicator would show vari- ation in pressure in the steam-chest. 568 EXPERIMENTAL ENGINEERING. [§4U CHAPTER XVIII. METHODS OF TESTING THE STEAM-ENGINE. 412. Standards Employed in Engine-testing. — The unit of work ordinarily used in engine-testing is the horse-power (H.P.), which may be either that shown by the indicator and known as the indicated horse-power (I.H.P.), or that delivered from the engine, which is known as delivered or brake horse- power (D.H.P.). The horse-power is equivalent to 33,000 foot-pounds or 42.413 B.T.U. per minute, or to 1,980,000 foot- pounds or 2545 B.T.U. per hour. Fuel, Steam,, and Heat Consumption. — The ordinary standard of comparison of the economy of the work done by different engines is the weight of fuel or steam, or the number of B.T.U- required by the engine for each horse-power of work indicated or delivered per hour. The heat consumption, B.T.U. per H.P. hour, presents the advantages over the others of being more concise and definite. Duty. — This term is applied to the work performed by pump- ing-engines, expressed in foot-pounds, for the consumption of 100 pounds of coal, 1000 pounds of steam, or 1,000,000 B.T.U. See Art. 254. Perfect Engine. — The performance of a perfect engine is frequently employed as a standard of comparison. The per- fect engine is one which transforms all the available heat received and not rejected into mechanical work. Such an engine operates in a reversible or Carnot cycle and has a thermodynamic efficiency of (Ti — T 2 )/Ti, in which T\ is the absolute temperature of the entering steam and T 2 that of the exhaust. The heat (B.T.U.) consumed per H.P. hour for an engine of this kind is evidently h = 2545 T 1 /(T 1 ~T 2 ). The least possible weight of steam will be used in the per- 5 6 9 '■&& 570 EXPERIMENTAL ENGINEERING. [§ 413 feet engine when the difference between the heat entering, A, and that discharged, q, has all been converted into work. Hence the least possible steam consumption per H.P. hour of the per- fect reversible engine is 2545 *-q \Ti Rankine Cycle. — The maximum amount of heat which can be transformed into work in the perfect non-reversible engine is given by Professor Rankine per pound of steam as follows: K = T 1 -T 2 -T 2 \o^ + r(i-^j. This expression is frequently used as a standard of com- parison by British engineers, and the cycle on which such an engine works is termed the Rankine cycle. The efficiency of the steam-engine is expressed in various ways as follows: 1. Thermal Efficiency. — This is the ratio of the work actu- ally done (A.W.), expressed in heat units, to the total heat sup- plied (Q) in the steam. It is equal to AW/Q. 2. Thermodynamic Efficiency. — This is the greatest possible ratio of work done by the working substance to the mechanical equivalent of the heat expanded on it to do that work. In the Carnot reversible cycle this efficiency equals (T 1 — T 2 )/T 1 . 3. Mechanical Efficiency. — This is the ratio of the work actually delivered (D.H.P.) to that done on the piston and shown by the indicator (I.H.P.). 4. Plant Efficiency. — This is equal to the product of the several efficiencies of the various parts or machines which com- pose the plant. 413. Objects of the Engine-test. — The test may be made: 1. To adjust the valves or working parts of the engine. 2. To determine the indicated or dynamometric horse-power. 3. To ascertain the friction for different speeds or conditions. 4. To determine the consumption of fuel or steam per horse- power per hour. 5. To investigate the heat-changes which ; § 4 1 4-] METHODS OF TESTING THE STEAM-ENGINE, 5/1 characterize the passage of the steam through the engine. The general method of the test will depend largely on the ob- ject for which the test is made ; in any event the apparatus to be used should be carefully calibrated, the dimensions of the engine obtained, and the test conducted with care. 414. Measurements of Speed. — The various instruments employed for measurement of speed are speed-indicators, ta- chometers, continuous counters, and chronographs. Where the number of revolutions only is required, it is usually obtained either by counting or by the hand speed- indicator. Counting can be done quite accurately without an Fig. 273. — Double-ended Speed-indicator. instrument, by holding a stick in the hand in such a position that it is struck by some moving part, as the cross-head of an engine, once in each revolution. The hand speed-indicator, of which one form is shown in Fig. 273, consists of a counter operated by holding the pointed end of the instrument in the end of the rotating shaft. In using the instrument, the time is noted by a watch at the instant the counting gears are put in operation or are stopped. A stop-watch is very convenient for obtaining the time. The errors to be corrected are princi- pally those due to slipping of the point on the shaft, and to the slip of the gears in the counting device in putting in and out of operation. The best counters have a stop device to prevent this latter error, and the gears are engaged or disengaged with 572 EXPERIMENTAL ENGINEERING. [§ 4H. the point in contact with the shaft. To prevent slipping of the point, the end of the instrument is sometimes threaded and screwed into a hole in the end of the shaft. The continuous counter consists of a series of gears arranged to work a set of dials which show the number of revolutions. The arrangement of gearing in such an instrument is shown in Fig. 274. The instrument can usually be made to register by either rotary or reciprocating motion, and can be had in a Fig. 274. square or round case. The reading of the counter is taken at stated intervals and the rate of rotation calculated. Tachometers (see Fig. 275) are instruments which utilize the centrifugal force in throwing outward either heavy balls or a liquid. The motion so caused moves a needle a distance pro- portional to the speed, so that the number of revolutions is read directly from the position of the needle on the graduated dial. The tachometer is arranged with a pointed end to hold against the shaft whose speed is to be determined, or with a pulley so that it may be driven by a belt. §4 I 5-] METHODS OF TESTING THE STEAM-ENGINE. 573 Brown s Speed-indicator consists of a U-shaped tube joined to a straight tube in the centre. The revolution of the U-tube around the centre tube induces a centrifugal force which ele- FlG. 275.— ICHAEFFER AND BUDEXBERG HAND TACHOMETER. vat£s mercury in the revolving arms and depresses it in the centre tube. A calibrated scale gives the number of revolu- tions corresponding to a given depression. 415. The Chronograph. — The chronograph,* Fig. 276, con- sists of a drum revolved by clock-work so as to make a Fig. 276. definite number of revolutions per minute. A carriage hav- ing one or two pens, h, g, as may be required is moved parallel * See Thurston's Engine and Boiler Trials, page 226. 574 EXPERIMENTAL ENGINEERING. [§4*5. to the axis of the cylinder by a screw which is connected with the chronograph-drum A by gearing. The pen in its normal condition is in contact with the paper, and it is so connected to an electro-magnet that it is moved axially on the paper whenever the circuit is broken. The cir- cuit may be broken automatically by the motion of a clock, or by hand with a special key, or by any moving mechanism. 1 wo pens are usually employed, one of which registers auto- matically the beats of a standard clock ; the other may be ar- ranged to note each revolution or fraction of a revolution of a revolving shaft. The distance between the marks made by the clock gives the distance corresponding to one second of time ; the distance between the marks made by breaking the circuit at other intervals represents the required time which is to be measured on the same scale. This instrument has been in use by astronomers for a long time for minute measurements of time, and by its use intervals as short as one one-hundredth (.01) part of a second can be measured accurately. Tuning-fork Chronograph. — A tuning-fork emitting a musi- cal note makes a constant and known number of vibrations. The number of vibrations of the fork corresponding to the musical tones are as follows : Note C D E F G A B C a Vibrations ) _ zr i /r 128 144 160 170I 192 213^ 240 256 per second. If now a small point or stylus be attached to one of the arms of a tuning-fork, as shown in Fig. 276,* — in which F\s one of the arms of the tuning-fork, and CAED a piece of elastic metal to which the stylus, AP, is attached, — and if the fork be put in vibration and the stylus permitted to come in contact with any surface that can be marked, as a smoked and var- nished cylinder moved at a uniform rate, the vibrations of the tuning-fork will be recorded on the cylinder by a series of wavy lines, as shown in Fig. 279; the distance between the *~See Thurston's Engine and Boiler Trials, page 233. §415-] METHODS OF TESTING THE STEAM-ENGINE. 575 waves corresponding to known increments of time. If each revolution or portion of a revolution of the shaft whose speed is required be marked on the cylin- der, the distance between such marks, measured to the same scale as the wavy lines made by the tuning-fork, would represent the time of revolu- tion. Fig. 278 (from Thurston's Engine and Boiler Trials) represents the Ran- son chronograph ; in this case the tun- ing-fork is moved axially by a carriage operated by gears, and is kept in vibration by an electro-magnet. The operation of the instru- ment is the same as already described. The form of the record being shown in Fig. 279; the wavy marks being those Fig. 277.— Stylus for Tuning- fork. Fig. 278. — Tuning-Fork Chronograph. made by the tuning-forks, those at right angles being made at the end of a revolution of the shaft whose speed is required. The tuning-fork with stylus attached,* as in Fig. 277, can be made to draw a diagram on a revolving cylinder connected See Engine and Boiler Trials, page 234. 576 EXPERIMENTAL ENGINEERING. [§ 4 J 7« directly to the main shaft of the engine, or the shaft itself may be smoked and afterward varnished. If the fork be moved axially at a perfectly uniform rate, the development of the lines drawn will be for uniform motion, straight and oi uniform pitch ; but for variations in speed these lines will be Fig. 279. — Speed-record from Chronograph. curved and at a varying distance apart. From such a diagram the variation in speed during a single revolution can be deter. mined. 416= Autographic Speed-recorder. — Variations in speed are shown autographically in several instruments by recording on a strip of paper moved by clock-work the variation in cen- trifugal force of revolving weights. In the Moscrop speed- recorder, shown in Fig. 280, the shaft B is connected with the shaft whose speed is to be measured. The variation in the height of the balls near B, caused by variation in speed, gives the arm C a reciprocating motion, so that an attached pencil makes a diagram, FED, on the strip of paper moved by clock- work. The ordinates of this diagram are proportional to the speed. 417. The Surface Condenser. — In the measurement of the steam used by the engine the surface condenser is fre- quently employed. The surface condenser usually consists of a vessel in which are a great many brass tubes. It is usually arranged so that the exhaust steam comes in contact with the outer surface of these tubes, and the condensing water flows through the tubes. The condensed steam falls to the bottom of the condenser and is removed by an air-pump ; the heat of the steam being taken up by the condensing water. If the condenser is free from leaks, the air-pump of ample size and with little clearance, and if the proper temperatures are main- §417-] METHODS OF TESTING THE STEAM-ENGINE, 577 tained, nearly all the atmospheric pressure can be removed from the condenser and the back-pressure on the engine cor- respondingly reduced. The surface condenser affords more accurate means of Fig. 280 —The Moscrop Speed-recorder. obtaining the water-consumption of a steam-engine than the measurement of feed-water during a boiler-test, since the effect of steam-leaks are to a great extent eliminated. The condenser should be tested for leaks by noting how 57 8 EXPERIMENTAL ENGINEERING. |_§ 418. long a given reading of the vacuum-gauge can be maintained when all the connecting valves are closed, or by turning on steam when the water-pipes are empty, or vice versa, and noting whether there is any leakage. FORM FOR TEST ON CONDENSER. Date Duration of test . . . . min. Barometer inches lbs. per sq. in. Temperature, entering steam C F. Temperature, condensed steam C , F. Temperature, cold condensing water C F. Temperature, hot condensing water C F. Hook-gauge reading (corrected) inches. (Hook-gauge reading) * Temperature at weir C F. Weight of condensed steam lbs. Breadth of weir inches. End area of tubes - sq. ft. Area steam surface sq. ft. Area water surface sq. ft. Weight steam condensed per hour lbs. Weight condensing water used per hour lbs. Weight steam condensed per pound of water .lbs. Weight steam condensed per sq. ft. steam surface per hour lbs. Weight steam condensed per sq. ft. water surface per hour lbs. Velocity of water through tubes ft. per sec. Heat acquired by condensing water used per hour B. T. U. Heat given up by steam condensed per hour. B. T. U. Signed , 418. Calibration of Apparatus for Engine-testing.— Before commencing any important test, all instruments and apparatus to be used should be adjusted and carefully com- pared with standards, under the same conditions as in actual oractice. The errors or constants of all instruments should be §4 l8 -] METHODS OF TESTING THE STEAM-ENGINE. 579 noted in the report of the test, and corresponding corrections made to the data obtained. The instruments to be calibrated are : 1. Steam-gauge. — Compare with mercury column, or with standard square-inch gauge, for each five pounds of pressure, reading both up and down throughout the range of pressures likely to be used in the test. (See Article 282, page 366.) 2. Steam-engine Indicat or -springs . — Put the indicator under actual steam-pressure (see Art. 393, p. 535) and compare the length of ordinate of the card with the reading of the mercury column or a standard gauge for the same pressure. Take ten readings, both up and down, through an extreme range equal to two and one-half times the number on the spring. The steam-pressure may be varied by throttling the supply and •exhaust. The ordinate may also be compared by a special method with readings of a standard scale ; the indicator being heated by the flow of steam through a rubber tube wound around it. 3. Speed-indicators. — The accuracy can be checked by hand counting. For the best work chronographs should be used. Continuous counters are necessary for accuracy in a long run. (See Articles 414 and 415.) 4. Indicator Reducing-motion. — This may be tested by divid- ing the stroke of the engine on the guides into twelve equal parts and noting whether the card is similarly divided. It should be tested for both return and forward stroke. When the form of the card is considered, this is an imports* matter, as many reducing-motions distort its shape. (See Article 390, page 528.) 5. Indicator-cords and Connections. — See that the connecting cords do not stretch at high speeds, and that the drum-spring of the indicator has a proper tension and gives a correct motion of the drum. This is important. (See Article 395.) 6. Weighing-scales. — Compare the readings with standard weights. 7. Water-meters. — Calibrate by actually weighing the dis- charge under conditions of use as regards pressure and flow. 580 EXPERIMENTAL ENGINEERING. [§418 In case meters are used, temperatures of the water must be taken in order to obtain the weight. (See Article 213, page 283.) 8. Thermometers. — Test the thermometer for freezing-point by comparison with water containing ice or snow ; test for boil- ing-point by comparison with steam at atmospheric pressure in the special apparatus described on page 381, the correct boiling- point being determined by readings of the standard barometer. The other tests of the thermometer can in general be left to the makers of the instrument. In cases where great accuracy is required the readings should be compared throughout the whole scale with a standard air-thermometer, as described on page 350. 9. Pyrometer. — Compare with a standard thermometer while immersed in steam for the lower ranges of temperature, and with known melting-points of metals for higher. The correction may also be determined by cooling heated masses of metals in large bodies of water and calculating the temper- ature from the known relations of specific heats. (See Articles 298 to 304). 10. The Planimeter, which is used for measuring the indi- cator-diagram, should be calibrated by making a comparison with a standard area, as explained in Article 38, page 52. The following form is useful to record the results of calibrations : BLANK FORM FOR CALIBRATION OF INSTRUMENTS. Steam-engine Indicator-springs. Used on Head. Crank. § 4!9-] METHODS OF TESTING THE STEAM-ENGINE. 58 1 Steam-gauges. Maker. Position. Number. Error, lbs. When Tested. How Tested. Thermometers. Position. Boiling-point. Registered Number. Read- Per Ba- ing. rometer. Error. Freezing-point. Read- ing. Error. Barometer. 419. Preparations for Testing. — The preparations re- quired will depend largely on the object of the test. They should always be carefully made, and in general are to include the following operations : 1. Weighing of Steam. — Prepare to weigh all the steam supplied the engine. This may be done by weighing or meas- uring all the feed-water supplied the boiler (see Article 375), provided there is no waste nor other use of steam ; or it may be done by condensing (see Article 417) and weighing all the exhaust from the engine. In the first case especial precaution must be taken to prevent leaks, and in the latter to reduce the temperature of the condensed steam to 1 io° F. before weigh- ing. The weights may in some cases be determined from a meter-reading (see Article 214). 2. Quality of Steam. — Attach a calorimeter (see Articles 330 co 336), which may be of the throttling or separator kind, to the main steam-pipe, near the engine. This attachment may be made by a half-inch pipe, cut with a long thread and ex- tending three fourths across the main steam-pipe. This pipe 5 82 EXP E RIM EN TA L ENGINEERING. [§ 4 1 <>• should be provided with large holes so that steam will be drawn from all parts of the main steam-pipe (see page 370). 3. Leaks. — The engine should be tested for piston-leaks by- turning on steam with the piston blocked and cylinder-cocks opened on the end opposite that at which steam is supplied. If leaks are found, they should be stopped before beginning the test. 4. Indicator Attachments. — Arrange a perfect reducing-mo- tion. The kind to be used will depend entirely upon circum- stances. The lazy-tongs or pantograph is reliable for speed* less than 125, and can be easily applied. The pendulum piv- oted above and furnished with an arc, although not perfectly accurate, is much used. Make yourself familiar with the vari- ous devices in use. (See Article 390). 5. An Absorption Dynamometer may be required ; if so, ar- range a Prony brake to absorb the power of the engine, and make provision for lubricating it and removing the heat gen- erated (see Article 178, page 528). In many commercial tests the power is absorbed by machinery or in useful work, and the efficiency is wholly determined by measurements of the amount and quality of steam and from the indicator-diagram. 6. Weight of c^z/.-^-This is generally taken during an engine, test, but will be treated here as pertaining to boiler-testing ; the methods of weighing are fully described under that head (see Article 375). An engine fitted completely for a test is shown in Fig. 272,. from Thurston's Engine and Boiler Trials. In this case two indicators are employed, the drum-motion being derived from a pendulum reducing-motion; a Prony brake is attached to absorb and measure the power delivered, water for keeping the brake cool being delivered near the bottom and on the inside of the flanged brake-wheel by a curved pipe, and drawn out by an- other pipe the end of which is funnel-shaped and bent so as to meet the current of water in the wheel. The speed is taken by a Brown speed-indicator mounted on top of the brake, and also by a hand speed-indicator. The steam-pressure is measured §421.] METHODS OF TESTING THE STEAM-ENGINE. 583 near the engine ; the quality of steam is determined by a sam- ple drawn from the vertical pipe near the engine. 420. Measurement of Dimensions of Engine. — Make careful measurements of the dimensions of engine ; the diam- eter of piston, length of stroke, and diameter of piston-rod, as may be required. Piston-displacement. — This is the space swept through by the piston ; it is obtained by multiplying the area of the piston by the length of stroke. For the crank end of the cylinder the area of the piston-rod is to be deducted from the area of the piston. Clearance is the space at the end of cylinder and between valve and piston, filled with steam, but not swept through by the piston. To measure the clearance, put the piston at end of its stroke and fill the space with a known weight of water, ascertaining that no leaks occur by watching with valve-chest cover and cylinder-head removed. Make this determination for both ends of the cylinder, and from the known weight of water compute the volume required. This is usually reduced to percentage, by dividing by the volume of piston-displacement. This last reduction may be obviated, as suggested by Prof. Sweet, by finding, after the clearance-spaces are full of water, how far the piston will have to move in order to make room for an equal amount of water ; this distance divided by the full, stroke is the percentage required. Another approximate way sometimes necessary is to fill the whole cylinder and clearance- spaces with water ; from this volume deduct the piston-dis^ placement and divide by 2. Preliminary Run. — It will be found advisable to make a pre- liminary run of several hours before beginning the regular test, to ascertain if all the arrangements are perfect. 421. Quantities to be observed. — The observations to be taken on a complete engine-test are given in the following list. Fill out the following blank spaces. 5 8 4 EXPERIMENTAL ENGINEERING. t& 422. Kind of engine Maker's name Brake-arm feet. Diameter cylinder inches. Length stroke feet Diameter piston-rod inches. Diameter crank-pin " Length crank-pin " Diameter wrist-pin " Travel valve " DESCRIPTION OF ENGINE. Lap of valve inches. Scale indicator-spring Piston area sq. in. Steam-port area " Exhaust-port area " Diameter fly-wheel inches. Clearance, head lbs. water. crank " " per cent P.D. head " " " crank Number Time Revolutions : Continuous counter Speed-indicator Gauge-readings : Boiler lbs. Steam-pipe " Steam-chest ** Exhaust .inches hg. Condenser " " Barometer " '* Temperatures : External air LOG Of TEST. Temperatures Engine-room Condensed steam, Feed-water Injection-water.. . Discharge- water. . Calorimeter : Steam-pipe Steam-chest Weights : Condensed steam. Feed-water Injection-water. . . Calorimeter.. 422. Special Engine- tests.— Preliminary Indicator Prac- tice. — A simple test with the indicator will be found a useful exercise in rendering the student familiar with the methods of handling the indicator and of reducing and conv puting the data to be obtained from the indicator-diagrams The directions are as follows : Apparatus. — Throttling calorimeter ; steam-gauge ; two indi' cators ; reducing-motion, and indicator-cord. 1. Obtain dimensions of engines. Measure the clearance \> see that indicators are oiled and in good condition, and that § 422.] METHODS OF TESTING THE STEAM-ENGINE. 585 the reducing-motion gives a perfect diagram. Adjust the length of cord so that the indicator will not hit the stops. Pre- pare to take cards as explained in Article 398, page 545. 2. Take diagrams once in each five minutes, simultaneously from head and crank end of cylinder ; take reading of boiler- gauge, barometer, gauge on steam-pipe or on steam-chest, vacuum-gauge if condenser is used, temperature or pressure of entering steam, temperature of room, and number of revolu- tions. 3. Measure or weigh the condensed steam during run. 4. From the cards taken compute the M. E. P. and I. H. P. for each card as. required by the log. 5. Take a sample pair of diagrams, one from head and one from crank end. (a) Find clearance from diagrams (see Article 407, page 561) ; (b) draw hyperbolae respectively from cut-off and release and find re-evaporation and cylinder condensation (see Article 408) ; (c) produce hyperbola from release to meet hori- zontal line- representing boiler-pressure; complete the diagram with hyperbola from point of admission. Compute the work (I. H. P.) from this new diagram. Draw conclusions from the form of card (see Article 409). 6. Compute the steam-consumption per stroke and per I. H. P. at cut-off and at end of stroke from the diagram (see Article 406). Compare this with the actual amount as deter- mined by the test. 7. From the weight of dry steam as shown by the indicator- diagram, and the actual weight as determined by the amount of condensed steam, determine the quality at cut-off and re- lease. 8. Make report of test on the following form : REPORT OF TEST ON ENGINE. Date Duration of test ....=... min. Revolutions per min Steam used per min. c lbs Barometer. in " 586 EXPERIMENTAL ENGINEERING. [§ 423. Piston-displacement Clearance (per cent of P. D.) Engine constant Cut-off (per cent of stroke) Release (per cent of stroke) , Compression (per cent of stroke). Pressure at cut-off Pressure at release Pressure at compression , Mean effective pressure Revolutions per minute Horse-power , Crank End. cu. ft. lbs. Head P.nd. cu. f t lbs. C. E. H. E. Per Stroke. C. E. H. E. Per Revo- lution. .Total. Per I.H.P. .lbs. Weight of steam at cut-off Weight of steam at release Weight of steam during compression. . . Re-evaporation per H. P. per hour Weight of water per revolution, actual '* Weight of mixture in cylinder per revolution " Per cent of mixture accounted for as steam at cut-off Per cent of mixture accounted for as steam at release Weight of water per H. P. per hour, actual lbs. Weight of water per H. P. per hour, by indicator " Signed. 423. Valve-setting. — This exercise will consist, first, in obtaining dimensions of ports and valves, and in drawing the valve-diagram corresponding to a given lead and angular ad- vance, and setting the valve by measurement with a lead cor- responding to that shown on the diagram. The valve-diagram may be drawn by Zeuner's * or Bilgram's method, as may be convenient ;f from the valve-diagram draw the probable in- dicator-diagram and compute its area, and from that figure the indicated horse-power.:): * See Valve-gears, by Halsey. D. Van Nostrand Co., N. Y. f Valve-gears, by Peabody. J. Wiley & Sons, N. Y. \ Valve-gears, by Spangler. J. Wiley & Sons. N. Y. § 4 2 3-] METHODS OF TESTING THE STEAM-ENGINE. 587 The method of drawing the indicator-diagram by projection from the valve-diagram is well shown in Fig. 281, from Thurs- ton's Manual of the Steam-engine. The steam-pressure and back-pressure lines being assumed, the various events as shown on the valve-diagram are projected upon these lines, and the indicator-diagram completed as shown. Secondly, in attaching the indicators and taking diagrams v Point of * T Admission Fig. 281.— Indicator-diagram constructed from Valve-diagram. from which the error in the position of the valve is determined. Its position is corrected as required, to equalize the indicator- diagrams taken from each end of the cylinder. The special directions are as follows : Apparatus. — Scale, dividers, and trammel-point, the latter consisting of a rod the pointed end of which can be set on a mark on the floor and which carries a marking point at the other end. I. Measure dimensions of valves and ports, throw of ec- centric, and other dimensions called for by engine-log. 588 EXPERIMENTAL ENGINEERING. [§ 423, 2. From these data, with a definite lead assumed, draw valve-diagram, and note position of piston for cut-off, release, compression, and admission. 3. Set the valve to the assumed lead, and with angular ad- vance as indicated by the valve-diagram. Turn the engine over and see that the lead is the same at both ends of the cylinder. This requires the engine to be set on its centre ; this is done by bringing the piston to the extreme end of the stroke at either cylinder-end, so that the piston- and connecting-rods form one straight line. As the motion of the piston is very slow near the end of the stroke, this position is determined most accurately as follows : Mark a coincident line on cross- head and guides corresponding to the position of the crank when at an angle of about 20 measured from its horizontal position ; then, from a fixed point on the floor, swing the trammel-point as a radius, and mark a line on the circumference of the fly-wheel ; turn the engine over until the marks again coincide with the crank on the other side of the centre and make a second mark on the fly-wheel with the trammel-point; bisect the distance on the wheel between these marks and ob- tain a third line ; turn the wheel until this line is shown by the trammel to be at the same distance from the reference-point, on the floor, as the other marks: the engine will then be on its centre. Move the valve the proper amount to make its position correspond with that shown on the diagram. In set- ting the valve remember that to change angular advance, the eccentric must be rotated on the shaft ; and to equalize events for both ends of cylinder, the valve must be moved on the stem. These adjustments must be made together, as they are to some extent mutually dependent. 4. From the valve-diagram draw an ideal indicator-diagram as explained, assuming initial steam-pressure to be (a) pounds per square inch, absolute back pressure 5 pounds absolute, and that expansion and compression curves are true hyperbolae. Calculate its area by formula. Area = PV{i + \og e r) - P V (i + log e r'), § 4 2 5-] METHODS OF TESTING THE STEAM-ENGINE. 589 in which V = volume at cut-off, and P ■— corresponding pres- sure ; V = clearance volume, and P = clearance pressure ; r = number of expansions, and r' = number of compressions. 5. Compute the horse-power of the diagram so drawn, and compare with that shown by the diagram taken. 424. Friction-test. — For this test the engine should be fitted with a Prony brake (see Article 169, page 239, to absorb and measure the power developed. Indicator-diagrams are to be taken and the indicated horse-power computed (see Article 402, page 552). The indicated horse-power being the work done by the steam on the piston of the engine, the dyna- mometer horse-power, that delivered by the engine, the dif- ference will be the power absorbed by the engine in friction, or the friction horse-power. It is customary to reduce this amount to equivalent mean pressure acting on the piston by dividing by product of area of piston in square inches and speed in feet per minute. In making the test for friction of the engine the loads on the brake-arm should be varied, with the speed uniform, or the load on the brake-arm should be constant with varied speed, noting in each case the effect on the frictional work. It has been shown by an extended series of experiments * that the friction of engines is practically constant regardless of the work performed, and that the work shown by the indicator-diagram, when the engine is running light or not attached to machinery, is practically equal to the engine-friction in case the speed is maintained uniform. In the case of variation in speed the friction work increases nearly in proportion to increase of speed. Detailed directions for this test are not considered neces- sary. 425. Simple Efficiency-test. — Engines are frequently sold on a guarantee as to coal or water consumption per in- dicated horse-power (I. H. P.), or in some instances per dyna- mometer horse-power (D. H. P.); in such a case a test is to be made showing the I. H. P. or the D. H. P. as may be required, and the water and coal consumed. * See Transactions Am. Soc. Mech. Engineers, Vol. VIII., page 86. 590 EXPERIMENTAL ENGINEERING. [§ 426. The I. H. P. is to be obtained as already explained in Article 402 ; the D. H. P. by readings from a Prony brake, Article 178. The coal-consumption is to be obtained by a boiler-test, Article 375 ; the total water consumed, by the feed water used in the boiler-test, corrected for leaks and quality; or by condensing the steam in a surface condenser, Article 417, The quality of the steam should be taken near the engine, as explained iiv Article 336, page 433. The principal quantities to be observed are quantities required for a boiler-test, quality of steam near engine, number of revolutions of engine per minute, and weight of feed-water or weight of condensed steam. These observations should be taken regularly and simultaneously once in ten or fifteen minutes, and at the same instant an in- dicator-diagram should be taken. From these data are com- puted the quantities required. 426. The Calorimetric Method of Engine-testing.— Hirris Analysis. — The calorimetric method of testing engines as developed from Hirn's theory by Professor V. Dwelshauvers- Dery of Liege enables the experimenter to determine the amount of heat lost and restored and that transformed into work in the passage of the steam through the cylinder.* The principle on which the method is founded is as follows: The amount of heat supplied the engine is determined by measuring the pressure, quality, and weight of the steam ; that removed from the engine is obtained by measuring the heat in the condensed steam and that given to the condensing water. The amount of heat remaining in the cylinder per pound of steam at any point after cut-off can be calculated from the data obtained from the indicator-diagram ; this multiplied bij the known weight gives the total heat. The heat supplied to the engine added to that already existing in the clearance-spaces gives the total amount of heat available ; if from this sum there be taken the heat existing at cut-off and the heat equivalent of the work done during admission, the difference will be the loss during admission, due * See Table Properties of Steam, V. Dwelshauvers-Dery, Trans. Am. Soc. M. E., Vol. XI. § 4 2 6.] METHODS OF TESTING THE STEAM-ENGINE. 59 1 principally to cylinder-condensation. The difference between the heat in the cylinder at cut-off and that at release after de- ducting the work equivalent is that lost or restored during expansion. This method applied to all the events of the stroke, and at as many places as required, gives full informa- tion of the transfer of heat to and from the metal. In the fundamental equations of this analysis which follow, the following symbols are used : Quantity. Symbol. Quantity. Symbol. Heat admitted per stroke. . . . Weight of steam per stroke. . . Absolute pressure of entering steam, per sq. inch Temperature, degrees Fahr. Heat of the liquid ........... Q M P t ? P r X D I — X c P Heat equivalent of energy of steam in the cylinder at any instant h Joule's equivalent Reciprocal of Joule's equiva- lent J A Weight of 1 cu. foot of steam. Vol. of r lb. of steam, cu. ft. . Volume of cylinder to any point under consideration moved through by the piston, cu. ft .' § Total latent heat Specific heat of steam of con- v Volume of clearance, cu. ft. . . External work in foot-pounds. Vol. of 1 lb. of water in cu. ft . w a The value of the quantity at any point under discussion i c denoted by the following subscripts : clearance, c ; beginning of admission, o ; cut-off, 1 ; release, 2 ; beginning of compression. The equations are as follows for wet or saturated steam ': Heat in the Entering Steam. — Q=M(a+xr); (I) if the steam is superheated D degrees, Q = M{q+r+c t D). (2) 592 EXPERIMENTAL ENGINEERING. [§426. Heat in the Cylinder. — Since the steam in this case is in- variably moist, we have the following equations : In the clearance spaces, h c = M (g c -\- x c p c ) ; ... '3) At admission, k = M (g + x p ) ; . . . (4) At cut-off, K = (M+M,)(q, + x lf >,)', . (5) At . elease, h, = (M + M )(g, + x A ) ; . (6) At compression, h % — M ( •iojBoipni-paads •jaianoo snonupuo3 •3TOIX | uaqtanM afl W Oh TO _C 55 W 6 in V jj , n « a • g | £ _ ""* .5 *** o .S a .5 aT .S § -* c «- rt OT ™ *- »- ^- rt s* b% e 1 2" cd rt c cs rt a* ._, .-, v ;~ <-■ rt Q Q J Q H a U c o rt ctj C I* .— u PQ D J § 4 28 -J METHODS OF TESTJNG THE STEAM-ENGINE. 599 Form No. I. APPLICATION OF HIRN'S ANALYSIS TO SIMPLE CONDENSING ENGINE. Data and Results. Test of steam-engine made by . at Cornell University, Kind of engine, slide-valve throttling. Diameter cylinder 6.06 inches. Length stroke 8 inches. Diameter piston-rod. . i^f " Volume cylinder crank end, o. 12921 cu. ft. ; head end, o. 13354 cu - ft* Volume clearance, cubic foot, head 0.01744 Clearance in per cent of stroke 13.06 Volume clearance, cubic foot, crank 0.01616 Clearance in per cent of stroke 12.51 Boiler-pressure by gauge 69.4. Barometer 29.276 Boiler pressure absolute, pounds 83.7 Boiling temperature, atmospheric pressure, deg. F 210.7 Revolutions per hour 11898 Steam used during run, pounds 716.424 Quality of steam in steam-pipe 0.99 Quality of steam in steam-chest 0.9941 Quality of steam in compression 1.001 Quality of steam in exhaust 0.9021 Weight of condensed steam per hour = . . . . 259.92 Pounds of wet steam* per stroke head, 0.0109707; crank, 0.0109383 Temperatures condensed steam 103.47 deg. F. Temperatures condensing water cold, 42.758 deg. F.; hot, 92.219 * Pounds of condensing water, per hour 5044.878 " " " " " revolution 0.42429 " " " " " stroke-head 0.212016 '* " " " " crank 0.212274 Symbols. To denote different portions of the stroke, the following subscripts are used: Admission, a; expansion, b; exhaust, c; compression, d. To denote different events of the stroke, the following sub-numbers are used* Cut-off, 1; release, 2; compression, beginning of, 3; admission,, beginning of, 0; in exhaust, 5. Quality of steam denoted by X. Cut-off, crank end, per cent of stroke. . . 20.544. Release, crank end. . 93.95$ Cut-off, head end, per cent of stroke... . 18.963. Release, head end. . . 94.971 Compression, crank end, per cent of stroke 52.341 Compression, head end, per cent of stroke 39-77<> Pounds of steam per I. H. P 39-351 Pounds of steam per brake H. P 55.314 I. H. P.- Head 3-3152. Crank 3-3Q54- Total 6.6206 Brake horse-power 4. 71 * Wet steam is the steam uncorrected for calorimetric determinations. 6oo EXPERIMENTAL ENGINEERING. Form No. II. [§ 428. ABSOLUTE PRESSURES FROM INDICATOR-DIAGRAMS AND CORRESPONDING PROPERTIES OF SATURATED STEAM. Cut-off. Release. Beginning Symbols. Com- pression. Of Ad- mission. Ran- kine. Clau- sius. Subscripts used I 2 3 P s I L H C K a u i S Head Absolute pressure. . -j Crank Heat of liquid j g^ Internal latent heat, j c , a a nk P 1 9 Latent-heat evapo- j Head ration ( Crank To-, heat | &* Vo.. I lb.cu.£,...j«- d k A K+r> V c +Vs ^c+^3 ^o+F c MEAN PRESSURES AND HEAT EQUIVALENTS OF EXTERNAL WORK. i/i .2* "C u CO £> 3 (A Head End. Crank End. Mean Pressures. External Work. Mean Pressures. External Work. Foot-lbs. B. T. U. Foot-lbs. B. T. U. Symbols a b c d MP w AW* MP W A IV* Admission, Expansion. ...... Compression Total * A = ij-fr . V c = volume in clearance-spaces. § 4 2 8.] METHODS OF TESTING THE STEAM-ENGINE. 6oi tv 00 00 I I O »0 t-» d rn t^« m m h m rr, os (r) pi (« JO CO o « 00 00 I I I " J* -s- ^° AfcT >^ sT T+ + £*3 + 6"^ + " + £ H c> Ci, s ^ >- e « 4) S « -2 S "2 rt S g « i o ° w o o £ rt *t<~ a s a 2 rt rt rt rt u u t> v •o ,_, j. .2 rt 13 £•3- - ! g'l g CO rt 3 5 « 4; r* *e 8 (H rt o CJ u »- rt rt rt co rt 1 II II T3 X X O 3 rt u u u So '3c ■- 2 « j= -3 « "= Cn in X V X X m S 8 8 ffi hJ hJ o c t> *£? 85 rt ~ J3 rt cj 3.2 (WO £* 602 EXPERIMENTAL ENGINEERING. L§ 428. c o a r^ a> >o 00 V ^ L . ° 00 A{P±p + s)xLxN = -jT X 1, 000,000 (foot-pounds). C X 144 2. Percentage of leakage = . j tj. X 100 (per cent). 3. Capacity = number of gallons of water discharged in 24 hours _ A x Lx Nx 7.4805 X 24 ~DX 144 A XLx NX 1.2467s D (gallons). 4. Percentage of total friction ( IHp _ A{P±p+s)xLxN \ _ ( J _ ^J D X 60 X 33>QQQ ) LH.P. x 100 r A{P±pXs)x Lx N~] , . = 1 1 - A s xM.E.P.xL s xN; 1 X ^o (per cent); or, in the usual case, where the length of the stroke and num- ber of strokes of the plunger are the same as that of the steam- piston, this last formula becomes — r A(P±p+s)~\ , x Percentage of total frictions = I — • . ^ n/r p p ]X iOO(p.c). § 43 2 -] TESTING PUMPING-ENGINES. 629 In these formulae the letters refer to the following quanti- ties : A — Area, in square inches, of pump-plunger or piston, corrected for area of piston-rod. (When one rod is used at one end only, the correction is one half the area of the rod. If there is more than one rod, the correction is multiplied accordingly.) P= Pressure, in pounds per square inch, indicated by the gauge on the force-main. p = Pressure, in pounds per square inch, corresponding to indication of the vacuum-gauge on suction- main (or pressure-gauge, if the suction-pipe is under a head). The indication of the vacuum- gauge, in inches of mercury, may be converted into pounds by dividing it by 2.035. S = Pressure, in pounds per square inch, corresponding to distance between the centres of the two gauges. The computation for this pressure is made by multiplying the distance, expressed in feet, by the weight of one cubic foot of water at the tempera- ture of the pump-well, and dividing the product by 144 ; or by multiplying the distance in feet by the weights of one cubic foot of water at the various temperatures. £, = Average length of stroke of pump-plunger, in feet. N= Total number of single strokes of pump-plunger made during the trial. A = Area of steam-cylinder, in square inches, corrected for area of piston-rod. The quantity A s xM.£.P. f in an engine having more than one cylinder, is the sum of the various quantities relating to the respective cylinders. L s = Average length of stroke of steam-piston, in feet. N s = Total number of single strokes of steam-piston during trial. M.E.P. = Average mean effective pressure, in pounds per 63O EXPERIMENTAL ENGINEERING. [§ 432. square inch, measured from the indicator-diagrams taken from the steam cylinder. I.H.P. = Indicated horse-power developed by the steam- cylinder. C — Total number of cubic feet of water which leaked by the pump-plunger during the trial, estimated from the results of the leakage-test. D = Duration of trial, in hours. H = Total number of heat-units [B. T. U.] consumed by engine = weight of water supplied to boiler by main feed-pump X. total heat of steam of boiler- pressure reckoned from temperature of main feed- water -f- weight of water supplied by jacket-pump X total heat of steam of boiler-pressure reckoned from temperature of jacket-water -|- weight of any other water supplied X total heat of steam reck- oned from its temperature of supply. The total heat of the steam is corrected for the moisture or superheat which the steam may contain. For moisture, the correction is subtracted, and is found by multiplying the latent heat of the steam by the percentage of moisture, and dividing the product by 100. For superheat, the correction is added, and is found by multiplying the number of degrees of superheating (i.e., the excess of the temperature of the steam above the normal tem- perature of saturated steam) by 0.48. No allow- ance is made for heat added to the feed-water, which is derived from any source, except the engine or some accessory of the engine. Heat added to the water by the use of a flue-heater at the boiler is not to be deducted. Should heat be abstracted from .the flue by means of a steam- reheater connected with the intermediate receiver of the engine, this heat must be included in the total quantity supplied by the boiler. The following example is one of those given by the com- 432.] TESTING PUMPING-ENGINES. 63 I mittee to illustrate the method of computation. The figures are not obtained from tests actually made, but they correspond in round numbers with those which were so obtained: EXAMPLE. — Compound Fly-wJieel Engine. — High -pressure cylinder jacketed with live steam from the boiler. Low-press- ure cylinder jacketed with steam from the intermediate re- ceiver, the condensed water from which is returned to the boiler by means of a pump operated by the engine. Main steam-pipe fitted with a separator. The intermediate receiver provided with a reheater supplied with boiler-steam. Water drained from high-pressure jacket, separator, and reheater col- lected in a closed tank under boiler-pressure, and from this point fed to the boiler direct by an independent steam-pump. Jet-condenser used operated by an independent air-pump. Main supply of feed-water drawn from hot-well and fed to the boiler by donkey steam-pump, which discharges through a feed-water heater. All the steam-pumps, together with the independent air-pump, exhaust through the heater to the at- mosphere. DIMENSIONS. Diameter of high-pressure steam-cylinder (one) 20 in. Diameter of low-pressure steam-cylinder (one) 40 " Diameter of plunger (one) 20 " Diameter of each piston-rod 4. " Stroke of steam-pistons and pump-plunger 3 ft. GENERAL DATA. 1. Duration of trial (Z>) 10 hrs. 2. Boiler-pressure indicated by gauge (barometric press- ure, 14. 7 lbs. ) 120 lbs. 3. Temperature of water in pump-well 60 degs 4. Temperature of water supplied to boiler by main feed- pump, leaving heater 215 5. Temperature of water supplied by low-pressure jacket- pump 225 6. Temperature of water supplied by high-pressure jacket, separator, and reheater-pump, that derived from separator being 340 , and that from jackets 200 .. 300 " 632 EXPERIMENTAL ENGINEERING. [§ 432. 7. Weight of water supplied to boiler by main feed-pump 18,863 lbs. 8. Weight of water supplied by low-pressure jacket-pump 615 " 9. Weight of water supplied by pump for high-pressure jacket, separator, and reheater-tank, of which 210 lbs. is derived from separator 1 ,025 " 10. Total weight of feed- water supplied from all sources 20,503 " 11. Percentage of moisture in steam after leaving sepa- rator 1.5$ DATA RELATING TO WORK OF PUMP. 12. Area of plunger minus \ area of piston-rod (A) 307.88 sq. in. 13. Average length of stroke (L and L s ) 3 ft. 14. Total number of single strokes during trial (N and N s ) 24,000 15. Pressure by gauge on force-main (P) 95 lbs. 16. Vacuum by gauge.on suction-main 7.5 in. 17. Pressure corresponding to vacuum given in preceding line (/) 3.69 lbs. 18. Vertical distance between centres of two gauges 10 ft. 19. Pressure equivalent to distance between two gauges (s) 4.33 lbs c 20. Total leakage of pump during trial, determined from results of leakage-test (C) 3,078 cu. ft. 21. Number of double strokes of pump per minute 20 22. Mean effective pressure measured from pump-dia- grams 105 lbs. 23. Indicated horse-power exerted in pump-cylinders.. .. H7-55 I.H.P. DATA RELATING TO WORK OF STEAM-CYLINDERS. 24. Area of high-pressure piston minus -£■ area of rod (A S i) 307.88 sq. in. 25. Area of low-pressure piston minus i area of rod (A s2 ) 1,250.36 " " 26. Average length of stroke, each 3 ft. 27. Mean effective pressure measured from high-pressure diagrams {M.E.P.i) 59-25 lbs. 28. Mean effective pressure measured from low-pressure diagrams (M.E.P. 2 ) 13-60 " 29. Number of double strokes per minute (line 21) 20 30. Indicated horse-power developed by H.-P. cylinder.. 66.33 I.H.P. 31. Indicated horse-power developed by L.-P. cylinder. . 61.82 " 32. Indicated horse-power developed by both cylinders. . 128.15 " 33. Feed-water consumed by plant per indicated horse- power per hour, corrected for separator-water and for moisture in steam 15.60 lbs. 34. Number of heat-units consumed per indicated horse- power per hour ... . 15,652.1 B.T.U* 3$. Number of heat-units consumed per indicated horse- power per minute ' 260.9 " § 43 2 TESTING PUMP1NG-ENG1NES. 633 TOTAL HEAT OF STEAM RECKONED FROM THE VARIOUS TEMPERATURES OP FEED-WATER, AND COMPUTATIONS BASED THEREON. 36. Total heat of 1 lb. of steam at 120 lbs. gauge-pressure, containing 1.5$ of moisture, reckoned from o° F.= i220.6-(i.5# of 866.7) 1,207.6 B.T.U. 37. Ditto, reckoned from 215° temperature of main feed- water = 1207.6— 215.9 99*.7 " 38. Ditto, reckoned from 225 temperature of low-pressure jacket-water = 1207.6 — 226. 1 981.5 " 39. Ditto, reckoned from 290 temperature of high-pres- sure jacket and reheater water = 1207.6— 292.3 = . . 915-3 " 40. Heat of separator-water reckoned from 340°= 353.9 — 343-8 io.i *• 41. Heat consumed by engine {H) = (18.863 X 991.7) + (615 X 981.5) + (815X915.3) + (210 X 10.1)= 20,058,150 " RESULTS. Substituting these quantities in the formulae, we have: a P p s L N 1 n„tv - 3 ° 7 - 8 8 X (95 + 3 ' 6g + 4 ' 33) X 3 X 24>QQQ — 1. Duty = — ■ X 1,000,000 20,058, 1 50 = 113,853,044 foot-pounds. C 2. Percentage of leakage = — £ I44 ^ x 100=2.0$. 307.88 X 3 X 24,000 3. Capacity = 3< * 88 X 3 X 2 ^°° X U2 &\ 10 = 2,763,716 gallons. 4. Percentage of total frictions a p p s 307.88 x (95 + 3.69 + 4.33 ) A a M.E.P., A S2 MJE~P~: 2 l XI 00 (307.88 X 59-25) + (1250.36 X 13.6) = 9-oJf. 634 EXPERIMENTAL ENGINEERING. [§434- In the use of a system like the preceding, every precaution should be observed in the adoption of methods, as well as in taking observations. The water discharged by a -pumping- engine, for example, should never be obtained by computation from the measured dimensions of the pump and the observed number of strokes, but should be measured directly. A weir is commonly arranged for this purpose. Where the delivery of the pump has been actually measured, and the pump thus standardized, its use as a meter is less liable to error, but it is best avoided whenever possible. 434. Standard Method of Testing Locomotives. — The following is a reprint of a report of a committee on standard methods of testing locomotives appointed by the American Society of Mechanical Engineers, and submitted at the San Francisco meeting in 1892 : Locomotive-testing is conducted under such unfavorable circumstances and surroundings that many of the exact methods employed in testing stationary engines or boilers cannot be used. It is desirable, therefore, that locomotive-tests be always made with a special train when possible, so that the same cars shall be used for the different trips, and the weight of train be uniform. The speed of the train can also be under control, and the tests not hampered by the rules governing a regularly scheduled train. Special and peculiar apparatus is employed by nearly every different experimenter as having some extra merit of convenience or accuracy, and we have endeavored to ascertain the best practical instruments and methods for the various measurements, and to illustrate or explain them. When a dynamometer-car is not used : As a final basis of comparison of locomotives, we recom- mend as a unit the number of thermal units used per indicated horse-power per hour. The object in view in testing a loco- motive will determine the methods employed and the extent and kind of data necessary to obtain. Some tests are made to ascertain the economy of a particular kind of boiler or fire- §434-11 TESTING LOCOMOTIVES, &ly box; others, the value of employing compound cylinders; others, to ascertain the relative merits of certain coals for locomotive use. As a practical and commercial unit the amount of coal consumed per ton-mile may be used. For a coal-test we give a separate method and test blanks, Form D, for tabulating results. For a unit of comparison of boiler-test we recommend the number of thermal units F. taken up every hour by the water and steam in the boiler. For a measurement of the resistance overcome in hauling a train, a dynamometer-car is essential, and we give a method of operating a dynamometer-car and of recording results. For a uniform method of recording results of indicator- tests, we recommend the blank Form A. For tabulating general results, Form B is presented. The waste from the injector should be ascertained by catch- ing it in a vessel conveniently attached, or by starting the in- jector several times in the engine-house and catching the over- flow in a tub. The total weight of the water caught divided by the num- ber of applications of the injector gives the average waste. The observer in the cab should keep a record of the number of times the injector is applied during the trips, and thus obtain data for estimating the total waste. FUEL MEASUREMENTS. The measurement of fuel in locomotive-tests is not difficult so far as a determination of the total amount shovelled into the fire is concerned. A weighed amount may be shovelled into the tank, and the amount remaining, after a given run, be weighed to determine the amount used, provided no water is used to wet down the coal. But it is next to impossible to determine the amount of coal used at any particular portion of a run when the coal is put in the tender in bulk. If coal is put in sacks containing 125 pounds each, with a small amount of "weighed coal on the foot-plate, even with heavy firing it is 636 EXPERIMENTAL ENGINEERING. [§434- found quite possible for the fireman to cut open the bags, and dump the coal on the foot-plate as needed. In this way the rate of consumption on difficult portions of the run could readily be estimated. The use of water-meters and of coal in sacks obviates any need of weighing the tender, and thus re- moves one of the largest inaccuracies incident to the ordinary locomotive-tests. To determine the amount of coal used dur- ing the trip, it is only necessary to count the number of bags which have been emptied. However, the determination of the amount of fuel used during a run is not all that is neces- sary for a test. The measurement of the fire-line before and after a test is very essential and extremely difficult. If the run is a long one, then the errors in the determination of the fire-line may not be great ; but for short runs there seems to be no way of measuring the difference between the heat-value of coal in the fire before the test and after with sufficient accuracy to give reliable data. In tests made on a heavy grade, one trip closely succeeding another, it is of course im- practicable to drop the fire and measure the amount of fuel in the ashes remaining. Such measurements are unsatisfactory and inaccurate in any case, because it is not practicable to draw the fire without wetting it, as the ashes rise into the machinery, and they are too hot to handle. When one run succeeds another within a short space of time, some other method is necessary for measuring fuel used than by dumping the coal. The test is commenced with a good fire in the furnace, and the height of coal estimated by two or more assistants engaged in the trial. At the end of the run the fire should be in the same condition as near as possible. No raw coal should be in the box and steam-pressure and pyrometer-pressure falling. APPLICATION OF THE INDICATOR. If the power of the engine is to be determined, the action of the valve-gear examined, or the coal and water used per unit of power in a unit of time, the indicator must be used. § 434- TES TING L O CO MO Tl FES. 637 This instrument should be attached to a three-way cock just at the outer edge of the steam-chest, in order that the con^ necting pipes (which should be { inch in diameter) can go directly in a diagonal direction to holes tapped into the sides of the cylinder rather than into the heads (Fig. 285). By this arrangement the pipes are shorter than when they pass over Fig 285. — Reducing-motion for Locomotives. the steam-chest into the heads, and have but short horizontal portions, thus facilitating the rapid draining of the pipes. Moreover, if a cylinder-head is knocked out th~ pipes are not dragged off, and the operator and indicator escape injury. The indicator should not be placed on horizontal pipes on a level with the axis of the cylinder-heads. The indicator-pipes and three-way cock should be covered with a non-conductor, wrapped with canvas and painted. The indicator itself should be wrapped as high as the vent-holes in its steam-cylinder. 6 3 8 EXPERIMENTAL ENGINEERING. [§434- The indicator-gear may be a rigid, true pantograph motion, either fixed or adjustable in height (Fig. 286) ; or it may be a simple pendulum connected by link to the cross-head with a wooden quadrant 2 inches thick, and having a radius such as will make the indicator-card 3 inches long. The cord of the indicator should be 8 or 10 inches long, and connected with a rod reaching forward from the panto- graph. In order to determine the steam-chest pressure, the indica- tor should be so piped that a steam-chest diagram can be Travel 3 mid-position Rigid Non Adjustable Fig. 286.— Reducing-motion. drawn by it. A steam-gauge on the chest is inaccurate and difficult to use. Indicator-diagrams should be taken at equal distances in- stead of at equal time-intervals, in order to properly average the power. They should therefore be taken at mile-posts. The signal for taking diagrams should be given by the observer in the cab, who can pull a cord and ring a bell at the front of the engine, or blow the whistle. For the safety of the operator at the indicator, it is recom- mended that the seat be on a piece of boiler-plate above the cylinder, and so arranged that a piston or cylinder-head can pass out without injuring him. § 434-3 TESTING LOCOMOTIVES. 639 The person who takes the indicator-diagrams should be thoroughly sheltered by a temporary box containing a seat placed on the front end of the engine. Besides the usual indi- cator, there should be located near the observer a revolution- counter, which should be so arranged that after starting out the instrument will continue to record the revolutions for a period of exactly one minute, starting every time from zero, and when the minute has elapsed the counter will stop. Such an instrument is already in existence for taking the continuous revolutions of dynamos and high-speed engines, and little or no difficulty would be experienced in obtaining an instrument capable of taking the revolutions from some reciprocating part of the machinery. It is desirable also to have an electric connection between the indicator and the recording apparatus in the dynamometer- car, so that at the instant an indicator-diagram is taken, the fact may be registered on the dynamometer-diagram, see Article 181, page 246; and the cards should be numbered con- secutively, and the record likewise. Besides the person taking the indicator-diagrams, another person should be located in the cab of the engine, whose duty it should be to observe the point of cut-off given by the posi- tion of the reverse-lever, the position of the throttle-lever, and the boiler-pressure, all of which conditions should be recorded in a log-book for this purpose. Besides recording on the dynamometer-diagram the fact that an indicator-card is being taken, a bell should be rung at the same time, so as to call the attention of the observers in the dynamometer-car to this tact. LOCOMOTIVE-BOILER TESTS.— GENERAL DIRECTIONS. First. The drawing of the boiler to accompany the report of tests should be particular in specifying the construction in de- tail, with reference to coal-burning and generating steam, such as heating surface, grate area and the distribution of openings through the grate, volume of fire-box, size and thickness of 64O EXPERIMENTAL ENGINEERING. [§434- flues, size of smoke-box, and the arrangement for draught, together with the thickness of walls between the heated gases and the water in the boiler ; the weight of the boiler itself should be given, and the number of cubic feet of water-space and of steam-space in the boiler, the division between the two to be taken at the middle of the range of the gauges. Second. Boilers for tests should be thoroughly cleaned on both sides of the heating surface, by a removal of the flues, before any test is commenced, and these surfaces should be kept clean by frequent washing during the test. Exception. — When it is desired to make a comparison of boilers for the purpose of determining a difference between them as to incrustation, they should first be tested as above when clean, and then tested again without cleaning further than the ordinary washing out of the boilers after the lapse of some months' service. The results are to be reduced to evaporation per square foot of heating surface ; both boilers using the same water during the period of testing. Third. In case the measure of the capacity of the locomo- tive boiler for generating steam be desired, without reference to the engines forming the locomotive, this capacity should be measured by the number of British thermal units, taken up per hour by the water and steam in the boiler, which may be readily determined from the observed data of temperature of water fed to the boiler, pounds of water evaporated per hour, and steam-pressure under which this evaporation occurs. Use any good set of steam-tables, such as Peabody's or Por- ter's, found in Appendix, or in Richard's Steam-engine Indica- tor. In such cases it will be necessary to specify all the perti- nent conditions under which such measure of the capacity of the boiler is made, so that in comparing with the capacity of another boiler all such conditions may be made as nearly alike as possible. It is, however, believed that a measure of the capacity of a locomotive boiler, without any reference to the capacity or efficiency and method of working of the engines on the locomotive which such boiler feeds, will not be of par- ticular value in comparison of boilers, unless the conditions § 434-] TESTING LOCOMOTIVES. 64 1 under which the entries are worked with different boilers are identical, or nearly so. Fourth. On account of the important influence which the temperature, and especially the moisture of the atmosphere, has upon the results obtained in a boiler-test, it is necessary to compare two or more boilers at the same place and at the same time, to get results which may be strictly comparable. The temperature of the air should then be noted for record. Fifth. To properly determine the amount of water fed to a locomotive boiler in service on a locomotive during any test, it is necessary to use a good water-meter, which should have its maximum error determined by previous tests and given with the report. Sixth. The coal used should be dry when weighed, and placed in sacks, each containing 100 or 125 lbs., care being taken to insure that all scales used are accurate. When an un- usually large amount of coal is needed, a weighed quantity of coal may be placed in the front of the tender and used first, and the test finished with coal from the sacks. An analysis of the coal used should accompany the report, which should show the volatile matter, the fixed carbons, etc., the moisture, and the ash contained in the coal. The ashes should be dried if they contain any moisture, and carefully weighed and re- corded after each test-run. Seventh. The temperature of the smoke-box gases should be measured by a good pyrometer, located near enough to the flues in the smoke-box to get the average temperature of the gases after they have passed the heating surface, and before they are mixed with the exhaust steam. It is suggested that pyrometers, such as that offered by Schaeffer & Budenberg, or Weiskopf, are suitable for this purpose. The location of pyrometers is shown in Fig. 288. These instruments cost about thirty-five dollars. They should register up to 1000 F. See Article 296. Eighth. The degree of exhaustion in the smoke-box should be measured and recorded by means of a simple manometer gauge. See Article 273. 6 4 : EXPERIMENTAL ENGINEERING. [§434- Ninth. The quality of the steam furnished by the boiler to the engines should be determined by the most approved methods: See Chapter XIII. Tenth. Samples of gases passing from the flues to the smoke-box should be analyzed and results reported. The Fig. 288. means of taking such gases so as to insure perfect samples is to be further considered, and definite means prescribed. See Article 358, page 473- COAL TESTS. Directions to be observed in Supervising and Conducting Coal- trials. — The locomotive selected should be in good condition, § 434-] TESTING LOCOMOTIVES. 643 and either a new engine or one that has lately undergone repairs. The boiler should be washed before commencing the trial, the steam-gauge tested, the flues cleaned, and the exhaust nozzles cleaned and measured, which operations should be per- formed also whenever the kind of coal is changed. Instruc- tions should be given to round-house foremen that no repairs or alterations of any sort be made to the engine without the approbation of the conductor of the trial. The same engine- man and fireman should operate the engine throughout the trial, and the same methods of firing and running should be strictly adhered to. The run selected should be one in which the same distance is covered on each trip. The trains should be through trains and unbroken from end to end of the run, and the same number of cars and same lading should be pro- vided each trip. The same speed should, if possible, be pre- served on all trips. The conductor of the trial should be familiar with correct methods of firing and running locomotives, and should insist that the fireman adhere to approved methods of firing, and that the same method's be preserved throughout the duration of the trial, so that all coals shall receive the same treatment. (See Chapter XIV, on Heating Values of Fuels, and Chapter XV, on Steam-boiler Trials.) He should also see that the coal supplied at coaling points is of the proper kind, and should weigh the coal personally, and keep an accurate record of the following items : The coal consumed. The amount of ash. The amount of cinders in smoke-box. The water evaporated. The number of cars in train. The weight of cars as marked thereon. The weight of lading. The state of the weather. The direction and estimated velocity of wind. The temperature of the atmosphere. 644 EXPERIMENTAL ENGINEERING. [§434- The temperature of the feed-water. The time on road. The steam-pressure. The exhaust-nozzles. The conductor should enter the above observations in a log-book, together with notes of repairs to engine, and any other items that might be of import. REPORT OF COAL-TRIALS. In order that coal-trials may be similar and consequently comparative, the following data should be observed (see Arti- cle 343, page 443) : First. Dates between which trials were conducted. Class of locomotive. Service in which trials were made, mentioning locality, etc. Name of conductor of trial. Second. Coal A. Kind of coal. Name of mine and operator. Location of mine. Physical quality of coal (appearance). Steaming quality of coal. Kind of fire made. Clinkers and ashes. Cinders in smoke box. Cleaning ash-pan and smoke-box. Labor involved in firing. Coal B. Same as above. GENERAL REMARKS. Comparison of evaporation (pounds of water evaporated per pound of coal). § 434-] TESTING LOCOMOTIVES. 645 Comparison of coal consumed per 100 tons hauled one mile. Value coal A, ioo#. Value coal B. Comparative value. Coal A is 100$ more or less valuable than coal B. A table of engine-performance and a table of general re- sults of engine-performance for each coal must accompany the report. (See Form D, page 646.) WATER-MEASUREMENTS. It has been found during the last year or two that meters are reliable and accurate within less than one per cent for measuring the water used by a locomotive. (The experience of the author does not accord with this statement — see Article 214, page 284.) The meters should be specially made for the purpose and, if possible, free from any material that is injured by contact with hot water. They should be placed so as to be read from the cab. In mounting these meters, all pipes should be thoroughly cleaned before they are put into position, and a sufficiently large strainer should be placed between the meter and the tank. A most essential feature is to have a good flap check-valve be- tween the injector and the meter ; otherwise the hot water may flow backward and ruin the rubber recording-disks in the meter. As a check upon the meter, however, other means of measuring the water should be employed. The most convenient method is to use a float attached to a wooden bar which slides upon a graduated rod, the lower end of which rests upon the bottom of the tank. This rod is graduated to show 1000 lbs., and subdivided to 250 lbs. The method of graduating the rod is as follows : Fill the tank, place the bar and float in the proper position for read- ing, and mark the stationary rod zero at a level with the top of the float bar. Draw from the tank 1000 lbs., place the measuring device in position again and mark the rod, calling this mark 1. Again draw off 1000 lbs., mark the rod 2, and so continue until the water is all drawn. If the tank has a uni- 646 EXPERIMENTAL ENGINEERING. [§434. J < c* H J < O U w 1 OT 1 < u u oq "z w • >* < £ : 8 S £ : « x £ • ^ o o : S Uh y o % w J 1 ^* «q w . > * r-- O s o u o -J M I u 1 1 "3[!IM jadsuoxooi J35° EXPERIMENTAL ENGINEERING, '% 434- measured from a base-line drawn upon the paper by a station- ary pen so located that when no force is exerted upon the draw-bar the base-line should coincide with zero pull. "B." — THE SPEED AT WHICH THE TRAIN IS RUNNING. This record should, if possible, be obtained in two ways : First. — By an accurate time-piece, preferably a chronometer furnished with an electric circuit-breaking device. It is of con- siderable importance that the time-piece should have its circuit- breaking device very carefully made, to produce exact intervals- of-time marks, because, when the matters of acceleration or re- tardation of speeds enter into the data required, it is important that the time-record should be correct. The question of length of intervals of time required is open to discussion. In most cases of ordinary work, five-second intervals, or twelve to the minute, are probably as satisfactory as can be decided upon ; for very careful work it would probably be advisable to have an auxiliary apparatus, something like the Boyer speed- recorder. Boyer Speed-recorder. — This instrument is constructed in such a manner that its accuracy and reliability are without question when it is properly mounted and cared for. It is not a delicate machine, and only needs ordinary attention. Its principle of operation is as follows : It consists of an oil- pump which works against a fixed resistance in the shape of an aperture through which the oil flows. The faster the pump runs, the greater is the pressure in the oil-cylinder. A piston in the oil-cylinder which moves against a spring rises in proportion to the increase of pressure. As the piston rises, a metallic pencil marks the movement on a roll of pre- pared paper, which moves in proportion to the longitudinal movement of the engine. In the cab is a dial which indicates at all times the speed of the engine with only a small error. The diagrams record all stops and make an accurate record of the rate of acceleration. Second. — It would be well to have, in addition to the § 434-] TES TING LOCO MO TI VES. 6 5 I apparatus just described, another one which produces a con- tinuous curve upon the diagram paper, the ordinate of which, measured from a base-line, would give the speed in feet per second, or any other convenient measurement ; this could be obtained by modification of the Boyer speed-indicator. « C " — THE LOCATION OF ANY POINT ALONG THE LINE USED FOR REFERENCE STATIONS. These location-marks are most easily produced by having, at various convenient parts of the car, electric press-buttons, and having a pen upon the dynamometer which will be deflected sidewise when the circuit is made or broken ; this pen to be operated by an observer whose special duty it is to attend to this part of the work. " D."— WIND-RESISTANCE. Very little attention has so far been given to measurements of wind-resistance, or the relation it bears to the frictional resistance of journals and wheels, and few experiments on this subject are recorded. The subject is very complex, owing to the fact that it is generally supposed, and we think with good reason, that the train is so very largely surrounded by eddies of air, and that it will be very difficult to obtain any reliable data, especially when it is remembered that the clearances of a rail- road are greatly circumscribed and reduced to a minimum, so that it will be impossible to put any apparatus which measures resistance of this kind far enough out from the car to get reliable data. The apparatus for measuring this resistance would probably be subdivided into three separate disks, one facing front and two facing toward the sides of the car, all three connected together to produce a single resultant curve drawn upon the diagram paper, and the scale upon which this is drawn could probably be best subdivided into ten points, as practised by the United States Government. 652 EXPERIMENTAL ENGINEERING. [§434- GENERAL. It is of very great advantage to have more than one relative speed on the paper upon which the diagrams are recorded, and the length of the paper consumed per mile run should bear some convenient relation to the distance travelled over. We would suggest that the rates of travel of paper per mile be such that 1 inch measured upon the diagrams shall represent 100 feet as the maximum, and that this distance be further subdivided so that \ inch shall represent 100 feet of track, and \ inch shall represent 100 feet of track. It is of course also necessary to have all of the registering pens located upon one line transverse to the direction of the movement of the paper, as in that way only can simultaneous data be recorded. The staff required to work the dynamometer is as follows : One chief, who has general supervision over the force, and whose duty it is to see that the records are properly obtained, and that all the location stations are properly marked upon the diagrams. One outlook, whose duty it is solely to observe the location stations, and to locate them upon the diagrams by means of an electrically moved pen. Besides this it is of considerable advantage to have a third person who is familiar with all the mechanism in the car, and who looks after the proper working of the mechanical parts oi the apparatus, and assists the general observer. TABLE OF ENGINE-PERFORMANCE. The following forms are recommended for tabulating the results of a locomotive-test, and in order to make the test com plete each test item should be entered. It is particularly im portant that the "equivalent evaporation from and at 21 2° per pound of coal " be entered, as it is only by this that evaporative comparisons can be made. § 434 ] TESTING LOCOMOTIVES. 653 O T3 C 3 C O O TO w c S #> (4 u o to m ro length of connect- ing-rod ; ft, the crank-angle measured from its position when parallel to the centre line of the cylinder ; M, mass of the piston, piston-rod, and cross head ; m, the mass of the connect- ing-rod ; r, angular velocity of crank-shaft ; 6, connecting-rod angle; P n and P c , forces exerted by the connecting-rod upon wrist-pin and crank-pin, respectively; P a , pressure of steam on the piston ; T, tangential component of the force P c acting on * See Thurston's Manual of the Steam-engine, Vol. II., page 425. 660 §437-] DETERMINATION OF INERTIA. tt\ the crank-pin ; N, radial component of the force P e acting at the crank-pin ; Z and P b , auxiliary quantities. We have 7 _ n 2 cos 2 6 - «'-sin a + sin 4 _ ( n * _ sin 2 fl) 3 ' />, = (M+ m)T*R(cos V + Z); T = (P a ~ P p ) sec./? sin (0+ fi) ; N = (P a - P p ) sec /?cos (0 + /?) ; P e =(P a -Ps) sec A When the accelerating forces are not included, r = P a sec/?sin(0 + /?); />, = P a sec /?. In this work is discussed only the experimental method of determining the inertia of an engine as developed by Mr. E. F. Williams of Buffalo, N. Y., and published in the American Machinist in 1884 and '5. 437. The Williams Inertia-indicator. — This instrument draws a curve (see Fig. 290) closely resembling the theoretical inertia-diagram, and similar in kind to an indicator-card. The horizontal length of the diagram corresponds to the stroke. The abscissa of any point of the curve identifies the position of the piston at a corresponding point in its travel, and its ordi- nate measures to a known scale the force required to give to a mass of known weight (one or two pounds) the acceleration, positive or negative, of the piston at that point of its stroke. The product of this force into the weight of the reciprocating parts, in pounds, gives for that point of stroke the positive 01 negative horizontal force at the crank-pin due to the inertia of the parts. The instrument is shown in Fig. 290 attached to the cross-head of an engine, and in Fig. 292 in plan. The frame P is rigidly attached to the cross-head A hy two studs / and r, the former serving also as a pivot for the arm IJ. The upper end of B is pivoted to one end of a horizontal bar y whose other end is attached by a pin to some fixed support. In this way B swings back and forth, its lower end, together 662 EXPERIMENTAL ENGINEERING. l§ 437- n fQi Fig. agu— The Williams Inertia-instrument. Plan View. Fig. 29a.— Spring to Inertia-instrument. d Fig. 29a— The Williams Inertia-indicator. §437-] DETERMINATION OF INERlIA, 663 with the frame P and the parts carried by it, travelling with the cross-head. Within the case or cage d (shown in section in Fig. 292) the weight h is free to slide horizontally on steel friction rollers, except as controlled by the spring. This spring, whose tension is known by calibration, is the only means by which the motion of the cross-head is communicated to the weight kj and it must therefore be extended or compressed by an amount which measures the force needed to overcome the inertia of the weight. For convenience h may be made to weigh, including the parts moving with it, exactly one pound. It is joined by a light rod e to the bent lever a which moves a pencil in a direc- tion at right angles to that of the cross-head motion. By the vibration of the arm B the paper is carried under the pencil on the curved platform b shown in Figs. 290 and 291. This can at pleasure be drawn upward by the cord m, and kept in contact with the pencil for one or more revolutions while the engine is in motion. The paper is put in place while the engine is at rest, and the neutral line x, Fig. 291, is drawn by swinging the arm B back and forth by hand. As soon as the engine is run- ning under the conditions desired, contact may be made and the diagram drawn. In using the instrument so as to make a diagram from 2 to 3 inches long, the arm B may be varied in length to suit the stroke of the engine. To maintain a given average length of ordinates for widely differing speeds, the scale maybe changed by changing the spring, or the weight, or both. For obtaining the effect per pound weight of the recipro- cating masses, determine the scale as follows : The force exerted by an 80-lb. indicator-spring when it is compressed or extended \ inch, causing a pencil-movement of one inch, is 80 lbs. per square inch of indicator piston-area. The latter being one-half square inch, the actual force on the spring is 40 lbs. If, then, an 80-lb. spring with a 2-lb. weight be used, a i-inch ordinate, will mean 40 lbs. exerted by thc spring in total, or a force of 20 lbs. per pound of the mass it moves. 664 EXPERIMENTAL ENGINEERING. [§ 438. Thus a scale 20 means a force, for each inch of ordinate measured from the neutral line, equal to twenty times the weight of the moving body under investigation. In other words, each twentieth of an inch in length of ordinate repre- sents a force equal to the weight of the reciprocating masses. An 80-lb. spring with a i-lb. weight, scale 40 " 80-lb. " " " 2-lb. " " 20 " 40-lb. " " " i-lb. " " 20 . " 20-lb. " " " I-lb. " " 10 438. The Inertia-diagram drawn by the Instrument. — In interpreting the diagram several points are to be noted : 1. The evenness and general form of the diagram are largely influenced by the smoothness of running of the engine, which depends on the accuracy of bearing surfaces, and the degree in which the weight of reciprocating parts, their veloci- ties, and the varying steam-pressures are suited to each other. 2. The curvature of the lines traced depends chiefly on the ratio of crank-length to that of connecting-rod ; this ratio should be determined by measurement. 3. In combining the diagram with an indicator-card the ordinates should represent forces in pounds per square inch of piston-area, and in the same scale as that of the indicator-card. For this we determine by independent measurement (1) the force exerted by the spring for a given length of ordinate from the neutral line ; (2) the ratio of the weight of the reciprocating parts of the engine to that of the parts of the instrument moved by the spring ; and (3) the area of the engine-piston. 4. The difference in length of the corresponding ordinates in the inertia and indicator diagrams, the latter corrected for back pressure or compression, represents the net horizontal force transmitted to the crank-pin. For combination with a steam indicator-card, the force per square inch of piston-area is required. This is best obtained by getting the weight-ratio or the weight of reciprocating parts per square inch of piston-area. This multiplied by the scale of the inertia-diagram gives the engine-scale or scale of pounds per 438-] DETERMINATION OF INERTIA. 665 square inch at the speed at which the diagram was taken. An example will make this clear. The inertia-diagram in Fig. 234, taken from a very smooth-running engine, was obtained with an Scale 40 revs, per min. Hi" as 1Q" Porter- Allen Fig. 293. — Inertia-diagram. Scale 40 265 revs, per min., 4.416 " " sec. Fig. 294. — Inertia and Indicator Diagrams. 80 spring and a one-pound weight. Hence the diagram-scale is 40. But for this engine the weight-ratio was 3. Hence 40 X 3 = 120 is the engine-scale. Having, now, this inertia-diagram (Fig. 234) whose engine- scale is 120, suppose we are to combine it with an indicator- diagram (Fig. 235) from the same engine at same spe The plus sign to be employed before s when the suction- water is supplied under pressure ; otherwise the negative sign is to be used. If the friction in the pipe be neglected, V= V2gn, and we have v V2gn , . y = 1. ...... hi\ ' 2gn — sg v 0/ 442. Limits of the Injector.— Maximum Amount of Water Lifted. — This may be obtained from equation (12) or (13), but it can be obtained with sufficient accuracy by neglecting the WV f momentum due to the suction-water in equation (7) ; in this case from which W v v 1400 , , v y = — = 77 — 1 = . — — 1 = . — — 1, nearly. (14) §44 2 THE STEAM-INJECTOR— THE PULSOMETER. 677 The maximum ratio of water to steam is shown by the fol- lowing table : Delivery Pressure Maximum Ratio Delivery Pressure Maximum Ratio above that on of Water to above that on the of Water to Injector. Steam by Weight. Injector. Steam by Weight. IO 36.5 55 15.5 15 29.8 60 14.7 20 25.6 65 14-3 25 23.8 70 13-7 30 20.9 75 13.3 35 19-5 80 12.9 40 17.87 85 12.6 45 17.0 90 12. 1 50 16.2 100 11. 5 1 The minimum amount of water required must be sufficient to condense the steam, in which case W h-q, y " w t' t' 05) in which h is the heat in one pound of entering steam ; q 9 , the heat of the liquid in the delivery, both reckoned from 32 ; /', the temperature of the delivery ; /, that of the feed-water, so that the ratio cannot be greater than shown in equation (14) nor less than that shown in equation (15). Temperature of Feed-water. — As the temperature of the feed-water increases vapor is given off which increases the pressure, b, in equation (9) on the surface of the supply-water, and reduces the height through which the water can be lifted. If the temperature of the feed-water is greater, the amount required to condense the steam must also be greater; but as the amount lifted by a given amount of steam cannot exceed the approximate value given in equation (14), we shall have at the extreme limit at which the injector works, the values of y as given in equations 14 and 15 equal to each other, from which the maximum temperature of feed-water becomes * = *'- {hj-q^v v- V = t' 1400 — 4/^ , nearly. 678 EXPERIMENTAL ENGINEERING. [§ 442'. The following table gives approximately the limiting values of suction-head in feet and temperature of feed-water : LIMIT OF SUCTION-HEAD IN FEET. Pressure of Limit of Suction- Steam-pressure 100 lbs. Absolute. Temperature of Feed-water. Vapor. Pounds head in case of Delivery 212 Fahr. Delivery 180 Fahr. Degs. Fahr. per sq. inch. Vacuum. Feet. Number of Pounds of Water to con- Number of Pounds of Water to con- dense one of Steam. dense one of Steam.. 70 O.36 32.96 7.04 8.8l 80 O.50 32.6 7-57 9.61 90 O.69 32.2 8.19 IO.76 IOO O.94 31.4 8.92 12. II HO 1.26 30.9 9.80 13.84 I20 1.6? 29.7 10.87 16.I5 I30 2.22 27-3 12,20 19.32 I40 2.87 25.9 13.89 24.22 I50 3-70 24.8 16.13 32.3 l6o 4.72 22.5 19.23 48.45 I70 5.98 19.6 23.81 96.9O I80 7-50 16.9 31-25 I90 9-33 9-9 45.46 200 11.52 9-3 83-33 2IO 14.12 1.1 500.9 MAXIMUM TEMPERATURE FEED-WATER. Maximum Temperature of Maximum Temperature of Gauge Press- ure. Pounds Feed-water. Degrees Fahr. Gauge Press- ure. Pounds Feed-water. Degrees Fahr. per sq. inch. Discharge Discharge per sq. inch. Discharge Discharge 180 Fahr. 212 Fahr. 70 i3o° Fahr. 212 Fahr. 20 142 173 109 139 25 137 168 75 I07 137 30 133 164 80 T o5 134 35 129 160 90 99 129 40 126 156 100 95 125 45 123 153 HO 91 121 50 I20 I50 I20 87 117 55 117 147 130 83 "3 60 114 144 I4O 80 no 65 III 141 ISO 77 107 § 444-] THE S TEA M-INJE C TOR - THE P UL SOME TEE. 679 A series of carefully conducted experiments* made at Sib- ley College, Cornell University, to determine the efficiencies of different steam injectors, confirm the results expressed in the preceding computations. 443. Directions for Handling and Setting Injectors. — Injectors are of two general classes, lifting and non-lifting. In the first class water is drawn in by suction and then discharged against a pressure; in the second class water flows in under pressure and is discharged against a greater pressure. As there is a limit to the temperature at which water will be handled by the injector, variations in steam-pressure will affect the discharge and may cause it to stop altogether. This may be regulated to a certain extent by manipulating the valves of the steam and water supply ; some injectors are self- adjusting in this respect and are termed automatic. The general directions for starting an injector are to open the overflow, turn on steam until the water appears at the overflow, and the temperature of the injector is sufficiently low to condense the steam. Then close the overflow and the in- jector should discharge against a pressure equal to or greater than the steam-pressure. In many of the injectors the over- flow valve will open whenever the pressure in the injector becomes greater than that of the atmosphere. In several kinds the overflow is closed by a valve regulated independ- ently or connected by a lever to the starting handle so as to be opened and closed at the proper time by the simple opera- tion of admitting steam. Injectors will not work with oily or dirty water, and are liable to be stopped by anything that will not pass the nozzles. In general they are to be connected by pipe-fittings made up without red lead and arranged so as to deliver water into a pipe leading to the boiler, in which is placed a check-valve to remove the boiler-pressure when starting the injector. 444. Directions for Testing. — For testing the injector use two tanks, both of which are to rest on weighing-scales. * See Cassier's Magazine, Feb. i8q2. 68o EXPERIMENTAL ENGINEERING. [§444 Fill one of the tanks with water, and locate the injector any convenient distance above or below this tank, and arrange it sc as to deliver water into the second tank. If the water that escapes at the overflow is arranged to run into the tank from which the water is taken, no correction will be requi/red ; otherwise it must be caught and weighed. Place a valve in the delivery-pipe, some distance from the injector or beyond an air-chamber, and regulate the delivery- head by partly opening or closing this valve. The delivery- pressure, which can be reduced to head in feet of water, can be measured by a pressure-gauge in the delivery-pipe ; the suction- pressure is observed in a similar manner by using a vacuum- gauge or a manometer. The water received, W, is that taken from the first tank ; the amount delivered, W-\- w, is that weighed in the second tank ; the difference is w, the steam used. Arrange thermometers to take the temperature of the water as it enters and leaves the injector. Make runs with discharge-pressures equal respectively to one-fourth, one-half, three-fourths, once, and one and one- fourth times that on the boiler. During each run take obser- vations, as required by the blank log furnished, once in two minutes. Determine the limits at which the injector stops working, for temperature of feed-water, suction-head and delivery-head. Careful trials show that the thermodynamic efficiency of any injector is ioo per cent ; by assuming this as true the sec- ond tank may be dispensed with, and the amount of steam computed from its heating effect and known quality on the water passing through the injector. In the report, describe the injector tested, explain method of action, and submit a graphical log, with time as abscissa, as well as an efficiency curve for varying pressures of discharge, also for varying temperatures of discharge. Fill out the log and make complete report, after the stand- ard form. § 445-] THE STEAM-INJECTOR— THE PVLSOMETER. 68 1 445. Form for Data and Results of Injector-test. Cu V bf, ■s "•5 a* 5 Cu c «> s <-> a .0 u 8 n v- e *- c H ~ Q c£ Q c£ cu > cu 3 £ S ?. o o .2 B a S £ e H H £ £ H 682 EXPERIMENTAL ENGINEERING. [§445- + V * g + + E + * ^ ■H V X ^ 4- k 4- * + 8 S CO *s, m o X 2 o o 8 i 3 Is, s5 f< J PQ £ SB :=! H a r* Q O U II 1^ £ ^ O 54 I Vo a s s £ £ £ ao £ e a « w w U U > § 44 6 -] THE STEAM-INJECTOR— THE PULSOMETER. 683 446. The Pulsometer. — This is a pump consisting of two bottle-shaped cylinders joined together with tapering necks, into which a ball C is fitted so as to move in the direction o5 least pressure, with a slight rolling motion, between seats formed in the passages. These chambers connect by means of open- ings fitted with clack-valves, E £, into the induction-chamber D. The water is delivered through the passage H, which is connected to the chamber by openings fitted with valves G. Between the chambers is a vacuum-chamber J which connects with the induction-passage D. Air is supplied the chambers by small air- valves moving inward, which open when the pressure is less than atmos- pheric. The method of working is as fol- lows : Conceive the left chamber full FlG - 303.-THE pulsometer. of water, and a vacuum in the right chamber; steam enters to the left of the valve C, presses directly on the surface of the water, and forces it past the check-valve G into the delivery- passage H and air-chamber J \ at the same time the right chamber is filling with water, which rushes in and by its momentum moves the valve C to the left. The steam in the left chamber condenses, forming a vacuum, and the operation described is repeated, except that the conditions in the two chambers are reversed. All the steam entering is condensed and forced out vith the water, increasing its temperature. The analysis is very similar to that of the injector, except that the steam acts by pressure instead of by impact. The theory is fully stated in "Thermodynamics," by Prof. DeVolson Wood, page 293. Thus: if w equal the weight of steam, W the weight of water raised, t the temperature of the supply, t x that of the delivery, r the latent heat of evaporation of the 684 EXPERIMEN TA L ENGINEERING. [§447- steam, T the temperature of the steam, n the delivery-head, n 1 the suction-head, n -\- n x the total head, — no allowance being made for variation, — we have w(T+r -t,)= W(t x -t). The heat equivalent of the mechanical work done, [7=A[Wn 1 +(W+w)n']. The heat expended, in thermal units, h = w( T — t -\- r). The efficiency, £ _U A[W7t 1 -\-{W+w)n-\ h w(T — t -\- r) Neglecting the work of lifting the condensed steam, r, A{n x + n) t x -t , nearly. The following form for data and results of test is used by the Massachusetts Institute of Technology : 447. Form for Data and Results of Test on Pulsometer. No. Date, , 189. . a Flow of Steam. Water. Heads. Calorimeter. Counter u u xi s 3 Total 3 09 to it ft ft u 2£ "0 n 6 u 3 10 co V a (J S s 3 0, V 0. rJ)) J) J) iMovimr Blades ft?' C C C C C (LCX C Statioil ( ar y Blades Moving Blades .1 ^ Fig. 306. — Blades of the Parsons Turbine. the moving blades, Pi, at the most effective angle, thence the steam is deflected to a row of stationary blades and thence again to a row of moving blades as shown by the arrows. Steam enters at A (Fig. 307) and passes in succession through the various rows of buckets on the parts F, G, H, and K. The last series of buckets are on an enlarged portion of the drum, O, which increases the volume and produces great expansion. From the rotating part it passes into the chamber, B, connected with the condenser. 690 EXPERIMENTAL ENGINEERING. [§45L To take the lateral thrust off the bearings, pistons or rotating collars, P, are arranged so as to receive the steam pressure and balance the thrust. The turbine is provided with a governor, L, which acts to turn the steam entirely on or off as may be necessary to maintain constant speed. The driving-shaft is extended for direct connection for an Fig. 307. — Parsons Steam-turbine. electrical generator for which the power generated by the turbine is generally used. The Parsons' steam-turbine is built by the Westinghouse Machine Co. and by the Allis- Chalmers Co. 451. Steam-turbine of Combined Reaction and Impulse Type. — The Curtis turbine as built by the General Electric Co. is a good illustration of a combined impulse and reaction turbine. In this turbine the steam passes through a set of nozzles arranged in multiple; it then strikes the first row of blades, after which it reacts on alternate rows of moving and stationary blades as in the Parsons turbine. The general arrangement of the buckets in this turbine appears in Fig. 308, which shows the valves connecting the steam- chest with the supply nozzles, the development of moving and stationary blades, and the nozzle diaphragm through which the steam flows against another set of moving blades on a wheel of larger diameter. §452. THE STEAM-TURBINE. 69I The number of stages may be made as great as necessary, there usually being four stages in large wheels. The large-size Curtis turbines are made of vertical form with a generator above the turbine and carried on the same vertical shaft, being supported below by a rotating collar resting on oil or water under pressure. The general arrangement is shown in Fig. 309, the generator being at G, the turbine at T. The steam-pipe is connected at 5, the exhaust-pipe at E. S'team Chest WIW1)1MWS)1)1)))D1)W Moving Blades ! Stationary Blades Moving Blades Moving Blades TO)TO)^DTOpPj£PPM Stationary Blades kC \.CjC\C-C, i C.CC^vC,\ \JC\CC,^^M • Moving Blades )W;W))W WW1)1M) ])1)U)\ Stationary Blades U «««««« «« <4<4 Moving Blades Fig. 308. \ i I • j i I -Nozzles and Buckets, Curtis Turbine. Fig. 309. -The Curtis Turbo- generator. 452. Testing of Steam-turbines. — Since there is a continu- ous flow of steam through the steam-turbine, at a uniform pressure and temperature for any one condition, there is no opportunity for taking a diagram similar to the indicator card, and conse- quently there is no means for measuring the mechanical work done by the entering steam on the rotating part. There may be, however, if the construction warrants, an opportunity of measuring the temperature and pressure at the 6c 2 EXPERIMENTAL ENGINEERING. [§453- various stages in a multiple-stage turbine, and these quantities if possible should be observed. Most of the steam-turbines are constructed for direct con- nection to an electrical generator, and as usually built do not permit the attachment of intermediate thermometers and pressure- gauges. The test for that reason must generally consist in the measurement of the total steam and heat supplied and the work done by the generator. This latter is measured by means of various electrical instruments. If the efficiency of the generator is known, the work delivered (D.H.P.) from the turbine can be computed. From the heat input and the electrical output measured as described the efficiency can be computed on the basis of delivered or electrical horse-power. The heat (B.T.U.) per electrical or delivered horse-power supplied per minute can also be computed. These quantities are usually sufficient for all commercial require- ments and serve for a comparison of the results obtained with those of reciprocating engines, which are already well known from numerous tests. 453. Log-sheets. — A log-sheet which suggests quantities to be observed and results to be computed in the test of a steam- turbine directly connected to an electrical generator is printed on the following page. The input H.P. is computed by adding all generator losses, reduced to horse-power units, to the output H.P. computed from the K.W. The thermodynamic efficiency is the ratio of the difference of temperature of steam centering and discharging, divided by the absolute temperature of the entering steam. The thermal efficiency is the ratio of the work, expressed in thermal units, AW, to the total heat supplied, Q. A perfect engine is assumed to be one that converts the differ- ence between the heat entering, Q, and that discharging, q, into work. § 453-J THE STEAM-TURBINE. 693 REPORT OF DIRECT-CONNECTED STEAM-TURBINE TEST. Made by Date Kind of Turbine Mfg. by Duration of run Hours Revolutions per minute Temperature of condensing water cold Temperature of condensing water warm Temperature of condensed steam Temperature of the engine-room Steam-chest pressure-gauge Barometer . . .inches Hg Condenser pressure " " Boiling temp. Exh. pressure Total steam per hr. condensed lbs Total condensing water per hr " Wt. condensing water per lb. steam. .'■ " Total heat supplied .B.T.U.— Q Total heat exhausted " — q Volts Amperes Series-field heat loss Shunt-field heat loss. . . : Armature heat loss Iron and friction loss K.W. hrs. useful output Total generator losses reduced to B.T.U Total input— H.P. (Calculated from K.W.) output Total D.H.P Efficiency of the plant Moisture in steam per cent Steam per input H.P. hr. (wet) lbs Steam per input H.P. hr. (dry) " Steam per D.H.P. hr. (dry) " Thermodynamic Eff (T-T') + T Tnermal Eff. . , AW+Q... Steam per H.P. hr. of perfect engine (dry) lbs. — (Q — q) -^-2545 Ratio actual to theoretical water consumption Heat supplied per minute B.T.U Heat utilized per min . . ' * Heat discharged per min " Heat radiated per minute ' ' CHAPTER XXIII. HOT-AIR AND GAS ENGINES. 454. Hot-air Engines. — Hot-air engines consist of engines in which the piston is driven backward and forward by the alternate expansion and contraction of a body of air caused by heating and cooling. Those now on the market are used prin- Fig. 311. Fig. 312. Ericsson Hot-air Pumhng-engine. cipslly for pumping-engines, and are arranged to use either coal or gas as fuel. 455. Ericsson Hot-air Engine. — This engine is shown in Fig. 311 in elevation, and in Fig. 312 in section. 694 §45^-1 HOT-AIR AND GAS ENGINES. 695 The method of operation is as follows : There are two pistons, viz., A, the displacing piston ox plunger, and B, the driv- ing-piston. The driving-piston is connected to the mechanism as shown. The displacing-piston, A, is a vessel made of some non-conducting substance, and its office is to move a body of air alternately from the space above to that below it. As shown in the figure, the piston A is at the upper end of its stroke, and the piston B is moving rapidly upward, being driven by the expansion of the air in the lower part of the receiver d. The air in the upper part of the receiver is cooled by water which has been raised by the pump r, and which circulates in the annular space xx. On the return stroke of the piston B the plunger A at first descends somewhat faster, and thus by transferring air main- tains a nearly uniform pressure upon the piston. When the piston B reaches the position shown in Fig. 312 on its down- ward stroke, the plunger A will be at the bottom of its stroke, and all the working air will have been transferred above and its temperature maintained at its lower limit, while it is com- pressed by the completion of the downward stroke of the piston B, after which the plunger will rise to the position shown in the figure and the temperature and volume are both increased at nearly constant pressure. The mass of air in the engine remains constant. 456. The Rider Hot-air Engine. — In this engine the compression-piston A and the power-piston C work in sepa- rate cylinders, which are connected together by a rectangular passage D in which are placed a large number of thin metallic plates, forming the regenerator, whose office is to alternately abstract from and return to the air the heat in its passage backward and forward. The same air is used continuously ; it may be admitted to the cylinders by a simple check-valve O, opening inward. The engine is used entirely as a pumping- engine, and the water so raised circulates around the compres- sion-chamber B. The operation of the engine is briefly as follows : The compression-piston A first compresses the cold air in 696 EXPERIMENTAL ENGINEERING. § 456.] Fig. 313.— The Rider Hot-air Pumping-engine. § 45 8 -] HOT-AIR AND GAS ENGINES. 697 the lower part of the compression-cylinder B, when, by the advancing or upward motion of the power-piston C and the completion of the down stroke of the compression-piston A, the air is transferred from the compression-cylinder B through the regenerator D and into the heater E without appreciable change of volume. The result is a great increase of pressure, corresponding to the increase of temperature, and this impels the power-piston up to the end of its stroke. The pressure still remaining in the power-cylinder and reading on the com- pression-piston A forces the latter upward till it reaches nearly to the top of its stroke, when, by the cooling of the charge of air, the pressure falls to its minimum, the power-piston de- scends, and the compression again begins. In the mean time, the heated air, in passing through the regenerator, has left the greater portion of its heat in the regenerator-plates to be picked up and utilized on the return of the air towards the heater. 457. Thermodynamic Theory. — The thermodynamic theory of the hot-air engine will be found fully discussed in Rankine's Steam-engine and in Wood's Thermodynamics, from which it is seen that these engines may work under the conditions of change of temperature with either constant press- ure or constant volume, or under the condition of receiving and rejecting heat at constant pressure. The thermodynamic efficiency is found by dividing the range of temperatures of the fluid by the absolute temperature of the heated fluid. 458. Method of Testing. — The method of testing hot-air engines does not differ essentially from that for the steam- engine. An indicator is to be attached so as to measure the pressures. Knowing the pressures and volumes, the corre- sponding temperatures can be computed from the formula £^ = Rz= 53.21, in which p is the pressure in pounds per square foot, v the 6 9 8 EXPERIMENTAL ENGINEERING. [§459- corresponding volume in cubic feet, and T the absolute tem- perature. From this T = pv The quantities which should be taken in each test are shown oc the following blank for data and results : 459. Forms for Data and Results of Test of Hot-air Engine. MECHANICAL LABORATORY, SIBLEY COLLEGE, CORNELL UNIVERSITY. Test of Hot-air pumping-engine. Fuel, At Date 189. By Log of Trial. Symbol. h' w p / 2f t' *" iV G «/ Water. Pressures. Temperatures. Revolutions. Fuel. Leakage u i .• ! ^ , ho 1 •« 3 (l Ok a P4 *J (4 . u u Jacket. ° u 3 O u V 0. 1 3 1 3 S3 '53 '-3 u ^8. 3 ST i £ si c e M rt hi of an induction-coil. The primary circuit of this coil is con- nected to a battery, B, at the proper moment by a contact cam on the secondary shaft, S. The primary circuit of the coil includes a vibrator, V, in many cases. With this arrangement a succession of sparks passes between the igniter terminals while the circuit-closing cam is in contact with its brush. In some cases, however, the vibrator is omitted, the circuit being broken only once, at the cam contact. The cut, Fig. 317, shows the construction of a recently designed four-stroke-cycle engine for gas or hydro-carbon vapor. In this engine, which is shown in section, the gas and air enter, through separate inlets, the mixing-chamber M, from which the mixture flows through the port N and inlet- valve J into the cylinder as the piston is beginning a down- ward stroke at the' commencement of a cycle of operation. The inlet-valve is opened once in two revolutions by the motion of the cam B, which makes one half as many revo« 706 EXPERIMENTAL ENGINEERING. [§ 46o. lutions as that of the main shaft of the engine. The charge is then drawn into the cylinder by suction. During the up- Fig. 317. — Section through Westinghouse Engine. stroke of the piston, the charge of gas and air is compressed in the cylinder. The charge is ignited by an electrical spark at about the time the compression is maximum and when both inlet- and exhaust-valves are closed. The ignition is performed by an igniter-cam arranged so as to bring two igniter-terminals into contact, completing the electric circuit, and then suddenly separating them by the energy in a coiled § 46o.] HOT-AIR AND GAS ENGINES. 707 spring located in the guide D. The rise of pressure following ignition drives the piston downward to the end of its stroke. Fig. 318. — Section of Lozier Engine. On its return-stroke the exhaust-cam A opens the exhaust- valve E and the burned gases are expelled by the rising piston into the exhaust-pipe O. One cycle of operation is then complete and requires, as thus described, four strokes of the piston or two revolutions of the engine. For the purpose of cooling, a jacket is provided through which water is made to circulate, entering at H and dis- charging at K. In the engine above described the speed is regulated by a governor, not shown in the cut, which throttles the mixture of gas and air. A two-stroke-cycle engine is shown in Fig. 318, in which the cycle of operation is completed in two strokes or one revo- 708 • EXPERIMENTAL ENGINEERING. [§ 460. lution of the engine, although the number of operations is the same as in the case of the four-stroke cycle. In the engine as shown in the figure, the mixed charge of gas and air is drawn into a chamber in the crank-case through the opening A, and is prevented from going backward by a check-valve opening inward which is located on the pipe supplying the charge. No valve other than the piston is employed to con- trol either the admission- or the exhaust-port. The admis- sion-port is in the lower part of the cylinder, at C, the exhaust-port is at the opposite side of the cylinder, at F. The charge enters when the piston is at the lower por- tion of its stroke through the open admission-port, due to the compression produced by the downward motion of the piston on the contents of the crank-chamber; at the same instant the burned gases are being exhausted through the open exhaust-port. On the return-stroke the fresh charge is compressed from the time the piston has covered the exhaust-port until the end of the stroke. The ignition is performed at about the time of greatest compression. We note that in this cycle of operation admission and exhaust take place simultaneously at the beginning of the upward stroke, and compression during the completion of the stroke; ignition takes place at or near the begin- ning of the downward stroke, expansion during the down- ward stroke, and beginning of exhaust near the end of this stroke. The advantages of this cycle of operation are claimed to be a greater number of impulses per revolution and a steadier motion for engines of the same weight. The disadvantages are the uncertainty of a clean cylinder for .the explosion and the probable loss of unburned gases in the exhaust, Actual tests show that the two-stroke- cycle en- gines are much less economical than those of the four-stroke- cycle type and fully as heavy per unit of power. 455. Method of Testing Gas-engines — The method of testing gas-engines is in many respects the same as for a hot- air engine, but if possible measurement should be made of the §461.] HOT-AIR AND GAS ENGINES. 709 vaporized and mixed with air, by a device called a carburetter, previous to its introduction into the engine cylinder. Engines designed for the use of gasolene are sometimes called "gasolene- engines," but they do not differ in any essential way from those designed for gas. The carburetter is always external to and independent of the engine, and is equivalent to a gas-machine in its results. Gasolene is the principal source of fuel for all portable or automobile motors, for which it is excellently suited, because of its great heating value per unit of volume and because of its easy volatilization in the carburetter without heat. Car- buretters are designed in various forms, but in all cases they provide means for passing the entering air over the necessary amount of gasolene while in a finely divided state. The regu- lation is frequently accomplished automatically by a float or other device. 461. Oil-engines. — This name is appropriately applied to engines designed to use as a fuel the heavy petroleum oils which are not readily vaporized. These engines are internal-combus- tion motors, which differ from gas-engines principally in the fuel employed and in the means required for vaporizing and ignition of the same. They may be either of the two-stroke or four-stroke cycle type, but usually are of the latter. The first oil-engines used flame ignition, but those now built are ignited wholly or in part by the heat of compression aided by a hot tube, hot surface, or electric spark. The oil-engines are generally of the class which ignite at constant volume and during increase of pressure and temperature, the charge having been previously compressed. Prominent exceptions are the Brayton, which is not now built, and the Diesel. The Brayton ignites from a constantly burning flame at constant pressure during increase of volume and temperature. The Diesel ignites from the heat of compression at constant temperature during increase of volume and decrease of pressure. Oil-engines, it is noted, may be divided into three classes, igniting, respectively, (1) at constant volume, (2) at constant pressure, (3) at con- stant temperature. JiO EXPERIMENTAL ENGINEERING. [§ 46l In the Brayton the oil is sprayed directly into the cylinder during ignition, which takes place for a portion of the forward stroke. At the same time compressed air is supplied by a com- pressor, so as to maintain constant pressure in the working cylinder. The speed is regulated by a governor which controls the admission- valve for air and oil. The diagram from this engine is much like one from a Corliss steam-engine. Fig. 319.— The Hornsby-Akroyd Oil-engine. A n the Priestman oil-engine there is an external vaporizer heated externally by the exhaust gases, and through which the entire charge of oil and air for combustion pass on the way to the engine. In the Hornsby-Akroyd engine, shown in Fig. 319, the oil- charge is pumped into a chamber connected to the working cylinder, where it is vaporized by the heat. The air is drawn into the cylinder through a separate inlet- valve and forced by the compression into contact with the oil-vapor, causing ignition. The Priestman and the Hornsby-Akroyd in other respects resem- bles the Otto gas-engine. § 462.] HOT-AIR AND GAS ENGINES, 711 462. Theoretical Relations of Pressure, Volume, and Temperature of a Gas. — The relations of pressure, p, volume, v, and temperature, /, of a unit of weight of a perfect gas during expansion or compression may be expressed by the following equations, in which T— absolute temperature, a = coefficient of expansion per degree of absolute temperature, a = number of degrees between freezing-point and absolute zero, po = pressure at o°, ^0= volume at o° of one unit of weight of the gas, and R = constant = poV a = poV Q /a. From Boyle's and Gay-Lussac's laws we have pv = poV (i+at); (1) • • (2) p v = ^T=^(a + t)=R(a + t)=RT, pv=RT may be considered the characteristic equation of a per- fect gas since it shows the relations, during expansion or com- pression, of a unit weight between the pressure, volume, and abso- lute temperature. R is a constant dependent on the nature of the gas, with values as follows for a few of the gases : Values of R. English Units. Metric Units. Hydrogen (H) 770.3 48.74 35-41 53-22 422.68 26.475 iQ-43 29.20 Carbon dioxide (C0 2 ) Air Expansion and compression may take place (1) isothertnally, in which case there is no change of temperature, or (2) adiabat- ically, in which case there is no increase or decrease in the total heat. For the first case, since the temperature remains constant, pv = p'v r . (3) The curve corresponding to this equation is an equilateral hy- perbola asymptotic to the axes of volume and pressure. Methods 7 12 EXPERIMENTAL ENGINEENING. [§ 462 of drawing this curve have already been given in Art. 404, pages 554 and 555. For the second case, or adiabatic expansion or compression, «$■ from which ptfVo k = pv k = a constant, (4) in which k = c P /c v . c P = specific heat at constant pressure and c = specific heat at constant volume. During adiabatic expansion the relations of temperature and volume are shown by the following equation: V) =T & The relation of pressure and temperature by 1— k z—k Tp k =T 1 p 1 k . ( 6 ) The following table (see next page) from Clausius (Mechanical Theory of Heat) gives the value of the two specific heats for a few of the gases. The adiabatic curve may be drawn when po, v , and k are known by assuming values of v and calculating, either with a table of logarithms or a slide- rule, corresponding values of p. The mechanical work, W, done during isothermal expansion between the volumes v 2 and v± is theoretically as follows: /f V2 dv v 2 pdv = p 1 v 1 J^ — = ftvilog,— . ... (7) The work done during adiabatic expansion from v 2 to Vi is as follows: -en-fen « §4^3. HOT-AIR AND GAS ENGINES. 713 Name of Gas. Air Oxygen Nitrogen Hydrogen Nitric oxide Carbonic oxide. . . Carbon dioxide. . . Steam Disulphide carbon Olefiant gas Ammonia Alcohol Symbol O N H NO CO co 2 H 2 cs 2 C 2 H 4 NH 3 C 2 H fi O Specific Heat. Constant Pressure. 2375 2I 75 2438 4090 2 3*7 2450 2169 4805 x 569 0.4040 0.5084 o-4534 Constant Values. O.1684 o-^S 1 o. 1727 2.4110 o. 1652 0.1736 o. 1720 0.3700 o. 1310 0-3590 0.3910 0.4100 406 403 416 414 402 413 261 298 198 J 25 3OO !5 The heat applied during isothermal expansion or received during isothermal compression is given by the following equation: / V2 dv Vo -=(^- Cs )r 1 io ge -, or Q=ART 1 log.^-Ap 1 v 1 log.^ i . (9) The complete derivation of these equations can be found in any work on thermodynamics; they are given here merely for convenience. 463. Cycle of Operation of Gas-engines. — A body is said to operate in a closed cycle when it returns to its original state after passing through a series of physical and chemical changes. When a change of composition occurs, as is the case during combus- tion in the internal- combustion engine, the body may return to its initial condition only so far as pressure and volume are con- cerned and not in other respects. For this reason the gas-engine operates in a cycle which is only approximately closed. If <2=heat received, q that exhausted, the highest possible 7H EXPERIMENTAL ENGINEERING. [§ 464. maximum efficiency would be for that condition (Q — q)/Q, which ratio has been called by A. Witz the "coefficient of economy." The Carnot cycle is an ideal one which differs materially from any actual cycle of the gas-engine, yet it is useful as a basis of comparison, since it represents the maximum return in work for a given fall of temperature. In this cycle there is isothermal and adiabatic expansion followed by isothermal and adiabatic compression. For this case it can be shown that Q-q T-T in which T is the absolute temperature during the isothermal expansion and T' that during isothermal compression. The thermal efficiency may be calculated from the I. H. P. by dividing the mechanical work shown by the indicator diagram, expressed in heat-units, by the heat value of the fuel consumed. It may also be expressed as the ratio of the delivered work in heat units to the heat value of the fuel. Thus if T^ = the mechan- ical work delivered, IW the mechanical work shown by the indicator diagram, then will the efficiency be as follows: Thermal from I. H. P. =IW/Q; Thermal from D. H. P. =W/Q. 464. Method of Testing Gas- or Oil-engines. — The method of testing gas- and oil-engines is essentially the same, the difference being principally due to the different methods of measuring the gaseous and liquid fuel. The object of the test in every case is to find the relation of the work performed to the thermal value of the fuel supplied, and the efficiency of the engine. To obtain these results the amount of air should be ascer- tained. This may be computed approximately by subtracting the volume occupied by the fuel from the cylinder displacement, but it is desirable whenever possible to meter or measure the entering air. In attaching the indicator it will be found necessary to use § 464.] HOT-AIR AND GAS ENGINES. 715 a heavy spring in order to resist the effect of the explosion. This spring, because of its stiffness, will show but little work on the intermediate strokes; for this reason it is advisable to use a second indicator with a light spring, in which is placed a stop for the piston so that the spring cannot be compressed to such an extent as to injure it. A pyrometer should be inserted in the exhaust, and a gas-bag placed between the gas-meter and Gas Meter ^yiomeW Fig. 320. — Plan of Arrangement for Gas-engine Trial. the engine. The proper arrangement of a gas-engine for trial i? shown in Fig. 320, from Thurston's Engine and Boiler Trials. The heat-units per cubic foot of gas used should be deter- mined by a calorimetric experiment (see page 451). The actual and ideal indicator-diagrams are shown in Fig. 321, the differ- ence being in great part due to losses of heat in the cylinder. The report of the test should contain a description of the engine, the method of testing, together with the log and the re- 716 EXPERIMENTAL ENGINEERING. [§ 464. suits properly tabulated. In connection with the test of a gas- engine, plot a curve with cubic feet of gas per I. H. P. at 32 F. and atmospheric pressure as ordinates, and I. H. P. as abscissae. In the test of gasoline- or oil-engines, plot a similar curve, using the weight of fuel instead of the volume of gas. Also plot a curve showing the relation of the total B. T. U. in the fuel supplied to the total I. H. P. and D. H. P. of the engine. Mean pressure 46o5 P.e-voluUons p.ermln, 18 »* 12 the loss known as cylinder con- densation; in addition, heat is radiated into the surrounding space. These losses reduce the working value of the steam 20 to 50 per cent. In the refrigerating machine similar losses of an opposite and negative character exist. The effect of the negative heat losses would be as follows : In the compression the cylinder becomes heated, and this heat is only partially discharged to the condenser; the remainder keeps the cylinder warmer than it otherwise would have been even at the end of expansion. This heat in the cylinder walls warms and expands the entering gas as it flows in, and has the effect of reducing its capacity, being thus exactly opposed in character, but otherwise similar to the loss of heat which occurs with a heat-engine. During a great part of the revolution the tem- perature in the cylinder is below that of the room, in which case heat will flow from the surrounding room into the working cylinder. 480. The Working Fluid. — The working fluids are usually selected among the fixed gases, or from liquids whose §480.] MECHANICAL REFRIGERATION. 739 boiling-point is very low. The principal freezing machines use either air, ammonia, or carbon dioxide, but water-vapor or steam may be employed. The properties desirable in a vapor or gas to be used for refrigeration purposes are: First, latent heat of vaporization large, which will permit the use of a small amount of working substance, since the capacity of a given weight to transfer heat is proportional to this quantity. Second, freezing-point low; as the capacity to absorb heat is a function of difference of temperature, the lower the tem- perature at which a given substance will remain liquid, the greater the capacity for a given weight, and also the lower the temperature which can be attained. It is hardly necessary to mention that a solid body cannot be pumped, and that as soon as it solidifies it becomes useless for refrigeration. Third, considerable change in temperature for moderate increase of pressure. In addition, commercial considerations render it necessary that the liquid shall be reasonable in cost, and shall be one that will not attack or destroy the machinery used. Water Vapor. — A steam-engine, run backward or as a com- pressor, with steam as a working substance, would convey heat from a lower to a higher temperature at the expense of the net work of compression. • In this case, however, the lower limit of temperature could not be much less than that of the freezing- point of water. In any case, when expansion occurred, an amount of heat equivalent to the latent heat of liquefaction would be absorbed from the surrounding medium. While steam or vapor of water has a very high latent heat, it becomes solid at a comparatively high temperature (32 F.), and consequently is not well suited for use in a refrigerating machine. In a pressure below that of the atmosphere considerable vapor is given off, and practical ice-making machines have been built to work under such conditions. These machines are known as water-vapor vacuum machines. Air. — An air-compressor would transfer heat, as already explained, by the mechanical work of compression. 74Q EXPERIMENTAL ENGINEERING [ § 480. Anhydrous Ammonia. — This material is produced as a waste product in various industries in an impure form, and it needs only to be purified and separated from water to fit it for refrig- eration purposes. The material exerts 1 o corrosive action on iron, and for this reason does not affect in any degree the ordinary machinery for conveying or compressing it. It will, however, attack brass or copper and must be kept from contact with these metals. Its important properties are given in the following table: At atmospheric pressure boiling-point is 2 8. 6° F. Weight at 32° F., combined with water, is 0.6364, or 39.73 pounds per cubic foot, or 5.3 pounds per gallon. Specific heat is 0.50836. Latent heat at 32 F. is about 560 B.T.U. The following table, giving the principal properties for each 10 degrees of temperature on the Fahrenheit scale, is taken from Professor Wood's Thermodynamics. PROPERTIES OF SATURATED ANHYDROUS AMMONIA. Degrees F. Pressure Absolute per Sq. Inch. Total Latent Heat. External Latent Heat. Internal Latent Heat. Volume of 1 Pound of Vapor Cu. Ft. Volume of 1 Pound of Liquid Cu.Ft. Weight of 1 Cu. Ft. in Pounds. r apw 5 -40 IO.69 579-67 48.25 531-42 24.38 0.0234 0.041 1 -3° 14-13 573 69 48 85 524 84 18.67 0.0237 0-0535 — 20 18.45 567 67 49 44 5i8 23 14.48 . 0240 . 0690 — 10 23-77 56i 61 5° 05 5" 56 11.36 0.0243 0.0880 30-37 555 5 5i 3^ 5°4 12 9.14 0.0246 0. 1094 10 38.55 549 4 5 1 13 498 22 7.20 O . 0249 0.1381 20 47-95 543 J 5 5 1 65 491 50 5-82 O.0252 0. 1721 3° 59-4i 536 92 52 02 484 90 4-73 0.0254 0.2111 40 73.00 53° 63 52 42 478 21 3.88 0.0257 0.2577 5° 88.96 5 2 4 3 52 82 47i 44 3.21 0.0260 °-3"5 60 107.60 5i7 93 53 21 464 76 2.67 0.0265 0-3745 70 129. 21 5 11 5 2 53 67 457 95 2.24 0.0268 0.4664 80 154. 11 5°4 66 53 96 45° 75 1.89 O.0272 0.5291 90 182.8 498 11 54 28 443 70 1. 61 0.0274 0.62 1 1 100 215.14 491 5 54-54 437-35 1.36 O.0279 o-735 6 § 48 1 .] ME CHA NIC A L REFRIGERA TION. 74 1 481. The Air-refrigerating Machine. — In this case air is compressed by mechanical means, and the heat which is generated is removed by a water-jacket, so that the temperature after compression is approximately the same as at the beginning. It is then permitted to expand adiabatically against a resistance so as to perform mechanical work, and in so doing falls in tem- perature. It can afterward take up heat from' the surrounding bodies. It was experimentally demonstrated by Joule that the temperature of air remains constant if it expands without doing external work. For the air-refrigerating machine W e in equation (5), the mechanical work done during expansion, is considerable; for the ammonia machine it is usually small and often zero. The heat capacity of any gas which does not change its state is small, and is equal to the product of specific heat, into weight, into change of temperature. On the other hand, when vapors are employed which are converted into liquids during the process of compression and cooling, and then changed into vapors during expansion, the heat capacity of a given weight is increased because of its latent heat, which is always comparatively large. It becomes quite evident from the latter consideration alone that the air machine must for a given capacity be many times greater in size than the ammonia machine. Two of the more successful machines of this type are described as follows: The Windhausen machine, which was operated during the Vienna Exposition, had a capacity of 30 cwt. of ice per hour. In its construction it consisted of a single cylinder, each end of which was alternately a compressed-air engine and a pump for compressing the air. The compressed air was de- livered to a cooling vessel, and from thence to one end of the cylinder, being admitted by a valve motion, and acting in its expansion to move the piston and help to compress the air drawn in at the other end. The exhaust air after, being deprived of its heat by the work of expansion, was passed to the cooling vessels, and utilized in lowering the temperature of a quantity of brine, or directly discharged for refrigeration purposes. The 742 EXPERIMENTAL ENGINEERING. [§ 482, power required over and above that provided by the compressed air was supplied by an engine. The Bell- Coleman machine, which is extensively used on shipboard for refrigeration purposes, is constructed in much the same manner as the Windhausen, but the operations of compressing and expanding are performed in separate cylinders. The machine consists of three tandem cylinders, and three pis- tons fixed to a common piston-rod. One cylinder is the air- compressor, the other the air-engine, while a third is a steam- engine which supplies the excess of power needed to move the pistons. The amount of work required and the change of temperature produced in the expansion and compression of air have been discussed quite fully in Art. 462. 482. The Ammonia Compressor. — A general outline of an ammonia compression system is shown in Fig. 331. It . . Water Supply AmmOniSl IlCondenssrC Compression Refrigerating Apparatus Three Parts MitiiwiiiniMiiii; 11 iiiiiiHiiuiiiirnrMriuiiiiiiiiiniiffiiiiiiuq 'iJiiiBimiiwiwiHiii^^^iniiwiuiiuiiiJitifmttiiiiuLW.HiiniiiffiiEi griii«iiiiiinuuiiiN'iiriuiiiiiiiiii(inu:uiriiiiiinjiiiin!nrniiin!iiiiiiii;iiiiKiiii::i h a T Brine Tank or Congealer A. Fig. -Outline Drawing of Mechanical Compression System. consists of a compressor or pump, B, which draws the ammonia vapor from the brine-tank or congealer, A, compresses it, and then delivers it to the large condenser, C, where it is cooled by water and is liquefied. The liquid ammonia under pressure is then permitted to flow through the expansion-valve shown § 482.] MECHANICAL REFRIGERA TION. 743 between the condenser and the brine- tank. In passing through the expansion-valve and into the expansion-pipe shown in the brine-tank, the liquid ammonia is vaporized by expansion, and the heat required is taken up from the material surrounding the coil. The apparatus as shown consists of three parts: (1) the expansion-valve and coil, in which the liquid is vaporized, (2) the compressor, in which the vapor is compressed; and (3) the con- denser, in which the vapor is reduced to a liquid. If there were no other heat losses, it is evident that the heat given off in the condenser would equal that drawn from the medium surrounding the expansion-coils. In the apparatus illustrated the expansion-coils are shown surrounded by brine. In many cases the expansion coils are in contact with the air of the room which is to be lowered in tem- perature. In some instances the brine, after being cooled by the expansion of ammonia, is circulated to the places where a low temperature is required. The compression cylinder for the ammonia refrigeration machine should be made with as small a clearance as possible, for the reasons which have already been given in the discussion of the air-compressor. Fig. 332 shows an enlarged view of a single-acting ammonia-compression cylinder surrounded with a water-jacket for removing heat during compression. In some instances ammonia compressors have been provided with means for keeping the clearance spaces filled with oil. In such cases an oil-separator is employed between the compressor and the condenser, which is arranged to take the oil out of the ammonia pipes and return it to the compressor. Refrigerating machines are used for the cooling of buildings and also for the manufacture of ice. For the manufacture of ice a brine- tank is usually employed which is maintained at low temperature by the expansion of ammonia in coils inserted in the tank substantially as shown in Fig. 331. The ice is usually made by freezing distilled water in cans of the desired shape. In nearly all ice-plants of this character, apparatus is required 744 EXPERIMENTAL ENGINEERING. [§483. not only for the ammonia system but also for supplying and purifying the water. Fig. 333 shows a section of an ice-making plant with all the principal parts named. The ' operation of the plant can be understood from a study of the drawing. Fig. 332. — Ammonia Compression Cylinder. Ice is also made by directly freezing water in contact with the expansion system. In such case the ice is frozen in large plates, and is usually removed by discharging hot ammonia liquid directly into the expansion system, which loosens it from the expansion plates. It is in such cases usually cut into small pieces by the use of jets of steam. 483. Relations of Pressure and Volume. — In the compression of ammonia the relations of pressure, volume, and temperature are essentially as those given in equation in Art. 462. The compression is usually very nearly adiabatic, as indicated by the diagrams taken with an indicator. For the adiabatic curve of ammonia vapor, £ = 1.3. § 483-: ME CHA NIC A L KEFRIGERA TION. 745 7 4 6 EXPERIMENTAL ENGINEERING. [§ 483. In Fig. 334 is shown a series of adiabatic curves for different pressures and volumes drawn by Mr. R. L. Shipman, which wilL be found extremely useful in making a comparison of the com- pression line obtained on an indicator diagram with an adia- batic curve corresponding to the same pressure and volume. Hll'm\l\l!l\\\M\1\\\lMM\\\ lllllillllml\M\Mv\\\\\\\\ ■MlllllHVMlMmiHHI ■■■■■■! ■■■■■■■■■■■■■■■■■■■■■■■■ ■■niiminiimm\u\i\\\\«HHi ■■■■■■■■■■■■ ■■■■ I l \M\\\\\vM\\i \1\\\m\V\\\mu uISiumSBs iiimvSsSmS I iWmIimsl tt( SISSlK sifiisBsEawM SiBsQiEffioSwu irtJlrnSlHSS JrpMliSHI jrtitsfifisKSsSSv iQKQlSSKBfflSM nnEvasssMo^ SiSSMSM^H ftjirMcMssMSv- IT SLUqQSvMMMM ZD irivVasssMsssSv % 3iGGGEGESSSS§S§5 + UJ IBrilAssssssSaSS^ cc IIMMYSV5SSSS|^ +XC\Xu$2ssSssSsSSs u\\ A v\ v\\\v V\ AA\VaXX^\ : ii\ Avssvss^gggSgs^ st^oSvxsSsSssSsSsi^ _. T3^SV3SX5SS5SSSS||S^^ ^xvHv5\$$S5S$§§§§s§a^ Sa_v$w5_^s§Ss§s§|§|I^ : X^\^$sosss§s^|s|||ll^^ 35_^_S5$s5§s§^l5l^l§§t§^ ^S\_;S^^s|_;§5^|5il§lPSI§^ x^^S^xxSSS^^^^^^^^SSs^^S^^^^s*. \ s ^v^n > \^\ n * VvN *^^^5^:§^^^5:^5^<^:§§^^=s»«. ^^\ \\^^^\SVS^5i;^^^g;;^g5^ ^5 = ^. \\\^^^^^^^^.^i;^555-^ ; 5;g5gg$5$§§§^S§§5S^ ^^N^V^^^vS^-^v^^^^^v^J^^^^^SS- ^^N^^S^^^^^^ii^^^^Ss^sS^sSSssisIs ^-^-i^-^^-^?^?^?^?^^^?^ =3S5=5 = =S| ^ """--^^-^^^^"-■^^^Sr^sS— := — = = = =1=5 _ = — ~ = =~=: — = =— = _i := =:= = = :_ = — ———======= , _____ Fig. 334.- VOLUME OR LENGTH OF STROKE -Adiabatic Curves for Different Pressures and Volumes. The following table gives the result of a series of tests on ammonia compression machines, made by C. Linde of Munich, and are of interest as showing the amount and character of the various quantities described The table is copied from a paper read before the American Society of Mechanical Enigneers, at the Chicago meeting, 1893. The units were reduced to one) 484] MECHANICAL REFRIGERA TION. 747 minute of time instead of one hour. It is noted that in every case AW is less than K — K\, and it should also be further noted that the smaller this difference the greater the economical per- formance of the machine. Number of Test. Temp, of brine: Inlet, deg. F. . . Temp, of brine: Outlet, deg. F. . Specific heat of brine per unit of volume Quantity of brine per hr., cu. ft. . . Cold produced, B.T.U. per min., Kx Temp, of cooling water: Inlet, degs. F Temp, of cooling water: Outlet degs. F Quan. of cooling water per hr. cu. ft Heat removed by condenser per minute, B.T.U., K Increase in heat, K—K\ I.H.P. in comp. cyl., W Heat equivalent of work, AW. I.H.P. in steam-engine cylinder. . Consumption of steam per hour, lbs Consumption of steam per min- ute, lbs Cold produced in B.T.U. per minute per I.H.P. in comp. cyl. Cold produced in B.T.U. per minute per I.H.P. in steam cylinder Cold produced in B.T.U. per minute per pound of steam. . . . Thermodvnamic efficiency (460 + f)+(t c -t)=E 1 Actual efficiency Ki-t-AW=E 2 . . Ratio of actual to thermodynamic efficiency AW-(K-Ki) * Lbs. of ice melted per lb. of steam Lbs. of ice melted per lb. of coal. . 43- 2 37-° 0.861 1039.4 57I5-I 48.8 66.7 338-7 6305-9 590.8 13.82 586.2 15.80 3H-5 5-i9 413-5 361.7 1 100 17.2 9-75 0.56 -4.6 7-5 2 75-2 28 22 o 908 4309 49 68 260 5° 2 3 724 14 606 16 336 5 3°7 9 851 267. 1 785-6 10.65 7.26 0.68 -118. 1 5.66 56.6 1 3 8 o 615 2781 49 67 187 3509 728 13 587 15 306 5 200 9 7 843 4 3 1 180.7 543-9 8.04 4-73 °-59 -141. 2 3-85 38.5 ~°-3 -5-9 0-837 915.0 2024.5 49.1 67-3 140.0 2648.7 624.2 11.98 508.2 14.24 278.8 4-65 169.0 142 .2 435-8 6.2 4-03 0.667 -116. o 3-i 31.0 28 23 o 800 3671 49 93 97 45i8 847 19 837 21 43° 7 185 169 512 6 4 o — 10 851 9 86 3* 637 4 64 4 * Latent heat of ice taken as 141 B.T.U. 484. The Absorption System of Refrigeration. — This system was invented by M. Carre, and dispenses with the ammo- 74 8 EXPERIMENTAL ENGINEERING. [§ 484. nia compressor. Instead of compressing the ammonia by pres- sure, water strongly impregnated with ammonia gas is heated by steam. The heat vaporizes the ammonia and, because of the low boiling temperature of the ammonia, causes as much pressure as required. The compressed ammonia is treated as in the other processes, that is, it is first passed through a con- denser and liquefied, thence to expansion-coils, where it takes up heat from the surrounding material. Instead of being pumped hack as in the first system, it is absorbed by water and the dilute liquid is pumped. Fig. 335 shows a view of an absorption system with all the principal parts named. It is worthy of a close study, as showing the economy practiced in the use of the heat employed. The strong ammonia liquid from the absorber is pumped through a heater, where it is surrounded by weak ammonia liquor which had been previously heated in the gene ator. It then flows, partially heated, to the analyzer, where it exposes a large surface to the heat. The principal part of the ammonia gas under pressure passes off above, the weak ammonia liquor falls to the bottom of the generator. The ammonia gas under the pressure due to. its temperature is received in the condensing coil. In this coil the pressure is maintained, but the tempera- ture is lowered by the use of condensing water, so that the ammo- nia gas is converted into liquid anhydrous ammonia. The anhydrous ammonia is used as in the other systems; it may be allowed to expand in a tank filled with brine, or it may be carried to the rooms where refrigeration is needed and then permitted to expand. In the figure the brine system is shown, the expansion taking place in the cooler, in which a circulation of brine is maintained by a pump. The weak ammonia from the generator, after parting with some of its heat in the heater, is brought in contact with the ammonia in a vessel called the absorber. The ammonia gas has a strong affinity for water, and is absorbed readily, convert- ing the weak ammonia liquor into strong ammonia liquor. This is pumped to the heater and completes the cycle. The exhaust 484.] MECHANICAL REFRIGERA TION. 749 75° EXPERIMENTAL ENGINEERING. [§ 484. steam from the pumps is utilized in heating under ordinary conditions, so that all the heat wastes are carried off in the con- densing water and in the drip from the generator. When a low back pressure is wanted, such as is required in production of ice, this system succeeds well, and is somewhat more economical than the compression system. For purposes of refrigeration where a high back pressure is maintained the compression system is more economical in its operation. The following sheets indicate the observations which are necessary for a complete test of an ammonia refrigerating machine : . LOG A. Test of Refrigerating Machine built by Style Tested at .' Date Size of Ammonia Cylinder — Diam Stroke Scale of Ind. Spring Capacity of Expansion Valve .... Specific gravity of Brine .... Barometer Test made by No Time Speed-counter Revolutions per minute Temperature, room . . . . : Temperature, external air Condenser: Temperature, entering gas Temperature, injecting water Temperature, discharging water Weight water lbs Compression gauge " Expansion Coils: Temperature, entering gas Deg- F- Temperature, discharging gas " Suction gauge lbs Brine Tank: Temperature, entering brine. Temperature, discharging brine Meter reading Cubic feet, brine "Weight of brine, pounds Revolutions of expansion valve Temperature, liquid NH 3 , at expansion valve § 4 8 4-] MECHANICAL REFRIGERATION. 7$ I LOG B. Test of Refrigerating Machine built by , Tested at Date Tested by Specific gravity of NH 3 Specific heat of NH 3 . Specific gravity of brine Specific heat of brine. Number Brine: Pounds, circulated Range, temperature B.T.U. discharge Condenser: Pounds, water Range, temperature B.T.U. discharge Gain B.T.U Compression cylinder: Absolute pressure admitted Absolute pressure discharged M.E.P D.H.P Work, B.T.U Ammonia: Pounds, circulated Heat of vaporizion, suction pressure Heat of vaporizion, condenser pressure Temperature due to pressure in refrigerating coils Absolute pressure in refrigerating coils SPECIFIC HEAT OF BRINE. 1. 170 1. 103 1.072 1.044 1.023 1. 012 .805 .863 .895 • 931 .962 .978 Specific Gravity 1 . 187 Specific Heat 0.791 SPECIFIC HEAT CHLORIDE OF CALCIUM SOLUTION. Specific Gravity 1.0255 1.163 Specific Heat 0.957 0.827 752 EXPERIMENTAL ENGINEERING. [§ 484. REPORT. Test of Refrigerating Machine built by ; Tested at Date Latent heat of ice 142.2 Tested by No. I 2 3 4 5 6 .7 8 9 10 11 12 13 14 15 16 17 18 J 9 20 21 22 23 24 25 26 27 Pounds of condensing water per hour Range of temperature of condensing water Pounds of brine per hour Range of temperature of brine Pounds of ammonia per hour Pounds of condensing water per £ound of NH 3 Average temperature outlet of brine Average temperature outlet of cooling water Temperature of NH 3 entering brine tank Corresponding sensible heat liquid above 32 in B.T.U. . Total heat NH 3 gas B.T.U. at suction pressure Temperature of gas leaving brine tank Temperature of gas corresponding to suction pressure Superheating of gas in degrees Fahrenheit Cooling per pound of ammonia in B.T.U Temperature of gas entering condenser Heat carried off by condensing H 2 per hour B.T.U. . . Heat taken from brine per hour B.T.U. (Refrigeration) D.H.P. ammonia cylinder Foot-pounds of work per hour, no friction Heat equivalent of work per hour B.T.U Heat carried from brine per pound NH 3 circulated. . . . Heat carried off by cond. H 2 per pound NH 3 cir Heat gained by system per hour B.T.U Thermodynamic efficiency Actual efficiency Ratio actual to thermal efficiency Ice-melting capacity pounds 24 hours at 100 revolutions Sym bols. Formulae. t-t 3 ^2—qi + o.^i d x QT QiTtX Spe. ht. AW K-Ki t + 4.61 t c -t Ki-i-AW Ei + E LIST OF TABLES. PAGE- I. U. S. Standard and Metric Measures • 754 II. Numerical Constants 756 III. Logarithms of Numbers 769 IV. Logarithmic Functions op Angles 771 V. Naturae Functions op Angles 777 VI. Coefficients of Strength of Materials 781 VII. Strength of Metals at Different Temperatures 782 VIII. Important Properties of Familiar Substances 783 IX. Coefficient of Friction 784 X. Hyperbolic or Naperian Logarithms 784 XI. Moisture Absorbed by Air 785 XII. Relative Humidity of the Air 785 XIII. Table for Reducing Beaume's Scale-reading to Specific Gravity 786 XIV. Composition of Various Facts of the United States 787 XV. Buel's Steam-tables 788 XVI. Entropy of Water and Steam 794 XVII. Discharge of Steam : Napier Formula 795 XVIII. Water in Steam by Throttling Calorimeter 795 Diagram for Determining Per Cent of Moisture in Steam. 796 XIX. Factors of Evaporation 797 XX. Wrought-iron Welded Pipes 798 XXI. Weight of Water at Various Temperatures 799 XXII. Horse-power per Pound Mean Pressure 800 XXIII. Water Computation Table 801 XXIV. Weirs with Perfect End Contraction 803 XXV. Weirs without End Contraction 803 XXVI. Electrical Horse-power Table 803 XXVII. Horse-power of Shafting 804 XXVIII. Horse-power of Belting , 804 Sample-sheet of Paper 804. 753 754 EXPERIMENTAL ENGINEERING. t/5 w < W Q r5 w W § ^ 5 Q J ^ i IE- N inNQ>H rf-O co >-< HJ-QO N O l-" in O enCO C* tMJN TO O »- inOmoOMOt-ii^. «*^ r*» O rt- r^ M -rj-co m OO-i'-'i-iNNNen in o rfco nNMO h O n Otfinoo m m co MnN Oco i^nMoo n tncn^ mo o u 3 h HH 3 C >- 5^1 M nm r^co O n ^ m MO O cn m O cm inco MO ■ttOH Oco O "3" w inco ** Tto O > t t-> ^f co r^O *wn h oco misH in o en r^ o t II !l II II II II II II II m N en tt inO l^co O - o Too m inco w coo menu Ocoo in in inO I s * OMMt-iMNMcnen Oco r^o in rt en (N >- N inco m rf r-» O cno c* en m r^ co O ►-< enin m O inO in m o i— O -t O enco w i^ fh o O II II II II II II II II II it m en tJ- ino r^co O o g j> g in o rj- o rt-co enco n cno O en r^ o -t r^ « Oco co r^-o o in rf ^f O >-> n en ■** ino r^co OC^COTfOOWCOrt en tJ-o co o >h n n- 3. " >3S cn TfinrxOM enino OOOOO--MMF- Ttco WOO Too m o -too en r^ n O O in o MW-tinr^coO'-iw Oco r^o in -*• tT en w O m 0* en rf inO t^oo i-c hh n N en T T m in OOOOOOOOO coo T l^M r^ en N inNO W inr^O II II II II II II II II M«»co in in u> »i b£ • ft) 2 2 £ £ o S g <-> rt *-> -> (tie Hi r: 4) OJ l- S C _^ G tt co ^ u . •C in t>. 00 p- N o o o ^-n2 O O 1- N JS ph N CO jj-Tj- II II II II Z II II £ g « ll-gS H3 g O 3 o g _^ cno en ajjo-alk'n *« 3 -2 5 o '3 « -e o-rt 2 o > 2 o a: vS C Oi rt J 2« coo - o m n en ^t" ino f^co O oo t^^O O -OCNr^-i -!f r^ o w in M H M H « « 2 « Oco co r^o in •tj- ^f en co r^-o inrtenN m O o o o o o o o o o w i u Mnmn or^incnM 2S§ •^fOrtoenco enco en ON OinNcoini-ico ih m cs encnTj-min II II II II II II II II II m n en tj- mo r^co o o •rJ-CO N O O -rtCO woo enco co r^ in rf m m oco O r^inenM or^-rj-M O "c5 •— 3 mr>H inco N O O **■ m m hi m m en en O noo d co c/i.JL, Mn« O N>tN O^\0 Fluid Ounce to Mill litres in m t~* enco ^ q in t-t O Oco oo nn r^o o c* inoo hh -pf r-» o eno M M M N M w luid ms to lilitres u.Cen- etres. O O O Oco co co r^.co r^eno r^'^j-Mco m« tnt>H 'rj-co m in o en ^2rz:ua m m m n cn n en QSg'5 1 II II II II II •!! II II II 1 M«lnt »«o r>»ao 0*1 rt "So *' « -■; - ;H u i o a Us 'MO.S O.S2 3H jC3 * 0."0 -HI 3 3 o ^S*^ >.«'•§ *j c ^ <« S C '-3 — - r 3 cQ to'-' to v'a'c^ £ c « -S fc, > ^ " C v II — " u S o tt'Q J3 "5 S"rt 5 « v «^ Lag's rt.S2 eS ° § JJOQ n v n a J» tn 'u-^'u «« S . *j «-• *j ™ 'rj *• x 2 a 2 -> o^a rt s « o s c ^ >» ^ t^ etf 2 C — i o — « rt -g o c o-s «« b£> S^Ig 1 ^ ™ o o fa c a U. S. STANDARD AND METRIC MEASURES. 755 03 D 3 £• cnO ON inco m ^-r> m w en invo **» On O m c h « u ; 3 « io* 5 Q c t o enco m r^ w o O eno O^N inco tN inco in o inMO m r^ tN r-* nr>o t r^ m too ■_> « i-i i-i tN . o N rJ-NOM tO CO hi OOOOmmmmm h n mt ino r-^co o O«00 tOO MOO T OO^i-it-ii-itNtNtN i-i cn en t ino r^co on O NOO t O o tN co t OnMCNenenttin OOOOOOOOO II II II II II II II II in cntino r^co o> o o m v • 3 1-3^ v U CO m tN en t in\d r^co o t^ t >-i co in cn OO en t too enco tN r^ cn tN tr^O^tN tr^QNCN O CN CO tOO tN CO t s oco co co r* i^o O >- cn in r-^ on »-i mmrs t-i cn en t »n r^co 6> O rt cu td 4; 3 »- 3 D u~< too cn in on cn r^ m t ON On in i-i CO t >-i X^ r^ in cn Ooo in cn m co h- o «n r^ enco t 0> en to t~» On O tN en O O O O O O cn en t ino r-co On Is §2 5 rt 3 fa 2 N"tHoo in tN 0>0 en ent^M too N in on cn m m tN en to r^oo o> O t-i tN en t inO r^co O OtNcotOOtNcoin en r-» O too m inco tN Onco oo r^o O in t t O ii cn en t invo r»co m coo tM Ocoo tN N inco m tO O «N in a- 3 OOOOOOOOO OOOOOOOOO tNTfHoo in tN O^O en en r-> m too c< m CT> en CT^oo co r^o o >n t t tor> m ino^enr^M in m w m (N n en en II II II II II II II II II I m c* en t mo r>oo O^ 6 ° H a e . en to ncjO n tn ~~ O N mNQ> O &> N inoo N N N 666666666 N tO co eno a O O O m o nco too woo t t o* tnco p-jnno ooi- OOiHi-tcNtNenent tN to co O n tO co tN to co m cfimNO 1 II II II II II II II II tN en t ino l^co O^ ej)0 tN to m c^mNO O tNoo ti-i t>num t on enco tONNO OOwMtNtNenent tN to oo O N to oo N to oo en in r^ o in O en r-^ tN O O tN C> r^ co o en in m O too tN O -r - oo O 0> « t M O tN t^ . tfl «I "go tN t eno too in O * to co On tN in on in O too tN oo enco On O tN en 2fl C S1 2 J bo eno O eno On eno On too en r-^ m in o too in O O i-i r^ tN oo enco m en to r^ on O tN en OOOOOOmmw OOOOOOOOO II II II II II II II II II i-i ei en t ino t^oo on in o in o in O in O in i O to r^ in tN o r-* in tN O x^ £*"oj COI^H moo tN o O en 3 8-S oo O in en tN moo m M QOOMfl t r^ On tN m H M l-l w tN tN t^ t M en in tN 0>O en m en ino co O >-< en in a** G tOO tN O O m on en r^ M «J o O tN On m tN Q- rt NlflNO en moo m en =o M M M M tN tN o . i^ t O r-- t hh co t >-i ■" 05 O en o O en O O en O in m r^ tN co t On m ■-> 82 S O M M tN tN en en t m 4J 3 a a m tN en t mo r^co on • °-, b5 CO O t tN m Onco O en •£+■"5 ™ miNH in ON tN o O t Cen litres Flu Ounc eno O O* 6 m eno o en r^ o m m M tN tN en HJ illilitre ubic Ce litres t uidDra r^ t m CO m tN OnO en tN moo o eno co m t ooo H M M M W tN Mu fe I II II II II II II II II II 1 i-i N en t mo r»o© on "3 3 2 «3 alii > S - ! >,-2 a -2 S crto o o O 1) *J m. j. 756 EXPERIMENTAL ENGINEERING. II. NUMERICAL CONSTANTS. n ffir 4 .. «s Vn 3 l.o 3.142 0.7854 1. 000 1. 000 I. OOOO I. OOOO I.I 3.456 0.9503 1. 210 1. 331 I.0488 I .0323 1.2 3- 770 1.1310 1.440 I.728 I.0955 I.0627 13 4.084 1-3273 1.690 2.197 I . 1402 I. O914 1.4 4.398 1-5394 1.960 2.744 I. 1832 I.II87 1.5 4.712 1.7672 2.250 3-375 1.2247 I . 1447 1.6 5.027 2.0106 2.560 4.096 I . 2649 I. 1696 1-7 5.341 2.2698 2.890 4.913 I.3038 I- 1935 1.8 5-655 2-5447 3.240 5.832 I. 3416 I. 2164 1.9 5.969 2.8353 3-6io 6.859 1.3784 I.2386 2.0 6.283 3.1416 4.000 8.000 I. 4142 I.2599 2.1 6-597 3.4636 4.410 9.261 I. 4491 I.2806 2.2 6.912 3.8013 4.840 10.648 I.4832 I . 3006 2-3 7.226 4-1543 5.290 12.167 I. 5 166 I.3200 2.4 7-540 4-5239 5.760 13.824 1.5492 1.3389 2.- 7-854 4.9087 6.250 15625 1.5811 1-3572 2.6 8.168 5.3093 6.760 I7.576 1. 6125 1. 3751 2.7 8.482 5-7256 7.290 19.683 1.6432 1.3925 2.8 8-797 6.1575 7.840 21.952 1.6733 1.4095 2.9 9. in 6.6052 8.410 24.389 1 . 7029 1.4260 3.0 9-425 7.0686 9.00 27.000 1. 7321 1.4422 3.1 9-739 7-5477 9.61 29.791 1.7607 1. 4581 3.2 10.053 8.0425 10.24 32.768 1.7889 1-4736 3.3 10.367 8.5530 10.89 35-937 1. 8166 1.4888 3.4 10.681 9.0792 11-56 39-304 1.8439 1.5037 3-5 10.996 9.6211 12.25 42.875 1.8708 r.5183 3-6 11. 310 10.179 12.96 46.656 1.8974 1.5326 3-7 11.624 10.752 13.69 50.653 1.9235 1 • 5467 3-8 11.938 11. 341 14.44 54.872 1.9494 1 . 56O5 3-9 12.252 11.946 15.21 59.3I9 1.9748 1 -5741 4.0 12.566 12.566 16.00 64.000 2.0000 1.5874 4-1 12.881 13.203 16.81 68.921 2.0249 1 . 6005 4.2 13-195 13-854 17.64 74.088 2.0494 1. 6134 4-3 13 509 14-522 18.49 79-507 2.0736 1. 6261 4-4 13.823 15-205 19.36 85.184 2.0976 1.6386 4-5 , 14 137 ! 15 90* ' 20.25 91.125 2.1213 1. 6510 4.6 14-451 14.765 16.619 1 17.349 1 21.16 97-336 2 . 1448 1. 6631 .4.7 22.09 103.823 2.I680 1 6751 NUMERICAL CONSTANTS. 7S7 Constants — Continued. n nit 4 »» »» Vn s 4-8 15.080 18.096 23.04 110.592 2 . I9O9 1.6869 4-9 15.394 18.857 24.01 117.649 2.2136 1.6985 5-o I5.708 19-635 25.00 125.000 2.2361 I. 7100 5.1 I6.022 20.428 26.0I 132.651 2.2583 1. 7213 5.2 16.336 21.237 27.04 140.608 2.2804 1.7325 5.3 16.650 22.062 28.09 148.877 2.3022 1 • 7435 5-4 16.965 22.902 29.16 157.464 2.3238 1-7544 5-5 17.279 23.758 30.25 166.375 2.3452 1.7652 5.6 17.593 24.630 3I-36 175-616 2.3664 1.7758 5.7 17.907 25.518 32.49 185.193 2.3875 1.7863 5.8 I8.22I 26.421 33-64 195. 112 2.4083 1.7967 5-9 18.535 27.340 34.81 205.379 2.429O 1 . 8070 6.0 18.850 28.274 36.OO 216.000 2-4495 1.8171 6.1 19.164 29.225 37-21 226.981 2.4698 1.8272 6.2 19.478 30.191 38.44 238.328 2 . 49OO 1. 8371 6.3 19.792 31.173 39-69 250.047 2.5IOO 1.8469 6.4 20.106 32.170 4O.96 262.144 2.5298 1.8566 6.5 20.420 33-183 42.25 274.625 2-5495 1.8663 6.6 20.735 34.212 43-56 287.496 2.569I 1.8758 6.7 21.049 35.257 44.89 300.763 2.5884 1.8852 6.8 21.363 36.317 46.24 3I4-432 2.6077 1.8945 6.9 21.677 37-393 47.61 328.509 2.6268 1.9038 7.0 21.991 38.485 49.00 343 . 000 2.6458 1. 9129 7.1 22.305 39-592 50.4I 357-9" 2 . 6646 1.9220 7.2 22.619 40.715 51.84 373-248 2.6833 1. 93io 7-3 22.934 41.854 53-29 389-017 2.7019 1-9399 7-4 23.248 43.008 54-76 405.224 2.7203 1.9487 7-5 23.562 44.179 56.25 421.875 2.7386 1-9574 7.6 23.876 45.365 57.76 438.976 2.7568 1. 9661 7.7 24.190 46.566 59-29 456.533 2-7749 1-9747 7-8 24.504 47.784 60.84 474-552 2.7929 1.9832 7.9 24.819 49.017 62.41 493-039 2.8107 1. 9916 8.0 25.133 50.266 64.00 512.000 2.8284 2.0000 8.1 25.447 51.530 65.61 531.441 2.846I 2.0083 8.2 25.761 52.810 67.24 551.468 2.8636 2.0165 8-3 26.075 54.106 68.89 571.787 2.88IO 2.0247 8.4 26.389 55-418 70.56 592.704 2.8983 2.0328 8.5 26 . 704 56.745 72.25 614.125 2.9155 2 . 0408 8.6 27.018 58.088 73.96 636.056 2.9326 2.0488 8.7 27.332 59-447 75.69 658.503 2.9496 2.0567 8.8 27.646 66.821 77-44 681.473 2.9665 2 . 0646 8.9 27.960 62.211 79.21 704.969 2.9833 2.0724 758 EXPERIMENTAL ENGINEERING. Constants — Continued. ft nw 4 «» «3 ^ h 9 o 28.274 63.617 81.00 729.OOO 3.0000 2.0801 9.1 28.588 65.039 82.81 753.571 3.OI66 2.0878 9.2 28.903 66.476 84.64 778.688 3 0332 2.0954 9-3 29.217 67.929 86.49 804.357 3-0496 2 . 1029 9.4 29-531 69.398 88.36 83O.584 3.0659 2.1105 9-5 29.845 70.882 90.25 857.375 3.0822 2.1179 9.6 30.I59 72.382 92.16 884.736 3.0984 2.1253 97 30.473 73.898 94.09 912.673 3-II45 2.1327 9.8 30.788 75.430 96.04 941 . 192 3.1305 2.1400 9.9 31.102 76.977 98.01 970.299 3.1464 2.1472 10. 3I.4r6 78.540 100.00 IOOO.OOO 3.1623 2.1544 10. 1 3I-730 80.II9 102.01 1030 . 30I 3.1780 2.1616 10.2 32.044 81.713 104.04 I06l.208 3-1937 2.1687 10.3 32.358 83.323 106 . 09 1092.727 3.2094 2.1757 10.4 32.673 84.949 108.16 II24.863 3.2249 2.1828 10.5 32.987 86.590 110.25 II57.625 3.2404 2.1897 10.6 33.30I 88.247 112.36 II9I.OI6 3-2558 2.1967 10.7 33-615 89.920 114.49 1225.043 32711 2 . 2036 10.8 33.929 91 .609 116.64 1259.712 3-2863 2.2104 10.9 34.243 93-313 118. 81 1295.029 3-3015 2.2172 11. 34-558 95.033 121.00 I33I.OOO 3-3166 2.2239 II. 1 34.872 96 . 769 123.21 I367.63I 3-3317 2.2307 11. 2 35-186 98.520 125.44 I4O4.928 3.3466 2.2374 "•3 35-500 IOO.29 127.69 1442.897 3-3615 2.2441 11. 4 35-814 I02.07 129.96 I48I.544 3-3764 2.2506 11. 5 36.128 IO3.87 132.25 1520.875 33912 2.2572 II. 6 36.442 IO5.68 134-56 I560.896 3-4059 2.2637 11. 7 36.757 I07.5I 136.89 l60I.6l3 3.4205 2.2702 11. 8 37-071 IO9.36 139.24 I643.O32 3-4351 2.2766 11. 9 37-385 III. 22 141. 61 I685.I59 3.4496 2.2831 12.0 37.699 113-10 144.00 I728.OOO 3.4641 2.2894 12. 1 38.013 114.99 146.41 I77I.56I 3.4785 2.2957 12.2 38.327 116.90 148.84 I815.848 3.4928 2.3021 12.3 38.642 118.82 151.29 I860.867 3 5071 2 . 3084 12.4 38.956 120.76 153.76 I906.624 3.5214 2.3146 12.5 39-270 122.72 156.25 1953.125 3-5355 2 . 3208 12.6 39.584 124.69 158.76 20OO.376 3-5496 2.3270 12.7 39-898 126.68 161.29 2048.383 3-5637 2.3331 12.8 40.212 128.68 163.84 2097.152 3.5777 2.3392 12.9 40.527 130.70 166.41 2146.689 3-59 J 7 2.3453 13.0 40.841 132.73 169.00 2I97.OOO 36056 2.3513 13. 1 41.155 134-78 171. 61 2248.O9I 3.6194 2.3573 13.2 41.469 136.85 174.24 2299.968 3-6332 2 . 3633 NUMERICAL CONSTANTS. Constants — Continued. 759 n nit 4 »* »3 Vn s 13-3 41.783 138.93 176.89 2352.637 3.6469 2.3693 13.4 42.097 I4I.03 I79-56 2406.104 3.6606 2.3752 13-5 42.412 143-14 182.25 2460.375 3.6742 2.3811 13.6 42.726 145-27 184.96 2515.456 3.6878 2.3870 13-7 43-040 I47.4I 187.69 2571.353 3.7013 2.3928 13.8 43-354 149.57 190.44 2628.072 3.7148 2.3986 13-9 43.668 I5L75 193.21 2685.619 3.7283 2.4044 14.0 43.982 153-94 196.00 2744.000 3.7417 2.4101 14. 1 44.296 156.15 198.81 2803.221 3.7550 2.4159 14.2 44.611 158.37 201 . 64 2863.288 3.7683 2.4216 14.3 44-925 160.61 204.49 2924.207 3-7^15 2.4272 14.4 45-239 162.86 207.36 2985.984 3-7947 2.4329 14.5 45-553 165.13 210.25 3048.625 3.8079 2.4385 14.6 45.867 167.42 213. 16 3112.136 3.8210 2.4441 14.7 46.181 169.72 216.09 3176.523 3.834I 2.4497 14.8 46.49° 172.03 219.04 3241 . 792 3.847I 2.4552 14.9 46.810 174-37 222.01 3307 -949 3 . 8600 2.4607 15.0 47-124 176.72 225.00 3375.000 3.8730 2.4662 15. 1 47-438 179.08 228.01 3442.951 3-8859 2.4717 15.2 47.752 181.46 231.04 3511-808 3.8987 2.4772 15.3 48.066 183.85 234-09 3581.577 3.9 JI 5 2.4825 15-4 48.381 186.27 237.16 3652.264 3.9243 2.4879 .15.5 48.695 188.69 240.25 3723.875 3.9370 2.4933 15.6 49.009 191. 13 243.36 3796.416 3-9497 2.4986 X5-7 49-323 193-59 246.49 3869.893 3.9623 2 . 5039 15-8 49,637 196.07 249 . 64 3944.312 3-9749 2 . 5092 1 15.9 49-951 198.56 252.81 4019.679 3.9875 2.5146 16.0 50.265 201.06 256.00 4096.000 4.0000 2.5198 16. 1 50.580 203.58 259-21 4173.281 4.0125 2.5251 16.2 50.894 206.12 262.44 4251.528 4.0249 2.5303 16.3 51.208 208.67 265.69 4330.747 4-0373 2.5355 16.4 51.522 211.24 268.96 4410.944 4.0497 2.5406 16.5 51-836 213.83 272.25 4492.125 4.0620 2.5458 16.6 52.150 216.42 275.56 4574.296 4-0743 2.5509 16.7 52.465 219.04 278.89 4657.463 4.0866 2.5561 16.8 52.779 221.67 282.24 4741.632 4.0988 2.5612 16.9 53-093 224.32 285.61 4826.809 4.1110 2 . 5663 17.0 53-407 226 98 289.00 4913.000 4.1231 2.5713 17. 1 53-721 229.66 292.41 5000.211 4.I352 2.5763 17.2 54-035 132.35 295.84 5088.448 4-1473 2.5813 i7o 54-350 235.06 299 . 29 5I77.7I7 4-1593 2.5863 17.4 54-064 23^.79 302 . 76 5268.024 4.I7I3 2.5913 y6o EXPERIMENTAL ENGINEERING. Constants— Continued. n nit 4 *» «» lTn h 17-5 54.978 240.53 306.25 5359-375 4-1833 2.5963 17.6 55.292 243.29 3O9.76 545L776 4.1952 2.6012 17.7 55.606 246 . 06 313-29 5545.233 4.2071 2.6061 17-8 55.920 248.85 316.84 5639.752 4:2190 2.6109 17.9 56.235 251.65 320.41 5735-339 4.2308 2.6158 18.0 56.549 254-47 324.00 5832.000 4.2426 2 . 6207 18. 1 56.863 257.30 327.61 5929.741 4.2544 2.6256 18.2 57.177 26o.l6 33L24 6028.568 4.2661 2 • 6304 18.3 57-491 263.02 334.89 6128.487 4.2778 2.6352 I8.4 57.805 265.9O 338.56 6229.504 4-2895 2.64OI 18.5 58.II9 268.80 342.25 6331.625 4.3012 2 . 6448 18.6 58.434 271.72 345.96 6434.856 4-3I2S 2.6495 18.7 58.748 274.65 349.69 6539.203 4-3243 2.6543 18.8 59.062 277.59 353-44 6644.672 4-3359 2.6590 18.9 59-376 280.55 357-21 6751.269 4-3474 2.6637 I9.0 59-690 283.53 36I.OO 6859.000 4.3589 2.6684 19. 1 60.004 286.52 364.8I 6967.871 4.3703 2.673I 19.2 60.319 2S9.53 368.64 7077.888 4.3818 2.6777 19-3 60.633 292.55 372.49 7189.057 4.3932 2.6824 19-4 60.947 295.59 376.36 7301.384 4.4045 2.6869 19- 5 61.261 298.65 380.25 7414.875 4-4159 2.6916 19.6 61.575 301.72 384.16 7529-536 4.4272 2.6962 19-7 61.889 304.81 388.O9 7645.373 4.4385 2.7008 19.8 62 . 204 307.91 392.04 7762.392 4.4497 2.7053 19-9 62.518 3".03 396.01 7880.599 4 . 4609 2.7098 . 20.0 62.832 3I4.I6 400.00 8000.000 4.4721 2.7144 20.1 63.146 317.31 4O4.OI 8120.601 4.4833 2.7189 20.2 63.460 320.47 4O8 . 04 8242.408 4-4944 2.7234 20.3 63.774 323.66 4I2.09 8365.427 4-5055 2.7279 20.4 64.088 326 85 4l6.l6 8489.664 4.5!66 2.7324 20.5 64.403 330.06 420.25 8615.125 4.5277 2.7368 20.6 64.717 333-29 424.36 8741.816 4.5387 2; 7413 20.7 65.031 336.54 428.49 8869.743 4-5497 2-7457 20.8 65-345 339-8o 432.64 8989.912 4-5607 2.7502 20.9 O5.659 343.07 436.81 9129.329 4.5716 2-7545 21.0 65.973 346.36 44I.OO 9261.000 4.5826 2.7589 21. 1 66.288 349-67 445.21 9393-931 4-5935 2.7633 21.2 66.602 352.99 449.44 9528.128 4.6043 2 . 7676 21.3 66.916 356.33 453-69 9663.597 4.6152 2.772O 21.4 67.230 359-68 457-96 9800.344 4.6260 2.7763 21.5 67.544 363-05 462.25 9938.375 4.6368 2.7806 21 ..6 67.858 366.44 466.56 10077.696 4.6476 2.7849 21.7 68.173 369.84 470.89 10218.313 4.6583 2.7893 NUMERICAL CONSTANTS. Constants— Continued. 761 It nit 4 «a «3 V„ 3 21.8 68.487 373-25 475.24 10360.232 4.6690 2.7935 21.9 68 . 801 376.69 479.61 IO5O3.459 4.6797 2.7978 22.0 69.115 380.13 484.00 IO648.OOO 4 . 6904 2 . 8021 22.1 69.429 383-60 488.41 IO793.861 4.7011 2 . 8063 22.2 69-743 387.08 492.84 IO94I.O48 4-7II7 2.8105 22.3 70.058 39°- 57 497.29 IIO89.567 4.7223 2.8147 22.4 70.372 394.08 501.76 11239.424 4.7329 2.8189 22.5 70.686 397.61 506.25 II39O.625 4-7434 2.8231 22.6 71.000 401.15 510.76 II543-I76 4-7539 2.8273 22.7 7I-3I4 404 .71 5I5.29 II697.083 4.7644 2.8314 22.8 71.268 408.28 519.84 11852.352 4-7749 2.8356 22.9 71.942 411.87 524-41 I2OO8.989 4-7854 2.8397 23.O 72.257 4I5-48 529.00 I2I67.O0O 4.7958 2.8438 23.1 72.571 419.10 533-6i 12326.391 4.8062 2.8479 23.2 72.885 422.73 538.24 I2487.168 4.8166 2.8521 23-3 73-199 426.39 542.89 12649.337 4.8270 2.8562 23-4 73.513 430.05 547-56 I28I2.904 4-8373 2 . 8603 23.5 73.827 433-74 552.25 12977.875 4.8477 2.8643 23.6 74.142 437-44 556.96 13144.256 4.8580 2.8684 23-7 74.456 441.15 561.69 13312.053 4.8683 2.8724 23.8 74.770 444.88 566.44 13481.272 4.8785 2.8765 23-9 75.084 448.63 571.21 I365I.9I9 4.8888 2.8805 24.0 75-398 452.39 57600 I3824.OOO 4.8990 2.8845 24.1 75-712 456.17 580.81 13997.521 4.9092 2.8885 24.2 76.027 459.96 585.64 I4172.488 4-9193 2.8925 24.3 76.341 463.77 590.49 I4348.9O7 4.9295 2.8965 24.4 76.655 467.60 595-36 14526.784 4.9396 2 . 9004 24.5 76.969 471.44 600.25 I4706.I25 4.9497 2.9044 24.6 77.283 475.29 605.16 I4886.936 4.9598 2 . 9083 24.7 77-597 479.16 610.09 I5O69.223 4-9699 2.9123 24.8 77.911 483-05 615.04 15252.992 4.9799 2.9162 24-9 78.226 486.96 620.01 15438.249 4.9899 2.9201 25.0 78.540 490.87 625.00 I5625.OOO 5 . 0000 2.9241 25.1 78.854 494.81 630.01 I58I3-25I 5-0099 2.9279 25.2 79.168 498.76 635.04 I60O3.OO8 5.0199 2.9318 25-3 79-482 502.73 640.09 I6194.277 5.0299 2.9356 25 4 79.796 506.71 645.16 I6387.064 5-0398 2-9395 25-5 80. in 510.71 650.25 I658I.375 5-0497 2.9434 25.6 80.425 5I4-72 655-36 16777.216 5.0596 2.9472 25-7 80.739 518.75- 660.49 I6974.593 5.0695 2.9510 25.8 81.053 522.79 665 . 64 I7I73.5I2 5-0793 2.9549 25-9 81.367 526.85 670.81 17373-979 5.0892 2.9586 762 EXPERIMENTAL ENGINEERING. Constants — Continued. n mt A «» « 9 v« 3 26.0 81.681 530.93 676.00 17576.000 5.O99O 2 . 9624 26.1 81.996 535.02 681.21 I7779-58I 5 . 1088 2.9662 26.2 82.310 539-13 686.44 17984.728 5.H85 2.9701 26.3 82.624 543.25 691.69 18191.447 5.1283 2.9738 26.4 82.938 547-39 696.96 18399.744 5.1380 2.9776 26.5 83.252 551-55 702 . 25 18609.625 5.1478 2.9814 26.6 83.566 555-72 707.56 18821.096 5.1575 2.985I 26.7 83.881 559-90 712.89 19034.163 5.1672 2.9888 26.8 84.195 564.10 718.24 19248.832 r.1768 2.9926 26.9 84.509 568.32 723.61 19465 . 109 5.1865 2.9963 27.O 84.823 572.56 729.00 19683.000 5 . 1962 3.0000 27.I 85-137 576.80 734.41 19902. 511 5.2057 3.0037 27.2 85.45I 581.07 739-84 20123.648 5-2153 3.O074 273 85.765 585.35 745.29 20346.417 5.2249 3-oni 27.4 86.080 589-65 750.76 20570.824 5.2345 3-OI47 27.5 86.394 59396 756.25 20796.875 5.2440 3.0184 27.6 86.708 598.29 761.76 21024.576 5.2535 3.0221 27.7 87.022 602 . 63 767.29 21253.933 5.2630 3.0257 27.8 87.336 606.99 772.84 21484.952 5-2725 3.0293 27.9 87.650 611.36 778.41 21717.639 5.2820 3-0330 28.0 87.965 615-75 784.00 21952.000 5-29I5 3-0366 28.1 88.279 620.16 789.61 22188.041 5.3009 3.0402 28.2 88.593 624.58 795-24 2 242 L. 768 5-3I03 3.0438 28.3 88.907 629.02 800.89 22 65. 187 5-3197 3-0474 28.4 89.221 633-47 806.56 22906.304 5-329I 3.0510 28.5 89-535 637.94 812.25 23149.125 5.3385 3.0546 28.6 89.850 642.42 817.96 23393-656 5.3478 3.0581 28.7 90. 164 646.93 823.69 23639.903 5.3572 3.0617 28.8 90.478 651.44 829.44 23887.872 5.3665 3.0652 28.9 90.792 655.97 835-21 24137.569 5-3758 3.0688 29.0 91 . 106* 660.52 841.00 24389.OOO 5-3852 3.0723 29.1 91.420 665.08 846.81 24642.I7I 5-3944 3.0758 29.2 91-735 669.66 852.64 24897.088 5.4037 3- 0794 29.3 92.049 674.26 858.49 25153.757 5.4129 3.0829 29.4 92.363 678.87 864.36 25412.184 5.4221 3.0864 29 5 92.677 683.49 870.25 25672.375 54313 3.0899 29.6 92.991 688.13 876.16 25934.336 5-4405 3.0934 29.7 93.305 692.79 882.09 26198.073 5-4497 3 . 0968 29.8 93.619 697.47 888.04 26463.592 5.4589 3.1003 29.9 93-934 702.15 894.01 26730.899 5.4680 3-1038 30.0 94.248 706.86 900.00 27OOO.OOO 5.4772 3.1072 30.1 94-562 711.58* 906.01 2727O.9OI 5.4863 3.1107 30.2 94.876 716.32 912.04 27543-608 5-4954 3.1141 NUMERICAL CONSTANTS. Constants — Continued. 763 n HIT 4 «» «* Vn 3 30.3 95.190 721.07 918.09 278l8.I27 5 • 5045 3-II76 30-4 95 • 505 725-83 924.16 28094.464 5.5I36 3.1210 30- 5 95.819 730.62 930.25 28372.625 5.5226 3.1244 30.6 96.133 735-42 936.36 28652.616 5.5317 3.1278 30.7 96.447 740.23 942.49 28934.443 5.5407 3.1312 30.8 96.761 745.06 948 . 64 29218. 112 5-5497 3.1346 30.9 97-075 749.91 954.81 29503.629 5.5587 3.1380 310 97-389 754-77 961.OO 29 7Q I. 000 5.5678 3.I4I4 311 97.704 759-65 967.21 30080.231 5.5767 3.1448 31-2 98.018 764-54 973-44 30371.328 5-5857 3.1481 31.3 98.332 769-45 979.69 30664 . 297 5.5946 3.I5I5 31.4 98.646 774-37 985.96 3O959.I44 5-6035 3-154* 31-5 98 . 960 779-31 992.25 31255.875 5.6124 3-1582 31-6 99.274 784.27 998.56 31554.496 5.6213 3-1615 3i-7 99.588 789.24 IOO4.89 3I855-OI3 5.6302 3.1648 31.8 99.903 794-23 IOII.24 32157.432 5.6391 3.1681 31-9 100.22 799.23 IOI7.61 32461.759 5-6480 3.I7I5 32.0 100.53 804.25 IO24.OO 32768.OOO 5-6569 3.1748 32.1 100.85 809.28 IO30.41 33076.161 5.6656 3-1781 32.2 101.16 8i4-33 1036.84 33386.248 5.6745 3.1814 32.3 101.47 819.40 IO43.29 3369S.267 5.6833 3-1847 32.4 101.79 824.48 IO49.76 34012.224 5.6921 3.1880 32.5 102.10 829.58 IO56.25 34328.125 5 7008 3-i9 T 3 32.6 102.42 834.69 IO62.76 34645.976 5.7096 3-1945 32.7 102.73 839.82 IO69.29 34965.783 5.7183 3.I978 32.8 103.04 844 . 96 1075.84 35287.552 5.7271 3.2010 32.9 103 . 36 850.12 I082.4I 356H.289 5-7358 3.2043 330 103.67 855.30 I089.OO 35937.000 5.7446 3-2075 33-1 103.90* 860.49 IO95.61 36264.69I 5.7532 3.2108 33-2 104.30 865.70 1102.24 36594.368 5.7619 3-2140 33-3 104.62 870.92 IIO8.89 36926.O37 5.7706 3-2172 33-4 104.93 876.16 III556 37259.704 5-7792 3.2204 33-5 105.24 881.41 1122.25 37595-375 5.7379 3.2237 33-6 105.56 886.68 II28.96 37933.056 5.7965 3.2269 33-7 105.87 891.97 II35.69 38272.753 5-8051 3-2301 33-8 106.19 897.27 I 142 . 44 38614.472 5.8137 3.2332 33-9 106.50 902.59 I I49. 21 38958.219 5.8223 3-2364 34- 106.81 907.92 II56.OO 39304.000 5-8310 3.2396 34- 1 107.13 913.27 Il62.8l 39651.821 5.8395 3.2428 34-2 107.44 918.63 II69.64 40001.688 5 . 8480 3-2460 34-3 107.76 924.01 II76.49 40353.607 5.8566 3.2491 344 108.07 929.41 II83.36 40707.584 5.8651 3 2522 764 EXPERIMEN TA L ENGINEERING. Constants — Continued. n nit 4 «? «• Vn s 34.5 108.38 934.82 1190.25 41063.625 5.8736 3.2554 34-6 108.70 940.25 1197.16 41421.736 5.8821 3.2586 34-7 109.01 945.69 1204.09 41781.923 5 . 8906 3.26I7 34-8 iog-33 951-15 1211.04 42144.192 5.8991 3 . 2648 34-9 109.64 956.62 1218.01 42508.549 5.9076 3.2679 35-o 109.96 962.11 1225.00 42875.000 5-9161 3-2710 35-i 110.27 967.62 1232.01 43243.551 5.9245 3.2742 j 35.2 110.58 973.14 1239.04 43614.208 5.9329 3-2773 35-3 110.90 978.68 1246.09 43986.977 5.9413 3 . 2804 35-4 in. 21 984.23 1253.16 44361.864 5-9497 3-2835 35-5 "I- 53 989.80 1260.25 44738.875 5.9581 3.2866 35-6 in. 84 995.38 1267.36 45118.016 5.9665 3.2897 35-7 112. 15 1000.98 1274.49 45499.293 5-9749 3.2927 35-8 112.47 1006 . 60 1281.64 45882.712 5.9833 3-2958 35-9 112.78 1012.23 1288.81 46268.279 5.9916 3.2989 36.0 113. 10 1017.88 1296.00 46656 . 000 6 . 0000 3-3019 36.1 H3-4I 1023.54 1303.21 47045.881 6.0083 3-3050 36.2 113.73 1029.22 1310.44 47437-928 6.0166 3 • 3080 36.3 114.04 1034. 91 1317-69 47832.147 6.0249 3-3HI 36.4 H4-35 1040.62 13249 6 48228.544 6.0332 3.3I4I 39-5 114.67 1046.35 1332.25 48627.125 6.0415 3.3I7I 36.6 114.98 1052.09 I339.56 49027.896 6.0497 3 • 3202 36 7 115-30 1057.84 1346.89 49430.863 6.0580 3.3 2 32 36.8 115. 61 1063.62 1354.24 49836.032 6.0663 3.3262 36.9 115.92 1069.41 1361.61 50243.409 6.0745 3.3292 37-0 116.24 1075.21 1369.00 50653.000 6.0827 3-3322 37.i 116.55 1081.03 1376.41 51064. 811 6 . 0909 3-3352 37-2 116.87 1086.87 1383.84 51478.848 6.0991 3-3382 37-3 117.18 1092.72 1391.29 51895. 117 6.1073 3-3412 37.4 117.50 1098.58 1398.76 52313.624 6.1155 3-3442 37-5 117. 81 1104.47 1406.25 52734-375 6.1237 3.3472 37-6 118. 12 1110.36 1413.76 53I57-376 6.1318 3.350I 37-7 118.44 1116.28 1421.29 53582.633 6.1400 3.3531 37-8 118.75 1122.21 1428.84 54010.152 6.1481 3.356I 37-9 119.07 1128.15 1436.41 54439.939 6.1563 3-3590 38.0 119.38 1134- 11 1444.00 54872.000 6.1644 3.3620 38.1 119.69 1140.09 1451.61 55306.341 6.1725 3.3649 38.2 120.01 1146.08 1459-24 55742.968 6.1806 3.3679 38.3 120.32 1152.09 1466.89 56181.887 6.1887 3-3708 38-4 120.64 1158.12 1474.56 56623.104 6.1967 3-3737 38.5 120.95 1164.16 1482.25 57066.625 6.2048 3.3767 38.6 121.27 1170.21 1489.96 57512.456 6.2129 3.3796 _38-7 121.58 1176.28 1497.69 57960.603 6.2209 3-3825^ NUMERICAL CONSTANTS. Constants — Continued. 765 n wn 4 «« «3 Tn 3 38.8 121.89 1182.37 1505.44 584II.072 b.io&q 3.3854 38.9 122.21 1188.47 1513.21 58863.869 6.2370 3-3883 39-o 122.52 1194.59 1521.00 593I9.OOO 6.2450 3.3912 39- J 122.84 1200.72 1528.81 59776.471 6.2530 3-3941 39-2 123.15 1206.87 1536.64 60236.288 6.2610 3.3970 39-3 123.46 1213.04 1544-49 60698.457 6.2689 3-3999 39-4 123.78 1219.22 1552.36 6II62.984 6.2769 3.4028 39-5 124.09 1225.42 1560.25 6l629.875 6.2849 3.405& 39-6 124.41 1231.63 1568.16 62O99.I36 6.2928 3-4085 ' 39-7 124.72 1237.86 1576.09 62570.773 6 . 3008 3 -4i 14 39-8 125.04 1244.10 1584.04 63044.792 6.3087 3.4142 39-9 125.35 1250.36 1592.01 63521.199 6.3166 3.4171 , 40.0 125 . 66 1256.64 1600.00 64OOO . OOO 6.3245 3.4200- 40.1 125.98 1262.93 1608.01 6448I.2OI 6.3325 3.4228 40.2 126.29 1269.23 1616.04 64964.808 6.3404 3.4256' 40.3 126.61 1275-56 1624.09 65450.827 6.3482 3.4285. 40.4 126.92 1281.90 1632.16 65939.264 6.3561 3.43I3; 40.5 127.23 1288.25 1640.25 66430.125 6.3639 3-4341 40.6 127.55 1294.62 1648.36 66923.416 6.3718 3- 4370 40.7 127.86 1301.00 1656.49 674I9.I43 6.3796 3-4398 40.8 128.18 1307.41 1664.64 679II.3I2 6.3875 3-4426 40.9 128.49 1313.82 1672.81 684I7.929 6-3953 3.4454 41.0 128.81 1320.25 1681.00 6892I.OOO 6.4031 3.4482 41. 1 129.12 1326.70 1689.21 69426.53I 6.4109 3-45IO 41.2 129.43 I333-I7 1697.44 69934.528 6.4187 3-4538- 41-3 129.75 I339.65 1705-69 70444.997 6.4265 3.4566 41.4 130.06 1346.14 1713.96 70957.944 6.4343 3-4594 41.5 130-38 1352.65 1722.25 71473-375 6.4421 3.4622 41.6 130.69 1359.18 1730.56 7I99I.296 6.4498 3.4650 41.7 131.00 1365.72 1738.89 725II.7I3 6-4575 3.4677 41.8 131.32 1372.28 1747.24 73034.632 6.4653 3.4705 41.9 131-63 1378.85 i755-6i 73560.059 6.4730 3-4733 42.0 131.95 1385.44 1764.00 74O88.O00 6.4807 3.4760 42.1 132.26 1392.05 1772.41 746l8.46l 6.4884 3.4788 42.2 132.58 1398.67 1780.84 75151.448 6.4961 3-4815 42.3 132.89 1405.31 1789.29 75686.967 6.5038 3-4843 42.4 133.20 141 1. 96 1797.76 76225.024 6.5115 3.4870 42.5 133-52 1418.63 1806.25 76765.625 6.5192 3.4898 42.6 133-83 1425-31 1814.76 77308.776 6.5268 3-4925 42.7 I34.I5 1432.01 1823.29 77854.483 6-5345 3-4952 42.8 I34-46 1438.72 1831.84 784.O2.752 6.5422 3-4Q8o 42.9 134.77 1445.45 1840.41 78953.569 6.5498 3.5007 766 EXfERIMEN TAL ENGINEERING. Constants — Continued. n nn «* - 4 «» «» Vn h 43 .0 I35.09 I452.20 1849.00 79507.000 6-5574 3-5034 43-1 135^40 1458.96 1857.61 80062.991 6.565I 3.5061 43-2 135.72 I465.74 1866.24 80621.568 6.5727 3.5088 43-3 136.03 1472.54 1874.89 81182.737 6.5803 3-5II5 43-4 136.35 1479-34 1883.56 81746.504 6.5879 3-5142 43-5 136.66 1486.17 1892.25 82312.875 6-5954 3.5169 43-6 136.97 I493-OI 1900.96 82881.856 6.6030 3.5196 43-7 137.29 1499-87 1909.69 83453.453 6.6IC6 3-5223 43-8 137.60 1506.74 1918.44 84027.672 6.6182 3-5250 43.9 137.92 1513.63 1927.21 84604.519 6.6257 3-5277 44.0 138.23 1520.53 1936.00 85184.000 6.6333 3.5303 44.1 138.54 1527.45 1944.81 85766.121 6.6408 3 -533Q 44.2 138.86 1534.39 1953-64 86350.888 6.6483 3-5357 44-3 139.17 1541.34 1962.49 86938.307 6.6558 3.5384 44.4 139-49 1548.30 1971.36 87528.384 6.6633 3- 54*o 44-5 139.80 1555-28 1980.25 88121.125 6 . 6708 3-5437 44.6 140.12 1562.28 1989.16 88716.536 6.6783 3-5463 44-7 140.43 1569.30 1998.09 89314.623 6.6858 3-5490 44-8 140.74 1576.33 2007 . 04 89915.392 6.6933 3-5516 44.9 141.06 1583-37 2016.01 90518.849 6 . 7007 3-5543 45-0 I4L37 1590.43 2025.00 91125.000 6.7082 3.5569 45- 1 141.69 1597-51 2034.01 9I733-85I 6.7156 3-5595 45-2 142.00 1604.60 2043.04 92345.408 6.7231 3-5621 45-3 142.31 1611.71 2052.09 92959.677 6.7305 3-5648 45-4 142.63 1618.83 2061 . 16 93576.664 6.7379 3-5674 45-5 142.94 1625.97 2070.25 94196.375 6-7454 3- 5700 45-6 143.26 1633.13 2079.36 94818.816 6.7528 3-5726 45-7 143-57 1640.30 2088.49 95443.993 6.7602 3-5752 45-8 143-88 1647.48 2097 . 64 96071.912 6.7676 3-5778 45-9 144.20 1654.68 2106.81 96702.579 6.7749 3.5805 46.0 144.51 1661.90 2116.00 97336.000 6.7823 35830 46.1 144.83 1669.14 2125.21 97972.181 6.7897 3 5856 46.2 145.14 1676.39 2134.44 98611.128 6.7971 3.5882 46.3 145.46 1683.65 2143.69 99252.847 . 6 . 8044 3-59o8 46.4 145.77 1690.93 2152.96 99897.344 6.8117 3-5934 46.5 146.08 1698.23 2162.25 100544.625 6.8191 3.5960 46.6 146 . 40 1705.54 2171.56 101194.696 6.8264 3-5986 46.7 146.71 1712.87 2180.89- 101847.563 6.8337 3. 601 1 46.8 147.03 1720.21 2190.24 102503.232 6.8410 3-6037 46.9 147-34 1727-57 2199.61 103 161. 709 6.8484 3.6063 47.0 I47.65 1734-94 2209.00 103823.000 6.8556 3.6088 47.1 147-97 1742.34 2218.41 104487. in 6.8629 3 6114 47.2 148.28 1749-74 ' 2227-84 105154.048 6.8702 3.6139 NUMERICAL CONSTANTS. Constants — Continued. 767 n nit 4 «a «8 r n 3 47-3 148.60 1757.16 2237.29 IO5823.817 6.8775 3.6165 47-4 148.91 1764.60 2246.76 IO6496.424 6.8847 36190 47-5 149.23 1772.05 2256.25 I07I7I.875 6.8920 3.6216 47.6 149-54 1779.52 2265.76 IO785O.I76 6.8993 3-6241 47-7 149-85 1787.01 2275.29 IO853I.333 6.9065 3.6267 47-8 150.17 1794- 51 2284.84 IO9215.352 6.9137 3.6292 47-9 150.48 1802.03 2294.41 IO99O2 . 239 6.9209 3.63I7 48.0 150.80 1809.56 < 2304 . OO IIO592.OOO 6.9282 3-6342 48.1 151.11 1817.11 2313.61 III284.64I 6.9354 3.6368 48.2 151.42 1824.67 2323.24 III980.168 6.9426 3-6393 48.3 I5L74 1832.25 2332.89 II2678.587 6 . 9498 3-6418 48.4 152.05 1839.84 2342.56 "3379 -9°4 6.9570 3.6443 48.5 152.37 1847.45 2352.25 1 14084. 125 6 . 9642 3.6468 48.6 152.68 1855.08 2361.96 114791.256 6.9714 3.6493 48.7 153.00 1862.72 2371.69 1 15501.303 6.9785 3.6518 48.8 153-31 1870.38 2381.44 116214.272 6.9857 3-6543 48.9 153-62 1878.05 2391.21 1 1 6930. 169 6.9928 3.6568 49.0 153.94 1885.74 2401.OO 117649.000 7 . 0000 3.6593 49.1 154.25 1893.45 2410.81 118370.771 7.0071 3.6618 49-2 154.57 1901.17 2420.64 119095.488 7.0143 3.6643 49-3 154-88 1908.90 2430.49 119823.157 7.0214 3.6668 49.4 155.19 1916.65 2440.36 120553.784 7.0285 3.6692 49-5 155-51 1924.42 2450.25 121287.375 7.0356 3.6717 49.6 155.82 1932.21 2460.16 122023.936 70427 3-6742 49-7 156.14 1940.00 2470.09 122763.473 7.0498 3.6767 49.8 156.45 1947.82 2480.04 123505.992 7.0569 3.6791 49.9 156.77 I955-65 2490.OI 124251.499 7 . 0640 3.6816 50.0 157.08 1963.50 2500.OO 125000.000 7.0711 3.6840 51.0 160.22 2042 . 82 2601.00 132651.000 7.I4I4 3.7084 52.0 163.36 2123.72 2704.OO 140608.000 7.2111 3-7325 53.o 166.50 2206.19 2809 . OO 148877.000 7.2801 3.7563 54-o 169 . 64 2290.22 2916.00 157464.000 7.3485 3.7798 55.o 172.78 2375.83 3025.00 166375.000 7.4162 3.8030 56.0 175 93 2463.01 3136.00 175616.000 7.4833 3.8259 57-0 179.07 255I-76 3249.00 185193.000 7.5498 3.8485 58.0 182.21 2642.08 3364.00 195112.000 7.6158 3.8709 59-o 185.35 2733-^7 3481.00 205379.000 7.6811 3.8930 60.0 188.49 2827.44 3600.00 216000.000 7.7460 3.9149 61.0 191.63 2922.47 3721.00 226981.000 7.8102 3-9365 62.0 194.77 3019.07 3844.00 238328.000 7.8740 3.9579 63.0 197.92 3117-25 3969.00 250047.000 7-9373 3-979 1 64.0 201.06 3216.99 4096.00 262144.000 8.0000 4 . 0000 65.0 204.20 3318.31 4225.00 274625.000 8.0623 4.0207 66.0 207.34 3421 . 20 4356.00 287496.000 8.1240 4-0412 768 EXPERIMENTAL ENGINEERING. C on st ants — Continued. ft nir 4 «» «3 Vh 3 67.0 210.48 3525.66 4489 . OO 3OO763.OOO 8.1854 4.0615 68.0 213-63 3631.69 4624.00 314432.000 8.2462 4 .0817 69.0 216.77 3739-29 4761 .00 3285O9.OOO 8 . 3066 4 1016 70.0 219.9I 3848.46 4900 . OO 343000.000 8.3666 4 1213 71.0 223.05 3959-20 5041.OO 3579II.OOO 8.4261 4 1408 72.0 226.19 4071.51 5184.OO 37324S.OOO 8.4853 4 1602 1 73-o 229.33 4185.39 5329.00 389OI7.OOO 8.5440 4 1793 74.0 232.47 4300.85 5476.OO 405224.000 8.6023 4 1983 75-o 235.62 4417.87 5625.OO 42I875.OO0 8 . 6603 4 2172 76.0 238.76 4536.47 5776.00 438976.OOO 8.7178 4 2358 77.0 241.9O 4656.63 5929.OO 456533.OOO 8.7750 4 2543 78.0 245.04 4778.37 6084 . OO 474552.O00 8. 318 4 2727 79.0 248.18 4901.68 624I.OO 493039.0OO 8.8882 4 2908 80.0 25I.32 5026.56 6400.OO 512000.000 8-9443 4 3089 81.0 254-47 5153-or 6561.OO 53I44I.OOO 9.0000 4 3267 82.0 257-61 .5281.03 6724.OO 55I368.OO0 9-0554 4 3445 83.0 260.75 5410.62 6889.OO 57I787.OO0 9. 1 104 4 3621 84.0 263.89 554I-78 7056.OO 592704.OOO 9.1652 4 3795 85.0 267.03 5674.50 7225.OO 6I4I25.000 9-"i95 4 3968 86.0 270.17 5808.81 7396.OO 636O56.OOO 9.2736 4 4140 87.0 273-32 5944.69 7569.OO 6585O3.OOO 9-3274 4 43io 8S.0 276.46 6082.13 7744.OO 68I472.000 9.3808 4 4480 89.0 279.60 6221.13 7921.OO 7O4969.OOO 9.4340 4 4647 90.0 282.74 6361.74 8IOO.OO 72900O.OOO 9.4868 4 4814 91.0 285.88 6503.89 8281.OO 75357I.OOO 9-5394 4 4979 92.0 289.02 6647.62 8464 . OO 7786S8.000 9-59*7 4 5144 93-o 292.17 6792.92 8649 . OO 804357.000 9-6437 4 5307 94.0 295-31 6939, 78 8836.OO 83O584.OOO 9.6954 4- 5468 95-o 298.45 7088.23 9025.OO 857375.000 9.7468 4 5629 96.0 301.59 7238.24 9216.OO 884736.OOO 9.7980 4 5789 97.0 304-73 7389.83 9409 . OO 9I2673.000 9.8489 4 5947 98.0 307-87 7542.98 9604.OO 94II92.000 9.8995 4 6104 99.0 311.02 7697.68 9801.OO 97O299.OOO 9.9499 4 6261 100. 314-16 7854.00 IOOOO.OO IOOOOOO.OOO 10.0000 4.6416 LOGARITHMS OF NUMBERS. 769 III. LOGARITHMS OF NUMBERS. No. 1 2 3 4 5 6 17 8 9 IO 0000 0043 0086 0128 0170 0212 0253 0294 0334 0374 11 0414 o453 0492 0531 0569 0607 0645 0682 0719 °755 12 0792 0828 0864 0899 0934 0969 1004 1038 1072 1 106 13 1 139 '"73 1206 1239 1271 1303 1335 1367 1399 1430 *4 1461 1492 i5 2 3 *553 1584 1614 1644 1673 1703 1732 15 J 761 1790 18I8 1847 1875 1903 1931 1959 1987 2014 16 2041 206S 2095 2122 2148 2175 2201 2227 2253 2279 3 2304 2330 2355 2380 2405 2430 2455 2480 2504 2529 2553 2577 2601 2625 2648 2672 2695 2718 2742 2765 19 2788 2810 2833 2856 2878 2900 2923 2945 2967 2989 20 3010 3032 3054 3075 3096 3"8 3i39 3160 3181 3201 21 3222 3243 3263 3284 3304 3324 3345 3365 3385 3404 22 3424 3444 3464 3483 3502 3522 3541 3560 3579 3598 23 3617 3636 3655 3674 3692 3711 3729 3747 3766 3784 24 3802 3820 3838 3856 3874 3892 3909 3927 3945 3962 25 3979 3997 4014 4031 4048 4065 4082 4099 4116 4i33 26 415° 4166 4183 4200 4216 4232 4249 4265 4281 4298 27 43H 433o 4346 4362 4378 4393 4409 4425 4440 445 6 28 4472 4487 4502 45 l8 4533 4548 4564 4579 4594 4609 29 4624 4639 4654 4669 4683 4698 4713 4728 4742 4757 30 477i 4786 4800 4814 4829 *4843 4857 4871 4886 4900 31 4914 4928 4942 4955 4969 4983 4997 501 1 5024 5038 32 5°5i 5065 5079 5092 5105 5"9 5^2 5H5 5 J 59 5172 33 5185 5198 5211 5224 5237 5 2 5° 5263 5276 5289 5302 34 5315 5328 5340 5353 5366 5378 5391 5403 54i6 5428 35 544i 5453 5465 5478 549o 55° 2 55H 5527" 5539 555i' 36 5563 5575 5587 5599 561 1 5 62 3. ,5635 5 6 47 5658 5670 37 56S2 5 6 94 570S 5717 5729 574o- 5752 5763 5775 5786 38 5798 5809 5821 5832 5843 5855 5866 5877 5888 5899 39 59i 1 5922 5933 5944 5955 5966 5977 5988 5999 6010 40 6021 6031 6042 6053 6064 6075 6085 6096 6107 6117 4 1 6128 6138 6149 6160 6170 6180 6191 6201 6212 6222 42 6232 6243 6253 6263 6274 6284 6294 6304 6314 6325 43 6335 6345 6355 6365 6375 63S5 6395 6405 6415 6425 44 6435 6444 6454 6464 6474 6484 6493 6503 6513 ^6522 45 6532 6542 6551 6561 65 7 1 6580 6590 6599 6609 6618 46 6628 6637 6646 6656 6665 6675 6684 6693 6702 6712 47 6721 6730 6739 6749 6758 6767 6776 6785 6794 6803 48 6812 6821 6830 6839 6848 6857 6866 6875 6884 6893 49 6902 691 1 6920 6928 6937 6946 6955 6964 6972 6981 50 6990 6998 7007. 7016 7024 7°33 7042 7°5° 7059 1 7067 5i 7076 7084 7093 7101 7110 7118 7126 7*35 7H3 7 X 5 2 52 7160 7168 7177 7185 7*93 7^02 7210 7218 7226 7 2 35 53 7 2 43 7251 7259 7267 7275 7284 7292 7300 73o8 73i6 54 7324 7332 7340 7348 735 6 7364 7372 738o 7388 7396 No. 1 2 3 4 5 6 7 8 9 770 EXPERIMENTAL ENGINEERING, Logarithms of Numbers — Continued. No. 1 2 3 4 5 6 7 8 9 55 7404 7412 7419 7427 7435 7443 745i 7459 7466 7474 56 7482 7490 7497 75°5 75J3 7520 7528 7536 7543 755i 57 7559 •7566 7574 7582 7589 7597 7604 7612 -7619 7627 58 7634 7642 7649 7657 7664 7672 7679 7686 7 6 94 7701 59 7709 7716 7723 773i 7738 7745 7752 7760 7767 7774 60 7782 7789 7796 7803 78ro 7818 7825 7832 7839 7846 61 7853 7860 7868 7875 7882 7889 7896 7903 7910 7917 62 7924 793i 7938 7945 795 2 7959 7966 7973 7980 7987 63 7993 8000 8007 8014 8021- 8028 8035 8041 8048 8055 64 8062 8069 8075 8082 8089 8096 8102 8109 8116 8122 65 8129 8136 8142 8i49 8156 8162 81.69 8176 8182 8189 66 8195 8202 8209 8215 8222 8228 8235 8241 8248 8254 67 8261 8267 8274 8280 8287 8293- .8299 8306 8312 8319 68 8325 8331 8338 8344 8351 8357 8363 8370 8376 838'2 69 8388 8395 8401 8407 8414 8420 8426 8432 8439 8445 70 8451 8457 8463 8470. 8476 8482 8488 8494 8500 8506 71 8513 8519 8525 8531 8537 8543 8549 8555 8561 8567 72 8573 8579 8585 8591 8597 8603 8609 8615 8621 8627 73 8633 8639* 8645 8651 8657 8663 8669 8675 8681 8686 74 8692 8698 8704 8710 8716 8722 8727 8733 ~8 7 39 8745 75 8751 8756 8762 8768 8774 8779 8837 8785 8791 8797 8802 76 8808 8814 8820 8825 8831 8842 8848 8854 8859 77 8865 8871 8876 8882 8887 8893 8899 8904 8910 8915 78 8921 8927 8932 8938 8943 8949 8954 8960 8965 8971 79 8976 8982 8987 8993 8998 9004 9009 9015* 9020 9025 80 9031 9036 9042 9047 9053 9058 9063 9069 9074 9079 81 9085 9090 9096 9101 9106 9112 9117. 9122 9128 9133 82 9138 9H3 9149 9154 9159 9165 9170 9175 9180 9186 83 9191 9196 9201 9206 9212 9217 9222 9227 9232 9238 B4, 9243 9248 9253 9258 9263 9269 9274 ,9279 9284 9289 85 9'294 9299 9304 93°9 93*5 9320 9325" 9330 9335 9340 86 9345 935° 9355 9360 9365 9370 9375 9380 9385 9390 87 .9395 9400 9405 9410 94i5 9420 9425 9430 9435 9440 88 9445 945° 9455 9460 9465 9469 9474 9479 9484 9489 85 9494 9499 95/>4 95°9~ 95*3 9518 95 2 3 9528 9533 9538 90 9542 "9547 9552 9557 9562 9566 9571 9576 9581 9586 91 959o 9595 9600 9605 9609 9614 9619 9624 9628 9633 92 9638 9643 9647 9652 9657 9661 9666 9671 9675 9680 93 9685 9689 9694 9699 9703 9708 9713 9717 9722 9727 94 9731 9736 974i 9745 975° 9754 9759 9763 9768 9773 95 9777 9782 9786 9791 9795 9800 9805 9809 9814 9818 96 9823 9827 9832 9836 9841 9845 9850 9854 9859 9863 97 9868 9872 9877 988 r 9886 9890 9894 .9899 9903 9908 98 9912 .9917 9921 9926 993o 9934 9939 9943 9948 995 2 99 9956 9961 9965 9969 9974 9978 9983 9987 9991 8 9996 9 No. 1 2 3 4 5 6 7 LOGARITHMIC FUNCTIONS OF ANGLES. 771 IV. LOGARITHMIC FUNCTIONS OF ANGLES. Angle. 0° 0' o° 10' o° 20' o° 30' o° 40' o° 5. V. Cot 7-4 6 37 .7648 .9409 8.0658 .1627 -2419 .3089 .3669 .4181 .4638 •5053 -5 431 •5779 .6101 .6401 .6682 ♦6945 .7194 ■7429 .7652 .7865 .8067 .8261 8.8446 "T8624 •8795 .8960 .91.18 .9272 8.9420 •95 6 3 .9701 .9836 .9966 9-QQ93 9.0216 ^0336 •0453 .0567 .0678 ,.0786 9.0891 •0995 .1096 •"94 Cot. 301. 1 176.I I24.9 96.9 ,79-2 67.0 58.0 '51.2 45-7 ' 41-5 37-8 .34-8 .32-2 30.0 . 28.1 26.3 24.9 23-5 22.3 21.3 20.2 19.4 18.5 ,17.8' 17.1 16.5 45.8 15-4 ?4-8 14-3 13.8 13-5 1-3.0 12.7' 12.3 12.0 -*i. 7 1 1.4 11. 1 10.8 10.5 10.4 10.1 9-8 D.l'. 2.5363 .2352 .0591 I.9342 •8373 •758l .69II .6331 .5819 .5362 4947 •4569 .4221 .3899 •3599 .3318 •3055 .2806 ■2571 .2348. .2135 •1933 •1739 1-1554 •1376 .1205 .1040 .0882 .0728 1.0580 0-0437 ' .0299 .0164 .0034 0-9907 09784 . .9664 •9547 ' -9433 .9322 .9214 0.9109 ^9005" .8904 .8806 Tan. 90° 0' 89 50' 89 40' 89 30' 89 20' 89°ro' 89° 6' 88° so 1 88° 40' 58° 30' 88° 20' 88° 10' 88° 0' 87 50' S 7 ° 40' 8 7 ° 3 c/ 87 p 2o A 87 10' 87° 0' 86° 50' 86° 40' 86° 30' 86° 20' 86° io / 86° 0' 8 5 °5o' 85 40' S5 30' 85 20' 85 10' 85° 0' 84 50' 84 40' 8 4 ° 30' 84 2d 84 io' 84° 0' 83 50' 83 40' 8 3 °3o' 8 3 °20' 83 10' 83° 0' 82P 50' 82 4 o' 82°3o' Angle. 7-J2 EXPERIMENTAL ENGINEERING. Logarithmic Functions of Angles — Continued. Angle. Sin. D.l'. Cos. D.l'. Tan. r>. v. Cot. 7° 3o' 9-1*57 9-5 9.9963 .2 9.1 194 9-7. O.8806 82° 30' 7° 4o' .1252 .9961 .1291: .8709 S2 20' 70.50/ 8° 0' •1345 9-I436 9-3 9.1 8-9. 8.4 8.2 •■ • 8.0 •9959 • 2 ' .2 .1385 9-4 9-3 9.1 8-9 8.7 8 6 .8615 82° JO' 82° 0' 9-9958 9-I478 O.8522 8 a 10'. .1525 •995° <2 •.1569 ~%V 8i 5 o / 8° 20' .1612 •9954 .2 .2 .1658 .8342 8i°- 4 o' 8 ° 3 °: .1697 •9952 •1745 •8255 8i° 30' 8° 40' .1781 .9950 .2 .2 •I8 3 I 84 8.2 .8169 8i° 20' 8° 50' .1863 •9948 .1915 .8085 8i° 10' 9° 0' 9-1943 7-9 .7.6 7-5 7-3 7-3 7-1 7.0 •6.8 '6.8' 9-9946 .2 9.1997 8.1 0.8003 81° 0' 9 C 10' .2022 •9944 .2 .2078 80 .7922 8o c 50' 9° 20' .2100 •9942 .2 •2. .2 .2 •3-. .2158 7.8 7-7 7.6 7-4 7-3 7-3 7-i 7.0 6.9. .6.8 .7842 8o° 40' 9° 30' .2176 •9940 .2236 •7764 8o° 30' 9 40' ..2251 •9938 . ^313 •7687 8o°2o' 9° 50' io° JL •7464 IO° 20' .2538 .9929 .2 •3 .2 • .2609 •739i 79° 40' io° 30' .2606 . .9927 .2680 .7320 79° 30' io° 40' .2674 6.6 .9924 .2750 .7250 79 20' io° 50' .2740 6.6 .9922 •3" .2 .28.19 .7181 79 10' 11° 0' 9.2806 6.4 ,64 6.3 6.1 9-99*9 9.28"S7" 6.6 "oT"3~ 79° 0' 11° io' .2870 .9917 .3' .2 ~9~53 67 6.5 6.4 6-3. 6-3 6.1 .7047 7 So 5 c/ 11° 20' •2934 .9914 .3020 ..6980 7S 40' U° 30' .2997 .9912 3 .2 .■3085 .6915 78° 30' .11° 40' .3058 ' 6.! • .9909 •3H9 .6851 78° 20' n° s& •3"9 6.0 • -9907 •3 _ 1 32I2' .67SS 7S 10' 12° 0' 9-3I79 5-9 5.8 5-7 5 V 7 5-6 5-5 5-4 5-4 5-3 5-2 5-2 5-i 5.0 5-° .•4.9 4-9 4.8 '4-7 9.9904 ^3275 0-6725 78° 0' 12° 16' •3238 .9901 .2 •3336 6.1 " .6664 77° 50' 12° 20.' .3296 •9899 •3 •3 •3 •3 •3 •3 2 -3397 6!i 5-9 5-9 5-8 5-7 5-7 5-6 5-5 5-5 5-4 5-3 5-3 5-3 5-i 5-2 5-i- .6603 77° 40'- 12° 30' •3353 .9896 •3458 .6542 77° 30' 12° 40' .3410 •9S93 '■3S l 7 •.64S3 77 20' 12° 50' •3466 ■ .9890 . ■ -3576 .6424 77 '10' 13° 0' 9-3521. "9^887 9-3634 0.6366 .77° 0' 13° 10' •3575 .0884 .3691 "^6309 76° 50' 13° 2d .3629 .9S81 •3748 .6252 76° 40' if 30' .36S2 .9873 —3804 .6196 76° 30' '3° 40' •3734 .9875 •3 •3 •3 •3 .3859 .6141 76° 20' 13° 50' .3786 -9872 _l39i£ .60S6 76 10' 14° 0' 9-3837 9.9869 9.396S 0.C032 76° 0' 14 . 10' •3887 "^9866" .4021 •5979 75° 50' 1 4° 20' •3937 .9863 .4074 .5926 75° 4o' 14° 30' .3986 .9859 •4 •3 •3 •4 .4127 .5S73 75°'3o' 14° 40' •4035 .9856 . .4178 .5822 75° 20' 14° 50' 15° 0' •4083 9-4130 .9853 .4230 •5770 o-57i9 75° 10' 75°" 0' 9.9849 9.4281 Cos. D.l'. Sin. D.l'. Cot. D.l'. Tan. Angle. LOGARITHMIC FUNCTIONS OF ANGLES. Logarithmic Functions of Angles — Continued. 773 Angle. Sin. D.-l'. Cos. D. 1'. Tan. r>. i'. Cot. 15° 0' i 5 ° io' 9.4130 4-7- 4-6: 4.6 . 4-5- 4-5" 44. ' 4.4 9.9849' •3 •3 •4 •3 •4 •4. •3 •4 9.4281 5-o- 5.0 4-9 4-9/ 4.8: 4.8,:' 4-7 4.7 o-57*9 ,5669 75° 0' 74°5o' •41.77 .9846 .•4331 i 5 ° 20' .4223 •9843 .4381 ,5619 ,74° 40' 15° 30' 15° 40' .4269 4314 .9839 ■•',9836 •4430 •4479 •5570 •552i. 74°: 30' 74° 2c' 15° 50' 16° Q' •4359- 9.4403 .9832. •4527 •5473 0.5425 74° 10' 74° 0' 9.9828 9-4575 i6 c 10' •4447 .9825 .4622 •5378. 73° 5°' ' 1 6° 20' •4491, 4-4.. .9821 .4669 •5331 73° 40' 1 6° 30' •4533 4.2 4-3. 4.2 4.1' 4.1 4-1. 4 A- 4-0. 4.0 3-9 3-9 3-8 3-8 ' 3-7 3-8 3-6 3-7. 3-6- 3-6 3-5 3-6 3-5 3-4 3-4 3-4 3-4 3-3 3-3. 3-3 3-3 3-2 3-2 31 3-2. 3-i ' 3-i 3-o •9817 •4 '•3- • -47 f 6 4-7 ■ 4-6 4-6 •4:5 *5 4-5 44 . 44 44 4-3 4-3 4.2 4.2 4.2 4.2 4.1 4.1 t°o 4.0. • 4.0 4.0 3-9 • 3-9 3-8 3-9 3-8 3-S 3-7 3-8 3-7 3-7 •5284. 73° 3o' 1 6°. 40' •4576 .9814 .4762 •5238 73 20' 1 6° 50/ 17° 0' 1 7 10' .4618 9.4659 .9810 •4 •4.. •4"' .,4 . •4. •4 . •4 ' •4 •4 - " •4 .4 . •5 . -4 .4 ■ •5 •4 •5 •4 • •5 • •4 •5. •4 : •5 ••5. •5- •4 •5 •5 •5 •5 •5 •5 •5 .6 •5 D. 1'. ' .480*8 •5192 73° 10' 73° 0' 7 2 ° 50' 9.9806 .9802 94853! 0.5147 .4700' • .4898: .5102 1 7 '20' .4741 • .9798 4943 •5057 7 2° 40' 170 30' 4781 •9794 • 4987 •5 OI 3 72° 30' 17° 4 o' .4821 •9790 • -5 3i .4969 72° 20' [7° 50' .4861 .97S6 •5075 4925- 72° IO' 18° 0' 9.4900 9.9782 9.51 18 0.4882 72° 0' 18° io' 1 8° 20' •4939 •4977 -.9778 •9774 .5161 •5203 4839 4797 7.1° 50; 71° 40' iS° 30' •5°i5 •9770 ' •5245 4755 71 30' 1 8° 40' .5052 •9765 .5287 4713 71° 20' 1 8° 50' .5090 .9761 •5329 .4671 71° 10' 19° 0' 19° 10' 9.5126 "5163" _757 •9752 9-537Q 04630 4589 71° 0'. 70° 50' .5411 19 20' •5' 99 ' .9748 •5451 4549 70 40' 1 9 30' 19° 40' •5235 • -5270 •9743 •9739 •.•5491 •5531 .4509- .4469 70 30' 7O 20' 19° 50' 20° 0'" .5306 •9734 •557i 9,5611 4429 0.4389 70° I& 70° 0' 9-5341 9-9730 2Q° IO f . -5375 •9725 ••5 6 5° 435° 69° 50 7 20° 2C/ 20° 30' .5409. ' -5443 • .9721 .9716 .5689 •5727 431 1 4273 • 69 40' 69° 30', 20°. 40' •5477 .9711. .5766 4234 69° 20' 20° 50' •55IO .9706 .5804 .4196 69° IO' 21° 0' 9-5543 9.9702 9.5842 0.4158 69° 0' 21° IO' •5576 .9697 .5879 .4121 68° 56* 21° 20' .5609 ..9692 •5917 4083 68° 40^ 21° 30' .5641 .9687 •5954 .4046 68° 30' 21° 4 O f •5°73 .96S2 .5991 .4009 68° 2C/ 21 50' 22° 0' •57°4 .9677 .6028 3-7 3-6 3-6 3-6 3-6 •3972 68° 10' 68° 0' 9-5736 9.9672 9.6064 0.3936 22° IO' •57^7 .9667 .6100 .3900 67° 50' 22° 20 f .5798 . .9661 .6136 .3864 67° 40' 22° 30' .5828 .9656 .6172 .3828 6 7 °3C/ Cos. X>.1'. Sin. Cot. D.l'. Tan. Angle. 774 EXPERIMENTAL ENGINEERING. Logarithmic Functions of Angles — Continued. Angle* Sin. D.l'. Cos. D.l'. Tan. D. 1'. Cot. 22^ 30' 9.5828 3.1 3-o 3-o 2.9 3-0 2.9 2.9 2.9 2.8 9.9656 •5 •5 9.6172 3-6 3-5 3-6. 3-5 3-4 3-5 3-4 3-5 3-4 3-4 3-3 3-4 3-3 3-4 3-3 3-3 •3-2 3-3 3-2 3-3 3-2 3-2 3.2 3-i .3-2 3-i •3-2 O.3828 6 7 ° 30' 22° 40' .5859 .9651 .6208 •3792 67° 20' 22° 50' _j889_ .9646 .6243 •3757 67° 10' 23° 0.' 9-5919 9.964O •5 ,6' •5 .6 •5 .6 9-6279 0.3721 67° 0' 23° io' •5948 ^9635 .6314 ..3686 66° 50* 23° 2o' .5978 .9629 .6348 .3652 66° 40' 23° 30' .6007 .9624 ••6383 •3617 66° 30' 23° 40' .6036 .9618 .6417 .3583 66° 20' 23° 50' .6065 •9613 ;6 4 52 •3548 66° 10' 24° 0' V6093 2.8 9.9607 «5. .6 .6 .6 •5 .6 9.6486 Q-35 H 66° 0' 24° 10' .6121 2.8 2.8 2.8 2.7 2.7 2.7 2-7 2.7 2.6 2.6 2.6 .9602 .6520 .3480 65° 50' 24° 20' .6149 •9596 •6553 •3447 65° 40' 24° 30' .6177 .9590 .6587 •34U 65° 30' 24° 40' .6205 .95 8 4 .6620 •3380 65° 2o' 24° 50' •6232 •9579 .6654 •3346 65° IO' 25° 0' 9.6259 9-9573 .6 9.6687 03313 65° 0' 25° 10' .62S6 •95 6 7 .6 .6 .6720 .3280 64° 50' 25° 20' 6313 .9561 .6752 .3248 64° 40' 25° 30' .6340 •9555 .6 .6785. •3215 6 4 ° 30' 25° 40' .6366 •9549 .6 .6 . .6817 •3183 64° 20' 25° 50' '6392 •9543 .685O •3150 64° 10' 26° 0' 9.6418 2.6 9-953X •7 .6 "9T688T 0.31 18 64° 0' 26° 10' ~~ [6444 2.6 2.5 2.6 •953o .69I4 .3086 .63° 50' 26° 20' .6470 .9524 .6 .6 .6946 •3054 63 40' 26° 30' .6495 .9518 .6977 •3023 63° 30' 26° 40' .6521 .9512 •7 .6 .7009 .2991 63° 20' 26° 50' •6546 2-5- . 2.4 •95°5 • 7°4Q .2960 63° 10' 27° 0' 27° ic/ 9-657 • 6 595 -2.5 -•2.5 9-9499 .9492 •7 • .6 9.7072 31 31 31 ? T 0.2928 63° 0' 62° 50' •7io3 27° 20' .6620 .9486 •7*34 .2866 62° 40' 27° 30' .6644 2.4 •9479 •7 .6. •7 •7 .6 .7165 .2835 62° 30' 27° 40' .6668 2.4 •9473 .7196 J- 1 3-o 3-i 3-0 3-o 3-i 3-o 30 3° 2804 62° 20' 27° 50' 28° 0' .6692 9.6716 2.4 2.4 2.4 2.3 .9466 .7226 9-7257 •2774 62° 1 6' 62° 0' 9-9459 Q-2743 28° 16' T6740 •9453 •7- •7 •7 •7 .7 .7287 •2713 61° 50' 28° .20' .6763 .9446 •7317 .2683 61° 40' 28° 30' .6787 2.4 •9439 7348 .2652 61° 3 c' 28° 40' .6810 2 -3 .9432 .7378 .2622 6l° 2G' 28° 50' •6833 2 -3 2.3 2.2 2.3 2.2 •9425 •74o8 •2592 61° 10' 29° 0' 29° jo' 9.6856 .6878. 9-94^8 .9411 •7 •7 •7 •7 •7 . .8. 9-7438 2.9 3-o 2.9 3-o 2.9 2.9 0.2562 ~^2533. 61 °0' 60° 50' .7467 29° 20' .6901 .9404 •7497 •2503 60° 40' 29° 30' .6923 •9397 .7526 .2474 60° 30'- 29° 40' .6946 2-3 •9390 •755° :2 4 44 60° 20' 29° 50' 30° 0' .6968 2.2 2.2 •9383 9-9375 .7585 •2415 60° io' 60° 0' 9.6990 9.7614 0.2386 " Cos. D.l'. ,Sin. D. 1'. Cot. D. 1 . Tan. Angle. LOGARITHMIC FUNCTIONS OF ANGLES. Logarithmic Functions of Angles — Continued. 77S Angle. Sin. D.l>. Cos. D.l'. Tan. D.i'. Cot. 30° 0' 30° 10' 9.6990 .7012 2.2 9-9375 •7 •7 .8 9.7614 3.0 2.9 2.8 O.2386 .2356 60° 0' 59° 50 7 .9368- •7644 30° 20' -7033 2.2 .9361 •7673 . .2327 59° 40' 3O 30' •7055 •9353 •7 .8 .7701 2.9. 2.9 2.9 2.8 2.9 2.8 2.9 28 .2299 59° 30 7 3 o° 40' 7076 2.1 .9346 •7730 .2270 59° 20' 30° 50' .7097 •9338 •7 .8 .8 •7759 .2241 59° 10' 31° 0' 31° 10' 9-7"8 7*39 2.1 9-9331 •9323 9.7788. 0.22I2 59° 0' 58*50" .7816 12184 31° 20' .7160 2.1 •9315 •7 8 •7845 •2155 58° 40' 310 30/ .7181 .9308 •7873 .2127 58° 30 7 31° 40' .7201 .9300 .8 .7902 .2098 5 8° 20 7 31° .50' 32° 0' .7222 2.0 . 2.0 .9292 9-9284 ,8 .8 . -7930 '2.8 28 .2070 O.2042 58° 10' 58° 0' 9.7242 9-7958 32° 10' .7262 2.0 2.0 .9276 .& 8 .7986 2.8 2.8 2.8 .2014 57° 50' 32°. 20' .7282 .9268 .8014 .1986 57° 40' 32° 30' .7302 .9260 .8 .8042 .1958 57° 30' 32° 40' .7322 .9252 8 .8070 2-7 2.8 2.8 ' .1930 57° 20' 32° 50' 33° 0' •7342 1-9 1-9 2.0 1.9 1:9 1.9 1.9 1,8 1.9 1.8 1.9 1.8 1.8. 1.8. ' fi.8 1.8 1.7 r.8 1.7 1.8 •9244 9-9236 .8 8 .8097 •I903 0.1875 57° 10' 57° 0' 9-736I 9.8125 33° 10' .738o .9228 •9 8 .8153 2.7 28 .1847 56° 50* 33° 20' .7400 •9219 .8180 .1820 '56° 40' 33° 3o' .7419 .9211 .8 •9 •8 •9 .8 •9 •9 •9 .8 •9 •9 •9 •9 •9 -9 1 .8208 2-7 2 8 .1792 56° 30' 33° 40'. .7438 -9203 .8235 •1765 56° 20' 33° 5^ 34° 0' 34° !<• '7457 '9-7476 •7494 .9194- .8263 2.7 2.7 2.7 2.7 2-7 2.7 2-7 2 -7 2-7 2.7 26 •*737 0.1710 56° 10' 56° 0' 55° 5o' 9.9186 9.8290 .9177 .8317 .1683 34° *• •75*3 .9169 •8344 ,1656 55° 40 34° 3o' •753i .9160 •8371 .1629 55° 3o' 34° 40' •755° •9i5i . .8398 .1JJ02 55° 2c/ 34° 50' 35° 0' .7568 .9142 .8425 •1575* ■ 55 °i7 4 S° 40' 4i° 30' .8213 .8745 1 .2 .9468 .0532 48° 30' 41° 40' .8227 .S733 ► I.I •9494 2.5 2-5 2.6 2-5. 2.6 .0506 48° 20' 41° 50' 42° 0' 42° IO / •8241 .8269 .8722 9871T .8699 I.I 1.2 I _ 1 ~95 x 9 .0481 0.0456 48° 10' 48° 0' 47° 50' 9-9544 •9570 .0430 42° 20' .8283 .86S8 1.2 •9595 .0405 47° 40' 42° 3 o' .8297 .8676 I.I .9621 2-5 2-5 2.6 2-5 2-5 2-5 2.6 .0379 47° 30/ 42° 40' .8311 .8665 1 .2 .9646 •0354 47° 20' 42° 50' 43° 0' 43° 10' .8324 9-8338 •S351 .8653 1.2 . 1.2 j j •967 ' 9-9697 .9722 •0329 0.0303 .0278 47° 10' 47° 0' 46° 50' 9.8641 .8629 • .13° 2o' .8365 .8618 1.2 •9747 .0253 46° 40' 43° 3o' .S378. .860-6 1.2 •9772 .0228 46° 30' 43° 40' .8391 • I -3 1.4 •*-3 1 -3. .1-3 '.'1.2 .8594 r.2 i-3 1.2 .9798 .0202 46° 20' 43° 50' 44° 0' 44° 10' .S405 9.8418 .8431 .S5S2 9-8569 •8557 .9823- 9.9S48 .9874 2-5 2-5 2.6 •0177 0.0152 .0126 46° IO' 46° 0' 45° 5°' 44° 20' .8444 .8545 1 .2 i-3 1.2 I 3 1.2 .9899 2-5 .0101 45° 40' 44° 3o' •8457 .8532 . .9924 2-5 2-5 2.6 2-5 .0076 45° 3o' 44° 40' 44° 50' 45° 0' .84C9 .8482 1-3 1-3 .8520 .8507. •9949 •9975 .0051 .0025 45° 20' 45° IP' 45° 0' 9.8495 9-8495 0.0000 0.0000 Cos. D.l'. Sin. r>. i'. Cot. D. V. Tan. Angle. NA TURAL FUNCTIONS OF ANGLES. 777 V. NATURAL FUNCTIONS OF ANGLES. A. Sin. Cos. A. Sin.- Cos. 1^ | A. Sin. Cos. 0° 10' 20' So' 40' 50' l d 10' 20' 30' 40' SO' 2° 10' 20' 30' 40' 50' 3 C - 10' 20' 30; 40' 50' 4° 10' 20' .30' 40' 50' 5° 10' 20' 30' 40' 50' 6° 10' 20' 30' i>' 50' 7° 10' 20' 30' .OOOOOO I. OOOO 90° SO,' 40' 30' 20' 10' 89° 50; 40' 3°' 20' 10' 88° 50; 40' 30' 20' 10' 87° 50' 40' 30' 20' 10' 86° 40' 30' 20' 10' 85° 50' 40' 30' 20' 10' 8-4° 50' 40' 30' 20 r IO' 83 d 50' 40' •30' 30' 40' 50' 8°- 10' 20' 30' 40' 50' 9° 10' 20' ^30' 40' 50' 10° 10' 20' 3°; 40' 5o' 11° 10' 20 f 30' 40' 50' 12° 10' 20' 30' 40' 5o' 13 c 10' 20' 30' 40' 50' 14° 10' 20' 3o' 40' 5o' 15° •1305 •1334 .1363 .99 14 .99II .9907 3°' 20' 82° 50; 40' 30' 20'. IO< 81° 50' 40' 30' 20' '10' 80f 5 °; 40' 30' 20' 10' 79 c 5 °; 40' 30' 20' 10' 78 c 50; 40 f 30' 20'- 10' 77 c 50; 40' 30' 20' 10' 76 c 50; 40' 30" 20' 10' 75° 15° 10' 20' 30' -40' 50' 16° .10' 20' 30' 4 o' 5o' 17° 10' 20' 30' 40' 50' .18° 10'' 20' 30' 40' 50' 19 c 10' 20' 30' 40' SO' 20° 10' 20' 30' 40' 50' 21° 10' 20' 30' 40' 5o' 22° 10' 20' 30' .2588 . -9659 75° .50' 40' 30'. 20' 10' 74° 5°; 40' 30' 20' 10' 73° 50; 40' 30' 20' 10' 72° 50; 40'. 30' 20 r IO' 71° 50; 40' 30' 20' 10' 70 c 5 o; 4 o' 30' 20' 10' 69° 5°' 40' 30' 20' 10' 68° 50; 40' 3o' .OO2909. .005818 .008727 .OU635 .014544 I .OOOO I .OOOO I. OOOO .9999 •9999 .2616 .2644 .2672 .2700 .2728 .9652 ,9644 .9636- .9628 .9621 .1392 •9903 .1421 .1449 .1478 •I507 •1536 .9899 .9894 .9890 .9886 .9881 .017452 .9998 .2756 .9613 .02036 .02327 .02618 .02908 .03199 .9998 •9997 •9997 .9996 •9995 .2784 .2812 .2840 .2868 .2896 ..9605 .9596 .9588 .9580 •9572 .1564 .9877 •1593 .1622 .1650 .1679 .1708 .9872 .9S68 .9863. ..9858 •9353 .03490 •9994 •2924 •9563 .03781 .04071 .04362 .04653 •04943 •9993 .9992 •9990 .9989 .9988 •2952 .2979 •3007 •3035 .3062 •9555 •9546 •9537 •9528 •9520 •1736 .9848 •1765 .1794 .1822 .1851 .1880 .9843 •9838 •9333 .9827 .9822 .05234 .9986 .3090 •95 " •05524 .05814 .06105 •06395 .06685 •9985 •9983 .9981 .9980 .9978 .3118 ■3*45 •3173 .3201 .3228 .3256 •3283 ■33" •3338 •3365 1.3J93 •3_4£o •344 _ 8 •3475 •3502 •35 2 9 :35_57 •3584 .9502 .9492 •9483 •9474 •9465 _945i .9446 •9436 .9426 .9417 •9407 •9~397 •9387 •9377 •9367 •935 6 _ : 934_6_ •9336 .1908 .9816 •1937 •1965. .1994 .2022 .2051 .98LI' .9805 . -9799 •9793 •9787 .06976 .9976 .07266 •07556 .07846 .08136 .08426 •9974 .9971 .9969 19967- .9964 .2079 .9781 .2108 .2136 .2164 .2193 .2221 •9775 .9769 •9763 •9757 •975° .08716 .9962 .09005 .09295 •095 8 5 .09874 .10164 •9959 •9957 •9954 •995 l •9943 •9945 .2250 .2278 .2306 •2334 .2363 £392 .2419 •2447 .2476 .2504 •2532 .2560 •9744 •9737 •9730 .9724 .9717 J?7J2_ _j97p3_ . .9696 .9689 .9681 .9674 .9667 •10453 .10742 .11031 .11320 .11609 .11898 .9942 •9939 •9936 •993 2 .9929 .3611 •363S .3665 .3692 •37^9 •9325 •9315 •9304 .9293 . 9 _2S 3 _ •9272 .12187 •9925 •3746 .12476 .12764 .13053 .9922 .9918 .9914 •3773 .3800 .3827 .9261 .9250 •9239 .2588 •9659 Cos. Sin. A. Cos. Sin. A. Cos. Sin. A. 778 EXPERIMENTAL ENGINEERING. Natural Functions of Angles— Continued. A. Sin. Cos. A. Sin. Cos. A. Sin. Cos. 1 30' 40; 23° 10' 20' 3 3o' 26' ! to 5000 to 72 1 13,000 5200 70 % J 150 J • 13,000 10-14 7000 15-16 35 10-14 28 8000 2800 8-13 5 5500 1500 22 6400 2200 1 1-23 4500-6000 I700 15-26 6000 24OO 2-3 7-10 5500 0.9 3 1000 3-7 4 1 800 H-3+ 2i 600 4 950 4-7 2-4 i 750 4-6 4 4-7 3i 2£-5 i£-3 i-6 650 From Vol. XXII., Encyc. Britannica. 7^ 2 EXPERIMENTAL ENGINEERING. VII. STRENGTH OF METALS AT DIFFERENT TEMPERATURES. [Experiments of A. Le Chatelier, Paris, 1891.] Cast-brass. Strength remains about constant until 500° C. Temperature Centigrade. Deg. Breaking-load per Square Inch. Lbs. Elongation. Per Cent. 15 155 230 480 540 690 19,457 17,864 17,508 17,693 11,677 5,66o O.24 O.71 0.35 O.89 0.54 O.71 , Tin-bronze. Temperature Centigrade. Deg. Breaking-load per Square Inch. Lbs. Elongation. Per Cent. Duration of Test. 15 140 230 250 300 350 415 22,614 23,582 20.524 18,717 17,124 15,574 9,03! 5-7 7.08 3-9 4.28 2.0 1.4 M. S. 8 30 5 30 6 30 21 17 16 2 30 Aluminium-brass. Temperature Centigrade. Deg. Breaking-load per Square Inch. Lbs. Elongation in 5.502 Inches. Per Cent. 15 140 230 320 49, l8 3 46,168 42,100 30,380 30.7 [ 37-o 33-2 f IMPORTANT PROPERTIES OF FAMILIAR SUBSTANCES. 783 VIII. IMPORTANT PROPERTIES OF FAMILIAR SUBSTANCES. Meta\s from 32 to 212 Aluminium Antimony Bismuth ......... Brass Copper Iron, cast Iron, wrought Gold Lead Mercury at 32 . .. Nickel Platinum... Silver. Steel Tin Zinc Stones — Chalk Limestone Mascnry Marble, gray Marble, white. .. . Woods — Oak Pine, white Mineral substances — Charcoal, pine Coal, anthracite. . Coke Glass, white Sulphur Liquids- Alcohol, mean. ... Oil, petroleum Steam at 212 Turpentine.... . .. Water at 62° Solid- Ice at 32 Gases — Air at 32 Oxygen Hydrogen Carbonic acid Specific Gravity. Water, 1. 61 to 2.65 6.712 9.823 8.1 8.788 7-5 7-744 19-258 "•352 13.598 8.800 16.000 10.474 7-834 7.291 7. 191 .784 .156 .240 .686 .650 .86 •55 0006 87 000 .00127 .000089 .00198 Specific Heat. Water, 1 .212 0508 0308 oy39 092 1298 1138 0324 03 r 4 0333 1086 0324 056 1165 0562 0953 .2149 .2174 .2694 .2158 .2415 .2411 .203 .1977 .2026 6588 3 1 847 416 .238 .2412 3-2936 .2210 Absorbing and Radiat- ing Power of Bodies in Units of Heat per Square Foot for Dif- ference of 1°. .049 .0327 .648 .566 .1329 .0265 .0439 .049 .6786 •735 •735 •735 •735 .5948 1.0853 Conducting Power in Units of Heat Weight per Square in Foot of Sur- Pounds face with Difference of 1°. Per cu. in. O.IIOO 0.2428 0-3533 0.2930 S*S-o 0.3179 233.0 0.2707 233.0 0.2801 . 6965 113.0 0.4106 0.4918 0.3183 0.5787 0.3788 0.2916 0.2637 225.0 0.26 Per cu. ft. 174.0 197.0 140.0 28.0 168.0 22.4 165.0 i-7 54-o .748 34-6 27-5 88.7 62.5 6.6 180.7 127.0 57-5 55-o • 050 54-37 62.35 57-5 .0807 .0892 •°o559 .1234 Melting Points. Degrees Fahr. 810 476 1692 1996 2250 2900 2590 608 —39 2640 3700 2000 4000 446 680 See also pages 338 and 383. 784 EXPERIMEN TA L ENGINEERING. IX. — COEFFICIENTS OF FRICTION. (Morin.) (Page I9 6.> No. Surfaces. Wood on wood, dry. " " " soaked Metals on oak, dry " " " wet " " " soapy \ " " elm, dry Hemp on oak, " ** " " wet Leather on oak . Leather on metals, dry " " " wet " " " greasy " " " oily Metals on metals, dry 44 44 4< wet.. Smooth surfaces, occasionally greased Smooth surfaces, continually greased Smooth surfaces, best results. . . . Bronze on lignum vitse, wet. . . . Angle of Repose. Deg 14 to 26I III to 2 26I to 31 13I to 14-i "1 ill to 14 28 1 8* 15 to 19I 29I 20 13 81 81 to ill 16I 4 to 4I 3 if to 2 3? Coefficient of Friction. J = tan <£ 0.25 to .5 .2 to .04 .5 to .6 . 24 to . 26 .2 .2 tO .25 •53 •33 .27 to .38 .56 •36 •23 • 15 .15 to .2 •3 .07 to .08 .05 .03 to .036 .05? +f 4 to 2 5 to 25 2 tO 1 67 4.17 10 3.85 5 5 to 4 1.89 3 3.7 to 2 . 86 1.79 2.78 4-35 6.67 6.67 to 5 3-33 14.3 to 12.5 33-3 20 to 27.O 20? Note.— The above table is defective since the pressure per square inch is not given. The coefficient of friction diminishes with increase of pressure, so that in some k cases the total friction remains constant- X. — HYPERBOLIC OR NAPERIAN LOGARITHMS. N. Log. N. Log. N. I .og. N. Log. N. Log. x.oo 0.0000 2.30 0.8329 3.60 1 2809 4.90 1.5892 6.40 18563 1.05 0.0488 2-35 0.8544 3-65 1 2947 4-95 1-5994 6.50 1. 8718 X.IO 0-0953 2.40 0.8755 3-7o 1 3083 500 1 6094 6.60 1. 8871 LIS 0.1398 2-45 0.8961 3-75 1 3218 5-05 1 6194 6.70 I.902t X.20 0.1823 2.50 0.9163 3.80 1 3350 5.10 1 6292 6.80 I. 9169 1. 25 0.2231 2-55 09361 3-85 3481 5-i5 1 6390 6.90 1-9315 J. 30 0.2624 2.60 o.9555 3.90 1 3610 5.20 1 6487 7.00 1-9459 1-35 0.3001 2.65 0.9746 3-95 1 3737 5-25 1 6582 7.20 1. 9741 x-4° 0.3365 2.70 o-9933 4.00 1 386.3 5-3o 1 6677 7.40 2.0015 *-45 0.3716 2-75 1.0116 4.05 1 3987 5-S5 X 6771 7.60 2.0281 1.50 0.4055 2.80 1.0296 4.10 1 4110 5-40 1 6864 7.80 2.0541 1-55 0.4383 2.85 i-»473 4-^5 1 4 2 3i 5-45 1 6956 8.00 2.0794 X.60 0.4700 2.90 1.0647 4.20 1 435* 5-5o 1 7047 8.25 2.1102 J- 65 0.5008 2-95 1. 0818 4.25 1 4469 5-55 1 7138 8.50 2 . 1401 I.70 0.5306 3-oo 1 .0986 4-3° * 4586 5- 60 1 7228 8.75 2 . 1691 1-75 0.5596 3-05 i-"54 4-35 1 4701 5-6 5 1 73i7 9.00 2.1972 x.80 0.5878 3.10 1.1314 4.40 1 4816 5-7o 1 7405 925 2.2246 I.85 0.6152 3-i5 1. 1474 4-45 1 4929 5-75 x 7492 950 2.2513 I.90 0.6419 3.20 1.1632 4.50 1 5041 5.80 1 7579 9-75 2 • 2773 i-95 0.6678 3-25 1. 1787 4-55 1 5151 5-85 1 7664 10.00 2 . 3026 2.00 0.6931 3-3o I-J939 4.60 1 5261 5-90 1 775o 11.00 2-3979 2.05 0.7178 3-35 1.2090 4.65 1 5369 5 95 1 7834 12.00 2.4849 2. IO 0.7419 3 40 1.2238 4.70 1 5476 6.00 1 7918 13.00 2 5649 2.15 0.7655 3-45 T.2384 4-75 1 SS81 6.10 1 8083 14.00 2.6391 2.20 0.7885 3 5o 1.2528 4 80 1 5686 6.20 1 8245 15.00 2.7081 a. 25 0.8109 355 1.2669 4.85 X 579<5 6.30 1.8405 16.00 2 . 7726 MOISTURE ABSORBED BY THE AIR— HUMIDITY, 785 XL MOISTURE ABSORBED BY AIR.* The Quantity of Water which Air is Capable of Absorbing to THE Point of Maximum Saturation, in Grains per Cubic Foot for Various Temperatures. Degrees Grains in a Degrees Grains in a Fahr. Cubic Foot. Fahr. Cubic Foot. — 20 O.219 55 4.849 — IO 0.356 57 5- 191 - 5 O.450 60 5-744 O.564 62 6.142 5 O.705 65 6.782 10 O.873 67 7.24I 15 I.075 70 7.98o 20 1. 321 72 8.508 25 1. 6ll 75 9-356 30 I.958 77 9.961 32 2. 113 80 10.933 35 2.366 85 12.736 40 2.849 90 14.791 45 3-414 95 17.124 50 4.O76 100 19.766 52 4.372 105 22.751 XII. RELATIVE HUMIDITY OF THE AIR.* Difference of Temperature, Wet and Dry Bulb. Temperature of the Air. 32° F. 70° F. 90 F. 0.5 I 2 3 4 5 6 7 8 9 10 12 14 16 18 20 22 24 95 90 79 69 59 50 40 3i 21 12 3 98 95 90 86 81 77 72 68 64 60 55 48 40 33 26 19 13 7 98 96 92 88 85 81 78 75 71 68 65 59 53 47 41 36 32 26 ♦From Weather Bulletin No. 127, U. S. Dept. of Agriculture, 1897, faf barometer 92.4 7 86 EXPERIMENTAL ENGINEERING. xni. (Page 202.) TABLE OF BEAUME'S HYDROMETER SCALE WITH CORRE- SPONDING SPECIFIC GRAVITIES. For Liquids Lighter than Water. Temp. 6o° Fahr. Beaume. Specific Beaume* . Specific Beaume^ Specific Specific Gravity. Gravity. Gravity. Gravity. 10 I. OOOO 31 O.8695 52 O.7692 73 O.6896 II O.9929 32 0.8641 53 O.7650 74 O.6863 12 O.9859 33 O.8588 54 O.7608 75 O.6829 13 O.9790 34 O.8536 55 O.7567 76 O.6796 14 O.9722 35 O.8484 56 O.7526 77 O.6763 15 O.9655 36 O.8433 57 O.7486 78 O.673O 16 O.9589 37 O.8383 58 O.7446 79 O.6698 17 O.9523 38 O.8333 59 O.7407 80 O.6666 18 O.9459 39 O.8284 60 0.7368 81 O.6635 19 0.9395 40 O.8235 61 O.7329 82 O.6604 20 0.9333 4i O.8187 62 O.729O 83 O.6573 21 O.9271 42 O.8139 63 0.7253 84 O.6542 22 O.9210 43 O.8092 64 O.7216 85 O.6511 23 O.9150 44 O.8045 65 0.7I79 86 O.6481 24 O.909O 45 O.8000 66 O.7142 87 O.6451 25 O.9032 46 0.7954 67 O.7106 88 O.6422 *6 O.8974 47 O.7909 68 O.7070 89 O.6392 ?7 O.8917 48 O.7865 69 0.7035 90 O.6363 ?8 O.8860 49 O.7821 7o O. 7000 29 O.8805 50 O.7777 7i 0.6965 1o O.8750 5i 0.7734 72 O.6930 For Liquids Heavier than Water. Temp. 6o° Fahr. Beau»ne". Specific Beaume. Specific Beaume\ Specific Beaume\ Specific Gravity. Gravity. Gravity. Gravity. I I.0069 19 1. 1507 37 1.3425 55 I.6III 2 I. OI39 20 1. 1600 38 1 3551 56 I.6292 3 1. 02 1 1 21 1. 1693 39 1 3679 57 I.6477 4 I.0283 22 1. 1788 40 I 3809 58 1. 1666 5 I.0357 23 1. 1885 4i I 3942 59 I.6860 6 1. 0431 24 I.I983 42 I 4077 60 I.7056 7 I.0507 25 I.2083 43 I 4215 61 1. 7261 8 I.0583 26 1. 2184 44 I 4356 62 I.7469 9 1. 0661 27 1.2288 45 I 4500 63 I.7682 10 I.0740 28 1.2393 46 I 4646 64 1. 790I 11 I.0820 29 I.2500 47 1 4795 65 1. 8125 12 I.O902 30 I.2608 48 1 4949 66 1.8354 13 I.0984 31 1. 2719 49 I 5104 67 I.8589 14 1. 1068 32 1. 2831 50 I 5263 68 1. 8831 15 I.II53 33 I.2946 5i 1 5425 69 1.9079 16 1. 1 240 34 I.3063 52 I 5591 7o 1-9333 17 1. 1328 35 I.3181 53 I 576o 18 I.1417 36 I.3302 54 1.5934 . COMPOSITION OF VARIOUS FUELS OF U. S. 787 XIV. COMPOSITION OF VARIOUS FUELS OF THE UNITED STATES. Mine or Name. Mount Pleasant Exeter (Rice) Exeter Coxe's No. 1. No. 11 Forty-foot. .. York Farm (Bkwt).. Jermyn Cayuga Manville Shalt Avondale Oxford Continental Woodward' Cumberland Eureka Antrim Long Valley New River Pocahontas Cardiff Union New Castle (Lump). Mt. Olive (Lump)... Big Muddy Streator (Lump) Gillespie Ladd (Lump) Wilmington (Lump). Indiana Block New Pittsburgh Vanderpoo! (Lump). Wills Creek Jackson Hiil. Hocking Valley Brier Hiil Weilsville Goshen Hastings Turtie Creek . .. "Voughiogheny Trotter Reynoldsville Pittsburgh Summer Hill (Slack) Monongahela Leisenring CanneH.... Cooperstown Locality. Scranton, Pa. Pittston, Pa.. Scranton, Pa., Slate out.... . Scranton. Pa Schuylkill Co., Pa. Pottsviiie, Pa Scranton, Pa Maryland Pennsylvania Towanda. Pa . West Virginia. Wales. Jerome Park, Colo. New Castle, Colo.. . Illinois Streator, 111 . Illinois Wilmington. 111. Brazil, Ind. Indiana Block .. Kentucky... Ohio ..... Nebraska Monongahela R.,Pa. Pennsylvania . Connellsville.Pa. . . Pennsylvania Monongahela R.. Pa Connellsville. Pa Peyton. W. Va Nova Scotia Coal as Received. B.T.U. per lb. Fixed C. Vol. Matter. Ash. Water B.T.U. Comb. 80.54 7-54 10.65 127 12.307 1.3-973 79-41 8.16 12.18 •25 12,400 14160 74 73 5-7 1 18.90 .66 11.360 14.122 87.96 2.50 6.77 2.97 13-324 14 760 83 98 4.99 9 91 I. 12 12,903 14503 7S 29 5-47 18.43 .81 11,430 14.152 81 6b 5-78 10.84 I.70 12,036 13.760 84 46 5 37 9.20 97 12,294 13.684 bs 70 5-95 7 3 1 1.04 12.934 14.120 86 68 5-89 b.15 1.28 13.051 14.095 9t 45 5-°3 2.17 1 35 13-254 13.736 83 '3 5-98 9 62 1.27 12.943 M.525 79 23 3 73 13 7 r 3 33 12,149 14.642 75 So 17.00 6 00 1 5o 14.700 15,900 7° 47 23.86 4.87 .80 14.195 15.046 69 30 18.57 10'. 90 1.23 13,528 15.397 67.32 25.01 11 .12 1-55 12,965 14.845 72.90 20.42 5.00 1.18 m.200 16200 68.88 21.81 6.75 2.56 14.580 16.070 67'45 20.41 " 33 .81 12.789 14-555 52.86 36.70 8.44 2.00 13.650 15.240 50.80 35.8o 10 90 2.50 11,900 13.750 44.10 33 10 14.70 8.10 10.600 13.730 53.80 30.70 8.00 7-5° 12.400 14-675 44 30 36 35 11 -40 7-95 n. 600 14,380 49 55 39-94 11.74 3-77 10.506 12.425 42.45 3230 13.25 12.00 10.900 14-583 39-9° 32 . 80 11 .80 15.50 10.200 14.030 53 70 30.60 11.00 9.70 11,300 14.250 40.40 42.23 11.48 5 89 11.546 13-97? 54.60 34.10 7-30 4.00 12.800 14.430 46. C 5 36.23 n.63 5 49 T2.060 14-550 55.50 30.72 10. 90 2 88 11 .800 13,685 48 90 36.3c 8 30 6.50 12.C12 14,100 56 30 34.. 60 4-3o 4.80 12.900 14.200 49-5? 33 50 15.50 i-45 12.400 I4.930 49 83 ',8.03 6 91 5 23 11.966 13.619 60.88 27,82 11.09 21 12.935 14.583 59-45 34.22 4.22 2 11 14.150 15.107 54.00 32.25 12-50 1.25 12.900 14.958 58 90 28. 27 9 «3 3.00 12.539 14,386 59.04 30.77 9.16 1 07. i4^4 2 15.746 S3 3o 34.60 9.70 2.4c 12,400 14.107 «> 60 33.00 1 3 40 3 00 12.750 15.250 58.61 31,29 7 83 2.27 13.126 14.600 63 .56 28.71 6 10 1.93 15,005 16,313 4T 32 42.84 15.36 .48 12.224 J 4-5 2 3 64 44 30.42 4 03 1. 11 15,266 16,091 a p - 3 J3 O a u c/i ANALYSES OF ASH, Specific Grav. Color of Ash. Silica. Alum- ina. Oxide Iron. Lime, Mag- nesia. Loss. Acids S.&P. Pennsylvania Anthracite " Bituminous Welsh Anthracite 1-559 1-372 1.32 1.26 1.27 Reddish Buff. Gray. 45-6 76.0 40.0 37-6 19-3 42.75 21.00 44-8 52.0 11. 6 9.43 2.60 5-8' 1. 41 12.0 3-7 23-7 o-33 trace 1.1 2.6 t 0.48 0.40 2.97 Lignite 33-8 < w O W H < > < x «« O w H CU C OS 788 ft 8 ?* flttP4fi ♦JrtOs 1* «3 a-° «& *~ rt O « (LI — .Q O rt w m 3 b 3 2 * o J> •Ss* a •23 ffl 8?S . c v a a cc 9 o w°£q .2 v ex 3 c o^ :^° ■S «iS s S2 83 23 &§ a EX PERI MEN TAL ENGINEERING. g<*88 2 I'll •n>«- rtJ3 SS"js-S *Ej«« 0, S be ,2 "2 -3 rt II lift ««rt- sis X ctJB C C *J u « «! oj 5 jS •O.S3 rt O «« rt fe ■S33j3ap iiaqnajqBj *ajini , u8dinaj > •qoni sjBnbs jsd spanod uj •tunnoBA b 9AoqB sjnsssj^ m m m^>n0 tXOO P« N M t^C « m w smi ro 1000 -< covo c t» r« t^ t^ t^oo O ->*• m vo -4-00 ON t> rOOO m avoo t^ ct> ■*■ onoo o> O on rooo •^•vo •^no n NO mOM 85 on o*c O On ON ( On-^iocoo com eiNO M m u-> nvo "*■ O O ( NO M NO txVO 'tOO H ooiflN o>oo ■<*• m ■<*■ « 1-1 M OnO MNHIO MOO 00NO'Tt-'<»-fO«MM<-l'-0 OnOnOnOnOnOnOnOnOnOn OCO •* m MH (OUNOi *frVO NO NVO O « IT) ONM O conn m-<*-w nnovj 1- o >on Nt^-^u-) moo r0*O m en m On On ro « h n cf . ■* io\c t^so ■;> «n m \o ON •*■ « O>00 h> o 00 no bO o "* O M NO r^NO t>» 0> PONO On rovo ro ■<• 00 vo 00 00 O O ON On O* ON00 00 00 o> |2 o ? 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P»00 00 ON On H M „„„„„„„„„„ ,„„„-., ^ r» m N*K OMnrnM ov o COVO CO 00 mscninooo Onpoooo Pv00 m 00 vo mvo *vo m o ■»*■ o 00 p» O O NO ■*■ CO PI O Onoo P».vo ■*■ 1 m^mNO On On On On OnOO OO CO 00 00 | P-«VO W rj- -f ■*oo rooo "/Onion On m pocnipiihihooOOnon cm j- ►- Onoo oo t^vo vo mm] ro m On oo h ovo p^mcM mo m o moo m ovo m o oo oo P^ r~vo vo m m m m ■*• co co rtn«Mffi«nnN pi it o •ooo m ■o-vo m niin PvCO CO t^vo to CO t-» O CONO On P" >OO0 h •*■ •*VO t-^00 On m PI CO «OVO 00 PI *vo OH niAN m N N « N « fOCOmf^ commrommmmcoco io»»oo oo r-» co m OO O PI pi to oo o m pi m moo on* m m ■* •*■ ■* mr^ONrOMNO O ■*• OvO ONroroO roPl ON Pi N Pi i- Ooovo rOMCOm ■■*- mvo P- P-.00 On H vo oo o pi - ■***-«no *noo o pi o in cm cjixih t-^ * o t^oo o « «im t^co o is M M M « ON (O lONnim nnno O n N O O m On mvo O vo 00 ONMOowOt^o-oom moo ON-pipimmpipi * 0_ cw 00000 O *0 m0V3 vo * m p^ o m mvo p^vo 15 < O On 00 lO OOOOOOOOmm 0000 OnOnOnOnOnOnOnOn pi -. 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O O ON00 no --i O P» •* N On lOOO 1 CONO O CM * P** m in OO MMMMPICMCMrOrOrO vo *(< mo « mN r-vNO NO CO PI ■* oo vo mvo oo m w m •*• O vo m moo « pi m m VO 00 Ob PnT m mvo t^OO PJ NO 00 CM 00 O -*00 O m 00 M M N M m O OOO VO CM PI NNNNNNNCINN COCO |O000000000O000CO0000 PI PI COflfO CO CO CO CO 00 mmm-j-*-H-Ti--. o vo Tt- in OS * m 00 VO -*• PI M ONCO P^ GN ■*■ 0^O m N^OiioOnO tl vo m m o w O- On ro IH pi moo •* n vo * cm oo moo i-i O oo f mvo co O O m r^ r-» ooo oo o« moo moo -i- Tt-00 M « m« o *oo o m ^-^-^-m ooo m o -*■ m o moo c^vo >o ro ro 1 cocmpimmoOOOO COOT) 00 00 CO OO 00 OO CO OO NN t^t^l p»p*p~p~p~p~c--p~p>p~ inn snj-m t^ PvVO NO NO t-» t-» r-~ r- t^ r~*>-oovo mooo mm inmm*'s-O'«- cm m o o , oo oo pvvo no vo ■*• ■*• m m r» N P^vo 1 vo vo VO vo vo vo vo vo VO VO * On CO *8 «im mm moo o< -*vo t^ "*• VO PI NMNNNO tow p^ cm co mon + o in PI 00 OnVO in OnO in vo O0O0 NON moo cmoo O t^mpxt^m •Hrvo mO mt^O mt>.m O m m o p~ m o mvo o 1 vovooon *N» ovoco* mo cm r- - in m o) m -too oo vo m ro co -*■ CM CM CO co * IT) invO NO P-« t^OO 0> On MNNONNCn'NMini * On * On CO ro ro •* ■*■ in ro ro ro ro ro co cmvo mr^o -.00 O O O m CM CM 1 ■>* t~» CM CM CO CM N in in CO m OxOOMNONOONn 00 ONNnO rOVO On W co^O in m vo mnO pi vjIvOnO pi no ■* PI CO in ro ro PI 00 rovo ovo un m m moo o m m ro p^co oo p^ m * m p» Np-incioo pop^o cm m VO CM CM N o ovo -vr O VO 00 *VO CM CM vo CM moo vo w o vo oo vo moo ro co ■«* in invd vo r^. t^co m in m m io in io io m in rooo N Si- vovo N r-~oo ro ro ro' ro ro momi^O Tj-r~M -*p^ OOOOOOOOOmmm mmmm*'*'<-*-0 CO'* H M M M n* vivo tvOO On HMHHHHMMHH O VO P»00 On oooooooooo m ci m * mvo pnoo o o ciciCiCincincMCMro m o m o m-«r ■♦m OOOOOOOOOO; mo mo mo mo moi mvo vo o ooa ao oi o o 794 EXPERIMENTAL ENGINEERING. XVI. ENTROPY OF WATER AND STEAM, Absolute Entropy per Pound. B.T.U. Absolute Entropy per Pound. B.T.U. Pressure, Pressure, Pounds per 1 Pounds per Square Inch. Water. Steam. Square Inch. Water. Steam. I 0.134 1.987 IJ 5 . 490 1 •586 2 0-175 1 .924 120 O.494 1 •583 3 O.201 1 .887 I2 5 O . 498 1 .580 4 0.220 1 .861 130 O.501 1 •577 5 °- 2 35 I .841 i35 O-505 1 •574 6 0.247 I .825 140 0.508 1 •57i 7 0.257 I 814 i45 0.512 1 569 8 0.268 I 800 J 5o o.5 J 5 1 566 9 0.277 1 79° 155 0.518 1 •563 IO 0.285 I 781 160 0.521 1 561 15 °-3*S 1 747 165 0.524 1 559 20 0.338 I 722 170 0.527 1 •557 25 o-356 I 704 175 0.530 1 555 30 0.370 I 689 180 0-533 1 552 35 0.384 I 677 185 0.536 1 55o 40 0-395 I 666 190 0-539 1 548 45 0.405 1 657 195 0.542 1 54& 5° 0-415 I 649 200 o.544 1 545 55 0.423 I 641 205 o.547 1 543 60 0.431 I 634 210 o.549 1 54i 65 0.438 I 628 215 0-551 1 540 70 0.444 1 623 220 0-554 1 538 75 0.450 1 617* 230 0-559 1 535 80 o.455 I 612 240 0.563 1 532 85 0.461 1 608 250 0.567 1 529 90 0.466 1 604 260 0.571 1. 526 95 0.476 1 596 270 o.575 1 523 100 0.480 I 593 280 o.579 I- 520 105 0.482 1 593 290 0.583 1. 5i8 no 0.485 I 59° 300 0.587 1. 5i5 DISCHARGE OF STEAM. 79$ XVII. (Page 302.) DISCHARGE OF STEAM IN POUNDS PER HOUR CALCULATED BY NAPIER'S FORMULA. Pounds of Steam Absolute Pressure. Pounds. Diameter of Diameter of Diameter of Orifice ^ inch. Orifice ^ inch. Orifice £ inch. I O.039 O.158 O.631 2 O.079 0.3:6 I.262 3 0.II8 0.473 I.893 4 O.158 O.631 2.524 5 O.197 O.789 3-155 6 O.237 0-947 3.786 7 O.276 1. 104 4.417 8 0.315 I.262 5.048 9 0.354 I.420 5.680 10 0.395 1.578 6.3IT 20 O.789 3.155 12.622 30 1. 183 4-733 18.937 40 1.578 6. 311 25.244 50 I.972 7.880 3I-556 60 2.367 9.467 37.867 70 2.761 n.045 44.178 80 3-I56 12.623 50.488 90 3-55Q 14.200 =6. 800 100 3-947 I5.778 63-115 XVIII. Page 4 2o.) PER CENT OF WATER AND STEAM EXHAUSTING INTO ATMOSPHERE.— BY THROTTLING CALORIMETER. (Per cent of moisture.) Tempt, in Calorimeter. Degrees Fahr. 215 220 225 230 235 240 245 250 255 260 265 270 275 280 285 Diff. i° Fahr Gauge-pressure on Main Steam-pipe. .0233 .0207 .0181 .0154 .0128 .0102 .0076 .0049 .0023 .0005 — .0030— .0057- .0083— .0109 — .0136— .00052 •0253 .0227 .0201 ■ 0173 .0147 .0122 .0095 .0069 .0042 .0016 .0010- .0037- .0063- .00052 0271 0245 0218 0192 0165 0139 0112 0086 0059 0033 0006 0026 — 0047— 0073— 0100 — .00053 .0290 .0263 .0237 .0210 .0184 •0157 .0130 .0104 .0077 .0051 .0024 .0002— .0029— .0056— .0082 — .00053 .0307 .0280 •0253 .0227 .0200 • 0173 .0147 .0120 .0093 .0066 .0040 .0013 .0013- .0040- .0067- .00053 65 0322 0296 0269 0242 0215 0189 0162 0135 0108 0081 0055 0028 0001 0026- 0053- .00054 •0338 .0311 .0284 .0257 .0230 .0204 .0177 .0150 .0123 .0096 .0069 .0042 .0015 .0011 — .0038— .00054 •o354 .0327 .0300 .0273 .0246 .0219 .0192 .0165 .0138 .0111 .0084 .0057 .0030 .0003 .0024- 80 0368 0340 0313 0287 0260 0233 0206 0179 0152 0125 0098 0069 0042 0015 ooia- 00054 ■ oc, 054 The minus sign indicates superheat. This amount divided by 0.48 and multiplied by the value of the latent hear uili give the degree of superheat. Diagram for Determining Per Cent of Moisture from Reading of Thermometer IN Throttling Calorimeter. (See text, page 425.) 796 ViCTOZS OF EVAPORATION. '97 V) a K w E B. 1/) O s h < 2 C z < w • X a X o. in O s I < 5 h H > C n < X y z w < o> t/J a w W s o (Li Z W as D (A u OS On W D < § „ eensNK nnhnn »miomio CO rO CM CM M mOOO-OnCOOOCv tvVO O flOi vo m m Tf ro ro CM CM M M 00 POOO fO r"N o o ov ooo « SB NCn 1 00 N N'O vo o o 1 P - 00 N On m vo m m o m n in O in o ^- On - ro CM CM m O On OnOO 00 oo en rv moo c^ nvo no in O d H H ,„ CM hid uiO in in ■<»- On ■>!- o- -*oo mti tt - » ooo ooo n mo vo m ro ro rooo cm in •* tj- ro ro r«. CM t-» CM VO CM CM M M M VO M NO O ON OnOO 00 m in o m o in n nvo vo in O o> H 00 ro 03 fflNN K N t-~ M N. m VO M VO M m CM CM m m O OOO 00 J-. C-VO VO IO m o m On in •>*■■* ro cm ■>*■ On •*■ On ro CM m M O O 00 rooo ro C-* N NO NM nvo no in m O - t-- N •>*■ On moo ro oo moo rf)ts CM. N CM N m cm m m o o ooo oo t-. t^vo vo mio N » O tt K HMMMM MMHHH vo h vo h in tJ- tJ- ro ro CM m o »n on CM M M O ON M M M M O •* Ov -t rooo rooo cm NU f~ CM VO M M O OV MVO m vo OnOO 00 N c~- O O O O in O in o in vo vo in m t- O o VO M ro CM CM O -^-oo moo moo rooo cm r-. CM t- CM vo 11 m o O Ov Ooo oo nn vOO "im-* mvo wvo -1- ro ro cm cm inomoi- m m O On On ■*■ On -*00 moo s nvo O vo m m - n M M On OnOO OO t-vVO OldlflNft flO rooo ro f-. cr, en CM CM m m O On On ooco n r>.vo no uiinNj-Nt vo h vo m m ro ro CM cm m O m o m On h o ooo ■«- On •<*■ On ro 00 N NVO vo oo moo mca in in - -t -t- en rn D j m N co mso n o rsN tsM io hio h in On Ovoo oo N r^vo vo in in -*■ ■<*■ m O in O m On ro cm cm m o Tf ON f On CO 2 f?0^ O oo moo m n n txvo vo in O O O CM C-. CM N CM io ■*■ •* CO —, CM H 1 m m on 8 vo m io m OmOiOOv ■"a-ON-*ONro O on Onoo oo t^ rvvo m m •*■*>■ en m «?<2^ On OnOO 00 m vo mvo m m n nvo vo in O io too lOfNtKim r - CM NO O rooo cmc~-cni t^CMt^CMvo mvomvoO On Onoo oo f». two vo io in -^- -^- ro ro m o m o *- CM CM M M o On t}- On Tf-00 On Onoo oo r^ O O O moo moo cm nvo vo in in O Ml Nl( N Nftnmn O c CI H M in CM N o~ Mvoomo iriOmO'<*- Ov-^-On -*oo On Onoo oo t- c-^vo vo in ■* ^- ro ro CM rooo rooo cm cm m M o t^ CM tv CM VO On OnOO OO t-^ O O O O m vo m vo c-n.no vo in in O O io o io io NtNtnmci O o M M o c lis 4) i w c « w - u 41 [V. J vo ■<*- CM t~- io ro i-i mvo tci o Mn ro m oo vo ■st- cm o t^ in ro M 00 no tj- CM n io m m < CO 11 •>!- f^ CM IO00 M rONO On o\ On fe m mOmOm omomo moiogio CO^-^inin NOVO t^ t>00 00 Ov On m o m o m M CM N ro >n o m m ro ■*■ -r m m m o m o IOnO N NOO in m o m 00 ON Ov o O 5 7 9 8 EXPERIMENTAL ENGINEERING. X XI 6 pa H w Q < z o I— I < w U 01 X! CD X! ~o£ u, CJ a oT'S 'S m2"m m ~£ OTMWWTO °ocoooooooi»ooooooc»oooooo Nominal Weight per Foot. Pounds. H O O lOOO -*oo ON ONO h m CM CM m o M IA00 UIh m -«- cm m co m no -a- o o mmo»o -<»- o no o o o no cm oo cm onh o o « -<*- IO00 HVO N«« MflOC oo m o cm m O ON OOO M 00 Pi HHCMCMCOIOOOOCM •*oo oooci ro d moo rOSNN <«) m h hi m cm cm ro-^Tj-T^-inirj-* u->no Length of Pipe Containing One Cubic Foot. Feet. tOVO H O Hi CM CO (ICO ON h K^-o OOO w MCI ^ ONio oh mmmo cm o ooo cm oo io cm o on ovo vo hco u>n ovo on o •*■ ro M M M K -8 O td gl O o> ►4 IO »O00 HCO SinN OOO O ^-00 O CM O ONOO 00 CO CO M lOONcnmm ti-vo t^-^--^--l-Hioovo^-r<-)« hi *c-.hvovo t-~ roco uin o 000 t^vo in**mnmc) cm « w « Tj- C^>0 *m«NHHHH 13 u c u -J v. ccj t m o hi o w o»n -*vo oo t-^o Tama o>Mom« h ■*■ vo in\o on ro "O m onoo t^vo lom'tmtonM cni n n n m ONt^lO-^CON N MM H HI to « w K W > in < K H 3 5 t-» o ro cni rv •*■ m -^-no on cm >noo r^ M-oo moN* tj-vo -*»o no •*■ m o> m ' N«VO ■* m ONO ONI^O * SNCnhcC (NOO ON o f^iome) tJ-VO O hi hi cm m ->j-\o oo t-^CMNO mno comoNmo on-^-ioo cm o ooo H H Ci B (OCI* tOVO 00 H CO tJ-VO O •*• U100 ccj g C >— i m w ooo rONO t^-^-Hi ij-n-iCMNOOONO -*oo o hi oo 00 O rooo tv ir> m o> rONO on ro moo oo oo rovo Onoo m^mmrr ooo oo ■*•«»■ w O h h ro iooo *0 t»)N rooo t-> on onoo r~ c^oo O oo -4- cm vo wcMro-^-f-ONCMin onoo oo o moo iocinoiKh io m,m hi cm rnioW t-« On - comoo m ro M M M Hi cm CM 1- 5 on onoo t(-no oo ■* m cm h vo m- iono cm -no o>* h cm cni ->*-no on m fiott moo CM 00 O CONO m no •<*■ h h m ci ntiflNOiO ci mNO n m M H m m CM CM CM w u 2 a « [I] to § & u PS u C M OO-tMNONCIinH-t rONO WOO N 0+ rovo NO t^OO NO 00 -* ■*• in moo O cono o m ro it- -*no -^- iono r^r^t^m mnoco n m oo hi mosmcM coo -^ ono i-voi-oooooo-^m ono N*m^ h h h cm co ■*■ mvo soih cm ij-mONCM moo h ■*• o h -*oo m ■* HHHHHdtltl CimCOttNflOm rt en £ 5 tj u H cmno h onOnm mONM cmnono r^oo r-. co mvo oo cm ■*■ m cm •<*• NONN COONCOI-NONC ro Onno COO r~ m mONCOOHi moo « NO M ID NiO n<3 CI m N OiNtO CMOb N -*-in m hi cm CM n -t ifl m N 0> O cm -4-mt^O cot>.o covo O co o O covo m m h hi hi cm cm cm m m m Nt Nt Nt UN io m Thick- ness. Inches. oooomoncotj- m-^--* ono ono o hi cm -<*-no m m m m •* iooo OO hi m + t>oO hi cm co ■>!- moo cm -^-no o c-» r-. t^oo ■*■ OOOHIM^MHiMCMCMCMCMCMCMCMCOCOCOCOCOCOCOCOCMCOCO PS w W s Q Is 1 ■*■ Tt- co -*oo h r--oo r^oo nooo mmrocM oo ONO O CM CM Tj-00 H. NO NO NO •*■ CM O 'tNO N CO CO H IT)«OCO CM cm co -<*-nc 00 cono O-^-OmomOOOOOOOOCMCM-^-^co HHHtittcoro't'f mvo o ooo hi c* co •<*■ mNO t> &3 mto >o mm coiommio o * ts -t io » no oo vocMCMCMCMmmm ■<*- mvo oo cono o cooo m m o unno vovcvo ooo-O O O O O MMMHCM«co-<*-T(-m mvo ooo o O « cm ■*■ iovo ooo rtlS en s is w m h h n « mm** «o«0 t^co OiO h ci m* mNO o DEN SIT V AND WEIGHT OF WA TEE. 799 XXI. WEIGHT OF WATER PER CUBIC FOOT FOR VARIOUS TEM- PERATURES.* Weight of Water per Cubic Foot, from to 2i2° F., and Heat- units per Pound, Reckoned Above 3? F. 05 X) O JO 3 ■J.3 H > X H~ X H £ X H £ X 32 62.42 0. 78 62.25 46.03 123 61.68 91.16 168 60.81 136.44 33 62.42 1. 79 62.24 47-03 124 61.67 92.17 169 60.79 *37-45 34 62.42 2. 80 62.23 48.04 125 61.65 93-17 170 60.77 138.45 35 62.42 3- 81 62 22 49.04 126 61.63 94.17 171 60.75 139.46 36 62.42 4- 82 62.21 50.04 127 61.61 95.18 172 60.73 140.47 37 62.42 5- 83 62.20 51.04 128 61.60 96 18 J 73 60.70 i 4 r. 4 8 38 62.42 6. 84 62.19 52.04 129 61.58 97.19 174 60.68 142.49 39 62.42 7- 85 62.18 53-o5 130 61.56 98.19 175 60.66 I43-50 -to 62.42 8. 86 62. 17 54-os 131 61.54 99.20 176 60.64 14451 4 r 62.42 9- 87 62.16 55-os 132 61.52 100.20 177 60.62 145-52 42 62.42 10. 88 62.15 56.05 133 61.51 IOI. 21 178 60.59 146.52 43 62.42 11. 89 62. 14 57-o5 134 61.49 102.21 179 60 57 x 47.53 44 62.42 12. 90 62.13 58.06 135 61.47 103 . 22 180 60.55 148 54 45 62.42 13. 91 62. T2 59.06 136 61.45 104.22 181 60.53 149-55 46 62.42 14. 92 62.II 60.06 *37 61.43 105.23 182 60.50 150.56 47 62.42 x 5- 93 62.IO 61.06 138 61 .41 106.23 183 60.48 151 57 48 62.41 16. 94 62.O9 62.06 139 61.39 107.24 184 60.46 152.58 49 62.41 *7- 95 62.08 63.07 140 6137 108.25 185 60.44 J53.59 50 62.41 18. 96 62.O7 64-07 141 61.36 109 25 186 60.41 154.60 5 1 62.41 19. 97 62.06 65.07 142 61.34 110.26 187 60.39 155-61 52 62.40 20. 98 62 05 66.07 143 61.32 in. 26 188 60.37 156.62 53 62.40 21.01 99 62.O3 67 08 144 61.30 112.27 189 60.34 157-63 54 62.40 22.01 loo 62.02 68.08 145 61 28 113.28 190 60.32 158.64 55 62.39 23.01 IOI 62.OI 69.08 146 61.26 114.28 191 60.29 159-65 56 62.39 24.01 1 02 62.OO 70.09 147 61.24 H5.29 192 60.27 160.67 57 62.39 25.01 103 61.99 71.09 148 61.22 116.29 193 60.25 161.68 58 62.38 26.01 104 61.97 72.09 149 61.20 117.30 194 60.22 162.69 59 62.38 27.01 105 61.96 73- 10 150 61.18 118. 31 195 60.20 163.70 JO 62.37 28.01 106 61.95 74.10 151 61.16 119. 31 196 60.17 164.71 61 62.37 29.01 107 61.93 75.10 J 52 61.14 120.32 197 60.15 165.72 62 62.36 30.01 108 6l.92 76.10 153 61.12 121.33 198 60.12 166.73 63 62.36 31.01 109 61.9I 77-n 154 61.10 122.33 199 60.10 167.74 64 62.35 32.01 no 61.89 78.11 155 61.08 J 23-34 200 60.07 168.75 65 62.34 33.01 III 61.88 79.11 156 61.04 124.35 201 60.05 169.77 66 62.34 34.02 112 61.86 80.12 157 61.06 125.35 202 60 . 02 170.78 67 62-33 35 02 "3 61.85 81.12 158 61.02 126.36 203 60.00 171.79 68 62.33 36.02 114 61.83 82.13 *59 61.00 127. 37 204 59-97 172 80 69 62.32 37.02 115 6l.82 83 13 160 60.98 128.37 205 59-95 173-81 70 62.31 38.02 116 6l.8o 84.13 161 60.96 129.38 2d6 59 -92 174-83 7 1 62.31 39.02 117 6T.78 85.14 162 60.94 130.39 207 59-8g 175-84 72 62.30 40.02 118 61.77 86.14 163 60.92 131.40 208 59-87 176.85 73 62.29 41.02 119 61.75 87-I5 164 60.90 132.41 209 59 84 177.86 74 62.28 42.03 120 61.74 88.15 165 60.87 J33-4I 210 59-82 178.87 75 62.28 43 °3 121 61.72 89.I5 166 60.85 134.42 211 59 79 179.89 76 62.27 44.03 122 61.7O 90.16 167 60.83 135-43 212 59-76 180.90 77 62.26 45-03 Weight of Water at Temperatures Above 212 F. Porter (Richards' " Steam-engine Indicator," p. 52) says that nothing- is known about the expansion of water above 212 F. Applying formulae derived from experiments made at tem- peratures below 212 F., however, the weight and volume above 212 F. may be calculated, but in the absence of experimental data we are not certain that the formulae hold good at .higher temperatures. * Kent's " Pocket-book for Mechanical Engineers. 8oo EXPERIMENTAL ENGINEERING. XXII. HORSE-POWER PER POUND MEAN PRESSURE. O i- Speed of Piston in Feet per Minute. G^£ 100 240 300 350 400 450 500 550 600 650 750 4 .038 .091 .114 .133 .152 .171 .19 .209 .228 .247 -*8 5 4* .048 "5 .144 .168 .192 .216 .24 264 .288 •312 .360 5 .06 .144 .18 .21 .24 • 27 • 30 3.3 •36 •39 •45o 5* .072 •173 .216 .252 .288 .324 .36 396 .432 .468 ■540 6 .086 .205 .256 .299 • 342 .385 .428 47i •5*3 •555 .641 6* .102 • 245 • 307 •39i .409 .464 .512 563 .614 .698 .800 7 .116 •279 .348 .408 .466 • 524 .583 641 .699 .756 .874 7* •134 .321 .401 .468 •534 .602 .669 735 .802 .869 1.002 8 • 152 .365 .456 • 532 .608 .685 .761 837 .912 .989 1. 121 8£ .172 •4*3 .516 .602 .688 •774 .86 946 1.032 1. 118 1.290 9 .192 .462 •577 .674 .770 .866 •963 1 059 i-i54 1. 251 1.444 9* .215 .515 .644 • 75i .859 .966 1.074 1 181 1.288 1-395 1. 610 >o .238 •57 1 .714 •83* .952 1. 071 1. 190 1 309 1.428 1-547 1.785 IOJ .262 .63 .787 .919 1.050 1. 181 1-3*3 1 444 1-575 1.706 1.969 II .288 .691 .864 1.008 1. 152 1.296 1.44 1 584 1.728 1.872 2.160 Ilj ■3*4 •754 •943 1.1 1-257 1. 414 1-572 1 729 1.886 2.043 2-357 12 .342 .820 1.025 1 • i95 1.366 I-540 1.708 1 880 2. 050 2.222 2.564 13 .402 .964 1.206 1.407 1.608 1.809 2.01 2 211 2.412 2.613 3-015 14 .466 1. 119 ^•398 1. 631 1.864 2.097 2.331 2 564 2.797 3.029 3-495 15 •535 1.285 1.606 1.873 2. 131 2.409 2.677 2 945 3.212 3-479 4.004 16 .609 1. 461 1.827 2. 131 2.436 2.741 3-°45 3 349 3-654 3-958 4-567 17 .685 1.643 2.054 2.396 2-739 3.081 3-424 3 766 4.108 4 -450 5-135 18 .771 1.849 2.312 2.697 3-o8 3 3.468 3-854 4 239 4.624 5.009 5.780 *9 •859 2.061 2-577 3 006 3-436 3.865 4-295 4 724 5- I 54 5-583 6.442 20 .952 2.292 2.855 3-331 3.807 4.285 4-759 5 234 5-731 6.186 7.138 21 1.049 2.518 3.148 3-672 4.197 4.722 5-247 5 771 6.296 6.820 7- 860 22 1. 152 2.764 3-455 4.031 4.607 5.183 5-759 6 334 6. 911 7.486 8.638 23 1.259 3.021 3-776 4.405 5-035 5.664 6.294 6 923 7-552 8. 181 9-44 24 1-37° 3.289 4. in 4-797 5-482 6.167 6.853 7 538 8.223 8.908 10.279 25 1.487 3-569 4.461 5.105 5-948 6.692 7-436 8 o 7 2 8 923 9.566 11.053 26 1.609 3.861 4.S26 5.630 6-435 7.239 8.044 8 848 9.652 10.456 12.065 12.99& 27 1-733 4.159 s-^o 6.066 6.932 7-799 8.666 9 532 10. 399 11.265 28 1.865 4-477 5-596 6.529 7.462 8-395 9-328 10 261 n. 193 12.125 13.991 29 2.002 4.805 6.006 7.007 8 008 9.009 10.01 11 on 12.012 13.013 I 5-oi5 30 2.142 5-141 6.426 7-497 8.568 9.639 10.71 11 781 12.852 13923 16.065 3 1 2.288 5.486 6.865 8.001 9.144 10.287 "•43 12 573 13.716 14.866 '7-145 32 2.436 5.846 7.308 8.526 9-744 10.962 12.18 13 398 14.616 15-834 18.270 33 2.590 6.216 7.770 9.065 10.360 11.655 12.959 14 245 15-54^ 16.835 19.425 34 2.746 6-59 8.238 9. 611 10.984 I2 -357 13-73 15 103 16 476 17.849 20.595 35 2.914 6 -993 8.742 10.199 11.656 I3.«3 14-57 16 027 17.484 18.941 21855 36 3.084 7.401 9.252 10.794 12.336 13.878 15.42 .16 962 18.504 20 . 046 23.130 37 3-253 7.819 9-774 11.403 13-032 14.861 16.29 ^7 919 I9-548 21.177 24 433 38 3-436 8.246 10.308 12.026 r 3-744 15-462 17.18 18 898 20.616 22.334 25 770 39 3.620 8.648 10.86 12.67 14.48 16.29 18. 1 19 9i 21.62 23-53 27.150 40 3.808 9-139 11.424 13 328 15.232 17.136 19.04 20 944 22.848 24-752 28.560 4i 4.002 9.604 12.006 14.007 T6.008 18.009 20.00 22 on 24.012 26.013 30.015 42 4.198 10.065 J2-594 14.693 16.792 18.901 20.99 23 089 25.188 27.287 31 485 43 4.40 10.56 13.20 15-4 17.6 19.8 22.00 24 2 26.4 28.6 33-00 44 4.606 11.046 13.818 16. 121 18.424 20.727 23-03 25 333 27 ■ 636 29-939 34-545 45 4.818 11.563 H-454 16.863 19.272 21.681 24.09 26 399 28.908 3*-3i7 36 135 46 5.043 12.086 15.128 17.626 20.144 22.662 25-18 27 698 30.216 32-754 37770 47 5-256 12.614 15.768 18.396 2 1 . 024 23.652 26.28 28 908 ^•536 34.164 39.420 48 5.482 12.846 16.446 19.187 21.928 24 . 669 27.41 3° 151 3a 152 35633 41 115 49 5-714 12.913 17.142 19.999 22.856 25 713 28.57 3i 427 34.284 3 ll A1 42.855 5° 5-95Q 14.28 17-85 20.825 23.8 26.775 29-75 32 725 35-7 38.675 44-6/25 51 6.180 14.832 18.54 21.665 24.76 27-855 30.95 34 045 37.08 40 . 205 46.425 52 6.432 !5-437 19.296 22.512 25.728 28.944 32.16 35 376 38.592 41.808 48 240 53 6.684 16.041 20 . 052 23-394 26.736 30.078 33-42 36 762 40.104 43-446 50.130 54 6.940 16.656 20.82 24.29 27.76 31.23 34-7 33 *7 41.64 45-" 5»'0 5 55 7.198 17-275 21-594 25-193 28.792 32. 39 1 35-99 39 589 43.188 46.787 .S3-985 56 7.462 17.909 22.386 26.117 29 848 33-579 3 l 3 l 41 041 44.772 48.503 55-965 57 7-73 2 i8.557 23.196 27.062 30.028 34 794 38.66 42 526 46.392 50.258 57-99 58 8.006 19 214 24.018 28, 021 32.024 36.027 40.03 44 033 48.036 52.039 60 . 045 59 8.284 19902 24.852 28.964 33-I36 37.278 41.42 45 562 48.704 53.846 62.13 60 8.566 20.558 25.698 29.981 34-264 38-547 42.83 47 "3 5I-396 55-679 64.245 WA TER-COMP U TA T/OAT TABLE. 801 10 & • 3 z w w H cn Oh O w < B o X H D Oh o u Oh w H «} U H W Oh O w H » O O co OO rJ- tJ- i^>co co co On O O O O O 00 in Oco m o t en t Mco OO O in co m co co co OO m cni«r> aNmtn O m O co O ino N cow hh rj-r^w rfr co co N in n Tt ■t n tj- O coco O^^O \0 O N mifiH loco Oco loi-iO <-> cocoa hoo wm r^cN mt^ OO O O O N CO COCO f>NH IflOCONO ^"l^O COO CO M TtO O <■* CO LOCO O '- i->CO >-h in 00 i-t n n cj n cococo^-Tj-rtLOvnir>000 t>> t>«i^co oo oo OOOO O O t» moo o i"^ i-* co t^O 'tn OO ^O hh coco-^-^-cor^rj-cN Oco n o -h co t^Oi^i-i eoo co-h co in in o coco m'tintoo oco co n s *-• tsooo O OO O O t>> »-i ^"Wt H r^cor>>0 O Oco m coco ^•oco^-r^co or* co O rt O in O ^-co NO Ocor^O -^r^ON moo O co inco O* n 4o oo tj- r^ w unco m loco N in O n in O N loco n loco n inoo n loco m t}-n m <-> « n n mntn^^twinifiooo t^r>r^cococo oooo o O «s O n n i-» O O r» n w hco n t^M n coo co co r)-o inOeor^eooinM ON •* O m in O Ocor^O coco ^J- i-t loo lo cn co tj- h o r>-^fOrtt^ i^o mcooo N r^o n tj-o r^o CJ>in«vO mo O ^Ocoo O cor^O coo On Lnr^o n Lnr^On coin tnt>.M Ttco « loco m loco n inco n Lnco m Lnco n loco i-i h-nm t r^» n i-c n N N cncncnftri-inin uio O O r^ r^ r>.co coco OOOO O O 13 oo inco O co O co O tnco unOco o O Oco O O cocoinLnm Lnco co co co rt-t-or^O O fNNNoo cor^cio OO r^-r^oo O^D O^O r^O Ln O w r^OunoOco n Lnr^O ^00 m tt t lom r^Nco n r>M Lnocor^o ^-t^O coo O m rfO O >-> ^-o co O n cor^O tj- r~~ •— i -3-00 >-< ^t ** inco m loco m t^-co m ^-r^>-c "^-r^O ^r^ m m m N N cococo^-^ri-io ununOOO r>. rs i>.oo co oo OOOO O O •# cn cn'trN O oo cnTtmHcoo in n h Lno O O Oco coOvom m \nOco co urtcntNcncn'tH OO Oco vnoo Ooooo OOcoO - H rcocO'5i--+0 co O coo rj-Lococo m cocoo r^N t~~0 >-> O OM'h t^-NOco O n con Noo Tt-O^Ococo NO O coi^O ^i-r^O N loco m cooco O coint^O coo O enr^o ^- r» m rtoo m tj-qo ** 'i-oo m ri-r^M ^fr^o ^r^o coo M i-i N N N COCOCOTfra-^LniOLnOOO i>i^r^cococo OOOO O O co OO^t^t-NOTfNM Ooo O m Or^cooooo lom O n rto co m o r>. OLOcooi^r^cOMO'-'OcocOH-LnoOooi-i'-ioo^J'OO^i-'coO'^l" '^■r^rj-oo Ooo cor^ooo coOrj-r^co r^o m o co >^ o ^toco O ++ O oo >tO lom vnO Ttco NO O eoi^»0 coo ON ir>i^.C covnr^ON ^fO no O cor^o ^t^»0 *rNH r^r^i-i r^-r^o ^r^O ^tt^O coo O coo »h m cm n N cococOTj-'^-^-LnLn m*0 O O r> t>> r^co coco OOOO O O « NNrfHiO O '-' O in t-xO CO CO CO in t->CO ^J- <*CO NincOrH OcOLOt^O t-t co m ino O ^"co oo m n O r^O coo oO'd-cON t^inr^Noo — O in t— ~ •— i Ocoin-^-ON rj-incooino Tj-ir^TfeON (J-\Q t-i r-» m rt inoo oco ■^■i-O n r^NO n inocoo O »4-r^O coo On tNOw *oco o n noo coo O cnt^o cniNO rf/^O rM>0 cor^o coo O coo O coo m m i-i n N cOcocOTl-'^-Tj-inin ino O O t>» **» t^»co oooo O^ O^ h co O in m oo rtO nloOm •-• OO O O'^ ^O O OO cow inOOr> O' in cn t^. O O ^too OiOinNr^i-iMNO cy^O co O in O n co in r^O m ismoo -1-co cor^NO ocor^O *1" r^ O comoo m cooco w coinr^o n inONO Ocoo O coo O cor^-o cn r> O coo O coo Ocoo ON in m t-i i-i c< N N cn cn -i- 't t m in ino O O t^» r~* r»co oo co co OOOO O tf> OOOOOOOOOOOOOOOOOOOOOOOOOOOQO Oco mH/H-Tftno -t« r^N ino oo O O O Oco O tmO Onco Oco cnoo no into ^i"0 r-^ in m co cn r^ o Oco o cn>-io n i^ o >-" enm^- t^.toOinO inO -too mo O cor->0 coo ON inco O cnmNO N ^i-O m iT) co NO Ocoo Ocoo O COO O COO OcoO OCOO ONO ON in hi M h n n n cn cn cn » f^ r^oo co co OOOO O co rf mo r>«oo O O m n cn tj- ino ^«co o O >-> n cn T ino r^oo O O •-• ^ MWMMMMMWMMMNNNNNNNNNCOeO 802 EXPERIMENTAL ENGINEERING. C« TO co mwMnmm coco O TtN O co o T N Ocovo nwowihn infstM^inoo i-i T r^ O co m T u">co co oco on nc^m co tco r^OO w Oco in T N O O h vo O^mMifl O TO co O O Oco O co O *-> N to N r^ o O n TO to o>h n mm r^co o •-• n ^ To o r^co o w w co t «^> m too m t i^ O co r» o coo o n o on moo w *t r^ o co r^ O coo O i_ i_ ,_ c-i n N cnnM^-fti-inifi mo O O r^ t>. r^oo oo co O O O O W H co o ^ s T CO MO 't * * 't -t rj- 't Tt O O «oo -tOO N oo T O mml^aH co inco O OO O Too wo O OOO -t-UM^oo N r» in in m n r>-o O t>» Oco r-» co N mod t O Too co O m o n in r^co Oco r^tnr^oO >-" N m cnmNON co TO co CO W W ino co O O m n co T mo f^ O O w n ■h T t^ O T r^ O coo O cOO ON inco >- inco m T r^ O COO O coo O m m m N N N cocococoTTTmin ino O O £>• r>. r^co co co co OOO *ClO N inininminuimO T O N O O Tco N O O Too O T N O CO inn n cor^N r-»N r^c< r^ co co in o O minNwco r^ r^co O O O O t>» r^ r-^ m n O oo coco coo n co coco m to r^co x^o T inco oo <■* O d <-?* _; co ^-o r^ O O N CO i/l\0 r^co O O >-< N CO T in r^-co O COO o COO O N in O N inco i-i T r^ O T r^ O COO O n inco £ M CS N N cOcococOTTTin in inO O O t^ t^ r^co co co oo OOO C-i Ocoo T T T T T T TO co O N TO oo O n TO oo conh in o co in i-i TO co T O O N co TO i^mo con coi-^n Oco O^^O co in in ooo inincoOco tMDH t-»i-i inOO NO O co inO r~^0 in co TO co O O O r» o i-i co TO co O m co TO r^ O O n co T ino r^co o O w n co t u"> O coi^O coo Ocoi^ON inoo m inco w T r->. O coo Ocoo ON inoo m m m m « N n cococoTTTinininooO M^t^t^oocooo OOO OOOOcococococococoOOOOOOOOOOOOcocococococo in n r^ O O^^O coOr^T'-'ONONOONONOONcoocoT Ooo co ^ m o^^ incoo i^>C Tj-OinO inON ^ ino O io co co in r^co oo oo rfOcoO'-"coinr^coOi-iN^tor^ooOt-cooOi-iN O coo O coo O N in o N inco i-i ^ r-- w -xj- t^ O coo O N inco n inco M M m m cm N N cococo-i-'vi-'^-inin ino O O r^. r^ r-^ r^oo co oo O O O X X < !Z! ^ c u tk H H < < u c-i w c^ uJ H OcoONOOOOOOO'^-NOcoO'^-NOcoO'^-N>-ir-~cooi^ k -' rtN ocoOcoo 'i-N Oco coo i-i r^o r^o m m o i-i ^ >-i ■«■ n coOO m m OMncnnto ^ON r^coOcor^O co^-nin^t-N N rfO r^r^-r^ m cotOco O N coinoco 0"-< N ^-in l^co O O *- N co rf inO r^co O O coo ONO On inco i-i ^too m ^ r-^ O coo O coo On inco w •+ r^ t-i hh hi i-i cm n N cococoTj-'^-Tj-inin ino O O r>. r-» r>. r^oo co oo o o O N O O ^f t^. J^ NNNtN »>>o NCO ^00 Nco ^Oi^-N n-o CO O N rf Tt co -I o O Oco i^>0 in ^O O in co co 'l-co com >i noco n O coOO O Oco in co hh O^kO n r^M m n r^NO Ow cO'^-^teoi-' O co ino O O r^ O M co in r^co d N co ino co o ^ N co inO r^co OO w N CO ■n- ino ONO O N in oo N inco m 'd- r^ o rh r- O N in O N inco -+■ i^ o 1-1 ^ M N N N CO CO CO Tf ^J- *J" in in ino O o O r^ r-~ r^co co co O^ O^ O^ ci'tcq om ^O coONrfinr^OONco ino co O O N co rf tnO r^ r^ O O "-i N co On in o n inco w rtoo m ^ r>. O coo O coo On inco w -too i-i -T r^ O m m i- n n n cococOTt'.r^r^t^O n to co o n TO coon ocor^Mino N TTN m NCOT inO r>i coco inTi^OTn O m inO Nco r> i-i co O in in T N Oco O co O Too N co T O COO OmnnmOcoONTTT i-i co in r^co o n T in r~»co o •-< to TO r^co O m n co t TO r^oo o O On inco i-i inco >-< TX-^O Tt~-»0 coO ONO ON inco m Tr^O cor~« O m m m n n n cococoTTTininininooo r>r>r^oococo a^ 0~- O^ 000000000000000000000000 TO co O N TO NOONONOONONOOOOCOO O Ti-ico cot^O t^ coco n inco O m i-i O o r^ O >h cocoT 00000000 N ino in N co co N O r-^O co O N T »n r>» O m N T»^ l">-co O t-i co T in r^co O O O w N T co n inco i- Tr^i-iTr^OcooOc-io ONincOMinooi-i Tr^ q m i-h hh N N N cococoTTTinir, in ino O O r^ f^ r^oo co oo COEFFICIENT OF DISCHARGE. 803 The following tables give coefficient of discharge as collated from Hamilton Smith's experiments by Professor Merriman. XXIV. WEIRS WITH PERFECT END CONTRACTION. Length of Wei r in Feet. Effective Head in Feet. 0.66 1 2 3 5 10 19 O.I 0.632 0.639 0.646 0.652 0.653 0-655 0.656 0.15 .6:9 .625 • 634 .638 .640 .641 .642 0.2 .611 .618 .626 .630 .631 , •633 •634 0.25 .605 .612 .621 .624 .626 .628 .629 °-3 .601 .608 .616 .619 .621 .624 .625 0.4 • 595 .601 .609 .613 .615 .618 .620 0.5 .590 • 596 .605 .608 .611 .615 .617 0.6 .587 •593 .601 .605 .608 .613 .615 0.7 •59o .598 .603 .606 .612 .614 0.8 •595 .600 .604 .611 .613 0.9 •592 • 598 .603 .609 .612 1.0 •59o • 595 .601 .608 .611 1.2 .585 • 591 •597 .605 .610 1.4 .580 •587 •594 .602 .609 1.6 .582 •59i .600 .607 * See p. 274. XXV. WEIRS WITHOUT END CONTRACTION. Length of Weir in Feet. Effective Head in Feet. 2 3 4 5 7 10 19 O.I 0.659 0.658 0.658 0.657 0.15 0.652 0.649 0.647 •645 •645 .644 • 643 0.2 • 645 .642 .641 .638 • 637 •637 .635 0.25 .641 .638 .636 •634 •633 • 632 .630 3 • 639 .636 .633 .631 .629 .628 .626 0.4 .636 •633 .630 .628 .625 .623 .621 0.5 •637 • 633 .630 .627 ;624 .621 .619 0.6 .638 •634 .630 .627 •623 .620 .618 0.7 .640 .635 .631 .628 624 .620 .618 0.8 .643 • 637 •633 .629 •625 .621 .618 0.9 .645 •639 •635 .631 .627 .622 .619 1.0 .648 .641 •637 .633 .628 .624 .619 1.2 .646 .641 .636 .638 .626 .620 1.4 .644 .640 •634 .629 .622 1.6 • 647 .642 .637 .631 .623 8o4 EXPERIMENTAL ENGINEERING. XXVI. HORSE-POWER LINE-SHAFTING WILL TRANSMIT WITH SAFETY Bearings, 8 to io ft. centres. Diameter of Horse-power Diameter of Horse-power Diameter of Horse-power Shaft in one Shaft in one Shaft in one in Inches. Revolution. in Inches. Revolution. in Inches. Revolution. 15 TF .008 2Tf .216 Sit .728 ifV .0156 3-h .272 61V 2.195 .027 3tV •343 6H 2.744 .043 3H .424 7* 3.368 i T f .064 3tI .512 711 4.O96 2A .091 4 ?f .728 8t 7 6 4.912 2 T V .125 4if I. OO 8if 5.824 2H .166 5tV I.328 9A 6.848 For jack-shafts, or main section of line-shafts, allow only three-fourths of the horse-power given above, and also provide extra bearings wherever heavy- strains occur, as in main belts or gears. XXVII. HORSE-POWER BELTING WILL TRANSMIT WITH SAFETY. Hors e-power per ioo Feet. Horse-power per 100 Feet. Width of Velocity of Belt. Width of Velocity of Belt. Belt Belt in Inches. in Inches. Sing! e Belt. Double Belt. Single Belt. Double Belt. I 09 .18 12 I.09 2.18 2 18 .36 14 I.27 2-55 3 27 •55 16 1-45 2.91 4 36 •73 18 I.64 3.27 5 45 .91 20 1.82 3-64 6 55 1.09 22 2.00 4.00 7 64 1.27 24 2.18 4-30 8 73 1.46 28 2-55 5 09 9 82 1.64 32 2.91 5.82 10 9 1 1.82 36 3-27 6.55 11 1 00 2.00 40 3.64 7.27 In the calculations for horse-power in the above table, the belt is assumed to run about horizontally; the semi-circumference of smaller pulley has been considered as the ordinary arc-contact of belt. Any reduction of this contact will make approximate proportional reduction of horse-power. DEFT. EXPERIMENTAL ENGINEFRINC, BIBL'EY COLLEGE, CORNELL UNIVERSITY. 4-i ~ r _|_ J_ i i . T X i i 1 " x 1 " ~r 1 1 1 | i "" ' i ' i ■ i 1 1 i i 1 :± __ "' : "^ "i 1 -J- -t- 1 -L -1 1 ! ' ! 1 1 1 ± ± j_ — _ ± ' i X _L i. i ) i _ _ i i T X i X ..it i 1 1 _L i ~r : 1 1 i 1 1 1 i 1 : 1 1 ■ " : ■ 1 ■ : " i i ::~ x x ± It _L i ; T j- h i !i 1 X i i i i i i i 1 I! 1 1 ■ 1 ■ '■"■ " ■ i nil nil 1 1 - ■ ■ - ■ " | I | ill 'ml Iiii ii ' 1 1 . i i 1 : 1 .j i_ . i 111 " 1 ! II MM 1 I 1 1 1 I i 1 II I || ~\- 1 . j 1 | I ~ II ■ 1 ^ -■ 1 1 1 1 1 II I :"~.::"~ :~: _ _i_ ~ _ ~ ~ " X , _ X ± :___ -± ± 1 i A. C. CARPENTER. ITHACA N. ANDRUS & CHURCH, Publ.shem. ITHACA, N- Y. INDEX. A PAGE Abrasion Test 186 " " Paving-brick 180 Absolute Pressure 336 " Zero........ 338 Absorber in Refrigeration 747 Absorption Dynamometer 235 Test of Bricks 179 Accelerated Cement Test. v 190 Accidental Errors 18 Accuracy of Numerical Calculations 19 Acidity Tests for Oil 215 Adiabatic Compression, Loss of Work by 729 ' ' Curve fer Gases 712 ' ' for Steam, Formula for 556 ' ' Curves for Ammonia 745 1 ' Definition 342 ' ' Expansion of Gases 711 w " Steam, Formula 554 Admiralty Tests 172 Admission -line Diagrams. . . 564 Air, Coefficients of Discharge 298 " Formulae for Adiabatic and Isothemal expansion 711 " " Flow of in Pipes 711 1 ' Measurement of Velocity. 306 " Velocity of Flow 297 1 ' of, Measured by Heating 726 " Volume Discharged. . . .' 296 " Weight " 298 807 80S INDEX. Air-compressor, Clearance Space 723 ' ' Data and Results, Tests of 730 " Formulae for Compression 711 " Types of — 720 Air -pyrometer 381 Air Refrigerating-machine 741 Air-thermometer 371 ' ' Construction. : ; 376 ' < Corrections ' 377 1 i Directions for 378 ' ' Form of 379 ' ' Formula for 374 ' l Uses of 377 Alcohol Thermometer 371 Alden Brake • 241 Allen's Draft-gauge 351 Ammonia Absorption System 748 Illustrated 750 ' ' Adiabatic Curves for 745 ' ' Anhydrous Properties of. . 740 ' ' Compression Cylinder 744 " u Relation of Pressure and Volume 711, 744 Gauge. . . 358 1 ' Refrigerating-machine 742 ' l Refrigeration Data and Result Sheets 749 Amsler's Planimeter 30 Analysis of Flue -gas 474 ' < Proximate, Coal and Coke 470 Analyzer in Refrigeration 747 Anemometer Calibration 307 ' ' Described 306 ' ' for Measuring Air 725 Angles, Functions of, Table 771 ' ' Table of Natural Functions 777 Anhydrous Ammonia, Properties of 738 Approximate Calculation, Formulas 16 Artificial Building Stone, Test of. 178 Ash Analysis, Table 787 Ash, Determination of 47° Ashcroft's Oil-testing Machine 227 Asphalt, Tests of 180 Aspirator for Flue-gas 478 INDEX. 809 PAGE Atmospheric Line 548 ' ' Pressure 336 Atomic Weight Definition 443 Autographic Apparatus, Olsen m " Diagrams 21 ' ' Extensometer 133 Torsion Machine 114 B Bachelder Dynamometer 255 ' l Indicator 523 Back -pressure Line 549 Barnett Gas-engine 702 Barrel Calorimeter 402 * ' " Directions 405 Barrus Continuous Calorimeter 410 ' ' Superheating Calorimeter 398, 416 Bauschinger's Extensometer 125 Beau de Rochas Cycle 702 Beaume's Hydrometer Scale, Table of 786 Belt Test, Directions 266 " " Forms 268 ' ' Testing Machine 264 ' ' Dynamometer 263 ' ' Friction '. 199 " Testing Methods 263 Belting, Table of H.P. 304 Bending Moment 76 Test 166 Bernoulli's Formula 276 Berthelot's Fuel-calorimeter 457 Berthier's Fuel-calorimeter 456 Blowers, Types of 723 Boiler Efficiency 493 ' ' Horse-power 494 ' ' Leakage Locomotive Test 648 1 ' Test, Abbreviated Directions 514 Form •• 5i3 " " Analysis of Coal 504 1 1 " Analysis of Flue-gas 504 " " Calculations of Efficiency 505 8io INDEX. Boiler Test, Calibration of Apparatus 497 " * ' Correction for Leakage 498 ' ' " Definitions 493 ' ' ' ' Duration 499 11 " for Locomotives 639 ' ' * ' Forms for Data and Results 507 " Fuel 49 6 " " Value 472 ' ' " Graphical Log . . 495 " " Heat Balance 506 ' ' ' ' Measurements 496 " Object 492 " ' - Pumping-engines 618 " " Quality of Steam 501 11 Records 501 " " Sampling of Coal 502 * ' ' ' Smoke Observations 506 " " Standard Method 495 " ( * Starting and Stopping 499 " ' ( Uniformity of Operations 500 Boiling-point, Table 423 Test for 380 1 ' Test for Cement 190 Bomb Fuel-calorimeter 457 Boston Extensometer 132 Boult's Oil-testing Machine 227 ' ' " ' ' Directions 230 Bourdon Gauge 357 Boyer Speed-recorder 650 Brake, Alden 241 ' ' Constants 244 ■ ' Designing. 236 1 ' Different Forms 239 ' ' Directions for Use 243 1 ' Fan Form 245 1 ' Horse-power 239 ' ' Hydraulic 242 " Prony 235 ' ' Pump Form 245 ' ' Self -regulating 241 ' ' Strap Stresses 235 4 ' Transfer of Heat 243 INDEX. 8ll Breast Water-wheels 313 Brick, Abrasion Test 180 " Test of 178 Bridge Material, Specifications 169 Tests '. 168 Brine, Specific Heat of 752 Briquettes, Form of 141 Brown Speed-indicator 573 Brumbo Pulley 531 Burning-point Test for Oils 212 Buzby Extensometer I2 7 Calibration of Anemometer 307 1 ' Apparatus for Engine Test 578 ' ' Differential Dynamometer 256 ' ' Drum Spring 542 Forms for Gauges 368 of Gauges 363 ' ' Gauges with Mercury Column 366 1 ' Indicator Spring 535 ' ' Morin Dynamometer 249 1 ' Planimeter 52 ' ' Tachometer 291 ' ' Testing-machins 97 " Venturi Tube 287 " Weir 285 Caliper, Micrometer 59 " Sweet 60 ' ' Vernier 57 Calorie 339 Calorific Power of Fuels 444 Calorimeter, Barrel 402 Barrus Continuous 410 ' ' Superheating 416 Chemical 440 Collecting- nipples 399 Comparative Value 441 Condensing 395 Continuous-jet Condensing 405 Diagram for Results from Temperatures 428 812 INDEX. Calorimeter, Diagram for Throttling 425 ' c Effect of Errors ,....' 396 Forms 4I4 Fuel, Bomb 457 " " Heat Equivalent 452 " Mahler's 4 6i 11 " Thompson 455 ' ' Hoadley 407 Injector 4 o6 1 ' Limits of Throttling 427 1 ' for Locomotive Tests 653 Measure of Water Equivalent 4 oi Method of Sampling Steam 399 Principles of Fuel 45! Separating 430 Formula for Use 436 Superheating 398 Table of Errors 397 Throttling 4I 8 Diagram for using '. 796 " " Formula. 398 " Table for using 795 Use of, on Pumping-engine 621 Calorimetric Method of Engine Testing 590 ' ' Pyrometer 381 Capacity of Pumps, Definition 329 How Computed 628 Carbon, Determination of 470 ' ' Dioxide Absorbents 475 ' ' Monoxide Absorbents 476 Carbonic Acid Absorbents 475 Carburetter 709 Car-wheel Tests 167 Carnot Cycle for Gas-engines 714 Carpenter Calorimeter for Steam 422 ' ' Draft-gauge 35 1 ' ' Fuel-calorimeter 463 ' ' Separating-calorimeter 435 Cast-iron Tensile-test Piece 139 Cathetometer 62 Cement, Definitions 181 1 ' Fineness Test 184 INDEX. 813 PAGE Cement Moulds i 4I ' ' Natural, Definition T g T * ' Normal Consistency Test 185 " Portland, Definition i 9I I c Sieves 184 II Specific Gravity Test 183 1 ' Specifications 190 ' ' Tensile Strength Required 192 " Test, Mixing 187 " Piece 140 ' ' Tests, Forms for 194 Testing 182 Tensile 189 1 ' Machine 119 Fairbanks 120 Olsen 121 Riehle 122 Centrifugal Blower, Data and Results 732 Theory of 729 Fans, Types of 724 Pumps, Test of 331 Chain-test Piece 139 Chemical Calorimeter 44 ' ' Equivalents, Table 444 Chill-point Test of Oil 214 Chloride of Calcium, Specific Heat 752 Chromous Chloride 475 Chronograph 573 " Record 576 Chronometer for Locomotive Testing 650 Cistern Manometer 347 Classification of Calorimeters 391 Clay-ball Pyrometer 389 Clearance, how measured 583 from Indicator Diagram 560 in Compressor, Effect of 728 ' ' Line 548 Coal and Coke, Proximate Analysis 470 " Calorific Tests 504 ' ' Method of Determining Moisture 502 ' ' Sampling 502 1 ' Test, Form of Report for Locomotives 644 8 14 INDEX. PAGE Coal Test on Locomotives 642 Coefficient of Discharge 271 ' ' " Friction .' I9 6 Coffin Planimeter 4I Cold Tests for Oil 213 Column Testing, Directions x ^ 4 Combined Diagram, Method of Drawing 566 ' ' Inertia and Indicator Diagrams 668 Combustible, Definition 403 Combustion, Definition 44 ^ Heat of, Table 44 6 Method of Determining when Perfect 452 ' ' Products, Object of Analysis . .' 4 73 ' ' Temperature, How Determined 448 Composition of Fuels, Table 4 ^ x Compound Engine Diagrams 565 ' ' " Hirn's Analysis 604 ' ' Pumping-engine Test Examples 631 Compressible Fluids, Flow of 295 Compression, Effect of Clearance 728 ' ' Formula 74 ' ' of Gases, Formula for y TI Test, Directions 154 1 ' Pieces 142 " Results I55 Compressor, Ammonia 742 " for Air, Test of 730 ' ' Types of 720 Computation Machine 64 Condensation in Cylinder 561 Condenser for Steam, Surface 576 Test 578 Condensing Calorimeters 395 Consistency, Normal, Test of 185 Constancy of Volume, Definition 189 " " Test I02 Constant Head Viscosometer 207 Contraction, Coefficient for 271 Cornell University Experimental Engine. 657 Corradi Roller Planimeter 45 Counter of Speed 572 Crosby Gauge-testing Apparatus 363 INDEX. 8 1 5 PAGE Crosby Indicator 521 Cross-section Paper 20 Curtis Steam-turbine 690 Curve, Adiabatic, Formula for Steam 556 - ' Isothermal, Formula for 557 ' ' of Expansion Steam 556 " " Saturation, Formula for 555 Cycle, Four-stroke 702 ' ' Two-stroke 702 ' ' of Gas-engine 713 ' ' " Refrigerating Machine 734 Cylinder Condensation 561 Loss by Diagram. 563 t i D Definitions, Friction Tests 196 Steam-engine Terms 569 Deflectometer 135 Degree of Superheat 390 " " " Formula for 393 DeLaval Steam-turbine, Description of 687 Density of Steam 342 ' ' Test, Oil 202 Diagram, Autographic 21 1 ' of Experiments 20 1 ' from Indicator, Combined 567 " " Indicators 563 1 ' Inertia '. 664 1 ' Locomotive Tests , . 652 1 ' Reduction of 22 Represents Work 21 " of Shaft Motion 567 11 Strain 69, 144 for Throttling-calorimeter . 405 Thurston's Torsion Machine 115 Diameters and Squares, Table of . ... . 756 Diaphragm, Discharge through . . . . . 280 Gau g e 359 Loss of Head through 279 Diesel Oil-engine . > JO g Differential Dynamometer 255 " " Calibration 256 8i6 INDEX. PAGE Dilution Coefficient 488 Dimensions, Experimental Engine, Institute of Technology 605 Sibley College 657 of Pipe, Table of 798 Directions for Belt Test 266 " Tension Tests 145 Discharge, Coefficient for 271 Draft Gauges 351 Draw-bar Pull of Locomotives 649 Drop Test, Directions 164 ' ' Testing Machine 119 Drum Motion of Indicator 540 ' ' Spring Calibration 542 " ' ' Testing Device 541 Ductility of Specimens 143 DuLong's Formula 445 Durability Test Lubricants 226 Duty, Definition 328 ' ' How Computed 628 ' ' Test, Pressure-gauge 620 1 ' Trial, Pumping-engines 618 Dynamometer, Absorption 235 1 ' Alden 241 Belt 263 ' ' Classes of 235 ' ' Differential 255 * ' Emerson's 259 1 ' Horse-power 517 1 '■ Lewis 252 " Locomotive Tests 651 " Pillow Block 252 1 ' Records, Locomotive Tests 649 " Steelyard 250 " Traction 246 ** Transmission 247 " Van Winkle : 261 " Webber 255 E Efficiency, Boiler 494, 5°5 1 ' of Ideal Refrigerating Machine 735 1 ' Mechanical, Definition 569 INDEX. 8l 7 Efficiency of Perfect Engine 570 " Plant ! 570 ' ' " Refrigerating Machine 736 1 ' Test of Pumps 330 1 ' " Steam-engines 589 " .- -.-. 3 Thermodynamic, Definition 570 Elastic Curve 159 Elasticity 68 ' ' Modulus 73 1 ' and Rigidity Modulus, Relation of 8^ Elbows, Loss of Head 277 Electric Ignition 704 ' ' Pyrometer 385 Elliott's Flue-gas Apparatus 479 Elongation, in Test Piece . . 68 Measure of 134 Emerson's Power Scale 259 Emery Scale Beam 106 ' ' Testing Machine 94, 96 1 ' Vertical Machine 102 1 ' Weighing System 106 Empirical Formula, How Deduced 10 Engine Fitting for Testing 582 1 ' Hot-air 694 1 ' Inertia of Parts 660 ' ' Locomotive Test. 652 1 ' Method of Measuring 583 " Methods of Testing 581 1 ' Water Pressure 309 1 ' Test, Calibration of Apparatus 578 Directions 585 Form for Results 584 Indicator Practice 584 for Leaks 582 Measurement of Speed 571 Object 570 Quality of Steam 581 Weighing Steam 581 Entropy, Definition '. 343 ' ' Table of 794 Ericsson Hot-air Engine 694 8 1 8 INDEX. PAGE Ericsson Hot-air Engine, Method of Operating 700 Errors, Classification of ' 5 1 ' Combination of 9 " Probability of 6 ' ' When to Neglect '. 18 Euler's Formula , . 75 Evaporation, Table of Factors 797 Expansion Curve, Method of Drawing 554 ■ ' Fuel Calorimeter 463 ' ' of Gases, Formula for 711 1 ' Ratio of = 550 Experiment vs. Theory 2 Experimental Engine Dimensions, Institute of Technology 605 " " Sibley College, Dimensions of 657 " Use of 656 Experiments, Classification 3 Objects of 1 Extensometer, Autographic 133 ' ' Bauschinger's 125 1 ' t Boston 132 " Buzby 127 " Henning 129 " How to Apply 148 " Johnson's 129 " Marshall 131 " Paine 127 " Riehle 128 " Roller and Mirror 125 " Strohmeyer's 126 " Thurston 129 a ' Unwin's 126 " Wedge 124 Eye-bars, Specifications of 171 F Factor of Safety 69 ' * ' ' Evaporation, Definition 493 Factors of " Table ■ 797 Fairbanks Cement Machine 120 ' ' Testing Machine 92 Fan Brake 245 Fan, Data and Results 732 INDEX. 819 PAGE Fan, Theory of 729 Fans, Types of 724 Fatigue of Metals 166 Favre & Silbermann Fuel Calorimeter 453 f eed-water Measurement 616 " Temperature, Determinations of 615 Fineness of Cement 192 Test 184 Flash Test of Oils 210 Floats 282 1 ' Use of 289 Flow of Air 296 " "in Pipes 299 1 ' Compressible Fluids ■ 295 1 ' Gas 302 ' ' Steam through Orifice 300 I * Water in Pipes 288 " " Measurement of 281 Flue-gas Analysis, Computations from 486 Forms and Computations 490 Methods 474 Object of 473 " " Process of 476 11 " Reagents 475 { ' Aspirator 478 1 ' Sampling of . 477 Flue-gases, Analysis of . . 504 Flue Losses from Flue-gas Analysis 488 Fluid Friction 200 P orging Test 166 Form for Data and Results Steam Injector. . 681 * * Record, Locomotive Tests 646 * * Report of Test, Steam-turbine 693 * ' " Report, Pumping Test 624 II Results of Engine Test 584 • ' Tension Test. 151 " Test of Pulsometer 684 Forms for Air Thermometer 379 * ' •"' Belt Test 268 11 rt Calibration of Gauges 368 ' ' • 4 Calorimeter 414 " " Cement Test 194 820 INDEX. Forms for Hirn's Analysis 598 " " Oil Test 233 " " Pump Tests 332 " " Separating Calorimeters 439 11 " Test, Hot-air Engine 698 " " Testing Hydraulic Motors 326 1 ■' " Throttling-calorimeter 430 Formula, Air Thermometer 374 1 ' Bernouilli 276 ' ' for Approximate Calculation 15 " Compression 74 ' ' Empirical, Deduction of 10 " " Friction 198 " " Pressure, Volume and Temperature, Relations of Gases. . . 711 Formulae for Hirn's Analysis 591 Freezing Machine, Cycle 734 Point of oil, Test for 380 Friction, Classification 197 ' ' Coefficient of 196 ' ' Formula . 197 1 ' Lubricated Surfaces 201 of Belts 199 " Fluids 200 " Gears 199 " " Journals 198 " " Pivots 198 Table of Coefficients 784 Test of Engine 589 1 ' Tests, Definitions 196 Frost Test for Stones 176 Fuel Calorimeter, Bomb 457 Calorimeters, Principle of 451 Consumption, Definition 569 Measurements, Locomotive Testing 641 Method of Sampling 452 Test, Locomotive 635 Value by Boiler Trial 472 Weight of, Engine -testing 582 Fuels, Composition of 451 ' ' Table of Composition 787 Fulcrums for Emery Machine 95 Fuller's Slide Rule 28 INDEX, 821 Furnace Efficiency from Flue-gas Analysis 489 ' ' Maximum Temperature from Flue -gas Analysis 488 Gas Analysis Apparatus 479 1 ' Composition of, Table '703 ' ' Measurement of Flow 302 Gas-engine, Classification 700 Compression Type 702 Cycles 713 Diagram 716 Four-cycle 706 Ignition 703 Indicator 524 Optical Indicator 525 ' ' Report of Test 716 Theory 711 Two-cycle 707 Gas Measurement, Dry Meter 305 " " Wet Meter 303 ' ' Meter, Testing Device 303 Gasoline Engines 708 Gas- or Oil-engine Testing 714 Gauge, Apparatus for Testing 363 " Calibration by Mercury Column 366 ' ' Correction of. 367 ' ' Makers, list of 36 1 1 ' Marking Device 113 ' ' Tension Test 147 Gauges, Recording 613 ■ ' for Steam-pressures 357 Gear-teeth Friction 199 Gibbs's Viscosometer 205 Giffard Injector 670 Graphical Log of Boiler Test 495 ' ' Multiplication 64 ' ' Representation of Data 20 Gumming or Drying Test 210 H Hammer Test 166 Hancock Inspirator 672 822 INDEX. PAGE Hardening Test 166 Head, Lost by Contraction 279 11 " at Elbows 279 * ' ' * " Entrance of Pipe 278 1 ' " in Perforated Diaphragm 279 1 ' ' ' " Pipes, Measurement of 289 " "by Valves , . 279 1 ' Producing Velocity 271 1 ' Relation to Pressure 324 1 ' of Water, Measurement of 281 Heat Application to Isothermal Expansion 713 1 ' Balance 494 " " in Boiler-testing 506 1 ' of Combustion 444 1 ' Consumption, Ideal Engine . . 569 1 ' Equivalent of Fuel Calorimeter 452 * ' Interchanges from Saturation Curve 612 * ' Losses in Refrigerating Machine 738 " Mechanical Equivalent of 339 " Specific, definition 338 " "of Brine 752 1 1 and Temperature 337 " Transfers of Refrigerating Machine 735 i { Units, definition 339 ' ' " per Horse-power 569 Heating Value Measured by Oxygen 446 Heisler Calorimeter 421 Hempel's Flue-gas Apparatus 483 ' ' Fuel Calorimeter 456 Henning Extensometer 129 Hennings's Mirror Extensometer 130 Higgins's Draft-gauge 353 Hirn's Analysis 590 11 " for Compound Engine 603 " " Directions for 595 " " Forms for 598 tc " Institute of Technology Engine 605 " " for Non-condensing Engine 603 11 il by Saturation Curve 611 " ' ' for Triple -expansion Engine 604 Hoadley Air-thermometer 372 ' ' Calorimeter 407 INDEX. 823 Hoadley's Calorimetric Pyrometer 384 Draft Gauge 353 Hook Gauge 282 Hornsby-Akroyd Oil-engine 711 Horse-power, Boiler 494 " Brake 239 1 ' Formula for 517 Method of Computing 552 " per Pound M.E.P., Table . . . 800 Hot-air Engines 694 1 ' Engine Forms 698 " Theory 697 Hot Test for Cement 192 ' ' Tube Ignition 704 Humidity of the Air, Table 785 Hydraulic Engines 309 ' c Machinery, Classification 308 ' ' Motor, Forms for Testing 326 ' ' Power System, Parts of ' 309 ' ' Ram 321 11 " Directions for Testing 325 ' ' Testing Machine 92 Hydraulics, Flow of Water 270 Hydrometric Pendulum 295 Hyperbola, Method of Drawing 554 Hyperbolic Logarithms, Table of 784 Ice-making Plant, Illustrated 746 Ignition, Methods of, in Gas-engines 703 Impact Test, Directions 163 ' ' Testing Machine 119 Impulse Steam-turbine, Description of 687 ' ' Water-wheel 314 Indicated and Dynamometric Power 516 ' ' Horse-power 517 " " Method of Computing 552 Indicator, Applied to Locomotive 636 " Attachment to Cylinder 543 ' ' Attachments, Engine -testing 582 Care of ( 545 824 INDEX. PAGE Indicator Cock 543 1 ' Cord 529 11 " Attachment of .■ 532 " ' * Tension on 541 " Diagram 516 * ' " Clearance, How to Find 561 " " Combined 567 " " Definitions 547 " " General Discussion 562 ' ' " Form for Ideal Case 553 " " Hot-air Engine 699 " " with Loop 552 ' ' * ' Weight of Steam from 557 1 ' Diagrams, Measurements of 551 " ' ' Method of Taking 544 ' ' Dimensions, Table of 528 1 ' Drum Motion 540 1 ' Early Forms 517 1 ' External Spring 523 1 ' for Gas-engines 524 Gas-engine, Use of 715 1 ' Gear for Locomotives. 638 ' ' for Inertia 661 Optical 525 ' ' Paper Drum.. 529 Parts • 526 1 ' Pencil Mechanism 526 " " Movement Test 539 1 1 Practice, Engine Test 584 ' ' Reducing Motions 529 Spring 527 " Calibration 535, 579 ' ' Standardization 534 1 1 of Steam-engine, Use of 515 ' ' Tests of Locomotive, Form for. 653 Inertia Diagram 664 ' ' Indicator 661 1 1 and Indicator Diagram Combined 668 ' ' Moment, Experiment for 80 ' ' Moments, Table 78 ' ' of Parts of Steam-engine 660 Injector, Directions for Testing 679 INDEX. 825 PAGE Injector, General Directions for Use 679 1 ' Limits of 676 ' ' Mechanical Theory 674 ' ' Thermodynamical Theory 672 Institute of Technology Engine Dimensions 605 Intercooler 721 Investigation, Method of 2 Involution by Diagram 20 Isothermal, Definition 342 ' ' Expansion of Gases 711 j Johnson's Extensometer 129 Jolly Air -thermometer 373 Journal Friction 198 Jump-spark Ignition 705 K Kellogg Testing Machine 93 Kent Calorimeter 409 Kent's Draft Gauge . . 355 Knife-edge of Testing Machine 95 L Latent Heat of Steam 34! " Table of 788 Lazy Tongs 532 Leakage of Boilers, Locomotive Tests 648 ' ' Test of Pumps 622 Leaks, Test for, in Engine 582 Least Squares 5 Le Chatelier Specific Gravity Apparatus 183 Lenoir Gas-engine 701 Lewis Dynamometer 252 Lime, definition of x 8i Limits of Throttling -calorimeter 429 Linde Ice-machine Test 748 Lloyd's Tests for Steel x y- Load Variation Diagram 564 Locomotive Boiler Test. 6™ Coal Tests 642 826 INDEX, PAGE Locomotive Test, Object 634 " Standard Method 634 ' ' Water Measurement 645 1 ' Tests, Form for 653 " " General Results 654 1 * " Speed Recorder 650 " Staff for 652 Logarithm Table, Use of 64 Logarithms, Common Table of 769 Hyperbolic, " " 784 Logarithmic Paper 23 Lubricants, Durability Test 226 Lubricant Testing 201 Lubricated Surfaces, Friction of 201 M McNaught's Steam-engine Indicator 517 Machinery, Hydraulic, Classification 308 Machines for Computation 64 Mack Non-lifting Injector 670 Mahler's Fuel Calorimeter .' 461 Maillard Testing Machine . 94 Manographie 525 Manometer 345 1 ' Cistern Form 347 1 ' U-shaped 345 Marshall Extensometer j^j Materials, Strength of, Table 781 Material Tests 67 Mean Effective Pressure 550 M.E.P., Table for Equivalent H.P 800 Mean Error 7 ' ' Ordinate, Length of 22 Measurement of Feed-water 616 Mechanical Efficiency 569 " " How Computed 628 1 ' Equivalent of Heat 330 Mercurial Thermometer. 369 1 ' Weight Thermometer 370 Mercury Column, Calibration of Gauges 366 " ' " Useof 351 INDEX. 827 PAGE Mercury Columns 349 " Table of Depression 350 Metal, Strength of, at Different Temperatures ~. . . . 782 Metals, Table of Specific Gravity. 783 " Table of Specific Heat 783 Metallic Pyrometer 381 Meter, Gas 303 1 1 Prover 304 Meters for Water 283 Method of Taking Indicator Diagrams 544 Metric Measures, Table of 754 Micrometer 50 1 ' Caliper 59 Mirror Extensometer 125 Mistakes, Rejection of 71 Modulus of Elasticity 73 " ''Rigidity 83 Moisture Absorbed by Air, Table 785 Moment of Flexure 76 Moments, External, Table 79 " of Inertia 80 " " " Table 78 Morin Dynamometer 247 Calibration 249 Morse Thermal Heat Gauge 386 Mortar 182 Moscrop Speed-recorder 577 Moulds for Cement 141 Multiplying Draft Gauges 355 N Naperian Logarithms, Table of 784 Napier's Formula, Table of Discharge of Steam 795 Necking of Test Specimen 143 Needle, Vicat 186 Noel's Optical Pyrometer 386 Normal Consistency Test. 185 Nozzle Calibration 287 ' ' Discharge, DeLaval Turbine 688 Nozzles, Discharge Through 275 Numerical Calculations, Accuracy of 19 1 ' Constants, Table of 756 828 INDEX. O Oil Adulteration 202 Density . 202 Engines 709 Test for Acids 215 ' ' Burning-point 212 1 ' Durability 226 1 ' Evaporation 212 Flash 210 Forms 233 for Freezing 213 ' ' Gumming 210 with Limited Feed 231 of Viscosity 204 Testing 201 ' ' Machine, Ashcroft's 227 ' ' Boult's 227 ' ' Directions 222 R.R 218 " Riehle's 224 " Theory '. 220 " Thurston's 217 " Machines. 215 Oleography 214 Olsen Autographic Apparatus in ' ' Cement Machine 121 " Testing Machine 92,110 ' ' Torsion Machine 188a Optical Indicator 525 ' ' Pyrometers 386 Ordinate, Mean 22 Orsat's Flue -gas Apparatus 482 Otto Cycle 702 Otto & Langen Gas-engine 701 Overshot Water-wheels 311 Oxygen Absorbents 475 ' ' Method of Measuring Heating Value 446 INDEX. 829 P PAGE Paine Extensometer 127 Pantograph 531 Paper Drum for Indicators 529 ' ' Logarithmic 23 Parsons' Steam-turbine 689 Paving Materials, Test of 179 Peabody Calorimeter 419 Peclet's Draft-gauge 353 Pelton Motor, Test of 324 ' ' Water-wheel 315 Pencil Mechanism of Indicator. 526 ' ' Movement on Indicator, Test of 539 Pendulum Reducing Motion 530 ' ' Viscosometer 209 Pennsylvania R.R. Viscosometer 204 Perfect Engine Efficiency 570 Perkins Viscosometer 205 Phcenix Testing-machine 93 Phosphorus 475 ' ' Determination of 470 Pillow-block Dynamometer 252 Pipe-fitting Calorimeter for Steam 422 Pipes, Flow Through 277 Pipe, Table of Standard Dimensions 798 Piston Air-compressor 720 ' ' Displacement, how measured 583 Pitot Tube 292 " " for High Pressures 294 " " Use of, for Measuring Air 726 Pivot Friction IQ 8 Planimeter Adjustment 50 Calibration •. 52, 780 Directions $j Errors 55 ' ' Measurement of Diagrams ^ z Roller 45 ' ' Suspended 4I Plant Efficiency ^ 70 Platinum Ball Pyrometer. . .' 38^ Polar Planimeter 30 Theory 32 830 INDEX. PAGE Portland Cement, Definition jgj 1 ' " Specifications 192 " Testing l82 Potassium Pyrogallate 475 Power-pumps, Tests of 031 ' ' Systems Testing Machines 89 Pressure of Atmosphere 336 ' ' by Gauge 336 ' ' Measured by Manometer 347 Units, Table of 336 " and Volume, Formulae for Compression of Gas 711 " Relations of, in Refrigeration 744 Preston Air-thermometer 372 Priestman Oil-engine , 710 Probable Error 7 Probability of Errors 6 Products of Combustion, Object of Analysis 473 Prony Brake 235 " " Designing 236 ' ' " Directions 244 1 ' " for Engine -testing 582 * i Brakes, Various Forms 239 Properties of Steam , 340 Pulsometer, Description of 683 ' ' Form for Tests 684 Theory of 684 Pump Brake 245 1 - Test, Computation and Results 628 ' ' Forms for 332 1 ' Form of Report 624 Pumps, Centrifugal, Test of 331 ' l Classification of .' 327 1 ' Duty and Capacity of 328 1 c Efficiency Test 330 ' ' Measurement of Work 329 ' ' Rotary 328 " sli P of 330 Pumping-engine, Leakage Test 622 1 ' Observations 620 Pumping-engines, Duty Trial 618 Punching Test 166 Puzzuolana 182 INDEX. 83 1 PAGE Pyrometer Calibration 780 ' ' for Locomotive -testing 641 Pyrometers 380 ' ' Comparison of 389 Q Quality of Steam, Definition 390 " " Duty Test 621 " " Formula for 393 ' ' " " Methods of Determining 394 ' ' tl " from Saturation Curve 610 R Ram, Hydraulic 32r Rankine's Formula 74 ' ' Oil-testing Machine 215 Reaction Steam-turbine 689 " Turbine 316 1 ' Water-wheel 319 Recording Gauges 361 Records of Boiler-test 501 Rectangular Weir 272 Reducing Motion for Indicators 529 " " " Locomotives 637 " Test of 579 1 ' Wheels 532 ' ' Wheel for Indicator ... 524 Re -evaporation 561 Refrigerating Machine of Air 741 " " Ammonia 742 Defined 734 " " Efficiency 736 11 " Heat Exchanges 735 M tl Ideal Efficiency 735 li " Negative Heat Losses 738 11 Test 748 " Plant, Illustrated 746 Refrigeration, Absorption System 747 ' ' Data and Result Sheets 749 Regenerator Hot-air Engine 695 Relation of Pressure and Temperature of Gases 712 832 INDEX. PAGE Report, Form of 3 ' ' of Test, Steam-turbine. 693 Residual 7 Resilience 6& ' ' Torsional 83 Revolution-counter ^ 2 Richards's Indicator q x g Rider Hot-air Engine 695 " Method of Operating 7 oo Riehle Cement Machine I2 2 ' ' Extensometer I2 8 ' ' Hydraulic Machine IO y 1 1 Oil-testing Machine 224 ' ' Power Machine 108 1 ' Testing Machine g Z ' ' Torsion Machine ug Rigidity 68 ' ' Modulus of Wire 83 Roller Planimeter 45 Rope Test-piece 140 Rotary Pumps 328 Rubber, Effects of Strain 86 S Sample of Steam for Calorimeter 399 Sampling of Flue-gas 477 " Fuel -....* 452 Sand, Standard 187 Saturation Curve, Formula for 555 " " Heat Analysis from 609 " " Heat Interchanges from 611 Screws, Micrometer 50 Seaman's Pyrometer 385 Sellers's Injector 671 Separating Calorimeter 43a " ' ' Forms 439 Formula 436 " " Table of Accuracy 431 " " Various forms 432 Setting of Cement 192 " " Valves of Steam Engine 586 INDEX. 833 Shaft Diagram 567 Shafting, Table of H.P 804 Shear, Parallel 77 Shearing Strain, Theory 81 " and Normal Stress 84 Sibley College Experimental Engine, Dimensions 657 Sieves for Cement 184 Signs and Tangents, Table of 777 Simple-lever Machines 90 Slide-rule, description 24 * ' Directions 25 Fuller's 28 " Thatcher's 27 Slip of Pumps 330 Smoke Observations in Boiler-testing 505 Specifications Bridge Material 169 for Cement 190 of Eye-bars 171 ' Iron Plate 172 ' for Steel, Lloyd's 173 ' Steel Plate 172 1 Water-pipe 1 74 Specific Gravity of Cement required 191 " " Metals, Table of 783 ' ' Table corresponding to Beaume's Scale 786 " " Test of Cement 183 Specific Heat, definition ^8 " ' ' of Brine 752 ' * " Chloride of Calcium 752 " " Determination ' 382 " " of i ? uel-gases, Table 450 "of Metals, Table of , 783 " " and Melting-point, Tables of 383 Speed-counter 571 Speed-indicator 571 " Calibration 579 Speed Measurement with Chronograph 573 • " Tachometer 572 Speed-recorder, Locomotive Tests 650 Square-inch Gauge-testing Apparatus 365 Squares and Diameter, Table of 576 Standard Form Test-pieces 136 834 INDEX. Standard Method of Testing Boilers 4Q - " " " Cement j8 2 " " " Locomotive Testing 634 1 1 Test of Pumping -engines 614 Steam-boiler Test Definitions 403 Steam-boilers, Object of Test 492 Steam Calorimeter for Locomotive Tests 655 Steam Calorimeters, Classification 391 Steam-chest Diagram 567 Steam Accounted for by Indicator, References to Tables 560 " Density and Specific Volume Formula 342 ' ' Dry and Saturated 340 1 ' Flow of, Through Orifice 300 1 ' Formula for Heat, Contents 393 " " Quality... 393 " Fuel- and Heat- consumption, of Engine Definitions 569 " per I.H.P. from Indicator-diagram 558 ' ' Measurement of Heat, Contents 394 1 ' Methods of Determining Quality 394 1 i Properties of 340 1 ' Quality of, Definition 390 " Relations of Pressure and Temperature 339 ' ' Sample for Calorimeter 391 1 ' Superheated Properties 340 1 ' Table of Entropy 301, 794 " Table of Properties 788 1 ' Weight Discharged Through Orifice 302 Steam-engine Clearance, how measured 583 ' ' Compound, Test of 631 1 ' Efficiency Test 589 " Indicator 515 " * ' Care of 545 " " Early Forms 517 Ci " for Locomotives 638 " " Parts 526 u Inertia of Parts 660 Methods of Testing 581 Optical Indicator 525 References. 325 Terms Defined 569 Test for Friction 589 Test, Hirn's Analysis 590 INDEX. 835 PAGE Steam-engine Valve-setting 586 Steam-engines, Water- consumption Tables. 802 Steam Gauges 357 Steam-gauge Calibration 579 Steam-injector, Description ; 670 1 ' Directions for Handling and Applying 679 " Testing 679 1 ' Form for Data and Results 681 ' ' Limit of Suction-head 678 1 ' Limits of Capacity 676 " "of Temperature 677 1 ' Mechanical Theory 674 Theory of 672 Steam Pumping-engines, Standard Test of 614 Steam-separator, Use of 615 Steam Tables 340 ' ' " Compared 344 " Use of 392 Steam-turbine, Description of 686 ' ' Testing 691 Steelyard Dynamometer 250 Stillman's Viscosometer 206 Stones, Frost Test 1 76 " Tests of 175 Straight Line Indicator 525 " Lyne " 525 Strain, Definition of 68 1 ' Diagram Torsion Machine n6 ' ' Diagrams 69, 144 " " Autographic 145 " Relation to Temperature 86 Strap-brakes 240 Strength at High Temperature 167 ' ' of Materials, Notation 72 " " Table of Coefficients 781 Strengths after Repeated Applications of Load 167 Stress, Definition 67 ' ' Twisting with Bending 85 " " " Longitudinal 84 Stresses, Brake -strap 236 ' ' Combination of 84 Strohmyer's Extensometer I2 6 836 INDEX. PAGE Sulphur, Determination of, in Coal 470 Superheating Calorimeters 398 Surface Condenser 576 Suspended Planimeter , 4I Sweet Measuring-machine 60 Swelling Test of Cement jg 2 T Table, Air, Moisture Absorbed by 785 " Angles, Natural Functions of 777 1 ' Analysis of Ash 787 ' * Anhydrous Ammonia, Properties of 740 Beaume Hydrometer Scale 786 of Boiling-points 423 Chemical Equivalents 444 Coefficients of Friction 784 Strength 781 Composition of Fuels 451 Fuels of U. S 787 ■■•- 703 ' ' ' ' Depression, Mercury Column 350 1 ' Dimensions of Wrought-iron Pipe 798 " Discharge of Steam by Napier's Formula 795 1 ' Entropy of Steam. 301 ' ' Errors in Calorimeters 397 ' ' External Moments 79 ' ' Factors of Evaporation 797 1 ' Heat of Combustion 446 ' ' Horse-power of Belting 804 per Pound M.E.P 800 " " of Shafting 804 1 ' Humidity of the Air 785 ' ' Hyperbolic Logarithms 784 1 1 Indicator Dimensions 528 1 1 Logarithmic Functions of Angles 771 Logarithms 759 Materials, Important Properties of 783 Maximum Temperature of Combustion 450 tt ci a 11 (i <( tt a (t ic " " " " Gases. tt tt " of Feed-water for Injector 678 tt Moisture Absorbed by Air 785 Moments of Inertia 78 INDEX. 837 Table of Numerical Constants 756 Pressure, Units of 336 Specific Heat of Gases 450 Specific Heat and Melting-points 383 Specific Heat of Water ^8 Steam -injector, Limits of 677 Steam, Properties of .' 788 Strength of Metal at Different Temperatures. . 782 Suction-head, Limit of, in Injector 678 Thermometric Scales .' 337 Throttling-calorimeter, Limits of 429 Throttling-calorimeter, Application 795 Transverse Loads 78 U. S. Standard and Metric Weights 754 Water, Density and Weight of 799 Water Consumption for Steam-engines 802 Weir Discharge 803 Tabor Indicator 520 ' ' External Spring 524 Tachometer for Measuring Speed 572 ' ' Water Measurements 290 Tagliabue Viscosometer 205 Temperature 342 Produced by Combustion 448 Effect on Strength 167 Maximum, Table of 450 Measured by Hot Body 381 Measurement of Steam 400 Relation to Heat 337 " Strain 86 Rise in Adiabatic Compression 729 Temperatures of Feed-water, How found 615 Tension, Specimen Gauge 147 Tensile Strength, Cement 192 Formula 72 Tension Test, Blank 150 1 ' Directions 145, 149 " Forms 152 " Necking I43 " Piece 137,138 " Report I49 Test by Abrasion T 66 838 INDEX. PAG E Test, Admiralty, for Iron Plate 172 " Steel Plate 172 of Asphalt 180 by Bending 166 of Bricks 178 ' ' Bridge Materials 168 " Car Wheels 167 ' ' Cement 182 ' ' Compound Pumping-engine 631 1 ' Condenser 578 ' ' Density 203 by Drop Method 164 of Efficiency 3 by Forging 166 of Belts 263 1 ' Gas- or Oil-engines 714 " Gauges 363 by Hammer 166 ' ' Hardening 166 of Hot-air Engine 697 by Impact, Directions 163 of Injector 679 ' ' Lubricants 201 " Materials 67 ' ' Paving Materials. 171 ' ' Power-pumps 339 ' ' Pulsometer 684 ' ' Refrigerating-machine 748 by Repeated Loading 166 of Specific Gravity of Cement 183 1 ' Steam-turbines 691 ' ' Stones . m 175 1 ' Torsion, Long Specimens 118& ' ' Viscosity 204 ' ' Water-pipe 1 74 Test-pieces, Cast-iron 139 ' ' Cement 140 1 i Chain 139 ' ' Compression 142 ' ' Form of 136 Rope ! 140 " Tension 138 INDEX. 839 u and Lever. PAGE Test-pieces, Torsion 142 Transverse 142 " of Wire-rope 140 " " Wood 138 Testing of Water-motors 322 " by Welding z 6$ Testing-machine, Calibration 97 Cement 119 Classification 90 Compound Lever 91 Differential Lever 91 Emery 102 Extensometer 124 Frame 97 Fulcrum 95 Hydraulic 92 93 Impact and Drop 119 " Olsen IIO Power System 89, 98 Requirements of 88 " Riehle, Hydraulic 107 " Power 108 " Shackle's 89, 98 Simple-lever 90 Torsion, Thurston 114 Varieties and Forms 88 Watertown Arsenal 100 Wedges 100 Weighing Devices 88 Weighing System 96 Thatcher's Slide-rule 27 Theory, Hot-air Engine 697 Thermodynamic Efficiency 570 Thermometers, Air 371 Thermometer, Alcohol 371 Calibration 380, 580 Cups 400 " Mercurial 369 Rules for Handling 370 Thermometric Scales, Table of 337 Thompson's Fuel Calorimeter 455 840 INDEX, Thompson Indicator 519 Three-way Cock ... 544 Throttling-calorimeter ; 398, 418 " Diagram 425 " " for use 796 " Forms 430 ' ' Limit of 427 ' ' Table for use 795 Thurston Extensometer 129 Thurston's Oil-testing Machine, Directions 222 Standard 217 Theory 220 " R.R. Oil-testing Machine 219 ' ' Torsion-machine 114 " " Diagram 115 " " Directions 161 Torsion-machine Thurston 114 " Olsen n8fl " Riehle 117, n 8 Torsion Strain, Theory 82 Torsion-test, Directions 160 Forms for Report 162 Torsion Testing-machine 114 Torsion-tests, Long Specimens 1186 Torsion Test-pieces '. 142 Torsional Resilience 8^ Traction Dynamometer 246 Transmission Dynamometer 247 Transverse Deflectometer 135 ' ' Formula 76 ' ' Loads, Table 78 ' ' Test, Directions 156 " ' ' Elastic Curve 159 " " Forms 157 ' ' Specimens 142 Trapezoidal Weir 272 Triangular Weir 272 Triple-engine, Hirn's Analysis 604 Triple -expansion, Diagrams. 565 Tuning-fork Chronograph 574 Turbine, Steam-, Description of 686 Water-wheel 315 INDEX. 84I PAGE Turbine, Water-wheel, Forms of Test 318 Theory , 316 Twisting and Bending Stress 85 ' ' ' ' Longitudinal Stress 84 Two-cycle Gas-engine 707 U Undershot Water-wheels 313 Unwin's Extensometer 126 U-shaped Manometer 345 V Vacuum Gauge 360 " " Calibration 367 Vacuum Line 548 Valve-setting 586 Valves, Loss of Head 279 Van Winkle Power-meter 261 Variation of Load, Diagram 564 Velocity of Approach 283 ' ' " Discharge, Coefficient for 271 ' ' ' ' Flow of Air ; . . 297 " Head 271 ' ' of Nozzle Discharge, DeLaval Turbine 688 Venturi Tube Calibration 287 ' ' Flow Through 275 Vernier 29 " Caliper 57 Vicat Needle 186 Viscosity of Materials 70 " " Metals 167 " Oil 203 ' ' Test, Directions 208 Viscosbmeter, Carpenter's 207 Gibbs's 205 ' ' Pendulum. 209 Pennsylvania R.R 204 Perkins 205 Stillman 206 ' ' Tagliabue 205 842 INDEX. ; PAGE Volume of Air Discharged 296 " " " Measured by Heat absorbed 727 W Water, Computation Table for Steam-engine 802 ' ' Energy of Falling 309 ' ' Equivalent of Calorimeter 401 ' ' Flow in Circular Pipes 277 " " through Nozzles 275 ' ' under Pressure 276 " "in Streams, Measurement of 289 " ll through Venturi Tubes 275 ' ' ' ' over Weirs 272, 281 ' ' Measurement of Flow 281 " " in Pipes 288 " with Pitot's Tube 292 ' ' Measurement of Head 281 ' ' Measurement with Hydrometric Pendulum 295 ' ' Measurements, Locomotive Tests 645 ' ' Meters 283 1 - Meter Calibration 579 " Errors . 284 1 ' Locomotive Test 64, 645 ' ' Motors, Measurement of Head 323 Testing of: 322 ' ' Table of, Density and Weight 799 ' ' Theory of Flow 270 Water-pipe Specifications 174 Water-pressure Engines \ 309 " Test of 325 Water-power System, Parts of 309 Water Ram 321 Water- vapor for Refrigeration 739 Water-wheels, Breast 313 Classified 310 " Impulse 314 Overshot 311 Poncelet 314 ' ' Reaction Type 319 Water-wheels, Test of 325 ' ' Turbines , 315 Undershot 313 INDEX. 843 PAGE Watertown Testing-machine 100 Watt Steam-engine Indicator '. ^7 Wearing-test Paving-brick x 8o Weathering Quality of Stone 178 Webber Dynamometer 255 Wedge Extensometer 124 Wedgewood's Pyrometer 381 Weighing Device, Testing-machines 88 Scales Calibration 579 System Testing-machine. 96 Weight of Steam from Indicator Diagram. . 557 Weir Calibration 285 Weirs, Coefficients for 274 Different Forms 272 ' Discharge over, Table of 803 Formula for 273 Measurement of Water, Errors in 282 Measurement of Head 281 Requirements for Accuracy 282 Welding Test 165 Welter's Method of Measuring Heating Value 446 Werder Testing-machine 93 Westinghouse Gas-engine 706 Williams's Inertia Indicator 661 Willis's Planimeter 45 Wilson's Flue -gas Apparatus 481 Wind Resistance, Locomotive Tests 651 Wipe Spark-ignition 704 Wire-drawing 550 Wire -rope Test-piece 140 Wooden Tension Test-pieces 138 Work -diagram 21 Work Lost due to Heating in Compression 729 ' * Mechanical, Isothermal Expansion 712 Y Yield Point 69 Z Zero Absolute 338 " Circle, Theory 3 g Zeuner's Valve-diagram 587 SHORT-TITLE CATALOGUE OF THE PUBLICATIONS OF JOHN WILEY & SONS, New York. 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Boiler's Practical Treatise on the Construction of Iron Highway Bridges. .8vo, 2 00 * Thames River Bridge " 4to, paper, 5 00 Burr's Course on the Stresses in Bridges and Roof Trusses, Arched Ribs, and Suspension Bridges. . . 8vo, 3 50 6 Burr and Falk's Influence Lines for Bridge and Roof Computations. . . 8vo, 3 00 Design and Construction of Metallic Bridges 8vo, 5 00 Du Bois's Mechanics of Engineering. Vol. II Small 4to, 10 00 Foster's Treatise on Wooden Trestle Bridges 4to, 5 00 Fowler's Ordinary Foundations 8vo, 3 50 Greene's Roof Trusses 8vo, 1 25 Bridge Trusses 8vo, 2 50 Arches in Wood, Iron, and Stone 8vo, 2 50 Howe's Treatise on Arches 8vo, 4 00 Design of Simple Roof-trusses in Wood and Steel 8vo, 2 00 Johnson, Bryan, and Turneaure's Theory and Practice in the Designing of Modern Framed Structures Small 4to, 10 00 Mtrriman and Jacoby's Text-book on Roofs and Bridges : Part I. Stresses in Simple Trusses 8vo, 2 50 Part II. Graphic Statics 8vo, 2 50 Part III. 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A Manual for Steel-users i2mo, Patton's Practical Treatise on Foundations 8vo, Richardson's Modern Asphalt Pavements 8vo, Richey's Handbook for Superintendents of Construction i6mo, mor., Rockwell's Roads and Pavements in France i2mo, Sabin's Industrial and Artistic Technology of Paints and Varnish 8vo, Smith's Materials of Machines nmo, Snow's Principal Species of Wood 8vo, Spalding's Hydraulic Cement 121H0, Text-book on Roads and Pavements nmo, Taylor and Thompson's Treatise on Concrete, Plain and Reinforced 8vo, Thurston's Materials of Engineering. 3 Parts Svo, Part I. Non-metallic Materials of Engineering and Metallurgy 8vo, Part II. Iron and Steel 8vo, Part III. A Treatise on Brasses, Bronzes, and Other Alloys and their Constituents 8vo, Thurston's Text-book of the Materials of Construction 8vo, Tillson's Street Pavements and Paving. Materials 8vo, Waddell's De Pontibus. (A P©cket-book for Bridge Engineers.) . . i6mo, m®r., Specifications for Steel Bridges i2mo, Wood's (De V.) 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Andrew's Handbook for Street Railway Engineers.. .. .3x5 inches, morocco, 1 25 Berg's Buildings and Structures of American Railroads 4to, 5 00 Brook's Handbook of Street Railroad Location i6mo, morocco, 1 50 Butt's Civil Engineer's Field-book i6mo, morocco, 2 50 Crandall's Transition Curve i6mo, morocco, 1 50 Railway and Other Earthwork Tables 8vo, 1 50 Dawson's "Engineering" and Electric Traction Pocket-book. . i6mo, morocco, 5 00 8 Dredge's History of the Pennsylvania Railroad: (1879) Paper, 5 00 * Drinker's Tunnelling, Explosive Compounds, and Rock Drills. 4to, half mor., 25 00 Fisher's Table of Cubic Yards Cardboard, 23 Godwin's Raiiroad Engineers' Field-book and Explorers' Guide. . . i6mo, mor., 2 50 Howard's Transition Curve Field-book i6mo, morocco, 1 50 Hudson's Tables for Calculating the Cubic Contents of Excavations and Em- bankments 8vo, 1 00 Molitor and Beard's Manual for Resident Engineers i6mo, 1 00 Uagle's Field Manual for Railroad Engineers. .' i6mo, morocco, 3 00 Philbrick's Field Manual for Engineers i6mo, morocco, 3 00 Searles's Field Engineering i6mo, morocco, 3 00 Railroad Spiral i6mo, morocco, 1 50 Taylor's Prismoidal Formulae and Earthwork 8vo, 1 50 * Trautwine's Method of Calculating the Cube Contents of Excavations and Embankments by the Aid of Diagrams 8vo, 2 00 The Field Practice of Laying Out Circular Curves for Railroads. i2mo, morocco, 2 50 Cross-section Sheet Paper, 25 Webb's Railroad Construction. . i6mo, morocco, 5 00 Wellington's Economic Theory of the Location of Railways Small 8vo, 5 00 DRAWING. 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W.) and Marx's Machine Design .8vo, Warren's Elements of Plane and Solid Free-hand Geometrical Drawing. i2mo, Drafting Instruments and Operations i2mo, Manual of Elementary Projection Drawing i2mo, Manual of Elementary Problems in the Linear Perspective of Form and Shadow i2mo, Plane Problems in Elementary Geometry i2mo, 9 3 00 1 50 1 00 2 50 4 00 2 50 2 00 2 50 2 00 1 50 3 00 3 00 5 00 4 00 1 50 1 50 1 50 3 50 2 00 5 00 2 00 3 00 3 00 3 00 2 50 3 00 1 00 1 25 1 SO 1 GO 1 25 Warren's Primary Geometry nmo, 75 Elements of Descriptive Geometry, Shadows, and Perspective 8vo, 3 50 General Problems of Shades and Shadows 8vo, 3 00 Elements of Machine Construction and Drawing , 8vo, 7 50 Problems, Theorems, and Examples in Descriptive Geometry 8vo, 2 50 Weisbach's Kinematics [and Power of Transmission. (Hermann and Klein.). . 8vo, Whelpley's Practical Instruction in the Art of Letter Engraving 12 mo, Wilson's (H. M.) Topographic Surveying 8vo, Wilson's (V. T.) 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W.) and Marx's Machine Design 8vo, 3 00 Spangler, Greene, and Marshall's Elements of Steam-engineering 8vo, 3 00 Thurston's Treatise on Friction and Lost Work in Machinery and Mill Work 8vo, 3 00 Animal as a Machine and Prime Motor, and the Laws of Energetics. nmo, 1 00 Warren's. Elements of Machine Construction and Drawing 8vo, 7 50 Weisbach's Kinematics and Power of Transmission. ( Herrmann — Klein. ) . 8vo , 5 00 Machinery of Transmission and Governors. (Herrmann — Klein. ).8vo, 5 00 Wood's Elements of Analytical Mechanics 8vo, 3 00 Principles of Elementary Mechanics nmo, 1 25 Turbines 8vo, 2 50 The World's Columbian Exposition of 1893 ... .• 4to, 1 00 15 METALLURGY. Egleston's Metallurgy of Silver, Gold, and Mercury: Vol. I. Silver 8vo, Vol. II. Gold and Mercury 8vo, ** Iles's Lead-smelting. (Postage 9 cents additional.) i2mo, Keep's Cast Iron 8vo, Kunhardt's Practice of Ore Dressing in Europe 8vo, Le Chatelier's High-temperature Measurements. (Boudouard — Burgess. )nmo. 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