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Heating and Ventilating off Buildings. 

8vo, XV 4- 5^3 Pi^KCS* '77 fiffures, cloth, $^oo. 

Experimental Engineering. 

For Entpneers and for Student! in Engineering 
Laboratoriet. 8vo, xix + ^43 P^Kei, 335 figures, 
cloth, $6.00. 






raonnsoB op bzfbkimbntal bmginbkxing, ti»LBV coll k ob, 





Lokdon: chapman & HALL. Limited. 






P 1911 L 

Copyright, 1899, 19061 



nOCIMT^ ONi>MMn*lO *>Kt C)lrH|tMY 

rrooklvn. h. r ', 


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, ^\^th 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 engincenng constructions 



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 A^-ill be verified by experiment, whereas 
no theory can be correct which does not accord with experimental 

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 observation^. 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 laborator}*^ 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 necessar>' 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- 


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 afiford 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 obsen'ation, 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 
obser\*ers, 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 obser\'er. 

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 laborator)' 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 


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. 


Junior Year. 
First Term. 

Strength of Materials — ^Tensile and Transverse; Calibratum — ^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; Doblc Water-wheel; Pelton Wheel; Refrigeration; Com- 
pound and Triple-expansion Engine by Him'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 


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 o^n language what he has learned 
respecting the subject under investigation in the laboratory and 
in the references, as well as to teach him methods of observing 
and recording the data and of computing the results of the test. 
For the purpose of performing the experiments the students are 
di\'ided 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 laborator}-. 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 • 

Exp-Timonlal Methods of Investigation. 

Reduction of Experimental Data Analytically and Graphically. 
Apparatus for Reduction of Experimental Data, including use of Slide-rule, 
I'lanimeter, etc. 


Strength oi 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. 
The 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-cngincs. 
Air-com pressors 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 Professgr H. Diederichs, and 
C. Hirshfeldt, and to Mr. R. L. Shipman, Mr. W. M. Sawdon, 
and Mr. G. B. Upton. 




1. Objects of Engineering Experiment i 

2. Relation of Theory to Experiment 2 

3. The Method of Investigation 2 

4. Classification of Experiments 1 3 

5. Efficiency-tests 3 




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 Formulae 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 



^^. The Slide-rule 24 

25. The Vernier 29 

26. The Polar Planimeter 30 

30. The Suspended Planimeter 41 

31. The Coffin Planimeter 41 



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 



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 



61. General Description of Machines 88 

65. Shackles or Holders 98 

66. Emery Testing-machine 100 

68. Riehl^ Bros.' Testing-machine 107 

70. Olsen Testing-machine no 

73. Thurston's Torsion Machines 114 

75. Richie's and Olsen's Torsion Machines 118 

76. Impact Testing-machine 119 

77. Cement-testing Machines 119 

Testing-machine Accessories 124 



78 to 86. Extensometers. 124 

87. Deflectometer 155 



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 

103. Elastic Cun-e 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 

111. 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 






Friction — Definitions — Useful Formulae 196 

Friction of Teeth 199 

** Cords or Belts 199 

** Fluids .*. 200 

* ' * * Lubricated Surfaces 201 

Testing of Lubricants — Density 201 

** '' '' Viscosity 209 

** ** ** Gumming 210 

'' ** '' Flash-test 210 

Testing of Lubricants — Cold Test 213 

Oil-testing Machines — Rankine's 215 

152. " ** Thurston's 217 




155. Coefficient of Friction 222 

157. Riehl^'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 



165. Absorption Dynamometer. The Prony Brake 235 

173. " *' *' AldenBrake 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 

Steelyard 250 

Pillow-block 252 

Lewis 252 

Differential 255 

Emerson 259 

Van Winkle 261 

Belt 263 

197. Belt-testing Machine, with Directions 264 

186. • 




192. * 

194. * 




200. Theory of the Flow of Water 270 

201. Flow of Water over Weirs — Formulae 272 


206. ** " ** in Circular Pipes 277 

207. ** ** " through a Diaphragm — ^Formulae 279 

209. Method of Measuring the Flow of Water by Weirs 281 

'* Meters 283 

* * Nozzles 287 

** Diaphragms 288 

*' in Streams 289 

" Pitot'sTube 292 





* * through Nozzles — Formulae 275 

" under Pressure — Formulae 276 





217. ^ 

219. ' 

220. ^ 

322. ^ 



225. Flow of Compressible Fluids, throu^ an Orifice 295 

229. '* ** '* *' inaPipe 299 

230. ** * * Steam 3cx> 

232. Gas-meters 304 

233. Anemometer 306 



235. Classification 308 

239. Water-pressure Engines 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 Pimip-test 332 



259. Books of Reference 325 

260. Units of Pressure 336 

261. Heat and Temperature .* 337 

264. Properties of Steam 340 

267. Steam-tables 344 



268. Manometers 345 

271. Mcrcur)' Columns 349 

273 Draught-gauges 351 



277. Steam-gauges 357 

381. Apparatus for Testing Gauges 363 



285. Mercurial Thermometers 369 

288. Air-thermometers 371 

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 



305. Definitions 390 

307. General Methods 391 

314. Errors in Calorimeters 396 

315. Sampling the Steam 399 

317. Water E>)uivalent of Calorimeter. 401 

318. Barrel Calorimeter 402 

321. Hoadley Calorimeter 407 

323. Barms Continuous Calorimeter 41 1 

326. ** Superheating ** 416 

328. Throttling Calorimeter 418 

336. Separator " 430 

341. Chemical '^ 440 



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 



347. Composition of Fuels 450 

348. Fuel<alorimeters — Principle 451 

352. * * Favre and Silbermann's 453 

353- " Thompson's 455 

354- " Berthier 456 

355. " Berthelot Bomb 459 

356. ** Caqxntcr 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 



369. Objects of Boiler-testing 492 

371. Efficiency of a Boiler 493 

375. Standard Method of Testing Steam-boilers 495 

377. Concise Directions for Testing Boilers. , 513 



378. Uses of the Indicator 515 

380. Early Forms 517 

381. Richards 518 

7,^2. Thompson ^19 

^S^. Tabor 520 

384. Crosby 521 

385. Indicators with External Springs 523 

387. Optical Indicators 525 

3QO. Reducing-motions 529 

393- Calibration 535 

397. Method of Attaching to the Cylinder 543 

398. Directions for Use 545 






400. Definitions ••••••••• 547 

401. Measurement of Diagrams 551 

403. Form of Diagram 553 

416. Weight of Steam from the Diagram 557 

407. Clearance from the Diagram 560 

40S. Cylinder-condensation and Re-evaporatioQ 561 

409. Discussion of Diagrams 563 

410. Diagrams from Compound Engines 565 

411. Crank-shaft and Steam-chest Diagrams 567 



413. 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. Him's Analysis 590 

430. ** ** of Compound Engines. 603 



433. Standard Method of Testing Pumping-engines 614 

434. '* ** ** ** Locomotives 634 

435. Experimental Engines 656 





436. General Effects of Inertia 660 

437. The-Williams Inertia-indicator 661 

438. " Inertia-diagram 664 



459. Description of the Injector 670 

440. Theory 672 

442. Limits of 676 

443-5. Diitctions for Testing 679 

446-7. The Pulsometer , 683 



448. General Principles 686 

449. Impulse Type (De Laval) 687 

450. Reaction Type (Parsons) 689 

451. Combined Type (Curtis) 690 

452. Testing . . 691 



454. General Principles 692 

455. Ericsson Hot-air Engine 692 

456. Rider Hot-air Engine 693 

457. Theor>' 695 

458. Method of Testing O95 

460. The Gas-engine 701 

461. Oil-engines 709 

462. Theoretical Formulse 711 

463. Cycle of Operation 713 



464. Method of Testing 714 

465. Data and Results of Test 717 



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 Blower 733 



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 




I. U. S. Standard and Metric Measures 75 

II. Numerical Constants . . 

in. Logarithms of Numbers 7I 

IV. Loganthmic Functions of Angles 7y x 



V. Natural Functions of 777 

VI. Qjefficients of Strength of Materials 781 

VII. Strength of Metals at DifiFerent Temperatures 782 

VIII. Important Properties of Familiar Substances 783 

IX. Coefficient of Friction 784 

X. Hyperbolic Naperian Logarithms 784 

XI. Moisture Absorbed by Air 785 

Xn. Relative Humidity of the Air 785 

XIII. Table for Reducing Beaiun^'s Scale-reading to Specific Gravity 786 

XIV. Composition of Fuels of U. S 787 

XV. BueFs 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 

XX\1I. '* *' Belting 804 

Sample-sheet of Cross-section Paper 805 


Moments of Inertia 78 

Units of Pressure Compared 336 

Thermomctric Scales 337 

Melting-points and Specific Heats of Metab 383 

Maximum Temperature of Combustion 450 

Av-eragc Composition of Fuels 451 

Properties of Saturated Ammonia 738 


X. Objects of Engineering Experiments. — ^The object ol 

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 coefKcients 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- 

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- 
lorining 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 
<^xactly repeated in each experiment, even provided no error 
^^ made. The object will then be to find average values of 
these coefficients, to obtain the variation in each specific test 


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^ 
ligation, before the test is commenced ; but in many cases this 
is not possible, and the experiment must precede a study of the 

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« 
tradictory 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 


conditions as nearly as possible the same as those in actual prac- 
tice. These methods later \i'ill be given in detail. The manner 
of performing the test will depend entirely on the experiment. 

The report should be \vritten in books or on paper of a pre- 
scribed form, and should describe clearly: (i) Object of the 
experiment; (2) Deduction of formulae 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 everj*^ case be clearly comprehended. 
The following subjects are considered in this treatise, under 
various heads: (i) The calibration of apparatus; (2) Tests of 
the strength of materials; (3) Measurements of liquids and 
gases; (4) Tests of friction and lubrication; (5) Efficiency- 
tests, which relate to {a) belting and machiner}' of transmission, 
(6) water-wheels, pumps, and hydraulic motors, (r) hot-air and 
gas engines, {d) air-compressors and compressed-air machinery, 
(t) 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 efficiencv of a machine is the ratio of the useful work 
delivered by the machine to the whole 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, j)lus the work lost in friction, dissi- 
pated in heat, etc. The lost work of a machine often consists 


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-iesls 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. 





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 fuliy 
studied in the work by Chauvenet published by Lippincott & 
Co., or in the work by Merriman publi')hed by John Wiley & 

6. Classification of Errors. — The errors to \vhich all ob- 
servations are subject are of two classef^ : systematic and 

Systematic errors are those which affect the same q jariti- 
tics in the same way, and may be fjrther clasiifi'rd as in'Jru- 
mental and personal. Th-j i: -t." jm-.r.tal '.rror-. are ^Ije 'o 
imperfection of the instrum---ri::» -zrr.'J. j-j'-Zi, ^r.^i ^t': 'Ir.^r.^- i , 
comparison with standard ir.^tr .rr. ■::.': r or by -.r.^:',; i! -^'h'. .- 
0( calibration. Personal err :.r- a-^: : .*: r.o a zyr. 
the "observer tending to nr»a!«:-t: h;- r^-^ :::.;/ 
a certain direction, ani are to ''.: iv.-:.'--^ - : : -, 

J > . 

,J . . ,J J . . m ..1., 


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. 

Accidental 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 probabiUty 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 = ^^-****, (l) 

in which c and h are constants, and e the base of the Napierian 

system of logarithms. 


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 
obser\ation 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 obser\'ations. The probable error is 0.6745 time the mean 
error. The error of the result is that of a single obscr\ation 
divided by the square root of their number. 

Thus let n represent the number of observations, 5 the sum 
of the squares of the residuals ; let e, ^, , ^, , 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 ± a / . . . (2) 

Mean error of the result i \/ ~? \- • (4) 


V ;/(//-!)• 

Probable error of the result ± 0.6745 \ / ^,,^, 7^. (S) 

In every case S = 2e^, 

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 




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 72° 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 0° Centigrade, and is known as the 
MHre des Archives. 

The following are some of these determinations. That 
made by Clarke in 1866 is most generally recognized as of 
the greatest weight. 



Name of Observer. 





Comstock . . . 

Mean value 





length of meter 

m inches. 

39 3701 5 
39 36985 


Difference from 

the mean. 

Residual = *. 

Square of the 


— 0.001460 
+ 8780 
~ 1818 

— 2100 

— 0.002400 



2^ = 5 = 0.0000907024, « = 5, n{n — i) = 20. 

Mean error of a single observation 

5on = ±y^x=^- 


Probable error of single observation = ± 0.00317. 

Mean error of mean value 

= =ty;j(^,5 = o.oo2ij 

Probable error of mean value 

= ± 0.00142. 


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. 

ID. 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 A' equal the calculated or observed result, F the 
error made in the result ; let x equal one of the observed 
quantities, and / its error. Then will 

P-fTx (^ 


in which t- 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'y etc., the probable error of the 

= ± yfF' + F'\ (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 //, the mean pressure by/, 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, 

F dW , r^ . r, 

j= -jp=lan, F=piaf\ 

F' dW 

T " ~dn =^^^- 


The error/" in the mean pressure is itself a complicated 
one, since/ 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 o.ook'j 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 = lOO square inches, 
/ = 2 feet, n = 300, / = SO pounds, /= 0.335, /' = O-S- 

F = 20,100, F = 5,000, W = 3,000,000. 

Probable error = ± VF* + 7^* = 20,712 ft.-lbs., which in this 
case is 0.0069 of the work done. 

12. Deduction of Empirical Formulae. — Observations arc 
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 


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 

}^=A-\'Bx-{'Cx' + Dx' + 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 • 

j^ = ^+^;r* + Cr*+Z?;r»+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 &x+B,cos &x + C, sin ^2X 

m m m 

+ Clcos^ — 2;r4-etc. . . . <lo) 

Still another form which is occasionally used is 

y^=^ A-\' B sixi mx + C sin* mx + etc. « . (11) 

13. General Methods. — A method of deducing the em- 
pineal 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'\ 


etc., and suppose that by means of the observations we have 
deduced the general equations of conditions as follows: 

e = A '\' ax '\- by + ^^^ 
e' =:A' •\-a'x +by +c'z, 
/' = A" + a''x + by + c''z, 
^'" = A"' + a'^'x + b"'y + c'"z, 
etc. etc. etc. 


Let it be required to find such values of x, y^ z, etc., that the 
values of the residuals e, e\ e'\ 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 

^ 4. ^« 4. ^'» 4. e'"^ + etc. = x'ia^ + a'^ + a"^ + etc.) 

+ 2x\{ah + ah' + a"h" + etc.)+ a{by + ^-? + etc) 
+ a\b'y + c'z + etc.) + etc. } + A' + h'^ + etc. 

This equation may be arranged with reference to ;r as 
follows ; 

u = e' + e'' + ^'* + etc. z=Px' + 2Qx+R + etc. ; 

in which the various coefficients of the different powers of s 
are denoted by the symbols P, Q, R, etc. 

Now in order that these various errors may be a minimum, 
^ + ^" + ^'" + ^^c. = « 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 (2> 

x{a^ + a'' + etc.) + ah + ah' + etc. J^a{by + cz + etc.) 

+ ^'{b'y + c'z + etc.) + etc. ■ 

Similar equations are to be formed for each variable. 


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 Itave simply to multiply tlie second member of each 
of the equations of condition by t/te 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 ordinarj' 
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 wf = 24 inches, n = 297 revolutions • 
w = 32 " « = 340 

w = 33 " « = 355 
/// z= 35 " n = 376 







Average values for w = 31 inches, ?i = 342 revolutions. 

Arranging the results in 

the following form, 

we have: 









+ 4 



— 2 

+ 13 

+ 34 

Assume that the equation of condition is of the form 

A ■{■ Bx -\- Cx' = j^. 




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: 

^-75 + 49C=-4S, 
A+ B+ C=- 2, 

A + 2B+ 4C= + i3, 


Multiplying each equation by the coefficient of A in that 
equation, we have 

^-7^+49^'= -45, 
^+ B+ C= - 2, 
^ + 2^+ 4C= + i3, 
^ + 4^+i6C= + 34. ^ 

- 11. 

Equations of minimum condi- 
tion of error with respect to A. 

4A +o5 + 7oC= 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+ ^+ C=- 2 
2A+ 4-5+ 8C= 26 
4^ + 16^+ 64C= 136 

Equations of minimum 
- IV. condition of error with 
respect to B. 

oA + 70-ff — 270C = 47S Sum of equations in group IV. 

Multiplying each equation in group I by the coefficient of 
C in that equation, we have 

49^ — 343-ff + 2401 C = — 2205 

A+ B+ C=- 2 

4^4- 85+ i6C= 52 

\6A+ 645+ 256^7= 544 

Equations of minimum. 
^ V. condition of error with 
respect to C. 

yoA — 268-ff + 2674C = — 1611 Sum of equations in group V. 


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 : 

4^ + o5 + 70C = 01 

oA 4- 70B — 270C = 475 > VL 
70A — 2685 + 2674^= — 1611 ) 

Solving the above, 

A = i.6oS; -5 = 7.140; C^=— 0.0919. 

Substituting in the original equation of condition, 

y = 1.608 + 7.i40tr — ao9i9;r*. 

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 j its value, n — 342 ; and for x 
its value, m — 31. In this case we shall have 

« — 342 = i-6o8 + 7.i4<> — 30 — o.09i9(;// — 31)"; 

which reduced gives the following equation as the most proba- 
ble value in accordance with the observations: 

n = 34.952 + 13.02;;/ — 0.09 1 9;;/'; 

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. 




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 

{flJ^dy =zor-\^ mcT'^d + m ^^ " ' V -'d' + etc., 

will become oT + ma'^'^S, if the higher powers of d be neglected. 
If d is equal to y^jVir P*^**^ ^^ ^» ^^^ error which results from 
omitting the remaining terms of the series becomes very 
small, as in this case the value of <^ = looltooo ^' 

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 : 

(I + ay 

(I + sy 


(I + 6)" 

= I + tnS, 
= I + 2d, 

= 1+4*. 
= 1+3*, 

= 1-6, 

(I - 8)" 

(1 - 6y 





= 1 + *; 

(I + *) 

; = I - 2d, 


;= I+2d; . 

= 1-4*, 

= 1+4*; 

Vi+S ' '' V\-S 

fi + *Xi+«Xi + C)--. i + d + e + C; 

(I _tf)(i _€)(, _C)...I- _6_C;. 








(I ±*Xl±€)(l±0...I±*±6±C; (21) 

(I ±<yX' ±Q tJ-rfO-n-;!-. too\ 

{X ± e)(i ± V) -li'iCTcTi,; .... (22) 

^^ =^^» (23) 

sin (jT -j- tf) = sinjr 4* ' cos x\ (24) 

cos (x + *) = cos x — * sinx; (25) 

tan (x + *) = tan x + rrT:i = tan x + rfsec*x; . . (26) 

cos Jv 

sin (jT — <J) = sin JT — * cos x ; (27) 

cos ( jT — <J) = cos JT + tf sin jr. (28) 

16. The Rejection of Doubtful Observations.* — It often 
happens that in a set of observations there are certain values 
which are so much at variance with the majority that the ob- 
server rejects them in adjusting the results. This might be 
done by application of Rule 3, Article 7, provided the magni- 
tude of the errors which could not occur were definitely deter, 
mined ; but to reject such observations without proper rules is 
a dangerous practice, and not to be recommended. 

This brings into sight a class of errors which we may term 
mistakes, and which are in no sense errors of observation, such 
as we have been considering. Mistakes may result from vari- 
ous causes, as a misunderstanding of the readings, or from re- 
cording the wrong numbers, inverting the numbers, etc. ; and 
when it is certainly shown that a mistake has occurred, if it 
cannot be corrected with certainty, the observations should 
be rejected. After making allowance for all constant errors, no 
results except tliose which are unquestionably mistakes should be 

The remaining discrepancies will then fall under the head 

* Sec Adjustment of Observations, by T. W. Wright. N. Y., D. VaD 


of irregular or accidental errors, and are to be corrected as ex- 
plained in the preceding articles ; the effect of a large error is 
largely or wholly compensated for by the greater frequency of 
the smaller errors. 

17. When to Neglect Errors.— Nearly all the observa- 
tions taken on any experimental work are combined with 
observations of some other quantity in order to obtain the 
desired result. Thus, for example, in the test of a steam- 
engine, observations of the number of revolutions and of the 
mean effective pressure acting on the piston are combined with 
the constants giving the length of stroke and area of piston. 
The product of these various quantities gives the work done 
per unit of time. 

All of these quantities are subject to correction, and it is 
often important to allow for such correction in the result. Just 
how important these corrections may be depends on the degree 
of accuracy which is sought. 

As the degree of accuracy increases, the number of influenc- 
ing circumstances increases as well as the difficulty of eliminat- 
ing them ; hence this part of the work is often the most difficult 
and sometimes the most important. To what limit these cor- 
rections may be carried depends on our knowledge of the laws 
which govern the experiments in question, as well as the 
accuracy with which the observations may be taken. It is 
evidently unnecessary to correct by abstruse and difficult cal- 
culation for influences which make less difference than the 
least possible unit to be determined by observation, and this 
consideration should no doubt determine whether or not correc- 
tions should be taken into account or neglected. 

Thus, in the case of the test of a steam-engine, we have 
errors made in obtaining the engine constants, i.e., length of 
stroke and area of piston. These errors may be simply of 
measurement, or they may be due to changes in the tempera- 
ture of the body measured. The errors of measurement depend 
on accuracy of the scale used, care with which the observations 
are made, and can be discussed as direct observations on a single 
quantity. The errors due to change of temperature can be cal- 


culated if observations showing the temperature are taken, anc^ 
if the coefficient of expansion is known. A calculation will, in 
case of the steam-engine constants referred to above, show that 
in general the probable error of observation is many times in 
excess of any change due to expansion, and hence the latter 
may be neglected. The effect of errors in the other quantities 
has already been discussed in Article 11. 

It is to be remembered that the method of correction 
outlined in the " Method of Least Squares" applies only to 
those accidental and irregular errors which cannot be directly 
accounted for by any imperfection in instruments or peculiar 
habit of the observer ; usually the correction for instrumental 
and personal errors is to be made to the observations them- 
selves, before computing the probable error. 

18. Accuracy of Numerical Calculations. — The results of 
all experiments are expressed in figures which show at best 
only an approximation to the truth, and this accuracy of ex- 
pression is increased by extending the number of decimal figures. 
It is, however, evidently true that the mere statement of an ex- 
periment, with the results expressed in figures of many decimal 
places, does not of necessity indicate accurate or reliable ex- 
periments. The accuracy depends not on the number oi 
decimal places in the result, but on the least errors made in 
the observations themselves. 

It is generally well to keep to the rule that the result is to 
be brought out to one more place than the errors of observa- 
tion would indicate as accurate : that is, the last decimal place 
should make no pretensions of accuracy; the one preceding 
should be pretty nearly accurate. In doubtful cases have one 
place too many rather than too few. No mistake, however, 
should be made in the numerical calculations; and these, to 
insure accuracy, should be carried for one place more than is 
to be given in the result, otherwise an error may be made that 
will affect the last figure in the result. The extra place is dis 
carded if less than 5 ; but if 5 or more it is considered as 10, and 
the extra place but one increased by i. 

In performing numerical calculations, it will be entirely 


unnecessary to attempt greater accuracy of computation than 
can be carried out by a four-place table of logarithms, except in 
cases where the units of measurement are very small and the 
numbers correspondingly great. In general, sufficient accuracy 
can be secured by the use of the pocket sUde-ruIe, the readings 
of which are hardly as accurate as a three-place table of loga- 
rithms. The sUde-rule will be found of great convenience in 
facilitating numerical computations, and its use is earnestly 

19. Methods of representing Experiments Graphically. 
— ^Nearly all experiments are undertaken for the purpose of 
ascertaining the relation that one variable condition bears to 
another, or to the result. All such experiments can be repre- 
sented graphically by using paper divided into squares. The 
result of the experiment is represented by a curve, drawn as 
follows: Lay off in a horizontal direction, using one or more 
squares as a scale, distances corresponding with the record values 
of one of the various observations, and in a similar manner, 
using any convenient scale, lay off, in a vertical direction from 
the points already fixed, distances proportional to the results 
obtained. A line connecting these various points often will be 
more or less irregular, but will represent by its direction the 
relation of the results to any one class or set of observations. 
A connecting line may form a smooth curve, but if, as is usually 
the case, the line is irregular and broken, a smooth curve should 
be drawn in a position representing the average value of the ob- 
servations. The points of observation, located on the squared 
paper as described, should be distinctly marked by a cross, or a 
point surrounded with a circle, triangle, or square; and farther, 
all observations of the same class should be denoted by the same 
mark; so that the relation of the curve to the obser\'ations can 
be perceived at any time. 

The value of the graphical method over the numerical one 
depends largely on the well-known fact that the mind is more 
sensitive to form, as perceived by the eye, than to large num- 
bers obtamed by computation. Indeed, when numbers are 


used, the averages of a series of observations are all that can 
be considered, and the effect of a gradual change, and the 
relation of that change to the result, which is often more im- 
portant than any numerical determination, is entirely disre- 
garded, and often not perceived. 

Every experiment should be expressed graphically, and stu- 
dents should become expert in interpreting the various curves 
produced. A sample of paper well suited for representing 
experiments is bound in the back portion of the present work. 

All important tests should also be accompanied by a 
graphical log; in this case time is taken as the abscissa, and the 
various observations corresponding to the time are plotted at 
convenient heights. The variation of these quantities from a 
horizontal line shows in a striking way irregularities which 
occur during the test, a horizontal line indicating uniform con- 

2a Area of the Diagram represents Work done.— 
In case the horizontal distances or abscissae represent space 
passed through, and the vertical distances or ordinates represent 
the force acting, then will the area included between this curve 
and the initial lines, represent the product of the mean force 
into the space passed through, — or, in other words, the work 
done. The units in which the work will be expressed will 
depend on the scales adopted. If the unit of space represent 
feet, the unit of force pounds, the results will be in foot-pounds. 
The initial lines in each case must be drawn at distances corre- 
sponding to the scales adopted, and must represent, respectively, 
zero-force and zero-space. 

21. Autographic Diagrams. — In various instruments used 
in testing, a diagram is drawn automatically, in which the ab- 
scissa corresponds to the space passed through, the ordinate 
to the force exerted, and the area to the work done. A 
familiar illustration is the steam-engine indicator-diagram, in 
which horizontal distance corresponds to the stroke of the 
piston of the engine, and vertical distance or ordinates to the 
pressure acting on the piston at any point. The absolute 
amount of the pressures may be determined by reference to the 


atmospheric line. The distance vertically between the lines 
drawn on the forward and back strokes of the engine is the 
effective pressure acting on the piston at the given position of 
its stroke ; the mean length of all such lines is the mean 
effective pressure utilized in work. The vertical distance from 
any point on the atmospheric line to the curve drawn while the 
piston is on its forward stroke is the forward pressure, the 
corresponding distance to the back-pressure line is the back 
pressure, and the areas between these respective curves give 
effective or total work per revolution. 

An autographic device is put on many testing-machines : in 
this case the ordinates of the diagram drawn represent pres- 
sure applied to the test specimen, and abscissae represent the 
stretch of the specimen. This latter corresponds to the space 
passed through by the force, so that the area of the diagram 
included between the curve and line of no pressure represents- 
the work done, — at least so far as the resistance of the test- 
piece is equal to the pull exerted, which is the case within the 
elastic limit only. 

Various dynamometers construct autographic diagrams, ia 
which ordinates are proportional to the force exerted and ab- 
scissae to the space passed through, so that the area is propor- 
tional to the work done. The diagram so drawn would repre- 
sent the work done equally well were ordinates proportional 
to space passed through, and abscissae to the force exerted, but 
such diagrams are not often used. 

22. Reduction of Diagrams. — In the reduction of auto- 
graphic diagrams the process is reversed as compared with the 
construction of the diagram. The important data required are^ 
first, the position of initial lines of force and of space ; second, 
the respective scales of force and of space. In computing the 
work, it is usually customary to find the mean pressure from 
the diagram, and multiply this result by the space through 
which the body actually moves, instead of multiplying by the 
length of the diagram. 

To find the length of the mean ordinate^ from which the 
mean pressure is easily obtained, vertical lines are drawn so 


close together that the portion of the curve included between 
them is sensibly straight ; the sum of these lines, which may 
be expeditiously taken by transferring them successively to a 
strip of paper and measuring the total length, is found ; and 
this result divided by the number gives the length of the mean 
ordinate. This length multiplied by the scale gives the pres- 
sure. An integrating instrument, the planimeter, is more 
frequently used for this purpose, and gives more accurate 
results. The theory of the instrument and method of using is 
of great importance to engineers, and is given in full in the 
following chapter. 

Logarithmic Cross-section Paper is very convenient for 
the reduction of certain forms of curves to algebraic or 
analytic equations. The rulings of this paper are made at 
iiistances proportional to the logarithms of the numbers which 
represent the ordinates and abscissae. Any curve which may 
be represented by a simple logarithmic or exponential equa- 
tion would be represented on paper ruled in this way by a 
straight line. Thus, an equation of the general form y = 
Bj^ can be reduced so that log^ = log B -\' n log jr, which 
is the equation of a straight line in logarithmic units. In 
this equation n is the tangent of the angle which the line 
makes with the axis of abscissae, and B is the intercept on this 
axis from the origin. Paper ruled in this manner can be ob- 
tained from most dealers in technical supplies. In case it 
cannot be obtained, ordinary cross-section paper, as shown in 
the Appendix to this book, may be used by numbering the 
graduations on the axes of abscissae and ordinates as propor- 
tional to the logarithms of the distances from the origin. 



23.The Slide-rule. — The slide-rule is made in several forms, 
but it consists in every case of a sliding scale, in which the 
distance between the divisions, instead of corresponding to the 
numbers marked on the scale, corresponds to the logarithms of 
these numbers. This scale can be made to slide past another 
logarithmic scale, so that by placing them in proper positions 
there may be shown the sum or difference of these scales, and 
the number corresponding. As these scales are logarithmic, the 
number corresponding to the sum is the product, that corre- 
sponding to the difference is the quotient. Operations involv- 
ing involution and evolution can also be performed. Scales 
showing the logarithmic functions of angles are also usually 

Pig. I.— Thb Slidb-ruls. 

The usual form of the slide-rule is shown in Fig. I. This 
form carries four logarithmic scales, one on either edge of the 
slide, and one above and one below. Either scale can be used; 
that above is generally to one half the scale of the lower, and 
while not quite as accurate, is more convenient than the one 
below. The trigonometrical scales are on the back of the slide. 


§ 24.] APPARATUS, 2$ 

The principal use to the computer is the solution of problems 
in multiplication and division. 

The following directions for use of the plain slide-rule, 
which is ordinarily employed, give a simple practical method 
of multiplying or dividing by the slide-rule, experience 
having shown that when these processes are fully understood 
the others are mastered without instruction. 

Suppose that a student has a slide-rule of the straight kind, 
and similar to the one in Fig. i, which consists of a stationary 
scale, a sliding-scale, and a sliding pointer or runner. These 
parts we will term, respectively, the ** scale," the slide, and the 

24. Directions for using the Slide-rule. — Holding the 
rule so that the figures are rfght side up, four graduated edges 
will be seen, of which only the upper two are used in the 
problem we are about to describe. (The method of using the 
two lower scales would be exactly the same, the difference 
being, that they are twice as long, and that the slide is above 
instead of below the scale.) 

Move the slide to such a position that the graduations 
agree throughout the length of the scale, and place the runner 
at a division marked i, and the rule is ready for use. Arrange 
the factors to be dealt with in the form of a fraction, with one 
more factor in numerator than in denominator, units being in- 
troduced if necessary to make up deficiencies in the factors. 

Thus, to multiply 6 by 7 by 3 and divide by 8 times 2, 
arrange the factors as follows : 


The factors in the numerator show the successive positions 
which the runner must take ; those in the denominator the 
positions of the slide. Thus, to solve above example, start (1) 
with runner at 6 on the scale, always reading from same side of 
runner; (2) bring figure 8 on slide to runner; (3) move runner 
to 7 on slide: the result can now be read on the scale; (4) 


bring 2 on slide to runner ; (5) move runner to 3 on slide. The 
result is read directly on the scale at position of runner. 

Another example : Multiply 11 by 6 by 7 by 8, and divide 
by 31. 

In this case arrange the factors 

II X 6x 7 X 8 
I X I X 31 

Start with runner at 1 1 on scale, move i on slide to runner, 
move runner to 6 on slide, move i on slide to runner, runner 
, to 7 on slide, move 31 on slide to runner, runner to 8 on slide: 
read result on scale at runner. 

The numbers on the slide-rule are to be considered signifi- 
cant figures, and to be used without regard to the decimal 
point. Thus the number on the rule for 8 is to be used as .8 
or 80 or 800, as may be desired, even in the same problenu 
The significant figures in the result are readily determined by 
a rough computation. In case the slide projects so much 
beyond the scale, that the runner cannot be set at the required 
figure on the slide, bring the runner to i on the slide, then 
move the slide its full length, until the other i comes under 
the runner. Then proceed according to directions above ; i.e., 
move runner to number on slide, and read results on the scale : 

6 X 25 X 35 X 7 X 7 X 31 _p 
;r X 426 X 914 X I X I "" 

Begin with the first factor in the numerator, and multiply 
and divide alternately, — 

X 6, -4- ;r, X 25, -5- 426, X 3-5» -^ 9i4» etc.,— 

until all the factors have been used, checking them off as they 
are used, to guard against skipping any or using one twice. 



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- 
arj- 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- 

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 

Thacher's calculating instrument consists of a cylinder 4 
inches in diameter and 18 inches long, working within a frame- 
work oE triangular bars. Both the cyhnders and bars are grad* 

|lnted with a double set of logarithmic scales, and results In 
Multiplication or division can be obtained from one setting of 
Pifce instrument, hence it is especially convenient when a series 
[ of numbers arc to be multiplied by a common factor. The 
I 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 

r of using is essentially similar to that of the plain slide-rule; 



[§ =4- 

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 wil! be read by noting that 
number on the triangular scale which registers with 1 on the 
cylindrical scale. The product of this quotient by any otlier 
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 lengtti, 

is graduated around the cylinder spirally, and the readings are 
obtained by means of two pointers or indices, one of which. ^, 
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 3 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 v4, fixed to the handle. t\\e fixed pointer, the other B^. 
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) -h- c. set the fixed pointer A to Ihft 
6rst number in the numerator, then bring the movable index 

§2$.] APPARATUS, zy 

P 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 maybe used for reading, as convenient, their distance 
apart corresponding to the entire length of the scale on the 
ty Under 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 // equal the number of subdivisions of 
the vernier which are equal to ;/ — i on the limb. Then the 

value of one subdivision on the vernier is ti[ 

The difference in length of one subdivision on the limb and 
one on the vernier is 

\ n / n 

Avhich evidently will equal the least reading of the vernier, and 
indicates the distance to be moved to bring the first line of 
tiie vernier to coincide with one on the linib. 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 


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 (A J — 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 ot^er 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, (i) the reading of the limb is 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, pivoted together at the point K, The arm PA' 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 TVS. 3 1 

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 A" and /^, or in A"/^ 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. 

Flo. 4-— AiuLu'i Paul PuHi 

The detailed construction of the record-wheel, and the ar- 
rangement of the counter C, showing the number of revolutions. 

is shown in Fig. j. The wheel D is subdivided into a given 
number of parts, usually lOO ; 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 



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. g.)—The Zero- 
circle. — If the two arms be clamped so that the plane of tlie 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 nil! 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 i' 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 -f 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 a line 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 »i'l^ 
(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 ^PdO. The total differ- 
ential of area is then dA'^ldp+^dd. I is always a. constwit 




during the operadon of a planimetery so that A ^jiA ^Ijip-^ 

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 JdO^ is zero. Hence A ^ifdp simply. But J dp is 

the net distance the arm has moved perpendicular to itself. 
Call this Rf and there results the equation of the planimeter 

Pio. 6. 

Fio. 7. 

If the polar planimeter is so used as to bring in the zero-drde, 
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 fdO is now 2;r instead of zero, T making 

a complete revolution about G. The linear turning of the edge 

of the recording- wheel is jdp—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 




zero-circle is traced by T when the plane of W passes through 

P. Then (dp^intij and the wheel records 2^ro. 

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. 

Pig. 8. 

Pio. 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 

Movefnent 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 £Z>'F"=go® 
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 £, 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 d6, 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^^ designated by dR^ which is the projection of 

(J Amsler instrument is usually constructed so that the 

is adjustable in length, and consequently it may be 

^ available for any scale or for various units. Gradua- 

are engraved on the arm which show the length required 

• vi; a record in a given scale or for given units. 

■e area of ike zero-circle is usually engraved on the top 

L arm /. In case it is not given, it may be found by 

iting the areas of two circles of known area, each greater 

the area of the zero-circle nr". Let the areas of such 

■i be respectively C and C, and the corresponding read- 

of the record-wheel i?and R, in proper units, TTien we 

C= Tr" + Jeand C = ;rr" + ^, 
2_ which 

'2nr'^ = C-\'C' -{R-^RT). (8) 

ving found r". we can compute », since r** = tw" + /* -|- ^^t 
\ m and I can both be obtained from measurement. 

Forms of Polar Planimeters. — Polar planimeters are 

.two forms: i. Withthepivot/, Fig. lo, fixed. 2. With 

movable, so that the arm / between pivot and tracing- 

Ytnv he varied tn Ipnirth. Sinre the area is in earh ra<» 




From the right triangle ED'F", 

r" = »»• + <• + 2«/ 


Substituting the values of r* and r'* in equation (2), we have 

dA :=^ l{m cos B — n)d6. 


By comparing equation (5), the differential equation for the 
area, with equation (i), the corresponding equation for the 

record, we see that 

Pig. xo. — Polak Plamimbtbs. 

dA = ldR\ . 


or by integration between limits o and R, since / is a constant. 

A = /R. 


This shows that the area is equai to the length of arm 
from pivot to the tracing-pointy multipliea by the space registered 

§28.] APPARATUS. 37 

cn the circumferenee of the rtcord-^whetl^ and is independent of 
the other dimensions of the instrument. 

That this is true for ^eas not adjacent to the zerd><irde, 
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 

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 the xero-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 srr'*. Let the areas of such 
circles be respectively C and C^ and the corresponding read- 
ings of the record-wheel R and R^ in proper units. Then we 

C= irr'« + ^and C = irr" + ^, 

from which 

2;rr" = C+r-(/? + ^0- (8) 

Having found r'*, we can compute «, since r" = «• + ^ + 2«/, 
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. i o, fixed. 2. With 
pivot f 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 h'neal 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 


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 lOO 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 = lO.O 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 ar 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 i, 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, 

100 ^3?/=^; (8) 

' " Too?' ••••••••(9) 

\i A^siXO square inches and d^-^ inchy 


f 29.3 APPARA TVS. 

\iA = 10 square inches and </ = sV '"^h, 

The length of the arm from centre to the pivot has no effect ] 
on tbe 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. ft 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, arc 
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 

39. The Mean Ordinate by tbe Polar Planimeter.— 
If we let / equal the length of the mean ordinate, and let L 
equal tbe length of the diagram, then the area A = Lfi, but 
the area A = IR [eq, (7)]. Therefore If = IR, from which 

l^L=f-irR. (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 recordwheel, to a scale to be determined. 

The method of making the adjustable arm the lengjth 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 /^ and mounting a similar point Kat the same distance 
back of the pivot C\ then in all cases the distance UV will be 
equal to the length of the adjustable arm /. The instrument is 
xeadily set by loosening the set-screw 5 and sliding the frame 




carrying the pivot and record-wheel until the points [/V are at 
the respective ends of the diagram to be traced, as shown in 
Fig. 1 1 . 

In the absence of the points [/ 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 Uie 
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. II.— Mbthod of Setting thb Planimeter for 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. 

T/ie scale of the record-ivJieel 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'\% 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 sul> 

I 32.] APPARA TVS. 41 

divisions of the circumference, corresponds almost exactly to 
a :.cale of forty subdivisions to the inch, and is the dimension 
usually adopted on foreign-made instruments. 

3a The Suspended Planiraeter. — In the Amsler sus- 
pended planimeter as shown in Fig. 12, pure rolling motion 
without slipping is assumed to tai;e place. The motion of the 
record-wheel, not dearly shown ia the figure, is produced by 
the rotation of the cylinder c in contact with the spherical 

segment K. The rotation of the segment is due to angular 
motion around the pole O, that of the cylinder f to its posi- 
tion with reference to the axis of the segment. This position 
depends on the angle that the tracing arm, ks, 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 

31. The CofEn Planimeter and Averaging: Instrument. 
— This instrument is shown in Fig. 13, (rom 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, 
ill 1874. The record-wheel travels over a special surface; one 
end of the arm travels in a slide, the other end passes around 
the iltagram. 

32, Theory of the Coflin Instrument — This planimeter 
may be considered a special form of the Amsler, in wh 
point P, see Fig, 14, page 43, moves in a right line insl 


swinging in an arc of a circle, and the angle CPT, correspond- 
ing to B in eq. (i), is a fixed right angle. The dififerential 
equation for area therefore is 

dA=lndy, (n) 




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. O.) by placing the diagram so that 

Fig. 14.— Coffin Avbkaging Instkumknt. 

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 
^^e tracing-point perpendicular to the base along a special 
guide provided for that purpose until the record-wheel reads 
^ at the beginning. This latter distance is the mean 


To prove, take as in Art. 29 tne M. O. = /, the length 
of diagram = Z, the perpendicular distance = 5. Then 

A=pL=ilR (14) 

Let C be the angle, EPTy 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 = S s\n C, (15) 

For the position at the end of the diagram 

sin C = L -^ l\ 

Substituting this in equation (14), 

Hence/ = 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- 

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 Planimeter. — This planimeter is of the 
same general type as the Amslcr 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 



e of a triangular scale which is supported in an ingenious man- 
, as shown in the accompanying figure. The planimeter-arm 
1 be adjusted as in the Amsler Planimeler so as to read the 

M. E. P. direct. An adjustable pin, £, is employed for the 

purpose of setting off the lengtli 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 

tmference of the wheel. The only conditions of accuracy 
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 the 

\^w''--_^ r 


^^x^^Jl^L^ V \ 


140. -Tub W.LL.S Pukiwbikr. 

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 liew of the instrument is shown in Fig. 1 5, 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 
by one &zing of the instrument is very lai^e; thirdly, the 




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 

The frame B is supported by the shaft of the two rollers 
Rjt^ . 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 Ji,R^ a minutely 

divided mitre-wheel R, is fixed, which gears into a pinion 
Ji . This pinion, being fixed upon the same spindle as the 
disk/i, causes the disk to revolve, and thereby induces the roll- 
ing motion of the entire apparatus. 

The measuring-roller £, 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^ , fixed upon 
the frame B. 

35, Theory. — The following theory of the roller-planim- 
eter is partly translated from an article by F. H. Reitz, in the 
Zeitschrifi 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 constniction 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 

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 
diagrani 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 tracinf^j-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 




correct, this quantity imist 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 dxy a point in the circumference of the rollers i?,/?, 
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 i?, must move 

an amount equal to -^dx. 

Fig. x6. 

Suppose that while the tracing-point moves a distance dx^ 
the disk A moves a distance ab, Fig. lo, since this disk is turned 
by the mitre-wheel whose pitch-circle is R^, and ^i^is the dis- 
tance from record-wheel to the axis of this wheel, we must 

R^ ad 
R "R 


ft iS^l APFARA TVS. 


Became <rf die posMcm erf the axis of the lecord-wheel JS» the 
motioD of the disk A to the extent of ab produces a shifting 
of a point in the drcumfeience of E equal to «^, while the 
record-wheel dips.a distance me. The distance cb is the reading 
of the record-wheel and is the quantity required. We have 
i^^ =:90^^)e^ = 90^; hence €af:sict^ zxAfab^fi^ and eak 
ssa + /7. So that since tf^^ s 90^ 

«^s4i^sin(4r-fi8)ss4i^(sinacoii9 + coiarsin>^ • (f7> 
Bat it is aeen that 




_af D-ag^^-j: 

*"'' = ^= .^ 

Substitute these values in equation (17) : 



P\\ ad 

Substitute the value of ab in {16), 

= <^-' ^^«) 

^ = ^^^^^^ = (constant) j^^, . . • • U9) 

was to be pn'>ved 


The differential distance cb is the reading of the record wheel, 
let this be represented by dr^ denote by C the constant wpoj^ : 

dr—Cydx\ /flJr=^; i ydx=^ i dr. 

This expression integrated gives 

Area = -g:(r,-rJ = -^^^(r, -r^; . . ^ao) 

in which r, and r, are the initial and final readings of the 

In the construction of the instrument ^,, ^,, Z>, and R^ are 
fixed quantities, but the length of the tracing-arm F can be 
varied, with a corresponding variation in the unit of measure* 

36. Care and Adjustment of Planimeters. — From the 
preceding discussion it is seen that the area in every case is 
the product of the distance actually moved by the circum- 
ference of the record-wheel into the length of the arm from 
the tracing-point to the pivot, into a constant which may be 
and is, in the polar planimeter, equal to one. It is also to be 
noticed that the record-wheel is so arranged as to register the 
distance moved by a point in a direction perpendicular to that 
of the tracing-arm, and that for other directions it slips. This 
indicates that any change whatever in the diameter of the 
record-wheel or gear-wheels, due to wear or dirt, will require a 
corresponding change in the length of tracing-arm ; and further, 
any irregularities in the edge of this wheel will make the rela^ 
tive amounts of slipping and rolling motion uncertain, and con* 
sequently impair its accuracy. 

Again, the plane of the record-wheel must be perpendicular 
to the tracing-arm, otherwise an error will result. 

In the planimeter the moving parts usually have pivot* 

§ 37-] APPARATUS. jr 

bearings which can be loosened or tightened as required. The 
revolving parts should spin around easily but at tlie same time 
accurately, and the various arms should swing easily and show 
no lost motion. The pitch-line of the record-wheel should be 
as close as possible to the vernier, but yet must not touch it; 
the counting-wheel must work smoothly, but in no way inter* 
fere with the motion of the record-wheel. 

37. Directions for Use. — i. Oil occasionally with a few 
drops of watch or nut oil. 

2. Keep the rim of the record-wheel clean and free from 
rust. Wipe with a soft rag if it Is touched with the fingers, 

3. Prepare a smooth level surface, and cover it with heavy 
drawing-paper, for the record-wheel to move over. Stretcb 
the diagram to be evaluated smooth, 

4. Handle the instrument with the greatest care, as the 
least injury may ruin it. Select a pole-point so that the instru- 
ment will in its initial position have the tracing-arm perpen- 
dicular either to the pole-arm or to the axis of the fluted 
rollers, as the case may be; for in this position only is the 
error neutralized, which arises from the fact that the tracer is 
not returned to its exact starting-point. Then marking some 
starting-point, trace the outline of the area to be measured la 
the direction of the hands of a watch, slowly and carefully, 
noting the reading of the record-wheel at the instant of start- 
ing and stopping. It is generally more accurate to note the 
initial reading of the record-wheel than to try and set it at zero, 

5. Sfecial Directions. — To obtain the mean ordinate with 
the polar planimeter, make the length of the adjustable arm 
equal to the length of the diagram, as explained in Art. 28, 
page 38. and follow di'ections for use as before. 

6. In using the Coffin planimeter, the grooved metal plate / 
is first attached to the board, upon which the apparatus is 
mounted as shown in the cut, page 42, being held in place by 
s thumb-screw applied to the back side. 

The diagram will be held securely in place by the spring-clips 
adjacent, A and C, Fig. 13. The area may be found by running 
the tracing-point around the diagram, as described for the 


polar planimeter, for any position within the limits of the arm. 
The mean ordinate may be found by locating the diagram as 
shown in the cut, with one extreme point in the line of the 
metal groove produced, and the dimension representing the 
length of the diagram perpendicular to this groove. Start to 
trace the area at the farthest distance of the diagram from the 
metal guide produced, as shown in Fig. 13 ; pass around in the 
direction of the motion of the hands of a watch to the point 
of beginning; then carry the tracing-point along the straight- 
edge, AK, which is parallel to the metal groove, until the record- 
wheel shows the same reading as at the instant of starting: 
this latter distance is the length of the mean ordinate. 

38. Calibration of the Planimeter. — In order to ascertain 
whether the instrument is accurate and graduated correctly, it 
is necessary to resort to actual tests to determine the character 
and amount of error. 

It is necessary to ascertain: I. If the same readings are 
given by different portions of the record-wheel. 2. Whether 
the position of the vernier is correct, and agrees with the con- 
stants tabulated or marked on the tracing-arm. 3. Whether 
the scale of the record-wheel is correct, and agrees with the 
constants marked on the tracing-arm. 

These tests are all made by comparing the readings of the 
instrument with a definite and known area. To obtain a defi- 
nite area, a small brass or German-silver rule, shown at Z, Fig. 
II, is used; this rule has a small needle-point near one end, 
and a series of small holes at exact distances of one inch or 
one centimeter from the needle-point. To use the rule the 
needle-point is fixed on a smooth surface covered with paper, 
the planimeter is set with its tracing-point in one of the holes 
of the rule, and the pole-point fixed as required for actual use. 
With the tracing-point in the rule describe a circle, as shown 
by the dotted lines (Fig. 17) around the needle-point as a 
centre. Since the radius of this circle is known, its area is 
known; and as the tracing-point of the planimeter is guided in 
the circumference, the reading of the record-wheel should give 
the correct area. 




The method of testing is illustrated in Figs. 17, 18, 19, and 
20. Figs. 17 and 18 show the method with reference to the 
polar planimeter; Figs. 19 and 20 show the corresponding 
methods of testing the rolling-planimeter. In Figs. 17 and 19 
P is the position of the pole, B the pole-arm, and A the tracing- 
arm. In Figs. 18 and 20 B \s the axis of the rollers and A is 
the tracing-arm. 

First Test. This operation, see Figs. 17 and 18, consists 
in locating the planimeters as shown, and then slowly and 

^ I y— tf [ I #**--> 

\ ^ / J \ K / J 

Fio. 17. 

Fig. 18, 

carefully revolving so as to swing the check-rule as shown 
by the arrow. Take readings of the vernier at initial point, 
and again on returning to the starting-point : the difference of 
these readings should give the area. Repeat this operation 
several times. 

The instrument is now placed in the position shown in 
Figs. 19 and 20 when the circle K appears on the r/^A/-hand 
side of the tracing-arm Ay and the passage of the tracer takes 
place in exactly the same way. 

If the results obtained right and left of the tracing-arm be 
equal to one another, it is clear that the axis ab of the measur- 
ing-wheel is parallel to the tracing-arm, and, this being so, the 
second test may now be applied. But if the result be greater 
in the first case, that is to say, when the circle lies to the left 




of the tracing-arm, the extremity a of the axis of the measur* 
ing-wheel must be further removed from the tracing-arm ; if it 
be Uss^ that extremity must be brought nearer to the tracing- 

Second Test. The tracing-arm is adjusted by means of the 
vernier on the guide and by means of the micrometer-screw^ 
in accordance with the formulae for different areas ; it then is 
fixed within the guide by means of the binding-screw. The 
circumference of circles of various sizes are then travelled over 

Pig. 19. 

Pi& so. 

with the check-rule, and the results thus obtained are multi- 
plied into the unit of the vernier corresponding to the area 
given for that particular adjustment by the formula. The fig- 
ures thus obtained ought to be equal to the calculated area of 
the circles included by the circumferences. If the results ob- 
tained with the planimeter fall short of the calculated areas to 

the extent of — of those areas, the length of the tracing-arm, 
that is to say, the distance between the tracer and the fulcrum 

of the tracing-arm, must be reduced to the extent of — of that 


length; in the opposite case it must be increased in the same 

proportion. The vernier on the guide-piece of the tracing-arm 

shows the length thus defined with sufficient accuracy, usually 

S 39.] APPARA TUS. S 5 

in half-millimeteni, or about fiftieths of an inch, on the gauged 
portion of the arm. 

In order to test the accuracy of the readings according to 
the two methods just described, some prefer the use of a 
check-plate in lieu of the check-rule. The check-plate is a cir- 
cular brass disk upon which are engraved circles with known 

It is advisable to apply the second test also to a lai^e dia^ 
gram drawn on paper and having a known area. 

The instrument having been found correct or its errors de- 
termined, it may now be used with confidence. 

The following form is used to record the results of the test : 

Calibration of Planimeter 189. « 

by 9 Dia. register- wheel, in. .. « 

Formula of Instmment Length of arms, pole to pivot, in ... . 

Pivot to register- wheel, in. . • • Pivot to tracing-point, in ... • 

In RoUer Pla. radios roller, in. • . • Pitch radius Gears. No. I. . • .No. II . . . • • 



Mean Okdinatb. 


Intt. Kcadiiw. 

Difference from 



Inst. ReMlinff. 

Difference from 




Mean error of one obsenratioQ, ± V^r* -1- (« — i) in 
Mean error of result. 

I. • . •» in ofdinate. . .in. 
k. . .« in ordinate. . .in. 
k. ...» in ordinate. . . in. 
Probable error of result, ±a67 f^2^-i-ii(«— i) in area. ...» In ordinate. . .in. 

± ^'Se^ -h n{n — i) in 
Probable error of one oba., ± a67 f^^^ -*-(« — i) in 

39. Errors of Different Planimeters. — Professor Lorber, 
of the Royal Mining Academy of Loeben, in Austria, made 




extensive experiments on various planimeters^ with the results 
shown in the following table : 










The error in one passage of the tracer amounts on an average to 
the following fraction of the area measured by — 

The ordinary 
Polar Plan- 
imeter Unit 
of Vernier: 

zo sq. mm. = 
.015 sq. in. 

Stark *s Linear 
Unit of Ver- 
X sq. mm. = 
.015 sq. in. 


IBB 7 

Unit of Ver- 

I sq. mm. =: 
.0015 sq. in. 


Rolling Planimeter^ 

Unit of Ver- 
X sq. mm. = 
.0015 sq. in. 



Unit of Ver 

.1 sq. mm. as 
joooi sq. io. 


The absolute amount of error increases much less than the 
size of the area to be measured, and with the ordinary polar 
planimeter is nearly a constant amount. 

The following table is deduced from the foregoing, and 
shows the error per single revolution in square inches: 

Error in one passage of the tracer in square inches— 


Polar Planim- 
eter Unit of 
10 sq. mm. r= 
.015 sq. inches. 

Suspended Plan- 
imeter Unit of 
X sq. mm. = 

.0015 sq. inches. 

Rolling Planimeter— 

Unit of Vernier: 

X sq. mm. = 
.0015 sq. inches. 



Unit of Vernier 

.X sq. mm. = 

.0001 sq. inches. 









These errors were expressed in the form of equations, as 
follows, by Professor Lorber. Let / equal the area corre. 



J to one complete revolution ot the record-wheel ; let 
is the error in area due to use of the planimeter. Then 
to different planimcters we have the (ollowing equations: 

1 planimeter, dF= o.oooSr/ +0.00087 VFf\ 

planimeter, <^= O.OOi26/'+o.ooo22 \F/; 

laon polar planimeter, a7^= o.ooo6g/"+ 0.00018 \ Ff; 

#nded planimeter, <tf'= 0.0006/ -f-0.00026 v^; 

log planimeter, 4F — aoooQ/" + 0.0006 vFf, 

Moment Planimeters much more complicated than those 
ribed have bfeii made for special purposes, of which we 
Intention Amsler's mechanical integrator for finding the 
lent of inertia, and "Coradi's" mechanical integrapii for 
Jng the deriviiy of any curve, the principal curve being 
i(n, thus giving a graphic representation of moment. 



an inch on the vernier. The reading of the vernier as it is 
shown in the figure is 1.650 from the scale, and 0.002 on ihc 
vernier, making the total reading 1.652 inches. This instru- 
ment is useful for accurate me.isurements of great variety ; the 
especial form shown in the tut has a heavy base, so that it will 
stand in a vertical position and may be used as a height-gauge. 
To use it as a caliper, the specimen to be measured is placed 
between the sliding-jaw and the base ; the reading of the vernier 
will give the required diameter. 

41. The Micrometer. — This instrument is used to meas- 
ure small subdivisions. It consists of a finely cut screw, one 
revolution of which will advance the point an amount equal to 
the pitch of the screw. The screw is provided with a gradu- 
ated head, so that it can be turned a very small and definite 
portion of a revolution. Thus a screw with forty threads to 
the inch will advance for one complete revolution ^ of an 
inch, or 25 thousandths. If this be provided with a head sub- 
divided to 250 parts, the point would be advanced one ten- 
thousandth of an inch by the motion sufficient to carry the 
head past one subdivision. 

The micrometer is often used in connection with a micro- 
scope having cross-hairs, and in such a case represents the 
most accurate instrument known for obtaining the value o( 
minute subdivisions; it is also often used in connection with 
the vernier. The value of the least reading is determined by 
ascertaining the advance due to one complete revolution, and 
dividing by the number of subdivisions. The total advance of 
.he screw is equal to the advance for one revolution multiplied 
jy the number of revolutions plus the number of subdivisions 
multiplied by the corresponding advance for each. 

The accuracy of the micrometer depends entirely on the 
screw ivhicli is used. 

Accuracy of Micrometer-screws. — The accuracy attained in 
cutting screws is discussed at length by Prof, Rogers in Vol. V. 
of Transactions of American Society of Mechanical Engineere, 
from which it is seen that while no screw is perfectly accurate; 
still great accuracy is attained. The following errors are those 




in one of the best screws in the United States, expressed in 
hundred-thousandths of an inch, for each half-inch space, 
reckoned from one end. 

Total Errors in Hundred-thousandths of an Inch. 

''o. of space. 

Total Error. 

No. of Space 

Total Brror. 

No. of Space. 

Total Brror. 




- 4 






- 7 






- 9 






- 7 






— 10 






— II 






— II 


— 7 




— lO 






— lO 






- 9 




— I 


— II 




— 2 


— 10 


— 2 


A recent investigation made by the author* of the errors in 
the ordinary Brown and Sharpe micrometer-screw, failed to 
detect any errors except those of observation, which were 
found to be about 4 hundred-thousandths of an inch for a 
distance equal to three-fourths its length. The errors in the 
remaining portion of the screw were greater; the total error 
in the whole screw being \2 hundred-thousandths of an inch. 
As the least reading was one ten-thousandth, the screw was in 
error but slightly in excess of the value of its least subdivision. 
In another screw of the same make the error was three times 
that of the one described. 

42. Micrometer Caliper consists of a micrometer-screw 
shown in Fig. 22, which may be rotated through a fixed nut. 
To the screw is attached an external part or thimble, which 
has a graduated edge subdivided into 25 parts. The fixed nut 
is prolonged and carries a cylinder, termed the barrel, on which 
are cut concentric circles, corresponding to a scale of equal parts, 
and a series of parallel lines, which form a vernier with refer* 


cnce to the scale on the thimble, the least reading of which is 
one tenth that on the thimble. If the screw be cut 40 threads 
per inch, one revolution will advance the point 0.025 inch : and 
if the thimble carry 25 subdivisions, the least reading past 
any fixed mark on the barrel would be one thousandth of an 

By means of the vernier the advance of the point can be 
read to ten-thousandths of an inch. Thus in the sketches of 


the oarrel and thimble scales in Fig. 16 the zero of the vernier 
coincides in the upper sketch with Ko. 7 on the thimble: bui 
in the lower figure the zero of the vernier has passed beyond 7, 
and by looking on the vernier we see that the 3d mark coincide! 
with one on the thimble, so that the total reading is 0.007-}- 
0.0003, which equals 0.0073 '"*^h. 

This number must be added to the scale-reading cut on the 
barrel to show the complete reading. The principal use of the 
instrument is for measuring external diameters less than the 
travel of the micrometer-screw. 

The Sweet Measuring-machine. — The Sweet mcasurir^- 
Tiachine is a micrometer caliper, arranged for measuring larger 
diameters than the one previously described. The general 

§ 43.] APPJff^ TUS. 6l 

form of the instrument is shown in Fig. 23. The micrometer. 
screw has a limited range of motion, but the instrument is fur- 
nished with an adjustable tail splndie, which is set at each 

observation for distances in even inche?, and the micrometer, 
strew is used only to measure the fractional or decimal parts 
of an inch. The instrument is fuinislied witii an external 

scale, graduated on the upper edge to read in binary fractions 
of an inch, and on the lower edge Id read in decimals of at 
inch ; this scale can be set at a slight angle with the axis to 
correct for any error in the pitch of the micrometer-screw. 



The graduated disk is doubly graduated ; the right-hand grad- 
uations corresponding to those on the lower side of the scale. 
The scale and graduated disk is shown in Fig. 24, and the rea<L 
itigs corresponding to the positions shown in the lligure art 
0.6822, the last-number being estimated. 

The back or upper side of the scale, and the left-hand disk, 
are (or binary fractions, the figures indicating 32ds, Fig. 25 
shows the arrangement of the figures. 
Beginning at o and following the Une of 
chords to the right, the numbers are in 
regular order, every fifth one being counted, 
and coming back to o after five circuitst 
This is done to eliminate the factor five 
' ' " from the ten-thread screw. In Fig. 24 the 

'^ portion to the left of o in Fig. 25 is seen. 

The back side of the index-bar is divided only to i6ths, the 
odd 32d3 being easily estimated, as this scale is simply used for 
a "finder;" thus: In the figure the reading line is very near 
the H mark, or six 32ds beyond the half-inch. This shows 
that 6 is the significant figure upon this thread of the screw. 
The other figures belong to other threads. The figure 6 is 
brought to view when the reading line comes near this division 
of the scale. Bring the 6 to the front edge of the index-batt 
and the measurement is exactly W without any calctilation. 
Thus every 32d may be read, and for 64ths and other binary 
fractions take the nearest 32d below and set by the intcrmo 
diate divisions, always remembering that it requires ^iv spaces 
to count one. 

43. The Cathetometer. — This instrument is used exten. 
sively to measure differences of levels and changes from a 
horizontal line. Primarily it consists of one or more telescopes 
sliding over a vertical scale, with means for clamping the tel& 
scope in various positions and of reading minute distances, 
The one shown in the engraving (Fig. 26) consists of a solid 
brass tripod or base supporting a standard of the same metal 
the cross-section of which is shown at different points by the 
«nall figures on the left. A sliding-carriage upon which is 


ecured the small levelling instrument, and whic has also a 
emter scale as shown, is balanced by heavy lead weights, sus- 

lended within the brass tubes on either side by cords attached 
o the upper end of the carriage, and passing over the pulleys 


shown at the top of the column. The column is made ver. 
tical by reference to the attached plumb-line. 

The movable clamping-piece below the carriage is fixed at 
any point required, by the screw, shewn at its side, after which 
the telescope can be raised or lowered by rotating the micro- 
meter-screw attached to the clamp. The telescope is provided 
with cross-hairs, which can be adjusted by reversing in the 
wyes and turning i8o degrees in azimuth. The vertical scale 
is provided with vernier and reading-microscope. 

Aids to Computation — Graphical methods for multiply- 
ing or dividing are usually given in treatises on geometry and 
ate often sufficiently accurate for the required results. Tables 
of logarithms and of products often save much labor. The 
Rechentafeln by A. L. Crelle of Berlin gives one million 
products and will be found of much value in multiplication 
and division. A very excellent logarithmic table has recently 
been issued by Prof. G. W. Jones. Ithaca, N. Y. 

Computation Machines Several very excellent ma- 
chines (or multiplying and dividing are now made, which 
give accurate results to from 14 to 17 places. Of these we may 
mention, as moderate in price and of perfect accuracy, the 
calculating machine of George B. Grant of Boston: the 
Brunsvega by Grimme-Natlis & Co., Brunswick, Germany, 
and the Comptometer, made by the Comptometer Co. of 
Chicago. Slide-rules of compact form but with with scales 
40 feet in length, as designed by Thatcher or Fuller, can also 
be obtained of the principal stationers. 

The processes of arithmetical calculation are almost entirely 
mechanical and involve no reasoning powers, yet they are of 
utmost importance in connection with experimental work. 
Unless the observations of the experiment are correctly 
recorded and the necessary calculations for expressing th' 
result made accurately.' the experimental work will either be d 
no value, or, what is worse, positively misleading. For thes* 
reasons mechanical methods of computation, which involve at 
best small errors of known magnitude, are to be adopted wheff 
ever possible in reducmg engineering experiments. 

§43-] APPARATUS. 65 

The calculating machine is of especial value, since if the 
mechanical processes are correctly performed the results will 
be given with accuracy for the number of places within limits 
of the machine. Numerous calculating machines have been 
designed, the most noted of which is the " difference engine " 
designed by Babbage in 1822 and on which the English Govern- 
ment expended more than $85,000 without bringing it to per- 
fection. The first practical machine which accomplished any- 
tiiing worthy of permanent record was invented by Thomas de 
Colmar in 1850, and since that time numerous others, designed 
on similar lines, have appeared, of which should be mentioned 
those invented by Tate, Burkhardt, Grant, Baldwin, and 
Odhner. The Grant machine, developed from 1874 to 1896, 
has now reached a high degree of perfection, and its price is 
within the reach of any engineering laboratory. The Odhner 
or Brunsvega, referred to above, was shown at the World's Fair 
in 1893, and differs from the Grant principally in the arrange- 
ment of parts, in the fact that, as now sold, it possesses an 
index or counter to register the multiplier during the process 
of multiplication. The Grant machine will on special order be 
fitted with this appliance ; its mechanism is much superior to 
that of the foreign instrument, and it is operated with less labor 
and noise. 

In both machines, the result is read on a series of wheels 
arranged on the same axis and so connected that ten revolu- 
tions of one of lower denomination are required for one of the 
next higher, etc., these wheels being readily and simultaneously 
set at zero. The numbers to be united are engraved on a key- 
board. By setting a lever opposite any number and turning a 
crank once, the sum will appear on the result-wheels ; by turning 
the crank twice, the result-wheels will show twice the sum, etc. 
The number keyboard can be shifted several places, so that it 


Js possible to multiply by numbers of any denomination, by 
^ess than ten revolutions of the crank. Subtraction is per- 
formed by starting with the larger number on the result-wheel 
^nd the smaller number on the keyboard and revolving the 
crank in the opposite direction from that required for addition. 


Division is computed as a sort of continued subtraction, and is 
a complicated operation. The machine is readily worked as a 
difference engine, thus permitting its use for computing com^ 
plicated tables. 

A trial made in the U. S. Coast Survey of the relative ra- 
pidity and accuracy of the Grant calculating machine and a 
seven-place table of logarithms, in multiplying seven figures by 
seven figures and retaining seven figures in the result, showed the 
average time of multiplication with the machine as 56 seconds, 
and with logarithms 157 seconds; the number of errors in lOO 
trials, with the machine 7, with logarithms I2. A trial made 
at Sibley College showed more favorable for the machine, 
probably because the observers were not as expert with loga* 





In this chapter a statement is made of the principal for- 
mulae required for the experimental work in " Strength of 
Materials." The full demonstration of these formulae is to be 
found in "Mechanics of Engineering," by I. P. Church; 
"Strength of Materials," by D. V. Wood ; " Materials of Con- 
struction," by R. H. Thurston: N. Y., J. Wiley & Sons. 

44. Object of Experiments. — ^The object of experiments 
relating to the " Strength of Materials " is to ascertain, firstly, 
the resistance of various materials to strains of different char- 
acter; secondly, the characteristics which distinguish the 
different qualities, i.e., the good from the bad ; thirdly, experi- 
mental proof of the laws deduced theoretically; fourthly, 
general laws of variation, as dependent on form, material, or 

The following methods of testing are ordinarily employed : 
(i) by tension or pulling; (2) by compression; (3) by trans- 
verse loading; (4) by torsion ; (5) by impact; (6) by repeated 
loading and unloading, or fatigue. 

45. Definitions. — Stress is the distributed force applied to 
the material ; it may be internal or external. 

Stress is of two kinds, normal or direct, and shearing or 
tangential^ the latter force acting at right angles to the first. 
A direct stress on an element is always accompanied by a 
shearing stress, which tends to move the particles at right 




angles to the line of action of the force. This is well shown in 
the simple break by tension, in which case the particles are not 
only pulled apart, but they are moved laterally, since the break 
is accompanied with an elongation of the original specimen, 
and a corresponding reduction in area of the cross-section. 

Strain is the distortion of the material due to the action of 
the force, and within the limits of elasticity is proportiona' to 
the stress. 

Each stress produces a corresponding strain. 

Elasticity is the property that most materials have of re- 
gaining their original form when the forces acting on them arc 
removed. This property is possessed only to a limited extent, 
and if the deformation or strain exceeds a certain amount, the 
material will not regain its original form. 

The critical condition beyond which the body cannot be 
strained without a permanent distortion or set is termed the 
elastic limit ; this point is gradually reached in most materials, 
and is indicated by an increase in the increment of strain due 
to a constant increment of stress. 

Rigidity or stiffness is the property by means of which 
bodies resist change of form. 

The coefficient of ultimate strength is the number of pounds 
per square inch required for rupture, and is obtained by calcu- 
lation from the known area and actual breaking-load. The ^tf- 
efficient of strength at the elastic limit is the number of pounds 
per unit of are? acting upon the material when a failing in 
strength is shown by an increased increment of distortion for 
an equal increment of load. 

The resilience is the potential energy stored in the body, 
and is the amount of work the material would do on. being re- 
lieved from a state of stress. Within the elastic limit, it is the 
work done by the force acting on the body, and is evidently 
equal at any point to the product of one half the load, into the 
distortion of the piece, this latter being the space passed 
through. The elongation is the total relative strain; it is 
usually expressed in percentage of the full length, and is 
calculated for the point of rupture. In connection with 


this should be measured the reduction of area of cross-sec- 
tion. The modulus of ttastkiiy is the ratio of the stress per 
unit of area to the deformation per unit of length. The 
modulus of rigidity is the amount of tangential stress per 
unit of area, divided by the deformation it produces, expressed 
in angular or n measure. The maximum load is usually greater 
than the load at rupture. 

The safe load must alwasrs be less than the Ipad at the 
elastic limit, and is usually taken as a certain portion of the 
ultimate or breaking load. The ratio of the breakmg-load to 
the safe load is termed ^factor of safety. 

The different kinds of stress, consequently the different 
kinds of strain produced, are : Longitudinal, divided into tension 
and compression ; Transverst;, :pto shearing and bending ; and 
Twisting or Torsional. 

46. Strain-diagrmms are diagrams which show the reku 
tions which the increments of strain bear to the stress. If the 
strain-diagrams of several specimens be drawn on the same 
sheet, the relative values of stress and of strain at elastic limit 
and at breaking can be determined by inspection. Within 
the elastic limit the diagram will be a straight line. 

Strain-diagrams are constructed (see Article 19, p. 20) by lay- 
ing off the strain on the horizontal axis to a scale that is readily 
apparent to the eye, and the corresponding loads as ordinates 
to a convenient scale, as 3000 or 5000 pounds per inch : a curve 
drawn through the extremities of these various ordinates will 
be the strain-diagram. When no part is perfectly elastic, as in 
cast-iron or rubber, no portion of the curve will be straight. 

The general form of the strain-diagram, as drawn auto- 
graphically, is shown in Fig. 27. In this diagram the strain is 
represented by distances parallel to OX, the stress as a certain 
number of pounds per inch parallel to OY. For a short dis- 
tance from Oto A the diagram is a straight line, showing that 
the increments of strain and stress are uniform ; at A there is 
a sudden increase in the strain, without a marked increase in 
load, shown by the curved line A to B. The point A is often 
spoken of as the yield-point. In most of the ductile materials 




this sudden increase of strain is accompanied with an apparent 
reduction of stress, as shown by the curve from B to C. This 
reverse curvature is often well marked on curves taken auto- 
matically, and is probably due to the fact that the increase in 

Fig. 97. — The Strain-diagram. 

strain Is so great that the scale-beam of the machine falls until 
the stress is increased. The curve then continues to rise, reach- 
ing its maximum position at D^ and falling soon after when 
the specimen breaks, as shown at E, 

47. Viscosity or Plasticity. — This is the term applied to 
denote the change of form or flow that results from the appli* 
cation of stress for a long time. It is the result of internal 
molecular friction, and the resistance exerted is proportioned 
to the rapidity of the change. The definition of viscosity if 
given by Maxwell (see Theory of Heat) as follows: "The vi?^ 
cosity of a substance is measured by the tangential or shearirg 


force on the unit of area of either of two horizontal planes at 
the unit of distance apart, one of which is ifixed, while the 
other moves with the unit of velocity, the qpace between being 
filled with the viscous substance." 

Let the substance be in contact with one fixed plane and 
with one plane movii^ with the velocity v ; denote the dis« 
tancc between the planes by ^. Let F be the coefficient of 
shearing-force, or the force per unit of area tending to move 
the substance parallel to either plane. Let /i be the coefficient 
^f viscosity. 

Then we have 

P'l^ (0 

If we let # s the breadth and a the length of the plane 
and R the total force acting, 



cF cR 

When C9 a^ and t each equal unity, 

> /Elsie. 

7t J? is the moving force that would generate a certain velocity 
« in the mass Jf in time A R will equal Jfv -f- /; from which 


afl of which quantities may be determined by experiment 




48. Notation. — The notation used is the same as that in 
Church's " Mechanics of Engineering/* and is as follows : 






Load applied 

Load per square inch. . . . « . 
Moduli of tenacity 



Total elongation 

Increment of elongation. . . . 

Relative elongation 



Relative shearing distortion, 

Transverse load — total 

Transverse shear 











































Compression. Sheariof. 


Modulus of Elasticity Et Ee 

Area sq. inches F 

Length. ** / 

Factor of safety • if 

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 distrih>- 

uted, we have 

P=:FT\ (^) 

^ = ?; (3) 

e := 



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 




Resilience U = mean force X total space = J/^'A" = 
\JP"€"l = \T'e'FL But Fl equals the volume V. 

.-. £/=irV'r=i/>'V7. .... (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 

We shall have finally 

V = 2nl\ 



from which 

E— — = (7) 

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 


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 

Pc^FC^ / = J (8) 


^=2" (9) 

Resilience U,^\F'V' ^\P'e''l^\C'€''Fl. . . (11) 

The compression-strain is accompanied with a shearing- 
strain acting at right angles to the specimen equal to P sin a 
•cos Of, being a maximum when a = 45°. Hence, brittle 
materials tend to fly to pieces at that angle, leaving two pyra- 
mids with facing points. 

Lon£^ 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, = FC ^ {1 -{- /sQ. . ..... (12) 


Breaking4oad for round-ended or two-pin column, 

P. — FC'i'\i+4P^ {i^a^ 

Breaking-load for one round end and one square end or pin 
and square end. 

Value or CoimaBNTS its giybn by Rankini. 





^ in douthIs ner im- inch. ...r. «,..«.. 



I -«- 36000 


fi (abstract number) 

I -«-6400 

Notation in above Formulas. 
F«area in square inches. 
/» length in inches. 
jr<= radius of gyration. 
K^^I^F. See page 78 for values of /. 
In case the modulus of elasticity is required, Euler*s for^ 
inula should b2 ased; in this 

for round-ended columns, in which /=/"— ^, 

For a column with flat ends 



P/'=4£/^2^/"^ V'^l-h .... (13a) 

For a column with one pin or round end and the other end 

P2" = |£/7:2-^/"2, r=/-; (136) 

Euler's formula has only been approximately verified by 



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 farce 
lie in what is called the neutral axis. The curve which the 
neutral axis assumes due to the forces acting is termed the 
ttastic 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 ' tp ed the transverse shear. 
In addition to this there is a sliearii.g-force tending to move the 
fibre" 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 
Woment of Flexure or Bending-moment, which is denoted by J/. 

The internal moment of resistance is equal to pi -^ e, in 
which p equals the intensity of strain on the outermost fibre 
of the piece, / 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 = pl-i-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 which p = radius of curvature = 1 — ~ 



±£/g = Jlf, (i6) 

which is the differential equation of the elastic curve. 

To find the external moment J/, 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 ^^x- 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 

integrate. The first integration will give the value of -~ or 

the tangent of the elastic curve ; the second integration will 
give^, the ordinate to the elastic curve. 

Tht 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- j I the distance of its 

tral axis (or \x\ centre of gravity }-; (i8) 
below) ) I from that axis. 



(§ 5»- 

in which / is equal to the moment of inertia, J the total trans- 
verse shear, and &o the thickness of beam in the neutral axis. 

In the ordinary cases of shearing-forces^ such an act on 
rivets or pins, the intensity is uniform; this case is considered 

The following tables of moments of inertia, of transverse 
loads, and of external moments will be useful in working up 
t' e results of the experiments. 

Moments of Inertia 

Reciangle, width b^ depth h 

Hollow reciangle, symmetrical.... 
Triangle, width = b, height = A.. . 

Circle of radius r 

Ring of concentric circles 

Rhombus h — vertical diagonal. . . 
Square with side (^) vertical.. . . . . . 

•• (^)at45' 

Ordinary Momeoc. 

Polw MaoMDt 

rt*-«(*» f *«j 

Max. Fibre 


Formulas for Transverse Loads. 

Deflection = d. 

Maximum fibre-strain/ 

Safe load •..•••••.. 

Coefficient A" 

Relaiive sircnjflh, equal length .. 

Rcl-it:vc stiffness, equal load 

" safe load 

Modulus elasticity 

Max. shear 


With one End 
Load P-. 

Wt.of Beam 

|/V» -I- £/ 
F/e -i- / 
R'l -+- U 

PI* -^ 3^7 
/'at support 

With Uni- 
form Load. 

WU -4- 2/ 

IVle -*■ a/ 




Beams with Two 

Load/*, in 


Wt. of Beam 


A«» -*- EI 



/»/• •<- 4W/ 



8^'/ 4 /# 
ly/e + 8/ 




= i 

5 i 
■ 5 


-, 'S 










"" ^ -. 

» i % . s ^1 






^ 1 1 



' ' ^ 

! A \L 

- ■<! \ 

» w 3 " 





" " T 

- 7 'jL \h ; -vl^ , 

-,1 ' 



Htf I • 



a s a s • 





- ' Jt?t^!' 


' - '" .1 - 




:% -1 4 \ 




a » » 

i d~ = 1 iK 


- - % ' \ 



•• is! 

1 ivl> 


1 IP 




2 " ^fisaS, s 

wlila Hi III 

S 3 a = . 

SB D i 

-^a J 

' > 


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 MIC equals moment of inertia. 

Then, by mechanics, 


or, by reduction. 

K} = % (19) 

In this equation K is reckoned from the point of suspension^ 
and the moment of inertia is the moment around the point of 

The moment of inertia about a parallel axis through the 
centre of gravity, may be denoted by MK^t and we shall have 

MK; + MS^ = MIC\ 

* See Weisbach, Vol. I., page 66a. 


from which 


MK; = M{/C - 5'). 

54. Shearing - stress. — 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-T-F. (30) 

The stress produces on the molecules of the material an 
angular distortion, which is usually expressed in tt measure, or 
the linear length of the degree of distortion to a radius unity, 
and is denoted by 6, 

Let /, be the stress per square inch. 

F.^p.-i-S (21) 

E, is termed the modulus of rigidity. 

The coeflficient of shearing-strength 5 can be obtained by 
direct experiments, by using the specimen in the form of pins 
or rivets holding Hnks 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 cJ, which is expressed in tc measure. 
This has the effect also of moving any particle in the surface of 


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 or. Letting / equal the length of the specimen, e equal 
its radius, we have, neglecting functions of small angles, 

ea^lS, (22) 


S-szea-^-L........ (22a] 

But since £, = ^, -5- tf, 

£, =//-7-^a; (22*) 

from which E, , 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^ the polar moment of inertia, we will have 

Pa = (pj;) ^e, (23) 

from which 

p,^P7i.e^I^ (24) 

For a circular rod of radius r, , 

Ia = — ^, also ^ = r. 
' 2 

Let the external moment /k = J/) . Then 



The torsional resilience, or work done, will equal the aver- 
age load multiplied by the space, or 

U,-hP,^a. •^ (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 verfical axis passing 
through its point of suspension. Let / equal its length in feet, 
f its radius in feet, /p the polar moment of inertia of the swing- 
irg weight, / the time in seconds of an oscillation. Let £«= 
be the modulus of rigidity. Then 

^-^ <^ 

57. Relation of E. and Et . — Let the distortion in direc* 
tion of the stress equal €, the angular lateral distortion =s cJ, the 
lineal lateral distortion = m ; then 

tan ^45° - -J = \IL7 = ^ -»»-€, nearly. 
Sut since 6 is small, 


(45'' -^ = I -<^, nearly. 

Hence, by substituting, 

(^ = III -|- 6. 


E, = ^ and E. = ^^ 



E, € € 

Et 2d 2{fn + €)' 

In cast-iron, by experiment, Prof. Bauschinger found for 
cast-iron m = .236 ; hence for this case E, = o^ojEf. 

58. Combination of Two Stresses. Intensity of combined 
Shearifig* 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 ^ with 
the transverse section. Then, from equilibrium of forces, 

{r —p)cosd =iqs\n6y and rsinS = ^cosft 
Hence g^ ^r{r — p\ 

t3Ln 2d = 2g -T- p (27) 

r = ip± ^/ + i/' (28) 

58a. Twisting combined with Longitudinal Stress.— In 

a circular rod of radius r, , a total longitudinal force P in the 
direction of the axis gives a longitudinal normal stress 

/, = P-T- area =/ -7- 7rr^\ 

A twisting-couple M applied to the same rod gives a shearing- 
stress whose greatest intensity 

g^ = 2jHt -r- Ttr*. 

Encyc. Briiannica, art. " Strength of Materials.' 


The two together give rise to a pair of principal stresses, ^ 

*i^=*=\/©^+^ <*«>> 

59. Twisting combined with Bending.— Thb important 
practical case is realized in a crank-shaft 

Let P be the force applied to the crank-shaft ; let J? be the 
radius of the crank-shaft ; let B eiqual 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^ = PR^ and bending-moment M^ = PB. 
The stresses per unit of area on the outer fibre would be/« = 
4!/^ -^ nr^ (in which r, is the radius of the crank-shaft) from 
formulae for transverse strength, and p, = 2if, -f- nr^ from for- 
mula for torsion. 

Combining these as in equation (27), we find for the prin- 
cipal stress 

r = 2(if. ± VM,' + M;)^nr^. 
By substituting values of M^ and M^ , 

r = 2P{B ±VB' + I^)'^n r/. . • • . (30) 

The greatest shearing-stress equals 

/, = 2PVB' 4-^ -^ nr,\ (31) 

The axes of principal stresses are inclined so that 

tan2tf = Jf, -5- J/, = ^-7-^. (32) 


60. Thermodynamic Relations.'*' — Thermodynamic theory 
shows that heat is absorbed when a solid is strained bjr '\ 
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 ih? temperature were raised. As, for 
example, a spiral 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 i: stead of to expand the rubber. 
this theory the rise in temperature can be calculated for a. 
given strain. Thus let/ equal the absolute temperature of the 
body; Q the elevation of temperature produced by suddett 
specific stress/ ; let e equal the corresponding strain ; y Joulc'» 
equivalent; k the specific heat of the body under constant 
stress ; S its density. Then 

» = ^ (33> 

in which both e and/ are infinitesimal, or very small quantitieft^ 
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. Thgrnson in Philosophical Magaiine 1877^ 
Ui, page 814, ninth edition Encyc. Britannica. 

6i. Testing-machines and Methods of Testing. — The 

tcsting-macliines consist essentially of, fir^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 tlie stress caused by 
rupture of the specimen. Machines are built for applying 

tensile, compressive, transverse, and torsional stresses; they 
vary greatly in character and form ; some are adapted for 
applying more thaii one kind of stress, while others are limited 
to a single specific purpose. 

In all 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 (or 
calibrating testing-machines from time to time; the weighing 
syst«m is usually independent of the system for applying 
power, although in certain early machines a single Icvef 
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] 
weight by the ratio of the lever-arms h/a. 



The power system, when independent of the weighing sys- 
Vtem.usually consists of ahydraulic press, as showniii Fig. 31, or 
■Stiain of gears, as shown in Fig, 32. The principal advantage 
Bo( liaving the power system independent from the weighing 

system is due to the (act that under such conditions the 
' stretching of the specimen, which almost invariably takes place, 

dues not affect the accuracy of weighing. 

The shackles or clamps for holding the specimen vary with 
I the strain to be applied. The clamps for tension-tests usually 
■consist of truncated wedges which are inserted in rectangular 

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 i:^ provided with a triangle or 
V-shaced 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 firmly and accurately in 




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 belter 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 

Fio. 33 — WicKSTEED, Martens, Michaelis, Buceton. 

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 breakiDg 
was obtained from the weighing mechanism. Fig. 33 shows 
a single-lever machine much used at the present time in Eng- 
lind, in which the power is applied to the specimen at 5, and 
the amount of stress is determine 1 by the position of the jockey 
weight w, and the amount of weight on the poise R, 



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- 

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 

distances from the fulcrum. A machine of this fonn • 
manufactured at one time by Richie Brothers.* 

Third, compound-lever machines. These have been r 
used in America for the last twenty years, and are manoTr:- 
by Riehli Brothers, Olscn, and Fairbanks. In tbcKm:: 

power is usually applied by gearing; at least, mich .«i=. 

tion is generally preferred in this country, ~ 

* The forces acting ii 

hine can be ie|iTeaenMa a 




Fig* 36, shows the arrangement of levers adopted in the Fair- 
banks machine. Power is applied at F, specimen is placed at x, 
and the stress is transmitted by the various levers P^ £, and c 









Fig. 36.— Fairbanks Machink. 

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 Riehl^ machines, power being applied to the lower 
draw-head B, and the stress a 

transmitted through the speci- 
men by means of the various 
levers to the weighing- scale zv. 
In this diagram P denotes the 
position of fixed fulcrums. By 
placing the specimen between 
the lower draw- head 7? and the 
platform B/I, it may be broken 












Fig. 37.— Olskn and RibhlA. 

by compression. By providing suitable support resting on 
the platform E/i a transverse stress can be applied. 

Yo\xx\.\i^ 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' for compression. 
Machines of this kind have been built of the verj' largest 
capacity, as for instance that designed by Kellogg at Athens, 
Pa., has a capacity of 1,250,000 pounds, and at the Phoenix 


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 


Fig. 38.^Kiillocc, 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 RFy while that 

"i'i| 1 1 j ||iiii>|iiiii|ii(i 


Fig. 39.~Ths Wkrdbr, 1853. 

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 


which the stress applied to the specimen reacts. This force 
ts measured on a hydraulic gauge similar in many respects 
to the weighing apparatus of the Emery testing- machine. 

FlO. 40.— M»11.L«BI>. 

Fifth, the Emery machine. The general principle of the 
Emery testing-machine is shown in Fig, 41. Power is 
applied by means of the double-acting hydraulic press ^ 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 

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 J, 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 
diaphraf;m, which in turn causes a liquid pressure which is 
measured on the weighing-scale as before. The springs which 


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 lOO 
pounds in 100,000. 

The fulcrums for supporting the levers in the Emery test- 
ing-machine are thin plates of steel rir/idly 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 ik 
flexible side or diaphragm, which transmits the pressure to a 
similar support in contact with the weighing apparatus. The 




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 

Fig, 42 gives a perspective view of the Emery machine 
with the working parts marked the same as in the diagram. 

In this figure M is the pump for operating the hydraulic 
press, hh' the connecting piping, TT screws forming a part 
of the (rame and used for adjusting the position of the press 
for different lengths of specimens, and of sufficient strength to 
withstand the shock due to breaking; Pis the weighing-case, 
which contains a very elaborate system of weights which can 
be applied without handling, as described in detail later, 

62. Weighing Systetn. — The weighing systetnm. the pres- 
ent Englif^h machines, and in former ones built in this countrj'. 
consists of a single lever or scale-beam, along which can be 



moved a poise, and which can be connected by one or more 
levers to the test specimen. Such machines are objectionable 
principally {rom the space occupied. 

The weighing device in nearly all recent machines consists 
of a series of levers, arranged very much as in plat form -scales, 
finally ending in a graduated scale-beam over which a poise is 
made to move. The machines are usually so constructed that 
the effect of the strain on the speciipen is transmitted into 
a downward force acting on the platform, and the effect of 
a given stress is just the same as a given load on the plat> 

Thc weighing-levers usually consist of cast-iron beams car- 
rying hardened steel knife-edgt-s, which in turn rest on har- 
dened-stee! bearing plates. This is the system adopted by most 
scale-makers for their best scales. 

In the Emery testing-machines, which are especially noted 
ir their accuracy and sensitiveness, the knife-edges and bear- 
;g plates arc replaced by thin plates of steel, Uie flexibility of 
'hich permits the necessary motion of the levers. 

The weighing device should be accurate, and sufficiently sen- 
hive to detect any essential variation in the stress. The 
t of sensitiveness required must depend largely on the 
irposes of the test. An amount less than one tenth of one 
:r cent will rarely make any appreciable difference in the re- 
ll, and probably may be taken as the minimum sensitiveness 
'Deeded for ordinary testing. Means should be provided for 
talibrating tht weighing device. This can be done, in the class 
of machines under consideration, by loading the lower platform 
with standard weights and noting the corresponding readings 
of the scale-beams. Testing-machines may be ca/iiraied with a 
limited number of standard weights, by the use of a test- 
specimen, which is not to be strained beyond the elastic limit. 
The weights are successively added and removed, and strain is 
iniintained on the test-piece, equal to the reading on the cali- 
brated portion of the scale-beam. 

63. The Frame. — The frame of the machine must be 
«uf5ciently heavy and strong to withstand the shock producod 


by a weight equal to the capacity of the machine suddenly ap> 

The weighing levers must sustain all the stress or force act- 
ing on the specimL-n, without sufficient deflection to affect 
accuracy of the weighing, and the frame must be able to sus- 
tain the shoclt consequent upon the sudden removal of the 
load, due to breaking, without permanent set or deflection. 

64. Power System. — The power to strain or rupture the 
specimen is usually applied through the medium of a train of 
gears or by a hydraulic press, operated by power or hand. 
The hydraulic machine is very convenient when tlie stress is 
less than 50,000 pounds; but if there is any leakage in the 
valves, the stress will be partially relieved the instant the pump 
ceases to operate, and difficulty may be experienced in ascer- 
taining the stretch for a given load. 

65. Shackles. — The shackles or clamps for holding the 
specimen vary with the strain to b^ applied. These clamps for 
tension tests usually consist of truncated wedges which are in- 
serted in rectangular openings in the heads of the testing-ma- 
chines, and between which the specimen is placed. The inte* 
rior face of the wedges is for flat specimens plane and serrated, 
but for round or square specimens it is provided with a trian- 
gular or V-shaped groove, into which the head of the specimen 
is placed. When the strain is applied to the specimen these 
wedges are drawn closer together, exerting a pressure on the 
specimen somewhat in proportion to the strain and often in- 
jurious to its strength. In tensile testing it is essential to the 
correct determination of the strength of the specimen that the 
force shall be applied axially to the material ; in other words, it 
shall have no oblique or transverse component. This requires 
that the wedge clamps shall be parallel to the specimen, and 
that the heads which contain the clamp shall separate in a 
right line and parallel to the specimen. 

This construction is well shown in the following description 
of the clamps used in the Olsen and Riehld testing-machines. 

A plan and section of the draw-heads used with the Olsen 
machine is shown in Fig, 43. The small numbers refer to 


the same part in each view, and also in Figs. 56 to 60, so that 
any part can be easily identified ; 60, 59 is a counterbalanced 
lever used to prevent the wedges (ailing out when the strata 
is relieved ; 63, 63, is a screw connected to a plunger for a<L 
justing the space into which the wedge-clamps arc drawn. A 
lateral motion of the specimen is obtained by unscrewing on 
ontt side and screwing up simultaneously on the other side : 



this adjustment is of advantage in some instances in centring 
the specimen. For use of the other parts shown in Fig. 43, 
nee Art- 64. 

The clamps used by Richie Brothers for holding flat speci- 
mens arc shown in Fig. 44 and Fig. 46, as follows : 



Fig. 45 is a plan of wedge-clamp, with specimen in posi- 
tion; CC, curve-faced wedges; D, specimen; A, draw-head; 
and BB tension-rods. 

Fig. 46 is a sectional view of same. Fig, 44 is a view ot 
the wedge-faced clamp. The inclination o( the surfaces of the 
wedges are exaggerated in the as to distinctly set 
forth their features. 

Wedges have been made with spherical backs, and a por- 
tion of the draw-heads mounted on ball surfaces in order to 
insure axial strains. Special holders into wliich screw-threads 
have been cut have been used with success, and in manv 
instances the specimens have been fastened to the draw-head! 
by right and left threaded screws. 

66. Specifications for Government Testing-machine.— 
The large machine in use by the United States Govemtnent at 
the Watcrtown Arsenal was built by Albert H. Emery. The 
machine is not only of large capacity, but is extremely drlical^ 
and very accurate. A perspective view of the machine i^s 
shown in Fig. 28. 

The requirements of the United States Government as e>^^ 
pressed in the specifications, which were all successfully me *^ 
were as follows : 



1st. A machine with a capacity in tension or compression 
of 800,t)00 pounds, with a delicacy sufficient to accurately reg- 
ister the stress required to break a single horse-hair. 

2d, The machine should have the capacity of seizing and 
giving the necessary strains, from the minutest to the greatest, 
without a large number of special appliances, and witliout 
special adjustments for the different sizes. 

3d. The machine should be able to give the stresses and 
/eceive the shocks of recoil prodnced by rupture of the speci- 
men without injury. The recoil from the breaking of a speci- 
men which strains the machine to full cap.icity may amount 
to 800.000 pounds, instantly applied. The machine must bear 
this load in such a manner as to be sensitive to a load of a 
single pound placed upon it, without readjustment, the next 

4th. The parts of the machine to be at all times accessible. 

5th. The machine to be operated without excessive cost. 

67. Description of Emery Testing-machine. — These ma- 
chines are now constructed by VVm. Sellers & Co. of Phila- 
delphia, under a license from the Yale & Towne Mfg. Ca of 
Stamford, Conn. 

The following Jescription will serve to explain the principle 
on which the machine acts : 

The machine consists of the usual parts: i. Apparalui 
to apply the power. 2. Clamps for holding the specimen. 
3. The weighing device or scale. 

1 . The apparatus for applying power consists of a large hy- 
draulic press, which is mounted on wheels as shown in the en- 
gravings, Fig, 28 and Fig. 47, and can be moved a greater or 
less distance from the fixed head of the machine. Two laige 
screws serve to fix or hold this hydraulic press in any position 
desired, according to the length of the specimen : and when 
rupture is produced the shock is rectived at each end of these 
screws, which tend to alternately elongate and compress, and 
take all the strain from the foundation. 

2. Clamps for holding the specimen. These are peculiar to 
the Emery machine, and arc shown in Fig. 47 in section. This 



figure also sfaows a section of the fixed head of the machine, 
.and a portion of the straining-press, with elevation of the 
holder for the other cnii of the specimen. 

The clamps, numbered 1484 in Fig. 47, ire inserted between 
two movable jaws (1477), which are pressed together by a 

hydraulic press (1480), resting on the fixed support (1476), By 
this heavy lateral pressure force equal to,ocx> pounds can 
be applied to hold the specimen. The amount of this force is 
shown by gauges connected to the press cylinder, and can be 
fulated as required. 

104 EXPRKi.MEXTAL E^;CJXEEf:li\'G. [g 76. 

For the vertical machines these shackles or holders are ar- 

ranged so as lo have sufficient lateral motion to keep in the 
line of the test-piece. 

3. The weighing device. This is the especial pecvliarity of 


try machine: instead of knife-edges, thin plates oE 
used, which are flexed sufficiently to allow tlic neces- 
ion of the levers. The steel used varies from 0.004 to 

I thick, and the blades are so wide that the stress 
exceed 40,000 to 60,000 pounds per square inch, 
ja shows the form of fulcrums used for light forces 
tsted fulcrums are in tension. 

method of measuring the load is practically that o- 
Sulic press reversed, but instead of pistons, diaphragms 
Wry little motion are used. Below the diaphragm it 
diallow chamber connected by a tube to a secont 



4;haiTiber covered with a similar diaphragm, but of a different 
diameter. Any downward pressure on the first diaphragm is 
transmitted to the second, giving a motion inversely as the 
squares of the diameters. This latter motion may be farther 
increased in the same manner, with a corresponding reduction 
in pressure, or it may at once be received by the system of 
weighing levers. The total range of motion given the first 
diaphragrr, in the so-ton testing-machine is jjVnm pa" of an 
inch, but the indicating arm of the scales has a motion of y|| 
of an inch fur each pound. This increase of motion and cor- 
responding reduction of pressure 'is accomplished practically 
without friction. These parts will be well understood by Figs. 
50, 51, and 52. The diaphram with connecting pipe,/, is 
shown between the abutments EE in Fig. 50. 

Fig. 48 showsthe elevation of the vertical machine arranged 
for transverse tests. Fig. 49 shows the scale-beam and case, and 
Fig. 50 is a section of the base-frame and hydraulic supports. 
In this last figure the diaphragm, filled with liquid, is pkced 
between the frames EE. These frames are allowed the ncces 
sary but .slight vertical motion by the thin fulcrum-strips b anJ 
c, but at the same lime are held from lateral motion. The 
frame EE and diaphragms are supported by springs d, so as 
to have an initial tension acting on the test-piece. The dia- 
phragm and its enclosing rings fill the whole space between 
the frame to within 0.005 i'leh, which is the maximum amount 
of motion permitted. 

The pressure on the diaphragm between the frames EE is 
communicated by the tube /to a similar diaphragm in com- 
munication with the weighing-levers. Fig. 51 represents the 
^weighing-leve^3fo^ platform-scales. Incaseadiaphragm is used 
it 13 placed beneath the column A ; the motion of the column 
A is communicated to the scale-beams by a system of levers 
as shown. 

The scale-beam of the testing-machine is shown in Fig. 49, 
and is so arranged that by operating the handles on the out- 
side of the case the weights required to balance the load can 
be added or removed at pleasure. The device for adding the 


weights is shown in Fig. 53- o, b, c, d, e, 
which are usually gold-plated to prevent 
not in use are carried on the supports . 
pins. When needed, these supports can 
side levers, and as many weights as are 
needed are added to the weighing-poise 

68. Richie Brothers' Hydraulic 
Testing-machines. — The testing-ma- 
chines built by Riehte Brothers of Phil- 
adelphia vary greatly in principles and 
methods of construction. In the ma- 
chines built by this firm, power is ap- 
plied either by hydraulic pressure or by 
gtaring, and the weighing device con- 
sists of one or more levers working over 
steel knife-edges, as in the usual scale 

Machines have been built by this firm 
since 1876. The form of the first 
machine constructed was essentially 
that of a long weighing-beam sus- 
pended in a frame and connected by 
differential levers to the specimen, the 
power being applied by a hydraulic 
press. The later forms are more com- 
pact. The standard hydraulic machine 
as constructed by this firm is shown 
in Fig. 54. In this machine the cylin- 
der of the hydraulic press, which is 
situated directly beneath the specimen, 
is movable, and the piston is fixed. 

This motion is transmitted through 
resisted by the weighing levers at the 
ivbich are connected by rods and levei 
Two platforms connected by a frame are 
ing levers: the upper one is slotted to n 

and /are the weights, 
rusting. These when 
A and B by means of 
be lowered by the out- 

the specimen, and is 
top of the machine, 
s to the scale-frame, 
carried by the weigH- 
jccive the wedges for 



licildiiig the specimen : tht- lower one forms a plane table. The 
intermediate platform, or draw-head, can be adjusted in dif- 
ferent positions by turning the nuts on the screws shown in 
the cut. For tension-strains the specimen is placed between 
the upper and intermediate head; for compression it is placed 
between the intermediate and lower heads. An attachment is 
often added to the lower platform, so that transverse strains 
can be applied. 

The cylinder is connected by two screwed rods to the 
intermediate platform or draw-head, and when it is forcsd 

Fio. S4. — Htduitlic Ti 

downward by the operation of the pump this draw-head i» 
moved in the same direction and at the same rate. 

69. Riehl^ Power Machines. — The machines in whidi 
power is applied by gearing are now more generally used than 
hydraulic machines. Fig. 55 shows the design of geared ina> 
chine now built by Riehl^ Bros., in sizes of 50,000, loo.cxx), and 
;;oo.ocX) pounds capacity. In this machine both the gearing 
for applying the power and the levers connected with the 
weighing apparatus are near the floor and below the specimen. 
thus giving the machine great stability. The heads for holii 
ing the specimen are arranged as in the hydraulic machine, and 
power is applied to move the intermediate platform up or down 


as required. The upper head and lower platform form a part 
of the weighing system. The intermediate or draw-head may 
be moved either by friction-wheels or spur-gears at various 

speeds, which are regulated by two levers convenient to the 
operator standing near the scale-beam. 

The poise can be moved backward or forward on the Kale- 



beam, without disturbing the balance, by means of a hanci* 
wheel, opposite the fulcrum on which the scale-beam rests. 

The scale-beam can be read to minute divisions by • 
*'ernier on the poise. 

70. Olsen Testing-machine. — General i-orm. — The mar- 

chines of Tinius OUeii & Co. of Philadelphia are all operated 
by gearing, driven by hand in the machines of small capacity, 
ucd by power in those of larger capacity. 

The general form of the machine is shown in Figs. 56 and 
57, from which it is seen that the principles of conetructioa 
rfic the same as in the machine last described. 

S7''J srm-.KGTH of materials— TESTINCMACHINES. Ill 

The interniediate platform or draw-head U operated by 
foyr screws instead of by two, and there is a marked difference 
in the arrangement of the weigh ingle vers and in the gearing. 

The machine can be operated at various rates of speed in 
either direction, and is readily controlled by convenient levers. 

71. The Olsen Autographic Apparatus. — This apparatus 
iTw drawing strain-diagrams is entirely automatic, and la 
operated substantially as follows : 

The diagram is drawn on a drum (103), parallel to the scale- 
( a pencil actuated by a screw-thread cut to a fine pitch 



on the end of the rod which actuates the poise (io6). so that 
the pencil will move in a definite ratio to that of the poise. 
The drum is actuated by tiie stretch of the specimen. This 
is brought about by four finders shown in Fig. 56, and on a 
larger scale in Fig. 58 by numbers 82 and 83. These fingers, 
shown in plan in Fig. Jig, tend to separate and follow any 
motion of tlie collars (65) placed on the test-piece, as shown in 
Fig, 56; the motion of these fingers is multiplied five times, 

and connected by steel bands to the drum, 102. in such a mai*^ 
ner thai the resultant (orce only is effective to rotate the drurm.- 
The poise is moved by a friction device attached to th^ 
main power system, which is thrown into or out of gear auto— 
matically by an electric current, as required to keep the beaw^ 
floating ; the current passes through the scale-beam in opposite 
directions, according as the place of contact is above or belong 



the beam. Finally, an alarm-bell is rung whenever the scale- 
poise moves beyond its normal distance, thus calling the at- 
tention of the operator. 

Gauge-marking Deince, — A special and very ingenious ar- 
rangement, shown in Fig. 60, is used to hold the test-piece and 
mark the extreme gauge-marks in any position desired. 

72. Parts of Olsen Machine. — The following reference 
numbers to the parts of the Olsen machine will serve to show 
the construction : 

1. Entablature. 

2. Columns. 

3. Platform supporting columns. 

4. Pivots. 

5. Lower moving head. 
2.*. Sic."'* ♦^n driving-shaft. 

24. Rock-shaft operating lever shifting 


25. Hand-lever operating 24. 

26. 27. Pulleys rotating driving-shaft. 
2S, 29. Friction-clutches engaging 26 

with driving-shaft. 

30. Sleeve operating clutches. 

31. Forked lever controlling sleeve 3a 

33. Hand-lever ope.ating 3a 

34. Grooved wheel on driving-shaft. 

40. Tilting bearing. 

41. Band-wheel. 

42. Endless band. 
44- Helical spring. 

46. Fulcrum of lever X17. 

4S. Specimen under lest. 

49- Gripping jaws. 

S"-^- Projecting flanges on jaws 49. 

51. Block-slide. 

52. Grooves in 51. 

53- Slotted slide supporting 49. 

54. Opening in 53. 
55 Eye in 53. 

5^- Bolt connecting 53 and 57. 
57.' Lever to open and shut jaws. 

55. Fulcrum of 57. 
5y Counterweight. 
^' Handle of lever 57. 

61. Plungers for slides 51. 

62. Screws for 61. 

63. Screw-bolt. 

64. Collars pr clamps for caliper bear- 
ingl* I' '^^ 

7a. Guiding- block. 

73. Cam. 

74. Lever moving 87. 

75. Sliding-blocks. 

78. Polygonal prism in 75, 
82, 83. Calipers. 

85. Arm of caliper. 

86. Clamps. 

95. Cord operating recofding-cyUndei; 

96. Pulley. 

97. Lever. 

98. Fulcrum to 97, 

99. Pulley or sheave. 

100. Drum or winding-barrel of I03. 
loi. Link. 

102. Recording-cylinder. 

103. Pencil. 

104. Screw. 

105. Screws shifting 106, 

106. Poise or weight. 

III. Balancing pivot of beam. 

117. Force multiplying lever. 

1 1 8. Weighing-beam. 

iiS . Slide to small poise on liS. 

119. Link. 

144. Endless band for moving poiae* 

145. Guiding-pulleys. 

146. Grooved wheel. 




73. Thurston's Torsion Testing-machine — Both the 
breaking-strength and the modulus of rigidity can be obtained 
(rom the autographic testing-machine invented by Professor 
Thurston in 1873. 

In this machine the power is applied by a crank at one 
side, tending to rotate the specimen, the specimen being con- 
nected at the opposite end to a pendulum with a heavj' 

The resistance offered by the pendulum is the measure o( 


e force applied, since it is equal to the length of the lever- 
in into the sine of the angle ol inclination, multiplied by the 
nstant weight P. A pencil is carried in the axis of the 
ndulum produced, and at the same time is moved parallel to- 
e axis of the test-piece by a guide curved in proportion to- 
e sine of the angle of deviation of the pendulum, so that the 
ncil moves in the direction of the axis of the specimen an 
lount proportional to the sine of this angle. A drum carry- 
% a sheet of paper is moved at the same rate as the end of 
e specimen to which the power is applied. Now if the pencil 

made to trace a line, it will move a distance around the 
urn which is equal to the angle of torsion {a) expressed in 
grees or x measure, and it wilt move a distance parallel to 
e axis of the test-piece proportional to the moment of ex- 
-nal forces, Pa. 

The diagram Fig. 62, from Church's " Mechanics of En- 
leering," shows the working portions of the machine very 
■arly. In the figure Pia the pendulum, the upper end of 

>hich moves past the guide WR, and is connected by the link 
'A with the pencil A T. The diagram is drawn on a sheet of 
aper on the drum, which is rotated by the lever b. The 


drum moves through the angle a, relatively to the pendulum 
which moves through the angle ft. The test-piece is inserted 
between the pendulum and drum. 

The value of a in degrees can be found by dividing the 
distance on the diagram by the length of one degree on the 
surface of the paper on the drum, which may be found by 
measurement and calculation. 

Application of the Equations to the Strain-diagram. — For 
the breaking-load apply equation (23) of Chapter III., 

Pa=pJ^^e. (23) 

The external moment Pa equals Pr sin /?, in which P is 
the fixed weight, r the length of the pendulum, /? the angle 
made with the vertical. Hence 

Pr sin /? = pjp -5- e. 

In this equation P and r are constant, and depend upon the 
machine ; I^ and e are constant, and depend upon the test- 

sin ft is the ordinate in inches to the autographic strain- 
diagram, and can be measured ; knowing the constant,/, may 
be computed. 

/, = Pr sin fte -^ Ip. 

For the modulus of rigidity, apply equation (22a), Chapter 
III., page 72. 

E^ =p,l -i- ea = Plr sin ft -*- I^a. 

In this equation sin ft is the ordinate to the strain-diagram, and 
a the corresponding abscissa, the other quantities are constant, 
and depend on the machine or on the test-piece. 

The Resilience (see equation (25), page 83) is the area of the 
diagram within the elastic limit, expressed in absolute units. 

U = iPaa = iPr sin fta. 



^ The Helix Angle (see equation (22). page 82) S = ta-^l,v\ 

pwhidi / is the length of the specimen in inches. The elongation 

of the outer fibre can be computed by multiplying / by secant rf. 

The per cent of elongation is equal to secant tf. (Sec 6 is 

equal to the square root of 1 + tan' i5.) 

74, Machine Constants.^ Tti obtain the Constants of the 
J/dcA/nc— First, the external moment Pa. TTiis isobtained on 
the principle that it is equal to any other external moment 
which holds it in equilibrium. Swing the pendulum until its 
centre-line is horizontal; support it in this position by a strut 
resting on a pair of scales ; the product of the corrected reading 
of the scales into the distance to the axis on the arm will give 
Pa. Check this result by trialswith the strut at different points. 
Correct for friction of journal. Second, the value of the scale of 
■jordinates can be obtained by measuring the ordinate for /3 = 90° 
'and for yS = 30°, since sine 90° = i and sine 30° = ^. Third, the 
value of the scale of abscissa can be obtained by dividing the 
abscissa on the diagram by the radius of the drum including 
the paper. This may be expressed in degrees by dividing by 
tlie length of one degree. 

Constants of the Material are obtained by measuring the 
dimensions of the specimen. The values of /and e are given 
on page 78. 

Conditions of Accuracy. — In obtaining these values, the fol 
lowing conditions are assumed ; Firstly, the test-piece is exactly 
in the centre of motion of the pendulum and of the drum ; sec- 
ondly, the pencil is in line of the pendulum produced ; thirdly, 
the curve of the guides is that of the sine of the angle of devia- 
tion : and, fourthly, the specimen is held firmly from rotation 
'by the shackles or wedges, and j tt allowed longitudinal motion. 
'These constitute the adjustments of the machine, and must 
be carefully examined before each test. Any eccentricity of 
the axis ol the specimen will lead to serious error. 

63, Power Torsion-machine, — This machine is shown in 
Fig. 63a. Power is applied at various rates of speed by means 
of [he gearing shown. Tlie specimen is held by means of two 
chucks : the one on the left is rotated an amount shown by the 


graduated scale in degrees; the one on the right is prevented 
(rom rotating by a lever, so connected to the scale-beam that 
when it is balanced the reading is proportional to the torsional 
force or external moment transmitted through the specimen, 
expressed in foot-pounds, inch-pounds, or any other units 
desired. The weighing head is suspended so as to permit free 
elongation of the specimen. The chucks used have self-cen- 
tering jaws which will hold the specimen rigidly and central 
during application of the stress. 

Machines of the general class shown in the figure arc made 
in Philadelphia both by Riehl6 Brothers and Tinius Olscn, 


which arc adapted to testing of specimens of varying diameters 
and lengths. In the Richie machine shown, the adjustment i 
for specimens of various lengths is made by moving the pow^r 
head ; in the Olsen machine the adjustment i? made by mov- 
ing the weighing head and scale-beam, which are arranged in | 
a plane at right angles to the specimen. 

The graduated scale attached to the machine for angle ot 
torsion should seldom be used tor that purpose, as the specimet* 
is quite certain to slip to greater or less extent in the machirve 
and considerable error will result. 



In the Olsen machine the angle of torsion may be measured 
by clamping dogs on the specimen at each end so as to engage 
the projections, shown at 6, Fig. 63a, of the index-rings, which 
are free to move over the graduated scales of the chucks. The 
angle of torsion of the specimen, for a length represented by the 
distance between the centres of the dogs, is the angle turned 
through by the movable chuck less the sum of the angles through 

Fio. 6ja.— Ols»h ToBsios Machisb. 

which the index-rings are pushed by the dogs. Let «i = angle 
through which movable chuck is rotated, «2 = anglc through 
which index-ring on the movable chuck is pushed by the dog, 
aj=angle through which index-ring on fixed chuck is pushed by 
the dog, and a=angle of torsion. Then 
a-Oi-(a2 + a3). 
This angle is measured through short ranges by means of two 
index-arms clamped to the specimen, as showTi at c. One arm 
•"arties a pointer which plays over an arc (*/), graduated in inches, 
""hose centre of curvature is the centre of the specimen. The 
fl'^tance traversed by the pointer divided by the radius of the arc 
P^'Ci the angle of torsion in circular measure. 

The constant of the machine, or the value of the graduations 






Fig. 636. 

on the scale-beam, may be found as follows (see Fig. 636) : The 
fixed chuck is rigidly connected to link K as shown. The tor- 
sion moment {Pa) on the specimen tends to rotate the chuck and 

link as indicated by the arrow. The 
only additional forces acting on K are 
the vertical forces of strut Pi and of 
the frame through the knife-edges at 
iJ. The right end of link K is pre- 
vented from dropping down, when no 
load is on the specimen, by a strut act- 
ing upward at R (not shown in fig- 
ure). R may therefore act either 
upward or downward, depending upon the intensity of Fa, 
The weight of K may, however, be entirely neglected since the 
counterpoise of the machine may be so set that the system is in 
equilibrium with no stress on the specimen. 

With the dimensions shown, weight of poise =40 pounds, 
length between divisions on scale-beam = § inch, consider if 
as a free body. Then J(Pa)=o and i'F=o. From which 

jPa = i2Pi-f8/? and Pi=i?, 
or Pa = 2oPi (i) 

Pi acts at a lever-arm of 2 inches in the lower lever G, and P2 
acts at a lever-arm of 30 inches. Then 

2Pi=3oP2 and Pi = i5P2 (2) 

P acts on scale-beam at a lever-arm of 2 inches, and this moment 
must be balanced by moving the poise W along the distance x. 
From which 

2P2=ir.v (3) 

From (i), (2), and (3) we have 

Pa = 20 X 1 5 X 20J1;. 

Make x= i scale division = § inch. 

Pa = 4000 inch-pounds. 

Since the value of each division as marked on scale-beam fc 
200, the constant of the machine is 20. 


For an accurate determination of the angle of torsion, it 
s important that the specimen be kept straight during the 
pplication of stress, and that the angle of torsion be measured 
rom arcs or scales having the same centre as the specimen. 
The method of measuring the angle of torsion, as described 
or a specimen in the Olsen machine, is accurate and generally 

ippli cable. 

76. Impact-testing Machine. — The Drop Test — Testing by 
Impact. — This test, see Art. 105, is recommended for material 
used in machinery, railroad construction, and generally when- 
ever the material is likely to receive shocks or blows in use. 

This test is usually performed by letting a heavy weight 
fall on to the material to be tested. The Committee on Stand- 
ard Tests of the American Society of Mechanical Engineers 
recommend that the standard machine for this purpose consist 
of a gallows or framework operating a drop of twenty feet, the 
weight to be 2000 pounds, the machine to be arranged sub- 
stantially like a pile-driver. The impact machine designed by 
Mr. Heisler consists of a pendulum with a heavy bob, which 
delivers a blow on the centre of a bar securely held on two 
knife-edge supports affixed to a heavy mass of metal. This 
n^achine is especially designed for comparative tests of cast- 
ii^on; it is furnished with an arc graduated to read the vertical 
tall of the bob in feet, and a trip device for dropping the ram 
^rom any point in the arc. A paper drum can be arranged 
''^•^automatically recording the deflection of the test-pieces. 

Let W = the weight of the bob; 

// = the distance fallen through; 
P=z centre load ; 
\ = deflection. 



Wh = iPK 


77. Machines for Testing Cement. — Cement mortar can 

^•^^^^rmed into cubes, and after hardening can be tested in the 


usual testing-machines for compression ; but tensile tests ar^ 
usually required, and for this purpose a dehcate machine wilha 
■special shackles is needed. In order that the tests may gis^ 
.correct results, it is necessary that the power be applied uni- 

formly, and absolutely in the line of the axis of the specifncni 
and to make different tests comparable, the specimen, or as it 
is called, the briquette, must be always of the same shape and 
size, and made in exactly the same manner. The engraving 
(Fig. 64) shows Fairdan/ts' ^lu/omatic Cement TVj/it, in which the 
power is applied by the droppiiig of shot into the paiI/\ The 1 
specimen is held between clamps, which are regulated at the ' 


proper distance apart by the screw P. At the instant of rup. 
Ijre the scale-beam D (alls, closes a valve, and stops the flow of 
shot. In Fig. 64 M is a closed mould foi' forming a briquette, 
^Ihe mould opened for removing the briquette, To. briquette 
which has hardened, and t'one which has been broken. 

Directions. — Hang the cup F ow the end of the beam D, as 
lown in the illustration. See that the poise R is at the zero- 
lark, and balance the beam by turning the ball L. 

Place the shot in the hopper B, place the specimen in the 
EUnps NN, and adjust the hand-wheel P so that the gradu- 

iled beam ZJ will rise nearly to the stop A'. Open the automatic 
'^alve /so as to allow the shot to run slowly. Stand back and 
Icive the machine to make the test. 

When the specimen breaks, the beam D drops and closes 
Ihc valve /. Remove the cup with the shot in it, and hang 
the counterpoise-weight G in its place. Hang the cup ^ on 
the hook under the large balance-ball E, and proceed to weigh 
the shot in the ordinary way, using the poise ^on the graduated 
beam D and the weights H on the counterpoise-weight G. 
The result will show the number of pounds required to break 
the specimen. 

An automatic machine designed by Prof. A. E. Fuertes has 
ten in use a long time in the cement-testing laboratory at 


Cornell University. In this machine water is supplied flowing 
from a constant head through a small glass orifice. The fall 
of the beam consequent on the breaking of the specimen in- 
stantly slops the flow of water ; the weight of this water, mul* 
tiplied by a known constant, gives the breaking-load on the 

The Ohen Cement-tester is shown in Fig. 65. The poweri) 
applied by the hand-wheel and screw, so that it strains ibe 

briquette very slowly. The poise on the scale-beam is mov<" 1 
by turning a crank so that the beam can readily be kept flo^t* f 
ing. The peculiar method of mounting the shackles or hold' 
ers to insure an axial pull is well shown in the engraving. 

The Riehl6 cement-tester is shown in Fig. 66. The briquette J 
to be tested is placed between two shackles mounted on pivot? f 
so as to be free to turn in every direction. 

Power is applied to the specimen by the hand-wheel belo"' I 
the machine, and is measured by the reading on the scale-bearn I 
at the position of the poise. Special crushing tools, consisting I 


of a set of double platforms, which may be drawn together by 
application of the force, is furnished with this machine. The 
specimen to be crushed is placed between these platforms, and 
the power applied as for tension. 

Besides the machines described, various machines for special 
testing are manufactured ; these machines have a limited use, 
and do not merit special description in a work of this character. 


78. General Requirements of Instruments for Measur- 
ing Strains. — In the test of materials it is necessary to meas- 
ure the amount of strain or distortion of the body in order to 
compute the ductility and the modulus of elasticity. The 
ductility or percentage of ultimate deformation can often be 
obtained by measurement with ordinary scales and calipers, 
since the latter is usually a large quantity. Thus in the 
tension-test of a steel bar 8 inches long, it will increase in 
length before rupture nearly or quite 2 inches ; if in the meas- 
ure of this quantity an error equal to one fiftieth of an inch 
be made, the resulting error in ductility is only one half of 
one per cent. In the measure of deformation or strain oc- 

Fig. 67.— Thb Wedgk Scalb. 

curring within the elastic limit the case is very different, 

the deformation is v^ery small, and consequently a very sma-1 

error is sufficient to make a great percentage difference in tb»^ 


The instruments that have been used for this purpose ar"^ 

called extensomcters, and vary greatly in form and in principle 
of construction. The instrument is generally attached to th^ 
test-piece, either on one or on both sides, and the strain is al> 
tained by direct measurement with one or two micrometer- 
screws, or by the use of levers which multiply the deformation 
so that the results can be read on an ordinary scale. As a 





rule, instruments which attach to one side of the test-piece 
will give erroneous readings if the test-piece either be initially 
curved, or strained so as to draw its axis out of a right line, 
and this error may be large or small, as the conditions vary. 

The extensometers in use generally consist of some form 
of a multiplying-lever the free end of which moves over a 
scale which may or may not be provided with a vernier, a 
micrometer-screw which is used to measure the distance 
between fixed points attached to the specimen or the roller 
and mirror and also various forms of cathetometers. 

The Paine Extensometer, which is described later, is a very 
simple and admirable form of the lever micrometer. 

The Bauschinger's Roller and Mirror Extensometer, — To 
Professor Bauschinger belongs the credit of first systematically 
taking double measurements on opposite sides of a test-bar* 



- -^-^5^ 



Fig. 68. — Bauschinger's Mirror Apparatus. 

The general principle of his apparatus is shown in the annexed 
figure. It is seen to consist of two knife-edged clips, b, by 
^^'hich 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, 
^'^, which rotate in the plane of the figure as the spindles 
rotate. A clip, aa, is (*»tened to each side of the test-piece 
at the opposite extremit} and is connected by spring-pieces, 



[8 78 

with the rollers. The spring-pieces are slightly roughened by 
file, and turn the rollers by fnctional 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 v, s, and telescopes 
at e, £, the reflection of the scale will be seen in the mirror in 
looking through the telescope, and any extension of the test- 
piece wiil 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 
itrc 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. 

Strohmcyir s Roller ExteiisomdiT 
\Pas designed in iS86, and is a double- 
roller extensoraeter similar in principle 
to Kuzby's and Johnson's. The appa- 
ratus consists of a roller carrying » 
needle which is centred with respect 
F.O. (~,-Thb St-..»mrver 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. Tlic objections to this form of 
cxtensometer are due, first, to slipping of side-bars on the 
roller, and second, to the difficulty in making the roller pef 
fectly round. 

Regarding the various forms of ex ten so meters, the writef 


would say that his experience has covered the use of nearly 
ever>' 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 
icvices 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 

80. The Paine Extensometer.— This 
iiistrunient, shown in Fig. 70, operates on 
ihe principle of the bell-crank lever, tli.e long 
arm moving a vernier over a scale at right 
angles to the axis of the specimen. It reads 
bj'the scale to thousandths of an inch, and 
by means of the vernier to one ten-tliou- 
andth of an inch. Points on the instru- 
ment are fitted to indentations in one side 
ol the test-piece, and the instrument is held 
in place by spring clips. It is of historical 
importance, having been invented by Col- 
onel VV. H. Paine, and used in the tests of 
material for the Brooklyn Bridge, and also 
in the cables of the Niagara Suspension 
Bridge when, a few years since, the question 
•j'its strength was under investigation. 

8:, Buzby Hair-line Extensometer. — 
This is an extensometer in which the strain 
"s utilized to rotate a small friction-roller 
fintiKted with a graduated disk as shown in 
% 71- A projecting pin placed in the 
i*isof the graduated disk is held between 
'*o parallel bars, each of which is connected F'=- ?» 

'0 the specimen. The strain is magnified an amount propor- 


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 

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 RichW Extensometer. — The Riehl^ extensometer is 
a combination of compound levers which are attached to both 
sides of the specimen, and arranged so that one side carrier i 
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 clami' 
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 

g 82.] 7£S TJNU'MA CH/XE A CCESSOXIES. 1 29 

readings taken in the same manner as any scale and vernier, 
the scale being graduated to thousandths and the vernier to 
ten thousandths. 

JofiHSon's Bxtensomeler. — Johnson's extensometer, shown 
in Fig. 73, is a modification of the 
Slrohmeyer. 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 o[ the two readings gives the 
total elongation. 

82. Thurston's Extensometer. — 
This extensometer was designed by Prof, 
R. H. Thurston and Mr, Wni. Ktnt, 
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 sa>.i.Twi. 
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 

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 tilt same plane, and at equal distances from the axis of the 

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 
»as designed by G. C. Henning and C. A. Marshall, is shown in 
Pig' 74- It is constructed on the same general principles as the 


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 arc unhooked from the upper head 


before stress is applied to the specimen. The micrometer is 
cenntctcd to an electric bell in the same manner as tin 
Thurston extensometer. 

Hcnniug's Mirror Extensometer* — In 1896 Gus. C, Henniiig 
designed a mirror extensometer differing in several particular= 
from that of liauscliiiiger. The instrument is intended lot 
accurate measurements of the extension or compression on 
botli sides of the test-piece within the elastic limit, and is said 
to fulfil the following conditions: \a) It is applicable (or 
measures of extension or compression, {b) Readings in either 
direction, negative or positive, can be taken without interrup- 
tion or adju.stnient. {<:) 'I'ho instrument is free from changes 
of shape during the test, (i/) There is neither slip nor playot 
the working parts. 

* Sec Transactions American SoLiely Mtchanical EnginecTt, vol. XVnl. 


kbe instrument consists of two parts ; the first is a telescope 
ded with level ling-screws, mounted on a horizontal and 
vrtical axis and furnished with supports tor two linear scales, 
(hich may be arranged so that the reflection will show in 
tiirrors attached to the specimen. The second part consists of 
a (ramc 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 

''.JV-IiH Maomm 

iHa's KiTdisoumTU. 

'5 brought in contact on one side with the test-piece, and on 
the other with the spring side-bar- The elongation of the 
Uii-piece causes an angular motion of the mirror, which in 
*um causes a multiplied motion ol the reflection of the scale 
*secn from the telescope. The miirors are so arranged that 
the reflections from both scales can be seen continually and 
Viihout adjustment of the telescope, and the apparatus as a 
whole has fewer parts and is more readily adjusted than the 
Bauschingcr. It is limited to a total elongation of about &04 

inch and hence is accurate only for measurements within the 

elastic limit. 

S4. Tbe Marshall Extensometer. — This extensomctcr, 

ihoiin in Fig. 75, is the latent design of the late Mr. C. A. 

Marshall. Its principal difference from the Thurston exten- 


someter is in the convenient form of clamps, which are wc- J 1 
shown in the cut, and in the spring apparatus for steadying 
the lower part. 

The micrometer-screw used w^ith this instrument has s^ 
motion of only one inch. When the motion exceeds th^ 
range of the micrometer-screws, the movable bars BP^ B'F^ 
^ are changed in position, and a new serieis 

, ri \ , of readings taken with the micrometer 

^-pjp ^ ^ screw. To facilitate the change of posi- 

J I < 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 whicli 
Fig. 77. 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. y6) 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 atPand 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. y^^ 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. 



The Brown and Sharpe micrometer can readily be u 
[ similar collars, thus forming an exten- 
der; the accuracy of this form is 
I considerably less than those in which i 
I the micrometers are flxtd, but it 
will, however, be found with careful 
handling to give good results. 

Of the various extensometcrs de- 
scribed, the Paine, Buzby, Marshall, 
and Richie are manufactured by 
Richie Bros., Philadelphia; the 
Thurston, by Olsen of Philadelphia; 
the others, by the respective de- 

86. Combined Extensometer 
and Autographic Apparatus. — An 
cxiensomettr designed by the 
aulhor, and quite extensively used 
iVi the tests of materials in Sibley 
College, is shown in Fig. 80 in elc- 
\-alion and in Fig. 81 in plan. In 
this cxtcnsometer 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 r«, «, and m' , n' , so tliat 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, , C, , C, and C, , which are arranged 
so that a cord ad can be fastened at C, and passed down and 
around the pulley C, , thence over the guide-pulley IV. Fig. S i , 
to pulley C7, , thence over the pulley C^ , and thence to a paper 




drum. It is at once evident that any extension of the speci- 
men 55' 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 

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 diairrams, 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 


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 
slrain, 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 
iinali 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 dcflectometcrs. 

The deflectometer usually used by the author consists of a 
tight metal-frame of the same length as the test-piece, and 
irched or raised sufficiently in the centre to hold a micrometer 
aflhe 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 
tliminates 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 Richly Bros., and is 
shown, together with the method of attachment, in Fig. 82, 


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, ai' 
well as by associations of the different manufacturers. The 
general and special standard methods adopted by these asso* 
<:iations form the basis of methods described in this chapter. 

88. Form of Test-pieces. — The form of test-pieces b 
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 Araerican 
Society of Mechanical Engineers is as follows:* 

" Specimens for scientific or standard tests are to be pfC- 
pared with the greatest care and accuracy, and turned accotd- 
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 crj 
pressed in English measures, exactly 0.4, 0.6, 0.8, and 1.010(1^ 
in diameter; but for all these different diameters the angle, Mtj 

* See Vol. XI. of Transactioni. 





■tot the length, of the neck is to remain constant. Ti..j necK 
■s a cone, not a iillet connecting the shoulders and body. The 
Jength of the gauged or measured part to be 8 inches, of ths 
cylindrical part 8.8 inches. The length of the coned neck to 
4)e 3j times the diameter, increasing in diameter from the 
«)'lindrical part to ij times the cylindrical part. The shoul- 
■«lers to have a length equal to the diameter, and to be con- 
vected with a round fillet to a head, which has a diameter 
•equal to twice that of the cylinder, and a length at least I^ 
the diameter. 

Fig. i<3 shows the form of the test-piece recommended 
A>r tension ; the numbers above the fi^re give dir 


— 1 ■ ) ■ aainclirn- -tlj * — itw-l^-i-J 

- &SUchE(- 

■fniliimeters, those below in inches. For fiat test-pieces the 
*hape as shown in Fig. 84 is recommended: such specimens 



obe cut from larger pieces ; the fillets are to be accurately 
1, and the shoulders made ample to receive and hold th* 
1 of the shackles or wedges. 
Tie length for rough bars is to remain the same as for fin 
li test-pieces, but the length of specimen from the gauge* 
Ic to the nearest bolder is to be not less than the diameter 



of the test-piece if round,.or one and a half times the gifate^ 
side if flat. 

For commercial testing the standard form cannot alwajl 
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 holdiif 
devices in common use produce undesirable effects on the 
cylindrical portion o( the specimen. 

The forms of test-specimens which have been heretofore 
used arc somewliat different from the standards recommendwi. 
These forms are shown in Fig. 85, No. l to No. 5, and are u 
follows : 

I No. 1. Sqiure or Oat ter, ■ 

I rolled. 

Ho. >. ftouad bar, ti roiM. 
No. 3. Standicd ataipc fuf fUu <* 

\. Standard thjpt Idriuurh 

Fio. B5. I'ouu or SriciKBH for Tuuili StvAiiu re 

89. Test -pieces of Special Materials.— IfiJo./.- 
■ difficult material to test in tension, as the specimen is II 
to be crushed by the shackles or holders. The author 
fairly good success with specimens, made with a very I: 
bearing-surface in the shackles, of the form shown in Fig.*!*"! 

* A diicuBsIon ot the effect u( varying proportton «( teM-picce* h Kinn >* I 
TInmlon't " Test-book of Matcrimli," paKCi 3S&4. 


p^e 137 forflat 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. S4. 

Cast-iroH. — 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 Riehl6 Bros, propose a form 
of gpecimea shown in Fig. 36. .-1,5, and C, cast with an enlarged 

, the projecting portion of which,' as shown in C has 
\ Knife-edge shape. The specimen is carried in holders o- 
'lackles, A and B, which rest on knife-edges extending 
t right angles to thc^ of the specimen. This permits 
play of the specimen in either direction, and renders 
llique strains nearly impossible. 

Chain. — In the case of chain, large links are welded at the 
ids u shown in Fig. S7 ; these are passed through the heads 
I the testing-machine and held by pins. 


Hemp Rope. — A similar method is used in testing hemp 
rope, the specimen being prepared as shown in Fig. 88, 

Special hoHow 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 

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 mouldi 
and permitted to harden for some time before being tested. It 
is found that the strength is affected by the form of the sped- 

roR Cburnt. 

men, by the amount of water used, and by the method of mix- 
ing the cement. To get resii,lts which may safely be compared, 
it is necessary to have the test-specimens or briquettes oi 
exactly the same form, and pulled apart in shackles or holden 




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. 

Pio. 91. — Cbubnt Moulds and Briqubtibs. 

The form of the mould for making- the briquettes, and the 
holders or shackles generally used, are shown in Figs. 91 to 93, 


Fio. 9a. 


Fio. 03. Fif''- 04. 

Stawdard Clip and Briqubttb 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. 


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 arc 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. Lofig Specimens, — For all other purposes, especially when 
the elastic resistances are to be ascertained, specimens one indi 
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 arc 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 ])recautions must be taken 
to prevent surface-chilling and porosity. 

Test-bars of wood are to be forty inches in length, and three 
inches sfjuare in section. 

92. Torsion-test Specimens. — For standard tests, cylin- 
drical s])ccimcns with cylindrical concentric shoulders are to be 
used; the two are connected by large fillets. The specimen 



mo 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.— i'hc character of the fracture 
oflcn affords important information regarding the material. 
The structure of the fractured surface should be described as 
7oar*e 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- 

Fic «. 

■atcly 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 
ihouM be a sketch of the fractured specimen. 

Fracture occurs u.iually as the result of a gradual yielding 
if tile particles of the specimen. The strain, so long as the 
sitcss is less than the maximum load, is distributed nearly uni- 
l"fmly over the specimen, but after that point is passed the dis- 
tortion becomes nearly local ; a rapid elongation with a corrc- 
sporiciing reduction in section is manifest as affecting a small 
poniim of the specimen only. This action in materials with 
Knsible 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 


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 li 
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 ;;/ equal parts, and repre- 
sent the number of these parts in the short portion after rupture 
by s. Note two points in the long portion, A and B^ at s and 
\ni 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 

94. Strain-diagrams. — The results of measurements of 
the strain should be represented graphically by a curve 
termed a straiji-diagram. 

Strain-diagrams are drawn (see Art. 46, page 70) by taking 
the loads per square inch {p) 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 -^ 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. 





Autographic Strain-diagrams are drawn automatically^ 
on a revolving drum. In most machines the drum is revolved 
by the stietch 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 1 1 1. This apparatus is verj 
perfect in all its details, and produces a diagram similar tc 
that shown in Fig. 96. 

The ordinates on this diagram are proportional to the 
load, the abscissce 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 docs 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. 


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 witl- 
a certain amount of ductility. 

£Hr€ctwns for Tension Tests. — Examine the test-piece cai& 


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, 01 
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 ihe 
specimen between the gauge-marks into inches and half inches, 
which may be marked with a special tool, or by rubbing chalk 
CO the specimens and marking each division with a steel scratch. 

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 
ol rupture cither way, as explained in Art. 93, page t43. 

See that the tesling-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 elatitic hmit. Take one 
tenth of this as the increment of load. The Committee on 
Standard Tests, American Society of Mechanical Engineers, 
ttcommend 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 
™*ding specimens up to 1000 or 2cxx) pounds per square inch 
ihe eflcct of Initial errors, such as occur generally at the com- 
'''cnccment of each test, are lessened. The auxiliary apparatus 


adjusts itself somewhat during this period of loading, and the 
specimen assumes a true position should any slight irregularltj 

96, Attachment of Extensometer. — Attach the auxiharj' 
apparatus for measuring stretcli, 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 exactl; 
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 Htnning extensometer (see Article 83, Fig, "4, 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- 

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 teat 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 o( 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 beV 
rings announcing contact, back off barely enough to stop ring 
ing, and advance the other until the bell rings. Back off as 


before, and read both micrometers. The vertical scale and the 
micrometer head are graduated so that readings to ^^^^^^ 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 

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 oa Standard Tests, Vol. XI., Am. Society Mech. 


The maximum load is to be the highest load carried by the 

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* 
(i) 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 20CX> 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 €, on 
the scale I 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. = io,ooo lbs. per sq. in., and i div. = o.Ol 
inch for ordinates and abscissa,*, respectively. 

A blank form for the log is shown below, which is to b<. 
filled out and filed. On this log is to be entered, value of th. 


modulus of elasticity, load at elastic limit, character of rupture, 
irca of least section, and measurenients between each mark. 
made on the specimen. 

The following form is used by the author for both tension 
and compression tests : 


Kind of Test... 
Utucfiml from. . 






P 1 * 






P„M. °'-i-- 

(^iginallength io. DUmeier in. Area sq. in. 

final " in. Diameter Area " 

Form of icction Fracture: position ; character. 

Moduli: resilience ; brealcing-sirenglh 

^*d per sq. inch: elastic limil max breaking 

^uivalcnl elongalion for 8 inches inches per cent. 

Elongation Reduction area per cent. Local elongation each 

''I'f-ineb, ftom top, ist, ..; 3d ; 3d ; 4ih ; 5th ■ 

^*> ; 7tb ; 8th ; 9th ; toth ; iiih ; i2lh ..,; 

'3«li ; 14th ; i5tb ; i6ih 

The following form, from Vol. XI. 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. 



! II 

i la 

a 3 

& 'f 


i I 1 III! * 



■)»1 JO ooiiBjna 

i 1 1 1 1 i 

i K !), 7 3; ?, 



: : 1 II 1 


; 1 1 II 1 

-innii 3!iwi»iv 

i 1 1 ! 1 1 


■a™»^. JO 

pol ICUMD mojj ajni 
■3mjj joig(odjoac]uoma 

^ 11 il 11 1 |i 

: s-i. S" ^i. >i, Si 

.: 1 

1 1 1 




J ; " S 8 a * 


■^H 11 ! f 


jn»dlJoaa«isqiii»oai 1 — ■ | 




j 1 1 tU ! 

' 1 ° 

-i,;Si»i imoj. 1 = ; :: :■ r ^ r | 



; -i -1 -1 -a -s 

. 1 ,.„„„,„„, 






ad,, "I"" "ON 

i' Is 1 





Prof. G. Lanza of the Massachusetts Institute of Tech- 
Dology uses the following forms for log and report of tension- 
tests : 





Length between clamps Tested by. 

Original section 


Per tq. in. 

— •! 









Per inch. 


Fractured section Breaking-stress per sq. in. fractured section. , 

Reduction of area of cross-section Modulus of elasticity 

Ultimate extension Modulus of elastic resilience 

Cross-section at maximum load Modulus of ultimate resilience. 

Tensile limit per sq. in ....•.•••••• • . . . . 




Ungth between clamps, 

Original section, 

Elastic limit, • • . 

Breaking-load, • • • 

Fractared section, 

Reductioa of area of cross-section, . . 

l/Itimate extension, 

Breaking-stress per square inch fractured 

Modulus of elasticity, 



• • • • • • ••••••• 

• • • • 

• • • • 

• • • • 


• • • • • • 


• •••••••• 

• • • • • • •••••*•• 

• * • • • • ••••' 

section, • a • • .••••*•• 

. . • • • 

• ••*•• * 



99. Methods of Testing by Compression, i. 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 i long division = lOOO 
pounds, and abscissae I long division = o.ooi 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 wiy, except that the heads of the extensometer will 
approach instead of recede from each other ; this makes it 


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 Chy Rankine's formula, and 
compare with the usual results. 

Compute the modulus of elasticity by Euler's formula: 

(i) P/' =£/;r*-f-r« (Church," Mechanics of Materials," p. 366). 
(2) E = nP:' -r- n'l. /'' = /- V\ (3) £ = (/ - X'JP' -f. Tt'I. 

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 

Submit a strain-diagram, and follow the same general direc- 
tions as prescribed in the report for tensile strain, Article 98. 


ICO. 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 


by putting in the supporting abutments, and by arranging the 
head for such tests, or else by using the special transverse 

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 -r- 4/. (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 135), from which 
compute the coefficient of resilience and the modulus of 

Balance the scale-beam with the test-bar in position and 
the deflectometer lying on the platform. Set the pois^ 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 witb 
the micrometer at zero make contact and record zeio-reading 
md zero-load. 

Apply the load in uniform increments equal to about one 
fifth the calculated load for the elastic limit, stopping only 



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. 

Id. Form of Report. — In the report describe the ma- 
:hine, method of making test, form of cross-section, peculi- 
irities 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 : 


Form of cross-section. • • • . • 

Length between supports ins. 

On Testing-machine. 

Time hrs mins. 

Date Observers 











Composition Specific Gravity 


\estin§ -machine 

^me hrs. ••• min. 

^e ,189 Observers: I 

Wt. per cu. ft ^bs. 



[§ 101. 





Diaineter •• 


•., in. 








Max. fibre distance 



Moment of inertia 



Reduced per sq. in. 
in Outer Fibre. 

Klastic limit .••••.•• 

Majcimum. ............. ■■ 


Maximum .•••••••.•••••••.•••••••*••••• 

MoHnliifl of Hanticitv. • • •• i 

• • • •■lbs. t>er so. in 


MnHnlnit nf KfliliencC . • « . • 

ft. lbs 



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 : 

Date •! 



Span Wt. of beam 

Position of load • , 

Tested by 

Wt. of yoke, etc...* 



M icrometer-read i ngs. 



Modulus of elasticity 

Modulus of rupture (including weight of beam). 
Maximum intensity of longitudinal shear 





Date. . . . 






• • • > • 



• •••••••••••• 

^P*n, ••••••■••• 

Dimensioas, •••••••• 

Weight of beam, 

Weight of yoke, etc., • • • • • 


Modulus of elasticity, • . • . • 
Modulus of rupture (includiog weight of beamX 
Maximum intensity of longitudinal shear, . . 


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 TJ. 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 

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 p 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. 


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. 


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- 

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-diagran: 
obtained. This diagram is on a large 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 sj)ecimen, and corrections 
made to the results obtained from the diagram. 

The characteristic form of diap^ram 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 (7\0, the abscissae are develop- 
ments of the an<^le of torsion {a). The value of one inch oi 
ordinate is to be found by measuring the ordinate correspond- 
ing to a known moment of torsion, and the abscissa corrc- 

♦ See ** Mechanics of Materials," page 240, by I. P. Church. Published bl 
Wiley & Son, N. Y. 



spending 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 

Fig. 98. 

fimit, 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^ 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^rms, 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 





o o 































*s Autogra 











o • 

•="2 Q 




h I 


1 '-' 













O •'O 

si > 












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8 0^5 



2 ii o o « 

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s ". i ". Ill 

§Q SQ |q 

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s i :? i 

c . 








3 ^ 

a ^ 

•^ 2. 

C V 



























•- s 

^ c 

^ 8 

2 i 
i i 








£ <• 



* t» 

• '?! 

TS CD i 

.S i> Cjl 
U V u 

M £ E e 

o *5 g - 


Note the variation of the pencil-point between the vertical 
and the horizontal positions of the pendulum. This distance 
laid down on the Kaxis of the record-sheet corresponds to 
ihe maximum moment obtained above, whence calculate the 
value of one inch of ordinate. Calculate the length corre* 
spending to one degree on the surface of the paper drum, 
pariliel to the vV-axis. This will be the unit to be used in 
akiilating the angle of torsion. Fix the paper on the drum 
ind draw the datum-line or A'-axis. Insert the test-piece be- 
tween the centres and screw in the centre until the neck of the 
test.picce is 2Dout 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- 
wence 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 
Of yielding of frame by reference to index-arms carried by the 
test specimen. 

The record of torsion-tests, page 1 62, is a numerical example, 
obtained Erom diagrams similar to those shown in Fig. gS. 


105- Directions for Testing Cast-iron by Impact with 
Heisler's Impact Testing-machine, (See Article 76, p. 1 19,) 

Uttkod. — Take a transverse test-bar of cast-iron and place 
tt 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 



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 coeilicients. 

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: 

JQrop'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 i^f ailing mass) shall weigh looo 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 rigW 
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 ^ \ 
the anvil-block. 

e. The length of guides on the ball should be more tbaft 
twice the width between the guides, which are to be made ol 
metal; i.e., rails so placed that the ball has but a minimutft 
amount of play between them. Graphite is recommended ^* 

y. The detachment or shears must not cause the balV 
oscillate between the guides, and must be readily and f 
controllable, with the point of suspension truly above 

I - 


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- 

g. When a constant height of drop is used, an automatic 
detaching device is recommended. 

k The bearings for the test-piece are to be rigidly attached 
to the scafifold 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 

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 
percent of the work due to impact are to be discarded. 

/. For large tests a ball weighing 2CXX) pounds is to be 

q, A sliding-scale is to be attached to the frame, and in 
<uch a manner that the zero-mark can always be placed on a 
kvel with the top of the test-piece. 


107. The following comparative tests are often useful : 
1. TAf Welding-iest. — This is to be done with a hammer 
•weighing eight to ten pounds, with a given number of blows. 






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 aflfords 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. Ptinc king-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 eff'ect of repeated stresses, is a 
matter of great practical importance, and was investigated 
very extensively by Wohler. These results are discussed n. 
full in a work by Weyrauch. It is well established that the 


saking-point is lowered by a large number of applications 
stress. The proportional loads (or wrought-iron» according 
Wdhler, being as follows : Breaking-load applied once, 4 ; 
iston alternating with no stress, 2 ; tension alternating with 
mpression, i. 

Rest of materials or removal of stress in some instances 
nns to restore both strength and elasticity. 

Viscosity or the fluidity of metals under certain conditions 
also well established. 

The effect of temperature on the strength of metals has now 
^n thoroughly investigated. The investigations at the 
^atertown Arsenal show that steel and wrought-iron bars in- 
ease slightly in tensile strength as the temperature increases 
I 6cx>^ F., and then decrease in proportion to increase of 
mperature, so that the breaking coefficients at 1600^ F. lie 
.tween lo^ooo and 20,000 pounds. See U. S. Report, Test 
Metals, 1888. 

I0& Tests required for Different Material.*— In general 
le material is to be tested in such a manner as to develop 
le same strains that will be called forth in the peculiar use to 
hich it is devoted. 

The table, page 148, shows the tests that are prescribed for 
aterials for various uses, by the Committee on Standard 
ests and Methods of Testing of the American Society of 
lechanical Engineers. 

Pipes and Pipe-fittings. — ^These should be subject to an 
ternal hydraulic pressure. 

Car-wheels. — Car-wheels are usually subjected to the drop- 
St. The following method is employed by the Pennsylvania 
ailroad Company for testing cast-iron wheels : 

For each fifty wheels which have been shipped, or are 
ady to ship, one wheel is taken at random by the railroad 
mpany's inspector, either at the railroad company's shops or 
the wheel-manufacturer's, as the case may be, and subjected 
the following test: The wheel is placed flange downward 
an anvil-block weigjiing 1700 pounds, set on rubble masonry 
D feet down, and having three supports not more than five 

^ For detailed information see Proceedings Am. Soc. Testing Materials. 


Required Tat denoted bf x. 


Mucri&l tued t«r 


















Building— wrought-iron 















Copper and Eofl melals 


* Repeat in both di 

inches wide for the wheel to rest upon. This arrangement 
being effected, the wheel is struck centrally on the hubbjri 
weight of 140 pounds, fiilliiig 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 w 
more pieces, the fifty wheels are accepted. 

109. Methodsof Testing Bridge-materials.— The follow- 
ing directions arc abstracted from th« standard specjficatioitt 
adopted by bridge-builders.* 

Wrought-iron. i. Appearance. — All wrought-iron must be 
tough, ductile, fibrous, and of uniforn\ r[<iality for each class; 

* S« Handbooli published by Carnegie, Ptliw^ ♦ ">!.- P'ilrH'^ 



-aight, smooth, free from cinder pockets or injurious flaws, 
ickles, blisters, or cracks. When rolls are working at maxi« 
um thickness, poorer finish will be accepted. 

2. Manufacture. — No special process of manufacture re- 

3. Standard Test-piece. — The tensile strength, limit of elas- 
city and ductility shall be determined from a standard test- 
ece, not less than one quarter-inch in thickness, cut from a 
lU-sized bar, and planed or turned parallel ; if the cross-sec- 
on is reduced, the tangent between shoulders shall be at 
:ast twelve times its shortest dimensions, and the minimum 
rea of cross-section shall not be less than one fourth square 
ich in area and not more than one square inch. Whenever 
racticable, two opposite sides of the piece are to be left as 
ley come from the rolls. A full-sized bar if less than the re- 
uired dimensions may be used as its own test-piece. 

The ductility, or per cent of strain, is obtained by measuring 
le elongation after breaking from the point of rupture both 
ays, on an original length, ten times the least cross-section, 
r 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- 
on of the size, and to be determined by the formulae in the 
blowing table : 


Character of the Iron. 

Dsion-iroo, pins and bolts, and ) 
>iate-iron less than 8 inches wide, f 

ite-iron S to 24 inches wide 

241036 " " 

361048 •• " 

iped iron not specified above : 

" less than \ inch thick. . . . 

" over \ inch thick 

Fonnulc for Ulti- 
mate Strength. 
Pounds per sq. in. 

52000 — 




50000 — 



Elastic Limit. 

Per cent of 


at Rupture. 

Per cent.. 







In above formulae A represents area in square inches, h 
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 

6. Rivet-iron, — Rivet-iron niust 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 a>^erage. 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 


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 pn 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 

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 3^ 
inches, or by 0.03 inch if over 3J 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 


specimens, rolled at the same time as those required for the 

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 

b. Or if more than one third break in the eye, the ten- 
sile strength is within 5 per cent required by the formula 

T= 52000 -^ 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 ^ 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. 

I/ofy to bend without fracture from 90® to 12*5**. 

Co/dy to bend without fracture to the following angles: 
i-inch plate., .lengthwise 10° to 15°, crosswise 5** 
|. " "... " 20° to 25^ " 5*» to lo' 

i- " " ..• " 30°to35^ " 10** to 15' 

i- « "... " 55°to70^ " 2o^to30' 

Tests for Plate Steel.* 

I. Sfren^f A.^Stnps 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. 


2. Temper. — Strips cut lengthwise of the plate \\ 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 

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. 

I, 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 

III. 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 

*Scc Thurston's " Steam-engine," Vol. II. 


test, except that inner radius of bend is three times the 

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.) 

I. 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 be 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 arc subjected principally to compression 


or crushing stresses. The important properties are strength 
\ and durability. Stone is usually tested for compressive and 
i transverse strength, brick for compressive strength, and cement 
I and mortar for tension. 

[ 114. Testing Stones. — The specimens for compressive 
j strength are cubes of various sizes, depending principally on 
t the capacity of the testing-machine. These cubes are to be 
r nicely made with the opposite sides perfectly parallel to pro- 
ide a uniform bearing-surface. It is found that the larger 
j 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 

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, (^) 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. 



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 formi 

I. Description of stone in its geological and tnincTalogical Tctatloof. 
1. Miner's c1as9iGca:i<>n (hard, very hard, ot extremelj' hard). 
%. Texmre ti. e.. coarse-grained, fine-grained, panllel.noniultOflrtacliMd 
^ axil of drill-hole). 

4. Specific gravity of the acoae. 

5. Diameter of hole drilled. 

6. Diameter of hole and core ivhen bofio^ 
;, Straight or curve edged drills. 

8. Angle of edge of drills. 

q. Number of blows per revolution of drilL 

10. Effective weight of drill. 

11. Mean effective drnp of drill. 

II. 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 woric done dDrir>2 boring staled In meter-U» 
grams per c. m. of hole bored. (When Dsing a hallow borer the annolui 4 
Stone cut away is alone (o be considered.) 

3. Find when possible the position tn the quarry originaltf 
occupied by the specimen tested. 

4. Find out the intended use of the stone, and determine 
the character of tests largely from that. g. Dry the stone 
until no further loss of weight occurs at a temperature of 30*C 
(86° K.). and test in a dry condition. 

Make the tests for strength as described, using as large 
specimens as possibSc. 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. "Wx^ frostJest consists of: 

a. The determination of the compressive strength of satir 
rated stones, and its compaiison with that of dried pieces. 


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 

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 seal* 
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 IS*' C. (59^ F.) to 20** C. (68*^ F.). 

c. The saturated blocks are to be subjected to temperatures 
of from — 10° 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 d 
distilled water at from 59** F. to 64** F. 


II. An investigation of ivcathering qualities — stability un- 
der influences of atmospheric changes — ciiji 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 M'ilh 
previous experience in the use of similar material. Obsfivc— 

a. The effect of the stin in producing cracks and rupfjres 
in stones, 

b. The effect of the air, afld whether carbonic-acid gas t 
given off, 

c. The effect of rain and moisture. 

d. The effect of temperature. 

115. Bricks or Artificial Building-stone. — BrUk art Uttti 
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. withoot 
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, stale 
the method of testing. Whole bricks are stronger per unit of 
area than portions of bricks, and should be used when practi- 

2. It is also recommended that brick be tested for compres- 
sion in the shape of two half-bricks superimposed, united hyi 
thin layer of Portland cement, and covered on top and bottom 
with a thin layer of such paste to secure even bearing- 

3. The transverse test for brick is believed to be a valuable 
index to its building properties. Support the brick on knifp 
edges 6 inches apart, and apply the load at the centre. Com' 
pute the modulus of rupture : 

' "2 bd" 

'See Vol. XI. (Standard Method of Testing), Ttanwttaooi or ) 
.K-ciely Mrchanical Engineers, regarding Ailicles IU-118. 



('equals the centre-load, /the length, b the breadth. 
\i, 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 \\\^ 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 
Iweuty-four hours ; then completely submerge for twenty-four 
hours, dry superficially, and weigh. Determine porosity (rom 
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 sails, 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 
'Ossification, the origin of the samples, etc., etc. : also ; 

2. Statement in regard to utilisation of same. 

3. Specific gravity of the samples is to be determined. 

4. All materials used in the construction of roads, provided 
'"cyare not to be used under cover or in localities without 


frosty are to be tested for \}^t\x 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 dc 
termining the wearing qualities by an abrasion-test described 
by Prof. I. O. Baker as follows :* The abrasionA^^X.'^ are made 
by putting the bricks and a number of pieces of iron into a re- 
volving horizontal cylinder. The cylinder used by Prof. Bakei 
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 \ 
pound each, thus making a total weight of 83t|^ 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 ^^ 
peating the trial on the same piece, and not merely testing a»/» 
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 bricb 
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^ August and September 1891. 


Opinion coinciding with the results of such trial may be formed 

(a) Determination of the quantity and quality of the bitu- 
men contained therein (whether the bitun:ien be artificial or 

{p) By physical and chemical determination of the resid'je. 

(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 1 8, p. 163.) 

{d) By the determination of the wear of such test-pieces by 
abrasion or grinding trials. 

(c) 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 metliod as here given is that recommended by 
the Committee on Standard Methods of Testing at Munich in 

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 
then moistened with water become wholly or partly pulverized 
Md slaked. According to local circumstances, these are .'^old 
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 
Oust be powdered by mechanical means. 

J. Portland cements Arc products obtained by burning clayey 
tnirls or artificial mixtures of materials containing clay and Hme 
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 


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 produ'-ed from a 
proper kind of volcanic tufa, blast-furnace slag, burnt clay. 

5. Puzzuolana cements are products obtained by most cart 
lully mixing hydrates of lime, pulverized, with hydraulic fluxes 
jn 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," ?t 
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 ^\\\ 
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 

118. Method of Testing Cements. — The principal prop- 
erties which are necessary to know are : (i) 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- 



ance with the directions in the Journal of the Society of Chemical 
Industry, published Jan. 15, 1902. 

Sptcip: Gravity. — ^This is most conveniently made with Le 
Cbateliei's apparatus, which consists of a Sask (£>), Fig. 99, of 

iw cu. cm, (7.32 cubic inches) capacity, the neck of which is about 
10 cm. (7.87 inches) long; in the middle of this neck is a bulb 
(C), above and below which arc 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- 
zinc (62" Baum€ naphtha), or kerosene free from water, should 
be used in making the determination. 

The specific gravity can be determined in two ways: (i) The 
flask is filled vrith either of these liquids to the lower mark (E), 
ind 64 gr. (2.25 ounces) of powder, previously dried at 100° C. 
{212° F.) and cooled to the temperature of the liquid, is grad- 
ually introduced through the funnel (B) [the stem of which ex- 
lends 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 
^liich has displaced 20 cu. cm. 


(2) The whole quantity of the powder is introduced, and the 

ievel 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 


r. .r . Weight of cement 

Specific gravity = fr: — \ -\ — \ . 

^ ^ J Displaced volume 

The flask during the operation is kept immersed in water in 
a jar, -4, in order to avoid variations in the temperature of the 
liquid. Different trials should agree within i 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 

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 
i^hould be used for the test, the sieves having previously been 

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 pladng 


I the sieve a small quantity of large shot, of, better, some flat 
ieces of brass or copper about the size of a cent. The residue 
weighed, then placed on a No. loo sieve and the operation 
jpeated. The results should be reported to the nearest tenth 
f one per cent. 

Normal Consistency. — ^The use of a proper percentage of 
ater in mixing the cement or mortar is exceedingly important. 
To method is entirely satisfactory, but the following, which con- 
sts in the determination of the depth of penetration of a wire 
f a known diameter carrying a specified weight, is recommended 
'he apparatus recommended is the ViccU needle shown in Fig. 
x>, which is also used for determining the time of setting. This 
Dnsists of a frame, 2C, bearing a movable rod, L, with a cap, 
>, at one end, and at the other the cylinder, G, i cm. (0.39 inches) 
I diameter, the cap, rod, and cylinder weighing 300 gr. (10.58 
z.). The rod, which can be held in any desired position by a 
m-ew, Fy carries an indicator, which moves over a graduated 
cale attached to the frame, K. The paste is held by a conical 
lard-rubber ring, /, 7 cm. (2.76 inches) in diameter at the base, 
[ cm. (1.57 inches) high, resting on a glass plate, 7, 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 tht 
briquettes (but not less than 500 grams) is kneaded into a past* 
and quickly formed into a ball Tjvnth the hands, completing th* 
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 i^ 
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. 



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, 

.—Vic AT Nbbdlb. 

Time oj Setting. — ^The object of this test is to determine the 
time which elapses until the paste ceases to be fluid and plasdCi 
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 (£), Fig, too; 
this rod when bearing the cap (D) weighs 300 gr, (10.58 otV 
The needle (H), at the lower end, is 1 mm. (0,039 inch) in 


^Mieicr, Then ihe needle is carefully brought in contact with 
' ihe surface of the paste and quickly released. 

The setting is said to have commenced when the_ needle ceases 
to pass a jwinl 5 mm. (0.20 inch) above the upper surface of the 
glass plate, and is said to have tenninated 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 b materially affected by the temperature of the 
inliing water, the percentage of the water used, and the amount 
of moulding the paste receives. 

Slartdard Sand. — The committee recommend at present the 
U5e of a natural sand from Ottawa, IIL, 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 
ami 0.01 12 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 
ihan ihe crushed quartz of the same size formerly employed 
for this purpose. 

Form oj Briqiiftle.— The form of briquette recommended is 
shown in Fig, 94. It is substantially like that formerly used 
Wcepi that the comers are rounded. 

Moulds. — The moulds should be made of brass, bronze, or 
Some equally non-corrodible material, and gang moulds of the 
form ^own in Fig. 92 are recommended. They should be 
wiped with an oily cloth before using. 

119. Afixing. — .-Ml proportions 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 mking water 


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 inmiersion, 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 houis 
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 doth 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 iin- 
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 

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 


glass shelves on which to place the briquettes. Care should be 
taken to keep the air in the closet uniformly moist. 

-Mter tweoty-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. 

Ttnsile 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- 
tad should be \ inch wide, and the distance between the centre 
of contact on the same clip should be i^ inches. 

Test-pieces should be broken as soon as they are removed 
from the water, tifc load being applied uniformly at the rate 
<if about 600 pounds per minute. The average tests of the 
briquettes of each sample should be taken as the strength, ex- 
duding any results which are manifestly faulty. 

Constancy oj Volume. — ^The object is to develop these quali- 
lifs which lend to destroy the strength and durability of a cement. 
^i il is highly essential to determine such qualities at once, tests 
of this diaracter are for the most part made in a verj- short dme, 
Md are known, therefore, as accelerated tests. Failure is re- 
italcd by cracking, checking, swelling, or disintegration, or all 
uf ihese phenomena. A cement which remains perfectly sound 
is said to be of constant volume. 

Tests for constancy of volume are di%'ided into two classes: 
(i) normal tests, or those made in cither air or water main- 
lined at about 21° C. (70° F.), and (2) accelerated tests, or 
lliofc made in air, steam, or water at a temperature of 45° C. 
(115° F.) and upward. The test-pieces should be allowed to re- 
raun iwenty-four hours in moist air before immersion in water 
or iteam, or preservation in air. 

For these tests, pats, about ■j\ cm. (2.95 inches) in diameter, 
i\ cm. (0.49 inch) thick at the centre, and tapering to a thin 
fdge, should be made, upon a dean glass plate [about 10 cm. 
(j-94 inches) square], from cement paste of normal consistency. 


Normal Tesl. — ^A pat is Immersed in water maintained u 
near 21° C. (70° F.) as possible for 28 days, and obser\-cd at 
intervals. A similar pat is maintained in air at ordinary tem- 
perature and observed at mten-als. 

Accdcraud Test. — A pat is exposed in any convenient w»y 
in an atmosphere of steam, above boiling water, in a loosely 
dosed 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 Icsis, 
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 fcr 
Testing Materials, Nov. 14, 1904: 

General Condilions. — i. All cement shall be inspected. 

2. Cement may be inspected either at the place of manufacture of 0" 
the work. 

3. In order to allow ample time for inspecting and testing, the teowi 
should be stored Jn a suitable weather-tight building having the floor properir 
blocked or raised from the ground. 

4. The cement shall be stored in such a manner as to pennil easy acffss 
for proper inspection and identification of each shipment. 

5. Every facility shall be provided by the contractor and a period of « 
least twelve days allowed for the inspection and necessary tests. 

6. Cement shall be delivered in suitable packages with the btand vi 
nsuae of manufacturer plainly marked thereon. 

7. A bag of cement shall contain 94 pounds of cement neL Each bvnl 
of Portland cement shall contain 4 l>ags, and each barrel of natural awfi 
shall contain 3 bags of the above net weight. 

8. Cement failing to meet the seven-day requirements may be held »%'- 
ing the results of the Iwenly-eight-day tests before rejection. 

9. All tests shall be made in accordance with the methods proposed t? 
the Committee on Uniform Tests of Cement of the American Society ol 


Civil Engineers, presented to the Society January ii, 1903, and amended 
JiniaiT 30, 1904, with al! subsequent amendments thereto. 

10. Tbe acceptance or rejection shall be based on the following require- 

11. Natltial CEiCEST.—De^niltoH. — This term shall be applied to the 
iatW pulverised product resulting from the calcination of an argillaceous 
lirocsiooe al a icmpetaluie only sulBcient to dri\-e off the carbonic acid gas. 

Ti. 5^rei/K Gravity. — The specific gravity of the cement thoroughly 
dried u ic»° C. shall be not less that 2.8. 

ij. Fineness.— It shall leave by weight a residue of not more than 10% 
on ibe No, 100 sieve, and jo^o on the No, 200. 

!<. Time oj Setting.— \\ shall develop initial set in not less than ten minutes, 
ixA hard set in not less than thirty minutes nor more than three hours. 

15. Tensile Slraiglk.— The minimum requirvments for tensile strength 
for briquettes one inch square in cross-section shall be within the following 
liotiis, and shall show no retrogression in strength within the periods specified:* 


14 hours in moist air 50-100 lbs. 

7 days ( I day in moist air, 6 days in water) loo-ioo " 

18 davs (i day in moist air, J7 days in water) 100-300 " 


7 days (i day in moist air, 6 days in water) a5-7S " 

jS days (1 day in mobt air, 27 days in water) 75-'50 " 

16. Constancy oj Voliime. — Pats of neat cement about three indies in 
diameter, one-half inch thick at centre, tapering to a thin edge, shall be kept 
in moisl air for a period of twenly-fours hours. 

(aj 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 pals are observed at intervals for at least 38 days, and, to 
utisfactorily pass the tests, should remain &rm and hard and show no signs 
ol distortion, checking, cracking, or disintegrating. 

t8. Portland Cement.— De^nifwn.— This term is applied lo the finely 
pulverised product resulting from the calcination to incipient fusion of an 
intimale miiture o( properly proportioned argillaceous and calcatvous mate- 

• For eiample, the mmimum rcquiremcnf for the Iwcmy-four-hour Qtat- cement 
tot tbould t>e some specified value within the limits of 30 and loo pounds, and 
U on for each period staled. 


rials, and to which no addition greater than 3% has been made subsequent 
to calcination. 

19. Specific Gravity. — ^The specific gravity of the cement, thoiougfalf 
dried at 100° 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 
mmutes, 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.** 


Age. Strength. 

24 hours in moist air 150-200 Vbi, 

7 days (i day in moist air, 6 days in water) 450-550 " 

28 days (i day in moist air, 27 days in water) 55o~65o " 


7 days (i day in moist air, 6 days in water) 150-200 ** 

28 days (i day in moist air, 27 days in water) 200-300 " 

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. 

(6) 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- 

25. Sulphuric Acid and Magnesia. — The cement shall not contain more 
than 1.75% of anhydrous sulphuric acid (SO3), 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. 



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 
Ae columns: No.; Time of Testing; Weight of Water; Ten; 
s:le Strength ; and Remarks. 

Prof. Iwau^a of Boston requires a report of the following 



^'*<3ftest« ,• •• 

I^ate of mixing 

No. of days sei, ^ 

Manner of setung <tn jJr or Ui water), . • 
Kind of cement, ••«•••••* 
Brand, •••••%•••••• 

• • 

• • 

• • 

• • 

Mixture (by wt.), jtf 

Breaking-strength per sq. in. (tensionX 

Crushing* load (2-10. cnbeX .... 



• • 

• • 

* • • • • 

• •*•.*••••••• 

• • • 

• . • 



• *••**..• 

• • 



• . • < 


*.••...*... ...I 

The cement-testing laboratory of Berlin, which has perhaps 

the best reputation for this line of work, makes observations as 

sWn 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 : 




^ i „ C S ^ 


nn M^ = ^ u 

; ^ , s s . : 5 ■ . 





8 \1\ : S K R ■« 



£■ 5 i if : s, a -e. s 




"^^^■S is^ffR 








« a a » a a A a « . 






>ft _ ■ „ « " c o o o - 








SK5S E.^ 




= 1? 




d „ - • • . o . . 

■a HUMS JO ™!i 

^. ^ t, , . fif . : 1 , 



tit^t s 7 % aiirc 


1.fcSS.^ K,S,1i,^^»- 

■wn "J )i«i»jtt 

r=I*?=l Ml ?5l»M?a*? ^ 


-;<-<aoaQ ;|as 





121. Coefficients of Strength. — It is desirable to know in 
dvance of the test the probable load the material under in- 
estigation will safely bear, in order that increments of stress 
lay be so proportioned as to make a reasonable number of 
bservations. It is also often desirable to know how the 
isults obtained compare with the standard values for the 
laterial under investigation. To provide this information a 
rief statement of the results of various tests are tabulated in 
he Appendix. These results are mainly obtained from " Ma- 
erials of Construction," by R. H. Thurston (3 vols.; N. Y., 
Viley & Son); and from "Applied Mechanics," by Prof. G. 
.anza (N. Y., J. Wiley & Son) ; and ** Materials of Engineer 
ig," by Prof. W. H. Burr (N. Y., J. Wiley & Son). These 
Doks will be found of great value for reference in the testing- 


122. Friction. — This subject is of great importance to oh 
gineers, since in some instances it causes loss of useful worlc, 
and in other instances it is utilized in transmission of power. 
The subject is intimately connected with that of measurement 
of power by dynamometers, treated in Chapter VII. ; in con- 
nection with these two chapters, the student is advised to read 
** Friction and Lost Work in Machinery and Mill-work," by R. 
H. Thurston ; N. Y., J. Wiley & Sons. 

Definitions. — Frictiony denoted by F, is the resistance to 
motion offered by the surfaces of bodies in contact in a direc- 
tion parallel to those surfaces. 

The fiormal force y denoted by Ry is the force acting perpen- 
dicular to the surfaces, tending to press them together. 

The coefficient of friction, f is the ratio of the friction, is to 
the normal force, R ; that \Syf^=F-^R. 

The total pressure y /*, is the resultant of the normal pressure, 
Ry and of the friction, Fy and its obliquity or inclination to the 
common perpendicular of the surfaces is the angle of rtpou^ , 
ox friction y whose tangent is the coefficient of friction. ! 

The angle of repose or friction y 0, is the inclination at which 
a body would start if resting on an Inclined plane. It is easyto 
show* that for that condition, if Wis the weight of thcbodyi 

Wcos(t>'=R\ also, fFsin0 = /^; 

* See Mechanics, by I. P. Church; p. 164. 




and since /*= F-^ i?. 

'^ IF cos 

It has been shown by experiment that for tliding fricium 
-(i) the coefficient / is independent of ^; (2) it is greater at the 
instant of starting than after it is in motion ; (3) it is indepencV 
«nt of the area of rubbing surfaces ; (4) it is diminished by 
lubrication ; (5) it is independent of velocity. 

223. Classification and Notation.— The subject of friction 
is naturally divided into the following sub-heads, all of which 
are intimately connected with methods of lubrication : 

A. Friction efrest^ occurring when a body is about to start. 
It is the resistance to change of position. 

R Friction of motion^ occurring during uniform motion, and 
being less than the friction of rest. 

The second kind, or friction of motion, is of principal im« 
portance, and consists of — 

1. Sliding friction. 

a. Bodies sliding on a plane. 

b. Axles or journals rolling in boxes. 

c. Pivots turning on a plane step. 

2. Rolling friction. 

a. One body rolling over a plane. 

b. One body rolling over another. 
124. Formulae and Notation. 

<i s angle of inclination of plane; 
^ s angle of friction ; 
A =^ arc of contact on journal; 
^= inclination of force with plane; 
^= normal force on a plane; 
/= coefficient of friction; 

r = radios of journal; 
/ = length of journal; 
a = space passed through; 
/ •*= intensity of pressure per sq. in.; 
P = total pressure; 
IV = weight of the body. 

The most important formulae relating to friction 
tabulated as follows : 

can be 






Force of friction ............ 


















fWz=zW\a.n a = frtan 0. 
Tan a = ian 0= f' ff < — i^ -1- ^. 
W (sin a ± / cos a) -i- (cos /5 ±/ 
sin E), 


Coefficient of friction ...••..•• 


Obliaue force. .•....•• 


F orce of friction 


/A* = «^sin9)s=/fr-f- Vi+Z*. 


ig Journal. 

Square of reaction of bearing. 
Weight on journal (squared) . . 
Moment of friction 

H^ •- F* = H^{i - sin« 0) = W^ 

cos' (f>, 
A^« + /•* = N\l +/») =r F\l +/) 

Fr = tVr sin 4> =flVr -¥- fi -f /». 
War sin = 2nnrlV sin 4> s 
27CnrfiV-¥- f'i+/«. 

Work of friction per minute. . . 





•— » 






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 

/ plr cos BdB. 

p -*- cos 0. 

p'lr 1 COS* 0^ as LSTflr. 

0.64^ COS 0-#-/r. 
0.64 ^-*-/r. 

0.64 PV r cos 0^0 as 1.27 fr. 

/P'PV=z 1. 27/lV. 

1. 27/ AT (space). 

P'/r =z 1.27/ IVr. 

Ma = 1.27/ IVr = 2,S4X/nrlV, 

Moment of friction 

Work of friction per minute . . 


Maximum pressure per sq. inch 
Total oressure 

IV -^ 2/r. 
p'l7tr = \itW= 1.57^. 

P'/r = j.i7/Wr. 

Ma = i.57«//f^r = ^nflVm. 

Uniform p 
ure on Joi 

Total force of friction 

Moment of friciion. 

Work of friction per minute. . . 

125- Friction of Journals in V or Triangular Bearings. 

— Force of friction F= P cos sin -r- cos or, in which P 
equals the force transmitted through the shaft. When co«? 
0= i,/^=/^sin 0-T- cos ^. 

126. Friction of Pivots on Fiat Rotating Surfaces - 
Intensity of pressure =/; total pressure = P. Moment o" 


iction, M=ifPr. Work of friction, U=\nnfPr. For a 
mical pivot, M = |//V -i- sin or. a = i angle of cone. 

For Friction on a Flat Collar. — Moment of friction, JIf = 
r/3(r•-r^-^(r*— r^ ; r= radius of collar ; r's radius of shaft 
1 which it is fitted. 

127. Friction of Teeth— RoUing: Prictiou.— Work lost in 
unit of time, U^=^nFPs^ in which s equals the sliding or slip- 
!ng; IT, number of teeth; other terms as before. For in 
>lute teeth, in which C, = length of arc of approach, C. that 
: arc of recess, 9 the obliquity of action, r, and r, respective 
itch-radii, we have for involute teeth 

U= nfPs ^ nfP{Q + o(^^ + ~) + 2 cos ft 

his is nearly accurate for any teeth. (See article ''Me* 
lanics," Encyc. Briiannica.) 

128. Friction of Cords and Belts— SlidUig Friction.— 
^ 7, be the tension on driving side of belt, 7. on the loose 
de, T the tension at any part of the arc of contact ; let <^ be 
le length of the arc of contact divided by the radius, i.e., ex* 
ressed in circular measure ; let c equal the ratio of the arc of 
ontact to the entire circumference ; let d equal the number of 
egrees in the arc of contact, c the base of the Napierian 
>garithms = 2.71828, m the modulus of the common loga- 
thms = 0434295 ; let F equal the force of friction. 

nr d nd 

_ d e 

360 2n ^ ' 

«/=-— = 360c (0 

lie tension at any point, dT^ is equal to the resistance TfdB. 


dT^ Tfdd, id' 

fd9 = Y' 



This integrated between limits T, and T, gives 

fB = log. Y= — (common) log ^^ ; . , 

. . M 


^ = e^= lO/*- = lo '»-"= 10'^'" = B, . 

■ . W 

l?rom the nature of the stress, 



,; '• <" 

T " 
■=: = the number corresponding f" .He'iogan'thm 

which t 


equal fOm, or "^^g—. or 2njcm, 

Substituting numerical values, 

fem = 0.4,14/^, —^ = Q.007S^M and 2ii/cm = 


From equations {/), 

common log ( =^1 = O4.34/I? ss 2.y2Sifs, 

By solving equations (/) and Cf), 


. . (« 

^ --^^- 

. . (« 

^^ 129. Friction of Fluids (!) 13 independent of 


^2) proportional to area of surface; (3) proportional 

to square 

of velocity for moderate and high speeds and to velocity fo' 

low speeds ; (4) is independent of the nature of the 


(5) is proportional to the density of the fluid, and is 

related to 


The resistance to relative motion in case of fluid frictiM 1. 

R=/AV = 2gh/A =fhwA; 



^^=Rs = RVt^fAJrt=fAkwVL 

ve formulae R = resistance of friction, A = areft 

= velocity of slipping, k -=. head correspondii^ 

= weight, f Ihe reastance per unit of area of 

^ coefficient of liquid friction, f = -^^. 

*. ^ and density of fluids do not affect to any s^ipreck 
« the retardation by friction in the rate of flow, but 

^fA influence 'Apqp the total expenditures of energy. 

'.or internal friction also exists. 
<4iibricated Surfaces. — Lubricated surfaces are no 
>be considered as solid surfaces, wholly or partially 

■ by a fluid, and the friction will vary, with different 

Ik from that of liquid friction to that of sliding fric* 

|cen solids. Dr. Thurston * gives the following laws, 

le to perfect lubrication only: 

le coefficient of friction is inversely as the intensity of 

lure, and the resistance is independent of the pressure. 

le coefficient varies with the square of the speed. 

lie resistance varies directly as the area of journal and 

lie friction is reduced as temperature rises, and as the 
' of the lubricant is thus decreased. 
!Ct lubrication is not possible, and consequently the 
ireming the actual cases are likely to be very different 
e above. The coefficient of friction in any practical 
likely to be made up of the sum of two components, 
d fluid friction. 


Determinations required. — The following determtna- 
j required in a complete test of lubricants : 
tie composition, and detection of adulteration. 
[le measurement of density. 

* Sec Friction and Lost Work, by Thurston. 


3. The determination of viscosity. 

4. The detection of tendency to gum. 

5. The determination of temperatures of decompositiont 
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 



9. The determination of its condition as to grit and foreigfi 

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 

133. Density of Oils. — The density or specific gravity is 
usually obtained with a hydrometer (see Fig. 10 1) adapted (or 
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 ifl 
pure water; the five-degree mark by immersing in a 
five-per-cent solution ; the ten-degree mark in a ten* 
Fig. ioi. per-ceut solution ; etc. For liquids lighter than 

Hydrometer. * . 

water the zero-mark is obtamed by immersing in a 
ten-per-ccnt solution of brine ; the ten-degree mark by inw 
mersing in pure water. After obtaining the length of a 
degree the stem is graduated by measurement. 

* Sec Friction and Lost Work, by R. H. Thurston. 


rhe density may be found by obtaining the loss of 
rht of the same body in oil and in distilled water. The 
> of loss of weights will be the density compared with 

[t may also be obtained by weighing a given volume on a 
of chemical scales. The density of animal oils varies from 
to .89; sperm-oil at 39^ F. has a density of .8813 to .88 IS ; 
:-seed oil has a density of .9168; lard-oil (winter) has a 
sity of .9175 ; cotton-seed oil a density of .9224 to .9231 for 
inary, and of .9128 for white winter; linseed-oil» raw, has a 
sity of -9299; castor-oil» pure cold-pressed, a density of 

134. Method of finding Density.— A. With Hydrometer 
mnometer^ and Hydrometer Cylinder. 

Method. — I. Clean the cylinder thoroughly, using benzine 
first with distilled water. Set the whole in a water-jacket, 
I bring the temperature to 60*^ F. Obtain the reading of the 
Irometer in the distilled water and determine its error. 
2. Clean out the cylinder, dry it thoroughly, and fill with 
oil to be tested ; heat in a water-jacket to a temperature of 
P., and obtain reading of hydrometer ; also obtain reading, 
:emperatures of 40**, 80**, 100°, 125**, and 150°, and plot a 
/e showing relation of temperature and corrected hydrome- 

Reduce hydrometer-readings to corresponding specific 
cities, by table given in Appendix. 

B. Weigh on a chemical balance the same volume of dis- 
ci water at 60** F., and of the oil at the same temperature; 
compute the specific gravity. 

r. Weigh the same metallic body by suspending from the 
om of a scale-pan of a balance: i. In air; 2. In water; 3. 
he oil at the required temperature. Carefully clean the 
r with benzine after immersing in the oil. The ratio of the 
of weight in oil to that in water will be the density. 
35. Viscosity. — Viscosity of oil is closely related but not 
ortional to its density. It is also closely related, and in 
\f cases it is inversely proportional, to its lubricating prop- 



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 sameastliox 
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 acceptti 
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 noiiit 
while maintained at a constant 
or constantly diminishing h«d 
and constant temperature, J 
comparison to be made witl 
water or with some well-kno»ii 

. as sperm, lard, > 

■ rape- 


under the same conditions oi 
pressure and temperature. 

136. Viscosimeter.— A pi- 
pette surrounded by a naia- 
jacket, in which the water can 
be heated by an auxiliary linip 
and maintained at anydesif™ 
temperature, is generally usw 
as a viscosimeter. Fig. 
shows the usual arrangemc" 
for this test. E is the heal« 
for the jacket-water. BB ll" 
Jacket, v4 the pipette. C a thermometer for determining l^* 
temperature of the jacket-water. The oil is usually allowed ''' 
run partially out from the pipette, in which case the lirii 
diminishes. Time for the whole run is noted with a stop-«aicti 





In the oil-tests made by the Pennsylvania R. R. Co. the 
pipette is of special (orm, holding 100 c.c. between two marks, 
-one drawn on the stem, the other some distance from ih: end 
of the discharge-nozzle. 

137. Tagliabue's Viscosimeten — In Taghabue's viscosim- 
eler, shown in Figs. I03 and 104, the oil is 
supplied in a basin C, and trickles dovvn- 
iiard through a metal coil, being dis- 
diirged at the faucet on the side into a 
vessel holding 50 c.c. The oil is main- 
tained at any desired temperature by 
healing the water in the vessel B sur- 
rounding the coil ; cold water is supplied 
from the vessel A. as required to main- 
Win 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 
ssme oil, even at the same temperature, 
isnoialways the same, — which Is probably ' iiMETm. 

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 Chic^o 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- 
lure of the discharged oil is measured near the point of dis- 

139. Perkins' Viscosimeter. — The Perkins Viscosimeter 
onsists of a cylindrical vessel of glass, surrounded by a water or 
il bath, and fitted with a piston and rod of glass. The edges 
f this piston are rounded, so as not to be caught by a slight 
igularity of motion. The diameter is one-thousandth of an 


inch less than that o( the cylinder. In practice the eylinderis | 
filled nearly full of the oil to be tested, and the piston inserted. ' 

The time required for the piston to sink a certain distance tnlo 
the oil is taken as the measure of the viscosity.* 

140. Stillman's Viscosimeter. — Prof. Thomas B. StiUmjn 
of Stevens Institute uses a conical vessel of copper, 6f incha 
in length and ij inches greatest diameter, surrounded bya 
water-bath, and connected to a small branch tube of glass- 
(vhich is graduated in cubic centimeters; the time taken foi 
25 c.c, to flow through a bottom orifice -^ 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 anil 
uniform standard. The temperature of the oil is taken at 
about the centre of the viscosimeter. 

Z41. Viscosimeter with Constant Head A form o( 

viscosimeter wiiich 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. Demon, Vol. IX., Tiaiisactjuns of Am. Sociely A 
Mccbankal Engineers. 




shown in the next figure. It is simple in form and can be 
-y readily cleaned. It is provided with a jacket, and oils 
ty be tested at any temperature. This instrument is now 
t principal standard used in the 
>Iey College Laboratories. 
Description. — A is a cup similar in 
nstruction to that of the kerosene 
;ervoir of a students' lamp, with a 
pacity of about 125 c.c, and is sur- 
unded with a jacket A in which may 
\ placed insulating materials to main- 
in a constant temperature while the 
1 is flowing; C is a thermometer-cup, 
) the bottom of which is secured a 
nail cap containing the orifice F ; N 
i a channel connecting chamber con- 
lining A with C; B is one of four 
mall tubes which admit air to the in- 
erior of the cup A and thus maintain 
tmospheric pressure on oil in it; this 
ction secures a constant level of the 
urface of the oil in the cup C and 
he surrounding space, at the height of the lower opening 
n the tube B, // is a valve to retain oil in A while placing 
t into D. M and N are brackets serving as guides for valve- 
tern K. 

The mechanism Z,, G, G^ is a device for opening and 
losing the orifice F readily, and is held in a closed position 
»y spring catch L, 

The instrument is supported by three legs about eight 
iches in length. 

Operation, — Withdraw cup A, fill it in an inverted posi- 
on with the oil, hold valve H on its seat while reinserting 
le cup into its former place as seen in figure, in which latter 
aeration the valve H is raised and the oil allowed to flow 
It of A until chambers N and C are filled a little above 

Fig. 105.— Viscosimbtsk. 


lower opening of tube B. A beaker graduated in cc.'s, of 
capacity of about no c.c, is placed under /^; L is released 
and G allowed to drop, permitting oil to flow through Ffreely 
into the beaker. When oil in C falls below the bottom of 
tube By 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 agaiin. This 
action continues throughout entire run, intermittently but sc 
rapidly that a constant head is maintained at /^ 

In ^T 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, 
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 ^ 
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 wth 
this instrument, the time of flow of 100 c.c. only need b^ 
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 frustutn 
of a cone, having dimensions as follows: bottom diametci 
1.25 inches, top diameter 1.95 inches, depth 6 inches. The 



2S place through a sharp-edged orifice in the centre- 
3ttom ^ inch in diameter. The whole height is 6^^ 

The instrument when made of copper requires a. 
•gauge, showing the height of the oil in the viscosi- 

This should be connected to the viscosimeter 3 
om the bottom. The time for the flow of 100 c.c. 

as the measure of the viscosity, during which time 
d changes from 6 to about 3.5 inches, the area of 

surface diminishes at almost exactly the rate of 

of velocity of flow, so that the fall of level is very 

comparative number of vibrations of a pendulum 
\ freely in the air, and when immersed in an oil dur- 
iven time, is also said to afford a valuable means of 
ling the viscosity. 

Viscosity Determinations of Oil, by Prof. Thomas 




ist run 
2d run. 

d oil — winter. 





Time of Flow in Seconds of 95 
c.c. through Orifice as explained. 


50° C 


150* c. 

68«* F. 

122* F. 

212« F. 













































with water 

at ao» C. 

(68« F.). 






Method of measuring Viscosity. — Apparatus. Stop- 
id viscosimeter. Fill the jacket of the viscosimeter 
er and arrange for the maintenance of the same at any 
remperature. This is most conveniently done by cir- 
from a water-bath. Fill the viscosimeter with the oil 


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 disciiarge a given amount. Make determinations 
at 60°, 100°, 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 oilsven' 

Methods of Testing, — NasjnytKs 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 eup. — In this case the oil to be tester 
if. placed in an open cup of watch-glass form, which rests 0^* 1 
.iand-bath. The cup is so arranged that a thermometer ^^ 
be kept in it. Heat is applied to the sand-bath, and as tVic° 


Komes heated a lighted taper or match is passed at intervals 
f a few seconds over the surface of the oil, and at a distance 

>f about one half-inch from it. At the instant of flashing the 

emperature of the water-bath is noted, which is the tempera- 

ure of the " flash-point." 

Fig, io6showsTagltabue's form of the open cup, in which 

■at is applied by a spirit-lamp to a water or sand bath sur- 

nunding the cup containing the oil. 

The method of applying the match is found to a have great 

nfluence on the temperature of the flash-point, and should be 

iistinctly stated in each case. When the vapor is heavier than 

Tva. loS.— Opbn Cuf. fr 

lower flash-point will be shown by holding 

|l the cup. 

Secondly. With the closed oilcup. — Fig. 107 is a view of Tag- 
lue's closed cup for obtaining the flash-point ; in this instru- 
nt the oil is heated by a sand-bath above a lamp. The 

^ennometcr gives the temperature of the oil, and the match 


applied from time to time at the orifice rf, 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° 
a quarter of an hour. At intervals of half a minute after a 
temperature of 100° 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- 

145. Method of Determining the Burning-point- The 
burning'pomt is determined by heating the oil to such a tern* 
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. 




147. Cold Tests. — Cold tests are made to determine the 
lavior of oils and greases at low temperatures. The method 
test is to expose the sample while in a wide-mouthed 
tie or test-tube to the action of a freezing mixture, which 
rounds the oil to be tested. Freezing mixtures may be 
de with ice and common salt, with ice alone, or with 15 
ts of Glauber's salts, above which is \ mixture of 5 parts 
riatic add and S parts of sold water. The temperature is 
d from a thermometer immersed in the oil. The melting- 
ni is to be found by first freezing, then melting. 
Tagliabue has a special apparatus for the cold test of oils 
(Wn in section in Fig. 108. The oil is placed in the glass 

ssel, which is surrounded with a freezing mixture. Thel 
iss containing the oil can be rocked backward and forwardj^ 
insure more thorough freezing, A thermometer i 
the oil and another in the surrounding air-chamber; the 
is frozen, then permitted to melt, and the temperature 



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 b\ 
3 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- 

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 mdiy be made by ob 
serving the effects on blue litmus-paper; or better by th« (oi 
lowing method described by Dr. C. B. Dudley : Have ready (l) 


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 J cubic centi- 
meters exactly neutralize 5 c.c. of a solution of sulphuric acid 
and water, containing 40 milligrams H,SO^ 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. I, 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. 


151. Oil-testing Machines. — Measurements of the coefficienU 
of frictioji are made on oil-testing machines, of which various 
^ornis have been built. These machines are all species o. 
dynamometers, which provide (i) means of measuring the total 
^vork received and that delivered, the difference being the work 
^f friction ; or (2) means of measuring the work of friction 
directly. Machines of the latter class are the ones commonly 
^rnployed for this especial purpose. 

Rankine's Oil-testing Machine, — Rankine describes two 
^orms of apparatus for testing the lubricating properties of oil 
^nd 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 coefficieii 
of friction determined by its deviation from a vertical. In this 
machine the axle was provided with reversing-gears, so that it 


-could be driven first in one direction and then in the opposite. 
With this class o( 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 hsM 
the product of the force W into the arm R sin ^ equal to tlu 
moment o£ resistance Fr. That is. 

Fr = WR s 


f_F_ lyRsi tup 
^ P Pr ~' 

II. Dynamic or Kinetic Apparatus. — In this case a loose 
f)y-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 th* 
normal. The driving-power is then disengaged, and thefiy 
disk rotates on the stationary axis until it comes to resL Th* 
coefficient of friction is obtained by measuring the retardation 
in a given time. Thus, let W equal the weight of the fly- 
wheel, i its radius of gyration, so that W)^ ~r g equals its 
moment of inertia. Let w equal number of revolutions at 
beginning, and n' at end of period /. Then the retardation lo 
-angular velocity per second is 

2?r(« — «') -«- /; 

the moment producing retardation, 

M = 

2ff(» — n') 


If we neglect the resistance of the air, this must equal tl* 
moment of friction /JFr. 
Equating these values, 

^- gt'r *^' 


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 
niichine permits variation in speed and in pressure on the 
juumal: it also affords means of supplying oil at any time, of 
fciiiing the pressure on the journal, and the friction on grad- 
vated scales attached to the instrument. 

This machine, as shown in the above cuts, Figs. 109 and 1 10, 
tonsists of a cone of pulleys, C, for various speeds carried be- 
tween two bearings, B, 0, and connected to an overhanging 
**is, F\ on this overhanging part is a pendulum, H, with 
plumber-block in which the axis is free to turn ; the pendulum 
"s supported by brasses which are adjustable and which may 
■J* set to exert any given pressure by means of an adjusting 
*trew, A"', acting on a coiled spring within the penduljm. 
The pressure so exerted can be read directly by the scale M, 
^'Uched to the pendulum; a thermometer, Q, in the upper 
trass gives the temoerature of the bearings. The deviation 


of the pendulum is measured by a graduated arc, /V, 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 jP, and on the other the pressure per square inch,/; 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. iii.) 
Explanation of symbols : 

T, thermometer, giving temperature of bearings. 

Ry 5, rubber tubes for circulation of water through the 

//, burette, furnishing supply of oil. 

M<, siphon, controlling supply of oil. 

P, candle-vvicking, for feeding the oil. 

//, 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,y, which is shown by solid black 
shading in Fig. 1 12, into the head K, which embraces the jour- 
nal and holds the bearings aa in their place. In this pipe ^ 
loose piece, b, is fitted, which bears against the under journal- 
bearing, <7'. Into the lower end of the pipe y a piece, ff» '^ 
screwed, which has a hole drilled in the centre, through which 



\ passes, the upper end of which is screwed into a cap, 
reen this cap and the piece cc a spiral spring is placed, 
iper end o( the rod bears against the piece b. whicli in 
ears against the bearing a' . The piece b has a key, /, 
i through it and the pipe /. This key bears 

;a nut, o, screwed on the pipe. By turning the nut 
ess on the journal produced by screwing the rod y" can 
mm on the key /, and the bearing relieved of pressure, 
t changing the tension on the spring. A counterbalance 
the pendulum is used when accurate readings are de- 


sired. The " brasses " arc cast hollow, and when necessaiya 
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. 

as in the standard machine, the total friction ; and on the 
pendulum, the total pressures (i) 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 a* 
follows: Let /"equal the total pressure on the journal ;/ tb* 
pressure per square inch on projected area of journal; /"tl** i 
tension of the spring; (f the weight of the pendulum; rtt»* ! 
radius of the journal; R the effective arm of the pcnduluil>' 


^ the angle of deviation of the pendulum from a vertical line ; 
^ the total force of friction ; / the coefficient of friction ; / 
he length of bearing-surface of each brass. 

Since in this machine both brasses are loaded, the pro- 
ected atea of the journal bearing-surface is 2(2r)/ = 4/r. We 
shall evidently have 

P=2T'\^W, (i) 

P 2T+W ,^ 

Jy detinition/= F-i-P. 

Since the moment of friction is equal to the external mo* 
lent of forces acting, 

Fr=^P/r=f(2T+W)r=^WRsine.. . . (3) 
Vom which 

^ F WR sin e 

f^-p^ — Vp — ' ^^^ 

In the machines WR sin 6^ -=- r is shown on the fixed scale^ 
nd the graduations will evidently vary with sin ^, since 
^R -T- r is constant. 

P, the total pressure, is shown on the scale attached to the 

In the standard machine the weight of the pendulum is 
Neglected, and P = 2 7"; but in the Railroad Oil-testing Machine 
the weight must be considered, and P=: 2T '\- fF, as in equa- 
tion (i). 

Constants of the Machine. — As the constants of the 
niachine are likely to change with use, they should be deter- 
niined before every important test, and the final results cor- 
rected accordingly. 


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(2/r). 


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 f 

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. 15 ii 
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 


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 in 
Article 154, 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 (01 pressures of lOO, 
ijO, and 200 lbs.; but do not in general permit the maximum 
pressure in pounds per square inch to exceed 44,800 -^ {r-|-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 nin read the revolution-counter and note the time. 

The velocity, v, in rubbing surface in feet per minute should 
he computed from the number of revolutions and circumfer- 
ence of the journal. 

I Make a second series of runs, with constant pressure and 
pdable speed. 

* In report of the test state clearly the objects, describe 
^paratus 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 
<•' the various tests as follows : 

1. With total friction as abscissae, and pressure per square 
idchas ordinates; for constant speed, 

2. With coefficient of friction as abscissa, and pressure per 
puare inch as ordinates ; for constant speed. 

3. With coefficient of friction as abscissx, and velocity of 
pbbing in feet per minute as ordinates; pressure constant. 


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 

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 bjr 

forcing oil or water through hollow brasses, 
r. Feed limited, temperature variable or temperature 
In all cases the object will be to ascertain the coefficient of 

157. Riehl6*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. 1 13 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 maybe arranged. A thermometer gives the 
temperature of the journal ; a counter the number of revolu- 

Let P equal the total pressure applied to the bearings- 
Let B equal the projected area of the journal-bearings,/ equal 


the pressure per square inch ; F equal the total friction ; /equal 

Fig. ii3.-B.BHl4'i OiL-i 

the coefficient of friction; « equal tlie arm of the bearingj 
40 the arm of the total pressure. Then do we have 

Sfn = aP, 


aP _ap 


If / be maintained constant, and a -^ nht, made the value 
of the unit of graduation on the scale-beam 

/*= 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 rail 
temperature to a fixed point — for instance, 160 F. — is in 
instances considered proportional to the durability. 

The Ashcroft (see Article 159, page 227) and the Boult(scc 
Article 160, page 228) machines are especially designed ford^ 
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 oH 
from the journals, which is sufficient, however, to make the 
results very uncertain. 

*See paper by Professor Denton, VoL XL, p. X013, Transactions of AmerW 
an Society of Mechanical Engineers. 


^ Ashcroft's Oil-testing Machine. — This machine 
II4)consi5t5 of an axie revolving in two bras^ boxes ; the 
ire on the axle is regulated by the heavy overhanging 
erpoise shown in the engraving. The tendency to lotate 
isted by a lever which is connected to the attached gauge. 
puge is graduated to show coefficient oi friction. 

e temperature is taken by an attached thermometer, and 
mberof revolutions by a rounter, as shown in the figure, 
i'this midline the weights and levers are constant, the 
les being the temperature and coefficient of friction. 
Is used exclusively with a limited supply of oil, the value 
t oil being supposed to vary with the total number of 
Itions required to raise the temperature to a given degree, 
bistance, to 160° F. 

Ik Boult's Lubricant-testing: Machine. — This machine, 
led by W. S. Boult of Liverpool, is a modification of 





the Thurston oii-tester, yet it differs in several essential 'm' 
ures. A general view of the machine is shown in Fig I'i 
and a section of its boxes and the surrounding bush in Fig;! 

The machine Is designed to accomplish the follow 
poses: I. Maintaining the testing journal at any desired v 

2. Complete retention on the rubbing surface 

the oil under test. 3. Application of 


le pressure lo 

rubbing surfaces. 4. Measurement of the friction betweei 
rubbing surfaces. 



S'o secure the complete retention of the oil, a complete bush 

A internal flanges is used instead of the brasses employed in 

ler oil-testing machines. On 

: inside of the bush is an ex- 

iding journal, /?£), Fig. I i6.the 

tsof which are pressed outward 

(tnst the surrounding bush by 

springs E, or they may be 
wn together by the set-screws 
?, compressing the springs E. A 
ited amount of oil is fed from 
lipette or graduated cylinder 

the journal, with the bush 
loved. This oil, it is claimed, 
I be maintained on the uut( 
face of the journal and on th 
:rior surface of the metallic 
h, so that it may be used to 
truciion. The bush is hollow, 
1 can be filled with water, oil, 
nehing ice and brine. 
The oil to be tested can bCp 
intaincd at any desired tem- t.5tki.. 

ature by a burner, F, which heats the liquid CC in the sur- 
nding bush. The temperature of the journal can be read 
a thermometer whose bulb is inserted in the liquid CC. 
The friction tends to rotate the bush ; this tendency is re- 
ed by a lever connected by a chain to an axis carrying a 
ghted pendulum, G, Fig. 115. 

The motion of the pendulum is communicated by gearing 
1 hand, passing over a dial graduated to show the total fric- 
1 on the rubbing surfaces. 

The formulx for use of the instrument would be as follows : 
:y equal coefficient of friction; G the weight of the bob 
the pendulum, R its lever arm; a the angle made by the 
dulum with the vertical; a the length of the connecting 
r; c the radius of the axis to which the pendulum is 


attached ; r the radius of the journal; A the projected area of 
the journal ; Pthe total pressure on the journal. Then 

• a R 

-.-.(7 sin a =/^P, 
re J ^ 

from which 

aGR sin or sin or , . 

/ = rcAP ~ "^ ~P'' (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 ot. 

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 

The instrument cannot be used with a constant feed of oil, 
nor can the pressures be varied except by changing the 
springs E. 

i6i. 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 tif:jhtcning the set-screws in order to de- 
press the sprint^. 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-screwe 
so as to allow the spring to have full pressure. The set-screw: 
should not be removed entirely when slackening. 


2. Light the Bunsen burner. 

3. The thermometer indicates the temperature to which 
lubricant has to be subjected in the steam-cylinder, being 
duated in degrees Fahrenheit, and their equivalent in pounds 
ssure. Thus, if the working steam-pressure is 60 lbs., the 
rmometer shows that the heat of steam at that pressure is 
** Fahr.; whilst at lOO lb9^ pressure its temperature is 358^ 
in, etc. Run the tester, say, until there is a rise of 50 per 
t; in some cases it is preferable to run the tester until 
re is a rise of 100 per cent of the friction first indicated, 
^e does not appear to be any advantage in going beyond 
^ as the oil is then practically unfit for further use, and 
re is danger of roughening the friction surfaces. 

^ When it is considered desirable to ascertain the distance 
'elled by the friction surfaces during a test, read off the 
nting-indicator before and after the test, and subtract the 
er from the greater total, and the difference will represent 
number of revolutions made during the test. As the fric- 
1 surfaces travel two thirds of a foot during each revolution, 
number of feet travelled is arrived at by simply deducting 
n the number of revolutions made, one third thereof. 
The value of the oil is proportional to the number of feet 
'clled by the rubbing surfaces. 

The speed at which the tester should be run should be 
ut five to six hundred revolutions per minute. For quick- 
*d engine-oil the speed may be increased to about a thou- 
i per minute. 

[62. Experiment with Limited Feed.— The object of this 
eriment is to ascertain the variation in the coefficient of 
tion due to a change in the rate of feed. 
The experiment is to be made with the feeding apparatus 
.nged so that the supply can be regulated. Different runs 
made with different rates of feed, and the variation in 
coefficient of friction determined. Fig. i Ii,p.2i9, repre- 
s the Thurston R. R. Lubricant-tester as arranged for tlic 
irriment, with a constantly diminishing rate of feed, by Pro 
jr G. W. Bissel. In this case oil is obtained by the siphon 





M from the burette N, and conveyed by the candle-wicldn 
to a copper rod H inserted in the bearings. The rate of £ 
will depend upon the height of the oil in the burette N^ 
the end of the siphon-tube M^ and as the head gradually 
minishes from loss of oil, the rate of flow will decrease. 

The quantity of oil used is to be determined by grad 
tions on the burette. The increase in coefficient of fricti 
due to the constantly diminishing rate of feed is shown h f 
86, the coefficients of friction being shown by the dott 
lines, corresponding to a given rate of feed and a given til 
jn minutes. 


.002 .OOS 

CkwfBcient oCJ'riotioB 



The experiment with head and feed maintained consta 
during each run would represent very closely the usual com 
tions of supplying lubricants. 

In this case, provided there was no loss of oil from 
journals, the experiment might show — 

1. The laws of friction for ordinary lubrication. 

2. The most economical rate of feed foi- a given lubrica 




The value of the lubricants on the joint basis of amount 
med and coefficient of friction. 

few tables showing coefficients of friction which has been 
led in various trials are given in the Appendix for refer- 

j. Forms for Report. — The following are the forms used 
ley College for data and results of lubricant test : 


f Lnbricaot 

Lab. No Date... 



lest. < 

e on joomal, lbs. per sq. inch . . . 

ressure on journal, lbs 

L of oil used on journal, m. g. . .. , 

t coeflBcient of friction , 

m coefficient of friction , 


eet travelled by rubbing surface. 
>n of temperature 





ing OD 

cient of 

] Min- 
' utes. 



ing oo 


cient of 




d from. 




.189... • 

Ash % 

"B. Tar % 

, water 100. Chill-pt * F. 

,• F. Loss at • F. for 3 hrs % 

.•F. Acid 

2 34 





Time of Flow of loo c.c. in Seconds. 

Degrees F. 

Value Lard-od 



I^rd oil. 



2. . . . 



C- . . - 








... 189 . 







Hiffhest readinc . - . . . 

I owpst rPAdinc 

Average readinc ..... 

.•••*•• ••••• 

Drons n#*r min 

Time of run min 


Rev oer min 

Miles ner hour 


Total lbs 

P#*r sn in Ih^ 

Coefficient of friction 


Flow on plane inclined degrees. 

Kind of plane. .. , Tempt, room. ••••••••••• 

Time in hrs.. Sample , Lard-oil ••••••» Water* •••••••m** 



164. Classes. — Dynamometers are instruments for measur*' 
J power. They are of two classes : i. Absorption; 2. TranS" 
ssioK, In the first class the work received is transformed 

friction into heat and dissipated ; in the second class the 
namometer absorbs only so much force as is necessary to 
ercome its own friction, the remainder being transmitted. 

165. Absorption Dynamometer.— The Prony Brake.* — 
le Prony brake is the most common form of absorption dy- 
imometer. This brake is so constructed as to absorb the 
ork done by the machine in friction, this friction being pro- 
Jced by some kind of a surface connected to a stationary 
art, and which rubs on the revolving surface of the v/heel 
ith which it is used. The brake usually consists of a por- 
ion which can be clamped on to a wheel (see Fig. 11 8, page 
39), with more or less pressure, and an arm or its equivalent, 
he part exerting pressure on the wheel is termed the brake* 
^rap ; the perpendicular distance from the line of action of 
lie weight, G^ to the centre of the wheel is termed the arin of 
le brake. The brake is prevented from turning by a definite 
ad which we term G, applied at a distance equal to the 
igth of the arm {a) from centre of motion. The work of 
sistance would then evidently be equal to the product of the 
ight of resistance, G, into the distance it would pass through 

•See Engine and Boiler Trials, by R. H. Thurston, page 157; Mechanics of 
lerials, by I. P. Church, page 269; Du Bois' Weisbach's Mechanics of En- 
rcring, page 13. 



if free to move. If n be the number of revolutions per minute, 
the horse-power shown by the brake would evidently be 

2nGan -^ 33000 (l) 

Brakes are made with various rubbing surfaces, and with 
various devices to maintain a constant resistance. 

166. Stresses on the Brake-strap. — FormuUB.—Vcit 
strains on the brake-strap are essentially the same as those 
on a belt, as given in Article 128, page 199. 

That is, if Z", represent the greatest tension, T^ the least 
tension, c the percentage that the arc of contact bears to the 
whole circumference, iVthe normal pressure, F the resistance 
of the brake, / coefficient of friction, 

1 -. Kf-vf^c^ Number whose log is 2.7288/J: = R 

^■=«^ (" 

^•=j^ « 

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 2C2 
also, " Friction and Lubrication." 


\ horse-power H^ shall not exceed 500 to looa* Call this 
ult K. Then 

^ wv 

400 to 5CX) is considered a good average value of K. 
The value of the coefficient of friction f should be taken 
:he lowest value for the surfaces in contact (see table of co- 
dent of friction in Appendix). This coefficient is about 0.2 
wood or leather on metal, and about 0.15 for metal on metal 
Let H be the work to be transmitted in horse-power, ;/ the 
nber of revolutions of the brake-wheel, D its diamete 
n the resistance F of the brake must be 

•• • 

^-"-^5:;- (4) 


* arc of contact is known or assumed, and may be expressed 
ronvenient (see Article 128) in circular measure d, degrees 
)r in percentage of the whole circumference c. 
Example. — Assume the arc of contact as 180 degrees 
= 0.5), the diameter of brake-wheel 4 feet, coefficient 01 
tion (/"=o.i5), face of brake-wheel 10 inches, revolutions 
horse-power 70. Find the safe dimensions of the brake- 
ip and working parts of the brake. 
Then, from page 236, 

It is, B equals the number whose logarithm is 0.2046 ; or, 

B = 1.602. 

S€C also •* Engine and Boiler Trials," by R. H. Thurston, pp. 272 and 279. 


Thus if the brake-wheel is 4 feet diameter revolving at 90 
revolutions per minute : from equation (4) 

^^ (33000) (70)^ ds, 

(^) (4) (90) ^^ ^ 

Taking B as above, and substituting in equations (2) and (3), 
we have 


^-^3(S) = 5436; 

y, 2043^ 

^* .602 ^^^5' 

iV= -— = 1362a 


From the value of 7", , 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— loooo = 0.55 square inch. 
The assumed width of brake-wheel is 10 inches; this gives 
for the value of K, by equation page 237. 

^ = (10) (i 1 32) -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 

o.t^S -T- 6 = 0.091 inch. 

To determine a convenient length of the brake-arm^ con- 
sider equation (i) for work delivered in horse-power. 

H = 27tGan -^ 33000. 




y dividing both terms by 2n^ 



168. Brake Horse-power. — ^The following table will often 
e convenient for determining the delivered horse-power from 


Length of Brake-arm, 

Factor to multiply 

Ratio of scale-read- 


scale-reading to give 
horae-power, H-t-G. 

ing to horse-power, 


































169. Different Forms of Prony Brakes. — ^Various forms 
of brakes are made. Fig. 118 shows a very simple form of 


Fig. 118. — Prony Brake. 

rony brake, in which the rubbing surfaces are made by two 
ooden beams clamped together by the bolts C C, Weight is 
^Plied to the arm E at the point G ; the stops D D prevent a 
^^^ range of motion of the arm ; the projection F is used to 
^ff on sufficient counterbalance to prevent the brake from 


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 weiglit at G and that at F, reduced to an equin> 
ient 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 tiie blocks should be fitted to thewli«l, 
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 a 
shown in Fig. 119 attached to a portable engine. 

17a Strap-brakes. — Brakes are sometimes made by tatdn^ 
one or more turns of a rope or strap around a wheel, as show 

in Fig. 120, In this case weights must be hung on both sid**' | 
and since the arm of action is equal, the resultant iotc^ 


ting is the difference between the two weights : that is, in 
e figure the resultant force is ^ — B\ the equivalent space 
ssed through is the distance travelled by any point of the 
cumference of the wheel in a given time. The work done 
the product of these quantities. 

171. Self-regulating Brakes.— Brakes with automatic 
gulating devices are often made ; in this case the direction of 
otion of the wheel must be such as to lift the brake-arm. If 
le tension is too great the brake-arm rises a short distance, 
id this motion is made to operate a regulating device of some 
nt, lessening the tension on the brake- 
heel ; if the tension is not great enough, 
e brake-beam falls, producing the oppo- 
e effect. 

172. Brake with oblique Arm. — ^A 
ry simple form of self-regulating brake 

shown in Fig. 121: in this case the 
T) is maintained at an angle with the 
rizontal. If the friction becomes too 
?at, the weight G rises, and the arm of 
e brake swings from A to E, thus in- p,^ „,.«self.rbgulatino 
casing the lever-arm from BC to LC; if brake. 

e friction diminishes, the lever-arm is correspondingly dimin* 
led, thus tending to maintain the brake in equilibrium. 

173. Alden Brake The Alden brake (see Figs. 122 to 12 5) 

an absorption dynamometer in which the rubbing surfaces 
^ separated by a film of oil, and the heat is absorbed by 
ater under pressure, which produces the friction. It is con- 
ructed by fastening a disk of cast-iron, A, Fig. 122, to the 
mer-shaft ; this disk revolves between two sheets of thii> 
pper E E joined at their outer edges, from which it is sepa- 
ted by a bath of oil. Outside the copper sheets on either 
le is a chamber which is connected with the water-supply at 

The water is received at 6^ and discharged at Hy thus main- 
ning a moderate temperature. Any pressure in the chamber 
ises the copper disks to press against the revolving plate, pro- 
ring friction which tends to turn the copper disks. As these 


are rigidly connected to the outside cast-iron casing and brakft 
arm P, the turning effect can be balanced and measured ihe 
same as in the ordinary Prony brake. The pressure of water 
is automatically regulated by a valveV.Fig. I25,wbich isp»f- 

tially closed if the brake-arm rises above the horizontal, and is 
partially opened if it falls below ; this brake with a constanl 
head gives exceedingly close regulation. 

174. Hydraulic Friction-brake.— The author has desigiwd 
a hydraulic friction-brake that can be applied to the surface 
of an ordinary brake-wheel. The brake consists of a tube o*^ 
copper with an oval or rectangular cross-section, which ver}' 
nearly encircles the brake-wheel, and has both ends dosed- 
The greatest dimension in its cross-section is equal to til* 
width of the brake-wheel, and its least dimension is one half 1** 
three fourths of an inch. One end of the tube is conned"' 
with the water-supply, the other to the discharge, which c»*^ 
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 braWe- 
arm, and also one end of the cupper tube, When waler-p'"**' 


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 
lends to revolve the tube and band of iron. This is resisted 
by Ihe weight on the arm of the brake. The water-pressure is 
icgulated automatically by a slight motion of the brake-arm, 
Mhich 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 
lube thin sheets of iron may be interposed, A lubricant is 
applied by means of lubricators fixed near the ends of the 

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 
'he axis and discharged at the other. Another way is to leave 
a deep internal flange on the brake-wheel, and in using the 
Sirake, 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 
lo meet the current of water near the opposite side of the 
*heeL Water is sometimes run on to the surface through a 
hose, but aside from the inconvenience due to flying water, 
if aiiv of the rubbing surfaces are of wood it is likely to make 
.sudden and irregular variations in the coefficient of friction 

It are difficult to control. 

176. Applying; Load. — In applying the load, care must be 
iiilten tiiat its direction is tangent to the circle that would be 
(escribed by the brake-arm were it free to move. In other 
'fOfds, the virtual brake-arm must be considered as perpendic- 
Wrto this force. If a vertical load or weight is applied, the 

iltcarm must be horizontal, and equal in length to the dis- 
'ce from this vertical line to the centre of the motion. 


It will be found in general safer and more satisfactory to 
have the motion of the brake-wheel such as to produce x 
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 pix)pcr 
length to hold the brake-arm horizontal. 

177. Constants of Brake. — All brakes with unbalanced 
arms have a tendency to turn, due to Aveight 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 twa 
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. Sec 
that the brake-w^heel is rigidly fastened to the main shaft. 
2. Provide ample means of lubrication. 


3. If the brake-wheel has an internal rim, provide means 
supplying and removing water from this rim. 

4. Find the equivalent weight of brake-arm to be taken 
irom or added to the load, depending on the direction of 
motion of the wheel. 

5. In applying the load, tighten the brake-strap \eiy 
slowly, and give time for the friction to become constant W 
(ore noting readings of the result, 

6. Note the time, number of revolutions, length of brake- 
rresponding load, and calculate the results. 

179. Pump Brakes. — A rotarj- pump which delivers water 
lugh an orifice that can be throttled or enlarged at will, has 

in used with success for absorbing power. 
H 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 
easured by the weight of water discharged multiplied by the 
light due to the greatest velocity of its particles multiplied 
a coefficient to be determined by trial.* 
A special form of the pump-brake, with casing mounted so 
tt it is free to revolve, has been used with success on the 
fens College experimental engine by Osborne Reynolds. 
this case the brake is practically an inverted turbine, the 
lleel delivering water to the guides so as to produce the 
imum resistance. The water forced through the guides 
one point is discharged so as to oppose the motion of the 
eel at another point. 

180. Fan-brakes. — A fan or wheel with vanes revolved in 
tor. oil, or air will absorb work, and in many instances fonns 
raluable absorption-dynamometer. 

The resistance to be obtained from a fan-brake is expreusd 
the formula t 

Rl = IKDA — . 

* Sec Rankine, Machiocry Had MiU-nork, page 404. 
f Ibid., page 406. 


in which ^/equals the moment 
of resistance, K 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 
she vane moves, Ka, coefficient, 
found by experiment by Pon- 
(^let to have tiie value 

/ir= 1.254 + 

1.6244 va 
l~s ' 

n which s is the distance in 
feet from the centre of the 
entire vane to the centre of 

bat half nearest the axis. 

vVhen set at an angle i with 

the direction of motion the 

value for Rl must be multi- 

,. , , 2 sin' i 
plied by — ; — -^^^■^ 

^ I + sm t 

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. 


ktcording Traction-dynamometers. — These are constructed 
rious forms. Fig. 127 shows a simple form of a recording 
ftian-dynamometer, designed by C. M. Giddings. Paper is 
Lced on the reel A, which is operated by clock-work; a 
[icil is connected at K to the band, and this draws a diagram, 
shown in Fig, i2S,the ordinates of which represent pounds 

Woo—/^ • — 



[pull, the abscissae the time. The drum may be arranged 
be operated by a wheel in contact with the ground : then the 
Kissa will be proportional to the space, and the area of the 
^am will represent work done. 

"I82. General Types of Transmission-dynamometers.* 
transmission-dynamometers are of different types, the ob- 
t in each case being to measure the power which is 
xived without absorbing any greater portion than is neces- 
y to move the dynamometer. They all consist of a set of 
lleys or gear-wheels, so arranged that they may be placed 
twecn the prime movers and machinery to be driven, while 
: power that is transmitted is generally measured by the 
Kure of springs or Liy the tendency to rotate a set of gears, 
BCh may be resisted by a lever. 

&83. Morin's Rotation-dynamometer. — In Morin's dy- 
faometer, which is shown in Fig. 129, the power is trans- 
ited through springs. FG, which are thereby flexed an 
cunt proportional to the power. The flexure of the springs 
recorded on paper by a pencil s fastened to the rim of the 

'flee Thurston's Engine and Boiler Trials, pa^e 264 ; also Weisbach** 
cs, VoL 11., pa^cB 39^73 ; also Rankitie's SCcBm-cngine, page 43. 




wheel. A second pencil is stationary with reference to llw „ 
frame carrying the paper. The paper is made to pass undet U 
the pencil by means of clock-work driven by the shafting, -^ 
-which can be engaged or disengaged at any instant by operating L 
the lever R. The springs are fastened at one end rigidly to L 
the main axle, which is in communication with the prime 
mover, and at the other end to the rim of the pulley, whid 
otherwise is free to turn on the main shaft. The power 11 
iaken from this last pulley, and this force acts to bend the 

springs as already described. In the figure ^ 19 a loose puQe/ 
B is fixed to the shaft. 

The autographic recoiding apparatus of the Morin dyn* 
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 sleevt slides longitudinally on tbe 
axis, and may be engaged with or disengaged from the frame al 
a:iy instant by means of a lever. When this sleeve is engaged 
with the frame and made stationary the recording apparatni 
i? put in motion by the concentric motion of the gearing. 5Fi 
with respect to the axis. The pencil attached to the sprioj 
will at this instant trace a diagram on the paper whose ordt- 


ates are proportional to the force transmitted. The rate ; t 
Dtation of the drums carrj'ing the paper, with respect to the 
nain axis, is determined in the same manner as though the 
>ears were at rest — by finding the ratios of the radii of the 
espective wheels. Thus the amount of paper which passes 
iff from one drum on to the other can be proportioned to the 
pace passed through, so that the area of the diagram may be 
iroportional to the work transmitted. 

To find the value of the ordinates in pounds the dyn^ 
aomater must be calibrated ; this may be done by a dead pull 
\i a given weight against the springs, thus obtaining the 
leflections for a given force ; or, better, connect a Prony brake 
lirectly to the rim of the fixed pulley B, and make a series of 
■ns with difiertnt loads on the brak^, and ^d the correspond- 
mt values of the ordinates of the card. ■ 
K|84. Calibration of the Morio Dynamometer. — Appara- 
K/^Speed-indicator, dynamometer-paper, and Prony brake. 
I I. Fasten paper on the receiving drum, wind off enough 
a pass over the recording drum, and fasten the end securely 
:o the winding drum. See that the gears for the autographic 
ipparatus are in perfect order, and that both pencils give 
legible lines. Adjust the pencil fixed to the frame of the 
^lock-work, so that it will draw the same line as the movable 
pencil, when no load is applied. 

3, With the apparatus out of gear apply the power. Take 
K card with no load. This card will be the friction work of 
the dynamometer. 

•\. 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 tine traced 
by the pencil affixed to the frame of the clock-work must io 
■Q 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 tran»> 
nitted 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-am^ 

2 50 



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 rf 
ordinate. Describe the apparatus. 

7. In using it, insert it betwetn the prime mover and re. 
aistance to be measured. Determine the power transmitted 
from the calibration. 

185. Form of Report— The following form is useful Id 
calibrating this dynamometer: 


Kind o( beakr used. .......,,,.... Len([th of braltc-arm 

Weigbt o( bcakc-Brm lbs. Zero-reading of scale*.... 

Badiui of driviag-pulky. fL Observers 

::. ; 



Load on 
pullejr, !U. 

Ordluie, lacbM. 







Eqnallon of Curve, 
.. K- 

186. Steelyard-dynamometer. — In this dynamometei the 
pressure of the axle of a revolving shaft is determined bjf 
shifting the weight G on the graduated scale-beam AC. 

The power is applied at P, putting in motion the train d 
gear-wheels, and is delivered at Q. 

Denote the applied force by P, the delivered force by {J 


:he radius KM by a, KE by r, LF by r, , NL by & the fon» 
lelivered at E by ^, that at Fby Ji,, 
We shall have 

llr = Pa, also «,r, =0*. 

lt(ELr) = RlFD); 
Id since £/) = /», 

The resultant force Z= R + /i,=3R 

.:R = IZ; 


= Kr, + .. 

If we know the number of revolutions, the space passed 
through by each force can be readily calculated, and the work 
/ound by taking the product of the force into the space 
passed through. 

CffnsidfratioH of Friction. — The friction of the axle and 
gear-teeth will increase the force R and decrease the force R^ 
Let ;< be the experimental coefficient expressing this frictioo. 

^ Par, + Q 


187. Pillow-block Dynamometer. — The pillow-block dy. 
namometer operates on the same principle as the fteelyaid 
dynamometer, but no intermediate 
wheel is used. This dynamometer, 
I shown in Fig. 131, consists of the 
fixed shaft L, which is rotated by 
the power Q applied at ^V, Thf 
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 ihe 
force delivered, let a equal the angle this force makes willi ihe 
horizontal, let A'J/ equal a and KE equal r , G equal the weight 1 
of shaft and wheel The weight on the pillow-block at t , 
must be 

Z= ^-HPain a +^/'= (?+i^8ln a+^\ 

Fveai which 

sin a -f 

When the belt is horizontal. 

«*=0 and P = (^Z-~G)-' 

188. The Lewis Dynamometer.* — This transmissioiwljl 
namometer is a modified form of the pillow-block dyn* 
Riometer, arranged in such a manner that the friction of tM 
gearing or journals will not affect the reading on the weighing- 
scales. This dynamometer is shown in Fig. 132, and also in Fig 
39, Article I95, page 265. The dynamometer consists of t»* 

c VflL VII., page 376, Tiaos. Am. Socicir M 

schanical Engiaeetli 

i 188.] 



i^ar-wheels A and C, whose pitch-circles are tangent at B; 
Uie gear-wheel A is carried by the fixed frame 7". the wheel Cis 
carried on the lever BD: the lever BD is connected to the 
ilxed frame 7" by a thin steel fulcrum, as used in the Emery 
Testing-machines (Article 67, page 105), The point ZJ, the 
centre of wheel C, and the fulcrum are in the same right tine. 
The fulcrum B permits vertical motion only of the point D. 
The point D rests on a pillar, which in turn is supported by 
■ pair of scales. The shaft leading from the wheel C is fur- 
nished with a universal joint (see Fig. 139), »o that its weight 
does not affect that on the journal C. In Fig. 132, A is the 


Lnm DvHjuiOMmR. 

driving and C the driven wheel, the force to be measured being 
deceived 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 torsiov 
of the sha.'t c. This will be readily seen by considering: 
L That any downward force acting at B will be resisted by 
the fixed frame T, and will not increase the pressure at D. 
X A downward force a' ting on the lever between B and D 
wiD produce a pressure proportional to its distance from B. 
y, It the driven wheel C were firmly clamped to its frame, no 
force acting at f would change the pressure at Z> ; and since 


journal-friction would have the effect of partially clamping the 
wheel to the journal ^, it would have no effect on the scal^ 
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 scal^ 
reading at D by W. Then from equality of moments 

Wa^Zr, Z=^ 


The effective lever-arm BD is to be obtained experimen. 
tally as follows : Disconnect the universal joint, shown in Fig. 
io8, so as to leave the wheel C, free to turn ; block the driving- 
pulley A ; fasten a horizontal arm, ^(dotted lines, Fig. loi), 
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 Gy and /the second position; let IV Sind W represent 
the corresponding scale-readings, after balancing scales without 
G on the lever, ef. 

Then we have 

"^ ^ DB' 


W'-W Jf B -eB) ef 

^~ DB ~^ DB ~^''DS 

Then will 

DB = ef. 




189. The Differential Dynamometer.— This is often 
jllcd the Bachelder, Francis, or Webber dynamometer ; was 

ented by Samuel Wliite, of England, in 17S0, and brought 

ills country by Mr. Bachelder in 1S36. 

The dynamometer portion consists of four bevel-gears, 
town in plan in Fig. 133. 

Power is appHed to the pulley M, which carries the bevel- 

heel EE^ ; the resistance is overcome by the pulley N, which 

ixries the bevel-wheel FF,. Both wheels run loosely upon 

fixed shaft XX^ , and are connected by the wheels EFand 

\, By the action of the force /'and the resistance Q, the 

vssure of the wheels ££, and FF, is downward at £ and F, 

Id upward at £, and F, , tending to swing the lever GG, 

Ound the axis XX, , one half as fast as the pulley M. The 

dght which holds the lever-arm stationary, multiplied by the 

:e it would pass through if free to move, is the measure of 

work of the force P. A dashpot is usually attached to the 

IVcr GG, at C, , to lessen vibrations and act as a counterbal- 

cc. Let Z equal the vertical force acting at £ and B, ; S, 

; vertical pressure between the teeth at each point of con- 

t; i, the distance of B and £, from the centre C; a, tho 

tance, AC, to the weight. 

Then we have evidently 

2^ = 4^, or Z= 2R; 

Ga = 2Zb = 4R6, 




If a' is 

the radius of the 

driving-pulley M, and 

r the radliii 

of each bevel-gear, 

Pa' = 2Rr, or P =~ = 

G r a 
' 2 b ^' 

If friction 

is considered, 



The mechanical work received is equal to /"multiplied by 
the space passed through in the given time. 

This instrument has been improved by Mr. S. Webber, 
shown in Fig, 134. 

Fig. 134.— Thi Wkb™ DTHAHDMrnic 

These dynamometers are used in substantially the saOW 
way as the Morin dynamometers. 

190. Calibration of the Differential Dynamomcter.- 
I. See that it is well oiled, in good condition, its axis horiion- 
tal, and also that the weighing arm is horizontal for no loaii. 

2. Observe constants of the apparatus : obtain weight of 
small poise ; of large poise ; of amount to balance beam W.' 
Measure the arm of each, and calculate the foot-pounds pw 
100 revolutions corresponding to weights and graduations. 

I go.} 



3. Make a preliminary run without load, and note the 
:ading of the poise required to balance the arm. This will 
^termine the friction of the dynamometer without load, 
letermine the length of the arm, and the value of each sub- 
ivision in foot-pounds. 

4. Attach a strap-brake (see Art. 169. p. 339) to the delivery 
uUcy of the dynamometer, and absorb all the force trans- 
litted. Make a series of ten runs, each ten minutes in length 
nd during each of which the load on the Prony brake-arm is 
ept as constant as possible, but which is increased by equal 
icrements, in the different runs. Take observations each 
linute during the run. 

5. The difference between the work absorbed by the brake 
nd that shown by the dynamometer should be carefully de- 
ermined. It is the error of the dynamometer. 

6. Note whether this error is a constant quantity, or is a 
■ercentage of the work delivered. 

7. In your report, describe the apparatus, give the results 
f the calibration, and draw a curve, using brake foot-pounds 
9 ordinates, and dynamometer foot-pounds as abscissa. 

8. To use the dynamometer insert it between the prime 
lover and the machinery to be run. 

Il ^cial Directions for Calibrating ike Webber Differeniial 
I Dynamometer. 

r Apparatus required : 

1. Ten small tension-weights. 2. Spnng-balance or plat- 
form-scales, 3. Measuring-scale. 4. Calipers. 5. Stop-watch. 

a. Weight of small tension-weights. 

A " ** fixed poise-weights. 

<; ** " dynamometer-arm. 

d. " " sliding poise. 

*. XtCngtb of dynamometer-arm to fixed poise. 

_/. Length of dynamometer-arm to sliding poise. 

g. Diameter of brake-pulley. 

il. Thickness of brake-strap. 




I. Friction-run. — Remove brake. Find time, in seconds, 
of looo revolutions (lO rings of bell). Balance dynamomctet. 
arm ; the reading is the " zero-reading" by the beam, and must 
be corrected to get the true friction-reading. 

II. Tesl-ritns. — Put on brake; hang one weight on iti 
slack side. Time. lOOO revs. Read simultaneously dynamont 
eter-arm and platform jcales. Repeat the same with succet- 
3!ve 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 tlie 
dynamometer-arm. and sliding-poise set at the zero-mark. 

191. Form of Report. — The following blank is used intbe 
exercises with the differential dynamometer in Sibley College: 

Calibration of Differential Dyi 

Kind of Brake used 

Length of Brake-arm ft. Weight of Bralce-«rfn. 

Zero-reading of Brake-scales lbs. 

Date. 1S9. . Observert 







rk in It. 

b». per >« 


















7-,- 7-, 











— . 



MomenlArm .. ft. 




Vilue, ft.. 



. . . = )r. 

Increase per Notch. 

♦-.^Zeto-rauJing by 

«'.+ M'.=Fti«ion-rea(». 

192. Emerson's Power-scale. — One of the most complete 
ttansmission-dynamometers is shown in Fig. 135, with attached 
numbers showing the dimensions of the various sizes manu- 
bctured. In this instrument the wheel Cis keyed or fastened 
toihe shaft: the wheel B is connected with the wheel Cneat 
lb outer circumference by projecting studs; the amount of 
^cssure on these studs is conveyed by bent levers to a collcr, 

'hich in turn is connected with weigiiing-levers. Small weights 
arc 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 
t*ower-scale are used by the Massachusetts Institute of Tech. 


K DYHAMOMrrsft. 

•Wb«. p 

:;l : I \. I.. 


Iferolotknii per mianle... 






■lion of leit 







P-b¥ brake 



,. Em,™, P.-.,«.l.. 






















umbtr I 








Constanls and Remarks. 

194. The Van Winkle Power- meter. —The Van Winkle 
>w'er-meter is shown in Fig. 1 36, complete, and with its parts 


separated, in Fig. 137. It consists of a sleeve with attached 
plate, B, that can be fastened rigidly to the shaft; and* 
plate A, which is revolved by the force communicated throogli 

the springs ss. The angular position of the plate A with refer- 
ence to B will vary with the force transmitted. This angular 
motion is utilized to operate levers, and move a loose sleeve 

longitudinally on the shaft. The amount of motion of the 
sleeve, which is proportional to the force transmitted, is imii 
cated by a hand moving over a graduated dial. The dial u 
graduated to show horse-power per 100 revolutions. 



>• Belt-d]rnamometers. — Belts ha^.'e been used in some 
ces instead of gearing in transmission-dynamometers, 
:cause of the great loss of power due to stiffness of the 
aind to the uncertainty caused 
pping, they have not been 
lively used. The following 
from Church's " Mechanics 
Lterials," is probably as sue- 
[ as any that has been de- 
It consists of a vertical 
carrying four pulleys and a 
lan, as shown in Fig. 138. 
cale-beam is balanced, the 
len adjusted, and power turned on ; a sufficient weight, 
placed in the scale-pan to balance the plate again. Let 
le arm of the scale>pan, and a that of the forces P and 
Then, for equilibrium, 

Pia. 138.— A Belt-dynamombtks. 

Gd=:Pa- P'a, 


° and P' on the right have no leverage about C, as the 
the belts produced intersects C. From (i) 

P-P' = 



e work transmitted in foot-pounds per minute 5s equal 
- P'^v, in which v is the velocity of the belt in feet per 
I to be obtained by counting. Another form employs 
larter-twist belts to revolve a shaft at right angles to the 
;haft. (See Vol. XII., Transactions Am. Soc. Mechaii- 

\, Method of Testing Belts.* — The object of this test 

etermine the coefficient of friction, and the power trans 

by various kinds of belting running under differer.. 




The required formulae are given in Aiticle 128, page 199, 
its follows: 7^1 y maximum tension; 7^,, minimum tension;/, 
the force of friction ; c^ the percentage of arc of contact to 
whole circumference ; B^ the arc of contact in circular measuie 
We have 

7;-7; = i^; 

Common log -^ = 0434/9 as 2.72SS/C 

From which 

/as Napierian log ("y^jz- 

Belt-testing machines must be arranged so that measares 
of T^f T^y 0, and c can be made. To determine loss due to 
resistance, it is necessary to supply the power by a transflusp 
sion-dynamometer, and absorb that delivered by a brake. 

197. The Sibley College Belt-testing Machine.— The 
belt-testing machine illustrated in Fig. 1 39 is used in the 
Mechanical Laboratory of Sibley College. It was designed by 
Wilfred Lewis of Philadelphia, and used in the tests described 
in Vol. VII. of Transactions of American Society of Mechanical 

The belt to be tested is placed on the pullesrs i?, F\ power is 
transmitted through the pulleys /^ to the Lewis transmitting^ 

* The student is referred to papers in Transactions of American Society ol 
Mechanical Engineers, Vol. VII.. by Wilfred Lewis and Prof. G. Lanza; also 
10 paper in Vol. XII., by Prof. G. Alden ; and to theHolman tests in the Jom 

nal of the Franklin Institute, 1885. 

J MaASUM£M£/tT Of fOltrZt, 


dynamometer (see Article i88, page 252), and thence through 
the shaft H to the pulley £. The power transmitted is absorbed 
by a Prony brake on the shaft M, The slip of the belt is 
measured by transmitting the motion of the pulley ^5" by gearing 
to the shaft /, and thence to a disk 5", whose edge is graduated 
The pulley F is connected to the gear-wheel Z, shown in a 
larger scale in centre of Fig. 96. The wheel L is so proportioned 
that if there is no slip it will revolve at the same rate as the 
disk S\ if there is slip it will fall behind S. The amount that 
it falls behind is read by the scale F, which may be clamped 
to the hub of L by the screw 71 As this device moves only 
one one-hundredth as fast as the main shafts, the amount of 
slip can be easily read. The pulley F and the brake M arc 
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- 

Weighing-scales are placed a,t A, B^ and C, respectivelyi 
that at A is termed the dynamometcr'Scales ; that at By the brah^ 
scales that at C, the tensioU'Scoles, The reading on the tension- 
scales C multiplied by the horizontal arm Ky divided by the 
height ^of the pulley E upon the knife-edge, gives the total 
tension on the belts 7", + 7,. The reading on brake-scales 
/>\ divided by the arm ^ of the brake, and multiplied by the 
radius D of the pulley Fy gives the difference of tensions. 
7,— 7, . The brake-scale reading, multiplied by the brake-arm 
by and by 27r;/, n being the number of. revplutions, gives the 
delivered work in foot-pounds. The dynamometer scale-read- 
ing Ay multiplied by the equivalent dynamometer-arm tf and 
by znuy gives the work received in foot-pounds. The dp* 
mometer-arm a is to be found as described in Article itt 
page 253. 

198. Directions for Belt-test 

I. Before starting: 

{a) Get speed-indicator and log-blanks. 

ib) Oil all bearings and loose pulley under main belt 


(f) Balance scales A and C^ and note their ''zero* 

3. With test-belt off : 

{d) Take friction-reading on scales A for driving-shaft; 
punting its revolutions. 

{e) Weigh brake-arm (see note below) to get zero- 
^ding of scale B and then remove brake from brake-pulley. 

3. With brake off : 

(/) Put on test-belt (while loose), first moving brake 
haft frame by unscrewing hand-wheel next the floor. Tightesi 
«lt to read while at rest 75 lbs. net, on scales C. 

{g) Take friction-reading again on scales A. Count 
■evolutions of driving-shaft and read " per cent of slip/' from 
irhich the speed of brake-shaft can be calculated. 

4. Run I. 

(A) For tension of belt: Set scales Cto read 50 lbs. net 
with belt at rest, by screwing up hand-wheel next the floor, 
^hich should not be changed during the run. Take reading 
of scales C for each load added on brake-scales B. 

{%) 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 revolutions. 

{k) For power put into Jbelt : Read scales A and take 
speed of driving-shaft. 

(/) For slip of belt : Read graduated " slip-disk,** which 
'^as icx) equal divisions. When vernier is set, it turns with the 
^Jsk, and shows one per cent of slip when falling back one 
division during one turn of the slip-disk. 

{ni) Thus continue to increase brake-load by 5 lbs. ol 
'J^crements on scales B. Each time keep it carefully balanced, 
^d take simultaneous readings on scales A^ scales B^ scales C^ 
^p-disk, and revolution-counter. 

5. Runs II., III., and IV. 

(«) For run II., set tension-scales to read 75 lbs. nei 
n'th belt at rest, and proceed as in run I. Increase this in'tiai 
*nsion-reading by 25 lbs. each, for runs III. and IV. 




6. Measurement of machine-constants : 

((?) Get length in feet of (i) brake-arm, (s) dynamufr 
eter<ann, (3) arms of bell-crank acting on tension-scalet, lal 
(4) circumferences of test-belt pulleys, — latter with steel tapt 
Calculate diameters. 

(/) If the pulleys differ in diameter, the reading V 
slip-disk, obtained while running " light " (see (^ above), wl 
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 oO face i' 
pulley. Balance arm on scales while turning pulley first back- 
ward and again forward. The nnean of the two readings nil 
be the weight required. 

199. Form of Log and Reports as used in Sibley Col- 

Test of Belting by ll^. 

Description of Belt, Material Hade by 

Length feet. Width iDcbe*. TbkkneM bcbu. 

Cooditioa , 



' Q 































Arm of transmission-dynamometer ft 

Arm of Prony brake. " 

Hor. arm on tension-scales * ' 

Ver. arm on tension-scales " 

Diameter driving pulley in 

Diameter driven pulley 

Face driving pulley 

Face driven pulley 

Area of bearings, driving wheel sq. in. 

•• " •* driven wheel " ** 

Weight on bearings, driving wheel lbs. 

* driven wheel *• 

Kind of pulley used 




esultsof Test of Belting. 

ade by 190.. 

Ayerage of Results. 

uration of trial 

evolutions driving shaft 

evolutions driven shaft 

elt-speed. feet per minute.. . . 

*y name meter-scales, lbs 

jrake-scales, lbs 

ension-scales, lbs 

ircumfercnce driving pulley. . 
ircumfercnce driven pulley... 
dynamometer horse-power. . . . 

^rake, horse-power 


^jp of belt, per cent , . 

'>p of belt, feet per minute . . . 
horsepower per inch in width. 

Maximum tension, Tx 

Minimum tension, T% 


f- + 7-, 

y c of contact, degrees 

-oefficient of friction, per cent, 

'OSS due to stififness 

'OSS due to journal-friction. . . • 

Test No. 

Test No. 

Test Na 

Test No. 



200. Theory of the Flow of Water. — General Farmuh of 
Discharge. — The theory of the flow of water is fully investigated 
in Weisbach's Mechanics, Vol. I.; in Church's Mechanics of 
Engineering; and in the article " Hydromechanics," Encyclo- 
paedia Britannica. A very concise statement of the principte 
involved and formulae required are given here, preceding the 
actual methods of measurement of the flow, but studentsarcad* 
vised to consult the foregoing works. In the flow of water the 
particles are urged onward by gravity, or an equivalent force, 
and move with the same velocity as bodies falling through a 
height equal to the head of water exerting the pressure. " 
this head be represented by //, and the corresponding velocity 
in feet per second by v^ we have, neglecting friction losses, 

V = ^flglt (0 

If we denote the area in square feet of the dischai?c ori- 
fice by F, the quantity discharged in cubic feet per second by 
Qy then, neglecting contraction. 

Qz:^vF=FV2gh (2) 

It IS found, however, in the actual discharge of water, that, 
except in rare cases, i. The actual velocity of discharge is k^s 
..lan the theoretical; 2. The area of the stream discharged^ 
less than the area of the orifice through which it passes. These 

.osses are corrected by introducing coefficients. The cofffi^ 


oa] jfjiASUXEMSJ^r of liquids and gases. 271 

velociiy is the ratio of the actual to the theoretical velocity^ 
1 is represented by c^ • The coefficient ofcontractum is the ratio 
the least area of cross-section of the discharged stream to 
I area of orifice of discharge, and is denoted by ^«. The 
ifBdent of effitix or discharge is the product of these two 
intitieSy and is represented by c. 
If v^ denotes the actual velocity of discharge, we shall have 

v^ = c^V2gk. (3) 

The coefficient c^ is to be determined by experiment ; it is 
iriy constant for different heads with well-formed simple 
Bees. It often has the value ap/. The difference between 
\ velocity of discharge and that due to the head may be 
mssed in terms of the equivalent loss of head. Thus the 
al head producing outflow consists of a part, A« » producing 
\ actual velocity v^\ and a second part, h^^ expended in 
^rooming velocity and friction. Denote the ratio of these 
rtsby^r* Then 

K^^. (4) 

e also have 

*«A;, + *. = *^^+l), (5) 


*--^ <^ 

Since k^ is the head-producing velocity. 

'• = V^. =y/^g-^' 

... (7) 


By equating (7) and (3) we obtain the relation of 1; to <^ 

as follows: 

• <;=-^-i. ® 

Tke actual discharge 

Qa^cQ^cvF^cFVT^ (9) 

Since c ^^ c^^ » 


^c^J^^h^cJ^KJ zg-^^^. . (10) 

From equation (9), 

201. Formulae for Flow of Water over Weirs.*— A wdr 

is primarily a dam or obstruction over which the water is made 
to pass ; but the term is often applied to a notch opening to 
the air on one side, through which the water flows. In cases 
where the opening is entirely below the surface, it is spoken of 
as a submerged weir. The head of water producing the flow 
is the distance to the surface of still water from the centre of 
pressure of the issuing stream. The depth of the weir is meas- 
ured from the surface of still water to the bottom or sill of the 

Rectangular Notch. — Denote the coefficient of efHux by^, 
the depth of the weir in feet by //, the area in sq. feet enclosed 
by the wetted perimeter by /% and the number of cubic feet 
per second by Q. We have, as a formula applicable to open 
rectangular notches, 

Q^\FcVlih (II) 

* See Church's Mechanics, page 684; Rankine's Steam-engine, p. 90; Encyc 
Britannica, Vol. XII. p. 470; Bulletin on Irrigation and Used Wein, by pioL 
L. Cr. Carpenter, Fort Collins, Colorado. 


With most areas c increases slightly with the length and 
diminishes with the head ; it probably depends on the ratio of 
wetted perimeter to area, although it is not quite constant for 
\ triangular notches, in which this ratio is a constant one. Very 
complete and extensive experiments were conducted by J, B, 
Francis at Lowell, Mass., and from these experiments he de- 
duced the value of the coefficient of contraction to equal one 
tenth the head, and consequently for rectangular weirs 

Q = lc{6 ^ o.ihA)A V2gA, .... (12) 

fa which n = number of contractions. Applying this correc 
: tion to an ordinary rectangular notch with two contractions^ 
^ have the well-known Francis formula for rectangular weirs» 

Q = 1^* — o.2h)h Vzgh = 5.35<* — o.2h)h^. . (13) 

For heads ranging from three inches to two feet it has been 
found by experiment that 

^ = 0.62 and (2 = "VK* — 0-2A)^« 

Triangular Notch. — For the triangular notch in which apex 
b down, b the base at water-level, h the depth, 

(2 = (4 -•- lS)cbh V^ = 4.2^bhK . . . (14) 

Iftbe angle is 6o^ 

' ^s2Atan jo^s 1.1547A and Q^TJ^df. 

f iTAe angle b90^ 

b^2h and Q — ^^ ^Tgk. 

Trapezoidal Notch, — ^To avoid the corrections for contrac-^ 
ia0s» Cippoletti of Milan in 1886 proposed to use a trap^ 






zoidal notch of such dimensions that the area of the strea 
flowing through the triangular portion should be justsufficic 
to correct for the contraction of the stream in a rectangul 
weir. The proportions of such a weir, in terms of the leng 
at bottom of the notch, is as follows : height equal to six tent 
the bottom length, width of top equal to the bottom pi 
one fourth the height added to either side; the tangent oft 
angle of inclination of the sides equal to 0.25. It is assert 
that such a weir will give the discharge with an error less th 
one half of one per cent. The formula for the use of sud 
notch would be simply 

Q = \cbh V^i = 3.33*A« (I 

Submerged orifices, rectangular or circular, are sometim 
used for the measurement of water. The required formu! 
are given in the table following. 

From table in Weisbach's Mechanics, ^ = on the averaj 
0.6. For small areas it diminishes with increase of head fro 
0.7 to 0.6, and for large areas it increases with increase of bcJ 
irom 0.57 to 0.60. 

These formulae are conveniently tabulated as follows: 

202. Table of Formulae for Flow over Weirs. 

Form of Notch. 





Usual form . . .• 




Submerged.. . 




Triangular: ] 


Ang. at b. 60* 
Ang. at b. 90° 
Cippoietti's. . .| 


th over 
p of notch 

dth of 
ch at water- 

rage value 


discharge c. 

0. /^ u 

X ^ 


V M 

















2h tan a 


1. 1547/5 






Formula for discharge in ^ 
feet per secood. 

\cbk ^7sh 
%cb i^2^**^2iil 

^bk* tan a \^\ 

A^>»» V2gk 


When still water cannot be found above the weir, and we 
lave a velocity ofcapproach that can be measured and is equal 

^ = ^2gh\ we can compute h\ Then 

e=S-35^*[(A + >4')*->4'*3.* .... (16: 

In above formula Q = discharge in cubic feet per second, 
the length of sill at bottom of notch. 

203. EfHux of Water through Nozzles, or Conical Con- 
erg^ng Orifices. — In this case, if we denote least area in 
quare feet by /% in which cf' is the coefficient of contraction, 
' that of velocity, and c that of discharge, 

Q^c'c'^F^Tzgh^cF^flgh. . . • . (17) 

In this case the head is to be measured by a pressure-gauge 
tached close to the nozzle. 

The value of r is a maximum when the sides of the nozzle 
ake an angle of 13° 24', attaining a value of 0.946. When the 
»gle of the nozzle is 3° 10', c = 0.895, and when 49°, c = 0.895. 
►ee Church's Mechanics, page 692 ; " Hydromechanics,** 
ncyc. Brit., page 475.) 

204. Efflux of Water through Venturi Tubes or Bell- 
outhed Orifices. — A conically divergent orifice, with 
'unded entrance to conform to the shape of the contracted 
*in, is now termed, from the first experimenter, Venturis tube, 
he dimensions of such a tube, as given in Encyc. Britannica^ 
ol. XII., page 463, are as follows, in terms of the small 
ameter {d). Large diameter {D) at opening equals 1.25^/; 
ngth equals .62 5^, or ,^D. The sides are in section a circular 
:, struck with a radius of 1.625^, from a centre in the line o^ 


■ Rankine's Steam-engine. Hamilton Smith writes formula 


The formula of discharge is 

Q-^c'FV2gh. 09 

in which F\s 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. Weisbacb 
gives the value of c* as .959, .975, and .994 for heads respcc 
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, ^ indi 
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 BemouiDi, 
which may be stated in a general form as follows : " Tlu exttt* 
nal and internal work done on a mass is equal to the change 0} 
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 Bernouilli's theorem, as the 
velocity increases the pressure must diminish, and we shall 
find least pressuie at the points where the cross-sections arc 
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, 13 

7/ p 

1 h -s^ = constant; 

2g ' Y 

*See "Hydromechanics," Encyc. Britannicay page 468. 


. which t^ -7- 2g' is the velocity-head, / is the pressure per 
[uare foot, y the weight per cubic foot ; so that /^ -i- y is the 
ressure-head, and s the potential head, or vertical distance 
om any horizontal reference line. 

206. Flow of Water in Circular Pipes.* — In this case 
lere is a loss of head, A\ due to friction. Denote the sine of 
le angle of inclination by 1, diameter by d, length by L, loss 
f head by A/, all in feet coefficient of loss of head by C. 

v=4v • <■») 

From experiments of Darcy, 

C = 0.005 ( I H ^j for clean pipes; 

C = 0.01 f I ^ -0 for incrusted pipes; 

C =s o.a\^i + -^ in general ; 


Q = \crv. (21) 

Loss of Head at Elbows. — In this case the loss b principally 
lue to contraction. Weisbach gives the following (onnuis : 

A/ = C.- (22) 


See " Hydromechanics^ " Encyc. BritannioL 




If <p equal the exterior angle. 

C = 0.9457 sin* "I + 2.047 sin* -^, • • • fel 

From this are deduced the following values: 








1. 861 


For pipes neatly bent the value of C« is much less. 

By equating /// and h^ 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 : 



On substituting the values of C, as above, and C as equal to 
0.006, this additional length will be found not to vary much 
from 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 




Weisbach found Cc = O.505. By making A/ of equation (19) 
qual to /i^\ and reducing, we find the additional length, L, of 
:raight: j>ip« producing the same loss of head. 


Lssu.n^ng C bms an average value of 0.006, and C as above, 

Z = 2od. 

Loss of tstad by abrupt Contraction of Pipe.^^\n this case 
/eisbach found 

v = 



hich would correspond to an additional length of pipe equal 
> about 13 diameters. When the mouth of the contracted 
ipe is jeduced by an aperture smaller than the pipe, Weis- 
ach found the following values of Zc In the tabic, F^ is area 
f orifice, F^ that of pipe into which the flow takes place. 














3 077 

1. 169 











Globe valves produce about one half more resistance than 
I right-angled elbow, or an amount equal to an additional 
ength of about 60 diameters. 

207. Loss of Head in flowing through a Perforated 
Oiaphragm in a Tube of Uniform Section. — Let F, be the 
area of the orifice, Fthat of the pipe in square feet, C the co- 
iifficient of discharge, c the coeflRcient of contraction. 




The loss of head in feet 

C = 

2^ .2.S" 


Weisbach gives the following values as the results d e» 
periments : 



























20& Volume flowing through a Perforated Diaphrag& 
—Let Ha represent the head in feet on side of grreatest pro- 
ure, and H^ that on the opposite side. 

The loss of head 


From equation (26), by transposing and substituting; 

v = yJ^ = ^^{^H,-H,). ... (art 

The quantity discharged in cubic feet per secondt 

e=/;«'=/^,>y/f*(^a-^i). . - • . (rfi 

From this 

C = Qi K {^%i^ 


209. Measurements of the Flow of Water. — General 
'ihads. — The measurement of the flow of water is of import- 
:e in connection with efficiency-tests of pumps, water-meters, 
d steam-engines, as well as in determining the amount of water 
at can be obtained from a given stream. x 

The methods used for measurement of the flow usually con- 
t in making the water pass through open notches over weirs» 
rough standard orifices or nozzles, or through meters. 

The coefficients that have been given are in every case to be 
nsidered approximations only, and should be tested by actual 
sasurement under the conditions of use. 

The head of water is the distance from the centre of press* 
e to the surface of still water under atmospheric pressure. In 
se the water is under pressure and at rest, this head can be 
:asured by a calibrated pressure-gauge. The gauge is usually 
iduated to show pressure in pounds per square inch, each 
und being equivalent to a head of 2.307 feet of water at a 
nperature of 70° Fahr., pr to 2.037 inches of mercury. 

Ill case the water-pressure is read in inches of mercury, one 
:h of mercury corresponds to a head equal to 1.I13 feet. 

A convenient table, showing relation of pounds of pressure- 
ad in feet of water or inches of mercury, will be found in 
tide 260. 

210. Flow of Water over Weirs. — Methods of measuring 

* Head. — The head is measured most accurately by the use of 
i hook-gauge, used first by Mr. U. Boyden of Bostoti in 
40. Many of the English engineers still depend on the use 
floats. The head in all cases is to be measured at a distance 
fficiently back from the weir to insure a surface which is un- 
ected by the flow. The channel above the weir must be of 
(ficient depth and width to secure comparatively still water, 
le addition of baffle-plates, some near the surface and some 
ar the bottom, under or over which the water must flow, or 

* introduction of screens of wire-netting, serves to check the 
rrent to great extent. Such an arrangement is sometimes 
led a tumbling-bay. * 

The object of the baffle-plates is to secure still wat^r for the 



accurate measurement of height of the surface above the siil of 
tht weir. The same object can be accomplished by connecting 
a box or vessel to the water above the weir by a small pipe 
entering near the bottom of the vessel ; the water 
will stand in this vessel at the same height as that 
above the weir, and will be disturbed but little bf 
waves or eddies in the main channel. The hcJ^ 
of water is then obtained from that in the vessel 
Prof. 1. P. Church has the connecting-pipe pass ova 
the top of the vessel and arranged so as to act as a 

The Hook-gauge. — This consists of a sharp- 
pointed hook attached to a vernier scale, as shown 
inFig. 140, in such a manner that the amount it it 
raised or lowered can be accurately measured. To 
use it, the hook is submerged, then slowly raised 10 
break the surface. The correct height is the lead- 
ing the instant the hook pierces the surface. To 
obtain the head of water flowing over the weir, set 
the point of the hook at the same level as the siil 
of the weir. The reading taken in this positioo 
will correspond to the zero-head, and is to be sub- 
tracted from ail other readings to give the head of 
the water flowing over the weir. 

In some forms of the hook-gauge the zero d 
the main scale can be adjusted to correspond to 
HcxiK-oAucB. ^^^g zero-head, or level of the sill of the weir. 
Floats. — Floats are sometimes used : they are made of hot 
low metallic vessels, or painted blocks of wood or cork, and 
carry a vertical stem ; on the stem is an index-hand or pcinta 
that moves over a graduated scale. 

211. Conditions affecting the Accuracy of Weirs.— 
I. The weir must be preceded by a straight channel of con- 
stant cross-section, with its axis passing through the middle ol 
the weir and perpendicular to it, of sufficient length to secure 
uniform velocity without internal agitation or eddies. 

2. The opening itself must have a sharp edge on thf u^ 


ream face, and the walls cut away so that the thickness shall 
>t exceed one tenth the depth of the overflow. 

3. The distance of the sill or bottom of the weir from the 
3ttom of the canal shall be at least three times the depth on 
le weir, and the ends of the sill must be at least twice the 
epth on the weir from the sides of the canal. 

. 4. The length of the weir perpendicular to the current shall 
e three or four times the depth of the water. 

5. The velocity of approach must be small ; for small weirs 
I should be less than 6 inches per second. This requires the 
hannel of approach to be much longer than the weir opening. 

4. The layer of falling water should be perfectly free from 
he walls below the weir, in order that air may freely circulate 

5. The depth of the water should be measured with accuracy. 
It a point back from the weir unaffected by the suction of the 
low and by the action of waves or winds. 

6. The sill should be horizontal, the plane of the notch 

212. Effect of Disturbing Causes and Error in Weir 
Measurements. — i. Incorrect measurement of head. This 
nay increase or decrease the computed flow, as the error is a 
)ositive or negative quantity. 

2. Obliquity of weir; the effect of this or of eddies is to 
•ctard the flow. 

3. Velocity of approach too great, sides and bottom too 
lear the crest, contraction incomplete, crest not perfectly 
•harp, or water clinging to the outside of the weir, tend in each 
asc to increase the discharge. 

The causes tending to increase the discharge evidently out- 
umber those decreasing it, and are, all things being taken into 
ccount, more difficult to overcome. 

213. Water-meters. — The water-meter is an instrument 
»r measuring the amount of water flowing through a pipe. 
night makes seven distinct classes of water-meters, as follows:* 

* Knight's Mechanical Dictionary, Vol. III. 


1. Those in which the water rotates a horizontal case, or a 
horizontal wheel in a fixed case, delivering a definite amount 
at each rotation. 

2. A piston or wheel made to rotate by the pressure of tie 
water, the meter in this case being the converse of the rotary 
engine or pump. 

3. A screw made to rotate by the motion of the water. 

4. A reciprocating piston in a cylinder of known capsciiy 
driven backward and forward by the pressure of the water, 

5. The pulsating diaphragm, in a vessel of known cap.icity, 
which is moved alternately as the side chambers are filled iwl 

6. The bucket and balance-beam, in which the buckets rf 
known capacity on the ends of the beam, are alternately pre- 
Bcnted to catch the water and are depressed and emptied as they 
become filled. 

7. The meter-wheel, in which chambers of known capacity 
are alternately filled and discharged as the wheel rotates. 

Besides these seven classes, it is evident that any madiint 
may be used in which the motion is proportional to the velocity 
of flow of water. 

These classes can be united into two general classes: I. Po* 
tive ; II. Inferential, In class I. the water cannot pass wi;houl 
moving the mechanism, and meters of this kind are consiocfrJ 
more delicate and accurate than those in class II. 

Each class of meter has a registering apparatus, which i» 
general consists of a series of gear-wheels, so arranged isto 
move a hand continuously around a graduated dial, from whicli 
the volume can be read. 

214. Errors of Water-meters. — In addition to the constant 
errors of graduation, meters are liable to be clogged by tJirt, 
be affected by air in the water, and by change in the tempe* 
ture, head, or quantity of discharge of the water pas»ii( 

While the meter is no doubt of sufficient accuracy foreoO* 
mercial purposes, it should be used with caution in the mcasiw 
ment of water for tests or for purposes of scientific invest^ 


on. Before and after such tests a careful calibration of the 
leter should be made under the exact conditions of the test. 

The following directions explain the method of calibrating 
le weir notch and meter, arranged in series. In this experi- 
lent the water is to be weighed. Either instrument may be 
alibrated separately. In case the weir has been calibrated, the 
leter could be calibrated by direct comparison, without the 
se of weighing-scales. 

215. Directions for Calibrating the Weir Notch and 
Aeter. — The object of this experiment is to determine the 
oefficient c of formula (9), Article 201, page 272, and the ac- 
uracy of previous determinations. 

Apparatus needed, — Hook-gauge, pair of scales, thermom* 
tcr, spirit-level, pressure-gauge, weir, and meter. 

1. Accurately level the sill of the weir, and see that the 
lotch is in a truly vertical plane. 

2. Take the zero-reading of the hook-gauge, by setting the 
)oint of the hook with a spirit-level, at the same height as the 
ill of the notch. In case the form of the notch is such as to 
>revent the use of the spirit-level, grease the edge of the notch 
ind set the hook by the water-level ; being sure that the water 
surface does not, through capillary action, rise above the 
ower edge of the notch. 

3. Start the water flowing, and after it has obtained a con- 
»tant rate, take measurements of weights and of head. The 
commencement of the experiment to be determined by the 
rising of the poise on the scale-beam, which previously must be 
set at a given weight. Note the time, scale reading, thermom- 
eter-reading, reading of the hook-gauge at the beginning and 
t>nce in five minutes during the run. As the experiment ap- 
proaches the end set the poise of the scale-beam in advance of 
the weight, terminate the run when the beam rises, accurately 
noting the time, weight, thermometer-reading, and reading of 
the hook-gauge. Make direct measurements of the coefficient 
)f contraction. Calculate coefficient of discharge. 

4. If the water to the weir first passes through a meter, take 
orresponding readings of the meter-dial. Note the pressure 




and temperature at the meter. Calculate the number of cubic 

5. Draw on cross-section paper a curve of discharge, in 
which cubic feet per second are taken as abscissae and the cor. 
responding heads as ordinates. Also draw in dotted lines 00 
the same sheet a curve of coefficients, of discharge in which co- 
efficients are taken as abscissae, and corresponding heads af 
ordinates. Also, draw a curve showing error of meter for eact 

216. Form of Report. — The following form has been 
used by the author for calibration of the weir notch and meter; 


Made by ... 

at Date 

Number of Run. 




i < 






f ( 

Duration, minutes 

Temperature discharge, deg. F 

Readings of hook-gauge — Zero 




Weight of water — Beginning (tare) lbs. 

End of run ibs. 

Total lbs. 

Cubic feet per second Q, 

Contraction gauge — Beginning ft. 

End fl. 

Area — Wetted orifice sq. ft. 

'* Contracted section sq. ft. 

Coefficients — Contraction, Ce 

" Discharge, c 

" Velocity, t> 

*' Loss of head, Cr 

Meter — Beginning 



Cubic feet per second 

Error per cent 

Pressure-j^auge, lbs 

Thermometer, F" 




IV. ; V. 

Constants of Weir, Form Length ft. Angle of sides. 

Remarks t 

Meter, manf. by General class Ko...- 

Remarks Formulae: r >■ <«^ ^r = — — <• 


217. Calibration of Nozzles and Venturi Tubes. — These 
re often more convenient to use than weir-notches, in the 
leasurement of the efflux of water. Before using these they 
lould be carefully calibrated by measurements of the head 
nd discharge. The Venturi tube is sometimes inserted in a 
ingth of pipe; in this case the pressure should be observed 
n either side of the tube, and the discharge measured. The 
fecial directions for calibrating when discharging into the air 
rould be as follows : 

1. Arrange the nozzle or Venturi tube, so that the discharge 
an be caught in tanks and measured or weighed. 

2. Attach a pressure-gauge, which has been previously cali 
rated, to the pipe near the nozzle. Since the pressure is a 
jnction of the area of cross-section, the position ot the gauge 
hould be described and the area of the cross-section at that 
oint measured. 

3. Make careful measurements of least and greatest inter- 
al diameters of nozzles, of length of nozzle, and note condition 
f interior surface. Make sketch showing the form. 

4. Make five runs, as explained in directions for calibrating 
»'eir-notches, Article 215, page 285, obtaining weight of water 
>y the same method. In case it is not convenient to weigh the 
^'ater, discharge into tanks which have been carefully calibrated 
iy weighing, arranged so that one is emptying while the other 
s filling. 

5. Observe during run, reading of pressure-gauge, temper^ 
ature of discharge-water, weight of discharged water. Com 
3ute corresponding head producing flow, volume of discharged 
vater, and the coefficient of discharge in the formula 

Q — cF V2gh. 

6. Draw a curve showing relation of discharge in cubic 
ret to head, as explained for weir-notches, page 285 ; also one 
lowing relation of coefficient to head. 

218. Measurement of Efflux of Water through an Ori- 
cc in End of Tube of Uniform Section. — ^A cap can often 


be arranged over the end of a tube, and an orifice made in 
this cap with a sharp edge on the side toward the current, 
This will be found to give very uniform coefficients of dis- 
charge. The special method of calibrating this orifice would 
be as follows: 

1. Arrange the tube with a cap in which is an orifice, the 
area of which is one third that of the pipe. Ream the sides of 
the orifice so that a sharp edge will be presented to the out- 
flowing water. Attach a calibrated gauge at a distance of two 
diameters of the pipe back from the orifice. Arrange to weigh 
or measure the discharged water. Measure the orifice. 

2. Make runs as explained for other calibrations with five 
different heads, and notereadingof pressure-gauge, temperature 
of discharged water, weight or volume of discharged water, and 
least diameter of stream discharged. The least diamelerof the 
discharged stream can be measured by arranging two sharp 1 
pointed set-screws in a frame, so that they can be screwed | 
toward each other. These screws can be made to touch the 
outflowing stream, and the distance between their points mea^ 

3. Compute head producing the flow, coefficient of con- 
traction, which is ratio of area of stream to area of orific(i 
coefficient of discharge, and loss of head. See equations (l) 
to (10), Article 200, page 272. 

4. Draw curves on cross-section paper showing the relation* 
of these various quantities. 

5. Repeat tiie experiment with orifices of different size*. 
Z19. Measurement of the Flow of Water in Pipes by 

use of a Perforated Diaphragm or of a Venturi Tube,— In 
this case the loss of head flowing through the orifice in the 
diaphragm or the Venturi fubf must be measured ; then, know- 
ing the coefficient of efflux and area of cross-section, the vol- 
ume discharged can be computed by equation (28), Article 
2o8, page 280; also Art. 204, p. 275. 




The difference of head is measured accurately by inserting 
tubes at a distance of two diameters on each side of the orifice, 
connecting each of tliese tubes to a U-shaped glass tube partly 
filled with water, very much as shown :n Fig. 145, page 294^ 
except that the ends of the tubes A and B are in each case 
perpendicular to the pipe, and are on opposite sides of the 
diaphragm. The difference in the height of the water in the 
two branches of the U-shaped tube will be the loss of head 
{H, — //,) caused by the orifice. It is essential that the tubes 
be connected into pipes having equal areas of cross-section, 
since the pressure, even in the same line of pipe, increases with 
the area (see Article 205). The coefficient C should be deter- 
mined by calibration, following essentially the same method a» 
that prescribed for nozzies and Venturi tubes in Article 217. 

220. Measurement of the Flow of Water in Streams.* — 
This is done by ([) Floating bodies; (2) Tachometer ; (3) Pilot's 
tube; (4) Hydrometric pendulum, 

Fioaling bodies, when used, should be small, and about the 
I density of the water. A floating body with a volume about 
1 one tenth of a cubic foot is belter than larger. They can be 
I made of wood and weighted, or of hollow metal and partially 
I filled with water. A coat of paint will ser\'e to render them 
■ "Haible. To obtain the velocity for different depths, the sur- 
I face velocity is first found, the float is then connected with a 
Iweighted ball that can be adjusted to float at any depth, and 
I the joint x-elocity observed. 

Call the surface velocity v, , the joint velocity v^ ; then will 
I the velocity of the submerged ball be 

W, = 2I'„ — V,, 

A floating staff that remains vertical in still water is some- 
poes used. 

e floats are used, the velocity is obtained by noting 
' time of passing over a measured distance. The measured 
nice should be marked by sights, so that the line of begin 

• Sec WeiBbaeb'* Mechanics, Vol. 1. 


ning and ending can be accurately determined. The float 
put in above the initial point, and the instant of pas^ tl 

firsi iiid last lines of the course is to be determined byS 

221. The Tachometer, or Woltman's Mill, c 
small water-wheel connected to gearing so as to repl 



of revolutions. The wheel is. anchored at the required 
the stream, and at a given instant, the time of which 
on a stop-watch, the gearing is set in motion by pull- 
lever ; at the instant of stopping the experiment, the 
: stopped by a trip. The machine is removed, and 
ber of revolutions multiplied by a constant /actor gives 
space moved by the water; this divided by the time 
: velocity. 

shape of the vanes of the revolving wheel are varied 
ent makers, and the wheel is made to revolve either in 
ital or a vertical plane. 

[41 shows a form used extensively, in which the gearing 
tering the number of revolutions is operated by an 
:urrent, and can be seen at any instant. 
;lectric register shown in Fig. 142 can be located at 
mce from the tachometer convenient to the observer, 
iration. — The constant (actor, which multiplied into 
reading gives the velocity, is obtained by calibration, 
iration is performed by attaching the instrument to 
• a boat, and towing it past fixed marks at a known dis- 
m each other. The velocity is obtained as for floating 
nd the constant is found by comparing this with the 
of the instrument. One method of calibrating the 

nt is as follows (see Fig. 143) : The instrument is 
to the bow of a boat, so as to remain in a vertical 
the water being still, and little or no current. The 
iropelled by a cord, which may be wound up by a 
; the motion must be in a right line, and over a known 





distance. Several trials are to be made, and the average results 
taken, and reduced by the method of Least Squares, as ex- 
plained in Chapter I. 

The tachometer is the most convenient, and if properly 
constructed the most accurate, niethod of measuring the ve- 
locity of running water. 

222. Pitot's Tube. — This is a bent glass tube, held in the 
water in such a manner that the lower part is horizontal and 
opposite the motion of the current. By the impulse of the 
current a column of the water will be forced into the tube and 

held above the lev^l of the water in 
the stream ; this rise, DE (see Fig. 
144) is proportional to the impulse 
or to the velocity of the water that 
produces it. If the height DE above 
the surface of the water equal h and 
the velocity of the water equal f, 
^ we have 

~ in which c equals the coefficient to be 
determined by experiment. 

To determine the coefficient c, 
F,G. ,44.-PiTOT's Tube. ^j^^ instrument is either to be held 

in moving water whose velocity is known, or else moved 
through the water at a constant velocity. From the known 
value of V and the observed value of k the coefficient ^ can be 

Weisbach found that with fine instruments, when the 
velocities were between 0.32 and 1.24 meters (1.04 and 4.06! 
feet) per second, that 

V = 3.545 V7i meters per second, 
or, in English measures, 

V = 6.43 i^/i feet per second. 


Pitot's tube, as ordinarily used, is shown in the diagram 
ig. 145. It consists of two tubes, one, AB, bent as in Fig. 
14, the other, CD, vertical. The mouth-pieces of both tubes 
-e slightly convergent, to prevent rapid fluctuation in the 

ibes. These tubes are so arranged that both can be closed at 
ny instant by pulling on the cord ss leading to the cock R. 
ktween the glass tubes dD and bB is a scale which can be read 
losely by means of the sliding verniers m and «. The tubes 
ire connected at the top, and a rubber tube with a mouth-piece 
5 is attached. 

In using the instrument it is fastened to a stake or post by 
he thumb-screws EF\ the bent tube is placed to oppose the 
Jrrent of water, the cocks K and R opened. The difference 
I height of the water in the tubes will be that due to the 
-locity of the current. The water in the column dD will nnt 
5e above the surface of the surrounding water, and the instru- 
*^nt may be inconvenient to read. In that case some oi the 
r may be sucked out at the moiith-piece O, and the cock K 
Osed; this will have the effect to raise the water in both 



18 "J- 

columns without changing the difference of level, so that (he 
readings can be taken in a more convenient portion; or by dos- 
ing the cock K, by pulling on the strings ss, the instnimeiK 
may be withdrawn, and the readings made at any convenieol 

223. Pilot's Tube for High Pressures. — A modifitd 
form, as shown in Fig. 146, of Pilot's tube is useful for obtain- 
ing the velocity of liquids or gases flowing under pressure. 
Tbf arrangement is readily understood from the drawiog. 

Pio. 1 4fi.— Sketch 

The ditTcrcnce of pressure is shown by the difference in hdghts 
of the liquid in the branches of the U-shaped tube Mll'\ this 
dilTcrencc is due entirely to the velocity, since both brandies 
are under equal pressure. Thus, if the liquid stand atM on 
one side and at .1/' on the other, the velocity is that due to the 
height of a column of liquid e(|ual to the distance that 2/ is 
above W. Call this distance /(; then 


The cocfTicicnt c is to be determined by experirae;its miJe 
on a lube iii which the vilocity of llow is known. 


224. Hydrometric Pendulum. — This instrument consists 

^ a ball, two or three inches in diameter, attached to a string. 

The ball is suspended in the water and carried downward by 

fte current; the angle of deviation with a vertical may be 

'Heasured by a graduated arc supported so that the initial or 

2ero-point is in a vertical line through the point of suspension. 

Jf the current is less than 4 feet per second an ivory ball can 

be used, but for greater velocities an iron ball will be required. 

The instrument cannot give accurate determinations, because 

of the fluctuations of the ball and consequent variations in the 

angle. The formulae for use are as follows : Let G equal the 

'^•eight of the ball, D equal the weight of an equal volume of 

'^•ater ; then G — D\s the resultant vertical force. Let F equal 

3.rea of cross-section of the body, v the velocity of the current, 

^ a coefficient to be determined by experiment ; then we have 

the horizontal force P = cFv^, Let angle of deviation be S\ 


P cFv" 

tan o = 

f rem which 


D ) tan d 

The best results with this instrument will be only approxi- 

225. Flow of Compressible Fluids through an Orifice. — 

General Case, — In this case, as heat is neither given nor taken 
Up, the flow is adiabatic. The formulae are deduced by prin- 
ciples of thermodynamics, and their derivation can be studied 
m treatises devoted to those subjects.* 

Denote the velocity by v, the weight per cubic foot by Gy 
/he pressure per square foot in the vessel from which the flow 

♦ Sc« Pcabody's Thermodynamics, p. 132; also, art. ** Hydromechanics, 
Encyc. Britannica. 



takes place by p^ , the pressure against which the flow takes 
place by/,, the volume of one pound in cubic feet by C, the 
absolute temperature corresponding to pressure/, by 7,, the 
ratio of specific heats by y. 




rr« — »j^ 311 Q ^ ,j^ — — ^ T^* • • • Kjr^l 

226. Flow of Air. — For air, /„ = 21 16.8, G. = 0.08075, 
7", = 492.6 at 32° Fahr., y = 1.405. Inserting these numerical 
values, we have the following equation for the theoretical 
velocity of flow of air through an orifice: 

g=,s3.6.,{--(irK- • <" 

Volume of Air discharged. — The volume of air discharged, 
in cubic feet per second at pressure of discharge, is to be com- 
puted by multiplying the area of the orifice F^ in square feet, by 
the velocity z/3, by a coefficient of discharge c. Then 


Substituting numerical values for the ratio of /, to /, , >»'C 

Q^= \o%.7cF,Voa6()^T^ (33* 

* See article *• Hydromechanics," Encyc. Britannica, Vol. XII, page 481 



To express this in terms of the volume discharged from the 
eservoir (2i » in which /, is reservoir pressure and /, pressure 
i discharge, we have 

a = mo,. 


Substituting numerical values for free flow, 

G. = (0.527)' *"<2, = 0.6339(2,; 

(2. = io%.7cF{ff' ^ T^ { . - l^^J'' I . . . (34) 

Substituting values of/, -r-/,* 

Q,=:6%.%cF,VoA6gsT, (35) 

227. Velocity of Flow of Air through an Orifice. — The 

elocity of flow is obtained by substituting numerical values in 
le preceding equations. We have, denoting by T^ the abso- 
ite temperature in the reservoir as the greatest velocity of 
ow of air, 

-^= 183.6 rxi -0.8305). 


Solving equation (36), we have the following theoretical 


Temperature of Air in Reservoir. 


Velocity of 
Flow in Feet 

Degrees Fabr. 


per Sec. 












1 105 














228. The Weight of Air discharged.— This is to be com- 
puted by multiplying the volume of discharge by the specific 

Thus the weight of air is 

(7, = ^ 'y. pounds per cubic foot, 

when /, and T^ are, respectively, pressure and absolute tcm- ^ 
perature in the reservoir. Hence the weight of air dis- 
charged is 

W, = Q,G, = ioZ.7cF,G,i^0^ T,{i -i^J" . • (17) 

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 I.I atmospheres 0.97 to a99 

Circular sharp-edged orifices 0.563 to 0.7 

Short cylindrical mouth-pieces O.81 to 0. 

The same rounded at the inner end O.92 to 0.93 

Conical converging mouth-pieces 0.90 to 099 

In the general formula for the flow of air, the weight de- 
livered becomes a maximum when 

P^-( 2 v-« 

p, \y + 1/ 

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 


brough a small tube or orifice, the pressure in the orifice may 
»c less than the back-pressure. 

229. Flow of Air in Pipes. — When air flows through a long 
ipe, a great part of the work is expended in overcoming fric- 
lonal resistances. This friction generates heat, which is largely 
sed in increasing the pressure in the pipes, tlie only loss being 
■om radiation, which is small. 

The expansion then is isothermal, the heat generated by 
iction exactly neutralizing the heat due to work. 

For pipes of circular section, when d is the diameter, / the 
riigth, /, the greater and /, the less pressure, T the absolute 
*mperature, C the coefficient of discharge, r^(= 53.15 foot-lbs.) 
le specific heat, we have the initial velocity 

his may be reduced to 

«. = (l- 1319 - 0-726^')y ■ 

4C/ • 

It has been found from recent experiments that fair values 
f the coefficient are as follows : * 

C = 0.005(1 +f^ 

ordinary pipes for velocities of 100 feet per second ; 

C = 0.0028 


T pipes as smooth as those at the St. Gothard Tunnel. 

• Sec " Hydromechanics," Encyc. Britannica, Vol. XII, p. 491. 




Weight of air flowing per second in circular pipes in pounds 
is given by the equation 

=0.61 1/ { ^fp.'-f!) \ . 


W^=(o.69i6a-o.4438A)(^) . . . . (39) 

230. Flow of Steam through an Orifice. — Velocity,—h 
this case, as in Article 226, the expansion is supposed to be 

Denote by A the reciprocal of the mechanical equivalent 
of one B. T. U. corresponding to the quantity 778; byjr, 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^ the latent heat 
per pound in reservoir, r, the same in the tube ; Z", and T^ the 
respective absolute temperatures, 6^ and 6^ the respective 
entropies of the liquids, c the specific heat of the liquid, ^, 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<r. 

jr, can be determined from the relation expressed in the 





no tables are at hand for S^ , its approximate value can be 
:ed, since 


(f,-d, = c\og,f^ 



■y = -y- + C log, y^. 

inating x, in equations (40) and (41), 

=yi(7;~7;)- 7;(^.-^.)+(^ -^,)+^a(^.-/0- (43) 

he following table, condensed from Peabody's steam 
5, gives the value of the entropy of the liquid : 







of the 


of the 














0.2842 1 




0.3143 ! 
















0.38 1 1 























I the above equations^ has a numerical value of I -$- 778, 
learly equal to 0.016, ^ to 32.16. 

* See Thermodynamics, by Peabody, page 138. 


It has been shown that in the flow of saturated steam/, 
will not fall below 0.58 of/,, 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 /, equal to 0.^,, 
the velocity will be found to be nearly constant, and to va^ 
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 



in which W''= weight discharged in pounds per second, /" = 
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, J", is a con- 
stant quantity. Thus 

/z/ _/W 
T " T,' 

If / and T can be kept constant, the quantity discharged 
will vary as the volume ; if/ and T are known, the quantity di**! 
charged can be computed. 

Gas-meters are instruments for measuring the volume 01 
gas passing them. They are constructed on various plans aw 
are known as Wet or Dry, depending on whether water is usei 
The volume is usually measured in cubic feet. 

Meter-prover. — This is the name given to a sort of gasotnetcfj 
arranged as shown in Fig. 147 It consists of an open vessd 



partly filled with water, into which a vessel, AF^ of some, 
smaller diameter is inverted. The weight of the vessel AF 
interbalanced by a weight )f^ which descends into a vessel 
ter CK at such a rate as to keep the sum of the displace- 
s of the two vessels constant, in which case the pressure 

Fia 147. 

he confined gas in the vessel AF will remain constant 
gas flows out through the pipe 7", its pressure being taken 
manometer at w, its temperature by a thermometer at /. 
*ig. 148 shows a form of meter-prover made by the Ameri- 
Vleter Co., in which the counterweight lifts an additional 
ht moving over an involute wheel, so calculated that the 
»ure on the outflowing gas remains constant. These instru- 
:s are used principally to calibrate meters ; they give very 
rate results, but are not suited for continuous measure- 

Vet-meter. — The wet-meter works on the same principle as 
meter-prover, but is arranged with a series of chambers 


which are alternately filled and emptied with gas. These 
chambers are usually arranged like an Archimedean screw, as 
shown in section in Fig. 149. 

Gas is admitted just above the surface of thewater.MiJ 
raises the partition of the chamber, bringing it above thewaW 
and filling it. The outlet-pipe is submerged until the chambtt 
is filled. It is connected with the case of the meter, asshoto 
in the figure. The gas is completely expelled as the cyliw''' 


The wet-meter is a very accurate measure of the gas pass- 
ng, provided the water-level be maintained at the constant 
tandard height. Any change of the water-level changes the 
tze of the chambers accordingly. The motion of the cylinde> 
tctuates the recording mechanism. 

The Dry Gas-rneler. — The dry gas-meter possesses the ad- 
^'antage of not being affected by frost, nor of increasing the 
fcinount of moisture in the gas. Tlie dry-meter is made in vari- 
'iiii forms, and generally consists of two chambers separated 
■rom each other by partitions. Each chamber is divided into 
t\i'o parts by a flexible partition which moves backwards and 
•oniards, and actuates the recording mechanism as the gas 
9ows in or out. This motion is regulated by valves somewhat 
Mmilar to those of a steam-engine. The gas-meter is calibrated 
by comparing with a meter-prover as already described, 
lliese meters are not supposed to be instruments of great 



IS =35 

233. Anemometers. — Instruments that are used to measurt 
the velocity of gases directly are termed anemometers, Tlicj 
consist of flat or liemispherical vanes mounted like arms of i 
light wheel so as to revolve easily. The motion of the wheel 
actuates a recording mechanism, Robinson's Anemomcler, 
which consists of hemispherical cups revolving around a vertic^ii 
axis, is much used for meteorological observations. 

A form shown in Fig, 150 with flat vanes, and with liie 

dial arranged in the centre as shown, or on top of thecs*' 
various positions, is much used as a portable instrument- 

The dial mechanism of the anemometer can be sta'^* 
stopped by a trip arranged convenient to the operator 1 '" 
instances the dial mechanism is operated by an electric cu' 
similar to that described in connection with the tacho"* . 
Article 221, page 262. It is also made self-recording, b>' * 
ing clock-work carrying an endless paper strip which i* 
under a pencil operated by the anemometer mechanist*" 


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 

'W'eight 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. 


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- 
eye. 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 follo>\'ing 
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 j 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-pmnps, in which the impulse of one mas:^ 
of fluid is used to drive another. 



237. Energy of Falling Water. — Hydraulic motors are 
Iriven either by the weight, pressure, or impulse of moving 
rater. Neglecting the losses due to friction or other causes, 
he energy of falling water is the same whether it act by (I.) 
vcight, (11.) by pressure, or (III.) by impulse. This is proved 
s follows : 

Let h equal the head or total height of fall, Q\\i^ discharge in 
ubic feet per second, G the weight per cubic foot,/ the pressure 
n pounds per square foot, v the velocity in feet per second, P 
he pressure in pounds per square inch. Since the work done 
s equal to the product of the force acting into the space moved 
hrough, we have for the work done per second in the several 

:ases (I.) GQh, (II.) (/0, (III.) GQ— ; but since / = Gh and 

4 = — , we have by substitution 


GQh =^ pQ ^ GQ- = \uPQ. .... (I.) 

238. Parts of an Hydraulic Power-system. — The hydrau- 

ic power-system in general requires — 

1. A supply-channel or tube leading the water from the 
li^hest accessible level. 

2. A discharge-pipe or tail-race conveying the water away 
rem the motor. 

3. Gates or valves in the supply-channel, and a wastcKrhao* 
lel or weir to convey surplus water away from the motor. 

4. The motor, which may belong to any of the classes jfc- 
cribed in Article 236. and suitable machinery for transmtttiK: 
he energy received from the motor to a place where it 
JscfuUy applied. 

239. Water-pressure Engines.*— Water-pressure 
^re well adapted for use where a slow motion is 
great pressure is accessible. 

♦ Sec Wcisbach's Hydraulics, Vol. II, p. 558. 


These engines resemble in many respects a steam^iigine, 
water being tlie motive force instead of steam. They consist 
of a cylinder (Fig. 151) in which a piston T is worked alter- 

Fig. ip.— Watih-i 

nately forward and backward, water being admitted altematelji 
at the two ends of the cylinder by the moving shde-valvc 5- 
While water is passing into one end of the cylinder llirough 
the passages D, E, C, it is being discharged through the pipe 
£, G, H, which is proportioned so as to afford a free exit lo 
the water. Near the end of the stroke of the piston the slid* 
valve S closes both admission-ports, and the pressure in the 
cylinder C, is increased by the diminution of volume caused 
by the motion of the piston. When the pressure in the chaow 
ber tT, exceeds that in the supply-pipe the valve W, 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 isW 
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 ne* 
stroke is commenced. 

240. Vertical Water-wheels.— There are four classes o( 
vertical water-wheels : 

I. Overshot, in which the water is received on the top of 




J 241.] 

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- 
fulse 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- 

suppiy of from 3 to 25 cubic 

feet per minute. On the 

outside of the wheel is built 

a scries 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 Fic. ij^.— sscnow or ovHKSHor wat»«- 
ttie top. The head of water whkil. 

above the wheel must be sufficient to give the falling water 
greater velocity than the periphery. The peripheral velocity 
■ n practice is from 5 to 10 feet per second, that of the falling 
Vatcr from 9 to 1 2 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 

(ust free from the discharged water. 

The principal formulse relating to the overshot-whcel arc as 

follows : 


Let d equal the depth of the buckets, b the width ol tlit 
wheel, r the radius of the wheel, « the number of revolutioni 
per second, v the peripheral velocity in feet per second, ^ibe 
water-supply in cubic feet per second, Q^ the capacity of lb»I 
part of the wheel that passes in one second, m the ratio odlw 
water actually carried to the capacity of the bucket! 

usually about one (ourth- 

ber of buckets. 

Then, supposing the wheel to be set just free of thett 

h= ■2r-\-{\\ to 2) all in feet; 
N =■ —J- = , usually, 6r ; 

= —{2rd—d') — bdv, nearly; 
= mQ^ z=.mbdv ; 




The efficiency is the ratio of the work delivered to the en- 
gy received from the falling water. 

The efficiency of the best wheels of this class reaches 75 
r cent. 

242. Breast-wheels. — The form of breast-wheel is shown 
Fig. 153. The water is received at a height slightly above or 
low the centre C of the wheel, and is prevented from falling 
ay from the wheel by the curved breast ABE; the water 
ts on the radial or slightly curved buckets, thus tending to 
/olve the wheel partly by weight and partly by impulse. 

The flow of water is regulated by a gate at S. 

The formulae applying to breast-wheels are essentially the 
ne as those for overshot-wheels. The efficiency of the best 
leels of this class varies from 58 to 62 per cent. 

243. Undershot-wheels. — The undershot-wheel differs 
>m the breast-wheel in receiving the water at or near the 
ttom ; the water flows in a guide under the wheel, which guide 

some cases extends some dis- 
ice up the sides. The usual form 

such wheels is shown in Fig. 
4; the buckets or floats are often 
dial, sometimes, however, of con- 
ve or bent form. 
If we let c equal the velocity of 
Iter as it strikes the wheel, v the 
ripheral velocity of the wheel, Q 
e quantity of water in cubic feet ^^^ »54.-Undkrshot-whebl. 
r second, G the weight per cubic foot, //, the portion of the 
ad corresponding to the elevation of the entering water as it 
"ikes the wheel over that of the discharge, P the force de- 
ered at the circumference of the wheel; then will the effi- 
-ncy 7 be obtained by the following formulas :* 


V = 



•Sec Wcisbach's Hydraulics, page 291. 


From experiments of Morin it was found that whent;-rf 
was less than 0.63, the efficiency 7 was 0.41. When v -5- r was 
between 0.63 and 0.8, r^ was 0.33. The efficiency obtained 
from the best form of these wheels is 0.55. 

Poncelefs Wheel. — When the floats of the undershot whed 
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 
:he 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 arc 
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, a 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, 

L = Pv = ~'{c — z)v\^i — cos a\. 

This is maximum when v = ^c. 

In case a hemispherical vane is used, a will equal 180®, and 
I — cos « = 2. For that case, a = 180** and v = ^c^ we have 

In case the absolute velocity of the particles leaving the 
vane equal zero, an efficiency equal to unity would be possible. 




tee or more jets of water are lifeed as necessary to produce 
aaximum power. Fig. 155 shows the Pelton wheel, provided 
four jets. The bucket of this wheel shown at B is of double 
spherical form with a sharp midriff, separating the two parts, 
I splits the jet and turns each part through an angle of 
The efficiency of is wheel has in some instances ex- 
9 80 per cent. 

Sere is a large number of motors in' this class, some of 
1 arc adapted for high heads and lai^c powers. The Doble 
! is proWdcd nith a ntiedle regulating- valve controlled by 
ovemor. The Cascade has buckets arranged on each side of 
heel, ihe edge of ihc wheel serving to divide the jet. Most 
; small hydraulic motors are of impulse type. 
fi. Turbines- — The turbine-wheels receive water con- 
fe and uniformly, and usually in each bucket simultane- 
j The buckets are usually curved, and tlie water is guided 
Hie buckets by fixed plates. The name was originally 
n in France to any wheel rotating in a horizontal plane, 

Lwheeb are now frequently erected so as to revolve in 
planes. The turbine was invented by Foumeyron in 
: original wheel being constructed to receive water near 



the axis, and to deliver it by flow outward at the circumlcf*|^ 
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 

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 dl^ 
charge-surface of the wheel, with its angular momentum rela- 
tive to the wheel changed. It must exert a couple —My 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^ , c^ be the tangential com- 
ponents of the velocity of the water at the receiving and di^* 
charging surfaces of the wheel, r, , r, the radii of these surfaces. 

___^ l^ 

♦Sec *' Hydromechanics, " Encyc. Britannica. 


is the angular velocity of the wheel, the work done on 
si is 

total head of the water h^ is reduced by friction and 
es hp in the channels leading to the wheel, so that 
:tive head h which should be used in calculating the 
yr is 

h = h,-h, (3) 

^e the construction of the turbine requires that it set 

lil-race d feet, the velocity of water in the turbine 

)e calculated for a head of //— rf^ but the efficiency for 

f h feet. The work of the turbine is partially absorbed 


T equal the total work, T^ the useful work, and 7i the 

id in friction. Then 

T=T,+ T, (4) 

>s efficiency 

raulic efficiency 

'' = -^ <^ 

hydraulic efficiency is of principal importance in the 
' turbines. Substituting this value of T in equation (2), 

the fundamental equation in the theory of turbines. 



IS 247. 

For greatest efficiency the velocity of the water 
should be o, in which case ^, = o and 

V — 

. (!) 

But r,a is the lineal velocity of the wheel at the inlet suriace; 
if we call this F, , 


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 preccd- 
ing formulae. The best values are the ones obtained by ex- 
periment. Let V^ equal the peripheral velocity at outlet, Pj 
at inlet, r^ and r< the corresponding radii of outlet and inlet 
surfaces. Then we shall have as best speeds* for 

axial-flow turbine F^ = Vi=. 0.6 \2gh to 0.66 f2p^; 


radial outward-flow turbine Vi = 0.56 \2gh ; V^—Vc'^ 


radial inward-flow turbine Vi = 0.66 V'2gA ; V^ = Vr 

247. Forms of Turbines. — Fourneyrons Turbine.—'V^^'^ 
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 insectioikl 
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 A A is supplied witli 
curved buckets bd^b^d^, so arranged as to absorb most oftbc 
energy of the water; the water enters the wheel at thcin*^*^ 
edges of the buckets and is discharged at the outer circu*^' 

* >« 

Hydromechanics " Encyc. Britannica. 


'etice. Gates for regulating the supply of water are shown in 
ction between the ends of the guides and the wheel. 

Fio. IS*.— luTw^BPTuow Timiu™. 

248. Reaction -wheels. —The simple reaction-wheel 

own in Fig. 157, from which it is seen to consist of a vertical 

Bndcr, CB. which receives the water, and two cylindric arms, 

and F\ on opposite sides of each 

i a circular orifice through which 

atcr is discharged. The effect 

this arrangement is to reduce the 

iure on the sides toward the ori- 

B, thus producing an unbalanced 

Bsure which tends to make the 

kI revolve. If we denote by // the ' 

liable fall measured from the level 

the water in the vertical pipe to tli'. 

tre of the orifices, r the radius nf 1 

Uion measured from the axis to 1 

tic of each orifice, v the velocity of discharge, a the angular 

Dcity of the machine, F the area of the orifices,— when at 

the velocity would equal '^zgh, but when in motion the 

iter in the arms moves with a velocity ar. which corresponds 

increased head due to centrifugal force of aV -— 2g. 




Hence the velocity of discharge through the orifices b 

V = V2gh + aV ; 
lhe quantity discharged 

Q^Fv = FV2gh + a^r^. 

Since the orifices move with a velocity ar, the velocity witk 
reference to a fixed point is 2/ — ar. 

If G be the weight per cubic foot, the momentum or mass 
times the velocity is 


(v — ar) 

This mass moves with an angular velocity a and arm r, hence 
the work done per second in rotating the wheel is 


{v — ar)ar foot-pounds. 

The work expended by the water-fall is GQ/L 
Hence the efficiency 

V = 

(v — ar\cir 

This increases as ar increases, or the maximum efficiencyiJ 
reached when the velocity is infinite. The friction considera' 
bly reduces these results, and experiment indicates the greatest 

efficiency when ar = ^2gh. In which 
case, by substitution, we should have 

V = 0.828. 

The best efficiency realized in pr>^ 
tice with these wheels is about O.60. 

The Scottish turbine, shown in Fig* 

1 16 in section, is a reaction-wheel with 

Fig. 158.-SCOTTISH Turbine, thrcc dischargc-jets, thc watcr being 

supplied from a tube filled with water under pressure beneath 

the wheel. 




249. The Hydraulic Ram. — ^The hydraulic ram is a ma* 
hine so arranged that a quantity of water falling a height k 
^rces a smaller quantity through a greater height h\ 

Pig. t59.-^ydrauuc 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 o^ opening into the chamber 
Cfrom the pipe ss. 

2. The waste-valve, Bd^ is a weighted clack or check* 
^ve, opening inward and connected to a stem df\ on the 
»tcm is a nut or cotter at f to regulate the length of stroke, i.e.^ 
^ount 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 
iJie backward wave-motion ; its length must not be less than 
five times the supply-head. The working parts of the ram are 
ie check-valve o and the waste-valve dB ; these parts move 
11 opposite directions, and alternately. 

The action of the ram is explained as follows : 




Water is supplied the ram by the pipe ss; the waste-vain 
dB being open, the water escapes with a velocity due to W 

height h. The water escaping at d suddenly closes the wasl^ 
valve. The acquired momentum of the moving column w 
water in the pipe ss is sufficient to raise the valve o and difr 
charge a portion of its weight to a height h'. As soon as the! 
pressure is reduced the valve o closes, the waste-valve rffi opeiwi 
md the water again flows down the pipe ss. These inotionsl 
are produced with regularity, and the water acquires a backward 
and forward wave-motion in the pipe ss. A small air-ch^mbcrj 
at/, with a small check-valve opening inward at c tosupplylln 
chamber with air, are found to add to its efficiency. 

The wave-motion has been utilized to operate a piston bacfc 
ward and forward beyond the waste-valve, the piston beiiq 
utilized as a pump in raising water from a different supply. 

Formula. — Let //equal the height of the reservoir abort 
the discharge- valve of the ram, h' the height to which tin 
water is raised above reservoir, Q the total water supplied 
the ram per second, q the amount raised to the height A'.Ctd 
weight per cubic foot. Then the useful work equals Gqli; iIK 
work which the water is capable of doing equals Gfi(_Q — q\ 

The efficiency 

Rankinc (see Steam-engine, page 212) gives the foliowiBJ 
formulae for obtaining the dimensions of a ram : 

Let L equal lengtli of supply-pipe, D the diameter * 
Bupply-pipe in feet; other symbols as above. Then 

L= k + h' 


Volume of air-chamber C equals volume of feed-piptl 

250. Methods of Testing Water-motors. — The metliBl 

j( testing hydraulic motors require in all cases the mcasuit 



ment (l) of volume or weight of the water dischai^ed, (2) of 
the net head, or pressure acting on the motor, or (3) the 
velocity of discharge. From these measuremeiUs may be com. 
puted the tncrgy received by the motor, by the formulas 
already given. 

1, Mtasurement 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 white 
:he other is emptying. Temperature observations must be 
taken, and from the known weight and temperature the volume 
{Q) may be computed, if required. The tanks may be previ- 
ously calibrated by filling to a kno\vn point, and be so con- 
aected 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. 

Thv measurement will usually have to be made by discharg- 
ing over XL'cirs ^see page274) or through noszlesor Venturi tubes; 
this will be especially true for targe motors. 

With water-pressure engines an approximate measurement 
may be made by the piston-displacement, corrected for slip. 
Adiscussion of the effect of slip is to be found on page 302. 

2. ifiasHrement of the Head [/t] may be made, in the first 
piace, by taking a series of iei'els from standing water in the 
tank or dam above, to the level of the water in the tail-race, 
1ms measurement must be corrected for loss of head by fric- 

I 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- 
'cvel 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 t<> the pressure-head only, and would be less than the true 
1«ad acting on the pipe. By inserting a tube well into the 
iurrcnt, and bent so as to face the current, thus forming & I'itot 


tube (Article 222, pago 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 hcai 
To the head so obtained must be added the dist^ince fromlhc 
centre of the gauge to the level of the water in the tail-rjci. 
In case the draught-tube is used, a vacuum gauge ormercur} 
manometer can be attached, and the suction-head calcubii 
from the gauge-reiding may be compared with the measun 
distance. In case two gauges are used, the vertical disum. 
between them must be measured, and considered a portioit el 
the head. 

To obtain the head corresponding to a given pressu 
pounds per square inch, multiply the gauge-reading bylhc 
height, in feet, of water corresponding to one pound of pressutt 

One pound of pressure per square inch corresponds W 
2.308, 2,309, 3.31, 2.312, 2.315, 2.319, and 2.32 feet of head of 
water at the temperatures of 40°, 50°, 60°, 70°, 80°, 90°, and 
100° F., respectively. 

The head of one inch of mercury corresponds to 1.15W 
of water z.':~:J' F. 

Knowing the quantity or weight of discharge and the hwdi 
the energy received may be computed by any one of the foi" 
forms in equation (i), Article 237, p. 309. 

3. The velocity of discharge z?in ^(Aiiom be measured directlyi 
it can be computed from measures of the pressure or net h"''' 
since the velocity V = V'lgh. It is rarely of importance. 

In case the motor is supplied with water through ano»I^ 
its least area may be determined by measurement; ihcn l^' 
quantity discharged may be computed as the product of ve- 
locity, least area, and coefficient. (See Article 304, p. aJ5. 

251. Special Tests. — Backus or PcUon Motors.—Appa.*^ 
needed. — Pressure-gauges, two receiving tanks on scales ofsmw' 
weirs, Prony brake, pipes to remove water, thermometer. 

Testing Directions. — Measure nozzle; note its position »"" 
the angle at which jet will strike buckets; attach preyuf 
gauge, and arrange to measure discharged water ; attach Proi')' 
brake. Vary the head of water by throttling the supply '' 


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 paper, 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 
ivith 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 
<lescribed 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- 
^red ifidependently. 

Hydraulic Ram. — Apparatus as before, with additional 
pressure-gauge for discharge-pipe, means of measuring the 
^ter delivered and the water wasted. 

Testing. — Measure head of water acting on the ram and of 
^hat 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 




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 

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 Capacity Diam 

At „ \ 

Date ^n 

Length of Brake-arm f t. ; Weir zero ; Temp. Water * F. 

G = 



D. H. P. ^ 







Head on 



o . 



Water used. 

Cu. ft. 
per sec. 

Lbfi. per 






per minute. 

H. P. de- 
veloped by 

per cent. 

Form and dimensions of Buckets , 

Number of Buckets .Form of Deli very -tube, 

Diameter , 

The following form for test of the Swain turbine is used at 
the Massachusetts Institute of Technology: 









ing of 

per — 










' Hook-1 



ture in 


eraire. . 

rrected . 

Lineter of wheel ft. Radius of brake ft. 

St of weir above floor of pit ft. 

iih of weir and pit ft. 

rection for hook-gauge ft. 

served depth on weir (corrected) ft. 

al head acting on wheel ft. 

tght of I cubic foot water at ° Fahr lbs. 

solutions of wheel per minute 

Lntity of water passing weir (uncorrected) cu. ft. 

** " *' (corrected) cu. ft. 

iilable work ft.-lbs. per sec. 

rk at brake ft.-lbs. per sec. 


per cent. 

rse-power of wheel 

ocity due to head acting on wheel ft. per sec 

ocity of outside of wheel ft. per sec 


253. Classification of Pumps. — The dififerent classes of 
rnps correspond almost exactly to the different classes of 
ter-motors, with the mechanical principles of operation 




Ordinary reciprocating pumps correspond to water-en gin «; 
chain- and buckeC-punips, to water-wheels in which the waW 
acts principally by weight. Scoop-wheels are similar to undet- 
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, doubU-acXat 
and diaphragm. 

B. Rotary, divided into : (i) inferential, in which the walcr 
is urged forward by the velocity of the working parts of the 
pump, as in the centrifugal pump ; {2) positive, in which ill 
the water that passes the pump is lifted or forced by the 
ing parts of the pump to a liigher level ; the working parlsof 
these pumps are usually gears or cams meshing together. 
These pumps are often spoken of as rotary, in distinction Irom 

Pumps are also classified by the power used to drive ihein. 
Thus, pumps driven directly by attached engines are tcrmrf 
steam pumping-cngines or steam-pumps; those driven from run- 
ning machinery by belts or gears are tsrmed power-pumps; thi« 
operated by hand, hami-piimps. 

254. Duty and Capacity. — The termV^/j is applied to the 
work done by steam-pumps. This term originally signified ihe 
number of pounds of water lifted one foot by the consumptim 
of one bushel (94 pounds) of coal ; more recently it has b«n 
the water lifted one foot by the consumption of 100 pounds of 
coal. It has, in recent tests, been customary to assume thil 
each pound of coal evaporates ten pounds of water, from JmI 
at 212°, under atmospheric pressure. As each pound of waW 
evaporated under such conditions requires 965.7 Britisli thermal 
units,* and each B. T. U. is equivalent to 778 fool-poundso' 
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 mainic 

* A British [hermal unil, symbol B. T. LT., i 
one pound ai water one dcKree Fahr, in (cmpen 



number of foot-pounds of water raised by 751,314,600 
unds of enei^ expended on the pump and accessories, 
ommittee appointed by the American Society of Me* 
1 Engineers (see VoL XL of Transactions American 

Mechanical Engineers, p. 668) recommend that in a 
d method of conducting duty trials, 1,000,000 therma} 
r 778,000,000 foot-pounds, be taken as the basis from 
he duty is computed. This is equivalent to the evapo«* 
Df 10.3s pounds of water per pound of coal, from and 
, and is likely to be adopted in future trials, in which 
e duty becomes the number of * foot-pounds of water 
!d for 1 ,000,000 British thermal units of eneigy supplied 

capacity of a pump is usually expressed as the number 
)ns of water that can be raised against a specified head 
>urs of time ; a gallon being considered as equivalent to 
pounds at a temperature of 39.2^. 

Measurement of Useful Work. — The useful work 
/ a pump is the product of the number of pounds of 
elivered into the head through which it is raised. 

head is the total vertical distance in feet from the sur- 
the water-supply tc the discharge, increased by friction, 
rasured most accurately by pressure-gauge connected to 
s tube (p. 292) with its nozzle facing the current inserted 
lischarge pipe, near the pump, and by a vacuum gauge 
ometer connected to the suction pipe. The head in 
equal to the distance between these gauges plus the 
adings of the gauges, reduced to equivalent heads of 
>ee p. 324). 

water delivered may be measured by discharging over 
or through a nozzle or tapering pipe called a Venturi 
See Article 204, p. 275.) 

discharge through a Venturi tube may be taken as 98 
t of the theoretical discharge, that through a straight 
nozzle as 977 per cent.* 

■ ■ m 

papers before Am. Soc. Civil Engineers, by Clemens Herschel, Nov. 
Jan. 1888, and by J. R. Freeman, Nov. 1S89. 


Delivery measured from Piston-displacement. — S/i/.— The 
water delivered in the case of piston-pumps is often computed 
by multiplying the total piston-displacement during llie test 
by 1, minus the slip. The total piston-displacement is equal lo 
the product of area of piston by length of strokes, by toul 
number of single strokes. In piston-pumps the length oi 
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-dispUce- 
ment; it can only be determined accurately by comparing liie 
volume actually discharged with the total displacement. The 
slip is caused by air in suction-pipe, leakage past piston, leak- 
age past valves in eitiier suction- or discharge-pipe, and imper- 
fect port-openings. The principal cause probably comes froni 
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 forvarious 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 Manuj]. 
published by the Harris-Corliss Engine Co., from which il i« 
seen that the slip for large pumps is about two per ccnt.and 
that it varies from one to five per cent, 

256. Efficiency-tests of Pumps. — An -efliciency-tcsi will 
require in each case measurements of, firstly, the cnci^« 
work supplied the pump ; secondly, the useful work ; thirdly, 
the lost work. 

The difference in methods of testing the various classeiof 
pumps, as described in Article 253, simply extends to the nie»> , 
urement of the power supplied the pump. 

The steam-pump, or steam pumpiHg-engine, is to be coo 
sidered as a combination of the steam-engine with a pump 
The power received by the pump is that delivered by tht 
engine, and is determined by a steam-engine test. TVe 
method cl testing =''eam pum ping-engines, and standard method 


ef making duty-trials, as adopted by the American Society o( 
Uechanical Engineers, will be given under special applications 
oftlie 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-dynamometcr (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 
upplJed in foot-pounds is the product of the circumference 
tiiat might be described by the arm as radius, number of 
revolutions, and the weight. Such a framework is termed a 
Vradie-dy namomcter. 

257. Special Efficiency-tests— Power-pumps. — Efficiency- 
lat of Centrifugal Pumps — Direct ions. 

Apparatus needed. — Pressure-gauge for delivery, manometer 
[or suction, transmission-dynamometer, thermometer, weir for 

Directions. — Connect suction-pipe to supply-tank, and ar- 
range discharge with throttle-valve to deliver water over a 
«eir. Connect delivery-gauge to an elongated air-chamber, 
*hich in turn is connected with the delivery.pipe, provided 
with a water gauge-glass opposite the pressure-gauge, and 
"leans 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- 
•lynamometer to receive the power, and drive the pump. 

During the test maintain the water in the air chamber at 
'eight of centre of the gauge. 

Testing. — Set the machinery in operation; arrange the 
'hrottie-valve 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 dynamomctei 




or power-scale. Continue the run for one hour with uniform 
pressure on dischai^e-gauge. 

Make a second run with an approximate head of 75 feet, 
and a third run with an approximate head of loo feet. 

Report. — In report, calculate efficiency, duty, and capadtjr 
for each head ; draw a curve of each test, using power in foot. 
pounds as ordinates, and total water delivered as abscissz. 
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 mcasurai 
by a weir, or it may be delivered into two weighing tanks, one 
of which is fi!Un<;. 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 Webbef 
centrifugal pump and on rotary power-pump: 


Diamcicr discharge-pipe 

Tiansverse area discliarge-pipe. . 
Distance between gauges 

§ 2S8.] 



Crest of weit above boiiom of channel .>.. f; 

WiJth of Teir ft. 

Kevolutkns o( pump per minuie 

Water pumped in Itw 

Duration of test inin$^ 

^ j Depth of water oo weir < ft. 

^ ( Teinperaiure «i weir (corrected) °C * F. 

Suction-gauge (corrected) int. ft. 

\ Discharge- gauge (corrected).. lbs ft. 

!£ Actual suction ft. 

Actual hem]. fL 

& ^ ■ J Scale-reading lbs, 

% ^-^ ( Revolutions per minuie 

Jl u ( Scale-reading lbs. 

a. I, ^ ( Revolutions per minute. .,...,. 

Water pumped in minutes lbs. 

Capacity in gallona per minute 

Tout work by power-scale (pumping) H. P. 

Tate H. P. 

Wotk given to pump H. P. 

Work delivered by pump H. P. 

EScicnc; per cent. 

I><.;y(fL-lbs. per 1,003.000 B. T. U.) 







Kaof L. 
Gog ;Tin«. 














r<«l ' . 1 


« «< 


No Date 

Duration of test mJA 

Power-scale, pumping, revolutions per minute 

weight Ibi 

tare, revolutions per minute •• .• 

weight lbs. 

Suction-head by gauge inches mercury ft. HiO 

Discharge-head by gauge lbs. per sq. in " 

Head on orifices *' 

Temperature * Q, 'F. 

Revolutions of pump per minute • 

Area of discharge at gauge s().ft. 

Vertical distance between gauges • ft 

Diameter of orifices, a.. . • , ^. . . ., ^ . . .., ^. . . ., ^. . . ., ^. . • ., g» • . ., >!...., i>><> 
v^oeixicientSy tf • ••*, ^■•••, ^■.••, a • « • •, ^* • • . , j * • • • , ^» • • •» ^ • •** ^' •* 

Constant for power-scale it 

Power- pumping, by scale H. R 

Tare H.P 

Power given to pump •••• H. P- 

Velocity-head of discharge • ^ 

Total head = press, heads ■\- vel. head 4- vert. dist. bet. gauges. ^ 

Water pumped lbs. per s^ 

Work done by pump ••••• H. P 

Efficiency of pump ••••• percent- 
Capacity of pump in gallons per minute •••••••.•• 

Duty of pump (ft.-lbs. per 1,000,000 B. T. U.) , 



• •• 






259. General Remarks. — The methods of testing the 
;teani-engine which are given here presume an accurate 
icnowledge of the principles of action of the engine, an ac- 
[{uaintance with the details of its mechanism, and a knowledge 
of the thermodynamic principles which relate to the transfop 
Riation 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. 
£tude Exp6rimentale Calorim^trique de la Machine k 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, i vol. London, Longmans^ 

Green & Co. 
Steam-engine, by J. M. Rankine. i vol. London, Chas. 

Griffin & Co. 
!team-making, by C. A. Smith, i vol. Chicago, American 

team-using. Ibid, 





Steam-engine, by James H. Cotterill. London, E. & F. N. Spon. 
Thermodynamics, by C. H. Peabody. N. Y., J.Wiley &Son& 
Thermodynamics, by De Volson Wood. N. Y., J. Wiley & 

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 /r/i5*rf 
as employed in engineering, refers to the force tending to com- 
press a body, and is expressed as follows: (i) 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: 


70® Fah. 

Pressure in 

Pressure in 
pounds per sq. 

pounds per sq. 



Inches of mer- 

Feet of water. 

laches of water. 


















8 . 05 1 2 





10. 1890 




























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 


the same units. Absolute pressure is always meant unless 
herwise specified. 

Pressure below the atmosphere is usually reckoned in inches 

mercury from the atmospheric pressure, so that 29.92 inches 

3uld correspond to a perfect vacuum at sea-level, latitude 49°. 

261. Heat and Temperature. — The term heat is used 
metimes as referring to a familiar sensation, and again as 
)plying to a certain form of energy which is capable of pro- 
icing the sensation. In this treatise it is used in the latter 
nse only. 

Temperature is essentially different from heat, and is merely 
le of its qualities ; it is difficult to define, but two bodies are 

equal temperature when there is no tendency to the trans- 
r of heat from one to the other. Temperature is measured 
r the expansion of some substance in an instrument termed 
thermometer. Two points, that of melting ice and of steam 
Dm water boiling at atmospheric pressure, are fixed tempera- 
res on all scales of thermometry. The expansion between 
ese points is divided into various parts according to the 
ale adopted, and each part is termed a degree. 

The following thermometric scales are in use in different 
>rtions of the world : 

Fixed Points, Temperature of Water. 

^rees between freezing and boil 

ng point 

mperature ai freezing point .... 
mparative length i degree 



Fahrenheit. ' Centigrade. 








Degrees of temperature taken on one scale can easily be 

iuced to any other; thus, let t^ be the temperature of a body 

the Fahrenheit scale, t^ on the Centigrade scale, and t^ on 

Reamur scale. We shall have, from the preceding table. 

ifc + 32° ; 
W/ - 32°) ; 

ifr + 32°. 




The Fahrenheit thermometer is used principally by Englislt 
speaking people, and unless otherwise mentioned is the 
us.-d in this treatise. 

The Thermometric Substances principally used are mercuiy, 
alcohol, and air, from the expansion of which the temperature 
is obtained. 

Absolute Zero, — This quantity is fixed by reasoning as tit 
point where gaseous elasticity or expansion would be lero. 
This is 492°, more exactly 491.8°, of the Fahrenheit scale 
273° +* of the Centigrade scale below the freezing-point 
water, so that in the Fahrenheit scale the absolute tempera- 
ture is 460°+ the reading of the thermometer, and on Iti: 
Centigrade scale 273° + the reading of the thermometer. 

Absolute Temperature, on any scale, is temperature recbnol 
from absolute zero. 

262. Specific Heat. — Specific heat is the ratio of thai re- 
quired to raise a pound one degree in temperature compafd 
with that required to raise one pound of water from 6o'to6i 

Specific heat of water is not quite constant, but varies 
follows : f 

specific heat of saturated steam at atmospheric prt*""* 
was found by Regnault to equal 0.478. Investigations mi« 
at Sibley College show that the specific heat of superheat™ 
steam increases with the pressure and temperature. 

The heat contained in different bodies of the sametenip«* 

• Encje. Brll., Vol. XI. p. S73. t See Pea body's Si eim-l ill" 


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/ 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 
4.26.9 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. 
*Jwelshauvcrs-Dery, Peabody, and Buel. 

The following empirical formula, deduced from Regnault*s 




experiments, gives the relation between the temperature and 
pressure of steam at a latitude of 45° : 

Yox steam* from 32° to 212° Fahr. pressure in pounds per 
square inch, 

\o^p = a — ba^-\-cB'^, 

in which a = 3.025908, log b = 0.61 174, log c = 8.13204 — la 
log a = 9.998181015 — 10, log B = 0.0038134, T=: t — 32". 
For steam from 212° to 428° Fahr., 

log/ = ^,-*,^/ + ^,5/, 

in which «, = 3.743976, log b^ = 04120021, log c^ = 7.74168- 
10, log tf, = 9.998561831 — 10, log ^, = 0.0042454, T—t-2n\ 
265. Properties of Steam. — Definitions, — Steam occurs in 
two different conditions: i, saturated ; 2, superheated. 

1. Dry and Saturated Steam, or, as frequently called, rfr; 
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 vioist or wet steam, in distinction from dry steam. Thus 
saturated steam may be either wet or dry. The percentage of 
dry steam in a ma^s 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. 


am at a pressure P. If / is the temperature of the steam, 
t total heat, A, is calculated by an empirical formula based on 
t experiments of Regnault. Expressed in English units, 

\ = 1081.4 + 0.305/. 

(p) Heat of the Liquid {g) is the number of thermal ftnits 
ed in heating one pound of water from 32° Fahr. to the tem 
rature required to generate steam. According to Regnault, 

g = t -{- 0.00002/' 4- 0.0000003/' 

r Centigrade units. And according to Rankine for English 
lits when /, is the initial and / the final temperature, 

V — * — A + 0.000000 1 03 [(/ - 39°- 0' — (A — 39°-0']- 

{c) Internal Latent Heat {p), — This is the work done, 
easured in thermal units, in separating the molecules of the 
sam beyond the range of mutual attraction. It is calculated 
Dm the formula 

p = 1061 — 0.791/. 

{d) External Late fit Heat {APu). — This is the work, ex- 
essed in heat-units, of expanding the steam against an 
eternal pressure which is equal to that of the steam generated, 
hus, let « = J — cr be the difference in volume of a pound of 
earn, s, and a pound of water, cr, at any pressure per square 
»ot, P, Then the work of expansion will be Pu foot-pounds or 
Pu thermal units. According to Zeuner, 

APu = 20.91 + i.096(/ — q). 

[e) Heat of the Steam (iL). — This is the heat which the steam 
ctually contains ; it is the total heat less the external latert 
eat. In thermal units, 

L=^\ — APu = q-\- p, since \ = q -\' APu -\- p. 


(/) Heat of Vaporization^ or total latent heat^ (f ,) is thatpor* 
tion of the total heat which is required to convert one pound 
of water at any temperature into saturated steam at the same 
temperature and at a pressure P\ it is the sum of exteraal 
and internal latent heats, or the total heat less the heat of the 
liquid. That is, 

r = p -|- APu = A. — J, 

&. formula for calculating r is 

r= 1081.4 + 0-305^ — ?. 

{£) Specific Volumes and Density of Steam. — These quanti* 
ties are usually calculated from thermodynamic equations. 


s j= volume rj{ <me pound of steam, cr = volume of one pound 
of water. 

It will be noticed that the different steam tables differ 
principally in respect to these quantities. 



266. Isothermal is a term used to denote a condition in 
which the temperature remains constant; the total amount of 
heat, or the pressure, may vary, 

Adiabatic is a term used to denote the condition in which 
the total quantity of heat is unchanged by heat-transfer. It 
may, however, be changed by transformation into work and 
vice versa. 

Temperature is the scale used to determine the relative 
values of different isothermal conditions ; and change of tern 


^rature is the change which occurs in passing from one 
^thermal condition to another. 

Entropy is the scale used to determine the relative values 
: different adiabatic conditions ; and change of entropy is the 
lange which occurs in passing from one adiabatic condition 
\ another. 

Change of temperature can be measured by the expansion 
■ some thermometric substance ; but change of entropy^ which 
just as real, cannot be measured or represented in any sim- 
e manner. If we represent the entropy by 0, the absolute 
mperature by 7", the heat at any adiabatic condition by (2> 
len by the second law of thermodynamics 

d<t>^^ (I) 

I case of a liquid, dQ = cdq^ in which c is the specific heat, 
id q the temperature. In this case denote the entropy by Q. 


'^ (2) 

For water this is readily calculated. 

In the case of steam the entropy, or change of entropy 
Dm water at the freezing-point to steam at any pressure is 
[ual to the entropy of the liquid, ^, plus that of the steam, 

• In which x is the quality of the steam, or per cent of dry 

In this case 

any other case 

0.=^ + ^.. 

-* 1 




Change of entropy, 


A short table giving the value of the entropy of the liquid 
is to be found in Article 230, page 301. 

267. Steam-tables. — The numerical values representing 
che various properties of steam, in relation to its pressure, art 
arranged in the form of tables termed steam-tables. The rela- 
tive accuracy of these various steam tables is discussed at 
length by Prof. D. S. Jacobus in Vol. XII. Transactions of 
American Society Mechanical Engineers, page 590, from whidl 
it is seen that the table compiled by Mr. Chas. T. Porter rcjv 
resents the experimental investigations of Regnault mostacco- 
rately ; but that possibly for scientific investigations the tabid 
of Peabody, Dery, and Buel, which are founded on thcnmh 
dynamical laws, are somewhat more accurate. Practically the 
tables are accordant for all working pressures and temperatures 
of steam : the difference is principally in the values given for 
the density. The tables of Chas. T. Porter* have been adopted 
as the tables to be used in reporting results of boiler triab 
and of duty trials of pumping engines, by the America 
Society of Mechanical Engineers (see Transactions, VoL VL, 
and also Vol. XII.), and for such tests the standard reports 
should be calculated from those tables. These tables are, how- 
ever, deficient for scientific purposes, since they omit values of 
some of the important properties of steam. In the Appendix 
is printed the table by Porter, and abo the table by Buel as 
printed in Weisbach's work on the steam-engine and in VoLL 
of Thurston's Manual of the Steam-engine. 

* The Ricnards Steam-engire ladicaicr, by Chas. T. Porter* 


Manometers.— The term manometer is frequently 
to any apparatus for the measurement of pressure-. 

h it is the practice of Amerj- 

gineers to use this term only for 

columns filled with mercury or 

ind used to measure small press- 

The pressure is measured, in all 

eiers used for engineering pur- 

bove the atmospheric pressure, and 

termination must be increased by 

Ssure equivalent to the barometer- 

' to give absolute pressure. The 

eters in common use are glass or 

ubes, either U-shape in form as in 

i, or straight and connected to a 

Hi large cross-section as shown in 


«ures below the atmosphere can 

surcd equally well by connecting 

ong branch of the tube and leav- 

short branch open to the atmos- 

U-shaped Manometer.— Tn the 
:d tube, with any form as shown in Fig. i6oorFig, i6i. 




water or mercury is poured in both branches of the tube, the 
pressure is applied to the top of one of the tubes, 
and the liquid rises a corresponding distance in the 
other. When no pressure is applied, the liquid will 
stand at the same level in both tubes ; when pressure 
is applied, it is depressed in one tube and raised in 
the other. The pressure corresponds to the vertical 
distance between the surface of the liquid in tin 
two tubes and can be reduced, as explained in Arti- 
cle 260, to pounds of pressure per square inch. 

An inch of water at a temperature of 70° Fahr. 
corresponds to a pressure of 0,036 pound ; an inch 
of mercury, to 0.493 pound. The principle of ac- 
tion of the U-shaped manometer-tubes is as follows: 
Consider the atmospheric pressure as acting oa 
one side of the tube, and the pressure which is 
to be measured and which is greater or less thaft 
atmospheric as acting on the other side. jThe total 
absolute pressure in each branch of the tube mustbci 
equal, consequently enough liquid will flow from the side of the 
greater to the side of the less to maintain equilibrium. Thus 
let / be the atmospheric pressure ; /, , the absolute pressure 
to be measured, expressed in inches of water or mercury; i» 
the height of the column on the side of the atmosphere; i,i 
the height on the side of the pressure. Then 

Fig. i6i. 


/> + /^=A + A,. 

from which 


Tlie U-shaped tube, in construction similar to HoadUj 

draught-gauge. Art. 275, can be used with two liquids oj dif* 

J event densities, using the heavier liquid on the side of the 

lighter pressure. Let d^ denote the density of the lighttf 

liquid, and d that of the heavier; A, and A, the correspondi< 


Its of the columns. We shall have as before, taking all 
urements from the lower surface of the heavier liquid, 


/, — / = h^d^ — ltd. 

'his instrument is much more delicate and is better suited 
neasuring small differences of pressure than when a single 
d is used ; the reason for which will be readily seen if we 
ider an example. Suppose that water be used as the 
ier liquid, of which the specific gravity is I, and that 
e olive-oil be used as the lighter liquid, of which the 
ific gravity is 0.916. Suppose that all pressures are meas- 
in equivalent height of a water column expressed in 
is, and that // = 6 inches,/, — / = ^ inch ; then A, , which 
e difference of level of the water in the two branches, will 
+ 6.(0.916) = 6.0 inches, whereas it would have been but 
lalf inch had there been only water, or 0.545 if the liquid 
been olive-oil. By making the density of the liquids more 
more nearly equal the instrument will become more and 
! delicate. A dilute mixture of water and alcohol of which 
lensity must be determined (see Article 275, page 354), for 
icavier, and of crude olive-oil for the lighter, gives excel- 
rcsults. If the instrument can be so manipulated that 


he calculation becomes very simple, as in that case the 
ng would have to be multiplied only by the differences oi 
ensities of the two liquids. 

70- Cistern-manometer. — In the case of a manometer oi 
\or\x\ of Fig. 162 or Fig. 163. the t/j/^r/^ or vessel intc 



which the tube is connected has a large area 
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 tiie 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, /: the correspond- 
ing rise of liquid in the tube, b the height 
required for one pound of pressure (see 
Article 360. page 336),^ the number of 
pounds of pressure. We have then 

and since the tube is supplied by liquid from the cistei 

HA = ha. 
Eliminating H in the two equations, 

<r^ = one pound, 

^^f^£AS[;/i£A/£A-r Of PKESSL-RE. 


\ the length the graduation should ' 


i to allow for fall of mercury in the 


ind give a value equal to one pound 


make this correction uniformly ap- ' 

M _ 


the area of cross-section of both 

3 cistern should remain uniform. 


Mercury Columns. — Mercury col- 

es - 

t used in the laboratories, are usually 

w - 

1 the principle of the cistern-ma nom- 


"he tube is very long and made of 

steel carefully bored out to a uniform 

2°. 50 

r. If the tube is of glass, the height 

5S. ia 

:ur\- can be readily perceived and 

of steel, the height of the mercury 

60 - 

y obtained by a float, which in some 

S5 ^ 

S is connected to a needle which 

» - 

ound a graduated dial. . 

~ !£ 


ne of these instruments electric con- 

^ 30 

are broken whenever the mercury 

40 yg 

certain point, and an automatic 

jj ~ 


a the reading is made. Fig. 163 

— »s 

fi usual form of the mercury col- 


(rhich the pressure is applied in the 

K » 

irt of the cistern, so as to come 

3 = 

ton the top of the mercury. In the 

I glass column Ihe graduations are 


»iade on an attached scale, and are 

_!t .Q 

■ as explained in Article 270 for the 


Srcurj' in the cistern. 

~n ~ 

Corrections to the Mercury Cot- 

-2- - 

'Ine mercury column is usually the 

si 1 

by which all pressure-gauges are ' 


1, and its accuracy should be 


Jj established in every particular. 


"^uircments for an accurate mer- ■ 

imnare: ^"^ 




1. Uniform bore in cistern and tube. 

2. Accurate graduations, spaced as explained in Article 27a 
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: 

I. 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 \ equal the coefficient of lineal expansion of the mcf. 
cury, and 3A that of the cubical expansion per degree Fahr.; 
let 6 equal the coefficient of lineal expansion of the metal of 
the cistern, and d' that of the metal of the tube. Let /^' equal 
the depression in the cistern, // 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 kvd 
corresponding to a pressure of one pound at a temperature of 
60° Fahr. Then, as before, 

//' = 

a ^ A''' a{\ -f 26') + ^(i + 26) 

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 

o. 10 






o. 141 

o . 04 1 


Diameter of 



' 0.40 


! 0.60 











3. There might also be considered a very slight correction 
lie to the fact that the force of gravity in different latitudes 
■lies somewhat. Since the weight of a given mass of mercury 
» equal to the product of the mass into the force of gravity, it 
tU vary directly as the force of gravity, or, in other words, 
le assumed weight of mercury may not be exactly correct, 
"his correction is a refinement not necessary in usual tests. 

4. Difference of barometer-readings at top and bottom of 
le tube might make some difference. 

While it is well to give all these corrections their true 
Tcight, yet a false impression should not be incurred concerning 
leir importance. It is hardly probable that the corrections for 
lange in temperature, or corrections for the difference in the 
irce of gravity from that at the sea-level on the equator, would 
I any event make a sensible difference in the readings. 

273, Direct-reading Draught-gauges. — The ascending 
•rce which causes smoke or heated air to rise in a chinmey is 
illed the draught. The pressure in such a case is below that 
E the atmosphere, and is usually measured in inches of 
•ater. Draught-gauges are U-shaped manometers adapted to 
leasure pressures less than that of the atmosphere. See Figs. 
60 and 161. To use this manometer, water is poured into the 
ibe until it stands at the point marked o, Fig. 161; one side 
► then connected by a pipe to the flue or chimney of which 
le draught is to be measured. The difference of level of the 
•^tcr, as shown by the manometer- tubes, is the draught ex- 
xessed in inches of water. An inch of water at a temperature 
f 70° Fahr. corresponds to 0.036 pound. 

Allen's Draught- gauge. — A very complete draught-gauge of 
le U-shaped manometer type, with attached thermometer and 

movable scale the zero of which can be set to correspond to 
le lower water surface, is shown in Fig. 164 as designed by 
. M. Allen of the Hartford Boiler Insurance Co. 

A draught-gauge designed by the author is shown in Fig. 
)4a, which is arranged so that one scale will give difference in 
?vation of the liquid in the two columns. This is accomplished 




by setting the collar i^ to the lower menisois of the liquid by ihcsofl 
£; then by setting the collar H to the meniscus of the liquk 
in the other column by means of the micrometer-screw Ji, lb 
height of the column may be read on the attadied scale and di 

micrometer-screw R. The reflection from the two edges of ^ 
meniscus enables the scales to be set with great accuracy. W 
inches and tenths of inches are read on the attached scak. »( 
hundredths of inches by the graduations of the micromeler-scft*! 
274. Draught-gauges with Diagonal and Level StiWI 
— PecMCs Draughl-gauge.—h. draughl-gaugc with diagonal stJj 
is shown in Fig. 165. It consists of a bottle, A, with a iw<i^ 
piece near the bottom into which a tube, EB, is inserted with u] 
convenient inclination. The upper end of the tube is bcnl ttf 
ward, as at BK, and connected with a rubber tube, KC, loiEi 
to the chimney. The tube is fastened to a convenient suppci 




a level, D, is attached. To use the instrument, first level 
lote reading of scale, then attach it to the chimney, and 
J the reading, which will be, if the inclination is one to five^ 

Fig 165. — Draucht-cai'Gb. 




Fig 166.— Hfggins's Draught^ 


times the difference of level in the bottle and tube. The 
e should be graduated to show differences of level in the 
tie, and thus give the pressure directly in inches of water. 
Higginss Draught-gaug€. — Another form of this class of 
jght-gauges is shown in Fig. 166, as designed by Mr. C. P^ 
gins of Philadelphia. The gauge « 
lied with water above the level of 
horizontal tube, in such a manner 

leave a bubble of air about one- 
inch long near one end of the hori- 

tal tube when the water is level in 
side tubes. The inside diameter 
he vertical tubes being the same, say one-half inch, and that 
iie horizontal tube one eighth of an inch, a draught equivalent 
>ne inch in water, or which will cause the water-level in the 
ical tubes to vary one inch, will cause the bubble in the 
t to move eight inches in the horizontal tube. In general 
air-bubble moves a distance inversely proportional to the 
. of the tubes, and hence it can be read more accurately 

1 in case of the ordinary draught-gauge. 

>75. Hoadley*s Draught-gauge. — This gauge was used in 
trials of a warm-blast apparatus described in Vol. VI. Tran- 
ions American Society Mechanical Engineers, page 725. 
)nsists of two glass tubes, as shown in Fig. 167, about 30 
t^s long, and about 0.4 inch inside diameter and 0.7 inch 
de, joined at each end by means of stuffing-boxes to 
ble brass tube connections, by which they are secured to a 



18 W 

backing of wood. The glass tubes can be put in communio 
tion with each other at top and bottom by opening a cock it 
each of the brass connections. Directly over each tube is a bn* 
drum-shaped vessel 4.2J 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 hquid, and crude olive-oil 
with a specific gravity of 0.916 for the lighter. 
In using the instrument tlie 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 tlie 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 tlie top connection opened ; 
the .surface of tile olive-oil would then become """' 
level in the two tubes, that of the water remaining at difiurent 
heights. It was then attached to the flue and these operation! 
repeated, until the heavier liquid would no longer flow lo ttt 
side of the lighter pressure; In that case we shouM have the 
condition of equilibrium between two liquids of different den- 
sities, Article 269, page 347, in which the lengths of columu. 



8 J?"-] 

of the two liquids are equal Hence, noting that p is here the 
greater, the difference of pressure in indies of water is 

p-f\ = h{d^~d), 
in which d\ and d aie the respective specific gravities of the 
liquids used. 

376. Multiplying Draugfat-g:aug:es. — Fig. i68a shows a 
Inught-gauge designed by Prof. Wm. Kent, the dimensions of 
rikich are marked on the figure, although they are not material for 
Is cq>eration. The gauge consists of a cup, B, which is partly filled 
lith water, and an mverted cup, A, suspended above the cup B 
y a spring, C, with the lower and open end submet;ged in the 
rmter of the cup B. The tube, E, extends through the side of 
lie cup B, with its upper end projecting above the surface of 
tie water in the cup j5, and is extended by suitable connection 
> the flue. 

By this connection the pressure in the inverted cup, -4, is re- 
■iced to that in the flue where the pressure is to be measured, 
Utting a greater load on the spring, C, which causes it to elongate. 
Tie amount of elongation will be proportional to the reduction 
1 pressure and can be determi.icd by the use of a suitable scale, 
le values of which are found by calibration. It is evident that 
le distance through which the cup A will move is dependent 
poo the area of its cross-section a:;d the strength and length 
f the spring, C, and the immersion in the water. 




Peclfet in his work, "Traitd de la Chaleur," published in 1878^ 
describes a similar gauge. 

In Vol. XI of the Transactions of the Am. See. Mech. En- 
gineers Prof. J. B. Welb describes a draught-gauge of similar 
principle, but in which the change in pressure is weighed on i 
pair of balances. 

A U-shaped gauge as shown in Fig. i68i, 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 Z) as thcl 
area is smaller; if, for instance, the area at a be one fourth that 
at i>, 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 w^hich the pres-i 
sure has been transmitted to the measuring manometer by & 
piston having faces or sides of unequal areas connected, hi 
this case the total pressure acting on each face of the pistott 
will be in equilibrium; consequently the pressure per square indlj 
on each face will vary inversely as the areas of the two fa 
of the piston. The objection to the instrument is the 
due to friction of the piston, which can in large measure bedinB-j 
nated by keeping it in rotation during its use. In place of I 
piston two diaphragms of unequal area with a connecting soM 
l)art have in some cases been employed for the purpose of elimina^| 
ing friction. 




277. Steam-gauges. — The steam-gauges in general use are 
f two classes, known respectively as the Bourdon and Dia~ 
•ragm Gauges, 

The Bourdon Gauge. — In the Bourdon gauge the pressure 
exiirted on the interior of a lube, oval in cross-section, bent 

fit the interior of a circular case ; the application of pressure 
Ends to make the cross-section round and thus to straighten 
tie tube. This motion communicated by means of racks and 
:ars rotates an arbor carrying a needle or hand. 

The various forms of levers used for transmitting the 
totion of the tube to the needle are well shown in the accom- 

.nying figures, 169 to 173. The levers are in general adjust- 
ile in length so that the rate of motion of the needle with 
spect to the bent tube can be increased or diminished at will. 
lus in Fig. 169, and also in Fig. 170, the lever carrying the 
ctor b slotted where it is pivoted to the frame; by loosen- 
j a set-screw the pivot can be changed in position, thus alter- 
; the ratio of motion of hand and spring in different parts of 
e dial. 

Pig, 170 shows a gauge with a steel tube or diaphragm For 
E with ammoniacal vapors which attack brass. 

In nearly ail these gauges lost motions of the parts 
lo some extent taken up by a light hair-spring wound aiu"" 
the neciile-pivot. 


The Diaphragm Pressure-gauge. — In the dia- 
rauge the pressure is resistetl by a corrugated plate, 
ay be placed in a horizontal plane, as in Kig. 1 72, or in a 
plane, as in Fig. 173. The motion given the plate is 
Led to the hand in ways similar to those Just explained. 

g. 172 the pressure is exerted on the corrugated dta- 
below the gauge, and the motion is transmitted to the 
the rods and gears shown in the engraving. 
:onstruclion shown in Fig. 1 73, in which the diaphragm 
il, is as follows: the lever is in two parts which are 
It the centre; one end is fixed to the frame, the other 
:d to the sector. The centre pivot is pressed outward 
;tion of thediaphragm, drawing the free end downward 
ting the sector, which in turn moves the needle. 
luges of usual construction of either class, when there 
ssure on the gauge, the needle rests against a stop, 
placed somewhat in advance of the rero-mark, so that 





minute pressures are not indicated by the gauge. In the uk 
of the instrument the needle sometimes gets loose on the pivot, 
or turned to the urong position with reference to the graduj- 
tions; in such a case the needle is to be removed entirely, and 
set when the gauge is subjected to a known pressure. Thest 

gauges are also affected by beat. Hence, when set up for 
bent lube, termed a siphon, or a vessel which will always conlMi: 
water, should be interposed between the gauge and the steam. 
279. Vacuum-gauges. — Vacuum-gauges are constmCKd 
in the same method as the Hourdon or diaphragm gauges; the 
removal of pressure from the interior of the bent tube or di* 
phragm causes a motion which is utilized to move the needlft 
These are graduated to show pressure below that of tlte »■■ 
mosphere corresponding to inches of mercury, zero being ^ 
atmospheric pressure, and 29.92 a perfect vacuum. Thediff* 
tnce between the reading by such a gauge and that of ll" 



neter would be the absolute pressure in inches of mer* 

K principal makers of steam-gauges in this country are the 
y Steam Gauge and Valve Co., Boston ; American Steam 
E Co., Boston; Ashcroft Steam Gauge Co., New York; 
Her & Budenberg, New York; Ulica Gauge Co., Utica, 

Recording:- gauges. — Recording-gauges are arranged 

t the pressure moves a pencil parallel to the axis of a 

»g drum which is moved at a uniform rate by ciock- 

The Edson recording- gauge is shown in Fig, 174. In 

nge the steam -pressure acts on a diaphragm which oper- 




Rtes a aeries of levers giving motion to a needle moving over 
^ graduated arc showing pressure in pounds : also to a pencB- 
arm moving parallel to the axis of a revolving drum. 

This instrument has an attachment, which is (urnished 
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-bails 
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- 
bcrg'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 
Ricliards steam-engine indicator. 

Fig. 176 shows a portion of a diagram made by a recorrfir* 
gauge. The drum is operated by an eight-day clock, and v 


inged to rotate once in twenty-four hours. In the diagram 
[le ordinates show pressure, and the abscissae time in hours 
nd fractions of an hour. 

281. Apparatus for Testing Gauges. — Apparatus for 
*sting gauges consists of a pump or other means of obtaining 
ressure, and some method of attaching the gauge to be tested, 
nd the standard with which it is to be compared. The form of 
unnp usually employed for producing the pressure is shown in 
ig. 177. The gauge is attached at E, the standard at E^ \ the 
and-wheel D is run back, and water is supplied by filling the 
jp between the gauges and opening the cock; after the cylin- 
er C is filled the cock below the cup is closed ; if the hand- 
heel D is turned, an equal pressure will be put on the standard 
nd on the gauge. 

The standards used for testing may be manometers or cal*^ 
fated gauges, or apparatus for lifting known weights by the 
ressure acting on a known area. Of these various standards, 
lie mercury column, as described in Article 271, page 349, is 
3 be given the preference, since the only errors of any prac- 
ical importance are those due to graduation. The readings 
iven by the mercury column are on a larger scale than those 
[iven by any other instrument, and no corrections for friction 
re required. The other standards, of which the short mer- 
ur>' columns have been described (see Article 264), will be 
ound to give excellent results in practice, since the graduations 
n the gauges to be tested are usually so close together that 
lie friction of the moving parts of the apparatus is inap- 

Apparatus for Testing Gauges with Standard Weights, 

There are two forms of this apparatus on the market, in one 
I which the pressure is received on a round piston, and in 
ic other on a surface exactly one square inch in area. The 
iction in both cases is practically inappreciable ; the errors in 
eas can be determined by comparison with a standard mer- 
uy column. 

The Crosby Steam-gauge Testing Apparatus. — This is shown 
Fig. 178, from which it is seen to consist of a small cylinder 

^Jil-aiMEKlAL £XGlriEEIllNC. 




riiich works a nicely fitted piston • this cylinder connects 
1 a U-shaped tube ending in a pipe tapped and fitted for 


piing a gauge. The tube is filled with glycerine, in 
a known weight added to the piston produces an 
jre on the gauge, less the friction of the piston in 
This is almost entirely ovt-rcome by giving the 
and piston a slight rotary motion. 
Square-inch Gauge. — This apparatus consists of a tube 
of which has an area of one square inch enclosed with 
■dges. This is connected to the test-pumps in place of 
indard (see Fig. 177, page 364); a given weight is sus- 
from the centre of a smooth plate which rests on the 
inch orifice. The gauge to be tested is connected a 
the pressure applied until the plate is lifted and watei 
from the orifice. 


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 pressurcis 
made too great at any time, run it some distance below the 
required amount and make a new trial, it being necessar}'to 
keep the mercury column and gauge hand moving continuaDy 
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 aJ 
explained in Article 272, page 350, and reduced to pounds w 
pressure, is the correct pressure with which the gauge-rcadiflj 
is to be compared. 

Second, with Water-pressure. — In this case a hand(orc^ 
pump (see Article 281) must be used after the limits of prcssurt 
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 
connecting-valve. Attach the gauge to be tested with >^ 
centre opposite the zero of the column. Open the coct 




)raw water from the mains until the gauge indicates 5 lbs. 
ressure. Shut off the water and adjust the pressure exactly 
t 5 lbs. by using the displacer. Note the height of the mer- 
ury in the tube. Increase the pressure to 10 lbs. and take 
ladings. Carry the pressure as far as desired by increments 
f 5 lbs. Use the pump alone when water-pressure fails. 
*rom the maximum pressure attained descend by increments 
f 5 lbs., taking readings as before. Tabulate data and plot a 
jrve, using gauge-readings as ordinates and actual pressures as 
bscissse. By inspection of the curve determine the fault in 
le gauge and give directions for correcting it. 

In these tests it may not be possible to set the centre of 
le gauge as low as the zero of the column. In that case the 
wading on the mercury column should be greater than that at 
lie centre of the gauge by a pressure due to the length of a 
olumn of water equal to the elevation of the centre of the 
;auge above the zero of the mercury column. This is a con- 
tant amount ; it should be obtained and the read- 
ngs of the column corrected accordingly. 

The method of calibrating gauges with other 
\tandards is to be essentially the same, except as to 
the manipulation of the apparatus, f'urther 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 
^r the equivalent. It is to be noted that the pin 
^o stop the motion of the hand is not placed at 
^cro, but in high-pressure gauges is usually set at u-sha"'bTma- 
^uree to five pounds pressure. 

283. Calibration of Vacuum-gauges. — This is best done 
^y a comparison with a U-shaped mercury manometer, as shown 

Fig. 179' 




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, aod 
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. 



Maker and No. of Gauge 


189 . Observers, \ 



Mercury Column. 









Temperature of Room .... deg. Fahr. 
Centre of Gauge above o of column . . ft. 
Correction to column reading .... lbs. 


Maker and No. of Gauge 

Date 189 . 




Load in lbs. on 





15. Mercurial Thermometers. — Measurements of tem- 

Lire are determined by the expansion of some ther- 

itric substance, mercury, alcohol, or air being commonly 


le mercurial thermometer is commonly used ; this con- 

>f a bulb of thin glass connected with a capillary glass 

on the best thermometers the graduations are cut on 

ibe, and an enamelled strip is placed back of them to facil- 

the reading. When the mercury is inserted, every trace of 

jst be removed in order to insure perfect working. There 

!rtain defects in mercurial thermometers due to perma- 

changc of volume of the glass bulb, with use and time, 

esults in a change of the zero-point. This defect is so 

IS as to render the mercurial thermometer useless for very 

:e subdivisions of a degree. In a good thermometer the 

Df the tube must be perfectly uniform, which fact can be 

I by separating a thread of mercury and sliding it from 

to point along the tube, and noting by careful measure- 

whether the thread is of the same length in all portions 

tube : if the readings are the same, the bore is uniform or 

ated by trial. In most thermometers the graduations are 

with a dividing engine ; in some thermometers the prin- 

grad nations are obtained by the thread of mercury, as 

bed ; in the latter case change in diameter of bore would 

Tipensated. To determine the accuracy of temperature 





measurements thermometers used should be frequently lesttd 
for freezing-point and boiling-point. The accuracy of inlcr- 
mediate points should be determined by comparison with \ 
standard mercurial or air thermometer. ' 

The mercurial-weight thermometer which was employed bjl 
Regnault, but is now very little used, consists of a glass vcssd 
with a large bulb and capillary tube, open at the top : it is filled 
with mercury when at the temperature of the freezing-poJfit; 
it is then heated to the temperature of boiling water, andt'ne 
amount of mercury that runs out is carefully weighed, anJ J^ 
terminesthevalueof the thermomelric scale. The temperalute 
of any enclosure is then found by placing in it the thermonie4 
ter, previously filled when at freezing-point and weighing thci 
amount that escapes; from this the temperature can becjK 
culated by simple proportion. , 

The expansion of mercury ia not perfectly uniform (otjII; 
temperatures, so that mercurial thermometers are never per' 
feet for extreme ranges of temperature. 

286. Rules for the Care of Mercurial Thermometers- 
The following rules for handling and using mercurial therowrof 
ters, if carefully observed, will reduce accidents to a minimuni: 

1. Keep the thermometer in its case when not in use. 

2. Avoid all jars ; exercise especial care in placing in tb«- 

3. Do not expose the thermometer to steam heat unlot 
the graduations extend to or beyond 350° F, 

4. In measuring heat given ofT by working-apparatus,ofiii 
continuous calorimeters, do not put the thermometers in ^ 
until the apparatus is started, and take them out befotei''' 
stopped. Be especially careful that no thermometer ii "** 

5. In general do not use thermometers in apparatus™'' 
fully understood or which is not in good working condilioi' 

6. Never carry a thermometer wrong end up. 

7. See that the thermometer-cups are filled with Q'lii"''' 
oil or mercury. If cylinder-oil is used, keep water oul w"" 
cups or an explosion will follow. 




I 288.] 

8. After a thermometer is placed in a cup, keep it (lom 
contact with the metal by the use of waste. 

287. Alcohol-thermometers. — Other Uqiiids, 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. 

2S8. Air-thermometers. — Air-thermometcrs,in which cither 
air or hydrogen may be used, are not open to the objections 
which hold with the mercurial thcrnnometer, 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- 

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- 
ited scale which can be read by a vernier to small divisions of 
inch ; a single mark is placed in the air branch, at a dis- 
nce 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 
1} inches by 6 inches ; the bulb is joined by a capillary tube, /v 
^raight or bent into any convenient form as may be required, 
n order that the bulb may be conveniently located for heat- 
j, this capillary tube is joined to a tube of glass about -jig 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 H. 
T~lie tee has a branch provided with a cock, and connection for 
•"ubber tubing. The opposite side of this tee is Joined in a 
similar way to a lube, BE, of the same bore, which is given a 
'cngth sufficient to measure the required temperatures. A mark 


a is made on the glass near F, at the junction of the capilbr; 
tube with the larger one (or the mercury, and serves to detcp 
mine the Umit o( volume o( air used. The bottle, ^, is fille<! 
with mercury, and connected by a rubber tube to the cock J. 
By opening the cock and elevating the bottle, mercuiy wl 

pass into the tubes : when it reaches the height of the markA 
the connecting cock B is closed, and the amount that the col- 
umn BE extends above the levul of this mark, or fails of 
reaching this level, is road on the scale. 

Hoadley Air-thermometer. — The Hoadley air-themotnfr 
ter. as described in the Transactions of the American Societ>of 
Mechanical Engineers. Vol. VI., page 282, is shown in Fig. 181. 
v.ith all the diinensions 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 
-jif inch diameter. The instrument consists of a U-tube about 


ich external diameter, -^ bore, having a 
It leg about 39 inches long, and the other 
longer by 12 inches or more, the latter sur- ' 
inted by a bulb blown out of the tube i| 
ics in diameter, 6|- inches in extreme length. 1 
- branches of the U-tube are 2 inches apart 

vertical ; these are separate tubes, each one 
t to a right at^Ie by a curve of short 
us, ground square and true at the ends 

united by a short coupling of rubber 
ng, ea, firmly bound on each branch with 
After it is filled with dry air according 
he directions in Article 290, page 376, it is 
:ned on a piece of board by annealed wire 
'les, and paper scales affixed as shown in 

figure. The difference in height of the 

columns of mercury is taken as the read, 
of the thermometer, and no correction is 
!e for slight variations in the volume of 
as shown by variation in the position of the 
;ht of the mercury column in the branch 
The error caused in this way is very small 

amounts to only 0.0030 inch per inch of 
;ht. This is equivalent to an error of about 

degrees in a range of temperature of 600 
fees F. 

The Jolly Air-thertnometeT. — An exceedingly 
lie form of the air-thermometer, and one also 
' accurate, consists of the air-bulb C, and a 
llary stem attached to three or four feet 
ubber tubing, which replaces the U-tube 
"ig. i8o; in the other end of the rubber 
ng is inserted a piece of glass tube 8 to 12 
es long and about -^ inch bore; on this 
$ tube, and also on the capillary tube, is 
ed a single mark ; the rubber tube is filled 

mercury, which extends up the glass tube i 
ic other branch. A fixed scale, similar to DE 


in Fig. 1 8 1 , is located near the instrunient. 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 Bh^ Fig. 180, will equal the 
weight of mercury in the other branch plus the weight of the 
atmosphere. Thus let / equal the pressure expressed in inches 
of mercury of the confined air, v its volume, m 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, / 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, 

pJ^m^m'-^-b', (i) 

/ = ;«' — /«-}- ^. 

Since m' -- m = h^ • (2) 

/ = A + * (3) 

From physics. 

pv , 

-Tp = constant ;..••••. U) 


V be made constant,/ will vary as T\ also 

7'=46of/; J5) 

p = 7\constant) = (460 -\-t)a; . . , . (6) 

{46o + /)a = 6 + k (7) 

^ same symbols with primes denote other values of the 
•onding quantities. Then 

(460 + 0^ = *^ + *' (8) 

iparing equations (7) and (8), 

460 + / _ d + A 
460 + /'"*' + A' 


vhich, by solving, 

'' = [l$77<46o + 0] - 460. . . . . (10) 

a/fp/y the formula, take readings of the instrument at 
or some known temperature, and ascertain the con- 
of the instrument. Thus suppose the air-bulb to be 
\n ice and the temperature reduced to 32° F. In this 
= 2)2^ ; b and // are to be observed and recorded. 


If / = 32° in equation (10), 

^ = ^/*' +>*')- 460; (11) 

which is an equation to determine any temperature. If b andi 
are constant, 492 -5- (^ -f- //) is constant and equals K. 

/ = A:(^' + //')-46o; (12) 

which is the practical equation for use in determining tem- 

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 J 
-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 dr)' 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 dr)'air 
is introduced. To effect the introduction of dry air, all the 
Hiercury 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 f inch internal diameter, filled withdt}' 
lumps of chloride of calcium and surrounded by crushed ice; 
the opening in the end of the air-chamber is connected by a 
ubber tube to an aspirator (a small injector supplied with 
water would act well as an aspirator), and air is drawn through 


»r three or four hours : at the end of this time the bulb and 
ibe should be filled with dry air. While the current of air is 

ill flowing, the cock B is opened and niercury allowed to pass 
ito the tubes until it rises to the point a in the tube BF\ the 
pening in the air-chamber is then hermetically sealed with a 
low-pipe, and the connections to the chloride-of-calcium tube 
'moved. This operation fills the bulb with air at atmospheric 
-essure. By closing the cock B before the mercury has risen 
► the point a the pressure will be increased ; by closing it ?fter 

has passed the point a it will be diminished. Packing the 
alb C in ice, or heating it, will also increase or dimini-sh the 
"essure as required. 

291. Corrections to Determinations by the Air-thennr>m- 
:cr. — The corrections to the air- thermometer are all lery 
nail, and affect the results but little if considered. They ; re : 

1. Capillarity, or adhesion of the mercury to the glass. In 
*neral the mercury in the two tubes ^/^and BE (Fig. ifto) is 
oving in opposite directions, and the effect of adhesion is 
iutralized. For error in other cases see table on page 35T. 

2. Expansion of the glass. This is a small amount, and 
lay usually be neglected. The coefficient of surface expun- 
on of glass is o.ooooi per degree F. ; it is entirely neutralized 

the column of mercur>' is not reduced in area at the point 
f meeting the air from the bulb. 

3. Expansion of the mercury should in every case be taken 
»to account by reducing all observations to 32*^ F., the coeffi- 
ient of expansion being o.oooi per degree F. Reduce all ob- 
-rvations before applying formulae. 

4. Errors in the fixed scale should be determined and 
bservations reduced before applying formulae. 

292. Practical Uses of the Air-thermometer. — The air- 
^ermometer may be used as a standard with which to compare 
'ercurial thermometers; in this case the bulb of the air-ther- 
'ometer is surrounded with a non-conducting chamber (Fig. 
^), in which the thermometer to be compared is inserted. 
Or low temperatures water may be circulated through this 
anibcr, and simultaneous readings taken ; for higher tem- 




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 vill 
increase rapidly for high temperatures. 

The air-tkermometer may also be used to measure tempac 
tares directly. When the bulb is connected with a long cap!! 
lary stem it may be introduced into flues, and temperatura 
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 Airthermometer. 
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 A and of the barometer (5; 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 readngi 
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 h', and that of 
barometer b' in the same room. The reading of the mercuiy 
column plus that of the barometer will correspond to^'-f-*" 
in the formula 

* + / 

+ A") - 460 =^ /ii;^' -f /o - 460. 

Third. To Compare a Mercurial Thermometer. — MakesfiB' 

taneous readings of the thermometer when hanging ii 
chamber with the air-bulb, and the height of the mercuJJ 
column. Perform reduction, and plot a calibration curve fo 
each 10° of graduation. 

Fourth. For general use of the air-thermometer, ^*iiB"J 




bulb so that it can be inserted into the medium whose 
iperature is to be measured, with the U-shaped tubes in an 
essible position for reading. Obtain the temperature a3 
iained above (see Second). 
294. Form for Reducing Air-thermometer Determina- 



loQ. • • • 

Determination op Constant. 






n^r&tnre of air-bulb. ......... 

nag tgr^— Reading ............ 


Reduced 10 32' 


Thermometer . 

Reduced to 32". 

cffAnt — Afk2 "f" (b '-4- fiS. ........ 


tfti^kUk ^^ f^^m m ^w 1 »»/• •••••••• 

Determination of Temperature. 

f^/ay+*') -460. 

























295. Determination of Boiling and Freezing Points, 
First. To ti si for Boiling-point. — Suspeid 

the llicrmometer so that it will becntirdy 
surrounded in the vapor of boiling waiK 
at atmospheric pressure but will not be in 
contact with the water. Note the reading. 
From the barometer-reading calcuiate the 
boiling-point for the same time. The dif- 
ference will be the error in position of the 

The engraving (Fig. 182) shows . 
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 iiKtni 
ment around the tube, and down on ttie 
outside, discharging into the air. oritmif 
be returned directly to the cup, thusob- 
viating the need of supplying water. 1" 
the form shown, the parts telescope into 
each other for convenience in canj'iog, 
which is entirely unnecessary for labo* 
tory uses. 

Secondly. To lest for Freesing-poiHl- 
Surround the bulb of the thermometer by 
a mixture of water and ice. or watei and 
snow; drain off most of the water. Tht 
TBsr'B^iuNo^^oi^^T.™ difference between the reading oblaintd 

and the zero as marked on the thermometer (32° for F»bt. 

scale) is the error in location of freezing-point. 

296. Metallic Pyrometers are instruments used formt* 
uring high temperatures. The ordinary instruments sold under 
this name are made of two metals which have different rates ol 
expansion, copper and iron generally being used. Thedifle^ 
ence in the rate of expansion is employed by means of Icvtts 
and gears to rotate a needle over a dial graduated to degrees. 

In usiiig the metallic pyrometer no reading should be takt* ' 
until it has had sufficient time to arrive at ^he tempecaturc o( 


e medium in which it is enclosed ; when one tube alone is 
:ated, the needle may be stationary on the dial, or even have 
retrograde motion. 

The metallic pyrometer is usually calibrated by immersing 
a pipe filled with steam under pressure and comparing the 
mperature with that given by a calibrated mercurial ther- 
jineter. The scale so obtained is assumed to be uniform 
roughout the range of the pyrometer and beyond the limits 
the calibration. Comparison might be made with an air- 
^rmometer. The extreme range of such pyrometers is about 
yf Fahr., but they are probably of little value for tempera- 
•es exceeding iocx)° Fahr. 

Wedgewood' s Pyrometer is based on the permanent contrac- 
n of clay cylinders due to heating. This contraction is 
termined by measurement in a metal groove with plane sides 
:lined towards each other. This pyrometer does npt give 
iform results. 

297. Air-pyrometer. — The air-thermometer with a bulb of 
rcelain, or platinum or other refractory material, affords an 
rurate method of measuring high temperatures. 

Mr. Hoadley* states that the ordinary air-thermometer made 
hard glass can be used to determine temperatures of 800° 

hr. With porcelain bulb it has been used to measure tem- 

ratures of 1900° Fahr. 

298. Calorimetric Pyrometers.— Pyrometers of this class 
termine the temperature by heating a metal or other refrac- 
y substance to the heat of the medium whose temperature 
to be measured. Suddenly dropping the heated body into a 
ge mass of water, the heat given ofT by the body is equal to 
at gained by the water ; from this operation and the known 
ecific heat of the substance the temperature is computed, 
lus, let A" equal the specific heat of the body, J/ its weight; 

Unequal the weight of water, / its temperature before, and 
ifter, the body has been immersed ; let T' equal the tempera- 
e of the heated body, t' its final temperature. Then 

KM{T-t')^ \V\^t' -/). 

* See Vol. VI., Transactions American Society Mechanical Engineers. 


From which 

In connection with pyrometrical work, the specific hcatol 
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 Z", its weight 3/ 
having been accurately determined, it is dropped suddenly 
without loss of heat into a vessel containing fF pounds of water 
at a temperature of 60'' Fahr. Let K be the specific heat of 
the body, and /' 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 /' 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' - 60^). 
From which 

W{t'- 60^) 

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 (i) 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 metak 
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* 








Specific Heat. 
Low Temperaturei. 



Pl«tiniiin • ■ . 

. . • » 


- 38 
• . • • 













• • ■ . 


Wrought- iroo . ... 









Sulohur. .... ..... 


he mean specific heat of Plati?mm* has been the subject of 
al investigation. It was found to vary from 0.03350 at 
C. to 00377 at 1100° C. by Poullet, the experiment being 
! with a platinum reservoir air-thermometer, 
he following were the determinations : 



:an|fe of Temperature. 

Mean Specific 

Range of Temperature. 

Mean Specific 

Degree Centi|pade. 


Degree Centigrade. 


10 100 


15 to TOO 


•* 200 


16 ** 172 


•* 300 


17 " 247 


'* 400 


•* 500 


" 600 


" 700 


" 800 


*• 90c 


" 1000 




* See Encyclopaedia Britannica, art. Pyrometer. 




YoT wrmtg/it-iron the true specific heat at a temperature/ 
on the Centigrade scale is given as follows by Weinbold: 

C, = o. 105907 + 0.00036538/ + aooooooo66477/'. 

Pore^f/ain or Fire-clajr ha,v\ns a specific heat from 0,17 tow, 
althoiigli not a metal, is well adapted for pyrometrical purpojf). 

301. Hoadley Calorimetric Pyrometer. — The Hoadlei' 
pyrometer Is described in Vol. VI., p. 712, Transactions p( 
the American Society of Mechanical Engineers, It consisid 
of a vessel. Fig. 183, made of several concentric vessels of 
copper, with water in the inner one, eider-down in the iiittr- 
mediate spaces, and a cover of the same nature. Also a sub- 

stance to be heated consisting of balls of platinum, or wrought- 
iron 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 
ma Je of hard rubber, with a hole in the centre for a the^nom^ 
tcr. The balls used as heat-carriers weighed about three qiw 
ters of a pound each ; the vessel held about twelve pouDt^ ot 
water. This apparatus is now at Cornell University. 


The balls were heated in crucibles and conveyed to the 
calorimeter in a fire-clay jar as shown in Fig. 142. The cover 

^f this jar was quickly removed and the balls dropped into the 
■vater in the calorimeter, 

302. Thermo-Couple Thermometers In thermometers 

>r pyrometers of this kind the temperature is determined by the 
aeasurement of the electro-motive force excited by differences 
if temperature in a metallic circuit composed of two different 
Dctals. The point of union of the metals is termed a junction. 
Vhen there are several junctions in series the device is called a 

This thermometer was first proposed by Becquerel in 1826, 
trst applied practically by Pouillet in 1836, it was considered 
inrt-Uable by Regnault, but was much improved by Edw. 
Secquerel in 1863, who introduced the platinum paUadin couples 
md it %vas finally made a practical commercial instrument by 
L* Chatelier. Le Chatelicr introduced a platinum and platinum- 
'hodium couple which gives extremely reliable results through 
I range of temperatures from 300° C, to 1500° C, 

The materials best adapted for couples depend upon the 
^uirements as to temperature and other conditions. The 
5ietals should be pure or at least homogeneous, since clectro- 
^notive force is set up by a change of structiu-e. The couples 
*ed ro be protected from corroding gases for reliable results. 
for bigfa temperatures a couple made of pure platinum and a 


length, and the thermo-couple inserted in the porcelain 

t £• Prof. W. H. Bristol has recently designed and put on 

nuurket a thermometer of this type which is fully described 

fsJL 25 of the Transactions of the Am. Soc. Mech. Engineers. 

Bristol's thermometer platinum rhodium is used for the hot 

tient and cheaper metals for the remaining portion. A 

ct reading special milli-voltmeter of the Weston type is 

1 to measure the electro- motive force and its equivalent 

perature. The instrument is considered acciuute to 2000® F, 

s provided with a recording devise when desiredi and an 

)matic compensator for changes of temperature of the cold 

rtion, thus making corrections for that purpose imnecessary. 

'he empirical formula applying to the use of the P/, Ptr-Rh^ 

to the P/, Ft^Jr thermometer is given by Dr. W. C. Waidner 


e = - a + & (r - /) + c (7^ - /») 

ch becomes when / = o 

1 the above formula e is the electro-motive force, T the 
igrade temperature of the hot junction and i that of the 
.. As there are three constants, a, b and c, in the above for- 
a, it is evident that in order to standardize, three points must 
ietermined from calibration, 
[olman has proposed the following formula 

e = m (T* - r) when / = o, 
e = mT^ 
1 which 

log e = n log T + log w. 

man's formula has been found sufficiently accurate for most 
Doses, and haWng only two constants requires only two points 
>e found by calibration. 

rofessor Brown of McGill University has devised a form of 
Callendar instrument in which the diflFerence of temperature 
etermined by the current required to make equal resistance 
vi'o different circuits, which condition is indicated by the use 
telephone which at that instant transmits no sound. 


303. Electrical Resistance Thermometer. — This instru- 
ment is based on the well known law of increase of electrical re- 
sistance with increase of temperature. From this law it can be 
deduced that the difference of temperature when a^constant cur- 
rent is flowing through a corniuctor is a function of the differ* 
ence in resistance. 

This thermometer was first constructed by Siemens about 
1874, in a form which did not give reliable results. It has 
been improved and perfected by Callendar, Griffiths and otheis» 
and is for many purposes the most accurate thermometer buik 
at the present time. 

Callendar constructs his thermometer by winding a coil of 
fine platinum wire on a serrated mica frame, so that the wire is 
in contact with its supporting frame for only a minute portion 
of its length. He connects leads of larger pt. wire at top and 
bottom of coil so as to compensate for varying depths of immer- 
sion. Leads and coil are then inserted in a protecting tube of 
porcelain which is glazed only on the outside. 

The resistance is measured by a Wheatstone bridge, a gal- 
vanometer or a potentiometer which may be specially constructed 
to read in degrees of temperature. Each thermometer must 
have a special calibration as the scales vary with the degree of 
purity of the metal. 

Full discussions of the various methods of measuring high 
temperatures is to be found in a work by Dr. Carl Barrus, pub- 
lished by the U. S. Geological Survey, and also in an aniclc 
by Dr. C. W. Waidncr published in the Transactions of 'is& 
Engineering Society of Western Pennsylvania in 1904. 

304. Optical Pyrometers. — From the fact that the color rf 
an incandescent body varies with the wave length and this again 
with the temperature, it is i)ossible to determine the temperal 
of such bodies by thcii ai)pearance. 

For this purpose a number of optical pyrometers haN-e 
devised. The Mesur^ and NouePs pyrometric telescope 
ures the temperatures by taking advantage of the rotation of 
plane of polarization of light passing through a quartz plate 




•erpendicular to its axis. The angle of rotation is directly pro- 
ortional to the thickness of the quartz, and approximately in- 
ersely proportional to the square of the wave length. 

Light from an incandescent object, passing through the 
lightly ground diffusing-glass G (Fig. 185), enters a polarizing 

Pic. 185. — MssuR* and Noubl Pyrombtric Tblbscopb. 

icol P, and, traversing the quartz plate Q, strikes the analyzer i4, 
nd is seen through the eye piece OL, 

In the use of the instrument the analyzer is turned until the 
bject appears to have a Temon-yellow color. The' position of 



Fio. 186. — Thb Morsb Thbrmo-gaugb. 

e analyzer is indicated by the graduated circle C, the reading 
which may be referred to a temperature scale. Because of 
e variations due to personal errors of different obser\Trs the 
icertainties of observations are likely to amount to fully 100° C. 
le instrument is very convenient for use and is approximately 


The Morse thenno-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 diflferent 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. 





305. Quality of SteSLtn.— Decree of Super heat. Sxtm 
may be dry and saturated, wet or superheated, as described in 
Article 265, page 340. The term quality is used to exprcs 
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 tk 
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 tkt 

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 'vor 
portance of correctly determining the quality of steam is great, 
because the percentage of water carried over in the steam ifl 
the form of vapor or drops of water may be large, and tltf 
water is an inert quantity so far as its power of doing work • 
concerned, even if not a positive detriment to the engine. ABf 
tests for the efficiency of engine or boiler not accompanied 
vith determinations of the amount of water carried over in tic 




^am would be defective in essential particulars, and might 
id to erroneous or even absurd results. 

307. Methods of Determining the Quality. — The methods 
measuring the amount of moisture contained in steam may 
considered under three heads: first, Calortmetry proper, in 

lich the method is based on some process of comparing the 
at actually existing in a pound of the sample with that 
own to exist in a pound of dry and saturated steam at the 
ne pressure. Secondly, Mechanical Separation of the water 
•m the steam, involving the processes of separation and of 
ighing. Thirdly, a Chemical Metliod, in which case a soluble 
t is introduced into the water of the boiler. This salt is not 
sorbed by dry steam, and if it is found in the steam it indi- 
:es the presence of water. The quality is equal to the ratio 

salt in the steam to that in an equal weight of water drawn 
>m the boiler. 

All methods for determining the quality of steam are 
:luded under the head of calorimetry, and instruments for 
termining the quality are termed calorimeters. 

308. Classification of Calorimeters. — The following das- 
cation of different forms of calorimeter is convenient and 
mprehensive : 



' Condensing. . . . >< 

Surface , . 

Barrel or Tank. 

Barrus — Continuous. 
Hoadley Calorimeter. 
Kent — Tank Calorimeter. 

o . . \ External — Barrus Superheatinir. 

Superheating ^ Internal-Peabody Throttling 

Directly determining moisture. 



309. Error in Calorimetric Processes. — The calorimetric 
►cesses proper depend on the method of measuring the heat 
ually existing in a pound of the sample steam at a known 
ssure. This measurement is then compared with the re- 
:s given in a steam-table for dry and saturated steam, and 
quality is computed as will be explained later. 




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 io 
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 34O, 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 : 


Properties of Sieam. 


Properties of Steam. 

Pressure, pounds per sq in.' / 'Total heat B. T. U. 

Pressure, pounds per sq. fool P ' Weight of cu. ft. of steam lbs. 

Temperature, degrees Fahr. / Vol. of i lb. steam, cubic ft. 

Temperature absolute T I'Vol. of i lb. water, cubic ft . 

Heat of the liquid ^ or 5 1 Change in volume v — <r . . . 

Internal latent heat f> ox I -Quality of steam 

External latent heat A Pu or iE > ! Per cent of moisture 

Total latent heat r or L , Degree of superheat 



vox C 






* Mathematical Papers, XLVIIL, p. 194. 


The quantities q^ p, APu^ r, and \ are given in B. T. U. 
r pound of saturated steam reckoned from 32° Fahr. 

311. General Formula for the Heat in One Pound of 
:eam. — The heat existing in one pound of steam with any 
lality X can be expressed by the formula 

•^P + ? = ^ (0 

The heat, however, which is required to raise water from 
:® F. and convert it into steam at a given temperature will 
dude the external latent heat, and will be expressed by the 

xr-\'q^h! (2) 

The heat that may be given out by condensation or change 
: pressure is expressed in equation (2) ; that which exists in 
le steam without change of pressure or external work, by 
juation (i). 

Since in all calorimetric processes the steam is condensed, 
r at least the pressure changed, equation (2) is to be employed 
> represent the available heat. 

If the pressure of the steam is known, r and q can be found 
om the steam-tables. If the heat h in B. T. U. above 32° 
m be found for the sample steam, all the quantities in the 
>ove equation with the exception of x are known, and we 
lall find 

-^ = —7-^ (3) 

case X is greater than unity, the steam is superheated, and 
c degree of superheat 

^ = ^^ (4) 

.en 0.48 equals the specific heat of steam, Cp, 
312. Methods of Determining the Heat in a given 
mple of Steam. — There arc two methods of determining 
^ heat ^ in a given sample of steam. 


I. Condensing the Steam at Atmospheric Pressure. — ^Inthis 
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 ol 
the condensed steam by iv\ the temperatuie of the condensing 
water cold by /, , the condensing water warm by /, ; the original 
temperature of the steam by /, 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 

W-\-k . 


(^-O (5) 

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, XT + /, 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 

;rr + /-/, = — ^-(/. -O; 

from which 

W^+/^(^-0_(^-0 (6) 

X = — • • • • • r/ 

w r r 

If the temperature of condensed steam equal that of the 
warm condensing water, /, = /,, which is the usual condition of 


2. Superheating the Steam.— li the pressure and tempera- 
ture of superheated steam is known, the degree of superheat 
can be found by deducting the normal temperature, as giv^» 
in the steam-table for that pressure, from the observed tcv.- 
perature. The total heat in a pound of the superheated stcatt 


equal to that in a pound of saturated steam, as given by the 
iam-tables, plus the product of the degree of superheat into 
e specific heat Cp of the steam ; that is, 

//- = A + CpD. 

The superheating may be done by extraneous means, as in 
\ Barrus superheating calorimeter, or by throttling, as in 
I throttling calorimeter. In the latter the heat required for 
)erheating is obtained by reducing the pressure, which, being 
ompanied by a corresponding reduction of boiling point, 
*rates heat sufficient to evaporate a small percentage of 
•isture only. 

In the case of the superheating calorimeter, the heat re- 
red to evaporate the moisture and superheat the steam is 
asured by the loss of temperature n in an equal weight of 
)erheated steam, so that 

Cpfi = r(i — ^) + ^/^; 
i-^ = V— ^-^ (7) 

In the case of the throttling calorimeter there is no change 
:be total amount of heat, but there is a change of pressure, so 
t the quantities in the first member of (8) correspond to the 
^inal pressures of steam before throttling, and those in the 
ond member to the calorimeter pressures after throttling, and 

313. Condensing Calorimeters. — Condensing calorimeters 
of two general classes : i. The jet of steam is received by 
condensing water, and the condensed steam intermingU- 
ctly with the condensing water. 2. The jet of steam i- 
densed in a coil or pipe arranged as in a surface condenser. 




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 

w r r 

In the first class t^=^ t^^ and 

^ ^r+>&(/,-o (/-/,) 

X = : ^-^ '-^ — :^ -V ..... (9) I' 

w r r m 

Both forms of condensing calorimeter can be made to act con- 
tinuously or at intervals, and there are several distinct typesol 

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 fonns 
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 t« 
be a variable and differentiate the equation 

4r = 




We have 

^x-^A IV= (/, - /,) -^ wr ; 

Jx -f- ^w 
Ax ~ At^ 
Ax -=- At^ 

W -T- wr. 



; Jr = —At, nearly, for ordinary pressures of steam, aiid 
er is a function of the pressure, wc have approximately 

J/ = ^p = — Jr ; 

Ax^4p= r^C- '.) - '- r + /,1 -i- r*. 

lie weight of condensing water usually held by the barrel- 
imeters is from 300 to 400 lbs., while the weight of the 
n condensed varies from t6 to 20 lbs., and the correspond- 
emperalures have a range of 50° to 70° F. For these cases 
11 be found that the percentage of error in quality, sup- 
ig other data correct, is approximately the same as the 
:ntage of error in the weights. The error in thermometer- 
rmination has nearly the same effect, whether made before 
ter the steam has been condensed. For the amounts usu* 
employed the error of one fifth of one degree in tempera 
has about the same effect as one half of one per cent error 
;ight ; that is, it makes an error of about the same amount 
e quality of steam. 

'he following shows in tabular form the effect of errors 
condensing calorimeters in which the ordinary weights of 
r and of steam are used : 


^ W>ur. 

Brror [a 
CooOcoed Stom, 









Jj.i 1 Pern. 


g.a.( 1 olca 




Per ct. 






= io'F- 



Pr. - 







- ! 


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 con* 
densed steam, of 0.53** F. in temperature of cold water, of a65* 
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 i per cent in weight or 1.2 and a6 
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 Suptf- 

heating Calorimeter, — In this, if /, — / is the gain of tempera- 
ture of the sample steam, and /,— /, is the loss of temperature 
in the superheated steam, we have, neglecting radiation, 

I - ;r = o.48[/, - /, - (/, - /)] -^ r. 

In the Throttlijig Calorimeter^ where the steam is super- 
heated by expanding, we have by equation (7), making f^ = 

_ A + 0.48/^ — q 

X — m 

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 


uld be correctly determined, however, especially if the 
)unt of superheating is small. 

^n error in gauge-reading has about one half the effect on 

quality of the steam as in the other class of calorimeters. 

115. Method of Obtaining a Sample of Steam. — It is 

illy arranged so as to pass only a very small percentage of 

total steam through the calorimeter, and it is important 

this sample shall fairly represent the entire quantity ol 

m. From experiments made by the author, it is quite cer- 

that the quality varies greatly in different portions of the 

e pipe, and th^t it differs more in horizontal than in verti- 

Dipes. Steam drawn from the surface of the pipe is likely 

:ontain more than the average amount of moisture ; that 

1 the centre of the pipe to contain less. The better 

hod for obtaining a sample of steam is to cut a long 

aded nipple into which a series of holes may be drilled, 

screw this well into the pipe. Half-inch pipe is gen- 

ly used for calorimeter connections, and it may be screwed 

the main pipe one half or three quarters of the distance to 

centre, with the end left open and without side-perfora- 

s, as shown in Fig. 187, or screwed three fourths the 


Fig. 187. CoLLECTiNC-NipPLBS. Fig. 188. 

ince across the pipe, a series of holes drilled through the 
5, and the end left open or stopped, as shown in Fig. 144. 
)ck-nut on the nipple, which can be screwed against the 
when the nipple is in place, will serve to make a tight 
The best form of nipple is not definitely determined, 
r\igh many experiments have been made for this purpose: 
m extending nearly across the pipe and provided with a 



slit or with numerous holes Js probably preferable. 
the current of steam is ascending in a vertical pipe, t 
seems to be more uniformly mixed than when Descend 
a vertical pipe or when moving in a horizontal ane. 
is, however, considerable variation ior tnis com 
especially if the steam contains .nore than 3 oer cent of 1 
316. Method of Inserting Thermometers. — In the 1 
calorimeters it is frequently necessary to insert thernton 

FlC, .S9.— STBAli|-rHBlt».0».TIll. FlG i 

into the steam in order to correctly measure the tempu 
For this purpose thermometers can be had mountrd 1 
brass case, as shown in Fig. 189. which will screw loB 
[lireaded opening In the main pipe. 

The author prefers to use instead a thermometer<up •*' 
form shown in Fig. 190, which is screwed into a lappedof 


n the pipe. Cylinder-oil or mercury is then poured into 
up, and a thermometer with graduations cut on the glass 
:ed. The thermometer-cups are usually made of a solid 

casting, the outside being turned down to the proper di- 
ions and threaded to fit a J-inch pipe-fitting. The inside 
is drilled \ inch in diameter, and the walls are left ^V i^ch 
The total length varies from 4J to 6 inches — depending 
e place where it must be used. In either case it is essen- 
hat the thermometer be inserted deep into the current of 
I or water, and that no air-pocket forms around the bulb 
e thermometer. The thermometer should be nearly ver- 

and as much of the stem as possible should be protected 

radiating influence. 

the thermometer is to be inserted into steam of very little 
are, the stem of the thermometer can be crowded into a 
cut in a rubber cork which fits the opening in the pipe. 
Lse the thermometer cannot be inserted in the pipe it is 
times bound on the outside, being well protected from 
tion by hair-felting; but this practice cannot be recom- 
cd, as the reading is often much less than is shown by a 
lometer inserted in the current of flowing steam. In the 
>f thermometers, breakages will be lessened by carefully 
ving the directions as given in Article 286, p. 370. 
[7. Determination of the Water-equivalent of the 
rimeter. — The calorimeters exert some effect on the 
ig of the liquid contained in them, since the inner sub- 
i of the calorimeter must also be heated. This effect is 
expressed by considering the calorimeter as equivalent to 
•tain number of pounds of water producing the same 
This number is termed the waler-equivalent of the 
meter. The water-equivalent, k, can be found in three 

By computing from the known weight and specific heat 
3 materials composing the calorimeter. Thus let c be the 
ic heat, Wc the weight; then 


2. By drawing into the calorimeter, when it is coolecl 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, /, the first and /, the final 
temperatures, and k the water-equivalent sought. Since the 
heat before and after this operation is the same. 

From which 


3. By condensing steam drawn from a quiescent boiler,anJ 
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), 

^ ^ «<r^. -^)_ _ j^^ .... (.0) 

For the barrel and jet condensing calorimeters generally, /,=A» 
and wc have 

k = - K^-^ + ^ - O _ y^^^ 

The cooling effect of superheating calorimeters is generally 
expressed in degrees of temperature in the reading of onco( 
the thermometers. 


318. Barrel or Tank Calorimeter. — The barrel caloriffi' 
eter belongs to that class of condensing calorimeters in whicb 
a jet of steam intermingles directly with the water of conden- 
sation. It is made in various ways ; in some instances the 



alls are made double and packed with a non>condensing 
ibstance, as down or hair-felting, to prevent radiation, and 
le instrument is provided with an agitator consisting of 
addles fastened to a vertical axis that can be revolved and 
le water thoroughly mixed ; but it usually consists of an ordi- 
ary wooden tank or barrel resting on a pair of scales, is 
10 wn in Fig. 191. 

Fig. 191.— The Barrkl Calorimrter. 

A sample of steam is drawn from the main steam-pipe by 
>nnections, as explained in Article 315, page 369, and con- 
ned by hose, or partly by iron pipe and partly by hose, to 
le calorimeter. In the use of the instrument, water is first 
dmitted to the barrel and the weight accurately determined, 
he pipe is then heated by permitting steam to blow through 
t into the air; steam is then shut off, the end of the pipe is 
ubmerged in the water of the calorimeter, and steam turned 
>n until the temperature of the condensing water is about 1 10° 
P. 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 
cnown, the quality can be computed as in equation (6), page 394. 

X = 

( W-^ k u, - O {I - /,) 




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 oflf. 

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 b\ 
weighing with and without the pipe in the water of the calo- 

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 arc 
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. 

Exuffipie. — Temperature of condensing water, cold, /,.is 
52°.8 F.; warm, /, , 109^.6 F. Steam-pressure by gauge, 79.7: 
absolute, 94.4. Entering steam, normal temperature, from 
steam-table, /, 323^.5 F. Latent heat, r, 888.2 B. T. U. 
Weight of condensing water cold, W^ 360 pounds ; warm, 
W -\- w, 379.1 pounds, wet steam, a/, 19.1 pounds. Calorim- 
eter-equivalent eliminated by heating. The quality 

j6o (1096 -- 52^ _ 323.5 - 109.6 _ 
1 9. 1 888.2 888.2 ^^*^ 


319. Directions for Use of the Barrel Calorimeter.— 

ipparatus, — Thermometer reading to \ degree F., range 32° 
o 212° ; scales reading to ^ of a pound ; barrel provided with 
neans of filling with water and emptying ; proper steam con- 
lections ; steam-gauge or thermometer in main steam-pipe. 

1. Calibrate all apparatus. 

2. Fill barrel with 360 pounds of water, and heat to 130 
legrees by steam ; waste this and make no determinations for 
noisture. This is to warm up the barrel. 

3. Empty the barrel, take its weight, add quickly 360 
K>unds of water, and take its temperature. 

4. Remove steam-pipe from barrel ; blow steam thfough it 
o warm and dry it ; hang on bracket so as not to be in contact 
¥ith barrel ; turn on steam, and leave it on until temperature 
)f resulting water rises to 110° F. Turn oflF steam; open air- 
rock at steam-pipe as explained. 

5. Take the final weights with pipe in barrel, in same po- 
ation as in previous weighings ; also take weights with the pipe 
■cmoved : calculate from this the displacement due to pipe, and 
X)rrect for same. 

Alternative for fourth and fifth operations, — Supply steam 
hrough a hose, which is removed as soon as water rises to a 
cmperature of 1 10° F. Weigh with the hose removed from 
lie barrel. Stir the water while taking temperatures. 

6. Take five determinations, and compute results as ex- 
>lained. Fill out and file blank containing data and results. 

7. Compute the value of the water-equivalent, ky in pounds 
>y comparing the different sets of observations. 

320. The Continuous-jet Condensing Calorimeter. — 
V calorimeter may be made by condensing the jet of steam in 
■ stream of water passing through a small injector or an equiva- 
^nt instrument. The method is well shown in Fig, 193. A 
^nk of cold water, B^ placed upon the scales R^ is connected 
c> the small injector by the pipe C\ the injector is supplied 
*^ ith steam by the pipe 5, the pressure of which is taken d}- 
Ke gauge P\ the temperature of the cold water is taken at <. 
hat of the warm water at g. Water is discharged into the 




weighing-tank^. The amount taken from the tankfisthc 
weight of cold water W; the difference in the respective 
weights of the water in tanks A and B is the weight of tk 
steam w. 

The quality is computed exactly as for the barrel caloriin- 

In case an injector is used, as shown in Fig, 19a, the tint 
7 is not needed : water can be raised by suction from tiie tint 
I through the pipe d. The original weight of A will be ihii 

of the cold water; the final weight will be that of steam adW 
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 cant* 
made of pipe-fittings, as shown in Fig. 193. In this cascstcii" 
of known pressure and temperature is supplied by the pipfl 
cold water is received at S' , and the warm water is disctiaig^l 
at S. The temperature of the entering water is taken b}> 
thermometer in the thermometer-cup 7", that of the dischai^t 
by a thermometer at T. The steam is condensed in front (( 
the nozzle C. 

This class of instruments present much better opportunitio 
of measuring the temperatures accurately than the band 
calorimeter, and the results are somewhat more reliable. 


In the use of continuous calorimeters of any class, the in- 
rument should be put in operation before the thermometers 
"c put in place or any observations taken. The poise on the 
eighing'scale can be set somewhat in advance of its baL 
icing position, and when sufficient water has been pumped 
It the scale-beam will rise \ this may be taken as the signal 

Fio. 17J.— Jbt Coin 

3r saving the water which has been previously wasted, and 
'commencing the run. 

The water equivalent of the calorimeter, k, will be small, 
Qd due principally to radiation. It can be found by passing 
ot water through the calorimeter and noting tlie loss in tem- 

321. The Hoadley Calorimeter. — This instrument be. 
ngs to the class of non-continuous surface calorimeters. The 


instrument is described in Transactions of the Americi 
ciety of Mechanical Engineers, Vol. VI.. page 716, and cot 
of a condensing coil for the steam, situated in the botloi 
tank-calorimeter, very carefully made to prevent rad 
losses. The dimensions were 17 inches diameter by 32 
deep, with a capacity of about 200 pounds of watet? 

calorimeter was made of three concentric vessels of gaM 
iron, the spaces being filled with hair-felt and eider-) 
The condenser consisted of a drum through which f 
a large number of half-inch copper tubes, the steam 
on the outside, the water on the inside, of these tubes 
agitator consisting of a propeller-wheel attached to ar 
that could be rotated by turning the external crank I 
ally stirring the water. The thermometer for measuf 
temperature was inserted in the axis of the agitatoj 



hands of Mr. Hoadley the instrument gave accurate 

practice the instrument was arranged as in Fig. 195; the 
leter E was placed on the scales /% and supplied by 
Iter from the elevated barrel A. The temperature of 
tering water was taken at C Steam was admitted to 
ndensing-coil until the temperature of the condensing 
reached, say, 1 10° F. The weights before and aftei 

Fig. 195.— Hoadlby*s Calorimbtbr Arrangbd rox Uss. 

steam were taken by the scales F\ the temperature ot 
rm condensing water was taken by a thermometer, G^ 
d in the axis of the agitator. The water-equivalent was 
ined as explained in Article 317, page 401, and the 
computed by equation (6), page 394, I'he rate of 
; was determined, and an equivalent amount added as a 
ion for any loss of heat by radiation. 
. The Kent Calorimeter. — This instrument differs 
le Hoadley instrument principally in the arrangement of 
ndensing coil. This when filled with steam could bf 
;d from the calorimeter, so as to enable the weight o* 


steam to be taken on a smaller and more delicate pair of 
than those required for the condensing water, thus | 
more accurate determinations of the weight of the stean 

323. The Barrus Continuous Calorimeter. — This 
rimeter is shown in Fig. 196 in section and in Fig. iQf ii 
spective. It consists of a steam-pipe, a/, surrounded 

FlC ,9*.-BAl.Sra CONT.NIOU5 Caloribitm. 

tub or bucket, O. into which cold water flows; the condc 
water is received as it enters the bucket in a small brass 
*. surrounding the pipe a, and is conveyed over and i 
baffle-plates, m, so as to be thoroughly mixed with thtfi 
in the vessel, and is finally discharged ate. Thermomete; 
placed at / and at .i; to tiike the temperature of the water 


lUid leaves, and finally the condensing water is caught 
he overflow and weighed. The condensed steam falls 

:he calorimirtcr : by mean': nf tlit walcc gauge glass at - 


be seen and kept at a constant height. The temperature 
ied steam while it is still under pressure is shown 
Tiometer at h. In order to use the calorimeter it is 
by to weigh the condensed steam ; this cannot be done 
E further cooling, as it would be converted into steam 
Ite pressure removed. For this purpose it is passed 
h a coil of pipe immersed in a bucket filled with water, 


shown at 5 in Fig. 197. The water used in the cooling bucket 
5 has no effect on the quality of the steam and is not cod- 
sidered in the results ; it is allowed to waste, but the condensed 
steam is caught at Wy Fig. 197, and weighed. 

The quality of steam is computed by omitting k in for- 
mula (6), page 394. Hence 

;r = — — • 

w r r 

w is the weight of condensed steam after correction for ^adi^ 
tion-loss as explained in Article 324 ; w being equal to vl-t, 

324. Directions for Using the Barms Continuous Calo* 
rimeter. — Apparatus needed, — Thermometers ; pail for receff* 
ing condensed steam ; tank and scales for the condensing wattt 

Directions. — i. Fill the thermometer-cups with cylinder- 
oil. (Do not put thermometers in place until apparatus i$ 

2. Turn on condensing water and steam ; regulate the flof 
of condensing water so as to keep the bucket O nearly fulLafl^ 
the temperature of the discharge-water as much above tetfr 
perature of the room as injection is below : this should be 
about 110° F. Regulate the flow of condensed steam soasW 
keep the water in the glass r at a constant level. Turn wattf 
on to the cooling coil in the bucket 5, 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 «» 
injection and discharge water, and having previously weigl^ 
the vessels, at a given signal, note time and commence t 
catch the condensed steam and the condensing water. ^■ 
tinue the run until about ^(x^ or 40c pounds of condensi 
water has run into the receiving tank. Without disturbi 
the condition of the apparatus, commence simultaneous!; i' 
waste the discharge from both pipes. Find the weight> 


lensed steam (z«/') and condensing water {W)\ note time of 
ng run. 

^ Make three more runs similar to the first. 
;. To find the radiation-correction of the instruments 
3ty the bucket O of condensing water, and surround the 
iensing tube a with hair-felting ; make a run of the same 
th, and with steam of same pressure as in the previous 
. The weight of steam conden-^ed will be the radiation- 
which we call 1/, and is to be deducted from the weight of 
lensed steam obtained in the previous runs of the same 
th. Find the condensation per hour. 
L Work up quality of steam by the formula 

= [^iiC. - O -(/-'.)] ^ r. 

4ake report as described for other calorimeters. 
Ixample. — The following is the result of a trial with the 
us continuous calorimeter: Temperature of injection-water, 
37°.5 Fahr. ; temperature of discharge-water, /, = 83^8 
r. : temperature of condensed steam, /, = 304.9 Fahr. ; 
n-pressure by gauge, 72.4 lbs. ; temperature of entering 
11,/ = 3 1 7*^.9 ; length of test, 40 minutes ; weight of cool- 
.vater, W = 573.5 lbs. ; weight of condensed steam, w' = 
p lbs. ; radiation-loss // = o. 13 lb. Neglecting value of «, 

^ ^ 573:5 ^ 83.8 - 37.5) _ (3 1 7-9 - 3Q4»9) 
29.89 891 891 

19.21 X 46.3— 130 876.4 

891 891 

= 984. 

98.4 if not corrected for radiation-loss. If corrected, 

("TIC \ 

29:76 "^^-^ - 1 30] ^ 891 = 98.9. 




325. Forms for Use with Condensing: Calorimeters. 



Priming Test with Condensing Calorimeter. 

Made by. 
Test of 


Kind of calorimeter 

189.. ' 


N. Y. 

Number of run 






Duration of run. minutes 


Gauce-oressure lbs . .... ... 

Absolute oressure. lbs 



fV-f- V 


Scale-readings, tare, lbs 

Tare and rold water lbs. .... 

ft* **^ 

Pinal weicht Ihs .... 

• • . • • 

• • ■ *t* 

Quantities : 

C!onflpnsiniy water lbs ...... 





CrtndenseH steam Ihs 

Temperatures, deg. Fahr. : 

Condensing water, cold 

Condensing water, warm 

f^nndensefl steam ... 


• • • • • 


Steam at pressure P 

Ratio water to steam. ... 


Oualilv oer rent ............. 


Per rent moisture .... . . 

Degree of super-heat 

• ••••• 

' '^ 

Correction due to displacement of water by hose ^ 


Calorimeter-equivalent lbs. How found 

Temp, rcom deg. Fahr. Barometer-reading. 

Quality x = 

W , 

- /i) -(/-/.) U- r. 

Degree of super-heat D = (x — i)r -*- 0.48. 


Dmle Ko. 












Weigh 1. 









ngbt o( sMam condensed lbs. 

;igbt of condensing water. " 

eiage temperalure of hot condensing water. . . -C; . . . .Fahr.; . . ■ .B.T.U. 
"cold '■ " ...." .... '• '• 

" " " condensed steam " .... " ..■■ " 

"room " ....deg.C. 

" pressure of air lbs. per sq. in. 

" absolute pressure of the steam . " " " 

ennal units in water corresponding 10 absolute pressure of steam.. ..B.T.U. 

at acquired by condensing water " 

at given up by condensed steam in cooling to temperature of tfaer- 

ight of water condensed by radiation lbs. 

»1 given up by each pound of steam in condensing B.T.U. 

rut heat o( one pound of steam at averagfr absolute pressure " 

cent of 





326. Bamis Superheating Calorimeters. — In the Bar 

Superheating Calorimeter, Fig. 198, the steam-pipe leading fn 
the main is bifurcated, one branch, E. m 
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 

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 jV. The superheated 
steam forms a jacket from / to A' outside 
the sample to be tested, and is discharged 
at the orifice .lA 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 ^.'^i^- 
at H, by reference to the steam-table. 

The theory of this calorimeter is as follows: 


1. An equal weight of steam flows through each branch of 
ic pipe. 

2. The steam, superheated by the gas-flame, is used as a 
cket for the other branch, and parts with as much heat, ex- 
rpt for radiation, as the other gains. 

3. This amount may be measured provided the steam dis- 
larged from the central tube is superheated. 

To measure this gain or loss of heat, thermometers are 
aced to take the temperature of steam as it enters and leaves 
le jacket, and on the central pipe near the same places. 

Formula. — Let (i — jr) be the amount of water to be evap- 
rated ; in so doing it will take up from the jacket-steam 
1 — jr) heat-units. Let / be the normal temperature of the 
cam at the gauge pressure ; let 7", be the temperature of the 
iperheated jacket-steam at entering, and T^ as it leaves; let 
", be the temperature of the superheated steam discharged 
om 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 
sat are equal, we have 

0.48( r» - 7; - /) = r(l - ;r) + 0.48(r. - /), 
.-. I - ;r = o.48[r, _ r^ _ / _ (T; - /)] -v- r ; 

cm which x may be found. 

To find /, the radiation-loss in degrees, shut off steam in 
le branch leading to the centre steam-pipe, and find reading 
thermometers Z", and 7", . After a run of same length as in 
St, take /= 7", — T",. 

Directions for using Barrus Superheating Calorimeler, — Ap- 
^ratus needed, — Three thermometers reading 400^ F. each, 
id pressure-gauge, superheating lamps, etc. 

First. Calibrate instruments, and ascertain by a run of 

enty minutes that equal amounts of steam are discharged 

^m each orifice. This may be done by condensing the steam. 

Second. Put cylinder-oil in oil-cups ; attach gauge. 


327. Thomas Electric Superheating Calorimeter. — An 

electric superheating calorimeter has recently been designed 
(see Vol. XXV, A.S.M.E.), by Prof. Carl C. Thomas, in whkh 
the steam flowing through the instrument is superheated by an 
electric current supplied for that purpose, the energy of which is 
m(jasured. The heat derived from the electric current is absorbed 
iji (i ) evaporating such moisture as the steam may contain (2) 
iiuperheating the steam from a temperature / to a temperature 
Tj (3) in overcoming the radiation loss. The equation repre 
senting this action would be as follows: 

|; = f (I - :v) + c (r, - /) + iJ 

from which i "■^^"TTV"^ (^s ~ "" ^ I 

In the above equations, E is the electrical energy expressed in 
B.T.U. (equal to the watts divided by 17.56), W the weight of 
st'^^am discharged, r the latent heat, x the quality, c the specific 
heat of steam (0.48 for low degrees of superheat and pressure), 
/ temperature of steam as it enters calorimeter, T temperature 
of superheated steam as it leaves calorimeter, and R the radiation 
pyprcssed in B.T.U. 

The instrument consists of a soapstone cylinder about 3 by 4 
inches, containing numerous holes in each of which is inserted a 
coil of German silver wire which constitutes the electric heater. 
The soapstone cylinder is inserted in a brass case \sith suitable 
connections for steam, the electric current, steam gauge and 
thermometers for the entering and leaving steam. The discharge 
steam flows through an orifice and its weight W is obtained Ij 
Napier's rule as explained on page 434 for the separating calon- 
meter. The electrical energ)' E is measured by suitable insti'J' 
ments as a wattmeter or a potentiometer, r is obtained ^^ 
steam tables, and the temperatures are measured. The radiatio"^ 
R^ which is ver\- small, can be determined by suppl}*!"? ^ 
instrument with steam of a sliirht degree of superheat. 

328. The Throttling Calorimeter This instrument ^ 

designed in 1888 by Prof. C. H. Peabody of Boston, and ^ 


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 nriginally, 
it consisted of a small vessel (our inches in diameter by six to 
eight inches long, and connected 
to the steam-supply with a pipe 
containing a valve, b, 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. Cau.»iiiit«ii. 

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 evaporatmj 
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 
IS in formula (2), Article 311. page 393, by xr -\- q. After 
'/caching the calorimeter the heat is that due to the press- 






ure in the calorimeter added to that due to the superheat, or 
A., + 0.48(7', — T^. Since these quantities are equal, 

;rr + ^ = A, + 048(7; - 7;); 

from which 

x = \^c-q-\- 0.48(7', - 7,)] -5- r; . 


m which r equals latent heat, and q heat of liquid due to 
pressure in main pipe as given in the steam-table. 

X^ = total heat in one pound of dry steam at calorimeter 
pressure; 7", = reading of thermometer in calorimeter, and 
T^ = normal temperature of steam in calorimeter due to calo- 
rimeter pressure. Care must be taken that both A, 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 barofli' 
eter-reading, and that the thermometer in the caloriineter 
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. . 



Dejf. F. 


Heat of 
B.T. U. 




B. T. U. 




• • • • 


a T. I'. 


From which 

•^= [1153 - 293.2 + 0.48(274,2 -233.1)] 4- 887.3; 
X = 99. 1 . 

Per cent of moisture, 100 — ;r = 0.9. 




»9. Recent Forms of Throttling Calorimeters These 

iciita differ from I'cabody's principally in size and 
They all work in the same general manner and 
iiled descriptions are hardly necessary. 

(dh^-Kbislxe'b Throttxino Calorimeteiu 
Reisler's throttling calorimeter is shown in Fig. 200, 
ft attached manometer for measuring the pressure in the 
orimeter chamber, it is of small size and keeps the current 
steam intimately in contact with the thermometer. 
Carpenter's throttling calorimeter, shown in Fig. 201 , is pro- 
led with an attached nuzzle for spraying the sample of 
am over the themometer-bulb. The instrument may be 
I with or without a thermometer-cup, but in every case 
Jiermomeler must be deeply immersed in the steam, 
(instrument is made by Schaffer and Budenberg, New York, 


Pre. ».— C»»r«HTmii-s C*LOK»in«>. 

Throttling: Calorimeter of Pipe-fittings.— A veo 
tsfactory calorimeter can be made of pipe-fittings, as s 

Fic. t^-Ti 
in Fig. 202. Connect 
as explained already 


is made to the main steam' 
wiiere. The calorimeter is 1 



ch fittings arranged as shown ; the steam-pipe W is of 
pipe, and the throttling orifice is made by screwing on a 
which is drilled a hole i or -ji^f inch in diameter, 
hermometer-cup, Fig. 1 90, page 400,1s screwed into the 
id an air-cock inserted opposite the supply of steam. A 
leter, B^ for measuring the pressure is attached by a 
)f rubber tubing as shown. The exhaust steam is dis- 
d at E. The back-pressure on the calorimeter can be 
ied any desired amount by a valve on the exhaust-pipe ; 
no valve is used the pressure is so nearly atmospheric 
manometer is seldom required. 

ithod of finding: Normal Temperature in the Calor- 
r. — It is essential to know the normal temperature 
the calorimeter; this will vary with the pressure on the 
leter, which pressure is equal to the barometer-reading 
e manometer-reading. 
5 following table gives the normal temperature corre- 



Total Pressure 


Toul Pressure 


on Calorimeter. 


on Calorimeter. 

Decrees F. 

Inches Hg. 

Degrees F. 

Inches Hg. 


























































































Difference i* F =.0.585 inch. Diflfcrcncc i inch = i*.709. 


spending to various absolute pressures nearly atmosphe 
pressed in inches of mercury: 

In the use of the instrument the total pressure 
calorimeter is to be taken as the sum of the barometer-i 
and the attached manometer. The degree of superheat 
steam in the calorimeter is the difference between the te 
ture as shown by the pressure and that shown by the ii 

Graphical Solution for Throttling-Calorimeter 
minations. — In the practical use of this instrument 
customary to exhaust at atmospheric pressure, so th 
normal temperature in the calorimeter is the boiling-p 
atmospheric pressure, and \ is 1 146.6; in which case f< 
(11) becomes 

1 146.6 + o^SC T*, — 212) — q 


1 146.6 — q , 0.48(7', — 212 ) 

— I 1 -* 

If in this form we suppose the steam-pressure constat! 

the degree of superheat and quality of steam alone to 

r and q will both be constant, and we shall have the eqi 

1 1 46.6 — q 
of a right line, in which is the distance abo\ 

origin that the line cuts the axis of ordinates, and 0.48- 
the tangent of the angle that the line makes with the a 
abscissa,\ Drawing lines corresponding to the different j 
or absolute pressures, a chart may be formed from uhic 
values of x may be obtained without calculation. 

Using degrees of superheat in the calorimeter as abi 
and absolute stcam-prcssure as ordinates, and drawing 
corresponding to various percentages of moisture, we h 
diagram shown in Fig. 203, from which the results of ob 
tions made with the throttling calorimeter may be tali 
once without further calculation. 



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 avtr- 
tical direction until you reach the required absolute pressufe 
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 prc5» 
ure in the calorimeter of 31. 3 inches, corresponding to a tem- 
perature of 2\J^.^^ Fahr. Steam-gauge, So pounds; absolute 
pressure, 94,7 pounds; thermometer-reading in calon'nicler, 
254° Fahr. From which the degree of superheat is found lo 
be2S4''-2i4°-27 = 39''-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 — 1.56 = 9S.34 per cent. While the diagram i» 
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 il 
under pressure, by considering that the ordinates represent the 
difference of pressures on the steam and in the calorimeter. 
Thus, in the example. Article 32S, page 390, the steam-presure 
was So pounds, calorimeter-pressure 8 pounds ; degree of s^lf►c^ 
heat 274.2 — 233.1 =41.1; resulting quality by calculation 59 !■ 
indicating 0.9 per cent of moisture. Using difference o( press- 
ure 80 — 8 = 72 as ordinate, and 41.1 as abscissa, we findfroo 
the chart that the percentage of moisture is 0.92 ; from which 
X = 99.08. 

The results for the throttling calorimeter may be cofll' 
puted from the temperatures instead of the pressure of tht 
original sample of steam as compared with the tcmperaturt 
in the calorimeter when at atmospheric pressure. Carpenter* 
calorimeter, Fig. 201, is especially adapted for such detennini- 
tions, since it provides an easy method of calibrating lU 
thermometer when in position. This is especially impoiunt 
since thermometers will ordinarily read two or three degrees 
low when there is 3 portion of the stem exposed. 


For using the instrument in this manner, the boiling- 
oint in the calorimeter is first determined by opening both 
lie supply and discharge valves C and D and showering the 
istrument and connections with water until the steam in the 
sdorimeter is moist, in which case the reading of the ther- 
ipmeter will be that due to the boiling-point. Second, close 
le discharge-valve with the supply-valve open and obtain 
lU boiler pressure in the calorimeter; when the thermometer 
ais become stationary note the temperature: this will be the 
oiling-temperature for the given pressure as read by the 
[yen thermometer. Third, open the discharge-valve of the 
Lstrument, and after the mercury has become stationary note 
ic reading of the thermometer. Deduct from this latter 
rading the reading first taken and we shall have the degree 
■ superheat in the calorimeter. From these two numbers 
le quality may be computed by reference to steam tables as 
cplained, but it is more easily done by reference to the 
Ilowing diagram, in which the temperature of the steam is 
Lc ordinate and is that given when the discharge- valve is 
Dsed, and the temperature in the calorimeter is the abscissa, 
I the supposition that the boiling-temperature at calorimeter 
essure is 212 degrees. If the boiling-temperature is more or 
5s than this amount, a corresponding correction must be 
ade to the result. As an illustration, suppose that the 
>iling-temperature in the calorimeter is 2 1 1 or one degree 
w, that the actual temperature in the calorimeter when both 
Ives are open is 265, and that the temperature of the steam 
stained with the discharge-valve closed is 320. To find the 
lality we look in the line over 266 and opposite 330, and 
ad the results by the diagonal lines, the quality as shown 
I the diagram being 98.8 (see Fig. 204). 

Limits of the* Throttling Calorimeter. — To deter- 
ine the amount of moisture that can be evaporated by 
rottling, make T, = T, in formula (11); then 

x^{\,- q)'^r (12) 

The amount of moisture that can be determined by the 

-JJ t- X J A — \J-.'.—Ui.J.^ _LT 







f throttling calorimeter in expanding from the given pressure 
i to atmospheric, as computed by substituting in formula (12), 
is as follows : 


Pressure, poaods per square in. 

Maximum per 
cent of prim- 

Quality of the 
steam, per cenL 








no. 3 












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 
lor 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- 
rfnlly removed any moisture from the cup. Place thermometer 
fin 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. 

*^ N. Y., 189.... 

with Throttling Calorimeter. 

rometei-readinf^ inches. S'.eam used during run lbs. 



meter miliaE (■Is- 
ObKrved teapenlu 

cent of cotniiud 
Degreci of HupcrbeiU. 



Duration ol icsl "» 

Baroineter io.; lbs. pei »q. i 

Boiler-pressure by gauge '' 

" " absolute ■' " 

CalorimeLer-pressure by gauge " "■ 

" absolute " ■" 

CaloiimeleT-lemperaluTC C; F. 


Uf IT 

Signed ..- 

336. The Separating Calorimeter. — The scparatinj 
calorimeter is an instrument which removes all water froB 
the sample of steam by some process of mechanical separ*" 
tion, and provides a method of determining the amount* 
water so removed and also the weight of the sample. TW 
process is dependent upon the greater density of water » 
compared with that of steam. Thus, for instance, steam it 
100 lbs. absolute pressure is more than 260 times lighter tlu* 
"water at the same temperature, and if the sample of steaJB 
when moving with considerable velocity can be made n" 
change its direction of motion abruptly, the water will bf 
deposited by the action of inertia. 



43 r 

lie accuracy of this instrument depends on the possibility 
rompletely separating the water from the s^.eam by 
iianical methods. To determine this a series of tests 
: conducted for the author by Messrs. Brill and Meeker 
steam of varying degrees of quality. The range in 
iture was from 33 to i per cent, yet in every case the 
ttling calorimeter attached to the exhaust gave dry steam 
in limits of error of observation. The following were the 
its of this examination. 


Examination of Exhaust 

Obaenrations on Entering Steam. 

Steam from Calorimeter by 

ThrottUniir Calorimeter. 








No. of 






Water in 




Steam in 



Temp, in 

Steam in 



per cent. 





I 1. 15 


79 46 















! 0.525 









1 0.150 




281. 8 





78. 5 











1 .150 



97.32 1 


















, 4 








i 83.5 

1. 15 

1 4 







Si. 6 


i 4 



262.7 9998 




■ m 






















Si. 5 








! 81.4 












93. Si 










, 95.8 





81. I 










l<t of 18 t 

rials* inv< 

>Iving 9S 



; 99.998 


Tills experiment indicates that the complete separation of 

sture from steam is possible by mechanial means. 

\ny radiation in the instrument will increase ttie apparent 

;ture in the steam, and must also receive consideration. 

cially if it be sufficient in amount to sensibly affect Hk 





337. Description of Various Forms. — The earliest 
of separating calorimeter used in experimental work, i 
Sibley College laboratory, consisted of a vessel with an in 

Fin. 905-— The SEPARATuk Cuouxn) 
nozzle, extending below tlie outlet and so arranged thJ 
turrcnt of steam would abruptly change direction and di 
tlio moisture into the bottom portion of the vessel. Tl 
steam was allowed to escape near the top. Fig. 205 


Drm, used in the early experiments, which was constructed 

This instrument, even when covered with hair felt, gave 

sufficient amount of heat to sensibly affect the results, and 
:orrection for radiation was essential. The amount of radia- 
n was determined by using two instruments of the same 
id and size, arranged so that the discharge from one was 
z supply to the other. 

The second instrument receives perfectly dry steam from 
i first, the water deposited is due to the radiation loss, 
ich, being the same in both instruments, provides a method 

determining its amount. In figuring the percentage of 
Msture, the amount thrown down by radiation in the second 
trument is to be deducted from the total amount caught 
the first calorimeter. 

In later forms of the instrument the amount of radiating 
•face has been made so small as to render the correction for 
liation, in all ordinary cases, negligible, by constructing 
i instrument in such a manner as to be jacketed by steam 
the same pressure and temperature as in the sample. The 
m of this instrument is shown in Fig. 207, in which the 
am is supplied through the pipe D^ the moisture being 
eived in the interior vessel E^ the discharge steam passing 
t of the chamber E at the top, into the jacket F, and thence 
t of the instrument through a small opening at L\ the 
ening at L being made sufficiently small to maintain the 
-ssure in the jacket the same as that in the sample. The 
^charged steam is then condensed in a can, J. This can is 
ovided with a small top in which is set a gauge-glass with 
tached scale, graduated so as to read to pounds and tenths 

pounds of water. A gauge-glass N attached to the 
lorimeter is provided with index, ;;/;/, arranged to move 
er a graduated scale, 5, which shows the weight of water in 
? vessel E in pounds and hundredths. In using this 
trument the condensing can / is filled with water to tlae 
o-point of the scale. The amount of condensed steam is 


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 S 
divided by the sum of the readings on both scales. 

The latest form of the instrument is shown complete with 
all accessories in Fig. 2o6, 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 ifl 
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 maybe 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. XI. 
1887, paper by Prof. C. H. Peabody. 


• less of the steam; the 
s then changed through an 

1 3370 

! cup 14, together with more 1 

: of the steam and water 

Blgle of nearly 180 degrees, 

puses the entire amount of water to 

e thrown outward through the meshes 

cup into the space 3, which con- 

ptitutcs the inner chamber. The cup 

> to prevent the current of steam 

rom taking up any moisture which has 

(Iready been thrown out by the force 

if inertia. The meshes or fins project 

into the inside of the cup, so 

iiat any water intercepted will drip into 

e chamber 3. The steam then passes 

[iward, and enters the top of the out- 

: chamber. It is discharged from 

; bottom of the outside chamber 

hrough an orifice 8 of known area, 

nuch smaller than any section 

If llie passages through the calorimeter, 

lothal the steam in the outer chamber 

Nffers no sensible reduction in pressure. The pressure in 

: outer chamber, being the same as in the interior, has 

■ same temperature, and consequently no loss by radia- 

ton can take place from the interior chamber except that 

I takes place from the exposed surface of the gauge- 

iss and fittings. The pressure in the outer chamber, and 

the flow of steam in a given time, is shown by suitably 
raved scales on the attached gauge. The scale for show- 

:he flow of steam is the outer one on the gauge, and is 
ited by trial, and gives the discharge of steam in pounds 
R ten minutes of time. The readings on the scale 12 show 
Ve weight of water in the interior vessel 3, and should be taken 
t the beginning and end of the interval. 

The total size of the instrument is about 12 X 2^ inches. 

1 its weight about 8 pounds. 



338. Formula for Use of the Separating' CaloriiiiH 

. — Let w equal the weight of dry steam discharged a^ I 
exhaust-orifice. IKlhe water drawn from the separator,^'' 
water thrown down during the run by radiation. Thcajj 
quality of the steam is 

H' + jc' 
the amount of moisture 

_ w — R 
' " ~ IV + w 


To reduce the radiation loss as much as possible the in- 
ment should be thoroughly covered with hair felt to the 
kness of 1/2 to 3/4 inch. In this case the total loss by 
iation will be about 0.4 B. T. U.* per square foot per hour 
each degree difference of temperature between the steam 
the surrounding air. This will amount to about 220 
r. U. per square foot per hour, or about 1/5 of a pound 
team under usual conditions of pressure and temperature. 

the instrument desc/ibed the actual exposed surface 
>unts to about 1/12 sq. ft., so that the condensation loss 
/ be considered as from 1/50 to 1/60 of a pound of steam 

hour. The total flow of steam through the instrument 
ally varies from 40 to 60 lbs. of steam per hour, so that if 

instrument is covered, the radiation loss would be less 
n 1/20 of one per cent. If the instrument be not covered, 

loss would be about five times this amount, or under usual 
ditiofis about 1/5 of one per cent. 

The radiation loss can in every case be determined by 
ig steam of known quality as determined by the throttling 
)rimeter, or better still by arranging two separating calori- 
ters of exactly the same size in series so that the steam 
lausted from the first is used as a supply to the second in 
lanncr already explained. 

The Limits of the Instrument. — The instrument will give 
rect determinations with any amount of moisture that the 
nple of steam may contain. With steam containing a very 
all amount of moisture, the radiation loss will have more 
ect than with steam containing a great amount. When the 
t IS considered, however, that a sample of steam cannot 
^bably be obtained but what differs more than 1/2 per cent 
^ the average, the futility of making this correction 
-mcs at once apparent. 

339- General Method of Using. — The general method of 
A ^<^ <^iven only for the latest instrument described, which 

^<^«^ numerous experimenis. Carpenter's Healing and Ventilation 
•• J- VVjley & Sons), Chapter IV. 


is briefly as follows: First, attach the instrument to a pipe 
leading to the main steam-pipe as already explained, and w 
as to obtain the fairest sample of steam. 

Second, wrap the instrument and connections thorougfaljr * 
with hair felt, to prevent loss of heat by radiation, leaving only 
the scales visible. 

Third, permit the steam to blow through the instrument 
until it is thoroughly heated, before making any determina- 

Fourth, take the initial and final readings on the scale 13 
at beginning and end of a period of ten minutes of time and 
note the average position of the hand on the gauge-dial during 
this time. The pressure should be kept as nearly constant 
as possible during the period of discharge, in which case this 
hand will remain constant. 

Fifth, compute the percentage of moisture as explained by 
dividing the reading on the scale 12 by the siun of the read- 
ings on scale 1 2 and the gauge-dial. 

Attention is again called to the difficulty of obtaining an 
average sample of steam for the calori metric determination. The 
principal cause of this difficulty is due to the great difference ui 
specific gravity of water and steam, as, for example, at a pressure 
of 100 pounds absolute per square inch a cubic foot of steam 
weighs 0.23 pound; a cubic foot of water at the corresponding 
temperature weighs about 56 pounds, or more than 225 times 
as much. If any great amount of water is contained in the 
steam, it is likely, if moving in a horizontal pipe, to be concen- 
trated on the bottom; if moving downward in a vertical pipCi 
to fall under the influence of gravity and inertia; if moving upward 
in a vertical pipe, it tends to remain at the bottom until absorbed 
or taken up by the current of steam. The amount of water by 
weight that will be absorbed as a mist or fog and carried by the 
steam is not definitely known, but it depends in a large measure 
on the velocity of flow. 

Because of the great difference in weight of water and steam 
nearly all the water can be deposited from a current of steam, 




in a vessel or reservoir conveniently connected to the steam-pipe, 
by action of gravity or inertia. Such a device is known com- 
mercially as a steam-separcUor. The water is removed from the 
separator either by an automatically controlled pump or trap or 
by hand. 

In the determination of quality it is desirable to remove the 
fee water by a steam-separator before making the connection 
to obtain the sample, as in that case the sample is more likely 
to be an average one. See papers on this subject in the Trans- 
actions of Am. Soc. Mechanical Engineers, Vol. XIII, by Prof. 
J). S. Jacobus, and Vol. XII, by the author. 



Priming Test with Separator Calorimeter. 


Test of . . . . 



N. Y. 

No. of 

lion of 



Weight of 



Weight of 












1 - X 



per ct. 









. i 


Diameler of orilice in. Area of orifice sq. in. SymbolA. 

Barometer'reading in. 

Formula of inslrumcnl, i - .t = < W - jP) + ( W-\- w). 
Napier's Rule, Flow of Steam, pounds per second = ^ FA. 

Melhod of delermining jf 


Method of determining W 

341. The Chemical Calorimeter,— This instrument it.- 
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 iht 
salt appears in the steam its presence indicates water. 

Various salts have been used, but common salt, chleridt 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 follou's: 

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 xvater and condense an equal weight of steam, which 
are to be kept in separate vessels. Add to each of them a {n 
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 tinift 
into each of the three solutions. The effect is to cause tb* 
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 ali been precipitated the liquid turn- 
red. The amount of nitrate of silver required is measured by 
the graduated pipette, and gives the information regarding the 
salt present. 




The detailed directions for the test are as follows : 
Take in each case ICX) cubic centimeters of liquid contain- 
g a few drops of neutral chromate of potassium, and drop 
om a triturated solution holding 10.8 grams of silver to 
e liter; the following data were obtained in a test: 


100 c. c. RED. 


c c of 

•ndensed steam .... 
Mer from the boiler 
■tilled water 

First Trial. 

O.I c. c. 
13 6 c. c. 
0.05 c. c. 

Second Trial. 

0.05 c. C. 
X4.0 c. c. 
0.05 c. c. 

Third Trial. 

O.I c. c. 

13.35 c. c. 
0.05 c. c. 



Letting the results witn these three samples be denoted by 
^, and c respectively, and the amount of moisture by I — jr, 
t have 

I — ;r = 

a — c 

This gives the following results : 

otint moiBtare. 

First Trial. 

o. I — 0.05 
13.6 — .05 

= 0037 

Second Trial. 

0.05 — 0.05 
14.0 — 0.05 

= o 

Third Trial. 

0.1 —0.05 
«3 35 -0.05 

= .00375 

Average = 0.0025. 

This method is evidently applicable only in determining 
c amount of moisture in the steam as it leaves the boiler, and 
U give no information regarding the additional moisture that 
^y be added to the steam by condensation. 

Instead of common salt, sulphate of soda is sometimes used, 
d the percentage of moisture determined by the percentage 

sulphuric acid present in the steam as compared wfth that 
Water from the boiler. 

34^. Comparative Value of Calorimeters. — These instru- 
*nts, arranged in order of accuracy, are no doubt as follows: 




throttling; separating; Barrus superheating ;'Hoadley; con- 
tinuous condensing ; chemical ; and lastly the barrel. 

The ease with which the throttling and separating instro- 
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 wth 
a small amount of moisture, as explained in Article 333 ; but 
the separating instrument is not limited by the amount A 
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 




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 
^t the same pressure and temperature. 

TYk^ 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 con: 
position of ordinary fuels : ^^^ 







Hydrogen , 



Sulphur , 





Carbonic oxide 

Carbonic acid 

Olefiant gas 

Marsh gas 

Sulphurous acid 

Sulphuretted hydrogen 
Bisulphuret of carbon. 








77N + 23O 

by Weight. 














by volume. 





79N -I- iiO 
+ 0, 
+ H. 

+ 0. 
+ H. 

+ S. 



344. Calorific Power or Heat of Combustion.— The 

calorific value of a fuel is expressed in British thermal Mnits 
or in calories f according as Fahrenheit or Centigrade thermo. 
metric scales are used. The calorific value may be detcr^ 
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 oxygec 
exist in a compound in the proper proportion to form waict, 
the combination of these constituents has no effect on tb( 
total heat of combustion. 

The calorimctric value, determined experimentally, of one 
pound of hydrogen is 62,032 B. T. U. ; that of one pound ol 
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, //, of combustion in B.T.U 



for each pound of the compound containing hydrogen and 
carbon would be 

A = i4,50o[c + 4.28(h - ^)] (I) 

For theoretical evaporative power, in pounds of water from 
^ndat 212 F., 

£ = A = X4.6[C + 4.28(h - -^)]. ... (2) 


I The number of pounds of air required to supply the oxygen 

[ necessary for the combustion of one pound of fuel to CO, can 
' be computed from the formula 

^ = .2[c + 3(h-§)]; ,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 

= I49[C 4- 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 212° is 966 units; hence 
we must deduct 966 X 9 = 8694 units from the tabular value 




of the heat due to the combustion of hydr(^eii. This leava 
53,338 units available. Therefore the actual value \w teniucf 
carbon is H = 3.67C, instead of 4.28C as stated in (1)^ and tlw 
heat of combustion actually available is 

*=I4,5oo[c + 3.67(h-2)] (S) 

The following table gives the heat of combustion of tke 
principal combustible substances : 


-^1 Ctl 

Hydrogen gas 

Carbon burned lo 
Carbon burned to 

Olefianl gas 

Liquid hydru-carb 
Sulphurlo SO,... 
Silicon ID SiO, . . 
Phosphorus K. P,I 
Maiahgas. C,il,- 
Crudc peirulcum.. 
Oil ol [urpenline. . 





:ohoI. . 

Methyl alcohol (wood-spirit).. 

Bisulphide a\ carbon, OS, 

Carbonic oxide 

345. Determination of the Heating Value b7 tbt 
Oxygen required. — It was observed by Welter* that those 

* Chemical Technology. Vol. I., p. 336 : Gtaret sod Thorp. 


onstituents of a compound which require an equal amount of 
ixygen for combustion evolve also equal quantities of heat ; 
rem which he concluded that since the oxygen required for 
he combustion of a body is in the same relation as the quan- 
ity of heat evolved, it might fairly be made the measure of 
he heating power. When, therefore, oxygen is consumed by 
he burning of carbon, wood, hydrogen, etc., the heat which 
s evolved must increase with the quantity that is consumed ; 
\T the same amount of heat is generated by a certain given 
/eight of oxygen, whether that quantity be employed in con- 
erting carbon into carbonic acid, or hydrogen into water. 

The oxygen required is 2f for one part of carbon ; 8 for one 
>art of hydrogen. 

One part by weight of carbon will raise the temperature of 
0.5 parts of water from freezing to boiling. 

One part by weight of hydrogen will raise 234 parts of 
/ater from freezing to boiling. 

One part by weight of oxygen in burning carbon will heat 

1O.5 - 

-y- = 29. 1 parts of water. 

One part by weight of oxygen in burning hydrogen will 
leat ^^ = 29.3 parts of water from the freezing to the boiling 

In round numbers, therefore, the heating effect of oxygen 
nay be assumed as sufficient to raise 29.2 parts of water from 
he 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 
herefore be the product of this number by the number of 
^arts of oxygen required. Thus let a equal the number of 
>arts of oxygen required for each combustible ; then the heat 
Produced by the combustion is 

h = 2920af in Centigrade units ; 
h = 5230^ in B. T. U. 

Thus, for example, in the combustion of carbon to CO,, 


2\ parts by weight of oxygen are required for ea«^ one of 
carbon ; hence for this case a = 2f , and 

h = 5230 X 2j = 14,10a 

In the combustion of hydrogen to water 8 parts by weight of 
oxygen are required, and in this case a = 8 ; hence 

A = 5230 X 8 = 41,840. 

This is about two thirds of the actual value of the calorific 
power of hydrogen, but does not difier 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, a, , «', , a, be the parts by weight of oxygen required 
by each. Then 

h = 2^2Q{aa -|- ba^ + ca^ -\- da^ in Centigrade units; 
= ^2iQ{aa -|- ba^ + ca^ -\- da^ in Fahrenheit units. 

346. Temperature produced by Combustion.— In the 

determination of the calorific value of a fuel two principa! 
factors are involved, namely, the calorific power, or the total 
amount of heat to be obtained from the perfect combustion o( 
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 
CO, will produce a much higher temperature when burned in 
oxygen gas than when in the air, since in the latter case it 
nust heat an additional quantity of nitrogen equal to rathei 
more than three times the weight of the o^t^^e**- 


The maximum temperature cannot be either computed or 
etermined experimentally with complete accuracy, partly be- 
ause the total combustion of a quantity of fuel in a given 
ime at one operation is practically impossible, but more par- 
icularly from the fact that dissociation of gaseous compounds 
roduced in burning takes place at temperatures far below 
lose indicated as possible by calculation. 

The maximum temperature is calculated as follows : 
The value of one pound of carbon is 8080 Centigrade heat- 
nits, or 14,500 B. T. U. The heat absorbed by any body is 
qual to the product of its weight, Wy specific heat, 5, and rise 
f temperature, /. Hence 

wst = 8080, or / = 8080 -T- wSy in Centigrade degrees, 


/ = 14,550-4- ws, in Fahrenheit degrees. 

In the case of combustion of carbon to CO, in oxygen gas, 
iie oxygen required for each part of carbon is 2f parts ; the 
pecific heat of CO, is 0.216. Hence the maximum temperature 


: 10,187° C, 

3.67 X 0.216 

3.67 X 0.216^ '^ ' 

In case it is burned in air an additional weight of 8.88 
ounds of nitrogen, with a specific heat of 0.24, must be 
lised to the temperature of combustion. Hence the maxi- 
lum rise of temperature will be 

3.67X0.2 16 + 8.888X0.24 = '73 1 C. or 4860° F. 

The maximum temperature to be attained by combustion 
the following substances, as calculated by R. Bunsen, is: 





In Oxygen. 

In Air. 


Carbonic oxide 

Olcfiant eras, t . t . . 1 1 r t . 

9873" c. 



i7,8o3' F. 
. 14,103 

2458* c. 


4456- F 



Marsh f?as 

H vdroflTcn 

If the air supplied to the fuel be in excess of that requin 
for perfect combustion, the temperature will be less. 

When the excess of air is 50 per cent, the maximum ten 
perature from combustion of carbon is 3515** F. ; when tl 
excess is 100 per cent, the maximum temperature is 2710** F 

The specific heats under constant pressure of the gases usi 
ally occurring in connection with combustion are 

Carbonic-atid gas a2i7 

Steam 0475 

Nitrogen 0.245 

Air 0.238 

Ashes (probably) 0.200 

Oxygen O.241 

Carbonic oxide 0.288 

Hydrogen 0.235 

347. Composition of Fuels. — The fuels in ordinary us< 
contain, in addition to the combustible compounds, more 01 
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 i" 
various boiler trials shows a wide variation, as follows: 

American coals 5 to 22 per cent 

English coals 2.9 to 27.7 

Prussian coals 1.5 to 1 1.6 

Saxon coals 7.4 to 63.4 







The following table gives the composition of the principal 
fuels and the weight of air required to produce perfect com- 
bustion : 



Charcoal from wood 

" from peat 

Coke, good 

.Coal, anthracite 

" dry bituminous 

" coking 

" cannel 

" dry, long-flaming... 

•' lignite 

Peal, dry 

"Wood, dry 

air-dried, 20% HiO. 
Af ineral oil 





































4 4 

5 to 15 



Pounds of 

Air required 

for one of 


II. 16 

II. 3 






9- 30 


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 (i) 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 
ivhich 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, E the heat evolved 
in heat-units by the combustion of one part, W the number of 
parts by weight of water heated from a temperature /' to /. 
Then if the escaping gases be reduced in temperature to that 
of the room, 

wE = {K+ Wyj - /'), 


from which ^H 

^^ {K^W){t-t\ ^ 

349. 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. Tr 
select a sample of coal for calorimetric examination sevenl 
lots of ten pounds each should be chosen from different por- 
tions of the coal to be tested. These should be put in onepile, 
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 lany 
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 calorimetm 
used in determining the quality of steam (see Article 3i7,pagt 
401), either by finding the sum of the products of the weights 
and specific heals 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 — a.'i for instance pure carbon in oxygen 
gas— or again by its cooling effect on steam of known prt 
and weight, or on warm water as explained on page 37 

351. Method of Determining Perfect Combustion.—' 
quality of the combustion is only to be determined by 
analysis of the resulting gases and of the products of cml"* 
tion. In case of perfect combustion all carbon is redi 


CO,, all available hydrogen to water, sulphur to sulphuric acid, 
and further, the sum of the weights of all the products of com- 
busnoii should, after deducting the air and oxygen obtained 
from the atmosphere, equal the original weight of the coal. 

The method adopted by Fa v re 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 oxidt 
was first oxidized to carbonic acid by heated oxide of copper 
and then absorbed by caust ic 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 o( substances containing car- 
bon, CO was always present to a variable extent with CO, , 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- 
'ily of heat evolved is the measure of the sum of the chemical 
anii 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 
*ith a cover through which solid combustibles could be intro- 
duced into the cage C. The cover was traversed by a tube, £, 
Connected bv means of a suitable pipe to a reservoir of the gas 
lo be used in combustion, and by a second tube, D, the lower 
end of which was closed with alum and glass, transparent but 
*di ithermic substances which permitted a view of the process 
5| cimbustion without any loss of heat. 

For convenience of observation a small inclined mirror wa' 
pliceJ above the peep-tube D. 

•See Conveision o( Heat into Work : Anderson. 



The products of combustion were carried off by a.\ 
the lower portion of which constituted a thin copper 
the upper part was connected to the apparatus in whii 
non-condensible products were collected and examined. 
whole of this portion of the calorimeter was plunged into 
copper vessel, G, silvered internal!)- and filled with watet 

— Favbh -t^ii Si 

was kept thoroughly mixed by means of agitators, J 
second vessel stood on wooden blocks inside a third 
sides and bottoms of which were covered with s' 
with the down on, and the whole was immersed in a 
k'essel,/, filled with water kept at the average temperal 
the laboratory. Thermometers, A', K, of great delicac 


yl to measure the increase of temperature in the water sur- 
anding the combustion-chamber. The quantity of heat 
veloped by the combustion pf a known weight of fuel was 
termined by the increase of temperature of the water con- 
ned in the vessel G. For finding the calorific value of gases 
ly, the cage C was removed and a compound jet, NO, sub- 
tuted for the single gas-pipe, ignition being produced by an 
ctric spark or by some spongy platinum fixed at the end of 
t jet. 

353. Thompson's Calorimeter. — Thompson's Calorimeter* 
often employed for determination of the heating values of 
*ls. It consists of a glass jar graduated to contain 1934 
ams of water; in this are inserted (i) a thermometer to indi- 
te elevation of temperature, and (2) a cylindrical combustion- 
amber with a capacity of about 200 grams of water. This 
amber is capped at the top, and a small tube furnished with a 
.Ive is screwed into it, to hold the fuel. The combustible to 
r examined, 2 grams, is mixed as intimately as possible with 22 
ams of a very dry mixture of 3 parts of potassic chlorate and 
part of potassic nitrate, and introduced into the combus- 
>n-tube ; a nitrate of-lead fuse is added and lighted. This 
be is introduced into the combustion-chamber, the cap 
rewed on, and the whole placed without delay in the water 

the calorimeter. The combustion takes place directly in the 
Iter, and the gases disengaged rise to the surface. The water 

proportioned to the fuel as 966 is to I, so that the rise in 
niperature in degrees F. is proportional to the evaporative 
>\ver. The oxygen required for the combustion is supplied 
^ the chemicals added. The water-equivalent of the calorim- 
er as above described is about ten per cent. When com- 
Jstion has ceased, the rise in temperature of the water is 
bserved ; to this one tenth is added for the water value of the 

The corrected number gives the number of grams of water 
hich a gram of the combustible can evaporate. 

*Scc Chemical Technology, Vol. I. 


354. The Berthier Calorimeter.*— This calorimeter, is 
based 011 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 powtr 
may be calculated by Welter's law, Article 345. One part of 
pure carbon being capable of reducing 344- limes its weight 
in lead. 

The operation is performed by mixing intimately the 
weighed sample (10 grams) with a large excess of pure lithai^ 
(400 grams). 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 tosiircii 
considerably have escaped, it is covered with fuel and strongly 
heated for about ten minutes, in order to collect the globults 
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 equin- 
lent of reduced metallic lead. 

The heating power is calculated as follows: i part of pureca^ 
bon requires 2.666 parts of oxygen by weight, which taken fwni 
litharge leaves 34.5 parts of metallic lead. The same weight A 
carbon is sufficient to heat 80 parts of water from 32° to3i:°. 
Hence every unit of lead reduced by any kind of fuel corre- 

sponds by Welter's law with 

: 2.23 parts of water rabtdj 

from the freezing to the boiling point, 

355. The Berthelot Calorimeter. — This caloHmet 
modified by Hcmpcl, consists of a very strong vessel 1 
capacity of about 250 c.c, into which the fuel is placed a 
being compressed into a solid form; the combustion U per* 


med in an atmosphere of oxygen gas under a pressure of 10 
12 atmospheres.* 

The fuel is ignited by an electric spark, and the heat gen- 
ted is known by measuring the rise in temperature in the sur- 
mding water, as in the Favre and Silbermann calorimeter. 
The oxygen gas is generated in a tube about one inch in 
meter connected to the calorimeter by an intervening tube 
3ut i inch in diameter. To this latter tube is attached r 
^sure-gauge to indicate the pressure, and a safety-gauge to 
!vent damage from explosion or excessive pressure. A 
p-cock is also inserted close to the calorimeter. For gen- 
ting the oxygen the tube is filled with 40 grams of a mix- 
e of equal parts of manganese dioxide and potassium 
orate. It is then heated by the full flame of a Bunsen 
Tier applied first at the end nearest the calorimeter and 
dually moved to the farther end. 

To use the instrument, the fuel, connected to platinum 
es for electrical ignition, is introduced and suspended in the 
trimeter, the top of which is firmly screwed on and the 
ve closed. Oxygen gas is then generated until the pressure 
ches 90 pounds, and exhausted into the air to remove other 
es from the calorimeter. The escape-valve from the calo- 
leter is closed and oxygen gas generated until the pressure- 
ige shows 150 to 175 pounds pressure per square inch; then 
connecting stop-valve is closed and the electric current ap- 
?d. After the heat of combustion has been absorbed the 
ermination is made as with the Favre and Silbermann calo- 

355. The Bomb Calorimeter. — This instrument was 
igned by the French chemist M. Bcrthelot, and consists 
a strong steel vessel provided with a tightly fitting cover 
) which the coal is placed for combustion. For the pur- 
e of combustion an excess of oxygen gas is supplied under 
-essure of from 20 to 30 atmospheres. The fuel is sup- 
ecJ by a cage of platinum connected to the cover. The 
is fired by an electric current passing through connecting 

* Sec Hempel's Gas Analysis, translaied by Dennis. 


wires and generated by a battery of ten bichromate cells. To 
prevent the oxidation of the instrument, the bomb built by 
Bcrthelot was lined with platinum. The heat given \A 
during the process of combustion was absorbed by water in i 
vessel surrounding the bomb. During the process of com- 
bustion this water was kept in motion by a stirrer, and the 
Jieat given off determined by its rise in temperature. 

Various modifications o( coal-calorimeters employing ific 
principle of Berthelol's instrument have been made and are 
in extensive use. The form built by Mahler, Fig. 2i2. is 
perhaps the best known, whicii difiers from that of Bcrthelot 
only in the form of the stirring apparatus and in the lining ol 
the bomb, whicli 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 intenw 
of which is protected by an oxidized surface wliich has beta 
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 mi? 

be made by heating a crucible filled with equal parts of 
ganese dioxide and potassium chlorate- Some chlorine «3 
usually pass over, which may be removed by passing throng* 

1 35 5-] 




^^k close roll of brass wire-gauze. The oxygen may be 
^^Kcetved into a small gasometer and compressed by the action 
^of a pump to the required density. O.xygen is also now 
manufactured as a commercial arlick- 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 n.ay be 
purchased in New York of Elmer & Amend. 

In the Hempel calorimeter, as shown in Fig. 210, the 
crucible for making the oxygen is attached directly to the 

calorimeter hy mcni)>^ nf connecting pipes. In this case the 
calorimeter is char-jcd before connecting the crucible. The 
crucible is filled with a mixture of equal parts dio.Nide 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 




crucible removed. To prevent danger from accidents during 
the generation of the oxygen, the crucible and gauge shuuld 
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 tlic 
calorimeter. The heat liberated in the formation of nitnc 

nt, but as this is seldom greater 

acid should be taken into 
than \ of one per cent, it is 

errors of observation. To avoid the numerous correction* 
and the tedious calculations which result therefrom, the 
chemist Hempel adopted the plan of standardizing his instni- 
mcnts 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 crystalhicd 
sugar several times in succession, driving off at a high heat all 
volatile matter. This process of calibration gave a scries of 
factors, which multiplied by thermometer-readings reduced 
the results to heat-units. The following example from 




•* Traits Pratique de Calorim^tre 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 carefullf 
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. 


Dried at a temperature of from 120 to 130 degrees C. until it bad attaioedt 
constant weight and permitted to cool in a closed vessel and in the presence 
of concentrated sulphuric acid. (Observations of time and temperatnre.) 

Preliminary Observations 
Before Combustion. 

o min., 







17.360 deg. C. 








Observations Dunog 

5 min., 18.500 ^^%. C. 

6 •• 18.782 

7 * 18.820 

8 •• 18.818 




Observatioos After 

9 min., 18.810 deg. 










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 

carbon = 3532.9 caloricSi 


Heat for one gram = — — ^ = 8 1 36.6 *• 



The latest determinations of Berthelot give the absolute 
ing power of amorphous carbon as 8137.4 calories = 
59.5 B. T. U. In the use of the calorimeter, the coal 
3 be first powdered and then reduced by pressure to a 
idrical cake or lump which is fired by the heat from an 
trie current. Corrections to the result are to be made 
:he heat disengaged by the oxidization of the iron and by 

formation of nitric acid and by the vapor of water 
aining in the atmosphere of the bomb. All these correc- 
s are very small and may be avoided by using the process 
Uibration employed by Hempel. 

\s noticed in the example above cited, the rise in tem- 
ture of the surrounding water is very small, and in order 
>btain accurate results this water must be thoroughly 
ited to produce a uniform temperature; the thermometer 
I must be capable of reading very small increments of a 
ee and must be read by a strong reading-glass or attached 
ier. The accurate determination of small increments of 
perature is nearly impossible with the apparatus to be 
d in an engineering laboratory. To overcome this difli- 
fr, the author has designed a form of calorimeter in which 
increase in temperature is determined by the expansion 
le entire amount of water in the vessel surrounding the 
rimeter. The value of the scale is determined by calibra- 
Two forms of this instrument are manufactured by 
leffer and Budenberg, Brooklyn, N. Y. In one form the 
bustion is performed in a steel bomb lined with enamel in 
y respects similar to the Mahler calorimeter. In the 
r the combustion is performed in a current of oxygen gas 
rr low pressure, and the heat of combustion is absorbed 
ater in the surrounding vessel, the products of combus- 
passing through a coil and being finally discharged into 
itmospheric air. 

36. Fuel-calorimeter in which Heat is Measured by 
ansion of Water. — The general appearance of the instru- 

\s shown in Fig. 212; a sectional view of the interior 




part is shown in Fig. 214, from which it is seen that,k! 
principle, the instrument is a large thermometer, in the but] 
of which combustion takes place, the heat being absorbed Ij' 
the liquid which is within the bulb. The rise in temperatiiK 
is denoted by the height to which a column of liquid rises ii| 
the attached glass tube. 

In construction, Fig. 214, the instrument consists of ij 
chamber, No. 15, which has a removable bottom, shown ■] 
section in Fig. 213, and in perspective in Fig. 214. 
chamber is supplied with oxygen for combustion throi 
tube 23, 24, 25, the products of combustion being dischar 
through a spiral lube, 29, 28, 30. 

Surrounding the combustion-chamber is a laiger dc 
chamber, i. Fig. 214, filled with water, and connecting*! 
an open glass tube, 9 and 10. Above the water-chamber 
is a diaphragm, 12, which can be changed in position 
screw 14 so as to adjust the zero level m the open glass tul 
at any desired point. A glass for observing the process 
combustion is inserted at 33, in top of the combuslic 
chamber, and also at 34, in top of the water-chamber, and 
36, in top of outer case. 

This instrument readily slips into an outside case, whic 
is nickel-plated and polished on the inside, so as to redi 
radiation as much as possible. The instrument is supper 
on strips of felting, 5 and 6, Fig. 214. A funnel forfillil 
is provided at 37, which can also be used for emptying 

The plug which stops up the bottom of the combustic 
chamber carries a dish, 22, in which the fuel for combustic 
is placed; also two wires passing through tubes of vulcanii 
fibre, which are adjustable in a vertical direction, and 
nectcd with a thin platinum wire at the ends. These vit 
are connected to an electric current, and used for firing 
fuel. On the top part of the plug is placed a silver mil 
38, to deflect any radiant heat. Through the centre of 
plug passes a tube, 25, through which the oxygen passesi 

§ 356.] 



supply combustion. The plug is made with alternate layers 
of rubber and asbestos iibre, 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 


^KThe instrument has been so designed that the combustion 
flr take place in oxygen gas having considerable pressure, 
»d in the form of a bomb; but in practice we have found 
aX very reliable results have been obtained with pressures 

, and are discharged through a very fine orifice in a cap 

of 2 to 5 pounds per square inch in an instrument of the fora 
described, and this has been commonly used in investigatioiu 
at Sibley College. 

For the purpose of making determinations of fuel, oxygtn 
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 accurait 
sample by a system of quartering, which shall commence wtb 
a very great amount, if possible, and finally terminate uilln 
very small fraction of a pound, 

3. Reduce to powder by grinding, in a mortar or a milL 
sufficient coal for several samples. A coffee-mill ansiroi 
excellently for this purpose. 

3.' Introduce the sample into a small asbestos cup, drin 
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) fWt 
the oxygen gas flowing; {b) tire the charge, which should tie 
done by pressing on a key; (c) at instant coal is lighted, 
throw off the current and note the reading of the scale »iii 
time. During combustion keep the discharge orifice opefc 
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 compieted 
note the scale reading and the lime. The difference bct*K> 
first and second reading is the actual scale reading. 

6. To correct for radiation note the amount, the waterii 
the column has fallen for the same time as required forco* 
bustion: add this to the actual reading to get the corrcctti 
scale reading. 

7. Divide the value as shown on the diagram by t^ 
weight in pounds of the sample burned. The result «"ill I" 
the value in B. T. U. of one pound of coal. 

8. Remove the dish in which the combustion took pUct! 
weigh it carefully with and without contents. If the 
bustion has been perfect, the difference of these weights 


the ash. Wipe the combustion-chamber dry for another 

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- 
:cnt lighting, may be used with success. 






Weight of crucible 1. 269 grams. 

** and coal 3.017 " 

•• and ash » 1.567 " 

combustibles • « 1*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 11.2 corresponds to 46.25 B. T. U.'siii 

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 

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 

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 


istrument in such a position that the glass-tube opening 
be its highest point and so enable all air and steam to 
through the connection to the smaller vessel. Also keep 
ater in the smaller vessel boiling until the calorimeter 
jlly cooled off. Remove rubber connection, fill the glass 
with boiled water and screw it tight. Take care not to 
it to pass so far into the calorimeter that air will be 

ut about two inches kerosene oil on top of water-column 
svent air from coming in contact with the water. Should 
found that the water in column stands too high after the 
meter has taken the temperature of the room, loosen 
>lug and allow water to leak out slowly until the scale- 
tig is about two inches, then close it securely. 

If the instrument is ready for calibration, follow in- 
tions given under method of using the calorimeter. The 
ence of weight between the weight of crucible and 
n (coke) and the weight of crucible and ash is the 
It of pure carbon burned. 

•ividing 14540 by the weight of burned carbon, we obtain 
umber of heat-units in the sample. 

y drawing the oblique line on the chart, take the num- 
f corrected scale-reading as ordinates, and the number 
T. U.*s in sample as abscissae, make a point on crossing 
raw a line to zero. 


ht of crucible and coke in grams 3.OO2 

•* '* *• ash ** ** 1.064 

** burned pure carbon 1-935 

1.935 grams reduced to pound = .00426 lbs. 

1.935 X. 002205 = .00426 lb<^. 
14540 X .00426 = 61.86 B. T. U. in sample. 

scale-reading, 3.33 inches, time ii o'clock, 15 minutes 

d " 16.85 ** " II ** 40 '* 

i« 16. '* ** 12 ** 10 ** 


Actual reading 16.85 — 3-35 = 13.50 indks 

For radiation 16.00—16.85= -8$ " 

Corrected scale-reading 14.35 " 





The sample should be finely pulverized in a mortar, aii 
then thoroughly mixed. 

Moisture. — Place the weighed sample (about I gram) in 
porcelain crucible, and dry in an air-bath for one hour, at 
temperature between 105 and 1 10 degrees C. Weigh as 
as cool. Loss is moisture. 

Volatile Matter. — Weigh about I J grams of the undri 
pulverized coal, place it in a platinum crucible and 
tightly. Heat it for 3J minutes over Bunsen burner (br^ 
red heat), and then immediately, without cooling, for 
minutes over blast-lamp (white heat). Cool and vc^ 
Loss, less the moisture, is volatile matter. 

Fixed Carbon. — If a coke be formed in the preceding 
tion, make a note of its properties, color, firmness, etc., 
place the crucible, with cover removed, in an inclined 
tion, and heat over Bunsen burner until all carbon is burn 
i.e., to constant weight. The combustion may be hasten^ 
by stirring the charge from time to time with a platinuini^t 
Difference between this and last weight is the fixed carbon. 

Ash. — Difference between last weight and weight of c 
ble is the ash. 

Total Sulphur in Coal and Coke. — Prepare a fusing mi 
by thoroughly mixing two parts calcined magnesia with 
part anhydrous sodium carbonate. Determine the sulph 
in the mixture. 

Thoroughly mix I gram of the finely pulverized coal 
li grams of fusing mixture. Heat over an alcohol lamp, 
an open platinum or porcelain crucible, so inclined that 

*See " Crooke's Select Methods/' 2d Edition, pp. 595-607. 


lower half may be brought to a red heat. The crucible 

ould not be over i or | full, and the heat should be gentle 

first, to avoid loss upon the consequent sudden escape of 

^^olatile matter, if present in large amount. Raise the heat 

dually (it must not at any time be high enough to fuse the 

ixture), and stir the contents of the crucible every five 

inutes with a platinum wire. The oxidation of the carbon 

complete when ash becomes yellowish or light gray (about 

^One hour). Cool crucible, add i gram pulverized NH^NO, to 

- 'tile ash, mix thoroughly by stirring with a glass rod, and heat 

-^.te> redness for five to ten minutes, the crucible being covered 

'Urith its lid. 

Cool, digest the mass in water, transfer the crucible con- 
i^Vtents to a beaker, rinse out the crucible with dilute warm 

■ HCl, dilute solution in beaker to about 150 c.c, acidulate 
,- "With HCl, and heat almost to boiling for five minutes. Filter 

and precipitate the sulphuric acid in filtrate by BaCl, in usual 

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. 
^Sce 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 remamed; it would 

then die down, and when the carbon commenced to burn 

irouid be decidedly blue. The operation to be always stopped 



[§ 35? 

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 \ihen 
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. \V. R. 
Johnson at the Navy Yard, Washington, in 1843, ^^'J^'^ a small 
cylindrical boiler, were as follows: 


Area of 



Coal p>cr Hour. 

^^- ^'^- Total. 

Anthracite (7 samples). . . 14 3^ 
Bituminous coals, free 

burning (11 samples). . MM 
Bituminous coking coals. 

Virginian (10 samples;.. I 14.1^ 


Water evaporated | 

per Hour. : Wiier 


, flOCD 

Per Sq. 
Ft of 



Per Sq 7u' F. ptf 
Fl. 0! lb. <A 


0.87 \ 9-^3 
0.97 . Q '? 

105.02 , 7.42 ; 12,16 0.86 s a^ 


14.20 ()9 71 

7.02 ! 12-75 0.90 0. 


358. Object of Analysis of the Products of Combustion. 

— The products resulting from the combustion of ordinary fuel 
contain principally a mixture of air, CO, , 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 
^ greater degree, as can readily be shown by calculation. 

From a careful examination of the products of combustion 
"^ve should be able to ascertain its character and make the 
siecessary corrections for such losses as may be due to imper- 
fect combustion. 

The methods to be employed must be such as any en- 
ineer can fully comprehend, and the apparatus portable 
nd convenient. The degree of accuracy sought need not 
such as would be required in a chemical laboratory 
here every convenience for accurate work is to be found. 
ndeed, considering the approximations to be made in its ap- 
lication, it is very doubtful if determinations nearer than one 
r cent in volume are required, or even of any value. Such 
^terminations are obtained readily with simple instruments, 
»id serve to show the approximate condition of the [gaseous 
oducts of combustion. The student is referred to ** Hand- 
fc^o ok of Technical Gas Analysis," by Clemens VV^inkler ( London, 
Xfohn Van Voorst), and to "Methods of Gas Analysis," by Dr. 
^Ai^. Hempel, translated by L. M. Dennis (Macmillan & Co.); 
^l50 to a paper on tests of a hot-blast apparatus by J. C. Hoad- 
^^y, Vol. VI. Transactions of the American Society of Mechani- 
^^I Engineers. 

In a thorough examination of the value of fuel, the ashc^ 
^liould also be analyzed, since if they contain any combustiblL, 


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 CO,, 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. 
\V. 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 i 
volumetric one, and consists of the following steps, which wii 
be described in detail later on. 

A. The sample is first collected and then introduced intoa 
measuring-tube ; 100 c.c. of the gas is retained, the remaindcf 

B. The constituents of the gas are then absorbed by sue* 
cessive operations, in the following order : carbonic acid (CO,i. 
free oxyi^en (O), carbonic oxide (CO), and hydrogen iH*. 
The absorption is accomplished by causing the gas to flo* 
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 
\nd the loss of volume measured. The loss is due to^bsorp" 

ion, the various absorbents used being as follows : 


For carbonic acid^ CO , , either potassium hydroxide (caustic 
lotash KOH), or barium hydroxide. 

For oxygen^ O, either (i) a strong alkaline solution of 
•yrogallic acid, (2) chromous chloride, (3) phosphorus, (4) 
letallic copper. 

For carbon monoxide^ CO, either an ammoniacal or a hydro- 
hloric-acid solution of cuprous chloride. 

For hydrogen, H, an explosion or rapid combustion in the 
resence of oxygen, or absorption by metallic potassium, 
odium, or palladium. The reagent usually employed as an 
bsorbent is the one first mentioned in each case. 

360. Preparation of the Reagents.— Absorbents of Oxy- 
gen. — I. Potassium pyrogallate. This is prepared by mixing 
ogether, either directly in the absorption pipette or in the 
pparatus, 5 grams of pyrogallic acid dissolved in 15 c.c. of 
/ater, and 120 grams of caustic potash (KOH) dissolved in 80 
:.c. of water. Caustic potash purified with alcohol should not 
>e used for analysis. The absorption of the gas should not be 
rarried on at a temperature under 15° C. (55° Fahr.) ; it may 
)e 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: 
t is to be kept in the solid form under water and in the dark ; 
he gas is to be passed over the reagent, displacing the water, 
^nd kept in contact with it for about three minutes. The end 
>f the absorption is shown by a disappearance of a light glow, 
vhich characterizes the process of absorption. The phosphorus 
vill remain in serviceable condition for a long time. 

4. Copper, at a red heat or in the form of little rolls of wire- 
?auze 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 
ie method of gas analysis. With the Elliot apparatus, a sola- 


tion of 3 to 5 per cent of KOH in distilled water is sufHciently 
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 CO, is very small ; in this case titration 
with oxalic acid will be required. 

Absorbents of Carbon Monoxide (CO). — i. {a) Hydrochh- 
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. 

{b) 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 <^t 
1. 124 specific gravity. A spiral of copper wire is then plaaJ 
in the solution, and the bottie 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. 

Ihc ajnmofiiaciai solution is to be used in case hydrogen :.> 
to be absorbed by palladium. This is prepared from the 
colorless solution {(j) as follows : Pour the clear hydrochloric 
acid solution into a large beaker-glass containing i^ to 2 litres 
of water, to precipitate the cuprous chloride. After the pre- 
cipitate has settled, pour off the dilute acid as completely a^ 
of possible, then wash the cuprous chloride with 100 to 15OC.C. 
distilled water, and add amuKMiia to the solution until the liqui" 
takes a pale-blue color. The solutions of cupric chloride vi 
compose readily, and in general should be used when fresh, ^^ 


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-tubt is intro- 
duced into the flue : this consists of a tube open at both ends, 
tile outside end being provided with a stop-cock and connected 
with the collecting apparatus by an india-rubber tube. There 

^ probably a great diversity in the composition of gases from 
■"arious parts of the flue. 

For obtaining an average sample, J. C. Hoadley employed 
t mixing-box B, * provided witli a large number of i-inch pipes, 
-widing in varioua parts of the cross-section of the flue A. An 
"levation of the inixlng-box is shown at B' . From the mix- 
'^g-box four tubes CC load downward from various parts to a 
*»ixing-chamber D, trom which a pipe E leads to the collecting 
"■^Jparatus. Two of these mixing-boxcs were used, one placed 
■* the flue a short distance above the other, and an aijreemcnt 
» J the samples obtained from each was regarded a.s prmif of tlie 
*jbstantral accuracy of tht sample. 
"""^ •Tr»n«. AtrT. Soe. M. E., Vol. Vi. 


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 aspjrating-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 hold 
opening in different portions of the chimney. The material 
for the aspirating-tube is preferably porcelain or glass, but 
iron lias no especial absorptive action on the gases usually lo 
be found in the flue, and may be used with satisfaction. Along 
length of rubber tubing may, however, sensibly affect the 

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, IcrmB) 
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 ind 
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 lop : the other bottle or tank is open to the atmos- 
phcre. 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!* 
made, and the stop-cocks opened, the empty vessel is brouglil 
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 gast 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 *slf'r 
which is an absorbent to a considerable extent of the p^ 



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: (l) 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 

In either case the steps are, as explained in Article 358: {a) 
Obtain 100 c.c. by measurement; {b) to absorb the CO,, bring 
the gas in contact with KOH, and measure the reduction of 
volume so caused ; this is equivalent to the percentage of CO, ; 
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 ; 
Crf) determine the other constituents in a similar manner. 

In performing these various operations it is essential that 
^le tubes be kept clean and that the reagents be kept entirely 
^fjparate from each other. This is accomplished by washing or 

lusing some water to pass up and down the tubes or pipettes 

jveral times after each operation. 

363. Elliot's Apparatus. — This is one of the most simple 
"^tetfits for gas analysis, and consists of a treating-tube AB and 




a measuring-tube A'B', Fig. 216, connected by a capillary tube 
at the top, in which is a stop<ock, 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 b}' 
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 /"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. Tliat 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 tn 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 tliat needud, the cock G is opened, the bottle A' de- 
pressed, tlie bottle /, elevated ; the gas will then pass over into 
the measuring-tube A' IV : the bottle K is then held so that ilif 
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. .ire 
in the mciisurinn;-tLibe : then the cock G is closed, the ciwrkf 
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 miasu ring-tube A' B' is surrounded with) 
jacket of water to maintain the gas at the uniform temperature 
of tlie room. After measuring the sample it is then run over 
into the trcating-tube Al>. and the reagent introduced through 


he funnel above F by letting it drip very slowly into the tube 
AB. After there is no farther absorption in the tube AB, the 
:ock F'\s closed and the gas again passed over to the measur- 
ng-tube.-I'fi', and its loss of volume measured. This operation 
s repeated until all the reagents have been used : in each case, 
when the gas is run back from the measuring-tube, pass over 
L little water to wash out the connections ; exercise great care 
:hat in manipulating the cocks A' or G no gas be allowed to 
jscape or air to enter. 

364, Wilson's Apparatus * — This apparatus is illustrated 
in Fig. S17. 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-lube d, a measuring- 
lube a. connected at the top by a 
capillary tube f. The measuring- 
tube ends in a vessel filled with 
Ticrcury, and in this case the press- 
aie on the tubes can be regulated 
»>■ towering and raising the single 
kottle filled with mercury, and the 
Cascan be manipulated as in the 
Slliot apparatus, using one bottle 
nstcad of two. Reagents are in- 
■Tjduced into the funnel e, and 
Ome in contact with the gas in 
tie treating-tubc d. 

The coliecting-tube used with 
fcais apparatus is shown at B, and 
Onusts of a vessel filled with mer- 
Mry. One side is connected to 
Ifcc aspiratOT-tube ; some of the 
• ercur>' is allowed to run out '"-'■'■—'""■«■"""'"•*"'■*'■■"»■ 
brough a cock, and the space is filled by the gas. Sufficient 
fc«r<:ur>' is retained to form a seal. 

365. Fisher's Modification of Orsat's Apparatus. — This 

• Thumon's Engine and Boiler Trials, p. 107. 



apparatus, shown in Fig. a 1 8, belongs to the class in 
each reagent is introduced in a concentrated form into a 
treating-tube. The apparatus consisls of a measurir 
surrounded by a water-jacket, into which the gas can h 
duced substantially as explained for the Elliot apparatus. 

reagent is introduced in a concentrated form into 4 
burettes connected at the bottom by a U-shaped tube 

In making an analysis the gas is first drawn int 
measuring-tube and lOO c.c. retained ; the cock in lh< 
leading to one of the treating- tubes is then opened, lilt 
raised, and the gas driven over into the treating-tube. 


aeration is facilitated by connecting a soft rubber bag to 
e opposite side of the treating-tube, by means of which 
:emate pressure and suction can be applied, and the reagent 
otected from the atmosphere. After the absorption is com« 
2te, which will take from one to three minutes in each tube, 
e gas is returned to the measuring-tube by lowering the 
►ttle and exerting pressure on the attached rubber bag. The 
bbei bag is not shown in Fig. 218, and is not required, pro- 
Jed the treating-tube is completely filled with the reagent 
I the side toward the measuring-tube. 

The treating-tubes are filled in order from the measuring, 
be with the following reagents: (i) with 33 per cent solution 

KOH ; (2) with a solution of pyrogallic acid and KOH, 

with sticks of phosphorus (see Article 360) ; (3) with a 
'drochloric-acid or an ammoniacal solution of cuprous chloride 
contact with copper wire (see Article 359). 

In the first treating-tube is absorbed CO,, in the second 0> 
d in the third CO. 

A modification of the Orsat apparatus has a fourth tube ;o 
ich hydrogen can be exploded ; the reduction in volume, duv 
the explosion, gives the amount of hydrogen present. 

An apparatus for flue-gas analysis has been designed by 
r author in which the treating-tubes are arranged as in the 
sat, but they are of such a form as to permit the use of solid 
gents for absorbing oxygen, and are much less liable to 
>ture. It is used exactly as described for the Orsat, but is 
ich more convenient and is somewhat more accurate. 

366. Hempel's Apparatus for Gas Analysis.* — This ap- 
ratus^ shown in Figs. 219 to 224, is especially designed for 
e accurate analysis of the constituents of various gases ; for 
boratory use it presents many advantages over the other 
)paratus described. The apparatus consists of the following 
irts: I. The measuring burette, shown in Fig. 220, which is 
instructed and used as follows: It is furnished with an iron 

♦See Hem pel's Gas Analysis, by L. M. Dennis. Catalogue of Eimer & 
cod. New York. 


base, which is connected by a rubber tube to an open ti 
(see Fig. 219) with a similar base. The stop-cock «/ is opi 
the tube a elevated, and water or mercury, whichever nu 


used, flows from a over to b. Gas is introduced as foil 
Tlie measuring-tube b is filled with liquid, the cocks ^ : 
closed, aiul connect ion made ;it c to the vessel containiii 
gas to be mcjsurtd ; the cocks d and c are then opeiie. 




c a lowered : the liquid will then flow from the measuring, 
e d to ((, and the gas will fill the measuring-tube. To ineas- 
the volume of gas. hold the tube a as shown in Fig. a 19, so 
\ the water-level shall be the same in both tubes, thus 
iging the gas under atmospheric pressure. Read the vol- 

■HElim.'E AfBOHl-tlQT. Blbsttbs, 

S directly by the graduation corresponding to the lower 
iEof the meniscus. 

n-pipt'tles are different in form from those used 
: Orsat apparatus, and are connected only as required to 
f measuring-burette, but are used in essentially the samt 
y. Several forms of these are employed as shown in Figs- 
I to 224. The forms shown in Fig. 222 and Fig. 224 are 




ordinarily used tor reagents in solution. In such a casell* 
measunng-lube is connected at e. Fig. 233, the reagent occupy- 
ing the bulbs a and b. The top of the measuring-burellc 
e. Fig. 219, is connected to the absorption-pipette, and the 
gas moved alternately forward and backward as required b)' 
raising or lowering the tube a. In case reagents in the soiid 
form are to be used, the absorption-pipette is made of the iorm 
shown in Fig. 223, in case regents which decompose verj- eaiily 
are used a pipette of the form shown in Fig. aai is employed. 
The general methods employed are the same as those prt 
viously described. 

367. Deductions and Computations from Flue^as 
Analysis.— The determinations give the percentage of volume 
of CO, , 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 nitro^a 
to oxygen existing in the atmosphere is 79 to 21 by volume: 
call this ratio S\ denote the percentage of volume of the gas« 
existing in the sample as follows: CO, by A'', oxygen by (T. 
CO by U' , nitrogen by N' . Then we shall have 

Ar' + C?'+ £/' + A" = 100 per cent, , 

N' = 100 - (^' + «■ + C/')- . 



If the oxygen were all derived from the atmosphere, both 
the amount of nitrogen A" and of carbonic oxide £/' could be 
computed, since in such a case the volume occupied by the 
free oxygen before combining would equal 

Hence the nitrogen 

N" = SKK-^0--^iU-). (J 


:uting this latter value in equation (i), 

£^'={ioo-(is:'+c?0(i+5){+(i+|). . (4) 

ce there is to be found from 2 to 5 per cent of oxygen 
fuel, equation (4) will generally give negative values for 
)y and should not be used. 

composition of the flue-gases is an index of the com- 
jss of the combustion. The flue-gases should contain 
trogen, oxygen, steam, and carbon dioxide, if thecom- 
i is perfect. Since the amount of CO and of hydrogen 
unds are always small, the excess of air can be com« 
very nearly from the amount of CO,. Thus, were the 
ts of combustion free oxygen, nitrogen, and carbon 
*, only, the volume of oxygen and carbon dioxide 
replace that of oxygen in the air, or would equal about 
jr cent. On account of slight losses, it is more nearly 
actual cases. The percentage of excess of air would 
t 20 less the per cent of carbon dioxide divided by the 
tage of carbon dioxide, 

20 - ^' 
•^=-^p- (5) 

: gives an approximate formula for the percentage of 

F, = 0.65 p^ = in centigrade units, (6) 

:h 7^= temperature of the flue; 

/ = temperature of air entering furnace, 
CO, = percentage of CO,. 

5 principal object of the flue-gas analysis may be con- 
as accomplished when the percentage of uncombined 




oxygen and of CO, is determined, since in every case the 
amount of the other 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 ly 
shows the volume- of air supplied to that required to furnisli 
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 

jr = 


N'- SO 

7 — (i H ^7 — )» nearly, . . (7) 

The analysis and the computations considered relate to 
volumes of the various gases. They ma> be reduced to pro- 
portiojial 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 combustion of a pound of 
carbon will be required 2.67 pounds of oxygen, for which will 
be required 1 1.7 pounds of air. If the ratio of air used to that 
required be X, then the weight of air per pound of fuel equal 
1 1.7X. 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 w.jX— 146.2X 

The maxivmm temperature 7",„ , that can possibly be attaint' 
in the furnace, is to be calculated as in Article 346, page 449- 

T = 


(3.67)(o.2i6) + (8.88X0.24) + (A' - i)(i2.6ya:3' 

14500 5000 

2-791 +2.84^A'-T)=-x' "pp^°^""^*^iy- 


ing the maximum temperature of the furnace and the 
iture of the escaping gases, the efficiency^ E^ of the 
nd grate may be calculated by the formula 

^= " " ^9) 

11 TJ is the excess of temperature of the furnace and 
excess of temperature of the escaping gases above that 
entering air. This hypothesis would be strictly true 
ere no loss of heat and were the weight of entering and 
je gases the same. The error in the calculation is not 
a serious one. 

kine, in his work on the steam-engine, pages 287 and 
'es formulae for computing velocity of flow in flues, 
d required to produce a given reading of the draught- 
ind the required height of chimney. 
se formulae are developed from the experimental work 
^t, and while they do not agree well with modern 
% still give interesting results for comparison. The 
.1 application is shown in the following example of an 

made at Cornell University, the coal burned being that 
d after deducting ashes and clinkers. 

Form for Data and Computations in Flue-gas 
is. — Test made Nov. 3, 1890. 

linations mad!' by F. Land, H. B. Clarke, and O. G. Heilman. 
»;/ of plants Ithaca, N, Y. 
Sy Cornell University. 

f ;^rat<\ sq.ft 181 

•/" chiniun\ sq ft. (symbol A) 12.5 

' if chimnt-y, in feet (sy m bol // ) lOO 

h of heateii flue (symbol / ), feet . 130 

perimeter of chimney ^ feet ^ I4 

v/ of boilers 3 

f boilers : one of 61 H. P., two of 250 H. P. 

of boilers : Water-lube, made by HabccKk & Wilcox. 

cter of draught, forced by sieam-blovvcrs. 


oxygen and of CO, 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 furnisii 
the oxygen for the combustion. 

It may be computed by comparing the total volume o( 
gases with that required to unite with the combined oxygen, 
from which 

„ N' / , 20-A'\ , ,. 

The analysis and the computations considered relate to 
volumes of the various gases. They ma> be reduced Xo ff^ 
portional weights by multiplying the volume of each gasbyits 
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 combustion of a pound of 
carbon will be required 2.67 pounds of oxygen, for which will 
be required 1 1.7 pounds of air. If the ratio of air used tothat 
required be X, then the ivcight of air per pound of fuel equal 
I i.^X, One pound of air at 32"^ Fahr. occupies 12.5 cubic left- 
Knowing which, the volume of air per pound of coal can be 
computed as equal 

12.5 X 11.7^"— 146.2X 

The ^naximuvi temperature T„, , that can possibly be attaint^' 
in the furnace, is to be calculated as in Article 346, page 449- 

y^ _ ^ _I4500 

^ *" (3.67)(o.2 16) + (8.88X0.24) + \X-- \){\2.e)\orJ 

14^00 5000 


aving the maximum temperature of the furnace and the 
jrature of the escaping gases, the efficiency^ E^ of the 
• and grate may be calculated by the formula 

E=^ "7- / — , (9) 

ich TJ is the excess of temperature of the furnace and 
e excess of temperature of the escaping gases above that 
e entering air. This hypothesis would be strictly true 
there no loss of heat and were the weight of entering and 
irge gases the same. The error in the calculation is not 
[y a serious one. 

ankine, in his work on the steam-engine, pages 287 and 
^ives formulae for computing velocity of flow in flues, 
ead required to produce a given reading of the draught- 
% and the required height of chimney, 
iiese formulae are developed from the experimental work 
^ci^t, and while they do not agree well with modern 
ice, still give interesting results for comparison. The 
ical application is shown in the following example of an 
sis made at Cornell University, the coal burned being that 
ned after deducting ashes and clinkers. 
)8. Form for Data and Computations in Flue-gas 
/sis. — Test made Nov. 3, 1890. 

rtnimitious madif by F. Land, H. B. Clarke, and O. G. Heilman. 
r//<>// of plant, Ithaca, N, Y. 
'cTj, Cornell University. 

r of -ratt\ sq. ft I Si 

' of chimney, sq ft. (symbol A) 12 . 5 

■ '/ ' of chimney, in feet (sy m bol // ) lOo 

'th of heated flue (symbol /), feet 130 

t'c p:ri meter of chimney, feet I4 

-f .'V/ of I'oilers ... 3 

'\t' boilers : <»ne of 61 H. P., two of 250 H. P. 
^d of boilers : Water-lube, made by Rabcock & Wilcox. 
^rajfr of draught, forced by sieam-blovvers. 










«<*• mJ O O^ CO 

* «^ * * * 

O o o o £ f^ O 


M r^ <^ tn 



O^ o « 






6 o 

e o 

8 ft 




> :S O O O 




^ Q. 




6 o 



e e 

• O^ m O 
S • • * 

£ o o 



ei ^ 

f^ c »^ 

























^^^>*sS«j bJ^^ ^^ 







x: 3 
bo (C 

2 Si 
-5 2 

be 2 

c o 

V V 




o ^ 





c o 
k. > 

2 ^ 



> c 

•*- ^ 

w V! -= 



E ^ 

3 O 

3 3 

(« CO 

k. u 

a. a. 

E E 

H H 




►^ o 






•S 8 


O O 







o 5 

I d 

o •*- 

u C 

O V 

O u 













o o* 
oo c« 









O r^ 




j^ OO 


O m 







^ + 





















S " 

eg « 

C u 

3 09 

JK ?» 

•3 09 

(0 .^ 

O (« 


2 § 

E ^ 

E '3 
£ E 

S > 


















































'Z g* 

JS _ 
3 2 

< H 
















— ft; 

c (h 

>c a; 

.y c 

•*= :5 

^ «; OS 

— 2 ** 

< t* 

o E 
o ft; 

09 ft; 



1 8 

- I 

<^ ft; 

c • 


•A ^ 


There are in use two methods of defining and calculating 
the efficiency of a boiler. They are: 

T-/3C • r^u u -I Heat absorbed per lb. combustible 

1 . Efficiency of the boiler = — — ^1 — — --• 

Heatmg 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 foraU 
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 anap- 
preciable amount of surface moisture, allowance is to be made 
for the heat lost in evaporating this moisture by adding tothe 
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 beat 
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 fl'JC 
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 ^ 
boiler is a conventional definition of capacity, since the boiler 
of itself does no work. As the weight of steam required fvX 
different engines varies within wide limits, an arbitrary rating 
was adopted by the judges of the Centennial Exhibition in 



a standard nominal horse-power for boilers. This 
1, which is now generally used, fixed one horse-power 
alent to 30 pounds of water evaporated into dry steam 
'from feed-water at 100° Fakr.^ and under a pressure of 
pounds per square inch above the atmosphere. This is 
> an evaporation of 34.488 pounds from and at 212** F. 
nit of evaporation '* being 966.7 B. T. U., the commer- 
5e-power is 34.488 X 966.7 = 33,391 B. T. U. 

Graphical Log. — The results of a boiler-test can be 
ited graphically by considering intervals of time as 
ional to the abscissse, and ordinates as proportional to 
ous pressures and temperatures measured, as shown in 
5, from Thurston's Engine and Boiler Trials. 

Indfeatod Hon* Power 

Foot Puands aach SO mhratei 

Mmn Prcanrt ta Low Yn m ma t CjUader 


Fig. 2*5. 

Method of Making a Boiler-test — A standard 
I of making a boiler-test was adopted by the American 
• of Mechanical Engineers in 1884; this was revised in 
The first report is published in the Transactions, Vol. 
I latter in Vol. XXI, with discussion on the same as 

49^ EXI'tKIMEiVTAL EXliI.yE£K*AG. ll9H 

cuDE uF isys. I 

L Determine at llie outset the specific object of the prfipowd 
trial, whether it be to ascertain the capacity of the boiler, il« 
efficiency as a steam generator, its efficiency and ita defects anJu 
usual vorkiiig coDditions, the economy of some particular kind 
of fuel, or the effect of changes of desigu, proportion, or oper*- 
tion ; and prepare lor the trial accordingly, i Appendix II.) 

11. J&(im'W //ic foi'/tT, lioth outside and inside; ascertain tb« 
dimensions of grates, heating surfaces, and all important parte; 
and make a full record, describing the same, and iUustnUing 
special features by sketches. The area of heating surfac? iito 
be computed from the surfaces of shells, tubes, furnaces, and file- 
boxes in contact with the fire or hot gases. The outside Jiam- 
eter of water-tubes and the inside diameter of fire-tubes 
to be used in the computation. Ail surfaces )>elow the mean 
water level which have water on one side and products of com- 
bustion on the other are to be considered as water-h6atii« 
surface, and all surfaces above the mean water level whici 
have steam on one side and products of combustion on tbe 
other are to be considered as superheating surface. 

TTT .Votice theijeneral condiliou of the boiler and its equipment, 
and record such facts in relation thereto as bear upon the objecU 
in view. 

If the object of the trial is to ascertain the maximum econamj 
or capacity of the boiler as a steam generator, the boiler aaJ ^t 
its appurtenances should be put in first-class condition. CImo 
the heating surface inside and outside, remove clinkers from 
the grates and from the sides of the furnace. Remove all JQ»t, 
soot, and ashes from the chambers, smoke connections, and 
fines. Close air leaks in the masonry and poorly fitted clean- 
ing doors. See that the damper will open wide and close tij^L 
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 fiame of a candle oTsr 
cracks in the brickwork. 

rV. DeUnnlne the eharacter of Ifte coal to be used. For teal* 
of the efficiency or capacity of the boiler for comparison willi 
other boilers the coal should, if possible, be of some kind whici 
is commercially regarded as a standard. For \ew England 


1 tbat portion of the country east of the Allegheny Moun- 
as, good anthracite egg coal, containing not over 10 per cent, 
ish, and semi-bituminous Clearfield (Pa.^, Cumberland (Md.), 
1 Pocahontas (Va.) coals are thus regarded. West of the 
egheny Mountains, Pocahontas (Va.) and New Biver (W. Va.) 
di-bituminous, and Toughiogheny or Pittsburg bituminous 
kls are recognized as standards.^ There is no special grade 
Boal mined in the Western States which is widely recognized 
of superior quality or considered as a standard coal for 
iler testing. Big Muddy lump, an Illinois coal mined in 
;kson County, HI., is suggested as being of sufficiently high 
ide to answer these requirements in districts where it is more 
iveniently obtainable than the other coals mentioned above. 
For tests made to determine the performance of a boiler with 
^articular kind of coal, such as may be specified in a contract 
the sale of a boiler, the coal used should not be higher in 
1 and in moisture than that specified, since increase in ash 
1 moisture ai)ove a stated amount is apt to cause a falling off 
1>oth capacity and economy in greater proportion than the 
^portion of such increase. 

7, Establish the correctness of aU, apparatus used in the test for 
Lghing and measuring. These are : 

• Scales for weighing coal, ashes, and water. 

L Tanks, or water meters for measuring water. Water me- 
s, as a rule, should only be used as a check on other measure- 
Ots. For accurate work, the water should be weighed or 
insured in a tank. (See Chapter VII.) 

• Thermometers and pyrometers for taking temperatures of 
steam, feed-water, waste gases, etc. (Chapter XII.) 

- Pressure-gauges, draught-gauges, etc. (Chapter XI, pagt-s 

to 369.) 
'The kind and location of the various pieces of testing appaia- 

must be left to the judgment of the person conductinor the 
t ; always keeping in mind the main object, i.e., to obtain 
^hentic data. 

Vl. See that the hoUer is thoroughly heated before the trial to 
^ usual working temperature. If the boiler is new and of a 

*These coals are selected because they are about the only coals which possess 
IfSBentialfl of exceUence of quality, adaptability to various kinds of furnaces. 
Mbb, boilers, and methods of firing, and wide distribution and general accessi- 
Ijjr In the markets. See various appendices in Vol. XXI, Trausiiciioos 


form provided with a brick setting, it should be in regular ua 
at least a week before the trial, so as to dry and heat the walk 
If it has been laid off aa<I become cold, it shoald be n-nrked 
before the trial until the walls are well heated. 

Vn. The hoilvr ami connectiong should be proved to be free fro« 
leaks before beginning a teat, and all water connections, inclo^ 
ing blow and extra feed pipes, should be disconnected, stopped 
with blank flanges, or bled through special openings beyond tis 
valves, except the particular pipe through which water ie to bt 
fed to the boiler during tlie trial During the test the blow^ 
and feed pipes should remain exposed to view. 

If an injector is used, it should receive steam directly throng 
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 injectcc 
If the quantity is determined before it goes to the injector Uw 
temperature should be determined on the suction side of tb* 
injector, and if no change of temperature occurs other than thil 
due to the injector, the temperature thus determined ia properly 
that of the feed-water. When the temperature changes hetwew 
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 tlw 
injector and that at which it enters the boiler should all In 
taken. In that case the weight to be used is that of the w&fer 
Iea\-Lng the injector, computed from the heat units if not 
directly measured, and the temperature, that of the waMt 
entering the boiler. 

Let w — weight of water entering the injector. 
X = '' " Hteam " " " 

/f, = heat units per pound of water entering injeotor. 
A, = " " " " " steam " " 

ft, = " " " " " water leaving '* 
Then, w + x = weight of water leaving injector. 

^ ~ *" A, - h' 

* Id feeding a bolkr undergalng wiili aa Injector taking sl«ain TraRi anotbt 
boil«r. or from ibe mBin sleam pipe from aevpral boileni, the evaporaUr« neulV 
maj b« modified bv a diSereiice in (lie quality nf tbe ateam from such wan* 
compared nitb that supplied b^tbelxiiler being tested, and in son)ectw*l)» 
coDiiectlon to tbe Injector nay act as a drip for tbe main sixain pipf. If ilil 
known thai the eleam (rora tlie main pipe \s of the s»tne pressure and qaalll; • 
tbat furnished bj the boiler undergoing tbe ti^it. the Hteam ma; be taken tn* 
main pipe. 


Jee that the steam main is so arrangeil that water of con- 
isation cannot ran back into the boiler, 

JHTT Biiraltono/thf Tesf. — For testa made to ascertain either 
I maximum economy or the maximum capacity of a boiler, irre- 
ictive of the particnlar class of service for which it is regularly 
k), the iloration should be at least ]0 hours of continuous run- 
ig. If the rate of combustion exceeds 25 pounds of coal per 
lare foot of grate surface per hour, it may be stopped when a tn- 
of '250 pounds of coal has been burned per square foot of grate. 
[n cases where the service requires continuous running tor 
1 whole 24 hours of the day, with shifts of firemen a number 
times during that period, it is well to continue the test for at 
Biii hours. 

When it is desired to ascertaia the performance under the 
iking conditions of practical ruuning, whether the boiler be 
{ularly in use 24 hours a day or only a certain number of 
nrs out of each 24, the fires being banked the balance of the 
u, the duration should not be less than 24 hours. 
K. Starting and Slopping n Test. — The conditions of the boiler 
i fomace in all respects should be, as nearly as possible, the 
ue at the end as at the beginning of the teat. The steam 
Bsaure should be the same ; the water level the same ; the fire 
on the grates should be the same in t^uautity and condition ; 
i the walls, fines, etc., should be of the same temperature, 
m methods of obtaining the desired equality of conditions of 
I fire may be used, viz. : those which were called in the Code 
1885 " the standard method " and " the alternate method," 
) latter being employed where it is inconvenient to make 
i of the standard method.* 

S, Standard Afelhoii of Starting and Stopping a 7'es^^Steam 
ing raised to the working pressure, remove rapidly all 
i fire from the grate, close the damper, clean the ash pit, 
3 as quickly as possible start a new fire with weighed 
lod and coal, noting the time and the water level! while 

'TbeCommillee eoDtiladeB iLal It is best to retaio tbu duaigaatlons "stnod- 
|'*Mi(I "Bllemale," idnce they have bccomo widelj knotm and catablishvd in 
iB^ds of enEioeeni and id the repriots of tbe Code of 1685, Mau; eDgineera 
Itrthe "alternate" to the " standard " method oo aocoUQt of Us being: less 
Ht to error dae to cooling of the boUer nt the beginning and end of a teat. 
The gKUgt-glass should not \ie blown out wilbin an hour before the water 
d ti taken at the beginolng and end of a, test, otherwise an error in the read- 
er level may be caased by a chnnge in Ibe temperature and di^naity 
n the pipe leading from the l)Otl<<iD of the glass into the bollei. 


the water is in a qnlesoent state, jost 'before ligLtiiig 

At tlie end of tlie test remove the wliole fire, vliifh t 
been burned low, clean the grates and aah pit, and nnte 1 
water level when the water ia in a quiescent stale. Ji 
record the time of hauling the fire. The water level s!i« 
be as nearly as possible the same as at the be|riiiiiiii^u[ll 
test If it is not the same, a correction should W mitikl 
computation, and not by operating the pump after tlie Mti 

XI. Alifrimic Mcthml of Starting and St^nng a Te>l-Ti 
boiler being thoroughly heated by a preliminary run, the (■ 
are to be burned low and well cleaned. Note the amoiull 
coal left on the grate as nearly ns it can be estimated; notei 
pressure of steam and the water level. Note the lime, i 
record it as the starting time. Fresh coal which has t" 
weighed should now be fii'ed. The ash pits should b* ll 
ouyhly cleaned at once after starting. Before the enii 
teat the fires should be burned low, just as before the si 
the fires cleaued iu siich a manner as to leave a bed of 
the grates of the same depth, and in the same conditi< 
the start. When this stage is reached, note the time and' 
it as the stopping time. The water level and steam pi 
should previously be brought as nearly as possible to 
point aa at the start. If the water level ia not the si 
the start, a correction should be made by computation, 
by operating the pump after the test is completed. 

Xn. Uniformity of drnditums. — In all trials made to 
masimum economy or capacity, the conditions should 
taiited uniformly constant. Arrangements should be 
dispose of the steam so that the rate of evaporation 
kept the same from beginning to end. This may be 
plished in a single, boiler by carrying the steam 
waste steam pij^e, the discharge from which can be ri 
desired. In a battery of boilers, in which only one is 
the draft may be regulated on the remaining boilers, li 
teat boiler to work under a constant rate of prodactioD. 

Uniformity of conditions should prevail as to the pi 
steam, the height ot water, the rate of evaporation, the ' 
of fire, the times of firing and quantity ot coal fired at 
and as to the intervals between the times of clutining 


The method of firing to be carried on in such tests should be 
stated by the expert or person in responsible charge of the 
5t, and the method adopted should be adhered to by the fire- 
iu throughout the test. 

XIIL K'ft'ping the Records. — Take note of every event con- 
cted with the progress of the trial, however unimportant it 
ly appear. Record the time of every occurrence and the 
ne of taking every weight and every observation. 
The coal should be weighed and delivered to the fireman in 
ual proportions, each sufficient for not more than one hour's 
n, and a fresh portion should not be delivered until the pre- 
Dus one has all been fired The time required to consume 
«h portion should be noted, the time being recorded at the 
stant of firing the last of each portion. It is desirable that at 
esame time the amount of water fed into the boiler should be 
curately noted and recorded, including the height of the 
iter in the boiler, and the average pressure of steam and tem- 
rature of feed during the time. By thus recording the 
lount of water evaporated by successive portions of coal, the 
jt may be divided into several periods if desired, and the de- 
ee of uniformity of combustion, evaporation, and economy 
alyzed for each period. In addition to these records of the 
^1 and the feed water, half hourlv observations should be made 
the temperature of the feed water, of the flue gases, of the 
berual air in the boiler-room, of the temperature of the fur- 
2e when a furnace pyrometer is used, also of the pressure of 
am, and of the readings of the instruments for determining 
5 moisture in the steam. A log should be kept on properly 
spared blanks containing columns for record of the various 

HVTien the '* standard method " of starting and stopping the 
t is used, the hourly rate of combustion and of evaporation 
1 the horse-power should be computed from the records taken 
ring the time when the fires are in active condition. This 
le is somewhat less than the actual time whicli elapses Uii- 
jen the beginning and end of tlie run. The loss of time du<' 
kindling the fire at the beginning and burning it out at ti^ 
[ makes this course necessarv. 

HV. QffaHty of Steam, — The percentage of moisture m U*- 
tm should be determined by the use of either a throliU^ *' 


a separating steam oalorimeter. Tbe sampling nozzle stu 
be placed in the vertical steam pipe rising from the boiler. 
should be made of J-inch pipe, and should extend across 
diameter of the steam pipe to within half an inch of the 
site side, being closed at the end and perforated with m 
than twenty |-iueh holes equally distributed along and 
its cylindrical surface, but none of these holes should be ueanr 
than \ inch to the inner side of the steam pipe. The calorin 
eter and the pipe leading to it should be well cohered wiA 
felting. Wheuever 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 bIiodM 
be checked by a steam separator placed in the steam pipe It 
close to the boiler as convenient, with a calorimeter in the steam 
pipe just beyond the outlet from the separator. The drip from 
tbe separator should be caught and weighed, and the perceDt- 
age of moisture computed therefrom added to that shown br 
the calorimeter. (See Chapter XIII, page 438.) ) 

Superheating should be determined by means of a tbermome 
ter placed in a mercury well inserted in the steam pipe. The 
degree of superheating should be taken as the difference lie- 
tween the reading of the thermometer for superheated steam 
and the readings of the same thermometer for saturated stwim 
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 correotioiii 
for quality of steam, see Chapter XIII, pages 393 aii<l 43o. 

SV. Samptin/f the Coal and Detefminintf it» i foist ure. — As 
each barrow load or fresh portion of coal is taken from the coal 
pile, a representative shovelful is selected from it and placed a 
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 prooeas of 
repeated quartering and crushing until a final sample weighing 
about five pounds is obtained, and the size of the larger pieoM 
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 Bam- 
ples are to be kept for subsequent determinations of moistuR 
and of heating value and for chemical analyses. Darii 

^50 TESTING steam-boilers. 503 

•oess of quartering, when the sample has been reduced to 
»at 100 pounds, a quarter to a half of it may be taken for an 
>roximate determination of moisture. This may be made by 
cing it in a shallow iron pan, not over three inches deep, 
rfaUy weighing it, and setting the pan in the hottest place 
i can be found on the brickwork of the boiler setting or flues, 
iping it there for at least 12 hours, and then weighing it. 
a determination of moisture thus made is believed to be ap- 
fzimately accurate for anthracite and semi-bituminous coals, 
1 also for Pittsburg or Toughiogheny coal ; but it cannot be 
ed upon for coals mined west of Pittsburg, or for other coals 
taining inherent moisture. For these latter coals it is impor- 
I that a more accurate method be adopted. The method 
Dmmended by the Committee for all accurate tests, whatever 

character of the coal, is described as follows : 
Ue one of the samples contained in the glass jars, and 
ject it to a thorough air-drying, by spreading it in a thin layer 

exposing it for several hours to the atmosphere of a warm 
m, weighing it before and after, thereby determining the quan- 

of surface moisture it contains. Then crush the whole of it by 
Ding it through an ordinary coffee mill adjusted so as to pro- 
B somewhat coarse grains (less than ^-inch), thoroughly mix 

crushed sample, select from it a portion of from 10 to 50 
3QS, weigh it in a balance which will easily show a variation 
mall as 1 part in 1,000, and dry it in an air or sand bath at 
mperature between 240 and 280 degrees Fahr. for one hour, 
i^h it and record the loss, then heat and weigh it ag^in 
^tedly, at intervals of an hour or less, until the minimum 
5ht has been reached and the weight begins to increase by 
U&tion of a portion of the coal. The difference between the 
inal and the minimum weight is taken as the moisture in the 
iried coaL This moisture test should preferably be made 
Implicate samples, and the results should agree within 0.3 
-4 of one per cent., the mean of the two determinations being 
^H as the correct result The sum of the percentage of 
Bture thus found and the percentage of surface moisture 
viously determined is the total moisture. 
tVl. Trecdmerd of Ashes and Refuse, — The ashes and refuse 
' ta be weighed in a dry state. If it is found desirable to 
^ the principal characteristics of the ash, a sample sliould 

lubjected to a proximate analysis and the actual amount 

504 hXPEKiMi..; TAL EAGi-\Et.f:JAG 

of incombustible material determined. For elaborate tria 
complete analysis of tlie asU ami refuse sbouUl be made. 

XVn. Oalori/h Tfsts ami Analysis of Q>al.—The qnalityol 
fuel should be determiued either by heat test or bv anslysi 
by both. 

The rational method of determining the total beat of com 
tiun is to burn the sample of coal in an atmosphere of oi; 
gas, the coal to be sampled as directed in Article XV. of 
code. (See Chapter XIV.) 

The chemical analysis of the coal should be made only b; 
espert chemist. The total heat of combustion computed ii 
the results of the ultimate analysis may be obtained bj 
uae of Dulong's formula (with constants modified by tea 
determinations), viz.: 14,600 + 62,000 0^-S) + 4-'W> 
in ivliich C, H, 0, and 5" refer to the proportions of carboB. i 
drogen, oxygen, and sulphur respectively, as determined bt tl 
ultimate analysis.* 

It is desirable that a proximate anaJysis should be mM 
thereby determining the relative proportions of volatile nuW 
and fixed carbon. These proportions furnish an iudicaOMI 
the leading characteristics of the fuel, and serve to fii ■ 
class to which it belongs, (I'nge 470.) Aa an aJilitioa 
indication of the characteristics of the fuel, the speciliv ^;n<^ 
should be determined. 

XVin. Analysis of Flue Gases. — The analysis of the fine p* 
is an especially valuable method of determining the n'JB 
value of different methods of firing, or of different kimifccf' 
naces. In making these analyses great care should bet^<'' 
procure average samples — since the composition is »ft t^" 
at different points of the flue pages 47o to 402). The k* 
position is also apt to vary from minute to minute, ami ft*" 
reason the drawings of gas should lost a considerable peri* 
time. Where complete deter mi nations are desired, th>i at*!,' 
shonld ha intrusted to an espert chemist. For apptou" 
determinations the Orsattor the Hempol ]: apparatus 01*^ 
osed by the engineer, (See pages 481 and 483.) 

*Favro nrni Silbcrman give 14.544 B.T.IJ. pi- r pound car Ikiii ■, BefiW*'' 
B.T.U. Fuvrennd Silberraau Rive 05,033 U.T.D. per pound lijdKflea; t** 
81,810 B.T.U. 

+ Se«H.8. [Iale'spaperoTi"Flu«Gu.iAiiiil)-8l8."7V((n»(icCi07ui.v*l stflL.|l 

{Sob Hempel'a " Methods of Oae Aaalysis" (MacmUlan & Oo.}. 


For the contiDUouB indication of the amonnt of carbonio acid 
present in the flue gases, an iustrumeut may be employed wbich 
shows the -weight of the sample of gaa passing throogh it. 

XIX. Smoke Ohser vat ions. — 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 sraokiuess 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 preferrp'l. {See Appendices XXXIV. and XXXV.) 

XX Misccf/anetiiis. — In tests for purposes of scientific re- 
search, in wiiich 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 
boilert 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. 

XXL Cakulatioiis of EiHcifiifj. — Two methods of defining and 
edculating the efficiency of a boiler are recommended. They are : 

. T.«. ■ . .1 i_ -1 Heat absorbed per lb. combustible 

1. Efficiency of the boiler — „-i — .w — , ^i,,.— , ■ ,.. , — 

Laloritic value of I lb. combustible 

a -r-n- ■ f .1 i_ -1 1 . Hoat absorbed ijer lb. coal 

2. Emciencv of the boiler and crate = „ , .„ , ', ,-„ ^ 

uaiorinc value of 1 lb. coal 

The first of these is sometimes called the efficiency based on 
combustible, and the second the efficiency baaed on coah 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 ia used without qualification. The 
second, however, should be included iu a report of a teat, to- 
gether with the first, whenever the object of the test is to detet- 
ptinft the efficiency of the boiler and furnace together with the 



[§ 375. 

grate (or mechanical stoker), or to compare difFerent fnniaoefl^ 
grates, fuels, or methods of firing. 

The heat absorbed per pound of combustible (or per pound 
ooal) is to be calculated by multiplying the equivalent eyapon- 
tion from and at 212 degrees per pound combustible (or coal) bj 

XXIL The Heat Balance. — An approximate " heat balance," or 
statement of the distribution of the heating value of the coal 
among the several items of heat utilized and heat lost may be 
included in the report of a test when analyses of the fuel and of 
the chimney gases have been made. It should be reported in 
the following form : 

Hbat Balance, or Distribution of the Heatino Valub of the CoxbubtiblIi 
Total Heat Value of 1 lb. of Combustible B. T. U. 

1. Heat absorbed by the boiler = evaporation from and at 212 

degrees per pound of combustible x 965.7. 

2. Loss due to moisture in coal = per cent, of moisture referred 

to combustible -*- 100 x [(212 — + 906 + 0.48 (T — 
212)] {t — temperature of air in the boiler-room, T = 
that of the flue gases) 
%, Loss due lo moisture formed by the burning of hydropen 
= per cent, of hvdrogen to combustible -i- 100 x 9 x 
r (212 - i) 4- 966 + 0.48 (r - 212)]. 
due to 

4.* Loss 

heat carried away in the dry chimney gases = 

weight of gas per pound of combustible x 0.24 x (7' — 0- 

6.t Loss duo to incomplete combustion of carbon = 

CO. + CO 

per cent. C in combustible *^ ^^ 
X j^^ X » . 

6. Loss due to unconsumed hydrogen and hydrocarbons, to 
heating the moisture in the air, to radiation, and unac- 
counted for. (Some of these losses may be separately 
itemized if data are obtained from which they may be 



*The weight of ga« per poQDd of carbon barned may be calcaUted from the gu •biIjki' 
follows : 

Dry gas per pound carbon » IL^l t3^ ^JL?. ^52jt2D, In which 00,, CO, 0, ind X « I* 

3 (COj + CO) ^ 

p»erci>ntaKP»4 by volume of the Hovcral ga!<e8. As the sampling and analysM of the 6**'*''' n! 
prej*ent btate of the art are liable to considerable errors, tne ret>nlt of this calcolatioD i« o*^ 
oniv an approximate one. The bent ))alniiC(' itself i;* aloo only approximate for this r e « W »y^ 
as for tlie fact that it is not iKL-i^ible tu deterniine accurately the percentage of anbamed M"*^ 
or hydrocarbons In the llur pis*"* __^ 

The weicrht of dry gas j)er pound of comr)Uf«tible is found by multiplying the dfj gM pvP"^ 
of carbon by the pcrc'-ntaK*; <>f carbon in the combustible, and dividing by 100. ,^ ^ 

t ("Oj and CO are respectivt'ly ibe percentage by volume of carbonic acid and carbonic »*f 
the flue gases. The Quantity 10,150 = Number of heat unita generated by bamiag to ctf^*^ 
acid one pound of caroon contained In carbonic oxide. 

XXIII. Report of the Trial — The data and results should^! 
reported in the manner given in either one of the two foBotriBfj 


tables, omitting lines where the tests have not been made as 
elaborately as provided for in such tables. Additional lines may 
be added for data relating to the specific object of the test. The 
extra lines should be classified under the headings provided in 
the tables, and numbered as per preceding line, with sub letters 
a, 6, etc. The Short Form of Beport, Table No. 2, is recom- 
mended for commercial tests and as a convenient form of 
abridging the longer form for publication when saving of space 
18 desirable.f For elaborate trials, it is recommended that the 
fall log of the trial be shown graphically, by means of a charL 
(See page 495.) 


Data and Results of Evaforatt^s Tbst, 

Amnged in accordance with the Complete Form advised by tlie Boiler Test 
Committee of the Ameiican Society of Mechanical Engineers. Code of 1899. 

Made bj of boiler at to 


incipal conditions governing the trial 

Mind of fuel* 

Xind of furnace .... 
State of the weather. 

Method of starting and stopping the test (" standard ** or " alternate," Art. X. 
mad XI., Code) 

1. DaUoftrial 

9. Duration of trial honil. 

Dimemions and Proportions. 

(A complete description of the boiler, and drawings of the same if of nnusaal 
^fpe, shonld be given on an annexed sheet. (See Appendix X.) 

1 Grate turface undth length area 

4. Height of farnace 

5. Approximate width of air spaces in grate 

9. Proportion of air space to whole grate surface 

7. WaUr-heaUng surface 

9. Superheating surfijice 

f. Ratio of water-heating surface to grate surface 

JOL Ratio of minimum draft area to grate surface 

sq. Tt. 



per cent. 

sq. ft 


— toL 

Ito — 

• Iba kflOM printed In Itallca correspond to the items in the " Short Fom of Coda.* 
t Also SM short form on page 513, uned in Coniell Univei-sity. 


Awragt Pre9ture9» 

11. Sieam prenure by gauge Ibe. per sq-to 

12. Force of draft between damper and boiler Ids. of witcr 

18. Force of draft in furnace •* •* 

14. Force of draft or blast in ashpit •• •* 

Average Temperatures. 

15. Ofeztemalair dtg, 

16. Of fireroom •• 

17. Of steam , .' " 

18. Of feed water entering beater • " 

19. Of feed water entering economizer • ** 

20. Of feed water entering boiler '* 

21. Of escaping gases from boiler " 

22. Of escaping gases from economizer • • *' 


28. Size and condition 

24. Weight of wood used in lighting fire • • •• Ibi. 

25. Weight of coal an fired* " 

26. Percentage of moisture in coal \ •• per cenu 

27. Total wdfjlit of dry coal consumed lbs. 

28. Total ash and refuse 

29. Quality of asli and refuse 

80. Total combustible consumed •• lbs. 

81. Percentage of ash and refuse in di g coal •• perecoL 

Proximate Analysis of Coat, 

(App. XII.) 

OfOoaL OrOombQftibk 

82. Fixed carbon per cent. per cent 

33. Volatile matter *' " 

34. Moisture " 

85. Ash " 

100 per cent. 100 per cent 
86. Sulphur, separately determined 

«< •< 

* Inclndiu^ eqn'valent of wood used Id lighting the fire, not incladini; onbant coal witbdn** 
from furnace at tuno* of cleaning and at end of teat. One poand of wood is taken to b« equl V 
0.4 pound of coal, or. In case greater accuracy is desired, as having a heat value eqalralent to t^ 
evaporation of 6 pounds of water from and at 212 dejrrees per pound. (8 x 965.7 = S,7M B.T. C.) 
The term "as fired '' means ii. Its actual condition, including moisture. 

t Thifl is the total moisture in the coal as found by drying it artificially, at descifbed in ^ 
XV. of Code. 


XJUiimaU ArudytU of Dry Coal. 

(Art. XVII., Code.) 

OfOod. OfOomboitible. 

rkrbon (C) pereent percent. 

ifjdrogen (H) " *• 


JJitrogen (N) " ** 

kJpbnr (8) •• «' 

fish •* 

100 per eent^ 100 per cent. 
Uoistare in sample of ooel as reeelred ** '* 

Anaiyii$ of Aih and R^im. 

Oarbon ••••• •••••••••••• percent. 

Barthj matter 


Fuel per Hour. 

Dry eoal eontumed por hour lbs. 

Combustible oonsnmed per hoar " 

Dry coal per square foci of grate surface per Tiour •* 

Combustible per sqoare foot of water-beating surface per boor. ** 

dalorifle Value of Fuel. 
(Art XVII., Code.) 

Calorifle value by oxygen calorimeter, per lb. of dry eoal RTl?. 

Caiorifle value by oxygen calorimeter, per lb. of combuetibtB ** 

Calorific value by analysis, per lb. of dry coal * •«• ** 

Calorific value bj analysis, per lb. of combustible. • ** 

Qualily of Steam. 
(App. XV. to XIX.) 

Pereentage of moisture in steam percent. 

Number of degrees of superheating deg. 

Quality of steam (dry steam = unity). (For exact determina- 
tion of tbe factor of correction for quality of steam see Ap- 
pendix XVIII.) 

(App. I. IV., VII., vm.) 

Total weight of water fed to boiler f lbs. 

Equivalent water fed to boiler from and at 212 degrees 

Water actually evaporated, corrected for quality of steam 

Sea fonaala for caloflllc Tslne under Article X VII. of Code. 

)omet6d for ineqaaUty of water level and of pteam preseiure at beglDDlng and end of test. 


60. Facto? of eyaporation * Il 

61. Equivalent water evaporated into dry steam from and at SIS 

degrees, f (Item 59 x Item 60.) " 

WaUr per Hour. 

63. Water evaporated per hour^ corrected for quality of tteam * 

63. Equivalent evaporation per hour from and at 212 decrees \ * 

64. Equivalent evaporation per hour from and at 213 degrees per 

square foot of water-heating surface \ * 


65. Horse-power developed. (84i lbs. of water evaporated per hour 

into dry steam from and at 312 degrees, equate one horse- 

power) X H. 

66. Builders* rated horse-pov>er * 

67. Percentage of builders^ rated horse-power developed pff 

Economic Results. 

68. Water apparently evaporated under actual conditions per pound 

of coal as fired. {Item 57 -t- Item 25.) I 

69. Equivalent evaporation from and at 213 degrees per pound of 

coal as fired, f {/tern 61 -*- Item 35.) 

70. Equivalent evaporation from and at 213 degrees per pound of dry 

coal, t {Item 61 4- Item 27.) 

71. Equivalent evap&ratitm from and at 313 degrees per pound of 

combustible. \ (Itnn 61 -t- Item 30.) 

(If the equivalent evaporation. Items 69, 70. and 71, is not cor- 
rected for the quality of steam, the fact should be stated). 


(Art. XXl., Code.) 

78. Efficiency of the boihr ; heat absorbed by the boiler per lb. ofeom- 

bustible diridtd hy the heat taluc of one lb. of combustible %, ... I» 

73. Efficiency of boiler^ including the grate; heat absorbed by the 
boiler, per lb. of dry coal, dividtd by the heat value of one lb. of 
dry coal 

• Factor of evnporation = vJr-i.. i" which // and h are respectiviriy the total betttni 

the Bverajfe observed preg^uro, an<l in water of the arera^ obeerred temperatore oftht fe* 
t The §yrabol *' l*. E." nuaninir '" Unit!* of Eva|)oration,*' may be convenleotlj Rib^r 

the expn'stj'ioii " EquivaKnt w a'cr ov:»pv>rattHi into dry »team from and at 8}2 dffrec^" l« 

lion iH'ini; ^iven in a foot iu>tt'. 
X Ueld to be the rquiralcnt of .3> lbs of wator per hoar eraporated from lOOdecnai fi 

dry steam at "JO Uh. pm^i^ prt'!*-urtv iSe^ l>a»^ 45M.) 
I In all cases where the wonl c<»mba:«ubU' i;* u^od. it means the coal wtthostSM^tut 

bQt inclnding all other consttitawotd. It i^ the same a(» what la called in Voropa ** coal drj 



OM of Evaporation. 

- Co9t of coal per ton of 1b9. delivered in loiter room $ 

Cost of fuel for evaporating 1,000 lbs of water under observed 

conditions $ 

Co9t of fiui lisedfor evaporating 1,000 Iba. of water from and alt 
212 degrees $ 

Smoke Observtitiona. 

(App. XXXIV. and XXXV.) 

Percentage of smoke as observed per cent 

^Veight of soot per hour obtained from smoke meter ounces. 

Volume of soot per hour obtained from smoke meter cub. in. 

Methods of Firing. 

Kind of firing (spreading, alternate, or coking) 

Average thickness of fire 

Average intervals between firings for each furnace during time 

when fires are in normal condition • . • 

. Average interval between times of levelling or breaking up. • • • 

Analyses of the Dry Gases. 

. Carbon dioxide (CO,) percent. 

. Oxygen (O) ** 

» Carbon monoxide (CO) *' 

> Hydrogen and hydrocarbons 

> Nitrogen (by difference) (N) 


100 per cent. 

Data and Results op Evapoeatitb Test, 

ranged in accordance with the Short Form advised by the Boiler Test Com- 
mittee of the American Society of Mechanical Engineers. Code of 1899. 

<]e by on boiler, at to 

ermine. • • 

id of fuel 

id of furnace 

Ieth<)d of starting and stopping the test (" standard" or " alternate," Art. X. 
I XL. Code) 

ite surface aq. ft. 

Yer-heating surface " 

^rheating surface " 

Total Quantities. 
Date of trial 

Duration of trial ham, 

Veight of coal as fired ♦ Ihs, 

Percentage of moisture in coal * per muL 

Total weight of dry coal consumed 

Total aah and refuse 

Percentage of aeh and refuse in dry coal 

* See foot-notes of Complete Form. 


8. Total weight of water fed to the boiler ♦ li 

9. Water actually evaporated, corrected for molBture or saper- 

heat in steam ** 

10. Equivalent water evaporated into dry steam from an^ *%! 812 

degrees* r. ... ** 

Howrly QtMiUUies. 

11. Dry coal consumed per hour h^ 

12. Dry coal per square foot of grate surface per hour r » 

13. Water evapomted per hour corrected for quality of steam. . r - 

14. Equivalent evaporation per hour from and at 212 degrees *. . 

15. Equivalent evaporation per hour from and at 212 degrees par 

square foot of water-heating surface * 



Average Preaw/rest Temperatures, et&» 

16. Steam pressure by gauge Ibi F**!'^ 

17. Temperature of feed water entering boiler dif> 

18. Tempei-ature of escaping gases from boiler. '* 

19. Force of draft between damper and boiler ing.of«ittf> 

20. Percentage of moisture in steam, or number of degrees of 

superheating peroioiordif- 


21. Horse-power developed (Item 14 -i- 84^) * H.P. 

22. Builders' rated horse-power • " 

23. Percentage of builders* rated horae-power developed • • MTcr.l 

Economic Results, 

24. N^'ater apparently evaporated under actual conditions per 

pound of coal as fired. (Item 8 -^ Item 3) ^^ 

25. Equivalent evaporation from and at 212 degrees per pound of 

coal as fired.* (Item 10 -j- Item 3) 

26. Equivalent evaporation from and at 212 degrees per pound of 

dry coal.* (Item 10 -i- Item 5) 

27. Equivalent evaporation from and at 212 degrees per pound of 

combustible.* [Item 10 -f- (Itt;m 5 — Item 6)] 

(If Items 25, 26. and 27 are not corrected for quality of stesiD, 
the fact should be stated.) 


28. Calorific value of the dry coal per pound RT.v- 

29. Calorific value of the C()ml)ustiblp per pound •.... *' 

30. Eflif ioncy of Imiler (based on combustible) * ptf €•*• 

31. Efficienry of boiler, including grate (l)ased on dry ooal) 

Cost of Evaporation, 

32. Cost ef coal per ton of lbs. delivered in boiler-room % 

33. Cost of coal required for evaporating 1,000 pounds of water 

from and at 212 drgroes. % 

♦See fo<)t-not«'5 of Complete Form. 




(Sibley CoIIckc. Cornell UniTcnitr.) 
Log of BoiLEk-TniAt.. 



Rkport of Boilbr-test. 


N. V „.ia 

ooITrUl Houn. 





A».o«„.u.ed Pound* 

"f.lewh ft.. 

;h fi. Sq-(t. 

utiDit Hirface. 

Ev.po,a»d. dry ..«» " 

Evap. from and at ir.*. - 

Ptr Ptumd •/ Fmtl. 

Actual PoDBd*. 

Eijui.. from-mJ.1,..* " 

draushKoloriiBCUT). " 

i-oer '■ 

'bi-uer 1^. 

silns lo anic *arf*ec. 

™«Ke Pound. 

I-Bange Incha-xer. 

Equi*. lioD and at 9i>° ■• 

Prr Sf. FI. //HHme^lir/mcI fr Mr. 

Actuid, ... Pound* 

Equiv. fromandM,.,*.... " 

Fr.m i'^'F.I,-p,F,u%d,hGM-f' 

Prr SfMarr Fatt >•/ Cralt. 

'""'""«' ^''>«"- 

Actual, from feed w.ier i«n- 

peraiu" Poumli. 

l\TSf.Fl.^f Wmlrr-AHtiK(Smr/mc€. 

Actual Pound*. 

EquiT.fromuida.,.,' ■■ 

PrrSf. FI. rf Lrail Drii,[l,l-tirra. 

Actual Poundi. 

per hour H. P. 

Builden- wioE ■• 

Ipo-hour. " 

1 per Kioare fool of 

T.ble per squa>c foot 

1 per «|uan foot o( 

e Heiling-autface. 



377. Abbreviated Directions for Boiler-testing.— -•}/- 

paratiis, — As in standard tests : tanks and scales for weighing 
water ; meter for measuring water ; apparatus for flue-gas 
analysis ; barometer and pyrometer. 

Directions, — Calibrate all apparatus, meters, scales, ther- 
mometers, and gauges; arrange throttling or separator calo- 
rimetef to obtain quality of steam delivered. Note conditior 
of Boiler and Furnace Rules, VII-IX. Start and close ih 
test either by standard or alternative method. Rules X and XI. 
During test proceed as in Rules XIII and XIV. Continue 
the test as long as time will permit, at least four hours, takinf 
simultaneous observations each 15 minutes at a signal given 
by a whistle ; keep record so that coal and water consumption 
can be computed for each hour. 

Put 100 pounds of coal in a box and dry in a hot place for 
24 hours ; if ashes are damp from use of a steam-blower, dry a 
sample of 100 pounds in same manner. In general, ashes may 
be removed at once and weighed. 

Report and Computation. — Make report on standard forms 
submitted and compute the required quantities. Submit with 
report 3. graphical log, in which time is taken as abscissa, and 
the various observed quantities as ordinates. 

Revised Code for Boiler-testing. — At the meeting of the 
American Society of Mechanical Engineers in December. 
1899, a revised code for boiler-testing was presented before 
the society by a special committee appointed for that pur- 
pose. The new code is given in the Appendix to this volume: 
it differs from the old one principally in the use of improve 



378, Uses of the Steam-engine Indicator. — The steam- 
engine indicator is an instrument for drawing a diagram on 
paper which shall accurately represent the various changes of 
pressure on one side of the piston of the steam-engine during 
both the forward and return stroke. 

Fig aa6.— Thb Indicator-diagram. 

The general form of the indicator-diagram is shown in Fig. 
226; the ordinates of the diagram, measured from the line 
GG, are proportional to the pressure per square inch above the 
atmosphere; measured from the line HH, are proportional to 
the absolute pressure per square inch acting on the piston. 
The abscissa corresponding to any ordinate is proportional to 
the distance moved by the piston. ABCDE is the line drawn 
during the forward stroke of the engine, EFA that drawn dur- 
ing the return stroke. The ordinates to the line ABCDE rep- 
resent the pressures acting to move the piston forward ; those 
to the line EFA represent the pressures acting to retard or 



Stop the motion of the piston on its back stroke. The ordi- 
nates intercepted between the lines represent the effective 
pressure acting to urge the piston forward. Since the abscissa 
of the diagram are proportional to the space passed througjj 
by the piston, and the intercepted ordinate to the effective 
pressure acting on the piston, the area of the diagram must be 
proportional to the work done by the steam on one side of the 
piston, acting on a unit of area and during both forward and 
return stroke. (See Article 21, page 21.) 

From this diagram can be obtained, by processes to be ex- 
plained later: i. The quantity of power developed in ihcr 
cylinder, and the quantity lost in various ways, — by wire-draw- 
ing, by back pressure, by premature release, by mal-adjustment 
of valves, leakage, etc. 

2. The redistribution of horizontal pressures at the crank- 
pin, through the momentum and inertia of the reciprocating 
parts, and the angular distribution of the tangential component 
of the horizontal pressure ; in other words, the rotative effect 
around the path of the crank. 

3. Taken in combination with measurements of feed-water 
or of the exhaust steam, with the amount and temperatures of 
condensing water, the indicator furnishes opportunities far 
measuring the heat losses which occur at different points 
during the stroke. 

4. The indicator-diagram also shows the position of the 
piston at times wlien tl^e valve-motion opens or closes the 
steam and exhaust ports of the engine. It also furnishes in- 
formation regarding the general condition of the engine, and 
the arrangement of the valves, adequacy of the ports and par 
sages, and of t!ie steam or the exhaust pipes. 

379. Indicated and Dynamometric Power. — The steaft. 
engine iiidicator is used in all steam-engine tests to measure 
the force of the steam acting on a unit of area cf the piston. A 
dynamometer of the ahst)rbing or transmission type (seepages 
235 to 2 50) is used to measure the work delivered by thesteanv 
eni;ine. The work of the en^^ine is usually expressed in hor>c- 
power; one horse-powei being equivalent to 33,000 foot-pour.GS 



5 '7 

er minute. The work shown by the steam-engine indicator* 
iagram is temiedthe/«(/jir<a/^rfAow<'-/oa'Cf (I.H.P.); that shown 
y the dynamometer, DyHamometric horse-power (D.H.P.). 

The mean effective pressure per unit of area act'ng on the 
iston is obtained from the indicator-diagram this quantity, 
tultiplied by the area of the piston and the distance travelled 
y the piston in feet per minute, will give the work in foot 
ounds. Thus let / equal the mean effective pressure, / tht 
:ngth of stroke of the engine in feet, » the number of revolu 
ons, a the area of the piston in square inches. Then the 
ork done per minute by the steam acting on one side of tl.e 
iston, in horse-power, is 

plan -~ 33,000. 

380. Early Forms of the Steam-engine Indicator. — 
Vatt and McNaught. — The steam-engine indicator was in- 
<nted by James Watt, and was extensive- 
J used by him in perfecting his engine, 
"he indicator of Watt,* as used in 1814, 
t-insisted of a small steam-cylinder AA, 
^ shown in Fig, 227, in whicli a piston 
'as moved by the steam -pressure, against 
ie resistance of a spring FC. The end 
F the piston-rod carried a pencil, which 

a?! made to press against a sheet of 
aper DD. moved backward and forward 
1 conformity to the motion of the piston. 
V this method a diagram was produced 
f^ilar to that shown in Fig. 227, 

ilcNaught's indicator, which succeeded 
lat of Watt and was in general use until 
>out i860, differed from the form u-^cd 

' Watt principally in the use of a verti- 

■I cylinder instead of the sliding; panel, 

hich was turned backward and forward *""'" i";.~T"r»**^ 

* a vertical axis, in conformity to the motion of the pistOO- 

* See Thureion'E Engine an'l boiler Trials, ;.aKe 130. 




381. The Richards Indicator.* — The Richards ind 
was invented by Professor C. B. Richards about 1S60; !< 
tains every essential constructive feature found in rccenl 
cators, and may be considered the prototype from whii 
other indicators differ simply in details of workmanship, 
and size of parts. 

The construction of this indicator is well shown in F^ 

from which it 

irom wim^ii ii is m:i.ii to consist of a steam-cylindcr A: 
which is a piston />', connected by a rigid rod with tiica 
Tlic movement of tht: piston is resisted by the spriiyt' 

Tlic m 

such aniann 

to the i>r 


• See ih 


tliat its motion in ciilier direction is f 
rt. The motion of tlic piston-rod is traibit 
A', by links which arc so arranj-cd that tiit-p 

lards Inaicaior, by C. U. Porter; New Vort, D VaT S- 


■noves parallel to the piston B, but through a considerably 
jreater range. The indicator-spring can be taken out by 
inscrewing the cap E, removing the top of the instrument and 
inscrewing the piston B, and another spring with a different 
.ension can be substituted, The drum OR is made of light 
netal, mounted on a vertical axis, and provided with a spring 
itranged to resist rotation. The drum is connected to the cross- 
lead or reducing motion by a coid, and is given a motion in one 
iirection by the tension transmitted through the cord and in a 
reverse direction by the indicator drum-spring. The paper op 
which the diagram is to be drawn is wrapped smoothly around 
ihe drum OQ, being held in place by the clips PQ. The indicator 
Is connected to the steam-cylinder by a pipe leading to the 
Jearance-space of the engine : a cock, T, being screwed into this 
pipe, and the indicator connected to the cock by the coupling U. 
382. The Thompson Indicator.— This indicator is shown 
31 Figs. 229 and 330, It differs from the Richards indicator 

dpally in the form of the parallel motion, form of indicator- 
, and details of workmanship. The parts of the instru- 


ment are much lighter, and it is better adapted for use on hig)i< 
speed engines. 

Tlie use is essentially the same as the Richards ; the method 
of citanging springs should be thoroughly understood, and U as 
follows: Unscrew the milled-edged cap at the top of steim- 
cylinder; then take out piston, with arm and connections: di^ 
connect pencil-lever and piston by unscrewing the small milled. 
headed screw which connects them ; remove the spring from thi 
piston, substitute the one desired, and put together in same 
manner, being careful, of course, to screw the spring up firmly 
against cap and well down to the piston-head. The method of 
changing springs is simple, easy, and convenient, and does not 
require the use of any wrench or pin of any kind. 

383. The Tabor Indicator. — The Tabor indicator, shown 
in Figs. 231 and 232, in the form now manufactured differs 
from other indicators principally in producing the paralld 

motion of the pencil by a pin moving in a peculiarly-sliil*'' 1 
slot. It also differs in details of construction and in tor'' J 
of the indicator-spring; the pencil-point being arranged^ 
move not only parallel to the piston, but uniformly fivel! 
a? fast as the piston at every part of the range. 


Tietliod of changing springs in the Tabor indicator is as 

Remove the cover of the 
remove the screw beneath 
n, unscrew the piston from 
ng and the spring from 
r, and replace the spring 
When the lower end 
piston-rod is introduced 
square hole in the centre 
iston, care must be taku:i 
icts fairly in the hole be- ' 
screw is applied. Unless 
e is observed, the corners 
h and cause derangement. 
sion OH (he drum-spring 
varied by removing the 

urn, loosening the thumb-screw wliich encircles the 
haft, lifting the drum-carriage so as to clear the stop, 

winding the carriage in the direction desired. 
The Crosby Indicai:or. — The Crosby indicator as at 
:onstructed is shown in Figs. 233 and 234. It differs 
se already described in the form of piston- and drum- 
nd in the arrangement for producing accurate parallel 

.pecial directions for this instrument are given by the 
:urers as follows: 

move ike piston, spring, etc., unscrew the cap, then, by 
■e, lift all the connected parts free. This gives ful' 
the parts to clean and oil them. 

ftach the spring, unscrew the cap from spring-head, 
crew piston-rod from swivel-head, then, with the hol- 
ed wrench, unscrew the piston-rod from the piston, 
tl a spring, simply reverse this process. Before setting 
x/i the spring unscrew G slightly, then, after the piston- 
been firmly screwed down to its shoulder, set G up 
;ainst the bead, and thereby take up all lost motion. 
jften desirable to change the position 0/ the atmosphei,: 




line on the paper. This can easily be done by unscrewing the 
cap from the cylinder and raising the sleeve BB which earne* 
Jhe pencil-movement. Then turn the cap to the right or left. 

and the piston-rod will be screwed off or on the swivel i,^™ 
the position of the atmospheric line will be raised or lowertii 

Never remove the pins or screws from the joints X./.i-*' 
but keep them well oHed with refined porpotse-jaw oil, •'li''' 
is furnished with each instrument. 

The tension on the drum-spring should be increawd " 
diminished according to the speed at which the instrument ■ 
used, by means of the thumb-nut on top of the drum-spiiwl^ 

Use a spring of suck a number that the diagram will noil* 



>ver one and three-quarter inches high; as, for instance, a No. 
p spring should not be used for pressures above 70 lbs. 

385. Indicators with External Springs.— The Bachclder 
ndicatoT, shown in Fig. 235, has a fiat spring thai is flexed over 
I movable fulcrum by the steam pressure acting on tlie piston, 
rhe scale of the spring is changed, through a limited range, by 
moving the fulcrum. This form is desirable when the spring 
is subjected to high temperatures; it is only open to the objec- 
tion that the scale may be somewhat unrchable due to an acci- 
dental motion of the fuknmi. 

.\n indicator with the spring entirely outside and above the 
Indicator cylinder is shown in Fig. 236, For indicating gas- 


386. Sundry Types of Indicators. — Many of the makcis 
of indicators provide reducing- wheels which may be adapted 10 

varying lengths of strokes either by changing gear-whcds 1" 
the train of gears, or by varying the diameter of the wheels dii^f 
by the cord from the cross-head. An indicator provided «i4 
one form of reducing-whecis is shown in Fig. 337. 


[n Figs, 238 and 238(1 are shown indicators with pencil-moving 
banism of different character from those described. In one 

se the iiencil is directed in a straight line by a slotted guide- 
ir, in the other case it is made to move in a right line by a species 

parallel motion links, 

387. Optical Indicators. — The ordinary steam-engine indi- 
tor is not adapted for a very high speed of rotation, because 
? inertia of the moving parts distorts the diagram. By arranging 

mirror, which may be illuminated so as to be deflected in 
e direction by changes of pressure in the cylinder, and in a 
■ectioQ at right angles by the motion of the piston, the indi- 
:or diagram will be traced by a beam of light thrown on a 
>und-glass screen or on a sensitive plate in a camera. The 
fen of the diagram may be studied by obsen'ing it on the ground 
pe, or it may be photographed and preserved. 

One form of this instrument is made by J. Carpcnticr of 

3B, and is called the Manograpkie. Another form is made by 
Elsassische Elektricitats-Werke, Strassburg, and is called J 
(^tical indicator, 
perspective view and section of the Manographie is shown ' 

figi. 339 and 339a. A small mirror is located at i4 in the 




back part of the camera E. It is deflected in one direction by 
a small crank operated in imison with the engine piston by the 

revolving shaft P, to 
which it is connected by 
the flexible shaft R, Fig. 
239; it is deflected in a 
direction at right angks 
against the resistance of 
a spring by the pressure 
from the engine cylinder 
acting through a pipe T 
Fig 239. upon a diaphragm di- 

rectly back of the mirroL 
The mirror is illuminated by light from a lamp at G ^ich 
is reflected by the prism shown at H. The indicator diagram 
is traced on the screen Z> 
by the ray of light, and ^-^^^^^^^^^^^^^W^^^^^^^^ 

may be photographed by 

the use of a sensitive 

plate. This apparatus 

has been successfully 

used to take indicator 

diagrams of gas-engines 

when moving at the rate 

of 2000 revolutions per fio. 2390. 


388. Parts of the Steam-engine Indicator. — ^The parts of 
the steam-engine indicator are essentially as follows: 

1. The Steam-cylinder. — This contains the piston, the in^ii* 
cator-s])ring, and attachments for the pencil mechanism, 

2. The Piston, — This is usually solid, with grooves or holes 
in its outer edge; it must move easily in the cylinder. \^'^^ 
in use it must be lubricated with cylinder-oil of best quality. 

3. The Pencil Mechanism. — This receives the motion fron^ 
the piston-rod, increases its amplitude, and transfers it to 1 
pencil by means of guides or parallel- motion links, so that the 



wes in a right line and usually four to six times the 
of tile piston. The height of the atmospheric line, or 

pressure, on the drum, can often be adjusted by 
a threaded sleeve fitting on the piston-rod. In the 

ilor the pencil swings in an arc of a circle. 
e Jiiduator- spring. — This is usually a helical spring; 
ise it has one end screwed to the upper head of the 
and the other screwed to the piston. To insure accu- 
ts the spring must be accurate, and there must be no 
>st motion between the piston and the cylinder-head, 
pring must receive and deliver the force axially. The 
if pounds pressure on the square inch required to move 

1 one inch is stamped on the spring, and the springs 
nated by that number. It is essential to know the 
ny, in this number. A spring can be readily removed 
tier substituted when desired ; the maximum compres- 
ably should not exceed one third of an inch. 

pring is in many respects the most important part of 
ator, as the (orm of the diagram is directly affected 
rror. The following cuts show some of the principal 

apted by a few of the makers, and it may perhaps be 
to state that within the range of action of tlie indi- 
• of these forms can be made practically perfect. 




































E 6 






























c — 











































o , 

0£ • 

o c/) 





C/5 1 


y^ ' 

c ^ 

W i 

X . 

s • 










o « 

en .t: 

d °^ 


CO rj 















? • 

l> o 

^ bo 

£ p 

































^ f' 















c . 
- : 



E . 

*L. O 

^ "^ 
















>- o 

6 « 

oo i_ 
























^- O. .Si 






















_ c 
c E 


o E 


o c 
•s o 








X z 
if V 

:i "l £ 



390.] THE steam-engine indicator. 529 

The Bachelder indicator (see Fig. 238) is made with a flat 
►ring, and to a certain extent the tension is regulated by 
langing its fulcrum. 

5. The Paper-drum^ to which the card is attached, consists 
a brass cylinder attached to a spindle which is connected 

. the drum-spring, the action of which has been described, 
he drum can be removed readily, and the tension on the 
•ring changed at pleasure. Two clips or fingers serve to hold 
e paper in position. 

6. The Cord used, although not a part of the indicator, 
ust be selected with great care; it must be of a character 
)t to be stretched by the forces acting on the indicator. 
;eel wire is sometimes used for this purpose. Any variation 

length of the connecting cord affects the abscissa in the 

7. T/ie Reducing-motions^ also not a part of the indicator, 
ust give an exact reproduction, on a smaller scale, of the 
lotion of the piston ; otherwise the length of the indicator- 
iagram will either not be accurately reduced, or the events 
ill not be properly timed. 

389. The table opposite gives the actual dimensions of the 
rincipal indicators described, as obtained by careful measure- 
ment of those owned by Sibley College. 

390. Reducing-motions for Indicators. — The maximum 
lotion of the indicator-drum is usually less than four inches; 
>nsequently it can seldom be connected directly to the cross- 
^ad of the engine, but must be connected to some apparatus 
hich has a motion less in amplitude but corresponding exactly 

all its phases to that of the cross-head. This apparatus is 
rmed a reducing-motioft. Since the horizontal components 
' the indicator-diagram and consequently its area and form 
-pend upon the motion of the piston, it is evident that the 
-curacy of the diagram depends upon the accuracy of the 
ducing-motion. Various combinations of levers and pulleys 
ave been used* for reducing-motions, a few of which will be 

* Sec Thurston's Engine and Boiler Trials. 



described. Several simply forms of reducing-moti 
given here as suggestions, but it is expected that the : 
will devise other motions if required, and ascertain the j 
of error, if any, in the motion used. 

Fig. 24a.— The Simple Pendulum Reducing-motion 

The cheaper and more easily arranged reducing-m 
consist usually of some form of swinging lever or pen 
(see Fig. 242) pivoted at one point, and connected 
lower end to the cross-head by a lever. The indicati 
is attached to the swinging lever at some point havii 
proper motion. These motions never give an exact re] 


of the motion of the piston ; but if the pendulum and 
head are simultaneously at the centre of the stroke, the 
is very small. 

form of the pendulum-moiion, called the Brumbo pulley, 
}'ientlyused as shown in Fig. 243. The pendulum issotne- 
modiBed, so that its lower ena is pivoted directly to a 

in the cross-head, its upper half moving vertically in a 
:ing tube. The cord is attached to an arc on this tube as 
?. 242. 




The pantograph, or lazy-tongs, as shown in Fig. 244 witi 
plan of method of attachment shown in Fig. 245, is a perfect 
reducing motion, but because of its numerous joints it is no! 
adapted to high-speed engines. 


Fio. 945"— MsTBOD OF ATTAcanrG tmb pAirroGKAra. 

A form of pantograph with four joints only, shown in Fig. 
246, is much better adapted to high-speed engines than the om 
with more numerous joints shown above. 

Fig. ^46.— Method of Using the Pantograph. 

Reducing'Wheels, — Reducing wheels, which consbt of 1 
lar^re and a small pulley (see Fig. 247) attached to the same 
axis, are extensively used by engineers. The method of ittacb 
\x\^ this reducin^-motion to an engine is shown in Fig. 24S. 

391. The Indicator-cord. — The indicator-cord should bei« 
nearly as possible incxtensible, since any stretch of the cor 
causes a corresponding error in the motion of the indicator 
urum. As it is nearly impossible to secure a cord that will not 


Rretch, it should be made as short as possible, and a fine wire u( 
•leeiorironorof hard-drawn brass should be used if practicable. 


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 anpt 
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 ovec 
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 cod. 
yenient form for such a loop, and one that can readily be ad- 
justed, is shown in Fig. 249. The indicator-cord is usually 

Pig. a49.'->THB Loop. 

provided with a hook fastened as shown in Fig. 182, which b 
hooked when diagrams are needed into the loop attached to 
the reducing-motion. 

The author would strongly urge that the indicator-cord bt 
arranged so as to avoid the necessity of frequent hooking aid 
unhooking, thus throwing severe and unnecessar}- strains 01 
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 b pulled 
toward the reducin^^^-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 sat isf actor)'. 
In case of compound engines when numerous indicators are re- 
quired these suggestions become of even greater importance. 

392. Standardization of the Indicator. — The accurac>of 


e indicator-diagram depends upon the following features, all 
which should be the subject of careful examination : 
(i) Uniformity of the indicator^pring. 

(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 

(5) Friction of the piston and pencil-movements. 

(6) Lost motion. 

The calibration of these parts should be made as nearly as 
•ssible under the conditions of actual use and as described 
the following articles. 

393. Calibration of the Indicator-spring. — The accuracy 
the indicator-spring is only to be determined by comparison 
th standardized apparatus. This may be done as follows : 

Firstly : with the open mercury column. This can be done 
th steam only, as the leakage of water past the loosely-fitting 
>ton would render it impossible to maintain the pressure, 
sert the spring; see that the indicator is oiled and in good 
ndition. Attach the indicator as previously explained for 
e calibration of steam-gauges, page 366 ; put paper on the 
um ; turn on steam-pressure until the instrument is warm ; 
m off the steam, and pressing the pencil lightly against the 
iper, turn the drum by hand, thus drawing the atmospheric 
le. Apply pressure by increments equal to one fifth that 
larked on the spring, keeping the motion continually upward, 
lopping only long enough to draw the line for the required 
ressure. Take ten increments first up then down ; the average 
osition of any line will give the ordinate corresponding to 
bat pressure ; the difference between any two lines (see Fig. 
50) will be twice the friction of indicator-piston at that point. 

Second : with the standard scales. This method was devised 
y Professor M. E. Cooley, of Ann Arbor. In this case the 
idicator is supported on a bracket above the platform of the 
ales. Force is applied to the indicator-piston by means of a 
d which can be raised or lowered by turning a hand-wheel ; 
is rod terminates above in a cap nicely fitted to the under 




Side of the piston, and below it rests on a pedestal standing 
the platform of the scales. Any force applied to compress 
spring is registered on the scale beam. The reading of \ 
scale-beam is that force acting on one-half square inch, as i 
piston is usually one-half square inch in area ; this is to be mu 
plied by 2 to correspond with the reading given by the indii 
tor-spring. The indicator can be heated by wrapping ruM 
tubing around the cylinder and passing steam through the tut 
























Ki<~,. aso. — Inuicatok-spking Calibration. 


By comparison with 

Make of indicator 

Mark and No. of spring 






I Inches ; Lbs. 


Ordi nates. 







Actual ^^ 
Pressure. P«*'*' 


e indicator-springs should be calibrated as nearly as possi- 
ider the conditions of actual use. The springs are elon- 
by increase in temperature and weakened because of that 

that the calibration of the spring cold will give results 
differ by approximately 3 per cent, from the calibration when 
ring is at a temperature approximating 212°, as has been 

1 by extended experiments,* 

■rious forms of apparatus have been devised for the testing 
icator-springs both cold and hot. A simple device is shown 

J. 251 consisting of a cylinder, A, supported on a bracket 
a pair of scales and fitted with a piston having an area of 
section exactly the same as the indicator-piston. A rod 
this piston extends downward on to a platform scale, as 
I in the 6gure. The indicator is connected by suitable 

iperiments, Marks and Bairaclough, \'o1. XV, Transattions A. S. M. E. 




piping to the upper end of the cylinder. The steam for th 
pose of calibration is adjusted in pressure by a valve, £, 
it enters the drum, B. The pressure in the steam in the 
is shown on the attached gauge. This steam-pressure 
an upward pressure on the mdicator-piston and a dow: 
pressure on the piston in the cylinder, i4, which latter 
rccted for dead weight, is measured on the weighing- 

A modification of this apparatus is shown in Fig. 
which consists of a vessel, A, into which steam can be adn 


at any desired i)ressure. The pressure in the vessel act! 
the piston, A', which is \ square inch in area and ma 
measured by tlie attached scale-beam. The same pre 
reacts on the indicalor-j)iston. By taking simultaneous i 
ings of the pressure on the piston, A", and on the indu 
j)iston, the calibration may be performed substantial! 

This aj)paratus has proved satisfactory after an cxtc 
use. It can be purchased of SchaelTer & Budenberg of Bnx^ 
N. Y. 


394. Test for Parallelism of the Pencil-movement to the 
Lxis of the Drum. — This is tested by removing the spring 
rem the indicator, rotating the drum, and drawing an atmos- 
heric Hne ; then hold the drum stationary in various positions 
nd press the piston of the indicator upward throughout its 
uU stroke, while the pencil is in contact with the paper. The 
ines thus drawn should be parallel to each other and perpen- 
licular to the atmospheric line. 

Parallelism of the piston-movetnent to the cylinder axis is 
hown when the increments for equal pressure are the same in all 
>ositions of the diagram. It is important that the piston is not 
ramped or pushed over by the spring, in any part of its stroke. 

Friction of the piston and penciUtnovement can be determined 
1 the calibration of the indicator-spring as explained. When 
le spring is removed from the indicator, the parts should 
ork easily and freely but without lost motion. 

395. Accuracy of the Drum-motion. — The accuracy of the 
rum-motion depends on the form of the drum-spring, the 
>ass moved, the length of the diagram, and the elasticity of 
le connecting cord. 

Indicator-drums would revolve in a harmonic motion if 
le inertia of the mass could be neglected. The speed of ro- 
.t:ion is greatest near the half-stroke of the piston ; therefore, 
the drum-spring tension can be adjusted so as to exactly 
>unterbalance the effect of the inertia of the moving parts, 
^e theoretical harmonic motion will be nearly realized. 

In most indicator drum-springs the tension increases directly 
^ proportion to the extension. Since the speed of the drum 
' greatest at half stroke, at this point the drum will run 
head of its theoretic motion if the spring tension is not %uffi- 
^cnt to counteract the eflfect of the inertia of the moving parts, 
therefore if the tension of the drum-spring is adjusted to 
-Xactly balance the effect of inertia at half-stroke, the card 
»lould be as nearly as possible theoretically correct. To ob- 
"^*n the value of this tension, use is made of the formulae for 
he harmonic motion of a body as follows. Let 


time of \ length of card = J of a revolution ; 

i length of card ; 

-—= ; (see Church's Mechanics.) 

IS 39: 

/ = 

s = 

t = 

P = pM = T, where T is the tension in the spring at J the 
length of the card. 

/ = - sa; 

J/ = — = mass of rotating parts ; 

a = 


a = — 



/' = 


T = 



The foot, pound, second system is used in the formulae^ 
The results are shown in the following table. 





Pounds of 


Pounds of 


Force to pull 


Force to pull 


Drum 1.75 in. 


Drum 1.75 in. 


















1. 15 











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, tlion 
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 


nertia etiect will be shown by an increase in the length of the 
liagram. This increase in length may be partly due to stretch 
n the indicator-cord caused by inertia of the rotating parts, as 
:ven with the best tension on the springs, determined as ex- 
>lained, it may be sensibly lessened by the use of wire. A 
imple arrangement, consisting of a pin and connecting-rod 
eading to the face-plate of a lathe, the tool-rest being utilized 
IS a guide, may be used instead of an engine for obtaining 
;omplete determination of this error. The amount of error 
:aused by over-travel of the drum has been found by experi- 
nent to be from 0.5 to 1.5 per cent at 250 revolutions, with the 
»cst tension on the drum spring. 

Uniform Tension on the Indicator -cord. — It is often impor- 
ant to determinewhether the drum-spring maintains a uniform 
ension on the cord, or whether it aJternateiy exerts a greater 

»r less stress; this may be determined by the instrument shown 
n Fig, 253. The testing instrument consists of a wooden 
plate. A, on one end of which is fastened the brass frame, BB, 
carr>'ing the slide, C with its cross-head, D. The head of 
ihe 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 
winging leaf /"holds the paperon which the diagram is to be 
aken. The indicator to be tested is clamped to the plate as 
hown. and the drum-cord connected with the free end of the 
pring. The crank is made to move at the speed at which 
t is desired to test the drum-spring. The paper is then 
^cssed up to the pencil and the diagram taken. If the tenaion 




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 na 
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 stretdi 
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. 280 revolutions 

I ndi c ato r . SOrtvolatlOH 
B • 

Indicator. 100 revolutions 

Indicator. 400 rerobittoiii 

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 tbc 
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 error 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.] 



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- 

Fic 355.— Sbctxon op Crosby Thskb-way Cock. 

Fig. 356.— Elkvatxok of Crosby 
Thrbb-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 exercisedjthat 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. 


194, to which the indicator is attached. The cock is located 
as nearly as possible equidistant from the two ends of the 

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. Direbtions for Taking Indicator-diagjams. 

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 

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 fi"^ 
di?»grams are required. 

When the load is varying, and the average horse-power is 
required, it is better to allow the pencil to remain during 1 
number of revolutions, and to take the mean effective pressure 
from the several diaijrams drawn. 


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. 

Dta^^ram from M Engine 

Oiameter of cylinder 

L.ength 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 


Built by 

Pressure . 

Barometer reads 




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. Partimlar 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 




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 spnng, di}* 
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 H rule 
only one way, but it requires no pounding to get it properly in 
place ; carefully close the box to protect it from dust. 



400. Definitions. — ^The indicator-diagram is the diagram 
iken by the indicator, as explained in Article 378, page 515. 

In the diagram the ordinates correspond to the pressures 
er square inch acting on the piston, the abscissse to the travel 

a^7.— Diagram from an Improved Greene Engine. Cylinder, x6 Inches in Diameter 
^ Inches Stroke. Boiler-pressure, ioo lbs. 8o Revolutions per minute. Scale, 50. 


the piston. During a complete revolution of an engine, 
^wx four phases of valve- mot ioyi which are shown on the indi- 
tor-diagram, viz. : admission, CDE, when the valve is open 
^d the steam is passing into the cylinder; expansion, EF, 
hen steam is neither admitted nor released and acts by its 



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^ 
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, OF, 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 tj the 
atmospheric line, and at a distance from it by scale equal to 
the boiler-pressure snown 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, Dli, is drawn when the steam- valve is open 
and steam is being admitted to the cylinder. 

The Point of Cut-off, P, is the point where the admission 
of steam is stopped by the closing of the valve. It is difficult 
to determine tlie exact point at which the cut-olT takes place. 


It is usually located where the outline of the diag^m 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 CurvCy EFy shows the fall in pressure as the 
steam in the cylinder expands doing work. 

The Point of Release, /% shows when the exhaust-valve 

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 Initial 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 pre.ssure is always measured from the Imc of 
perfect vacuum, hence it is the absolute terminal pressure. 

Admission Pressure is the pressure acting on the piston ;A 
end of compression, and is usually less than initial pressure. 


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 
tlie 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 footol 
area = />z'(i + ^y ^^^ ^)- 

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. 


401. Measurement of Diagrams. — The diagrams taken 
tK on a small scale, they are often irregular, and the boundary 
ines 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 
Ihree-way cock (see Article 398), in which case the two dla- 
^ms will be drawn on the same card as shown in Fig. 258. In 
Ac latter case each diagram is to be considered separately ; that 
I, the area of each diagram, as CDEBFC and GHI/KG, is to 

pi I I I k 

* determined as though on a separate card. The object of 
diagram -measurements is principally to obtain the mean effect- 
»-« pressure (M. E. P.). 

Two methods are practised. 

First, the method of ordinates. In this case the atmos> 
wieric tine AB is divided into ten equal spaces, and ordinates 
^x erected from the centre of each space. The sum of the 
>i^h of these various ordinates divided by the number gives 
W mean ordinate. This multiplied by the scale of the dia- 
Cram gives the mean effective pressure. The sum of the 
ndinates is expeditiously obtained by successively transferring 
*e length of each ordinate to a strip of paper and measuring 
s length. 

Secondly, vnth the planimeter. The planimeter gives the 
«an ordinate much more accurately and quickly than the 


method of ordinates. The various planimeteis are 
described, pages 32 to 55. 

With any planimeter the area of the diagram can 
tained, in which case the mean ordinate is to be fou 
dividing by the length of the diagram. Several of th 
nimeters give the value of the mean ordinate, or M. 

In some instances the indicator-diagram has a loop 
Fig. 2 59, caused by expanding below the back-pressure lii 
this case the ordinates to the loop are negative and shoi 

subtracted from the lengths of the ordinates above. In 
of measurement by the planimeter, if the tracing-point 
made to follow the expansion-line in the order it was dram 
the indicator-pencil, the part within the loop will be cin: 
iicribed by a reverse motion, and will be deducted automaiJc 
by the instrumciit, so that the reading of the planimelr 
be the result sought. 

402. Indicated Horse-power. — Indicated horse-po" 
the horse-power computed from the indicator-diagram, b- 
obtained by the product of M. E. P. (/). length of slroV 
feet (/), area of piston in square inches (a), and number of «>' 
tions {«), as represcnttd in the formula plan -h- 33,000. In 
computation the area on the crank side of the piston i-i' 
corrected for area of piston-rod, and the two ends of thec) 
ders computed as separate engines. Further, in this conip 
tion, it will not in genera! answer to multiply the avH 
M.E.P. of a number of cards by the length of stroke and by 


erage of the number of revolutions, but each card must be 
bjected to a separate computation and the results averaged, 
his can be readily done for each engine by computing a table 
ade up of the products of the average value of n by length 

stroke and area of piston, and for different values of M. E. P. 
om I to 10. Take from this table the values corresponding to 
le given M. E. P., increase or diminish this as required by 
le per cent of change of speed from the average. A very 
mvenient table for this purpose, entitled " Horse-power per 
ound, Mean Pressure," is given in the Appendix to this work, 
ranged with reference to diameter of cylinder in inches and 
ston-speed in feet per minute. 

403. Form of the Indicator-diagram. — The form of the 
dicator-diagram has been carefully worked out for the ideal 
Sse by Rankine and CotterelL* In the ideal case the steam 
orks in a non-conducting cylinder, and all loss of heat is due 

transformation into work, the expansion in such a case being 
liabatic. In the actual case the problem is much more com- 
icated, since a large portion of the heat is utilized in heating 
e cylinder, and is returned to the steam at or near the time 

exhaust, doing little work. It is found, however, in the best 
gines working with quick-acting valve-gear, that the steam 
d back-pressure lines are straight and parallel to the atmos- 
»eric line, and that the expansion and compression lines are 
ry nearly hyperbolae, asymptotic to the clearance line and 

the vacuum line. 

If we denote by/ the pressure measured from the vacuum 

le, and by v the volume corresponding to a distance meas- 

ed from the clearance line, so that pv shall be the co-ordinates 

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- 
ndensible gases, since, according to that law, the pressure 
ries inversely as the volume. 


Steam-engine, by James H. Couerell. 




Rankine found by examination of a great many actual caies 
that the expression pi^ = 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 i 
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 
fi( drawing an hyperbola, the clearance and vacuum fines beiitg 
given, are as follows : I 

First Method. (See Fig, 260.) — CB, the clearance line, and J 
CD, the vacuum line, being given, draw a line parallel to the 

B K_- 

atmosphcric line through B\ find by producing the steam a"^ 
expansion lines the point of cut-off, c. Draw a series « 
radiating lines from tlic point C to the points £, F. G, H.vA 
A, taken at random, and a line cb intersecting these lin* 
drawn from c parallel to BC. From the points of the intc- 
sfction of fiiwith these radiating lines draw horizontal lines to 
meet vertical lines drawn from the points E, F, G, H, W^ 




A ; the intersections of these lines at ^, /, gy A, 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 a, and the 
vertical lines are extended above AB instead of below. 

Second Method, (See Fig. 261.) — The hyperbola may be 
drawn by a method founded on the principle that the inter- 
:epts made by a straight line intersecting an hyperbola and its 
isymptotes are equal. Thus if abed represent an hyperbola, 
3C and CD its asymptotes, then the intercepts aa! and bb' 
lade by the straight line a'b' are equal. 

To draw the hyperbola : Beginning at any point, as a^ draw 

■--^ — . e 

Fig. 26i.^Mkthod of Drawing an Hypkrbola. 

^le straight line a'b\ and lay off from the line CD b'b, equal to 
'a ; then will b be one point in the hyperbola. Draw a similar 
ine (fd' through by making d'c equal c'b ; then will c be another 
>oint in the hyperbola. This process can be repeated until a 
•citable number of points is found ; the hyperbola is to be 
irawn through these points, A similar method can be used 
^o draw the hyperbola EF. 

405. Construction of Saturation and Adiabatic Curves. 
— The saturation curve of steam is represented almost exactly 
t)ythe equation /zHl = a constant. This is the curve whose 






volumes and pressures correspond to those given in the steam- 
tables; no doubt the easiest way to construct such a cun-eis 
to take the volumes from the steam-tables corresponding to 
given pressures and set them off along the volume axis; lav 
off the corresponding pressures as ordinates ; then a curve 
drawn through the extremities of the ordinates will be the ex- 
pansion curve, which, as the form of the equation shows, does 
not differ greatly from an hyperbola. 

The adiabatic curve^ or that corresponding to neither gain 
nor loss of heat, is expressed approximately by/t/V=: constant.* 
and differs somewhat more from the hyperbola than the satu- 
ration curve. 

Any of the exponential curves which are represented by 
the equation /r" =/,7'," = A^'a" ^^^ ^^ drawn as follows: 

From the above expression 

n log 7' + log/ = « log %\ + log/, , 

from which 

log/ = 71 log i\ + log/, — « log t/ ; 

from which, if ;/, t*, , and v are known,/ may be determined. 
The values of ;/ arc as follows : 

Equilateral hyperbola, n -= \ \ 
Saturation curve — steam, 7/ = -[^ = I.0646; 
Adiabatic curve — steam, ;/ = I-035 +O.14; 

" gas, ;/ = 1.408; 
Isothermal " ** ;/ = 1.0. 

These three expansion curvesf are represented in Fig.-''-'* 
tl;e pressures from o to 90 pounds per square inch are repr^ 
senieil f)\' the ordinates, and the volumes in cubic feet cortc- 
spoiKJiiiL^ to one pound in weight are represented by abscis>^ 

* Raiikine's Steam-engine, page 3S5. 

f See Thurston's Engine and Boiler Trials, page 251. 




In the figure the curve A to G is the hyperbola, A to I the 
iaturation curve, and A to L the adiabatic curve. ON is the 
ixis of the hyperbola, of which OB and O// are asymptotes. 
It is to be noticed that the saturation curve corresponds to a 
iniform quality of steam, the adiabatic curve to a condition 
n which the moisture is increasing, and the hyperbolic curve 

1 1 •■ 





:|thm|pT[t ft:i:,'zi:;-_:::. _|^--l_ 

i \ uu\' 

llHJIIlJlll 1 1 Mf^ f "^ ^' ■iriiiH' 

l^tt-'HBji t 



m xo tw 

o a condition in which the moisture is decreasing, the latter 
greeing more closely with the .ictiiaj condition. 

406. Weight of Steam from the Indicator-diagram. — 
The diagram shows by direct measurement the pressure and 
■otume at any point in the stroke of the piston; the weight 
»er cubic foot for any given pressure may be taken directly 
rom a steam-table. The method, then, of finding the weight 
»f steam for any point in the stroke is to find the volume in 
:ubic feet, including the clearance and piston displacement to 
-he given point, which must be taken at cut-off or later, and 
triulliply this by the weight per cubic foot corresponding to 
the pressure at the given point as measured on the diagram, 
i'ht:^ will give the weight of steam in the cylinder accounted 
'' ■r by the indicatordiagram, per stroke. In an engine work- 
ing with compression, the weight of steam at terminal pressure 




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 thenumbff 
of strokes required to develop one horse-power per hourol 

The method of computing would then be : Find the weighi 
per cubic foot, from a steam-table corresponding to the abso- 
lute pressure, at the given point, multiply this by the corrc- 
sponding volume in cubic feet, including clearance, and this by I 
the number of strokes per hour. Correct this for the steal 
imprisoned in the clearance-space. Divide this by the hor» 
power developed, and we shall have the consumption in poun(ii| 
of dry steam per I. H. P. as shown by the diagram. Thus let 

A -= area of piston in square feet ; 

a— ** ** " " " inches; 
iV— number of strokes per hour; 

«= " " ** ** 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 ; /' = 4 -}~ ^'j ^ = correspondin{j 
per cent; 
w' = weight of cubic foot of steam at compression pressurtl 

Then the consumption of dry steam in pounds per hour per] 
horse-power (indicated). 

NAl^, ,, 6ohia{b7u — cw') \'\.7^o\h%v—nv^\ 

H.P.^ ^ 144 plan p 


The above equation corrects for the steam caught in 
clearance spaces during compression. 

As an example: Compute the steam consumption as she 
in Fig. 257 at point of cut-off E and at terminal pressure. 



The absolute pressure shown by the diagram is 97 pounds 
at cut-off and 37 at end of the stroke. Neglect steam in clear- 

The length of stroke total is 3 feet, at cut-off is } foot. 

Clearance is 3.2 per cent. M. E. P. (/) is 50 pounds. 

Steam-consumption at Cut-off. — From steam-table 7f/=o.22o8. 

_ (0.2 208) (0.7 5 +0.09) ^ ,- T TT T. 

5 = 1375Q ^Q ' ^^ = 16.17 IBs. per I.H.P. per hour. 

Steam-consumption at End of Stroke. — From steam-table 
w = 0.0896. 

(0.0896) (3+0.09) „ , ,, ^ 

S = 13,750 -^' ^^^ ^^ = 25.37 lbs. per I.H.P. per hour. 

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+f/'^p, 
in which r is the ratio of the areas of the cylinders, // the M. E. P. 
of the high-, and //' that of the low-pressure cylinder. 

If we consider the steam-consumption only for the end of 
the stroke, /« of equation (i) becomes equal to /, and the equation 
reduces to the following form: 

•5/ = i3>75Ot(i+0 (2) 



Neglecting the clearance, 

5. =13,750-; (3) 

in which / = the M. E. P. of the diagram, and zv 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 ' f 
1 3,750«/, 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 

must be multiplied by the weight of a pound of steam corre- 
sponding to the terminal pressure, to give the steam-consump- 

Williams's tables, published in the Crosby catalogue, give 

values of — -—-y and the results in each case have to be multi- 

plied by 32.32t£/ to give the steam-consumption. 

A graphical correction is made in all cases for compressi'">n 
by drawing a horizontal line through the terminal pressure i-^ 
compression line of diagram, and multiplying the result giv-n 
in the table by the ratio of the portion of this line intcrceptcii 
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 ami 
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: Layoff the vacuum line 
CD (Fig. 207) parallel to the atmospheric line FT, and ai 
a distance corresponding to the atmospheric pressure. The 
position of the clearance line can be determined by twometh(xk I 
corresponding to those used in di awing the hyperbola. ¥1^^* 




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 ab\ to 
meet the vacuum line CD : the point of intersection C will be 

_^'_i V- ii^-0 

Fig. 263. — Methods of Finding thb Clbarancb. 

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 ofl nn equal to mm\ or on the 
line e'f lay ofl ee' equal to ff'\ then will either of the points 
e' or «' 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 




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 Hne at b, and remain below it nearly to the end of the 
stroke. The amount by which the expansion line rises abov; 
the hyperbola may be considered as due ^o re-evaporatlDfi 
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 

C ^^ h' d' 

Fig. 264.— Work Restored by Rb-bvaporation. 

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 methoti 
are approximations which may vary much from the truth. 

409. Discussion of Diagrams. — Diagrams are often taken 



!. In case the valve 

• at K. 

of a compound or 

r in anv noticeable 

_• as already 

springs for 

or exactly 

reduced tj 

bv the fnl- 


le line of 




effects in the drum-motion, which is sometimes sufficient to 
make the compression line concave when it should be conve::^ 
as shown in the lower diagram of Fig. 267. Vertical cuncs 
arc 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 ninninir 
under variable loads, each revolution will show a different d;. 
gram, as shown in Fig. 267. 

Fig. 267.— V'akiai ion uf Luau. 

Differe^U 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 CD and E the valve 
opens late, and after the piston has started on its return stroke. 
In F ?ix\i\ G^ the exhaust-valve closes late, so that live steam 
escapes. H and / are familiar examples of extreme compre- 
sion, produced on high-speed automatic engines working witl'. 
a liglit load. J shows a sharp corner above the compressi^' 

♦ u 

Power, September 1891. 

§ 4IO.] 



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 


Fic. a6S.— Tymcal Admission-links. 

particular from those taken from a simple engine as already 
described. They are usually taken with different springs for 
tlie different cylinders, but may have very nearly or exactly 
tlie same lengths. 

The diagrams from a compound engine may be reduced \.o 
nn 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 




highest steam-pressure acting in the small cylinder. \Ay 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 KGH^r- 
ailel to POQ, intersecting both diagrams, and lay off upon it 
HL ==■ KG] and GL = GH-\- KG represents the total volume 



B C 

G Hy\ 


_/ -^ 

"* ■*•• 






D I 



Fig. a09. 

in both cylinders when the pressure is OG^ and Z 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 CD LM 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 : 2.4-'. 
and the total ratio of expansion is 8. The length of each du- 
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-ofT 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 20a. 




|.ii. Crank-sbaft and Steam-chest Diagrams. — Dia- 
ns may be taken with the motion of the indicator^rum 
)ortional to any moving part of the engine, as for instance 

Fig. 370.-K30MBINBD Diagram from Triple-expansiun Engine. 

[n such a case, shown by Fig. 271 the ordinates will be as 
)re proportional to the pressures per square inch acting on 
piston, but the abscissae will correspond to distances moved 

Fig. 971,— Shaft-diagram. 

)ugh by the crank-pin. In Fig. 271, ^ to ^ is the exhaust, 
xi B to C compression, D to E steam line, E to A expan- 
i. Diagrams may also be taken with the indicator mounted 
the valve-chest ; in this case the indicator would show vari- 
n in pressure in the steam-chest. 



[2. Standards Employed in Engine-testing. — The 

of work ordinarily used in engine-testing is the horse-power 
.), which may be either that shown by the indicator and 
n as the indicated horse-power (I.H.P.), or that delivered 

the engine, which is kno^Mi as delivered or brake horse- 
r (D.H.P.). The horse-power is equivalent to 33,000 
>ounds or 42.413 B.T.U. per minute, or to 1,980,000 foot- 
is or 2545 B.T.U. per hour. 

uel, SUam^ and Heat Consumption, — ^The ordinary standard 
mparison of the economy of the work done by different 
es is the weight of fuel or steam, or the number of B.T.U. 
red by the engine for each horse-power of work indicated 
slivered per hour. The heat consumption, B.T.U. per 

hour, presents the advantages over the others of being 

concise and definite. 

uty. — ^This term is applied to the work performed by pump- 
igines, expressed in foot-pounds, for the consumption of 
K>unds of coal, 1000 pounds of steam, or 1,000,000 B.T.U. 
LTt- 254. 

sr/ec/ Engine, — The performance of a perfect engine is 
endy employed as a standard of comparison. The per- 
ngine is one which transforms all the available heat received 
lot rejected into mechanical work. Such an engine operates 
eversible or Carnot cycle and has a thermodynamic efficiency 
\ — T2)/Tx, in which Ti is the absolute temperature of the 
ng steam and T2 that of the exhaust. 
Kc heat (B.T.U.) consumed per H.P. hour for an engine 
is kind is evidently 

/z=2 545 Ti (Ti-To), 

le least possible weight of steam will be used in the per- 



feet engine when the difference between the heat entering, x, 
and that discharged, g, has all been converted into work. Hence 
the least possible steam consumption per H.P. hour of the per- 
fect reversible engine is 


G = 



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: 


T2^( m 

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 eflicicncy of the steam-engine is expressed in various 
ways as follows: 

1. Thermal Efficiency. — This is the ratio of the work acm- 
allv done (A.W.), expressed in heat units, to the total heat sujh 
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 
ecjuivalcnt of the heat expanded on it to do that work. In the 
Carnot reversible cycle this efficiency equals (Ti — T2)/Ti. 

3. Mechanical Efficiency. — This is the ratio of the work 
actuallv (IcHvercd (D.H.P.) to that done on the piston andsho^^n 
by the indicator (l.H.P.). . 

4. Plant Efficiency. — This is equal to the product of the 
several clVicicncics of the various parts or machines which com- 
pose the plant. 

413. Objects of the Engine-test. —The test may be 
made: i. To adjust the valves or working parts of the engin^' 

2. To determine the indicated or dynamometric horse-po^'^^- 

3. To ascertain tlie friction for different speeds or conditionN 

4. To determine the consumption of fuel or steam per honff 
])ower j)er hour. 5. To investigate the heai-changes ^^^ 


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, eontinuotts counters, and elironographs. 

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 

L CN^ 

instrument, by holding a stick in the hand in such a position 
that it is struck by some moving pan, as the cross-head of an 
engine, once in each revolution. The hand specti-imiicalor, of 
which one form is shown in Fij;. 373. 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 preven. 
this latter error, and the gears are engaged or disengaged with 



the point in contact with the shaft. To prevent slipfiiiii;'.i 
the point, the end of the in^^trunicnt is sometimes tlircadci 
and screwed into ii hole in tlie end of the shaft. 

The continuous couitler consists of a series of geare arrangtii 
to work a set of dials which show the number of revoluiiuti>. 
The arrangement of gearing in such an instrument is shown 
Fig. 274. The instrument can usually be made to register by 
either rotary or reciprocating motion, and can be bad 'm.t 

square or round case. The reading of the counter b take 
stated intervals and the rate of rotation calculated. 

Tachometers (see Fig. 275) are instruments which utilitefl 
centrifugal force in throwing outward either heavy balisfl^ 
liquid. The motion so caused moves a needle a distance^ 
portional to the speed, so that the number of revolutions ii I 
read directly from the position of the needle on the graduslw I 
dial. The tachometer is arranged with a pointed end lo hwj 
against the shaft whose speed is to be determined, or wila 
pulley so that it may be driven by a belt. 


Brozms Speed-indicator consists of a U-shaped tube joined 
to a straight tube in the centre. The revolution of the U-tube 
iround the centre tube induces a centrifugal force which ele- 

Fic. *7S.— ScHAtmn amd Budikbibc Hakd T* 

rates mercury in the revolving arms and depresses it in the 
:entre tube. A calibrated scale gives the number of revolu- 
ions corresponding lo a given depression. 

415. The Chronograph.— The chronograph,* Fig. 276, con- 
iists of a drum revolved by clock-work so as to make a 

number of revolutions per minute. A carnage hav- 
Hg one or two pens, h, g, as may be required is moved parallel 
' See Thurstoa's Engine and Boiler Trials, psgc 136. 


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. 
Two pens are usually employed, one of which registers auto 
matically the beats of a standard clock; the other may bear- 
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 intends 
as short as one one-hundredth (.oi) 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 vibratio.i.v 
The number of vibrations of the fork corresponding to the 
musical tones are as follows : 

Note C D E F G A BQ 

Vibrations ) „ ^ o i 

per second. S '-S '44 i6o 170I 192 213J 240:50 

If now a small point or stylus be attached to one of the 
arms of a tuning-fork, as shown in Fig. 2^6* — in which F'lsom 
of the arms of the tuning-fork, and CAED a piece of clastic 
metal to which the stylus, AP, is attached, — and if the furtc 
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 <^' 
wavy lines, as shown in Fig. 279; the distance between the 

* See Thurston's Engine and Boiler Trials, page 233. 




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 cyUn- 
der, the distance between such marks, 
measuri^d to the same scale as the 
wav>- lines made by the tuning-fork, 
would represent the time of revolu- 

Fig. 278 (from Thurston's Engine 
and Boiler Trials) represents the Ran- 
soi) 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- 
ndcnt Is the same as already described. The form of the 
record being shown in Fig. 279; the wavy marks being those 


e by the tuning-forks, those at right angles being made At 
tend of a revolution of the shaft whose speed is required. 
, The tuning-fork with stylus attached,* as in Fig. 277, can 
k made to draw a diagram on a revolving cylinder connected 

* See Eagine and Boiler Trials, page ■34. 




J 41; 

directly to the main shaft of the engine, or the shaft it»cil 
may be smoked and afterward varnished. If the fotlc Ix 
moved axially at a perfectly uniform rate, the development ol 
the lines drawn will be for uniform motion, straight and >! 
uniform pitch ; but for variations in speed these lines will bf 

curved and at a varying distance apart. From such a diagran 
the variation in speed during a single revolution can bedet«- 

416. Autofi:raphic Speed-recorder.— Variations in spcrf 
are shown autographically in several instruments by recordmj 
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 tht 
shaft whose speed is to be measured. The variation inlht 
height of the balls near B. caused by variation in speed, p'tt 
the arm C a reciprocating motion, so that an attached [wid 
makes a diagram, FED, on the strip of paper moved bj'doct 
work. The ordinates of this diagram are proportional to She 

417. The Surface Condenser. — In the measurement of 
the steam used by the engine the surface condenser is fft- 
quently employed. The surface condenser usually consisU'' 
a vessel in which are a great many brass tubes. It isusu»ll]' 
arranged so that the exhaust steam comes in contact withtte 
outer surface of these tubes, and the condensing water flo»' 
through the tubes. The condensed steam falls to the boItoB 
ol the condenser and is removed by an air-pump : the heat ^ 
the steam being taken up by the condensing water. If'* 
condenser is free from leaks, the air-pump of ample sizew' ' 
with httle clearance, and if the proper temperatures are m"' 



I, nearly all the atmospheric pressure can be removed 
the condenser and the back-pressure on the engine cor- 
ftdingly reduced. 
Vt surface condenser affords more .Tccurate means o{ 

Ung the water<oii sumption of a steam-engine than the 
Itement of feed-water (iiiring a boiler-test. since the 
of steam-leaks are to a great extent eliminated. 
IC condenser should be tested for leaks by noting how 



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 z^ersa, and noting 
whether there is any leakage. 



Duration of test 

Barometer inches lbs. per sq. io. 

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) incb«. 

(IJook-gauge reading)* 

Temperature at weir C F. 

Weight of condensed steam IK 

Hreadth of weir inch*?. 

End area of tubes >q. :. 

Area steam surface s. - 

Area water surface 5 ■'- 

\Vcit;ht steam condensed per hour !:■<. 

Weight condensing water used per hour > 

Weight steam condensed per pound of water - 

Weight steam condensed per sq. ft. steam surface per hour ^ 

Weight steam condensed per sq. ft. water surface per hour "'■'* 

Velocity of water through tubes fl. per f^" 

Heat acquired by condensing water used per hour B. T. ' 

Heat given up by steam condensed per hour R T '^ 


418. Calibration of Apparatus for Engine-testiflg- 

iVjforc commciicin^:^ any important test, all instruments 3"^ 
apparatus to be used should be adjusted and carefully con*- 
pared with standards, under the same conditions as in act- 
practice. The errors or constants of all instruments snouW^c 


oted in the report of the test, and corresponding corrections 
lade to the data obtained. 

The instruments to be calibrated are : 

1. Steam-gauge, — Compare with mercury column, or with 
:andard square-inch gauge, for each five pounds of pressure, 
wading both up and down throughout the range of pressures 
ke!y to be used in the test. (See Article 282, page 366.) 

2. Steam-engine Indicator springs. — Put the indicator under 
3tual steam-pressure (see Art. 393, p. 535) and compare the 
;ngth of ordinate of the card with the reading of the mercury 
3lumn or a standard gauge for the same pressure. Take ten 
.^adings, both up and down, through an extreme range equal 
) two and one-half times the number on the spring. The 
cam-pressure may be varied by throttling the supply and 
jchaust. The ordinate may also be compared by a special 
lethod with readings of a standard scale : the indicator being 
eated by the flow of steam through a rubber tube wound 
round it. 

3. Speed-indicators, — The accuracy can be checked by hand 
Dunting. For the best work chronographs should be used, 
ontinuous counters are necessary for accuracy in a long run. 
ice Articles 414 and 415.) 

4. Indicator Redncing-motion. — This may be tested by divid- 
ig the stroke of the engine on the guides into twelve equal 
arts and noting whether the card is similarly divided. It 
lould be tested for both return and forward stroke. When 
le form of the card is considered, this is an imporU-Tt matter, 
s many reducing-motions distort its shape. (See Article 390, 
age 528.) 

5. indicator-cords and Connections, — See that the connecting 
ords do not stretch at high speeds, and that the drum-spring 
f the indicator has a proper tension and gives a correct motion 
{ the drum. This is important. (See Article 395.) 

6. Weighing-scales, — Compare the readings with standard 

7. Water-meters, — Calibrate by actually weighing the dis- 
harge under conditions of use as regards pressure and flow. 




\n case meters are used, temperatures of the water must be 
taken in order to obtain the weight. (See Article 213, page 

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 specia/ 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 accurac}' 
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 Artides 
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: 



Used on 



Maker's name 

Maker's number 

Scale of SDriner 

Number of spring. 

When tested 

How tested 

F'er cent error 






Error, lbs. 

When Tested. 

How Tested. 



i>#««s*t«%ii Registered 
*^*''**^ Number. 





Read- ' Per Ba- 
ing. rometer. 





419. Preparations for Testing. — The preparations re- 
[uired will depend largely on the object of the test. They 
hould always be carefully made, and in general are to include 
he following operations : 

1. Weighing of Steam. — Prepare to weigh all the steam 
upplied the engine. This may be done by weighing or meas- 
iring all the feed-water supplied the boiler (see Article 375), 
provided there is no waste nor other use of steam ; or it may 
>e done by condensing (see Article 417) and weighing all the 
xhaust from the engine. In the first case especial precaution 
aust be taken to prevent leaks, and in the latter to reduce the 
emperature of the condensed steam to 1 10° F. before weigh- 
n^^ The weights may in some cases be determined from a 
net er- read ing (see Article 214). 

2. Quality of Steam. — Attach a calorimeter (see Articles 33c 
o 336), v/nich may be of the throttling or separator kind, to the 
nair steam-pipe, near the engine. This attachment may be 
Hade by s half-inch pipe, cut with a long thread and ex- 
•ending three fourths across the main steam-pipe. This pipe 


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 supplieil 
If leaks are found, they should be stopped before beginning 
the test. 

4. Indicator Attachments, — Arrange a perfect reducing-mo 
cion. The kind to be used will depend entirely upon circum- 
stances. The lazy-tongs or pantograph is reliable for speeds 
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 Dynaviometcr 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 theamoi:r.: 
and quality of steam and from the indicator-diagram. 

6. Weight of Coal. — This is generally taken during an eni^inc- 
test, but will be treated here as pertaining to boiler-tcsiin^. 
the methods of weighing are fully described under that head 
(see Article 375). 

An engine fitted completely for a test is shown in Fig. 2;:. 
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 brakx 
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 istakenby 
a Brown speed-indicator mounted on top of the brake, andal^o 
by a hand speed-indicator. The steam-pressure is measured 


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 pis*^on-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 
(or 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 

Fill out the following blank spaces. 



I? 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 valv^ *' 






Lap of valve incboL 

Scale indicator-spring 

Piston area sq. ia. 

Steam-port area 

Exhaust-port area 

Diameter fly-wheel inches. 

Clearance, head lbs. wiier. 

crank " 

percent P.D. head. 




« < 

< ( 

• < 



Time .• 

Revolutions : 

Continuous counter 


Gauge-readings : 

Boiler lbs. 

Steam-pipe " 

Steam-chest *' 

Exhaust inches bg. 


Barometer ** 

Temperatures : 

Exteriial air 


Temperatures : 

«« u 


Condensed steam. .. 



Discharge-water. . . . 
Calorimeter : 



Weights : 

Condensed steam.. . 



Calorimeter. . 

422. Special Engine-tests.— Pr^/fW«^?ry 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 com 
puting the data to be obtained from the indicator-diagram> 
The directions are as follows: 

Apparattis. — Throttling calorimeter ; steam-gauge ; two indi- 
cators ; reducing-motion, and indicator-cord. 

I. Obtain dimensions of engines. Measure the clearanct 
see that indicators are oiled and in good condition, and that 


he reducing-motion gives a perfect diagram. Adjust the 
ength of cord so that the indicator will not hit the jstops. Pre- 
pare to take cards as explained in Article 398, page 545. 

2. Take diagrams once in each five minutes, simultaneously 
rem head and crank end of cylinder ; take reading of boiler- 
auge, barometer, gauge on steam-pipe or on steam-chest, 
acuum-gauge if condenser is used, temperature or pressure of 
ntering steam, temperature of room, and number of revolu- 

3. Measure or weigh the condensed steam during run. 

4. From the cards taken compute the M. E. P. and I. H. P. 
3r eacii card as required by the log. 

5. Take a sample pair of diagrams, one from head and one 
-om crank end. {d) Find clearance from diagrams (see Article 
57, page 561) ; (p) draw hyperbola respectively from cut-off and 
please and find re-evaporation and cylinder condensation (see 
Lrticle 408); {c) produce hyperbola from release to meet hori- 
ontal line representing boiler-pressure ; complete the diagram 

ith hyperbola from point of admission. Compute the work 
[. H. P.) from this new diagram. Draw conclusions from the 
)rm of card (see Article 409). 

6. Compute the steam-consumption per stroke and per 
. H. P. at cut-off and at end of stroke from the diagram (see 
Article 406). Compare this with the actual amount as deter- 
lined bv the test. 

7. From the weight of dry steam as shown by the indicator- 
iagram, and the actual weight as determined by the amount 
f condensed steam, determine the quality at cuf off and re- 


8. Make report of test on the following form : 



[)uration of test . . .min. 

Revolutions per min 

Sieam used per min. . lbs 

Barometer in *• 




Piston -displacement 

Clearance (per cent of P. D.) 

Engine constant 

Cut-ofif (per cent of stroke). 

Release (per cent of stroke) 

Compression (per cent of stroke). 

Pressure at cut-ofif 

Pressure at release 

Pressure a^ compression 

Mean efifective pressure 

Revolutions per minute 

Horse-power C. E. ; 

Crank Bnd. 
ca. ft. 







Per Stroke. 


C. B. 


Per Revo-f 


Weight of steam at cut-ofif 

Weight of steam at release 

Weight of steam during compression. . . . 

Re-evaporation per H. P. per hour U«. 

Weight of water per revolution, actual " | 

W^eight of mixture in cylinder per revolution *' 

Per cent of mixture accounted for as steam at cut-ofif 

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 maybe 
convenient ;f from the valve-diagram draw the probable in 
dicator-diagram and compute its area, and from that figure 
the indicated horse-povver.:^ 

* See Valve-gears, by Halsey. D. Van Nostrand Co., N. Y. 
f Valve-gears, by Peabody. J. Wiley & Sons, N. Y. 
t Valve-gcars, by Spangler. J. Wiley & Sons. N. Y. 


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 Unes 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 

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 s 
mark on the floor and which carries a marking point at the 
other end. 

I. Measure dimensions of valves and ports, throw of «*- 
centric, and other dimensions called for by cnginc-Iog, 



2. From these data, with a definite lead assumed, dn* 
valve-diagram, and note position of piston for cut-off, reles«. 
compression, and admission. 

3. Set the valve to the assumed lead, and with angular jJ- 
vance as indicated by the valve-diagram. Turn the engine 
over and sec that the lead is the same at both ends of the 

This requirL-s the engine to be set on its centre; tb;s ii 
done by bringing the piston to the extreme end of the strnl.t 
at either cylinder-end, so that the piston- and connecting-rodi 
form one straight line. As the motion of the piston isvcn- 
slow near the end of the stroke, this position is dctermiiirti 
most accurately as follows : Mark a coincident line on aoiy 
head and guides corresponding to the position of the cnni 
when at an angle of about 30^ measured from its horitotilil 
position ; then, from a fixed point on the floor, swing ibt 
trammel-point as a radius, and mark a line on the circumfocna 
of the fly-wheel ; turn the engine over until the marks agiin 
coincide with the crank on the other side of the centre anJ 
make a second mark on the fly-wheel with the trammel-pomi: 
bisect the distance on the wheel between these marks and ob- 
tain a third line : turn the wheel until this line is shown byli* 
trammel to be at the same distance from the refercnce-poiiti 
on the floor, as the other marks: the engine will then be on 
its centre. Move the valve the proper amount to makf iL< 
position correspond with that shown on the diagram. /«»* 
ti«£' the i-alve remember that to change angular advanit.'^ 
eccentric must be rotated on the shaft; and to etpialisf ernH 
for both ends of cylinder, the valve must be moved on iht 
stem. These adjustments must be made together, as thcyut 
to some extent mutually dependent. 

4. From the valve-diagram draw an ideal indicator-diagnn 
as explained, assuming initial steam-pressure to be (a) ponnib 
per square inch, absolute back pressure 5 pounds absoiute.and 
that expansion and compression curves are true hyperbol 

Calculate its area by formula. 

Area = PVil + log.r) - F.l'll + logX). 


in which V =^ volume at cut-off, and P = corresponding pres- 
sure: K = 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. Frictioc-test. — For this test the engine should be 
ritted with a Prony brake {see Article 169, page 259, to absorb 
and measure the power developed. Indicator-diagrams are 
to be taken and the indicated horse-power computed (see 
Article 40-. 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 horsepower. It is customary to reduce this 
annount 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 
llie 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 machinerj', 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- 

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 TraDMclioni Am. Soc. Mecb. Engiuetrs. Vol. VIII.. page 86- 


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 bj- t 
boiler-test. Article 375 ; the total water consumed, by the leci 
water used in the boiler-test, corrected for leaks and qualil/; 
or by condensing the steam in a surface condenser. Article 41;. 
The quality of the steam should be taken near the engim;, u 
explained in Article 336, page 433. The principal quantilic. 
to be observed are quantities required for a boiler-test, quality oi 
steam near engine, number of revolutions of engine per ininutt, 
and weight of feed-water or weight of condensed steam. That 
observations should be taken regularly and simultancousijr 
once in ten or fifteen minutes, and at the same instant ail in- 
dicator-diagram should be taken. From these data are com- 
puted the quantities required. 

4.26. The Calorimetric Method of Engine-testing.- 
Hirn's Analysis. — The calorimetric method of testing engina 
as developed from Hirn's theory by Professor V. D\vclshauvcf» 
Dery of Lifege 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 b)' 
measuring the pressure, quality, and weight of the steam ; thai 
removed from the engine is obtained by measuring the hcatm 
the condensed steam and that given to the condensing w.itrr. 
The amount of heat remaining in the cylinder per pound o! 
steam at any point after cut-off can be calculated from the Jali 
obtained from the indicator-diagram ; this muItipUed bj tbt 
known weight gives the total heat. 

The heat supplied to the engine added to that i^xKiM 
existing in the clearance-spaces gives the total amount of he»t 
available; if from this sum there be taken the heat i^xistirrg at 
cul-ofi and the heat equivalent of the work done during 
admission, the difference will be the loss during admission, due 

•See Table Properties ol Steam. V. OneUhau vera- Dery, 
M. E., Vol XI. 

. Trans. Am. Sot I 


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 : 


Heat admitted per stroke. . . . 
Weight of steam per stroke . . . 
Absolute pressure of entering 

steam, per sq. inch 

Temperature, degrees Fahr. 

Heat of the liquid 

Internal latent heat 

Total latent heat 

Euality of the steam 
egree of superheat 

Per cent of moisture 

Specific heat of steam of con- 
stant pressure 







I — jr 


Heat equivalent of energy of 
steam in the cylinder at any 

Joule's equivalent 

Reciprocal of Joule's equiva- 

Weight of I cu. foot of steam. 

Vol. of I lb. of sieam, cu. ft. . 

Volume of cylinder to any 
point under consideration 
moved through by the piston 
cu. ft , 

Volume of clearance, cu. ft. . 

External work in foot- pounds 

Vq^. of I lb. of water in cu. ft 









The value of the quantity at any point under discussion i« 
denoted by the following subscripts : clearance, c ; beginning of 
admission, o ; cut-off, i ; release, 2 ; beginning of compression. 


The equations are as follows for wet or saturated steam : 

Heat in the Entering Steam, — 

Q=M{q + xry, 


^ the steam is superheated D degrees, 

Q = M{q+r+c^ (2) 


Heat in the Cylinder. — Since the steam in this case is in* 
variably moist, we have the following equations : 

In the clearance spaces, h^ = Mj^q^ + x^p^ ; . . . I3) 
At admission, A, = M^{q^ + x^p^ ; . . . (41 

At cut-off, A. = (^+^A)(^. + ^.P.); . (5- 

Al release, A, = {M + M.){q^ + xj)^; . (61 

At compression, A, = ^^.(9% + x»Pt) .... {? 

The external work is to be determined from the indicator- 
diagram. Let the heat equivalent of this work be represented 
as follows: 

During admission, AlV^; (|) 

During expansion, AlV^; (o> 

During exhaust, ^^c\ 1*0 

During compression, AW^ (11 

The volume in cubic feet, Vy of a given weight of steam. 
My can always be expressed by the formula 

V = M{xti -{- a)\ (i:' 

in which u equal the excess of volume of one pound of steam 
over that of one pound of water ; u =^ v — cr. 

Substituting the value of u in the above equation, 

V = M(xv + (r{i ^ x)) ^13) 

As (T is a very small quantity, (i — x)<t can be sa'cly 
dropped as less than the errors of observation, and in all piac« 
ice) applications the formula used is 

y= Mxv 114 



In the exact equation (13) or the approximate equation 
(14), if the pressure, weight, and volume of steam are known, 
its specific volume, z/, can be found, and x may be computed. 

At any point in the stroke after the steam-valve is closed. 
the volume and pressure of steam in the cylinder can be 
determined from the indicator-diagram if the dimensions of 
the engine and its clearance are known. If the weight of steam 
used is known from an engine-test, there can be determined 
from the indicator-diagram both the quality and amount of 
heat in the cylinder at any point, with the single exception of 
the steam remaining in the clearance spaces. Thus let V^ 
«qual volume of clearance; F, + Vc volume at admission, 
usually equal to Vc\ V^-{- V^ volume at cut-off ; f^, + F^ , at 
release ; F, + f^^ , at compression ; M, the weight of steam 
used; M^, the weight of steam caught and retained in the 
clearance spaces. Then, by method used in equation (12), 

F, = J/.Ki/, + <r,) ; (15) 

F.+ F, = J/„K//. + (r,); (16) 

V,+ K^{M,+M){x,u,+ <r,); . . . (17) 

K+yc = {M.-^Af){x,u,+ (T;); . . , (18) 

K+K = m.{x,u, + (t;) (19) 

In the above equations we know the volumes and pressures 
#or each point, and the weight of steam, J/, passing through 
the engine. So that in the five equations there are six un- 
known quantities : il/„ , ;r^ , .r„ , .r, , or, , and x^ , of which x^ may 
t>e assumed as i.oo without sensible error. In the above equa- 
"^ions, (15) and (16) are usually identical ; they differ from each 
other only when there is a sensible lead which shows on the 

The weight of steam in the clearance space is computed 
trom equation (15): 

J^. = ( f^c) -^ i^cK + <^c) = Vc-^ XcV, , nearly. 


Assume x = i.oo: 

M.^ Vc^V, (20) 

In computing the Iieat at any point, it is customary to com- 
pute the sensible and internal heat in two operations. Thus 
in equation (4) make //, the total heat, equal to /^, the sensible 
heat, plus H\ the internal heat ; then 

or II,= M,q„ (21) 

If,'= xji,M, ; {li] 

and in equation (5), 

If, = q,{M, + M), ........ (2ji 

H,' = {x,p,){M, + M). (241 

From equation (17), 

M. + M^ i±ii = -£+i^ = ^^•, nearly. PJ 

By substituting in (24), 

which form is used in the computations that follow. 

The analysis determines the loss of heat during a given 
period, by finding the difference between the heat in the cylin- 
der at the bcgiiinin<:^ of the period and the sum of that utilized 
in work during the period and that remaining at the end oi 
tbe period. 

The following directions and example should make the 
method clearly understood. 


The total heat received and discharged per stroke is obtained 
qr testing. The distribution of the heat and its relations to the 
W)rk performed is obtained by measurements from the indicator 
liagram. For this purpose the diagram is divided as indicated 
1 Fig. 282, so that the mechanical .work for the respective periods 
f admission, expansion, release, and compression can be com- 
uted. The heat received at the beginning and discharged al 
le end of each of these periods is compared with the mechanical 

b d 

:^. aSa. — Diagram prom a Grbbnb Enginb. Cylinder, a6 inches in diaubtbr bt 


ork expressed in heat-imits done during that period. From 

Us comparison the amoimt of heat interchanged, plus or minus, 

computed for each period. It is to be noted that work done on 

le forward stroke is positive and that on the back stroke negative. 

427. Directions for Engine-testing by Hirn's Analysis. 

Directions, — i. Make a complete engine- test with a constant 
oad, weigh the condensing water, and measure its temperature 
^ore and after condensing the steam. Obtain the quality of 
le entering steam either in the steam-pipe or steam-chest; if 
^nvenient, make calorimetric determinations of the quality of 


the steam in the exhaust, which may be used as a check on the 
results, but which is necessary In case the exhaust steam is 
not condensed. 

2. Calibrate all the instruments used, and correct all obsa 
vations where required. 

3. From the average quantities on the log. corrcclcd a; 
shown by the calibration, fill out form I, of data and result- 
The steam and condensing water used per revolution to be t; 
vided between the forward and backward strokes of the piaon 
in proportion to the M. E. P. of these respective strokes, 
shown on the log. 

4. Draw on each diagram as explained lines corresponding (o 
zero volume and to zero pressure, and divide the diagrams » 
shown in Fig. 226 into sections, by drawing lines to points A 
admission W, cut-off en, release Oe, and compression od. 

Measure for each diagram the percentages of cut-oH, release 
and compression, calling the original length of the diagrsa 
without clearance 100 per cent. 

5. Measure the absolute pressure from each card and enter 
the averages in blank form No II, using subscripts as follows; 0, 
admission ; 1, cut-off : 3, release : 3, compression ; c, clearanft 

Take from a steam-table the heat of liquid, internal latcnl I 
heat, total latent heat, total heat, and specific volume, cofI^ I 
spending to each of the above pressures. 

6. Compute the volumes in cubic feet for clearance, toti 
volumes, including clearance, at admission, cut-ofT, release, laf 
compression, and place the average results in the props 

7. Compute the area corresponding to each period inu 
which the diagram is divided and find the mean pressure if 
that period. Also find the work done in each period, exprt»^ 
in foot-pounds and also in B. T. U. (It is to be noted Ihittl* 
work done during the return stroke is negative.) Enter tl* 
average of these results in the proper place, noting the usee' 
the subscripts a, b. t, and d. 

8. Calculate the heat-losses as indicated on Form III, whii' 
is an account of the heat used during 100 strokes of the cngif* 


The weight of steam, Mj in pounds is 100 times the amount used 
for one stroke as given on Form I. The weight of steam in 
clearance is to be calculated for admission, pressure, and volume, 
and with x equal I. CO. J/,, to be calculated in the same manner. 
Calculate from known weights and temperatures the heat ex- 
hausted from the engine in the condensed steam AT and in the 
condensing water K. 

Calculate by the formulae, aj explained, the heat supplied 
the engine, and the sensible and internal heat, at each event in 
the stroke of the engine. 

9. Calculate the cylinder-loss at admission as the difference 
between that supplied added to that already in the clearance, 
and that remaining at cut-off added to that used in work. If 
the heat is flowing from the metal, the sign will be negative, 
otherwise positive. 

10. Perform the same operation for each period of the 
engine ; the difference between the heat at the beginning of 
each period and that at the end, taking into account the work 
done, is the loss. 

1 1. Take the algebraic sum of these losses and of the heat 
equivalent of the external work, and if no error has been made 
in the calculations, this sum, which is the total transformation, 
will equal the difference between the heat supplied and that 
exhausted. That is, using the symbols of the analysis, D = D/ 
It is also evident that this quantity is the loss by radiation. 

The importance of this check on the accuracy of the com- 
putations should not be overlooked. If no errors of computa- 
tion are made, in each case the value of D will equal that of ly, 

12. Make the remaining calculations as on Form IV; these 
give the quality which the steam must have at various portions 
of the stroke to correspond with the foregoing calculations. 
The quality is calculated from the volume remaining in the 
Cylinder. Compute the various efficiencies. 

Note that the heat lost during admission is in some respects 
^ measure of the initial cylinder-condensation. 

The following forms are given partially filled out with the 
•"esults of a test made by application of Hirn's analysis. 





Forms for Hirn's Analysis. 


■aoiidi ,u iiMs 



-d-H a 




s^ • ■ ■ ■ 


■dH I 

■J aw 









J- *' 

MaiC«-UO|13i(U| j 

-„,...^, 1 

S s- 1 !i 


■j»p«!tXo j 


'l«qj.(nriis 1 

•ad.diD«is 1 

■iaiKju-aajiriiHia 1 


■»„.«-uo(,»ru, j 

■""--P"J 1 


'lOMlS piWjpOOa 

■u,«,>3mSug ; 




.i«ujpuo3 1 

■16h»q«a 1 


■,«qj>D.BJIS 1 

£ . ; : : 

•«bd-n.«,s 1 


■jsiiog 1 


1 i -Ji 

8 °!i; 


-^ix 1 

1= in 



Form No. I. 



Data and Results. 

Test of sieam-tngine made by at Cornell University, 

Kind of engine, slide-valve throttling. Diameter cylinder. . . . 6.06 inehes. 

Length stroke 8 inches. Diameter piston-rod. . x^ " 

Volume cylinder crank end, 0.X2921 cu. ft.; head end, 0.13354 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 i.ooi 

Quality of steam in exhaust 0.9021 

W^eight of condensed steam per hour 259.92 

Pounds of wet steam* per stroke head, 0.0109707; crank, 0.0109383 

Femperatures 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 0.2x2274 


To denote different portions of the stroke, the following subscripts are used: 
Admission, a; expansion, b\ exhaust, r; compression, d. 

To denote different events of the stroke, the following sub-numbers are used. 
I^ut-off. i; release, 2; compression, beginning of, 3; admission,, beginning of, 
>; in exhaust, 5. Quality of steam denoted by X. 

3ut-off, crank end, per cen^of stroke. . . 20.544. Release, crank end. . 93.958 
3ut-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 39-770 

F*ounds of steam per I. H. P 39.35' 

bounds of steam per brake H. P 55-314 

^. H. P.* Head 3-3152. Crank 3-3054. Total 6.6106 

^rake horse-power 4.71 

* Wet steam is the steam uncorrected for calorimetric determinations. 



[§ 428. 

Form No. II. 







Of Ad- 



SubscriDts used 





Absolute pressure.. ■ rrank 

Heat of liquid {"^rlt^i 

Internal latent heat, j q ^^x\)ii 





Latent-heat cvapo-j Head 
ration. Crank 


^ . . Head 

Total heat ^rank 


., , ., , Head 

Vol. lib. cu. ft....- ^^^^j^ 

C r 

Volumes svmbols 

f'.+ v^ 




y • 

Volumes head. cu. ft 

'^9 ' 

Volumes crank, cu. ft 






Head End. 

Crank End. 

il Wc^k. 


External Work. 



Foot-lbs. B. T. U. 


B. T. (• 















\ ^ . 


* // = y^j^ . Kq = volume in clearance-spaces. 

















rs, •• «o m 00 cb m 

m c« ■• o m o « 

♦ 00 » ro 00 O' ^ 
n r^ 00 O M M «h 
00 •• m >o oo \o ^ 


^ « ^ 00 <«t 

•C 00 00 

M e« N 

'S ? 

??> <>.!!*_<««««« 

O "T «C 00 

00 00 

I I I 


00 « <•• 

«n •■ ^ r« m ■• m 
«^ ^O 'O «• 9> 00 00 
••00 "^ 1^ o M *■ 

M 00 •• 00 m t^ 
(^ e« ^ 00 m 

m 00 m ^ 

♦ C* T •*» 
•« m in « 

I I I - 








.. o. 


VD J^ ^ 






s :^ 


+ -' J ^' + , 







*^ * * " 

,• ^r« ^ ,w -•• ^ ,• « ^ • « ^ 

•n < 5: <: 5: "C <: o«o*oo»«q'^s 








, e 

i> -3 « S 

i i I. ^ 

i - 5 § 

8 E a 2 

« « ^ (« 

V u V u 

^ ^ U) X 

•O w' 


=. %i 

, -o 

• c 

** c 

^ 2 

.5 f 

•) > 

v ^ 

^ «-> 

c « 

U X 

" e 


















e e 


3 3 



» .S 
n c 
ju c 

S 8 .2 .2 - g 

J3 C 

(/) M J) 1^ Ji 


S c 









.„ c 3 r ^ 

a a^ a o 

•O K K C ^ 

r8 l> U u 

.£ <« 






.::: u 

1 ^ S? 

»1 o o 

X U nJ 





















. j2 

I o 

























• • • 

O^ IT 





8 « « n M 


« M »«. Ok tft 


M M fv) m 









n lo «o m 


^ s. 







n <*) M 


<o - 

t^ o> 







S 3 3 3 

« . 








S ft; 















p8 rt 

3 3 































S « 

g C 3 iJ 

.5 .2 s.j's -a 

I -o -c* a - 

« 2i ii S 1 

•rf -f u w ;= 

JssJ i 

(4 f rt (4 (1 

3 i> bi V V 

Ot Z X X X 





^ s ^ 

u C V 

.2 2 c « 

S r- V U 

2 c ii — 

••5 .s *{ e 

w 2 c c 

- .2 .2 S 

(fl w w U 

X P^ Stf H 




>^ 2. 

^ E 

a -if 

3 u 

o e 

< aJ 


7 1 

> . 

t r 


429. Hirn's Analysis applied to Non-condensio^ En- 
gines. — In this case : 1. Determine the weight of water used 
by weighing that supplied the boiler, taking precautions to 
prevent loss of steam between the engine and the boiler by 
leaks. Apply the calorimeter ant! ascertain the quality near 
the engine. The heat in one pound of steam above 32° Falir. 
win be represented by the formula xr -\- q, as previously 
explained. This quantity multiplied by the weight, M, is the 
heat supplied. J/ may be taken for i or for 100 strokes, as 

2. Determine the quality of the exhaust-steam by attaching 
a calorimeter in the exhaust-pipe, close to the engine, The 
heat discharged by one pound will be, as explained in Article 
l\\, x.r,-\- q,: in which the symbols denote quantities taken 
at exhaust-steam pressure. This quantity multiplied by the 
weight, M, is the heat discharged, and is equal to K-\-JC in 
the Form III, page 543. 

3. With these exceptions, the method is exactly as explained 
for the condensing engine, and the same forms are to be used. 

In obtaining the quality of the exhaust-steam, a separating 
calorimeter (see Art. 337) through wliich the steam is drawn 
by suction, can be used with success. 

430. Application of Hirn's Analysis to Compound 
Engines. — Compound engines are usually run condensing, and 
the special directions are for that case: but in case the engine 
is run non-condensing the method of Article 429 can be appUed. 

Directions. — Wilh calorimtttr between the cylinders: 

1. Attach a calorimeter in the exhaust of the high-pressure 
cylinder, and determine the heat exhausted from the high- 
pressure cylinder as explained for non-condensing engines. 

Treat the high pressure cylinder as a simple non-condensing 
engine, as explained in Article 429. 

2. Determine by the calorimeter between the cylinders the 
heat supplied to the low-pressure engine. This quantity will 
be the same as that e.\hausted from the high-pressure, correcteil 
for steam used by the calorimeter and for radiation from the 
connecting pipes. 




W C- 

3. Fill out the forms for each cylinder as a separate engine. 

By using two calorimeters between cylinders the same 
method can be applied to a triple-expansion engine. 

In case the pressure of the steam between the cylinders is 
less than atmospheric a calorimeter can be used by attaching} 
special air-pump and as to secure a flow of steJiE 
through the calorimeter. 

Without calorimeter between the cylinders : 

1. Determine the weight of steam, J/, for both cylinders 
from the condensed steam of the low-pressure cylinder. Tliii 
will give the quantity M. 

2. For the high-pressure cylinder compute the quantilio 
as in Form III, omitting those terms containing A' and A", the 
heat exhausted. 

3. Determine K and A" as follows; A"-|- A" is evidcnlly 
equal to the heat supplied the high-pressure engine, less tht 
heat transformed into work, expressed in B. T. U., less the loss 
by radiation. The total loss by radiation in the whole engine 
is equal to the heat supplied the first cylinder, less the Borl: 
done by all the cylinders, less the heat discharged from the list 
one. As an approximation, divide this total radiation-Iitu 
equally between the cylinders, assuming that the lower ttm- 
perature of the low-pressure cj'linder will offset its increa-tJ 
size. This will give us in Form III the value o{ D = Q- B. 
Compute 5, substitute this value in the equation B = K^ 
K'-\-A\V. Compute A -|- A' and complete the analysis Mr 
the high-pressure cylinder. 

4. For the lozv-pressure cylinder, determine the enterinj 
heat as that discharged from the high-pressure cylinder, A-t-JT- 
plus the assumed radiation as given above. 

Make a complete analysis for each cylinder as explained Iw 
a simple engine, 

431. Him's Analysis applied to a Triple-expansion En- 
gine. — When the quality of the steam between I he cylinJci^ 
can be determined, treat the engine as three separate engii" 
as explained. 



When the quality cannot be determined, treat the case as 
ixplained for a compound engine, as follows : 

1. Find the entire loss as equal to the difference between 
hat supplied to the first cylinder and that discharged from the 
ast, increased by the work done in the whole system reduced 
o thermal units. Divide this by the number of cylinders to 
ind the assumed radiation-loss from each. 

2. Take the cylinders in series, and assume the discharged 
leat to equal the heat supplied, diminished by that transformed 
ito external work, and make a separate analysis for each 
ylinder as explained for a simple engine. 

The following is an application of Hirn*s analysis to a 
riple-expansion engine by Prof. C. H. Peabody at the Massa- 
husetts Institute of Technology. 

The main dimensions of the engine are as follows: 

Diamett. of the high-pressure cylinder 9 inches. 

Diameter of the intermediate cylinder 16 " 

Diameter of ihe low-pressure cylinder 24 " 

Diameter of the piston-rods 2^ " 

Stroke 30 ** 

Clearance in per cent of the piston displacements : 

High-pressure cylinder, headend, 8.83; crank end, Q.76 
Intermediate ** ** 10.4 ** 10.9 

Low-pressure *' ** 11.25 ** 8.84 

The following table gives the data and results of a test 
ith Hirn*s analysis, made by the graduating class: 

uration of test, minutes 60 

3tal number of revolutions 5299 

evolutions per minute 88.3 

eam-consumption duiing test, pounds: 

Passing through cylinders 1 193 

Condensation in high-pressure jacket 57 

in first receiver jacket 61 

in intermediate jacket 85 

in second receiver jacket 53 

in low-pressure jacket 89 


Toul 1538 


Condensing water for test, pounds.. 22S47 

Priming, by calorimeter aois 

Temperatures, Fahrenheit: 

Condensed steam 95.4 

Condensing water^ cold 41.9 

Condensing water, hot 96.1 

Pressure of the atmosphere, by the barometer, lbs. per sq. in 14.8 

Boiler-pressure, lbs. per sq. inch, absolute 155.3 

Vacuum in condenser, inches of mercury 25.0 

Events of the stroke: 

High-pressure cylinder — 

Cut-off, crank end aiqs 

" headend 0.215 

Release, both ends i.oo 

Compression, crank end 005 

** headend aoj 

Intermediate cylinder — 

Cut-off, both ends aag 

Release, both ends i.oo 

Compression, crank end ao3 

*' headend 0.04 

Low-pressure cylinder — 

Cut-off, crank end a59 

" headend 0.59 

Release, both ends i.oo 

Quality of the sieam in the cylinder — (at admission and at compression 
the sieam was assumed to be dry and saturated:) 
High-pressure cylinder — 

At cut-off Xi a7§5 

At release Xt 0.5/) 

Intermediate cylinder — 

At cui-off X| o.S<^^ 

At release x« >J4 

Low-pressure cylinder — 

At cut-off X, m:J 

A'^^^^^^^ ^« heTeSd 

Interchanges of heat betvveen the steam and the walls of the cylinders, 
in B. T. U. Quantities affected by the positive sign are 
absorbed by the cylinder-walls; quantities affected by the 
negative sign are yielded by the walls. 
High-pressure cylinder — 

Brought in by steam Q 132 q: 

During admission Q^, 23^. 

During expansion Q^ — iS .^^ 

During exhaust • Q( — 8.36 


During compression Qi 0.45 

Supplied by jacket Qj 4. 56 

Lost by radiation Qt 1.50 

First intermediate receiver — 

Supplied by jacket Qjr 4.92 

Lost by radiation QtR o. 58 

Intermediate cylinder — 

Brought in by steam (J 131.89 

During admission Qa 13.62 

During expansion Qh — 18.65 

During exhaust Qc 0.22 

During compression Qd 0.44 

Supplied by jacket Qj* 6.82 

Lost by radiation Q^ 2.45 

Second intermediate receiver — 

Supplied by jacket Qjr 4.20 

Lost by radiation Q^r, 1.20 

Low-pressure cylinder — 

Brought in by steam • • Q' 132.14 

During admission Q^' 5.85 

During expansion Qb' — 9.51 

During exhaust Qe* 2.53 

During compression QJ* 0.00 

Supplied by jacket Q' 7.08 

Lost by radiation , Q* 4.34 

Total loss by radiation : 

By preliminary test 2Q« 10.07 

By equation (49) ix.68 

Absolute pressures in the cylinder, lbs. per sq. inch : 

High-pressure cylinder — 

Cut-off, crank end 145*9 

*' headend M3*2 

Release, crank end 41.3 

" headend 41.5 

Compression, crank end 43.7 

" headend 1 48.7 

Admission, crank end 64.5 

" headend 75.3 

Intermediate cylinder — 

Cut-off, crank end 37.2 

" headend 35.0 

Release, crank end 13.6 

'* headend -3.4 

Compression, crank end 16.3 

" headend 17.9 


Admission, crank end ao.4 

" headend 31. i 

Low-pressure cylinder — 

Cut-off, crank end 12. i 

'* headend X3.o 

Release, crank end 5.6 

** headend 5.4 

Compression and admission, crank end 3.7 

headend 4.3 

Heat equivalents of external work, B. T. U., from areas on indicator- 
diagram to line of absolute vacuum : 
High-pressure cylinder — 

During admission, A Wa , crank end 5.71 

" *• headend 6.61 

During expansion, A Wb t crank end xo.65 

•* *• headend laSi 

During exhaust, A IVc, crank end 7.73 

headend 8.0S 

During compression, A fVd , crank end 0.43 

" •* headend 0.62 

Intermediate cylinder — 

During admission, A fVa , crank end 7.53 

** '* headend 7.43 

During expansion, A Wt, crank end 9.54 

** " headend 9.22 

During exhaust, A fVc , crank end 0^" 

** " headend 9.27 

During compression, A IVd , crank end 0.3; 

*• ** headend oto 

Low-pressure cylinder — 

During admission, A IVa^ crank end 7.75 

headend 7.99 

During expansion, y^ Af^A, crank end 6.i3 

" headend 6.S7 

During exhaust, A Wc , crank end 5.0S 

" headend 5.05 

During compression, A IVd , crank end aoo 

** *• headend aoo 

Power and economy : 

Heat equivalents of work per stroke — 

High-pressure cylinder yi ff^ S.44 

Intermediate cylinder , jf ff ' -U 

Low-pressure cylinder AW" ^M 

Total 2:» 

Toul heat furnished by jackets r.p 



Distribution of work : 

High-pressure cylinder i.oo 

Intermediaie cylinder 0.84 

Low-pressure cylinder 1. 14 

Horse-power 104.9 

Steam per horse-power per hour 14.65 

B. T. U. per horse-power per minute 358.3 

The Saturation-curve. — By drawing on the indicator- 
iagram a curve corresponding to the volume of an equal 
weight of dry and saturated steam, the quality may be 
etermined at any point during the expansion, and by calcula- 
ions similar to those used in Hirn's analysis the heat exist- 
ig in the cylinder may be computed. The method of 
rawing the saturation-curve may be explained as follows: 
rst, determine the weight of steam per stroke by the usual 
lethods of engine-testing. Second, find the corresponding 
olume for dry and saturated steam by multiplying the weight 
►f steam per stroke by the volume corresponding to one 
»ound as obtained from the steam tables, for several points in 
he expansion-curve. Third, draw in connection with the 
ndicator-diagram a clearance-line and a vacuum-line in 
Lccordance with the scale of volume and pressure, from which 
nitial measurements can be taken. 

Fourth, determine the volume occupied by the steam 
:aught in the clearance-space when compressed to the steam- 
ine; for this operation we can assume with little error that 
the steam is dry and saturated at the end of compression, and 
that it remains m this condition during compression. Thus 
in Fig. 283 the compression-line is produced from a^ to a 
by drawing a saturation-curve, which is drawn by taking 
^rdinates proportional to pressures and abscissa proportional 
'0 volumes as given in the steam table, those for a^ being 
s^nown. This curve may be considered the curve of volume 
Or dry and saturated compression. Very little error would 
*e made by assuming the compression-curve hyperbolic. By 
roducing the saturation-curve aa^ downward the quality 
Uring compression could be determined. 




Fifth, lay off from the compression-curve for saturated 
steam horizontal distance corresponding to the volume of di)- 
and saturated steam at different pressures, obtained as ex- 
plained above. Through the various points so determined 
draw a curve; such a curve will be the saturation-curve. 

To obtain the quality of the steam at any point en the 
expansion-tines divide the horizontal distance measured fion 
the clearance-line to the expansion-line by the correspond] r; 
distance to the saturation -curve. Thus in Fig. 283 the 

F.O. >8j. 

quality at d, is equal to b^djb,c^ — that is, the quality is tlif 
ratio of the actual volume of the steam to that of dn- and 
saturated steam, and this is true provided the volume occupifd 
by the condensed steam, which is exceedingly small in eve^ 
case, is neglected. The quality at different points dunn;: 
expansion can be determined in a similar manner, and a cunt 
showing the variation of quality may be laid off as shown tn 
the lower portion of Fig, 283. 

The comparative quality during compression can t< 
obtained in a similar manner by comparing the volume durin;; 
compression with that of an equal volume of dry and satunlcd 


The error involved in the above construction is the same 

that made in Hirn*s analysis, since in both cases the 

lality of the steam at end of compression is assumed and the 

Fig. 284. 

»lume of water entrained is neglected ; such errors are, how- 
ler, exceedingly small. Fig. 284 shows the saturation- 
irves of a combined diagram reduced from cards taken on 
ic Sibley College experimental engine. It will be noticed 
lat the saturation-curve is not continuous for the three 




cylinders, which is due to the fact that clearance and com- 
pression of the different cylinders is not uniform. 

To calculate the interchanges of heat in an engine during 
expansion and compression, first determine the quality as 
explained. -Also determine the weight of steam used per 
stroke, the weight of and the rise in temperature of the con- 
densing water. Using the same symbols as for Him's 
analysis, the heat supplied to the engine will be 


that discharged from the engine is equal to the heat of the 
condensed steam above 32® F., Mq^ plus that absorbed by the 
injection-water G{qk — q) that utilized in work A IV. The 



Obtain by measuranent : 

Weight of steam, in pounds 

Weight of injection water, 
in pounds 

Temperature of condensed 
steam above 32° F 

Rise in temperature injec- 

Wt. of steam in clearance . . 

Quality steam entering 

Quality cut-off, release, and 


Quality end of compres'n, % 

Obtain by computation : 

Total heat A/(xr -f </) 

Heat at cul-ofT, 

(.l/-hi^/o)(^i/^. -f ^.) 
Heat at release, 

(J/-f- A/„){x^fJi -f gi) 
Heat at compression. 

Heal discharged, condensed 

Heat discharged, injection 

Heat loss, total 




X\ , X\ ^ and x% 

Mqg = K 
M{qk - qt) = Kx 

Heat transformed into wrrkl 
Admission {a) A W'a = a 

Expansion (^) A IVb = ^ 

Exhaust (<:) A lVc-=. c 

Compression {d) A li'j^d 

Heat'tntef chani^es : 
Admission // — (/A -f j) 

Expansion //| — (//, -f- ^) 
Exhaust iVa — (A'-t- A, -f <^- A'«) 

Compression Hi — {d-\-/it) 

Total loss equals algcbr^c k« 
of heat-interchanges, and :** 
affords a check on the nctst^ 
ical work. 



difference between that received and that discharged is the 
total loss due to radiation. 

The heat remaining in the steam at any point can be 
obtained by multiplying the weight of steam used per stroke, 
increased by that caught in the clearance, by the sum of 
sensible heat and product of internal latent heat and quality. 

The work done while the piston is passing from point to point 
under consideration may be obtained by integrating the 
diagram and reducing to heat-units by dividing by 778. The 
table on the foregoing page indicates the operations to be 
performed in calculating the heat-interchanges by the satura- 

Note. — The method of determining the heat interchanges in a steam 
engine which have been g^iven apply directly to the use of saturated or 
wet steam only. The same general method is applicable when sup)er- 
lieated steam is used, but for that case the relai ion of volume and weights 
»o heat values will be essentially different. 




432. Special Methods of Engine-testing. — Engines em- 
ployed for certain specific purposes, as for pumping water or 
for locomotive service, are constructed with peculiar features 
rendered necessary by the work to be accomplished. In such 
cases it is frequently difficult to arrange to make all the 
measurements in the manner prescribed for the tests of the 
general type of the steam-engine ; further, it is often of impor- 
tance that the amount and character of the work accomplished 
be taken into consideration. To secure results that can safely 
be compared, it is essential that certain methods of testing be 
adopted and that the results be expressed in the same lonn 
and referred to the same standards. 

433. Method of Testing Steam Pumping-engines.--^ 

standard method of testing steam pumping-engines has been 
adopted by the American Society of Mechanical Enfjineer? 
(see Vol. XL of the Transactions). The method is as follows: 


The plant is subjected to a preliminary run, under the con- 
ditions determined upon for the test, for a period of three 
hours, or such a time as is necessary to find the temperature 
of the feed-water (or the several temperatures, if there is more 
than one supply) for use in the calculation of the duty. During 
this test observations of the temperature are made ever)' iifteeo 
minutes. Frequent observations are also made of the spct^ 
length of stroke, indication of water-pressur^ gauges, and othci 



instruments, so as to have a record of the general conditions 
under which this test is made. 

Directions for obtaining Feed-water Temperatures, — When 
the feed-water is all supplied by one feeding instrument, the 
temperature to be found is that of the water in the feed-pipe 
near the point where it enters the boiler. If the water is fed 
by an injector this temperature is to be corrected for the heat 
added to the water by the steam, and for this purpose the 
temperature of the water entering and of that leaving the 
injector are both observed. If the water does not pass through 
a heater on its way to the boiler (that is, that form of heater 
which depends upon the rejected heat of the engine, such as 
that contained in the exhaust-steam either of the main cyHn- 
ders or of the auxiliary pumps), it is sufficient, for practical 
purposes, to take the temperature of the water at the source 
of supply, whether the feeding instrument is a pump or an 

When there are two independent sources of feed-water 
supply, one the main supply from the hot-well, or from some 
other source, and the other an auxiliary supply derived from 
the water condensed in the jackets of the main engine and in 
the live-steam reheater, if one be used, they are to be treated 
independently. The remarks already made apply to the first, 
or main, supply. The temperature of the auxiliary supply, if 
carried by an independent pipe either direct to the boiler or to 
the main feed-pipe near the boiler, is to be taken at convenient 
points in the independent pipe. 

When a separator is used in the main steam-pipe, arranged 

so as to discharge the entrained water back into the boiler by 

gravity, no account need be made of the temperature of the 

^^vater thus returned. Should it discharge either into the 

-atmosphere to waste, to the hot-well, or to the jacket-tank, its 

temperature is to be determined at the point where the water 

leaves the separator before its pressure is reduced. 

When a separator is used, and it drains by gravity into the 
jacket-tank, this tank being subjected to boiler-pressure, the 


temperature of tiie separator-water and jackebwater are eadi 
to be taken before their entrance to the tank. 

Should there be any other independent supply of water, the 
temperature of that is also to be taken on this preliminarytrat. 

Directions for Measurement of Feed-water. — As soon a; 
feed-watcr temperatures have been obtained the engine ii 
stopped, and the necessary apparatus arranged for determin- 
ing the weight of the feed-water consumed, or of the various 
supplies of feed-water if there is more than one. 

In order that the main supply of feed-water may be mcas. 
ured, it will generally be found desirable to draw it from the 
cold-water service-main. The best form of apparatus for 
weighing the water consists of two tanks, one of which rests 
upon a platform-scale supported by staging, while the other is 
placed underneath. The water is drawn from the service-main 
into the upper tank, where it is weighed, and it is then emptied 
into the lower tank. The lower tank serves as a reser\'oir, and 
to this the suction-pipe of the feeding apparatus is connected. 

The jacket-water may be measured by using a pair of small 
barrels, one being filled while the other is being weighed and 
emptied. This water, after being measured, may be thrown 
away, the loss being made up by the main feed-pump. To 
prevent evaporation from the water, and consequent loss on 
account of its highly heated condition, each barrel shouM be 
partially filled with cold water previous to using it for collect- 
ing the jacket-water, and the weight of this water treated as 

When the jacket-water drains back by gravity to the boiler, 
waste of live steam during the weighing should be prevented 
by providing a small vertical chamber, and conducting the 
water into this receptacle before its escape, A glass water- 
gauge is attached, so as to show the height of water inside the 
chamber, and this serves as a guide in regulating the discharge- 

When the jacket-water is returned to the boiler by mesiw 
of a pump, the discharge-valve should be throttled during lh« 
test, so that the pump may work against its usual pressure 

} 432.] 



that is, the boiler-pressure as nearly as may be, a gauge being 
attached to the discharge-pipe for this purpose. 

When a separator is used and the entrained water dis- 
iharges either to waste, to the hot-weli, or to the jacket-tank, 
the weight of this water is to be determined, the water being 
jrawn into barrels in the manner pointed out (or measuring 
:he jacket-water. Except in the case where the separator dis- 
:harges into the jacket-tank, the entrained water thus found is 
ireated, in the calculations, in the same manner as moisture 
ifaown by the caiorimeter-test. When it discharges into the 
iacket-tank, its weight is simply subtracted from the total 
weight of water fed, and allowance made for heat of this water 
ost by radiation between separator and tank. 

When the jackets are drained by a trap, and the condensed 
rater goes either to waste or to the hot-well, the determination 
)f the quantity used is not necessary to the main object of the 
luty trial, because the main feed-pump in such cases supplies 
Jl the feed-water. For the sake of having complete data, how- 
rver, it is desirable that this water be measured, whatever the 
ise to which it is applied. 

Should live steam be used for reheating the steam in the 
nternnediate receiver, it is desirable to separate this from the 
icket-steam, if it drain into the same tank, and measure it 
ndependently. This, likewise, is not essential to the main 
ibject of the duty trial, though useful for purposes of in- 

The remarks as to the manner of preventing losses of live 
team and of evaporation, in the measurement of jacket-water, 
pply to the measurement of any other hot water under press- 
ixe, which may be used foi feed-water. 

Should there be any other independent supply of water to 
be boiler, besides those named, its quantity is to be deter- 
lined independently, apparatus for all these measurements 
ciiig set up during the interval between the preliminary run 
t die main trial, when the plant is idle. 



The duty-trial is here assumed to apply to a complde 
plant, embracing a test of the performance of the boiler it 
well as that of the engine. The test of the two will go M 
simultaneously after both are started, but the boiler-test »HI 
begin a short time in advance of the commencement of tbt 
engine-test, and continue a short time after the enginc>lcstii 
finished. The mode of procedure is as follows : 

The plant having been worked for a suitable time under 
normal conditions, the fire is burned down to a low point and 
the engine brought to rest. The fire remaining on the grate it 
then quickly hauled, the furnace cleaned, and the refuse witi- 
drawn from the ash-pit. The bniler-test is now started, J«l 
this test is made in accordance with the rules for a staniUri 
method recommended by the Committee on Boiler Tests oi 
the American Society of Mechanical Engineers. This melhoi 
briefly described, consists in starling the test with a newfiit 
lighted with wood, the boiler having previously been healed ta 
its normal working degree; operating the boiler in accordifl* 
with the conditions determined upon; weighing coal, »siia 
and feed-water; observing the draught, temperatures of fed 
water and escaping gases, and such other data as may bcii»| 
dentally desired ; determining the quantity of moisture ifl>^, 
coal and in the steam ; and at the close of the test haulingtJej 
fire, and deducting from the weight of coal fired whaK* 
unburned coal is contained in the refuse withdrawn from '■'] 
furnace, the quantify of water in the boiler and the stcam-pre* 
ure being the same as at the time of lighting the fire at tbej 
beginning of the test. 

Previous to the close of the test it is desirable that 
should be burned down to a tow point, so that the unl 
coal withdrawn may be in a nearly consumed state, 
perature of the feed-water is observed at the point wbi 
water leaves the engine heater, if this be used, or at 
where it enters the flue-heater, if that apparatus be ent| 
Where an injector is used for supplying the water, a dedi 


is to be made in either case for the increased temperature of 
the water derived from the steam which it consumes. 

As soon after the beginning of the boiler-test as practicable 
the engine is started and preparations are made for the begin- 
ning of the engine-test. The formal commencement of this 
test is delayed till the plant is again in normal working con- 
dition, which should not be over one hour after the time of 
lighting the fire. When the time for commencement arrives 
the feed-water is momentarily shut off, and the water in the 
lower tank is brought to a mark. Observations are thei made 
of the number of tanks of water thus far supplied, the height 
of water in the gauge-glass of the boiler, the indication of the 
counter on the engine, and the time of day ; after which the 
supply of feed-water is renewed, and the regular observations 
of the test, including the measurement of the auxiliary supplies 
of feed-water, are commenced. The engine-test is to continue 
at least ten hours. At its expiration the feed-pump is again 
momentarily stopped, care having been taken to have the 
water slightly higher than at the start, and the water in the 
lower tank is brought to the mark. When the water in the 
gauge-glass has settled to the point which it occupied at the 
beginning, the time of day and the indication of the counter 
are observed, together with the number of tanks of water thus 
far supplied, and the engine-test is held to be finished. The 
engine continues to run after this time till the fire reaches a 
condition for hauling, and completing the boiler-test. It is 
then stopped, and the final observations relating to the boiler- 
test are taken. 

The observations to be made and data obtained for the 
purposes of the engine-test, or duty-trial proper, embrace the 
weight of feed-water supplied by the main feeding apparatus, 
that of the water drained from the jackets, and any other water 
which is ordinarily supplied to the boiler, determined in the 
manner pointed out. They also embrace the number 01 hours' 
duration, and number of single strokes of the pump during the 
test ; and, in direct-acting engines, the length of the stroke, 
together with the indications of the gauges attached to the 



\% *>1 

force and suction mains, and indicator-diagrams from the stcjtn- 
cylinders. It is desirable that pump-diagrams also be obtained 

Observations of the length of stroke, in the case of direct 
acting engines, should be made every five minutes; observe 
tions of the water-pressure gauges every fifteen minutes; 
observations of the remaining instruments— such as stcaro 
gauge, vacuum-gauge, thermometer in pump-well, thermomc' 
ter in feed-pipe ; thermometer sliowing temperature of engm^ 
room, boiler-room, and outside air; thermometer in flue, thd- 
mometer in steam-pipe, if the boiler has steam-heating suifjct 
barometer, and other instruments which may be used— even 
half-hour. Indicator-diagrams should be taken every half-hour. 

When the duty-trial embraces simply a test of the engint 
apart from the boiler, the course of procedure will be the sane 
as that described, excepting that the fires will not be hauled 
and the special observations relating to the performance of Itt 
boiler will not be taken. 

Directions regarding Arrang(mcnt and Use of tnstrumnu. 
and other Provisions for the Test. — The gauge attached to Ibe 
force-main is liable to a considerable amount of fluctuatioe 
unless the gauge-cock is nearly closed. The practice ol 
choking the cock is objectionable. The difficulty may be 
satisfactorily overcome, and a nearly steady indication * 
cured, with cock wide open, if a small reservoir having an *ir 
chamber is interposed between the gauge and the forcc-miit 
By means of a gauge glass on the side of the chamber and u 
air-valve, the average water-level may be adjusted to thf 
height of the centre of the gauge, and correction for ihi* 
element of variation is avoided. If not thus adju.ited. tbc 
reading is to be referred to the level shown, whatever ite 
may be. 

To determine the length of stroke in the case of dirccucl- 
ing engines, a scale should be securely fastened to the trafflt 
which connects the steam and water cylinders, in a posilion 
parallel to the piston-rod, and a pointer attached to the rodw 
as to move back and forth over the graduations on the scjIe. 
The marks on the scale, which the pointer reaches at thetvD 


ends of the stroke, are thus readily observed, and the distance 
moved over computed. If the len^h of the stroke can be de- 
termined by the use of some form of registering apparatus, 
such a method of measurement is preferred. The personal 
errors in observing the exact scale-marks, which are liable to 
creep in, may thereby be avoided. 

The form of calorimeter to be used for testing the quality 
of the steam is left to the decision of the person who conducts 
the trial. It is preferred that some form of continuous calo- 
rimeter be used, which acts directly on the moisture tested. If 
either the separating calorimeter* or the wire-drawing f 
instrument be employed, the steam which it discharges is to be 
measured either by numerous short trials, made by condensing 
it in a barrel of water previously weighed, thereby obtaining the 
rate by which it is discharged, or by passing it through a sur- 
face-condenser of some simple construction, and measuring the 
whole quantity consumed. When neither of these instruments 
is at hand, and dependence must be placed upon the barrel 
calorimeter, scales should be used which are sensitive to a 
change in weight of a small fraction of a pound, and thermom- 
eters which may be read to tenths of a degree. The pipe 
which supplies the calorimeter should be thoroughly warmed 
and drained just previous to each test. In making the calcu- 
lations the specific heat of the material of the barrel or tank 
should be taken into account, whether this be of metal or of 

If the steam is superheated, or if the boiler is provided 
with steam-heating surface, the temperature of the steam is to 
be taken by means of a high-grade thermometer resting in a 
cup holding oil or mercury, which is screwed into the steam- 
pipe so as to be surrounded by the current of steam. The 
temperature of the feed-water is preferably taken by means of 
1 cup screwed into the feed-pipe in the same manner. 

Indicator-pipes and connections used for the water-cylin- 

* Vol. VII, p. 178, 1886, Transactions A. S. M. E. See page 430 of this 

f Vol. XI, 1890, p. 193, Transactions A. S. M. E. See page 419 of this volume. 


ders should be of ample size, and, so far as possible, free from 
bends. Three-quarter-inch pipes are preferred, and the indi- 
cators should be attached one at each end of the cylinder. It 
f»hould be remembered that indicator-springs which are correct 
\inder steam heat are erroneous when used for cold water. When 
such springs are used, the actual scale should be determined, 
if calculations are made of the indicated work done in the 
water-cylinders. The scale of steam-springs should be deter- 
mined by a comparison, under steam-pressure, with an accurate 
steam-gauge at the time of the trial, and that of water-springs 
by cold dead-weight test. 

The accuracy of all the gauges should be carefully verified 
by comparison with a reliable mercury-column. Similar veri- 
fication should be made of the thermometers, and if no stand- 
ard is at hand, they should be tested in boiling water and 
melting ice. 

To avoid errors in conducting the test, due to leakage of 
stop-valves either on the steam-pipes, feed-water pipes, or 
blow-ofT pipes, all these pipes not concerned in the operation 
of the plant under test should be disconnected. 


As soon as practicable after the completion of the main 
trial (or at some time immediately preceding the trial) the en- 
gine is brought to rest, and the rate determined at which le:k- 
age takes place through the plunger and valves of the pump 
when these are subjected to the full pressure of the force- 

The leakage of the plunger is most satisfactorily determined 
by making the test with the cylinder-head removed. A wide 
board or plank may be temporarily bolted to the lower par. of 
the end of the cylinder, so as to hold back the water in the 
manner of a dam, and an opening made in the temporar\'head 
thus provided for the reception of an overflow pipe. The 
plunger is blocked at some intermediate point in the stroke for. 
if this position is not practicable, at the end of the stroke), and 



the water from the force-main is admitted at full pressure be. 
hind it. The leakage escapes through the overflow pipe, and 
it is collected in barrels and measured. 

Should the escape of the water into the engine-room be 
objectionable, a spout may be constructed to carry it out of the 
building. Where the leakage is too great to be readily meas- 
ured in barrels, or where other objections arise, resort may be 
had to weir or orifice measurement, the weir or orifice taking 
the place of the overfliow-pipe in the wooden head. The ap- 
paratus may be constructed, if desired, in a somewhat rude 
manner, and yet be sufficiently accurate for practical require- 
ments. The test should be made, if possible, with the plunger 
in various positions. 

In the case of a pump so planned that it is difficult to re- 
move the cylinder-head, it may be desirable to take the leakage 
from one of the openings which are provided for the inspection 
of the suction-valves, the head being allowed to remain in 

It is here assumed that there is a practical absence of valve- 
leakage, a condition of things which ought to be attained in all 
well-constructed pumps. Examination for such leakage should 
be made first of all, and if it occurs and it is found to be due 
to disordered valves, it should be remedied before making the 
plunger-test. Leakage of the discharge-valves will be shown 
fcy water passing down into the empty cylinder at either end 
A\hen they are under pressure. Leakage of the suction-valves 
AA'ill be shown by the disappearance of water which covers 

If valve-leakage is found which cannot be remedied, the 
cjuantity of water thus lost should also be tested. The deter- 
ination of the quantity which leaks through the suction-valves^ 
here there is no gate in the suction-pipe, must be made by 
indirect means. One method is to measure the amount of 
'v\.'ater required to maintain a certain pressure in the pump 
cr;ylinder when this is introduced through a pipe temporaril) 
^ rected, no water being allowed to enter through the discharge^ 
V-^ves of the pump. 


The exact methods to be followed in any particular case, io 
determining leakage, must be left to the judgment and ingcnu. 
ity of the person conducting the test. 


In order that uniformity may be secured, it is suggested 
that the data and results, worked out in accordance with the 
standard method, be tabulated in the manner indicated in the 
following scheme: 

Duty-trial of Engine. 


I. Number of steam-cylinders •• 

3. Diameter of steam-cylinders ios. 

3. Diameter of piston-rods of steam-cylinders ins. 

4. Nominal stroke of steam-pistons fi« 

5. Number of water-plungers 

6. Diameter of plungers • ins. 

7. Diameter of piston-rods of water-cylinders ins. 

8. Nominal stroke of plungers ft 

9. Net area of plungers sq. iflS- 

10. Net area of steam-pistons sq ini 

11. Average length of stroke of steam-pistons during trial fi. 

12. Average length of stroke of plungers during trial ft. 

(Give also complete description of plant.) 


13. Temperature of water in pump- well degs. 

14. Temperature of waier supplied to boiler by main feed-punnp. dcgs. 

15. Temperature of water supplied to boiler from various other 

sources degs. 


16. Weight of water supplied to boiler by main feed-pump lbs. 

17. Weight of water supplied to boiler from various other sources, lbs. 

18. Total weight of feed-water supplied from all sources. lU- 


Ig. Boiler- pressure indicated by gauge lbs. 

20. Pressure indicated by gauge on force-main lbs. 

21. Vacuum indicated by gauge on suction-main ins. 

22. Pressure corresponding to vacuum given in preceding line lbs. 

23. Vertical distance between the centres of the two gauges.. ... ins. 
14. Pressure equivalent to distance between Uie two gauges. UiP* 




Miscillaneous Data, 

35. Duration of trial hrs. 

26. Total number of single strokes during trial 

27. Percentage of moisture in steam supplied to engine, or num- 

ber of degrees of superheating ^ordeg; 

38. Total leakage of pump during trial, determined from results of 

leakage-test lbs. 

29. Mean effective pressure, measured from diagrams taken from 

steam-cylinders M. E. P. 

Principal Results, 

30. Duty ft.-lbs. 

31. Percentage of leakage % 

32. Capacity gals. 

33. Percentage of total frictions % 

Additional Results* 

34. Number of double strokes of steam-piston per minute 

35. Indicated horse-power developed by the various steam- 

cylinders I. H. P. 

36. Feed-water consumed by the plant per hour lbs. 

^ 37. Feed-water consumed by the plant per indicated horse-power 

per hour, corrected for moisture in steam lbs. 

38. Number of heat-units consumed per indicated horse-power per 

hour B. T. U. 

39. Number of heat-units consumed per indicated horse-power per 

minute B. T.U. 

40W Steam accounted for by indicator at cut-off and release in the 

various steam-cylinders lbs. 

41. Proportion which steam accounted for by indicator bears to 

the feed-water consumption 

Sample Diagrams taken from Steam-cylinders, 

[Also, if possible, full measurements of the diagrams, embracing pressures 
at the initial point, cut-off, release, and compression ; also back- pressure, and 
the proportions of the stroke completed at the various points noted.] 

42. Number of double strokes of pump per minute 

43. Mean effective pressure, measured from pump-diagrams M. E.P. 

44. Indicated horse-power exerted in pump-cylinders. I. H. P. 

* These are not necessary to the main object, but it is desirable to give thetn. 


Sample Diagrams taken from Pump^yUnders. 

Data and Results of Boiler-test. 

[in accordance with the scheme recommended by the boiler-test 

commutes of the society.] 

1. Date of trial 

2. Duration of trial hrs. 

Dimensions and Proportions, 

3. Grate-surface wide long Area sq.ft. 

4. Water-heating surface sq. ft. 

5. Superheating-surface sq. fL 

6. Ratio of water-heating surface to grate-surface 

(Give also complete description of boilers.) 

Average Pressures, 

7. Steam-pressure in boiler by gauge lbs. 

8. Atmospheric pressure by barometer lbs. 

9. Force of draught in inches of water ins. 

Average Temperatures, 

10. Of steam degs. 

11. Of escaping gases degs. 

12. Of feed-water 


13. Total amount of coal consumed * lbs. 

14. Moisture in coal . . % 

15. Dry coal consumed lbs. 

16. Total refuse (dry) lbs. 

17. Total combustible (dry weight of coal, item 15, less refuse, 

item 16) lbs. 

18. Dry coal consumed per hour lbs. 

Results of Calorimetric Test, 

19. Quality of steam, dry steam being taken as unity 

CO. Percentage of moisture in steam ^ 

21. Number of (it* j^rees superheated degs. 

* Including equivalent of wood used in lighting fire. One pound of '^^'>'' 
equals 0.4 of a pound of coal, not including unburned coal withdrawn from fire 
at end of test. 



93. Total weight of water pumped into boiler and apparently 

evaporated * lbs. 

23. Water actually evaporated corrected for quality of steam lbs. 

34. Equivalent water evaporated into dry steam from and at 

212' F.f lbs. 

3f. Equivalent total heat derived from fuel, in British thermal 

units B.T.U. 

26. Equivalent water evaporated into dry steam from and at 

212° F. per hour lbs. 

Economic Evaporation, 

37. Water actually evaporated per pound of dry coal from actual 

pressure and temperature lbs. 

28. Equivalent water evaporated per pound of dry coal from 

and at 212° F lbs. 

29. Equivalent water evaporated per pound of combustible from 

and at 212° F lbs. 

50. Number of pounds of coal required to supply one million 

British thermal units lbs. 

Rate of Combustion, 

31. Dry coal actually burned per square foot of grate-surface per 
hour lbs. 

Rate of Evaporation, 

32. Water evaporated from and at 212* F. per square foot of 

heating-surface per hour lbs. 

To determine the percentage of surface moisture in the coal 
a sample of the coal should be dried for a period of twenty- 
four hours, being subjected to a temperature of not more than 
212°. The quantity of unconsumed coal contained in the 
refuse withdrawn from the furnace and ash-pit at the end of the 
test may be found by sifting either the whole of the refuse, or 

* Corrected for inequality of water-level and of steam-pressure at beginning 
and end of test. 

f Factor of evaporation = — , H and k being, respectively, the toul 

heat-units in steam of the average observed pressure corrected for quality, 
and in water of the average observed temperature of feed. 


a sample of the same, in a screen having f-inch meshes. This^ 
deducted from the weight of dry coal fired, gives the weight 
of dry coal consumed, for line 15. 

Results of actual trial, as illustrated by the committee, 
would be computed by the use of the following formuls : 

Foot-pounds of work done 
'^ ~" Total number of heat-units consumed ' ' 

= -jr X 1, 000,000 (foot-pounds). 

C X 144 

2. Percentage of leakage = . y. ^ X 100 (per cent). 

3. Capacity = number of gallons of water discharged in 24 


__ A X Lx Nx 7.4805 X 24 
"" /^ X 144 

A xLx Nx 1.2467s , ,, . 
= -^ (gallons). 

4. Percentage of total friction 

/ jjfp __ A(P±fi+s)xLxN ^ 
I ■ ' * Z> X 60 X 33»ooo 
= V fJTP. / X '«> 


r A(P ±px s)x Lx Nl , . 

= I — —. T-^r^rr- — r Tr " X lOO (per cent) ; 

L A,x M,E.P. X L,X N,J ^ ' 

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 — 

Percentagre of total frictions = ^~' a\( M FP P^ '^^(p.c) 


In these formulae the letters refer to the following quanti« 

> . 

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 bj 
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 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. 

L = Average length of stroke of pump-plunger, in feet. 

iV^= 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, x M.E.P.^ 
in an engine having more than one cylinder, is 
the sum of the various quantities relating to the 
respective cylinders. 

Lg = Average length of stroke of steam-piston, in feet. 

Ng = Total number of single strokes of steam-piston 
during trial. 
\EJ^. = Average mean effective pressure, in pounds pel 


square inch, measured from the indicator-diagrams 
taken from the steam cyh'nder. 
I.H.P. = Indicated horse-power developed by the steam- 
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 -|- 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 prodi;c: 
by 100. For superheat, the correction is added, 
and is found by multiplying the number 01 
degrees of superheating (i.e., the excess of the 
temperature of the steam abov^e 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 stean- 
reheater connected with the intermediate receiver 
of the engine, this heat must be included i^ ^^^ 
total quantity supplied by the boiler. 
The following example is one of those given by the rom' 


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. — Cofnpound Fly-wheel 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- 


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-plu