title: Dynamometers,
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A v >■ c'v ♦ V > / V> » v > A \ v 0 N c "Ap * * AV * V 1 B f J „fN *P .'V V ^ ^0' ^ 3 N 0 > \ ^ s"'!** V v x V ^ ^ .o * : ^ ^ \0 o A *<> v>^ V o o x V v» J . * « , 0 O y * * \ V ^ < Z^//i\j^P % ^ ^ / 0%’ c^r *- ' ' ' v X y V X ^ ' * 0 A > X 0 v /jaVa V ^ ^ * **■ ' 1.. ® V ® i? *w 2 j ° </\ © * "' ' S s ^ . . . %> y 0 * A. &'"• ^ v - - ■> <V </^ V \V * Cs ^ / *-.W^./ ' V A .v, %,'-‘V ^ ** /J)J0 * A O 'y ; A- V vl 0 O * 0 V S S T /y C> A - ^ aV ^ iP ,\V > ^ A yV DYNAMOMETERS DYNAMOMETERS BY REV. FREDERICK JOHN JERVIS-SMITH, M.A., F.R.S. EDITED AND AMPLIFIED BY CHARLES VERNON BOYS, F.R.S. NEW YORK D. VAN NOSTRAND COMPANY 25 PARK PLACE 1915 Printed in Great Britain EDITOR’S PREFACE In completing and preparing for the press the unfinished manuscript of the author, I have had the advantage from long and intimate association with him of knowing his views on the subject generally. Unfortunately I had not had any dis¬ cussion with him upon the scheme of his book, and where the parts succeed one another in a manner which is somewhat disjointed I do not know whether he intended to introduce paragraphs which would connect these part©. From his table of contents I have learned without doubt the order he intended to follow, and to this I have adhered faith¬ fully. I have occasionally made minor corrections or explana¬ tions where I thought them desirable, and these are not indicated. Additional paragraphs are indicated by square brackets [ ], For any faults in these the author was in no way responsible. I have not thought it necessary or desirable to abstract every printed account of a dynamometer which I have found, but I have described in sufficient detail some for which he had left blank spaces, and a number of others which seemed to me to be of sufficient interest. My regret is that I may have overlooked so many that should have been included. It has been a pleasure to me to do my best to complete this book; for it shows how the author from the time that he was acting as his father’s curate at Taunton, and while he was Millard Lecturer on Mechanics at Oxford, devoted himself consistently to the science and art of dynamometry, and in that time devised and constructed nearly every known type of instrument, in many cases being the pioneer. C. V. B. OBITUARY NOTICE (From the Proceedings of the Royal Society.) FREDERICK JOHN JERVIS-SMITH, 1848—1911. The Reverend Frederick John Jervis-Smith, the only son of the Reverend Prebendary Smith, of Taunton, was born at Taunton on April 2, 1848. He was educated at Pembroke College, Oxford. While still a boy at home he had the great advantage of meeting constantly William Ellis Metford, by whom his natural aptitude for science and mechanics was stimulated so that his genius, which was so marked in these directions, forced him at a later date to break away from the narrower life which his father wished him to follow. In obedience to this wish he entered the Church and acted for some years as his father’s curate and organist, becoming later Vicar and Patron of the living of St. John’s, Taunton. It must have been at this time also that with the help of Sir John Stainer he attained that knowledge of music and skill at the organ and piano that his friends so greatly admired, for a touch such as his could not have been acquired in later life. While at Taunton he followed the bent that was so strong in him and carried on experimental work in his own workshop, acquiring by various means an intimate knowledge of workshop practice such as the amateur rarely possesses. In 1886 he was invited to take charge of the Millard Engineering Laboratory attached to Trinity College, Oxford, and it was here that his best work was done. A good indication of the variety of Jervis-Smith’s investiga¬ tions may be found by reference to the Philosophical Magazine in the twenty years from 1882 to 1902. The subject to which OBITUARY NOTICE viii he devoted himself most particularly was that of work-measuring machines and integrators, and many of the papers are on this subject. Several papers refer to the measurement of the torsion of rotating shafts with a view to determine the power being transmitted, and one of his early papers describes the means now adopted on large steamships, where, owing to the engines being turbines, indicated power cannot be ascertained and the torsional method is the only one available. Other enquiries which interested him were the magnetic properties of metals as affected by mechanical stress or by heat ; electric sparks and the influence on them of flame or pressure. Under this heading, probably, should be mentioned his beautiful electrically produced images of coins that he called inducto- script. One of the most valuable results of Jervis-Smith’s ingenuity and mechanical aptitude is his tram chronograph. Those who have used the old pendulum myographs so usual in physiological laboratories, where the time records are rendered tiresome by the variable speed of the recording surface, should be the first to appreciate this beautiful instrument, in which trouble from this cause is entirely eliminated. A still greater value has been given to this instrument by the perfection of the electro¬ magnetic styles that he invented and made. By making his electromagnets extremely small and the yoke relatively short and thick he reduced the latent period, so that this chronograph is now not only the most convenient but the most accurate instrument for ballistic and other measurements of the kind. Other subjects of less interest perhaps in which Jervis-Smith made investigations or inventions were in relation to mer¬ cury pumps and means for raising the mercury continuously and automatically, quick distillation of mercury in vacuo , recalescence of iron, and high resistances made of graphite and plaster of Paris. During the last few years since his retirement to his charming house near Lymington Jervis-Smith was greatly interested in glowing phenomena in vacuous bulbs moved or spun in electric OBITUARY NOTICE ix and magnetic fields. On these he made numerous original experiments, but up to the present these results are not well understood. Jervis-Smith was awarded a medal at the Paris Exhibition of 1878 for a dynamometer, and at the Inventions Exhibition at South Kensington he was awarded a silver medal for his work on dynamometers! He also received a medal from the Royal Humane Society for rescuing a person in danger of being drowned. He was a member of the Committee on Explosives appointed by the Home Office in 1895—96. He became a Fellow of the Royal Society in 1894. He was keenly interested in the historical side of Physical Science, and often brought to light curious anticipations of more recent inventions. He found, for instance, that the tele¬ phone had been made and described in Italy as an instrument for recording taps upon it by movement at the receiving end. The former inventor had apparently invented the same instru¬ ment as Bell, but he never thought of speaking into it. This historical appreciation made the selection of Jervis-Smith to represent the University of Oxford at the tercentenary of Torricelli at Faenza in 1898 singularly appropriate. Throughout his career one subject was constantly receiving his attention, and that was dynamometry in its widest sense. On this he had been collecting papers all his life, and in his later years he was putting these in order in the hope of seeing the great work completed which had gained so much from his originality. It is hoped that this will appear this year. He married Annie Eyton, second daughter of T. Taylor, Esq., who with one surviving son remains to mourn his loss. The singular charm, humour, and modesty of Jervis-Smith, no less than his genius, made his friendship a valued possession. The writer of this notice found in addition a community of taste and a mutual sympathy, and he has lost his closest and most valued friend and counsellor. C. Y. B. CONTENTS PAGE Editor’s Preface ........ v Obituary Notice .vii CHAPTER I Introduction Importance of dynamometric tests—Ergometer—Gravity, Fric¬ tional and Transmission Dynamometers—Ideal gravity method—Smeaton : Wind-mill test—Unit of work: the inch- ounce—De Borda—Atwood—Watt, and Farey on Watt— Horse-power unit of Watt—Horse-power first mentioned— Sliding rule : Watt—Edgeworth : his method applied to modern vehicles—Poncelet on Coulomb: The work done by man—Work done in unloading ships—Gravity test of engine — Hirn : his band machine — Joule’s gravity method — Acknowledgment to authors and institutions ... 1 CHAPTER II Friction The laws of friction—References to authors of researches on friction —Experimental determination of friction, and table of results—Method of least squares applied to the calculation of the coefficient of friction — Diagram on square ruled paper deduced from experimental results—[Graphic treat¬ ment preferable in certain cases]—[Logarithmic and semi- logarithmic ruled paper]—Graphic method of showing the value of friction between a band and a pulley. (Cotterill’s method)—Mechanical method of drawing the equiangular spiral, by the author—Coefficient of friction between band T and pulley, equation == e ^ e —[Use of Dr. Roget’s log log slide rule for calculating e ^ e ]—Automatic machine by the author for finding the friction of a belt on a pulley—Experi¬ ments by Imray—Experiments by the author—[Simple experiment with umbrella and tape]—[Use of bollard friction in drawing wire]—[S. G. Brown’s mechanical relay]—[Dr. J. G. Gray’s use of mechanical relay]—[Lateral friction] 17 xii CONTENTS CHAPTER III Planimeters PAGE The earliest application of the area method of finding the product of force and space : the Watt-Southern steam engine indi¬ cator—Recording apparatus used in conjunction with work¬ measuring machines—General Morin and Ernst integrator— Disc and roller—Ashton and Storey steam engine integrator —Record of work on paper band—Application of method by Mr. A. Denny and by Herr Frahm—Two integrators by the author—The area of a figure, how found—References to authors of papers on integrators and planimeters—Description of the Amsler planimeter, showing how areas are integrated mechanically, with Henrici’s explanation — Mechanical integrator by the author, applied to power-measuring machines—[The steam engine power integrator of Boys]— Example of application of the planimeter to diagram from model ship dynamometer, Admiralty experimental works .......... 44 CHAPTER IV Friction Brakes Some early applications of coiled ropes (Horner)—Bollards and hawsers—Resistance due to coils of rope on a cylinder—Sir Christopher Wren’s “ Engin ”—The rope dynamometer brake —Equation for the rope brake—W. Thomson’s (Lord Kelvin) application of the coiled rope as a dynamometer brake—. Abstract of Thomson’s patent: this brake invented in connection with laying the Atlantic cable—Unwin’s dynamo¬ meter—Society of Arts motor trials, use of the rope brake —Modification of Thomson’s brake by Capt. Sankey—Rope brake at the City and Guilds Technical College, London— Friction brake formerly at Cooper’s Hill College, showing method of cooling—Dynamometers by James Thomson, Imray, Carpentier, Raffard, Reckenzaun, Scheibe — Block brake dynamometers, by Prony, Coope, Appold and Amos, Balk, Garrett and Sons (water-cooled brake wheel), [Griffin Engineering Co.]—[Alden dynamometer]—[Nicholson’s lathe tool dynamometer] ........ 67 CHAPTER V Water Brakes Historical — Hirn — Perry — Reynolds — Froude—Heenan and Froude—Brotherhood ....... 95 CONTENTS xiii CHAPTER VI Am Brakes page Walker—[Renard]—[Morgan and Wood]—[White and Poppe]— [Logarithmic chart of air brake]—[Observations on air brake] 113 CHAPTER VII Magnetic Brake Dynamometer Arago’s observation—Foucault’s observation — Violle’s measure¬ ments— Morris and Lister . . . ..  — [Froude’s lecture at the Royal Institution]—[Osborne Reynolds and critical velocity] . . . . .128 CHAPTER X Transmission Dynamometers The function of this type of dynamometer—A. Morin : Translation from the French of his description of original dynamometers : Ernst’s integrator—Dynamometers of Messrs. Easton and Anderson — William Froude — Jervis-Smith — Dynamic weighing by Taring—Dynamometers of Ayrton and Perry, F. Von Hefner Alteneck, Matter, King, [Boys], Bourry, Megy, Ruddick, Valet, Neer, Latchinoff, Tatham, Farcot, Parsons, Saurin, Dalby, [Amsler], [Moore]—[Worm testing machine of Lanchester]—[Draw-bar dynamometers] . .144 CHAPTER XI Torsion Power-measuring Machines or Torsion Meters The necessity for this kind of power measurer—Remarks by Mr. Archibald Denny—The principle underlying the con¬ struction of torsion power-measuring machines—Method of calculating the torsion, the transverse elasticity G being known—Experimental determination of G for a small rod .......... 190 XIV CONTENTS CHAPTER XII Torsion Power-measuring Machines of Different Inventors page Him—Jervis-Smith—Mechanical and optical methods of reading the angle of torsion—The rotostat—Lord Rayleigh : quota¬ tion on this subject—Application of the rotostat for comparing the speed of two engines—Jervis-Smith : Another optical method of reading the angle of torsion, and an electrical method of reading the torsional angle—Mr. Archibald Denny on the electrical method of reading the torsional angle— H. Frahm’s torsion meter — The torsion meter of Dr. Fottinger, with efficiency and power diagrams—The Denny- Johnson torsion meter—The torsion meter of Hopkinson and Tliring — [Dr. Alfred Amsler’s torsion meter, with comments by H. H. Broughton]—[Fritz Lux]—[Johnson]— [Thurston] . ....... 195 CHAPTER XIII The Cradle Dynamometer Jervis-Smith : Ergometer for small electromotors—The cradle dynamometers of C. F. Brackett and Dr. Drysdale—Marcel Deprez: knife edge suspension—The cradle dynamometer of Davis and Shaw ........ 218 CHAPTER XIV Dynamometric Tests of Motor-car Engines and High Speed Internal Combustion Engines. Peculiar difficulties and necessity for flexible couplings—Use of calibrated dynamo—“Milling machine” supports—[Insta¬ bility of speed with friction brakes] — [Dr. W. Watson’s investigations] — [Wimperis accelerometer for brake horse¬ power tests of motor-car engines]. 223 CHAPTER XV Ship Model Dynamometer Froude’s original researches—Admiralty tank and equipment at Haslar—List of other tanks. .236 CHAPTER XVI The Aeronautic Dynamometer National Physical Laboratory apparatus—Vickers, Sons and Maxim’s apparatus 247 ILLUSTRATIONS PAGE 1. Smeaton’s Whirling Machine ..... 6 2. Hirn’s Dynamometer, modified by the Author. 12 3. Diagram of Curve of Friction on Square-ruled Paper 24 4. [Semi-Logarithmic Chart] ...... 27 5. Professor Cotterill’s Graphic representation of the Friction of a Belt on a Pulley .... 29 6. Automatic Friction Machine by the Author. 33 7. Graphic Representation of Naperian Logarithms. 35 8. Regulation of Arc of Contact ..... 35 9. [Diagram of S. G. Brown’s Mechanical Relay]. 40 10. The Watt-Southern Indicator ..... 45 11. The Watt Indicator ....... 45 12. Mechanical Integrator by the Author ... 48 13. Area Diagram ........ 49 14—21. The Amsler Polar Planimeter. 51—57 22—24. Mechanical Integrator by the Author. 58, 59 25—26. [Engine Power Integrator by C. V. Boys]. 61, 62 27. Record from Model Ship Dynamometer ... 65 28. Rope coiled on Cylinder ...... 68 29—31. Wren’s “Engin”.70 32. William Thomson’s Rope Dynamometer ... 74 33. Sankey’s Dynamometer.78 34. Dynamometer at Central Institute .... 79 35. Dynamometer at Cooper’s Hill. .81 36. Dynamometer of James Thomson .... 82 37—38. Dynamometer of Imray. 83, 84 39. Prony’s Brake Dynamometer.87 40. Appold’s Brake Dynamometer.89 41—42. [Griffin Engineering Company’s Brake Dynamo¬ meter] ... .... 91, 92 43. Perry’s Liquid Friction Apparatus .... 97 44_51. Froude’s Turbine Dynamometer. 100,101 52_53. Heenan and Froude’s Dynamometer. 109, 110 54. Brotherhood’s Dynamometer. .112 XVI ILLUSTRATIONS PAGE 55. Air Brake, Walker.• 113 56. [White and Poppe Diagram].117 57. [Logarithmic Chart of Air Brake Resistance]. • 118 58—59. Eddy Current Brake, Morris and Lister. 123 60. Jervis-Smith’s End Thrust Ergometer. 126 61. De Borda, Stream Lines ...... 134 62—63. [Hele-Shaw’s Stream Lines] .... 137, 138 64—72. Morin’s Dynamometers. 148—160 73—80. Froude’s Transmission Dynamometer. 163—167 8i—84. Jervis-Smith’s Transmission Dynamometer. 169, 170 85. [Amsler’s Transmission Dynamometer]. .182 86. [Diagram of Moore’s Electrical Dynamometer]. 183 87—88. [Lanchester’s Worm-gear Testing Machine] 185—187 89. Torsion of Shaft, Diagram ...... 191 90—91. Dynamometers by the Author 197, 198 92—93. Bays in Reflecting Prism ... 200 94. Atwood . . .. The inventions of these pioneers of the subject are remark¬ able. Prony was the first to employ the friction set up between two surfaces, as a measured resistance to a pulley wheel rotated by a prime-mover. Hirn made his torsional dynamometer totalise the work done during a given period of time. Morin added an integrator to his transmission dynamometer, and also an automatic recording apparatus, which exhibited the work done as an area, generated on a moving paper band ; by this means not only was the total ivorlc shown, but also the way in which it was built up during any period of time. Thomson devised a brake machine in which the moment of inertia of the brake, namely a rope, was reduced to the least workable value, thereby minimising the tendency to oscillate in the brake itself, and rendering the dynamometer steady when running. To Froude is due the turbine brake, in which enormous resistance to rotation is obtained in a small space by the useful application of the vortical rotation of a liquid. INTRODUCTION 3 Some years ago I published a pamphlet in which a short account was given of certain forms of work-measuring machines. It was little more than a sketch of some experiments which were made in Paris in 1881, and at Taunton in a private laboratory, on dynamometric measurements. Since then more experiments on the same subject have been carried on by me and some of the students at the Millard Engineering Laboratory at Oxford (1886 to 1903). Believing that some portions of the work may be of interest to engineers, science students and others not directly engaged in the design of machines and engines, I have collected in the following pages some further accounts of dynamometric experiments and calculations bearing on the subject, so that the reader may be able to compare the different methods which have been employed by investigators of eminence in estimating the output and efficiency of prime-movers and mechanical combinations of many different kinds. Now that a certain class of machinery, including the dynamo, the electric motor, and many kinds of engines, employed in ships and launches, railways, trams, motor cars, and flying machines, has undergone rapid develop¬ ment, and in some cases reached a high degree of perfection, it has become necessary that some adequate method of testing the comparative merits of such machines should be in the hands of those who make them and use them. One of the leading features of excellence of machinery, either of prime-movers or machines driven by them, is economy of working, so that accurate dynamometric tests of such machines is of paramount importance. An observation made by John Penn, the celebrated marine engineer, chairman of the Institution of Mechanical Engineers, in 1858, at the close of a paper by William Froude on dynamo¬ meters, is interesting in connection with my subject. It is as follows :—“ He ” (Mr. Penn) “ thought there could not be too many dynamometers, as they were of such importance.” Penn’s words were spoken at a time when the available methods for measuring efficiency were quite few and not much known ; he evidently felt that progress in the construction of the steam engine could be best gauged by dynamometric measurements of work. The masterly experiments of the late W. Froude, F.R.S., on the power absorbed by marine engines, and ship B 2 4 DYNAMOMETERS resistance, decided certain dynamometrical questions so per¬ fectly that the importance of this class of measurement was thrust with great force upon naval architects and the builders of marine engines. Dynamometric tests bearing on the structure of our battleships are now carried on daily at the Admiralty experimental works at Haslar under the direction of Mr. E. Froude, F.R.S., and similar testing plants have been laid down by shipbuilders who wish to conduct their own testing. [These have been added to recently by the con¬ struction of a tank at the National Physical Laboratory at Bushy.] Some few makers of electrical machines long ago (1881) realised the importance of dynamometric tests ; also excellent tests of this kind were made from time to time under the supervision of the Royal Agricultural Society of England. In 1888-89 the Society of Arts conducted exhaus¬ tive trials of motors for electric lighting. At Messrs. Willans and Robinson’s Engineering Works, Rugby, a complete department for engine testing has been arranged by Captain Riall Sankey and Mr. C. H. Wingfield. In a well- illustrated paper by Mr. W. W. Beaumont,* will be found detailed descriptions of dynamometers of the friction-brake type. My own observations from having visited many engineering works and technical colleges, both in England and in the colonies of Australia and New Zealand, lead me to believe that much has yet to be done in this most interesting and necessary branch of experimental work. It has been customary with engineers to call the machine used for measuring work a dynamometer. The name does not seem to have been well chosen, since the word, derived as it is from the Greek Bvvapis = force, and ^erpov = a measure, would imply that only force was measured, whereas work, i.e., the product of force into the space through which it acts, is measured by the machine. Since this is the case, a word * Proceedings of the Institution of Civil Engineers, Yol. XCV., November, 1888. INTRODUCTION 5 compounded of the Greek words epyov = a work, and j uerpov — a measure, would be preferable. Machines whereby work is measured have been called ergometers (see “ Elements of Natural Philosophy,” Thompson and Tait, p. 134, Part I., 2nd ed., 1879). But as the word “ dynamometer ” has been so universally employed and applied to work-measuring machines it will be adhered to in this book. Dynamometers may be divided into three classes, the gravity, the frictional (including absorption machines), and the transmission forms. These and some of the methods used for obtaining numerical results will be considered in order. If we wished to measure the work done by any engine, whether driven by water, steam, gas, electricity, or any other agent, we could make such a measurement by causing the engine or motor to wind up a known weight from a deep shaft in the earth ; then the height in feet through which the weight is raised, at a uniform velocity, multiplied by the numerical value of the total weight in pounds raised would give the numerical value of work done in raising the load in foot-pounds. In order that this very simple method might be practically employed the winding-rope should be continuous, so that the rope in itself may be in equilibrium. If an unbalanced rope were employed, its weight must be known ; then the product of the height through which its centre of gravity is raised multiplied by its weight = the work done in raising the rope. The sum of the two products equals the whole work done. Probably the earliest instance of carefully-conducted experi¬ ments on the determination of the work done by a machine in a certain time is due to John Smeaton, E.R.S. I give two instances of his methods of measuring work. The vanes of a small windmill were carried on an axle mounted on an arm FG (Fig. 1) perpendicular to its length, the arm being capable of rotation in a horizontal plane, on the axle DE, mounted on the frame ABC. By means of a cord ZH coiled on the vertical axle, the little windmill was driven through the air at any required velocity ; while the windmill was thus impelled against the air it raised known weights P placed in a pan ST to a known height by means of pulleys and a cord MNO. Smeaton’s experiments were made on wind¬ mills furnished with vanes varying in shape and angular set. 6 DYNAMOMETERS A comparison between the values of the weights raised in different cases indicated the relative values of the different 4 forms of vanes and their angular set. A pendulum VX was used to show the time in which work was done. In another INTRODUCTION 7 set of experiments Smeaton employed a somewhat similar method to determine the work done in generating angular velocity in a certain given mass, starting from rest when impelled by a force acting through a given space, whereby he essayed to find the relationship existing between rotating bodies and a falling weight which propelled them. Here we see probably for the first time work expressed as a product. Smeaton writes thus : “ And this mechanic power we shall express by the number 202, the product of ounces in the scale multiplied by the inches in its perpendicular descent, for 8 x 25J = 202 ”—about T06 foot-pounds. Smeaton’s unit of work was the inch-ounce, a product like the foot-pound now used by the modern engineer. It will be noted that Smeaton, by means of his pendulum, determined the time also in which work was done ; so that the rate of doing work , that is power, was found by him. In these days of aeroplane flights the earliest definite research in windmill sails should be of interest to those who are working on the behaviour of air screw pro¬ pellers. It will be seen in what follows that Smeaton’s excellent method has recently been developed into elaborate machines for testing the power of aerial propellers (Chap. XVI.). Some excellent experiments were made by M. Le Chevalier De Borda on the horizontal impulse wheel by means of the gravity method (“ Memoire sur les Roues Hydraulique,” par M. le Chevalier De Borda, Hist, de 1’Acad. Royal des Sciences, 1767). The water struck the vanes or curved blades of the wheel at an angle to the vertical; De Borda caused the hydraulic wheel to raise a weight by means of a pulley and a cord wrapped on the axle of the wheel, and by this means determined the condition of the maximum efficiency. Atwood, the inventor of the well-known machine which bears his name, when writing on the dynamics of rotating bodies (1784), gives an illustration of Smeaton’s instrument, but in his calculations the kinetic energy of the driving mass is included in the reckoning, and also other important points (“A Treatise on the Rectilinear Motion and Rotation of Bodies,” G. Atwood, M.A., F.R.S., Cambridge, 1784). An experiment involving the same dynamic condition is described in “ Applied Mechanics,” by Prof. John Perry, F.R.S., ed. of 1897, p. 247. 8 DYNAMOMETERS Soon after the steam engine of James Watt had shown itself to be an excellent prime-mover and the horse began to be replaced by it, the need of some method for determining the comparative power of the steam engine and the horse was felt. The following quotation from John Farey shows clearly how the early estimates of horse-power were arrived at and determined. The passage is important historically, and therefore I give it at full length. Estimation of the Force of Steam Engines by Horse-power, 1784 (“ The Steam Engine,” by John Farey: London, 1827) :-— “ The only unequivocal mode of expressing the mechanical power exerted by an engine or by an animal is the weight which can be raised through a certain space in a given time by that exertion; and unless we define what a horse-power is in those terms, it is a very vague expression, on account of various degrees of strength which different horses possess, and their capacity of enduring fatigue.” “ When Messrs. Boulton and Watt first began to introduce their rotative steam engines into manufactories, about 1784, they found it necessary to adopt some measure of the power which they were required to exert; this they endeavoured to do in such terms as would be readily understood by the persons who were likely to want such engines. The machinery in the great breweries and distilleries in London was then moved by the strength of horses, and the proprietors of those establish¬ ments, who were the first to require Mr. Watt’s engines, always inquired what number of horses an intended engine would be equal to. “ In consequence, Mr. Watt made some experiments on the strong horses employed by the brewers in London, and found that a horse of that kind, walking at the rate of two and a half miles per hour, could draw 150 lb. avoirdupois, by means of a rope passing over a pulley, so as to raise up that weight, with vertical motion, at the rate of 220 ft. per minute. “ This exertion of mechanical power is equal to 33,000 pounds (or 528 cubic ft. of water) raised vertically through a space of one foot in one minute, and he denominated it a horse-power, to serve for a measure of the power exerted by his steam-engines ; that is, of the resistance actually overcome, in addition to the friction of the engine itself, and the resistance of the air pump. . . . Messrs. Boulton and Watt’s standard for the horse-power is very much beyond the actual power of any horse, except the very strongest, and they cannot long endure the exertion of raising 33,000 lb. at the rate of 1 ft. per minute. Mr. Smeaton and other INTRODUCTION 9 engineers made many observations on the work actually performed by horses when working regularly in mills, and the results seem to show that 22,000 lb., raised at the rate of 1 ft. per minute, may be taken for a real horse-power, or as the exertion that a good horse can overcome with so much ease as to continue work for eight hours per day.” It may be noted that the first mention of horse-power in print occurs in Vol. II. of the first edition of the “ Mechanics ” of Olinthus Gregory, 1805. Farey was a friend of James Watt, and a man of much ability, and moreover the inventor of an excellent form of slide rule, which appears to have been much used in the cal¬ culation of the dimensions of Watt’s engines. Some of the slide rules were devised by Watt himself and one of his en¬ gineers, by name Southern. These instruments were known as the Soho sliding rule, and formed one of the everyday tools of the workmen employed by Watt (pp. 531—532 idem), as is evident from the following words :—“ and having observed the facility with which the Soho workmen performed their ordinary calculations by it.” I mention this, as I have heard some engineers speak of the slide rule as a new sort of instru¬ ment, and therefore one to be avoided. As a matter of fact the slide rule dates from a much earlier period, probably 1662 (see Nature, Vol. LXXXII.). Experiments were made with much care by R. L. Edgeworth, F.R.S., on the relative work required to pull carriages of varied construction along ordinary roads. The results are collected in a volume entitled “ An Essay on the Construction of Road Carriages,” by R. L. Edgeworth, 1813. One experiment whereby the pull on two carriages carrying different loads was found deserves especial notice. The two carriages to be compared were pulled along a road by means of a rope attached to each, which passed round a horizontal pulley, the axle of which was fixed to another carriage in front, pulled by a horse. When the friction of each carriage was the same in value they advanced side by side, but when different, by loading, the friction of one of them was changed, one advanced on the other as both were pulled along (ibid., p. 191). Two carts, one of wdiich was furnished with springs, were tested ; while the load of the cart having springs was as 15 to 12, the carts remained abreast of one another, thus showing the 10 DYNAMOMETERS advantage of the introduction of springs. The results are brought together in a paper by Mr. Ward, in the Third Report for 1809 of the House of Commons Committee upon Road Wheels and Roads. A somewhat similar method has been used for comparing the friction of two boats drawn through still water, but in this case the relative friction was found by knowing the lengths of the arms of a lever, which took the place of the pulley in the former experiment. The author has also employed a modification of the same method, in which the horizontal wheel in Edgeworth’s experiment was furnished with a Salter’s balance, which indicated the difference of pull on the two bodies drawn along by the front carriage ; in this way the relative resistance of two motor cars may be easily estimated— the two cars under comparison not using their own engines during the experiment. In many other experiments the same method of reading the difference of pull has been found to give excellent results—for example, in testing the surface friction between two pairs of similar surfaces, in one set the rubber moving in a straight line, in the other the rubber having in addition a small simultaneous lateral movement. Coulomb investigated with great care the conditions under which men best performed work (Memoires de l’lnstitut National des Sciences et Artes : Coulomb, “ Science, Math, et Phys.,” T. II.). His work is commented on by Poncelet in his “ Mecanique industrielle ” : Paris, 1841, p. 237. The table exhibited by Poncelet, taken from the results of Coulomb, is most instructive, as it is a summary of his experiments, made with great care and extending over many years of observation. The following translation describes one of the most remarkable discoveries of Coulomb :— “ Concerning the best method for utilising the strength of man, the table shows that the greatest amount of work which a man can yield per day without undue fatigue consists in raising his own body, and this equals 280,800 kilogram-metre units of work in eight hours. Since the kilogram-metre = 7-233 foot-pounds, 280,800 kilograms = 2,031,026 foot-pounds in eight hours, or 4,231-2 foot-pounds per minute, so that the rate of doing work was 0-128 horse-power—a result at least seven times that of a simple worker with a shovel, and one which surpasses by INTRODUCTION 11 nearly two-thirds that of a workman employed in turning a winch handle. In order to utilise that amount of work at disposal there is no question, as Coulomb observes, but to make use of the descent of the weight of the man in raising a weight equal to his own to the height which he reaches each time, i.«., each journey. Amongst the con¬ trivances devised to fulfil this end the most simple, and that which has been practically used by Captain Coignet in the construction of the earthworks of the fort of Vincennes, near Paris, consisted of a rope passing over a pulley, furnished at its ends with boards, one of which carried the man and the other the weight to be raised. These opera¬ tions, in which each workman raised the weight of his own body (70 kilograms) 310 times daily to the height of 13 metres, have been thoroughly authenticated.” The process will perhaps be better understood if we imagine a grooved pulley, running on a horizontal axle fixed at the top of a building, furnished with a rope having its lower end attached to the load to be raised. Before he left his seat the load at the top would be removed, another man would take its place, and the man below who had made the descent would be replaced by the next load, which would ascend in the same manner. At the same time the first man would be walking up again to the top of the building, to be ready for the next load. To-day one may see ships and colliers unloaded by men employing the same principle as that just described. A basket filled with coal by men in the hold of a collier is hauled up by means of a rope passing over a pulley suspended from a spar ; the rope is furnished with numerous ends, four or five ; each end is seized by one of a group of men standing on a platform. The men jump from the platform at the same moment, and their joint weight brings up the load : this is then upset down a shoot into a lighter or truck ; the men then return to the platform for their next load. It is difficult to determine the date of this method of employing manual labour, but 12 DYNAMOMETERS it is probably a very early one. A very simple and not to be despised method of test¬ ing a prime-mover such as a gas engine or steam engine (the ports being open to the air) with a view to finding its internal friction is to set the engine in motion by means of a rope coiled on the fly¬ wheel, the rope being fur¬ nished with a weight sufficient to give the flywheel some con¬ venient slow rotation. The weight may either descend into a dry pit, or, if high buildings are available, the rope may be taken over a pulley at such a height that the weight may have the required fall while rotating the flywheel of the engine slowly. The method, which will be found instructive, can be easily applied for testing any small machine in which rota¬ tion takes place. The weight can be most conveniently applied and increased by means of an open cylinder or bucket attached to the cord, into which dry sand p IG . 2 . poured from a hopper furnished with a sliding gate, by means of which the sand can be shut off at any instant. It is convenient to determine the weight of the cylinder, so that only the sand has to be weighed in each experiment. 