/055 
 . 34 
 
 C/i 
 
 8 
 
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George Davidson 
 1825-1911 
 
 

 
 Kftorfc^flfteasunncj 
 
 F. J. (SMITH. 
 
Gift 
 
ON SOME 
 
 NEW FORMS OF 
 
 WORK-MEASURING MACHINES 
 
 AS APPLIED TO 
 
 2)\mamo6 ant) lElectroflDotore. 
 
 FREDERICK JOHN SMITH, B.A., 
 
 Associate Tel. Eng., Memb. Phy. Soc. Ldn. 
 
 LONDON : E. AND F. N. SPON, 16 CHARING CROSS. 
 NEW YORK: 35 MURRAY STREET. 
 
Sntrotwction. 
 
 [i] In the following pages will be found the results 
 of some work which has been carried on by the author 
 since the year 1880, the object in view being to produce 
 some machines and apparatus for measuring the work 
 done by electro-motors, and also the work done by prime 
 movers, such as water wheels, turbines, steam and gas 
 engines, in working dynamos. Two kinds of work- 
 measuring machines have been dealt with, viz., the 
 absorption machine and the transmission one. 
 
 Many questions of late as to how dynamos, &c., 
 should be tested have led the author to publish the 
 following few pages, in the hope that some of the 
 methods shown may possibly be of use to others who 
 may be engaged in this exceedingly interesting branch 
 of measuring. Many of the methods have already been 
 made known in a brief form in the Electrician, 1881, 
 p. 261, Electrical Review, 1881, p. 397, Philosophical 
 Magazine, vol. xv., pp. 87, 424, and vol. xvii., p. 59. 
 The method of making an electro - motor or dynamo 
 into its own ergometer is taken from a paper read in 
 November, 1883, before the Physical Society of Bristol. 
 
worb 5>\mamometer. 
 
 [2] The term dynamometer has usually been applied 
 to that class of instruments by which weighing is per- 
 formed by means of a spring, as in the dynamometer of 
 Regnier and the Salter balance, and if the instruments 
 were only used for this purpose the term dynamometer 
 would be correct, coming as it does from the two Greek 
 words cvi/a/u?, force, and pe-rpov, a measure. But the 
 word dynamometer is also applied to that class of in- 
 struments by which work is measured. Now since work* 
 is force multiplied by length, the word dynamometer or 
 force-measurer appears no longer to be the correct one 
 to be applied to an instrument by which work is mea- 
 sured ; for this reason the word ergometer, or work- 
 measurer, from the Greek words ep^ov, a work, and 
 /j-erpov, a measure, will be used in this little book instead 
 of dynamometer, as the name of that class of instru- 
 ments by which work is measured. 
 
 * The abstract equations which express the "dimensions" of 
 the Physical quantities, "velocity" and "acceleration," with respect 
 to the fundamental quantities, length and time, are as follows. 
 From this it will be clearly seen how WORK is made up : 
 
 
 
 UNITS. 
 
 DIMENSIONS. 
 
 
 Fundamental 
 Length 
 
 
 L 
 
 
 Mass 
 
 
 M 
 
 
 Time 
 
 
 T 
 
 
 
 
 
 
 Derived 
 Area L x 
 
 L 
 
 L 2 
 
 
 Volume L 
 
 x L x L 
 
 L 8 
 
 " 
 
 Velocity - L 
 
 
 L T' 1 
 
 a 
 
 Acceleration 
 
 Velocity L 
 
 L T- 2 
 
 f 
 
 Force = Mass 
 WORK Fore* 
 
 Time T 2 ' 
 x Acceleration = 
 
 1 x Length ^* 
 
 MLT-* 
 
 
 
 
 
[3] If we wish to measure the work done by any 
 engine, either steam, gas, or electrical, we could do so 
 by causing it to wind up, by means of a drum and rope, 
 a certain weight from a shaft in the earth of indefinite 
 depth. Then the number of feet through which it is 
 lifted per second, multiplied by the numerical value of 
 the weight in pounds, gives us the work done in foot 
 pounds per second. Since such an experiment could 
 not be carried out, some constantly opposing force 
 acting at a tangent to the face of the drum must be 
 used instead of the weight lifted out of the shaft. 
 
 [4] This end may be obtained by 
 using a friction break acting on the face 
 of the drum ; friction thus set up takes 
 the place of the weight just mentioned. 
 In Fig. i we see how this may be arranged : 
 A is the side view of the drum driven by 
 the machine which is being tested, this is 
 partly covered by a cord or belt J5C, which 
 also passes round the wheel D, the pull of 
 the spring transmitted through the wheel 
 D causes the pull on each of the sides B 
 and C to be equal, and by means of an 
 adjusting screw any necessary pressure 
 may be put on. The spring balance F is 
 attached to the side of the cord or strap 
 B so that its pull is tangential to the face 
 of the drum A , and the pull due to friction 
 at the effective radius is shown on the 
 scale of the spring balance F. 
 
 In using this instrument, the \salue of 
 the pull on F in pounds is multiplied by 
 the velocity of the circumference of the drum in feet per 
 second ; this gives foot pounds per second ; or taking n 
 the number of revolutions of the drum per minute, v the 
 radius of the drum, w the pull on the balance F, and 
 
 7T = 3.I4I59. 
 
 Work done ) _27rrnw _7rrnw , * 
 
 per second) 6o~~ ~$o~ 
 
 [5] It will be noticed that this form or instrument, 
 although springs are used, differs very materially from 
 
Navier's" ;: form ; in it a drum was embraced by a belt 
 and a spring balance was put on one side and a weight 
 on the other until the required friction was produced, 
 recently Navier's method appears to have been greatly 
 improved on by Professor W. C. Unwin.f If the drum 
 be made of cast iron, truly cylindrical and well polished, 
 and the band be hard twisted cord, constantly lubri- 
 cated, very good results may be obtained. Messrs. 
 Ayrton and Perry J have recently invented a very beau- 
 tiful form of friction ergometer, in which the friction is 
 kept constant by the cord which passes over the drum 
 being of different diameter on the two sides of the 
 drum, which in their machine is a grooved wheel. 
 The effect of any increase of the coefficient of friction 
 is to wind the thicker end off the drum and at once 
 reduce the coefficient of friction. Should the coefficient 
 of friction diminish then the thicker end rises on to 
 the drum and so the coefficient of friction is increased, 
 the result of all this being that changes in the coefficient 
 are compensated for rapidly and a practically uniform 
 coefficient of friction is the result. 
 
 [6] When small electro-motors have to be tested 
 great care should be taken not to introduce any extra- 
 neous friction from the instrument employed to measure 
 the work done by them. To obviate this difficulty the 
 author devised the following plan, first used in testing 
 some Trouve motors in the year 1881. 
 
 B 
 
 Fig. 2. 
 
 * Weisbach Mechanics of Engineering, vol. ii., p. 66. 
 t Paper read before G section British Association, 1883, by 
 Professor W. C. Umvin. 
 
 J Proceedings Telegraph Engineers and Electricians, vol. xii., 346. 
 
 A 2 
 
The motor as a wl /irtually converted into 
 
 its own ergometer. T 1 magnets and frame are 
 
 balanced with counteri ights so that the whole 
 
 motor, when the axis of lature is placed between 
 
 suitable centres, is in equilibria n, the bearings in which 
 the spindle of the armatnfv rQ s are carried on friction 
 wheels so as to prevent arrj r.mecessary friction from 
 the weight of the field magnel s and frame. When the 
 motor is doing work th: < action of the armature is 
 against the field magi. I frame; now if the frame 
 
 be attached to a spring : ace and so prevented from 
 revolving, the moment of the couple can at once be 
 determined, and if the spring be applied to a point in the 
 frame at a distance from the axis equal to the radius of 
 the driving pulley, then th \v r ork done will be expressed 
 by the equation (i) used in the question of the friction- 
 break ergometer, the spring being so placed that the 
 direction of its pull is tangential to the face of the 
 driving pulley ; or, instead of a spring, a lever and 
 weight may be used, thus (see Fig. 2) : B D are the 
 field magnets, E the armature. If the armature re- 
 volve within the field magnets certain tangential forces 
 /i>/2>/3 will be acting, tending to turn the frame A BCD 
 and field magnets in the direction of the arrow, these 
 forces acting at the effective radius will give us the 
 moments fa, f >/,/& = ^ fr about the centre O, and we 
 have another moment Pd, the whole frame without the 
 weight P is balanced, so that the weight P alone acts 
 at the distance d. When equilibrium in the system is 
 obtained we have 
 
 *fr=Pd. ... (A) 
 
 Next take the angular velocity at a unit distance from 
 O, then the work due to the above-mentioned forces for 
 one revolution will be 
 
 2/7 27T. 
 
 Let n denote the number of revolutions per minute of 
 the machine, and W f the work done against the mag- 
 netic friction in a second, then 
 
 TTT 2 fr 2.7DI 
 
II 
 
 Put the value of 2// in (A) into equation (B) and we 
 have 
 
 W f = Pd. 
 30 
 
 Thus a dynamo-machine has become its own ergometer. 
 This process is reversed when a dynamo is tested on 
 a similar system of supports ; instead of the dynamo 
 driving, it is driven. The same line of calculation as 
 that given shows the amount of work done in giving its 
 armature rotation when yielding a current. 
 
 There is a curious and interesting similarity in the 
 action of the dynamo ergometer just mentioned and the 
 turbine ergometer of the late Mr. W. Froude ; in each 
 the resisting couple increases as the velocity increases, 
 the regenerative action in the turbine ergometer being 
 closely allied to that of a dynamo during the period of 
 time that the field magnets are getting saturated. This 
 is only a rough statement of what takes place in each 
 machine ; the points of similarity are now being care- 
 fully compared and worked out. 
 
 [7] When dealing with small motors it is necessary 
 to count the revolutions of the motor without introducing 
 friction by attaching a speed-counter to the motor direct; 
 the author's plan of doing this is as follows : In the first 
 experiments, one, of two cog wheels having the same 
 number of teeth, was fixed on the spindle of the armature 
 of the motor, the other was fixed on the spindle of a 
 speed-indicator Young's speed-indicator, now so much 
 used, is a considerable improvement on the one used in 
 these first experiments two metallic springs pressed 
 very lightly against the teeth of the cogs ; in the earliest 
 experiments these springs were placed on sound boards 
 attached to resonators, so that a very loud and clear 
 note was given out both by the wheel and spring 
 attached to the motor, and the wheel attached to the 
 speed-indicator, now when the speed-indicator was 
 so driven by hand that the note produced by its 
 spring and cog was of the same pitch as that of the 
 spring and cog of the motor the speed of revolution 
 shown by the indicator was recorded, and therefore, 
 
12 
 
 evidently, the speed of the motor, because the same 
 number of revolutions would give the same note in each 
 instrument. When the revolutions are very high a 
 wheel cut with three cogs will be found to answer. 
 
 This method has since given way to either of the two 
 following plans, if the spaces between the cogs are filled 
 up with a non-conductor, and turned off so as to be 
 smooth, then a telephone and battery placed in circuit 
 with the two wheels and springs on the motor and speed 
 indicator tells one very accurately when the same note 
 -is produced by both motor and speed indicator. It will 
 be found most convenient to use a telephone wound 
 with two distinct circuits, one being in connection with 
 the spring and wheel of the motor, the other in connec- 
 tion with the spring and wheel on the speed indicator. 
 An attempt was made to affect the telephone by a 
 current induced by that which was driving the motor, 
 but experience showed that the former of these methods 
 was the best. This way of measuring the revolutions, 
 not only of electro-motors, but anything which is easily 
 stopped by friction, might be introduced in many 
 instances in the physical laboratory. 
 
 {Transmission jergometer. 
 
 [8] It may be well to preface the description of 
 this class of work-measuring instrument by shewing 
 
 briefly the general 
 principle involved 
 in Transmission 
 Ergometers. Fig. 
 (3) shows what 
 has to be put into 
 a practical form. 
 
 Fig. 3. 
 
Let it be supposed that E is the driving wheel of a 
 prime mover such as a steam engine, and that D is the 
 pulley of a dynamo, and that E drives D by means of a 
 strap ; then if we could make spring balances parts 
 of the strap T T', and if we could read the difference of 
 the tensions T and T', and if we multiplied this T T', 
 expressed in pounds by the velocity of the belt in feet 
 per second, we should then have the foot pounds per 
 second necessary to drive the dynamo, and from this 
 the H.P. if we wished by dividing it by 550. 
 
 Or H.P. = - 7-^ where v denotes velocity of belt 
 
 in feet per second. 
 
 [9] Now since such an arrangement as this cannot 
 be easily carried out the usual method is to place between 
 the engine and dynamo some instrument capable of 
 showing the tension of the belt in Ibs. and the velocity 
 of the belt, and in certain cases a continuous record of 
 the work done. The following machine and apparatus 
 has been devised by the author to obtain such a com- 
 bination. 
 
 A side view of the machine Fig. (4) [see front page 
 
 Fig. 4. 
 
 also] , shows how the ergometer has been arranged. 
 The central steel* shaft C B, which is tubular at each 
 end and link shaped between E F, carries two pullies, 
 D and G. G is keyed to the shaft, and carries two 
 bevel wheels K M, these engage with the bevel wheel 
 //, which is part of the pulley D which is loose on C B. 
 
 * The tubular steel shaft was made by Sir J. Whitworth and Co. 
 of their compressed steel. 
 
K and M are each furnished with a cylindrical drum y 
 on these either gut or steel tape is coiled over three- 
 fourths of their faces, and the gut or tape is attached 
 to a cross head L, which is attached to the spring A, 
 placed within the link, and from which a rod of 
 steel passing through one end of the link actuates the 
 pointer of the dial Q, whereby the pull on the spring 
 attached to the end of the link is shown. R is the 
 speed indicator. 
 
 If a continuous record of work is required the steel 
 rod is attached either to a recording drum or to an 
 integrating apparatus; see section (13). 
 
 The machine having been placed between a prime 
 mover and a machine to be tested, the belt from the 
 prime mover drives the pulley D and another belt from 
 the pulley G drives the machine to be tested. The 
 tension on the driving side of the belt causes the spring >;c 
 to be extended by means of the bevel wheels, and there- 
 fore this tension is made known by the pointer of the 
 dial Q. The instrument is calibrated by hanging known 
 weights from strong thin cords or cat gut passing round 
 the pullies and marking the dial in accordance with the 
 weights. 
 
 [n] There is another method of calibrating which 
 the author believes to be new ; it is as follows : Let a 
 prime mover (a water wheel appears to be the most 
 steady) drive the transmission ergometer, and let the 
 ergometer drive a pulley on a shaft embraced by either 
 a Prony, Appold or suitable friction ergometer, and let 
 the work done against friction be calculated. This 
 should agree with the results of the transmission machine: 
 If it does we may conclude that it has been correctly 
 calibrated. The advantage of this method is that the 
 transmission machine is tested while running in its 
 usual condition. When testing a dynamo care should 
 be taken that the speed indicator be well attached to 
 the shaft the velocity of which it is measuring. A piece 
 
 * The spiral springs were made by Messrs. Salter and Co. After 
 many severe tests they seem to be quite unaltered in their value of 
 pull. It is convenient to use four sizes of springs, which may be 
 extended to two inches respectively by 50, 100, 150 and 200 Ibs, 
 
of coil spring such as is t 
 well to connect it to the 
 
 [12] The leading ft 
 position of the spring in 
 of the shaft coincide ; 
 hardly at all affected 
 spiral spring is whirled : 
 occupied in ergometers 
 the effect of centrifugal 
 pull are used and the 
 velocity the deformatk 
 introduce considerable t 
 
 The deformation of 
 ciated by Schuckert, :;: a 
 spiral springs of his ergi 
 
 When the spring is ] 
 with that of the mach 
 troduced, and the fricti* 
 avoided. 
 
 dentist's lathe answers 
 with. 
 
 this instrument is the 
 axis of the spring and 
 L- of this is that it is 
 ugal force. When a 
 
 M! in the position it usually 
 
 le to deformation from 
 
 When springs of slight 
 
 r is driven at a great 
 
 , considerable, and would 
 the result. 
 
 ^ has been fully appre- 
 .>re he has placed the 
 cylindrical cases. 
 
 : h its axis coincidental 
 .uch error can be in- 
 uring against a case is 
 
 [13] When a contin 
 a cylinder not shown ii 
 9 to the right hand) is 
 instrument, it carries a 
 a continuous trace from 
 pen is attached to the 
 extension of the spring, 
 proportional to the am 
 at any instant ; the sec 
 of an electro -magnet i 
 trolled by a seconds p 
 marking at each seconc. 
 line, the ox line in geom 
 perpendicular. 
 
 The recording drum 
 convenient ratio to the i 
 
 im. 
 
 :cord of work is required 
 . 4 (but shown in Fig. 
 J at the dial end of the 
 i of paper which receives 
 self- feeding ink pens ; one 
 which is moved by the 
 ites ordinates directly 
 if extension of the spring 
 pen, attached to the lever 
 tized by a current con- 
 urn, describes a V-shaped 
 ; third pen traces a datum 
 to which the ordinates are 
 
 be made to revolve at any 
 ations of the belt wheels. 
 
 * See list of Tran .ion Ergometers, p 30. 
 
i6 
 
 n Q 
 
 Fig. 4 a. 
 
 [14] OX is the datum line previously spoken of, let 
 the curve be referred to rectangular axes, the ordinate y 
 represents the tension of the spring, and RQ is propor- 
 tional to a small length of belt that has passed over the 
 pulley of the machine, then the rectangle PQ represents 
 the work done at the point P when the RQ is indefinitely 
 diminished, if then we take the sum of all such reel- 
 angles we have the whole area of the curve, which 
 therefore represents the work done during any time 
 recorded on the time line A B. 
 
 For the purpose of seeing at a glance the value of 
 the height of any of the ordinates of a curve traced out, 
 it will be found convenient to have a rectangular wooden 
 frame of the size of the edges of the diagram taken from 
 the recording drum. Thin wires are stretched the long 
 way of the frame, so that their distance apart equals the 
 ordinate which represents any given pull of the spring 
 experimentally determined. 
 
 Suppose that such a spring be used that the increase 
 of extension is not directly proportional to the increase 
 of weight (this is sometimes the case in very light 
 springs), then if a frame be wired to suit the conditions 
 of the extension of the spring it will enable one to make 
 quickly a correct interpretation of the value of the 
 ordinates of the diagram. The correction is very slight, 
 but in certain experiments in connection with the 
 mechanical equivalent of heat and the laws of viscosity 
 it was necessarily introduced. 
 
[15] The process of integration is carried out prac- 
 tically by cutting out the area of the curve and finding 
 out by weighing how many times it contains the weight 
 of a piece of paper the area of which represents a 
 certain known amount of work done ; if the paper be 
 well selected and be of uniform thickness excellent 
 results may be obtained, and by properly adjusting the 
 speed of the drum, 1000 foot pounds may be represented 
 by 0*5 grm. This method of calculating work-done by 
 weight of paper is due to General Morin (see " Descrip- 
 tion des Appareils Dynamometriques," Morin. 
 
 gjjdrautic gnteorating gtptwrattt toy tte gUttlta*. 
 
 [16] In using the ergometer it is not always neces- 
 sary to attach the recording drum unless some special 
 curve be sought for, such as that which is produced 
 when the instrument is measuring the work done in 
 charging an accumulator or secondary battery. The 
 following apparatus has been devised by the author to 
 take the place of a disc integrator. 
 
 A very small double- 
 acting pump, D, oscillat- 
 ing about the point H and 
 having a long rod E G,* 
 not shown at full length 
 B in Fig. 5 is actuated by a 
 
 :z= ^ L link A B (rocking about 
 
 PT~ the point B), to which 
 
 reciprocal motion is given 
 by the connecting rod C. 
 
 <^^^\ J This rod receives its 
 
 L_| I motion from the revolu- 
 
 tion of the shaft ; the 
 position of the end of the 
 pump-rod , and hence 
 the length of the stroke is 
 controlled by the rod EF, 
 which is connected to the 
 spring of the instrument, 
 
 ','; so that any extension of 
 
 \\ pjg 5 < the spring moves E to- 
 
 j: wards A and consequently 
 
 * For the method of making the connecting rod, virtually of 
 infinite length, see p. 21. 
 
 L 
 
 I 
 
i8 
 
 lengthens the stroke of the pump. Now, when no 
 energy is being transmitted the spring of the ergometer 
 is not extended and E has a definite position between 
 C and B ; and then the water discharged by the pump 
 is proportional to the number of revolutions of the 
 shaft ; but as soon as energy is transmitted the spring 
 is extended and the discharge of water is increased by 
 the stroke being thus lengthened : the discharge then 
 becomes a measure of the work done in driving any 
 given machine. 
 
 In this pump arrangement it will be noticed that the 
 volume of the water discharged varies directly as the 
 length of the stroke when the speed of the stroke is 
 constant, and directly with the speed of the strokes 
 when the length is constant, hence the volume varies 
 directly as the product of these two, viz., length of 
 stroke and speed when both vary ; now since its speed 
 is proportional to the speed of the belt, and the length 
 is proportional to the tension, therefore the volume varies 
 directly as the product of tension of spring by speed of 
 belt, and is thus a measure of work done. 
 
 Wnt 
 
 tec ami 
 
 Fig. 6. 
 
 [17] The integrator attributed to General Morin is 
 as follows: The disc A is driven at a velocity pro- 
 portional to the pullies of an ergometer, the roller B 
 can be pulled out from the centre of the disc towards 
 the circumference of it, this pulling out being propor- 
 tional to the tension on the belt of the ergometer, the 
 numerical value of the revolution of B becomes a 
 measure of the work done. 
 
Then if, when the roller is at any distance from the 
 centre, the speed be constant the angular velocity of 
 the roller is proportional to the tension. If the tension 
 be constant, then the angular velocity of the roller is 
 proportional to the angular velocity of the disc, and 
 therefore when both the tension and the angular velo- 
 city of the disc vary together the angular velocity of the 
 roller varies as the product of these two, and therefore 
 is proportional to the tension of the belt multiplied by 
 the velocity of the belt, or to the work done. 
 
 Beautiful as this arrangement is, there are two things 
 which are somewhat against it. The first is that the 
 roller in contact with the disc has a grinding action, 
 and it has this because while the edges have the same 
 linear velocity they have to travel in paths which are 
 concentric circles on the disc by which the roller is 
 driven. The second defect is that, since the roller has 
 to be moved with its axis parallel to a radius of the 
 driving-disc, its edge has to be scraped across the disc. 
 The result of this is, that while a certain amount of 
 friction is required to ensure good rolling contact this 
 very friction prevents the roller from being easily moved 
 with its axis parallel to a radius of the driving-disc. 
 
 [18] In the form of this apparatus devised by the 
 writer of these lines * instead of the roller being solid 
 
 * See Phil. Mag., vol. xvii., p 59. 
 I Y . II 
 
 i 
 
 Fig. 7 
 
20 
 
 the face of it is notched in a dividing engine with a 
 circular saw ; each notch so formed carries a little disk, 
 the edge of which is rounded to the curvative of the 
 circle C B, Fig. 7 ; a ring of steel piano wire forms the 
 axis of all the little disks placed round the circumference 
 of the roller R (only two little disks d and d' are shown 
 in Fig. II.). In Fig. i D is part of the large driving disk 
 which drives the roller R, Y Y' is the axis of the disc D, 
 X X' that of the roller R. The roller so constructed is 
 found to move with the utmost freedom in the two 
 directions required, and it will do so without any "slip," 
 whether the motions are simultaneous or not so. By 
 making the number of little disks large, and facing the 
 disc D very carefully, the action even at an unnecessarily 
 high speed is quite smooth and free from vibration. Q 
 shows a portion of the roller, with only three disks 
 attached, full size. 
 
 [19] Ratchet and link integrator by the author, 
 Fig. 8, shows the construction, L K is a link vibrating 
 about the point M. A connecting rod from the ergo- 
 meter attached at K moves it to and fro, or it may in 
 practice be driven much faster than the ergometer 
 pullies by means of intermediate gearing, so that its 
 vibrations are proportional to the revolutions of the 
 pullies. The T-shaped piece S is controlled in its 
 movement by the spring of the ergometer. Motion in 
 the direction of the arrow would result from the exten- 
 sion of the spring. To this T-piece the piece H is 
 attached by means of a rolling contact R. E is con- 
 nected by the same device at R. The piece H is con- 
 nected to F by a pin which slides in the link J^. The 
 piece E works the two arc shaped pieces C D. These 
 are furnished with pauls acting in opposite directions. 
 The ratchet wheels are denoted by the inner circles, 
 the outer ones denote cog wheels in gear at their point 
 of contact. It is evident that whichever way E moves 
 it will be driving round the wheels A B. These wheels 
 drive an ordinary recording train of wheels. The arc 
 ended pieces H and F are used so to connect the systems 
 together that the effect is the same as if connecting rods 
 of infinite length were used. What has been said about 
 
21 
 
 K 
 
 fl 
 
 the hydraulic integrator 
 applies exactly to this 
 integrator, with this differ- 
 ence, that the motion to 
 and fro of E causes the 
 wheels to revolve instead 
 of working the double 
 acting pump. 
 
 The ratchet wheels used 
 in the instrument are small 
 pullies faced with leather, 
 and the paul consists of a 
 small bundle of steel wires, 
 by this means whatever 
 position the paul is in it 
 at once engages with the 
 wheel to be driven, and 
 consequently there is no 
 loss of time in the action. 
 
 ) 
 
22 
 
 to 
 
 [20] The two pullies .4 B, each carrying a bevel 
 wheel and running loose on the same fixed shaft, are in 
 gear with a third bevel wheel of equal diameter, the 
 axis of which is carried at right angles to the axis of 
 the other two by a sector shaped casting. This sector 
 while carrying the intermediate wheel is capable of 
 angular displacement, this displacement being con- 
 trolled by a spiral spring within the case F. The spring 
 is so attached to the sector that its pull acts tangentially 
 to it. An upper sector H, fixed to the under sector and 
 counterpoised, carries the light rod G D, attached to 
 the sector by two cross cords. The section of the rod is 
 thus, the cords lie side by side within the groove. 
 A connection such as this prevents any "back 
 lash" in the movement of the point D. The 
 point D traces on the drum E an ordinate proportional 
 to the extension of the spring. The drum is driven 
 by a screw and tangent wheel at a given ratio to the 
 speed of the pulleys A or B. The counter K records 
 the number of revolutions. The area of the curve traced 
 on E when interpreted, as in the case of the diagram 
 previously mentioned, shows the work done. The 
 hand wheel L was added to this instrument when it 
 was exhibited in the International Exhibition of 
 Electricity, Paris, 1881.* A lever M", carrying another 
 tracer and controlled by an electro-magnet in connection 
 with a seconds pendulum, records on the drum the time 
 during which any experiment has lasted. 
 
 [21] A torsion ergometer (Fig. 10). This form of 
 ergometer is very different from any already described. 
 It was used to control the motion of a dynamo worked 
 by a windmill. The first windmill to which this arrange- 
 ment was applied was nearly destroyed by the storms 
 of September, 1882, at Taunton. Since then the plan 
 of placing the dynamo in the head cap of a windmill, 
 
 * This exhibit was awarded a medal and decree. 
 
Fig. 10. 
 
 thus avoiding the introduction of long shafts to bring 
 down the motion has been found to answer well, the con- 
 ductors alone are brought down, the connexion with the 
 head cap being made through rubbing contacts of copper 
 on rings of the same metal. The wheel B is attached 
 to the pulley A by means of two links, L L, as shown 
 at K M N. The wheel A is fast on the shaft C D, and 
 B is loose. If B be turned as shown by the arrow on 
 the belt M the tendency of the links is to make the pulley 
 B approach A , and thereby compress the spiral spring S. 
 A gun-metal wheel E, kept by means of a spring against 
 the disk F, which is part of the pulley, moves a jointer 
 over the dial H, and thus the tension of the belt at the 
 effective radius is read. A speed indicator is attached 
 as in the other machines. The central spring at the 
 end where it comes in contact with the pulley B is 
 furnished with a sleeve which slides on the central 
 shaft. The end face of the sleeve is grooved, and the 
 part of the pulley opposite to this groove is also grooved 
 in a similar way. Several steel balls are placed between 
 the grooves, and render the contact between the spring 
 
and the pulley as frictionless as possible. The pulley B 
 has a larger face than A, to permit of the slight side 
 motion necessary to act on the spring. 
 
 [22] Mercurial speed indicator. This part of the 
 apparatus belonging to the ergometer is based on the 
 principle involved in the velocimeter of Ramsbottom. 
 In his instrument oil in a glass cylinder is caused to 
 rotate, and the depression of its surface caused by 
 rotation is used to denote the velocity of 
 the shaft to which it is attached. As this 
 instrument does not admit of sufficiently 
 close reading for the ergometer, mercury 
 has been used instead of oil ; this is whirled 
 round in a cup with inverted edges A Fig. 
 (n). Into the centre of the mercury a 
 fixed glass tube (B) dips ; the end of the 
 tube in the mercury has fifty times the 
 capacity of the rest of the tube. The 
 tube is partly filled with a tinted liquid, the 
 column of liquid being supported by the 
 mercury. Now when the mercury is 
 whirled, the centre in sinking alters the 
 capacity of the large end of the tube, and this 
 alteration of capacity, even when slight, is 
 Fig. II. clearly shown by the displacement of the 
 liquid in the stem of the tube. The cup is caused to 
 rotate by means of any two wheels of a set of change- 
 wheels attached at C, these wheels being used either to 
 reduce or augment the speed of rotatation as any par- 
 ticular case might require. The relationship between 
 the depression and the angular velocity is that the de- 
 pression varies as the square of the angular velocity. 
 
 [23] When using ergometers in testing a dynamo or 
 electro-motor, it is hardly, perhaps, necessary to mention 
 that the mechanical h.p. may be compared at once with 
 the electrical by testing the circuit with an Am-meter 
 and Volt-meter during the trial. Instruments suitable 
 for this purpose are the graded galvanometers of Sir 
 \V. Thomson, the Am-meters and Volt-meters of Pro- 
 fessors Ayrton and Perry, and the combination instru- 
 ment of Siemens. 
 
26 
 
 [24] Electrical energy in terms of foot pounds and 
 horse power. 
 
 A Watt, which is the received unit of power, is 
 defined as " The power conveyed by a current of an 
 Ampere through the difference of potential of a Volt," 
 so that the Watt expresses the rate of an Ampere 
 multiplied by a Volt.* The English horse power is 
 equal to nearly 746 Watts, and the French Cheval de 
 Vapeur to 735 Watts. 
 
 In the centimetre gramme second system the value 
 of the Ampere is lo" 1 C. G. S. units, and the Volt is 
 io 8 C. G. S. units ; therefore the Ampere x Volt or Watt 
 = io 8 x lo" 1 = io 7 C. G. S. 
 
 Now i foot Ib. = 1.356 x io 7 ergs.f 
 
 . . one erg. = ft. Ib. 
 
 1.356 X io 7 
 
 and the Watt or io 7 ergs. = * * Ic>7 7 = 0.73747 ft. Ib. 
 
 1.356 x io' 
 
 per sec. Now 550 ft. Ib. per sec. = i h.p. 
 
 and 55 _ = 746 nearly, so that there are nearly 746 
 
 -73747 
 Watts in the English horse power. 
 
 * See Report of the British Association," Nature," vol. xxvi., p. 391. 
 t See Units and Physical Constants, by Prof. Everett, p. 16. 
 
SHORT NOTES, WITH REFERENCES, 
 
 ON 
 
 TRACTION, FRICTION, AND TRANSMISSION, 
 ERGOMETERS. 
 
 {Traction Brgometers. 
 
 McDouGALES. Rees 1 Cyclopedia, plate xxvi., vol. A. 
 This is one of the earliest machines of the traction ergo- 
 meter type, the date of the plate is 1809. A spiral 
 spring was placed between the load and the horse 
 drawing it, the spring was furnished with a rack and 
 pinion ; by this means the extension of the spring was 
 indicated on a dial. 
 
 SALMON. Rees' Cyclopedia, plate xxvi., vol. A. A 
 similar device attached to a horse when working a 
 horse-mill. 
 
 MORIX. Description des Appareils Dynamometrique. A 
 Poncelet spring balance, made of two flat springs, was 
 placed between a wagon and the horse drawing it ; the 
 extension of the spring was recorded on a band of paper. 
 
 MESSRS. EASTON AND ANDERSON. Report of Royal 
 Agricultural Society. A machine for testing the draught 
 of ploughs and implements. A spiral spring is placed 
 between the horse and the implement drawn, a record 
 of the work done is made by means of an integrating 
 apparatus; a "dash-pot" is introduced to diminish the 
 vibration of the machine when in use. 
 
 MM. VAILLEMIN, GUEBARD AND DIEUDONNE. Span's 
 Dictionary of Engineering, p. 1306. A traction ergometer 
 railway car, used to test the resistance of a train ; in 
 this machine a composite spring is used, one side of 
 each spring being flat the other slightly curved ; an 
 integrating apparatus records the work done. 
 
 SMEATON. Traces on Hydraulics, p. 48. Small wind- 
 mills, having different forms of sails to be compared, 
 were placed on the end of a radial arm to which motion 
 
28 
 
 could be given by means of a handle, this caused the 
 windmill sails to strike against the wind and raise 
 weights by means of a cord attached to a drum con- 
 nected to the sails. 
 
 transmission JErgometers* 
 
 INVENTOR : MORIN. Descriptions des Appareils Dyna- 
 mometvique. Two pullies are placed on the same shaft, 
 one of them is fixed, if the other, which is loose on the 
 shaft, be angularly displaced with regard to the fixed 
 one, its displacement deflects a straight bar spring, the 
 centre of which is fixed to the shaft. A recording drum 
 attached to the pullies and going round with them, re- 
 cords in the form of a diagram on a strip of paper, a 
 curve, which being duly interpreted shows the work 
 done. 
 
 MESSRS. EASTON AND ANDERSON. Report of the Royal 
 Agricultural Society. Two pullies are used as in the pre- 
 ceding machine, instead of the bar spring two curved 
 ones are used, and a continuous record of the work 
 done is kept by .means of an integrating apparatus of 
 the disc and roller type. 
 
 HACHETTE. Mechanics of Engineering, Weisbach, vol, 
 ii., p. 46. Three cog wheels are placed side by side in 
 gear in the same straight line, the central one is attached 
 to the end of a steelyard and is forced down when work 
 is being done, the pressure on the cogs is estimated by 
 means of the steelyard, this being known and also the 
 velocity of the wheels, the energy transmitted may at 
 once be adduced. 
 
 SHINZ. Mechanics of Engineering, Weisbach, vol. ii., 
 p. 49. Essentially the same as the preceding. 
 
 RITTINGER. Same reference. The same improved ; it 
 is called the pillow-block ergometer. In this machine 
 only two cog wheels are used, and the pressure on the 
 bearing is used to indicate, as in the preceding machine. 
 A portable hand machine similar in action to this is 
 shown on p. 510 of Span's Dictionary of Engineering. 
 
 WHITE. Span's Dictionary of Engineering. Two 
 pullies, each attached to a bevel wheel and running on 
 
2 9 
 
 the same fixed axis, are in gear with two other bevel 
 wheels carried with their axes at right angles with the 
 common axis of the former on a lever to the other end 
 ot which weights are applied, by this means the pres- 
 sure between the cogs is measured, and the velocity 
 being known, the energy transmitted is at once deduced. 
 
 FREDERICK J. SMITH. See p. 22 of this book and 
 p. 17 Paris Elettrical Exhibition list in Proceedings of the 
 Telegraph Eng., 1881, also Electrician, Sept. 10, 1881. 
 
 7. WAGNER. Mechanics of Engineering, Weisbach, vol. 
 ii., p. 55. Three bevel wheels are in gear instead of 
 four as in White's, and the difference of pressure on the 
 teeth of the wheels causes a lever carrying a weight at 
 its end to be raised through an arc, as in an ordinary 
 index balance for weighing letters ; the pressure on the 
 cogs is estimated by means of this. 
 
 HAGENBACH. Telegraphic Journal, 1881, p. 65. The 
 same in principal as Hachette, a spiral spring taking 
 the place of the weights in the former machine. 
 
 PROFESSORS AYRTON AND PERRY. Proceedings of 
 the Soc. Tel. Eng., 1881, p. 163. A fast and loose pulley 
 on the same shaft are connected by means of four spiral 
 springs, angular displacement' between the two pullies 
 causes the springs to be extended, the extension is made 
 known by means of the change of position of a bright 
 bead attached to a light lever moved by one of the 
 pullies. 
 
 RAFFARD. Proceedings of the Soc. Tel. Eng., 1882. A 
 train of cog wheels are so arranged that the pressure on 
 the teeth may be estimated by means of a lever and 
 weights. The reference and diagram should be seen to 
 understand the construction. 
 
 HARTIG. Polytech. Centralblatt, 1857, No. i ; also 
 Separat-Abdruck aus dem Bayerischen Industrie-und Gewer- 
 beblatt, 1883, heft. i. Six cog wheels are so engaged that 
 the pressure on the teeth of a pair of wheels can be es- 
 timated by means of a Poncelet spring. The diagram 
 of the machine should be examined. 
 
 FREDERICK J. SMITH. Philosophical Magazine, vol. xv., 
 p. 87. Fully described in this book at pp. 13, 14, 15. 
 
W. FROUDE. Proceedings Inst. Mec. Eng., 1858. The 
 tension of the belt driving a machine is measured while 
 moving, the pullies over which it runs being placed on 
 a scale-beam controlled by a spring balance, by it the 
 tension of the belt is estimated, a recording drum is 
 attached and by it a continuous record is kept of the 
 work done. 
 
 EDISON. Scribner's Monthly, vol. xix., p. 543. The 
 driving belt of a dynamo is passed under a small pulley 
 attached to a weight placed on the platform of a weighing 
 machine, the tension of the belt when running causes 
 the weight to be lifted and its force on the weighing 
 machine to be diminished, by this means the tension of 
 the belt is estimated and from it (the speed of belt being 
 known) the horse power. 
 
 F. VON HEFNER ALTENECK. Professor M. Schroter 
 (Separat-A bdruck aus den Bayerischen Industrie-mid Gewerbeb- 
 latt, 1883, heft. i.). The difference of tension on the two 
 sides of a driving belt is estimated by causing pullies 
 over which it runs to be displaced. The reference 
 should be consulted, the description is quite beyond 
 the scope of a mere note. 
 
 E. THOMPSON. The Scientific American, quoted from 
 the English Mechanic, vol. xxxii., p. 607. A modifi- 
 cation of the machine of Alteneck. The tension of the 
 driving belt is estimated by means of a steelyard and 
 weights, the lever being so graduated as to read off 
 horse-power at once, the velocity of the driving pulley 
 being kept constant. 
 
 EMERSON. Journal of the Franklin Institute, Sept., 1882, 
 and Spon's Die. Eng., p. 628. This machine is designed 
 to attach to any shop machine ; the pulley of the machine 
 to be tested is removed and is replaced by the ergometer, 
 the tension of the belt causes a weight to be raised 
 through an arc, as in the machine of Wagner, and a 
 pointer on a dial shows the amount of tension, a speed 
 indicator driven by a worm wheel gives the number of 
 revolutions made by the machine. 
 
 SCHUCKERT. Professor M. Schroter (Separat-Abdmck 
 mis den Bayerischen Industvie-und Gewerbeblatt, 1883, heft. i.). 
 
3 1 
 
 A fast and loose pulley are placed on the same shaft 
 and they are connected by springs, as in Messrs. Ayrton 
 and Perry's machine, but in Schuckert's machine the 
 spiral springs are placed in cylindrical cases. The 
 angular displacement of the two pullies is made known 
 by means of a rod thrust out in the line of the axis of 
 the wheels, and the machine registers its results. 
 
 RIELER. Same reference. Three cog wheels are in 
 gear as in Hachette's machine, a spring taking the place 
 of the weight in Hachette's, and a registering apparatus 
 has been added. 
 
 ^friction JErgometers. 
 
 PIOBART AND FARDY, 1820. Applied a brake to 
 determine the power of water wheels. 
 
 PRONY. Spans. Die. Eng., p. 616. A pulley or shaft 
 of the machine to be tested is embraced by two jaws of 
 wood ; these jaws are furnished with an arm to which 
 weight may be attached to prevent them being carried 
 round with the shaft. When the shaft is running at its 
 usual speed weights are applied to the arm till it 
 assumes a horizontal position, then the moment result- 
 ing from the co-efficient of friction is balanced by the 
 moment due to the weight on the end of the arm. From 
 this the work done is calculated, as shown at page 8. 
 The same sort of machine has been used by Lowell in his 
 hydraulic experiments on turbines with the plane of 
 rotation horizontal. See Mechanics of Eng., Weisbach. 
 Vol. ii., p. 67 for illustration. 
 
 PONCELET. Spans. Die. Eng. To Prony's machine 
 Poncelet added a rod at right angles to the end of the 
 arm attached to the jaws, and pointing downwards. To 
 the end of this rod the weights were attached. By this 
 device if the coefficient of friction were to increase the 
 weight would be carried into a new position, which 
 would make its arm longer and its effect greater, and 
 thus equilibrium would be restored. 
 
 APPOLD. A pulley driven by the machine to be 
 tested is embraced by a steel strap armed with wood 
 blocks, which press against the pulley. The pressure 
 
of the strap is regulated by means of a lever, one end of 
 which is fixed in a vertical line just under the axis of 
 the pulley. To the other end of lever which hangs a 
 little below the length of the strap the weighted side of 
 the strap is attached by means of a short link. The 
 other end of the strap is attached to the same lever at a 
 point just within the length of the radius of the inner 
 faces of the wood blocks. The effect of such a device 
 is that if the coefficient of friction should increase, the 
 weighted side of the strap is turned upwards. This 
 causes the lever to be turned in the same direction and 
 pressure to be taken off the strap. This at once restores 
 equilibrium. The reverse takes place should the co- 
 efficient of friction decrease. 
 
 DEPREZ. Two jaws are brought together by means 
 of a similar lever to that used in the Appold machine, 
 but the fixed point in Appold's becomes a weighted point 
 placed in the line of the axis of the pulley on which the 
 jaws act. 
 
 FROUDE. Proceedings of the Inst. Mech. Eng., July, 
 1877, P- 2 37- I n this machine a turbine of peculiar con- 
 struction takes the place of the pulley and wood jaws of 
 the Prony machine. It will well repay the trouble of a 
 close examination of the original description. Span's 
 Dictionary of Engineering gives a good history of it at page 
 513 supplement. 
 
 This is by no means an exhaustive list of the many forms of 
 ergometers now used, but more have not been mentioned as they 
 so nearly resemble some in this list, only differing in small Uetails 
 of construction. 
 
 A. HAMMETT, PRINTER, TAUNTON. 
 
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