276 



NATURE 



[Feb. 4, 1875 



Thus we see what interest there is for astronomy to determine 

 the parallax of the sun by three independent methods ; I trust 

 that the experiments that I have the honour to submit to the 

 Academy will justify, by their precision, the theoretical im- 

 portance of the physical method. R- M. 



ON THE MUSCULAR MECHANICAL WORK 



DONE BEFORE EXHAUSTION* 



II. 



ONE of the principal sources of error in the series of experiments 

 before discussed, was the fatigue caused by the downward- 

 plunging weight. To elirninate this, the apparatus shown in 

 vertical section in Figs, i and 2 was constructed. The shelf 0, 

 armed with a plate of car-spring caoutchouc, serves as a support 

 for the weight. This shelf is fastened by the iron bands, /, and 

 a vertical backpicce, B, to the slide, u, being further supported 

 by a crosspiece. By suitable blocks, a, the slide may be raised 

 to any desired height, which height is read off on a scale marked 

 on the upright pieces, A. j is a support for the arm during the 

 interval of rest, and it can be adjusted to any desired height ; 

 IV h a wire, from which a small cord, />, passes horizontally to the 

 wall of the room. By some modifications this cord can also be 

 male movable, which will become necessary when I come to 

 investigate the influence of elevation of the arm, upon the work 

 done. The weight is a bucket of shot, provided with a stiff 

 bail and a wooden handle, so that for any position of the arm 

 while lifting the weight, the line passing through the centre of 

 the hand and the centre of gravity of the weight is a vertical. 

 Placing the bucket upon the shelf 0, the experimenter stands to 



the right of the apparatus (as in Fig. 2), and lifts the weight 

 until his knuckles touch the cord b. The instant of beginning 

 and close of this interval of work is marked by the sharp click 

 of a metronome, the time of whose beat is /. At the instant 

 when the knuckles touch the string, the weight is grasped by an 

 assistant, + and by him lowered to the shelf 0, the arm of the 

 experimenter being entirely relaxed, and resting upon the stiii 

 bail of the bucket and the support s. X This is continued until 

 the arm becomes unable to lift the weight to the required height. 

 Tlie determin.ation of the number of lifts should lu-vcrht made by 

 the experimenter, who should furthermore try to lose all estimate 

 of time during the process. In the earlier experiments it became 

 evident that the arm not only grew gradually stronger, but also 

 that it varied greatly from day to day. In order to get some 

 measure of the strength, the arm was exhausted on each day of 

 experiment, by a constant weight (5 'o kilos.) lifted through a 

 height h = 070 metres in a time t = I '25 sec. The values of 



* Continued from p. 257. 



+ I am under many obligations to friends, among whom I may mention 

 Mr. W. C. Preston and Mr. D. A. Myers, for aid in this very laborious 

 work. 



J The arm is raised in the plane which make an angle of 45° with the 

 vertical plane passing through the centres of the shoulder-joints. 



« were all reduced to the mean strength, as shown by the con- 

 stant experiment. 



In the series here given, w was variable, h = 070 metres, and 

 T = I '25 sec, the interval of rest being equal to the interval of 

 work. The mean value of n for the constant experiment for 

 the weights ro = 3-0, 3-5, 4'o, &c. — 7'5, in all 100 experiments, 

 is 35 '79- Taking these values, c, as the measure of the strength, 

 and assuming that the work done with any weight at different 

 times is proportional to the strength,* and we have — calling 

 ;/ the number of lifts before exhaustion, and « the number 

 reduced to the basis of the mean constant (3579) — 

 K= 3579 



from which we have the following values of n, which hereafter 

 we shall call >i (obs. ) Each of these values is a mean of ten 

 independent determinations. 



Table II. 



The determination of it for w = 7 '5 and 8 "O was consciously 



velocity, so that I was obliged to stop li^forc- the arm was ex- 

 hausti\i.\ The values of n for w less than 3'o were also dropped 

 in the final calculation, as with such light weights the work is 

 found to vary greatly with a slight variation of strength. 



Assuming the arm to be a uniform cylinder, and denoting by 

 a. one half tlie weight of the arm, and we have as the dynamical 

 work done before exhaustion — 



/F=(w; + :«)/,« (6). 



The value of a can be determined directly by means of a 

 spring-balance. Exhaust the arm thoroughly, then grasp the 

 hook of the spring-balance, the dial of which should be turned 

 from the face of the experimenter, the reading being done by an 

 assistant. After several minutes the muscles tire, and the prac- 

 tised experimenter can then gradually relax them fully. Un- 

 trained muscles, when thus tried, act involuntarily, and precise 



* This is only approximately trne, but is accurate enough for our purpose. 

 We shall develop tliis point further on. 



t This is a highly import.int point. Try to lift 20 kilos, in a second of time 

 through o"7 metres. You will fail to lift it once, and yet not be exhaitsied. 

 The problem of maximum velocity attainable with different weights, is 

 wholly different from the one under consideration. I think Mr. Haughton 

 has overlooked this influence on his own experiments. 



