Apnl I'j, 1S75J 



NATURE 



465 



in, tJie total icoriaV^wf multiplied by the rate ofvim-k is constant." 

 The words constant action are here to be understood in the sense 

 in which all muscular action used by animals is constant, viz., 

 short periods of contraction followed by short intervals of rest, 

 as in walking, climbing, &c. And the velocities employed are 

 understood to be, v/ithin certain limits, such as are used in all 

 descriptions of labour. 



The " Law of Fatigue" (thus stated) is based by me upon 

 several and various classes of experiments. 



Mr. Nipher's experiments (employed in my book, pp. 462-65) 

 consisted in raising various weights at a fixed rate and at regular 

 intervals through a fixed height, as described in page 462 of my 

 book. The ' ' Law of Fatigue " in this case led me to the 

 formula — 



« (to + o)'' = ^ (I) 



which is a cubical hyperbola. 



As stated in Nature by Mr. Nipher, the comparison of this 

 formula with observation is given in pp. 464-65, and is most 

 complete and satisfactory. I here give it for the right arm, and 

 refer for that of the left arm (which is equally satlsfactoiy) to the 

 book itself. 



Mr. Nipher^Right Arvi (raising weights at constant rate). 



A — 1,000* 

 0=1 



Mr. Nipher admits (Nature, vol. xi. p. 257) that this com- 

 parison of his observations with formula (i) deduced from the 

 "Law of Fatigue" is satisfactory, but proposes (Nature, vol. 

 xi. p. 276) to substitute fur his observations used by me, another 

 set of similar obseivalions submitted to a series of reductions; 



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these observations are given in his Table II., and will be fuUy 

 consideted by me hereafter. I may here observe that the percentage 

 error in the above table is less than that given by him in com- 

 paring Table II. with an empirical formula. 



Other experiments, in which the same weight was lifted at 

 varying r.ites, were made by Dr. Alexander Macalister, Mr. 

 Gilbert Haughton, and by Mr. Nipher (vide "Animal Me- 

 chanics," pp. 46S to 477). Mr. Nipher now rejects his own 

 experiments, and, as I believe, with good reason. These 

 experiments are given in Nature, vol. xi. p. 256, Table I., 

 with the exception of the fir;t line, which is taken from 

 the experiments just given. The reason why I transferred 

 the first experiment from the former series is this. The 

 column for « ought to show a maximum in passing from very 

 rapid to very slow motions ; for if the motions be very rapid, 

 respiratory distress sets in, and the work done will be less than 

 with a slower motion ; and 'f the motion be very slow, the useful 

 work done will be also less, owing to the fatigue work spent in 

 holding up the weight ; from this it follows that there is a certain 

 rate of lift at which the maximum work is done. 



If we omit the first line in Mr. Nipher's experiments. Table I., 

 we find no trace of a maximum in the column for «, which may 

 be regarded as internal evidence of something wrong in the 

 observations. At the time of publishing my book, I thought 

 (and still think) that Dr. Macalister's and Mr. Gilbert 

 Haughton's experiments were better than those of Mr. Nipher, of 

 which, however, I made use as well as of the other experiments, 

 as I wished to employ all the materials at my disposal in dis- 

 cussing the Law of Fatigue. I now fully concur with Mr. 

 Nipher's estimate of the value of his observations, made at vary- 



ing rates, which he states " were merely published as a pre- 

 liminary" (Nature, vol. .xi. p. 256, note). 



The withdrawal of Mr. Nipher's experiments at varying rate 

 from the controversy disposes at once of the greater part of the 

 criticisms, which are based on the difference between his experi- 

 ments at var)'ing rate and at fixed rate. 



Mr. Nipher, however, not only withdraws his experiments at 

 varying rate, but criticises Dr. Macalister's and Mr. Gilbert 

 Haughton's experiments of the same class. 



I shall first answer his criticisms on the experiments of Dr. 

 Macalister and Mr. Gilbert Haughton, and then notice his own 

 new experiments at fi.xed rate and empincal formula. 



The relation between n and t in Dr. Macalister's and Mr. 

 Gilbert Haughton's experiments is represented by a central 

 cubic, viz. :— 



n = "" ., (2) 



This formula is plotted and compared with the experiments in 

 Diagrams, pp. 472 to 474, and the agreement is evidently close. 

 Mr. Nipher transforms equation (2) into the following : — 



-^' = ^ - /3 (nt), (3) 



and adds : — "Anyone who will take the trouble to calculate and 



co-ordinate the values of — and «/ from Prof. Haughton's ob- 



* If we correct these values by the method of least squares, we find A = 

 '933> °- = i'o94. and may reduce the sum of the squares of the percentage 

 differences from 3r6'33to 242 '56, thus making the agreement between theory 

 and observation somewhat closer. 



