Aug. 5, 1875J 



NATURE 



271 



LETTERS TO THE EDITOR 



[The Editor does not hold himself responsible for opinions expressed 

 by his correspondents. Neither can he undertake to return, 

 or to correspond with the writers of, rejected manuscripts. 

 No notice is taken of anonymous communications.^ 

 On the Mechanical Work done in exhausting a Muscle 

 I BEG leave to make some reply to the comments (Nature, 

 vol. xi. pp. 464, 488) of Prof. Haughton on my paper, 



I. In regard to the relative value of my earlier and later expe- 

 riments, it is to be said, that in one sense they are all equally 

 valuable. My object, however, was to find the work of exhaus- 

 tion when the intervals of work and rest were equal, the work to 

 be expended only in lifting the weight. Hence the experiments 

 were made in such a way as to eliminate the fatigue caused by 

 the falling weight. Prof. Preston and myself practised for several 

 weeks, until we were able to keep accurate time, before the 

 published series was begun. All who saw the experiments were 

 then satisfied that the later method of experiment was an im- 

 provement. The two series first published were made with equal 

 care, an I I am therefore at some loss to know what has been 



Prof. Haughton's criterion in deciding that one was good and 

 the other bad. 



2. In dealing with Prof. Haughton's equation — 



A.t 



fif' 



(2) 



when it was said that the co-ordmated values of " and «V formed a 



t 



curve, the meaning could only have been that p is not a constant. 

 Prof. Haughton is of course right in saying that the observations 

 thus co-ordinated " may be represented by a straight line." He 

 might also have added that for properly chosen limits, any other 

 observations may also be represented by a straight line. ^ The 

 point is, whether these lines give any evidence qf regular devia- 

 tions. It seems to me that " any one accustomed to such obser- 

 vations" ought to be able to see such evidence in .the diagrams 

 of Prof. Haughton in Nature, loc. cit. In this connec- 

 tion I wish to give a series of experiments, the time of lift i 

 being variable and equal to the interval of rest. The values of 

 « are the means of four experiments, and are uncorrected;for 

 variations in strength. The experiments were made with the 



a^KB^^^^^^^^^^^^HBI^^Ii^B^S^^^BD^^^^^^^^^^^^^^^^^^^^^^^^^^B^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^I 



apparatus described in my last paper (Nature, vol. xi. pp. 256, 



276) and my right arm. 



JRaising weight of^'S kgr. through 070 in t sec. 



The values of n and t are represented in the diagram by the 

 dotted line. It will be seen that « reaches a maximum where 

 t = 3-4- 



The values of / — j and {n't) are also represented by the 



full line. It will be observed tliat the observations on 

 opposite sides of the maximum n are not continuous. A com- 

 parison of this line with those given by Prof. Haughton in 

 Nature, vol. xi. p. 465, will be found instructive. 



3. In the case just considered, the time of exhaustion depends 

 upon the velocity of disintegration and recuperation of the 

 muscles. It is well known that the velocities of such operations, 

 taking place in time, are represented by the binomial curve. I 

 have satisfied myself that the values of n in the above series are 

 represented by the terms of the expanded binomial (/> + ^)"» 

 where p -^q = I ; where / and q are unequal, and where 

 m — I represents the total number of chances. This point is 

 reserved for future investigation. 



4. In my paper in the American Journal of Science (Feb. 

 1875, pp. 130-137), the accuracy with which Prof. Haughton's 

 formula represents my experiments, was shown. Assuming 



(w+ o) hn = ,, 



(w + a) 



where a is the reduced weight of the arm, and Prof. Haughton's 

 law demands that v = unity. It turns out to be 2 •6. Prof. 



