ANIMAL MECHANICS. 



445 



The calculated distances contained in the foregoing Table 

 were obtained by Mr. Jevons, by assuming the following 

 empirical Law : 



where 



x = distance thrown, 

 w = weight thrown, 



p, q, unknown constants to be determined. 



The experiments gave Mr. Jevons eight distinct equa- 

 tions by which to determine the two unknown quantities p 

 and q ; and by means of the method of least squares, Mr. Je- 

 vons found their most probable values to be 



P = 1 15-7 

 3-9 



Mr. Jevons correctly stated that the agreement between 

 observation and calculation is so close as to prove the accu- 

 racy of the empirical law (115), but he professes his inability 

 to explain it on mechanical principles. I subsequently suc- 

 ceeded in doing so, and published my results in Nature. My 

 investigation is as follows : — 



In throwing weights by the hand in the manner described 

 by Mr. Jevons, the arm, after a little practice, instinctively 

 pitches the weight at the angle (45 0 ) corresponding to the 

 maximum range (#), and as the maximum range is propor- 

 tional to the square of the velocity of projection, it may be 

 used to replace that quantity, in estimating the work done by 

 the arm. The total work done by the arm is the same as if 

 the weight used and the weight of the arm were concentrated 

 at the centre of Gyration of the loaded arm, regarded as a 

 compound pendulum. 



