446 ANIMAL MECHANICS. 



Let 



us assume 



w = weight held in hand, 



a = weight of arm, 



v = velocity of centre of Gyration. 



By the law of Constancy of Work, we have 



(w + a) v 2 - constant. ( 1 1 6) 



Let 



V = velocity of the hand, 

 k - radius of gyration, 

 a = length of the arm. 



We now have the additional equations, 



v-V* (i i 7 ) 



and since the arm may be assumed to be approximately 

 cylindrical, we have 



y + — J a 2 = (w + a)k-. 

 3/ 

 or, 



a 



72 w + ~ 

 3 



a 2 w + a ^ ' 



Substituting from (117) and (118) in equation (116), we 

 find 



F 2 \w + - j = Const. : 

 and finally, writing x for V 2 , as before explained, we have 



x = -£— d (119) 



w + - 

 3 



This equation is identical with the empirical formula (115) 

 employed by Mr. Jevons, and shows that his constant, q, 



