ANIMAL MECHANICS. 



447 



represents one- third of the weight of the moving arm ex- 

 pressed in pounds. The weight of Mr. Jevons' arm, includ- 

 ing the scapula and its muscles actually in motion, is therefore 

 1 1.7 lbs. 



The remarkable agreement between the observations and 

 equations (115) and (119) which may be derived directly, as 

 I have shown, from the Law of constancy of work done in a 

 single contraction of a group of muscles, proves completely 

 the accuracy of that Law. 



Although the work done by the contraction of the muscles 

 is constant, the useful work done is not constant, and it may 

 be worth while to inquire how it varies, and whether it 

 admits of a maximum, a circumstance which would have an 

 important practical significance. 



Using the same notation as before 



The useful work done = wx = rj. 

 The weight thrown — w = £. 



If £ and y] be used to designate the abscissa and ordi- 

 nate of a curve, by constructing this curve of useful work 

 done, we may ascertain whether its ordinates admit of a 

 maximum or not. Multiplying Mr. Jevons' equation (115) 

 by w, we find 



pw 



wx = — 



w + q 



or *? = ,f • (120) 



% + q v y 



This represents an equilateral hyperbola referred to axes 

 parallel to its asymptotes, and intersecting on the curve 

 itself. 



In Fig. (102) I have constructed from calculation the 

 curve of useful effect, which is an equilateral hyperbola, 

 having OX and OY {or asymptotes. 



