ANIMAL MECHANICS. 



43 



our difficulty is to find what kind of curve is best. Having 

 found that a curve of the fifth degree will not answer, I shall 

 now show that the relation between w and t may be repre- 

 sented by a cubical hyperbola. 

 By equation (7), 



Total work = tua '^w + - ) t ; 



Rate of work = am ( w + 



But, assuming the truth of the Law of Fatigue, the product of 

 these two expressions will be constant. Hence 



o> 2 a 2 [ w + - ) t = constant, 



w + - ) t = A. (12c) 



This equation represents a cubical hyperbola, whose 

 asymptotes are 



t = o, 

 a 



w + - = o. 



2 



This curve is free from the objections made to the curve 

 of the fifth degree, for t becomes zero when w is infinite, and 

 increases continuously, as w diminishes, and becomes infinite 



when w + - = o, which corresponds to the case of statical 

 equilibrium ; and t has no intermediate maximum between 

 zero and positive infinity. In fact, if we differentiate the 

 equation (12c), we find 



