458 



ANIMAL MECHANICS. 



which X'OX is the single asymptote, corresponding to t = o, 

 and ApA is the double asymptote corresponding to 



a 



w + — = o, 



and having a cusp at negative infinity. 



Fig. 105. 



There is an hyperbolic branch lying between pX' and pA'. 

 The curve passes through the origin 0, and the positive 

 weights are measured on OX, while negative weights are 

 measured on OX', The asymptote A A' lies at a distance from 



YY' equal to - ; which signifies that if the hand were lifted 



by a weight equal to that of half the arm, it could be held 

 out for an infinite time, without being tired, as is evident. 



The portion of the curve with which we are concerned 

 lies between OX and 0 Y. 



The ordinate (or useful effect) attains a maximum mm', 

 when the weight Om' is equal to half the weight of the arm ; 

 and the point n corresponding to On' equal to the weight of 



