ANIMAL MECHANICS. 455 



Now, we have 



, a 

 (w + a) x = wu + a -, 

 2 



where a is the length of the arm, supposed to be an uniform 

 cylinder ; therefore 



(w + a) x = a^w + 



substituting in equation (127), we obtain (assuming w 2 to be 

 an unknown constant) 



w +-]t = A. (12%) 



This equation represents a cubical hyperbola, whose 

 asymptotes are 



t = o. (129) 



w -f - = o. 

 2 



Solving equation (128) for t, we find 

 + - 



03°) 



The useful effect is found by multiplying ( 1 30) by w, and is 

 Useful effect = wt = - . (ni) 



/ (I .2 v -» ' 



This equation represents a cuspidal cubic, whose shape I 

 shall presently describe. 



I find the following values of A and a to give me the best 

 agreement between theory and observation, viz. :— 



A = 7730. 

 a = 8.5 lbs. 



