182 



ANIMAL MECHANICS. 



The total amount of work inherent in the muscle may be 

 found as follows : if I denote the length of any fibre Ox, then 

 IdO will be proportional to the work of its contraction ; and 

 the total inherent work will be — 



Inherent Work of Triangular Muscle =/ 



mo 



If we call j3 the angle BXO (Fig. 28), we have 

 b sin j3 



sin (j3 - 0) 

 Inherent Work = f$b sin j3 



, and 



dO 



n (j3 - 0) 



This result admits of a geometrical illustration (Fig. 30). 

 In the triangle A OB draw the bisector of the vertical angle 



0 



Fig. 30. 



OX, and from the point X let fall the perpendicular XY= q. 

 Produce the sides AO and AB, and draw the exscribed circle, 



