974 



ANIMAL MECHANICS. 



COS 2 0dQ 

 cos 9 



sin me 



cos 0 



P = sin j3 sin j3' (6 + a cos 0) (6' + a cos </>), 



Q = cos j3 cos j3' . a 2 cos <£ 2 , 



2 (6 - 6') sin j3 sin |3' 



If, as before, we write 



/ = PI+ QY, 



x - a cos 0, 



we obtain the equation of the curve the square of whose ordi- 

 nate represents the work done by the contraction of the 

 muscle, the axis of rotation corresponding to the ordinate in 



y 2 = X sin j3 sin /3' (b + x) (b' fa?) + Fcos j3 cos fix' 2 . (53) 



This is the equation of a central conic, whose major axis lies 

 on the bisector OX, and whose centre is situated at a distance 

 from 0 towards X represented by 



Since X and Fare essentially positive, and since the con- 

 dition B = o requires /3 and j3' to be both acute, § will be 

 essentially negative, and the centre of the conic will lie inside 

 the vertex of the triangle A OB. 



The positions of the axis on the bisector of A OB, which 

 correspond to neutral equilibrium, are found by equating (53 > 



or, 



1 (b + 6')Xsin/3sin/3' 



2 " Xsm |3 sin |3 + Fcos i?'cos j3" 



(54) 



