ANIMAL MECHANICS. 



281 



3 0 . The equilibrium of the plane muscle will be unstable 

 when y 1 is negative. 



4°. The stability of the equilibrium increases indefinitely 

 as the axis of rotation becomes more and more remote 

 from 0. 



5°. The instability of the muscle reaches a maximum at 

 a position of the axis of rotation passing through the centre 

 of the conic determined by equation (6o). 



The definite integrals, X, Y, Z, are readily found as 

 follows. We have 



sin 'OdO 

 A cos 6 + B sin 



where 



.A 



B 



(b - b') sin j3 sin j3' 



b sin j3 cos j3' - b' sin fi' cos /3 



Assume 



R sin a = A, 



B cos a - B\ 



then we have 



and 



i c cos me 



# Jsin (a + 8) 



