278 



ANIMAL MECHANICS. 



zero also ; and the hyperbola will be reduced to its asymptotes, 

 while the ellipse disappears altogether. Hence, in this case, 

 the equilibrium of the plane quadrilateral muscle will be 

 always stable for every axis of rotation, except that passing 

 through the intersection of the asymptotes ; for which axis of 

 rotation the equilibrium will be neutral ; and, finally, there is 

 no position of axis possible for which the equilibrium becomes 

 unstable, so that the contraction of the muscle would convert 

 the plane quadrilateral into a skew muscle. 

 3 0 . If the expression (55) 



(b - b') 2 X sin j3 sin j3' - 4W Y cos /3 cos /3' 

 be negative, m 2 and ?i 2 will both be negative ; and there is no 

 possible position of the axis which will render y 2 either zero 

 or negative. The construction for this case becomes the 

 following (Fig. 75): — 





p 



B 









A 



X 



' t 











0 



■i 





b 



Fig. 7 5- 



Construct, with the same axes and asymptotes as before, the 

 conjugate hyperbola, whose real axis is CB = n, on the line 

 CB, perpendicular to OX, the bisector of the angle made by 

 the muscular fibres. If a rotation take place round any chord 

 ab, cd, the work done by the muscle will be proportional to 

 the square of the chord of rotation, and its contraction will 

 always restore the skew muscle to the plane, and the equi- 

 librium will never become neutral or unstable. 



