ANIMAL MECHANICS. 



271) 



In the three cases now considered, we have : 



i°. The axis of rotation passing through the centre of the 

 conic (56, 57), is the axis of maximum instability. 



2°. The axis of rotation passing through the centre of the 

 conic (56, 57), is the axis of neutral equilibrium. 



3 0 . The axis of rotation passing through the centre of the 

 conic (56, 57), is the axis of minimum stability. 



The condition contemplated in the second of the foregoing 

 cases, viz., that the expression (55) 



(b - b') 2 X sin /3 sin j3' - $b' Y cos j3 cos j3' = o 



may be readily found. For, since 



b tan [3 = b' tan [3\ 



we have 



tan /3' = — tan j3, 



b' 



which reduces (55) to the following : 



tan ,p m _ _ „, 



or 



When the angle [5 exceeds the value determined by 

 equation (58), the expression (55) will be positive, and a 

 position of axis of unstable equilibrium will be possible ; but 

 when f3 is less than the value assigned by equation (58), the 

 equilibrium will, in all cases, be stable, and there is no position 

 of axis of rotation which will render it unstable. 



We shall now consider the general expression (48) for 

 the work done by a quadrilateral muscle revolving round an 

 axis in its plane, and perpendicular to the bisector of the 

 angle AOB, contained between its extreme fibres. 



