ANIMAL MECHANICS. 239 



quadrilateral muscle ; it is required to find the motion of AB, 

 when the muscle contracts. 



The most general possible movement of AB may be re- 

 presented by a movement of translation parallel to itself, and 

 a movement of rotation round a point. 



Produce AA1 and BB' to meet at 0, and draw OX, the 

 bisector of the vertical angle. I say that no work is done by a 



o 



rotation of the bone AB round an axis passing through X 

 the foot of the bisector, and perpendicular to the plane of the 

 muscle, and, therefore, that the muscle by its own contraction 

 can never produce such a rotation. For, let xy be the new 

 position of the bone AB, when turned through a small angle 

 of rotation, xXA = yXB = w. 



Let aa'O be the original direction of any muscular fibre, 

 and let ab be the path described by the point a during the 

 rotation; draw bp perpendicular to ad and join a'b. Let 

 Oa = I 

 Oa' = I 

 aOX = 0 

 BX0 = (3 

 OX = b. 



