ANIMAL MECHANICS. 



271 



shortening of the muscular fibres joining the bone AB with 

 the vertex 0. 



The preceding investigation leads to the following : — 



Proposition C. 



If, in a triangular muscle A OB, the moveable bone AB ro- 

 tate round an axis, perpendicular to OX, the bisector of the 

 angle A OB — 



1°. The contraction of the muscle will tend to restore the 

 bone to its original position, if the axis of rotation intersect the 

 bisctor OX, beyond either 0 or X ; and its restoring power 

 will increase with the distance of the intersection of the axis from 

 0 or X. 



2°. If the axis of rotation pass through 0 or X, the contrac- 

 tion of the muscle can have no effect in moving the bone. 



8°. The contraction of the muscle will tend further to clis- 

 place the bone, if the axis of rotation intersect the bisector OX, 

 between 0 and X ; and its displacing power will be a maximum 

 when the point of intersection of the axis bisects the bisector 

 OX. 



In addition to the construction shown in Fig. 71, for the 

 work done by the muscle, whether positive or negative, the 

 following construction may be used, and is interesting, be- 

 cause it is a particular case of the construction belonging to 

 the general equation (48). 



Let us suppose the work done to be represented by the 

 square of the ordinate of a curve, whose abscissa is a cos 0 

 = x. Then, by equation (50), we have, for the triangular 

 muscle, 



f = x{b + x). (51) 

 When if is positive, this is the equation of an equilateral hy- 



