306 



ANIMAL MECHANICS. 



3 0 . For the bisector itself, taken as axis of rotation, the 

 equilibrium of the muscle is neutral, and for all other positions 

 it is stable, and never becomes unstable. 



If we compare these results with the corresponding results 

 for rotation round axes perpendicular to the bisector of the 

 angle of the muscular fibres (pp. 269, 270), we see very im- 

 portant consequences, which may be thus stated : — 



Proposition E. 



No triangular muscle, by the contraction of its fibres, can 

 compel the bone that forms its base to revolve round an axis of 

 rotation lying in the plane of the muscle, unless the socket of the 

 joint lie between the perpendiculars drawn at each extremity of 

 the bisector of the vertical angle of the muscle. 



For, if the rotation be resolved round two rectangular axes, 

 parallel and perpendicular to the bisector, the equilibrium of 

 the muscle, with respect to the first component axis of rota- 

 tion, is always either stable or neutral ; and, with respect to 

 the second component axis of rotation, the equilibrium is also 

 either stable or neutral, unless the axis lie between the per- 

 pendiculars drawn at each extremity of the bisector. 



I have already shown, in the latissimus dorsi of Man, of the 

 Tiger, and of the Albatross (pp. 246, 249, 256), and in the 

 hamstring muscles of the Tiger (p. 258), that the socket of 

 the joint is placed upon the perpendicular at the vertex to the 

 bisector of the muscle, and that the object of that arrangement 

 is to produce the maximum amount of Work possible by a 

 rotation round an axis perpendicular to the plane of the muscle. 

 It follows from Prop. E, that these muscles can produce no 

 rotation whatever round any axis lying in the plane of the 

 muscle. 



These muscles are, therefore, intended to cause rotation 

 round one axis only, and to do so with a maximum amount 

 of useful work. 



