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ANIMAL MECHANICS. 



2°. That if the axis of rotation pass through either 0 or X 

 (the vertex of triangular muscle or foot of bisector of vertical 

 angle), the bone AB will remain, indifferently, in any position 

 in which it is placed, for no work is done in altering its 

 position, 



3°. That if the axis of rotation lies between 0 and X, a 

 contraction of the muscular fibres will immediately cause a 

 motion of the bone round the given axis, for any change of 

 position will be accomplished by a total shortening of the fibres, 

 which is possible. 



4°. The triangular muscle will exert a maximum effect 

 in displacing the bone AB, round the axis passing through 

 the socket joint, when that axis of rotation bisects the line 

 OX, because in this case the total shortening of the fibres will 

 be a maximum. 



The positions of the axis of rotation, beyond 0 or X, 

 which correspond to positive values of the work done, denote 

 positions of stable equilibrium, and the work done by the 

 muscle consists in forcing back the bone into the plane con- 

 taining itself and the axis of rotation. 



The positions of the axis of rotation, passing through 

 0 or X, correspond with positions of neutral equilibrium, 

 when the bone and muscle are indifferent to the position in 

 which they are placed, and no work is done by the contrac- 

 tion of the muscle, tending to rotate the bone round the 

 axis. 



The positions of the axis of rotation, lying inside 0 and X, 

 which correspond to negative values of the work done, denote 

 positions of unstable equilibrium, and the work done by the 

 muscle consists in pulling the bone out of the plane contain- 

 ing itself and the axis of rotation. 



All the preceding results may be verified, geometrically, 

 by drawing the cone described by the bone AB round the 

 axis of rotation, and considering, in detail, the lengthening or 



