302 



ANIMAL MECHANICS. 



the contraction of the. muscle will produce no effect, and the 

 equilibrium of the bones ivill be neutral. 



3 0 . If the axis of rotation lie inside these points, the contrac- 

 tion of the muscle will tend to convert the plane quadrilateral 

 into a skew muscle ; and this effect will be a maximum, when the 

 axis passes through the point midway between these points ; and 

 the equilibrium of the bones will be unstable. 



The Divine Architect of the Universe has placed the axis 

 of rotation of the wings of birds in the position of maximum 

 work, or so that a given amount of work shall be performed 

 by the minimum amount of muscle ; which is in conformity 

 with the " Principle of Least Action" observable in all de- 

 partments of Nature. Hence we may regard the Postulate 

 of page 238 as proved for this class of muscles, and as thus 

 having additional probabilities in its favour. 



In Propositions A and B, we have considered the case of 

 two bones, lying in the same plane, and united by a quadri- 

 lateral sheet of muscle, one bone being supposed fixed, and 

 the other compelled to turn round an axis of rotation perpen- 

 dicular to the plane. 



In Propositions C and D, we have considered the same 

 case, when the axis of rotation lies in the original plane of the 

 quadrilateral muscle, and is perpendicular to the bisector of 

 the muscular fibres. 



In order to complete the consideration of the action of the 

 muscle, when the bone rotates round any axis whatever, we 

 shall now consider its action when the bone rotates round an 

 axis, perpendicular to both the former axes of rotation ; that 

 is to say, when the rotation of the moveable bone takes place 

 round an axis parallel to the bisector of the muscular fibres. 



Let AB and A'B (Fig. 82) be the bones, and let the 

 same notation be used as before. Let S be the socket of the 

 joint, and SZ the axis of rotation, parallel to OX, the bisector 

 of the angle made by the fibres. Draw SY perpendicular to 

 FOX and let 



