240 



ANIMAL MECHANICS. 



It is plain that ap denotes the change in length of the fibre 

 ad during the rotation, and the work done by it is 



but 



me - ap x dO, 

 ap = ab x sin (j3 - 0) 

 ab = u) + aX = to x OX x — 



sin 0 



sin (j3-0)' 

 ap = u) x OX x sin 0, 

 to0 = tob sin 0rf0. 

 Integrating this element from AO to we find 



Therefore, 

 and 



Work done • 



ujb sin 0<i0 - o. 



Hence, no work is done by the muscle in any rotation of the 

 bone AB round an axis passing through the foot of the bi- 

 sector OX, and perpendicular to the plane of the muscle. 



0 



?-U£-.-i 



AS- 



/x 



y 



Fig. 6 1. 



Let us now suppose the bone AB, Fig. 6i, to be moved 

 parallel to itself into the position ocy, and let 

 xAB = <j) ; 



