ANIMAL MECHANICS. 



323 



Hence we obtain the following preliminary condition : — 

 Condition. 



Whenever two bones, joined by muscular fibres , tend to turn 

 each other round an axis of rotation formed by the intersection 

 of two planes passing through the bones, the work done by th e 

 contraction of the fibres will be a maximum, when the axis of 

 rotation is formed by the intersection of planes at right angles to 

 each other. 



Let us now consider the simple case of a single muscular 

 fibre, of a given lengthy, the ends of which are required to 

 remain in two planes at right angles to each other, in con- 

 formity with the foregoing preliminary condition ; it is required 

 to find the position of the fibre, so that the moment of the 

 force causing one bone to rotate round the line of intersection 

 of the planes shall be a maximum. 



Let 01 (Fig. 86) be the line of intersection of the two 



p' 



p 



Fig. 86. 



rectangular planes, and let P, P', be the ends of the fibre, 

 whose length, PP =p, is given. Draw Pa, Pa, each in its 

 own plane, perpendicular to 01; and let 



PF=p, 

 Pa = 7T, 



PV=7T', 



ad = u. 



y 2 



