ANIMAL MECHANICS. 



325 



at right angles, their extremities being joined by fibres, p,p\ 

 of given length, and we are required so to place the bones, 

 that the work done by the contraction ofthe fibres in rotating 

 one plane upon the other shall be a maximum. 



a' 



o / 



\ ^^^E 



I 





/ a 



B 



A 



Fig. 87. 



Let 01 (Fig. 87), as before, be the intersection of the 

 planes, and let AB and A'B' be the given bones lying in the 

 two planes, respectively. Produce the plane ABA'B to meet 

 O/in the point b ; and imagine the fibres AA' and BB' to be 

 produced to meet, and that X'X is the bisector of the angle 

 under which they meet. The resultant of all the fibres joining 

 A B and A'B\ lies in the line XX\ which may be regarded 

 as the only fibre with which we have to deal. The line XX' 

 must, therefore, be placed in a plane perpendicular to the 

 planes containing AB and A'B\ and the perpendiculars 

 Xa = Tr and X'a = 7r', must be equal to each other. Now, in 

 the triangles, Xab and X'ab, we have Xab = X'ab = 90 0 ; Xa «= 

 X'a\ and ah common to both. Hence we have Xb = X'b, 

 and therefore bXX'=bX'X. 



