242 



ANIMAL MECHANICS. 



following restriction on the free motion of the bone A B. Let 

 A'B' (Fig. 62) be the fixed bone, and AB the moveable bone, 

 which is subject to the condition of always turning round a 



B 



if 



Fig. 62. 



joint, or socket, placed at the point S. Hence, we have the 

 following problem. 



Proposition B. (Problem.) 



Given a fixed bone A'B, and a moveable bone AB lying in 

 the same plane, subject to the condition of always turning round 

 an axis passing through a certain point S, and perpendicular to 

 the plane of the bones AB and A'B' ; it is required to find the 

 locus of the joint S, so that the work done by the muscle^ in con- 

 tracting, shall be a maximum. 



Let aa' be any fibre, and let the bone AB receive a small 



