ANIMAL MECHANICS. 



245 



Hence, the moment of the force round the socket will be 

 Moment = ikf sin 9 sin 0, 



which agrees with equation (44). 



If we suppose the angle 6 to be given, the work done will 

 be a maximum when k sin 0 = SP is a maximum ; and if k, 

 the distance of the socket from the vertex, be also given, 

 then (p = 90 0 , or OS perpendicular to OX, will be the ar- 

 rangement capable of producing the maximum effect. 



Illustrations of Prop. B. — On examining, in nature, the 

 actual relative positions of the socket of the joint, and vertex 

 of the triangular or quadrilateral muscle, we find them always 

 placed in accordance with the result just found ; so that, at 

 the moment at which the muscle makes its most vigorous 

 contraction, the direction of its resultant is perpendicular to 

 the line SO, and, therefore, produces the maximum effect in 

 turning the bone round the socket of the joint. 



(a). Latissimus dor si in Man. — In Fig. 64, let *S represent 

 the socket of the shoulder joint, and 0 the insertion of the 

 latissimus dor si, whose ^ 

 extreme fibres make 

 with each other an 

 angle of 35 0 (p. 191). 

 The bisector OX of 

 the vertical angle o 

 the muscle passes, very 

 nearly, through the 

 spinous process of the 

 first lumbar vertebra. 

 Draw SH horizontal, 

 and place the arm SO 

 in such a position that 

 the angle SOX shall 

 be a right angle. The following measurements arc readily 

 made : — 



