244 



ANIMAL MECHANICS. 



so formed ; it is necessary, in order to produce the maximum 

 work due to a rotation round the socket 8, that this socket shall 

 be placed somewhere upon a right line drawn through the vertex 

 of the triangle, and perpendicular to the internal bisector of that 

 angle. 



'<0 



i 



Fig 63. 



The same result may be thus obtained without integra- 



tion, from the principles laid down in p. 181. Let AB, AB', 

 Fig. 63, be the quadrilateral muscle, and let OX be the bi- 

 sector of the vertical angle A OB. 



08 = k, 

 SOX = 0, 



aox = e. 



The resultant of all the forces of the muscular fibres lies in 

 the right line OX, and its moment, in turning the bone 

 AB round the socket 8, will be a maximum when the per- 

 pendicular SP, let fall from the socket upon OX the direction 

 of the force, is a maximum. The resultant force (p. 181), is 

 2 / sin 6 ; 



and from the figure, 



SP = k sin (j). 



