284 



ANIMAL MECHANICS. 



any curved origin (Fig. 77) of a muscle, whose fibres con- 

 verge to the point 0. The work done by this muscle is 

 represented by \ldd, where / is the length of each fibre — and 

 this integral is readily found by construction, by drawing a 

 number of radiating lines from the point 0, and drawing per- 

 pendiculars, pq, pq, from the points of intersection with the 

 0 



Fig. 77. 



curve AB, upon the consecutive radiating lines. The sum 

 of all these perpendiculars, added together, will be equal to 

 the integral \ld9, when the radiating lines are taken sufficiently 

 near to each other. 



Let us draw the line AB (Fig. 76), joining the extremities 

 of the bone AB; and seek to find a right line A"B", parallel 

 to AB, and included between the extreme fibres, OA, OB, 

 whose mechanical effect shall be the same as that of the 

 curved bone. 



The work inherent in a triangular muscle, with a right 

 line for base, is, by equation (31), proportional to 



b sin j3 loge 



t an £ Q3 + fl) . 



tan fQ3 - 0) 1 



where b is the bisector of the vertical angle, and (3 is the 

 angle made by it, with the base. 



