189 



ANIMAL MKCHANICS. 



lying to the right of xy will be lengthened. No Work at all 

 is done by the fibre Ox, or those to the right ; and of the 



0 



A 



A 



B 



B 



Y/ 



Fig. 34- 



fibres to the left of xy, all do some Work ; but the Work done 

 by them, with the single exception of the fibre OY, is less 

 than their inherent Work. Taking the sum of all the Work 

 done by each fibre, we have — 



a result that coincides with the Work done, found directly 

 from the resultant of all the forces (30). 



When a fan-shaped muscle, instead of being triangular in 

 shape, has a curved base, as in the pectoral fin of the Angel 

 Shark, Fig. 29, the Work done by the muscle will still be re- 

 presented by double the perpendicular let fall from the foot 

 of the bisector of the vertical angle upon the side ; and the 

 work inherent in the muscle will depend upon the integral 

 of IdOy taken all round the curve. 



If this curve be a portion of a circle whose centre coin- 

 cides with the vertex of the radiating fan-shaped fibres, the 

 comparison of the inherent Work and Work done becomes 

 very simple. This case is nearly realized in the great pectoral 



Work done -= f§b cos OdO = sin 0, 



-0 



