ANIMAL MECHANICS. 



267 



a» 2 - ~, fsi 



+ — a 2 cos 2 0 cos p cos p J - 



i 2 0^0 



2 



to 2 



a cos rf> x 



2 r 



{ (a cos 0 + 6) sin j3 cos /3' + (a cos 0 + _>') sin ]3 cos |3} x 

 fsin 0 cos 0 f?0 

 J A ' 

 Previous to integrating the general expression for the 

 work done by the skew quadrilateral muscle (48) ; it will be 

 interesting to discuss the simpler case of a triangular muscle, 

 which is deduced from the general expression by reducing 

 the bone A'B to a point coinciding with the vertex 0. This 

 may be best done by combining the general expression for 

 the work done, viz., 



to 2 C(a cos (j> + I cos 0) (a cos 0 + V cos 0) dQ 



_____ . 



with the condition, I' =0. 

 Hence, we obtain, 



&> 2 C a cos <f> (a cos (f> 4 I cos 0) dO 



which becomes, by substituting for its value 

 _ b sin )3 



sin (0-0)' 

 after a few reductions 



J spdo = f . « C0S A(_p<__*)j cos m (49) 



^ 2 a 2 cos 2 <ft cot 8 f . ^ 7/1 

 . ~ ' sin Vdf). 



20) 



Integrating this expression from + 0 to - 0, the second 

 term will disappear, and we find for the work done, 



TtT . . f - . . n a cos 0 (a cos d> + 6) , x 

 Work done = SpdO •= w 2 sin 0 . ^ — -' (50) 



