ANIMAL MECHANICS. 



195 



bisecting the angle A OB ; and from X, X\ let fall XF t 

 XY, perpendicular to OA. 



0 



Fig. 39- 



The quadrilateral muscle may be regarded as a triangular 

 muscle, A OB, from which a portion A' OB' has been cut 

 off, and the properties of the quadrilateral muscle may be 

 readily deduced from those of triangular muscles. 



I have^ shown (equation 30) that the work done by the 

 triangular muscle A OB, is proportional to the perpen- 

 dicular XY; but the work done by the part cut off, A' OB', 

 is proportional to the perpendicular X Y f ; hence the total 

 work done by a quadrilateral muscle is proportional to the 

 difference of X Y and X Y'. Hence, whatever be the shape 

 of two quadrilateral muscles, if the difference between X 1 

 and X' Y' be the same in both, the two muscles will do the 

 same work in contracting : also, if the inclination, A OB 

 between the extreme fibres of two quadrilateral muscles, be 

 the same, the work done by each will be proportional, simply, 

 to the length of the right line XX'; for 

 XY= XO. sin 0 



x r = xo. sin e 

 0 2 



