326 



ANIMAL MECHANICS. 



Let Fig. 88 represent the plane of the quadrilateral 

 ABAB', in which YXX' is the bisector of the angle A YB. 



Y 



Fig. 88. 



Hence, we have 



BXX' = BYX+XBY 

 BX'X = A' YX' + X'A' F; 



but BYX= A' YX' \ therefore 



XBY= X'A'Y\ 



or, in the quadrilateral ABA'B', the external angle is equal 

 to the opposite internal angle ; or the sum of two opposite 

 angles is equal to two right angles ; hence the quadrilateral 

 ABA'B' is inscribable in a circle. 

 Hence, 



If two bones, joined by muscular fibres forming a plane quad- 

 rilateral, lie in two planes at right angles to each other, the 

 maximum work done in rotating the planes round their axis of 



