ANIMAL MECHANICS. 



307 



This consideration affords us a glimpse of the reason why 

 so many muscles are made to act in various ways round the 

 shoulder and hip joints of animals ; each muscle is intended 

 to produce a rotation round some axis or definite group of 

 axes ; and, in order to enable it to do so with maximum effect, 

 its power to cause rotations round other axes is taken away.* 



We shall now consider, in detail, the case of rotation round 

 an axis parallel to the bisector, with respect to the five birds 

 already discussed. 



If we expand equation (69), writing 



10 J 



y m a sin 0, 



we find 



x 1 = Py 2 + Qy + R; (72) 



where 



r r/0 f ([+ 0 sin Q r lV sin 2 0 



Equation (72) represents a central conic, whose centre lies 

 upon the axis of?/, on the perpendicular drawn at 0, to the 

 bisector 0X y and at a distance from 0, determined by the 

 equation 



iPy+Q = o. (73) 



When the equation (72) is referred to axes of co-ordinates 

 passing through the centre, it becomes 



± S-£- 1 - (74) 



* May not the remarkable similarity in the bones and muscles of various 

 animals, in corresponding parts of their structure, be the result of some such 

 geometrical and mechanical necessity, foreseen by the Divine Contriver, instead 

 of being the result of common descent from a remote ancestor possessing a similar 

 arrangement of bones and muscles ? 



x 2 



