ANIMAL MECHANICS. 



311 



of the Albatross, the two conies represented by the equa- 

 tions, 



y 2 = Lx 1 + Mx 4 N\ 

 x 2 = Pf + Qy + R, 



referred to OX and OY as co-ordinate axes. 



The ellipse whose centre is C may be called the ellipse of 

 instability, and the axis of rotation, LM, passing through its 

 centre, is the axis of maximum instability. The hyperbola 

 whose centre is D may be called the hyperbola of stability, 

 and the axis of rotation, PQ, passing through its centre, is the 

 axis of minimum stability. The intersection of these two axes, 

 Z, determines the exact position of the centre of the socket 

 of the shoulder joint, which fulfils the conditions imposed by 

 the principle of " least action because if the wing rotate 

 round any axis passing through this point, and lying in the 

 plane of the muscle, the contraction of the muscle will produce 

 a maximum amount of work done, by the component rotation 

 parallel to OX ; and, although the contraction of the muscle 

 cannot produce any rotation round an axis parallel to OY, 

 yet, if any such rotation take place from external causes, the 

 contraction of the muscle will restore the bones to their 

 original positions, with the minimum amount of work lost. 



The near approach of the calculated socket Z to the 

 observed socket 8 is a proof of the truth of the Postulate 

 (p. 238) ; and we shall see that the wings of the remaining 

 birds confirm the conclusion here drawn. 



(b.) Wing of the Wood Pigeon. — The following measure- 

 ments on the Wood Pigeon and other birds are made in 32nds 

 of an inch : — 



