316 ANIMAL MECHANICS. 



From these values we find 



Q 2 -4Pi? = - 15.361, 



showing that the equilibrium is always stable, and 



« . 3.1896 



§ = i. — = 0.-27. 



2 0.17018 y3/ 



The actual distance of the socket from the line OF is ^fnds 

 of an inch. 



Collecting together into one Table the co-efficients of 

 equation (72), we obtain — 



Bird. 



P 



Q 



M 



Q - aPR 



Albatross, . . 



0. 09620 



2.8308 



103.37 



- 3 1 • 7 6 3 



Wood Pigeon, . 



O.M433 



3.059 2 



34-21 



- 10.391 



Heron, . . . 



0.15370 



1. 1230 



15-9° 



- 8.514 



Macaw, . . . 



0. 13062 



0.5014 



3 r -36 



- 16. 134 



Pheasant, . . 



0. 17018 



3. 1896 



37-51 



- 15.361 



1 



From the foregoing investigation, it appears that Prop. E 

 may be extended to the curved quadrilateral muscles which 

 form the great pectoral in the wings of birds, and that the 

 contraction of the muscle cannot produce a rotation of the 

 wing round any axis lying in its plane, unless the socket of 

 the joint be placed somewhere in that plane lying between 

 the tangents drawn to the ellipse of instability at the extremities 

 of its diameter on the line OX, which bisects the angle formed 

 by the fibres of the muscle. 



The exact position of this socket, required to fulfil the 

 conditions of maximum ivork clone and minimum work lost, is 

 found by the intersection of the axes of maximum instability 

 and minimum stability. 



The difference between the calculated and observed posi- 

 tions of these two axes is shown in the following Table : — 



