ANIMAL MECHANICS. 301 



Condition of Unstable Equilibrium in the Wings of Birds. 



Bird. 



L 



M 



N 



M 2 



Albatross, . . 



0.0962 



22.78:3 



1 104.51 



+ 93-9 1 



Woodpigeon, 



o.i4433 



19.7449 



557 05 



+ 68.27 



Heron, . . . 



o.r537o 



14.9375 



193.90 



+ 103.90 



Macaw, . . . 



0.13062 



11.3202 



101.17 



+ 75-27 



Pheasant, . . . 



0.17018 



19.5805 



342-4* 



+ 150.29 



The positive values in the last column of this Table show, 

 that in every case there exists a real axis of maximum insta- 

 bility, or tendency in the plane muscle to become skew. 



If we compare together the preceding examples, and bear 

 in mind the necessary errors of observation, and also that we 

 have been compelled to employ summation instead of integra- 

 tion, so that our results are only approximations ; there can 

 be no doubt that, in the wing of the bird, the socket of the 

 humerus is so placed, in relation to the origin and insertion 

 of the pectoral muscle, as to produce the maximum amount 

 of work possible by the contraction of that muscle. 



From all the preceding cases and calculations, we are 

 entitled to lay down the following : — 



Proposition D. 



When a quadrilateral muscle unites any two bones whatever, 

 and motion takes place round an axis lying in their plane, and 

 perpendicular to the bisector of the angle made by their extreme 

 fibres ; two points may be found on that bisector, such that — 



i°. If the axis of rotation lie outside these points, the con- 

 traction of the muscle will tend to replace the bones in the same 

 plane, and their equilibrium will be stable. 



2°. If the axis of rotation pass through either of these points, 



