290 



ANIMAL MECHANICS. 



which may be regarded as a useful approximation to the true 

 position of the maximum axis, which is 5.70 inches. 



The method of finding a quadrilateral muscle, with straight 

 bones, equivalent to a given muscle with curved bones which 

 has just been gi-ven, leads to difficult calculations; and, 

 moreover, does not seem to bring the calculated axis PQ, 

 sufficiently near to the actual axis 8T t to satisfy the require- 

 ments of exact science ; it may, therefore, be useful to give 

 another mode of computation, somewhat less laborious, and 

 which may be made to approximate as near as we please to 

 the conditions imposed by the actual curves formed by the 

 bones of origin and insertion. 



The general expression (47), 



iv 2 [(a cos (\> \ I cos 6) (a cos </> 4- /'cos 0) 

 I - I' ' 



for the work done during a rotation (to) round an axis per- 

 pendicular to the bisector may be thus written, making 

 a cos 6 = x : 



7 J**-/ 



(x + I cos 9) (x + 1' cos 0) 



- ( SpdO = if- Lx 1 + Mx + TV, (65) 



*> 2 J 



r f -d0 - %r ((1+ t) cos Odd Ar [W cos *6<t0 



L = J Try M = J T^i — ' A ~ J ~i ~- r" 



Now, if the bones of the wing be carefully laid down to scale, 

 and a number of radii drawn through the point 0, the definite 

 integrals L, M, N 9 may be found, by construction, to any 

 degree of approximation, as shown by the following example 

 of the Albatross, in which the measurements are made in 

 twenty-fourths of an inch : — 



