ANIMAL MECHANICS. 



217 



To do this wo must find the value of 

 P 



in an eliipse. 

 Assume 



x = a sin 0 



y = b cos 0, 



then 



is 



ds = d(p y/ a 1 cos 2 ip + 6* sin 2 0 



V a' a cos + 6^ sin 2 0 

 c?s (a' 2 cos 2 0 4- />- sin 



The integral of this expression taken all round the ellipse 



(ds a 2 + b 2 



= 7T - 



J y; ab 



[ds ■ (\ i \ 



final 



Pi p% j 



where p x and p % are the radii of curvature of the surface 

 along the axes of the ellipse. 



The vertical component of all the elementary tensions, 

 just found, must be now equated to the sum of all the perpen- 

 dicular pressures acting on the indicatrix, which is 



P x fopds = Px nab, 



