ANIMAL MECHANICS. 215 



section, and wzStw the circle of curvature at the point S, 

 having its centre at R ; then 



c= OS = SC 

 p = zO . Z C 

 9 = Rz = RC. 

 In the right angled triangle RzO, we have 

 (zO) 2 = ROx CO; 



or 



P 2 =2C 9 , ( 37 ) 



Since 2c, the height of the vertex of the tangent cone, is the 

 same for all points of the indicatrix, we see that 



9 * P\ 



and since (because P is constant), by equation (36) T varies 

 as p, it must vary as p 2 . Hence, we have the following 

 elegant theorem. 



Fig. 51. 



Let Fig. 5 1 represent the indicatrix ellipse at any point 

 of a convex surface ; let C be its centre, and CR, CP, the 

 radius vector and perpendicular on tangent at any point. The 

 surface forms an elliptic dome, of very small height, standing 



