212 



ANIMAL MECHANICS. 



of the tangent cone xyO. Let 2 be the centre of the circle 

 Sx or Sy, and p its radius. Since 0 is very near the surface, 

 Oy and Cy are to be considered equal ; let each of them be 

 called a. 



The perpendicular pressure acting on the element Cxy is 

 P x §a 2 dB 



where dO is the angle xCy; and the tangential strain in the 

 element of the cone is 



T x add. 



This must be resolved along the line OR, and equated to the 

 perpendicular pressure. This gives us 



TxadO x cos (yOR), 



or 



T x adO x -. 



P 



Equating this expression to the perpendicular pressure, we 

 find that a 2 d6 goes out, and leaves us the equation 



• p = *l. 



e 



This is the well known equation which is used by architects 

 in the problem of the equilibrium of a spherical dome. 



When the surface has a spherical curvature at any point, 

 as in the preceding case, the tangential strain T, is the same 

 in every azimuth at each point ; but when the curvature, 

 becomes ellipsoidal, and the indicatnx is an ellipse, the tan- 

 gential strain T is different in different azimuths, while the 

 perpendicular pressure P remains constant. 



Let us now examine the general case. 



Let S (Fig. 49) be the point of the ellipsoidal surface in 

 question ; and let txyt be the indicatnx ellipse formed by a 



