42 Mr. C. Chree. Isotropic Elastic Solid Ellipsoids under 



(2 + 3 17 + l5, / 2 ) 



..... (12), 



2a 2 ?r c 2 . 



- - t 1 -'- 4 '') 



...... (13). 



The other stresses may lie written down from symmetry. 

 With the notation of 2, 



1 - A 2V.c(3--, y ) f 20-- c 2 (2- 

 V 



It will be noticed that 



P*.. x = px'(l r 2 // 2 ), 

 \ 



where r= y(* 2 + 2/ 2 + 2 2 ), / = */(x'* + y' z + z"-) t 



x' t y', e being the coordinates of the point where the radius vector r 

 produced cats the surface of the ellipsoid, and p being the perpendi- 

 cular from the centre on the tangent plane at a/, T/', z'. Near the 

 surface we may put 



1 r 2 /r' 2 = 2(1 r/r'), 



and so conclude that t x and the other stress components across the 

 tangent planes to (q) vary approximately as the distance from the 

 surface. 



As the stresses at the surface itself are of special interest in the 

 event of any application to the earth, I shall briefly consider them 

 for a spheroid in which b = a. The principal stresses are nn, tt, 00, 

 directed respectively along the normal, the tangent to the meridian, 

 and the perpendicular to the meridian. Using cylindrical coordinates, 

 r, 0. z where 



r = v / (* 2 +2/ ! ), = tarry/as, 



