Purser — On Ether Stress, Gravitational and Electrostatical. 197 

 The expression for the cubical dilatation will then be given by 



dr 

 Now, in the interior stress conditions are 



ax a 



Hence, (A + 2^.) ?"'^ = - • Ir + C''^ + 6''; 



ft 10 o 



- ^ .. (X + 2^)i2 = -.- + .-+-, 



where C^ must evidently vanish. Outside the surface we have ^ = A ^ B -, 



r,-A 



.r- 



whence (A + 2/i) r'E = A- + B^ + B\ 



o 2 



In order that the displacement should vanish at cc , we must have 

 A= B = 0; r. R = -- 

 This gives now A = at surface, and for all external points 

 .. ^ = -^, .. (A + 2;^)i^^--^--^-«. 



The continuity of B inside and outside the surface gives now 



B' 



This gives the complete law of displacement, .sc always radial in direction, 

 and in magnitude = rBi\ i.e. for all internal points 



(— |- - ^p ^ J / A + 2/i, and for all external, - "^p - / A + 2u • 



These dis]placements, then, will give a resultant action on any element of 

 ether equivalent to the action of gravitation on the matter contained in the 

 element, and thus solve our problem. 



