in an ellipsoid 361 



saturated. But, on trying this distribution, we find that it is not consistent 

 with equilibrium. For when n is less than 2, the effect of a shell of fluid on a 

 particle within it is a force directed from the centre. If, therefore, a sphere of 

 saturated matter is surrounded by a shell of electric fluid, the fluid in the sphere 

 will be drawn towards the shell, and this process will go on till the different 

 parts of the interior of the sphere are rendered undercharged to such a degree 

 that each particle of fluid in the sphere is as much attracted to the centre by 

 the matter of the sphere as it is repelled from it by the fluid in the sphere and 

 the shell together. This is the same conclusion as that stated by Cavendish. 



Green solves the problem, on the hypothesis of two fluids, in the following 

 manner. 



Suppose that the sphere, when saturated, contains a finite quantity, E, of 

 the positive fluid, and an equal quantity of the negative fluid, and let a quantity, 

 Q, of one of them, say the positive, be introduced into the sphere. 



Let the whole of the positive fluid be spread uniformly over the surface of 

 the sphere whose radius is a, so that if P' is the surface-density, 



Green then considers the equilibrium of fluid in an inner and concentric 

 sphere of radius b, acted on by the fluid in the surface whose radius is a, and 

 shows that if the density of the fluid is 



p = 2 P'a sin "-^ 77 (a 2 - 6 2 )^" (a 2 - r 2 )- 1 (6 2 - r 2 ) ~ 2 ~ , 



there will be equilibrium of the fluid within the inner sphere. 



The value of p is evidently negative if n is less than 2. 



Green then determines, from this value of the density, the whole quantity 

 of fluid within the sphere whose radius is b, and then by equating this to E, 

 the whole quantity of negative fluid, he determines the radius, b, of the inner 

 sphere, so that it shall just contain the whole of the negative fluid. 



The whole of the positive fluid is thus condensed on the outer surface, the 

 whole of the negative fluid distributed within the inner sphere, and the shell 

 between the two spherical surfaces is entirely deprived of both fluids. 



At the outer surface, the force on the positive fluid is from the centre, but 

 the fluid there cannot move, because it is prevented by the insulating medium 

 which surrounds the sphere. 



In the shell between the two spherical surfaces the force on the positive 

 fluid would be from the centre. Hence if any positive fluid enters this shell, it 

 will be driven to the outer surface, and if any negative fluid enters, it will be 

 driven to the inner surface. 



But all the positive fluid is already at the outer surface, and all the negative 

 fluid is already in the inner sphere, where, as Green has shown, it is in equili- 

 brium, and thus the fluids are in equilibrium throughout the sphere. 



It may be remarked that this solution, according to which a certain portion 

 of matter becomes entirely deprived of both fluids, is inconsistent with the 



