Various laws of force considered 39 



except that the fluid on the outside of the globe is immoveable, and dis- 

 posed in such manner as everywhere to saturate the matter, and that the 

 electric attraction and repulsion is inversely as some other power of the 

 distance than the square. 



I am not able to answer this problem accurately; but I think we may 

 be certain of the following circumstances. 



24] CASE i. Let the repulsion be inversely as some power of the 

 distance between the square and the cube, and let the globe be over- 

 charged. 



It is certain that the density of the fluid will be everywhere the same, 

 at the same distance from the center. Therefore, first, There can be no 

 space as Cb, within which the matter will be everywhere saturated; for 

 a particle at b is impelled towards the center, by the redundant fluid in 

 Bb, and will therefore move towards the center, unless Cb is sufficiently 

 overcharged to prevent it. Secondly, The fluid close to the surface of the 

 sphere will be pressed close together; for otherwise a particle so near to 

 it, that the quantity of fluid between it and the surface should be very 

 small, would move towards it; as the repulsion of the small quantity of 

 fluid between it and the surface would be unable to balance the repulsion 

 of the fluid on the other side. Whence, I think, we may conclude, that 

 the density of the fluid will increase gradually from the center to the 

 surface, where the particles will be pressed close together: whether the 

 matter exactly at the center will be overcharged, or only saturated, I 

 cannot tell. 



25] COR. For the same reason, if the globe be undercharged, I think 

 we may conclude, that the density of the fluid will diminish gradually 

 from the center to the surface, where the matter will be intirely deprived 

 of fluid. 



26] CASE 2. Let the repulsion be inversely as some power of the 

 distance less than the square; and let the globe be overcharged. 



There will be a space Bb, in which the particles of the fluid will be 

 everywhere pressed close together; and the quantity of redundant fluid 

 in that space will be greater than the quantity of redundant fluid in the 

 whole globe BDE ; so that the space Cb, taken all together, will be under- 

 charged : but I cannot tell in what manner the fluid will be disposed in 

 that space. 



For it is certain, that the density of the fluid will be everywhere the 

 same, at the same distance from the center. Therefore, let b be any point 

 where the fluid is not pressed close together, then will a particle at b be 

 impelled towards the surface, by the redundant fluid in the space Bb; 

 therefore, unless the space Cb is undercharged, the particle will move 

 towards the surface. 





