rOL. LXI.] PHILOSOPHICAL TBANSACTIONS. MQ 



all the rest of space the matter will be exactly saturated. The demonstration is 

 exactly similar to the foregoing. 



Corol. 2. The fluid in the globe bde will be disposed in exactly the same 

 manner, whether the fluid without is immoveable, and disposed in such manner 

 that the matter shall be every where saturated, or whether it is disposed as above 

 described; and the fluid without the globe will be disposed in just the same 

 manner, whether the fluid within is disposed uniformly, or whether it is disposed 

 as above described. " 



Prop. 6, prob. 2. — ^To determine in what manner the fluid will be disposed in 

 the globe bde, supposing every thing as in the last problem, except that the 

 fluid on the outside of the globe is immoveable, and disposed in such manner 

 as every where to saturate the matter, and that the electric attraction and repul- 

 sion is inversely as some other power of the distance than the square. 

 ' I am not able, says Mr. C, to answer this problem accurately; but I think 

 we may be certain of the following circumstances. I ,i9dJi 



Case 1 . Let the repulsion be inversely as some power of the distance between 

 the square and the cube, and let the globe be overcharged. It is certain that the 

 density of the fluid will be every where the same at the same distance from the 

 centre. Therefore, first, there can be no space, as cb, within which the matter 

 will be every where saturated; for a particle at b is impelled towards the centre, 

 by the redundant fluid in hb, and will therefore move towards the centre, unless 

 cb is sufficiently overcharged to prevent it. Secondly, the fluid close to the sur- 

 face 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, he thinks, we may conclude, that the density of the 

 fluid will increase gradually from the centre to the surface, where the particles 

 will be pressed close together. Whether the matter exactly at the centre will be 

 overcharged, or only saturated, he cannot tell. 



Corol. For the same reason, if the globe be undercharged, he thinks we may 

 conclude, that the density of the fluid will diminish gradually from the centre to 

 the surface, where the matter will be entirely deprived of fluid. 



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 sb, in 

 which the particles of the fluid will be every where 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 ci, taken all together, 

 will be undercharged. But he cannot tell in what manner the fluid will be dis- 

 posed in that space. For it is certain that the density of the fluid will be every 



