VOL. LXI.] VHILOSOPHICAL TRANSACTIONS. 233 



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

 the square and the cube, and let ad be overcharged. 1st. It is certain that the 

 density of the fluid must be every where the same, at the same distance from the 

 planes Ka and nd. 2d. There can be no space, as bc, of any sensible breadth, 

 in which the matter will not be overcharged. And, 3d. The fluid close to the 

 planes Ka and d^ will be pressed close together. Whence he thinks, we may 

 conclude, that the density of the fluid will increase gradually from the middle of 

 the space to the outside, where it will be pressed close together. Whether the 

 matter exactly in the middle will be overcharged, or only saturated, he cannot tell. 

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

 the square and the simple power, and let ad be overcharged. There will be two 

 spaces, AB and dc, in which the fluid will be pressed close together, and the 

 quantity of redundant fluid in each of those spaces will be more than half the 

 redundant fluid in AD ; so that the space bc, taken all together, will be under- 

 charged; but he cannot tell in what manner the fluid will be disposed in that 

 space. The demonstrations of these two cases are exactly similar to those of the 

 two cases of prob. 1. 



Case 3. If the repulsion is inversely as the simple, or some low power, 

 of the distance, and ad is overcharged, all the fluid will be collected in the 

 spaces AB and cd, and bc will be entirely deprived of fluid. If ad contains just 

 fluid enough to saturate it, and the repulsion is inversely as the distance, the 

 fluid will remain in equilibrio, in whatever manner it is disposed; provided its 

 density is every where the same, at the same distance from the planes ku and nd , 

 but if the repulsion is inversely as some less power than the simple one, the fluid 

 will be in equilibrio, whether it is either spread uniformly, or whether it is all 

 collected in that plane which is in the middle between Aa and i>d, or whether it 

 is all collected in the spaces ab and cd; but not, he believes, if it is disposed in 

 any other manner. The demonstration depends on this circumstance; namely, 

 that if *he repulsion is inversely as the distance, two spaces, ab and cd, repel a 

 particle, placed either between them, or on the outside of them, with the same 

 force as if all the matter of those spaces was collected in the middle plane 

 between them. It is needless mentioning the 3 cases in which ad is undercharged, 

 as the reader will easily supply the place. 



Though the 4 foregoing problems do not immediately tend to explain the 

 phenomena of electricity, Mr. C. chose to insert them ; partly because they seem 

 worth engaging our attention in themselves; and partly because they serve, in 

 some measure, to confirm the truth of some of the following propositions, in 

 which he was obliged to make use of a less accurate kind of reasoning. 



In the following propositions, Mr. C. always supposes the bodies he speaks of 

 to consist of solid matter, confined to the same spot, so as not to be able to alter 



VOh. XIII. H H 



