VOL. LXI.] PHILOSOPHICAL TRANSACTIONS. '241 



A on tlie column cd, in the direction CD, is equal to the fluxion of the repulsion 

 of F on CG ; and when ad equals AC, the repulsion of both a and f, on their 

 respective coluinns;, vanishes ; and therefore the repulsion of a on the whole 

 column CD, equals that of f on CG ; and when cd and cg are both infinitely 

 extended, they may be considered as the same column. 



Prop. 17. Let two similar bodies, of dift'erent sizes, and consisting of 

 different sorts of matter, be both overcharged, or both undercharged, but in 

 difierent degrees; and let the redundance or deficience of fluid in each be very 

 small, in respect of the whole quantity of fluid in them: it is impossible for the 

 fluid to be disposed accurately in a similar manner in both of them ;* as it has 

 been shown that there will be a space, close to the surface, which will either be 

 as full of fluid as it can hold, or will be entirely deprived of fluid ; but it will be 

 disposed as nearly in a similar manner in both, as is possible. To explain this, 

 let bde and bde, fig. 12, be the two similar bodies; and let the space com- 

 prehended between the surfaces bde and fgh (or the space bp as he calls it for 

 shortness) be that part of bde, which is either as full of fluid as it can hold, or 

 entirely deprived of it : draw the sariace fgh, such that the space bf, shall be to 

 the space bf, as the quantity of redundant or deficient fluid in bde, to that in 

 BDE, and that the thickness of the space i/ shall every where bear the same pro- 

 portion to the corresponding thickness of bf : then will the space bfhe either as 

 full of fluid as it can hold, or entirely deprived of it ; and the fluid within the 

 space _/o-A will be disposed very nearly similarly to that in the space fgh. 



For it is plain, that if the fluid could be disposed accurately in a similar 

 manner in both bodies, the fluid would be in equilibrio in one body, if it was in 

 the other ; therefore draw the surface ^Si such that the thickness of the space j3/| 

 shall be every where to the corresponding thickness of bf, as the diameter of 

 bde to the diameter of bde ; and let the redundant fluid or matter in ^be spread 

 uniformly over the space (3/"; then if the fluid in the space Tg'A is disposed exactly 

 similarly to that in fgh, it will be in equilibrio ; as the fluid will then be disposed 

 exactly similarly in the spaces ^Si and bde : but as, by the supposition, the 

 thickness of the space jS/" is very small in respect of the diameter of bde, the fluid 

 or matter in the space bf will exert very nearly the same force on the rest of the 

 fluid, whether it is spread over the space (3/j or whether it is collected in bf. 



Prop. 18. — Let two bodies, a and b, be connected to each other by a canal of 



• By the fluid being disposed in a similar manner in both bodies, Mr. C. means that the quantity 

 of redundant or deficient fluid, in any small part of one body, is to that in the corresponding small 

 part of ihe other, as the whole quantity of redundant or deficient fluid in one body, to that in the 

 other. By the quantity of deficient fluid in a body, he means the quantity of fluid wanting to satu- 

 rate it. Notwithstanding the impropriety of this expression, he begs leave to make use of it, as it 

 will consequently save a great deal of circumlocution. 

 VOL. XIII. I I 



