rOL. LXI.] PHILOSOPHICAL TRANSACTIONS."* 231 



if both spaces are overcharged, or which contains the least redundant matter, if 

 both are undercharged ; or, if one is overcharged, and the other undercharged, 

 let AD be the overcharged one. Then, first, there will be two spaces, ab and gh, 

 which will either be entirely deprived of fluid, or in which the particles will be 

 pressed close together; namely, if the whole quantity of fluid in ad and eh 

 together, is less than sufficient to saturate the matter therein, they will be 

 entirely deprived of fluid; the quantity of redundant matter in each being half 

 the whole redundant matter in ad and eh together: but if the fluid in ad and 

 EH together is more than sufficient to saturate the matter, the fluid in ab and gh 

 will be pressed close together; the quantity of redundant fluid in each being half 

 the whole redundant fluid in both spaces. 2d. In the space cd the fluid will be 

 pressed close together; the quantity of fluid in it being such, as to leave just 

 enough fluid in bc to saturate the matter in it. 3d. The space ef will be entirely 

 deprived of fluid; the quantity of matter in it being such, that the fluid in fg 

 shall be just sufficient to saturate the matter in it: consequently the redundant 

 fluid in CD will be just sufficient to saturate the redundant matter in ef ; for as ab 

 and GH together contain the whole redundant fluid or matter in both spaces, the 

 spaces BD and eg together contain their natural quantity of fluid; and therefore, 

 as BC and fg each contain their natural quantity of fluid, the spaces cd and ef 

 together contain their natural quantity of fluid. And, 4th, the spaces bc and 

 pg will be saturated in all parts. 



For, 1st. if the fluid is disposed in this manner, no particle of it can have any 

 tendency to move: tor a particle placed anywhere in the spaces bc and fg, is 

 attracted with just as much force by ef, as it is repelled by cd; and it is repelled 

 or attracted with just as much force by ab, as it is in a contrary direction by 

 GH, and consequently has no tendency to move. A particle placed any where in 

 the space cd, or in the spaces ab and gh, if they are overcharged, is indeed 

 repelled with more force towards the planes orf, aq, and hA, than it is in the 

 contrary direction ; but as the fluid in those spaces is already as much compressed 

 as possible, the particle will have no tendency to move. . 



2d. It seems impossible that the fluid should be at rest, if it is disposed in any 

 other manner: but as this part of the demonstration is exactly similar to the 

 latter part of that of problem the first, it is omitted. 



Corol. 1 . If the two spaces ad and eh are both overcharged, the redundant 

 fluid in CD is half the difference of the redundant fluid in those spaces: for half' 

 the difference of the redundant fluid in those spaces, added to the quantity in ab, ' • 

 which is half the sum, is equal to the whole quantity in ad. For a like reason, 

 if AD and eh are both undercharged, the redundant matter in ef is half the ' 

 difference of the redundant matter in those spaces; and if ad is overcharged, 

 and EH undercharged, the redundant fluid in cd exceeds half the redundant' 



