Plane Parallel Plates 41 



Let AD be that space which contains the greatest quantity of re- 

 dundant fluid, 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 intirely de- 

 prived 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 intirely 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. Secondly, 

 In the space CD the fluid will be pressed close together; the quantity of 

 fluid therein being such, as to leave just enough fluid in BC to saturate 

 the matter therein. Thirdly, The space EF will be intirely deprived of 

 fluid ; the quantity of matter therein being such that the fluid in FG shall 

 be just sufficient to saturate the matter therein: consequently, the re- 

 dundant 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 ED 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 fourthly, The spaces BC and FG will 

 be saturated in all parts. 



For, first, If the fluid is disposed in this manner, no particle of it can 

 have any tendency to move : for 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 anywhere in the space CD, or in the spaces 

 AB and GH, if they are overcharged, is indeed repelled with more force 

 towards the planes Dd, Aa and Hh, 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. 



Secondly, 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, I shall 

 omit it. 



31] COR. I. 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 





