(fSO PHILOSOPHICAI, TRANSACTIONS. [aNNO 1771. 



where the same at the same distance from the centre. Therefore, let b be any 

 point where the fluid is not pressed close together, then will a particle at b be 

 impelled towards the surface, by the redundant fluid in the space ub; therefore, 

 unless the space cb is undercharged, the particle will move towards the surface. 



Carol. For the same reason, if the globe is undercharged, there will be a 

 space B^, in which the matter will be entirely deprived of fluid, the quantity of 

 matter in it being more than the whole redundant matter in the globe; and con- 

 sequently the space cb, taken all together, will be overcharged. 



Lemma 6. — Let the whole space comprehended between two parallel planes, 

 infinitely extended each way, be filled with uniform matter, the repulsion of 

 whose particles is inversely as the square of the distance; the plate of matter 

 formed thereby will repel a particle of matter with exactly the same force, at 

 whatever distance from it, it be placed. : ' mho? aa tclagrv/ni ji 



For, suppose that there are two such plates, of equal thickness, placed parallel 

 to each other, let a (fig. 3) be any point not placed in or between the two plates: 

 let BCD represent any part of the nearest plate: draw the lines ab, ac, and ad, 

 cutting the farthest plate in b, c, and d; for it is plain, that if they cut one plate, 

 they must, if produced, cut the other; the triangle bcd is lo the triangle bed, 

 as ab^ to A^^; therefore a particle of matter at A will be repelled with the same 

 force by the matter in the triangle bcd, as by that in bcd. Whence it appears, 

 that a particle at a will be repelled with as much force by the nearest plate, as 

 by the more distant; and consequently will be impelled with the same force by 

 either plate, at whatever distance from it it be placed. 



Carol. If the repulsion of the particles is inversely as some higher power of 

 the distance than the square, the plate will repel a particle with more force, if 

 its distance be small than if it be great ; and if the repulsion is inversely as some 

 lower power than the square, it will repel a particle with less force, if its dis- 

 tance be small, than if it be great. 



•' Prop. 7, prab. 3. — In fig. 4 let the parallel lines Aa, Bb, &c. represent parallel 

 planes infinitely extended each way: let the spaces* ad and eh be filled with 

 uniform solid matter: let the electric fluid in each of those spaces be moveable 

 and unable to escape; and let all the rest of the matter in the universe be satu- 

 rated with immoveable fluid; and let the electric attraction and repulsion be in- 

 versely as the square of the distance. It is required to determine in what manner 

 the fluid will be disposed in the spaces ad and eh, according as one or both of 

 them are over or undercharged. 



Let AD be that space which contains the greatest quantity of redundant fluid, 



* By the space ad or ab, &c. is meant the space comprehended between the planes Aa and vd, 

 OT between Aa and ei — Orig. 



