40 First published Paper on Electricity 



27] COR. For the same reason, if the globe is undercharged, there 

 will be a space Bb, in which the matter will be intirely deprived of fluid, 

 the quantity of matter therein being more than the whole redundant 

 matter in the globe; and, consequently, the space Cb, taken all together, 

 will be overcharged*. 



28] LEMMA VI. 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. 



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 furthest plate 

 in b, c, and d; for it is plain that if they cut one F - 



plate, they must, if produced, cut the other: the 

 triangle BCD is to the triangle bed, as AB 2 to Ab z ; 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 bed. 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. 



29] COR. 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 distance be small than if it be great. 



30] PROP. VII. PROB. 3. In Fig. 4, let the parallel lines Aa, Bb, &c. 

 represent parallel planes infinitely extended 

 each way: let the spaces f AD and EH be jj~^ir -~r~ 



filled with uniform solid matter: let the elec- c 



trie fluid in each of those spaces be moveable 



and unable to escape: and let all the rest of I s1 



the matter in the universe be saturated with & . 



immoveable fluid ; and let the electric attrac- F ~~ ~~~f 



tion and repulsion be inversely as the square jg 



of the distance. It is required to determine in 



what manner the fluid will be disposed in the 



spaces A D and EH, according as one or both of them are over or undercharged. 



* [Note 2, p. 358.] 



f By the space AD or AB, &c. I mean the space comprehended between the 

 planes Aa and Dd, or between Aa and Bb. 



