5 2 First published Paper on Electricity 



64] COR. III. Suppose now that the matter of the plate is denser near 

 the circumference than near the middle, and that the density at and near 

 the middle is to the mean density, or the density which it would every- 

 where be of if the matter was spread uniformly, as S to i ; the repulsion 

 of the plate on EC will be less than if the matter was spread uniformly, 

 in a ratio approaching much nearer to that of 8 to I, than to that of 

 equality. 



65] COR. IV. Let everything be as in the last corollary, and let n be 

 taken to one, as the force with which the plate actually repels the column 

 DC, (DC"- 1 being very great in respect of AC n ~ l ), is to the force with which 

 it would repel it, if the matter was spread uniformly; the repulsion of the 

 plate on EC will be to its repulsion on DC, in a ratio between that of 

 EC 3 ~" x 8 to AC 3 ~ n x TT, and that of EC 3 ~ n to AC 3 ~ n x -n, but will 

 approach much nearer to the former ratio than to the latter. 



66] LEMMA XI. In the line DC produced, take CF equal to CA : if 

 all the matter of the plate AB is collected in the circumference, its re- 

 pulsion on the column CD, infinitely continued, is equal to the repulsion 

 of the same quantity of matter collected in the point F, on the same column. 



For the repulsion of the plate on the column in the direction CD, is 

 the same, whether the matter of it be collected in the whole circumference, 

 or in the point A . Suppose it therefore to be collected in A ; and let an 

 equal quantity of matter be collected in -F; take FG constantly equal to 

 AD; and let AD and FG flow: the fluxion of CD is to the fluxion of FG, 

 as A D to CD ; and the repulsion of A on the point D, in the direction CD, 

 is to the repulsion of F on G, as CD to AD; and therefore the fluxion of 

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

 fluxion of the repulsion of F on CG; and when AD equals AC, the re- 

 pulsion of both A and F on their respective columns vanishes ; and there- 

 fore 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 looked 

 upon as the same column. 



67] PROP. XVII. Let two similar bodies, of different sizes, and con- 

 sisting of different sorts of matter, be both overcharged, or both under- 

 charged, but in different 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 shewn that there will be a space, 



* By the fluid being disposed in a similar manner in both bodies, I mean that 

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

 that in the corresponding small part of the other, as the whole quantity of re- 

 dundant or deficient fluid in one body, to that in the other. By the quantity of 

 deficient fluid in a body, I mean the quantity of fluid wanting to saturate it. Not- 

 withstanding the impropriety of this expression, I must beg leave to make use of 

 it, as it will frequently save a great deal of circumlocution. [See Note i.] 



