58 First published Paper on E/ectricity 



everywhere be of, if it was spread uniformly, in the ratio of 8 to i ; and 

 if the distance of the two plates is so small, that EC"* 1 is very small in 

 respect of AC"- 1 , and that EC s ~ n is very small in respect of AC 3 -", the 



B AC 

 quantity of redundant fluid in AB will be greater than - x -^^. 



2 



3-n 



, and 



B AC 3 ~" 

 less than -* x -,^ 

 28 EC 



than the former. For, in this case, PIT is, by Lemma X, Corol. IV, less 



, but will approach much nearer to the latter value 



EC 



3 -" EC 



3-n 



, and greater than -^-' x S, but approaches much nearer to 

 A C ( 



the latter value than the former; and if EC 3 '" is very small in respect 

 of AC 3 ~ n , P is very small. 



76] REMARKS. If DF was not undercharged, it is certain that AB 

 would be considerably more overcharged near the circumference of the 

 circle than near the center ; for if the fluid was spread uniformly, a particle 

 placed anywhere at a distance from the center, as at N, would be repelled 

 with considerably more force towards the circumference than it would 

 towards the center. If the plates are very near together, and, consequently, 

 DF nearly as much undercharged as A B is overcharged, AB will still be 

 more overcharged near the circumference than near the center, but the 

 difference will not be near so great as in the former case: for, let NR be 

 many times greater than CE, and NS less than CE ; and take Er and Es 

 equal to CR and CS; there can be no doubt, I think, but that the deficient 

 fluid in DF will be lodged nearly in the same manner as the redundant 

 fluid in AB; and therefore, the repulsion of the redundant fluid at R, on 

 a particle at N, will be very nearly balanced by the attraction of the 

 redundant matter at r, for R is not much nearer to N than r is; but the 

 repulsion of S will not be near balanced by that of s ; for the distance of S 

 from N is much less than that of s. Let now a small circle, whose diameter 

 is ST, be drawn round the center N, on the plane of the plate; as the 

 density of the fluid is greater at T than at S, the repulsion of the redundant 

 fluid within the small circle tends to impel the point N towards C ; but as 

 there is a much greater quantity of fluid between N and B, than between 

 N and A , the repulsion of the fluid without the small circle tends to balance 

 that; but the effect of the fluid within the small circle is not much less 

 than it would be, if DF was not undercharged ; whereas much the greater 

 part of the effect of that part of the plate on the outside of the circle, is 

 taken off by the effect of the corresponding part of DF: consequently, 

 the difference of density between T and S will not be near so great as if 

 DF was not undercharged. Hence I should imagine, that if the two plates 

 are very near together, the density of the redundant fluid near the center will 

 not be much less than the mean density, or 8 will not be much less than i ; 

 moreover, the less the distance of the plates, the nearer will 8 approach to i. 



