Corresponding points 9 1 



and the repulsion of the two particles when transferred to T on the column CE, 



TE TC 

 or the repulsion of T, as I shall call it for shortness, is 2 ~rr ^ . 



But as ME differs in a very small ratio from CE, and RM differs in a very 

 small ratio from RC, RE - RM or E differs in a very small ratio from TE TC. 

 In like manner SC NC or S differs in a very small ratio from TE TC, and 

 ER and CS both differ in a very small ratio from TE, and SE differs in a small 

 ratio from TC. 



Therefore =7; ^p + c -^~r-cr differs very little from 2 x == =^ , that 



RC x RE SC + SE 7 E x TC 



is, from the repulsion of T. 



Moreover, as EM and SN differ very little from each other, D is very small in 

 respect of TE TC, and ^ ^= is very small in respect of the repulsion of T. 



.. RC - SE . CM + RN CE , RE - SC . 



Moreover, ^^ is less than =^ or than -^=- 7 , and jj^ is 



KL KL L V Kt. 



RM - CN , RC -SE 



hardly greater than - , and is therefore still less than ^^ ; 



Kc, A.C 



RC RE 



therefore =-=- and ^ each differ from one in a less ratio than that of CE to 



o/i oO 



RC x RE 



CV, and therefore ^= - differs from one in a less ratio than that of 2CE 

 SE x SC 



toCV. 



r C C -C f RC x ~ 



Consequently, - ^-^ + ^-^ or ^^^ x (i - g 



^= ^ 



SE x SC 



is 



less than ^^ =-= x -^^ , which is less than 



KL x Kh Lv -^ 



CE x RC zCE 2CE* 



x 





CV x RC x RE CV CV 2 x RE ' 



zCE 2 

 which is very small in respect of ~=. 5^ , that is, of the repulsion of T. 



/ / , X ./ O X i \ i '. 



Therefore the sum of the repulsions of R and S differs very little from the 

 repulsion of T. 



N.B. Though the distance CR is ever so great, it may be shewn that the 

 sum of the repulsions of R and 5 cannot be more than double that of T*. 



156] COR. I. Let the edges of the plates ACB and DBF correspond, that is, 

 let them be such that if a line is erected on any part of the circumference of 

 one plate perpendicular to the [tangent] plane of the plate in that part, that 

 line shall meet the other plate in its circumference. Let the two plates be of 

 an uniform thickness, and let the thickness of DF bear such a proportion to 

 that of AB that the quantity of matter shall be the same in both. Consequently 

 the quantity of matter in each part of DF will be very nearly equal to that in 

 the corresponding part of AB. Also let the size of the plates be such that CE 



[* Note 14, p. 389.] 



