94 Preliminary Propositions 



First, if CR is considerably greater than MC, as 

 CR> - MR* - MC- - 2 MC x CN = MR* x {i - *ejJg+_2OV) J , 



i i I 3MC(MC + 2CN)\ 



^ 3 differs not much from ^- 3 x |i - - - MRi 



CN CN . CN - iMC (MC + zCN) 



, 

 and 



MR* ~ CR* 



MC - 3CN (MC + zCN) , MC 



or from x - V wnicn is very small in respect of ^p , 



provided CR is small in respect of CV. 



CR* 



For as CN is less than -?=-. , 

 20 r 



3 CN (MC + 2 CN) . 3 CR* x MC 



2 M# 2 2 



"CF" 4CF 2 ' 

 Therefore as j - = is very small in respect of ^^ , and as 



x C7 4 Mfl 2 x CF 2 ' 

 3MC 3C# 2 

 "" 



differs very little from , 3 + 3-3. or the difference of the 



AfC 

 repulsions of R on the points M and C differs very little from JTTJ^ , the 



difference of the repulsions of T on the same points. 



Secondly, if CR is not considerably greater than MC, CN must be very 

 small in respect of CR, and consequently must be very small in respect of MC. 



Therefore p - T is very small in respect of , and therefore the 



MC 

 difference of the repulsions of R on C and M differs very little from 



159] COR. Therefore by the same method of reasoning as was used in Cor. 

 to Lemma XVI, the difference of the repulsions of the whole plate ACB on 

 the points M and C is very nearly the same as if each particle of matter in it 

 was transferred to the plane Tt and placed at the same distance from C as 

 before, and therefore its repulsion on M is very nearly equal to its repulsion 

 on C, provided MC is very small in respect of the least distance of the circum- 

 ference of the plate from C, and that the thickness of the plate is everywhere 

 very nearly the same, except at such a distance from C as is very great in 

 respect of MC. 



160] PROP. XXXIV*. Fig. 8. Let NnvV be a plate of glass or any other 

 substance which does not conduct electricity, of uniform thickness, either flat, 

 or concave on one side and convex on the other, and let the electric fluid be 

 unable to penetrate at all into the glass or to move within it. 



Let ACB and DEF be thin coatings of metal, or any substance which 

 conducts electricity, applied to the glass. 



* This proposition is nearly the same as Prop. XXII, only made more general. 



