Comparison of capacities 133 



though x is ever so great ; for in that way it was before said that we were 

 liable to an error of four. But if x is equal to f , which is as great an error 

 of strength as I think can well arise in charging the vials, even when the 

 first mentioned electrometer is used, the error in finding the required 

 surface is only ^ of the whole surface, or only J part of what might arise 

 the other way. 



251] Having thus found what surface must be given to the trial plate, 

 in order that the deficience of fluid in it shall be equal to the redundance 

 in B, I take away the body B and put the other body b, which I want to 

 compare with it, in its room, and if I find on repeating the experiment 

 that the trial plate must be drawn out to the same surface as before, in 

 order that the deficience of fluid in it shall be equal to the redundance 

 in b, or, in other words, if the required surface of the trial plate is the same 

 in trying b as in trying B, I am well assured that if B and b were succes- 

 sively made to communicate with one of the vials, or with any other 

 third body, and were positively electrified, they would each of them contain 

 the same quantity of redundant fluid, supposing the quantity of redundant 

 fluid in the third body to remain the same each time. On the other hand, 

 if I find that the required surface of the trial plate is greater in trying b 

 than in trying B in the ratio of t 2 to T 2 , I am well assured that the quantity 

 of redundant fluid in b would exceed that in B in the ratio of t to T, sup- 

 posing, as was said before, that the deficience of fluid in the trial plate is 

 in proportion to the square root of its surface. 



252] If the reader should think that this conclusion requires any proof 

 it may be thus demonstrated : 



Suppose that in trying B it was found that the required surface of 

 the trial plate was T 2 and that in trying b it was t z , and let us first suppose 

 that the vials are charged in exactly the same degree in trying b as in 

 trying B, then is the conclusion evident, for then are B and b successively 

 made to communicate with the vial A, the charge of this vial being 

 exactly the same each time, and the quantity of redundant fluid com- 

 municated to b is, actually, to that communicated to B as t to T. But it 

 is plain that the conclusion is equally just, though the vials are charged 

 higher in trying one than in trying the other. For though, in this case, 

 the redundant fluid actually communicated to b will not be to that com- 

 municated to B in the ratio of / to T, yet we are sure that it would have 

 been so if the vials had been charged in the same degree each time, for the 

 required surfaces which must be given to the trial plate in trying b must 

 evidently be the same whether the vials are charged to the same degree 

 as they were in trying B, or to a different degree. 



253] Though it is of no signification whether the vials are charged to 

 the same degree in trying b as in trying B, yet it is necessary, as I said 

 before, that in trying either B or b the vials should be charged nearly 



