44 ^1 Method of Determining Capacities. 



the prjbable errors give, when we put r 1 = r 2 =c, 



e, _ {Y 1 '( 8 -V 1! )» + V 1 ,»(g.-V,)»}» £ 



c s - (V.-V,) ■«• 



Ci + Uj-^V,-^ 



(3) 

 (5) 



So far as C 2 is concerned, equation (4) shows that the 



V 



accuracy increases with the ratio ^~, i. e. with n ° n . 



But for d the relation is more complex and involves the 



9 

 ratio -—. However, we can avoid using G ± explicitly, bv 



taking as the "auxiliary' 3 condenser an ionization vessel 



which forms part of the measuring system. Cj. is then the 



capacity of the rest of the measuring system, and we are 



concerned only to know the value of Cx + CV The accuracy 



C 



of C + C 2 increases also steadily with the ratio ~ -^ , 



Kji + 2 



Hence, by the method of measurement here proposed, the 

 greatest accuracy is attained, when the standard condenser 

 used has as great a capacity as possible. The use of such 

 large standards is convenient on other grounds. A limit is 

 set to the possible magnitude of C by the condition that 

 both Y : and Y 2 must fall within the limits of measurement 

 by the potentiometer ; but a capacity as large as O'l m.f. 

 would be convenient for determining the capacity of a system 

 including an ionization vessel of reasonable size and an 

 electrometer. 



If the insulation of the electrode is not perfect, a correction 

 will have to be made for the time which elapses between 

 raising c 2 f to V x or V 2 and reading the electrometer. The 

 correction is easily determined by watching the decay of the 

 deflexion of the electrometer for a short time ; and such 

 observations will give the value of the insulation resistance, 

 a quantity of which the knowledge is important apart from 

 measurements of capacity. 



It will be observed that the method is useful for deter- 

 mining the variation of the capacity of the electrometer with 

 its deflexion — a troublesome relation to measure by any of 

 the ordinary methods. For this purpose it is only necessary 



