i 



Theory of the Quadrant Electrometer. 247 



Hence, at the intersection ^ must be positive, that is, 

 a^-lis >1-V'. ^6 



AVe have seen that the capacity of the plate per unit of 

 length perpendicular to the plane of the paper is 



4K^ 

 K ' 



and K^ is the same function of k'^ that K is of k^. 



Xow let AX-^2 be the variation of ^'^ from its value in the 

 symmetrical position, then 



Hence the capacity 



By a curious formula in elliptic functions we have 



1 BK^ 1 BK ^ 



l^''dk'-' "^ K -dk^ - 4F^'2KK'* 



Hence the capacity 

 and we have 



'2 



h'=i-b„" 



1 A 7 /9 Jl. /i 



an 



A//2- l7rV7W^(a^-l)^ 



where the suffix refers to the values when 7 = 0. 

 Hence the capacity is 



This formula corresponds to the formula which I gave in 

 the early part of this paper for the capacity of the needle, 

 viz. 



6 being the angular deflexion. 



I showed there that if 62 was a positive quantity of order 

 -j^Q of an electrostatic unit, the experimental peculiarity of 

 the electrometer for increasing potential of the needle could 

 be accounted for both qualitatively and quantitatively. 



