﻿Behaviour of the Quadrant Electrometer. 381 



produced by Rontgen Rays (Phil. Mag. Dec. 1898) only 

 deals with a particular problem which arose in the course of 

 the experiments therein described. 



Fig. 1 requires no explanation. It is merely a plan of the 

 electrometer, the circle outside representing the metallic 

 case. If Y l5 V 2 , V 3 denote the potentials of the two pairs of 



quadrants and the needle, the corresponding charges are 

 given by the equations 



Qx^CuV^OnV^ + CV,, 

 Q s =C 11 V 1 + C M V, + C tt V Sl 



Suppose the case of the instrument to be earthed, that 

 V 2 > V l3 and that the axis of figure of the needle makes an 

 angle 6 with QP in the position of equilibrium, and suppose 

 also that vanishes when everything is earthed. A very 

 little consideration will make it clear that,, up to and including 

 the second power of 0, we have 



C n = b + /36, O 12 =-(o-fp0 2 ), 



Cn=-(a + a0), 22 = /,-/3<9, 



( '23 ——(a — u6), C 33 = 2a + q — k6 2 . 



C M , it may be remarked, is the charge on the needle when 

 V 8 = l, and V2 = Vj = 0. The greater part of the comple- 

 mentary negative charge is on the quadrants and is equal to 

 — 2a; the rest, — </ + /c0 2 , is on the case of the instrument in 

 the neighbourhood of Pand Q. In the symmetrical position 

 the charge on the needle will be 2a + q, the charge on each 

 pair of quadrants —a, and the charge on the case —7. It' 

 not in the symmetrica] position, the charge on the case will 



