﻿382 Prof. A. Anderson on the Theory oj the 



be less, and tc, which is an important factor in determining 

 the sensibility of the electrometer, is numerically the decrease 

 in this negative charge per unit increase of 2 . If F be the 

 torsion couple required to turn the lower end of the suspen- 

 sion fibre through unit angle, we have 



(F4-aV + 2^Y 1 Y 2 )^=(Y 2 -Y 1 )[2aV 3 -/3(Y 1 + y 2 )]. 

 But, evidently, must vanish when Y 2 — V 3 =V S — V l3 and 



therefore a=/3, and 



(F + «V 3 2 + 2j 5 V 1 V 2 )0=2«<T 2 -V 1 ) (v 3 -^±^- 2 ). 



If Y 2 = 0, this equation becomes 



2«Y 2 (V 3 -^) 



°~ F + *V 3 2 * 

 If Y 2 can be neglected in comparison with Y 



6 = 



2ccV 2 Y 3 



F + *V 3 2 ' 

 which, for a given value of Y 2 is maximum when 



F = «V 3 2 , or V 3 =\/-' 



the condition of maximum sensibility. 



It will be interesting now to consider the case where, as 

 often happens, the axis of figure of the needle is not strictly 

 along QP when everything is earthed. Let the angle which 

 it makes with QP be y, and let 7 be measured in the direc- 

 tion from the pair of quadrants whose potential afterwards 

 becomes Y 2 to the pair whose potential afterwards becomes 

 Vj. will now be measured, not from QP, but from the 

 position of the axis of the needle when everything is earthed. 

 The values of C n , C J2 , &c, will be obtained by writing + y 

 for 6 and 



(F+ay +2 i ;V 1 v 2 )0=2<v 2 -vo [v 3 -^4^] 



-2 7 («V 3 2 + 2^V 1 V 2 ), 



which, when Yi = and Y 2 is very small in comparison with 

 Y 3 , reduces to 



a_ 2*Y 2 V 3 -2y«V/ 



When both quadrants are earthed the value of is 



-2y«Y 3 2 



F + kY 3 2 ' 



