QUADRANT ELECTROMETER. 185 



d and d' being the distances from these faces to the opposite sides 

 of the box. The charge of the surface S x is therefore 



which gives for the constant 



^sj^A'ft 



This expression is a minimum for d=d' that is to say, when the 

 needle is exactly at the centre of the bbx ; the sensitiveness is then 

 a minimum. 



The value of a is in general somewhat difficult to calculate 

 directly by measurement of S 1? d, and d 1 ; it will in general be 

 better to determine this constant directly by comparison with an 

 absolute electrometer. 



^ 813. The capacity of the electrometer itself varies with the 

 deflection. Let a be the capacity of each ' half of the needle on 

 either side the long axis of symmetry, m the charge of the needle 

 when it occupies a symmetrical position in reference to the quad- 

 rants, and m the charge when it is deflected through the angle 6 

 we have evidently 



We see already that in the position of equilibrium the charge of 

 the needle depends not only on the potential of the needle, but on 

 those of the quadrants. It is only independent of the potential of 

 the quadrants when V 1 + V 2 = ; it is then equal to 2aV. 



When the deflection is 0, we have, supposing V-V 2 >V-V 1 , 



l + V 2 ) + a6 (V l - V 2 ) 



