184 ELECTROMETRY. 



symmetrical with the plane of separation of the quadrants. The 

 radii are then in the mean part of the quadrants that is to say, in a 

 position in which the action they experience is sensibly zero. 



t 811. Let us suppose that each pair of quadrants and the needle 

 are kept at constant potentials, which are respectively equal to V 1? V 2 , 

 and V. If the needle turns through a very small angle 0, it is in the 

 conditions of the movable cylinder in the case of three cylinders (98) ; 

 if a is the capacity of the needle for unit angle, the change in energy 

 of the system for the displacement 0, or what amounts to the same 

 thing, the work done by electrical force during this displacement, 

 will be expressed by 



(16) W - W = 



The value of the moment of the couple acting on the needle is 



(17) - 



Equilibrium is obtained when this couple is equal to C sin 0, due to 

 the rotation of the bifilar, which gives the equation 



ft 



(18) "(Vj-Vjj) v-^I- 2 I -Cab*. 



The sine of the deflection may be replaced by the angle if the 

 deflections are very small or the suspension is uninlar. 



The sensitiveness of the apparatus is proportional to the ratio 



that is to say, to the capacity of the needle and to the length of 

 the wire, and is inversely as the weight of the needle and of the 

 square of the displacement of the wire. 



/ 812. The constant a may be calculated. If S x is the surface of 

 the circular band which corresponds to unit angle, that portion of 

 the needle comprised within the pair of quadrants at potential V l 

 has on its two faces electrical layers, the densities of which are 

 respectively (82) 



