POTENTIAL AND CAPACITY 91 



The increase of torsional energy in the same displacement is 



\6d0 



where is the total angle of displacement from zero and \0 is the 

 corresponding couple. 



Then for equilibrium we may equate these and 



t - v t ) (v n - 



If V n be great compared with V 1 and V 2 we may take as an 

 approximation 



If the needle and one pair of quadrants be both connected to 

 the same source at potential V n and the other pair be earthed, 

 V, = V w V t = 



and 



This is independent of the sign of V n , and the electrometer 

 may then be used to measure an alternating potential, giving the 

 mean square of V n . 



By taking into account the increase or decrease of charge induced 

 on the two pairs of quadrants as well as the increase on the needle 

 it is easy to verify directly for this particular case the fact that 

 the sources supply double the energy added in the field within the 

 quadrants.* 



The attracted disc, or the trap -door electrometer. In 

 Thomson's trap-door electrometer two parallel plates are arranged 

 as a condenser, one being connected to the source of which the 

 potential is required, the other being, say, to earth. We might 

 measure the pull of one plate on the whole of the other, and in 

 the first instrument of the kind Harrises attracted disc electro- 

 meter this was actually done. If we could express the potential 



* The formula found above is quite sufficiently exact for many of the ex- 

 periments in which the quadrant electrometer is used. The explanation of the 

 voltage for maximum sensitiveness will be found in Thomson's Elements of 

 Electricity and Magnetism, 61. 



