120-122] The Attracted Disc Electrometer 105 



pieces, originally at different potentials, are now brought to the same 

 potential by the flow of electricity over the surface of the conductor. 

 Electricity can only flow from places of higher to places of lower potential, 

 so that electrical energy is lost in this flow. Thus the introduction of the 

 new conductor has diminished the electric energy of the field. 



If we now put the new conductor to earth there is in general a further 

 flow of electricity, so that the energy is still further diminished. 



Thus the electric energy of any field is diminished by the introduction of 

 a new conductor, whether insulated or not. 



Consider the case in which the new conductor remains insulated. Let 

 the energy of the field before the introduction of the new conductor be 



(p u E l * + 2p l2 E 1 E, + ...+p nn E n *) .................. (53). 



After introduction, the energy may be taken to be 



where p u ', etc., are the new coefficients of potential. Further coefficients of 

 the type pi >n +i, P^n+z, > Pn+i,n+i are of course brought into existence, but 

 do not enter into the expression for the energy, since by hypothesis E n+1 = 0. 



Since expression (54) is less than expression (53), it follows that 



is positive for all values of E 1} E 2 , .... Hence pu pu i g positive, and other 

 relations may be obtained, as in 111. 



ELECTROMETERS. 

 I. The Attracted Disc Electrometer. 



FIG. 40. 



122. This instrument is, as regards its essential principle, a balance in 

 which the beam has a weight fixed at one end and a disc suspended from 

 the other. Under normal conditions the fixed weight is sufficiently heavy 



