106 Systems of Conductors [OH. iv 



to outweigh the disc. In using the instrument the disc is made to become 

 one plate of a parallel plate condenser, of which the second plate is adjusted 

 until the electric attraction between the two plates of the condenser is just 

 sufficient to restore the balance. 



The inequalities in the distribution of the lines of force which would 

 otherwise occur at the edges of the disc are avoided by the use of a guard- 

 ring ( 90), so arranged that when the beam of the balance is horizontal 

 the guard-ring and disc are exactly in one plane, and fit as closely as is 

 practicable. 



Let us suppose that the disc is- of area A and that the disc and guard- 

 ring are raised to potential V. Let the second plate of the condenser be 

 placed parallel to the disc at a distance h from it, and put to earth. Then 

 the intensity between the disc and lower plate is uniform and equal to V/h, 

 so that the surface density on the lower face of the disc is a = Vj4nrh. The 

 mechanical force acting on the disc is therefore a force 27rcr 2 A or V 2 A/87rh 2 

 acting vertically downwards through the centre of the disc. If this just 

 suffices to keep the beam horizontal, it must be exactly equal to the weight, 

 say W, which would have to be placed on this disc to maintain equilibrium 

 if it were uncharged. This weight is a constant of the instrument, so that 

 the equation 



8irh* 



enables us to determine V in terms of known quantities by observing h. 

 The instrument is arranged so that the lower plate can be moved parallel 

 to itself by a micrometer screw, the reading of which gives h with great 

 accuracy. We can accordingly determine V in absolute units, from the 

 equation 



If we wish to determine a difference of potential we can raise the upper 

 plate to one potential V ly and the lower plate to the second potential F a , 

 and we then have 



A more accurate method of determining a difference of potential is to 

 keep the disc at a constant potential v, and raise the lower plate succes- 

 sively to potentials Fj and F a . If h^ and h 2 are the values of h which bring 

 the disc to its standard position when the potentials of the lower plate are 

 F! and F 2 , we have 



877^ 



STI 



