168 ELEMENTS OF STATIC ELECTRICITY. 



different potentials, near each other, as A and B in the 

 electrometer, the attraction of each for the other is 

 equal ; the air being the dielectric between them. 

 Hence the force, exerted at any point between them, 

 equals the force on both surfaces, represented b} T ^TIQ; 

 and tends to draw the movable disc C towards B. 

 But this force is also equal to the difference of poten- 

 tial, divided by the distance between the discs. Hence 

 when x represents difference of potential, and d the 



or 

 distance, the resultant force, at any point, equals . 



x x 



Hence 4 ?*(>= , and Q = 

 a 



Now if the surface of the movable disc O be repre- 

 sented by s, its attractive force will equal s Q : hence 

 the total attractive force equals 2 TCQ x s Q = 2 it s if. 



nr 



And substituting for Q its value, -7 , we have 



4t Tt Ct 



/ x V x 2 sx 2 



2 ^M A - -j)=^ nS 1X 2^2 = Q - ^2' 



\4 it d' 16 a* d 2 Sad 2 



Now since the attractive force equals the weight w, 

 multiplied by the acceleration produced by gravity, 



s x 2 



represented by #, we have w g = - : therefore x 



" 



n 



= d ^ (1), which expresses x in absolute meas- 



ure. But x represents the potential of the first body 

 tested by the electrometer. 



By a similar process the potential, 2, of the second 



body is expressed by the equation, z = h I ^ (2). 



Subtracting (2) from (1), we have x z = (d Ji) 

 n w g 



J 



