CHAP, iv.] ELECTRICITY AND MAGNETISM. 215 



a second disc, A, supported on an insulating stand. This 

 lower disc can be raised or lowered at will by a micro- 

 meter screw, great care being taken in the mechanical 

 arrangements that it shall always be parallel to the 

 plane of the guard -plate. Now, since the disc and 

 guard-plate are in metallic connection with one another, 

 they form virtually part of one surface, and as the 

 irregularities of distribution occur at the edges of the 

 surface, the distribution over the surface of the disc is 

 practically uniform. Any attraction of the lower plate 

 upon the disc might be balanced either by increasing 

 the weight of the counterpoise, or by putting a torsion 

 on the wire ; but in practice it is found most convenient 

 to obtain a balance by altering the distance of the lower, 

 plate until the electric force of attraction exactly 

 balances the forces (whether* of torsion or of gravity 

 acting on the counterpoise) which tend to lift the disc 

 above the level of the guard-plate. 



The theory of the instrument is simple also. The 

 force F just outside a charged conducter is 4717) (Art. 

 252); and since electric force is the same thing as 

 the rate of change of potential per unit of length 

 (Art. 241), it will be equal to g, where V is the 

 difference of potentials between the upper and lower 

 plates, and D the distance between them : hence p = == 



If the surface of the movable disc be S, the quantity of 

 the charge on it will be S/o. Now, let us suppose that 

 the electricity on the lower plate has an equal density 

 but of opposite sign, as will be the case if either plate is 

 connected to "earth." Since its density is-p it will 

 exercise a force of-z-rrp on a + unit placed near the disc; 

 (but as this force is a force exerted from the upper side 

 of the plate we must change its sign again and call it 

 + 27rp, where the + sign signifies a force tending to 

 move a + unit downwards.) Now on the disc there are 



