92 STATIC ELECTRICITY 



difference in terms of this pull the instrument would be a satisfac- 

 tory electrometer. But the density in a condenser is not uniform 

 near the edges, and when the plates are some distance apart the 

 edge effect may extend some distance inwards. We cannot there- 

 fore apply the results of p. 83 to the whole plate. In the central 

 part of each plate, however, the density is practically uniform ; the 

 lines of strain go straight from plate to plate and these results 

 apply. Taking tha surface density as cr, the difference of potential 

 as V, and the distance of the plates apart as d, 



V = 



Since the pull per square centimetre is ZTTO*, the total pull P on a 

 central area A is 



AV* 



=_ (i). 



In practice the pull is measured on a " trap-door," i.e. on a 

 movable plate nearly filling a hole in one of the plates ot t he- 

 condenser, but with free edges. The surrounding plate is tern ml 

 the guard-ring, its function being to guard the density on the trap- 

 door from variation. The trap-door and guard-ring are electrically 

 connected and the force measured is that which is required to 

 keep the two in the same plane against the electrical pull of the 

 opposite plate. The effective area A is approximately (Maxwell, 

 Electricity and Magnetism, 3rd ed. vol. i. p. 333) the mean between 

 the aperture of the guard-ring and the area of tlu disc or trap-door. 

 Fig. 67 is one form of the instrument,* showing only the essential 

 parts. The guard-ring is fixed, while the movable disc or trap- 

 door is hung by metal wires from the end of a metal lever ha\ 

 a counterpoise at the other. The lever is supported by a wire 

 stretched horizontally between two insulated metal pillars connect id 

 to the guard-ring so that disc and ring are in connection. The 

 position of the trap-door is indicated by a hair stretched across 

 the forked end of the lever. This is viewed by a lens, and is so 

 adjusted that when it is midway between two black dots on a white 

 upright passing up through the fork behind the hair, the trap-door 

 and guard-ring are coplanar. Suppose that a known weight P is 

 placed on the disc and that a movable rider is adjusted on the 

 lever until the hair is in the central position when there is no 

 charge on the plates. Now remove P and connect the plates to 

 bodies at different potentials, adjusting the distance d of the 

 lower plate until the hair is again central. Evidently the electrical 

 pull is equal to P, and if V is the difference of potential we have 

 from (1) 



* Thomson's Papers on Electrostatics and Magnetitm, p. 281. 



