POTENTIAL AND CAPACITY 87 



with radius O'Ol cm. (about 36 S.W.G.) runs parallel to and 

 10 cm. above a conducting table, the formula shows that the 

 capacity per cm. length is more than 1 /3. 



Condenser of any form. A condenser consists essentially 

 of two conducting plates everywhere the same distance apart, this 

 distance being usually very small compared with the linear 

 dimensions of the plates, and the curvature being everywhere small. 

 We may then apply the treatment already used for two parallel 

 plane plates, and we have, when air is the insulator, 



V = 4<7T<Td 



and c = 



where A is the area of the inner surface of either plate and d is 

 their distance apart. 



INSTRUMENTS USED TO MEASURE DIFFERENCE 

 OF POTENTIAL 



The quadrant electrometer. The quadrant electrometer 

 devised by Lord Kelvin is the most sensitive instrument for the 

 measurement of differences of potential. We shall describe first 

 a simple form of the original instrument represented in Fig. 66.* 



Four hollow brass quadrants, like that shown in Fig. 66 (a), are 

 mounted on insulating pillars fixed on a metal base so as to form 

 a horizontal circular box, cut across two diameters at right angles, 

 >ince the quadrants are insulated from one another by narrow 

 air spaces. The opposite quadrants are connected in pairs by very 

 fine wires. Under the quadrants and between the supporting 

 pillars is an open Leyden jar lined outside with tinfoil and con- 

 taining inside strong sulphuric acid, the surface of contact of the 

 acid with the glass serving as the inner coating of the jar. The 

 acid also serves to dry the air within the case of the instrument and 

 so maintain^ tin- insulation of the various parts. Within the 

 hollow space made by the quadrants is a " needle," really a" figure- 

 of-eight' 1 shaped piece of sheet aluminium, Fig. 66 (6), the sectors 

 being each about a quadrant. The needle is supported from the top 

 of the case by an insulating suspension which also introduces torsion 

 wlim the needle is displaced from its " zero " position. The torsion 

 may be obtained from a bifilar suspension, a quartz fibre suspension, 

 or from a small magnet fastened on to the needle system. The 

 position of the needle is indicated by a beam of light reflected 

 on to a scale from a mirror above the quadrants and rigidly 

 attached to the needle. 



From two adjacent quadrants two brass rods pass vertically 



* In Lord Kelvin's Papers on Electrostatics and Electro-magnetism a form of 

 the instrument salted for exact work is described in the Report on Electrometers. 



