o 



500 KEPORT— 1867. 



tlie hollow corresponding to the continuous plate on the one side, and that 

 corresponding to the disk and guard-ring ou the other side, we see immediately 

 that they must be very nearly plane, from very near the disk all the way 

 across to the corresponding central portion of the opposite plate, but that 

 there will be a convexity towards the annular space between the disk and 

 uard-ring. 

 § 21. Thus we see that the resultant electric force will, to a very close 



approximation, be equal to — for all points of the aii* between the plates at 



distances from the outer bounding edges exceeding two or three times the 

 distance between the plates, and at distances from the interstice between the 

 guard-ring and disk any less than the breadth of this interstice. Hence if p 

 denote the electric density of any point of the plate or disk far enough from 

 the edges, wo have 



V 

 ■" = 4^- 

 But the outward force experienced by the surface of the electrified conduc- 

 tor per unit of area at any point is 2wp^, and therefore if F denote the force 

 experienced by any area A of the fixed plate, anj- part of which comes near 

 its edge, we have 



which ynU. clearly be equal to the attraction experienced by the moveable 



/Sn-F 



disk, if A be the mean area defined above. This gives V=D^ /— — , the 



formula by which dilference of potentials in absolute electrostatic measure 

 is calculated from the result of a measurement of the force F, which, it must 

 be remembered, is to be expressed in kinetic units. Thus if W be the mass 

 in grammes to which the weight is equal, we have 



where fj is the force of gravity in centimetres per second. 



The difficulty which, in first applying this method about twelve years ago, 

 I found in measuring accurately the distance I) between the plates and in 

 avoiding error from their not being rigorously parallel, I now elude by 

 measuring only differences of distance, and deducing the desired results from 

 the difference of the corresponding diflercnccs of potentials. Thus let Y' be 

 the difference of potentials between the plates required to give the same force 

 F ; when the difference of potentials is V' instead of Y, we have 



Y'-Y=(D'-D). /^. 



§ 22. The plan of proceeding wliich I now use is as foUows : — Each plate 

 .(fig. 11, Plate YI.) is insulated ; one of them, the continuous one, for instance, 

 -is kept at a potential diftering from the earth by a fixed amount tested by aid 

 of a separate idiostatic® electrometer; the other plate (the guard-ring and 

 moveable disk in metallic communication with one another) is alternately 

 connected with the earth and with the bod)' whose ])otential is to be 

 measured. The lower plate is moved iip or down by a micrometer- screw 

 imtil the moveable dislv balances in a definite position, indicated by the hair 

 (with background of white with black dots) seen through a lens, as shown in 

 fig. 11. Before and after commencing each series of electrical experiments, 



* See § 40 below. 



