532 Prof. Thomson on the Electro-statical Capacity of 



or any liquid or solid dielectric, and of other analogous arrange- 

 ments, such as the copper wires in gutta-percha tubes under water, 

 with which Faraday has recently performed such remarkable ex- 

 periments*. 



Thus, for a Leyden phial ; let us suppose a portion S of the 

 surface of a conductor A to be everywhere so near the surface of 

 a conductor A', that the distance between them at any point is 

 a small fraction of the radii of curvature of each surface in the 

 neighbourhood ; and let z be the distance between them at a 

 particular position, P. Then, by the analogy with heat, it is 

 clear that if the two surfaces be kept at different electrical poten- 

 tials, V and V, the potentials at equidistant points in any line 

 across from one to the other will be in arithmetical progression. 



V— V 

 Hence — - — will be the rate of variation of the potential per- 

 z 



pendicularly across in the position P. If, in the first place, 



the dielectric be air, the electric force in the air between the two 



V— V 



about the position P will consequently be — - — , and therefore 



the electrical density (according to the theorem proved in the 



1 V— V' 



first article) on one surface must be + - , and on the 



1 V— V . z 



other — . The quantity of electricity in the position 



1 V— V 



P, on an area ds of the surface S, is therefore ds, and 



47T Z 



therefore the whole quantity on S is 

 y-y/ Wg 

 4tti/ z' 



which is Green's general expression for the electrification of 

 either coating of a Leyden phial. If the thickness of the dielec- 

 tric be constant and equal to t, it becomes 



V-Y'S 



4fTT T ' 



Xow if A' be uninsulated, we have V' = ; and then, to charge 



g 

 S to the potential V, it takes the quantity V x -j — . Hence the 



" capacity " of S is S 



47TT* 



If instead of air there be a solid or liquid dielectric of inductive 

 capacity, k, occupying the space between the two surfaces, the 



* Deserioed in a lecture at the Royal Institution, Jan. 20, 1854, and 

 subsequently published iu vol. vii. p. l!>7 of the Philosophical Magazine. 



