160 Formula for capacity of plate condenser 



I have frequently seen a narrow fringed ring of dirt on the glass all round 

 the coating, the space between the ring and the coating being clean, and 

 in general about T \y inch broad*. This must in all probability have pro- 

 ceeded from some dirt being driven off from the tinfoil by the explosions, 

 and deposited on the glass about the extremity of that space over which 

 the electricity spreads instantaneously, and therefore seems to show that 

 the distance to which the electricity spreads instantaneously is not very 

 different from -fo of an inch. 



309] From some experiments which will be mentioned by and byf, 

 I am inclined to think that the distance to which the electricity spreads 

 instantaneously is about ^ of an inch when the thickness of the glass 

 is about I of an inch and about ^ of an inch when its thickness is about 

 jij of an inch; or more properly the quantity of redundant fluid which 

 spreads itself on the surface of the glass is the same that it would be if 

 the distance to which it spread was so much, and that the glass in all 

 parts of that space was as much charged as it is in the coated part. 



310] If I charged and discharged a coated plate several times running, 

 in the dark, with intervals of not many seconds between each time, I 

 commonly observed that the flash of light round the edges of the coating 

 was stronger the first or second time than the succeeding ones, which 

 seems to shew that the electricity spreads further the first or second time 

 than the succeeding ones. Accordingly I frequently found in trying the 

 following experiments that the pith balls would separate rather differently 

 the first or second time of trying any coated plate than the succeeding ones. 

 Observing that I now speak of the half dozen trials which, as I said in [Art. 

 299], I commonly took with the same plate immediately after one another. 



311] Before I proceed to the experiments it may be proper to remind 

 the readerj that if a plate of glass or other non-conducting substance, 

 either flat or concave on one side and convex on the other, provided its 

 thickness is very small in respect of its least radius of curvature, is coated 

 on each side with plates of metal of any shape, of the same size and placed 

 opposite to each other, its charge ought by the theory to be equal to that 

 of a globe whose diameter is equal to the square of the semidiameter of 

 a circle whose area equals that of the coating divided by twice the thick- 

 ness of the glass, supposing the coated plate and globe to be placed at 

 an infinite distance from any over or undercharged body, and to be 

 connected to the jar by which they are electrified by canals of incom- 

 pressible fluid ; provided also that the electricity does not penetrate to any 

 sensible depth into the substance of the glass, and that the thickness of 



* [See Art. 538, Feb. 13, 1773.] f [See below, Arts. 314 to 323.] 



} [See Art. 166, Prop. XXXIV, Cor. VI.] { The generalisation, to values of capacity 

 and distribution for condensers with varying thickness of dielectric, had to await 

 Green's Easay of 1828, where it follows immediately from his use of the potential 

 function. Cf. end of Note 3, p. 366.} 



