68 Royal Society : — 



and the length indefinitely increased, the surface remaining constant, 

 then, as observed by Volta, the least quantity which can be accumu- 

 lated under a given electrometer indication is when the given surface 

 is a circular plate, that is to say, when the boundary is a minimum, 

 and the greatest when extended into a right line of small width, 

 that is, when the boundary is a maximum. In the union of two 

 similar surfaces by a boundary contact, as for example two circular 

 plates, two spheres, two rectangular plates, &c, we fail to obtain 

 twice the charge of one of them taken separately. In either case 

 we fail to decrease the intensity (the quantity being constant) or to 

 increase the charge (the intensity being constant), it being evident 

 that whatever decreases the electrometer indication or intensity must 

 increase the charge, that is to say, the quantity which can be accu- 

 mulated under the given intensity. Conversely, whatever increases 

 the electrometer indication decreases the charge, that is to say, the 

 quantity which can be accumulated under the given intensity. 



10. If the grouping or disposition of the electrical particles, in 

 regard to surrounding matter, be such as not to materially influence 

 external induction, then the boundary extension of the surface may 

 be neglected. In all similar figures, for example, such as squares, 

 circles, spheres, &c, the electrical boundary is, in relation to sur- 

 rounding matter, pretty much the same in each, whatever be the 

 extent of their respective surfaces. In calculating the charge, there- 

 fore, of such surfaces, the boundary extensions may be neglected, 

 in which case their relative charges are found to be as the square roots 

 of the surfaces only ; thus the charges of circular plates and globes 

 areas their diameters, the charges of square plates are as their sides. 

 In rectangular surfaces also, having the same boundary extensions, 

 the same result ensues, the charges are as the square roots of the sur- 

 faces. In cases of hollow cylinders and globes, in which one of 

 the surfaces is shut out from external influences, only one-half the 

 surface may be considered as exposed to external inductive action, 

 and the charge will be as the square root of half the surface, that 

 is to say, as the square root of the exposed surface. If, for example, 

 we suppose a square plate of any given dimensions to be rolled up 

 into an open hollow cylinder, the charge of the cylinder will be to the 

 charge of the plate into which we may suppose it to be expanded 

 as 1: sl 2. In like manner, if we take a hollow globe and a circular 

 plate of twice its diameter, the charge of the globe will be to the 

 charge of the plate also as 1 : V2, which is the general relation of the 

 charge of closed to open surfaces of the same extension. The charge 

 of a square plate to the charge of a circular plate of the same dia- 

 meter was found to be 1 : 1*13; according to Cavendish it is as 

 1 : 1*15, which is not far different. It is not unworthy of remark 

 that the electrical relation of a square to a circular plate of the same 

 diameter, as determined by Cavendish nearly a century since, is in 

 near accordance with the formulae C= VS above deduced. 



1 1 . The author enumerates the following formulae as embracing 

 the general laws of quantity, surface, boundary extension, and inten- 

 sity, practically useful in deducing the laws of statical electrical force. 



