1864.] 



of JBIecfrical Force. 



367 



versely with the square of the surface. In such cases, of which the author 

 gives some examples, the above formula does not apply. 



9. From these inquiries it is evident, as observed by the early electricians, 

 that conducting bodies do not take up electricity in proportion to their sur- 

 faces, except under certain relations of surface and boundary. If the breadth 

 of a given surface be indefinitely diminished, and the length indefinitely in- 

 creased, the surface remaining constant, then, as observed by Volta, the 

 least quantity which can be accumulated under a given electrometer indi- 

 cation 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 de- 

 creases the electrometer indication or intensity must increase the charge, 

 that is to say, the quantity which can be accumulated under the given in- 

 tensity. Conversely, whatever increases the electrometer indication de- 

 creases 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 induc- 

 tion, then the boundary extension of the surface may be neglected. In all 

 similar figures, for example, such as squares, circles, spheres, &c., the elec- 

 trical boundary is, in relation to surrounding matter, pretty much the same 

 in each, whatever be the extent of their respective surfaces. In calculating 

 the charge, therefore, 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 

 are as 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 surfaces. 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 dimen- 

 sions 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 ex- 

 panded as 1: In bke 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 : V 2, 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 diameter was found to be 1 : 1*13 ; 



