Applied Mathematicsematics

Mathematical papers of the late George Green by George Green

By George Green

This publication is a facsimile reprint and will comprise imperfections comparable to marks, notations, marginalia and fallacious pages.

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The total quantity of electricity contained in the interior of any number of equal and similar jars, when one of them communicates with the prime conductor and the others are charged by cascade, is precisely equal to that, which one only would receive, if placed in communication with the same conductor, its exterior surface being connected with the common reservoir. This method when any of charging batteries, therefore, must not be employed great accumulation of electricity is required. been shown by M.

Thus far perfect conductors only have been considered. In order to give an example of the application of theory to bodies which are not so, we have, in the thirteenth article, supposed the matter of which they are formed to be endowed with a constant coercive force equal to /5, and analogous to friction in its operation, so that when the resultant of the electric forces acting upon any one of their elements is less than /3, the electrical state element shall remain unchanged; but, so soon as it exceed /3, a change shall ensue.

Having thus proved, that F' the value of any point p within the surface is tion F, at the potential funcgiven, provided its GENERAL PRELIMINARY RESULTS. value V is known it by we will now show, that what- V V deduced may be, the general value of the formula just given shall satisfy the equation ever the value "of from at this surface, 33 For, the value of V at any point p whose co-ordinates are x, y, z, deduced from the assumed value of V, by the above written formula, is U being the total potential function within the surface, arising from a unit of electricity concentrated in the point p, and the electricity since T is induced on the surface itself by evidently independent of x, y, its action.

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