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By George Green

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Mathematical papers of the late George Green

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

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De 1'Acad. de Sciences, 1821 et 1822), that It has when an placed in the interior of a hollow spherical conducting shell of uniform thickness, it will not be acted upon in the slightest degree by any bodies exterior to the electrified body is however intensely they may be electrified. In the ninth Essay this is proved to be generally true, whatever may be the form or thickness of the conducting shell. In the tenth article there will be found some simple equations, by means of which the density of the electricity induced on a spherical conducting surface, placed under the influence of any electrical forces whatever, is immediately given and thence shell, article of the present ; the general value of the potential function for any point either within or without this surface is determined from the arbitrary value at the surface itself, by the aid of a definite integral.

1), that the will be carried to their surfaces, all perfect whole of the and therefore there con- electricity is here no place for the application of the theory contained in this article ; but as there are probably no perfectly conducting bodies in becomes indispensably necessary, if we would electrical the phenomena in all their generality. investigate nature, this theory Having in this, and the preceding articles, laid down the most general principles of the electrical theory, we shall in what follows apply these principles to more special cases; and the necessity of confining this Essay within a moderate extent, will compel us to limit ourselves to a brief examination of the more interesting phenomena.

Then imagining a to begins solid of revolution to turn continually about its axis, and to be of this f acting in parallel "right subject to a constant electrical force electrical state at which the the determine we lines, permanent The result of the analysis is, that will ultimately arrive. in consequence of the coercive force /3, the solid will receive a new polarity, equal to that which would be induced in it if it body were a perfect conductor and acted upon by the constant force to one in the body's equator, making /3, directed in lines parallel the angle 90 + 7, with a plane passing through its axis and being supposed resolved into two parallel to the direction of/ : / one in the direction of the body's axis, the other b directed along the intersection of its equator with the plane just forces, mentioned, and 7 being determined by the equation In the latter part of the present article the same problem is considered under a more general point of view, and treated by a different analysis : the body's progress from the initial, towards it was the object of the former part to de- that permanent state and the great rapidity of this progress made by an example.

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