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Does any one know when it was first proved that a conducting surface of any shape, not just a sphere with no charges inside it, but arbitrary charges outside it, has no total charge inside it? As late as 1925 one sees vague arguments to this effect, but only much later the argument using uniqueness of solutions of Laplace's equation for given boundary values.

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I should apologize for placing this question here, because I've just found the answer. It was George Green (of Green's functions); it occurs on page 49 of his mathematical papers, originally published in 1828.

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