Abstract
MR. G. W. WALKER tells me that he has sent to NATURE his interesting problem of the mutual attraction between two uniform concentric hemispherical shells, bounded by a common diametral plane. The following elementary solution has occurred to me. Call the outer shell A and the inner B. Now let another hemisphere A′ be added to A so that instead of the hemisphere A we have a complete and uniform spherical shell surrounding B. The attraction between the complete sphere and B is zero, if, as is here understood to be the case, the attraction between the particles follows the Newtonian law. Hence the attraction F of A on B is equal and opposite to the attraction of A′ on B. But the force exerted by A′ on B is obviously equal and opposite to the attraction which would be exerted by A on a hemisphere added to B so as to convert it into a complete spherical shell. Hence the force exerted by A on the inner sphere thus completed would be 2F, and this attraction is the same as that which would be exerted on a particle of double the mass of B placed at the centre. The attraction F of A on B is therefore that which would be exerted by A on a particle of mass equal to B placed at the centre, and the same thing holds for the reaction of B on A. Mr. Walker's result is therefore established.
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GRAY, A. Attraction between Concentric Hemispherical Shells. Nature 69, 560 (1904). https://doi.org/10.1038/069560b0
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DOI: https://doi.org/10.1038/069560b0
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