Abstract
THE theorem of attraction stated by Prof. T. Alexander in NATURE of January 19, is a particular case of a more general theorem which I have not seen stated, though very likely it is not new. The well-known theorem of couches de glissement. is also a case of it. Imagine two spheres, one of radius r and made of positive or attracting matter of density σ, the other of radius ŕ and made of negative or repelling matter of the same density σ, to coexist even if they overlap. In the space common to the two spheres the one kind of matter neutralises the other, so that the space may be considered as empty. The force on a unit particle of positive matter, placed at any point on the circle of intersection of the two surfaces, is parallel to the line of the centres A, B, of the two spheres and of amount 4/3πσkc where σ is the common density of the spheres, c the distance between their centres, and k is the usual attraction constant. For the positive sphere attracts the particle towards the centre with a force 4/3;πσkr, and the other sphere repels the particle from its centre with a force πσkŕ. These forces give the resultant 4/3πσkc parallel to the line joining the centres of the spheres and from the repelling centre towards the other.
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GRAY, A. Attraction in a Spherical Hollow. Nature 59, 341 (1899). https://doi.org/10.1038/059341a0
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DOI: https://doi.org/10.1038/059341a0
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