Abstract
THE solid is one of revolution (evidently), and the attraction being a maximum is unaltered by shifting a small elementary ring of matter from one point to another of its bounding surface. If dM is the mass of a ring formed by the revolution of the point r, θ, then the attraction is dM cos θ/r2. Hence the equation of the generating curve of the boundary is cos θ/r2=const., or r2=k2 cos θ say, or (x2 + y2)3=k4x2. The curve may be traced by drawing the circle r=k cos θ, and taking on each radius vector a mean proportional between that radius and k.
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BRYAN, G. Maximum Gravitational Attraction on a Solid. Nature 75, 439 (1907). https://doi.org/10.1038/075439d0
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DOI: https://doi.org/10.1038/075439d0
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