The life and work of Robert J. Adcock. Part I: the figure of the Earth

Abstract

The American mathematician Robert Jackson Adcock (1826–1895) is an obscure figure, hitherto associated with the history of regression analysis and least-squares, whose identity and life are described in Part II of this work. In 1872, he self-published a pamphlet, ‘Gravitation to the sphere and the two ellipsoids of revolution: ratio of the axes of a rotating fluid mass’, which seems to have been largely ignored at the time. It effectively became lost thereafter, until a copy was recently discovered in the Library of the Royal Society. In it, he determined the degree of flattening assumed by a rotating homogeneous ellipsoidal fluid Earth with a uniform density, subject to gravitational attraction and in hydrostatic equilibrium—a problem previously considered, but not solved, by Newton, Laplace, Gauss and Dirichlet. Adcock successfully obtained an explicit solution for the potential of a homogeneous ellipsoid and correctly calculated the flattening of such a model. Until now, this result was believed to have first been obtained by a German engineer, Otto Heymann, in 1935. Adcock's pamphlet is transcribed here with a commentary on its contents. It is hoped that recognition of his remarkable achievement will enhance his reputation as a mathematician.