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.

美国数学家罗伯特·杰克逊·阿考克（Robert Jackson Adcock，1826-1895年）是一个晦涩的人物，迄今与回归分析和最小二乘法的历史有关，其身份和生活在本书第二部分中有所描述。1872年，他自行出版了一本小册子，“引力到球体和两个椭球公转：旋转流体质量的轴之比”，这在当时似乎已被很大程度上忽略。此后实际上丢失了，直到最近在皇家学会图书馆发现了副本。在其中，他确定了旋转均质椭圆体假定的展平程度密度均匀的流体地球，受到重力吸引并处于静水平衡状态，这是牛顿，拉普拉斯，高斯和狄利克雷以前曾考虑但尚未解决的问题。Adcock成功地获得了均质椭球势的显式解，并正确计算了该模型的展平度。到目前为止，据信该结果最早是由德国工程师Otto Heymann于1935年获得的。此处抄录了Adcock的小册子，并附有其内容的评论。希望表彰他的杰出成就将提高他作为数学家的声誉。