In his 1687 Philosophiæ Naturalis Principia Mathematica Newton correctly stated that a rotating fluid of uniform density under the influence of gravity would take the form of a spheroid and that the gravity (including the effect of centrifugal force) would be weaker at the equator than at the poles by an amount equal (at least asymptotically) to five fourths the centrifugal force at the equator. In 1742, Colin Maclaurin published his treatise on fluxions, in which he showed that the spheroid was an exact solution. If we designate the equatorial radius by r e , the polar radius by r p , and the eccentricity by ϵ ϵ , with