  Of the other results developed in the group of propositions following the deduction of universal gravity, the most heralded at the time were the defense of Copernicanism in Proposition 12 and the identification of the cause of the tides in Proposition 24 — two topics that Kepler, Galileo, and Descartes had all addressed. Nevertheless, the two Propositions that proved most important were 19 and 20, which respectively derive the non-spheroidal figure of the Earth and the variation of surface gravity with latitude under the assumption that the density of the Earth is uniform. This is the only passage in the Principia that Newton reworked extensively in both the second and then again in the third edition. As Newton was fully aware, and Huygens and a few others realized, these are the only results in the Principia that depend on universal gravity — that is, inverse-square gravity directed toward every particle of matter forming the Earth — and not merely macroscopic celestial gravity — inverse-square gravity directed toward celestial bodies. In his Discourse on the Cause of Gravity, Huygens offered an alternative theoretical account of the figure of the Earth and the variation of surface gravity, and he claimed to have evidence confirming it and hence refuting Newton's universal  gravity.[51] In part because evidence on the figure of the Earth and the variation of gravity with latitude were accessible in expeditions to the equator, these were the results in the Principia that were the first to receive concerted critical attention during the 1730s and 1740s. There was a complication in all this, however. The extremely precise results for both the figure of the Earth and the variation of gravity that Newton tabulated in the second and third editions were based on uniform density, and hence, just like Keplerian motion, represented an idealization, departures from which would point to non-uniformities of density. Not until Clairaut's Theory of the Figure of the Earth did means become available to calculate the effects of non-uniformities in the  density.[52]