E619 -- Enodatio difficultatis super figura Terrae a vi centrifuga oriunda.

(English Translation of Title)

(based on Eric J. Aiton's introduction (written in English) to Opera Omnia Series 2, Volume 31)
Euler finds that in the figure of the earth determined by the gravity towards its center and the centrifugal force arising from its rotation, the ratio of the diameter of the equator to the axis is 577 : 576. He says that the discrepancy between this ratio and that derived from geodetic measurements shows that in addition to the gravity to the center of the earth and the centrifugal force, the earth must also be subject to a lateral force that results from universal gravitation. Euler defines universal gravitation in terms of its required mathematical properties. He then says that if the entire earth were fluid, its surface could never arrive at an equilibrium state.


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