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published in 1743. Newton had assumed in his calculations that the Earth was homogeneous, and had made erroneous claims about the effect that a variable density would have. Clairaut showed that, for a shape built up from ellipsoidal layers of different densities, the acceleration due to gravity g at a latitude p would be related to that at the equator g0 through the equation g - go = go (2A - e) sin2 p, where A is the ratio of the centrifugal to the gravitational force at the equator, and e is the ellipticity (assumed small) of the Earth. This result is known as

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