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Ivory studied applications of mathematics, in particular the attraction of ellipsoids, orbits of comets, refraction, equilibrium of fluids and rotating ellipsoids based on methods of Jacobi and Liouville. His work led to him becoming a Fellow of the Royal Society, receiving both the Copley Medal and the Royal Medal and he was knighted. He made a critical commentary of Laplace's Méchanique céleste which was praised by Laplace.
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