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minant, a concept for which no formal theory existed. The results depended on the convergence of this infinite determinant - something Hill was not able to establish - but which was later proved by Poincare. Poincare was influenced greatly by Hill's approach and, in particular, he employed the idea of using non-trivial periodic solutions as the starting point for a perturbation theory to great effect.

Hill's theory was turned by E. W. Brown into a practical method for computing lunar positions. Brown completed his theory in 1908, and the tables derived from it were published in 1919. These served as the basis for British and American lunar ephemerides until 1959. The Hill-Brown theory represents an order of magnitude increase in accuracy over that of Delaunay and the pinnacle of success for quantitative perturbation techniques. In the hands of some of the world's finest mathematical astronomers, perturbation theory had become a hugely powerful tool with which to study Solar System dynamics, but

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