In 1818 Laplace proposed that the Academie des Sciences in Paris set up a prize to be awarded to whoever succeeded in constructing lunar tables based solely on the law of universal gravity. In 1820 the prize was awarded to Carlini and Plana and Damoiseau by a committee of which Laplace was a member. But Laplace strongly criticized the Carlini-Plana approach to the lunar theory. A dispute ensued that is reconstructed on the basis of hitherto unknown letters exchanged between Carlini-Plana (...) and Laplace, and on the basis of papers published in Connaissance des temps and in Zach's Correspondance. After the exchanges, public and private, between Carlini-Plana and Laplace, the latter concluded that the results of the Italian astronomers and those arrived at by Damoiseau following the method of his Mecanique Celeste were fairly close, and that the purpose of the Academie in establishing the prize had been reasonably fulfilled. (shrink)