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368 Tables de la Lune (1824 and 1828) were for some time in general use.

Some special problems of both lunar and planetary theory were dealt with by Siméon Denis Poisson (1781–1840), who is, however, better known as a writer on other branches of mathematical physics than as an astronomer. A very elaborate and detailed theory of the moon, investigated by the general methods of Laplace, was published by Giovanni Antonio Amadeo Plana (1781–1869) in 1832, but unaccompanied by tables. A general treatment of both lunar and planetary theories, the most complete that had appeared up to that time, by Philippe Gustave Doulcet de Pontécoulant (1795–1874), appeared in 1846, with the title Théorie Analytique du Système du Monde; and an incomplete lunar theory similar to his was published by John William Lubbock (1803–1865) in 1830–34.

A great advance in lunar theory was made by Peter Andreas Hansen (1795–1874) of Gotha, who published in 1838 and 1862–64 the treatises commonly known respectively as the Fundamenta and the Darlegung, and produced in 1857 tables of the moon's motion of such accuracy that the discrepancies between the tables and observations in the century 1750–1850 were never greater than 1" or 2". These tables were at once used for the calculation of the Nautical Almanac and other periodicals of the same kind, and with some modifications have remained in use up to the present day.

A completely new lunar theory—of great mathematical interest and of equal complexity—was published by Charles Delaunay (1816–1872) in 1860 and 1867. Unfortunately the author died before he was able to work out the corresponding tables.

Professor Newcomb of Washington (§ 283) has rendered valuable services to lunar theory—as to other branches of astronomy—by a number of delicate and intricate calculations, the best known being his comparison of Hansen's tables with observation and consequent corrections of the tables.