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 or homogeneity of form which is characteristic of a mathematical theory properly so called." These functions have been studied by C. Th. Anger of Danzig, 0. Schlömilch of Dresden, R. Lipschitz of Bonn (born 1832), Carl Neumann of Leipzig (born 1832), Eugen Lommel of Leipzig, I. Todhunter of St. John's College, Cambridge.

Prominent among the successors of Laplace are the following: Siméon Denis Poisson (1781–1840), who wrote in 1808 a classic Mémoire sur les inégalités séculaires des moyens mouvements des planètes, Giovanni Antonio Amadeo Plana (1781–1864) of Turin, a nephew of Lagrange, who published in 1811 a Memoria sulla teoria dell' attrazione degli sferoidi ellitici, and contributed to the theory of the moon. Peter Andreas Hansen (1795–1874) of Gotha, at one time a clockmaker in Tondern, then Schumacher's assistant at Altona, and finally director of the observatory at Gotha, wrote on various astronomical subjects, but mainly on the lunar theory, which he elaborated in his work Fundamenta nova investigationes orbitœ verœ quam Luna perlustrat (1838), and in subsequent investigations embracing extensive lunar tables. George Biddel Airy (1801–1892), royal astronomer at Greenwich, published in 1826 his Mathematical Tracts on the Lunar and Planetary Theories. These researches have since been greatly extended by him. August Ferdinand Möbius (1790–1868) of Leipzig wrote, in 1842, Elemente der Mechanik des Himmels. Urbain Jean Joseph Le Verrier (1811–1877) of Paris wrote, the Recherches Astronomiques, constituting in part a new elaboration of celestial mechanics, and is famous for his theoretical discovery of Neptune. John Couch Adams (1819–1892) of Cambridge divided with Le Verrier the honour of the mathematical discovery of Neptune, and pointed out in 1853 that Laplace's explanation of the secular acceleration of the moon's mean motion accounted for only half the observed acceleration.