Once again Halley’s suggestion became an inspiration for the mathematical astronomer. Clairaut, assisted by Lalande, found that Saturn would retard the comet 100 days, Jupiter 518 days, and predicted its return to perihelion on April 13th, 1759. In his communication to the French Academy, he said that a comet travelling into such distant regions might be exposed to the influence of forces totally unknown, and “even of some planet too far removed from the sun to be ever perceived.” The excitement of astronomers towards the end of 1758 became intense; and the honour of first catching sight of the traveller fell to an amateur in Saxony, George Palitsch, on Christmas Day, 1758. It reached perihelion on March 13th, 1759. This fact was a startling confirmation of the Newtonian theory, because it was a new kind of calculation of perturbations, and also it added a new member to the solar system, and gave a prospect of adding many more. When Halley’s comet reappeared in 1835, Pontecoulant’s computations for the date of perihelion passage were very exact, and afterwards he showed that, with more exact values of the masses of Jupiter and Saturn, his prediction was correct within two days, after an invisible voyage of seventy-five years! Hind afterwards searched out many old appearances of this comet, going back to 11 B.C., and most of these have been identified as being really Halley’s comet by the calculations of Cowell and Cromellin[4] (of Greenwich Observatory), who have also predicted its next perihelion passage for April 8th to 16th, 1910, and have traced back its history still farther, to 240 B.C. Already, in November, 1907, the Astronomer Royal was trying to catch it by the aid of photography. FOOTNOTES: [1] Born 1736; died 1813. [2] Born 1749; died 1827. [3] This sentence does not appear in the original memoir communicated to the Royal Society, but was first published in a posthumous reprint. [4] _R. A. S. Monthly Notices_, 1907-8. 9. DISCOVERY OF NEW PLANETS—HERSCHEL, PIAZZI, ADAMS, AND LE VERRIER. It would be very interesting, but quite impossible in these pages, to discuss all the exquisite researches of the mathematical astronomers, and to inspire a reverence for the names connected with these researches, which for two hundred years have been establishing the universality of Newton’s law. The lunar and planetary theories, the beautiful theory of Jupiter’s satellites, the figure of the earth, and the tides, were mathematically treated by Maclaurin, D’Alembert, Legendre, Clairaut, Euler, Lagrange, Laplace, Walmsley, Bailly, Lalande, Delambre, Mayer, Hansen, Burchardt, Binet, Damoiseau, Plana, Poisson, Gauss, Bessel, Bouvard, Airy, Ivory, Delaunay, Le Verrier, Adams, and others of later date.