ing month Dr. Galle of the Berlin Observatory received from Leverrier a request to search for it, and on the same evening found close to the position given by Leverrier a strange body shewing a small planetary disc, which was soon recognised as a new planet, known now as Neptune.
It may be worth while noticing that the error in the motion of Uranus which led to this remarkable discovery never exceeded 2', a quantity imperceptible to the ordinary eye; so that if two stars were side by side in the sky, one in the true position of Uranus and one in the calculated position as given by Bouvard's tables, an observer of ordinary eyesight would see one star only.
290. The lunar tables of Hansen and Professor Newcomb, and the planetary and solar tables of Leverrier, Professor Newcomb, and Dr. Hill, represent the motions of the bodies dealt with much more accurately than the corresponding tables based on Laplace's work, just as these were in turn much more accurate than those of Euler, Clairaut, and Halley. But the agreement between theory and observation is by no means perfect, and the discrepancies are in many cases greater than can be explained as being due to the necessary imperfections in our observations.
The two most striking cases are perhaps those of Mercury and the moon. Leverrier's explanation of the irregularities of the former (§ 288) has never been fully justified or generally accepted; and the position of the moon as given in the Nautical Almanac and in similar publications is calculated by means of certain corrections to Hansen's tables which were deduced by Professor Newcomb from observation and have no justification in the theory of gravitation.
291. The calculation of the paths of comets has become of some importance during this century owing to the discovery of a number of comets revolving round the sun in comparatively short periods. Halley's comet (chapter xi., § 231) reappeared duly in 1835, passing through its perihelion within a few days of the times predicted by three independent calculators; and it may be confidently expected again about 1910. Four other comets are now known which, like Halley's, revolve in elongated elliptic orbits, completing a revolution in between 70 and 80 years;
