We shall mention but one other achievement of the methods of celestial mechanics. Those visitors of the skies, the comets, which become so prominent only to fade away and vanish perhaps forever, had interested astronomers from the earliest times. Soon after the discovery of the law of gravitation, Newton had worked out a method by which the elements of a comet’s orbit can be computed from observations of its position. It was found that the great majority of these bodies move in nearly parabolic paths and only a few in ellipses. Of the latter the most prominent is the brilliant comet first observed by Halley in 1681. It has reappeared regularly at intervals of seventy-six years; the last appearance in the spring of 1910 is no doubt well remembered by the reader. Kant had considered comets to be formed by condensing solar nebulæ, whereas Laplace had maintained that they originate in matter which is scattered throughout stellar space and has no connection with the solar system. A study of the distribution of inclinations of comet orbits by H. A. Newton (=16=, 165, 1878) of New Haven substantiated Laplace’s hypothesis, and led to the conclusion that the periodic comets have been captured by the attraction of those planets near to which they have passed. Of these comets a number have comparatively short periods, and are found to have orbits which are in general only slightly inclined to those of the planets, and are traversed in the same direction. Moreover, the fact that the orbit of each of these comets comes very close to that of Jupiter made it seem probable that they have been attached to the solar system by the attraction of this planet. Further confirmation of this hypothesis was furnished by H. A. Newton’s (=42=, 183 and 482, 1891) explanation of the small inclination of their orbits and the scarcity of retrograde motions among them.