or that possibly it may be subject to disturbances from some unseen planet revolving about the sun beyond the present boundaries of our system. If, after a lapse of years, the tables formed from a combination of numerous observations should be still inadequate to represent the motions of Uranus, the discrepancies may reveal the existence, nay, even the mass and orbit, of a body placed for ever beyond the sphere of vision.”[5] That prediction has been fulfilled since the seventh edition of this book was published. Not only the existence of Neptune, revolving at the distance of three thousand millions of miles from the sun, has been discovered from his disturbing action on Uranus, but his mass, the form and position of his orbit in space, and his periodic time had been determined before the planet had been seen, and the planet itself was discovered in the very point of the heavens which had been assigned to it. It had been noticed for years that the perturbation of Uranus had increased in an unaccountable manner (N. 139). After the disturbing action of all the known planets had been determined, it was found that, between the years 1833 and 1837, the observed and computed distance of Uranus from the sun differed by 240,000 miles, which is about the mean distance of the moon from the earth, while, in 1841, the error in the geocentric longitude of the planet amounted to 96ʺ. These discrepancies were therefore attributed to the attraction of some unseen and unknown planet, consequently they gave rise to a case altogether unprecedented in the history of astronomy. Heretofore it was required to determine the disturbing action of one known planet upon another. Whereas the inverse problem had now to be solved, in which it was required to find the place of an unknown body in the heavens, at a given time, together with its mass, and the form and position of its orbit, from the disturbance it produced on the motions of another. The difficulty was extreme, because all the elements of the orbit of Uranus were erroneous from the action of Neptune, and those of Neptune’s orbit were unknown. In this dilemma it was necessary to form some hypothesis with regard to the unknown planet; it was therefore assumed, according to Bode’s empirical law on the mean distances of the planets, that it was revolving at twice the distance of Uranus from the sun. In fact, the periodic time of Uranus is about 84 years, and, as the discrepancies in his motions increased slowly and regularly, it was evident that it would require a planet with a much longer periodic time to produce them—moreover, it was clear that the new planet must be exterior to Uranus, otherwise it would have disturbed the motions of Saturn.