It will be remembered that at the latter part of the eighteenth century William Herschel had immortalized himself by the discovery of a great planet, to which was presently assigned the name of Uranus. After the movements of Uranus had been carefully studied, it was found that on many previous occasions Uranus had been unwittingly observed by astronomers, who regarded it as a star. When these observations were all brought together, and when the track which Uranus followed through the heavens was thus opened to investigation, it was found that the movements of the planet presented considerable anomalies. The planet did not move precisely as it would have moved had it been subjected solely to the supreme attractive power of the sun. Astronomers are, of course, accustomed to irregularities of this description in the movements of the planets. These irregularities have as their origin the attractions of the various other members of the solar system. It is possible to submit these attractions to calculation and thus to estimate their amount. The effect, for instance, of Saturn in disturbing Jupiter can be allowed for, and the nature of Jupiter's motion as thus modified can be precisely estimated. In like manner, the influence of the earth on Venus can be determined, and so for the other planets; and thus, generally speaking, it was found that when the proper allowances had been made for the action of known causes of disturbance, then the calculated movement of each planet could be reconciled with observation.
The circumstances of Uranus were, however, in this respect wholly exceptional. Due allowance was first made for the attraction of Uranus by Saturn, and for the attraction of Uranus by Jupiter, as well as by the other planets. It was thus found that the irregularities of Uranus could be to some extent explained, but that it was not possible in this manner to account for those irregularities completely. It was therefore evident that some influence must be at work affecting the movement of Uranus, in addition to those arising from any planet of which astronomers hitherto had cognizance. The only available supposition would be that some other planet, at present unrecognized, must be in our system, and that the attraction of this unknown body must give rise to those irregularities of Uranus which remained still outstanding.
A great problem was thus proposed for mathematicians. It was nothing less than to affect the determination of the orbit and the position of this unknown planet, the sole guide to the solution of the problem being afforded by the discrepancies between the places of Uranus as actually observed and the places which were indicated by the calculations, when every allowance had been made for known causes. The problem was indeed a difficult one, but,