70 ASTRONOMICAL TABLES. [SECT. viir. 



buted to the attraction of some unseen and unknown planet, 

 consequently they gave rise to a case altogether unprece- 

 dented in the history of astronomy. Heretofore it was re- 

 quired 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, to- 

 gether 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 di- 

 lemma it was necessary to form some hypothesis with re- 

 gard to the unknown -planet ; it was therefore assumed ac- 

 cording to an empirical law observed by Baron Bode, in 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 dis- 

 crepancies 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. 



Another circumstance tended to lessen the difficulty ; the 

 latitude of Uranus was not much affected, therefore it was 

 concluded that the inclination of the oroit of the unknown 

 body must be very small, and, as that of the orbit of Uranus 

 is only 46' 28"'4, both planets were assumed to be moving 

 in the plane of the ecliptic, and thus the elements of the 

 orbit of the unknown planet were reduced from six to four. 

 Having thus assumed that the unknown body was revolving 

 in a circle in the plane of the ecliptic, the analytical ex- 

 pression of its action on the motion of Uranus, when in nu- 

 merous points of its orbit, was compared with the observed 

 longitude of Uranus, through a regular series of years, by 

 means of which the faulty elements of the orbit of Uranus 



