SECT. VIII. ASTRONOMICAL TABLES. 61 



its motions, 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." * 



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 24,000 

 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 96". 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 de- 

 termine 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 ail unknown body in the heavens, 

 at a given time, together with its mass, and the form and posi- 

 tion 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. 



* Neptune was discovered in the year 1846. 



