Prof. Challis's Observations relative to the New Planet. 35 



of disturbances caused by an undiscovered planet more distant 

 than Uranus. But there is no evidence of this hypothesis 

 having been put to tlie test of calculation previous to 1843. 

 The usual problem of perturbations is to find the disturbing 

 action of one body on another by knowing the positions of 

 both. Here an inverse problem, hitherto untried, was to be 

 solved ; viz. from known disturbances of a planet in known 

 positions, to find the place of the disturbing body at a given 

 time. Mr. Adams, Fellow of St. John's College, showed me 

 a memorandum made in 1841, recording his intention of at- 

 tempting to solve this problem as soon as he had taken his 

 degree of B.A. Accordingly, after graduating in January 

 1843, he obtained an approximate solution by supposing the 

 disturbing body to move in a circle at twice the distance of 

 Uranus from the sun. The result so far satisfied the ob- 

 served anomalies in the motion of Uranus as to induce him to 

 enter upon an exact solution. For this purpose he required 

 reduced observations made in the years 1818-26, and re- 

 quested my intervention to obtain them from Greenwich. The 

 Astronomer Royal, on my application, immediately supplied 

 (Feb. 15, 1814) all the heliocentric errors of Uranus in lon- 

 gitude and latitude, from 1754 to 1830, completely reduced. 

 Mr. Adams was now furnished with ample data from obser- 

 vation, and his next care was to ascertain whether Bouvard's 

 theoretical calculations were correct enough for his purpose. 

 He tested the accuracy of the principal terms of the pertur- 

 bations caused by Jupiter and Saturn, and concluded that the 

 small terms which Bouvard had not taken into account would 

 not sensibly affect the final results, the chief of them being 

 either of long period, or of a period nearly equal to that of 

 Uranus. Besides which he introduced into the theory several 

 corrections which had been derived from observation and cal- 

 culation by different astronomers since 1821. The calcula- 

 tions were completed in 1845. In September of that year, 

 Mr. Adams placed in my hands a paper containing numerical 

 values of the mean longitude at a given epoch, longitude of 

 perihelion, eccentricity of orbit, mass, and geocentric longitude, 

 Sept. 30, of the supposed disturbing planet, which he calls by 

 anticipation "the new planet," evidently showing the convic- 

 tion in his own mind of the reality of its existence. Towards 

 the end of the next month, a communication of results slightly 

 dilferent was made to the Astronomer Royal, with the addition 

 of what was far more important, viz. a list of the residual 

 errors of the mean longitude of Uranus, for a period extend- 

 ing from 1690 to 1840, after taking account of the disturbing 

 effect of the supposed nianet. This comj)arisoii of observation 



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