36 Prof. Challis's Ohservatiojis relative to the New Planet. 



with the theory implied the determination oi all the unknown 

 quantities of the problem, both the corrections of the elements 

 of Uranus, and the elements of the disturbing body. The 

 smallness of the residual errors proved that the new theory 

 was adequate to the explanation of the observed anomalies in 

 the motion of Uranus ; and that as the error of longitude was 

 corrected for a period of at least 130 years, the error of radius 

 vector was also corrected. As the calculations rested on an 

 assumption made according to Bode's law, that the mean di- 

 stance of the disturbing planet was double that of Uranus, 

 without the above-mentioned numerical verification, no proof 

 was given that the problem was solved, or that the elements 

 of the supposed planet were not mere speculative results. The 

 earliest evidence of the complete solution of an inverse pro- 

 blem of perturbations is to be dated from October 184-5. 



Although the comparison of the theory with observation 

 proved synthetically that the assumed mean distance was not 

 very far from the truth, it was yet desirable to try the effect 

 of an alteration of the mean distance. Mr. Adams accord- 

 ingly went through the same calculations as before, assuming 

 a mean distance something less than the double of that of 

 Uranus, and obtained results which indicated a better accord- 

 ance of the theory with observation ; and led him to the con- 

 clusion, which has since been confirmed by observation, that 

 the mean distance should be still further diminished. This 

 second solution, taken in conjunction wilh the first, may be 

 considered to relieve the question of every kind of assumption. 

 The new elements of the disturbing body, and the results of 

 comparing the observed with the theoretical mean longitudes 

 of Uranus, were communicated to the Astronomer Royal at the 

 beginning of September 1846. These were accompanied by 

 numerical values of errors of the radius vector, the Astronomer 

 Royal having inquired alter the reception of the first solution, 

 whether the error of radius vector, known to exist from ob- 

 servation, was explained by this theory. It would be wrong 

 to infer that Mr. Adams was not prepai'ed to answer this 

 question till he had gone through the second solution. Errors 

 of radius vector were as readily deducible from the first solu- 

 tion as from the other. 



The preceding details are intended to point out the circum- 

 stances which led astronomers to suspect the existence of an 

 additional body of the solar system, and the theoretical reasons 

 there were for undertaking to search for it. No one could 

 have anticipated that the place of the unknown body was in- 

 dicated with any degree of exactness by a theory of this kind. 

 It might reasonably be supposed, without at all mistrusting 



