BIOGRAPHICAL NOTICE. xix 



taken a considerable number of observations, but that his progress was slow as he 

 thought it right to include all stars to the 10-11 magnitude. He found that to scrutinise 

 thoroughly, according to his plan, the proposed part of the heavens would require more 

 observations than he could take in the year. On the same day Adams wrote to the 

 Astronomer Royal a letter, the opening paragraphs of which are as follows : " In the 

 investigation, the results of which I communicated to you last October, the mean distance 

 of the supposed disturbing planet is assumed to be twice that of Uranus. Some assumption 

 is necessary in the first instance, and Bode's law renders it probable that the above dis- 

 tance is not very remote from the truth : but the investigation could scarcely be considered 

 satisfactory while based on anything arbitrary ; and I therefore determined to repeat the 

 calculation, making a different hypothesis as to the mean distance. The eccentricity also 

 resulting from my former calculations was far too large to be probable ; and I found that 

 although the agreement between theory and observation continued very satisfactory down 

 to 1840, the difference in subsequent years was becoming very sensible, and I hoped 

 that these errors as well as the eccentricity might be diminished by taking a different 

 mean distance. Not to make too violent a change, I assumed this distance to be less 

 than the former value by about ^th part of the whole. The result is very satisfactory, 

 and appears to show that, by still further diminishing the distance, the agreement be- 

 tween the theory and the later observations may be rendered complete, and the eccentricity 

 reduced at the same time to a very small quantity. The mass and the elements of the 

 orbit of the supposed planet, which result from the two hypotheses, are as follows : 



Hypothesis I. Hypothesis II. 



Mean Longitude of Planet, 1st October, 1846 ... 325 8' 323 2' 



Longitude of Perihelion ............ 315 57' 299 11' 



Eccentricity ............... 016103 012062 



Mass (that of Sun being 1) ......... 000016563 0'00015003." 



Adams also gave the errors of mean longitude, exhibiting the difference between 

 theory and observation on the two hypotheses, and, after pointing out that the errors 

 given by the Greenwich Observations of 1843 are very sensible on both hypotheses, he 

 proceeds : " By comparing these errors it may be inferred that the agreement of theory 



and observation would be rendered very close by assuming = - 57, and the corresponding 



a 



mean longitude on October 1, 1846, would be about 315 20', which I am inclined to 

 think is not far from the truth. It is plain, also, that the eccentricity corresponding to 



this value of , would be very small." In consequence of the divergence of the results 



fl 



of the two hypotheses, Adams asked for two normal places near the oppositions of 1844 

 and 1845. In the Astronomer Royal's absence on the Continent, these were sent by 

 Mr Main ; and on September 7 Adams wrote : " I hope by to-morrow to have obtained 

 approximate values of the inclination and longitude of the node." 



Two days earlier, on August 31, 1846, Le Verrier had presented to the French 



