8 ON THE PERTURBATIONS OF URANUS. [2 



Observations being then in process of reduction, I applied to Mr Airy, 

 through the kind intervention of Professor Challis, for the observations of 

 some years in which the agreement appeared least satisfactory. The 

 Astronomer Royal, in the kindest possible manner, sent me in February 

 1844 the results of all the Greenwich Observations of Uranus. 



4. Meanwhile the Eoyal Academy of Sciences of Gottingen had pro- 

 posed the theory of Uranus as the subject of their mathematical prize, and 

 although the little time which I could spare from important duties in my 

 college prevented me from attempting the complete examination of the 

 theory which a competition for the prize would have required, yet this 

 fact, together with the possession of such a valuable series of observations, 

 induced me to undertake a new solution of the problem. I now took into 

 account the most important terms depending on the first power of the 

 eccentricity of the disturbing planet, retaining the same assumption as 

 before with respect to the mean distance. For the modern observations, the 

 errors of the tables were taken exclusively from the Greenwich Observations 

 as far as the year 1830, with the exception of an observation by Bessel 

 in 1823; and subsequently from the Cambridge and Greenwich Observations, 

 and those given in various numbers of the Astronomische Nachncliten. 

 The errois of the tables for the ancient observations were taken from those 

 given in the equations of condition of Bouvard's tables. After obtaining 

 several solutions differing little from each other, by gradually taking into 

 account more and more terms of the series expressing the perturbations, 

 I communicated to Professor Challis, in September 1845, the final values 

 which I had obtained for the mass, heliocentric longitude, and elements 

 of the orbit of the assumed planet. The same results, slightly corrected, 

 I communicated in the following month to the Astronomer Royal. The 

 eccentricity coming out much larger than was probable, and later obser- 

 vations shewing that the theory founded on the first hypothesis as to 

 the mean distance was still sensibly in error, I afterwards repeated my 

 investigation, supposing the mean distance to be about ^th part less than 

 before. The result, which I communicated to Mr Airy in the beginning 

 of September of the present year, appeared more satisfactory than my 

 former one, the eccentricity being smaller, and the errors of theory, com- 

 pared with late observations, being less, and led me to infer that the 

 distance should be still further diminished. 



5. In November 1845, M. Le Verrier presented to the Royal Academy 

 of Sciences, at Paris, a very complete and elaborate investigation of the 



