1] ACCOUNTING FOR PERTURBATIONS OF URANUS. 3 



determined to repeat the calculation, making a different hypothesis as to 

 the mean distance. The eccentricity also resulting from my former calcu- 

 lations 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 y^th part of the whole. The result is very satisfactory, and appears 

 to shew that, by still further diminishing the distance, the agreement 

 between 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. 



(,4=0-6) ( a 4=o,i 5 ) 



Mean longitude of Planet, 1st Oct. 1846... 325 8' 323 2' 



Longitude of Perihelion 315 57' 299 11' 



Eccentricity 0'16103 0'12062 



Mass (that of Sun being 1) 0-00016563 0'00015003 



The investigation has been conducted in the same manner in both 

 cases, so that the differences between the two sets of elements may be con- 

 sidered as wholly due to the variation of the fundamental hypothesis. The 

 following table exhibits the differences between the theory and the obser- 

 vations which were used as the basis of calculation. The quantities given 

 are the errors of mean longitude, which I found it more convenient to 

 employ in my investigations than those of the true longitude. 



ANCIENT OBSERVATIONS. 



(Obs. -Theory.) n t (Obs. - Theory.) 



Date - Hypoth. I. Hypoth. U. Date ' Hypoth. I. Hypoth. II. 



1712 +67 +6-3 1756 4-0 4-0 



1715 -6-8 -6-6 1764 5-1 4-1 



1750 -1-6 -2-6 1769 + 0'6 + 1-8 



1753 +57 +5-2 1771 +H'8 +12-8 



12 



