THEORBITOFURANUS. 53 



CHAPTER III. 



PERTURBATIONS PRODUCED BY XEPTUXE AND JUPITER. 



The perturbations of Uranus by Neptune were originally computed with ele- 

 ments of both planets quite different from those finally adopted. But the last 

 computations, on which the concluded values of the perturbations depend, were 

 made with the concluded elements of Neptune found in my investigation of the 

 orbit of that planet.' They are as follows : 



Hence follow the following functions of the elements of Neptune and Uranus: 



a = 0.638195 

 ij = 12° 44' 58" 

 J = 247 45 20 

 - y = 1 30 29.6 

 cr = sin|j/= 0.013161 



31= 37.522 (in units of 6th place of decimals). 

 From these values of the elements are obtained the following values of the 

 various terms in the development of the perturbative function, and of v. As the 

 developments have been formed on the same principle as in the case of Saturn, it 

 is deemed unnecessary to give the details of the process. It is only necessary to 

 remark that the indices i' and { are the coefficients of I' and g respectively, the 

 mean longitude of Neptune, or T, being counted from the perihelion of Uranus. 



• Suiithsouiau Contributions to -Knowledge, Vol. NV. 



