THE ORBIT OF URANUS. 

 Derivatives with respect to (log a = .) 



Second derivatives. 



82.0 

 81.0 

 77.7 

 70.5 

 60.4 

 48.7 

 37.6 



The notation B ( % and E ( % is that of Le Verrier in his development in the first 

 volume of "Annales de V Observntoire Imperial de Paris." 



Numeric jl expression of R and its derivatives. 



We next proceed to the computation of the coefficients h and their derivatives. 

 As an example of the most convenient form of computation we present in full that 



vn f 



of the coefficient of cos (i% (i 1)2, o) in the expression of E for the action 

 aj 



of Saturn on Uranus. In this computation I use the tables given by Le Verrier 

 in his "Annales de V Observntoire," tome i, pages 358-383, comparing the develop- 

 ment with that of Professor Peirce in the Astronomical Journal, vol. i, as a control. 





