34 THEORBITOF URANUS. 



Derivatives with respect to (log a = ».) 



Second ilerivatives. 

 a^Dr,B<-'> a,D-oB^^ 2a^Dr,B<'^ 



82.0 

 81.0 

 77.7 

 70.5 

 60.4 

 48.7 

 37.6 



a,E<*'' «,£'? Sflj^'i' 6a,E'2 a,DvE^'> a^D^E'i> 2a,DvE<l> 



1.267 4.111 13.46 54.1 4.111 17.57 81.0 

 1.313 3.856 12.95 54.0 3.856 16.80 79.8 



The notation B^2 ^"(1 E''^ is that of Le Verrier in his development in the first 

 vohime of '■'■ Annales de V Ohservntoire Imj^erial de Paris." 



Numeric d 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 



of the coefficient of — cos {_i7J — (i — l)/l — u) in the expression of R for the action 



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

 in his '■'■Annaies de VOhservatoire" tome i, pages 358-383, comparing the develop- 

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



