THE ORBIT OP URANUS. 



Supposing the mass of Neptune to be uncertain by one-fiftieth of its entire 

 amount, which is quite possible, it will be seen the longitude of the mean peri- 

 helion is from this cause uncertain by more than two minutes, the mean longitude 

 of I "ranus itself by nearly a minute, and the mean motion by nearly two seconds 

 in a century. 



It will be seen that the logarithm of the mean distance just given does not 

 accurately correspond to that of elements 1 V plus the constant term of hv X " 1 ; * l ; K 

 as it should. This difference arises from the rejection of the terms of the second 

 order in ?>*>, which can not atfect the geocentric longitude of the planet by a tenth 

 of a second for a number of centuries. 



It is to be remarked that these mean elements are those to be used in the 

 general theory of the secular variation of the planetary orbits. 



Concluil (/ Tln'nry of Uranus. 



The elliptic longitude and radius vector of Uranus, affected by the secular and 

 long period perturbations of the elements, will be given by the following equations. 

 Put 



l a = n a t -f e m 



I =1 +11, 



9 = 1 Tto, 



h = M, 



the /eros indicating elements IV, and </*, M-, and H being the perturbations of 

 these three elements just given. Then 

 Elliptic longitude in orbit = I 



_ _ sn - e cos 



~ 64 *' 



.' _ 6A- 



J 



-7t + h ') sin 4j (Wh Wi") cos 4j j 



(& _ ipfcVi' -|- 5M 1 ) sin 5<7 (5k'h 10*W + V cos 5 

 Nepcrian logarithm of r = TO + fa* -\- ^c 1 

 |l !' J |/.- 



24 May, 1873. 



