20 



THE ORBIT OF NEPTUNE. 



§ 12. Adopted elements and masses. 



The elements of Neptune adopted in the computation of the perturbations are 

 obtained by correcting those of Walker so as to agree with the Lalande obser- 

 vations, and as nearly as possible with seven normal places derived from the 

 modern observations from 1846 to 1863. The latter series is thus represented 

 within a second of arc. As these elements are merely provisional, it is not worth 

 while to give any details of the corrections, except their amounts, which are as 

 follows : 



^Tt = — 4° 11' 18".6 ; 7t = 43° 3' 18".6 

 ^e = — .00025451; e = .00846495 

 hi — — 8".406 ,; n = 7864".368 



8s z= — ?yry'.92; E= 335 5 31.10 

 log a =1.4780405 



i 1°47'1" 



D. 130 7 20 

 Epoch, Jan. 0, 1850, Greenwich, M. noon. 



To obtain the value of log a, the mean motion was diminished by the secular 

 variation of the longitude of the epoch z= 21".354. A more exact value of this 

 quantity will appear, in the course of our computations, to be 21".4426. 



The provisional inclination and longitude have been taken from Walker without 

 change, as the small corrections which his values of these elements may require 

 will not aifect the perturbations. 



The adopted elements of Uranus, Saturn, and Jupiter, with their functions 

 used in the theory for the same epoch, are as follows : 





Uranus. 



Saturn. 



Jupiter. 



71 



167° 34' 21" 



90° 4' 0" 



112 54' 51" 



S 



28 27 14 



14 48 40 



159 56 20 



i 



46 30 



2 29 28.8 



1 18 41.1 



6 



73 14 14 



112 22 14 



98 56 10 



n 



15425.030 



43996.127 



109256.72 



e — 



.0466972 



.0560050 



.0482273 



.ga 



1.2837047 



0.9802225 



0.7162201 



T 



335°38' 



77°56' 



355°52' 



U 



.0131517 



.0083880 



.0082735 • 



a 



0.638195 



0.317301 



0.1727703 



nm. 



1 



1 



1 



These elements of Uranus have been obtained by applying to Peirce's values 

 of the mean elements (Appendix to American Ephemeris and Nautical Almanac, 

 1860-64, p. 4) approximate long-period perturbations of the elements produced 

 by Neptune at the epoch 1850. The elements of Jupiter and Saturn are from 

 Hansen's prize memoir on the mutual perturbations of those planets, and are, sub- 

 stantially, the same as Bouvard's. 



