28374 ; 



CO, = 215 



48 



3.99— 44.1 



X(n 



— 30.27717) 



82831 ; 



u, = 327 



14 



1.39 — 227.6 



X 0\ 



; — 29.98530) 



82321 ; 



c, = 328 



7 



.57.92 + 163.8 



X (n 



, — 29.98530) 



83294 ; 



CO, = 328 



57 



45. .52 + 1.0 



X (r, 



, — 29.98530) 



31 



sequel that the new discussion of these Elements, with the corrected Ephemeris 

 of the values of the perturbations & v and a r, which are given from October, 

 1846, to January, 1851, by that eminent astronomer, together with the value for 

 May 9, 1795, has indicated only slight modifications of the first approximation 

 towards the Elliptic Elements. 



No. 41. Although the discrepancy between theory and observation for 

 Elhptic Elements I was small, yet the modification of the values of 5 w, and 6 r, 

 rendered a small correction of them necessary. Wishing to leave nothing 

 undone towards a complete discussion of the theory of Neptune, as far as cir- 

 cumstances permitted, I resumed the study, and reduced the observations extant 

 to the 1st of February, 1848, and compared them with the Ephemeris from 

 Disturbed Elements IV, already referred to. 



The four fundamental places derived from this discussion were : 



SJECOND HELIOCENTRIC NORMAL PLACES. 



° I II II 



I 1795, May 9, 



II 1846, Nov. 7, 



III 1847, April 6, 



IV 1849, Aug. 22, 



where co is the true longitude on the orbit, and /• the elliptic portion of the 

 radius vector. A new discussion of the value of the disturbed radius vector, 

 and daily angular motion for the middle date between II and III, by the pro- 

 cess of No. 38, indicated no change in the mean motion of Elliptic Elements I. 



It was only necessary to assume a value of the elhptic portion of the radius 

 vector for the last place IV, and then by the subsidiary equation of No. 39, to 

 converge to the remaining elements, which must perfectly represent places I 

 and IV. The elements so found were tested by comparison of the Ephemeris 

 which they gave with observed normal Right Ascensions and Declinations of 

 1846, November 7; 1847, April 6 and November 16. If the representation was 

 not satisfactory, a new trial radius vector for August 22, 1847, was selected, and 

 the converging and testing process repeated. Several repetitions resulted at 

 last in the following values, wlijch I have called Elliptic *Elements II of Neptune : 



The corrections of Elliptic Elements I from these last computations were, 

 respectively, 



dn = — r 8' 56". 43 

 dQ,= — 14 .22 



di = — .57 



de = + 0.00014205 

 d/x. = 0".00 



dm = + 47 .84 



dT = Qy.O 



*See Appendix No. I to Volume II, Smithsonian Contributions. See, also, my letter of March 6, 1848, to Prof. Peirce. 

 Proceedings, A. A. A. S. for April 4, 1848, where dels erroneously printed = 0.000014205. 



