12 



very nearly. In other words, the orbit approaches very nearly to the circular 

 form ; and that which was at first inferred from the analogies of the solar sys- 

 tem, (viz., the smallness of the eccentricity,) seemed to be confirmed by deduc- 

 tions* from actual observation. 



No. 25. Being now prepared to commence a rigorous computation of 

 the circular elements, on the hypothesis of a uniform radius vector, r = a,I 

 used a normal place of the 26th of September, and another place deduced from 

 my own observations with the Washington Equatorial, December 26. On that 

 night I compared Neptune in right ascension, by transits, 33 times with each of 

 the two Enckian stars, which have been used for such comparisons, from its 

 discovei-y by Galle, to the middle of January last. I also compared it 11 

 times, in declination with the same stars, with the filar micrometer. 



After correcting the observed places for parallax, and the dates for aberra- 

 tion time, (which amounts to about 4 hours,) I computed the elements in the 

 table below. The data for the computation were obtained as follows: The pla- 

 net's mean place, as a fixed star, for January 1, 1847, was derived from the 

 observations; the correction for planetary parallax was applied. The R. A. and 

 Dec. were then reduced to their equivalent geocentric longitude a, and latitude s, 

 referred to the mean equinox of January 1, 1847, with the mean obliquity. The 

 places are — 



1846>' 268". 33333 + 

 — 0.16755 

 268.1.165783 

 325° 49' 1".48 



— 

 326 



— 

 + 



326 

 + 



tGreenwich mean time - - - 

 Aberration time ------ a 



Reduced time ------ 



Planet's geo. Ion. 



Planet's geo. lat. ----- 

 Concluded hel. Ion. - - - - 

 Concluded hel. lat. - - - - 



Orbital longitudes 

 True sid. mot. 

 Daily do. 

 Mean daily do. for r 



- rt -|- V 



/3 , li' 

 13 — ji' 



7t -|— V' 



= 29.93995 



31 



57 .81 



59 



5.40 



31 



7 .089 



32 



53 .60 



59 



32 .73 



32 



5-1 .36 



21" 



658575 



21" 



658575 



1846>' 359" 



5 





— 0.17563 





359". 32437 



326° 



21' 2".64 



— 



31 26 .37 



327 



31 59 .0 



— 



32 4 .791 



+ 



57 .702 



327 



32 27 .09 



"The possible accidental case of r = a, in a very eccentric orbit, was rejected from its extreme improbability. This case 

 occurred in a solution which I obtained about the 90th of January, 1847. The elements obtained were — 



rt = 237° 23' 2" mean equinox. January 1, 1847. 



a, = 129 48 23 " " 



i = 1 45 20 



e = 0.1927122 



^c = 21".5416 



True anomaly v = 89° 48' 0" September 28, 1846, mean no'on, Greenwich. 



This solution was rejected, because it was found that a change of one second in either of the four geocentric places used 

 would be sufficient to remove more than half this eccentricity. It may not, perhaps, be improper to remark, that the orbits 

 obtained by M. Valz, of IWarseilles, and published in the Comptes Rendus, and in the Astronomische Nachrichten, which 

 resemble this result, may have owed their large eccentricity to the very small errors of the Marseilles observations. 



t The earth's true place is taken out for the time B, and 8'. The earth's latitude was not taken into account. Its maxi- 

 mum eiTect is 0".02 on the computed geocentric place of Neptune. 



