WITH A STAR OBSERVED BY LALANDE. 



145 



In this manner I obtained from the above list of observations of Levcrricr sixteen 

 normal places, which I subjoin, together with the corrections of the ephemeris. In this 

 list a and & are the mean places of Lcverrier as a fixed star in latitudes and longitudes 

 referred to the mean equinox and mean obliquity of January 1st, 1847, corrected for 

 planetary parallax, but not corrected for planetary aberration. 



NORMAL PLACES OF LEVERRIER. 



No.of Place. Mean Time, Creenwich. 



Obs. Geo. Lon. 



1 



2 



3 



4 



5 



6 



7 



8 



9 



10 



11 



12 



13 



14 



15 



16 



1816 215 J .5G696 



223 54405 



270 5 



276 5 



282 5 



290 5 



298 5 



306 5 



313 5 



319 5 



325 5 



334 5 



345 5 



353 5 



359 5 



372 5 



327 57 



325 46 

 39 

 34 

 28 

 24 

 22 

 22 

 24 

 26 

 23 

 44 

 54 



326 4 

 326 26 



49 .31 

 9 .04 



25 .82 

 54 .23 

 16 .11 

 21 .99 



25 .25 

 32 .46 

 40 .00 



6 .41 



50 .59? 

 9 .44 



26 .93 

 58 .01 



2 .54 

 39 .11 



No. of Obi. 



To 



(16) 



(13) 

 (13) 

 (12) 

 (18) 

 (6) 

 (4) 

 (4) 

 (4) 

 (') 

 (4) 

 (2) 

 (3) 

 (3) 



Obs. Ceo. 

 & 



0°31'36 

 44 

 57 

 56 

 56 

 53 

 51 

 47 

 45 

 41 

 37 

 33 

 30 

 27 

 26 

 23 



Lai. 



/ 



'.24 



.09 



.99 



.14 



.09 



.16 



.13 



.01 



.15 



.51 



.30? 



.92 



.79 



.10 



.04 



.60 



Obs. Eph. Obs. Eph. 

 A a A 6 



(1 

 (1 



(16 



(13 



(13 



(12 



(19 



(6 



(3 



(6 



(4 



(6 



(4 



(2 



(3 



(3 



A slight examination of the corrections of the ephemeris from Elements (I.) deviates 

 Blightly though sensibly from the circular form. Accordingly, the next step in the inves- 

 tigation was to remove the restriction r = a, n = /u, and merely suppose the radius 

 vector constant during the observed interval, and leaving n to take such a value as the 

 observations should require. 



For this purpose let x = 



,V = 



z = 



50 X A r 



10 x A v 



A x ..o = correction of hel. lon. by Eph., October 29th, 1846. 



daily motion in hel. lon. 



From the sixteen normal places nine equations of condition were formed, with equal 

 weights. No. 11 was rejected. Equation 1 is the third of the mean of Nos. 1 and 2. 

 Equations 2, 3, 4, 5 and f>, are Nos. 3, 4, 5, 6 and 7, respectively. Equation 7 is the 

 mean of Nos. 8, 9 and 10; Equation 8 of Nos. 12 and 13; Equation 9 of Nos. 14, 15 

 and 16. 



After reducing the correction of the geocentric to those of heliocentric longitudes and 

 latitudes, and computing the coefficients of x and y (that of z is always 1,) the nine con- 

 ditional equations from the latitudes were, 



