15 



FIRST GEOCENTRIC NORMAL PLACES OF NEPTUNE. 



No. of 



Mean time. 



ObsMGeo.Lona:. . 



No. of Obs. 



Obs'd Geo. Lat. 



No. of Oba. 



Obs.- 



-Eph.I. 



Obs.— Eph. I. 



place. 



Greenwich, 1846. 



A 





a 



r~^-^ 



5 



.-^ 





II 



A S 





r \ 

 d 



' o 



/ // 



o / /; 



II 



1 



215.56696 



327 



9 49.34 



(1) 



31 36.24 



(1) 



— 



16.75 



— 0.63 



2 



223.54405 



326 57 9.04 



(1) 



44.09 



(1) 



— 



7.27 



— 1.03 



3 



270.5 



325 



46 25.82 



(16) 



57.99 



(16) 



— 



1.02 



+ 0.84 



4 



276.5 





39 54.23 



(13) 



56.15 



(13) 



+ 



0.27 



+ 1.51 



5 



282.5 





34 16.11 



(13) 



56.09 



(13) 



+ 



1.12 



+ 0.03 



6 



290.5 





28 21.99 



(12) 



53.16 



(12) 



+ 



3.13 



+ 0.80 



7 



298.5 





24 25.25 



(18) 



51.13 



(19) 



+ 



4.19 



+ 0.56 



8 



306.5 





22 32.46 



(6) 



47.61 



(6) 



+ 



3.02 



+ 0.23 



9 



313.5 





22 40.00 



(4) 



45.15 



(3) 



+ 



2.40 



— 0.68 



10 



319.5 





24 6.40 



(4) 



41.51 



(6) 



+ 



1.95 



+ 0.51 



*11 



325.5 





26 50.59.' 



(4) 



37.30.> 



(4) 



+ 



3.77.? 



+ 2.21? 



12 



334.5 





33 9.44 



(7) 



33.92 



(6) 



+ 



2.46 



— 1.13 



13 



345.5 





44 26.93 



(4) 



30.79 



(4) 



+ 



0.96 



— 0.03 



14 



353.5 





54 58.01 



(2) 



27.10 



(2) 





0.72 



+ 1.51 



15 



359.5 



326 



4 2.54 



(3) 



26.04 



(3) 



— 



0.23 



+ 0.77 



16 



372.5 



326 



26 39.11 



(3) 



31 23.60 



(3) 



— 



4.40 



+ 1.28 



A slight examination of the corrections of the Ephemeris from Disturbed 

 Elements I, seemed to show that the orbit deviated sensibly from the cir- 

 cular form. Accordingly the next step in the investigation was to remove the 

 restriction r =r a, " = f ? by merely supposing the radius vector constant 

 during the observed interval, and leaving t- to take such a value as the observa- 

 tions should require : 



For this purpose, let x = 50 X ^ r 

 y = 10 X A v 



z = A fgoo = correction of Neptune's true long, by Ephem., Oct. 29, 1846. 

 t'l = daily motion in true long. 



From the 16 normal places, 9 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, 6, were formed from Nos. 3, 4, 5, 6, 7, respectively. 

 Equation 7 is the mean of Nos. 8, 9, and 10. Equation 8, of Nos. 12 and 13; 

 and equation 9, of Nos. 14, 15, and 16. 



After reducing the corrections of the geocentric to their equivalent projections 

 in heliocentric longitude and latitude, (a ^k and a /3,) and computing the 

 coefficients of x and y, (that of z is always + 1,) the 9 conditional equations 

 from the longitudes were, 



*The 11th normal place was properly rejected in consequence of its difference from the others. I have since found 

 that one of the four observations used was erroneous. 



