70 THE ORBIT OF NEPTUNE. 



= 0.25& 



— 



1.39Xl0ic' 



+ 6.14i 



+ 9.36'i^ 



+ 8.6^ 



— 0.3 



2.04 



— 



044 



+ 0.18 



— 0.02 



+ 2.3 



— 1.8 



5.20 



— 



1.20 



+ 0.50 



+ 0.15 



+ 6.7 



— 3.0 



5.13 



— 



1.57 



+ 1.06 



+ 0.90 



+ 8.6 



— 0.2 



4.04 



— 



1.28 



+ 0.90 



+ 0.84 



+ 7.1 



— 3.2 



2.08 



— 



0.24 



— 0.22 



— 0.16 



+ 2.3 



— 3.4 



7.28 



— 



0.36 



— 1.68 



— 0.34 



+ 10.2 



— 2.6 



8.24 



— 



0.64 



— 1.84 



+ 0.23 



+ 13.5 



— 2.2 



5.05 



— 



0.23 



— 1.43 



+ 0.22 



+ 8.9 



— 2.4 



1.04 



+ 



0.30 



— 0.62 



— 0.20 



+ 1.8 



+ 0.3 



6.24 



+ 



1.68 



— 3.72 



— 0.86 



+ 12.1 



— 3.0 



5.16 



+ 



1.34 



— 3.20 



— 0.37 



+ 11.2 



— 3.4 



4.04 



+ 



1.05 



— 2.53 



— 0.15 



+ 9.3 



"— 3.8 



8.33 



+ 



4.99 



— 5.58 



— 1.37 



+ 23.8 



— 6.0 



7.31 



+ 



4.38 



— 4.99 



— 0.87 



+ 22.1 



— 4.4 



7.23 



+ 



4.00 



— 5.10 



— 0.36 



+ 22.7 



— 4.9 



7.13 



+ 



4.01 



— 5.10 



— 0.19 



+ 23.1 



— 3.0 



8.32 



+ 



7.52 



— 3.98 



— 0.82 



+ 35.7 



— 5.4 



9.42 



+ 



8.16 



— 4.95 



— 0.42 



+ 40.6 



— 4.8 



8.29 



+ 



7.09 



— 4.52 



+ 0.14 



+ 37.1 



— 5.2 



9.10 



+ 



7.65 



— 5.13 



+ 0.36 



+ 41.2 



— 10.8 



7.28 



+ 



8.83 



— 0.10 



— 0.01 



+ 43.8 



— 8.9 



9.44 



+ 11.07 



— 0.75 



+ 0.42 



+ 56.4 



— 14.7 



9.36 



+ 10.68 



— 1.29 



+ 1.02 



+ 56.7 



— 15.6 



7.14 



+ 



8.31 



— 0.69 



+ 1.07 



+ 44.9 



— 8.0 



3.11 



+ 



4.58 



+ 1.80 



+ 0.20 



+ 23.3 



— 4.4 



7.35 



+ 



10.38 



+ 3.33 



+ 0.93 



+ 54.5 



— 18.1 



7.27 



+ 



10.17 



+ 3.07 



+ 1.45 



+ 55.2 



— 15.2 



6.12 



+ 



8.52 



+ 2.37 



+ 1.35 



+ 46.7 



— 14.4 



(7) 



1277.71a; 



+ 935.29(10^) 



— 8.50.59 . 5 + 22.46^ 



93.5.29 



+ 1010.58 



— 190.60 



+ 24.58 



— 350..59 



— 190.60 



+ 805.88 



+ 90.80 



22.46 



+ 24.58 



+ 90.30 



+ 101.33 



§ 31. Treating these equations by the method of least squares, but leaving [j. 

 indeterminate for the present, we have the four normals 



+ 5431.7,a —1268.89 = 



+ 5178.1 — 1240.38 (8) 



— 935,5 + 146.81 



+ 817.9 — 74.89 



The solution of these equations gives the following values of the unknown 

 quantities in terms of ^u. 



& =+ 0.650 — 2.067^t 



&' = + 0.0800 — 0.342^ (9) 



8h=+8.76 —12.1Sfi 



8k=z — n.79 — 7Mfi 



