38 



THE ORBIT OF NEPTUNE. 



The constant terms in the coefficients -B^.i and 5<,.i, which give the perturbations 

 of the latitude, may be omitted without any error amounting to one hundredth 

 of a second. 



§ 19. The form of the preceding perturbations being different from that of the 

 perturbations computed by Professor Peirce, the ellijDtic elements are next pro- 

 visionally altered, so that the provisional theory shall be substantially identical 

 with that already adopted. Small corrections have also been applied to the 

 constants which determine the plane of the orbit. 



The provisional elements finally adopted for correction are as follows : 



s = 



335° 5' 25" 



.97 



71=: 



7864 



.421 



h = 



+ 1192 



.93 



k = 



+ 1279 



.36 



p = 



+ 4910.17 



q = 



— 4137.46 



Epoch, 1850, Jan. 0, Greenwich mean noon. Unit of time, 305.25 days. 



e= 0.00848055 

 e (in seconds) 1749".24 



* 1°47' 1".95 



7t 42 59 52 .0 



Q. 130 7 6.7 



log a 1.4787523 



The perturbations of the preceding elements are expressed in the following 

 form : 

 Put ■ M=z 21' — I 



Then, 

 and 



Tz= Number of centuries after 1850, Jan. 0. 

 M= 281° 43' 48" + 8° 26' 10".7 Tj 



M = 125".42 sin ( ilf _ 0° 16'.3) 

 + 36.08sin(2if+l°50') 

 + 3.58sin(3ilf+ 3°42') 



+ 1".32 7^+ constant. 



^/^ = 126".17 cos ( Jf— 0° 6'.2) 

 + 36 .08 cos (2 ilf + 1°50') 

 + 3 .58 cos (3 if + 3° 42') 



+ 0".31 r+ constant. 



^Z = 2247".52 sin ( if —170° 32' 23") S log a = 1286 cos ( if+9°8') 



+ 98.57sin(2ilf+ 183°24'.l) + 115 cos (2 ilf + 4° 0') 



+ 6 .81 sin (3 Jf + 186° 14') + constant. 



+ 2144".26 7^+ const. + const. X T. 



Sjy^V'MsmM 



+ 2.98sin(2ilf— 155°38') 



+ 1".107'+ constant. 



5(? z= 0".87 cos ( M— 61° 0') 



+ 2. 98 cos (2 ilf— 155° 38') 



+ 0".01 y+ constant. 



