26 



SECULAR VARIATIONS OF THE ELEMENTS OF 



(118) 



b = |0.1489647. . . [9. 1730832] \ iT r +[7.5931 242]i\ rF +[95.5264270]iV" 



• +[94.8701084LV" J 



V ={ 0.7286137 . . . [9.8624973] ji\r JF +[8.2750461LV r +[96.2059S93]i\ r " 



+[95.5492142]^"' 

 b" = { 1.690254 . . . [0.2279520] ji^ r +[8.6307197]iV F +[96.5586316]J\ r " 



+[95.9012715]^"' 

 Z/"= \ 5.307482 . . . [0.7248886] ^ F +[9.0992151LV F +[97.0186122].A r " 



+[96.3596252L¥ m 

 b 1= \ 0.000008754742 . . . [94.9422434] } ^+[96.8635004]^' 

 +[97.3236905] i^"+[97.0504994]i^'"; 

 Z> 2 ={ 0.0000005681531 . . . [93.7544654] jiV+[9o.6682302]xV 

 +[96.1186392] ^"+[95.8170069]^'"; 

 Z> 3 = \ 0.00000002443536 . . . [92.3880187] jiV+[94.2994239]JV' 

 +[94.7468016] i\T"+[94.4366545hV'"; 

 \= \ 0.000000003249184. . . [91.51177-13] ^+[93.4227230]^' 

 +[93.8695157] i\T"+[93.5577417hV"'; 

 We have given the natural and logarithmic coefficients of N and N IV , in the 

 values of b, b', b", &c, because the values of the other quantities are determined in 

 functions of these, and they will therefore be wanted. 



14. If we now suppose the second members of equations (82) and (83) to be 

 equal to nothing, we shall obtain the following values of g, g x , g 2 , &c: — 



(119) 



g= 5".46370645 

 9l = 7.24769852 

 # 2 =17 .01424590 

 <7 3 =17 .78441063 

 We must now transform equat 

 spectively less by g, g x , g 2 , and g s 



9i = 0",61668516; 

 g b = 2.72772365; 



# 6 = 3.71780374; 

 <7 7 =22 .46058485. 

 ion (82) in four others whose roots shall be re- 

 Putting Sg for the root of the first transformed 



equation, we shall have the following equation to determine §g. 



he/— 25.6552&/ 3 +184.8969fy 2 — 253.8812^+^=0. 

 But since 8g, Sg^ Sec. are very small quantities, we may neglect 8g B , Sg i , in these 

 transformed equations, and we shall then get by dividing by the coefficients of Sg 



z 184.8969 



lg-- 



■¥ 



253.8812 ' 253.8812' 



We may first neglect the last term of this equation, and we shall obtain a first 



approximation to the value of $g, with which we can compute the last term of the 



equation. If we perform the same process with the other roots, we shall obtain the 



following equations for determining $g, $g u <5r/ 2 , &c. 



hg =+[7.59537 ] z +[9.8623 ]3<f 



hg x =— [T.73616 ] Zl — [9.5602 ]Bg* 



S<7 2 =+[8.061074] Z2 +[0.04511% 2 2 



S<7 3 =— [8.00000 ]^ 3 — [0.16856]^ 3 2 



% 4 =+[7.84466 ]£4+[9.92529]^ 2 



^=-[8.38464 ]^ 6 +[9.76868]Sflr B a 



fy 6 =+[8.23997 ] Z6 -[0.10692]^ 6 2 



fy 7 =-[6.09265 ] Z7 -[9.17554% 7 2 



(120) 

 (121) 

 (122) 

 (123) 

 (124) 

 (125) 

 (126) 

 (127) 



