26 SECULAR VARIATIONS OF THE ELEMENTS OP 



b = 1 0.1489647 . . . [9.1730832] ^"+[7.5931242].V r +[95.5264270].V r/ 



+[94.8701084].V"' 



I' =^0.7286137 . . . [9.8624973]^+[8.2750461].V+[96.2059893].V r ' 



+[95.5492142],V" , n , 



b" = \ 1.690254 . . . [0.2279520] | A rJT +[8.6307197].r+[96.5586316]iV r ' 



+[95.9012715]^ 



i"'={5.307482 . . . [0.7248886]| jy /r +[9.0992151]AT r +[97.0186122]iV" 



(119) 



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



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



b z = \ 0.0000005681531 . . . [93.7544654] \ ^+[95.6682302]^' 



+[96.1186392] ^"+[95.81 70069]iV"; 



b 3 = \ 0.00000002443536 . . . [92.38801 87] ^+[94.2994239]^' 



+[94.7468016] AT"+[94.4366545]JV'"; 



^={0.000000003249184 . . . [91.51 17743] j JV+[93.4227230]^V' 



+[93.8695157] ^"+[93.557741 7] A T/ "; 

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

 values of 6, b\ b", &c., because the values of the other quantities arc 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^ g 2 , &c. : 

 = 5".46370645 ; g t = 0",61668516; 



ffl = 7.24769852; g,= 2.72772365; 



g t = 17 .01424590; g 6 = 3.71780374; 



<7 3 =17 .78441063 ; J7 7 =22 .46058485. 



We must now transform equation (82) in four others whose roots shall be re- 

 spectively less by g, <j lt g 2 , and g 3 . Putting $g for the root of the first transformed 

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



W 25.6552V+184.8969V 253.88 125y+ z =0. 



But since &/, &7j, &c. are very small quantities, we may neglect &g 3 , fy/ 4 , in these 

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



to - 4- 



g ~ 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 lt fy/< 2 , &c. 



tg =+[7.59537 ] x +[9-8623 ^ . (120) 



^i= -[7.73616 ]^-[9.5602 ]^ 2 ; (121) 



^2=+[8.061074]^+[0.04511]^ 2 a ; (122) 



% 3 = [8.00000 -]% a [G.16856^3 2 ; (123) 



^=+[7.84466 ]^ 4 +[9.92529% 4 2 ; (124) 



$7 4 = [8.38464 ]^ 6 +[9.76863% 6 2 ; (125) 



fye=+[8.23997 ]^-[0.10692]^ a ; (126) 



^ 7 = [6.09265 ]^ 7 [9.17554]^ 7 2 . (127) 



