58 SECULAR VARIATIONS OF THE ELEMENTS OF 



29. These numbers are now to be substituted in equations (134) and (135). We 



ffn tJt ft I 



must also add the logarithm of (1+/O to those of --, li", and _ /, in order 



r fL Ct 7i ft ?Z> Cb 



to obtain the numbers which are to be used in this computation. 



For the root 0=5".5095453, we get, 



1853601 J3698.3,, _1Q443191 



X 1Q20 "' y 1 1Q20 Z ~ 



Whence 0=87 43' 23".3 ; log. ^=9.2495260. 



N =+0.1776340 ; N' r =0.000008865 ; 



N" =+0.0083657 ; N T =0.000007939 ; 



N" =4-0.0053866; N TI =+0.000003416 ; 



^'"=-(-0.00085332 ; ^"'=+0.0000000640. 



For the root ^=7". 3 15380, we get, 



1595251 4450991 180052670 



&\ - H --- TQM "! 2^1 - I JQiM "! Z l - I 1Q 20 ** 



Whence fr=19 43' 4".3 ; log. ^=98.4192990. 



JV t =+0.0262603; N^ =+0.000010694; 



^'=0.0197843; NJ =+0.000010986; 



^"=0.0152679 ; Nj" =0.0000027265 ; 



JVi"'= 0.00261793 ; ^^"=0.00000011315. 



For the root <7 2 =17".217532, we get, 



_ 27629730 51666060 __a432446 



" 2/2 - + 20 "t 2 2 iO 



1 JQ20 



Whence /? 2 =331 51' 47".6 ; log. ^ 2 =97.2322182. 



N t =+0.00170694; ^"=0.0000012756; 



JV 2 ' =0.01 31662 ; N 2 r =0.000008639 ; 



Ai" =+0.0122912; N," =+0.0000005187; 



^'"=+0.0325334 ; ^ 2 m =+0.0000000382. 



For the root j7 3 =17".931057, we get, 



__ ^104020250 108060520 _ 8.174639 



X *~ 3; y*~ 20 3 * z *~ ~~ s< 



Whence &=136 5' 29".0 ; log. JV 3 =97.2635963. 



N 9 =+0.0018348; N 3 rr =+0.0000007482; 



JV S ' =0.0152412 ; N 3 r =+0.000008946 ; 



2V 3 " =+0.0171912; N 3 VI = 0.0000005014; 



AV= 0.0694007 N s r "= 0.0000000372. 



