64 SECULAR VARIATIONS OF THE ELEMENTS OF 



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

 must also add the logarithm of (1+/O or 0.0413927 to those of ,,, ~Ji" t and 



?Z (I ?i Ct 

 tt 



~ii a l", in order to obtain the numbers to be used in this computation. 



For the root #=5". 5550002, we get, 



1859252 982149.1 _10422045 



10 20 ' y ~ "TO 20 ' 2 1() 20 ' 



Whence /3=87 28" 12".8, log. #=9.2518088. 



# =+0.1785701; N" =-0.000008745 ; 



#'=+0.0081595; # r =0.000007856; 



#" =+0.0053002; #"=+0.000003321; 



N m =+0.00086522; #"'=+0-0000000649. 



For the root ^=7".3790776, we get, 



. 1535521 , 4548921 186590940 



, _ 



> 2/1 ~~ 20 ' Z i~ 



"1 I 1020 > yl~ 1020 



Whence /3,=18 39' 8".9 ; log. #!=98.4104497. 



#, =+0.0257306 ; # 1 ' r =+0.00001075$ ; 



#/ =0.0194493 ; #j r =+0.000011106; 



#,"= 0.0151823; #"= 0.000002714; 



#^=0.00269026 ; #/"= 0.0000001142. 



For the root gr 2 =17".4034121, we get, 



__? 9 _ 188 _ 05 J) .65870040 4.079210 



10io 



Whence ^ 2 =329 15' 1".2; log. # 2 =97.2739118. 



# 2 =+0.0018789 ; # 2 /r =0.000001477 ; 



# 2 ' =0.0145930 ; #/ =0.000011248 ; 



# 2 " =+0.0125684; # 2 " =+0.0000006631 ; 



# 2 '"=+0.0449428 ; # 2 "'= +0.00000004893. 



For the root <7 3 =18".09 84790, we get, 



__ j _82704460 _8J L 987110 _5.806087 



2/3 into 5 2 3 fmo 



Whence /3 S =134 45' 1".6 ; log. JV 8 =97.3022770. 



N 3 =+0.0020058 ; N^ =+0.0000004469 ; 



JV 3 ' =0.0167491 ; N s r =+0.0000065211 ; 



^"=+0.0173974; ^"=0.0000003597; 



W= 0.0572983 ; # 8 r "= 0.00000002674. 



