52 SECULAR VARIATIONS OF THE ELEMENTS OF 



For the root #, we get, 



fl e =3*.7167656 ; 



N t =+0.54047 W log. 9.7327733; 



JV 6 ' =+0.3822413tf 6 ' v " 9.5823376; 



N; =+0.3758324^" " 9.5748787; 



N 6 " =+0.4347748tf 6 ' r " 9.6382644 ; 



N t r =+0.7901 155N 6 IV " 9.8976906; 



# 8 "= 1.039253^" " 0.0167214n; 



JV "=+0.03290012JV 6 "' " 8.5171974. 



For the root 7,, we get, 



<7 7 =22".4609133; 



N, = 0.006641048JV/ r log. 7.8222366rc ; 



JW =+0.02354937^"" " 8.3719794; 



N," = 0.1 585801 NT " 9.2002488n; 



jff = 0.96475442V/'' " 9.9844168?i; 



^ 7 " = 3.091771JV/ r " 0.4902072ft; 



JV r 7 "=+0.1154698JV/ r " 9.0624686; 



JV J r "=+0.008728388^ 7 /r " 7.9409340. 



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



t t t 



must also add the logarithm of (1+^') to the logarithms of -^ --K, and --/, 



7Z tt 72 Ct lid 



which were used for the adopted masses ; and by this means they will become, 

 log -^=88.2471963; log. -^h' =85.9698939; log.-^ T=86.8867Q56. 



We shall therefore get for the root gr=5".5978504; 



1853795.. , 41624.4 v 10625807 



K y=-\ M-^' 2= 



Whence ^=88 42 1 49".4 ; log. JV=9.2418092. 



N =+0.1745056; ^"=0.0000092603; 



N' =+0.0093216; N r =0.000008345; 



N" =+0.0060728; N ri =+0.000003470; 



N" =+0.00094333 ; JV r// =+0.0000000703. 



For the root flr!=7".252874, we get, 



1689761 3937391, 138888320.. 



" 2l= ~~ l 



Whence ^,=23 23' 37".0 ; log. ^=98.4892507. 



AJ =+0.0308497; ^,^=+0.000010862; 



JV,' =0.0202303; JV/ =+0.000011101 ; 



N' =0.0154897; ^"=0.0000027974; 



Ni" =0.00258544; JV/"= 0.000000 11452. 



