130 SECULAR VARIATIONS OP THE ELEMENTS OF 



For the root y y = — 6".631323, we get, 



, 0.768973 Ar 0.6414600 , T 33.22066 ,_, 

 Nil Vi= TTxn ^ z l= Tau— ^i 



-1— I 10 1* -1. 91— 10 u -1, "1— jq; 



Whence /3 1 =129° 50' 4".4; and log. ^=8.4791971. 



N, =+0.030144, N ± ir =+0.00001026, 



JVi' =—0.008215, N/ =+0.00001454, 



^"=—0.006664, .^"=—0.000007438, 



iVi'"=— 0.001441, iVi"=— 0.0000004539. 



For the root g 2 =— 17".5137898, we get, 



6.914 692 A7 , 3.461327 A7 _60 89.390 AT2 



X 2 ^Q13 ""2> 2/2 + JQ13 -N2I Z 2 Jq13 -^2 • 



Whence /3 2 =296° 35' 29".2; and log. iV 2 =7.1037540. 



N 2 =+0.001270, N 2 IT =— 0:000002201, 



iV 2 ' =—0.007063, N 2 V =—0.000019926, 



N 2 " =+0.00521 1, 2V 2 " =+0.0000019167, 



iV 2 "=+0.048560, ^"=+0.0000002206. 



For the root g s =— 18".667944, we get, 



6.844087 __ 2.032363 A7 _ 1 783.3974 A7i 



~"6 JQ13 "11 Vt JQ13 ^'3> "3 JQ 



Whence /? 3 =253° 27' 40". 1 ; and log. iV 3 =7.6024178. 



JV 3 =+0.004003, ^=—0.00000018, 



N 3 ' =—0.024768, JV 3 r =—0.00000318, 



N 3 " =+0.025376, N 3 VI =+0.00000027, 



N 3 "'=— 0.033934, ^"=+0.000000031. 



For the root # 4 =0", we get, 



, 0.7256453 „ 0.2113461 „ 27.24508 



Whence &=106 o 14' 18".0; and N^=Nl=Nl'= &c, 

 — +0.02774066, log. 8.4431168. 



For the root g & = — 0".6616647, we get, 



, 0.1016673 „ IT , 0.2717444 , TJr 241.9412 AT 



N b IY ; y b =-\ t^is — N b ' r ; %= 1A10 iV a 



JT2 



•"6 ^ -^Qlo -*-'5 J #5 1 JQ10 -"6 J ~5 JQ 



Whence /? 5 =20° 30' 57".6 ; and log. iV 5 jr =7.0789098. 



JV 5 =+0.001476, N b IT =+0.00119925, 



N 6 ' =+0.001356, N/ =+0.00115768, 



JV 6 " =+0.001329, JV 6 "=— 0.00112471, 



iV 5 '"=+0.001259, iV 5 "=— 0.01178812 



