114 SECULAR VARIATIONS OF THE ELEMENTS OF 



In like manner we shall find for the root # 1 =6".592128, 



, 0.692850 ._ 0.6389472 Ar 33.24236 , 72 



^=H — io^— ^' v*~ ic»s — N i'> z i= — m~ x 



Whence /3 1 =132° 40' 57".8; and log. iV;=8.4525867. 



Therefore, for the root g x , we have, 



JV; =+0.028352, iV/ r =+0.00000952, 



iV/ =—0.007838, iV/ =+0.00001345, 



iV x " =—0.006321, ^"=—0.00000696, 



N™ =—0.001325, ^"=—0.00000042. 



For the root g 2 =— 17". 393390, we find, 



6.863228 , 2.889470 Ar __ 488.6204 AJ2 



~* JQ13 ^'2' V2 I JQ13 ^'25 "2 jq 



Whence /? 2 =292° 49' 53".2; and log. iV 2 =7. 1829906. 



N 2 =+0.001524, iV/ r =— 0.00000251, 



jy 2 ' =—0.008478, N 2 V =—0.00002140 , 



N 2 " =+0.0069546, N 2 " =+0.00000208, 



JV 2 "=+0.0506672 5 . N 2 TI =+0.00000024. 



For the root g 3 —— 18".408914, we get, 



6.724398 __ 2.217061 ^ T 1925.3617 . 72 



Xt= w*~ * ; Vs= 16*5—-^ %= — W* — 3 



Whence /3 3 =251° 45' 8".6; and log. iV 3 =7.5655490. 



N s =+0.003677, N z ir =— 0.000000072, 



N z ' =—0.022428, N z r =—0.000000557, 



N s " =+0.024477, N S TI =+0.0000000463, 



#3'"=— 0.0375951, N 3 TI '=+0.000000005. 



For the root g i =0", we get, 



0.7256453 0.2113461 _ 27.24403 Ar2 



Whence /3 4 =106° 14' 18".(); log. iV 4 =8.4431335. 



And N i =N^=N^=N/"=N i IV =N i r =N 4 ri =NJ 1 =+0.027741 73. 



For the root g & = — 0".661666, we get, 



0.1016992 _ 0.2717211 _ 24.19165 



^o "1 Jqio iV 5 > 2/5 ^0^ ° ' 5 10° 6 ' 



Whence /? 5 =20° 31' 24".6 ; and log. iV 5 /r =7.0789383. 



jV 5 =+0.001478, N b IT =+0.0011994, 



JV 5 ' =+0.001357, N b T =+0.0011577, 



iV 5 " =+0.001329, N i TI =— 0.00112485, 



^'"=+0.001259, NJ"=- 0.0117882. 



