120 SECULAR VARIATIONS OF THE ELEMENTS OF 



11. Substituting these values in equations (408) and (409), we shall get the 

 following values: — 



For the root g= — 4".815328, we get, 



, 1.524075 __ , 3.435486 „ 36.65228 %n 



*=H — jqu— &; y=-\ — w^~ '■ z=z — lo^ - 



Whence /3=23° 55' 15".6 ; and log. #=9.2108901. 



N =+0.162514, N IT =— 0.0000635, 



N' =+0.034037, N r =—0.0000790, 



N" =+0.02391 3, N n =+0.0000806, 



#'"=+0.004754, # F "=+0.0000014. 



For the root g x = — 7".064535, we get, 



, 1.725880 ._ 46 ST , 75.88155 STa 

 a'l—H jo«— -Nil 2/i=-p^i; Sx=H ioiir-^i- 



Whence ^=90° 0' 7".l ; and log. ^=8.3568764. 



JVi =+0.022744, #/" =+0.0000103, 



#/=— 0.009114, N X T =+0.0000150, 



#"=—0.007694, #/'=— 0.0000068, 



#'"=—0.001649, # r "=— 0.000000046. 



For the root g 2 — — 17".043656, we get, 



6.709998 , 3.568591 Ar 582O032 



#J 2/2 — + -im3 #> z 2 — -im 3 #• 



-2— 10 ,s r », Z* I 1( p -2, ~2 1Q 



Whence /3 2 =298° 0' 19". 7 ; and log. # 2 =7.1158842. 



# 2 =+0.001306, # 2 ' r =— 0.00000228, 



# 2 ' =—0.007211, #/ =—0.00001988, 



# 2 " =+0.005538, #"=+0.00000193, 



#'"=+0.048623, #"'=+0.00000022. 



For the root g 3 = — 18". 5 40625, we get, 



6.589852 _ 1.924650 _ 1774.373 7 



X 3 ^Q13 -"3; V% JQ13 -"3 5 Z 3 JQ13 #• 



Whence /? 3 =253° 43' 8".0 ; and log. #=7.5876055. 



# =+0.003869, #' r =— 0.000000154, 



#' =—0.023626, # F =—0.000002255, 



#" =+0.025066, #" =+0.0000001931, 



#'"=— 0.033482, # 3 " '=+0.0000002213. 



For the root # 4 =0, we get, 



. 0.7257772 ... 0.2112211 -_ 27.24551 xrs 



*4=H jQio f*l ft= Jqio ^ ^4= 1^0^^ 



Whence ft=106° 13' 35".2 ; #=+0.0277436, log. #=8.4431625. 



