58 SECULAR VARIATIONS OP THE ELEMENTS OP 



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



must also add the logarithm of (1+u") to those of——. —^-Ji", and — — J', in order 



nana n a 



to obtain the numbers which are to be used in this computation. 



For the root gr=5".5095453, we get, 



.1853601,. . 73698.3, T 10443191 



Whence /?=87° 43' 23".3 ; log. iV=9.2495260. 



tf = _j_o. 1776340 

 N' =+0.0083657 

 N" =+0.0053866 



N IT =—0.000008865 : 

 N r =—0.000007939 ; 

 N" =+0.000003416; 



i\r" '=+0.00085332 ; i\T" =+0.0000000640. 



For the root (/ 1 =7".315380, we get, 



, 1595251 „ , 4450991 „ , 180052670 



-"i> V\ — ~\ TT^o Nil Z 1 — -j =-fm -"l 



■~i — i io 20 ' 1() 20 10 2 



Whence ft=19° 43' 4".3; log. ^=98.4192990. 



Nj, =+0.0262603 

 NJ =—0.0197843 

 #"=—0.0152679 



JV/ r =+0.000010694; 

 NS =+0.000010986; 

 N 1 TI =— 0.0000027265; 



#'"=—0.00261793 ; #^=—0.00000011315. 



For the root <7 2 =17".217532, we get, 



_ 27629730 _ 51666060 _ 3.432446 Af2 



X 2 1Q20 -" 2 '■> V-2. + 1Q20 ""2J Z 2 Jqio ■" 2 • 



Whence /3 2 =331 51' 47".6; log. #=97.2322182. 



# =+0.00170694; # /r =— 0.0000012756; 



#' =—0.01 31662 ; #" =—0.000008639 ; 



#"=+0.01 22912; # rj =+0.0000005187; 



#'"=+0.0325334 ; # r/ =+0.0000000382. 



For the root <7 3 =17'"931057, Ave get, 



, 104020250 , r 108060520 , T 8.174639 ,„ 



#; y 3 = tt^o — #; z 3 = — Tm = — # 2 



io 20 io 20 — 10 



Whence /3 3 =136° 5' 29".0; log. #=97.2635963 



# =+0.0018348 

 #' =—0.0152412 

 N 3 " =+0.0171912 



N 3 ir =+0.0000007482; 

 # F =+0.000008946 ; 

 #"=— 0.0000005014; 



#'"=— 0.0694007 # r// =— 0.0000000372. 



