THE ORBITS OF THE EIGHT PRINCIPAL PLANETS. 65 



For the root # 4 =0".6 166870, we get, 



3.357912_ 1.360959 56997.71 



10 10 10 10 



Whence &=67 56' 42".3 ; log. # 4 /r =95.8032384. 



JV 4 =+0.000007676 ; JV 4 /F =+0.000063565 ; 



JV 4 ' =+0.000011687 ; NJ =+0.000071695 ; 



N t ' =+0.000013561 ; ^"=+0.00155764; 



^'"=+0.000021841 ; JV 4 " '=+0.01003850. 



For the root <7 5 =2".7277089, we get, 



0.6477216 0.1749684 _345.4842 



x * I TTiTo > 2/5 five ' 2 5 inio 



10 

 Whence &=105 6' 59".3 ; log. ^=97.2882538. 



N b =+0.00055404; N & ' r =+0.0019420; 



Nj =+0.00054913 ; N t r =+0.0017682; 



JV 6 " =+0.00057941 ; ^"=+0.0297289; 



JV 5 '"=+0.00077160 ; N 6 '= 0.00290997. 



For the root r7,j=3".7172386, we get, 



0.4583439 0.8566511 _22.50983 



x *~ "UF ' 2/6 ~ "TO 1 " ' Z ~ ~10 15 ' 

 Whence /S 6 =28 8' 55". 1 ; log. ^ 8 "=98.6350978. 



N 6 =+0.0233180; N 6 ir =+0.0431616 ; 



NJ =+0.0162078 ; N t r =+0.0341038 ; 



N,' =+0.0161491 ; JV 6 r/ = 0.0448343 ; 



JV a '"=+0.()186903 ; JV a r/J =+0.00141840. 



For the root <7 7 =22".46H216, we get, 



1.009450 , 0.7872062 81.85450 



10 10 ; Vn ~ 10 10 ; 2 ''~ xv 



Whence /3 7 =307 56' 54".3 ; log. ^/1=98.1942049. 



N, =0.00011217; N, ir =+0.0156388; 



AY =+0.0005 1216; ^T T F =0.0483500; 



JV 7 "= 0.0024585; N =+0.0018057; 



N= 0.0155133 ; .#7"=+0.00013650.' 



32. We shall now suppose ^"'=+1 ; and the mass of Mars will become, 



m , = i+i_ j_ 



"2680637~ 1340318.5' 

 Using this mass, we shall find, 



AFT]D= 0".0279815 ; AR3=0". 0031027 ; ] 



. ! 



AQTTj^0. 1020355; A^^ -0003297 ; , (26 g. 



AH7g= .2982001; A[T]=0 .0000275; | 



A[sTs]= 0. ; AQT3= .0000057. J 



9 November, 1871. 



