THE ORBITS OF THE EIGHT PRINCIPAL PLANETS. 



For the root </ 3 , we get, 



<7 3 =17".9310572; 

 JVj' = 8.306614/V 3 

 JV," =-|- 9.36934^ 

 N a m =37.82400^3 

 N a "+ 0.000407767JV, 

 N 3 r =4- 0.00487549^3 

 N 3 VI = 0.0002732457^3 

 N 3 ra = 0.00002027655JV 3 



For the root g^ we get, 



(7 1= 0".6166859; 

 Nj, =+ 0.1210308JV/ r 

 JV 4 ' =+ 0.1 8409 70^ 4 /r 



/ =+ 1.127857JV 4 / 

 J'=+ 24.50277^ 4 /r 



For the root # 6 , we get, 



(7 5 =2".7276841 ; 

 N, =+ 0.2888086JV 5 /r 

 JV 5 ' =-j- 0.284631 1JV 5 /F 

 iV 5 " =4- 0.2991 853 JV B /r 

 N s " =-{- 0.3984217^V 5 /r 



A; W = 1.497941iV 5 j 

 For the root <7 6 , we get, 



A;' =+0.3799388^" 

 ^ 6 " =-j-0.3762970JV a " 

 ^ 6 '" =-i-0.4342462iV 6 " 

 N e r =+0.790124^/ r 

 N= 1.0390902V." 



For the root gr 7 , we get, 



# 7 =22".4609846 ; 

 N 7 =0.006671589^ 

 N 7 ' =+0.02618465JV/ r 



Nj r = 3.091724JV/" 

 JV/'=-f0.1154676A7 r 



log. 0.9194240n; 

 " 0.9717089; 

 " 1.5777676?i ; 

 " 96.6104120; 

 " 97.6880184; 

 " 96.4365534n; 



log. 9.0828960 ; 



" 9.2650466 ; 



" 9.3292589 ; 



" 9.5372136; 



" 0.0522542 ; 



" 1.3892152; 



" 2.1984055. 



log. 9.4606101; 



" 9.4542824 ; 



" 9.4759404; 



" 9.6003430 ; 



" 9.9592404 ; 



" 1.1847750; 



0.1754948n. 



log. 9.7430272; 



" 9.5797136; 



" 9.5755308 ; 



" 9.6377360; 



" 9.8976952; 



0.0166530^; 



8.5170337. 



log. 7.8242293w; 



" 8.4180469 ; 



" 9.1888659n; 



9.9896951n; 



" 0.4902020ra ; 



" 9.0624601 ; 



" 7.9409255. 



8 November, 1871. 



