THE ORBITS OF THE EIGHT PRINCIPAL PLANETS. 153 



Substituting these roots in succession in equations (503-514), we shall get the 

 following values: 



For the root g, we get, 



#= 5".1262710; 

 N' =+0.12276772V 

 N" =+0.0879386^ 

 N" =+0.0175667# 

 N IV = 0.000208367JV 

 N T =0.00026463^ 

 N VI =+0.000232174^ 



N "'=+0.00000549425^ 



For the root g^ we get, 



1= 6".5922959; 

 Nf =0.276494^, 

 JV," =0.222958^ 

 JVr = 0.0467327tf, 

 JV," =+0.000336574^ 

 NS =+0.000474690^ 

 NS 1 = 0.000245839 JV, 

 N l r "= 0.0000143346JV1 



For the root g 2 , we get, 



/ 2 = 17".3938608; 



=+ 

 =+ 

 = 0.00165952.V 2 



log. 9.0890840; 

 " 8.9441794; 

 " 8.2446904; 



6.4226422w; 



6.3658128; 



4.7599088. 



#/'=+ 0.00136629^ 

 JV2 r/ '=+ 0.000156224^ 3 



For the root g^ we get, 



<7 3 = 18".4092048; 



N 3 = 6.098831^ 8 

 N 3 " =+ 6.65618#3 ' 

 N 3 '" = 10.22645JV 3 

 N 3 ZV = 0.0000196421 jy 3 

 N 3 T 0.000150200JV; 

 iV 3 r/ =+ 0.0000125074^3 

 JV 3 r// =+ 0.000001 39286 N 3 



For the root g 4 , we get, 



log. 9.4416856; 



" 9.3482238/i; 



" 8.6696208i; 



" 6.5270807; 



" 6.6764098; 



" 6.3906513; 



" 5.1563868?z. 



log. 0.7453350; 



" 0.6593380; 



" 1.5216464; 



" 7.2199837; 



" 8.1468598n; 



" 7.1355420; 



" 6.1937476. 



log. 0.7852466%; 



" 0.8232250; 



" 1.0097248? i; 



" 95.2931878n; 



" 96.1766688n; 



" 95.0971660; 



" 94.1439073. 



20 March, 1872. 



