THE ORBITS OF THE EIGHT PRINCIPAL PLANETS. 



now give the following values: 



123 



The solutions of equations (431-442) will 

 For the root </, we get, 



</= 5".201065, 



N' =+0. 13743982V 

 2V" =+0.10005562V 

 IV"' - -+0.02016892V 

 N ir = 0.0002330312V 

 N r = 0.0002980262V 

 2V"=+0.0002525282V 

 2V"'=+0.000007542082V 



For the root g it we get, 



</!= 6".6347695, 

 2V/ = 0.23729002V! 

 2V," =0.19356762^ 

 2V/" =0.04095122^ 

 2V/ r =+0.0002920342V, 

 NS =+0.0004138182^ 

 2V x r/ = 0.0002115382V, 

 N 1 V "= 0.00001292222^ 



For the root g^ we get, 



&= 17".459300, 

 2V 2 ' = 5.2349372V 2 



2V 2 "' =+40.010222V 2 

 N 2 lr = 0.001842382V 2 

 2V 2 r == 0.016221342V 2 

 2V 2 "=+ 0.0015690542V 2 

 2V 2 " r =+ 0.0001805562V 2 



For the root g s , we get, 



=5.839411^3 

 =+6.569047JV 3 

 =7.879027^3 

 =0.0000520881^ 3 



= 0.0009631222V; 

 =+0.0000818396^ 



N 3 r 

 N 3 TI 

 iV 3 rj/ =+0.000009421622v" 3 



log. 9.1381124, 

 " 9.0002416, 

 " 8.3046820, 



" 6.4742546, 

 " 6.4023092, 

 " 4.8774912. 



log. 9.3752793, 



" 9.2868326n, 



" 8.6122666n, 



" 6.4654333, 



" 6.6168096, 



" 6.3253889, 



5.1113360w. 



log. 0.7189114n, 



" 0.6243470, 



" 1.6021710, 



" 7.2653793n, 



" 8.2100866, 



" 7.1956378, 



6.2566120. 



log. 0.7663690, 



" 0.8175024, 



" 0.8964726, 



" 5.7167383, 



" 6.9836813, 



5.9129634, 



" 4.9741254. 



For the root g^ we get, 



4 =0", and N t = JV 4 '=iV 4 "=, &c. 



