THE ORBITS OF THE EIGHT PRINCIPAL PLANETS. 



123 



The solutions of equations (431—442) will now give the following values: 



For the root g, Ave get, 



g=— 5".201065, 



N' =+0.1374398iV log. 9.1381124, 

 N" =+0.1000556iV " 9.0002416, 



N'" — )-0.0201689iV " 8.3046820, 



N" —— 0.000233031iV " 6.3674143n, 



N T =— 0.000298026iV " 6.4742546m, 



N TI =+0.0002525 28iV " 6.4023092, 



jy r "=+0.00000754208IV 



" 4.8774912. 



For the root g v , we get, 



J7l== _6".6347695, 

 N{ =—0.2372900^ 

 iV," =—0.1935676^ 

 N{" = —0.0409512^ 

 JV/ r =+0.000292034JV, 

 N x r =+0.000413818^ 

 ^"=—0.000211538^, 

 N x ra =— 0.0000129222^ 



For the root g 2 , we get, 



&=— 1T.459300, 



JV 2 ' =— 5.234937JV 2 

 N{ =+ 4.210629JV 2 

 N't" =+40.01022iV 2 

 N 2 ir =— 0.00184238^ 

 N/ =— 0.01622134iV 2 

 iV 2 "=+ 0.001569054iV 2 

 iV 2 rJ =+ 0.000 180556iV 2 



For the root g 3 , we get, 



^ 8= _18".666221, 



JVy =—5.839411^ 

 jV 3 " =+6.569047^ 

 N, m =— 7.879027iV 3 . 

 JV 3 /r =—0.0000520881^ 

 N S T =^-.0.000963122^ 

 N 3 TI =+0.0000818396^ 

 iV 3 r/ =+0.00000942162iV3 



log. 9.3752793», 



" 9.2868326n, 



" 8.6122666?i, 



" 6.4654333, 



" 6.6168096, 



« 6.3253889», 



« 5.1113360?*. 



log. 0.7189114;?, 



" 0.6243470, 



" 1.6021710, 



« 7.2653793k, 



" 8.2100866w, 



" 7.1956378, 



« 6.2566120. 



log. 0.7663690n, 



" 0.8175024, 



" 0.8964726??, 



" 5.7167383n, 



" 6.9836813m, 



" 5.9129634, 



" 4.9741254. 



For the root g 4 , we get, 



g 4 =0", and N t =N t '—N^ 



=, &c. 



