THE ORBITS OF THE EIGHT PRINCIPAL PLANETS. 



153 



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

 following values: — 



lor the root g, we get, 



g=— 5".1262710; 

 TV' =+0.12276772V 

 N" =+0.08793867V 

 N'" =+0.0175667iV 

 N ir =— 0.0002083672V 

 2V r =— 0.000264632V 

 2V r/ =+0.0002321742V 

 2V " =+0.000005494252V 



For the root g u we get, 



g x =— 6".5922959; 

 2V/ =— 0.2764942V, 

 2V," =— 0.2229582V, 

 NT =— 0.04673272V; 

 2V/ r =+0.0003365742V, 

 iV 1 r =+0.0004746902^ 

 2V," =— 0.0002458392V, 

 2^"=— 0.00001433462V, 



For the root g 2 , we get, 



</ 2 = — 17". 3938608; 

 2V 2 ' =— 5.563332V, 

 2V 2 " =+ 4.563922V, 

 2V 2 '" =+33.23S92V 2 

 2V/ r =— 0.001659522V 2 

 2V 3 r =— 0.01402362V 2 

 2V 2 "=+ 0.001366292V, 

 2V 2 r/ =+ 0.0001562242V, 



For the root g s , we get, 



g 3 =— 18". 4092048; 

 2V 3 ' =— 6.0988312V 3 

 iV" 3 " =+ 6.656182V; 

 N," =— 10.226457V;, 

 2V/ r = — 0.00001964212V 3 

 2V 3 r =— 0.0001502002V S 

 2V 3 "=+ 0.00001250747V; 

 7V 3 r/ =+ 0.000001 39 2867V 3 



For the root <7 4 , we get, 



^=0", 2V 4 =2V7=2V 4 ' =2V7' '= &c. 



log. 9.0890840; 



" 8.9441794; 



" 8.2446904; 



" 6.3188297%; 



" 6.4226422ft; 



" 6.3658128; 



« 4.7599088. 



Los 



9.4416856ft 



9.3482238ft 



8.6696208m 



6.5270807; 



6.6764098; 



6.3906513ft; 



5. 1563868m. 



log. 0.7453350ft; 



" 0.6593380; 



" 1.5216464; 



« 7.2199837ft; 



" 8.1468598ft; 



« 7.1355420; 



" 6.1937476. 



log. 



0.7852466ft 

 0.8232250; 

 1.0097248n 

 95.2931878ft 

 96.1766688ft 

 95.0971660; 

 94.1439073. 



20 March, 1872. 



