THE ORBITS OF THE EIGHT PRINCIPAL PLANETS. HI 



^ we get, 

 g,= 0".661G66, 

 5 =+1.232212JV/ 



For the root 



JV 5 " =+1.108223^." 

 N =+1.049477 A;" 

 N 5 r =+0.9653287 A/' 

 N t "= 0.9379252 N & ' r 

 N t ru = 9.829270^'" 



For the root g 6 , we get, 



<7 6 = 2".9 16082, 

 JV 6 = + 3.557327A 6 ' r 

 AV =+ 2.059 163 A~ jr 

 A7 =+ 1.845317AV r 

 JV 6 '" =+ 1.314187JV 6 ' r 

 N a r =+ 0.8164588W 8 /r 

 JV r/ = 20.11300W /r 



log. 0.0906854, 

 0.0535832, 

 0.0446270, 

 0.0209706, 

 9.9846752, 

 9.9721682, 

 0.9925212. 



log. 0.5511238, 



" 0.3136906, 



" 0.2660709, 



" 0.1186570, 



" 9.9119342, 



" 1.3034768n, 



" 0.3347880. 



log. 8.6240604, 



" 8.6677625n,' 



" 9.6363826?i, 



" 0.1667598n, 



" 0.3963230n, 



" 9.0387886, 



" 8.0882343. 



5. Having thus determined all the roots of the equation of the eighth degree, 

 together with the ratios of the constant quantities N', N'\ N"\ &c., corresponding 

 to each root, the complete integrals of equations (E) will be 



For the root </ 7 , we get, 



fr= 25".934567, 

 N 7 = 0.04207851aV 

 JV,' = 0.04653315JV 

 N 7 " = 0.4328950JV 

 N 7 " =1.468114 

 Nj r = 2.490709JV 



r 

 " 



' 

 " 



=N cos 



cos 



cos 



&c.; 



p =N sin 



&c. 



sin 



sn 



The analysis of 16 will conduct us to the following equations for the deter- 

 mination of the arbitrary constants corresponding to each root. 



