TUB ORBITS OF THE EIGHT PRINCIPAL PLANETS. 



31 



r 4 = 0".6166849; 



=+ 0.1213144^' 



=4- .1843578^ 



=4- .2135417^7" 



=-f .3454671AV r 



=4- 1 .127803^ 4 /F 



.8892$, 



<7 6 = 2". 7276592; 

 N & =+ 0.2925180^ 

 N; =4- .2866292# 6 /r 

 JV 5 " =+ .3000735 Ar/ F 

 Nf =4- .3995364^/ F 



^ 5 r =+ C 

 ^ 5 "=+15.29769iV 5 J 



^ s r// =- 1 



,= 3".7166075; 

 =+0.5675117^ 



=4- .3847378^ 6 /^ 

 =+0 . 



JV 6 r =-0 - 

 N ri = 1 .0394174 



g,= 22".4608479; 

 __ 0.006236689^" 

 ' =+ 0.02030250^ 



= O.J 



- 3.091803^ /F 

 '=+ 0.1154716^/ r 

 '=4- 0.00872852^ 



log. 9.0839135; 



" 9.2656615; 



" 9.3294826; 



" 9.538406T; 



" 0.0522322; 



" 1.389161T; 



" 2.1983503. 



log. 9.4661526; 



" 9.4573205 ; 



" 9.4772276; 



" 9.6015563; 



" 9.9592151 ; 



" 1.1846258; 



" 0.1753554n. 



log. 9.7539748; 



" 9.5851649 ; 



" 9.5782040 ; 



" 9.6389698;. 



" 9.8976854; 



" 0.0167908; 



" 8.5173628. 



log. 97.7949541n; 



" 98.3075494; 



" 99.1820317n; 



" 99.9829761w; 

 " 0.49021 18/i ; 



" 99.0624752; 



" 97.9409405. 



16. We have thus determined all the roots appertaining to the equation of the 

 eighth degree, together with the ratios of the constant quantities N', N", &c., to N; 

 NI, JVy, &c., to Ni ; and the ratios of the similar quantities relative to each of the 

 other roots. The complete integrals of the equations (A) will therefore be the 

 sums of all the corresponding terms depending on g, g^ g 2 , &c., and we shall there- 

 fore have 



