THE ORBITS OF THE EIGHT JPUINCIPAL PLANETS. 



87 



For the root 



^ we get, 

 c/ 4 =0".628()0419 ; 



N t =+ 

 iV 4 ' =4- 

 N t " =-{- 

 N t " =+ 

 tf 4 r =+ 



0. 121 7541 ^i 

 0.1847141jV/ 

 0.2138538.V/ 

 0.3456976.V, 



1. 127368 NI" 



=+ 23.96983.V/ 



For the root g b , we get, 



// 5 =2". 7265 1823 ; 

 TV; =+ 0.2923210^ 5 /r 

 JV7 =+ 0.286536^ 6 /r 

 JV 6 " =+ 0. 299996 W 

 Nf =+ 0.3994943^'" 

 7V 8 F =+ 0.91 07594 N,,' r 

 ^"=4-14.68646^" 

 N a r "= 1.519462JV 5 ' r 



For the root r/ 6 , we get, 



/r 



=+0.5714777# 6 



JV a " = 



'" =+().4358324JV; /r 

 " =+0.7893470^ a /|r 

 " = 1.030466 N 6 ' r 



For the root fa, we get, 



# 7 =22".4729002; 

 N, = 0.0()622292JV/ r 

 JV 7 ' =+0.02016987JV/ r 

 JV 7 " = 0.1518602JV 7 /r 

 A 7 '" = 0.9593122AV 

 JV/ = 3.093542iV/ r 



log. 9.0854837 ; 



" 9.2665000; 



" 9.3301171; 



" 9.5386963 ; 



" 0.0520657 ; 



" 1.3796650; 



" 2.1862708. 



log. 9.4658600 ; 



" 9.4571790; 



" 9.4771160; 



" 9.6015106; 



" 9.9594036 ; 



" 1.1669170; 



" 0.1816899. 



log. 9.7569992; 



" 9.5864288; 



9.5792102; 



" 9.6393195; 



" 9.8972680; 



" 0.0130335n; 



" 8.5527582. 



log. 7.7939944r t ; 



" 8.3047032 ; 



" 9.1814440n; 



" 9.9819600n; 



" 0.4904560n ; 



" 9.0624906 ; 



" 7.9386915. 



39. These numbers are now to be substituted in equations (134) and (135). We 



VI VI VI 



must also add the logarithm of 1+u", to those of , 7i", and - ' f .l rr , in 



n a n a n a 



order to obtain the numbers which are to be used in this computation. 



