THE ORBITS OF TIIE EIGHT PRINCIPAL PLANETS. 



87 



For the root r/ 4 , we get, 



gr 4 =0".62800419 ; 



^4 



=-4- 0. 1217541 N t ' 



w 



=4" 0.1847141^ 



w 



=-f 0.2138538JV, 



Ni" 



=+ 0.3456976A7 



n; 



=+ 1.127368^' r 



K' 



=4- 23.96983 A7'' 



iV 4 r,/ =+153.5574iV/ r 



For the root r/ b , 



we get, 



9 



,=2'. 72651823; 



N b 



= _|_ 0.2923210AV" 



w 



= _f- ().286536A r 5 /r 



n: 



= j r 0.2999964iV/ r 



n:- 



— _[- 0.3994943AV 



nj 



=+ 0.9107594JV r 6 " r 



NJ' =+U.686±6N b ' v 

 N & r "=— 1.519462^" 



For the root g 6 , we get, 



^ 6 =3".7251312; 

 N e =+0.5714777^" 

 Nj =+0.3858590iV/ r 

 JV 6 " =4-0.3794987^' 

 N," =+0.4358324iV 6 /r 

 N/ =4t0.7893470JV/" 

 ^"=—1.030466^/" 

 JV7 ,, =4-0.0357074iV/ r 



log. 9.0854837; 



" 9.2665000 ; 



" 9.3301171; 



" 9.5380963 ; 



" 0:0520657; 



" 1.3796650; 



" 2.1862708. 



log. 



log. 



9.4658600 

 9.4571790 

 9.4771160 

 9.6015106 

 9.9594036 

 1.1669170 

 0.1816899» 



9.7569992: 



9.5864288 : 



9.5792102 



9.6393195 



9.8972680: 



0.0130335/*; 



8.5527582. 



For the root r/ 7 , we get, 



£ T =22".4729002 ; 



N 7 =— 0.00622292JV/" log. 7.7939944n ; 



TV/ =+0.02016987iV 7 ' r " 8.3047032; 



N 7 " =— 0.1518602iV 7 ' r " 9.1814440// 



A/" =— 0.9593122AV " 9.9819600;* 



JV/ =— 3.093542Ay r " 0.4904560?* 



7V 7 "=+0.1154757iV7 r " 9.0624906; 



iV 7 r "=-|-0.008683434A r / r " 7.9386915. 



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



must also add the logarithm of l-|-^ r/ , to those of 



/// 7 rr l "I 7 jv • 



,, J' 1 and r, J . in 

 n a n a 



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



