THE ORBITS OF THE EIGHT PRINCIPAL PLANETS. 137 



E = [9.9807377J6"; 

 E> = j^+22.3515875 j [8.9723624]Z>" ; 

 E"= J0+17.5618825 j[9.7501125]6"; 

 E'"= [1.0016537J6". 



F =+[8.4689676]&'"; 



F'= [9.4463886J6'"; 



F"= ^0+14.902331 |[0.7927855]Z/" ; 



F"= J0+34.490730 } [9.6907241]&'". 



(471) 



? 1= {0+4.5202496 } 6 i; 2 ={0+ 0.7124602 



:;:} 



C l = {0+4.1330154 j[9.5433087] 2 ; 

 C 2 = {0+0.73073414 j [9.434971 l]6 a ; 

 <7,=+[0.8644527]& a ; 

 ^=+[0.8654649]^. 



Ej= [8.331 7448]6 3 ; 

 ^ 2 = {0+39.7660231 } [8.74377 18]6 3 ; 

 E B = { 0+ 0.64863718 } [0.7242832]& 3 ; 

 E t = [0.9647514]5 3 . 



^=+[7.7244692]& 4 ; 



J?i= [0.3564628]6 4 ; 



^=10+ 2. 7805744 }[1.5514854]6 4 ; 



F t = {0+45.7639253 }[9.4626364]J t . 



(472) 



(473) 



(474) 



(475) 



(476) 



Sr*+47.9382786./+787.7033176./ ) _ , 47? , 



+5108.828105.r/+11271.52356 j = 



^ 4 +29.5262630./+95.1517832.^ 2 ) , 



+51.352675.^+0.624611 ) 



The values of b, b', b", and b'" are given by equations (405), and the values of 

 b 2 , 6 3 , and 6 4 are given by equations (406), by merely multiplying the coefficients 

 ' 



If we put equations (477) and (478) equal to nothing, they will give 



g 1 = 5".1830604, &= 0".0124492, 



* g 2 = 6 .7024834, y 5 = .6632208, 



3 = 17 .3261252, 9= 2.9170763, 



04= 18 .7266096, g,= 25 .9335168. 



18 March, 1872. 



