T11E ORBITS OF THE EIGHT PRINCIPAL PLANETS. 137 



E =—[9.98073771//'; 

 E'=— {^+22.3515875 } [8.9723624]& w ; 

 E" = — {^+17.5618825} [9.7501 125]Z>"; [ 

 E m =— [1.0016537]6". 



F =+[8.4689676]Z/"; 



.F'=— [9.4463886]Z>'"; 



-F"=— j</+ 14.902331 j[0.7927855]6'"; 



F'"= — ^+34.490730* [9.69072-11]//'. 



(471) 



(472) 



£,= ^+4.5202496^; B 2 =\g+ 0.7124602J6, ; ) 

 J B 3 =[<7+18.8179534JZ» 1 . i 



G x = — 1^+4.1330154 }[9.5433087]& 2 ; 

 t7 2 =— j^+0.73073414} [9.434971 1]& 2 ; 

 C 8 =+[0.8644527]6 2 ; 

 <7 4 =+[0.8654649]& 2 . 



(473) 



(474) 



E 1= — [8.331 7448JA; 

 E a =:— 1^+39.7660231 }[8.7437718]& 3 ; 

 E z =— \g+ 0.64863718 }[0.7242832]6 8 ; 

 Ei=— [0.9647514]5 3 . 



(475) 



^=+[7.7244692]^; 



F 2 =— [0.3564628T&; 



F s =—\g+ 2.7805744} [1.5514854]6 4 ; 



F 4 =— [^+45.7639253 } [9.4626364]6 4 . 



(476) 



Sr*+47.9382786./+787.7033176.^1 , 477) 



+5108.828105.^+11271.52356 J W> u **>**'' <> ' 



^+29.5262630.^+95.1517832^1 , 478) 



+51. 352675.^/ +0.624611 J ^ 4 '* 5 '* '^- v 



The values of b, b', b'\ and V" arc given by equations (405), and the values of 

 &o ^25 hi an( i b* arc given by equations (406), by merely multiplying the coefficients 

 ofiT'by l+p"=2. 



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



</,= - 5".1830604, g,= — (V.0124492, 



g b =— 0.6632208, 



g 2 =— 6.7024834, 

 g z =— 17 .3261252, 

 g A =— 18 .7266096, 



# 6 =— 2.9170763, 

 g 7 =—25 .9335168. 



18 March, 1872. 



