THE ORBITS OF THE EIGHT PRINCIPAL PLANETS. 



29 



Having found the values of N' r , N v , N rr , and N T ", we must now substitute them 

 in equations (118), and we shall get the following values of b, V, 6", and V". 

 b =—0.00000774510827 log. 94.8890274» ; 

 Z/ =—0.0000378706927 " 95.5783033»; 

 b"=— 0.0000878174627 « 95.9435809n; 

 V=— 0.000275438327" " 96.4400243». 



Substituting these quantities, together with 

 B =+0.000225931427 

 B =+0.0000937430727 

 B" =+0.0000541194027 

 C =—0.000103711027 

 C =—0.0000339789327 

 C" =+0.00006651 12327 

 C""=+0.0000697851627 

 E =—0.000036878727 

 E' =—0.0000630726027 

 #" =—0.000460902527 

 E'"=— 0.0007S6090027 

 F =+0.0000012300827 

 F' =—0.0000249898027 

 2"" =— 0.0163207227 

 2™=— 0.00265712527 



g, in equations (110-113), we get 

 log. 96.3539766 ; 



" 95.9719391; 



" 95.7333530; 



" 96.0158248w; 



" 95.5312097?*; 



" 95,8228950 ; 



" 95.8437631 ; 



" 95.5667753«; 



" 95. 7998407m; 



" 96.6636091«; 



" 96.8954722«; 



" 94.0899334; 



" 95.3977626n ; 



" 98.2127394»i ; 



" 97.42441 19n. 



These quantities being substituted in equations (51) Ave shall obtain 



/ =+0.000085341727 

 f =+0.0000609942227 

 /" =+0.0000575580327 

 /'"=— 0.000392149227 

 /" = — 0.0168808827 

 / r =— 0.00253322027 



log. 95.9311615; 

 " 95.7852886; 

 " 95.7601059; 

 " 96.5934513«; 

 " 98.227395bi; 

 " 97.4036729?*. 



Now substituting /, /', &c, D, D, D\ in equations (96), each one of them will 

 give x =+0.0243677. 



This value of % is to be substituted in equation (120), and we shall find 

 ^=+0".00009598, 

 and consequently g= 5".4638024. 



We have thus obtained a first approximation to the values of the required 

 quantities. In order to get a closer approximation we must repeat the whole 

 computation by using the corrected value of g, and the values of /,/',/", &c, 

 already found. But instead of computing new values of A, A', A", &c, D, D, D", &c, 

 by the formulae (98-109), it is much more convenient, as well as less laborious, to 

 compute corrections to these quantities depending on hg by formula? similar to 

 the following: — 



8 A =2g$g+$g*— 5^40.22178 ....;) 



8A'=2gfcj+Sg 2 — ^23. 14584 ....;) 



(128) 



