THE ORBITS OF THE EIGHT PRINCIPAL PLANETS. 29 



Having found the values of N ir , N r , N rt , and N" 1 , we must now substitute them 

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

 b =0.000007745108^ log. 94.8890274; 

 Z/ =0.00003787069^ " 95.5783033 ; 

 If _ 0.00008781746 JV " 95.9435809%; 

 b'"= 0.0002754383JV " 96.4400243. 



Substituting these quantities, together with #, in equations (110-113), we get 



B =+0.0002259314^ log. 96.3539766 ; 



B' =+0.00009374307JV " 95.9719391 ; 



B" =+0.00005411940JV " 95.7333530; 



C = 0.00010371 10JV " 96.0158248%; 



C' = 0.00003397893JV " 95.5312097%; 



C" =+0.00006651123JV " 95.8228950; 



e""=+0.00006978516JV " 95.8437631 ; 



E 0.0000368787^ " 95.5667753%; 



.#' =_ 0.00006307260JV " 95.7998407%; 



E'= 0.0004609025 N. " 96.6636091; 



E"= 0.0007860900^" " 96.8954722?i; 



F =+0.00000123008^" " 94.0899334; 



^'^0.00002498980^ " 95.3977626; 



F"= 0.01632072iV " 98.212739471 ; 



^'"=0.002657125^ " 97.42441 19n. 



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



/ =+0.000085341 IN log. 95.9311615; 



/' =+0.00006099422^ " 95.7852886; 



/" =+0.00005755803^V " 95.7601059 ; 



/'"= 0.0003921 492iV " 96.5934513n; 



/ /r = 0.01688088^" " 98.2273951; 



/^ == _0.002533220A r " 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 



and consequently #= 5".4638024. 



We have thus obtained ar 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 </, 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 tig by formulae similar to 



the following: 



U =2^+^-^40.22178 ....;) 

 ^23.14584 ....;] 



