44 LECTURES ON THE LUNAR THEORY. [LECT. 



But if we refer to the second equation, we see that 6 5 must be deter- 

 mined by means of a small divisor, and this puts any method of approxi- 

 mation at a disadvantage. In order to obtain readily satisfactory values 

 for the new coefficients, we shall treat the six equations simultaneously, 

 substituting first the numerical values of the known quantities. 



We have found 



a. = -00717,95, b,= '01021,20, n/a*= i '17 150,3. 

 Hence 

 3-52105a 6 -0-1747636.,+ -065405 6 --0293936 6 +-067727 7 --0326956 7 



= |n' 2 x 0-969364, 

 0-l74763a 5 - 0'0067366 5 - -039197a 6 + -0177536, + -042499a 7 - -0200756, 



= |' 2 x -0-040848, 



039009a.,+ '0081536 6 + 7'19766a ( ,-4-148586 (i = - n'" x 3'50, 



001651a 5 - 0086436 B + 4 > 14858a,- 3-683356, =-' 2 x-3'50, 



036687a.- '0114556., + 7'84443a 7 -4-4981l6 7 



= |w' 2 x -0-50, 

 001651a 5 + -0109656., +4-49811a 7 -4'330126 7 



= | w' 2 x 0-50. 

 From the second and third pairs we find 



0161 86 5 + -0070846., + li = ?n' 2 x 2 '94739, 



:-n' 2 x 4-26994, 

 -n' a -x -0-321398, 



011072a 5 --0100156 5 +6 7 = |n' 2 x -0'449338. 

 Eliminate a,, 6 6 , a,, b, from the first pair. 



