36 LECTURES ON THE LUNAR THEORY. [LECT. 



We notice that the first equation is not very different from the 

 second doubled ; it is this fact that makes successive approximation a 

 disadvantageous method and renders it advisable to include small quantities 

 from the beginning. 



Eliminate 3 , 6 3 in succession from the third and fourth equations, 

 thus : 



Multiply the third equation by 



9-00020 -[12-51451 x 9'00020-6'48508 X 6'48508]= 0'127523, 

 and the fourth by 



-6-48508 -[12-51451 X 9'00020 - 6'48508 X 6'48508] = -0'091887, 

 and add ; 6 3 will be eliminated. 



Again multiply the third equation by '091887 and the fourth by 

 -177317 and add; a., will be eliminated. Hence we find 



001 119a,- -0060526, + a 3 = '-n'*x 1 '09776, 



8 



- -001463a, - -0070346, + 6, = | n" x 1-34669. 



8 



Multiply these by - -08093 and '05137 respectively and add to the 

 first equation : 



4'56672a, - 2-172326, + '08093a 3 - '051376 3 = | n'- x 2'87937, 



8 



-0-000090, + 0-000496,- '080930, =-n' 2 x -G'08884, 



8 



-0-OOOOSo,- 0-000366, + -051376 3 = | >i' 2 x 0'06918 ; 



8 



hence 



4'56665fl, - 2-172196, = | n' 2 x 2-85971. 



8 



Eliminate a 3 , 6 3 in a similar manner from the second equation ; 



2-141280, -0-995466, + -061270, --033386,= --n' 2 x 0-91416, 



8 



-0-000070, +0-000376,- -06127o, =-- n '*x 0'06726, 



8 



-O'OOOOSa,- 0-000236, + "033386,= --n' 2 x -0'04495; 



8 



