6] A METHOD OF SOLVING THE EQUATION -g + Qw-Q. 135 



and so on. If we stop at this stage the equations to determine k 

 and c, are 



For example, take the equation of Lecture XIV. for finding the 

 Moon's latitude ; here with our present notation 



q a - = 1-17803,9, ?, = '01261,5, q,= '00012,6. 



Hence 



&= -01261,5 + 00012,6c_ I , Q_,= '00012,6 + '01261, 5c_ lt 



and taking k = q a as sufficient approximation in ^Q,, 8 l Q l we have 



8,^0 ='00001,9, 8 1 ^>_ 1 = -00002,2c_ 1 , 

 and the equations for k and c_ l are 



Jf - '01261, 5c_! = 1-17805, 8, 



c, [(Jfc-2) ! - 1-17806,1] = -01261,5, 



whence 



=1-08517,1, c_,= -'03698,3, 



which may be compared with the results of p. 103.] 



