22 LECTURES ON THE LUNAR THEORY. [LECT. 



It may be readily seen that the additional terms introduced are the 

 following : 



in - ~. 1 6 (n - n')- a t cos 4</, 



8n (n n') 6 4 



1 6 (n n')- b t sin 4i/, 



2 dr dd 



-= j- 8n(n n)a,sm4:\u, 



r at at 



and also that we may neglect the terms added in the expressions for 

 | n' 2 cos 2 (0 - n't - e'), | n' 2 sin 2 (0 - n't - e 7 ). 



If we write the terms thus produced along with the several terms left 

 outstanding in our equations and then equate the whole to zero, we have 



1 6 (n - nj 4 - 8n (n - n') b 4 + -^ 3a 4 - 6 (n - nj of - 2 (TO - nj b* 



ct 



- 1 6 (n - n')" 6 4 + 8n(n- n') a 4 + 4 (n - n') 1 A -2n(n- n') a.; + - n'*b, = 0, 



Zi 



from which we must determine a 4 and b t . 



