4:83] 
537 
483. 
ON A PAIR OF DIFFERENTIAL EQUATIONS IN THE LUNAR 
THEORY. 
[From the Monthly Notices of the Royal Astronomical Society, vol. xxxn. (1871—72), 
pp. 201—206.] 
I consider the differential equations 
'dv 
odt 
It cl “ p ^ + ^ = km2p & + $ C0S ^ V ~ 
d ( n dv 
dt V dt 
=jm 2 p 2 { — f sin (2v — 2mt)}, 
which when j = k = 1 give the following equations in the lunar theory (D — t— mt): 
I 1 W 2 _ 1 7 9 w 4 _ 9 7 TO 5 _ 757 w 6 _ 4039 m 7 _ 34751 189 m 8 _ 155067635 m 9 
rj ™ '288 m 4^ m T6l m 432 T¥£06 56 nt 4976640 //i 
• cos 2D [m 2 + -^ 9 - m 3 + w 4 + if + YoWf 1 m<i + 2 IItosir m? 
. 355021217 w 8 | 27888590059^91 
^ £331200 * 34992000 J 
30S 4R [1 m 4 + m* + AfffF m* + mJ + + gg <1 
.os6D[Mf m» + YWffi m* + 2 6 9 !?^- 3 - m *+ £ fSHfl№O 
'0033633 m 9] 
:os6R [fif m 6 + + - 
os 8D TO 8 + YoWnuf 
as m 7 , 
m 2 + m 4 + ff m s + -Wo¥' 
vo 9 /1 T /m2 — if m 3 - m 4 - £££ 
os 2D [— m 2 — 
os 4 Z> [- f m‘ - -Wif m* - W *»* - FIFF 
os 6D [- ih r "‘ ~ FjVev ™ 7 3> 
W ™ s - VAW »• - FSFF “ 7 ] 
[otF”» 7 ] 
68