813 
The coordinates of the moon are developed in the lunar theory 
in series depending on the four arguments /, /’, # and D, where 
/ and /’ are the mean anomalies of the moon and sun, / the mean 
argument of the moon’s latitude, and D the difference of the mean 
longitudes of the moon and sun. For the mean opposition we have 
D=0. The other three arguments are contained, under the names 
of 1, Il and III, in Opporzer’s “Tafeln zur Berechnung der Mondfin- 
sternisse’. We have 
erp ge ae 2F NE artan 66) 
ef Tees BE KOR IA net RO 
Denoting the mean longitudes by 4 and 4’, and the true longitudes 
by w, w’, we have 
wdd + AA, Deed 
l 
where 
5 
dl = 2e sinl + ri e* sin 21 — y? sin 2F 
. nes 
represents the elliptic term (" = tin gi). and 4A the sum of all 
perturbations in longitude. The perturbations in the motion of the 
earth can be neglected. Then, denoting the values for mean opposition 
by the suffix 1, we have 
À,—À,!' = 180°, ww, = 180° + dl, + Ad, — dl,'; 
for the instant of central eclipse on the other hand we have 
4 w—w' == 180° — y? sin 2F. 
We now put 
A = (w,—w,') — (w—w’) = dl, + AA, — dl, + y'sin 2F, 
Then, n (1—c) and n(1—g) being the mean motions of the perigee 
and the node, we have, neglecting perturbations *) : 
dw 0 
w= —=n(l + Zee cos l + — ce? cos 2l — 2gy? cos 2F), 
dt . 2 
due! 
n= nt (1 + 2e cosl +... ), 
The time elapsed between the epochs of mean opposition and 
central eclipse is then 
| A 
At = — — 
uu 
At the instant of central elipse we have thus 
l=l, + ncAt, v=l + dl + Al, 
i) See however the next footnote. 
