815 
corresponding term in K is zero, since 2D, = 0 *). The evection-term 
has the argument #«—2/—2). The resulting term in K therefore 
has the same argument as the principal term. Finally I found in this way 
K = e, {0.858 sin 1, — 0.081 sin 21, + 0.033 sin (1, + 1,} 
= 0.0471 {sin 1, (1--0.072 cos 1,) + 0.039 sin (i, + 1,3 . . (8) 
In order to verify this result, I have also computed the formula 
(6). The values of a and w—A expressed in the arguments /, 7, D 
and #’ were taken from Brown’s lunar theory. From these we easily 
derive gs and a 
dt dt 
We must then substitute for the arguments their values 
baa son At D = 180° + (1—m) nt 
—=I,' + mn At 2F = 2F, + 2gnÂt 
The value of At is given in OppoizEr’s “Syzygien-Tafeln für den 
Mond”, page 4. The value there given is the interval of time between 
mean and true opposition. To get the value for the epoch of central 
eclipse it is sufficiently accurate to omit the term +0.0104 sin (2g’+20’). 
The interval thus computed must then be reduced to our unit of time 
(see below). The developments, which are rather long, finally led to 
the following formula, where nothing is neglected that can affect the 
third decimal place : 
dx 
ys OP 0.95404 $0.8075 sin 1, — 0.0300 sin 21, 
i + 0.0300 sin (l, + L,') — 0.0020 sin (20, + 1) 
— 0.0033 sin I’, — 0.0050 sin (l,—U',) 
+ 0.0016 sin ZF, — 0.0055 sin a cos l, 
= 0.0114 eos AF sind. EPE en (3). 
Eclipses occur near the node. Consequently sin 24 Sah Thus, if 
we neglect all but the first three and the last term, none of the 
1 
neglected terms exceeds PG: Further cos 2#’ is always included 
between the limits 1 and 0.866. Therefore if we take cos 2/’, = 0.96 
1 
throughout, we cannot make a larger error than about sa of the 
last term. This latter then becomes 0.0110 sin 7, and can be added 
to the principal term. We thus finally get the formula 
1) The influence of the variation on the osculating values of a and n, is consi- 
derable, but it is the same in all oppositions, so that a?n is a constant. The same 
thing is true of the error which is produced by our taking in z, in the computation 
of At, the mean instead of the osculating value of n. 
