r example, the golden number of the year
1832 is ((1832 + 1) / 19)_r = 9, and the epact, as found in Table III., is
twenty-eight. This epact occurs at the 3rd of January, the 2nd of February,
the 3rd of March, the 2nd of April, the 1st of May, &c., and these days are
consequently the days of the ecclesiastical new moons in 1832. The
astronomical new moons generally take place one or two days, sometimes even
three days, earlier than those of the calendar.

There are some artifices employed in the construction of this table, to
which it is necessary to pay attention. The thirty epacts correspond to the
thirty days of a full lunar month; but the lunar months consist of
twenty-nine and thirty days alternately, therefore in six months of the
year the thirty epacts must correspond only to twenty-nine days. For this
reason the epacts twenty-five and twenty-four are placed together, so as to
belong only to one day in the months of February, April, June, August,
September and November, and in the same months another 25', distinguished
by an accent, or by being printed in a different character, is placed
beside 26, and belongs to the same day. The reason for doubling the 25 was
to prevent the new moons from being indicated in the calendar as happening
twice on the same day in the course of the lunar cycle, a thing which
actually cannot take place. For example, if we observe the line B in Table
III., we shall see that it contains both the epacts twenty-four and
twenty-five, so that if these correspond to the same day of the month, two
new moons would be indicated as happening on that day within nineteen
years. Now the three epacts 24, 25, 26, can never occur in the same line;
therefore in those lines in which 24 and 25 occur, the 25 is accented, and
placed in the calendar beside 26. When 25 and 26 occur in the same line of
epacts, the 25 is not accented, and in the calendar stands beside 24. The
lines of epacts in which 24 and 25 both occur, are those which are marked
by one of the eight letters b, e, k, n, r, B, E, N, in all of which 25'
stands in a column corresponding to a golden number higher than 11. There
are also eight lines in which 25 and 26 occur, namely, c, f, l, p, s, C, F,
P. In the other 14 lines, 25 either does not occur at all, or it occurs in
a line in which neither 24 nor 26 is found. From this it appears that if
the golden number of the year exceeds 11, the epact 25, in six months of
the year, must correspond to t