the year, must, in the course of
centuries, have all different values from one to thirty inclusive,
corresponding to the days in a full lunar month. Hence, for the
construction of a perpetual calendar, there must be thirty different sets
or lines of epacts. These are exhibited in the subjoined table (Table III.)
called the _Extended Table of Epacts_, which is constructed in the
following manner. The series of golden numbers is written in a line at the
top of the table, and under each golden number is a column of thirty
epacts, arranged in the order of the natural numbers, beginning at the
bottom and proceeding to the top of the column. The first column, under the
golden number 1, contains the epacts, 1, 2, 3, 4, &c., to 30 or 0. The
second column, corresponding to the following year in the lunar cycle, must
have all its epacts augmented by 11; the lowest number, therefore, in the
column is 12, then 13, 14, 15 and so on. The third column corresponding to
the golden number 3, has for its first epact 12 + 11 = 23; and in the same
manner all the nineteen columns of the table are formed. Each of the thirty
lines of epacts is designated by a letter of the alphabet, which serves as
its index or argument. The order of the letters, like that of the numbers,
is from the bottom of the column upwards.

In the tables of the church calendar the epacts are usually printed in
Roman numerals, excepting the last, which is designated by an asterisk (*),
used as an indefinite symbol to denote 30 or 0, and 25, which in the last
eight columns is expressed in Arabic characters, for a reason that will
immediately be explained. In the table here given, this distinction is made
by means of an accent placed over the last figure.

At the Reformation the epacts were given by the line D. The year 1600 was a
leap year; the intercalation accordingly took place as usual, and there was
no interruption in the order of the epacts; the line D was employed till
1700. In that year the omission of the intercalary day rendered it
necessary to diminish the epacts by unity, or to pass to the line C. In
1800 the solar equation again occurred, in consequence of which it was
necessary to descend one line to have the epacts diminished by unity; but
in this year the lunar equation also occurred, the anticipation of the new
moons having amounted to a day; the new moons accordingly happened a day
earlier, which rendered it necessary to take the epacts in the next highe