r
line. There was, consequently, no alteration; the two equations destroyed
each other. The line of epacts belonging to the present century is
therefore C. In 1900 the solar equation occurs, after which the line is B.
The year 2000 is a leap year, and there is no alteration. In 2100 the
equations again occur together and destroy each other, so that the line B
will serve three centuries, from 1900 to 2200. From that year to 2300 the
line will be A. In this manner the line of epacts belonging to any given
century is easily found, and the method of proceeding is obvious. When the
solar equation occurs alone, the line of epacts is changed to the next
lower in the table; when the lunar equation occurs alone, the line is
changed to the next higher; when both equations occur together, no change
takes place. In order that it may be perceived at once to what centuries
the different lines of epacts respectively belong, they have been placed in
a column on the left hand side of the table on next page.

The use of the epacts is to show the days of the new moons, and
consequently the moon's age on any day of the year. For this purpose they
are placed in the calendar (Table IV.) along with the days of the month and
dominical letters, in a retrograde order, so that the asterisk stands
beside the 1st of January, 29 beside the 2nd, 28 beside the 3rd and so on
to 1, which corresponds to the 30th. After this comes the asterisk, which
corresponds to the 31st of January, then 29, which belongs to the 1st of
February, and so on to the end of the year. The reason of this distribution
is evident. If the last lunation of any year ends, for example, on the 2nd
of December, the new moon falls on the 3rd; and the moon's age on the 31st,
or at the end of the year, is twenty-nine days. The epact of the following
year is therefore twenty-nine. Now that lunation having commenced on the
3rd of December, and consisting of thirty days, will end on the 1st of
January. The 2nd of January is therefore the day [v.04 p.0996] of the new
moon, which is indicated by the epact twenty-nine. In like manner, if the
new moon fell on the 4th of December, the epact of the following year would
be twenty-eight, which, to indicate the day of next new moon, must
correspond to the 3rd of January.

When the epact of the year is known, the days on which the new moons occur
throughout the whole year are shown by Table IV., which is called the
_Gregorian Calendar of Epacts_. Fo