ulian calendar, every omission of the
centenary intercalation would require them to be placed one line lower,
opposite the 6th, for example, instead of the 5th of the month; so that,
generally speaking, the places of the golden numbers would have to be
changed every century. On this account Lilius thought fit to reject the
golden numbers from the calendar, and supply their place by another set of
numbers called _Epacts_, the use of which we shall now proceed to explain.

_Epacts._--Epact is a word of Greek origin, employed in the calendar to
signify the moon's age at the beginning of the year. [v.04 p.0995] The
common solar year containing 365 days, and the lunar year only 354 days,
the difference is eleven; whence, if a new moon fall on the 1st of January
in any year, the moon will be eleven days old on the first day of the
following year, and twenty-two days on the first of the third year. The
numbers eleven and twenty-two are therefore the epacts of those years
respectively. Another addition of eleven gives thirty-three for the epact
of the fourth year; but in consequence of the insertion of the intercalary
month in each third year of the lunar cycle, this epact is reduced to
three. In like manner the epacts of all the following years of the cycle
are obtained by successively adding eleven to the epact of the former year,
and rejecting thirty as often as the sum exceeds that number. They are
therefore connected with the golden numbers by the formula (11 n / 30) in
which n is any whole number; and for a whole lunar cycle (supposing the
first epact to be 11), they are as follows:--11, 22, 3, 14, 25, 6, 17, 28,
9, 20, 1, 12, 23, 4, 15, 26, 7, 18, 29. But the order is interrupted at the
end of the cycle; for the epact of the following year, found in the same
manner, would be 29 + 11 = 40 or 10, whereas it ought again to be 11 to
correspond with the moon's age and the golden number 1. The reason of this
is, that the intercalary month, inserted at the end of the cycle, contains
only twenty-nine days instead of thirty; whence, after 11 has been added to
the epact of the year corresponding to the golden number 19, we must reject
twenty-nine instead of thirty, in order to have the epact of the succeeding
year; or, which comes to the same thing, we must add twelve to the epact of
the last year of the cycle, and then reject thirty as before.

This method of forming the epacts might have been continued indefinitely if
the Julian