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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.
Encyclopaedia Britannica, 11th Edition, Volume 4, Part 4 "Bulgaria" to "Calgary"

The new moons indicated by the epacts also differ from the astronomical new moons, and even from the mean new moons, in general by one or two days.
Encyclopaedia Britannica, 11th Edition, Volume 4, Part 4 "Bulgaria" to "Calgary"

Hence, for the construction of a perpetual calendar, there must be thirty different sets or lines of epacts.
Encyclopaedia Britannica, 11th Edition, Volume 4, Part 4 "Bulgaria" to "Calgary"

When the solar equation occurs, the epacts are diminished by unity; when the lunar equation occurs, the epacts are augmented by unity; and when both equations occur together, as in 1800, 2100, 2700, &c., they compensate each other, and the epacts are not changed.
Encyclopaedia Britannica, 11th Edition, Volume 4, Part 4 "Bulgaria" to "Calgary"

Instead, however, of employing the golden numbers and epacts for the determination of Easter and the movable feasts, it was resolved that the equinox and the paschal moon should be found by astronomical computation from the Rudolphine tables.
Encyclopaedia Britannica, 11th Edition, Volume 4, Part 4 "Bulgaria" to "Calgary"

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.
Encyclopaedia Britannica, 11th Edition, Volume 4, Part 4 "Bulgaria" to "Calgary"

This method of forming the epacts might have been continued indefinitely if the Julian intercalation had been followed without correction, and the cycle been perfectly exact; but as neither of these suppositions is true, two equations or corrections must be applied, one depending on the error of the Julian year, which is called the solar equation; the other on the error of the lunar cycle, which is called the lunar equation.
Encyclopaedia Britannica, 11th Edition, Volume 4, Part 4 "Bulgaria" to "Calgary"

The thirty epacts correspond to the thirty days of a full lunar month; but the lunar months consist of twentynine and thirty days alternately, therefore in six months of the year the thirty epacts must correspond only to twentynine days.
Encyclopaedia Britannica, 11th Edition, Volume 4, Part 4 "Bulgaria" to "Calgary"

When 25 and 26 occur in the same line of epacts, the 25 is not accented, and in the calendar stands beside 24.
Encyclopaedia Britannica, 11th Edition, Volume 4, Part 4 "Bulgaria" to "Calgary"

The numbers eleven and twentytwo are therefore the epacts of those years respectively.
Encyclopaedia Britannica, 11th Edition, Volume 4, Part 4 "Bulgaria" to "Calgary"
chained_bear commented on the word epacts
"Epacts, in chronology, the excesses of the solar month above the lunar or synodical month, and of the solar year above the lunar year of twelve synodical months; or of several solar months above as many synodical months, and several solar years above as many dozen of synodical months.
"The epacts are either annual or menstrual.
Menstrual Epacts, are the excesses of the civil or calendar month above the lunar month....
Annual Epacts, are the excesses of the solar year above the lunar...."
—Falconer's New Universal Dictionary of the Marine (1816), 685
October 12, 2008