The
epact (from Greek:
epaktai hèmerai = added days) is a quantification of the difference between the solar and lunar calendars. It was defined by the second canon of the
Gregorian calendarThe Gregorian calendar is the internationally accepted civil calendar. It was first proposed by the Calabrian doctor Aloysius Lilius, and decreed by Pope Gregory XIII, after whom the calendar was named, on 24 February 1582 by the papal bull Inter gravissimas...
reformA calendar reform is any significant revision of a calendar system. The term sometimes is used instead for a proposal to switch to a different calendar.Most calendars have several rules which could be altered by reform:...
as "the number of days by which the common solar year of 365 days surpasses the common lunar year of 354 days".
Epacts are used to find the date in the lunar calendar from the date in the common solar calendar.
A (solar) calendar year has 365 days (366 days in
leap yearA leap year is a year containing one or more extra days in order to keep the calendar year synchronized with the astronomical or seasonal year....
s).
The
epact (from Greek:
epaktai hèmerai = added days) is a quantification of the difference between the solar and lunar calendars. It was defined by the second canon of the
Gregorian calendarThe Gregorian calendar is the internationally accepted civil calendar. It was first proposed by the Calabrian doctor Aloysius Lilius, and decreed by Pope Gregory XIII, after whom the calendar was named, on 24 February 1582 by the papal bull Inter gravissimas...
reformA calendar reform is any significant revision of a calendar system. The term sometimes is used instead for a proposal to switch to a different calendar.Most calendars have several rules which could be altered by reform:...
as "the number of days by which the common solar year of 365 days surpasses the common lunar year of 354 days".
Lunar calendar
Epacts are used to find the date in the lunar calendar from the date in the common solar calendar.
Solar and lunar years
A (solar) calendar year has 365 days (366 days in
leap yearA leap year is a year containing one or more extra days in order to keep the calendar year synchronized with the astronomical or seasonal year....
s). A lunar year has 12 lunar months which alternate between 30 and 29 days (in leap years, one of the lunar months has a day added).
If a solar and lunar year start on the same day, then after one year, the start of the solar year is 11 days after the start of the lunar year; after two years, it is 22 days after. These excess days are epacts, and are added to the day of the solar year to determine the day of the lunar year.
Whenever the epact reaches or exceeds 30, an extra (embolismic or intercalary) month is inserted into the lunar calendar, and the epact is reduced by 30.
Leap days extend both the solar and lunar year, so they do not affect epact calculations for any other dates.
19-year cycle
The
tropical yearA tropical year is the length of time that the Sun takes to return to the same position in the cycle of seasons, as seen from Earth; for example, the time from vernal equinox to vernal equinox, or from summer solstice to summer solstice.A tropical year can equivalently be defined as the time taken...
is about 365¼ days, while the synodic month is also slightly longer than 29½ days on average. This gets corrected in the following way. Nineteen tropical years are as long as 235 synodic months (
Metonic cycleThe Metonic cycle or Enneadecaeteris in astronomy and calendar studies is a particular approximate common multiple of the tropical year and the synodic month. The Greek astronomer Meton of Athens observed that a period of 19 tropical years is almost exactly equal to 235 synodic months, and...
). A cycle can last 6939 or 6940 full days, depending on whether there are 4 or 5 leap days in this 19-year period.
After 19 years the lunations should fall the same way in the solar years, so the epact should repeat after 19 years. However, 19 × 11 = 209 , and this is not an integer multiple of the full cycle of 30 epact numbers (209
moduloIn mathematics, modular arithmetic is a system of arithmetic for integers, where numbers "wrap around" after they reach a certain value—the modulus...
30 = 29, not 0). So after 19 years the epact must be corrected by +1 in order for the cycle to repeat over 19 years. This is the
saltus lunae (jump of the moon). The sequence number of the year in the 19-year cycle is called the
Golden NumberA golden number is a number assigned to each year in sequence to indicate the year's position in a 19-year Metonic cycle. They are used in the computus and also in the Runic calendar. The golden number of any Julian or Gregorian calendar year can be calculated by dividing the year by 19, taking...
. The extra 209 days fill 7 embolismic months, for a total of 19×12 + 7 = 235 lunations.
Lilian (Gregorian) epacts
Despite the statement in the second canon of the Gregorian reform quoted above, the epacts in this calendar can no longer be interpreted exactly as days. The designer (
Aloysius LiliusAloysius Lilius , also Luigi Lilio or Luigi Gigliowas an Italian doctor, astronomer, philosopher and chronologist who devised the Gregorian Calendar.The crater Lilius on the Moon is named after him...
) broke the pure Metonic relation when allowing centennial corrections of the epacts by one unit:
- a "solar equation" by decrementing the epact for the years whenever the Gregorian calendar drops a leap day (3 times in 400 Gregorian years)
- a "lunar equation" by incrementing the epact 8 times in 2500 Gregorian years.
In the Gregorian calendar, there are 30 possible values for the epact. Epacts always are computed modulo 30, and always indicate the New Moon. Therefore the epacts are in units of of a lunation (also called a
tithiIn vedic timekeeping, a tithi is a lunar day, or the time it takes for the longitudinal angle between the moon and the sun to increase by 12°. Tithis begin at varying times of day and vary in duration from approximately 19 to approximately 26 hours. There are 30 tithis in each lunar month,...
). However a lunation is less than 30 days, so the epact unit is less than a full day.
This can also be understood from the following fact (please read
computusComputus is the calculation of the date of Easter in the Christian calendar. The name has been used for this procedure since the early Middle Ages, as it was one of the most important computations of the age....
for an explanation of the terms and procedures referred to here):
Almost half of the lunations last only 29 days. In the
Calendarium 12 days in the year have a double epact label (xxiv,25 and xxvi,25; one of these is used depending on the Golden Number). Therefore the correction of the epact by one unit does not always result in a shift of all dates of the New Moon (and Full Moon) by one day: for epacts
25 in short lunar months there is no difference. So the epact corrections are less than one day on average, and therefore the epact itself is not measured in calendar days.
It may be argued that Lilius applied the "solar equations" in order to bring the lunar calendar back in sync with the original Julian calendar; the "lunar equations" would then make a long-term correction to the approximate Metonic relation between the Julian year and the mean lunation. However, the "lunar equations" are applied at the beginning of Gregorian years, not Julian years. The Gregorian epact tables have a period of 5,700,000 years. When counting epacts as days, the lunar calendar does not repeat however with this period, neither in this many Gregorian nor in Julian years. The unit of the epact must be counted as
tithi for the tables to match the calendar.
External links
alternative site
- Epacts from the Catholic Encyclopedia
The Catholic Encyclopedia, also referred to today as the Old Catholic Encyclopedia, is an English-language encyclopedia published in the United States. The first volume appeared in March 1907 and it was completed in April 1914...