Epact
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The epact (
Lunar calendar
Epacts can also be used to relate dates in the lunar calendar to dates in the common solar calendar.
Solar and lunar years
A
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. These excess days are epacts, and have to be added to the lunar year to complete the solar year; or from the complementary perspective they are added to the day of the solar year to determine the day in the lunar year.
After two years the difference is 22 days, and after 3 years, 33 days. Whenever the epact reaches or exceeds 30 days, an extra (embolismic or intercalary) lunar month is inserted into the lunar calendar, and the epact is reduced by 30 days.
Leap days extend both the solar and lunar year, so they do not affect epact calculations for any other dates.[further explanation needed]
19-year cycle
The
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 modulo 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 ("leap of the moon"). The sequence number of the year in the 19-year cycle is called the golden number. The extra 209 days fill 7 embolismic months, for a total of 19 × 12 + 7 = 235 lunations.
Lilian (Gregorian) epacts
When the Gregorian calendar reform was instituted in 1582, the lunar cycle previously used with the Julian calendar to complete the calculation of Easter dates was adjusted also, in accordance with a (modification of the) scheme devised by Aloysius Lilius.[4] There were two adjustments to the old lunar cycle:
- a "solar equation", decrementing the epact by 1, whenever the Gregorian calendar drops a leap day (3 times in 400 calendar years), and
- a "lunar equation", incrementing the epact by 1, 8 times in 2500 calendar years (7 times after an interval of 300 years, and the 8th time after an interval of 400 years).
The revised "solar equation" was intended to adjust for the Gregorian change in the solar calendar, if they were applied at 1 January of the Julian calendar instead of the Gregorian calendar as the reformers implemented it; moreover the corrections to the solar calendar are leap days, whereas there are 30 epact values for a mean lunar month of 29+1/2 days and a bit: Therefore changing the epact by 1 day does not exactly compensate for a dropped leap day. The "lunar equation" only approximately adjusts for what had (by 1582) been seen after many centuries of recording, that the Moon moves a little faster than the expectation of the rate used for it in the old lunar cycle. By 1582 it was noted (for example, in the text of the bull Inter gravissimas itself) that the new and full moons were at that point occurring "four days and something more" sooner than the old lunar cycle indicated.
History
The discovery of the epact for computing the date of Easter has been attributed to Patriarch Demetrius I of Alexandria, who held office from 189–232 AD. In the year 214 he used the epact to produce an Easter calendar, which has not survived, which used an eight-year luni-solar cycle.[5] A subsequent application of the epact to an Easter calendar, using a sixteen-year cycle, is found in the Paschal Table of Hippolytus, a 112 year list of Easter dates beginning in the year 222 which is inscribed on the side of a statue found in Rome.[5] Augustalis, whose dates had been disputed from the third to the fifth century,[6](pp 224–228) computed a laterculus ("little tablet") of Easter dates. As reconstructed, it uses epacts (here the age of the moon on 1 January) and an 84 year luni-solar cycle to compute the dates of Easter using a base date of 213 AD. If we accept Augustalis's earlier dates, his laterculus extends from 213–312 AD and Augustalis originated the use of epacts to compute the date of Easter.[7](pp 40–45)
As early as the fourth century we see Easter
Two factors led to the creation of three new forms of the epact in the fifteenth and sixteenth centuries. The first was the increasing error of computistical techniques, which led to the introduction of a new Julian epact around 1478 AD, to be used for practical computations of the phase of the Moon for medical or astrological purposes. With the
See also
- Computus
- Wikisource English translation of the (Latin) 1582 papal bull 'Inter gravissimas' instituting Gregorian calendar reform
References
- ISBN 0-85323-693-3,
The epacts noted in the 19-year cycle specifically stand for the age of the moon on the 11th kalends of April [22 March], the beginning of the Paschal feast.
- ISBN 978-1-891389-85-6, archived from the original(PDF) on 2019-04-30, retrieved 2017-01-24,
The Epact of a year … is the age in days (0 to 29) of the ecclesiastical moon on the first day of the year (January 1).
- ^ Latin text and French translation of the Second Canon of the Gregorian calendar
- ^
Moyer, G. (1983). "Aloysius Lilius and the Compendium novae rationis restituendi kalendarium" (PDF). In Coyne, George V.; Hoskin, Michael A.; Pedersen, O. (eds.). Gregorian Reform of the Calendar. Vatican Conference to commemorate [the Gregorian Reform's] 400th Anniversary, 1582–1982 (PDF). Vatican City, IT: Pontifical Academy of Sciences, Vatican Observatory. p. 171. Archived from the original(PDF) on 16 November 2019. Retrieved 20 January 2024.
- ^ a b
Mosshammer, Alden A. (2008). "The 8 year cycle and the invention of the epacts". The Easter Computus and the Origins of the Christian Era. Oxford Early Christian Studies. Oxford, UK: Oxford University Press. pp. 109–125. ISBN 978-0-19-954312-0.
- ^ a b
Mosshammer, Alden A. (2008). The Easter Computus and the Origins of the Christian Era. Oxford Early Christian Studies. Oxford, UK: Oxford University Press. pp. 39–40, 109–125, 224–228. ISBN 978-0-19-954312-0.
- ^ a b
Coyne, G.V.; Hoskin, M.A.; Pedersen, O. (eds.). Gregorian Reform of the Calendar. Vatican Conference to commemorate [the Gregorian Reform's] 400th Anniversary, 1582–1982 (PDF). Vatican City, IT: Pontifical Academy of Sciences, Vatican Observatory (published 1983). pp. 39–59. Archived from the original(PDF) on 25 May 2015. Retrieved 13 May 2023.
- ^ a b .
External links
- Epacts from the Catholic Encyclopedia