 | This articleneeds additional citations forverification. Please helpimprove this article byadding citations to reliable sources. Unsourced material may be challenged and removed. Find sources: "Epact" – news ·newspapers ·books ·scholar ·JSTOR(May 2018) (Learn how and when to remove this message) |
Theepact (Latin:epactae, fromAncient Greek:ἐπακται ἡμεραι (epaktai hēmerai) = added days) used to be described by medievalcomputists as the age of aphase of the Moon in days on 22 March;[1] in the newerGregorian calendar, however, the epact is reckoned as the age of theecclesiastical moon on 1 January.[2] Its principal use is in determining thedate of Easter by computistical methods. It varies (usually by 11 days) from year to year, because of the difference between the solar year of 365–366 days and the lunar year of 354–355 days.[3]
Epacts can also be used to relate dates in the lunar calendar to dates in the common solar calendar.
Asolar calendar year has 365 days (366 days inleap years). Alunar calendar year has 12 lunar months which alternate between 30 and 29 days for a total of 354 days (in leap years, one of the lunar months has a day added; since a lunar year lasts a little over354+1/3 days, a leap year arises every second or third year rather than every fourth.)
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 orintercalary) 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]
Thesolar calendar year is slightly shorter than365+ 1 /4 days, while thesynodic month, on average, is slightly longer than29+ 1 /2 days meaning both are non-integers. This gets corrected in the following way. Nineteen tropical years are deemed to be as long as 235 synodic months (Metonic cycle). 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 (209modulo 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 thesaltus lunae ("leap of the moon"). The sequence number of the year in the 19-year cycle is called thegolden number. The extra 209 days fill 7 embolismic months, for a total of19 × 12 + 7 = 235 lunations.
When theGregorian calendar reform wasinstituted 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 byAloysius Lilius.[4]There were two adjustments to the old lunar cycle:
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 of29+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 bullInter 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.
The explicit formula for the numerical value of the Gregorian epact can be derived from the solar and lunar equations.[5]For a given year define, respectively, the century number and the golden number,
The epact is then given by
For 2026 the century number is 21.
For 2026 the golden number is 13.
The Gregorian epact of 2026 is (143 - 15 + 6 + 27) mod 30 = 161 mod 30 = 11.
The discovery of the epact for computing the date of Easter has been attributed toPatriarchDemetrius 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-yearluni-solar cycle.[6]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.[6] Augustalis, whose dates had been disputed from the third to the fifth century,[7](pp 224–228)computed alaterculus ("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, hislaterculus extends from 213–312 AD and Augustalis originated the use of epacts to compute the date of Easter.[8](pp 40–45)
As early as the fourth century we see Eastercomputus using the epact and the nineteen-yearMetonic cycle in Alexandria, and subsequent computistical tables were influenced by the structure of theAlexandrian calendar. The epact was taken as the age of the Moon on 26 Phamenoth (22 March in the Julian calendar) but that value of the epact also corresponded to the age of the Moon on the lastepagomenal day of the preceding year. Thus the epact can be seen as having been established at the beginning of the current year.[7](pp75–80) Subsequent Easter tables, such as those of BishopTheophilus of Alexandria, which covered 100 years beginning in 380 AD, and of his successor BishopCyril, which covered 95 years beginning in 437 AD discussed the computation of the epact in their introductory texts. Under the influence ofDionysius Exiguus and later, ofBede, theAlexandrian Easter Tables were adopted throughout Europe where they established the convention that the epact was the age of the Moon on 22 March.[8](p 52) This Dionysian epact fell into disuse after the introduction of a perpetual calendar based on thegolden number, which made the calculation of epacts unnecessary for ordinary computistical calculations.[9]
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 theGregorian reform of the calendar in 1582, two additional epacts came into use. The first was the Lilian epact, developed byAloisius Lilius as an element of the ecclesiastical computations using the Gregorian calendar. The Lilian epact included corrections for the motions of the Sun and the Moon that broke the fixed relationship between the epact and the golden number. The second new epact was a simple adjustment of the practical Julian epact to account for the ten-day change produced by the Gregorian Calendar.[9]
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.
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).
.png)