Date of Easter

[5] It was originally feasible for the entire Christian Church to receive the date of Easter each year through an annual announcement by the pope.

By the early third century, however, communications in the Roman Empire had deteriorated to the point that the church put great value in a system that would allow the clergy to determine the date for themselves, independently yet consistently.

[6] Additionally, the church wished to eliminate dependencies on the Hebrew calendar, by deriving the date for Easter directly from the March equinox.

A possible consequence of this intercalation is that 14 Nisan could occur before the equinox, which some third-century Christians considered unacceptable (this cannot happen in the fixed calendar in use today).

[12] Consequently, it was decided to separate the dating of Easter from the Hebrew calendar, by identifying the first full moon following the March equinox.

By the time of the First Council of Nicaea (AD 325), the Church of Alexandria had designated 21 March as an ecclesiastical date for the equinox, irrespective of actual astronomical observation.

[a] Although a process based on the 19-year Metonic cycle was first proposed by Bishop Anatolius of Laodicea around 277, the concept did not fully take hold until the Alexandrian method became authoritative in the late 4th century.

Charles Wheatly provides the detail: "Thus beginning the year with March (for that was the ancient custom) they allowed thirty days for the moon [ending] in March, and twenty-nine for that [ending] in April; and thirty again for May, and twenty-nine for June &c. according to the old verses: Impar luna pari, par fiet in impare mense; In quo completur mensi lunatio detur.

The Julian calendar handles it by reducing the length of the lunar month that begins on 1 July in the last year of the cycle to 29 days.

Its fourteenth day, therefore, always falls on a date between 21 March and 18 April inclusive (in the Gregorian or Julian calendar, for the Western and Eastern system, resp.

Then label all dates with a Roman numeral counting downwards, from "*" (0 or 30), "xxix" (29), down to "i" (1), starting from 1 January, and repeat this to the end of the year.

Treat the 13th period (last eleven days) as long, therefore, and assign the labels "xxv" and "xxiv" to sequential dates (26 and 27 December respectively).

To avoid this, in years that have epacts 25 and with a Golden Number larger than 11, the reckoned new moon falls on the date with the label 25 rather than xxv.

The reason for moving around the epact label "xxv/25" rather than any other seems to be the following: According to Dionysius (in his introductory letter to Petronius), the Nicene council, on the authority of Eusebius, established that the first month of the ecclesiastical lunar year (the paschal month) should start between 8 March and 5 April inclusive, and the 14th day fall between 21 March and 18 April inclusive, thus spanning a period of (only) 29 days.

Lilius's original work has not been preserved, but his proposal was described in the Compendium Novae Rationis Restituendi Kalendarium circulated in 1577, in which it is explained that the correction system he devised was to be a perfectly flexible tool in the hands of future calendar reformers, since the solar and lunar calendar could henceforth be corrected without mutual interference.

In Britain, where the Julian calendar was then still in use, Easter Sunday was defined, from 1662 to 1752 (in accordance with previous practice), by a simple table of dates in the Anglican Book of Common Prayer (decreed by the Act of Uniformity 1662).

For the British Empire and colonies, the new determination of the date of Easter Sunday was defined by what is now called the Calendar (New Style) Act 1750 in an annexe that declares its effect on the Book of Common Prayer.

[55] The annexe to the act includes the definition: "Easter-day (on which the rest depend) is always the first Sunday after the Full Moon, which happens upon, or next after the Twenty-first Day of March.

The claim by the Catholic Church in the 1582 papal bull Inter gravissimas, which promulgated the Gregorian calendar, that it restored "the celebration of Easter according to the rules fixed by ... the great ecumenical council of Nicaea"[59] was based on a false claim by Dionysius Exiguus (525) that "we determine the date of Easter Day ... in accordance with the proposal agreed upon by the 318 Fathers of the Church at the Council in Nicaea.

[citation needed] Francia (all of western Europe except Scandinavia (pagan), the British Isles, the Iberian Peninsula, and southern Italy) accepted it during the last quarter of the eighth century.

The range of dates in the Gregorian calendar of the Eastern Paschal full moon moves one day later every time there is a solar correction, so from 2100 to 2199 it will be 5 April to 9 May.

Due to the discrepancies between the approximations of Computistical calculations of the time of the mean (northern hemisphere) vernal equinox and the lunar phases, and the true values computed according to astronomical principles, differences occasionally arise between the date of Easter according to computistical reckoning and the hypothetical date of Easter calculated by astronomical methods using the principles attributed to the Church fathers.

[67] In his Kalendarium of 1474, Regiomontanus computed the exact time of all conjunctions of the Sun and Moon for the longitude of Nuremberg according to the Alfonsine Tables for the period from 1475 to 1531.

[68] The discrepancies are even larger if there is a difference according to the vernal equinox with respect to astronomical theory and the approximation of the computus.

[68] Equinoctial paradoxes are always valid globally for the whole Earth, because the sequence of equinox and full moon does not depend on the geographical longitude.

In contrast, weekly paradoxes are local in most cases and are valid only for part of the Earth, because the change of day between Saturday and Sunday is dependent on the geographical longitude.

[69] When expressing Easter algorithms without using tables, it has been customary to employ only the integer operations addition, subtraction, multiplication, division, modulo, and assignment as it is compatible with the use of simple mechanical or electronic calculators.

The constant N provides the starting point for the calculations for each century and depends on where 1 January, year 1 was implicitly located when the Gregorian calendar was constructed.

For reasons of historical compatibility, all offsets of 35 and some of 34 are subtracted by 7, jumping one Sunday back to the day of the full moon (in effect using a negative e of −1).

[73][74] It has been reprinted many times, e.g., in 1877 by Samuel Butcher in The Ecclesiastical Calendar,[75] in 1916 by Arthur Downing in The Observatory,[76] in 1922 by H. Spencer Jones in General Astronomy,[77] in 1977 by the Journal of the British Astronomical Association,[78] in 1977 by The Old Farmer's Almanac, in 1988 by Peter Duffett-Smith in Practical Astronomy with your Calculator, and in 1991 by Jean Meeus in Astronomical Algorithms.