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Uses of Radioactive Isotopes. The second half-line gives the ferial regular , or weekday displacement, of the day of that year's paschal full moon from the concurrent , or the weekday of 24 March. For Julian dates before and after , the year in the table that differs by an exact multiple of years is used. For Gregorian dates after ,the year in the table that differs by an exact multiple of years is used. The values " r0 " through " r6 " indicate the remainder when the Hundreds value is divided by 7 and 4 respectively, indicating how the series extend in either direction.

Both Julian and Gregorian values are shown — for convenience. If a year ends in 00 and its hundreds are in bold it is a leap year. Thus 19 indicates that is not a Gregorian leap year, but 19 in the Julian column indicates that it is a Julian leap year, as are all Julian x 00 years.

Use Jan and Feb only in leap years.

Note that the date and hence the day of the week in the Revised Julian and Gregorian calendars is the same up until 28 February , and that for large years it may be possible to subtract or a multiple thereof before starting so as to reach a year within or closer to the table. To look up the weekday of any date for any year using the table, subtract from the year, divide the number obtained by , multiply the resulting quotient omitting fractions by seven and divide the product by nine. Note the quotient omitting fractions.

Enter the table with the Julian year, and just before the final division add 50 and subtract the quotient noted above. For remaining digits To find the dominical letter , calculate the day of the week for either 1 January or 1 October. If it is Sunday, the Sunday Letter is A, if Saturday B, and similarly backwards through the week and forwards through the alphabet to Monday, which is G. Leap years have two letters, so for January and February calculate the day of the week for 1 January and for March to December calculate the day of the week for 1 October.

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Revised Julian calendar — all years divisible by , except those with a remainder of or when divided by When expressing Easter algorithms without using tables, it has been customary to employ only the integer operations addition , subtraction , multiplication , division , modulo , and assignment plus minus times div mod assign. That is compatible with the use of simple mechanical or electronic calculators.

But it is an undesirable restriction for computer programming, where conditional operators and statements, as well as look-up tables, are always available. More importantly, using such conditionals also simplifies the core of the Gregorian calculation. In , the mathematician Carl Friedrich Gauss presented this algorithm for calculating the date of the Julian or Gregorian Easter.

In he limited his algorithm to the 18th and 19th centuries only, and stated that 26 April is always replaced with 19 April and 25 April by 18 April. In he thanked his student Peter Paul Tittel for pointing out that p was wrong in the original version. An analysis of the Gauss's Easter algorithm is divided into two parts. The first part is the approximate tracking of the lunar orbiting and the second one is the exact, deterministic offsetting to obtain a Sunday following the full moon.

The first part consists of determining the variable d , the number of days counting from March 21 for the closest following full moon to occur. The formula for d contains the terms 19 a and the constant M. In older times, 19 calendar years were equated to lunar months the Metonic cycle , which is remarkably close since lunar months are approximately The year cycle has nothing to do with the '19' in 19 a , it is just a coincidence that another '19' appears.

The '19' in 19 a comes from correcting the mismatch between a calendar year and an integer number of lunar months. The difference is 11 days, which must be corrected for by moving the following year's occurrence of a full moon 11 days back. But in modulo 30 arithmetic, subtracting 11 is the same as adding 19, hence the addition of 19 for each year added, i.

The range of days considered for the full moon to determine Easter are 21 March the day of the ecclesislastical equinox of spring to 19 April—a day range mirrored in the mod 30 arithmetic of variable d and constant M , both of which can have integer values in the range 0 to Once d is determined, this is the number of days to add to 21 March the earliest possible full moon allowed, which is coincident with the ecclesiastical equinox of spring to obtain the day of the full moon.

The second part is finding e , the additional offset days that must be added to the date offset d to make it arrive at a Sunday. Since the week has 7 days, the offset must be in the range 0 to 6 and determined by modulo 7 arithmetic. These constants may seem strange at first, but are quite easily explainable if we remember that we operate under mod 7 arithmetic. Hence, each consecutive year, the weekday "slides one day forward", meaning if May 6 was a Wednesday one year, it is a Thursday the following year disregarding leap years.

Both b and c increases by one for an advancement of one year disregarding modulo effects. And to subtract by 1 is exactly what is required for a normal year — since the weekday slips one day forward we should compensate one day less to arrive at the correct weekday i. For a leap year, b becomes 0 and 2 b thus is 0 instead of 8—which under mod 7, is another subtraction by 1—i. The expression 6 d works the same way. Increasing d by some number y indicates that the full moon occurs y days later this year, and hence we should compensate y days less.

Adding 6 d is mod 7 the same as subtracting d , which is the desired operation.

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Thus, again, we do subtraction by adding under modulo arithmetic. In total, the variable e contains the step from the day of the full moon to the nearest following Sunday, between 0 and 6 days ahead. The constant N provides the starting point for the calculations for each century and depends on where Jan 1, year 1 was implicitly located when the Gregorian calendar was constructed.

This means that 26 April is never Easter Sunday and that 19 April is overrepresented. These latter corrections are for historical reasons only and has nothing to do with the mathematical algorithm. Using the Gauss's Easter algorithm for years prior to is historically pointless since the Gregorian calendar was not utilised for determining Easter before that year.

Using the algorithm far into the future is questionable, since we know nothing about how different churches will define Easter that far ahead. Easter calculations are based on agreements and conventions, not on the actual celestial movements nor on indisputable facts of history.

## Pre/Post-Test Key

In the New Scientist published a version of the Nature algorithm incorporating a few changes. Some tidying results in the replacement of variable o to which one must be added to obtain the date of Easter with variable p , which gives the date directly. Jean Meeus, in his book Astronomical Algorithms , p.

Faster and more compact algorithms for Gregorian Easter Sunday exist. From Wikipedia, the free encyclopedia. Retrieved 13 April Retrieved 9 August A History of the Christian Councils , pp. The Reckoning of Time , Liverpool: Cyprus Action Network of America. A Choice of Hallelujahs". The Reckoning of Time. Retrieved 28 October Retrieved 9 August — via Google Books. Baker and Michael Lapidge, eds. The reckoning of time , tr.

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Liverpool University Press, p. Spencer Jones, General Astronomy London: Longsman, Green, Archived from the original on 27 February Blackburn, Bonnie, and Holford-Strevens, Leofranc. The Oxford Companion to the Year: An exploration of calendar customs and time-reckoning.

First published , reprinted with corrections The Ordering of Time: In the fifth volume of Opera Mathematica Gregorian reform of the calendar: Proceedings of the Vatican conference to commemorate its th anniversary, — , Vatican City: Pontifical Academy of Sciences, Specolo Vaticano, Revised and edited with a new introduction by Andrew Louth. Penguin Books, London, Neue Folge, Band viii. Weidmannsche Buchhandlung , Berlin, Stern, Sacha, Calendar and Community: Liturgical year of the Catholic Church.

Based on the General Roman Calendar Computus Liturgical colours Solemnity Older calendars: Time in religion and mythology. Retrieved from " https: Calendar algorithms Easter date Christian terminology. Articles containing Ancient Greek-language text CS1: Julian—Gregorian uncertainty Articles with French-language external links Use dmy dates from June Commons category link is on Wikidata Articles with German-language external links.

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