Thursday, November 13, 2014

Article Number: 9948


-Date: 29 Aug 1996 06:39:37 GMT



-From: ct@login.dknet.dk (Claus Tondering)



-Newsgroups: sci.astro,soc.history,sci.answers,soc.answers,news.answers



-Followup-To: sci.astro,soc.history



-Subject: Calendar FAQ, v. 1.3 (modified 20 Aug 1996)





Archive-name: calendars/faq



Posting-Frequency: monthly



Last-modified: 1996/08/20



Version: 1.3



URL: ftp://login.dknet.dk/pub/ct/calendar.faq





FREQUENTLY ASKED QUESTIONS ABOUT



CALENDARS





Version 1.3 - 20 Aug 1996





Copyright and disclaimer



------------------------



This document is Copyright (C) 1996 by Claus Tondering.



E-mail: ct@login.dknet.dk.



The document may be freely distributed, provided this



copyright notice is included and no money is charged for



the document.





This document is provided "as is". No warranties are made as



to its correctness.





Introduction



------------



This is the calendar FAQ. Its purpose is to give an overview



of the Christian, Hebrew, and Islamic calendars in common



use. It will also provide a historical background for the



Christian calendar.





Comments are very welcome. My e-mail address is given above.





I would like to thank



- Dr. Monzur Ahmed of the University of Birmingham, UK,



- Michael J Appel,



- Chris Carrier,



- H. Koenig,



- Marcos Montes,



- Waleed A. Muhanna of the Fisher College of Business,



Columbus, Ohio, USA,



- Paul Schlyter of the Swedish Amateur Astronomer's Society



for their help with this document.





Changes since version 1.2



-------------------------



A few minor corrections. Especially in the articles about the



Roman and French Revolutionary calendars.





Writing dates and years



-----------------------



Dates will be written in the British format (1 January)



rather than the American format (January 1). Dates will



occasionally be abbreviated: "1 Jan" rather than "1 January".





Years before and after the "official" birth year of Christ



will be written "45 BC" or "AD 1996", respectively. I prefer



this notation over the secular "45 B.C.E." and "1996 C.E."





The % operator



--------------



Throughout this document the operator % will be used to



signify the modulo or remainder operator. For example, 17%7=3



because the result of the division 17/7 is 2 with a remainder



of 3.





The text in square brackets



---------------------------



Square brackets [like this] identify information that I am



unsure about and about which I would like more



information. Please write me at ct@login.dknet.dk.







Index:



------



1. What astronomical events form the basis of calendars?



2. The Christian calendar



2.1. What is the Julian calendar?



2.1.1. What years are leap years?



2.1.2. What consequences did the use of the Julian



calendar have?



2.2. What is the Gregorian calendar?



2.2.1. What years are leap years?



2.2.2. Isn't there a 4000-year rule?



2.2.3. Don't the Greek do it differently?



2.2.4. When did country X change from the Julian to



the Gregorian calendar?



2.3. What day is the leap day?



2.4. What is the Solar Cycle?



2.5. What day of the week was 2 August 1953?



2.6. What is the Roman calendar?



2.6.1. How did the Romans number days?



2.7. Has the year always started on 1 January?



2.8. What is the origin of the names of the months?



2.9. What is Easter?



2.9.1. When is Easter? (Short answer)



2.9.2. When is Easter? (Long answer)



2.9.3. What is the Golden Number?



2.9.4. What is the Epact?



2.9.5. How does one calculate Easter then?



2.9.6. Isn't there a simpler way to calculate Easter?



2.9.7. Is there a simple relationship between two



consecutive Easters?



2.9.8. How frequently are the dates for Easter repeated?



2.9.9. What about Greek Easter?



2.10. How does one count years?



2.10.1. Was Jesus born in the year 0?



2.10.2. When does the 21st century start?



2.11. What is the Indiction?



2.12. What is the Julian period?



2.12.1. What is the modified Julian day?



3. The Hebrew Calendar



3.1. What does a Hebrew year look like?



3.2. What years are leap years?



3.3. What years are deficient, regular, and complete?



3.4. When is New Year's day?



3.5. When does a Hebrew day begin?



3.6. When does a Hebrew year begin?



3.7. When is the new moon?



3.8. How does one count years?



4. The Islamic Calendar



4.1. What does an Islamic year look like?



4.2. So you can't print an Islamic calendar in advance?



4.3. How does one count years?



5. The French Revolutionary Calendar



5.1. What does a Republican year look like?



5.2. How does one count years?



5.3. What years are leap years?



5.4. How does one convert a Republican date to a Gregorian one?



6. Date







1. What astronomical events form the basis of calendars?



--------------------------------------------------------





Calendars are normally based on astronomical events, and the two most



important astronomical objects are the sun and the moon. Their cycles



are very important in the construction and understanding of calendars.





Our concept of a year is based on the earth's motion around the sun.



The time from one winter solstice to the next is called a "tropical



year". Its length is currently 365.242190 days, but it varies. Around



1900 its length was 365.242196 days, and around 2100 it will be



365.242184 days.





Our concept of a month is based on the moon's motion around the earth,



although this connection has been broken in the calendar commonly used



now. The time from one new moon to the next is called a "synodic



month", and its length is currently 29.5305889 days, but it



varies. Around 1900 its length was 29.5305886 days, and around 2100 it



will be 29.5305891 days.





Note that these numbers are averages. The actual length of a



particular year may vary by several minutes due to the influence of



the gravitational force from other planets. Similary, the time between



two new moons may vary by several hours due to the eccentricity of the



lunar orbit.





It is unfortunate that the length of the tropical year is not a



multiple of the length of the synodic month. This means that with 12



months per year, the relationship between our month and the moon



cannot be maintained.





However, 19 tropical years is 234.997 synodic months, which is very



close to an integer. So every 19 years the phases of the moon fall on



the same dates (if it were not for the skewness introduced by leap



years). 19 years is called a Metonic cycle (after Meton, an astronomer



from Athens in the 5th century BC).





So, to summarise: There are three important numbers to note:



A tropical year is 365.2422 days.



A synodic month is 29.53059 days.



19 tropical years is close to an integral number of synodic months.





The Christian calendar is based on the motion of the earth around the



sun, while the months have no connection with the motion of the moon.





On the other hand, the Islamic calendar is based on the motion of the



moon, while the year has no connection with the motion of the earth



around the sun.





Finally, the Hebrew calendar combines both, in that its years are



linked to the motion of the earth around the sun, and its months are



linked to the motion of the moon.







2. The Christian calendar



-------------------------





The "Christian calendar" is the term I use to designate the calendar



commonly in use, although its connection with Christianity is highly



debatable.





The Christian calendar has years of 365 or 366 days. It is divided into



12 months that have no relationship to the motion of the moon. In



parallel with this system, the concept of "weeks" groups the days in



sets of 7.





Two main versions of the Christian calendar have existed in recent



times: The Julian calendar and the Gregorian calendar. The difference



between them lies in the way they approximate the length of the



tropical year and their rules for calculating Easter.







2.1. What is the Julian calendar?



---------------------------------





The Julian calendar was introduced by Julius Caesar in 45 BC. It was



in common use until the 1500s, when countries started changing to the



Gregorian calendar (section 2.2). However, some countries (for



example, Greece and Russia) used it into this century, and the



Orthodox church in Russia still uses it, as do some other Orthodox



churches.





In the Julian calendar, the tropical year is approximated as 365 1/4



days = 365.25 days. This gives an error of 1 day in approximately 128



years.





The approximation 365 1/4 is achieved by having 1 leap year every 4



years.







2.1.1. What years are leap years?



---------------------------------





The Julian calendar has 1 leap year every 4 years. This means that:





Every year divisible by 4 is a leap year.





However, this rule was not followed in the first years after the



introduction of the Julian calendar in 45 BC. Due to a counting error,



every 3rd year was a leap year in the first years of this calendar's



existence. The leap years were:





45 BC, 42 BC, 39 BC, 36 BC, 33 BC, 30 BC,



27 BC, 24 BC, 21 BC, 18 BC, 15 BC, 12 BC, 9 BC,



AD 8, AD 12, and every 4th year from then on.





There were no leap years between 9 BC and AD 8. This period without



leap years was decreed by emperor Augustus and earned him a place in



the calendar as the 8th month was named after him.





It is a curious fact that although the method of reckoning years after



the (official) birthyear of Christ was not introduced until the 6th



century, by some stroke of luck the Julian leap years coincide with



years of our Lord that are divisible by 4. (But, of course, this may



been deliberate on the part of Dionysius Exiguus who introduced our



current year reckoning.)







2.1.2. What consequences did the use of the Julian calendar have?



-----------------------------------------------------------------





The Julian calendar introduces an error of 1 day every 128 years. So



every 128 years the vernal equinox moved one day backwards in the



calendar. Furthermore, the method for calculating the dates for Easter



was inaccurate and needed to be refined.





In order to remedy this, two steps were necessary: 1) The Julian



calendar had to be replaced by something more adequate. 2) The extra



days that the Julian calendar had inserted had to be dropped.





The solution to problem 1) was the Gregorian calendar described in



section 2.2.





The solution to problem 2) depended on the fact that it was felt that



21 March was the proper day for vernal equinox (because 21 March was



the date for vernal equinox during the Council of Nicaea in AD



325). The Gregorian calendar was therefore calibrated to make that day



vernal equinox.





By 1582 vernal equinox had moved (1582-325)/128 days = approximately



10 days backwards. So 10 days had to be dropped.





[Dropping 10 days in the 1500s brought the Gregorian calendar in sync



with the Julian calendar of the 3rd century. But AD 325 is in the 4th



century. Was that deliberate?]







2.2. What is the Gregorian calendar?



------------------------------------





The Gregorian calendar is the one commonly used today. It was decreed



by Pope Gregory XIII in a papal bull in February 1582.





In the Gregorian calendar, the tropical year is approximated as



365 97/400 days = 365.2425 days. This gives an error of 1 day in



approximately 3300 years.





The approximation 365 97/400 is achieved by having 97 leap years



every 400 years.







2.2.1. What years are leap years?



---------------------------------





The Gregorian calendar has 97 leap years every 400 years. This means



that:



Every year divisible by 4 is a leap year.



However, every year divisible by 100 is not a leap year.



However, every year divisible by 400 is a leap year after all.





So, 1700, 1800, 1900, 2100, and 2200 are not leap years. But 1600,



2000, and 2400 are leap years.





(Destruction of a myth: There are no double leap years, i.e. no



years with 367 days. See, however, the note on Sweden in section



2.2.4.)







2.2.2. Isn't there a 4000-year rule?



------------------------------------





It has been suggested (by the astronomer William Herschel (1738-1822)



among others) that a better approximation to the length of the



tropical year would be 365 969/4000 days = 365.24225 days. This would



dictate 969 leap years every 4000 years, rather than the 970 leap



years mandated by the Gregorian calendar. This could be achieved by



dropping one leap year from the Gregorian calendar every 4000 years,



which would make years divisible by 4000 non-leap years.





This rule has, however, not been officially adopted.







2.2.3. Don't the Greek do it differently?



-----------------------------------------





When the Orthodox church in Greece finally decided to switch to the



Gregorian calendar in the 1920s, they tried to improve on the



Gregorian leap year rules, replacing the "divisible by 400" rule by



the following:





Every year which when divided by 900 leaves a remainder of 200



or 600 is a leap year.





This makes 1900, 2100, 2200, 2300, 2500, 2600, 2700, 2800 non-leap



years, whereas 2000, 2400, and 2900 are leap years. This will not



create a conflict with the rest of the world until the year 2800.





This rule gives 218 leap years every 900 years, which gives us an



average year of 365 218/900 days = 365.24222 days, which is certainly



more accurate than the official Gregorian number of 365.2425 days.





However, to my knowledge, this rule is *not* official in Greece. [Is



this true?]





[I have received an e-mail indicating that this system is official in



Russia today. I'm investigating that. Information is very welcome.]







2.2.4. When did country X change from the Julian to the Gregorian calendar?



---------------------------------------------------------------------------





The papal bull of February 1582 decreed that 10 days should be dropped



from October 1582 so that 15 October should follow immediately after



4 October, and from then on the reformed calendar should be used.





This was observed in Italy, Poland, Portugal, and Spain. Other Catholic



countries followed shortly after, but Protestant countries were



reluctant to change, and the Greek orthodox countries didn't change



until the start of this century.









Changes in the 1500s required 10 days to be dropped.



Changes in the 1600s required 10 days to be dropped.



Changes in the 1700s required 11 days to be dropped.



Changes in the 1800s required 12 days to be dropped.



Changes in the 1900s required 13 days to be dropped.





(Exercise for the reader: Why is the error in the 1600s the same as



in the 1500s.)





The following list contains the dates for changes in a number of



countries.





Albania: December 1912





Austria: Different regions on different dates



5 Oct 1583 was followed by 16 Oct 1583



14 Dec 1583 was followed by 25 Dec 1583





Belgium: Different authorities say



14 Dec 1582 was followed by 25 Dec 1582



21 Dec 1582 was followed by 1 Jan 1583





Bulgaria: Different authorities say



Sometime in 1912



Sometime in 1915



18 Mar 1916 was followed by 1 Apr 1916





China: Different authorities say



18 Dec 1911 was followed by 1 Jan 1912



18 Dec 1928 was followed by 1 Jan 1929





Czechoslovakia (i.e. Bohemia and Moravia):



6 Jan 1584 was followed by 17 Jan 1584





Denmark (including Norway):



18 Feb 1700 was followed by 1 Mar 1700





Egypt: 1875





Estonia: January 1918





Finland: Then part of Sweden. (Note, however, that Finland later



became part of Russia, which then still used the



Julian calendar. The Gregorian calendar remained



official in Finland, but some use of the Julian



calendar was made.)





France: 9 Dec 1582 was followed by 20 Dec 1582





Germany: Different states on different dates:



Catholic states on various dates in 1583-1585



Prussia: 22 Aug 1610 was followed by 2 Sep 1610



Protestant states: 18 Feb 1700 was followed by 1 Mar 1700





Great Britain and Dominions (including what is now the USA):



2 Sep 1752 was followed by 14 Sep 1752





Greece: 9 Mar 1924 was followed by 23 Mar 1924





Hungary: 21 Oct 1587 was followed by 1 Nov 1587





Italy: 4 Oct 1582 was followed by 15 Oct 1582





Japan: Different authorities say:



19 Dec 1872 was followed by 1 Jan 1873



18 Dec 1918 was followed by 1 Jan 1919





Latvia: During German occupation 1915 to 1918





Lithuania: 1915





Luxemburg: 14 Dec 1582 was followed by 25 Dec 1582





Netherlands:



Brabant, Flanders, Holland, Artois, Hennegau:



14 Dec 1582 was followed by 25 Dec 1582



Geldern, Friesland, Zeuthen, Groningen, Overysel:



30 Nov 1700 was followed by 12 Dec 1700





Norway: Then part of Denmark.





Poland: 4 Oct 1582 was followed by 15 Oct 1582





Portugal: 4 Oct 1582 was followed by 15 Oct 1582





Romania: 31 Mar 1919 was followed by 14 Apr 1919





Russia: 31 Jan 1918 was followed by 14 Feb 1918





Spain: 4 Oct 1582 was followed by 15 Oct 1582





Sweden (including Finland):



17 Feb 1753 was followed by 1 Mar 1753 (see note below)





Switzerland:



Catholic cantons: 1583 or 1584



Zurich, Bern, Basel, Schafhausen, Neuchatel, Geneva:



31 Dec 1700 was followed by 12 Jan 1701



St Gallen: 1724





Turkey: 18 Dec 1926 was followed by 1 Jan 1927





USA: See Great Britain.





Yugoslavia: 1919





Sweden has a curious history. Sweden decided to make a gradual change



from the Julian to the Gregorian calendar. By dropping every leap year



from 1700 through 1740 the eleven superfluous days would be omitted



and from 1 Mar 1740 they would be in sync with the Gregorian



calendar. (But in the meantime they would be in sync with nobody!)





So 1700 (which should have been a leap year in the Julian calendar)



was not a leap year in Sweden. However, by mistake 1704 and 1708



became leap years. This left Sweden out of synchronisation with both



the Julian and the Gregorian world, so they decided to go *back* to



the Julian calendar. In order to do this, they inserted an extra day



in 1712, making that year a double leap year! So in 1712, February had



30 days in Sweden.





Later, in 1753 Sweden changed to the Gregorian calendar by dropping 11



days like everyone else.







2.3. What day is the leap day?



------------------------------





24 February!





Weird? Yes! The explanation is related to the Roman calendar and is



found in section 2.6.1.





>From a numerical point of view, of course 29 February is the extra



day. But from the point of view of celebration of feast days, the



following correspondence between days in leap years and non-leap



years exist:





Non-leap year Leap year



------------- ----------



22 February 22 February



23 February 23 February



24 February (extra day)



24 February 25 February



25 February 26 February



26 February 27 February



27 February 28 February



28 February 29 February





For example, the feast of St. Leander is celebrated on 27 February in



non-leap years and on 28 February in leap years.





The EU (European Union) in their infinite wisdom have decided that



starting in the year 2000, 29 February is to be the leap day. This



will affect countries such as Sweden and Austria that celebrate "name



days" (i.e. each day is associated with a name), but I doubt that the



EU can force the Catholic church to celebrate certain feast days for



saints on a new set of dates?







2.4. What is the Solar Cycle?



-----------------------------





In the Julian calendar the relationship between the days of the week



and the dates of the year is repeated in cycles of 28 years. In the



Gregorian calendar this is still true for periods that do not cross



years that are divisible by 100 but not by 400.





A period of 28 years is called a Solar Cycle. The "Solar Number" of a



year is found as:





Solar Number = (year + 8) % 28 + 1





In the Julian calendar there is a one-to-one relationship between the



Solar Number and the day on which a particular date falls.





(The leap year cycle of the Gregorian calendar is 400 years, which is



146,097 days, which curiously enough is a multiple of 7. So in the



Gregorian calendar the equivalent of the "Solar Cycle" would be 400



years, not 7*400=2800 years as one might be tempted to believe.)







2.5. What day of the week was 2 August 1953?



--------------------------------------------





To calculate the day on which a particular date falls, the following



algorithm may be used (the divisions are integer divisions, in which



remainders are discarded):





a = (14 - month) / 12



y = year - a



m = month + 12*a - 2



For Julian calendar: d = (5 + day + y + y/4 + (31*m)/12) % 7



For Gregorian calendar: d = (day + y + y/4 - y/100 + y/400 + (31*m)/12) % 7





The value of d is 0 for a Sunday, 1 for a Monday, 2 for a Tuesday, etc.





Example: On what day of the week was the author born?





My birthday is 2 August 1953 (Gregorian, of course).





a = (14 - 8) / 12 = 0



y = 1953 - 0 = 1953



m = 8 + 12*0 - 2 = 6



d = (2 + 1953 + 1953/4 - 1953/100 + 1953/400 + (31*6)/12) % 7



= (2 + 1953 + 488 - 19 + 4 + 15 ) % 7



= 2443 % 7



= 0





I was born on a Sunday.







2.6. What is the Roman calendar?



--------------------------------





Before Julius Caesar introduced the Julian calendar in 45 BC, the



Roman calendar was a mess, and much of our so-called "knowledge" about



it seems to be little more than guesswork.





Originally, the year started on 1 March and consisted of only 304 days



or 10 months (Martius, Aprilis, Maius, Junius, Quintilis, Sextilis,



September, October, November, and December). These 304 days were



followed by an unnamed and unnumbered winter period. The Roman king



Numa Pompilius (c. 715-673 BC) allegedly introduced February and



January (in that order) between December and March, increasing the



length of the year to 354 or 355 days. In 450 BC, February was moved



to its current position between January and March.





In order to make up for the lack of days in a year, an extra month,



Intercalans or Mercedonius, (allegedly with 22 or 23 days though some



authorities dispute this) was introduced in some years. In an 8 year



period the length of the years were:



1: 12 months or 355 days



2: 13 months or 377 days



3: 12 months or 355 days



4: 13 months or 378 days



5: 12 months or 355 days



6: 13 months or 377 days



7: 12 months or 355 days



8: 13 months or 378 days



A total of 2930 days corresponding to a year of 366 1/4 days. This



year was discovered to be too long, and therefore 7 days were later



dropped from the 8th year, yielding 365.375 days per year.





This is all theory. In practice it was the duty of the priesthood to



keep track of the calendars, but they failed miserably, partly due to



ignorance, partly because they were bribed to make certain years long



and other years short.





In order to clean up this mess, Julius Caesar made his famous calendar



reform in 45 BC. We can make an educated guess about the length of the



months in the years 47 and 46 BC:





47 BC 46 BC



January 29 29



February 28 24



Intercalans 27



March 31 31



April 29 29



May 31 31



June 29 29



Quintilis 31 31



Sextilis 29 29



September 29 29



October 31 31



November 29 29



Undecember 33



Duodecember 34



December 29 29



--- ---



Total 355 445





The length of the months from 45 BC onward were the same as the ones



we know today. Or were they?





There are two versions of the story:





1. The lengths of the months from 45 BC were the same as they are



today.





2. Julius Caesar made all odd numbered months 31 days long, and all



even numbered months 30 days long (with February having 29 days in



non-leap years). In 44 BC Quintilis was renamed "Julius" (July) in



honour of Julius Caesar, and in 8 BC Sextilis became "Augustus" in



honour of emperor Augustus. When Augustus had a month named after



him, he wanted his month to be a full 31 days long, so he removed



a day from February and shifted the length of the other months



so that August would have 31 days.





Which version is true? Some sources claim that version 2 is a 14th



century fabrication with no basis in actual fact. [Can anybody help me



here?]







2.6.1. How did the Romans number days?



--------------------------------------





The Romans didn't number the days sequentially from 1. Instead they



had three fixed points in each month:



"Kalendae" (or "Calendae"), which was the first day of the month.



"Idus", which was the 13th day of January, February, April,



June, August, September, November, and December, or



the 15th day of March, May, July, or October.



"Nonae", which was the 9th day before Idus (counting Idus



itself as the 1st day).





The days between Kalendae and Nonae were called "the 4th day before



Nonae", "the 3rd day before Nonae", and "the 2nd day before



Nonae". (The 1st day before Nonae would be Nonae itself.)





Similarly, the days between Nonae and Idus were called "the Xth day



before Idus", and the days after Idus were called "the Xth day before



Kalendae (of the next month)".





Julius Caesar decreed that in leap years the "6th day before Kalendae



of March" should be doubled. So in contrast to our present system, in



which we introduce an extra date (29 February), the Romans had the



same date twice in leap years. The doubling of the 6th day before



Kalendae of March is the origin of the word "bissextile". If we



create a list of equivalences between the Roman days and our current



days of February in a leap year, we get the following:





7th day before Kalendae of March 23 February



6th day before Kalendae of March 24 February



6th day before Kalendae of March 25 February



5th day before Kalendae of March 26 February



4th day before Kalendae of March 27 February



3rd day before Kalendae of March 28 February



2nd day before Kalendae of March 29 February



Kalendae of March 1 March





You can see that the extra 6th day (going backwards) falls on what is



today 24 February. For this reason 24 February is still today



considered the "extra day" in leap years (see section 2.3).





Why did Caesar choose to double the 6th day before Kalendae of March?



It appears that the leap month Intercalans/Mercedonius of the



pre-reform calendar was not placed after February, but inside it,



namely between the 7th and 6th day before Kalendae of March. It was



therefore natural to have the leap day in the same position.







2.7. Has the year always started on 1 January?



----------------------------------------------





For the man in the street, yes. When Julius Caesar introduced his



calendar in 45 BC, he made 1 January the start of the year, and it was



always the date on which the Solar Number and the Golden Number (see



section 2.9.3) were incremented.





However, the church didn't like the wild parties that took place at



the start of the new year, and in AD 567 the council of Tours declared



that having the year start on 1 January was an ancient mistake that



should be abolished.





Through the middle ages various New Year dates were used. If an



ancient document refers to year X, it may mean any of 8 different



periods in our present system:





- 1 Mar X to 28/29 Feb X+1



- 1 Jan X to 31 Dec X



- 1 Jan X-1 to 31 Dec X-1



- 25 Mar X-1 to 24 Mar X



- 25 Mar X to 24 Mar X+1



- Saturday before Easter X to Friday before Easter X+1



- 25 Dec X-1 to 24 Dec X



- 1 Sep X-1 to 31 Aug X [or 1 Sep X to 31 Aug X+1. Which is right?]





Choosing the right interpretation of a year number is difficult, so



much more as one country might use different systems for religious and



civil needs.





Since about 1600 most countries have used 1 January as the first day



of the year. Italy and England, however, did not make 1 January official



until around 1750.





In England (but not Scotland) three different years were used:



- The historical year, which started on 1 January.



- The liturgical year, which started on the first Sunday in advent.



- The civil year, which



from the 7th to the 12th century started on 25 December,



from the 12th century until 1751 started on 25 March,



from 1752 started on 1 January.







2.8. What is the origin of the names of the months?



---------------------------------------------------





January Latin: Januarius. Named after the god Janus.



February Latin: Februarius. Named after Februa, the purification



festival.



March Latin: Martius. Named after the god Mars.



April Latin: Aprilis. Named either after the goddess Aphrodite or



the Latin word "aperire", to open.



May Latin: Maius. Probably named after the goddess Maia.



June Latin: Junius. Probably named after the goddess Juno.



July Latin: Julius. Named after Julius Caesar in 44 BC. Prior



to that time its name was Quintilis from the word



"quintus", fifth, because it was the 5th month in the old



Roman calendar.



August Latin: Augustus. Named after emperor Augustus in 8



BC. Prior to that time the name was Sextilis from the



word "sextus", sixth, because it was the 6th month in the



old Roman calendar.



September Latin: September. From the word "septem", seven, because



it was the 7th month in the old Roman calendar.



October Latin: October. From the word "octo", eight, because it



was the 8th month in the old Roman calendar.



November Latin: November. From the word "novem", nine, because it



was the 9th month in the old Roman calendar.



December Latin: December. From the word "decem", ten, because it



was the 10th month in the old Roman calendar.







2.9. What is Easter?



--------------------





In the Christian world, Easter (and the days immediately preceding it)



is the celebration of the death and resurrection of Jesus in



(approximately) AD 30.







2.9.1. When is Easter? (Short answer)



-------------------------------------





Easter Sunday is the first Sunday after the first full moon after



vernal equinox.







2.9.2. When is Easter? (Long answer)



------------------------------------





The calculation of Easter is complicated because it is linked to (an



inaccurate version of) the Hebrew calendar.





Jesus was crucified immediately before the Jewish Passover, which is a



celebration of the Exodus from Egypt under Moses. Celebration of



Passover started on the 14th or 15th day of the (spring) month of



Nisan. Jewish months start when the moon is new, therefore the 14th or



15th day of the month must be immediately after a full moon.





It was therefore decided to make Easter Sunday the first Sunday after



the first full moon after vernal equinox. Or more precisely: Easter



Sunday is the first Sunday after the *official* full moon on or after



the *official* vernal equinox.





The official vernal equinox is always 21 March.





The official full moon may differ from the *real* full moon by one or



two days.





(Note, however, that historically, some countries have used the *real*



(astronomical) full moon instead of the official one when calculating



Easter. This was the case, for example of the German Protestant states,



which used the astronomical full moon in the years 1700-1776. A



similar practice was used Sweden in the years 1740-1844 and in Denmark



in the 1700s.)





The full moon that precedes Easter is called the Paschal full



moon. Two concepts play an important role when calculating the Pascal



full moon: The Golden Number and the Epact. They are described in the



following sections.





The following sections give details about how to calculate the date



for Easter. Note, however, that while the Julian calendar was in use,



it was customary to use tables rather than calculations to determine



Easter. The following sections do mention how to calcuate Easter under



the Julian calendar, but the reader should be aware that this is an



attempt to express in formulas what was originally expressed in



tables. The formulas can be taken as a good indication of when Easter



was celebrated in the Western Church from approximately the 6th



century.







2.9.3. What is the Golden Number?



---------------------------------





Each year is associated with a Golden Number.





Considering that the relationship between the moon's phases and the



days of the year repeats itself every 19 years (as described in



section 1), it is natural to associate a number between 1 and 19



with each year. This number is the so-called Golden Number. It is



calculated thus:



GoldenNumber = (year%19)+1





New moon will fall on (approximately) the same date in two years



with the same Golden Number.







2.9.4. What is the Epact?



-------------------------





Each year is associated with an Epact.





The Epact is a measure of the age of the moon (i.e. the number of days



that have passed since an "official" new moon) on a particular date.





In the Julian calendar, 8 + the Epact is the age of the moon at the



start of the year.



In the Gregorian calendar, the Epact is the age of the moon at the



start of the year.





The Epact is linked to the Golden Number in the following manner:





Under the Julian calendar, 19 years were assumed to be exactly an



integral number of synodic months, and the following relationship



exists between the Golden Number and the Epact:





Epact = (11 * (GoldenNumber-1)) % 30





If this formula yields zero, the Epact is by convention frequently



designated by the symbol * and its value is said to be 30. Weird?



Maybe, but people didn't like the number zero in the old days.





Since there are only 19 possible golden numbers, the Epact can have



only 19 different values: 1, 3, 4, 6, 7, 9, 11, 12, 14, 15, 17, 18, 20,



22, 23, 25, 26, 28, and 30.







The Julian system for calculating full moons was inaccurate, and under



the Gregorian calendar, some modifications are made to the simple



relationship between the Golden Number and the Epact.





In the Gregorian calendar the Epact should be calculated thus (the



divisions are integer divisions, in which remainders are discarded):





1) Use the Julian formula:



Epact = (11 * (GoldenNumber-1)) % 30





2) Adjust the Epact, taking into account the fact that 3 out of 4



centuries have one leap year less than a Julian century:



Epact = Epact - (3*century)/4





(For the purpose of this calculation century=20 is used for the



years 1900 through 1999, and similarly for other centuries,



although this contradicts the rules in section 2.10.2.)





3) Adjust the Epact, taking into account the fact that 19 years is not



exactly an integral number of synodic months:



Epact = Epact + (8*century + 5)/25





(This adds one to the epact 8 times every 2500 years.)





4) Add 8 to the Epact to make it the age of the moon on 1 January:



Epact = Epact + 8





5) Add or subtract 30 until the Epact lies between 1 and 30.





In the Gregorian calendar, the Epact can have any value from 1 to 30.





Example: What was the Epact for 1992?





GoldenNumber = 1992%19 + 1 = 17



1) Epact = (11 * (17-1)) % 30 = 26



2) Epact = 26 - (3*20)/4 = 11



3) Epact = 11 + (8*20 + 5)/25 = 17



4) Epact = 17 + 8 = 25



5) Epact = 25





The Epact for 1992 was 25.







2.9.5. How does one calculate Easter then?



------------------------------------------





To find Easter the following algorithm is used:





1) Calculate the Epact as described in the previous section.





2) For the Julian calendar: Add 8 to the Epact. (For the Gregorian



calendar, this has already been done in step 5 of the calculation of



the Epact). Subtract 30 if the sum exceeds 30.





3) Look up the Epact (as possibly modified in step 2) in this table to



find the date for the Paschal full moon:





Epact Full moon Epact Full moon Epact Full moon



----------------- ----------------- -----------------



1 12 April 11 2 April 21 23 March



2 11 April 12 1 April 22 22 March



3 10 April 13 31 March 23 21 March



4 9 April 14 30 March 24 18 April



5 8 April 15 29 March 25 18 or 17 April



6 7 April 16 28 March 26 17 April



7 6 April 17 27 March 27 16 April



8 5 April 18 26 March 28 15 April



9 4 April 19 25 March 29 14 April



10 3 April 20 24 March 30 13 April





4) Easter Sunday is the first Sunday following the above full moon



date. If the full moon falls on a Sunday, Easter Sunday is the



following Sunday.







An Epact of 25 requires special treatment, as it has two dates in the



above table. There are two equivalent methods for choosing the correct



full moon date:





A) Choose 18 April, unless the current century contains years with an



epact of 24, in which case 17 April should be used.





B) If the Golden Number is > 11 choose 17 April, otherwise choose 18 April.





The proof that these two statements are equivalent is left as an



exercise to the reader. (The frustrated ones may contact me for the



proof.)





Example: When was easter in 1992?





In the previous section we found that the Golden Number for 1992 was



17 and the Epact was 25. Looking in the table, we find that the



Paschal full moon was either 17 or 18 April. By rule B above, we



choose 17 April because the Golden Number > 11.





17 April 1992 was a Friday. Easter Sunday must therefore have been



19 April.







2.9.6. Isn't there a simpler way to calculate Easter?



-----------------------------------------------------





For the Gregorian calendar, try this one (the divisions are integer



divisions, in which remainders are discarded):





century = year/100



G = year % 19



K = (century - 17)/25



I = (century - century/4 - (century - K)/3 + 19*G + 15) % 30



I = I - (I/28)*(1 - (I/28)*(29/(I + 1))*((21 - G)/11))



J = (year + year/4 + I + 2 - century + century/4) % 7



L = I - J



EasterMonth = 3 + (L + 40)/44



EasterDay = L + 28 - 31*(EasterMonth/4)





This algorithm is based on the algorithm of Oudin (1940) and quoted in



"Explanatory Supplement to the Astronomical Almanac", P. Kenneth



Seidelmann, editor.







2.9.7. Is there a simple relationship between two consecutive Easters?



----------------------------------------------------------------------





Suppose you know the Easter date of the current year, can you easily



find the Easter date in the next year? No, but you can make a



qualified guess.





If Easter Sunday in the current year falls on day X and the next year



is not a leap year, Easter Sunday of next year will fall on one of the



following days: X-15, X-8, X+13 (rare), or X+20.





If Easter Sunday in the current year falls on day X and the next year



is a leap year, Easter Sunday of next year will fall on one of the



following days: X-16, X-9, X+12 (extremely rare), or X+19. (The jump



X+12 occurs only once in the period 1800-2099, namely when going from



2075 to 2076.)





If you combine this knowledge with the fact that Easter Sunday never



falls before 22 March and never falls after 25 April, you can



narrow the possibilities down to two or three dates.







2.9.8. How frequently are the dates for Easter repeated?



--------------------------------------------------------





The sequence of Easter dates repeats itself every 532 years in the



Julian calendar. The number 532 is the product of the following



numbers:





19 (the Metonic cycle or the cycle of the Golden Number)



28 (the Solar cycle, see section 2.4)





The sequence of Easter dates repeats itself every 5,700,000 years in



the Gregorian calendar. The number 5,700,000 is the product of the



following numbers:





19 (the Metonic cycle or the cycle of the Golden Number)



400 (the Gregorian equivalent of the Solar cycle, see section 2.4)



25 (the cycle used in step 3 when calculating the Epact)



30 (the number of different Epact values)







2.9.9. What about Greek Easter?



-------------------------------





The Greek Orthodox Church does not always celebrate Easter on the same



day as the Catholic and Protestant countries. The reason is that the



Orthodox Church uses the Julian calendar when calculating easter. This



is case even in the churches that otherwise use the Gregorian



calendar.





[One source says that the when the Greek Church decided to change to



the Gregorian calendar, they chose to use the astronomical full moon



as seen along the meridian of Jerusalem as the basis for calculating



Easter, rather than to use the "official" full moon described in the



previous sections. I would like more information about this.]







2.10. How does one count years?



-------------------------------





Around AD 525 a monk by the name of Dionysius Exiguus (in English



known as Denis the Little) was requested by Pope John I to prepare



calculations of the dates of Easter. At that time it was customary to



count years since the reign of emperor Diocletian; but in his



calculations Dionysius chose to number the years since the birth of



Christ, rather than honour the persecutor Diocletian.





Dionysius (wrongly) fixed Jesus' birth on 25 December 753 AUC (ab urbe



condita, i.e. since the founding of Rome), thus making the current era



start with AD 1 on 1 January 754 AUC.





How Dionysius established the year of Christ's birth is not



known. Jesus was born under the reign of king Herod the Great, who



died in 750 AUC, which means that Jesus could have been born no later



than that year. The English chronologist Bede questioned Dionysius'



calculations as early as the 8th century.





It was also Bede (673-735) who started dating years before 754 AUC



using the term "Before Christ". Bede's 1 BC immediately precedes AD 1



with no intervening year zero.





See also the following section.





[In this section I have used AD 1 = 754 AUC. This is the most likely



equivalence between the two systems. However, some authorities state



that AD 1 = 753 AUC or 755 AUC. I would appreciate it if someone could



enlighten me on this subject.]







2.10.1. Was Jesus born in the year 0?



-------------------------------------





No.





There are two reasons for this:



- There is no year 0.



- Jesus was born before 4 BC.





The concept of a year "zero" is a modern myth (but a very popular one).



Roman numerals do not have a figure designating zero, and treating zero



as a number on an equal footing with other numbers was not common in



the 6th century when our present year reckoning was established by



Dionysius Exiguus (see the previous section). Dionysius let the year



AD 1 start one week after what he believed to be Jesus' birthday.





Therefore, AD 1 follows immediately after 1 BC with no intervening



year zero. So a person who was born in 10 BC and died in AD 10,



would have died at the age of 19, not 20.





Furthermore, Dionysius' calculations were wrong. The Gospel of



Matthew tells us that Jesus was born under the reign of king Herod the



Great, and he died in 4 BC. It is likely that Jesus was actually born



around 7 BC. The date of his birth is unknown; it may or may not be 25



December.





Note, however, that astronomers frequently use another way of



numbering the years BC. Instead of 1 BC they use 0, instead of 2 BC



they use -1, instead of 3 BC they use -2, etc.







2.10.2. When does the 21st century start?



-----------------------------------------





The first century started in AD 1. The second century must therefore



have started a hundred years later, in AD 101, and the 21st century must



start 2000 years after the first century, i.e. in the year 2001.





This is the cause of some heated debate, especially since some



dictionaries and encyclopaedias say that a century starts in years



that end in 00.





Let me propose a few compromises:





Any 100-year period is a century. Therefore the period from 23 June 1996



to 22 June 2096 is a century. So please feel free to celebrate the



start of a century any day you like!





Although the 20th century started in 1901, the 1900s started in



1900. Similarly, we can celebrate the start of the 2000s in 2000 and



the start of the 21st century in 2001.





Finally, let's take a lesson from history:



When 1899 became 1900 people celebrated the start of a new century.



When 1900 became 1901 people celebrated the start of a new century.



Two parties! Let's do the same thing again!







2.11. What is the Indiction?



----------------------------





The Indiction was used in the middle ages to specify the position of a



year in a 15 year taxation cycle. It was introduced by emperor



Constantine the Great on 1 September 312 and abolished [whatever that



means] in 1806.





The Indiction may be calculated thus:



Indiction = (year + 2) % 15 + 1





The Indiction has no astronomical significance.





The Indiction did not always follow the calendar year. Three different



Indictions may be identified:





1) The Pontifical or Roman Indiction, which started on New Year's Day



(being either 25 December, 1 January, or 25 March).



2) The Greek or Constantinopolitan Indiction, which started on 1 September.



3) The Imperial Indiction or Indiction of Constantine, which started



on 24 September.







2.12. What is the Julian period?



--------------------------------





The Julian period (and the Julian day number) must not be confused



with the Julian calendar. The Julian calendar is named after the Roman



leader Julius Caesar (c. 100-44 BC), whereas the Julian period is



named after the Italian scholar Julius Caesar Scaliger (1484-1558).





Scaliger's son, the French scholar Joseph Justus Scaliger (1540-1609),



introduced the Julian period and named it after his father. His idea



was to assign a positive number to every year without having to worry



about BC/AD.





Scaliger's Julian period starts on 1 January 4713 BC (Julian calendar)



and lasts for 7980 years. AD 1996 is thus year 6709 in the Julian



period. After 7980 years the number starts from 1 again.





Why 4713 BC and why 7980 years? Well, in 4713 BC the Indiction (see



section 2.11), the Golden Number (see section 2.9.3) and the Solar



Number (see section 2.4) were all 1. The next times this happens is



15*19*28=7980 years later, in AD 3268.





Astronomers have used the Julian period to assign a unique number to



every day since 1 January 4713 BC. This is the so-called Julian Day



(JD). JD 0 designates the 24 hours from noon UTC on 1 January 4713 BC



to noon UTC on 2 January 4713 BC.





This means that at noon UTC on 1 January AD 2000, JD 2,451,545 will



start.





This can be calculated thus:



From 4713 BC to AD 2000 there are 6712 years.



In the Julian calendar, years have 365.25 days, so 6712 years



correspond to 6712*365.25=2,451,558 days. Subtract from this



the 13 days that the Gregorian calendar is ahead of the Julian



calendar, and you get 2,451,545.





Often fractions of Julian day numbers are used, so that 1 January AD



2000 at 15:00 UTC is referred to as JD 2,451,545.125.





Note that some people use the term "Julian day number" to refer to any



numbering of days. NASA, for example, use the term to denote the



number of days since 1 January of the current year.







2.12.1. What is the modified Julian day?



----------------------------------------





Sometimes a modified Julian day number (MJD) is used which is



2,400,000.5 less than the Julian day number. This brings the numbers



into a more manageable numeric range and makes the day numbers change



at midnight UTC rather than noon.







3. The Hebrew Calendar



----------------------





The current definition of the Hebrew calendar is generally said to



have been set down by the Sanhedrin president Hillel II in



approximately AD 359. The original details of his calendar are,



however, uncertain.





The Hebrew calendar is used for religious purposes by Jews all over



the world, and it is the official calendar of Israel.





The Hebrew calendar is a combined solar/lunar calendar, in that it



strives to have its years coincide with the tropical year and its



months coincide with the synodic months. This is a complicated goal,



and the rules for the Hebrew calendar are correspondingly



fascinating.







3.1. What does a Hebrew year look like?



---------------------------------------





An ordinary (non-leap) year has 353, 354, or 355 days.



A leap year has 383, 384, or 385 days.



The three lengths of the years are termed, "deficient", "regular",



and "complete", respectively.





An ordinary year has 12 months, a leap year has 13 months.





Every month starts (approximately) on the day of a new moon.





The months and their lengths are:





Length in a Length in a Length in a



Name deficient year regular year complete year



------- -------------- ------------ -------------



Tishri 30 30 30



Heshvan 29 29 30



Kislev 29 30 30



Tevet 29 29 29



Shevat 30 30 30



(Adar I 30 30 30)



Adar II 29 29 29



Nisan 30 30 30



Iyar 29 29 29



Sivan 30 30 30



Tammuz 29 29 29



Av 30 30 30



Elul 29 29 29



------- -------------- ------------ -------------



Total: 353 or 383 354 or 384 355 or 385





The month Adar I is only present in leap years. In non-leap years



Adar II is simply called "Adar".





Note that in a regular year the numbers 30 and 29 alternate; a



complete year is created by adding a day to Heshvan, whereas a



deficient year is created by removing a day from Kislev.





The alteration of 30 and 29 ensures that when the year starts with a



new moon, so does each month.







3.2. What years are leap years?



-------------------------------





A year is a leap year if the number year%19 is one of the following:



0, 3, 6, 8, 11, 14, or 17.





The value for year in this formula is the 'Anno Mundi' described in



section 3.8.







3.3. What years are deficient, regular, and complete?



-----------------------------------------------------





That is the wrong question to ask. The correct question to ask is: When



does a Hebrew year begin? Once you have answered that question (see



section 3.6), the length of the year is the number of days between



1 Tishri in one year and 1 Tishri in the following year.







3.4. When is New Year's day?



----------------------------





That depends. Jews have 4 different days to choose from:





1 Tishri: "Rosh HaShanah". This day is a celebration of the creation



of the world and marks the start of a new calendar



year. This will be the day we shall base our calculations on



in the following sections.





15 Shevat: "Tu B'shevat". The new year for trees, when fruit tithes



should be brought.





1 Nisan: "New Year for Kings". Nisan is considered the first month,



although it occurs 6 or 7 months after the start of the



calendar year.





1 Elul: "New Year for Animal Tithes (Taxes)".





Only the first two dates are celebrated nowadays.







3.5. When does a Hebrew day begin?



----------------------------------





A Hebrew day does not begin at midnight, but at sunset (when 3 stars



are visible).





Sunset marks the start of the 12 night hours, whereas sunrise marks the



start of the 12 day hours. This means that night hours may be longer



or shorter than day hours, depending on the season.







3.6. When does a Hebrew year begin?



-----------------------------------





The first day of the calendary year, Rosh HaShanah, on 1 Tishri is



determined as follows:





1) The new year starts on the day of the new moon that follows the last



month of the previous year.





2) If the new moon occurs after noon on that day, delay the new year



by one day. (Because in that case the new crescent moon will not be



visible until the next day.)





3) If this would cause the new year to start on a Sunday, Wednesday,



or Friday, delay it by one day. (Because we want to avoid that



Yom Kippur (10 Tishri) falls on a Friday or Sunday, and that



Hoshanah Rabba (21 Tishri) falls on a Sabbath (Saturday)).





4) If two consecutive years start 356 days apart (an illegal year



length), delay the start of the first year by two days.





5) If two consecutive years start 382 days apart (an illegal year



length), delay the start of the second year by one day.







Note: Rule 4 can only come into play if the first year was supposed



to start on a Tuesday. Therefore a two day delay is used rather that a



one day delay, as the year must not start on a Wednesday as stated in



rule 3.







3.7. When is the new moon?



--------------------------





A calculated new moon is used. In order to understand the



calculations, one must know that an hour is subdivided into 1080



'parts'.





The calculations are as follows:





The new moon that started the year AM 1, occurred 5 hours and 204



parts after sunset (i.e. just before midnight on Julian date 6 October



3761 BC).





The new moon of any particular year is calculated by extrapolating



from this time, using a synodic month of 29 days 12 hours and 793



parts.







3.8. How does one count years?



------------------------------





Years are counted since the creation of the world, which is assumed to



have taken place in 3761 BC. In that year, AM 1 started (AM = Anno



Mundi = year of the world).





In the year AD 1996 we will witness the start of Hebrew year AM 5757.







4. The Islamic Calendar



-----------------------





The Islamic calendar (or Hijri calendar) is a purely lunar



calendar. It contains 12 months that are based on the motion of the



moon, and because 12 synodic months is only 12*29.53=354.36 days, the



Islamic calendar is consistently shorter than a tropical year, and



therefore it shifts with respect to the Christian calendar.





The calendar is based on the Qur'an (Sura IX, 36-37) and its proper



observance is a sacred duty for Muslims.





The Islamic calendar is the official calendar in countries around the



Gulf, especially Saudi Arabia. But other Muslim countries use the



Gregorian calendar for civil purposes and only turn to the Islamic



calendar for religious purposes.







4.1. What does an Islamic year look like?



-----------------------------------------





The names of the 12 months that comprise the Islamic year are:





1. Muharram 7. Rajab



2. Safar 8. Sha'ban



3. Rabi' al-awwal (Rabi' I) 9. Ramadan



4. Rabi' al-thani (Rabi' II) 10. Shawwal



5. Jumada al-awwal (Jumada I) 11. Dhu al-Qi'dah



6. Jumada al-thani (Jumada II) 12. Dhu al-Hijjah





(Due to different transliterations of the Arabic alphabet, other



spellings of the months are possible.)





Each month starts when the lunar crescent is first seen (by an actual



human being) after a new moon.





Although new moons may be calculated quite precisely, the actual



visibility of the crescent is much more difficult to predict. It



depends on factors such a weather, the optical properties of the



atmosphere, and the location of the observer. It is therefore very



difficult to give accurate information in advance about when a new



month will start.





Furthermore, some Muslims depend on a local sighting of the moon,



whereas others depend on a sighting by authorities somewhere in the



Muslim world. Both are valid Islamic practices, but they may lead to



different starting days for the months.







4.2. So you can't print an Islamic calendar in advance?



-------------------------------------------------------





Not a reliable one. However, calendars are printed for planning



purposes, but such calendars are based on estimates of the visibility



of the lunar crescent, and the actual month may start a day earlier or



later than predicted in the printed calendar.





Different methods for estimating the calendars are used.





Some sources mention a crude system in which all odd numbered months



have 30 days and all even numbered months have 29 days with an extra



day added to the last month in 'leap years' (a concept otherwise



unknown in the calendar). Leap years could then be years in which the



number year%30 is one of the following: 2, 5, 7, 10, 13, 16, 18, 21,



24, 26, or 29. (This is the algorithm used in the calendar program of



the Gnu Emacs editor.)





Such a calendar would give an average month length of 29.53056 days,



which is quite close to the synodic month of 29.53059 days, so *on the



average* it would be quite accurate, but in any given month it is



still just a rough estimate.





Better algorithms for estimating the visibility of the new moon have



been devised. One such algorithm is implemented in a program called



'Islamic Timer' by professor Waleed A. Muhanna. Interested readers may



find the program on the World Wide Web at



http://www.cob.ohio-state.edu/facstf/homepage/muhanna/IslamicTimer.html





Another WWW site that contains information about the Islamic calendar



is http://www.ummah.org.uk/ildl/









4.3. How does one count years?



------------------------------





Years are counted since the Hijra, that is, Mohammed's flight to



Medina, which is assumed to have taken place 16 July AD 622 (Julian



calendar). On that date AH 1 started (AH = Anno Hegirae = year of the



Hijra).





In the year AD 1996 we have witnessed the start of Islamic year AH 1417.





Note that although only 1996-622=1375 years have passed in the



Christian calendar, 1416 years have passed in the Islamic calendar,



because its year is consistently shorter (by about 11 days) than the



tropical year used by the Christian calendar.







5. The French Revolutionary Calendar



------------------------------------





The French Revolutionary Calendar (or Republican Calendar) was



introduced in France on 24 November 1793 and abolished on 1 January



1806. It was used again briefly during under the Paris Commune in



1871.







5.1. What does a Republican year look like?



-------------------------------------------





A year consists of 365 or 366 days, divided into 12 months of 30 days



each, followed by 5 or 6 additional days. The months were:





1. Vendemiaire 7. Germinal



2. Brumaire 8. Floreal



3. Frimaire 9. Prairial



4. Nivose 10. Messidor



5. Pluviose 11. Thermidor



6. Ventose 12. Fructidor





(The second e in Vendemiaire and the e in Floreal carry an acute



accent. The o's in Nivose, Pluviose, and Ventose carry a circumflex



accent.)





The year was not divided into weeks, instead each month was divided



into three "decades" of 10 days, of which the final day was a day of



rest. This was an attempt to de-Christianize the calendar, but it was



an unpopular move, because now there were 9 work days between each day



of rest, whereas the Gregorian Calendar had only 6 work days between



each Sunday.





The ten days of each decade were called, respectively, Primidi, Duodi,



Tridi, Quartidi, Quintidi, Sextidi, Septidi, Octidi, Nonidi, Decadi.





The 5 or 6 additional days followed the last day of Fructidor and were



called:



1. Jour de la vertu (Virtue Day)



2. Jour du genie (Genius Day)



3. Jour du travail (Labour Day)



4. Jour de l'opinion (Reason Day)



5. Jour des recompenses (Rewards Day)



6. Jour de la revolution (Revolution Day) (the leap day)





Each year was supposed to start on autumnal equinox (around 22



September), but this created problems as will be seen in section 5.3.







5.2. How does one count years?



------------------------------





Years are counted since the establishment of the first French Republic



on 22 September 1792. That day became 1 Vendemiaire of the year 1 of



the Republic. (However, the Revolutionary Calendar was not introduced



until 24 November 1793.)







5.3. What years are leap years?



-------------------------------





Leap years were introduced to keep New Year's Day on autumnal



equinox. But this turned out to be difficult to handle, because



equinox is not completely simple to predict. Therefore a rule similar



to the one used in the Gregorian Calendar (including a 4000 year rule



as descibed in section 2.2.2) was to take effect in the year 20.



However, the Revolutionary Calendar was abolished in the year 14,



making this new rule irrelevant.





The following years were leap years: 3, 7, and 11. The years 15 and 20



should have been leap years, after which every 4th year (except every



100th year etc. etc.) should have been a leap year.







5.4. How does one convert a Republican date to a Gregorian one?



---------------------------------------------------------------





The following table lists the Gregorian date on which each year of the



Republic started:





Year 1: 22 Sep 1792 Year 8: 23 Sep 1799



Year 2: 22 Sep 1793 Year 9: 23 Sep 1800



Year 3: 22 Sep 1794 Year 10: 23 Sep 1801



Year 4: 23 Sep 1795 Year 11: 23 Sep 1802



Year 5: 22 Sep 1796 Year 12: 24 Sep 1803



Year 6: 22 Sep 1797 Year 13: 23 Sep 1804



Year 7: 22 Sep 1798 Year 14: 23 Sep 1805







6. Date



-------





This version 1.3 of this document was finished on





Tuesday after the 11th Sunday after Trinity, the 20th of



August, anno ab Incarnatione Domini MCMXCVI, indict. IV,



epacta X, luna V, anno post Margaretam Reginam Daniae natam



LVI, on the feast of Saint Amadour.





The 5th day of Elul, Anno Mundi 5756.





The 5th day of Rabi' al-thani, Anno Hegirae 1417.





Julian Day 2,450,316.


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