1609 lines
63 KiB
Plaintext
1609 lines
63 KiB
Plaintext
-Date: 29 Aug 1996 06:39:37 GMT
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-From: ct@login.dknet.dk (Claus Tondering)
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-Newsgroups: sci.astro,soc.history,sci.answers,soc.answers,news.answers
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-Followup-To: sci.astro,soc.history
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-Subject: Calendar FAQ, v. 1.3 (modified 20 Aug 1996)
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Archive-name: calendars/faq
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Posting-Frequency: monthly
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Last-modified: 1996/08/20
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Version: 1.3
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URL: ftp://login.dknet.dk/pub/ct/calendar.faq
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FREQUENTLY ASKED QUESTIONS ABOUT
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CALENDARS
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Version 1.3 - 20 Aug 1996
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Copyright and disclaimer
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------------------------
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This document is Copyright (C) 1996 by Claus Tondering.
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E-mail: ct@login.dknet.dk.
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The document may be freely distributed, provided this
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copyright notice is included and no money is charged for
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the document.
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This document is provided "as is". No warranties are made as
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to its correctness.
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Introduction
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------------
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This is the calendar FAQ. Its purpose is to give an overview
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of the Christian, Hebrew, and Islamic calendars in common
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use. It will also provide a historical background for the
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Christian calendar.
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Comments are very welcome. My e-mail address is given above.
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I would like to thank
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- Dr. Monzur Ahmed of the University of Birmingham, UK,
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- Michael J Appel,
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- Chris Carrier,
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- H. Koenig,
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- Marcos Montes,
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- Waleed A. Muhanna of the Fisher College of Business,
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Columbus, Ohio, USA,
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- Paul Schlyter of the Swedish Amateur Astronomer's Society
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for their help with this document.
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Changes since version 1.2
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-------------------------
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A few minor corrections. Especially in the articles about the
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Roman and French Revolutionary calendars.
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Writing dates and years
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-----------------------
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Dates will be written in the British format (1 January)
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rather than the American format (January 1). Dates will
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occasionally be abbreviated: "1 Jan" rather than "1 January".
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Years before and after the "official" birth year of Christ
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will be written "45 BC" or "AD 1996", respectively. I prefer
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this notation over the secular "45 B.C.E." and "1996 C.E."
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The % operator
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--------------
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Throughout this document the operator % will be used to
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signify the modulo or remainder operator. For example, 17%7=3
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because the result of the division 17/7 is 2 with a remainder
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of 3.
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The text in square brackets
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---------------------------
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Square brackets [like this] identify information that I am
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unsure about and about which I would like more
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information. Please write me at ct@login.dknet.dk.
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Index:
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------
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1. What astronomical events form the basis of calendars?
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2. The Christian calendar
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2.1. What is the Julian calendar?
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2.1.1. What years are leap years?
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2.1.2. What consequences did the use of the Julian
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calendar have?
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2.2. What is the Gregorian calendar?
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2.2.1. What years are leap years?
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2.2.2. Isn't there a 4000-year rule?
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2.2.3. Don't the Greek do it differently?
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2.2.4. When did country X change from the Julian to
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the Gregorian calendar?
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2.3. What day is the leap day?
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2.4. What is the Solar Cycle?
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2.5. What day of the week was 2 August 1953?
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2.6. What is the Roman calendar?
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2.6.1. How did the Romans number days?
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2.7. Has the year always started on 1 January?
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2.8. What is the origin of the names of the months?
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2.9. What is Easter?
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2.9.1. When is Easter? (Short answer)
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2.9.2. When is Easter? (Long answer)
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2.9.3. What is the Golden Number?
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2.9.4. What is the Epact?
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2.9.5. How does one calculate Easter then?
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2.9.6. Isn't there a simpler way to calculate Easter?
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2.9.7. Is there a simple relationship between two
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consecutive Easters?
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2.9.8. How frequently are the dates for Easter repeated?
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2.9.9. What about Greek Easter?
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2.10. How does one count years?
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2.10.1. Was Jesus born in the year 0?
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2.10.2. When does the 21st century start?
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2.11. What is the Indiction?
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2.12. What is the Julian period?
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2.12.1. What is the modified Julian day?
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3. The Hebrew Calendar
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3.1. What does a Hebrew year look like?
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3.2. What years are leap years?
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3.3. What years are deficient, regular, and complete?
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3.4. When is New Year's day?
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3.5. When does a Hebrew day begin?
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3.6. When does a Hebrew year begin?
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3.7. When is the new moon?
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3.8. How does one count years?
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4. The Islamic Calendar
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4.1. What does an Islamic year look like?
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4.2. So you can't print an Islamic calendar in advance?
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4.3. How does one count years?
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5. The French Revolutionary Calendar
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5.1. What does a Republican year look like?
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5.2. How does one count years?
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5.3. What years are leap years?
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5.4. How does one convert a Republican date to a Gregorian one?
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6. Date
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1. What astronomical events form the basis of calendars?
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--------------------------------------------------------
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Calendars are normally based on astronomical events, and the two most
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important astronomical objects are the sun and the moon. Their cycles
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are very important in the construction and understanding of calendars.
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Our concept of a year is based on the earth's motion around the sun.
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The time from one winter solstice to the next is called a "tropical
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year". Its length is currently 365.242190 days, but it varies. Around
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1900 its length was 365.242196 days, and around 2100 it will be
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365.242184 days.
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Our concept of a month is based on the moon's motion around the earth,
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although this connection has been broken in the calendar commonly used
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now. The time from one new moon to the next is called a "synodic
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month", and its length is currently 29.5305889 days, but it
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varies. Around 1900 its length was 29.5305886 days, and around 2100 it
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will be 29.5305891 days.
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Note that these numbers are averages. The actual length of a
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particular year may vary by several minutes due to the influence of
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the gravitational force from other planets. Similary, the time between
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two new moons may vary by several hours due to the eccentricity of the
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lunar orbit.
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It is unfortunate that the length of the tropical year is not a
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multiple of the length of the synodic month. This means that with 12
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months per year, the relationship between our month and the moon
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cannot be maintained.
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However, 19 tropical years is 234.997 synodic months, which is very
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close to an integer. So every 19 years the phases of the moon fall on
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the same dates (if it were not for the skewness introduced by leap
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years). 19 years is called a Metonic cycle (after Meton, an astronomer
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from Athens in the 5th century BC).
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So, to summarise: There are three important numbers to note:
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A tropical year is 365.2422 days.
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A synodic month is 29.53059 days.
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19 tropical years is close to an integral number of synodic months.
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The Christian calendar is based on the motion of the earth around the
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sun, while the months have no connection with the motion of the moon.
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On the other hand, the Islamic calendar is based on the motion of the
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moon, while the year has no connection with the motion of the earth
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around the sun.
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Finally, the Hebrew calendar combines both, in that its years are
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linked to the motion of the earth around the sun, and its months are
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linked to the motion of the moon.
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2. The Christian calendar
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-------------------------
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The "Christian calendar" is the term I use to designate the calendar
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commonly in use, although its connection with Christianity is highly
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debatable.
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The Christian calendar has years of 365 or 366 days. It is divided into
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12 months that have no relationship to the motion of the moon. In
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parallel with this system, the concept of "weeks" groups the days in
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sets of 7.
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Two main versions of the Christian calendar have existed in recent
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times: The Julian calendar and the Gregorian calendar. The difference
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between them lies in the way they approximate the length of the
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tropical year and their rules for calculating Easter.
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2.1. What is the Julian calendar?
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---------------------------------
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The Julian calendar was introduced by Julius Caesar in 45 BC. It was
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in common use until the 1500s, when countries started changing to the
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Gregorian calendar (section 2.2). However, some countries (for
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example, Greece and Russia) used it into this century, and the
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Orthodox church in Russia still uses it, as do some other Orthodox
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churches.
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In the Julian calendar, the tropical year is approximated as 365 1/4
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days = 365.25 days. This gives an error of 1 day in approximately 128
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years.
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The approximation 365 1/4 is achieved by having 1 leap year every 4
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years.
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2.1.1. What years are leap years?
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---------------------------------
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The Julian calendar has 1 leap year every 4 years. This means that:
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Every year divisible by 4 is a leap year.
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However, this rule was not followed in the first years after the
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introduction of the Julian calendar in 45 BC. Due to a counting error,
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every 3rd year was a leap year in the first years of this calendar's
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existence. The leap years were:
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45 BC, 42 BC, 39 BC, 36 BC, 33 BC, 30 BC,
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27 BC, 24 BC, 21 BC, 18 BC, 15 BC, 12 BC, 9 BC,
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AD 8, AD 12, and every 4th year from then on.
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There were no leap years between 9 BC and AD 8. This period without
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leap years was decreed by emperor Augustus and earned him a place in
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the calendar as the 8th month was named after him.
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It is a curious fact that although the method of reckoning years after
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the (official) birthyear of Christ was not introduced until the 6th
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century, by some stroke of luck the Julian leap years coincide with
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years of our Lord that are divisible by 4. (But, of course, this may
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been deliberate on the part of Dionysius Exiguus who introduced our
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current year reckoning.)
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2.1.2. What consequences did the use of the Julian calendar have?
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-----------------------------------------------------------------
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The Julian calendar introduces an error of 1 day every 128 years. So
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every 128 years the vernal equinox moved one day backwards in the
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calendar. Furthermore, the method for calculating the dates for Easter
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was inaccurate and needed to be refined.
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In order to remedy this, two steps were necessary: 1) The Julian
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calendar had to be replaced by something more adequate. 2) The extra
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days that the Julian calendar had inserted had to be dropped.
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The solution to problem 1) was the Gregorian calendar described in
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section 2.2.
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The solution to problem 2) depended on the fact that it was felt that
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21 March was the proper day for vernal equinox (because 21 March was
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the date for vernal equinox during the Council of Nicaea in AD
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325). The Gregorian calendar was therefore calibrated to make that day
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vernal equinox.
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By 1582 vernal equinox had moved (1582-325)/128 days = approximately
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10 days backwards. So 10 days had to be dropped.
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[Dropping 10 days in the 1500s brought the Gregorian calendar in sync
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with the Julian calendar of the 3rd century. But AD 325 is in the 4th
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century. Was that deliberate?]
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2.2. What is the Gregorian calendar?
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------------------------------------
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The Gregorian calendar is the one commonly used today. It was decreed
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by Pope Gregory XIII in a papal bull in February 1582.
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In the Gregorian calendar, the tropical year is approximated as
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365 97/400 days = 365.2425 days. This gives an error of 1 day in
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approximately 3300 years.
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The approximation 365 97/400 is achieved by having 97 leap years
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every 400 years.
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2.2.1. What years are leap years?
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---------------------------------
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The Gregorian calendar has 97 leap years every 400 years. This means
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that:
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Every year divisible by 4 is a leap year.
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However, every year divisible by 100 is not a leap year.
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However, every year divisible by 400 is a leap year after all.
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So, 1700, 1800, 1900, 2100, and 2200 are not leap years. But 1600,
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2000, and 2400 are leap years.
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(Destruction of a myth: There are no double leap years, i.e. no
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years with 367 days. See, however, the note on Sweden in section
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2.2.4.)
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2.2.2. Isn't there a 4000-year rule?
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------------------------------------
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It has been suggested (by the astronomer William Herschel (1738-1822)
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among others) that a better approximation to the length of the
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tropical year would be 365 969/4000 days = 365.24225 days. This would
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dictate 969 leap years every 4000 years, rather than the 970 leap
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years mandated by the Gregorian calendar. This could be achieved by
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dropping one leap year from the Gregorian calendar every 4000 years,
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which would make years divisible by 4000 non-leap years.
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This rule has, however, not been officially adopted.
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2.2.3. Don't the Greek do it differently?
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-----------------------------------------
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When the Orthodox church in Greece finally decided to switch to the
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Gregorian calendar in the 1920s, they tried to improve on the
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Gregorian leap year rules, replacing the "divisible by 400" rule by
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the following:
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Every year which when divided by 900 leaves a remainder of 200
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or 600 is a leap year.
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This makes 1900, 2100, 2200, 2300, 2500, 2600, 2700, 2800 non-leap
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years, whereas 2000, 2400, and 2900 are leap years. This will not
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create a conflict with the rest of the world until the year 2800.
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This rule gives 218 leap years every 900 years, which gives us an
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average year of 365 218/900 days = 365.24222 days, which is certainly
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more accurate than the official Gregorian number of 365.2425 days.
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However, to my knowledge, this rule is *not* official in Greece. [Is
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this true?]
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[I have received an e-mail indicating that this system is official in
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Russia today. I'm investigating that. Information is very welcome.]
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2.2.4. When did country X change from the Julian to the Gregorian calendar?
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---------------------------------------------------------------------------
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The papal bull of February 1582 decreed that 10 days should be dropped
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from October 1582 so that 15 October should follow immediately after
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4 October, and from then on the reformed calendar should be used.
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This was observed in Italy, Poland, Portugal, and Spain. Other Catholic
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countries followed shortly after, but Protestant countries were
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reluctant to change, and the Greek orthodox countries didn't change
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until the start of this century.
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Changes in the 1500s required 10 days to be dropped.
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Changes in the 1600s required 10 days to be dropped.
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Changes in the 1700s required 11 days to be dropped.
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Changes in the 1800s required 12 days to be dropped.
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Changes in the 1900s required 13 days to be dropped.
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(Exercise for the reader: Why is the error in the 1600s the same as
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in the 1500s.)
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The following list contains the dates for changes in a number of
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countries.
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Albania: December 1912
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Austria: Different regions on different dates
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5 Oct 1583 was followed by 16 Oct 1583
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14 Dec 1583 was followed by 25 Dec 1583
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Belgium: Different authorities say
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14 Dec 1582 was followed by 25 Dec 1582
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21 Dec 1582 was followed by 1 Jan 1583
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Bulgaria: Different authorities say
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Sometime in 1912
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Sometime in 1915
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18 Mar 1916 was followed by 1 Apr 1916
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China: Different authorities say
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18 Dec 1911 was followed by 1 Jan 1912
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18 Dec 1928 was followed by 1 Jan 1929
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Czechoslovakia (i.e. Bohemia and Moravia):
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6 Jan 1584 was followed by 17 Jan 1584
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Denmark (including Norway):
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18 Feb 1700 was followed by 1 Mar 1700
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Egypt: 1875
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Estonia: January 1918
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Finland: Then part of Sweden. (Note, however, that Finland later
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became part of Russia, which then still used the
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Julian calendar. The Gregorian calendar remained
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official in Finland, but some use of the Julian
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calendar was made.)
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France: 9 Dec 1582 was followed by 20 Dec 1582
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Germany: Different states on different dates:
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Catholic states on various dates in 1583-1585
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Prussia: 22 Aug 1610 was followed by 2 Sep 1610
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Protestant states: 18 Feb 1700 was followed by 1 Mar 1700
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Great Britain and Dominions (including what is now the USA):
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2 Sep 1752 was followed by 14 Sep 1752
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Greece: 9 Mar 1924 was followed by 23 Mar 1924
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Hungary: 21 Oct 1587 was followed by 1 Nov 1587
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Italy: 4 Oct 1582 was followed by 15 Oct 1582
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Japan: Different authorities say:
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19 Dec 1872 was followed by 1 Jan 1873
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18 Dec 1918 was followed by 1 Jan 1919
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Latvia: During German occupation 1915 to 1918
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Lithuania: 1915
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Luxemburg: 14 Dec 1582 was followed by 25 Dec 1582
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Netherlands:
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Brabant, Flanders, Holland, Artois, Hennegau:
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14 Dec 1582 was followed by 25 Dec 1582
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Geldern, Friesland, Zeuthen, Groningen, Overysel:
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30 Nov 1700 was followed by 12 Dec 1700
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Norway: Then part of Denmark.
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Poland: 4 Oct 1582 was followed by 15 Oct 1582
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Portugal: 4 Oct 1582 was followed by 15 Oct 1582
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Romania: 31 Mar 1919 was followed by 14 Apr 1919
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Russia: 31 Jan 1918 was followed by 14 Feb 1918
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Spain: 4 Oct 1582 was followed by 15 Oct 1582
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Sweden (including Finland):
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17 Feb 1753 was followed by 1 Mar 1753 (see note below)
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Switzerland:
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Catholic cantons: 1583 or 1584
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Zurich, Bern, Basel, Schafhausen, Neuchatel, Geneva:
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31 Dec 1700 was followed by 12 Jan 1701
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St Gallen: 1724
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Turkey: 18 Dec 1926 was followed by 1 Jan 1927
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USA: See Great Britain.
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Yugoslavia: 1919
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Sweden has a curious history. Sweden decided to make a gradual change
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from the Julian to the Gregorian calendar. By dropping every leap year
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from 1700 through 1740 the eleven superfluous days would be omitted
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and from 1 Mar 1740 they would be in sync with the Gregorian
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calendar. (But in the meantime they would be in sync with nobody!)
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So 1700 (which should have been a leap year in the Julian calendar)
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was not a leap year in Sweden. However, by mistake 1704 and 1708
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became leap years. This left Sweden out of synchronisation with both
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the Julian and the Gregorian world, so they decided to go *back* to
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the Julian calendar. In order to do this, they inserted an extra day
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in 1712, making that year a double leap year! So in 1712, February had
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30 days in Sweden.
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Later, in 1753 Sweden changed to the Gregorian calendar by dropping 11
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days like everyone else.
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2.3. What day is the leap day?
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------------------------------
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24 February!
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Weird? Yes! The explanation is related to the Roman calendar and is
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found in section 2.6.1.
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>From a numerical point of view, of course 29 February is the extra
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day. But from the point of view of celebration of feast days, the
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following correspondence between days in leap years and non-leap
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years exist:
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Non-leap year Leap year
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------------- ----------
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22 February 22 February
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23 February 23 February
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24 February (extra day)
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24 February 25 February
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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
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2. Brumaire 8. Floreal
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3. Frimaire 9. Prairial
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4. Nivose 10. Messidor
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5. Pluviose 11. Thermidor
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6. Ventose 12. Fructidor
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(The second e in Vendemiaire and the e in Floreal carry an acute
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accent. The o's in Nivose, Pluviose, and Ventose carry a circumflex
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accent.)
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The year was not divided into weeks, instead each month was divided
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into three "decades" of 10 days, of which the final day was a day of
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rest. This was an attempt to de-Christianize the calendar, but it was
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an unpopular move, because now there were 9 work days between each day
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|
of rest, whereas the Gregorian Calendar had only 6 work days between
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each Sunday.
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The ten days of each decade were called, respectively, Primidi, Duodi,
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Tridi, Quartidi, Quintidi, Sextidi, Septidi, Octidi, Nonidi, Decadi.
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The 5 or 6 additional days followed the last day of Fructidor and were
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|
called:
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1. Jour de la vertu (Virtue Day)
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|
2. Jour du genie (Genius Day)
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|
3. Jour du travail (Labour Day)
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|
4. Jour de l'opinion (Reason Day)
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|
5. Jour des recompenses (Rewards Day)
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|
6. Jour de la revolution (Revolution Day) (the leap day)
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|
Each year was supposed to start on autumnal equinox (around 22
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|
September), but this created problems as will be seen in section 5.3.
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5.2. How does one count years?
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------------------------------
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|
Years are counted since the establishment of the first French Republic
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|
on 22 September 1792. That day became 1 Vendemiaire of the year 1 of
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|
the Republic. (However, the Revolutionary Calendar was not introduced
|
|
until 24 November 1793.)
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5.3. What years are leap years?
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-------------------------------
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Leap years were introduced to keep New Year's Day on autumnal
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|
equinox. But this turned out to be difficult to handle, because
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|
equinox is not completely simple to predict. Therefore a rule similar
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|
to the one used in the Gregorian Calendar (including a 4000 year rule
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|
as descibed in section 2.2.2) was to take effect in the year 20.
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|
However, the Revolutionary Calendar was abolished in the year 14,
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|
making this new rule irrelevant.
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|
The following years were leap years: 3, 7, and 11. The years 15 and 20
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|
should have been leap years, after which every 4th year (except every
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|
100th year etc. etc.) should have been a leap year.
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5.4. How does one convert a Republican date to a Gregorian one?
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---------------------------------------------------------------
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|
The following table lists the Gregorian date on which each year of the
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|
Republic started:
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|
Year 1: 22 Sep 1792 Year 8: 23 Sep 1799
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|
Year 2: 22 Sep 1793 Year 9: 23 Sep 1800
|
|
Year 3: 22 Sep 1794 Year 10: 23 Sep 1801
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|
Year 4: 23 Sep 1795 Year 11: 23 Sep 1802
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|
Year 5: 22 Sep 1796 Year 12: 24 Sep 1803
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|
Year 6: 22 Sep 1797 Year 13: 23 Sep 1804
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|
Year 7: 22 Sep 1798 Year 14: 23 Sep 1805
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6. Date
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-------
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This version 1.3 of this document was finished on
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Tuesday after the 11th Sunday after Trinity, the 20th of
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August, anno ab Incarnatione Domini MCMXCVI, indict. IV,
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epacta X, luna V, anno post Margaretam Reginam Daniae natam
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LVI, on the feast of Saint Amadour.
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The 5th day of Elul, Anno Mundi 5756.
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The 5th day of Rabi' al-thani, Anno Hegirae 1417.
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Julian Day 2,450,316.
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