Leap year

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A leap year (or intercalary year) is a year containing an extra day, week or month in order to keep the calendar year synchronised with the astronomical or seasonal year. For example, February would have 29 days instead of just 28. Seasons and astronomical events do not repeat at an exact number of days, so a calendar which had the same number of days in each year would over time drift with respect to the event it was supposed to track. By occasionally inserting (or intercalating) an additional day or month into the year, the drift can be corrected. A year which is not a leap year is called a common year.

Leap years (which keep the calendar in sync with the year) should not be confused with leap seconds (which keep clock time in sync with the day).

Contents

[edit] Gregorian calendar

The Gregorian calendar, the current standard calendar in most of the world, adds a 29th day to February in all years evenly divisible by 4, except for centennial years (those ending in -00), which receive the extra day only if they are evenly divisible by 400. Thus 1600, 2000 and 2400 are leap years but 1700, 1800, 1900 and 2100 are not.

The reasoning behind this rule is as follows:

  • The Gregorian calendar is designed to keep the vernal equinox on or close to March 21, so that the date of Easter (celebrated on the Sunday after the 14th day of the Moon that falls on or after 21 March) remains correct with respect to the vernal equinox.
  • The vernal equinox year is currently about 365.242375 days long.
  • The Gregorian leap year rule gives an average year length of 365.2425 days.

This difference of a little over 0.0001 days means that in around 8,000 years, the calendar will be about one day behind where it should be. But in 8,000 years' time the length of the vernal equinox year will have changed by an amount which can't be accurately predicted (see below). So the Gregorian leap year rule does a good enough job.

Image:Gregoriancalendarleap.png
This graph shows the variation between the seasonal year versus the calendar year due to unequally spaced 'leap days' rules. See Iranian calendar to contrast with a calendar based on 8 leap days every 33 years.

[edit] Rules for determining when to have a leap year

In order to get a closer approximation, it was decided to have a leap day 97 years out of 400 rather than once every 4 years. To implement the model, it was provided that years divisible by 100 would be leap years only if they were divisible by 400 as well. So, in the last millennium, 1600 and 2000 were leap years, but 1700, 1800 and 1900 were not. In this millennium, 2100, 2200, 2300 and 2500 will not be leap years, but 2400 will be. The years that are divisible by 100 but not 400 are known as "exceptional common years". By this rule, the average number of days per year will be 365 + 1/4 - 1/100 + 1/400 = 365.2425.

[edit] Which day is the leap day?

The Gregorian calendar is a modification of the Julian calendar first used by the Romans. The Roman calendar originated as a lunar calendar, or more exactly a lunisolar calendar (though from the 5th century BC it no longer followed the real moon) and named its days after three of the phases of the moon: the new moon (Kalenda, or "calend", hence "calendar"), the first quarter (Nonis, or "none") and the full moon (Idis or "ide"). Days were counted down (inclusively) to the next named day, so 24 February was ante diem sextum Kalendas Martii ("the sixth day of the calends of March", understood as the sixth day before the calend of March). Note that Romans were counting days inclusively in all their calendars, so the first day of the calend of March was always 1 March at noon, marking the Roman new year (and historically the last new moon before the vernal equinox which should have remained close to 21 March).

The last quarter of the moon was not named specifically in the Roman calendar, but included as part of the days before the calend (which covered the half of most months, historically during the whole fall of the moon). However this last quarter of the moon (the 6th day of the calends) was used as the point before which a 23-days or 24-days intercalary month (intercalaris mensis) was inserted with the previous republican Roman calendar (this should normally have occured in February about once every two years), and was also used when Julius Caesar inserted three small intercalary months in 46 BC (22 days in October, 23 days in November and 22 days in December) and in 45 BC (23 days in February) to realign the Roman calendar with the solar cycle.

When an intercalary month was inserted, its first day was a calend (normally a new moon). The days of the splitted month before the intercalary month where counted down from the calend of this intercalary month, and the last 5 days of the splitted month (as well as the last days of the intercalary month after its ides) were all counted down from the calend (new moon) of the next month.

In the few days before 1 March 45 BC, there was still only one day named "the sixth day of the calends of March", because this day occured just after the last intercalary month inserted in February by Caesar. Some authors are arguing that 45 BC would have been a leap year, and that it would have been preceded by a leap day somewhere in the last days of February, but in fact the 6th day before the calend of March 45 BC was preceded by a small 23-days intercalary month, which was normal for the republican Roman calendar if it has been correctly applied, followed by the last 5 days of February (counted down from the calends of March). The Julian calendar was applied only starting on 1 March 45 BC, and terminated the historic republican Roman calendar with irregular intercalary months.

Starting in 1 March 45 BC, with the new Julian calendar created by Caesar, intercalary months were definitely abolished, and the length of the 12 months were adjusted so that the year would count 365 days, or 366 days in leap years, which should have occured every 4 years starting in 41 BC. The calendar was no longer luni-solar, but now a pure solar calendar, but the tradition of calendes, nones and ides were still used to name and count the days inclusively within months down from the traditional "moon days". Note that the days will be numbered inclusively foreward from the old calend (1st day of each month) only a few centuries later, after the old Roman tradition of "moon days" had eroded because it no longer had any sense within this solar calendar.

Every 4 years, February just before a leap year should have had two days called "the sixth day of the calends of March", understood as the sixth day before the calend of March:

  • ante diem sextum Kalendas Martii (abbreviated a.d. VI Kal. Mar.), meaning February 23 in all years, and:
  • ante diem sextum bissextilis Kalendas Martii (abbreviated a.d. VI bis Kal. Mar.), meaning February 24 only during leap years, which was the leap day. Hence the term bissextile day for 24 February in a bissextile year.

However this event occured only starting in 42 BC, the first bissextile year after the death of Caesar, where there was two such "sixth days of the calends", the second one (24 February) being the leap day. This occured one year too early, due to an interpretation error (and then every 3 years instead of every 4 years), an error that Augustus started correcting only 36 years later starting in 6 BC by temporarily dropping all bissextile years, up to 8 AD where a bissextile year occured again regulary every 4 years (up to the Gregorian reform of the Julian calendar in 1582, which also made January the first month of the year, so that the leap day occurs in February, within the same year as the leap year).

Where this custom is followed, anniversaries after the inserted day are moved one day later during leap years. For example, the former feast day of Saint Matthias, which occured "the fifth day of the calends of March" (understood as the fifth day before the calend of March, ante diem quintum Kalendas Martii, abbreviated a.d. V Kal. Mar.), meaning 24 February in ordinary years, would be 25 February in leap years.

This historical nicety is, however, in the process of being discarded: the European Union declared that, starting in 2000, 29 February rather than 24 February would be leap day,[citation needed] and the Roman Catholic Church also now uses 29 February as leap day[citation needed]. The only tangible difference is felt in countries that celebrate feast days, but in the general catholic calendar, all the last days of February, starting on the 24 February, are feria, meaning that the honored saints depend on the national rites. Today, most catholic countries observe feast days in February on fixed days of the Gregorian calendar, with the exception of some oriental catholic churches, who still celebrate the same saints as those celebrated by the orthodox churches.

[edit] Julian, Coptic and Ethiopian Calendars

The Julian calendar adds an extra day to February in years divisible by 4.

The Coptic calendar and Ethiopian calendar also add an extra day to the end of the year once every 4 years before a Julian 29-day February.

This rule gives an average year length of 365.25 days. The excess of about 0.0076 days with respect to the vernal equinox year means that the vernal equinox moves a day earlier in the calendar every 130 years or so.

[edit] Revised Julian Calendar

The Revised Julian calendar adds an extra day to February in years divisible by 4, except for years divisible by 100 that do not leave a remainder of 200 or 600 when divided by 900. This rule agrees with the rule for the Gregorian calendar until 2799. The first year that dates in the Revised Julian calendar will not agree with the those in the Gregorian calendar will be 2800, because it will be a leap year in the Gregorian calendar but not in the Revised Julian calendar.

This rule gives an average year length of 365.242222… days. This is a very good approximation to the mean tropical year, but because the vernal equinox tropical year is slightly longer, the Revised Julian calendar does not do as good a job as the Gregorian calendar of keeping the vernal equinox on or close to 21 March.

[edit] Chinese calendar

The Chinese calendar is lunisolar, so a leap year has an extra month, often called an embolismic month after the Greek word for it. In the Chinese calendar the leap month is added according to a complicated rule, which ensures that month 11 is always the month that contains the northern winter solstice. The intercalary month takes the same number as the preceding month; for example, if it follows the second month (二月) then it is simply called "leap second month" (Traditional Chinese: 閏二月; Simplified Chinese: 闰二月; pinyin: rùn'èryuè).

[edit] Hebrew calendar

The Hebrew calendar is also lunisolar with an embolismic month. In the Hebrew calendar the extra month is called Adar Alef (first Adar) and is added before Adar, which then becomes Adar bet (second Adar). According to the Metonic cycle, this is done seven times every nineteen years, specifically, in years, 3, 6, 8, 11, 14, 17, and 19.

In addition, the Hebrew calendar has postponement rules that postpone the start of the year by one or two days. These postponement rules reduce the number of different combinations of year length and starting day of the week from 28 to 14, and regulate the location of certain religious holidays in relation to the Sabbath. In particular, the first day of the Hebrew year can never be Sunday, Wednesday or Friday. Accordingly, the first day of Pesah is never Monday, Wednesday or Friday. This rule is known in Hebrew as "lo badu Pesah", which has a double meaning - "Pesah is not a legend", but also "Pesah is not Monday, Wednesday or Friday" (as the Hebrew word badu is written by three Hebrew letters signifying Monday, Wednesday and Friday).

One reason for this rule is that Yom Kippur, the holiest day in the Hebrew calendar, must never be adjacent to the weekly Sabbath (which is Saturday), i.e. it must never fall on Friday or Sunday, in order not to have two adjacent Sabbath days (Yom Kippur can be on Saturday, however).

[edit] Calendars with Leap Years synchronised with Gregorian

The Indian National Calendar and the Revised Bangla Calendar of Bangladesh organise their leap years so that the leap day is always close to February 29 in the Gregorian calendar. This makes it easy to convert dates to or from Gregorian.

[edit] Hindu Calendar

In the Hindu calendar, which is a lunisolar calendar, the embolismic month is called adhika maas (extra month). It is the month in which the sun is in the same sign of the stellar zodiac on two consecutive dark moons.

[edit] Iranian calendar

The Iranian calendar also has a single intercalated day once in every four years, but every 33 years or so the leap years will be five years apart instead of four years apart. The system used is more accurate and more complicated, and is based on the time of the March equinox as observed from Teheran. The 33-year period is not completely regular; every so often the 33-year cycle will be broken by a cycle of 29 or 37 years.

[edit] Long term leap year rules

The accumulated difference between the Gregorian calendar and the vernal equinoctial year amounts to 1 day in about 8,000 years. This suggests that the calendar needs to be improved by another refinement to the leap year rule: perhaps by avoiding leap years in years divisible by 8,000.

(The most common such proposal is to avoid leap years in years divisible by 4,000 [1]. This is based on the difference between the Gregorian calendar and the mean tropical year. Others claim, erroneously, that the Gregorian calendar itself already contains a refinement of this kind [2].)

Hypothetical 128 year based leap years has been proposed, and it can be adopted directly without any modification to current leap year calculations until the year 2048.

However, there is little point in planning a calendar so far ahead because over a timescale of tens of thousands of years the number of days in a year will change for a number of reasons, most notably:

  1. Precession of the equinoxes moves the position of the vernal equinox with respect to perihelion and so changes the length of the vernal equinoctial year.
  2. Tidal acceleration from the sun and moon slows the rotation of the earth, making the day longer.

In particular, the second component of change depends on such things as post-glacial rebound and sea level rise due to climate change. We can't predict these changes accurately enough to be able to make a calendar that will be accurate to a day in tens of thousands of years.

[edit] Marriage proposal

There is a tradition, said to go back to Saint Patrick and Saint Bridget in 5th century Ireland, but apparently not attested before the 19th century, whereby women may make marriage proposals only in leap years.

Supposedly (but disputed), in a 1288 law by Queen Margaret of Scotland (then age five and living in Norway), fines were levied if the proposal was refused by the man; compensation ranged from a kiss to £1 to a silk gown, in order to soften the blow.<ref>Virtually no laws of Margaret survive. Indeed, none concerning her subjects are recorded in the twelve volume Acts of the Parliaments of Scotland (1814–75) covering the period 1124–1707 (two laws concerning young Margaret herself are recorded on pages 424 & 441–2 of volume I).</ref> Because men felt that put them at too great a risk, the tradition was in some places tightened to restricting female proposals to 29 February.

Others regard these supposed folk traditions as unhistorical.<ref>The Privilege of Ladies by Barbara Mikkelson</ref>

[edit] Birthdays

A person who was born on 29 February may be called a "leapling". In non-leap years they usually celebrate their birthday on 28 February or 1 March.

For legal purposes, their legal birthdays depend on how different laws count time intervals. In Taiwan, for example, the legal birthday of a leapling is 28 February in common years, so a Taiwanese leapling born on 29 February 1980 would have legally reached 18 years old on 28 February 1998.

If a period fixed by weeks, months, and years does not commence from the beginning of a week, month, or year, it ends with the ending of the day which proceeds the day of the last week, month, or year which corresponds to that on which it began to commence. But if there is no corresponding day in the last month, the period ends with the ending of the last day of the last month.<ref>Article 121 of the [[s:Civil Code Part I General Principles|]] of the Republic of China in effect in Taiwan</ref>

There are many instances in children's literature where a person's claim to be only a quarter of their actual age turns out to be based on counting their leap-year birthdays. A similar device is used in the plot of the Gilbert and Sullivan operetta The Pirates of Penzance.

[edit] References

<references/>

[edit] See also

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Leap year

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