Leap year

A leap year (or intercalary year) is a year containing an extra day, week or month in order to keep the calendar year in sync with an 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).

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.

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.

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". A mathematical formula used for this calculation is called "Zeller's congruence", which is also used to determine what day of the week a specific date falls upon.

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 (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 (calends, hence "calendar"), the first quarter (nones) and the full moon (ides). Days were counted down (inclusively) to the next named day, so 24 February was ante diem sextum calendas martii ("the sixth day before the calends of March").

Since 45 BC, February in a leap year had two days called "the sixth day before the calends of March". The extra day was originally the second of these, but since the third century it was the first. Hence the term bissextile day for 24 February in a bissextile year.

Where this custom is followed, anniversaries after the inserted day are moved in leap years. For example, the former feast day of Saint Matthias, 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, and the Roman Catholic Church also now uses 29 February as leap day. The only tangible difference is felt in countries that celebrate feast days.

The Decree of Canopus, which was issued by the pharaoh Ptolemy III, Euergetes of Egypt in 239 BC, decreed a leap year system.

Julian calendar

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

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.

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.

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 then it is simply called "leap second month".

Hebrew calendar

The Hebrew calendar is also lunisolar with an embolistic 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).

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.

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.

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 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 [http://www.straightdope.com/mailbag/mleapyr.html.)

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:

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.
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.

Marriage proposal

There is a tradition, said to go back to Saint Patrick and Saint Bridget in 5th century Ireland, whereby women may make marriage proposals only in leap years.

Saint Patrick and the leap year

Saint Patrick, having driven the snakes out of the bogs was walking along the shores of Lough Neagh, when he was accosted by Saint Bridget in tears, and was told that a mutiny had broken out in the nunnery over which she presided, the ladies claiming the right of proposing for marriage.

Saint Patrick said he would concede them the right every seventh year, when Saint Bridget threw her arms round his neck, and exclaimed, "Arrah, Pathrick, jewel, I daurn't go back to the girls wid such a proposal. Make it one year in four." Saint Patrick replied, "Bridget, acushla, squeeze me that way again, an' I'll give ye leap-year, the longest of the lot." Saint Bridget, upon this, popped the question to St Patrick himself, who, of course, could not marry: so he patched up the difficulty as best he could with a kiss and a silk gown.

(Source: Evans, Ivor H, Brewer's Dictionary of Phrase and Fable, Cassell, London, 1988)

According to a 1288 law in Scotland, fines were levied if the proposal was refused by the man; compensation ranged from a kiss to a silk gown to soften the blow. 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.

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.

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.

Gourt Home::Gourt :: Leap year