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).
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.
 | 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. |
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
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.
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.
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".
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).
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.
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.
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:#
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.
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.
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.
*
leap second*
Intercalation*
Leap week calendar
