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The Calendar, Leap Years and the Year 2000 AD

Thanks to the Science and Engineering Research Council
of the Royal Greenwich Observatory. This information
is reprinted from files found in the World Wide Web


A calendar is a system of reckoning the time over extended intervals by combining days into longer groupings which are linked to the way in which we live. The groupings often have religious significance and some of the groups are linked to astronomical periods.

Our calendar is made up of days, weeks, months and years. The day is the rotational period of the Earth; the week is a purely artificial period linked to the Biblical story of creation; the month is linked to the period of the Moon and the year is linked to the Earth's period of rotation around the Sun.

Other Calendars

The Jewish calendar and the Moslem calendar are intimately connected with the Moon. The Jewish calendar is now a fixed calendar with rather complex rules for its construction. The length of the Jewish year may be 353, 354 or 355 days or 383, 384 or 385 days. Each month has 29 or 30 days.

The Moslem calendar is also a fixed calendar, but the religious festivals depend on visual sightings of the New Moon. The length of the Moslem year is 12 months of alternate lengths 30 and 29 days, except for the 12th month which can have either 29 or 30 days. The calendar is kept in adjustment with the Moon using a cycle of years of different length.

The Day

The definition of the day seems very simple. It should be the time taken for one passage of the Sun across the meridian to its next crossing. Unfortunately the Earth's movement around the Sun is not circular and this causes the time indicated by a sundial to be different from that measured by a clock. (The difference is called the Equation of Time and is describy a clock. (The difference is called the Equation of Time and is described in a separate pamphlet.) Nor is the Earth's rotation period constant, although the variations are very small. So we use a length for the day which represents the Earth's average rotation period. Occasionally we have to insert `leap-seconds' to correct from this exact measure to the slightly irregular rotation of the Earth.

The Week

Mosaic law forbidding work on every seventh day established a seven-day period as a measure of Jewish time. This passed over into the Christian church and gradually became established in the Roman calendar. The astrological practice of naming the days using the names of the Sun, Moon and the five known planets also yielded a seven day period.

The names that we give to the days of the week are still based on this nomenclature. In English Sunday and Monday are named after the Sun and Moon while the other days of the week are named after the teutonic versions of the gods that correspond to each planet. Tiu = Mars, Woden = Mercury, Thor = Jupiter and Freya = Venus, Saturday keeping its latin connection with Saturn.

The Month

Many ancient calendars were based on the lunar cycle. The lunar month is 29.530589 days and the number of lunations in a year is 12.368267. The most common scheme was to have 12 montommon scheme was to have 12 months of 30 days with either arbitrary or calculated additional days or months to bring the system into accord with the solar year.

Originally the Roman calendar had 10 months Martius (named after Mars and indicating the time for resumption of war), Aprilis (after the word for `to open', hence Spring), Maius (after Maia, the goddess of growth), Junius (after juvenis, meaning youth), Quintilius, Sextilis, Septembris, Octobris and Decembris (meaning the fifth to tenth months). The Romans had a dislike of even numbers as these symbolized death and so the months had either 29 or 31 days. King Numa increased the number of months to 12 by introducing Januarius (after the god Janus, the protector of doorways and hence the opening of the year) and Februarius (after Februalia, the time for sacrifices at the end of the year). The order of the months was later changed.

In order to reconcile the solar and lunar years,at the recommendation of Sosigenes Julius Caesar altered the lengths of the months and the change to our present format was completed by Caesar Augustus. They both claimed the names of one of the months and this gave rise to Julius and Augustus which replaced Quintilius and Sextilis.

The Year

The number of days in one revolution of the Earth around the Sun is f the Earth around the Sun is 365.2422 days. Unfortunately, this is not a whole number and so if we wish to keep the calendar in track with the seasons we must adopt some form of variable year length.

The first major attempt to accomplish this was by Julius Caesar. Besides pinching a day from the last month of the year (then February) to make `his' month, July, have 31 days he introduced the Julian calendar. February was further despoiled by Augustus Caesar who also purloined a day so as to make `his' month, August, also have 31 days. As some sort of compensation the leap-day was given to February.

The Julian calendar introduced a year of length 365 days with a leap-year every 4 years. It also moved the start of the year from March 25 to January 1, supposedly the longest day. The adopted length of the year, 365. 25 days, is only slightly different from the actual length, 365. 2422 days, but over the centuries the difference mounts up and by the 16th century had become noticeable. The effect is to move Spring and the date of Easter, which is related to the vernal equinox, closer to the date of Christmas.

The Gregorian reform to the calendar altered the rule for determining if a year should be a leap-year by stating that centenary years should only be leap-years if they were divisible by 400. It also dropped several days from the caled several days from the calendar so that the vernal equinox was brought back to March 21. The mean length of the calendar year is now 365. 2425 days and the error compared with the true value amounts to only 3 days in 10,000 years.


The year is defined as being the interval between two successive passages of the Sun through the vernal equinox. Of course, what is really occurring is that the Earth is going around the Sun but it is easier to understand what is happening by considering the apparent motion of the Sun in the sky.

The vernal equinox is the instant when the Sun is above the Earth's equator while going from the south to the north. It is the time which astronomers take as the definition of the beginning of Spring.The year as defined above is called the trove is called the tropical year and it is the year length that defines the repetition of the seasons. The length of the tropical year is 365.24219 days.

In 46 BC Julius Caesar established the Julian calendar which was used in the west until 1582. In the Julian calendar each year contained 12 months and there were an average of 365.25 days in a year. This was achieved by having three years containing 365 days and one year containing 366 days. (In fact the leap years were not correctly inserted until 8 AD).

The discrepancy between the actual length of the year, 365.24219 days, and the adopted length, 365.25 days, may not seem important but over hundreds of years the difference becomes obvious. The reason for this is that the seasons, which depend on the date in the tropical year, were getting progressively out of kilter with the calendar date. Pope Gregory XIII, in 1582, instituted the Gregorian calendar, which has been used since then.

The change from the Julian calendar to the Gregorian involved the change of the simple rule for leap-years to the more complex one in which century years should only be leap-years if they were divisible by 400. For example, 1700,1800 and 1900 are not leap-years whereas 2000 will be.

The net effect is to make the adopted average length of the year 365.2425 days. The dhe year 365.2425 days. The difference between this and the true length will not have a serious effect for many thousands of years. (The error amounts to about 3 days in 10,000 years.)

The adoption of the Gregorian calendar was made in Catholic countries in 1582 with the elimination of 10 days, October the 4th being followed by October 15th. The Gregorian calendar also stipulated that the year should start on January 1. In non-Catholic countries the change was made later; Britain and her colonies made the change in 1752 when September 2nd was followed by September 14 and New Year's Day was changed from March 25 to January 1.


A millennium is a period of 1000 years. The question of which year is the first year of the millennium hinges on the date of the first year AD.

Unfortunately the sequence of years going from BC to AD does not include a Year 0. The sequence of years runs 3 BC, 2 BC, 1 BC, 1 AD, 2 AD, 3 AD etc. This means that the first year of the first millennium was 1 AD. The one thousandth year was 1000 AD and the first day of the second millennium was 1001 AD.

It is thus clear that the start of the new millennium will be 1 Jan 2001.


The year 200="br1">

The year 2000 AD will certainly be celebrated, as is natural for a year with such a round number but, accurately speaking, we will be celebrating the 2000th year or the last year of the millennium, not the start of the new millennium. Whether this will be an excuse for more celebrations in the following year will have to be seen! /html>