The year is measured as one orbit of the earth around the sun. Called a solar year, tropical year, or seasonal year, a month was calculated by ancient skyward looking peoples as simply the time between two full moons, or the number of days for the moon to circle the earth, 29.5 days. This measurement, the lunar month, resulted in a lunar year of 354 days, which is 11 days shorter than the solar year.

In modern calendars, however, the days in each month are not based on the phases of the moon. The lengths of the months are approximately one-twelfth of a year, 28 to 31 days, and adjusted to fit the 12 months into a solar year.

Variations in the many calendars used from ancient times developed from the original, inaccurate ideas of the length of the year. These educated guesses, combined with the fact that a year cannot be divided evenly by any of the time units, days, weeks, or months, created a system of time that could not be sustained through centuries. The earliest calendars based on lunar months eventually failed to agree with the seasons and a month occasionally had to be added, to reconcile lunar months with the solar year.

The ancient Egyptians were the first to replace the lunar calendar with a calendar based on the solar year. They measured the solar year as 365 days, divided into 12 months of 30 days each, with 5 extra days at the end. About 238 BC King Ptolemy III ordered that an extra day be added to every fourth year, similar to the modern leap year.

In ancient Greece a lunar/solar calendar was in use, with a year of 354 days. Julius Caesar, upon the advice of his astronomer Sosigenes, decided to use a purely solar calendar, known as the Julian calendar, which fixed the normal year at 365 days, and the leap year, every fourth year, at 366 days. A leap year is so named because the extra day causes any date after February in a leap year to "leap" over one day in the week, and to occur two days later than it did in the previous year, rather than just one day later as in a normal year. The Julian calendar also established the order of the months and the days of the week as they exist in present-day calendar, and named the days of the week in honor of the sun, moon, and various planets. Unfortunately, the Julian year was 11 minutes and 14 seconds longer than the solar year and would eventually suffer the similar inaccuracies of earlier calendar systems.

Although the Julian method of intercalation was the most convenient that could be adopted, it could not, without correction, preserve the same interval of time between the beginning of the year and the equinox. It had been shown long before, by the observations of Hipparchus in 125 BC, that the excess of 365 1/4 days beyond a true solar year would amount to one day in 300 years. The real error is actually more than double this--one extra day every 128 years--but in the time of Caesar the length of the year was not a very well defined astronomical phenomenon. In the course of a few centuries, the inadequacies of the system were felt as the equinox retrograded towards the beginning of the year. When the Julian calendar was introduced, the equinox fell on the 25th of March. At the time of the Council of Nicea, which was held in 325, the equinox fell on the 21st.

The situation was increasingly seen as a scandal. By 700 AD it had become customary to count the years from the birth of Christ. But the equinox kept slipping backwards on the calendar one full day every 130 years. By 1500 the vernal equinox fell on the 10th or 11th of March and the autumnal equinox on the 13th or 14th of September.

The most important feast day on the Christian calendar is Easter. In the New Testament we find that Christ's crucifixion occurred a week after Passover. On the Jewish calendar, Passover was celebrated at the full moon of the first month of spring. In developing their own calendar, Christians put Easter on the first Sunday after the first full moon after the spring equinox. This is why Easter always fall between March 21 and April 18th depending on the full moon. If the equinox was wrong, then Easter was celebrated on the wrong day. Most other Christian observances (e.g., the beginning of Lent, Pentecost) are reckoned backward or forward from the date of Easter.

An error in the equinox thus introduced numerous errors in the entire religious calendar. Something had to be done. After several false starts, a commission under the leadership of the Jesuit mathematician and astronomer Christoph Clavius succeeded. In 1582 Pope Gregory XIII (hence the name Gregorian Calendar) ordered ten days to be dropped from October, thus restoring the vernal equinox at least to an average of the 20th of March, close to what it had been at the time of the Council of Nicea. In order to correct for the loss of one day every 130 days, the new calendar dropped three leap years every 400 years. Henceforth century years were leap years only if divisible by 400. Therefore 1600 and 2000 are leap years and 1700, 1800 and 1900 are not.

The new calendar, although controversial among technical astronomers, was pushed from Rome and adopted immediately in Catholic countries. Protestant countries like Germany, and the northern regions of the Netherlands adopted the calendar several decades later. The English, always suspicious of Rome during this period, retained the Julian Calendar and furthered the confusion: while other countries now began the new year uniformly on January 1st, the English maintained their older custom and began the New Year March 25th. The date February 11, 1672 in England was February 21, 1673 on the Continent. After 1700 in which the Julian Calendar had a leap year but the Gregorian did not, the difference was eleven days. The English and their American colonies finally adopted the Gregorian Calendar in the middle of the eighteenth century. George Washington was born on 11 February on the Julian Calendar, however we celebrate his birthday on 22 February.

OK, so let's run the calculations: The period of time from one vernal equinox to another is 365 days, 5 hours, 48 minutes and 45.5 seconds and is again known as a solar year. The Gregorian calendar approximates the solar year with a combination of common years of 365 days and leap years of 366 days.

A common year differs from a solar year by 5 hours, 48 minutes and 45.5 seconds. After 4 years this totals 23 hours, 15 minutes and 4 seconds, so a day is added to the year and it becomes a leap year.

However, at the end of a leap year we are short almost 45 minutes of making a whole day. After 100 years this leap year deficit comes to 1123.3 minutes, or 18 hours and 43.3 minutes. This is why century years (1700, 1800, 1900, etc.) are not leap years, even though they are divisible by 4. There is no need to add in an extra day since we are 18 hours and 43.3 minutes short.

Not adding in this day on century years gives us a 5 hours and 16.7 minutes surplus. After 400 years this equates to 21 hours and 6.8 minutes. Therefore century years that are divisible by 400, like the year 2000, do become leap years. Because of this simple fact, which most programmers either forgot or didn't anticipate, many software programs do not calculate the year 2000 as a leap year. So besides checking your computer for Y2K compliance, you should also check to see how your computer and various software programs handle the date change after 28 Feburary 2000.

Unfortunately, Christoph Clavius' solar year was a bit off and his calculations stopped at the every 400-year adjustment believing that it was sufficient. Today we know that this 400-year compensation still leaves a 3 hour and 53 minute deficit and some astronomers have proposed that century years divisible by 4000 not become a leap year. If accepted, the year 4000, normally a century leap year (divisible by 400) will not become one and the Gregorian calendar will once again come into close alignment (only 42 minutes in error) with the solar year. Since we have 2000 years to think about it, we should be able to solve the problem. Besides, by then it really won't matter very much to us.

Historical sources: *Funk & Wagnalls New Encyclopedia.*, 29v., K-III Reference Corp., 1996.