The earliest calendars were lunar based. With a month being the length of time marked by the revolution of the Moon around the Earth. In many traditional societies, the appearance of the first tiny crescent moon after the New Moon signaled the start of the month. The lunar month is the average interval between two successive moments of New Moon. Its length is 29.5 days.

The lunar calendars that best approximated a solar-year calendar are based on a 19-year period, with seven of these 19 years having 13 months, containing 235 months. Still using the lunation value of 29.5 days, this made a total of 6,932.5 days, while 19 solar years added up to 6,939.7 days, a difference of just one week per period and about five weeks per century.

Even the 19-year period required adjustment, but it is the basis of the calendars of the ancient Chinese, Babylonians, Greeks, and Jews. The Arabs also used this same calendar, but Muhammad later forbade shifting from 12 months to 13 months, so that the Islamic calendar, even today, has a lunar year of 354 days. As a result, the months of the Islamic calendar, as well as the Islamic religious festivals, migrate through all the seasons of the year.

When Rome emerged as a world power, they complicated their lives with their superstition that even numbers were unlucky. The Roman months were 29 or 31 days long, with the exception of February, which had 28 days. However, four months of 31 days, seven months of 29 days, and one month of 28 days added up to only 355 days. Therefore, the Romans created an extra month called Mercedonius of 22 or 23 days was added every second year.

Even with this extra month, the Roman calendar eventually became so far off that Julius Caesar, advised by the astronomers, ordered a sweeping reform in 45 B.C. One year, made 445 days long by imperial decree, brought the calendar back in step with the seasons. The solar year (with the value of 365 days and 6 hours) was made the basis of the calendar. The months were 30 or 31 days long, and to take care of the 6 hours, every fourth year was made a 366-day year. Caesar decreed the year began with the first of January, not with the equinox in late March.

This calendar is named the Julian calendar, after Julius Caesar, and it continues to be the calendar of the Eastern Orthodox churches to this day. However, despite the correction, the Julian calendar is still 11.5 minutes longer than the actual solar year, and after a number of centuries, even 11.5 minutes adds up.

By the 15th century, the Julian calendar had drifted behind the solar calendar by about a week, so that the vernal equinox was falling around March 12 instead of around March 20. In 1545, the Council of Trent authorized Pope Paul III to reform the calendar. The mathematical and astronomical work was done by Father Christopher Clavius, S.J. The correction advised by Father Clavius and ordered by Pope Gregory XIII, was that Thursday, Oct. 4, 1582, was to be the last day of the Julian calendar. The next day would be Friday, Oct. 15. For long-range accuracy, a formula was adopted: every fourth year is a leap year unless it is a century year like 1700 or 1800. Century years can be leap years only when they are divisible by 400 (e.g., 1600 and 2000). This rule eliminates three leap years in four centuries, making the calendar sufficiently accurate.

For in spite of the revised leap year rule, an average calendar year is still about 26 seconds longer than the Earth's orbital period. However, this discrepancy will need 3,323 years to build up to a single day.

Earth's orbital period. However, this discrepancy will need 3,323 years to build up to a single day.

The Gregorian reform was not adopted throughout the West immediately. All the Protestant princes in 1582 chose to ignore the papal bull; they continued with the Julian calendar. It was not until 1698 that the German professor Erhard Weigel persuaded the Protestant rulers of Germany and the Netherlands to change to the new calendar. In England, the shift took place in 1752, and in Russia, it needed the revolution to introduce the Gregorian calendar in 1918. Greece switched over in 1923.