Handout 1

A Brief History of Calendar Time

The Julian calendar was implemented by Julius Caesar in 46 BC It defined the year as having an average length of 365.25 days. Establishing that every fourth year (the leap year) would comprise 366 days while the remaining years (the common years) would comprise 365 days recognized the extra day (called a leap day) that occurred every four years. This arrangement resulted in inaccuracies. By setting the year at 365.25 days. The calendar was setting the duration of a single revolution of the earth around the sun at 365 days, 6 hours. In fact, a single revolution takes 365 days, 5 hours, 49 minutes, and 12 seconds. The defined calendar year was 10 minutes and 48 seconds (or 10.8 minutes) too long. Over the course of 400 years, this difference resulted in the calendar being 3 days ahead of itself.

As time passed, the problem worsened, and by the sixteenth century, the calendar was 12 days ahead. In 1582, Pope Gregory XIII decided to trim the extra days the Julian calendar had added, and to redefine which years were leap years, so that they better reflected the astronomical reality. He cut ten days from October: October 4, 1582 was followed by October 15, 1582. In addition, he mandated that from then on all years evenly divisible by four would be leap years except those that were evenly divisible by 100 and not divisible by 400. In the period 1599 to 1999, all years that are evenly divisible by 4 are leap years except for 1700, 1800, and 1900. Years 1600 and 2000 are leap years. The effect of this change is that 3-century years out of every 400 years are not leap years. This step corrects the Julian calendar error of 3 extra days every 400 years. The new calendar was named the Gregorian calendar after the pope.

The modifications proclaimed by Pope Gregory applied only to lands over which the Catholic Church had dominion. Protestant countries, such as England, refused on principle to go along with any papal edict and hence moved to the Gregorian calendar at separate times. While most Protestant countries adopted the new calendar in the 1699-1701 time frame, England (and hence the American colonies) did not switch over until 1752. By the time they made this move, another spurious day from the Julian calendar had crept into the error between the two calendars. So, in September 1752, England cut eleven days from the calendar: September 2, 1752 was immediately followed by September 14, 1752. After 1752, most major Western countries were on the Gregorian calendar. However, smaller nations held out much longer for all sorts of political reasons. Romania did not convert until 1919; Turkey not until 1927. Even today, countries under the dominion of the Eastern Orthodox Church use a variant of the Gregorian calendar to formulate their own dating system.

The Gregorian calendar made one additional change: it set the starting date of the New Year as January 1. Previously, individual countries celebrated the New Year on different days--some as early as December 25 and others as late as March 25. Before 1752, England and the American colonies used March 25 as New Year's Day. That is, March 24, 1701, was followed by March 25, 1702. Because of this change, George Washington's birthday, which today is given as February 22, 1732, was actually recorded on that day as February 11, 1731. Hence, if you need to talk exactly about any date prior to 1752, you must know where the event was recorded and whether the date has been converted to a Gregorian calendar.

Most calendar systems use the conventions:

1582 is used as the switch over point, and the current calendar convention of starting the new year on January l is projected backward over previous years. It is commonly understood that this projection means that the dates will occasionally be at odds with the dates, as they would have been recorded on the given day.
Most calendars used on computers today seek to do one thing: to give every day a unique, identifying sequential code that allows the user to compute dates relative to the current period. Beyond that, all bets are off.

Determining Leap Years

Year year is a leap year if it is divisible by 400 or it is a year that is divisible by 4 and not divisible by 100. Algorithmically this can be written as:

((year%4 == 0) && (year%100 != 0)) || (year%400 == 0)

returns true for leap years.

Some Time References

``Calendrical Calculations'', Dershowitz, N. & Reingold, E. M. 1990 Software-Practice and Experience 20 899
``Calendrical Calculations, II: Three Historical Calendars'', Reingold, E. M., Dershowitz, N., & Clamen,
Stewart, M. 1993 Software-Practice and Experience 23 383.

* Portions from Binstock and Rex, Practical Algorithms for Programmers.