History of Roman calendar

• The oldest form of roman calendar known in history used lunar months (also called synodic months). Since a lunar month comprises of 29.53054 (approximately 29 and half) days, romans used to have months alternately having 29 and 30 days. They had 10 months (and hence 295 days) in a year's calendar. The first one was called March and the last four September, October, November and December (implying their positions (7th, 8th, 9th and 10th) in the year).

• It's not clear when the concept of a 12 month year was first conceived by the romans. Legend says that the months January and February were added during the reign of Numa Pompilius (738 B.C.). Afterwards the 5th king of Rome, Tarquinius Priscius (616 - 579 B.C.) supposedly introduced the roman republican calendar that had 12 months and 355 days. A special month was inserted between Feb 23 and 24 once every two years to cope up with the imbalance of 365 - 355 = 10 days per year.

• The use of a 365-day calendar came eventually. February used to have 28 days, April, June, September and November 30 days and others 31 days. This means that months no longer remained lunar.

• Julian reform: Absence of leap years and also of strict enforcement of the rules finally led to enough confusions. It was in 46 B.C. when the Roman emperor Julius Caesar with the help of the Greek astronomer Sosigenes incorporated a major change in the roman calendar. In the first place Julias Caesar intercalated (that is, added) 85 days to the year 46 B.C. (making it quite a long year!!!). Secondly, the concept of a leap year was introduced, since it was known by that time that a solar year has 365.25 days. It was decided to add a day to February once every four years (more precisely, in the years that are multiples of 4). The roman calendar with all these amendments (called the Julian calendar) was finally inaugurated officially on Jan 1, 45 B.C.

  [Note: The solar (or tropical) year is the time interval between successive passages of the Sun through the vernal equinox. Equinox is the time of the year when the lengths of the day and the night are equal. This happens twice in the year when the sun crosses the equator - once around March 21 (vernal or spring equinox) and once around September 22 (autumnal equinox).]

• The solar year actually consists of 365.242199 solar days. The practice of having a leap year every 4 years, therefore, had the over-compensation of about 0.0078 day per year, that is, 3 days per 4 centuries. The first ecumenical council held at Nicaea in 325 A.D. talked about the resulting lag of 4 days in the Julian calendar (actually, 3 days can be accounted for the inexact calculation of the solar year; the other day was probably due to an error of Sosigenes). The people at the council attributed this discrepancy to faulty calculations by Sosigenes and moved the date of (vernal) equinox from March 25 to March 21.

• Gregorian reform: But the drift continued and the discrepancy went larger and larger with time. The deviation was 10 days at the time of Pope Gregory XIII (late 16th century). The equinox of 1582 fell on March 11 rather than on the expected March 21. By that time, people have calculated the solar year more accurately (compared to 365.25 days as in the time of Julius Caesar). Gregory removed 10 days - October 5 to October 14 - from the year 1582 and proclaimed that from that time onwards 3 days would be dropped from the calendar every 400 years. The years that are multiples of 100 would not be leap years with the exception that those that are multiples of 400 would be leap years. Thus, the years 1700, 1800, 1900, 2100 etc would not be leap years, whereas years 1600, 2000, 2400 etc would be leap years.

  France and Netherlands incorporated the Gregorian correction in 1582, the catholic states of Germany in 1584, Poland in 1586 and the protestant states of Germany and Switzerland in 1700. England and its colonies and Sweden accepted the Gregorian calendar at 1752 when the discrepancy was 11 days. Many other countries including Japan, China and Soviet Union, accepted the modifications much later, some even in the 20th century (this time the lag was 13 days).

• The Gregorian correction leaves us with an inexactness of 0.0003 day per year, that is, 3 days per 10,000 years. This need not be corrected for the time being, because the probability of change of rotation timings of earth and sun is assumed to be larger than this error. That is, deviations are likely to occur due to astronomical reasons at a rate larger than 3 days per 10,000 years. When such situations come, our descendents will deal with them accordingly. We should not and need not adopt advance preventive measures now.

hcal (also cal of UNIX and calendar of NCSA) follows the British convention of roman calendar. That is, before 1752, a year is a leap year if and only if it is a multiple of 4. After 1752, a year is a leap year if and only if it is divisible by 4 and is a multiple of 400 whenever it is a multiple of 100. The year 1752 was a leap year (in the 29-days-in-February sense) that comprised of 355 days - 11 days were cut from the month of September (September 3 to September 13).

References

[1]

Encyclopedia Americana, Volume 5, Grolier Inc., 1994.

[2]

The New Encyclopædia Britannica, Volume 2, 1985.