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The description of the calendar

The Gregorian solar calendar^[1] is an arithmetical calendar. It counts days as the basic unit of time, grouping them into years of 365 or 366 days.

The solar calendar repeats completely every 146,097 days, which fill 400 years, and which also happens to be 20,871 seven-day weeks. Of these 400 years, 303 (the "common years") have 365 days, and 97 - the leap years - have 366 days.

This gives an average year length of exactly 365.2425 days - or 365 days, 5 hours, 49 minutes and 12 seconds. 

A Gregorian year is divided into twelve months of irregular length (but note that there is a period of 153 days divided over 5 months in an alternating pattern from March to July that repeats from August to December):

A calendar date is fully specified by the year (numbered by some scheme beyond the scope of the calendar itself), the month (identified by name or number), and the day of the month (numbered sequentially starting at 1).

Leap years  are all years divisible by 4, with the exception of those divisible by 100, but not by 400. These 366-day years add a 29th day to February, which normally has 28 days. Thus, the essential ongoing differential feature of the Gregorian calendar, as opposed to the Julian calendar, is that the Gregorian omits 3 leap days every 400 years. This difference would have been more noticeable in modern memory were it not for the fact that the year 2000 was a leap year in both the Julian and Gregorian calendar systems.

The intercalary day  in a leap year is known as a leap day. Since Roman times 24 February (bissextile) was counted as the leap day, but nowadays 29 February is regarded as the leap day in most countries.

Although the calendar year runs from 1 January to 31 December, sometimes year numbers were based on a different starting point within the calendar. Confusingly, the term "Anno Domini" is not specific on this point, and actually refers to a family of year numbering systems with different starting points for the years. (See the section below for more on this issue.)

The history

The motivation of the Catholic Church in adjusting the calendar was to celebrate Easter at the time it thought the First Council of Nicaea had agreed upon in 325. Although a canon of the council implies that all churches used the same Easter, they did not. The Church of Alexandria celebrated Easter on the Sunday after the 14th day of the moon (computed using the Metonic cycle) that falls on or after the vernal equinox, which they placed on 21 March. However, the Church of Rome still regarded 25 March as the equinox (until 342) and used a different cycle to compute the day of the moon. In the Alexandrian system, since the 14th day of the Easter moon could fall at earliest on 21 March its first day could fall no earlier than 8 March and no later than 5 April. This meant that Easter varied between 22 March and 25 April. At Rome, Easter was not allowed to fall later than 21 April, this being the day of the Parilia or birthday of Rome and a pagan festival. The first day of the Easter moon could fall no earlier than 5 March and no later than 2 April. Easter was the Sunday after the 15th day of this moon, whose 14th day was allowed to precede the equinox. Where the two systems produced different dates there was generally a compromise so that both churches were able to celebrate on the same day. By the tenth century all churches (except for some on the eastern border of the Byzantine Empire) had adopted the Alexandrian Easter, which still placed the vernal equinox on 21 March, although Bede had already noted its drift in 725—it had drifted even further by the sixteenth century.

Worse, the reckoned Moon that was used to compute Easter was fixed to the Julian year by a 19 year cycle. However, that approximation built up an error of one day every 310 years, so by the sixteenth century the lunar calendar was out of phase with the real Moon by four days.

The Council of Trent approved a plan in 1563 for correcting the calendrical  errors, requiring that the date of the vernal equinox be restored to that which it held at the time of the First Council of Nicaea in 325 and that an alteration to the calendar be designed to prevent future drift. This would allow for a more consistent and accurate scheduling of the feast of Easter.

The fix was to come in two stages. First, it was necessary to approximate the correct length of a solar year. The value chosen was 365.2425 days in decimal notation. This is 365; 14,33 days in sexagesimal notation—the length of the tropical year, rounded to two sexagesimal positions; this was the value used in the major astronomical tables of the day. Although close to the mean tropical year of 365.24219 days, it is even closer to the vernal equinox year of 365.2424 days; this fact made the choice of approximation particularly appropriate as the purpose of creating the calendar was to ensure that the vernal equinox would be near a specific date (21 March).

The second stage was to devise a model based on the approximation which would provide an accurate yet simple, rule-based calendar. The formula designed by Aloysius Lilius was ultimately successful. It proposed a 10-day correction to revert the drift since Nicaea, and the imposition of a leap day in only 97 years in 400 rather than in 1 year in 4. To implement the model, it was provided that years divisible by 100 would be leap years only if they were divisible by 400 as well. So, in the last millennium, 1600 and 2000 were leap years, but 1700, 1800 and 1900 were not. In this millennium, 2100, 2200, 2300 and 2500 will not be leap years, but 2400 will be. This theory was expanded upon by Christopher Clavius in a closely argued, 800 page volume. He would later defend his and Lilius's work against detractors.

The 19-year cycle used for the lunar calendar was also to be corrected by one day every 300 or 400 years (8 times in 2500 years) along with corrections for the years (1700, 1800, 1900, 2100 et cetera) that are no longer leap years. In fact, a new method for computing the date of Easter was introduced.

Lilius originally proposed that the 10-day correction should be implemented by deleting the Julian leap day on each of its ten occurrences during a period of 40 years, thereby providing for a gradual return of the equinox to 21 March. However, Clavius's opinion was that the correction should take place in one move and it was this advice which prevailed with Pope Gregory XIII. Accordingly, when the new calendar was put in use, the error accumulated in the 13 centuries since the Council of Nicaea was corrected by a deletion of ten days. Thus the papal bull of February 1582 decreed that 10 days should be dropped from October 1582 so that 15 October should follow immediately after 4 October, and from then on the reformed calendar should be used. And so the last day of the Julian calendar was Thursday October 4, 1582 and this was followed by the first day of the Gregorian calendar, Friday October 15, 1582 (the cycle of weekdays was not affected).

Adoption of the new calendar was essentially immediate within Catholic countries. In the Protestant countries, where papal authority was neither recognized nor appreciated, adoption came more slowly.