Topic: From the Old-Style Julian Calendar to the New-Style Gregorian Calendar

The duration of the Julian Calendar (365 days and 6 hours or 365.25 days) is not exactly equal to the real duration of the tropical year, which is 365 days, 5 hours, 48 minutes and 45 seconds (or 365.24219879 days), resulting to a delay of one day every 128 years. This led to the need of a new reformation from the Old Style (Julian) Calendar to the New Style (Gregorian) Calendar in 1582 in the Catholic countries.

The weakness of the old calendar was evident as a shift with respect to the seasons. The excess of the calendar in relation to the real position of the sun in the ecliptic, which determines the seasons, results to a delay of the dates to the seasons. It means that the spring equinox, which should be on March 21st in the 1500s it occurred when the calendar showed March 11th.

Various philosophers and scientists, such as Roger Bacon (1214-1292) and Nicephorus Gregoras (1295-1360) had spoken and written about the necessity of the reformation. At last the man who undertook officially this great project was Pope Gregory XIII (1502-1585) in 1582 under the scientific help of doctor Aloysius Lilius (Luigi Lilio) (1510-1576) and the support of Antonio, brother of Aloysius and the Jesuit astronomer Christofer Clavius (1538-1612). Clavius was the man behind the scenes who championed Lilius's ideas, in the time of the great scientific and ecclesiastic controversy before and after 1582 (David Ewing Duncan, The Calendar, Publ. by Fourth Estate Limited, London, 1998).

The Pope with a bull ordered that the day following October 4th 1582 AD would be not 5th but 15th of October, with 10 days lost. This caused a lot of strange reactions and sentiments in all the classes of the people, from uneducated full of superstitions considering that they had lost 10 days of their life to educated officials considering that the calendar reformation was a strategic tool for the dominion of the Papal Church. For this reason the protestant countries admitted the calendar correction after nearly 2 centuries. United Kingdom and its colonies aligned with the Gregorian Calendar used by the Catholic countries in September 2nd of 1752 AD, deciding that the next day would not be the 3rd but the 14th (11 days later, one more day had been lost due to the year 1700, taken as leap in Julian but normal in Gregorian. The reaction of the people supported by the party of the Tories against the party of Whigs was tremendous. The slogan 'give us our eleven days' was heard for years. Another financial consequence of the reform was the day of tax paying. The start of the official and financial year of England from 1155 until 1751 was March 25th (Lady Day). After the calendar loss of 11 days, the day for the obligation of tax payment was transferred 11 days later, on April 5th and after 1800, a year, which the Gregorian Calendar does not consider as leap, it resulted to be April 6th, until nowadays.

Other countries adopted Gregorian Calendar even later. Alasca decided that the day following October 5th of 1867 would become 18th. In Soviet Russia the day after January 31st of 1918 became February 14th. In Greece the day after February 15th of 1923 became March 1st.
The most strange strategic was that of Sweden. In 1700, a year considered as leap in Julian Calendar but not leap in Gregorian, they decided that the day following February 28th would not be 29th (as the Julian did) but March 1st. This resulted to a very strange situation. Swedish Calendar after March 1st of 1700 was 1 day in advance to the Julian calendar and 10 days behind the Gregorian Calendar. They decided to correct it and realign it to the Julian Calendar in February 29th of 1712, by inserting one more leap day, February 30th (1712 in Sweden lasted 367 days). At last on February 17th of 1753, they decided that the next day would be March 1st, aligning their calendar to the Gregorian.

Which is the algorithm for definition of a year as a leap year in the Gregorian Calendar? Every year divisible by 4 is leap (this is the same as in the Julian Calendar). Exception: Every year divisible by 100 (as 1700, 1800, 1900) is not leap. Exception to the exception: Every year divisible by 400 (as 1600, 2000, 2400) is leap. According to this definition, the number of leap years in the duration of 400 years is 400/4 – 400/100 + 400/400 = 97. Therefore the mean duration of the Gregorian year is d = (303*365+97*366) / 400 = 365.2425 days, much closer to the real duration of the tropical year (365.21249879 days) than the mean duration of the Julian year, which is d=365.25 days.

The Gregorian calendar will be 3 days, 17 min, 33 s behind the Sun after 10,000 years. This inaccuracy could be corrected if we de-characterize a leap year as leap every 3200 years.