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A calendar defines, among many other things, the length of each year. Calendars with different year lengths must use different numbering systems.
However within a single calendar, it is possible to have several year numbering systems. This occurs for both the Gregorian calendar currently in common use and also the Julian calendar which preceded it.
Calendars with identical year lengths can share a numbering system, as has been proposed for several proposed reformed calendars based on Gregorian years.
The average year length within the Gregorian calendar is almost exactly one solar year, and continuing corrections will keep this true. There are several systems of year numbering, and several different names for the most common system.
See Anno Domini for a discussion of the arguments for and against various terms.
The Julian calendar was in use from 45 BC to AD 1582, and in many parts of the world until AD 1752, Russia until AD 1918, Greece until AD 1924 and Turkey until AD 1926.
It has a very slightly longer average year length than the Gregorian calendar, and therefore falls slowly out of step with the solar year. It is still used by Orthodox Churches for reckoning the date of easter, but no longer for year numbering.
In the period in which the Julian calendar was in official use, the similarly-marked Julian and Gregorian year numbers for a particular date will either be equal or the Julian year number will be one less than the Gregorian (and of course the day of the month and perhaps the month will differ, but the day of the week will be the same).
Julian dates will also sometimes be encountered for events outside the period of the calendar's use, see Proleptic Julian calendar.
Within this period, there are two reasons for the difference. Firstly, as Gregorian dates were set to be identical to Julian in 45 BC, the differing year length meant that by AD 1582 a ten day difference had accumulated. Secondly and more significantly, while the Julian year originally started on January 1, early in church history was moved to March 25, the supposed date of the Resurrection, where it remained until the introduction of the Gregorian calendar. This is extremely confusing, for example March 30, AD 501 is almost a year before March 20, AD 501 in this system. This led to the use of separate ecclesiastical and legal year ends, the legal year ending on December 31 preceding the ecclesiastical end of the same year. Sometimes these two will be seen combined, for example Francis BaconFor others individuals named Francis Bacon see: Francis Bacon (disambiguation Francis Bacon, 1st Viscount St Albans ( January 22, 1561 April 9, 1626), more commonly known as Sir Francis Bacon achieved fame as an English philosopher, statesman, and essayis's birth-date could be given as January 22nd, 1560-61 (OS). This style of year also gives a clue that a Julian date is probably intended.