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Julian & Gregorian Calendars
The Julian calendar is based on a 12-month year - the modern names of months still derive from the Julian calendar, and with generally the same number of days in each month as the modern Gregorian calendar. In the Julian system, February normally has 28 days, but has 29 days every fourth year - leading to a year that averages exactly 365.25 days long. This unfortunately does not match the exact period that the Earth takes to orbit around the sun (known as the "tropical year" or "solar year"), as a result the Julian calendar gains about 1 day, against the solar year, every 128 years.
The Julian calendar remained in widespread for many centuries after the fall of the Roman Empire, and gradually this discrepency began to become more and more noticeable. To correct this problem, Pope Gregory XIII introduced a revised calendar, known as the Gregorian calendar, in 1582.
Under the Gregorian system, February still has 28 days in most years and 29 in leap years, but the system for determining leap years is more complex - a year is a leap year if it is evenly divisible by 4, but not evenly divisible by 100, except when it is divisible by 400. So, for example, 1896 was a leap year (divisible by 4), 1900 was not a leap year (divisible by 100), and 2000 was a leap year (divisible by 400).
The result of this extra complexity, is that years in the Gregorian system average to 365.2425 days, which is much closer to the solar year. As compared to the large cumulative errors in the Julian system, the Gregorian calendar accummulates much smaller errors - it only gains 1 day every 3,226 years.
Additionally, one other incidental change with the Gregorian system is that the beginning of the year was moved from March to January, although this was purely a matter of convenience rather than accuracy.
The Gregorian calendar was gradually adopted by all European countries as their civil calendar, but different countries took different amounts of time to switch to it - in some cases it took hundreds of years before it was adopted. The last two countries to switch over were Russia (1917) and Greece (1923). Even today however, the Julian calendar still has some remaining niche uses - for example, certain churches use it in calculate the dates of religious feasts and festivals.
One final consequence of the introduction of the Gregorian, was the same day may be given as two different dates. This is because when the Gregorian calendar was first introduced, some dates were removed to deal with the discrepencies that had already occurred (in some countries there were riots about the "lost" or "stolen" days!), and of course since the Julian calendar remained in use in many places, the discrepencies grew wider over time. Thus you can often see the same event, or date of birth, or date of death, given different during the period of the switch-over, depending on whether the date is given according to the Old Style Julian calendar, or the New Style Gregorian calendar. For example the "October Revolution" (which the Bolsheviks gained power in Russia in 1917), actually took place on the 7th and 8th of November 1917, according to the currently used Gregorian calendar.
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