The problem: a year that is not 365.25 days
The Julian calendar, introduced by Julius Caesar, made every fourth year a leap year, giving an average year of 365.25 days. The solar year that governs the seasons is shorter, close to 365.2422 days. The difference is about 0.0078 of a day per year, which is roughly one day in 128 years.
That sounds small, and for centuries it did not matter much. But it accumulates. By the sixteenth century the calendar date of the spring equinox had slipped from about 21 March, the date Church authorities had treated as the fixed reference when setting Easter in the fourth century, to about 11 March. The calendar was running about ten days ahead of the seasons.
What the reform did
The correction was issued by Pope Gregory XIII in a document dated February 1582, usually known by its opening words, Inter gravissimas. It made two changes.
First, it removed ten days to bring the calendar back in line. In the countries that adopted it immediately, Thursday 4 October 1582 was followed by Friday 15 October. The days of the week continued without a break; only the dates were skipped.
Second, it changed the leap-year rule so the drift would not return. A year divisible by 4 remains a leap year, except that years divisible by 100 are not leap years unless they are also divisible by 400. So 1600 and 2000 were leap years, while 1700, 1800 and 1900 were not.
Checking the arithmetic
In every 400 years the Julian rule would have 100 leap years. The Gregorian rule has 97, because it drops the century years that are not divisible by 400, which are three out of every four. The total days in 400 Gregorian years is 400 times 365 plus 97, or 146,097. Divided by 400, that gives an average year of 365.2425 days.
This is very close to 365.2422. The remaining difference of about 0.0003 of a day per year adds up to roughly one day over 3,000 years or so, which is why the Gregorian calendar is considered accurate enough for ordinary use. Calendars in this sense are approximations, a theme also found in the approximations of pi that mathematicians refined over the centuries.
Why different countries switched at different times
The reform was a papal decree, which meant its acceptance depended on religion and politics as much as astronomy. The pattern of adoption is a good illustration.
- Catholic states acted quickly. Spain, Portugal, much of Italy and the Polish-Lithuanian Commonwealth changed in October 1582, and France followed in December of that year.
- Many Protestant German states, along with Denmark and Norway, kept the old system for over a century and changed around 1700. Some objected to taking a calendar from the pope.
- Britain and its colonies switched in 1752. By then the gap was eleven days, because 1700 had been a leap year in the Julian calendar but not in the Gregorian. In that year 2 September was followed by 14 September. The same act moved the start of the legal year from 25 March to 1 January. There were complaints about lost days, though the popular story of riots demanding them back is generally considered exaggerated.
- Sweden took an unusual path: a gradual change begun in 1700 was abandoned, and the country finally switched in 1753.
- Russia adopted it after the 1917 revolution: in 1918, 31 January was followed by 14 February. By then the gap was thirteen days.
- Greece adopted it for civil purposes in 1923, and Turkey changed its civil calendar in the 1920s.
- Japan moved to the Gregorian calendar in 1873, and China officially adopted it at the start of the Republic in 1912, though traditional lunisolar dates remained in use.
Several Eastern Orthodox churches continued to use the Julian calendar for religious dates, and some adopted a revised version in the 1920s. For the current period the Julian calendar runs thirteen days behind the Gregorian.
Living with the gap
For historians, the switch means that dates from the period of change need careful labelling. A document might be marked “Old Style” or “New Style”, and two correspondents in different countries could date the same day ten or eleven days apart. Famous cases include events in Britain and on the continent that happened on the same day but carry different dates.
For ordinary people, the reform also left small cultural traces. The special case of a leap day, 29 February, creates its own puzzles in anniversary traditions, such as when a person born on that day marks a birthday. Different legal systems answer in different ways.
What the reform shows
The Gregorian reform did not give any number a new meaning, but it shows how a number that looks simple, 365, hides a messy fraction. Calendar numbers are tuned to the sky over time, and where the tuning is done by an institution with religious authority, the results spread unevenly. The 1582 date marks the start of a process that took more than three centuries to complete, and in some religious calendars it is not complete today.