The day after September 2, 1752 — it was a Wednesday — was September 14. At least it was in Great Britain and all the British colonies. That was the day of the big switch from the Julian to the Gregorian calendar. The two calendars were off by 11 days at the time (the amount varied), and the correction had the slightly odd result that September 3 through 13 never happened that year. Although 1752 was a leap year, it only had 355 days — in the British Empire, that is.
The change was mandated by the Calendar (New Style) Act that Parliament passed in 1750. Besides changing the calendar and erasing 11 days, the Act also changed the start of the year from March 25 to January 1. That is, the start of the legal year changed. The United Kingdom also has a tax yea” for the calculation of income taxes; that starts on April 6.
Nobody seems to be quite sure why the tax year starts on April 6. A 1921 book by Alexander Philip included the observation that April 6 is 12 days after March 25, and theorized that in 1752, when 11 days were erased by the shift in calendars, the tax year was lengthened by 11 days (from March 25 to April 5) to make sure they didn’t fall short on their tax collections. Then an extra day was added in 1800, according to Philip, because that year was one day shorter in the Gregorian calendar than in the Julian.
That’s all just theory, though. Other historians claim that the tax year before 1752 didn’t start on March 25, it was the 26th, so the 11 day addition was the only one ever. If you look up the records of the British Treasury, no addition of 11 days in 1752 is mentioned. It wouldn’t have mattered anyway, because the taxes in those days weren’t calculated on the basis of days. That’s because they didn’t care about your income. They just looked at the amount of land you owned, counted the number of windows you had in all your buildings, figured out how much rent that probably added up to, and calculated your tax on that basis. Really. Windows. It was called the Land and Window Tax.
Another questionable story about the change of calendars was that there was rioting in the streets by people demanding their missing eleven days be returned. Although anyone whose birthday or anniversary fell on the missing days did have a legitimate grievance, there probably weren’t any riots. The whole idea came from a painting by William Hogarth in 1755. The painting was about the elections that year, and one of the members of Parliament who had helped pass the Calendar (New Style) Act was opposed by a candidate who used the confusion caused by the switch as a campaign issue. Hogarth’s painting, An Election Entertainment, was meant to be humorous, and if you look really closely you can see someone with a sign that says Give Us Our Eleven Days. That painting is probably where the story of the riots came from.
The Calendar (New Style) Act of 1750 applied to British colonies, and that caused some minor oddities in what was eventually the US. The laws in most US states are based on British laws, sometimes very explicitly. But the various colonies went about it in different ways; some referred to “the laws of England in 1607” (that was British common law), while others refer to British law as of July 4, 1776. Some states even include written portions of the Calendar (New Style) Act. Beyond that, there isn’t any national or Federal calendar law in the US. So if you really wanted to argue about it (and just wait; sooner or later somebody will), you could make a case that the Julian calendar is still technically in effect in some parts of the US.
Alaska really did stay on the Julian calendar until 1867, because until then it was part of Russia, where the Julian calendar was used. On Saturday, October 7, when the US bought Alaska from Russia, the date changed to Friday, October 18. The switch from Saturday to Friday wasn’t because of the calendar change though; they also switched Alaska to the other side of the International Date Line so it would be the same day there as it was in the rest of the US. Russia, by the way, stuck with the Julian calendar until 1918 and only changed after the October Revolution.
Even today the Gregorian calendar isn’t used everywhere. Ethiopia has its own calendar, which has 13 months. Nepal uses a Hindu calendar called the Vikram Samvat. It’s a lunar calendar, but instead of a leap day every four years there’s an extra “month” added according to a fairly complex formula. And the Solar Hijri calendar is official in Iran and Afghanistan.
Most calendars try to identify all the days in a year, but there have been some that didn’t. The Romans had a succession of calendars, and one of their early ones had a period of about three months that was just called “winter.” No months. Not even any special identification of individual days. In other words, in early Rome, winter was pretty much like our experience nowadays — the days just proceeded grimly, one after the other, all pretty much the same.