A day here, a day there - pretty soon it adds up

kw: calendars, analysis

In the wake of the holidays, I was thinking about the origin of "Twelve Days of Christmas." It got me to thinking about the changes to the calendar that led to the 12 days, and the manipulations of the year that led to that. In the Science Q&A section of eNotes.com I find the following, posted by fact-finder:

The longest year on record was 46 B.C., when Julius Caesar (100-44 B.C.) introduced his Julian calendar. In order to make up for the difference between the calendar date and the season (determined by the position of the Earth in its yearly journey around the sun), Caesar inserted 2 extra months and added 23 extra days to February. Thus, 46 B.C. was 455 days long.

The shortest year on record was 1582, when Pope Gregory XIII (1502-1585) introduced his calendar, the Gregorian calendar. He decreed that October 5 would be October 15, eliminating 10 days, to make up for the accumulated error in the Julian calendar.

The world only gradually changed over to the Gregorian calendar. Catholic Europe adopted it by the year 1584. Many Protestant continental countries did so between 1699 and 1700; England imposed it on its colonies in 1752 and Sweden adopted it in 1753. Many non-European countries adopted it in the nineteenth century, with China doing so in 1912, Turkey in 1917, and Russia in 1918.

Sources: Famighetti, Robert, ed. The World Almanac and Book of Facts 1995, p. 288; Trefil, James. 1001 Things Everyone Should Know About Science, p. 138.

Based on the entire Gregorian correction, the year 1600 was a leap year, while 1700, 1800 and 1900 were not. In the late 1700s, there were some in England who went along with the calendar change and some who did not. The former practiced Christmas Day on December 25, according to the Gregorian Calendar. Those who stuck with the Julian calendar used their December 25, which fell on January 5. Over time, neighbors accommodated neighbors, and many began to celebrate the whole twelve days as the Christmas Season. Sometime thereafter, the familiar song was written (or perhaps it accumulated).

Since that time, the loss of two leap days in 1800 and 1900, followed by 2000 having a leap day, has shifted "Old Christmas Day" to January 7. It would be humorous to coin a new song of the fourteen days of Christmas!

All this takes care of making the average calendar year work out to a length of 365.2425 days, by mixing 365- and 366-day years. Since 1582, all the years have been of one of these two lengths. But there is more. The actual Tropical Year has a length of 365.2422 days (in 2000: 365.242189). This difference of 0.000311 days yearly means an extra leap year needs to be skipped about every 3,215 years. 3215+1582=4797. That is long enough that the gradual change in the length of the tropical year must be taken into account; the date we need to skip a leap year will be a year or two later, like in about the year 4799 or maybe 4800. 4800 has a nice ring to it. Let's use that.