There are a number of explanations on the Internet, the most plausible being this and this, which both say that date was the last co-incidence of the starts of the following three cycles:

- The
**Metonic Cycle**of 19 is a quirk of two totally unrelated physical phenomena: the__sidereal lunar month__, which is the average time the moon takes to go through a complete cycle of phases, reckoned to have averaged 29.53058868 days over several centuries; and the__solar year__, reckoned to have averaged 365.242190 days. These come together as frequently as every 235 lunar months: 6939.68834 days which, taking into account the true length of a solar year, gives 19.0002375 years. The Metonic Cycle always starts with a New Moon. - The
**Solar cycle**of 28 is the number of years that dates and days of the week repeat themselves in the Julian Calendar. The Solar Cycle always starts with a leap-year whose 1st January is a Monday (curiously,__not__Sunday). This proposal was fine in the days of Joseph Justice Scaliger (who first proposed the Julian Date system in 1583 - the first complete year of the Gregorian calendar), but now we are well into in the Gregorian age, this cycle of 28 * 365.25 = 10227 days no longer starts on 1st January, but a bit later in the appropriate leap-year to account for days omitted by the Gregorian correction. We are currently in the 240th Solar cycle, which started on Monday 14th January 2008. - The
**Indiction cycle**of 15 is the number of years in the Roman tax cycle. It had ramifications throughout Catholic Europe until Napoléon had the sense to abolish it in 1806 - ’Nuff said!

The last two are both man-made (particularly the latter)
- but then, so are calendars....

Trying to make sense of all this is **very** difficult:

- If one projects back from the new moon of 1999-Aug-11 CE (the date of the last total solar eclipse visible from much of Europe), either 83012 or 83013 moons might have passed since JD zero – these numbers give either slightly more or slightly less than 29.53058868 days for a lunar month.
- The lunar month changes sinusoidally by plus or minus 6 hours throughout the year owing to the sun’s gravitational pull (the shortest is at the June solstice).
- According to moon cycle data throughout the 20th Century, there were 1249 cycles between the new moons of 1900-Jan-01 13:52 and 2000-Dec-25 17:22, which gives a somewhat shorter average lunar month of 29.5301408 days during the 20th century.
- Add to this, although the average length of a lunar month over the last two years of the 20th century was only 29.5110833 days, it is increasing overall because the moon is gradually moving away from the earth.

Who knows? – but the very comprehensive
Celestia
program reckons there was an __annular eclipse of the sun__ at

The ‘Julian Cycle’, which is considered to be the product of
19, 28 and 15 (ie. 7980 years) will **not** end on
3267-Dec-31 CE – as is stated in many places
because of two things:

- There will then be 22 ‘lost days’ introduced by the Gregorian system that need to be accounted for;
- The Metonic cycle is not
**exactly**19 years (nor is there any reason why it should be). The fraction 0.0002375 is 2 hours, 4 minutes and 53.44 seconds, which will add up to 36 days, 10 hours and 14 minutes over 7980 years. We can take out one moon cycle of 29.53 days to get nearer.... (But this still leaves 7 days unaccounted for.)

Thus, the true start date of the next Julian Cycle would work out as being 29 days further into the year 3268 (assuming the average lunar month remains 29.53058868 days), ie. 3268-Jan-30: still a Monday!

However, Celestia reckons there will be a new moon 6 days later, on 3268-Feb-05: a Sunday. Oh well....

Steve Glennie-Smith Dec 29th 2012