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Here's some more detail. In particular, Adar II does not happen every 4 years. Here's how the calendar works:

The month-length is taken to be 29 days, 12 hours, and 793 "parts," where a "part" is 1/1080 of an hour, or 1/25920 of a day, or 3-1/3 seconds. This is taken to be the mean length of a lunar month (between new moons). The beginning of the Year 1 is taken to have occurred on a Sunday night, at 5 hours and 204 parts (counting hours from sunset. That's actually before Creation: 12 months later the new moon was at 8am on Friday, the day Adam and Eve are considered to have been created.

Anyway, you add 12 months of 29:12:793 (days:minutes:parts) each, or 13 for each leap year. Specifically, there are 7 leap years for every 19 years. So for each cycle of 19 years, the time and day-of-the-week of the new moon moves by 2 days, 16 hours, and 595 parts. Whatever.

So now you know when the new moon beginning a given year is, and also where in the 19-year cycle of leap-years it is, and thus whether or not it's a leap year. Leap years do not happen every four years: they happen in years 3, 6, 8, 11, 14, 17, and 19 of the 19-year cycle, which is rather more frequently. You may have to change the day of the New Year (Rosh Hashanah), though. If nothing interferes, it happens on the day of the new moon you just calculated. But more often than not, something changes it:

1. If the moment of the new moon is after midday (halfway between sunrise and sunset), delay to the next day.
2. If it's on Sunday, Wednesday, or Friday, either because it fell out there or was delayed, delay it again. Rosh Hashanah can not, under any circumstances, be on a Sunday, Wednesday, or Friday (well, the first day; the second day of course may wind up there).
3. If it's after 9 hours and 204 parts on Tuesday (counting from sunset, remember!), in a non-leap year, delay it. This prevents some interactions that would result in an unacceptable year-length.
4. If it's after 15 hours and 789 parts (from sunset!) on a Monday, for a non-leap year following a leap year, delay it.

OK! So this gives us a year-length of 353, 354, or 355 days in a non-leap year, and 383, 384, or 385 days in a leap year, or an average length of about 365.2428 days. A trifle long, I think, but quite close.

And then the months proceed as mentioned above; the month of Adar is repeated if it's a leap year. Technically, it's the first month of Adar that's the added one: Adar II, the second one, is considered the real month. The holiday of Purim, which falls in Adar, happens in Adar II, not Adar I, and birthdays and death-anniversaries are kept in Adar II, etc. The months are 29 or 30 days long, on a fixed schedule, with the months of Kislev and Heshvan being variable between the two, to accomodate the varying year-lengths (only three of the four combinations are possible: they're either both long, both short, or Heshvan is short and Kislev long).

Because of the 19 year cycle, often the hebrew date coincides with the same english date every 19 years. Which means that for just about everyone, their 19th birthday will take place on the same day in both the english and hebrew calendars. This is not always the case. The Gregorian calendar and the Jewish calendar only synchronize every 80,000 years and change. (It takes about 230 years for the Jewish Calendar to fall a full day (and change) behind the Gregorian calendar.)< P>As a Result some people may be unfortunate enough to be born during a year where the skew has become significant enough to warrant just enough shift that the date changes, and then their english and hebrew 19th birthdays won't coincide. This does not mean that we added an extra day, all the changes (ie. additions) that happen in the 19 year cycle happen in the 19 year cycle so those changes would repeat as well. Instead it means simply that the extra few (375 or so) seconds which accumulate each year which are not accounted for, just happen to be the last 375 seconds in a day, pushing us into the next day.

There is actually a table printed in most editions of the Tur, a major halachic work, in which there is an error regarding when the two calendars coincide. More details will be added when/if I can find the source in question.

corrections appreciated

Jew"ish cal"en*dar.

A lunisolar calendar in use among Hebraic peoples, reckoning from the year 3761 b. c., the date traditionally given for the Creation. It received its present fixed form from Hillel II. about 360 a. d. The present names of the months, which are Babylonian-Assyrian in origin, replaced older ones, Abib, Bul, etc., at the time of the Babylonian Exile. Nineteen years constitute a lunar cycle, of which the 3d, 6th, 8th, 11th, 14th, 17th, and 19th years are leap years. The year 5663 [1902-3 a. d.] was the first year of the 299th lunar cycle. The common year is said to be defective, regular, or perfect (or abundant) according as it has 353, 354, or 355 days. The leap year has an intercalary month, and a total of 383 (defective), 384 (regular), or 385 (perfect, or abundant) days. The calendar is complicated by various rules providing for the harmonious arrangement of festivals, etc., so that no simple perpetual calendar can be constructed. The following table gives the months in order, with the number of days assigned to each. Only three months vary in length. They are: Heshvan, which has 30 days in perfect years; Kislev, which has 30 days in regular and perfect years; and Adar, which has 30 days in leap years. The ecclesiastical year commences with Nisan and the civil year with Tishri. The date of the first of Tishri, or the Jewish New Year, is also given for the Jewish years 5661-5696 (1900- 1935 a. d.). From these tables it is possible to transform any Jewish date into Christian, or vice versa, for the years 1900-1935 a. d.

```
1 Tishri . . . . . . 30
2 Heshvan . . . . .  29 (r. & d.)
or 30 (p.)
3 Kislev . . . . . . 29 (d.) or
30 (r. & p.)
4 Tebet . . . . . .  29
5 Shebat . . . . . . 30
6 Adar . . . . . . . 29 or
30 (l.)
-- Veadar . . . . .  29
(occuring only in leap years)
7 Nisan . . . . . . .30
8 Ivar . . . . . . ..29
9 Sivan . . . . . . .30
10 Tammux . . . . . . 29
11 Ab . . . . . . . . 30
12 Elul . . . . . . ..29```

5661 p. begins Sept. 24, 1900 5662 d.l. " " 14, 1901 5663 p. " Oct. 2, 1902 5664 r. " Sept. 22, 1903 5665 p.l. " " 10, 1904 5666 p. " " 30, 1905 5667 r. " " 20, 1906 5668 d.l. " " 6, 1907 5669 p. " " 26, 1908 5670 d.l. " " 16, 1909 5671 r. " Oct. 4, 1910 5672 p. " Sept. 23, 1911 5673 p.l. " " 12, 1912 5674 r. " Oct. 2, 1913 5675 d. " Sept. 21, 1914 5676 p.l. " " 9, 1915 5677 r. " " 28, 1916 5678 p. " " 17, 1917 5679 d.l. begins Sept. 7, 1918 5680 r. " " 25, 1919 5681 p.l. " " 13, 1920 5682 p. " Oct. 3, 1921 5683 d. " Sept. 23, 1922 5684 r.l. " " 11, 1923 5685 p. " " 29, 1924 5686 p. " " 19, 1925 5687 d.l. " " 9, 1926 5688 r. " " 27, 1927 5689 p.l. " " 15, 1928 5690 d. " Oct. 5, 1929 5691 r. " Sept. 23, 1930 5692 p.l. " " 12, 1931 5693 p. " Oct. 1, 1932 5694 r. " Sept. 23, 1933 5695 d.l. " " 10, 1934 5696 p. " " 28, 1935

d. = defective year; d.l. = defective leap year; p. = perfect year; p.l. = perfect leap year; r. = regular year; r.l. = regular leap year.

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