19-year cycle

Dr John Stockton wrote:
JRS: In article
.com
, dated Fri, 11 Feb 2005 08:16:44, seen in news:sci.space.science,
David
Grossmann posted :
I have heard every 19 years (235 lunar months) the moon and the
solar
year are synchronised. However, after looking at the times for new
moons in the almanacs, and comparing new moon times with a year and
a
year 19 years later, the new moon can be off as much as one day.
March
16 in the first year and March 15 in the 20th, which is 19 years
later.
Why is this? Is there any truth to the 19-year cyle?

Were you looking at the times for full moons, or for the dates only?

That is the Metonic Cycle, q.v. - Meton and Euctemon of Athens.

It is not an exact relationship; and, as far as I know, has never
been
generally considered to be exact. Using Javascript :

235 * new Date("1970/01/30 12:44:03 GMT") 599589105000
19 * 365.24220 * 864e5 599581595520
Difference 7509480 ms
02:05:09.48 s
Ratio 1.0000125245

There are 12.368266145863343 months per year, and that is best
approximated by
12:1, 25:2, 37:3, 99:8, 136:11, 235:19, 4131:334, 12628:1021
error 0.37 0.13 0.03 0.007 0.0046 0.00015 0.000027 0.00000026


The Metonic cycle is the shortest one that usually gets the date
right.

The ratio 99:8 was also anciently known - the octaeteris of
Cleostratus
of Tenedos.

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Thanks to everyone who responded. I appreciate your time,

Sincerely,
David Grossmann