The details of the Jewish calendar is rather involved for a complete
description to be given here, but a good discussion can be found in the
Encyclopedia Judaica, vol. 5, pp. 43-50. Books on the subject include
"Understanding the Jewish Calendar", Rabbi Nathan Bushwick, Moznaim
Pub. Corp., NY 1989, and on a more technical level, "Jewish Chrononomy"
by Prof. Leo Levi (published by the Assoc. of Orthodox Jewish
Scientists).
I only wish to add a few observations. Both Maimonides (Rambam) in his
magnum opus, Mishne Torah, Zemanim, Kiddush Hachodesh, sixth chap., and
Rabbi Yaacov ben Asher ("Tur"), Orech Chayim, chap. 427 set out the
offset in days, hours, and fractions of an hour from one month to the
next (mean lunar period), from one regular (12 lunar months) year to
the next, from one leap year (13 lunar months)to a regular year, and
from one year on the 19 year calendrical cycle to the corresponding
year in the next cycle. The mean lunar monthly cycle that is given
corresponds to the modern determination. This period was known in
Talmudic times (Babylonian Talmud, Rosh Hashanna, 25a). Thus the Molad
for any month, based on the mean lunar period, can be calculated once
an accurate or acceptable starting Molad is agreed upon. The Rambam is
very careful, however, in distinguishing between such a mean Molad and
the "true" astronomical lunar conjunction. The latter requires
accurate observation and a mathematical description of the lunar and
earth orbits, or an understanding of the involved method used by the
Sages in deriving such information (Sod Hamolad). A knowledge of the
"true" Molad was used by the High Court in Talmudic times, according to
the Rambam, to corroborate the testimony of eyewitnesses to the new
moon. The substitution of a fixed calendar for new-moon sightings,
with the demise of the Patriarchate (the authority of the House of
Hillel), lead to the adoption of the mean lunar month as the basis of
the new moon determinations. Both the Rambam and the Tur use the value
2 days, 5 hours, and 204/1080 hours as the "date" of the "first" Molad,
which is then used to establish the date of all subsequent Molados.
"Tosfos" in Talmud Bavli, Rosh Hashanna, 8b, "derives" the above "date"
by extrapolating the presumed Molad Tishrei of year one marking the
creation of Adam to the "Molad Tishrei" of the previous "period", using
the usual offset for a 12 month year. The calculation is interesting,
but still seems arbitrary, and is based on the view that creation was
in Tishrei (Rabbi Eliezer's opinion), not Nisan (Rabbi Yehoshua's
view). I think it reasonable, therefore, to assume that the Molad
Tishrei for year one (or zero) of creation was arrived at by back
calculation from a year in Talmudic times in which Molad Tishrei was
established from observation and accurate calculation of the "true"
lunar conjunction, assuming the traditional count of years from
creation (a.m.). The calculation using the a.m. value is then purely a
convenience.
With regard to Mordechai's second comment. I am not contending that
the world must end after 6000 years. The statement in Talmud to that
effect is Midrashic in nature. I was merely reflecting a thought by
Rabbi Preil in a previous posting that is appropriate for this time of
year.
Have a good year!
Yitzchok Zlochower