The 16th century Code of Jewish Law, the Shulchan Aruch (Orach Chayim, 117:1), written by Rabbi Joseph Caro (d. 1575) rules that in the 'Bar-aich Aleynu' berachah of the weekday Amidah prayer, there is a seasonal adjustment for winter. The phrase 'Ve-tain berachah' (and give blessing) is replaced in the winter with 'Ve-tain tal u'matar' (and give rain and blessing). See page 218 in the green Singer’s Siddur and page 270 in the Artscroll Siddur for an example of such usage.
Curiously, this adjustment is made according to a secular calendar to coincide with 60 days after the autumn equinox.
Why do we need to make this adjustment and why is it not based on the Jewish calendar?
The Talmud (volume Ta’anit 2a), the major work of rabbinic law and ethics, discusses when we should start praying for rain. For our purposes, this refers to what we say in the berachah of Bar-aich Aleynu, as noted above. It does not refer to the phrase Mashiv Haruach umorid hagashem, which is praise of G-d, not a request for rain, as evidenced by its placement in the first section of the Amidah which deals solely with praise.
According to the Talmud (Ta’anit 10a), the prayer for rain is seasonal and therefore different customs arose in Israel and the Diaspora (for these purposes, the Diaspora means Babylon), depending on when the rainy season came.
In Israel, the switch to ve-tein tal umatar is always made according to the Jewish calendar, on 7 Cheshvan, which is still current practice in Israel. This suits the needs of the Land of Israel and in Temple times allowed pilgrims a couple of weeks to get home from the Temple in Jerusalem to other parts of Israel, or even the Diaspora, after Shemini Atzeret without praying for themselves to get soaked on the way!
By contrast, Babylon in Talmudic times was run according to a different calendar. The optimum time for rain in Babylon was 60 days after Tekufat Tishrei (the autumnal equixox - this is one for calendar lovers) and so the Halacha as applied in Babylon meant that 60 days after Tekufat Tishrei was the time to start saying Tein Tal Umatar. Since the Babylonians did not use a Jewish calendar but used a calendar more similar to the Gregorian calendar we, who in the Diaspora are considered like the Babylonians for this purpose to ensure consistency throughout different communities, follow the 60th day after the autumnal equinox which currently falls on 4 or 5 December depending on the particular civil year, as explained in the Siddurim cited above.
The ruling of the Shulchan Aruch, mentioned at the top, is based on the Rambam, Hilchot Tefilah 2:16. In addition, the Beit Yosef, initially citing the ruling of the Rosh (Responsa 4:10), confirms after some lengthy discussion that Babylonian practice is applicable to the rest of the Diaspora as well.
For those who like the maths behind this, I am indebted to Philip Baigel and Russell Grossman of the Yeshurun Federation Syangogue in Edgware for their mathematical explanation on Yeshurun's website in 2007:
Tal Umatar Has Started!
"We started saying Tal Umatar from the evening of 5th December in the weekday Amidah, 60 days after an event known as Tekufat Tishrei - the first day of the Autumn season, which starts on the 23rd September. This is when the area of Babylonian exile, roughly modern day Iraq and representing the diaspora, needed rain. Sixty days after 23rd September is November 21st. But we don't say Tal Umatar until the 4th of December because the calculation was originally based on a solar year of 365.25 days. We now know the solar calendar is 365.2425 days and this discrepancy of 11 minutes and 14 seconds means the Tekufah has moved forward at a rate of one day every 128 years.
By 1582 the discrepancy had reached 10 days. The Catholics, led by Pope Gregory XIII (that's him pictured [on the Yeshurun site], looks like a frum bloke) decided to drop the extra ten days from the then Julian calendar by making the day after Thursday, October 4, 1582 Friday October 15, in a new calendar named “Gregorian” in the Pope's honour. As a result the day which would have been September 23 according to the Julian calendar is October 7 of the Gregorian The 60th day following which is December 5. Since we begin Tal Umatar during Maariv, that's the night of December 4. Every fourth year, however the Tekufah begins after the time that stars are visible ('Tzeit hakochavim') on October 7. The 60th day on those years is therefore December 6, and Tal Umotor begins on the evening of December 5."
This works well for us Northern Hemisphere guys but what about countries in the Southern Hemisphere or those close to the Equator? One posek who dealt with this question was the famed Rabbi Shmuel Salant, (1816-1909) who for many years was the Rav of Jerusalem.
In 1898, Rabbi Avraham Avar Hirshovitz, perhaps a student of Rabbi Salant, sent Rabbi Salant a question from Melbourne asking whether Tein tal umatar should be recited in Australia from 4/5 December, a time which is the middle of the Australian summer. Interestingly for those who like Rabbinic history, R'Hirshovitz was not the only Australian petitioner to approach Rabbi Salant (see Rabbi Salant’s halachic writings, Torat Rabeinu Shmuel Salant 1:3, for more details)
Rabbi Salant noted that Chief Rabbi Nathan Marcus Adler of London had already ruled that the Jews of Australia should say Tein Tal Umatar despite the Australian summer, presumably for the reasons we outlined above. Rabbi Hirshovitz disagreed with Rabbi Adler but Rabbi Salant replied that Rabbi Adler had authority to make this ruling and that Rabbi Hirshovitz should follow Rabbi Adler's ruling. This is a different kind of example of the unity that Tein Tal Umatar brought to Jewish communities, rather than being considered as a local prayer.
In conclusion, the Diaspora follows the custom of Babylon, unifying the Diaspora. May God answer our prayers favourably.