Mishnah/Seder Moed/Tractate Rosh Hashanah/Chapter 1/3
Seder Moed, Tractate Rosh Hashanah: Chapter 1, Mishnah 3
The first of the month (Rosh Chodesh) was originally decided not by a mathematical system as it is today, but by observation. Whenever a person observed the new moon, he was to go to the Sanhedrin and testify of what he saw. The Sanhedrin would then declare the day Rosh Chodesh, and the new month would begin. However, even then, there were many Jews who did not live in the Land of Israel and thus would need to be informed when Rosh Chodesh was declared so that they could coordinate their observance of the Jewish holidays with the Jews in Israel.
There were six months of the year where messengers would be dispatched so that people would know when Rosh Chodesh is for all of the major holidays. These months are discussed in this mishnah.
Hebrew Text 
- על שישה חודשים שלוחים יוצאים:
- על ניסן, מפני הפסח;
- על אב, מפני התענית;
- על אלול, מפני ראש השנה;
- על תשרי, מפני תקנת המועדות;
- על כסליו, מפני חנוכה;
- ועל אדר, מפני הפורים.
- וכשהיה בית המקדש קיים--יוצאין אף על אייר, מפני פסח קטן.
English Translation 
- On six months messengers go out:
- On Nisan, because of Pesach;
- On Av, because of the fast
- On Elul, because of Rosh Hashnanah;
- On Tishrei, to correct for the festivals
- On Kislev, because of Chanukah;
- On Adar, because of Purim;
- And when the Temple existed, they also went out on Iyar, because of the little Pesach.
The fast: i.e. Tisha B'Av
Because of Rosh Hashanah: As Rosh Hashanah is the first of Tishrei and is celebrated for two days everywhere (even in the land of Israel) just to be safe, the date of Rosh Chodesh Elul needed to be declared so that Jews in the diaspora could observe in unison with Israel.
Correct for the festivals: i.e. to set the correct dates for Yom Kippur and Sukkot.
Little Pesach: The little Pesach, or Pesach Sheni as it is often called, is the second opportunity to bring the Pesach sacrifice to the Temple if one had missed the first opportunity. As there is no Temple now, this holiday is not observed.