1. The Gemara discusses whether partial fasts are considered valid fasts.
2. Rebbi Yochanan sometimes remarked, "I am fasting until I come to my house."
3. To be a valid, private fast, one must accept the fast the previous afternoon.
4. There is a dispute about when one should accept the fast.
5. The Mishnah continues discussing what happens if it does not rain, even after all of the fasts.
A BIT MORE
1. The Gemara says that one whose fast does not last until sunset is not considered a valid fast. The Gemara gives examples of people who did not fast until sunset and yet the Beraisa says that they fasted. The Gemara refutes these examples by saying that they were not considered Halachically-valid fast days.
2. The Gemara says that this was not considered a Halachic fast, but rather a vow that would excuse him from having to eat at people's houses.
3. The Gemara says that a person who merely decided not to eat one day is not considered as though he Halachically fasted. The Gemara compares him to a bellows full of air.
4. Rav: He may do so anytime in the previous afternoon. Shmuel: He should do so specifically during the Minchah prayer.
5. If it does not rain after the second series of three fasts, Beis Din announces another three fasts for the public. These three fasts are more restrictive (more like Tish'ah b'Av) than the first series of public fasts.