Gemara

(Mishnah): If a Nazir became Tamei several times, he brings only one Korban (i.e. one set of Korbanos Tum'ah).

(Rav Chisda): This is like R. Yosi b'Rebbi Yehudah, who holds that Nezirus Taharah begins on day seven. (He became Tamei on day seven. This is like a new Tum'ah, but before he could bring his Korban, so it does not obligated another Korban.)

According to Rebbi, Nezirus Taharah begins on day eight. If he became Tamei on day seven, this is like one long Tum'ah. If he became Tamei on day eight, since he could have brought his Korban, he would need another Korban!

Question: Why didn't Rav Chisda explain that the Mishnah is like Rebbi, in a case when the Nazir became Tamei on the night of the eighth!

Suggestion: He holds that the previous night is not Mechusar Zeman. (Rather, it is as if the time for the Korban has arrived, and he would need to bring a Korban for each Tum'ah).

Answer (Rav Ada bar Ahavah): No, one must bring another Korban only if Nezirus Taharah began. (In any case the Mishnah cannot be like Rebbi:)

If the previous night is Mechusar Zeman, Nezirus Taharah does not start until morning (it is like one long Tum'ah).

If the previous night is not Mechusar Zeman, Nezirus Taharah starts on the night before the eighth (and he must bring a Korban for each Tum'ah)!

Kerisus 8a - Beraisa #1: If a Zav had three sightings on the eighth night, he brings a (second) Korban.

Beraisa #2: He does not bring a Korban.

Suggestion: They argue about when new Tum'ah obligates another Korban. Tana #1 holds that night is not Mechusar Zeman. Tana #2 holds that it is.

Rejection (Rav Huna bar Acha): No, both hold that night is Mechusar Zeman. Beraisa #1 discusses a Zav l'Tum'ah (he saw only twice before. Only now he became obligated to bring a Korban.) Beraisa #2 discusses one who already saw three times (and needed to bring a Korban. He is exempt from a second Korban.)

R. Yochanan: If a (full) Zav had one sighting on night eight and two more on day eight, he brings a (second) Korban.

Question: R. Yochanan holds (elsewhere) that night is Mechusar Zeman!

Chizkiyah: If a Nazir became Tamei on the eighth day (of Taharah from Tamei Mes), he brings another Korban Nazir Tamei. If he became Tamei on the eighth night, he does not bring another Korban for this;

R. Yochanan: In either case he brings another Korban.

Answer: R. Yochanan exempts the Zav according to the opinion that night is Mechusar Zeman. (He himself disagrees.)

Zevachim 12a (Rav Papa): A Korban Pesach Hukdash on the night of the 14th is considered Kosher from the start, since it will become Kosher the same day;

(Tana d'Vei R. Yishmael): One may tithe an animal on its eighth night (since it may be offered the coming day, is considered Kosher for a Korban).

Contradiction (R. Aftoriki): "V'Hayah Shiv'as Yomim Tachas Imo" implies that the night before its eighth day it is Kosher for a Korban. "Umi'Yom ha'Shemini va'Hal'ah Yeratzeh" implies that the night before it is not Kosher!

Answer (R. Aftoriki): One can make it Hekdesh the night before, but it cannot be offered until the eighth day.

Menachos 5a (Reish Lakish): If Kemitzah of Minchas ha'Omer was Lo Lishmah, it is Kosher. The Shirayim may not be eaten until a second Omer will be offered (Lishmah, to permit Chadash).

Question (Rav Papa): If Chatas Metzora was slaughtered before the Asham, we do not offer the Asham, and then finish offering the Chatas. Rather, we leave the Chatas to become Nosar, and it is burned in Beis ha'Sereifah.

If Mechusar Zeman does not apply to something that will become permitted that same day (like Reish Lakish taught), slaughter should be valid out of order! We should offer the Asham, and then finish the Chatas!

Answer (Rav Papa): Reish Lakish permits Chadash from dawn of the 16th (of Nisan, the day the Omer is brought).

Rishonim

Rambam (Hilchos Isurei Mizbe'ach 3:8): It is a Mitzvah to offer all Korbanos from the eighth day and onwards - "V'Hayah Shiv'as Yomim Tachas Imo umi'Yom ha'Shemini va'Hal'ah Yeratzeh". All seven days it is called Mechusar Zeman. Even though Mechusar Zeman is Pasul, one who transgressed and offered it is not lashed because it is a Lav derived from an Aseh.

Question (Mishneh l'Melech b'Sof, DH v'Lo): Why doesn't the Rambam bring the Isur to be Makdish Mechusar Zeman? The Gemara (Zevachim 12a) says that one can make it Hekdesh on the eighth night, but it cannot be offered until the eighth day. This implies that one may not be Makdish it beforehand! Tosfos (Zevachim 114b DH Heter) explicitly forbids.

Question: Rav Papa's question shows that he holds that Mechusar applies to something that will become permitted that same day. In Zevachim (12a) he does not consider the night before the eighth day to be Mechusar Zeman!

Answer (Tosfos Menachos 5a DH Ela): Rav Papa disqualifies something offered before it will become permitted that same day. However, he holds that Hekdesh of something that will become fitting for a Korban that same day is not like Hekdesh of Mechusar Zeman.

Rambam (Hilchos Bechoros 6:15): One who buys animals is exempt from Ma'aser Behemah only if he bought them after they may be tithed. Therefore, if one bought lambs within seven days, when the time comes he must tithe them. Since Mechusar Zeman cannot be tithed, it is as if he bought fetuses and they were born when he owned them.

Question (Kesef Mishneh 14): Zevachim 12a says that animals may be tithed on the night before the eighth day. Why did the Rambam omit this?

Answer (Shirei Korban Yevamos 8:1 (45b) Sof DH v'Osan): The Rambam relied on what he wrote here, that one who bought lambs within seven days must tithe them when the time comes. This implies that he need not tithe animals bought on the eighth night, for it is not like Mechusar Zeman. Also in Hilchos Isurei Mizbe'ach (3:8) he says that within seven days is Mechusar Zeman, implying that the eighth night is not.