(Gemara) Question: What is the meaning of "it is improper to have more than eight"?

Answer #1 (Rav Huna): Chachamim say that it is improper to be Me'aber more than eight months.

Question: Presumably, it is improper to Me'aber nine months, for then Rosh Hashanah will occur (almost) three days after the Molad. (People will deride the Chachamim, saying that they fix the months whenever they want, without regard to the Molad. Each Molad is about 29 days, 12.7 hours after the previous one. Over 12 months, this amounts to about 354 (and a third) days. If the months alternate between 29 and 30 days, there are 354 days. If nine months have 30 days, there are 357. Therefore, if a year has nine Ibur months, assuming that last Rosh Hashanah started at the Molad of Tishrei, the next Rosh Hashanah will be (almost) three days after the Molad.)

Likewise, it is improper to be Me'aber eight months, for then Rosh Hashanah will occur (almost) two days after the Molad!

Answer: We answer like Rav Mesharshiya answered (a different question). The case is, the previous (Rashi; Tosfos - current) year was (is) Me'uberes (had 13 months). The added month was Chaser (29 days, a half-day less than its Molad; Rashi - and last Rosh Hashanah was a half-day before the Molad), which compensates for one of the Ubar months. This Rosh Hashanah is only one (and a half) day(s) after the Molad, people will not deride the Chachamim for this. (Really, when we subtract the extra third of a day (that 12 Moldos exceed 354 days), it is only about one and a sixth days.)

Answer #2 (Ula): Chachamim say that it is improper to be Mechaser more than eight months;

This explains the previous law. We are not Me'aber less than four months in a year, for it is improper to be Mechaser more than eight.

Question: Presumably, it is improper to be Mechaser nine months, for then Rosh Hashanah will occur three (and a third) days before the Molad (people will deride the Chachamim);

Likewise, it is improper to be Mechaser eight months, for then Rosh Hashanah will occur (more than) two days before the Molad!

Answer: We answer like Rav Mesharshiya answered (elsewhere). The case is, the previous (Tosfos - current) year was (is) Me'uberes. The added month had 30 days, this cancels the effect of one of the Chaser months, this Rosh Hashanah is only one (and a half - counting the extra third, it is almost two) day(s) before the Molad;

People will not deride the Chachamim. They will assume that the Molad came shortly after Rosh Hashanah, just Chachamim did not notice it.

Question: What do Rav Huna and Ula argue about?

Answer: They argue about how many days are in the Ibur (added) month in a leap year:

(Beraisa): We add 30 days to make an Ibur Shanah;

R. Shimon ben Gamliel says, we add a month (29 or 30 days. Rav Huna assumed that the added month has 29 days. Ula holds like the first Tana, that it has 30.)

Question (Beraisa #1): Shavu'os is always on the same day (of the week) as (Nisan 16, the day we offer) the Omer (it is exactly seven weeks later). Rosh Hashanah is on that or the next day. (A regular year, with six Chaser and six full months, has 50 weeks and four days. A half year from Nisan 1 until Rosh Hashanah has 25 weeks and two days (if three of these six months are full). In this case, Rosh Hashanah is two days (in the week) later than Nisan 1 (or 15), i.e. the same day as Nisan 17, the day after the Omer. If only two of the months are full, it will be one day earlier, on the day of the Omer.)

We understand according to Ula. He says that we may be Mechaser eight months, but we may not be Me'aber eight. (Therefore, less than four summer months will be full);

Rav Huna says that we may be Me'aber eight months. If so, four summer (and four winter) months will be full. Rosh Hashanah will be two days after the Omer!

Counter-question: This is difficult also for Ula. He agrees that we may be Me'aber seven months. Sometimes four of them will be in summer!

Answer to both questions: The Beraisa is like Acherim;

(Beraisa #2 - Acherim): Shavu'os is always four days later in the week than the previous Shavu'os. (The months always alternate Chaser-full. A year is 50 weeks and four days.) Rosh Hashanah is always four days later than the previous Rosh Hashanah;

If it was a leap year, they are separated by five days. (The extra month has four weeks and one day.)

Question: Beraisa #1 says that Rosh Hashanah can be on the same day as the Omer (i.e. when four summer months are Chaserim). This is unlike Acherim!

Answer (Rav Mesharshiya): Acherim do not require perfect alternation of months in a leap year. If the extra month was full, we are Mechaser an extra summer month to compensate.

Question (Rav Ada bar Ahavah): Why didn't Acherim simply teach that the months always alternate? Do they come to teach arithmetic (i.e. the number of days in a year with six full months)?!

Answer (Rava): They teach that there is no Mitzvah to be Mekadesh the month according to witnesses who saw the new moon. (A full month is always followed by a Chaser month. Even if witnesses do not come on day 30 of a month that should be Chaser, we are Mekadesh it to be Rosh Chodesh.)

Question (Ravina): Acherim's law is not always true! (A lunar year exceeds 354 days by about 8.8 hours.) We must add a day to the year (i.e. be Me'aber an extra month) every third year (to compensate for eight extra hours in each of the three years), and we must add another day every 30 years (to compensate for 0.8 extra hours in each of 30 years)!

Answer: Since this day is not added every year, Acherim do not discuss it. (This compensation (every third and 30th year) is almost exact if we ignore leap years. However, seven years out of 19 are leap years, in which a month is added. If the added month has 29 days, this is 12.7 hours less than a Molad, we must add another (89 hours, or almost) four days for every (seven leap years in) 19 years! R. Gershom says that Acherim could hold that a leap year has 30 extra days (like Chachamim of R. Shimon ben Gamliel, unlike Rav Mesharshiya. Since the leap years have an extra seven days,) instead of adding four days in 19 years, we must subtract three. Instead of adding six or seven days in 19 years (every third and 30th year, like Ravina asked about), we must add only three or four. Perhaps Ravina asked that no matter what is Acherim's opinion about the leap month, other days must be added! Over a 19 year cycle, days must be added to 10 or 11 (regular or leap) years, i.e. more than half the time.)

Shmuel agrees with Rav Huna;

(Shmuel): A lunar year is always between 352 and 356 days.

If two (normally Chaser) months are made full, there are 356 days. If two (normally full) months are Chaserim, there are 352. If the months alternative (as usual), there are 354 days.

Question (Beraisa): If Reuven said "I am a Nazir like (i.e. as many times as) the (number of) days of the solar year," he is a Nazir 365 times. (After every 30 days, he brings Korbanos and starts the next Nezirus.) If he said "Like the days of the lunar year," he is a Nazir 354 times.

If a lunar year can be 356 days, he should be a Nazir this many times! (We could also ask according to Ula, that he should be a Nazir 355 times.)

Answer: Vows are interpreted according to the way people speak. They refer to the usual lunar year (354 days).

Also Rebbi holds like Rav Huna;

(Beraisa): It once occurred that Rebbi was Mechaser nine months in a year, and still, the moon was seen on (Tosfos - only one day after) Rosh Hashanah. He could not understand this.

Suggestion (his son, R. Shimon): Perhaps this year was a leap year, the extra month was full, and last year had two extra full months (eight in all). These extra three full months (almost) compensate for the extra three Chaser months! (Really, there were 13 Chaser months and 12 full months over the last two years. If two years ago the Molad was at Rosh Hashanah, last year it was almost two days early (before Rosh Hashanah. The new moon is not seen in Bavel until 18 hours later, about one day before Rosh Hashanah). This year it is about one day late.)

Rebbi: You enlighten Yisrael!