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1)

(a) The day before and the day after one of the days listed in Megilas Ta'anis was included in the prohibition. This does ...

1. ... not apply to a Yom-Tov d'Oraysa (such as Rosh Chodesh) - because Torah- Mitzvos do not need to be reinforced.
2. ... not apply to one of the fast-day in the times of the Beis-Hamikdash (such as Tzom Gedalyah), because 'Divrei Kabalah' (Mitzvos instituted by the Nevi'im) do not need to be reinforced either, which explains why it was necessary to include the third of Tishri as a Yom-Tov in Megilas Ta'anis (i.e. in order to include the day before).

(b) Yehudah ben Shamu'a and his colleagues went to ask advice from an aristocratic Roman woman who was familiar with all the great men of Rome - concerning the decrees against Torah-study, B'ris Milah and Shabbos (see Agados Maharsha, who explains how these three Mitzvos set us aside from all the other nations).

(c) She advised them - to stage a demonstration at night in all the public places (to evoke the mercy of the Roman dignitaries.

(d) They cried out 'For the sake of Hashem, are we not your brothers, children of the same father and mother? In what way are we different than all the other nations, that you issue harsh decrees against us?'

(a) On the twenty-eighth of Adar they received the good news - that their efforts had paid off, and that the decrees had been abolished.

(b) We ask the same Kashya on Rav as we asked above (if the *old* dates in Megilas Ta'anis became obsolete, how could they now add *new* ones to the list?). We cannot however, answer that this Beraisa speaks in the time of the Beis Hamikdash (like we answered there) - because Rebbi Yehudah ben Shamu'a was a disciple of Rebbi Meir, who lived after the time of the Churban.

(c) Raban Gamliel quotes Yehudah ben Shamu'a in the name of Rebbi Meir, who renders glass vessels which became holed, and which were stopped-up with lead, Tamei - because we go after the 'Ma'amid' (that what holds the vessel together (in this case, the lead).

(a)

1. If Yehudah ben Shamu'a is speaking about Tum'ah Yeshanah - then he means that the moment they are stopped up, they regain the Tum'ah that they lost when they became holed. Normally, glass vessels (unlike metal ones) do not regain their Tum'ah; here they do (for the reason that we just gave in the previous answer).
2. If he is speaking about the original Din of Tum'ah - then he is saying that, even though glass vessels are only subject to Tum'ah, mi'de'Rabbanan, the vessels under discussion are Tamei mi'd'Oraysa, seeing as we go after the lead that stops up the vessel, and lead vessels are subject to Tum'ah mi'd'Oraysa.

(b) The Chachamim go after the chief material which comprises the vessel (glass, in this case) and not after the material holds it together. Consequently, in the first case, the vessels will not regain their Tum'ah, and in the second case, they are only subject to Tum'ah mi'de'Rabbanan.

4)

(a) We resolve the Kashya against Rav from the Tana of the Beraisa that we just learned, who added a new Yom-Tov to the list after Megilas Ta'anis had become obsolete - pointing out that this is a actually a Machlokes Tana'im: Rebbi Meir holds that Megilas Ta'anis did *not* become Batel (and one is forbidden to fast on all the days mentioned there even today); whereas Rebbi Yossi holds that they *did* became Batel (and Rav holds like Rebbi Meir).

(b) Rebbi Yossi's reason is - because nowadays, the joy in celebrating those days has turned into mourning.

(c) When the Gemara finally rules 've'Hilchesa Batlu, ve'Hilchesa Lo Batlu' - it means to say that, although all other Yamim-Tovim mentioned in Megilas Ta'anis became Batel and no longer apply, those of Chanukah and Purim are exceptions, and still apply today.

(a) The Gemara asks why it was necessary for the Sh'luchim to go out in Tishri - since they had already gone out in Av, so that everybody knew when Rosh Chodesh Elul had been, and based on a statement in the name of Rav (who said that, since the time of Ezra, it had never happened that Elul had been full, they could safely assume that Elul would be a short month)?

(b) They nevertheless went out in Tishri - because the only reason that Elul had not been declared a full month since the days of Ezra is because it was not necessary to do so; but should it ever be necessary, the Chachamim had a right to do it (indeed, we see that it happened twice after the time of Rav - [see 21a.]).

(c) They would declare Ellul a full month to protect the proper observance of the other Yamim-Tovim, even if it meant throwing the Rosh Hashanah of the B'nei Golah out of gear - because three Yamim-Tovim (Yom-Kipur, Sukos and Shemini Atzeres) takes precedence over one.

(d) We prove this answer from our Mishnah - which writes 'Al Tishri Mipnei Takanas ha'Mo'ados', from which we see that Chazal were more concerned about the collection of Mo'ados than about Rosh Hashanah.

(a) The author of our Mishnah (which does not mention anything about going out in Adar Sheini) cannot be Rebbi - who says that if they declared a leap- year, the Sh'luchim would go out in Adar Sheini, too.

(b) Initially - we explain that according to the Chachamim, if the Chachamim fix a leap-year after Purim has already been celebrated, one has fulfilled all the Mitzvos of Purim (and it is therefore not necessary to celebrate Purim again); whereas Rebbi holds that one is obligated to celebrate Purim in Adar Sheini, and not in Adar Rishon, in which case, the Sh'luchim need to go out for Adar Sheini.

(a) We conclude that, in fact, even the Chachamim agree that in a leap-year, someone who observes Purim in Adar Rishon is not Yotze, and we connect their Machlokes to that of Raban Shimon ben Gamliel and the Tana Kama. The Tana Kama says there that, in a leap-year, the extra Adar (i.e. Rishon) is thirty days - whereas according to Raban Shimon ben Gamliel, it is 'a Chodesh' (twenty-nine days).

(b) If we take the Tana Kama's opinion at surface value, it will be impossible to connect that Machlokes with that of Rebbi and the Chachamim - because just as, according to Raban Shimon ben Gamliel, we know to add *two* days (because of the leap year), so too, according to the Tana Kama, we know that we have to add *one*. Consequently, according to which Tana will Rebbi require the Sh'luchim to go out for Adar Sheini?

(c) Consequently, when the Tana Kama says 'Chodesh' - he must mean that Adar Sheini may consist of twenty-nine days, should the Beis-Din wish (but not to preclude the thirty days of the Tana Kama).

(d) So Rav Papa finally establishes Rebbi's statement - to conform with the opinion of the Tana Kama; since it is impossible for the people in the Golah to know whether Adar Sheini was full or short, the Sh'luchim had to go out in Adar Sheini too; whereas the Chachamim hold like Raban Shimon ben Gamliel, in whose opinion Adar Sheini was always short. Consequently, it was not necessary to go out in Adar Sheini.

(a) Rebbi Yehoshua ben Levi testified in the name of the Holy Kehilah of Yerushalayim that one sanctifies both Adarim on the day of their 'Ibur' - i.e. on the thirtieth of Adar (which means that both Adarim are short months).

(b) Rebbi Sima'i in the name of Chagai, Zecharyah and Mal'achi, is quoted as saying that any combination of the two Adarim is possible. In Bavel however, Rav Nachman bar Chisda adds, the Minhag was to treat the *first* Adar as a full month, and the *second* one, as a short one. Rav is quoted as saying that - in Bavel, unless one knew that the Beis-Din in Eretz Yisrael also fixed the *first* Adar as a short month, they should treat the first Adar as a *full* month and the second Adar, as a *short* one (like Rav Nachman bar Chisda).

(c) The same ruling was sent to Mar Ukva. Rav Nachman however, queried this from the Mishnah later (which rules that the witnesses were even permitted to desecrate the Shabbos, if necessary, on the months of Nisan and Tishri). If Adar Sheini was always twenty-nine days, on what grounds did they permit the desecration of Shabbos?

(d) We answer that the desecration of Shabbos was not just so to ascertain which day will be Rosh Chodesh - but also because of the Mitzvah to declare Rosh Chodesh through the sighting of the new moon (even if they knew anyway when Rosh Chodesh was due to fall anyway (as we shall see later).