THE SONGS FOR THE WEEK
A Beraisa, citing R. Akiva, lists the songs that the Levi'im would sing for each day of the week:
On Sunday, they would sing "The world is Hash-m's," as that was the day when He established ownership of the world.
On Monday, they would sing "Hash-m is great," as He separated His works and reigned over them.
On Tuesday, they would sing "Hash-m stands in the Divine assembly" as He revealed the land and prepared it for His assembly.
On Wednesday, they would sing "Hash-m is the G-d of vengeance," as He will exact vengeance from those who worship the sun and moon which were created then.
On Thursday, they would sing "Rejoice to Hash-m" because He created birds and fish which give cause to praise Him.
On Friday, they would sing "Hash-m has reigned" because he finished His work and reigned over it.
On Shabbos they would sing "Mizmor Shir le'Yom ha'Shabbos" - referring to future era which is entirely Shabbos.
(R. Nechemiah): The song of Shabbos shouldn't be different in referring to the future; rather, it refers to Hash-m having rested on Shabbos.
The dispute between R. Akiva and R. Nechemiah is based on a dispute about whether the future era of Shabbos is equivalent to one day or two:
(R. Katina): The world will exist for 6000 years and be desolate for 1000.
(Abaye): It will be desolate for 2000 years.
On Musaf of Shabbos, they would sing Ha'azinu, referred to by the acronym of the sections HaZiYV LaCh.
The Parashah is broken up this way for leyning also.
On Minchah of Shabbos, they would sing Shiras ha'Yam, Mi Kamocha, and Alei Be'er.
Question: Were all the parts of Ha'azinu read each Shabbos, or was it split up?
Answer: A Beraisa states that in the time that the Shirah of Musaf was completed, the Shirah of the Minchah Tamid was repeated twice (i.e. six weeks), so we see that it was split up.
THE JOURNEYS OF THE SHECHINAH
The Shechinah journeyed ten tourneys during the Destruction of the First Beis ha'Mikdash, as derived from Pesukim:
From the Aron-cover, to a Keruv, to the other Keruv, to the threshold, to the courtyard, to the altar, to the roof, to the wall, to the city, to Har Zeisim, to the wilderness, to its place in Heaven.
(R. Yochanan): The Shechinah lingered for six months in the wilderness, hoping that the Jews would repent; it cursed them when they didn't.
Correspondingly, the Sanhedrin suffered ten exiles after the Destruction of the Second Beis ha'Mikdash, as we know from Oral Tradition:
From the Lishkas ha'Gazis, to Chanus, to Yerushalayim, to Yavneh, to Usha, back to Yavneh, back to Usha, to Shefar'am, to Beis She'arim, to Tzipori, to Tiveria, which was the deepest exile of all.
(R. Eliezer): There were only six exiles, as derived from a Pasuk.
(R. Yochanan): They are destined to be redeemed, as we see from a Pasuk.
MISHNAH: R. YOCHANAN'S DECREE ABOUT WITNESSES
Another decree of R. Yochanan ben Zakai was that even if the Rosh Beis Din was elsewhere, the witnesses need only go to the Beis Din.
WHETHER WITNESSES NEED TO TRAVEL
Ameimar excommunicated a woman summoned for litigation who failed to follow him when he left his Beis Din to Mechuza.
R. Ashi challenged him from our Mishnah which states that the witnesses do not need to go to the Rosh Beis Din.
He replied that that only applies to witnesses for the moon, who we don't want to discourage, but not to this litigation, where the debtor is subject to the wishes of the creditor.
THE DECREES OF R. YOCHANAN BEN ZAKAI
(Beraisa): Kohanim may not Duchen while wearing shoes.
This is one of the nine decrees of R. Yochanan ben Zakai.
This is the sixth one mentioned in this Perek (following Shofar on Shabbos in all towns with Beis Din, Lulav all seven days, Chadash forbidden on the 16th, all-day acceptance of testimony, and witnesses only going to the Va'ad).
Another was in the first Perek (of witnesses only transgressing Shabbos for Nisan and Tishrei.
The eighth is that a convert must separate a quarter-shekel for his bird-offering (to be brought when the Beis ha'Mikdash is rebuilt).
(R. Shimon ben Elazar): This has been annulled, because of the risk of his taking benefit from it.
The ninth is subject to a dispute between R. Papa and R. Nachman bar Yitzchak:
(R. Papa): It concerns Kerem Revai (fourth year fruit):
(Mishnah): Kerem Revai was brought to Yerushalayim (instead of redeemed) from everywhere within a day's walk, encompassing Eilas, Akrabas, Lod, and the Yarden.
This was done in order to decorate Yerushalayim with fruit.
R. Eliezer had Kerem Revai that he wanted to give to the poor instead, and his students told him that his colleagues had already decreed that it was permitted to do so.
These "colleagues" refer to R. Yochanan ben Zakai.
(R. Nachman bar Yitzchak): It concerns the strip of red wool:
(Beraisa): Originally, they would hang a strip of red wool up on Yom Kipur; if it turned white, the people would rejoice, but otherwise, they would despair.
It was decreed that it should be hung inside the Ulam of the Beis ha'Mikdash, but people would still peek in.
R. Yochanan ben Zakai therefore decreed that half of it should be tied to a rock and the other half tied to the goat thrown to Azazel.
R. Nachman bar Yitzchak disagreed with R. Papa's explanation as R. Yochanan ben Zakai was not a colleague of R. Eliezer but a teacher.
R. Papa would respond that it would be disrespectful for R. Eliezer's students to refer to him that way.
R. Papa disagreed with R. Nachman bar Yitzchak's explanation as R. Yochanan ben Zakai ruled only for his last forty years, some of which was after the Destruction, and we know that the wool never turned white within the last forty years of the Beis ha'Mikdash.
R. Nachman bar Yitzchak would respond that even before he ruled, he might have said it to his teacher, who would have enacted it in his name.