(Beraisa - R. Yochanan ben Nuri): Whom should we follow (regarding Tzaras Ervah)?

If we follow Beis Shamai (and allow Yibum), the child is a Mamzer according to Beis Hillel;

If we follow Beis Hillel, the child is blemished according to Beis Shamai.

We should enact that the Tzarah do Chalitzah and not Yibum.

They were unable to make the enactment in time.

R. Shimon ben Gamliel: What should we do for previous Tzaros?

Question: If Beis Shamai followed their teachings, we understand this. However, if they didn't, what was his concern?

Answer (Rav Nachman bar Yitzchak): He was concerned for the Tzarah herself (not for her children);

What should we do for Tzaros of Beis Hillel (who remarried without Chalitzah) according to Beis Shamai?

If we require them to do Chalitzah, their husbands will despise them! We cannot do so, for "(Torah's) ways are pleasant... its paths are Shalom!"

(Beraisa - R. Tarfon): I desire that a Tzaras ha'Bas will come to my hands. I will marry her (do Yibum. He was from Beis Shamai. This shows that they followed their own teachings!)

Rejection: Rather, he said that he will marry her off (to others. Even Beis Shamai did like Beis Hillel).

Question: If so, what was his great desire? (Everyone rules like Beis Hillel!)

Answer: He desired to demonstrate that we do not hold like R. Yochanan ben Nuri.

(Beraisa): It happened that R. Gamliel's daughter married his brother, and his brother died without children. R. Gamliel did Yibum with the Tzarah.

Objection: R. Gamliel was from Beis Hillel!

Answer: His daughter was an Ailonis.

Question (Seifa - Others): She was an Ailonis.

This shows that the first Tana holds that she was not an Ailonis!

Answer #1: They argue about whether or not her husband knew that she was an Ailonis.

Answer #2: They argue about whether or not an Ervah forbids a Tzarah if the Ervah was divorced after her husband married the Tzarah.

Answer #3: They argue about whether or not Bi'ah may be done on condition (i.e. if she is an Ailonis, Bi'ah should not be Kidushin).

Question (Rav Mesharshiya - Beraisa): It once occurred that R. Akiva picked an Esrog on the first of Shevat and took two tithes, one like Beis Shamai and one like Beis Hillel.

This shows that Beis Shamai followed their own teachings.

Answer: (No, R. Akiva wanted to follow Beis Hillel.) He was unsure if Beis Hillel hold that Shevat 1 is Rosh Hashanah for trees, or Shevat 15.

Question (Mar Zutra - Mishnah): Shamai's daughter-in-law gave birth on Sukos. He enlarged the Sukah to make room for the baby.

This proves that they followed their own teachings!

Answer: One cannot learn from there, for one who saw would think that he wanted more air.

Question (Mar Zutra - Mishnah): There was a stone through which water flowed into a Mikveh; all Taharos in Yerushalayim relied on this Mikveh. Beis Shamai enlarged the hole, since they hold that the majority must be open.

(Mishnah): Mikva'os may be joined by an opening as big as Shefoferes ha'Nod (the circumference of a hollow reed put into a leather pouch from which one draws out the liquid), i.e. a circle two fingers wide.

This shows that Beis Shamai followed their own teachings.

Answer: There, it appeared that they wanted more water to flow.

Question: R. Tzadok once sent olives to R. Yochanan ben Hachorani. When R. Yochanan saw that they were wet he said that he does not eat olives. R. Tzadok informed him that they were collected in a punctured basket that became sealed with sediment:

(Mishnah - Beis Shamai): There is no need to puncture a basket of densely packed olives (the liquid that exudes is not Machshir);

Beis Hillel says, it must be punctured (to show that he does not want the liquid, for otherwise it is Machshir);

Beis Hillel agree that if it was punctured and became sealed with sediment, it is not Machshir.

Even though R. Tzadok was from Beis Shamai, he acted according to Beis Hillel.

Summation of question: If Beis Shamai followed their own teachings, we understand why it was recorded that R. Tzadok acted like Beis Hillel. However, if they did not, there was no need to say this!

Question (Beraisa): They asked R. Yehoshua about the law of a Tzaras ha'Bas.

R. Yehoshua: Beis Shamai and Beis Hillel argue about this.

The questioner: Whom does the Halachah follow?

R. Yehoshua: You seek to put my head between two great mountains. I fear to answer, lest they (children whom I say are Mamzerim) kill me! I can testify about two great families in Yerushalayim that came from Tzaras Ervah (who married without Yibum or Chalitzah) and members of these families served as Kohen Gadol.

If they followed their teachings, we understand R. Yehoshua's fear. However, if not, why was he afraid? (This question is not answered.)

Counter-question: Even if they followed their teachings, why was he afraid?

(R. Yehoshua): A Mamzer results only from Arayos punishable by Misas Beis Din.

Answer: Granted, (he holds that) the child (of Tzaras Ervah) is not a Mamzer, but a Kal va'Chomer teaches that his lineage is Pagum (forbidden to Kehunah):

If a widow marries a Kohen Gadol, even though the Isur is not Shavah b'Chol, the child is Pagum. Tzaras Ervah is Shavah b'Chol, all the more so the child is Pagum!

Question: R. Yehoshua was asked about Tzaras Ervah. Why did he answer about the children?

Answer: They asked two questions.

What is the Halachah regarding Tzaras Ervah?

If the Halachah follows Beis Hillel, if Tzaras Ervah married without Yibum or Chalitzah, what do Beis Shamai say about the children?

Question: Why did they ask the second question? (If the Halachah follows Beis Hillel, why are we concerned for Beis Shamai's opinion?)

Answer: This teaches about Machazir Gerushaso (after his ex-wife married someone else):

Do we say that when a widow marries a Kohen Gadol, even though the Isur is not Shavah b'Chol the child is Pagum, and all the more so the child of Machazir Gerushaso is Pagum, for the Isur is Shavah b'Chol?

Or, perhaps the Kal va'Chomer is invalid. There, the widow herself becomes Pagum. Here, she does not.

R. Yehoshua testified about Bnei Tzaros (that some were Kohanim Gedolim).