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1)

(a)&(b) Beis Hillel first argued with Beis Shamai regarding all eighteen issues, taking the lenient view that the decrees should not be issued. However, they eventually relented, and, when the count was taken, it was found that Beis Shamai had the majority. So together, Beis Hillel, together with Beis Shamai, voted to issue the eighteen decrees.

(a) According to the Chachamim, five quarters of a Kav (one and a quarter Kabin - originally one and a half - is Chayav Chalah).

(b) According to Rebbi Yossi, one and a quarter Kabin is still Patur from Chalah, one and a quarter Kabin plus a fraction (one twentieth of an egg-volume per egg volume) is Chayav.
The reason that Rebbi Yossi is lenient is because, in his opinion, the eggs in the desert (at the time when the Torah was given) were slightly larger than the eggs of today.

(a) Hillel means that, if one Hin of drawn water falls into a Mikveh before it contains forty Sa'ah, it invalidates it (but once the Mikveh is Kasher, it will remain so even if one pours a thousand Sa'ah of drawn water into it).

(b) The term used by the Tana'im to describe the Torah's 'Hin' is twelve Lugin, not 'Hin'. Nevertheless, Hillel used the term 'Hin, because that was the way his Rebbes (Shemayah and Avtalyon) used to describe it, and a person is obligated to copy his Rebbe's manner of speech.

(c) According to Shamai, nine Kabin (three Hin) invalidate the Mikveh.

(d) The two weavers, testifying in the name of Shemayah and Avtalyon, gave the Shiur of drawn water that will invalidate a Mikveh as three Lugin (a quarter of a Hin).

(e) The Tana stated their profession and their location of work, to teach us the importance of never missing a day in the Beis Hamedrash; for you see, these two weavers, who worked in one of the lowliest of professions, and whose location of work, was one of the most insignificant in Yerushalayim, yet their testimony was accepted, against the opinions of the greatest sages.

(a) 'Kol ha'Nashim Da'ayan Sha'atan' means that a woman who sees blood, renders Tamei the Taharos with which she deals, only from the time that she actually saw blood, but not retroactively.

(b) According to Hillel, she renders Tamei any Taharos with which she dealt retroactively since the last time that she examined herself and was Tehorah.

(c) Rav Huna did not count the Machlokes between Shamai and Hillel regarding Semichah on Yom-Tov, because he was only listing those Machlokos where *they alone* argue, but not Machlokos which *other Tana'im* also disputed.

(a) According to Shamai, grapes that one picked for the wine-press become 'Muchshar le'Kabel Tum'ah' through their own juice, despite the fact that the juice that drips from the grapes just goes to waste through the holes in the wickerwork baskets (and in order to be Machshir food for Tum'ah, one needs liquid which originates to the owner's satisfaction). Shamai however, decrees on account of grapes that are picked into cemented baskets, where there are no holes for the juice to drip from.

(b) This case too, Rav Huna omitted, because Hillel ultimately conceded to Shamai.

(a) The significance of the statement that the Sanhedrin moved from the Lishkas ha'Gazis forty years before the Churban, is (the Gemara initially thought) that they no longer judged the laws of 'Kenas' (fines), but which it then changes to 'matters which involved the death-sentence' (an area of judgment which could only be judged as long as the Sanhedrin sat in the Lishkas ha'Gazis).

(b) The decree of Tum'ah on the gentile lands took place in stages, as we shall see shortly. Therefore it is possible for Yossi ben Yoezer and Yossi ben Yochanan to have decreed one stage of Tum'ah, and the Rabbanan of eighty years, another.

(c) Hillel was 'Prince of Israel' one hundred years before the Churban of the second Beis Hamikdash.

7)

(a) We are suggesting that they initially decreed *Vaday* on Terumah which touched gentile lands, and the Rabbanan of eighty years only added Tum'ah on Terumah which entered them suspended in the air (for example, in a closed wagon whose bottom is open). But that is impossible, in light of Ilfa, who said that it is only the decree of hands that from its inception, was decreed as a Vaday - all other decrees were decreed initially as a Safek (and Tum'ah is not burnt upon touching it).

(b) Nor can we say thatYossi ben Yoezer decreed Safek Tum'ah on Terumah which touchede gentile lands, and the Rabbanan of eighty years added Vaday Tum'ah on touching, and Safek Tum'ah on its air. Why not?
Because we have a tradition that Vaday Tum'ah was not introduced until the time of the Rabbanan of Usha (who lived many years after the Churban).

(c) We are therefore forced to say that Yossi ben Yoezer and Yossi ben Yochanan decreed a Safek Tum'ah on someone who touched the actual land, and nothing on the air. Came the Rabbanan of eighty years and added the air to the decree. And the saga ended when the Rabbanan of Usha decreed Vaday Tum'ah (to burn Terumah) on the land itself - but Terumah in the air remained a Safek.

(a) If Terumah has contact with any of the following Sefeikos, it must be burnt:

1. A Safek Beis ha'Peras: a field in which a grave was lost (i.e. we know it was there, but we are now unable to locate it).
2. Safek earth that came from gentile lands (which we just discussed a little earlier).
3. Clothes of an Am ha'Aretz, on which, we suspect, his wife may have sat.
4. Vessels that were found in the street, and which may be Tamei.
5. Spittle which is found in the street, and which may be that of a Zav.
6. Urine which is found in the street, and which may be that of a Zav.

(b) The last case is more stringent than all the others, inasmuch as we are even strict when it is a 'S'fek Sefeika' - i.e. if we do not know whether the urine is that of a human or of an animal, Terumah which touches it must still be burnt.

(c) Rebbi Yossi says that even if one is not certain that the Terumah actually touched them, if the Safek occurred in a Reshus ha'Yachid, it has to be burnt.

(d) The Chachamim maintain, that in a Reshus ha'Yachid, a Safek Negi'ah is only a Safek Tum'ah (and is not burnt), and in a Reshus ha'Rabim, it is Tahor.

(a) The reason that they decreed Tum'ah on glass vessels is because they are made of sand, and are therefore similar in their make-up to earthenware vessels.

(b) The Mishnah in Mikva'os, which permits Tevilah in a Mikveh, speaks when the glass vessel had a hole, which was soldered with lead. The author of the Mishnah is Rebbi Meir, in whose opinion we go after the material which was used to solder the vessel, and lead, like all metals, can be Toveled.

(c) According to the Rabbanan, we go, not after the material with which the vessel was soldered, bit after the material which comprises the main part of the vessel. Consequently, it remains a glass vessel, which, like earthenware, becomes Tahor when it breaks, even it has been soldered with lead.