1)

(a)There are two statements, one which says that they argue over eighteen things, and the other that they agree over eighteen things. To reconcile the two conflicting statements, we explain that - initially, Beis Hillel 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 Beis Hillel, together with Beis Shamai, agreed to issue the eighteen decrees.

2)

(a)When the measurements in Yerushalayim were enlarged by one sixth, the original Shiur Chalah changed from seven a half Lugin plus a fifth of a Lug to six Lugin. In Tzipori, they enlarged them again, so that six Lugin now became five. The Torah's Shiur for Chalah is a tenth of an Eifah (1 Eifah = 3 Sa'ah = 18 Kabin = 72 Lugin = 432 egg-volumes). According to Shamai, one Kav of flour is Chayav Chalah, according to Hillel, it is two Kabin. 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 - but one and a quarter Kabin plus a fraction (one twentieth of an egg-volume per egg) 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.

3)

(a)Hillel says that one Hin of drawn water invalidates a Mikvah (1 Hin = 3 Kabin = 12 Lugin = 72 egg-volumes) - meaning 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). 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 worked in one of the lowliest of professions, and their location of work was one of the most insignificant in Yerushalayim, yet their testimony was accepted, against the opinions of the greatest sages.

4)

(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 going back to the last time that she examined herself and was Tehorah.

(c)Rav Huna omitted 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 argued over, too.

5)

(a)They also argue about whether grapes picked for the wine-press are Muchshar (ready) to receive Tum'ah or not, where Shamai says that they are, and Hillel says that they are not.

1. ... Hillele's reason is - because 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).

2. ... Shamai however, decrees because of grapes that are picked into cemented baskets, where there are no holes for the juice to drip through.

(b)Rav Huna not include this case in his list - because Hillel ultimately conceded to Shamai.

6)

(a)Rome turned against Yisrael 180 years before the Churban Bayis Sheini; 80 years before the Churban, the Chachamim decreed Tum'ah on the lands of the gentiles and on glass vessels, and 40 years before, the Sanhedrin moved from the Lishkas ha'Gazis (in the Beis Hamikdash) to the 'Chanuyos' - from which time on, they no longer judged'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 Gemara's first contended - that it was the laws of 'Kenas' (fines) that could only be judged as long as the Sanhedrin sat in the Lishkas ha'Gazis

(c)In spite of the first part of the statement, we can still attribute the decree of Tum'ah on the lands of the gentiles to Yossi ben Yoezer and Yossi ben Yochanan - because this decree 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.

(d)Hillel was the Nasi one hundred years before the Churban of the second Beis Hamikdash.

7)

(a)The Gemara initially suggests that Yossi ben Yoezer and Yossi ben Yochanan decreed that only Terumah which actually touched the ground of the gentile lands would be Tamei to be burnt; whereas if it entered suspended in the air it would remain Tahor, and that that is the Tum'ah that the Rabbanan of eighty years added (to become Tamei, but not to be burnt). This suggestion is unacceptable however - due to 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 Terumah is not burned in cases of Safek Tum'ah).

(b)We also reject the contention that Yossi ben Yoezer and Yossi ben Yochanan decreed that, upon contact with the ground of the gentile lands, Terumah would be Tamei, though not to be burnt, whilst in the air, it would remain Tahor; and the Rabbanan of 80 years added that the former should be burnt, and the latter, Tamei, but not burnt - because of 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 Teumah that entered in the air. The Rabbanan of eighty years added the air to the decree. And the the Rabbanan of Usha decreed Vaday Tum'ah (to burn Terumah) on the land itself - but Terumah in the air remained a Safek.

8)

(a)The Rabbanan of Usha decreed that in the following six cases of Safek, one burns Terumah. The case of ...

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 when she was a Nidah.

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 stringent even when it is a 'S'fek Sefeika' - i.e. if we do not even know whether the urine is that of a human or of an animal, Terumah which touches it must still be burnt.

(c)According to the Tana Kama, it must be certain that the Terumah actually touched any of these, before it will become Tamei. Rebbi Yossi - renders them Tamei to be burned, even if one is not, if the Safek occurred in a Reshus ha'Yachid.

(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.

9)

(a)One of the eighteen things is that glass vessels (which are Tahor min ha'Torah), are subject to Tum'ah. The reason for this is - because they are made of sand, and are therefore similar in their make-up to earthenware vessels, which are subjesct to Tum'ah min ha'Torah.

(b)The Mishnah in Mikva'os, which permits Tevilah in a Mikveh, speaks about a glass vessel which had a hole, and 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. Ordinary glass vessels cannot be Toveled when they become Tamei, any more than earthenware can.

(c)According to the Rabbanan, we go, not after the material with which the vessel was soldered, but 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 without being Toveled in a Mikvah), even it has been soldered with lead.