1)

(a)Min ha'Torah, earthenware utensils receive and pass on Tum'ah through their insides exclusively . This applies also to 'me'Achoreihen' (possibly only mi'de'Rabbanan) - which refers to the back of a receptacle that is itself carved in such a way that it is a mini-receptacle (i.e. that it is able to hold water.

(b)Despite the fact that earthenware utensils receive and pass on Tum'ah through their insides exclusively, and despite the fact that glass utensils are subject to Tum'ah only because of their similarity to earthenware vessels, Chazal nevertheless decreed Tum'ah through contact with the outside of glass utensils - because they are also similar to metal vessels, inasmuch as, like metal vessels (but unlike earthenware ones), they can be repaired when they break.

2)

(a)Metal vessels which broke, lose their Tuma'h. When they are repaired, they regain it, retroactively, mi'de'Rabbanan - vessels made of wood, leather, bone and glass regain their ability to become Tamei when they are repaired, but not retroactively.

(b)The Rabbanan restricted the comparison of glass vessels to metal to Tum'os d'Oraysa; it does not apply to cases of Tum'ah de'Rabbanan (of which retroactive Tum'ah is one). There, they gave it the Din of earthenware, to which retroactive Tum'ah does not apply.

(c)They also gave flat vessels made of glass the leniency of flat earthenware vessels (which are not subject to Tum'ah at all) - as a reminder that the Tum'ah of glass vessels is only mi'de'Rabbanan, si that eople will remember not to burn Terumah and Kodshim which touch them.

3)

(a)We know that Tum'ah does not apply (min ha'Torah) ...

1. ... flat vessels made of wood and leather - because by virtue of their juxtaposition (in the Torah) to sack (which can receive Tum'ah only in the form of a receptacle, we learn that they too, must be receptacles before they can be subject to Tum'ah.

2. ... vessels made of bone must be receptacles before they can be subject to Tum'ah, because, elsewhere in the Torah, they are compared to wood and leather vessels.

4)

(a)The Tum'ah of metal vessels is indeed d'Oraysa - but Shimon ben Shetach decreed retroactive Tum'ah on metal vessels which broke and were repaired.

(b)The first person to be effected by the decree was - none other than his sister, Queen Shel Tziyon (otherwise known as Alexandra Shalomis, wife of King Yanai), who once prepared a banquet for her son. When all her vessels became Tamei, she broke them all and gave them to the metal-smith to repair, in order to be able to use them immediately, and not to have wait seven days. That was when Shimon ben Shetach decreed retroactive Tum'ah on all those vessels, and established it as a decree.

(c)We initially attribute the decree to the need to ensure the continuity of the ashes of the Parah Adumah. Otherwise, now that a way had been discovered to circumvent the need of the Eifer ha'Parah, there was a real danger that, in order to avoid having to wait for seven days, everyone would simply break their metal vessels, and then have them repaired. Shimon ben Shetach was afraid that the whole institution of the Eifer ha'Parah, at least as far as Tamei vessels was concerned, would now become obsolete. This wxplanation however, is acceptable only according to those who confine the decree to vessels that became Tamei Mes, but not according to those opinions who extend it to all kinds of Tum'ah, which have no connection with the Eifer ha'Parah.

(d)Abaye ultimately attributes the decree to the fact that one may not break the vessel properly (i.e. a hole at least the size of a pomegranate) - Rava ascribes it to people who see the owner using his vessels on the same day that they became Tamei, and who will then say that Tevilah helps to permit Tamei vessels on the same day that they were Toveled (even for Terumah, which requires 'Ha'arev Shemesh'), even before nightfall. The difference between Abaye and Rava will manifest itself - in a case where one smashed the vessel completely, then, according to Abaye, we must still suspect that he may leave a large piece intact without a hole the size of a pomegranate, which is still subject to the decree; whereas according to Rava, the vessel will be Tahor when he re-makes it, since everyone can see that the vessel has been re-formed.

5)

(a)'ha'Meini'ach Kelim Tachas ha'Tzinor Lekabel Meihem Mei Geshamim ... Poslin Es ha'Mikvah' (Mishnah - Mikva'os). For a pipe not to invalidate the Mikveh - it must have been permanently fixed in place, before being carved out in the shape of a pipe.

(b)If the vessels were placed there on purpose, everyone agrees that if the water then flows from into the Mikveh, the Mikveh is Pasul, because it has been filled with drawn water. The initial Machlokes (and ultimate case in which Beis Hillel concede to Beis Shamai, speaks when they were placed there inadvertently, though we have yet to see exactly what that means).

(c)The Mishnah mention 'even small or large vessels' and 'vessels made of earth or stone or marble'. The Tana meantions small vessels to teach us that, in spite of their apparent insignificance, they are sufficiently Chashuv to render the Mikveh Pasul; and he mentions large ones (see Tosfos DH 'Echad'), vessels made of plain (unmixed) earth, stone or marble to teach us that, even though they themselves are not subject to Tum'ah, they are nevertheless capable of rendering the Mikveh Pasul.

6)

(a)According to Rebbi Meir, Beis Shamai concede that if the water fell into vessels lying in the courtyard, the Mikvah is not Pasul because of 'Mayim She'uvin - because, since he did not leave the vessels under the pipe, their is no evidence that he intended the water to flow into the vessels, in which case it will not invalidate the Mikveh.

(b)If he placed the vessels under the pipe (and forgot them there) ...

1. ... when the sky was overcast, they will all agree that the Mikveh will be Tamei, since, he definitely intended the rain to fill his vessels, and even if he then forgot about them and went away, his original intentionremains.

2. ... when the sky was clear, they all agree that the Mikveh remains Kasher, since there is no indication that he wanted the vessels to be filled.

(c)Beis Shamai and Beis Hillel initially argue over vessels that were placed under the pipe and forgotten there, when the sky was overcast, and then cleared before becoming overcast again. Beis Hillel hold that, since the clouds cleared, he thought that the rain would no longer fall, and negates his original intention. Whereas according to Beis Shamai, his original intention does not become negated, since the sky became overcast again.

7)

(a)According to Rebbi, the twelfth decree of the eighteen is that of 'B'nos Kutim, Nidos me'Arisasan'. (According to Rebbi Meir, that decree was not issued then, but on another occasion.)