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1)

(a) According to ...

1. ... Rebbi Yehudah (who defines a Chatzi Peras as 'Sh'tei Beitzim Chaser Kim'a') - Rebbi Nasan and Rebbi Dosa, who describe the k'Beitzah of Tum'as Ochlin as 'Kamo'ah u'Kelifasah', should have given a slightly smaller Shiur.
2. ... Rebbi Yossi (who describes it as 'Sh'tei Beitzim Shochkos') - they should have given a slightly larger Shiur.
3. ... Rebbi (who added one twentieth of a k'Beitzah to every k'Beitzah) - they should have given a larger Shiur still.

(b) The Chachamim who give the Shiur of Tum'as Ochlin as a k'Beitzah u'Mechtzah Shochkos - are none other than Rebbi Yochanan ben Berokah (of our Mishnah), who gave the Shiur of Eruv as a quarter of a Kav - six k'Beitzim; half of that (three k'Beitzim) for a plagued house; and half of that (one a half k'Beitzim) for the half a Peras of Pesul Gevi'ah. Note: By the same token, the k'Beitzah of Tum'as Ochlin will be one and a quarter k'Beitzim according to him.

(c) Rav Chisda needs to teach us this here (despite the fact that he has already explained Rebbi Yochanan ben Berokah above), to teach us that the one and a half k'Beitzim of Rebbi Yochanan ben Berokah are large ones (Shochkos).

(a) There are 144 k'Beitzim in a Sa'ah Midbari.

(b) When we say that they added *a sixth* to the Sa'ah - what we really mean is a fifth (28 4/5 of a k'Beitzah, which is the equivalent to a sixth of the new total of k'Beitzim in a Sa'ah = 172 4/5 [173 to all intents and purposes]).

(c) There were 207 k'Beitzim in a Sa'ah Tzipori.

(a) The Shiur Chalah of 207 k'Beitzim is only eight k'Beitzim (one twenty- fourth of 192) plus - which would still only total 215, and not the 217 that Rebbi reckoned.

(b) In fact, Rebbi added ten (and not eight) to the Ne'usian Sa'ah - on account of the twentieth that he added to each k'Beitzah (see above 1a, 3.). In reality, he ought to have reckoned slightly more (1/20 of 207 = almost ten and a half. However, he the Gemara does not bother with fractions.

(c) When the Beraisa states that the Sa'ah Yerushalmi is one sixth more than the Sa'ah Midbari, and the Sa'ah Tzipori one sixth more than the Sa'ah Yerushalmi, and that consequently, the difference between the Sa'ah Midbari and the Sa'ah Tzipori is *one third* - it cannot mean that the difference between the Sa'ah Midbari and the Sa'ah Tzipori is one third of the Sa'ah Midbari - because, whereas one third of the Sa'ah Midbari is 48 k'Beitzim, the difference between the two is 63; nor can it be referring to one third of the Sa'ah Yerushalmi - because that amounts to 57 2/3 k'Beitzim (and not 63); nor can it refer to one third of a Sa'ah Tzipori - since a third of Sa'ah Tzipori is 69 k'Beitzim (even more than 63).

(a) The Gemara rejects the suggestion of Rebbi Yirmiyah [that what the Beraisa means is that the difference between the Sa'ah Tzipori and the Sa'ah Midbari (63) is close to *a third* of its own total (69), and that a third of its own total (69) is close to *a half* of the Midbari Sa'ah (72)] - because who mentioned 'close to'. The Beraisa says that it is exactly one third, not approximately.

(b) We finally explain the Beraisa to mean that - one third of a Sa'ah Tzipori 207 k'Beitzim) including the extra ten k'Beitzim (1/3 of 217 = 72 1/3) is only a third of a k'Beitzah more than half of the initial Sa'ah Midbari (1/2 of 144 = 72).

5)

(a) We know the Shiur of 'a dough of the Midbar' - from the Pasuk in Beshalach "ve'ha'Omer Asiris ha'Eifah Hu".

(b) There are three Sa'ah in an Eifah.

(c) Given the facts that an Eifah is the equivalent of a Bas, and that a Kur equals thirty Sa'ah, we learn from the Pasuk in Yechezkel "Ma'aser ha'Bas min ha'Kur" - that one Eifah equals three Sa'ah. (d) The Omer of Man that fell daily, contained ...

1. ... .3 Sa'ah.
2. ... 1.8 Kabin.
3. ... 7.2 Lugin.
4. ... 43.2 k'Beitzim.

(a) 'Shiv'ah Reva'im Kemach ve'Od' - simply means a little more than seven quarters of a Kav i.e. 7 Lugin and 1 1/5 k'Beitzim, which is the Shiur of Chalah.

(b) When this was transferred into ...

1. ... the Yerushalmi measurements - it came to 6 Lugin (36 k'Beitzim).
2. ... and then into the measurement of Tzipori - it came to 5 Lugin (30 k'Beitzim).

(c) The Beraisa concludes that someone who eats this amount is eating healthily; if he eats more than that, he is greedy; and if he eats less, it is harmful.

(a) If the residents of the Chatzer and those of the balcony (which is at least ten Tefachim high) forgot to make a combined Eruv - it is the residents of the Chatzer who are permitted to use the Chatzer.

(b) The residents of the balcony exclusively are permitted to use any part of the Chatzer that extends beyond the height of ten Tefachim (e.g. a mound of earth) - provided it is within four Tefachim of the balcony.

(c) The one does not forbid the other to carry - because the ladder that connects them has the Din of a Mechitzah Lehakel (as we learnt above 59b).

(d) If there is a pit with a mound of earth surrounding it next to the balcony, then it may be used exclusively ...

1. ... by the residents of the balcony - provided it is within four Tefachim of the balcony; otherwise it may be used ...
2. ... by the residents of the Chatzer.

(a)

1. ... 'la'Zeh ba'Pesach, ve'la'Zeh ba'Pesach' - means that each of the two courtyards are able to use the intervening domain with ease. The Din here is the same as that of a window between two domains (76a) - where they are permitted to make a combined Eruv or separate Eruvin, as they please. If they did not make a combined Eruv, then, if the window-ledge is four Tefachim wide, then neither Chatzer may use it; if it is not, then they may.
2. ... 'la'Zeh bi'Zerikah, ve'la'Zeh bi'Zerikah' - means that the intervening domain is more than ten Tefachim high, and one would only use it by throwing. Its Din is equivalent to that of a high wall, where both courtyards are forbidden to use it (if it is four Tefachim wide, as we explained in 1.).
3. ... 'la'Zeh be'Shilshul ve'la'Zeh be'Shilshul' - means that the intervening domain is lower than ten Tefachim, and it can only be used by lowering things into it. Here too, neither Chatzer is permitted to use it.

(b)

1. ... 'la'Zeh ba'Pesach, ve'la'Zeh bi'Zerikah' - is in the domain of the former, since it is far easier for them to use.
2. ... 'la'Zeh ba'Pesach, ve'la'Zeh be'Shilshul' - is likewise in the domain of the former, for the same reason.

(c) Shmuel holds by 'la'Zeh be'Shilshul ve'la'Zeh bi'Zerikah' - that since lowering it is slightly easier than throwing it, we place it in the domain of the upper-Chatzer, that needs to lower into it, and *they* are the ones who are allowed to use it.

(a) The Gemara initially thought that when the Tana taught 'Anshei Chazter ve'Anshei Mirpeset she'Shachechu ve'Lo Ervu, Kol she'Gavo'a mi'Yud Tefachim, le'*Mirpeset*' - means the residents of the attic, who live above the balcony, in which case, we have here a case of 'la'Zeh be'Shilshul ve'la'Zeh bi'Zerikah', which the Mishnah gives to the attic - because lowering is easier than throwing (like Shmuel).

(b) Rav Huna (a little later in the Sugya) will establish 'le'Mirpeset' to mean to the residents of the *Mirpeset* (and not the *attic*), which is a case of 'la'Zeh ba'Pesach, ve'la'Zeh bi'Zerikah', which, even Rav agrees, goes to the former.