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1) BIRDS THAT FLEW BACK AND FORTH

(a) (Mishnah 1): If one bird of a Ken Stumah (or many Stumos) flew away, or it became mixed with birds that must die (e.g. a Chatas whose owner died), or it died, we take another bird to replace it, to be offered with the remaining bird.
(b) If the bird became mixed with Kereivos (birds that can be offered; we assume that they are not all Olos, nor all Chata'os), it is Pasul and Posel. (Pasul means, on account of it we must refrain from offering one of the birds in the mixture -- we cannot offer an extra Olah (above the number of Olos in the Kereivos), lest all the Olos will be from the Kereivos; likewise, we cannot offer an extra Chatas. Posel means, it prevents us from offering one bird from the Ken or Kinim it left. (We can only offer whole Chovos, but not the "odd" (unpaired) bird left -- if we would offer the odd bird for Olah [or Chatas], this would mandate the Pore'ach (the bird that flew) to be a Chatas [or Olah], we would not be allowed to offer any Olos [or Chata'os] from the mixture). The coming Mishnayos discuss only being Posel, but indeed it is also Pasul.)
(c) (Mishnah 2): For example, if Rachel and Leah each had two Kinim, and one of Rachel's birds flew to [and became mixed with] Leah's birds, it is [Pasul, we offer only four birds of Leah's mixture, and] Posel (we offer only two of Rachel's [remaining] birds);
(d) (The Mishnayos discuss birds "returning" -- this is what it looks like, but since the birds became mixed, we really do not know whether or not it is the same bird.) If it [or one of Leah's birds] flew "back" to Rachel's birds, it is [Pasul, we may offer only two of Rachel's birds, just like before it returned, and] Posel (before, we could not offer one bird of Leah's mixture -- now we must refrain from offering two of the remaining four. We cannot offer three Olos [or Chata'os] in all, for any three birds we select could all be from the same woman.)
(e) If it [or another] flew again to the other birds and returned, even many times, it does not detract from what we may offer -- even if all the birds were mixed together, we could take any four and offer two Olos and two Chata'os, no matter whose birds they are.
(f) (Mishnah #3): If seven women had, respectively, one, two, three,... seven Chovos (we call their groups of birds A, B, C,... G), and a bird flew from A to B, then it [or another] flew from B to C,... from F to G, then "returned" from G to F,... and from B to A:

1. On the trip from A to G, it is Posel [one Chovah] from every group it leaves; likewise, on the return trip it is Posel one from every group it leaves. The numbers of Chovos we may offer from A, B,... G are 0, 0, 1, 2, 3, 4, 6. (It only left G once, on the return trip. Really, the reason it is Posel is because we do not want to "fix" the Pore'ach (see the end of (b)) -- since we do not offer anything from A or B, according to the letter of the law we could offer another Chovah from B *or* C (but not both -- if we offer from B, we may not fix what left C)! However, Chachamim decreed not to, lest other women think that they do not lose on account of the return.)
2. If afterwards a bird flew from C to D, then [it or another] to E, F, and G, then "returned" to F, ...C, it is Posel one from every group it leaves on the way to G, and also on the return; the numbers we may offer from C, D,... G are 0, 0, 1, 2, 5. (As above, according to the letter of the law we could offer more from some of these, since we are not offering anything that returned to the first groups, but Chachamim decreed not to. We explained like Bartenura, who says that the second journey could not have begun from A or B, for we may not offer any of them, they are like birds that must die, which forbid everything they get mixed with. Rosh explains, it started from and returned to A, like the previous clause. A and B are not like Chata'os ha'Mesos that surely must die -- rather, we do not offer them on account of Sefekos, we are lenient in cases of Sfek Sfeika (multiple doubts, we transgress only if all of them turn out the "wrong" way). Indeed, if we would know that both birds of A flew to and remained in G, we could not offer even two Olos [or Chata'os] from G, lest both are from A!)
3. If afterwards a bird went [Bartenura - from E; Rosh - from A] to G and back, it is Posel one on the way and on the return, we offer nothing from every group except for G, from which we offer four;

4. Some say, because we do not offer from any other group, G does not lose anything (on account of this third journey, it still offers five. Tiferes Yisrael - since after the second journey we ruled that it offers only five, the other two were Nidchim and can never be offered. Gra - we offer all seven of G.)
5. If Mesos (birds that must die) became mixed with any group, we may not offer anything from the mixture.

(g) (Mishnah 4): If a bird flew from a Ken Stumah to a Ken Mefureshes (the Chatas and Olah were designated, but later became mixed, so they must die), we take another bird to replace it, to be offered with the remaining bird of the Stumah.

1. If it returned, or if [nothing left the Stumah, just] a bird from the Mefureshes flew to the Stumah, all must die.

(h) (Mishnah 5): If there were three piles of birds, Chata'os on the right, Olos on the left, and Stumos in the middle:

1. If one bird from the middle went to the Olos, and another went to the Chata'os, nothing is lost -- we offer all the Chata'os including the Stumah (it becomes a Chatas), and all the Olos including the Stumah, and all the remaining Stumos (half Olos and half Chata'os);
2. If the [same or other] birds returned from both sides to the middle, all those in the middle must die, the Chata'os and Olos may still be offered;
3. If afterwards birds from the middle returned to the sides, all the birds must die.

(a) We may not bring a Tor (turtledove) and [Ben] Yonah (common dove) for a Chovah (rather, we must bring two Torim or two Yonim):

1. If a woman brought a Tor Chatas and [then] Yonah Olah, she must bring a Tor for an Olah;
2. If she brought a Tor Olah and [then] Yonah Chatas, she must bring another Olah, a Yonah (she must bring an Olah like the Chatas);
3. Ben Azai says, the first bird offered determines the latter (therefore, she must bring a Tor Chatas).

(b) If a woman brought her Chatas and died (before bringing her Olah), her heirs bring her Olah (some Amora'im say that this is only if she herself was Makdish the Olah; others say, there is a lien on her property, her heirs must buy and offer it);
(c) If she brought her Olah and died, her heirs do not bring her Chatas (Chatas can be offered only to atone, it may not be offered for the deceased).