The next three Tractates are relatively short, and their pages are numbered as if they were part of the Me'lah Tractate. They deal respectively with bird pairs brought as sacrifices, order of the day in the Temple, and dimensions of the Temple.
A pair of birds is brought in a number of cases, such as anyone who has to bring an animal sin-offering but is too poor for the expense, a woman who gave birth, or a spiritual leper on his purification. The birds have to be either two turtledoves, or two young pigeons.
One of the birds is a burned offering, whose blood is sprinkled on the upper part of the Altar wall, above the red line that designates the middle, and the other one is a sin-offering, and its blood is applied on the lower part of the wall. Therefore, the offerings are completely incompatible, and if one is brought as another, it is invalid. For example, if in a pair two birds were already designated, one as a burned offering, and the other as a sin-offering, and then they become mixed, the offering cannot be brought at all, and the birds have to die.
Therefore, the owner would prefer not to designate the birds, but allow the Kohen to do it, just before sacrificing them, and the Kohen is given the power of designating them. The owner can actually designate the birds when he or she buys them, and these are the only to moments in time when a designation can be done.
If a bird pair of one woman mingled with the the pair of another, only two out of four birds can be brought. Why? We can definitely bring one pair, since the mixture contains two undesignated burned offerings, and two sin-offerings. However, we cannot bring the second pair, because perhaps the first two birds were really burned offerings, and there are no more burned offerings left. The same is true if two pairs mixed with two pairs, three with three pairs, and so on – half of them can be brought, but not more.
Art: (After) Pieter Aertsen - A woman holding a duck and a bird cage with chickens and a dove