Chullin, Chapter 2, Mishnah 1. Having dealt in the first chapter with who is fit to perform shechitah, the Mishnah now turns to the act itself: how much of the neck must actually be cut for the shechitah to be valid. Our mishnah lays down the basic measurements, distinguishing between a bird and an animal, and closes with a case involving korbanot.
"Hashochet echad ba'of ushnayim babehemah, shechitatah kesherah."
A bird's throat contains two simanim, the trachea (windpipe) and the esophagus (food pipe), and one who slaughters a bird and severs either one of them has performed a valid shechitah. With an animal the rule is stricter: both simanim have to be cut. For a bird, a single siman is enough.
The Chachamim explain that this is bedi'eved, after the fact. Ideally a person slaughtering a bird should aim to cut through both pipes. But if in the end only one of them was cut, the shechitah is not disqualified, and the bird is kosher.
"Verubo shel echad kamohu."
In both cases, bird and animal alike, cutting the majority of a pipe has the same status as cutting it completely. There is no requirement to sever the pipe from end to end. Once the greater part of it has been cut, the shechitah is valid.
The Mishnah now moves to a related matter: the blood of the slaughtered creature, which the Torah forbids us to consume.
"Rabbi Yehudah omer: ad sheyishchot et haveridin."
Rabbi Yehudah teaches that even where the shechitah of a bird was performed entirely properly, the bird may not be eaten until the veridin, the major blood vessels of the neck (the carotid arteries), have been cut so that the blood drains out.
Why is this raised specifically regarding a bird? With ordinary animals, the standard processes of salting and roasting draw out the blood. A bird, however, is typically cooked or roasted whole, so salting and roasting will not succeed in extracting all the blood from within it. The veridin must therefore be opened so that the blood can drain away. Practically, this should be done at the time of the shechitah itself, so that the blood does not congeal in the vessels.
It is worth noting that opening the veridin does not need to be performed in the manner of shechitah. One may simply puncture them, or drain the blood by any means. This is not part of the act of shechitah at all; it merely takes place at the same time.
"Chatzi echad ba'of ve'echad vachatzi babehemah, shechitatah pesulah."
Now the opposite case. A bird whose one siman was cut only halfway through, or an animal in which the first siman was fully severed but the second was cut only to its midpoint, has not been validly slaughtered. Half is not a majority, and anything less than a majority achieves nothing at all in the cut. The requirement is fifty one percent, and fifty will not do.
"Rov echad ba'of verov shenayim babehemah, shechitatah kesherah."
Where a majority of the single siman was severed in a bird, or a majority of each of the two simanim in an animal, the shechitah is valid. But has this not just been taught? The Mishnah returns to it because it is now discussing korbanot.
One might have reasoned as follows: the purpose of a korban is the placing of the blood on the mizbe'ach. If that is the whole objective, perhaps the pipes must be cut through entirely, so that the blood should flow out as freely as possible. The Mishnah tells us otherwise. Even in the case of a korban, cutting the majority of each pipe is sufficient.