Pesachim, Chapter 6, Mishnah 3. In the previous mishnayos we dealt with the question of which parts of the service of the Pesach offering override Shabbos and which do not. Our Mishnah takes up another matter connected to the Pesach offering: the chagigah offering.
What is the chagigah offering:
The chagigah is a peace offering brought on the festivals, and bringing it is a mitzvah on every day of Yom Tov. Here, however, we are speaking of a special chagigah, one brought on Erev Pesach, and only when certain conditions are met.
The purpose of this chagigah is that the eating of the Pesach offering should be "al hasova" - that a person eat the Pesach when he is already satisfied. The Pesach offering by itself is not enough to satisfy a person: it comes from the sheep, and it is valid only within its first year, so it is small, while the demand for it was great. Very often many people were registered on a single Pesach offering, and each one received only a kezayis, exactly the required measure. To reach the point of satisfaction, then, additional food was needed.
Nowadays we eat matzah in generous quantities, but in earlier generations people were more exacting with the measures and ate less, and they frequently needed additional meat, so that by the time they came to the Pesach offering they would already be satisfied from it. For this purpose they would bring the chagigah offering beforehand.
Its source in the Torah:
This is hinted at in the Torah, which says that one slaughters the Pesach "tzon uvakar" - from the flock and from the herd. Yet cattle, the large animal, are not valid for the Pesach offering at all. Our Sages therefore said that the verse is speaking of the chagigah offering, which comes together with the Pesach offering so that it may be eaten al hasova.
When is a chagigah brought with the Pesach:
On a weekday - only when the Pesach offering is brought in the middle of the week. The Pesach offering overrides Shabbos, but the chagigah offering that accompanies it does not override Shabbos. If Erev Pesach falls on Shabbos, one must reach satisfaction with other foods and not with the meat of the chagigah.
In purity - only when the Pesach is brought in a state of purity. It is known that when the majority of the community or the kohanim are tamei, the Pesach is brought in tumah, since tumah is set aside (or permitted) for the community. In such circumstances, however, no chagigah is brought with it, for the chagigah comes only in purity.
When there is little - only when the Pesach offering is not enough for all those registered on it. But if the group is small and there is enough in the Pesach to satisfy all its members, no chagigah is needed.
Corresponding to this the Mishnah says: "Uvizman shehu ba b'Shabbos, bimrubeh uvtumah - ein mevi'in imo chagigah" - when the Pesach is brought on Shabbos, or when the group is large and there is enough in it to satisfy them, or when it is brought in tumah, no chagigah is brought with it.
In summary: the chagigah offering that comes with the Pesach is not an absolute obligation but depends on the circumstances. It comes only in order to complete the eating of the Pesach al hasova, and only when the Pesach is brought on a weekday, in purity, and when there is little. When the circumstances do not require it, it is not brought at all.