Zevachim Chapter Five, Mishnah Two. The mishnah continues to survey the order of the service for the various sacrifices, and opens with the words: "Par hanisrafim use'irim hanisrafim" - the burned bull and the burned he-goats. As we have already learned, there are five inner sin-offerings - chatas sacrifices whose blood is brought into the Heichal, to the inner altar.
Two of them were discussed in the previous mishnah: the bull of the Kohen Gadol (for himself and his household) and the he-goat offered to God, both from the Yom Kippur service. The remaining three sacrifices, which our mishnah addresses, are:
Par he'elem davar - when the Sanhedrin issued a ruling permitting something whose punishment is kares, and the majority of the public acted according to them. In this case, the entire public brings a bull, instead of each individual bringing a regular chatas.
Se'ir avodah zarah - when the Sanhedrin's ruling concerned a matter of idol worship, and afterward they said, "We erred," and the majority of the congregation followed them. In such a case, they bring a he-goat instead of a bull.
Par kohen mashiach - a Kohen Gadol anointed with the anointing oil, who issued a halachic ruling for himself in the manner that the Sanhedrin rules and acted upon it, and subsequently realized he committed a transgression whose penalty is kares when done intentionally. Instead of a regular chatas he brings a special bull, as one of the inner sin-offerings.
And if you ask: Why did the mishnah use the plural form, "he-goats that are burned," since we only have one he-goat left to discuss, as the other was mentioned in the previous mishnah? One answer is that the halachah is that when they bring the par he'elem davar or the he-goats, each of the twelve tribes brings a sacrifice for itself, and the Sanhedrin does not bring just one. Therefore, it says "he-goats" in the plural - the twelve he-goats brought by the twelve tribes.
The order of their service:
"Shechitasan batzafon" - their slaughter is on the northern side, because they are most holy offerings.
"Vekibul daman bikli shareis batzafon" - the blood is received in a ministering vessel, also in the north, for that exact same reason.
"Vedaman ta'un haza'ah al haparoches ve'al mizbach hazahav" - the blood is sprinkled toward the paroches, the curtain dividing between the Holy and the Holy of Holies within the Heichal, and also on the golden altar, which is the inner altar we mentioned.
The eleven sprinklings:
The reason the inner sin-offerings were divided into two separate mishnayos is that in the previous mishnah we dealt with the bull and the he-goat of Yom Kippur, which have forty-three sprinklings, as enumerated there; whereas in the three sacrifices before us there are only eleven sprinklings. How so?
Seven sprinklings toward the paroches in front of the Holy of Holies - as opposed to the eight we counted in the previous mishnah, both for the bull and the he-goat.
Four placements - blood that is placed, and actually dripped, onto the four corners of the golden altar. In the previous mishnah there were eleven placements on the golden altar: four on the four corners and seven on its top, the central surface; whereas here there are not these seven.
"Matanah achas meihen me'akeves" - every single one of the eleven sprinklings is indispensable, meaning that if one of them was done improperly, the sacrifice is not valid, and it must be done again properly.
"Shiray hadam hayah shofeich al yesod ma'aravi" - of the outer altar. The blood that remains after the eleven sprinklings is brought from the Heichal, from the Holy, to the outer altar. As we have learned, in the yesod - the ledge encompassing the lower level of the altar - there were two small holes in the southwestern corner, one on the southern side and one on the western side. Here it specifies the western side, which faces the Heichal, the building, and the leftover blood is poured into that hole.
"Ve'im lo nasan lo ikeiv" - if for any reason the blood did not reach the yesod or the hole, for instance, if it was spilled by mistake, this is not indispensable and the sacrifice is valid. Ideally it should be done, but after the fact, it does not invalidate it.
Burning in the Beis Hadeshen:
"Eilu v'eilu nisrafin b'veis hadeshen" - all five inner chatas offerings, the three bulls and the two he-goats, are burned in the Beis Hadeshen. "Deshen" is the Torah's term for ashes: on top of the Altar there were ashes from the burning. This should not be confused with Terumas Hadeshen - every morning there is a mitzvah to take a single scoop of it and place it on the floor of the Azarah, and the rest of the ashes were built into a "tapuach", a large pile of ashes, and from there taken out to a place outside Jerusalem called the Beis Hadeshen, the place of the ashes. According to the Rambam, this was done every day as a mitzvah; according to Rashi and the Chumash, it was only done periodically as needed, and not as an independent mitzvah.
That same place where the ashes are taken is called the Beis Hadeshen, the place of the ashes, and there the five inner chatas offerings are burned. The eimurim, the standard parts that are offered up, are burned on top of the Altar, but the rest of the meat is not eaten by the kohanim like other chatas offerings. Instead, it is burned in the Beis Hadeshen outside Jerusalem. Hence their name - "the burned bulls and the burned he-goats": instead of being eaten, they are burned there, outside Jerusalem, in the Beis Hadeshen.