Yoma, Chapter Four, Mishnah Two
After having drawn the lots to determine which goat would be slaughtered and which sent away, the days ceremonies continue.
1) He bound a thread of crimson wool on the head of the goat which was to be sent away, and he placed it at the gate where it was later to be sent away, and on the goat that was to be slaughtered [he placed a thread of crimson wool on its neck] at the place of the slaughtering.
2) He came to his bull a second time, pressed his two hands upon it and made confession.
a) And thus he would say: Please, Hashem! I have done wrong, I have transgressed, I have sinned before You, I and my house and the sons of Aaron Your holy people. Please, Hashem! Forgive the wrongdoings, the transgressions, the sins which I have committed and transgressed and sinned before You, I and my house and the sons of Aaron Your holy people, as it is written in the torah of Moses Your servant: For on this day shall atonement be made for you [to cleanse you of all your sins; you shall be clean before the Lord] (Leviticus 16:30).
b) And they answered after him: Blessed be the name of His glorious kingdom for ever and ever!
Section one: After determining the goats, the priest would tie a piece of crimson wool on the sacrificial goat between its horns and then set it near the gate from where it will be later sent into the wilderness. He would also tie a thread around the neck of the goat which will later be slaughtered. We have actually already mentioned this piece of wool in Shabbat 9:3 and Shekalim 4:2 and we shall discuss it and its function again in Yoma 6:6, and 6:8. The Talmud on this mishnah explains that the purpose of these threads was to make sure that these goats didnt get mixed up with others. They placed the threads in different places so that these two could be distinguished from one another.
Section two: He now comes back to the bull (he was already there at mishnah 3:8) and offers up another confession. This time the confession is not only for him and his household but for all of the other priests as well. The words of the confession are the same as those in 3:8 above, except here he adds and the sons of Aaron Your holy people.