The Kohen Gadol left the Sanctuary and slaughtered the goat designated for God. He collected its blood in a vessel and re-entered the Kodesh Ha-kodashim. He stood facing the two poles of the Ark and sprinkled the goat’s blood, once upward and seven times downward. As we read, “He shall then slaughter the people’s goat of sin offering, bring its blood beyond the parokhet, and do with its blood as he has done with the blood of the bull: he shall sprinkle it over the kaporet and in front of the kaporet. Thus he shall atone for the Kodesh from the impurity and transgression of the Israelites, whatever their sins” (Vayikra 16:15-16).
The Kohen Gadol then exited the Kodesh Ha-kodashim, placed the vessel of goat’s blood on a second stand, and picked up the vessel of bull’s blood. He sprinkled it toward the parokhet separating the Kodesh from the Kodesh Ha-kodashim, upward once and downward seven times. He then did the same with the goat’s blood. These sprinklings fulfilled the mandate, “He shall do the same for the Ohel Mo’ed, which abides with them in the midst of their impurity” (Vayikra 16:16).
After that, the Kohen Gadol took the vessels and mixed the blood of the two animals together. He walked from the parokhet to the golden altar in the Kodesh and sprinkled blood on its four corners. He cleared away coal and ash from the altar until its golden color became visible, whereupon he sprinkled it with blood seven times. As we read:
He shall go out to the altar that is before the Lord and atone for it: he shall take some of the blood of the bull and of the goat and apply it to each of the horns of the altar; and the rest of the blood he shall sprinkle on it with his finger seven times. Thus he shall cleanse it of the impurity of the Israelites and consecrate it. (Vayikra 16:18-19)
He then went out to the copper altar and spilled what was left of the blood on the western side of its base. Having finished atoning for the defilement of the Temple and its sacrifices, the Kohen Gadol began the process of atoning for all other sins. He approached the scapegoat, placed both hands on it, and confessed in the name of all Israel, as we read:
When he has finished atoning for the Kodesh, the Ohel Mo’ed, and the altar, the live goat shall be brought forward. Aharon shall lay both his hands upon the head of the live goat and confess over it all the iniquities and transgressions of the Israelites, whatever their sins, putting them on the head of the goat. (Vayikra 16:20-21)
This was the formula of the third vidui:
Please, Lord, Your people, the house of Israel, have sinned, have done wrong, have rebelled before You. Please, by Your name, grant atonement for the sins and for the wrongs and the rebellions that they have sinned, and done wrong, and rebelled before You – Your people, the house of Israel. As it is written in the Torah of Moshe Your servant, at the word of Your glory: “For on this day, you will be atoned for and made pure of all your sins before the Lord.”
A we learned, each time the kohanim and the people heard the Tetragrammaton, they would kneel, prostrate themselves, and proclaim, “Barukh shem kevod malkhuto le-olam va-ed.” Thus, during the course of the three confessions, the people prostrated themselves nine times. Together with the prostration when the Kohen Gadol pronounced the Divine Name upon casting the lots, we reach a total of ten prostrations.
The Kohen Gadol then sent the scapegoat to the wilderness with a designated agent, as we read, “It shall be sent off to the wilderness through a designated man. Thus the goat shall carry on it all their iniquities to an inaccessible region; and the goat shall be cast away in the wilderness” (Vayikra 16:21-22). The man walked to a mountain that was approximately twelve mil (about 11 km) into the wilderness. He then divided the ribbon that was tied to the goat’s horns in two, leaving one part on the goat’s horns and tying the other part to a rock. He cast the goat off the cliff; before it got halfway down the mountainside, it was already dashed to pieces (Yoma 67a).