Yoma Chapter 6, Mishnah 8. In order for the Kohen Gadol to continue with the order of the Yom Kippur service after the goat was sent to Azazel, he must know that the goat had reached the wilderness. It is not necessary that it already be pushed off the cliff, but until the goat reaches the wilderness the Kohen Gadol cannot proceed with the order of the service, for the Torah says: "And he shall send the goat into the wilderness," and only afterward does it say: "And the fat of the sin offering he shall burn" - at that point he burns the fats on the altar and performs all the other accompanying services.
The words of the Mishnah:
"Amru lo l'Kohen Gadol: higia sa'ir lamidbar" - they informed the Kohen Gadol that the goat had reached the wilderness, and from that point on he was permitted to continue with the order of the service.
"Me'ayin hayu yod'in shehigia sa'ir lamidbar?" - from where did they know that the goat had reached the wilderness?
"Dirkaos hayu osin, u'menifin b'sudarin, v'yod'in shehigia sa'ir lamidbar" - in the absence of any means of communication, they set up observation towers, and from the spot where the beginning of the wilderness could be seen they would wave cloths from tower to tower, and in this way the news arrived that the goat had reached the wilderness.
Rabbi Yehudah's sign:
Rabbi Yehudah says: "Vahalo siman gadol hayah lahem" - they had a clear sign, and there was no need for this entire process. And so it was: "MiYerushalayim v'ad Beis Chidudo shloshah milin" - Beis Chidudo is a place at the edge of Jerusalem, from which the wilderness begins, and the distance from Jerusalem to it is three mil (each mil being two thousand amos). And from here comes the calculation of the time:
"Holchin mil" - the distinguished men of Jerusalem, the notables of the city, who would escort the goat as far as the first booth, walked one mil.
"V'chozrin mil" - and they returned one mil.
"V'shohin k'dei mil" - and they waited the amount of time it takes to walk an additional mil.
"V'yod'in shehigia sa'ir lamidbar" - for the time it takes to walk three mil is the time required for the goat to reach the wilderness, and with these three measures - walking, returning and waiting - the time was completed.
The Rashash's precision:
The Rashash raises the question: how did they "wait the amount of time it takes to walk a mil"? The time required for the designated man to arrive is the time it takes to walk three mil, and one mil they walked and one mil they returned - but by what did they measure that final waiting period of "k'dei mil"? The Rashash suggests: the Temple Mount was five hundred amos by five hundred amos, and its perimeter was two thousand amos, which is the measure of a mil. Therefore a person would circle the Temple Mount, and by this that final wait of k'dei mil was measured, and in this way they knew that the goat had reached the wilderness.
Rabbi Shmuel's sign - the crimson thread:
Rabbi Shmuel brings an additional sign: a thread of crimson wool was tied at the entrance to the Sanctuary, and when the goat reached the wilderness that thread would turn white, as it says: "If your sins be as scarlet, they shall become white as snow."
Now, in the Mishnah we learned earlier it stated that the crimson thread was sent along with the goat to Azazel. On this the beraisa in the Gemara explains that Rabbi Shmuel is describing the practice as it was originally, and this is how matters developed:
At first they would tie the thread at the entrance to the Ulam, which is in front of the Sanctuary, and when it did not turn white the people would become distressed.
Therefore they moved it inside the Ulam, but the people would peek in and see.
Therefore they instituted that it be sent along with the goat to Azazel, as we learned in the previous Mishnah.
In summary: in this Mishnah we learned that the continuation of the Kohen Gadol's service depends on knowing that the goat had reached the wilderness, as derived from the order of the verses "And he shall send the goat into the wilderness" and "And the fat of the sin offering he shall burn." Three ways were stated for obtaining this knowledge: the observation towers and the waving of the cloths; Rabbi Yehudah's sign in the calculation of the mil - they walk a mil, and return a mil, and wait the time of a mil (and according to the Rashash the waiting was measured by circling the Temple Mount, whose perimeter is two thousand amos); and Rabbi Shmuel's sign in the whitening of the crimson thread tied at the entrance to the Sanctuary, which was the practice as it originally was, until they instituted that the thread be sent along with the goat to Azazel.