Yoma, Chapter 3, Mishnah 1. From here onward the Mishnah turns to the continuation of the order of the service on Yom Kippur, and to the way the time for slaughtering the daily Tamid offering was determined.
The words of the Mishnah:
"Amar lahem hamemuneh: tze'u ur'u im higia zman hashechitah" - the officer in charge in the Beis HaMikdash would send men out to check whether the time for the Tamid offering had arrived.
"Im higia - haro'eh omer: Barkai" - the watchman would announce that the light of morning had appeared, a light that can be seen even before sunrise.
"Matisya ben Shmuel omer: he'ir p'nei kol hamizrach" - in his opinion, they would not slaughter the Tamid until the watchman announced that the entire eastern sky had lit up.
"Ad sheb'Chevron":
After the announcement they would ask the watchman: "He'ir ad Chevron?" - has the light reached as far as Hebron? And he would answer: "Hen" - yes.
Why Hebron in particular?
The Mishnah explains that the question does not stem from any need for the light actually to reach Hebron, but from the desire to recall the merit of those buried in Hebron - the Avos. By mentioning their merit, they would help bring it about that the offerings be accepted favorably.
In summary: in this Mishnah we learned how the time for slaughtering the Tamid was determined: the watchman's announcement of "Barkai," and according to Matisya ben Shmuel, only once "the entire eastern sky had lit up"; and the reason for the question "He'ir ad Chevron" - recalling the merit of the Avos buried in Hebron, so that the offerings would be accepted.