Sukkah, Chapter Five, Mishnah 6. On every day of Sukkos, as on every Yom Tov, the Mussaf offerings were brought in the Beis HaMikdash. What is unique about Sukkos is the bulls: their number decreases from day to day - on the first day thirteen bulls were brought, and on the last day only seven, while the rest of the offerings remained the same on every one of the days.
The count of the animals on the first day of the festival was therefore as follows:
Thirteen bulls.
Two rams.
One goat as a sin offering.
Fourteen sheep.
Thirty animals in all.
Dividing the service among the watches:
Throughout the year the service in the Beis HaMikdash is divided among the twenty four watches, the groups of kohanim. On Yom Tov, however, all the watches take part together, at least in the offerings that come on account of the festival itself, and they divide those offerings among themselves. On the first day there were thirty animals set against twenty four watches: each watch received one animal, and six watches were awarded an additional animal. Since one bull was reduced each day, the number of watches that received two animals was reduced along with it: twenty nine animals on the second day, twenty eight on the third day, and so on.
The words of the Mishnah:
"Yom tov harishon shel chag hayu sham shloshah asar parim, eilim shnayim v'sa'ir echad" - that is sixteen animals, which were divided among sixteen watches, one animal per watch. The Mishnah continues: "Nishtayru sham arba'ah asar kevasim lishmoneh mishmaros" - the remaining eight watches divided fourteen sheep among themselves. From here comes the calculation for all the days of the festival:
On the first day: "Shishah makrivin shnayim shnayim, v'hashe'ar echad echad" - six watches brought two sheep each, and the rest of the watches brought only one animal. The two additional animals that those six watches received were the sheep.
On the second day: five watches brought two sheep each, and the rest one each.
On the third day: four watches brought two each, and the rest one each.
On the fourth day: three watches brought two each, and the rest one each.
On the fifth day: two watches brought two each, and the rest one each.
On the sixth day: one watch brought two, and all the rest of the watches one each.
On the seventh day: all of them were equal, since only seven bulls were brought on that day, and with them two rams, one goat and fourteen sheep - twenty four animals, exactly the number of the watches, one animal for each watch.
On Shemini Atzeres:
On Shemini Atzeres the Mussaf offerings were reduced considerably: one bull, one ram, one goat and seven sheep - only ten animals. In such a case they returned to the usual practice of the other festival days, in which a lottery is held to determine which watches will merit to bring the offerings.
They further said regarding the other days of the festival: a watch that brought bulls on one day does not bring bulls the next day; rather, the watches rotate in turn, so that each and every one is given the opportunity to bring different animals according to the day. Some will be assigned to the bulls on one day, to the rams on another day, to the goat on another day, and on another day they will bring the sheep.
In summary: in this Mishnah we learned the calculation of how the festival Mussaf offerings were divided among the twenty four watches: on the first day thirty animals, and from there one animal fewer each day as the bulls decreased, until the seventh day when the count stood at exactly twenty four with one animal for each watch. We also learned that on Shemini Atzeres, the small number of Mussaf offerings returned the arrangement to a lottery as on the other festival days, and that the watches rotated among themselves in the types of animals so that each one would have an equal opportunity.