Before us is Mishnah 7 in the fifth chapter of Maseches Yoma, which deals with the order of the Yom Kippur service and the law governing one who performs one act before another.
The rule established by the Mishnah:
"Kol ma'aseh Yom HaKippurim ha'amur al haseder" - every act and service of the Yom Kippur service that was stated in a particular order, "im hikdim ma'aseh la'chavero lo asah k'lum" - if one act was performed before another, not at its proper time and not in its chronological order, it has no validity, and it must be repeated in its proper order.
First example - performing the blood of the goat before the blood of the bull:
"Hikdim dam hasa'ir l'dam hapar - yachzor v'ya'aseh min dam hasa'ir l'achar dam hapar" - if he sprinkled from the blood of the goat before the blood of the bull, contrary to the proper order, he must go back and sprinkle from the blood of the goat after he has sprinkled from the blood of the bull.
The Gemara explains that the application of the blood with which the Mishnah is dealing is that of the second set - not the sprinklings in the Holy of Holies, but the sprinklings opposite the Paroches in the Heichal. The reason: had he reversed the order in the Holy of Holies, it would not have been enough to repeat the blood of the goat; he would have had to slaughter a new goat, since the halachah is that a goat slaughtered before the application of the blood of the bull in the Holy of Holies is invalid. This is a special halachah, that the goat must be slaughtered after the application of the blood of the bull in the Holy of Holies.
And since our Mishnah rules that it is enough to repeat the blood of the goat and there is no need to slaughter a new goat, it is proven that the case is one in which the application of the blood of the bull in the Holy of Holies was already done properly, and the reversal of the goat's blood before the bull's blood occurred only in the sprinklings before the Paroches.
The blood spilled before the applications were completed:
"Im ad shelo gamar es hamatanos shebifnim nishpach hadam - yavi dam acher v'yachzor v'ya'aseh batechilah bifnim" - if before he completed all the applications inside, within the Heichal, the blood spilled - one of the two bloods, the blood of the bull or the blood of the goat - he must bring other blood, slaughter another animal, and go back and begin the sprinklings from their beginning inside.
The Gemara explains that this ruling was stated regarding the blood of the goat. But if the blood of the bull spilled before he completed the process inside, and he must bring a new bull, he will have to bring new Ketores as well. The reason: as you will recall, they slaughter the bull, and one kohen stirs its blood while the Kohen Gadol is engaged in the service of the Ketores, and afterward the Kohen Gadol returns and takes the blood of the bull for its sprinkling - because the slaughter of the bull must always precede the Ketores. Therefore, when the slaughter of a new bull is required because the blood spilled, the Ketores must be done over as well.
The three sets of sprinklings - each one on its own:
The Mishnah continues and rules that this law was stated not only regarding the sprinklings inside, in the Holy of Holies, but also regarding the sprinklings in the Heichal - the sprinklings before the Paroches, and likewise the sprinklings on the Ketores altar, the golden altar. In each of them, if the blood spilled, a new animal must be brought and that set must be repeated from its beginning. However, the three sets are separate and distinct from one another:
The sprinklings inside the Holy of Holies.
The sprinklings before the Paroches.
The sprinklings on the golden altar.
Since each set stands on its own, there is no need to repeat the sets that have already been completed. If the blood spilled, he repeats only the sprinklings of the Heichal - if he has not yet performed them - and afterward those of the golden altar.
The opinion of Rabbi Elazar and Rabbi Shimon:
Rabbi Elazar and Rabbi Shimon say that from the place where he stopped, from there he begins. In their view, each and every sprinkling, even within the three sets, is considered an atonement in its own right, a separate atonement. Therefore he need not return to the beginning of the set, but continues with the new blood that was slaughtered from that very point at which he stopped.
In summary: in this Mishnah we learned the rule that all the acts of Yom Kippur that are stated in order, if one performed one act before another he has accomplished nothing; the law of performing the blood of the goat before the blood of the bull - which was stated regarding the sprinklings before the Paroches, for had it been in the Holy of Holies a new goat would have been required; the law of blood that spilled before the applications were completed, and the need for new Ketores when a new bull is slaughtered; the division of the sprinklings into three separate sets; and the opinion of Rabbi Elazar and Rabbi Shimon, that from the place where he stopped, there he begins.