Yoma, Chapter 5, Mishnah 5. In the previous Mishnah we learned about the sprinkling of the blood of the bull and the blood of the goat before the curtain, facing the partition. Now the Kohen Gadol approaches the incense altar - the golden altar that stood inside the Heichal.
"V'yatza el hamizbe'ach asher lifnei Hashem":
The Mishnah quotes the wording of the verse, that the Kohen Gadol went out to the altar that is before Hashem, and explains: "zeh mizbach hazahav" - this refers to the golden altar that stood inside the Heichal, and not to the altar in the courtyard, in the Azarah.
"Hischil mechatei v'yored":
The Kohen Gadol began to apply the blood with a downward motion. The blood was placed on each of the four corners - the small horn at each and every corner - and according to this opinion in the Mishnah, the Kohen places the blood on the horn directly in front of him. He therefore had to make a downward motion and not an upward one, for otherwise the blood would run down onto his arm and soil his garments.
The term "mechatei" is understood as an expression of purification, based on the verse in Vayikra: "v'chitei es hamizbe'ach" (and he shall purify the altar).
"Me'heichan maschil":
From where does he begin, and on which of the four horns does he place the blood first? The Mishnah details the order of the applications:
"Keren mizrachis tzefonis" - the northeast corner, and there he begins.
"Tzefonis ma'aravis" - the northwest horn.
"Ma'aravis deromis" - southwest.
"Deromis mizrachis" - southeast.
"Makom shehu mesayem b'chatas shel hamizbe'ach hachitzon" - that same southeast horn where he finishes here is the horn where he begins placing the blood of a chatas offering brought on the outer altar. For at the outer altar, one who ascends the ramp on the southern side and turns to the right encounters the southeast horn first; here, however, it is the last horn he reaches.
The opinion of Rabbi Eliezer:
"Rabbi Eliezer omer" - in his view the Kohen does not walk around the altar in order to place the blood, but rather "bimkomo hayah omed u'mechatei": he stands in one place - for example, at that same northeast corner where he began - and from that very spot he applies and places the blood on all the horns.
Therefore he says: "al kulan hayah nosen l'matah l'malah" - at the three other corners, which are not directly in front of him, he would place the blood from below upward, with an upward motion. The exception is the corner in front of him, where he would make a downward motion, since it is close to him, and an upward motion would cause the blood to run up his sleeve and soil it.
In summary: In this Mishnah we learned about the placing of the blood on the golden altar in the Heichal. According to the first Tanna, the Kohen walks around the altar and places the blood in the order of northeast, northwest, southwest and southeast - the horn at which one begins the placing of the chatas blood on the outer altar - and the application is done with a downward motion, so that the blood should not run onto his garments. According to Rabbi Eliezer, the Kohen stands in his place and applies the blood from there, placing it on all the horns from below upward, except for the horn nearest him, where he places it from above downward.