Commentary for Yoma 5:5

היה מחטא ויורד – this Tanna/teacher held that the Kohen would walk on his feet to each and every corner. And each and every sprinkling was in the corner that was before him and nearest him. And for this reason, [the Mishnah] takes [the words] “purifying [the altar by sprinkling], that is to say, that he would give sprinkling from above to below, for if he had given [sprinkling] from below to above in the corner that was before him, the blood would flow into his handle and soil his clothing. But Rabbi Eliezer held that the Kohen would stand in one corner and from there give sprinklings on all the corners, for the entire altar was not other than one cubit by one cubit squared, and since the three corners were near him, he can sprinkling from below to above without soiling his clothing, except for this corner that he was standing near, for it was impossible for him to turn sideways the tops of his fingers downward but [only] upwards, for if he would turn the tops of fingers downward and give a sprinkling from the bottom to the top, the blood would flow into the handle of his undercoat. But the Halakha is not according to Rabbi Eliezer.

Introduction After having sprinkled the blood of the goat and bull inside the Holy of Holies and onto the curtain separating the Hekhal from the Holy of Holies, the priest now turns his attention to the golden altar that is inside the Hekhal.

“And he shall go out to the altar that is before the Lord” (Leviticus 16:18): that is the golden altar. The mishnah identifies the altar mentioned in v. 18 with the golden altar inside the Hekhal, upon which the incense is offered. This is explicit in Exodus 30:10 which in reference to this golden incense altar states, “Once a year Aaron shall perform purification upon its horns with blood of the sin offering of purification; purification shall be performed upon it once a year throughout the ages. It is most holy to the Lord.”

He then began to purify [the altar by sprinkling] in downward motion. From where does he begin? From the northeast horn [of the altar], then the northwest, then the southwest, then the southeast. From the place where he begins [sprinkling when offering] a sin-offering on the outer altar, there he completes [sprinkling] on the inner altar. He now begins to purify the altar by sprinkling blood upon its four horns (corners), going counter-clockwise and starting at the northeast corner. The mishnah notes that he completes his sprinkling on the southeast corner, the same corner where he begins to sprinkle blood when offering a sin-offering on the outer altar. This is a sort of mnemonic used by the mishnah to remember which corner is last on Yom Kippur.

Rabbi Eliezer says: he remained in his place and sprinkled. And on every horn he would sprinkle from below upwards, with the exception of the horn at which he was standing, which he would sprinkle from above downwards. Rabbi Eliezer disagrees with the notion that he walks around the altar while sprinkling on the four horns. Rather, he remains in his spot. The whole altar was only one cubit by one cubit wide so sprinkling while standing in place would not have been difficult at all. On all of the other corners he would reach over and sprinkle with an upward motion. The exception was the corner where he was standing where for practical considerations he would sprinkle with a downwards motion.