Notes on the Bible, by Albert Barnes, [1834], at sacred-texts.com
On the eighth day - i. e., on the first day after the week of consecration.
A young calf - A bull calf, which might have been what we should call a yearling ox.
A kid of the goats - A shaggy he-goat. See Lev 4:23 note.
The glory of the Lord - Compare Exo 16:7.
It is to be remarked that Aaron offers no peace-offering for himself. It was enough that he should participate in the peace-offerings of the consecration Lev 8:31, and in the two peace-offerings about to be sacrificed for the people.
His sin-offering was probably regarded not so much as a sacrifice for his own actual sins as a typical acknowledgment of his sinful nature and of his future duty to offer for his own sins and those of the People. See marginal references. "The law maketh men high priests which have infirmity; but the word of the oath, which was since the law, maketh the Son, who is consecrated (in the margin perfected, see Lev 8:22 note) forevermore, Heb 7:28.
Aaron did not act according to the ordinary Law Lev 4:5-7, Lev 4:16-18, but as Moses had done in the sin-offering of the consecration ceremony (Lev 8:15; compare also Lev 4:25, Lev 4:30, Lev 4:34). The probable reason of this was that he had not yet been formally introduced as the high priest into the holy place of the tabernacle.
Brought the blood - They most likely held the basons in which the blood was received as it ran from the victim, and then handed them to their father. See Lev 1:5.
In this first complete series of offerings made by the high priest, the sacrifices take their appointed order; first, the sin-offering to make atonement; then the burnt-offering, to signify the surrender of the body, soul and spirit to Yahweh in heaven; and lastly the peace-offering, to show forth the communion vouchsafed to those who are justified and sanctified. See Lev 8:14 note.
Aaron having completed the offerings, before he came down from the stage surrounding the altar on which the priests used to stand to officiate (see Exo 27:8), turned toward the people, and blessed them; probably using the form which became the established one for the priests Num 6:24-26, and which is still maintained in the synagogues.
Aaron, having now gone through the cycle of priestly duties connected with the brass altar, accompanies Moses into the tent of Meeting. It was reasonable that Moses, as the divinely appointed leader of the nation, should induct Aaron into the tabernacle.
Blessed the people - This joint blessing of the mediator of the Law and the high priest was the solemn conclusion of the consecration and Inauguration. (Compare Ch2 6:3-11.) According to one tradition, the form used by Moses and Aaron resembled Psa 90:17. But another form is given in the Targum of Palestine, "May your offerings be accepted, and may the Lord dwell among you and forgive you your sins."
The very ancient Jewish tradition has been widely adopted that the sacred fire of the altar originated in this divine act, and that it was afterward preserved on the altar of the tabernacle until the dedication of the temple, when fire again "came down from heaven." Ch2 7:1. But according to the sacred narrative the altar-fire had been lighted in a natural way before this occasion. (Compare Lev 8:16; Lev 9:10, Lev 9:13, etc.; Exo 40:29.) It would therefore seem that the fire which "came out from before the Lord" manifested itself, according to the words of Lev 9:24, not in kindling the fuel on the altar, but in the sudden consuming of the victim. For the like testimony to the acceptance of a sacrifice, see Jdg 13:19-20; Kg1 18:38; Ch1 21:26, and probably Gen 4:4. The phrase to turn a sacrifice to ashes, became equivalent to accepting it (Psa 20:3, see the margin). The fire of the altar was maintained in accordance with Lev 6:13.