Charles Ellicott Commentary Exodus 29:27-29

"And thou shalt sanctify the breast of the wave-offering, and the thigh of the heave-offering, which is waved, and which is heaved up, of the ram of consecration, even of that which is for Aaron, and of that which is for his sons: and it shall be for Aaron and his sons as [their] portion for ever from the children of Israel; for it is a heave-offering: and it shall be a heave-offering from the children of Israel of the sacrifices of their peace-offerings, even their heave-offering unto Jehovah. And the holy garments of Aaron shall be for his sons after him, to be anointed in them, and to be consecrated in them." — Exodus 29:27-29 (ASV)

THE LAW OF THE WAVE AND HEAVE OFFERINGS, AND OF THE CONSECRATION GARMENTS.

The wave offering. —For the future, in every case of offerings made at a consecration, both the breast and the right shoulder (Leviticus 7:32) were to be given to the officiating priest, who was to “wave” the one and “heave” the other before the Lord. “Heaving” was a single movement, an uplifting of the thing heaved; “waving” was a repeated movement, a swaying of the thing waved backwards and forwards horizontally. Both were modes of presenting the thing to God.

The holy garments of Aaron shall be his sons’ after him. —That Eleazar was consecrated in his father’s holy garments we learn from Numbers 20:28; but nothing is recorded as to the investiture of later high priests. Still, it is reasonable to suppose that the injunctions here given were carried out so long as the garments worn by Aaron held together.

To be anointed therein. —The anointing of each successive high priest is here commanded by implication. Jewish tradition affirms the practice to have been in conformity.