It is like the precious ointment upon the head. The anointing oil of the sanctuary was an ointment composed of many "precious" ingredients, as myrrh, cinnamon, sweet calamus, and cassia, besides oil olive, which was its basis (Exodus 30:23, Exodus 30:24).
Not only Aaron (Le 8:12), but all later high priests, were anointed with it (Exodus 30:30). That ran down upon the beard, even Aaron's beard. This would be the natural result of a copious "pouring" of the oil upon the top of the head.
Though not mentioned historically in Leviticus, it presents itself to the eye of the poet, on whose mental vision the whole scene rises. That went down to the skirts of his garments. Streamed even to the lower fringe of his long vesture (Kay).
The high priest at his consecration was a type and symbol of unity. He bore on his breastplate the names of the twelve tribes, so that the holy oil, typical of the grace of God, when it was poured upon him, flowed down on all the tribes, diffusing everywhere an odor of fragrance.