Then thou shall take the anointing oil, After ordered to be made of principal spices, myrrh, cinnamon, calamus, cassia, and oil olive, Ex 30:23and pour it upon his head, and anoint him; this was done, according to Jarchi, in the form of the letter "chi" as before; the oil was put upon his head and between his eyebrows, and he joined them with his finger: Aben Ezra thinks this was done before the mitre was put upon his head, for upon the head was the oil only poured; but Nachmanides was of opinion that the mitre was so folded about the head that the middle of the head was open, and upon that the oil was poured; and so the Talmudists say that his (the high priest's) hair was seen between the plate of gold and the mitre; but however this was, it seems plain from the text that this anointing was after the mitre was put on, and the priest habited with all his garments; and it is also as clear a case, that the ointment was poured on his head, which ran down to his beard, Ps 133:2, and I see no difficulty in supposing that the mitre and crown might be taken off again while the ceremony of anointing was performed.
This unction denotes the investiture of Christ with his office in eternity, who is said to be anointed so early, Pr 8:22, and the donation of the Spirit to him in time, without measure; with which he is said to be anointed, both at his incarnation and at his baptism, and also at his ascension to heaven, and hence comes the name of the Messiah, which signifies anointed; and so his people, his priests, are anointed of God, with an unction from him, with the oil of grace, with the graces of the Spirit, which is necessary for their instruction, for the presentation of themselves to as an holy sacrifice, and to make them meet for the heavenly glory.
T. Bab. Zebachim, fol. 19.