On the Catholic Priesthood
A priest is not one merely chosen to read public prayers, or preach, or take a leading part in local good works. No sacramental symbol is required to enable a man to discharge these offices. The main function of the priest is to sacrifice; and, in the new law, to absolve from sin. Divine service is not necessarily Divine sacrifice. The rite of sacrifice, as essential, indeed , the main central act of worship, can never perish from the earth, not a priesthood to offer it. Forms, rites and ceremonies may change - not the priestly offering.
The abrogation of the sacrifices of the old law was only the introduction of the one majestic sacrifice of the new, still carried on in the Mass, and offered daily by the new priesthood " from the rising to the setting sun."
There is, and was, only one sacrifice worthy of God, and adequate to atone for sin - that of Christ on Calvary. That one sacrifice is still offered in an un-bloody manner in the Mass by the visible priesthood, representing and sharing in the power of our one invisible High Priest, Christ. Mystic powers are conveyed in Holy Orders, the chief of which is the perpetuation of the sacrifice of the Cross, "Do this in commemoration of me." This command to sacrifice, i.e., offer Christ's precious Body and Blood, the Church faithfully carries out through her priests. The Victim is the same, the priest the same, Jesus Christ, speaking through His priest, the manner only differs.
The Mass is the Sun of Divine worship. It sums up in solemn splendor and spiritual beauty all other outward forms of sacrifice. We may say, in a reverent sense, that the old and new law survive in the Mass. Nature, in the form of grape and wheat, all that men can bring in the way of art, and wealth, and taste, flowers,a nd music, and, on occasions, majestic rites, are embodied in the great Eucharistic Sacrifice of the Mass. All men's gifts to God circle round the altar, or are collected in the church, where holy Mass is offered by the priest, "first for his own sins, then for the people's" (Heb. VII, 27). The Mass is the one changeless Sacrifice of the Cross, offered up all the world over, to the quick and the dead.
Source: Holy Orders, by the Rev. William Graham. A Pulpit Commentary on Catholic Teaching: The liturgy of the ecclesiastical year. 1910