From the
Catholic Encyclopedia eucharist.
The name given to the Blessed Sacrament of the Altar in its twofold aspect of sacrament and Sacrifice of Mass, and in which Jesus Christ is truly present under the bread and wine.
Sacrifice of the Mass
The simple fact that numerous heretics, such as Wyclif and Luther, repudiated the Mass as "idolatry", while retaining the Sacrament of the true Body and Blood of Christ, proves that the Sacrament of the Eucharist is something essentially different from the Sacrifice of the Mass. In truth, the Eucharist performs at once two functions: that of a sacrament and that of a sacrifice. Though the inseparableness of the two is most clearly seen in the fact that the consecrating sacrificial powers of the priest coincide, and consequently that the sacrament is produced only in and through the Mass, the real difference between them is shown in that the sacrament is intended privately for the sanctification of the soul, whereas the sacrifice serves primarily to glorify God by adoration, thanksgiving, prayer, and expiation [NOTE: Propitiation is not used]. The recipient of the one is God, who receives the sacrifice of His only-begotten Son; of the other, man, who receives the sacrament for his own good.
The Blessed Eucharist as a Sacrament The Real Presence of Christ in the Eucharist
If, then, natural, literal interpretation were false, the Scriptural record alone would have to be considered as the cause of a pernicious error in faith and of the grievous crime of rendering Divine homage to bread (artolatria) — a supposition little in harmony with the character of the four Sacred Writers or with the inspiration of the Sacred Text. Moreover, we must not omit the important circumstance, that one of the four narrators has interpreted his own account literally. This is St. Paul (1 Corinthians 11:27 sq.), who, in the most vigorous language, brands the unworthy recipient as "guilty of body and of the blood of the Lord". There can be no question of a grievous offense against Christ Himself unless we suppose that the true Body and the true Blood of Christ are really present in the Eucharist...
In order to forestall at the very outset, the unworthy notion, that in the Eucharist we receive merely the Body and merely the Blood of Christ but not Christ in His entirety, the Council of Trent defined the Real Presence to be such as to include with Christ's Body and His Soul and Divinity as well. A strictly logical conclusion from the words of promise: "he that eateth me the same also shall live by me", this Totality of Presence was also the constant property of tradition, which characterized the partaking of separated parts of the Savior as a sarcophagy (flesh-eating) altogether derogatory to God. Although the separation of the Body, Blood, Soul, and Logos, is, absolutely speaking, within the almighty power of God, yet then actual inseparability is firmly established by the dogma of the indissolubility of the hypostatic union of Christ's Divinity and Humanity. In case the Apostles had celebrated the Lord's Supper during the triduum mortis (the time during which Christ's Body was in the tomb), when a real separation took place between the constitutive elements of Christ, there would have been really present in the Sacred Host only, the bloodless, inanimate Body of Christ as it lay in tomb, and in the Chalice only the Blood separated from His Body and absorbed by the earth as it was shed, both the Body and the Blood, however, hypostatically united to His Divinity, while His Soul, which sojourned in Limbo, would have remained entirely excluded from the Eucharistic presence...
There is, furthermore, a fourth kind of multilocation, which, however, has not been realized in the Eucharist, but would be, if Christ's Body were present in its natural mode of existence both in heaven and on earth. Such a miracle might be assumed to have occurred in the conversion of St. Paul before the gates of Damascus, when Christ in person said.to him: "Saul, Saul, why persecutest thou me?" So too the bilocation of saints, sometimes read of in the pages of hagiography, as, e.g., in the case of St. Alphonsus Liguori, cannot be arbitrarily cast aside as untrustworthy.