Epiklesis

Definition

The Greek word means invocation and refers to the prayer that originally appeared in all rites of the early church and continues in the Orthodox churches, but it has been dropped from most of the liturgies of the west. It's place in the Latin Mass was after the words of Institution that begin Hoc est enim corpus meum..., ("This is my Body..."). In the Epiklesis the celebrant prays that God will send his Holy Spirit to change the bread and wine into the Body and Blood of Christ. An example of the epiklesis is taken from Orthodox Liturgy of St. John Chrysostom that reads in part:
Priest (silently): Again we offer to You this spiritual and unbloody sacrifice, and we implore and pray, and entreat You, send down Your Holy Spirit upon us and upon these gifts here present. (Blessing the bread) And make this bread the precious body of Your Christ. (Blessing the chalice) And that which is in this chalice, the precious blood of your Christ. (Blessing both) Having changed them by Your Holy Spirit:

Controversy

And here lies a great controversy between the Eastern and Western churches. If the "magic" of transubstantiation takes place at the words of Institution as maintained by the Roman Church, then the Epiklesis is unnecessary. If, however, the transformation of the elements of bread and wine into the Body and Blood of Christ takes place during the Epiklesis, then any rite without it is defective in an essential part. As I understand Orthodox theology, what happens at the Epiklesis is not as finely defined as transubstantiation in the Roman Church. Still, there does not seem to be a resolution to the problem of what happens when.
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References:
http://www.newadvent.org/cathen/05502a.htm
http://www.byzantines.net/SaintAthanasius/liturgy.htm