The doctrine of transubstantiation became a contentious issue during the Protestant Reformation. Martin Luther believed that during the Eucharist, Christ is actually present. Wine and bread are offered as sacrifices and placed on the altar. The celebrant prays a prayer of gratitude. The institution's history is read aloud. One calls upon the Holy Spirit. The Holy Gifts are given out, and each communicant hears the powerful words of the gospel: "the Body of Christ," "the Blood of Christ." The Council of Trent appropriated Aquinas' analysis of substance and accidents in the eucharistic conversion in its Decree on the Holy Eucharist. The Council ruled that Christ truly offers his Body and Blood under the guise (species) of bread and wine. How did this doctrine change?
Now it cannot be that it is the actual body of Christ which is broken. First, it is outside all change and we can do nothing to it. Second, it is present in all its completeness under every part of the quantity, as we saw above, and that runs counter to the whole idea of being broken into parts. It remains then that the fraction takes place in the dimensive quantity of the bread, where all the other accidents also find their subject. … Whatever is eaten as under its natural form, is broken and chewed as under its natural form. But the body of Christ is not eaten as under its natural form, but as under the sacramental species. For this reason Augustine, commenting on the text of John, the flesh availeth nothing, says, understand this as spoken of the flesh in the way some people understand Christ carnally. They thought of eating his flesh as if it had been treated like butcher’s meat. The body of Christ in itself is not broken, but only in its sacramental appearance. And this is the sense in which we should understand Berengarius’s profession of faith; the fraction and the chewing with the teeth refer to the sacramental species, underneath which the body of Christ is really present. (Aquinas' ST 3a.77.8 [Blackfriars ed.])
The main idea of the passage is apparent: the Eucharistic Body and Blood of Christ are present in such a way that the spatial, dimensional, and visible properties of the bread and wine cannot be attributed to them. The purpose of Aquinas' division of accidents from substance is illustrated by the fact that while the accidents of the bread and wine remain, their substance is changed into the substance of the Body and Blood, which can only be understood intellectually. Christ may be found where the accidents are, where they now denote his presence; he is contained beneath them in a manner similar to how substance is joined to accidents; however, he is not the accident's subject.