In the Ordinariate Ordo Missae authorised by the Holy See, there is a very interesting Prayer taken from the Book of Common Prayer: called the 'Prayer of Humble Access' (Often frivolously called the humble crumble. We do not presume to come to this thy Table, O merciful Lord, trusting in our own righteousness, but in thy manifold and great mercies.). It begins with a paraphrase of the 'Ambrosian Prayer' given in your S Pius V Missals for use by the celebrant before Mass: Ad mensam dulcissimi convivii tui, pie Domine Iesu Christe, ego peccator de propriis meis meritis nihil praesumens, sed de tua confidens misericordia et bonitate, accedere vereor et contremisco.
Just before its end, the Anglican Prayer reads as follows: Grant us therefore gracious Lord, so to eat the Flesh of thy dear Son Jesus Christ, and to drink his Blood, that our sinful bodies may be made clean by his Body, and our souls washed through his most precious Blood, and that we may ever more dwell in him, and he in us.
This association of the Lord's Body with the needs of our bodies, and of his Blood with the needs of our souls, is a medieval idea going back to an unknown writer whose works were mixed up with those of S Ambrose, so that he is for convenience known as Ambrosiaster. S Thomas Aquinas, who in the Summa (III, lxxiv, 1) teaches this distinction (as had that enthusiastic Carolingian upholder of the Real Presence, S Paschasius Radbertus), quotes it as from S Ambrose; and I think it is clearly what the Angelic Doctor had in mind when he wrote the third stanza of his Verbum supernum prodiens; I give a literal translation: To whom [i.e.the disciples] He gave flesh and blood under twofold appearance that He might feed the whole Man of double substance. That is to say, He gave himself in the two species so that He might feed the entirety of Man who is composed, doubly, of both body and soul.
In his first (1548) liturgical experiment in the Eucharistic Liturgy, Cranmer carried this Thomistic distinction even into the formulae for Communion: The Body of our Lord Jesus Christ .... preserve thy body ... and The Blood of our Lord Jesus Christ ... preserve thy soul .... After a year he gave this distinction up.
Successive generations of Anglican liturgists have been nervous about the conclusion of the Prayer of Humble Access with its Thomist, non-Biblical distinction between the effect of the Body upon our bodies and of the Blood upon our souls; Dix cattily remarked "there is no particular reason why people should be made to pray medieval speculations in a Reformed church"*. The Puritans asked for its removal in the abortive negotiations which followed 1660 on the ground that it appeared to accord more efficacy to the Blood than to the Body... which seems to me potentially Manichaean. It has been eliminated from many modern Anglican rites including the American Prayer Book upon which the old (Anglican Use) Book of Divine Worship was based. So its happy re-appearance in the Ordinariate Ordo Missae is a significant bit of Magisterium. Delightfully distinctive! To paraphrase the catch-phrase of GloriaTV, The more distinctive the better!
Our erudite correspondent Joshua once told me ... I never got round to verifying it ... that Garrigou Lagrange argued for the Blood being more eficacious than the Body, because the reception of the Body ipso facto remitted all venial sins repented of, thus leaving the soul the more cleansed and ready to profit from the Chalice (medieval monarchs at their coronations were given the Chalice "ad augmentum gratiae"). GL also held that a desire thus to profit was a sufficient motive for desiring the Holy Order of priesthood!
Lex orandi lex credendi. Yes? The Ordinariates even have distinctive doctrine!
*One of his favourite themes - it never ceased to amuse him - was that sixteenth century Protestant liturgical compositions, far from being (as their authors had fondly supposed) 'Biblical' or 'Primitive', were in fact Late Medieval in both thought and expression. Indeed, the whole Prayer of Humble Access exemplifies a very Dixian point: it takes inspiration from a medieval private priest's prayer and makes it part of the public Liturgy. The great classical Western liturgical texts would be very unlikely to have the priest, saying publicly and 'in the name of the people,' a prayer with phrases like "We are not worthy so much as to gather up the crumbs under thy Table. But thou art the same Lord, whose property is always to have mercy".