The Roman liturgy, as it existed at the dawn of the 20th century, could be mistaken for an Arian rite if not for the Athanasius Creed at Prime, the Gloria Patri doxologies at the psalms, and the qui tecum vivit et regnat concluding orations. That is not to say the old Roman liturgy is in the least Arian, but it has every trace of being an ante-Nicene tradition that the Church enriched after the Christological clarifications of the first four councils. Unlike the explicitly didactic Greek rite, which preaches a small Trinitarian sermon at the sessional hymns and the troparia, the Latin rite rarely teaches about the nature of the Trinity, it simply directs the faithful in worship to God in the persons of the Trinity. I recall some time ago reading in an introduction to the writings of St. Gregory Nazianzen that the Byzantine Church saw the Trinity as three Divine persons Who, in virtue of the first commandment, must be one God, whereas the Latin Church saw one God Who, in virtue of the New Testament, must exist as three Divine persons. The Greek tradition narrates the active role of the Paraclete in every act of the Church, while the Latin tradition simply assumes it.
In the middle of the anaphora of the Greek liturgy the celebrant asks that the Father might "send down Your Holy Spirit and upon these gifts here offered," transforming them into the Body and Blood of Christ. The Roman Church quietly assumes that the Holy Spirit came down upon the Church once and is passed on by the laying of hands at exorcisms, Confirmation, absolution of sins, the conferral of Holy Order, and other blessings. The Holy Spirit need not descend upon the Church, He is already in it. St. Bernard writes in one reflection on the Song of Songs that the Holy Spirit ensures us of "truth of our interior life," guiding the faithful in the three so-called "theological" virtues (Song of Songs sermon 18). The Holy Spirit does not transubstantiate the gifts, He raises the priest to offer them to the Father, Who transforms them by his acceptance of them (Quam oblationem).
Perhaps the indwelling, as opposed to descending, Latin view of the Paraclete is why Roman Christians are more concerned than Easterners with having a pure Church at any given moment of history and why turbulent times are more difficult for them to endure (cf. Rorate Caeli every day). If the indwelling Spirit guides the Church "in all truth" then is the Church to be found in Pope Francis? Or in the "Novus Ordo"? Or in the Borgia era? The wise reply to those troubled hearts is the same Fr. Capreolus gave at Mass, that the Spirit lives in the Church, is passed on from age to age, and lifts up saints at the most dire of times. Perhaps the Church suffers today not from the lack of potentially great saints, but from bureaucratic obstruction of their work.
Regardless, the Lord sent forth His Holy Spirit fifty days after the Resurrection; henceforth, every generation of the Church has been created in the Spirit.