This festival may be seen as an appropriate ending of the first half of the Christian Year and at the same time an introduction to the second half.
The events commemorated in the Gospel readings from Advent to Pentecost in the BCP (following the Sarum Lectionary) reveal the Father acting through His Son and by His Spirit. The content of the Gospel readings after Trinity Sunday until Advent focus on what Jesus taught, and underlying all He taught is the revelation of the Father through the Son and by the Holy Ghost.
Such was the enthusiasm in England for this Feast that the English Missals (see e.g., the Sarum Missal) reckoned the Sundays from then on and until Advent as Sundays after Trinity rather than (as in Rome) Sundays after Pentecost. At the Reformation Thomas Cranmer, the Archbishop of Canterbury, in editing The Book of the Common Prayer  for the reformed Church of England simply followed the English usage rather than that of Rome.
The Latin Collect in use in the Ecclesia Anglicana until 1549 was:
Omnipotens sempiterne Deus, qui dedisti famulis tuis in confessione verae fidei aeternae Trinitatis gloriam agnoscere, et in potentia majestatis adorare Unitatem: quaesumus ut ejusdem fidei firmitate ab omnibus semper muniamur adversis..
Cranmer's translation in the 1549 BCP was:
Almighty and everlasting God, which hast given unto us thy servants grace by the confession of a true faith to acknowledge the glory of the eternal Trinity, and in the power of the divine majesty to worship the unity: we beseech thee, that through the steadfastness of this faith, we may evermore be defended from all adversity, which liveth and reigneth one God, world without end. Amen.
The translation as amended by the revisers in 1661 for the 1662 BCP:
Almighty and everlasting God, who hast given unto us thy servants grace, by the confession of a true faith, to acknowledge the glory of the eternal Trinity, and in the power of the Divine Majesty to worship the Unity: we beseech thee, that thou wouldest keep us steadfast in this faith and evermore defend us from all adversities, who livest and reignest, one God, world without end. Amen.
[Note: This 17th Century rendering changes the meaning of the original Latin from the beginning of the petition "we beseech thee." In contrast to the original Latin [& 1549 BCP] where the church prays for protection from "all adversities" through steadfastly believing in the vital Reality of the Holy Trinity, the revision creates two petitions, one for steadfastness in the Faith and another for defense from adversities.]
The American 1928 BCP follows precisely the wording of the 1662 BCP. It will be noticed that the Collect in these instances is address to God who is the Holy Trinity.
In contrast, the Rite I Collect of the 1979 Prayer Book of the Episcopal Church departs from the tradition of the BCP from 1549 - 1928:
Almighty and everlasting God, who hast given unto us thy servants grace, by the confession of a true faith, to acknowledge the glory of the eternal Trinity and in the power of the Divine Majesty to worship the Unity: we beseech thee that thou wouldest keep us steadfast in this faith and worship, and bring us at last to see thee in thy one and eternal glory, O Father; who with the Son and the Holy Spirit livest and reignest one God for ever and ever. Amen.
[Here there are major changes from "we beseech thee." In The Commentary on the American Prayer Book by M.J. Hatchet, we are told: "The present revision again addresses the prayer to the Father and changes the petition to bring it into parallel relation to the address." Here the claim is that the collect originally existed as addressed to the Father through the Son. However, we are not told where the Latin original is and so this rendering is a reconstruction of what is believed to have been the case or ought to have been the case. Whether it makes theological or grammatical sense is open to debate.]
To whom prayers are addressed
The normal way of Christian prayer is to address the Father through His Son, our Lord Jesus Christ, and to do so believing in the presence of the Holy Ghost to make the prayer effectual. However, to address prayer directly to the Lord Jesus Christ is permissible for he is not only "very God of very God" but also our Lord and Saviour. Thus we find that prayer to the Lord Jesus is central to the Litany in the western Church and in the BCP. Rarely but yet within the realms of orthodoxy it is right to pray to the Holy Ghost, especially when He is asked to descend upon God's people (see the Prayer "Come Holy Ghost" BCP 1928 p. 543).
Addressing the One, Holy, Undivided and Blessed Trinity of the Father and the Son and the Holy Ghost is not common but is appropriate in public prayer when it is the Feast of the Same!
The original Latin prayer and the English translation of 1549 (as well as the amended translation of 1662) are addressed to the Holy Trinity as Three Persons, One God. This is obvious because the prayer does not end - as is normal - "through Jesus Christ our Lord." Further, this is an instance of "worshipping the Unity" as the confession of Three Persons in One God, and One God in Three Persons is held clearly in mind.
To go with this Collect, the Preface for Trinity Sunday in the Order for Holy Communion of the classic BCP is also addressed to the Holy Trinity. (see further my piece on the Preface for Trinity Sunday)
The Rev'd Dr. Peter Toon
Minister of Christ Church, Biddulph Moor,
England & Vice-President and Emissary-at-Large
of The Prayer Book Society of America