From Pope Pius XII’s encyclical Mystici Corporis Christi (1943):

If we consider closely all these mysteries of the Cross, those words of the Apostle are no longer obscure, in which he teaches the Ephesians that Christ, by His blood, made the Jews and Gentiles one “breaking down the middle wall of partition . . . in his flesh” by which the two peoples were divided; and that He made the Old Law void “that He might make the two in Himself into one new man,” that is, the Church, and might reconcile both to God in one Body by the Cross.”⁴⁰

The Church which He founded by His Blood, He strengthened on the Day of Pentecost by a special power, given from heaven. For, having solemnly installed in his exalted office him whom He had already nominated as His Vicar, He had ascended into Heaven; and sitting now at the right hand of the Father He wished to make known and proclaim His Spouse through the visible coming of the Holy Spirit with the sound of a mighty wind and tongues of fire.⁴¹ For just as He Himself when He began to preach was made known by His Eternal Father through the Holy Spirit descending and remaining on Him in the form of a dove,⁴² so likewise, as the Apostles were about to enter upon their ministry of preaching, Christ our Lord sent the Holy Spirit down from Heaven, to touch them with tongues of fire and to point out, as by the finger of God, the supernatural mission and office of the Church.

⁴⁰ Cf. Eph., II, 14-16.
⁴¹ Cf. Acts, II, 1-4.
⁴² Cf. Luke, III, 22; Mark, I, 10.

— Mystici Corporis Christi 32-33

From Pope Pius XII’s encyclical Mystici Corporis Christi (1943):

On the Cross then the Old Law died, soon to be buried and to be a bearer of death,³⁶ in order to give way to the New Testament of which Christ had chosen the Apostles as qualified ministers;³⁷ and although He had been constituted the Head of the whole human family in the womb of the Blessed Virgin, it is by the power of the Cross that our Savior exercises fully the office itself of Head of His Church. “For it was through His triumph on the Cross,” according to the teaching of the Angelic and Common Doctor, “that He won power and dominion over the gentiles”;³⁸ by that same victory He increased the immense treasure of graces, which, as He reigns in glory in heaven, He lavishes continually on His mortal members; it was by His blood shed on the Cross that God’s anger was averted and that all the heavenly gifts, especially the spiritual graces of the New and Eternal Testament, could then flow from the fountains of our Savior for the salvation of men, of the faithful above all; it was on the tree of the Cross, finally, that He entered into possession of His Church, that is, of all the members of His Mystical Body; for they would not have been untied to this Mystical Body through the waters of Baptism except by the salutary virtue of the Cross, by which they had been already brought under the complete sway of Christ.

³⁶ Jerome and Augustine, Epist. CXII, 14 and CXVI, 16: Migne, Patrologiæ Cursus completus, Series Latina, XXII, 924 and 943; St. Thos., Summa Theologiæ [ST] I-II, q. 103, a. 3, ad 2; a. 4; ad 1; Council of Flor. pro Jacob.: Mansi, Sacrorum Conciliorum Nova et Amplissima Collectio XXXI, 1738.
³⁷ Cf. II Cor., III, 6.
³⁸ Cf. ST III, q. 42, a. 1.

— Mystici Corporis Christi 30