Peter raised to his cross (Introit, Gospel), like Christ rises above the world. He seals in his blood his confession of faith (Gospel of to-morrow) and love (Gospel) in Jesus, and henceforth it will be in His name (Ibid.) and as His vicar that he will be king of souls.
Paul, by sharing his labours and martyrdom, shares his kingship and his triumph.
Dicit Dominus Petro: Cum esses junior, cingebas te, et ambulabas ubi volebas: cum autem senueris, extendes manus tuas, et alius te cinget, et ducet quo tu non vis: hoc autem dixit, significans qua morte clarificaturus esset Deum. Caeli enarrant gloriam Dei: et opera manuum ejus annuntiat firmamentum.
The Lord saith to Peter: When thou wast younger, thou didst gird thyself, and didst walk where thou wouldst: but when thou shalt be old, thou shalt stretch forth thy hands, and another shall gird thee, and lead thee whither thou wouldst not: and this He said, signifying by what death he should glorify God. *The heavens show forth the glory of God: and the firmament declareth the works of His hands.
(St John 21:18-19 and Psalm 18:1 from the introit of Mass)
Praesta, quaesumus, omnipotens Deus: ut nullis nos permittas perturbationibus concuti, quos in apostolicae confessionis petra solidasti.
We beseech Thee, almighty God, that Thou suffer no disturbance to shake us, whom Thou hast founded as on a rock on the confession of Thine apostles.
From the Catholic Encyclopaedia on the Eves of Feasts: http://www.newadvent.org/cathen/05647a.htm