From Dom Guéranger's The Liturgical Year.
The Church makes a commemoration, on this same day within the octave, of the holy Pope Melchiades. This illustrious Pontiff, whom St. Augustine calls ‘the true child of the peace of Jesus Christ, the worthy father of the Christian people,’ ascended the papal throne in the year 311, that is, during the very fiercest storm of persecution. It is on this account that he is honoured with the title of martyr. Though he did not shed his blood for the name of Jesus, yet he shared in the glory of the martyrs, by reason of the great trials he had to suffer during the persecution, which afflicted the entire Church. It was the same with many of his predecessors. But the pontificate of Melchiades marks a very important period of the Church—the transition from persecution to peace. As early as the year 312, liberty was granted to the Christian religion by Constantine. So that Melchiades had the glory of governing the Church at the commencement of her period of temporal prosperity. His name now graces the calendar of the liturgical year, and reminds us of that peace which will soon descend upon us from heaven.
Deign then, O father of the Christian people, to pray for us to the Prince of peace, that, in His approaching visit, He may quell our troubles, remove the obstacles to His grace, and reign as absolute Master over our heart, our mind, and our senses. Pray also that peace may reign in the holy city and Church of Rome, of which thou wast the Bishop, and which will honour thy venerable memory to the end of time: help her by thy intercession now that thou art face to face with God, and hear the prayers which she addresses to thee.
Prayer
Infirmitatem nostram respice, omnipotens Deus, et quia pondus propriæ actionis gravat, beati Melchiadis Martyris tui atque Pontificis intercessio gloriosa nos protegat. Per Christum Dominum nostrum. Amen.
Have regard, O almighty God, to our weakness; and as we sink under the weight of our own doings, let the glorious intercession of blessed Melchiades, thy Martyr and Bishop, be a protection to us. Through Jesus Christ our Lord. Amen.