4 For since man is of twofold nature, soul and body, the purification also is twofold, the one incorporeal for the incorporeal part, and the other bodily for the body: the water cleanses the body, and the Spirit seals the soul; that we may draw near unto God, having our heart sprinkled by the Spirit, and our body washed with pure water. When going down, therefore, into the water, think not of the bare element, but look for salvation by the power of the Holy Ghost: for without both you can not possibly be made perfect. It is not I that say this, but the Lord Jesus Christ, who has the power in this matter: for He says, Unless a man be born anew (and He adds the words) of water and of the Spirit, he cannot enter into the kingdom of God. Neither does he that is baptized with water, but not found worthy of the Spirit, receive the grace in perfection; nor if a man be virtuous in his deeds, but receive not the seal by water, shall he enter into the kingdom of heaven.
A bold saying, but not mine, for it is Jesus who has declared it: and here is the proof of the statement from Holy Scripture. Cornelius was a just man, who was honoured with a vision of Angels, and had set up his prayers and almsdeeds as a good memorial before God in heaven. Peter came, and the Spirit was poured out upon them that believed, and they spoke with other tongues, and prophesied: and after the grace of the Spirit the Scripture says that Peter commanded them to be baptized in the name of Jesus Christ; in order that, the soul having been born again by faith, the body also might by the water partake of the grace.
Source: Catechetical Lectures (New Advent)