"About midnight Paul and Silas were praying and singing hymns to God, and the prisoners were listening to them. Suddenly there was an earthquake, so violent that the foundations of the prison were shaken; and immediately all the doors were opened and everyone’s chains were unfastened. When the jailer woke up and saw the prison doors wide open, he drew his sword and was about to kill himself, since he supposed that the prisoners had escaped. But Paul shouted in a loud voice, ‘Do not harm yourself, for we are all here.’ The jailer called for lights, and rushing in, he fell down trembling before Paul and Silas. Then he brought them outside and said, ‘Sirs, what must I do to be saved?’ They answered, ‘Believe on the Lord Jesus, and you will be saved, you and your household.’ They spoke the word of the Lord to him and to all who were in his house. At the same hour of the night he took them and washed their wounds; then he and his entire family were baptized without delay. He brought them up into the house and set food before them; and he and his entire household rejoiced that he had become a believer in God." Acts 16
I was always taught this passage as a quintessential message of salvation and I still always like to read "believe on" or "believeth on" rather than "believe in" because as one fundamentalist Baptist pastor explained to me, to believe in is to refer to yourself and your heart, to believe ON is to believe on what Jesus has already done on the cross. But as a Catholic I also like to see that St. Paul also had the sacramental side as well.
St. Augustine, On Baptism, Book 5 Chapter 28 (39): "Wherefore, if those appear to men to be baptized in Catholic unity who renounce the world in words only and not in deeds, how do they belong to the mystery of this ark in whom there is not the answer of a good conscience? Or how are they saved by water, who, making a bad use of holy baptism, though they seem to be within, yet persevere to the end of their days in a wicked and abandoned course of life? Or how can they fail to be saved by water, of whom Cyprian himself records that they were in time past simply admitted to the Church with the baptism which they had received in heresy? For the same unity of the ark saved them, in which no one has been saved except by water. For Cyprian himself says, "The Lord is able of His mercy to grant pardon, and not to sever from the gifts of His Church those who, being in all simplicity admitted to the Church, have fallen asleep within her pale." If not by water, how in the ark? If not in the ark, how in the Church? But if in the Church, certainly in the ark; and if in the ark, certainly by water. It is therefore possible that some who have been baptized without may be considered, through the foreknowledge of God, to have been really baptized within, because within the water begins to be profitable to them unto salvation; nor can they be said to have been otherwise saved in the ark except by water. And again, some who seemed to have been baptized within may be considered, through the same foreknowledge of God, more truly to have been baptized without, since, by making a bad use of baptism, they die by water, which then happened to no one who was not outside the ark. Certainly it is clear that, when we speak of within and without in relation to the Church, it is the position of the heart that we must consider, not that of the body, since all who are within in heart are saved in the unity of the ark through the same water, through which all who are in heart without, whether they are also in body without or not, die as enemies of unity. As therefore it was not another but the same water that saved those who were placed within the ark, and destroyed those who were left without the ark, so it is not by different baptisms, but by the same, that good Catholics are saved, and bad Catholics or heretics perish."
I just highlighted the interesting word that Thomists/Augustinians, and Calvinists alike despise "foreknowledge" and also that in the end St. Augustine says baptism saves but ultimately what makes the baptized saved or unsaved is the position of the heart.
Once again, may our hearts be better than our heads.