Proclamations and Conversions Discussed in Both Acts and Epistles: Philippi
Philippi was a Roman colony in Macedonia, the southern area of modern-day Greece. It was a destination of God's choosing for Paul and Silas. The Holy Spirit prevented them from preaching in other areas, then one night Paul had a vision of a Macedonian man asking for help. Paul concluded that God himself was directing them to Macedonia. There were two particular individuals whose conversions are discussed in Acts: the merchant Lydia and the anonymous jailer.

Paul went on to establish quite a close relationship with this church. The Philippians helped support him in other misionary activity in the area (Phil. 4:15), and Paul's companion Luke appears to have stayed in this city for quite some time even as Paul moved on (ref. Acts 16:11, 16:40-17:1; notice the "we" vs. "they" pronouns).

He later wrote to the Philippians in appreciation for their support, but made no mention of matters surrounding their conversion. The church was evidently susceptible to the Judaizing influence that he urged them to reject (Phil 3:2ff). This suggests that the church primarily consisted of Gentiles or God-fearers.
 

Text Observations
AC 16:11 Therefore putting out to sea from Troas, we ran a straight course to Samothrace, and on the day following to Neapolis; [12] and from there to Philippi, which is a leading city of the district of Macedonia, a Roman colony; and we were staying in this city for some days.  The exact length of time is not known; but their stay in Philippi was long enough to reach at least a few people.
AC 16:13 And on the Sabbath day we went outside the gate to a riverside, where we were supposing that there would be a place of prayer; and we sat down and began speaking to the women who had assembled.  Interestingly, Paul and his companions went to the riverside and not a synagogue on the Sabbath. Perhaps there was no synagogue-- or perhaps God continued working to assure that some particular people were able to hear and respond to the message.

(research why women might have gathered apart from the synagogue-- were they God-fearers? Jews?)

AC 16:14 And a certain woman named Lydia, from the city of Thyatira, a seller of purple fabrics, a worshiper of God, was listening; and the Lord opened her heart to respond to the things spoken by Paul. [15] And when she and her household had been baptized, she urged us, saying, "If you have judged me to be faithful to the Lord, come into my house and stay." And she prevailed upon us. Lydia was among the women who had gathered by the river to pray. What exactly Paul said is unknown, but the Lord opens her heart to respond. She and her household were then baptized. No husband or children are mentioned; "household" is probably referring to servants or companions. 
AC 16:16 And it happened that as we were going to the place of prayer, a certain slave-girl having a spirit of divination met us, who was bringing her masters much profit by fortunetelling. [17] Following after Paul and us, she kept crying out, saying, "These men are bond-servants of the Most High God, who are proclaiming to you the way of salvation." [18] And she continued doing this for many days. But Paul was greatly annoyed, and turned and said to the spirit, "I command you in the name of Jesus Christ to come out of her!" And it came out at that very moment.

[19] But when her masters saw that their hope of profit was gone, they seized Paul and Silas and dragged them into the market place before the authorities, [20] and when they had brought them to the chief magistrates, they said, "These men are throwing our city into confusion, being Jews, [21] and are proclaiming customs which it is not lawful for us to accept or to observe, being Romans." [22] And the crowd rose up together against them, and the chief magistrates tore their robes off them, and proceeded to order them to be beaten with rods. [23] And when they had inflicted many blows upon them, they threw them into prison, commanding the jailer to guard them securely; [24] and he, having received such a command, threw them into the inner prison, and fastened their feet in the stocks. 

This place of prayer by the river evidently became a common meeting place for them, and having the river water close by certainly made baptizing more convenient. 
AC 16:25 But about midnight Paul and Silas were praying and singing hymns of praise to God, and the prisoners were listening to them; [26] and suddenly there came a great earthquake, so that the foundations of the prison house were shaken; and immediately all the doors were opened, and everyone's chains were unfastened. [27] And when the jailer had been roused out of sleep and had seen the prison doors opened, he drew his sword and was about to kill himself, supposing that the prisoners had escaped. [28] But Paul cried out with a loud voice, saying, "Do yourself no harm, for we are all here!" [29] And he called for lights and rushed in and, trembling with fear, he fell down before Paul and Silas, [30] and after he brought them out, he said, "Sirs, what must I do to be saved?" 

[31] And they said, "Believe in the Lord Jesus, and you shall be saved, you and your household." [32] And they spoke the word of the Lord to him together with all who were in his house. [33] And he took them that very hour of the night and washed their wounds, and immediately he was baptized, he and all his household. [34] And he brought them into his house and set food before them, and rejoiced greatly, having believed in God with his whole household.

Paul and Silas respond to the beating by singing hymns of praise while the other prisoners listen in. Perhaps these hymns has some words that expressed various elements of the gospel message.

This local earthquake seems to have more or less destroyed the prison, yet there is no mention of any other damage in the city. It seems that none of the prisoners escaped, though the prison doors were opened and the chains were unfastened. The jailer was about to kill himself when Paul said they were all still present. 

The jailer brings out Paul and Silas (doesn't say anything about the others) and wants to know what to do to be saved. Paul tells him believe in the Lord, then he speaks the message to him and his household. They jailer and his household were then baptized. 

On the question of whether the "household" could have consisted in fants or children, we observe that the "household" heard and believed the message and was baptized-- not something young children or infants could do.

 AC 16:35 Now when day came, the chief magistrates sent their policemen, saying, "Release those men." [36] And the jailer reported these words to Paul, saying, "The chief magistrates have sent to release you. Now therefore, come out and go in peace." [37] But Paul said to them, "They have beaten us in public without trial, men who are Romans, and have thrown us into prison; and now are they sending us away secretly? No indeed! But let them come themselves and bring us out." [38] And the policemen reported these words to the chief magistrates. And they were afraid when they heard that they were Romans, [39] and they came and appealed to them, and when they had brought them out, they kept begging them to leave the city. [40] And they went out of the prison and entered the house of Lydia, and when they saw the brethren, they encouraged them and departed. Paul and Silas met with the other brothers at the house of Lydia prior to leaving town. Who else had been converted in town besides the households of Lydia and the jailer, we do not know. 

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