16:35 But when it was day, 
the magistrates sent the sergeants, saying, "Let those men go." 
16:36 The jailer reported these words to Paul, saying, 
"The magistrates have sent to let you go; 
now therefore come out, and go in peace." 
16:37 But Paul said to them, 
"They have beaten us publicly, without a trial, men who are Romans, 
and have cast us into prison! Do they now release us secretly? 
No, most assuredly, but let them come themselves and bring us out!" 
16:38 The sergeants reported these words to the magistrates,
and they were afraid when they heard that they were Romans, 
16:39 and they came and begged them.
When they had brought them out, they asked them to depart from the city. 
16:40 They went out of the prison, and entered into Lydia's house. 
When they had seen the brothers, they encouraged them, and departed. 
 

vs 25 It is unclear why Timothy isn't with them. But I don't think too much can be clearly  inferred from that fact. Paul and Silas were very courageous, very vocal and very public spreading the message. How many today being imprisoned unjustly would nonetheless pray and sing in prison in a very public fashion? I commend the work of Chuck Colson and others involved in such prison ministries. Furthermore we find them praying at midnight rather than sleeping.

vs 27 Prison guards were severely punished if their prisoners escaped. We saw in Acts 12:19 that the guards were put to death when Peter escaped prison. But it is surprising to me that this guard would have tried to kill himself before checking whether the prisoners had escaped. Perhaps we can infer that he deduced there being sufficient time for the prisoners to have escaped. As such it seems to me that the prisoners purposely remained with Paul and Silas, who themselves were determined to remain so as to not be perceived as outlaws and fugitives.

So we have here a situation which calls for wisdom in response to circumstances. For many would presume that this situation may be likened to that of Peter's in which God miraculously provided an escape from prison. Many would presume that the earthquake was for the purpose of Paul and Silas escaping. But they didn't interpret the event in that way, submitting themselves to the governing authorities. And this was no doubt also a testimony to the whole society, both to the other prisoners and to the authorities and other citizens alike, that the gospel did not advocate rebellion against the secular authorities. 

vs 30-31  "Sirs, what must I do to be saved?" They replied, "Believe in the Lord Jesus, and you will be saved— you and your household." That's as simple as the gospel gets. Important to note, however, is the mention of Jesus' Lordship. For faith in Christ is a pledge of allegiance to do what he says, as it is written, for "he died for all, that those who live should no longer live for themselves but for him who died for them and was raised again." 2Cor 5:15 And as for his household being saved, he's not saying that if one member of the household is saved, then the rest will be. Rather he's saying that the same condition for salvation holds for each member of his household. And in fact it came to pass according to verse 34 that his whole household came to believe, and thus were saved.

vs 35-40 As I mentioned previously, they intentionally remained in prison as a matter of their public reputation. They didn't want the reputation of being escaped prisoners. And this particularly becomes clear as Paul insists upon a public apology in light of the magistrates having violated Roman law in how they were treated. Yes, it's Christian to invoke secular law. To the extent the law allows for evangelism, we should utilize it to that end.