The duty sergeant was going through his routine of asking each brawling set of prisoners who the Billy and who the Tim was. If the handshake is right he will let the Billy go and slap the Tim around a bit. That way everybody's happy. The Billy gets to feel superior and delude himself that being a non-churchgoing 'protestant' is somehow important; the Tim gets to feel persecuted and indulge his paranoia about masonic conspiracies; the sergeant gets to slap the Tim around.