What do Jem and Scout do after Atticus leaves the house, and why?

Around 10:00pm, Jem starts changing his clothes and tells Scout that he's going downtown. Scout insists on coming, and they pick up Dill on the way. They look for Atticus in his office, but finally spy him sitting outside the county jail, with the light bulb providing light for him to read his book. The children stay a safe distance away so Atticus won't notice them. The children wanted to see where their father had gone and what he was doing.