Eragon wakes up from a nap at sunset. It's almost time for Operation Mystery-Thingy.
He straps on his bow and meets up with Jeod and Brom. They head off toward the castle.
When they get to the castle, Jeod gets them past the guard by claiming that Eragon left something in his office. The guard buys it. They're in.
They find the records office. The door's locked. But wait! Some of us know magic! Brom opens the door with his magical powers.
The room is filled with scrolls, and they get to work rummaging through them, taking notes of any mention of Seithr oil shipments.
They continue searching until Eragon hears Solembum in his head. He appears as a small boy with slanted eyes and shaggy black hair. He warns Eragon that guards are on their way.
They race through as many scrolls as they can before picking up their stuff and heading out the door. Just in time, too, as they can hear the guards coming down the hall.
The guards show up, but they claim to have gotten lost. Since the door is locked now, these world's-smartest guards decide to let them go on their way. Even better, they march them back to the gate and actually help them escape. Nice.
Back at Jeod's house, they break out the notes they took and a map. Through their knowledge of Alagaësian geography and process of elimination, they determine that the most likely place for the Ra'zac to be is the city of Dras-Leona. Easy as pie.
Eragon groans. Dras-Leona is really far away from Teirm. Jeod hands over his map; it looks like he and Brom are going to need it. He has to stay put and tend to his business.
Brom is resigned to heading back on the road again. Cue Willie Nelson.