Holmes, Watson, and Jones prepare to catch Small and his accomplice in the evening. Holmes recommends Watson bring his old service revolver. They take a police boat onto the river and hide near the wharf where Holmes knows the Aurora to be. He warns the police that the Aurora has a reputation for speed, and they will need to catch it quickly when it appears. While they wait, Holmes explains the logical suppositions he made to find the boat. He supposed that because Small had been in London watching the Sholtos for some time, he would need a day or two to prepare before he could make his final escape from the city. Therefore, Holmes concluded that he must have hidden the boat somewhere safe while he completed his business, and that the easiest place to hide a boat would be in a repair shipyard. So, in his disguise, he had visited every shipyard along the river until he found the right one.

Holmes shares another piece of his deductive reasoning process, explaining:

[W]hile the individual man is an insoluble puzzle, in the aggregate he becomes a mathematical certainty. You can, for example, never foretell what any one man will do, but you can say with precision what an average number will be up to.