Bob realized that he was not talking to Jimmy when he did not recognize his nose.
This is a story about two friends who made an agreement when they were young to meet twenty years later. Both of them actually keep the date, but they are on opposite sides of the law when they do it, ironically. Neither of them realize this at first.
Jimmy Wells is a cop. He is on patrol in the area at the beginning of the story, out of habit, and is very alert. When he first sees Bob, he is in the dark. Then he lights a cigar and his face can be clearly seen.
The man in the doorway struck a match and lit his cigar. The light showed a pale, square-jawed face with keen eyes, and a little white scar near his right eyebrow. His scarfpin was a large diamond, oddly set.
From this, Jimmy recognizes him as a wanted man. However, his friendship for the man he used to know and his sense of fair play presents him with a dilemma. He solves it by not identifying himself and pretending he doesn’t recognize Bob. He leaves, and finds another plain clothes cop who pretends to be him.
Bob goes along with it at first, until he realizes that there is no way this man could be Jimmy. His facial features are just too dissimilar.
"You're not Jimmy Wells," he snapped. "Twenty years is a long time, but not long enough to change a man's nose from a Roman to a pug."
The cop then tells him he has been under arrest the entire time, and gives him a note from Jimmy. In the note, Jimmy explains why he did it. He says he couldn’t do it (arrest Bob) himself.
This is a story about friendship, honor, and duty. It also is about the fact that people do not change. Both Jimmy and Bob are the same as they have always been. Their personalities remain as they were when they were young, but cemented now as adults. Jimmy was a steadfast man as a young man, that is how Bob knew he would keep the appointment. That is why he became a cop. Bob was always slick, and he became a crook.