Discuss the plainclothes detective.

O. Henry emphasizes that the plainclothes policeman who comes to arrest Bob is quite tall. The author's purpose is to suggest that the man is bigger than Bob and could overcome him with force if that should become necessary. O. Henry did not want the arrest to involve physical force, guns, or handcuffs. Any force used in arresting Bob would reflect badly on Jimmy Wells. Arresting his old friend who had come a thousand miles to meet him seems questionable enough. Some readers seem to think Jimmy should have let Bob go. Jimmy himself had such qualms about the problem that he turned the job over to another policeman. O. Henry is trying to soften Jimmy's betrayal by making Bob's arrest as painless as possible. This explains why Bob and the plainclothes detective go off together arm in arm, why there is only one man making the arrest, and why there is no use or threat of force. When Bob realizes that the man with whom he is walking arm in arm cannot be Jimmy Wells, he does not try to resist or make a run for it because the arresting officer is obviously bigger and stronger. This explains why the detective says:

"Going quietly, are you? That's sensible."

The whole arrest could not be more peaceful. Bob is "sensible" because the detective could easily overpower him.
O. Henry also ameliorates the seriousness of Bob's predicament. He may not be facing jail time at all. The plainclothes detective tells him:

"Chicago thinks you may have dropped over our way and wires us she wants to have a chat with you."

Referring to the Chicago police as "she" makes them seem polite and hospitable, like a hostess. Also the word "chat" suggests that the Chicago police haven't charged Bob with any crime and may only want to interrogate him. Since he is a slick operator and a smooth talker, Bob may be able to talk his way out of a tight spot when he gets to Chicago. All of this is intended to palliate Jimmy's act of turning his old friend over to the law.