York, but this city used to be his home. Jimmy's feelings are hidden, just as he himself is practically invisible throughout the story. Bob fails to recognize him because it is a fact that a uniform tends to obscure the wearer's identity. We see a cop and not the individual. This is probably the reason for uniforms, including military uniforms.

Jimmy is especially invisible in this story because the New York cops must have worn navy-blue uniforms and it was nighttime on an unlighted street. Jimmy would have blended into the darkness. Then Jimmy does not reveal himself or make the arrest personally; he passes that job on to another man. Jimmy seems like a sensitive man, judging from the note he has the other man hand to Bob. No doubt Jimmy was sorry for doing what he did, but he knew he would be equally sorry, if not sorrier, if he didn't do it. He was in a lose-lose situation. All of us have to make such choices in our lifetimes.

Jimmy had to make a decision, and he was guided by the training he had received at the police academy. He had been taught that as a police officer he could not be guided by personal feelings but that he had to uphold the law as he had sworn to do. He was taught this rule of conduct because his teachers knew that sooner or later he would need to remember it.

O. Henry rarely seemed terribly sympathetic to cops, but in this story he shows that his famous compassion for humanity includes cops along with the rest of humanity.

When an author portrays a character, he uses what he says about the character, what other characters say about him/her, and the actions and words of the character himself.  

What the author says: We find out at the end of the story that Jimmy Wells is a policeman.  However, O'Henry describes him in the first sentence of the story.

"The policeman on the beat moved up the avenue impressively.  The impressiveness was habitual and not for show, for spectators were few." (page one)

Jimmy makes a fine impression of a police officer even though there is no one to impress.  It is just the way he is, and he is not putting on airs.  O'Henry also tells us that he was,

"...twirling his club with many intricate and artful movements, turning now and then to cast a watchful eye down the pacific thoroughfare" (page one)

 This tells the reader that he has been at his job for a while because he has developed an art of handling his billy club.  A billy club, in case you do not know, is the stick that police officers carry when they walk their territory (beat).  He is also very observant.  This is reinforced later in the story.  O'Henry continues by telling the reader that Jimmy,

"....with is stalwart form and slight swagger, made a fine picture of a guardian of peace." (page one)

This shows Jimmy as a sturdy, robust character who looked as a policeman should look.

What other characters say about him: When Silky Bob is telling the police officer about Jimmy, he describes him as ,

"...the finest chap in the world." (page one)
"....raised here in New York." (page one)
"I was eighteen and Jimmy was twenty." (page one)
"You couldn't have dragged Jimmy out of New York; he thought it was the only place on earth." (page two)
"...he was always the truest, stauchest old chap in the world." (page two)
"He'll never forget." (page two)
"He was a kind of plodder though, good fellow as he was." (page two)

So Jimmy was two years older than Silky Bob.  He had been raised in New York and loved the city.  However, he did not crave the excitement that Silky Bob did, and he generally just lived day by day, taking a rather humdrum existence over the excitement that Silky Bob craved.  However, he is a good friend and a fine person.  If he could make the appointment, he would be there. When Silky Bob realized that the man who meets him is NOT Jimmy, he says,

"Twenty years is a long time, but not long enough to change a man's nose from a Roman to a pug." (page 3)

So we know that Jimmy has a Roman or long, straight nose.

The characters actions or words: Jimmy shows that he is observant when he write in his note to Silky Bob.

"When you struck the match to light your cigar, I saw it was the face of the man wanted in Chicago." (page 3)

He shows that he is a good friend when he writes,

"Somehow I couldn't do it myself, so I went around and got a plainclothesman to do the job." (page three)

He also shows that he is a moral, law-abiding person because he does have his friend arrested.  He cannot ignore it.

Bob said that if Jimmy could be there, he would because he was a good friend,and Jimmy was there.  He also says in the note.

"I was at the appointed place on time." (page three)

My copy of the story is off the internet.  The pages may differ from your version.  However, I have tried to put everything in order, and you should find the quotes relatively easily.

O. Henry's description of Bob's face by the light of his match has a double purpose. First, it is necessary to enable Jimmy to recognize Bob as the man who is wanted by the Chicago police. Second, it gives the author an opportunity to show the reader what Bob looks like. We must remember that both these men have changed a lot over the past twenty years. They are not a couple of kids talking to each other, but men who are both approaching middle age and who have acquired great stores of "street smarts" in their respective vocations. They are two mature men standing in the same spot where they said goodbye as mere boys twenty years before. The "white scar" near Bob's right eyebrow serves a dual purpose as well. It helps to identify him as the wanted man, and it suggests that he is a tough customer who has been in fights during his years in the West.

O. Henry's description of Jimmy's manner of patrolling his beat is largely intended to show that he has been a cop for a long time. This fact has had an indelible effect on his character and personality. He has become a cop through and through, a man who is dedicated to upholding the law. The reader will not discover until the end of the story that the policeman is in fact Jimmy Wells, but the reader will have formed a strong impression of Jimmy by that time and will understand why he found it impossible either to arrest his old friend or to let his him escape from the long arm of the law. We do not know exactly how long Jimmy has been a cop, but it could have been almost twenty years. He was twenty years old when he and Bob said goodbye in "Big Joe" Brady's restaurant. That would be about the age when he would be thinking about finding good steady employment. O. Henry's description of the policeman in the opening paragraphs suggests a man who has had many years in law enforcement and is thoroughly set in his ways as well as content in his character as a uniformed cop.

Both men are steadfast friends, but Bob is a criminal and Jimmy is a cop.

Both Bob and Jimmy are described physically.  First, Jimmy is described.

[The] officer, with his stalwart form and slight swagger, made a fine picture of a guardian of the peace

The Bob is described.

The light showed a pale, square-jawed face with keen eyes, and a little white scar near his right eyebrow

There is a stark contrast between Bob and Jimmy, yet they both came from the same place.  In a way, the story is about different paths we all have.  Jimmy chooses to stay behind and follow the straight and narrow, while Bob is ambitious and hopes to make his fortune.  Bob actually falls into the American metaphor of going west and becoming rich.  Sometimes that involved less than virtuous activities.  Jimmy becomes the law, and Bob becomes the law-breaker.

Bob arrives first.  Jimmy makes his way in a leisurely way.  Is this because he suspects that Bob might have become less than savory over the years? 

Bob seems nice enough.

"It's all right, officer," he said, reassuringly. "I'm just waiting for a friend. It's an appointment made twenty years ago. Sounds a little funny to you, doesn't it?

He kept the appointment.  So did Jimmy, but Jimmy still lived nearby.  It was more a stretch for Bob. Why did Bob return?  It shows that he was willing to risk going back where he may be recognized, because he wanted to be faithful to his friend.

Bob describes Jimmy as a "plodder" and says he never would have left New York.  Being a cop is very important to Jimmy.  His “impressiveness was habitual and not for show” and he walks down the street checking doors to make sure they’re locked.  He cares about his neighborhood and his role.  Yet he also cares about his friend.  He cannot arrest him himself, so he gets another cop to do it.  He is not willing to break the law and let his friend go, but he has not the heart to arrest him himself.

Jimmy Wells was once the best friend ("chum") of Bob, now a noted criminal. They grew up as if they were brothers, but went their separate ways twenty years before. Bob headed out west when he was 18 while Jimmy stayed in New York. The two best friends agreed to meet at a certain spot twenty years later—in front of Big Joe Brady's restaurant (which has since closed)—no matter what.

Unbeknownst to Bob, who thinks of Jimmy as a bit of a "plodder," Jimmy has become a police officer. When he recognizes his old friend as a notorious criminal with an expensive watch and flashy jewels, Jimmy asks another police officer he knows to pretend to be him. Jimmy himself doesn't have the heart to meet with and then arrest his old friend.

Jimmy is a sharp contrast to Bob. While Bob has pursued a life of crime, Jimmy has devoted himself to fighting crime. When Bob calls Jimmy the "truest, stanchest old chap," he doesn't realize the irony of his words. The integrity and loyalty that Bob remembers Jimmy having will now be used against him as Jimmy shows his loyalty to the police force and his integrity in pursuing justice by arresting his old friend.

O. Henry shows great literary skill in his depiction of Jimmy Wells. By introducing him as a cop in uniform patrolling his beat, O. Henry actually succeeds in disguising him. The man we see twirling his club and trying doors along the block has obviously been a beat cop for many years, and I visualize him as nearly forty years old, probably somewhat overweight, sure of himself, satisfied with his job--in fact, a typical middle-aged beat cop, often called a flatfoot. Readers think they know him, but they don't! We don't connect him with Jimmy Wells, because we learn from 'Silky' Bob that Jimmy was only twenty years old when they parted twenty years earlier; and we cannot help visualizing Jimmy as a young man who is just beginning to find his way in life. Even 'Silky' Bob cannot realize that this stereotypical uniformed New York Cop he is talking to is his old pal Jimmy Wells. If Bob is deceived, it is not surprising that the reader should be deceived as well. It never occurs to us that this cop, of all people, could be Jimmy Wells. One of the ways in which we are deceived is by O. Henry showing the cop trying doors along the way. We naturally assume that this is his beat and that he is just doing his job. He is not there to meet anybody. But the fact is that he is there on the scene both because it is his beat and because he intends to meet his old friend at exactly ten o'clock. When Bob looks at his fancy watch, he tells the cop that it is three minutes to ten. Jimmy was early. That is likely why he was taking his own leisurely time about approaching the site of their rendezvous. All the description of the club-twirling is intended to show that Jimmy has been a cop for a long time and that he is walking in a leisurely fashion. O. Henry has to introduce Jimmy, one of his principal characters, without really "introducing" him. That was a problem the author handled beautifully. His stories are worth studying just for the many little details he handles so adroitly.

The real Jimmy Wells in the story is the uniformed policeman who stops to talk to Bob, who is standing in the darkened doorway of a hardware store. O. Henry does a masterful job of introducing a character and at the same time deceiving the reader as to his identity. Jimmy fully intended to introduce himself to Bob, but he didn't get a chance to speak. Bob thought he was just a New York cop checking him out and began talking first.

“It's all right, officer,” he said, reassuringly. “I'm just waiting for a friend. It's an appointment made twenty years ago. Sounds a little funny to you, doesn't it? Well, I'll explain if you'd like to make certain it's all straight. About that long ago there used to be a restaurant where this store stands— ‘Big Joe’ Brady's restaurant.”

“Until five years ago,” said the policeman. “It was torn down then.”

The man in the doorway struck a match and lit his cigar.

Bob is a big talker. If he is a crook wanted by the Chicago police, we can assume that he is a con artist. Sometimes a man can talk too much and talk himself into trouble. When the plainclothes man arrives later in the story and the two men go off arm in arm, Bob does more talking. He is telling the officer pretending to be Jimmy Wells about his exploits in the West.

The man from the West, his egotism enlarged by success, was beginning to outline the history of his career. The other, submerged in his overcoat, listened with interest.

Naturally he listened with interest. He was gathering evidence about Bob's criminal activities over the past twenty years. Here again Bob was talking too much.

Getting back to the hardware-store doorway, Bob struck a match and lit his cigar. Jimmy had intended to introduce himself, but not after he saw the man's face lighted up by the match. Proof that the uniformed cop introduced at the beginning of the story is Jimmy Wells is contained in the note the arresting officer hands Bob at the very end of the yarn.

Bob: I was at the appointed place on time. When you struck the match to light your cigar I saw it was the face of the man wanted in Chicago. Somehow I couldn't do it myself, so I went around and got a plainclothesman to do the job.     JIMMY

The plainclothesman has told Bob why he is under arrest.

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

It would have been impossible to send a photo or even a sketch of the wanted man by "wire." Jimmy Wells, the uniformed cop, recognized Bob as the wanted man by the verbal description contained in the telegram. It would have contained the usual details such as height, weight, and age, but it would have also provided some special identifying details. Jimmy sees these when Bob lights his cigar in the doorway, but the reader does not realize that they have special significance.

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 scarf pin was a large diamond, oddly set.

The wanted man, according to the telegram, has a little white scar near his right eyebrow. The scarf pin would have been described in much more detail than that it was "oddly set." It would have been a one-of-a-kind scarf pin and would have been a dead giveaway of Bob's identity as the wanted man.