There is a cartoon in the public information office of the Prince George's County Police Department which depicts a county police officer shaking hands with John Q. Public. Looming over the two, guiding one toward the other, is Police Chief John W. Rhoads.

The message is clear. Since the day he became chief on May 6, 1975, Rhoads had tried desperately to change the image of his department from the hard-headed, shootfirst, ask-questions-later image of the late 60s and early 70s to an organization that works with the community. That was what Rhoads' boss, County Executive Winfield M. Kelly Jr., hired him to do.

In some ways, the campaign has worked. The phoned-in community support the police received during their recent job action can be traced to what Rhoads calls the "remarriage" of the police officers and the people they serve.

But many of the men on the force do not like what Rhoads has done to bring about that remarriage.

"You have to understand one thing about this department," said Sgt. Ralph Ross, an 18-year veteran. "Up until the mid-70s it was a known fact that if you came into Prince George's County and made trouble the police would kick your head in. Simple as that.

"The county had that image and it wanted that image. The police were encouraged to be that way. But times changed and that sort of thing wasn't allowed any more.

"But the men didn't change. Now, you're asking them to competely change their ways in midstream. They're bound to resent that. And Rhoads is the one put in the position of asking them-telling them - to change."

Kelly appointed Rhoads chief because he represented the kind of administrator Kelly wanted to help him embark on his much-touted "New Quality" program for the county.

Kelly was looking for men who were young and attractive, who had the background, looks and style to go with the "New Quality" campaign. Rhoads, now 43, fit the bill. He is a family man with a wife and two children, and a lifetime Prince Georgian who chose to remain in the county he grew up in. Just like Kelly.

Rhoads is also articulate, able to deal with the public and the media smoothly and comfortably. He has been involved in administration in one form or another for 20 fo his 21 years in the police department. Because of that, he rarely acts in haste or anger. He thinks, then acts.

Those qualities made him Kelly's choice for police chief in 1975. Ironically, many of those qualities bother rank-and-file officers the most.

Rhoads is not a police chief in the paramilitary tradition of most police departments. He does not rail publicly against the criminal element. He does not cry for revenge when one of his men has been wronged. And he does not publicly defend his men, right or wrong - only when he believes they were right.

Because of all that, and because they see Rhoads as a Kelly man with little freedom or inclination to act on his own, the rank and file unanimously passed a "no confidence" vote on their chief June 29.

But one decision apparently crystallized all those pent-up feelings and, more than anything else, may have led to the no-confidence vote: the June 21 firing of Officer Peter F. Morgan, who had fatally shot an unarmed, fleeing shoplifting suspect Christmas Eve.

According to the unspoken rules of the rank and file, Rhoads had committed an unpardonable sin: he admitted a police officer was wrong. He had not stood up for his man. Worse, many officers saw the firing as a public relations move, designed to placate the black community and the media.

"Pete was the victim of an election year we all know that," said a Seat Pleasant officer who has worked with Morgan. "Kelly needs the black vote. He told Rhoads to jump and Rhoads jumped. Pete never had a chance."

One of the criticims of Rhoads has been his relationship with the media. Generally, it is good. To most policemen, that is bad.

"Listen, John Rhoads is a great guy, one of the nicest guys you'll ever meet, but he doesn't know how to deal with his men or what they need," said Jack Cornett, former police union president. "As chief, John reacts too much to what looks good in the media. He does things to satisfy reporters. You can't run a police department that way.The men resent it."

The men also resent Rhoads lack of street experience. Many say that having been an administrator for 20 years, he is not capable of understanding the problems they deal with daily.

"That's just it," Seat Pleasant detective Nick Valatose said. "John Rhoads is an administrator not a policeman. He's politician, controlled by a politician. He doesn't know what it's like on the street."

Rhoads is keenly aware that his support among the rank and file has diminished greatly in recent months. After the no-confidence vote he said he might consider resigning.

"When I hear some of the things that I know are being said about me, it just tears me up inside," he said recently. "The men feel I should stand up for them and say they're 100 percent right 100 percent of the time. I wish I could do that, it would be nice.

"Sometimes I feel like a father figure with the men.One of the things a father has to do when something is wrong is punish, no matter how hard it is.

"The dismissal of Morgan was traumatic for a lot of the men and it has played a part in what's going on now. It played heavily on the men's emotions. They think the chief didn't do everything he could for one of their own."

There are many who say Rhoads had no choice. Relations between the largely white police force and the country's black population have always been strained.

That was one thing Rhoads has tried to change. But Morgan's shooting of shoplifting suspect William Ray, a black, and the shooting a month later of black burglary suspect Abraham Dickens IV rekindled tension between the department and the black community.

"I was fired the day after it happened," Morgan said, "Kelly made up his mind to appease the black community and that was it. He told Rhoads, 'fire him' and that was that.

So while Morgan and other officers see Morgan as a victim, and see themselves betrayed by their leader, Rhoads finds himself surrounded by a hostile force.

Rhoads admits that he is frustrated. He feels caught in the middle. He is unable to critize Kelly publicly even if he disagresss with him. But he still must try to retain the loyalty of 865 men, most of whom dislike Kelly's policies.

"Sometimes I think I should have stayed a lietunant colonel and not taken this job," he said with a straight face. Quickly, he added, "I'm only kidding.

"Look, in the end everything comes back to the guy sitting in this chair," he said, suddenly serious. "I realize that I'm the guy in the middle. I think I am loyal to my men. I think they've done an outstanding job in dealing with the changes this county has undergone.

"I always try to do what's best for them. But I have to do what's best for the community too. I have to do what I have to do."

One of the things Rhoads has done is to begin hiring more black officers. The Prince George's police force is still 91 percent white, but that is a drop from the 97 percent of four years ago. And classes of recruits are now 50 percent white, 50 percent black.

Integrating the force was one of Kelly's and Rhoads' primary objectives. The black population in the county has grown considerably the last 10 years and blacks now constitute 25 percent of the population.

This great influx of blacks into a community with a lily-white police department played a large role in creating the problems between the police force and the community.

"There was definitely an 'Us vs. Them,' feeling among a lot of the guys," current police union president Laney Hester said. "Lately I think that some of that feeling has changed. Now, 'Them' is the administration. A lot of guys feel like they're getting it from both sides. First, the community, then the administration."

Many men feel Rhoads has missed a chance to recoup some of their lost loyalty the last two weeks during the contract dispute with the county and the aftermath of the shooting deaths of Officers Albert M. Claggett IV and James Brian Swart.

"John Rhoads had his chance last week," said Officer Sherman Baxa. "All he had to do was come out and take a stand for his men, say he was sorry about the two officers' deaths." (Public Information spokesman John Hoxie said Rhoads was too upset to talk about the deaths.) Rhoads also could have said "that the men deserved a good contract and the county was wrong. But he wouldn't do that. He wouldn't mess with Winnie Kelly," Baxa added.

Or, as another officer put it, "John Rhoads doesn't go to the bathroom without making sure it's OK with Kelly first."

That is a fairly widespread feeling. Rhoads denies it. "When I make a decision," he said, emphasizing the work 'I.' "I have to take all sides into consideration. No matter what I do I'm going to make someone unhappy. I'm in the middle of something everyday. That's my job. A lot of the decisions are hard, but they're mine."

And, according to Kelly, they will continue to be his as long as he remains county executive. "There is no doubt in my mind about John Rhoads," he said last week. "I think he is one of the finest police chiefs in the county."

But many of the men on the street, some of whom fondly remember the old pre-Kelly days, want nothing to do with Kelly's New Quality.