The money is here. The FBI is here. The state police are here. Pschics are here. Frank Sinatra and Sammy Davis Jr. were here Tuesday night to raise $140,000. Burt Reynolds is here. He gave $10,000. The mayor says he spends about 80 percent of his time on it. But they keep finding little black bodies.

At last count there were 20 black children -- still another is missing -- linked to a killer who usually strangles his small victims, sometimes with his hands, sometimes with a white rope. The children, age 7 to 16, 2 girls and 18 boys, have been found dumped in streams, abandoned buildings and wooded areas. Some have been carefully placed with arms and legs extended, heads turned to the side. Only one victim, a girl, was sexually molested, and a boy was found wearing only his underclothes. Except for the unsubstantited surmise that the killer may get sexual gratification from strangling the children, however, there is little to suggest that the killings are sexually motivated. In fact, there is no known motive.

But the bodies keep coming. The panic is escalating as the killer picks up speed. In the last month, the killer has left three bodies for investigators to find, the most yet.

Yet despite the killer's non-stop work for nearly two years -- essentially in one neighborhood, along one major street filled with fast-food restaurants and working-class homes -- the police remain baffled. One investigator told The Atlanta Constitution recently, "We ain't got nothing."

Mayor Maynard Jackson says that is a lie. "We've made a policy decision not to make our case public," he says. But how does it keep happening? The same way you had someone who was the Boston Strangler, the argument goes, the same way Gacy got away with it in Chicago with some 30 kids, the same way you had the Zebra killer in San Francisco or the Columbus, Ga., strangler who was never caught.

"Homicides, normally to be broken," the mayor says, his face filled with lines, "require one of three elements -- an eyewitness, some physical evidence or a confession. None of those is present in this case."

So, theories fill Atlanta. It's all people talk about.

One theory has it that the killer is a black person, probably someone who wears a uniform, maybe a member of the Atlanta police, who in years past were often accused of brutal treatment of poor blacks. Atlanta police are now combing files of former members of the force to see if there are any likely suspects. "I'll tell you straight," says Camille Bell, the mother of one of the dead children. "The feeling in the community is that if it ain't the Klan, it's the cops."

The killer is thought to be black because, for over a year now, no black child would get into a car with or get near any white stranger. A second reason, police say, is that child molesters rarely cross racial lines to find victims. The former Atlanta chief of homicide has been quoted as saying that the killer is probably a black man 20 to 30 years old, "a religious kook but well educated, smart enough to have these turkeys [the police] running around."

"We may have someone, a black person I mean," says Mayor Jackson, "who is so demented by a racist society that his mind could be twisted enough to make his motive one of saving these kids from growing up in a racist society."

If the killer is black, that would in some ways be a relief to this city, which prides itself as an example of good racial relations in the South. If a white person is found to be stalking and strangling black children, there are fears that it could mean riots by blacks or retribution killings of white children. One theory already has it that the murders are retribution by whites for the murder of a white secretary on a downtown street by a black man and the murder of a prominent white doctor by two other black men only weeks before the little bodies started disappearing.

There is also concern here that Atlanta's image of sophistication will be trampled by Jesse Jackson and other national black leaders who are ready to turn Atlanta into a buzzword that for years to come will mean to all of America that the nation is still capable of virvulent racism.

"Even if it's the worst scenario," says Mayor Jackson, "if it turns out to be the Klan or the American Nazi Party, I think it will be an exclamation point behind our worst fears, and it will have serious political and social consequences. But I do not believe there will be a riot in Atlanta. If the killer is white, there may be some people who will draw the general from the specific. But I believe Atlanta is strong enough to avoid leaping to the conclusion that because one white person is rotten, all white people are rotten."

The Atlanta police department is under fire from all sides, white and black, for not solving the case yet. Poor blacks are particularly upset that the police department did not link the murders of the children together for over eight months -- even after the mothers of some of the dead children held a press conference to say "No one gives a damn."

"It's a class thing," says Camille Bell, who after the death of her 9-year-old son, Yusuf, became the spokeswoman for the parents of the dead children and the object of digs from people who say she revels in the celebrity that her son's death has brought her. "If it were Mayor Jackson's son or some big-time black, then you would have seen some quick response. But certain people's deaths in our society don't seem to mean anything. They were just ghetto kids.

"Sad, but you know what," Bell adds, talking to a writer in the swirl of furs and Las Vegas stars at a post-concert reception for Sammy Davis Jr., "these killings wouldn't have gone on so long without nothing being done if it was not for black people with a little something not caring about black people who ain't got nothing. . . . It's a matter of class. You know you got to ignore me, get away from me, if another group that you're trying to get in with masses you and me together, and you're trying to say you have arrived."

To the Atlanta of the black colleges, the Southern Christian Leadership Conference and the Martin Luther King Jr. Family, Bell's words burn. Coretta Scott King comes over to Mrs. Bell at the reception to ask how she's holding up under the strain. Suddenly TV cameras swarm around, and Mrs. Bell says to Mrs. King that she will see her inside, away from the bright lights. But Mrs. King continues to talk.

"I don't need all this," Mrs. Bell snaps back. "Seems like a bake sale to buy a bomber to me. This ain't no celebration. They'd have found the killer if people in this city cared anything."

Mrs. King quickly says goodbye, and the TV cameras shut off.

The tension runs so high in this town that even the parents and relatives of the children are under suspicion. Police study films of the funerals, looking for the killer.Some investigators believe there could be three sets of killers at work. First and foremost: the child killer, a crazy man. Second: a copycat, who sees the chance for a cheap shot, the opportunity to murder a black kid and get someone else blamed. And then the third group of suspects: the parents, who may have abused their children and, with the killings going on, found a quick way to get out of trouble. One child was supposedly taken from her bed by the killer. Police believe that would have to be a relative. So some parents have been given lie-detector and voice-stress tests.

Still, no solution. The little bodies keep turning up in Atlanta: about half apparently strangled or suffocated; others too decomposed to tell how they died; scratches on the boy's face that indicate he may have fought with the killer, apparently the only; child to do so. The gallery of faces belonging to the dead children includes a 9-year-old math whiz -- Camille Bell's son -- but more often the faces are of children who did better on the street than in school or at home. Eleven of them are described as "hustlers," selling cotton candy at the Omni, running errands, carrying bags from the grocery store, anything for a quarter. One of the children's last words, the newspapers report, were, "Mama, we'll find some [aluminum cans] to turn in for a penny apiece and make some money so you can wash the clothes." Five of the children were in juvenile homes for running away or committing crimes; 13 came from broken homes; four knew each other.

As the murders continue unsolved, they obsess the city, holding its leaders in a tight grip and defining their careers, much as the Iranian hostage situation did for another Georgia politician, Jimmy Carter.

"In many ways it's unfair," says Andy Young, the unannounced favorite to be the city's next mayor (Maynard Jackson cannot run again). "Nobody questioned the competence of the New York City policy or New York City's leaders during the Son of Sam murders. . . . Somehow Atlanta is on trial in this thing."

Following are excerpts of an interview by Juan Williams with Altanta Mayor Maynard Jackson.

Q. People are saying that if the children being killed were white, the government would have stopped it by now. How do people here in Atlanta react to that?

A. Insofar as that comment might be applied to Atlanta's administration, it is absurd. I've heard it said that if the children were white, things might have got started faster. This administration can show by its record that this claim is totally fallacious. If I died this minute, and the only thing I had done was to eliminate police brutality as an issue in the black community, I'd be happy. Before I became mayor, there were more civilians killed, almost all black, by the Atlanta police than by the police in any other city.

What about the reaction from the national government?

A. It's hard to say. It's probable, possible, that in some corners of our society, not all, the reaction to the death of white children would have been immediate. The official action in certain quarters might have been faster. But to say that alone is to speak an injustice. The fact is that America is pouring its heart out to Atlanta. People from all walks of life are looking to express their sympathy, trying to do anything they can to help. The money the White House gave us was targeted to the juvenile justice and prevention act. Now we have three corcerns here: One is the investigation, two is prevention and three is mental health. It is in the second category that the Reagan money, almost $1 million, falls. I believe the response from the White House, although not as complete as we would like it to be, has been sincere and direct.

Q. Are you making progress in this case or are you stymied?

A. The more evidence we accumulate, the more confident we become that we are going to solve these cases. This is not a guess. I am absolutely confident we will solve it.

Q. Have the killings signaled a change in life for Atlanta?

A. Certain southern traditions have changed. People still speak to you on the streets here; the people are very friendly. [There are] still great southern traditions in family, church. But there's very, very little of it the way it used to be. Only 25 percent of the people who live in Atlanta are Atlanta natives. We are the transportation hub of the South, the third-largest convention center in the nation. The sense of neighborhood that used to be is not as pronounced as it once was. What you had in a neighborhood before was a feeling that no matter whose child you were, if you were walking down the street going to school and if you didn't act right, somebody would get on you, say that they were going to call your mama and daddy and in fact did so. They wanted to see Rev. and Mrs. Jackson's little boy, Maynard, to well. Segregation, for all its evils -- I'm not defending it, but this is one of its factual historical byproducts -- drew black people together. In my opinion, we are still in a period of adjustment, evolving in social definition within a context of integration in American society.

Q. Do you believe that if the children were middle-class blacks there would have been a more swift response?

A. On a scale of 1 to 100, I'd say that issue ranks a 15 or 20 among black people here. I have an opinion of the natinal debate now going on about class among black people. Without going into detail, I'll tell you that one of the biggest lies being said today is that middle-class black people don't care about poor black people. That's not true.

I believe that we will solve this case. It's just a matter of when.