A 9-year-old boy goes to school in Los Angeles with an abrasion on his nose and a reddened eye socket. He tells his teacher he was hit by a ball. She sends him to the nurse.

The boy tells the nurse he was hit by a ball. She calls the principal. The boy repeats his story. The principal calls the child protective service workers, who call the police.

By this time, school is over. The boy's aunt -- his mother is in the hospital -- arrives looking for him. She also has the boy's 18-month-old sister. The authorities, fearing abuse, take custody of both children.

The family hires a lawyer, who gets the children back after eight days. The baby girl has bruises from her stint in custody. Eventually, the case is unconditionally discharged.

A distressing incident, to be sure. So, in a different way, is another case.

This one happens in Washington state. A father is charged with physically abusing his 3-year-old boy. The father claims to have been trying to discipline the child for drinking water out of the toilet. He says he was aiming for the child's bottom but missed. This broke the boy's femur -- one of the body's strongest bones. The father says he had kicked the child before and the child hadn't been harmed.

The father is charged with felony assault, but is found guilty only of simple assault. Says the prosecutor: "The fact that it was his own child diminished the seriousness of his conduct in the jury's eyes."

Two different cases. In the first, well-meaning officials were watching for abuse, made the wrong assumptions, and caused more trouble than if they had done nothing. In the second, the prosecution's efforts were hampered by the general belief that kicking your own kin -- even if he's only 3 and you break his leg -- isn't quite as consequential as kicking someone else.

Child abuse is an urgent problem -- and one where the definitions, society's responses, the causes and even the exact number of incidents are quite hard to determine. It's the iceberg of social issues: Most of it exists beneath the surface.

The stereotypes of child abuse do not always fit the statistics. Battering and sexual maltreatment are the most common images of abuse, yet according to an estimate by the American Association for Protecting Children (a division of the American Humane Association that collects state abuse figures), at least half of the abuse cases instead involve neglect -- failure to provide nourishment, shelter, clothing, health care or supervision.

And while the stranger lurking in the bushes or hanging around the schoolyard gates is still a potent fear, the figures say that the vast majority of abuse -- 84.6 percent in 1984 -- involve a parent-child relationship. Even with sex abuse, 55.6 percent of the offenders were the parents; another 18.7 percent were a relative.

These numbers, however, are based on reported incidents. What feeds most of the anxiety about maltreatment is that no one knows what is not being reported. A conservative estimate is that there are an equal number of undisclosed cases.

Start, however, with what is known. There were 2.2 million reports of physical or sexual abuse or neglect in 1986, a level that was more than triple that of a decade earlier. Roughly 40 percent of cases are substantiated -- i.e., the authorities concluded the child is in fact at risk. (Lack of substantiation, however, does not mean that there is no abuse. The case of Lisa Steinberg, the Manhattan 6-year-old who was beaten to death last November, was unsubstantiated right up until she was killed.)

"The number of reports are increasing from a combination of factors," says Patricia Toth, director of the Alexandria-based National Center for the Prosecution of Child Abuse and the prosecutor in the Washington state case.

"Awareness has increased greatly, and it's led to increased reporting. Also, the fact that there does exist a system for responding better to those reports has led to an increase in reporting. Overall, people are more educated, more willing to believe that the kind of abuse that goes on is indeed possible."

Unfortunately, the surge in abuse reports has not been accompanied by a parallel increase in state financing to deal with the problem. The system, especially in inner cities, is frequently overburdened, as protective service workers struggle to determine which cases are real and which aren't. The problem, says Victims of Child Abuse Laws (VOCAL), a small but influential group, is that over-zealous reports are flooding the system and wasting valuable time and resources.

Allen R. McMahon, a Santa Ana, Calif., lawyer who represented the L.A. boy with the reddened eye socket, is the legal adviser and a spokesman for VOCAL. "Child abuse is an extremely serious problem," he says. "But there are children being abused by the system supposedly set up to protect them."

The public, the lawyer says, "has been whipped to a frenzy on the issue of child abuse," somewhat in the same fashion as with the recent missing children scare. Because of several well publicized abductions by strangers, the fact that the great majority of missing children were runaways was ignored.

"I can give examples of malicious reports, where one parent is seeking to exclude the other in the course of a custody dispute; or where medical or school personnel overreacted; or of alarmist reactions," McMahon says.

As a result, he declares, "children are taken into custody, families are destroyed, children traumatized ... Every bruise on a child is not abuse. Every vaginal discharge is not molestation. Every dirty kid is not neglected. A lot of people act as if they had never heard of those ideas."

While abuse experts agree that there are sometimes false allegations and spurious reports, they don't think the total is as high as VOCAL suggests. "The claim by some people that these charges are made too easily is not really true," says David Finkelhor, associate director of the Family Violence Research Program at the University of New Hampshire. "Being accused of child abuse is not a minor matter."

The National Center for the Prosecution of Child Abuse's Toth says: "There is also a danger in assuming that a bruised child is not abused. There is no simple checklist that will tell you the truth. You don't know without taking steps to find out more information. I don't believe the solution is to have fewer investigations, but to have better ones -- more thorough, prompt, sensitive. If our presumption is wrong that abuse is not going on, who will be the one to suffer? The child."

David Hechler, author of the just-published study The Battle and the Backlash: The Child Sexual Abuse War, thinks the debate has led to "sweeping generalizations from all parties. To say children never lie, which some supporters of publicized cases have said, is simply false. And to say there is a witch hunt in this country, and anyone can point a finger and have a man tossed in jail as a child molester, is equally false."

While VOCAL and the child abuse establishment both would like protective service workers to be better trained, the advocacy group also wants a streamlined approach, including taking fewer kids into custody and dismissing more cases on initial review. The question is, will that also lead to the inadvertent dismissal of actual cases? Any permanent solution is going to take money, and no one seems overly optimistic about its appearance.

The conventional view of child abuse is that, however pervasive in our own society, it was even more prevalent in centuries past. Lloyd deMause, in his influential article "The Evolution of Childhood," writes: "The further back in history one goes, the lower the level of child care, and the more likely the children are to be killed, abandoned, beaten, terrorized, and sexually abused."

John Demos, an award-winning Yale University historian, takes exception to that idea. After reviewing the records of colonial New England, he concluded that physical abuse of children by their parents was essentially unknown in that society. Since record keeping was so good in this particular setting, and since the public authorities were so attentive to what was going on in their communities, he believes that if the abusive behavior was there, there would be some evidence.

"Most childhoods in pre-modern society knew their own forms of severity," he writes in his article "Child Abuse in Context." "But they seem not to have known the particular sufferings which the term 'child abuse' now calls so vividly and painfully to mind."

In an interview, Demos said that "if my article has any utility for the present, I hope it's in countering what I see as a way of letting ourselves off the hook by saying, 'However bad the problem is today, it's much better than it was long ago.' That's the wrong perspective."

Demos' argument that child abuse is a relatively modern invention is not widely accepted. Finkelhor of the Family Violence Research Program says that "colonial America is probably unusual. Child abuse is associated with urbanization and social stratification, and colonial America was pretty rural and was relatively classless." In the history of the West, however, "you'll find an enormous amount of child abuse in the 17th and 18th centuries. It's certainly not a condition of the 20th century."

Finkelhor offers this analogy: "We got exercised about poverty at a time when we had reduced it. When everybody's poor, it's not a social problem."

Similarly, he says, "when all children are abused and beaten and whipped, you don't make a fuss. It's when you get the idea that it doesn't have to be a state of nature that you decide no one should have to suffer this thing."

If Demos is correct -- that child abuse is bred in our culture as easily as garbage produces flies -- the problem may never be wholly eliminated. The historian suggests that our smaller families yield more intensive interaction, while on-the-job alienation and the pressures of modern life encourage a tendency to see abuse as an answer. He also sees the endemic violence in American life as a significant factor, along with our extreme tendency to social isolation.

"Study after study finds {abusive parents} rootless, friendless, virtually unknown even to next-door neighbors," he writes. "Are they overwhelmed by real or imagined adversities? There is no one else to share the load. Do they lash out at the nearest available human targets? There is no one to see the hand rise, and to stay its swift descent."