Two-year-old Lance Hosmer and his 4-year-old brother Absalom were sleeping in the back of the old blue Chevy Malibu with the dingy stuffed duck hanging from the rear-view mirror when the policeman rapped on the window.

Lance started crying.

His mother and father quickly woke up, startled in the dark by the noise. They asked what was wrong. The policeman told them they couldn't sleep in the park.

Lance and Absalom's daddy told the policeman that the family didn't have anywhere else to sleep -- they didn't have any money. The policeman told their daddy that he would have to take the boys and their mother out of the park.

That night the family slept uneasily on a side street in a strange neighborhood.

A few days later, after their money for food had run out, Lance wanted milk. Absalom watched as his father gave blood to get $8. Other times, 25-year-old John Hosmer had panhandled for change.

"John has a good heart," said the children's mother, Victoria, 26. "He don't like to see the children wanting."

But when the 2-year-old threw up one night from eating bad meat from a food line, his mother could only hold him. There was no money to pay a doctor.

Ab, as his mother calls him, and Lance are two of America's children living in poverty. Their hungry, sometimes confused faces are the sad reality behind statistics from Washington that show a dramatic increase in the number of American children who are poor -- statistics that many comfortable Americans find difficult to believe.

One of every five American children under 18 and one of every four under six live in poverty. There are more poor children in the United States than at any time since 1965, before the Great Society programs began.

The statistics come from the Census Bureau, the Congressional Research Service and the Children's Defense Fund. The most dramatic rise in the poverty rate among children between 1979 and 1983 was the 63 percent increase in poverty among white children in two-parent families, like Ab and Lance. About one-sixth -- 16.9 percent -- of all white children are in poverty.

And like Ab and Lance, who in the past month have slept in a car, in shelters and now in a temporary church home, one of every five American children, excluding runaways, is homeless.

With most of the elderly buoyed above the poverty line by Social Security cost-of-living adjustments, children are now the largest age group in poverty; 37.8 percent of all the poor are children.

"In 1985 affluent America, poverty is the greatest child killer," said a report released by the Children's Defense Fund last week. "More American children die each year from poverty than from traffic fatalities and suicide combined. Twice as many children die from poverty than from cancer and heart disease combined."

According to the statistics, this latest surge in childhood poverty is unlike the poverty that came before it. It is not due solely to an increase in the number of single-parent, female-headed households.

Instead, the major problem is the economy. The recession, according to poverty specialists, has not ended for children or for the young adults who are the parents of children.

If Ab and Lance had been born to a two-parent family during the 1960s or 1970s, the statistical odds are that they would not have lived in poverty.

Ab and Lance's father, John Hosmer, has not been able to find a steady job for three years. The mechanical skills Hosmer learned in the Army, where he put together nuclear devices, got him a job in Texas after he left the service, but he wanted to move back to his home town, Bolivar, N.Y., near Buffalo.

Hosmer got a job there doing mechanical work at an ice cream company. Later, around the time Ab was born, he found a slightly better paying job as a forklift operator. In early 1982 he was laid off that job, knocked around for a few months and got work as a groundskeeper on an estate. That job ended in late 1982, three years ago.

So Lance, now 2 1/2, was born to an unemployed father. His mother, a high school graduate, had worked as a cook and a waitress. But she quit her job after Absalom was born in April 1981.

"They just weren't hiring up there," Hosmer said of New York. "So, I said, 'Babe, there's nothing I can do but go out here and let them know I want to work' -- but we didn't see no work. Nobody's hiring."

This May, John and Victoria Hosmer said they were "tired of feeling sorry for ourselves" and decided there might be jobs elsewhere. They took their food stamps and cash -- about $300 in all -- and decided to drive until John could find work.

The money ran out about a week later, after four stops and no work. They were in Columbus, where they had heard the economy was good.

Although the boys have been in Ohio less than a month, they fit a pattern here, too. Ohio has had a 321 percent increase in the number of two-parent families on welfare during the 1979-83 period. Single-parent families on welfare increased by 15 percent during the same time. Currently, two of three welfare recipients in the state are children and 85 percent of those children are in elementary school, according to state records.

So far, Charles Dickens-like tales of children roaming the streets begging for food, working illegally or becoming involved in rampant prostitution and drugs have not been widely seen in America, despite the upswing in childhood poverty.

"I cut their hair myself," said Ab and Lance's mother. "I keep them clean as I can. Just because we're going through hard times don't mean they're going be looking torn up and dirty."

According to child sociology specialists, many parents keep alive the hope of education and a better life for their children. But the poverty facing children is deepening. Federal and local funds to house homeless families in Columbus ran out more than two months early in the first half of this year.

"The Reagan recession has not ended for children and the young adults who are in the child-bearing years," said Marian Wright Edelman, president of the Children's Defense Fund. "The young adults who lost jobs when plants were closed or there were layoffs are the last to be rehired. And when they are rehired, they are getting jobs that do not pay as much, they may be part time, they do not have the benefits that provide medical coverage for the children."

The Hosmers had been living on money from New York state welfare and food stamps. Their parents had helped a little but, John Hosmer said, "They ain't rich -- they can't take care of me and my family."

Ab, Lance and their parents slept in the car, eating in food lines. Their mother remembers the boys asking when they would go home.

"I would tell them we would get to a TV tomorrow so they could see cartoons to calm them down," said their mother.

Economists note that the nation has never had such a prolonged period of high unemployment as in the last five years.

In the 1960s a "natural" unemployment rate, according to government officials, was about 4 percent. But unemployment has not been under 7 percent since 1980. And both government and private organizations project that unemployment will continue in the 7 percent range until 1987.

Young adults -- often the parents of children -- have suffered most from this chronically high unemployment rate, according to many economists.

Even a new job does not always guarantee an end to poverty for the children.

For example, after two weeks of looking, John Hosmer got a job through an employment agency in a pipe company putting duct work together.

He is paid daily through the employment agency, but he is earning only the minimum wage -- not enough to pay for a motel room, not enough to lift his family above the poverty line.

The congressional report said more than 2.5 million of the 13.8 million children below the poverty line live in families where at least one person has a full-time job.

This belies the widespread view," the congressional report said, "that a full-time job throughout the year is near-insurance against poverty."

The damaging effects of unemployed parents has been compounded, according to the Children's Defense Fund and the congressional study, by cuts in federal programs since 1971. Sen. Daniel Patrick Moynihan (D-N.Y.) agrees.

"In the 1970s we allowed the benefits for children under the AFDC program to decline by one-third," Moynihan said. "We cut the childrens' allowance by one-third while we indexed benefits for everyone else. Only the children got left out. If you are under six years old in the U.S. you are six times more likely to be poor than if you are over 65. We are the first industrialized nation in the world in which children are the poorest age group."

In their short lives, Ab and Lance have not been hungry. They received food stamps and their parents got welfare in New York state.

"It's no kind of life to live depending on a little bit of welfare," said Victoria Hosmer. "It's no life for my children. That's why I said I'd come with John. We got to find work."

The Hosmers have not been in Ohio long enough to qualify for food stamps and welfare. They say they hope that John will hold his job at the pipe-fitting company or find a better job.

However, the prospect of a better job coming through economic recovery is not good, according to the congressional report.

"Unless recent trends are reversed," the report said, "it might take as long as 12 years . . . for the poverty rates of male-headed families with children to drop back to the levels of 1979."

Last week, Hosmer hurt his foot while doing an errand to earn some money. The injury kept him off the job for most of the week.

The pipe company provides no sick leave or benefits, so Hosmer and his family have no income at the moment although he has been promised that he can keep the job if he returns by Monday.

Asked if they are embarrassed by their poverty, the Hosmers looked away.

After a pause Victoria said, "It ain't nobody's fault. We pray, and it ain't like we're not trying. It's hard on the children, I know, but we do the best for them we can."

"It's a matter of your attitude," said John Hosmer. "We keep going. Nobody likes being down, right? But I say, 'Babe, we got a lot to be thankful for. People have been nice to us when we didn't know what we were going to do.' So you got to keep on pushing."

"One day," he said, "we're going get a job and then a place, maybe even one day a house. Man, we're going to hold on to that."

The family did have one lucky moment. Another poor family was evicted from a row of houses owned by Catholic Social Services, and the Hosmers' social worker, Mary Beth Buynak, arranged for the Hosmers to get the house for three months.

"We're concerned about the children in a situation like this," Buynak said. "These children are doing well by comparison with most . . . . The parents' optimism comes through.

"But children are very sensitive to what is happening," she added. "They are often disturbed by the whole thing. Being uprooted as a child is hard and the couples don't cope well with it . . . . The men are shamed. The children pick up the parents' fears and anxieties and reflect it in their behavior and insecurity. It is a very sad thing to see."

Lance and Ab don't talk much. While their parents were interviewed, they fought over two toys.

Their mother said she brought a bag of toys with them from New York and sometimes she buys a 99-cent toy for them, but "the boys like toys -- they want more, you know."

"You have any toys at home?" Ab asked.