The Fairfax County Board of Supervisors said yesterday it is prepared to provide police with extra money to investigate what the supervisors perceive as an increase in cases of child molestation.

"We want to do anything we can to protect the children," said Springfield Supervisor Elaine McConnell, who operates a private school for handicapped children.

An 11-year-old girl was attacked while walking to school in the Springfield District last week, an incident that may have prompted yesterday's board action.

In its 7-to-0 vote calling for stepped up investigations into child abuse, the board joins a nationwide effort to fight child abuse spurred by recent reports of child molestation at large day care centers and schools in California, Florida and New York.

"If additonal funds are needed," said Board Chairman John F. Herrity, "the police department should just let us know."

Fairfax County Police Maj. Andrew Page, commander of staff services, said yesterday that "incidences of molestation are few and far between, fortunately. It's hard to give you a number, but they're very rare."

Still, he said, police might need more money if they decide to start a new unit for investigating all crimes against children. That proposal is being studied by county officials.

"This is not because we have a problem," Page said, "but because we want to be able to specialize in this sensitive area and be better prepared to investigate."

"Child molesting happens in the home, as well as by strangers, and it happens in the home a lot more than people realize," said William McDonnell, assistant director of Child Welfare Services for Fairfax County.

He said reported instances of sexual abuse involving children under 18 has increased steadily by 10 to l5 percent during the last three years. "It's not so much that it's occurring more, it's just getting reported more," he said.

Virginia Ratliff, coordinator of the Victim Assistance Network, a county program, said her group also seems to be fielding more calls related to child molestation.

In the past 10 months, 51 victims have sought help from Ratliff's group, she said. Of those, 12 were under the age of 18 and six were in elementary school. The youngest was 7 and all but one were female.

She said the problem in Fairfax is no worse than it is elsewhere. "I think it's serious all over," she said.

A recent report by the National Association of Social Workers estimated that one in eight females in the United States will be a victim of sexual abuse before the age of l8.