Virginia law is silent about cats. In that silence, many Fairfax County cats are running amok.

Take, for example, the greasy-looking cats who have moved into the basement of the Value Inns of America motel on Richmond Highway. These cats, witnesses say, dance into motel rooms and persuade strangers to give them food. Then they bite the hand of the motel manager who chases them.

There's a tomcat near Mount Vernon who likes to flight neutered cats in his neighborhood, and that tomcat's case is due in Fairfax Court today. Mary K. Rose, who owns a black-and-white neutered cat that has suffered at the claws of the tomcat, says that somehow that tomcat must be stopped.

A Springfield man, who requests anonymity, has a system for coping with cats who do not respect his property line. The system is a Siberian husky and it has killed two cats and crippled a third.

Into the legal viod that condones such carnage, has come Fairfax County government. The Board of Supervisors has requested an inquiry into the feasibility of regulation. Attorneys are researching common law and the cat. The director of animal control on Friday asked, "How do you catch a cat?"

In 1949, Adlai Stevenson, who then was governor of Illinois, addressed the issue of cat regulation and his words have been studied closely in Fairfax.

Stevenson said, as he vetoed a bill that would have leashed Illinois cats, "To escort a cat abroad on a leash is against the nature of cat . . ."

Said Stevenson in reference to the bird lovers who fought for the cat law, "The problem of cat versus bird is as old as time. If we attempt to resolve it by legislation who knows but what we may be called upon to take sides as well in the age-old problems of dog versus cat, bird versus bird or even bird versus worm."

Supervisor Marie B. Travesky (R-Springfield), who notes that "cats roam with impunity" in her neighborhood, says a leash law for cats is unrealistic.

"We had a cat once," Travesky said in an interview about possible regulation of the county's estimated 104,000 cats. "It would stalk along in the gutter when I went for a walk. If I had put him on a leash he wouldn't have moved."

Travesky said she supports cat licensing, which would not get the cats off the streets but would, she said, help distinguish cats who belong in a neighborhood from those who do not.

The legal problem of even licensing cats, according to assistant county attorney John W. Henderson, is not simple.

To begin with, there is the unreliable and aloof nature of the cat. The law recognizes this and has a Latin term for it, ferae naturae, which means that because nobody knows what a cat will do, nobody is responsible for what it does.

"If my cat manages to get away from me," said Henderson, explaining the law, "he has reverted to the status of ferrae naturae. I am not responsible for what that cat does."

Cats aren't really anybody's property when they are running around, Henderson said. He said it is difficult under the law to require a cat owner to buy a license for a creature that does not legally belong to the owner when it is roaming around the county.

Furthermore, the Virginia General Assembly has written no statutes that mention cats. Efforts to bring cats under state animal control laws have been laughed off the floor of the House of Delegates.

The county will have to be "relatively creative" in finding the legal authority to control cats, according to one informed source close to the cat question.

The man who will have to enforce a cat law, if one is ever enacted, is Richard F. Amity, director of the county Department of Animal Control. Amity, who has said that his cat won't come to him when he calls, said last week he does not believe his department has the manpower or the knowledge to handle cats who violate the law, whatever the law may be.

Cat catching, Amity added is difficult business. "I defy you to fence a cat in," he said.

The animal control department now has no authority to pick up a cat unless it bites someone. To people who complain about cats in their flower beds, Amity rents cat traps for 25 cents a day.

The only legal recourse a county resident now has against a marauding cat is under an ordinance about wild animals, which requires that one go to a county magistrate and get a warrant to force a cat owner to take away his cat.

It is under that ordinance that Mary K. Rose of Mount Vernon will seek redress against the tomcat that has scratched and chewed on her cat, which she says stays in its own yard.

The manager of the Value Inns of America motel, which has the greasy-looking cats in its basement, has pleaded with the county to help her control the cats.

"They told me felines are cold blooded or hot blooded or something crazy like that and that they couldn't help me because of the law," said Darlene Graven. She rented a cat trap, baited it with milk and it did not catch a single cat.

"These cats are not stupid," Graven explained. CAPTION: Illustration, Last night I heard a cicada, Drawing by Booth, Copyright (c) 1978., The New Yorker Magazine Inc.