So what do you do with that rusted Ford Falcon after its third reincarnation as a working car and its final gasp on the way to the corner drugstore?

In Arlington, more drivers are abandoning their junk cars on streets and in parking lots, say county officials.

Because of the significant increase in abandoned cars, the County Board voted last week to spend $12,000 to expand the impoundment lot where the police department stores these autos to await their owners, the auction block or the scrap heap.

"One reason for the increase is that we have an initiative to clean up the county. We've been doing it for a little over a year," said Deputy Chief Robert Dreischer, commander of the services division of the Arlington Police Department.

Corporal Cynthia Wesem, supervisor for the parking enforcement unit of the Arlington police, said that people are reporting more autos left by the wayside.

The county code forbids parking of cars longer than 24 hours in a public place without being moved. When police find a possibly abandoned vehicle, they put a fluorescent green sticker on it with the police telephone number. The tires are chalked to determine whether the car has been moved. If the car has not been moved for 10 days, it will be then be towed by a private contractor, Crystal City Towing.

"We're trying to improve the environment by removing cars that are junkers and eyesores," Wesem remarked.

Only a few of the junk cars are claimed by the owners during the 40-day period during which owners can respond to a registered letter sent out by the police. "The majority of times the people have either moved or left the area. Those are the ones that are usually junk cars and sent to the crusher," Dreischer said.

Cars appraised at less then $150 are sold to a junk dealer. Those cars worth more than $150 are sold at public auctions at the impoundment lot on South Taylor Street, according to a police spokesman. Of the 30 or so cars put on the auction block, a small number remain unsold.

Over the past two years, the number of abandoned cars more than doubled -- from 309 in 1982 to 793 in 1984, according to county statistics. These statistics include cars left on private property, which numbered 156 in 1984, up from 29 in 1982. Cars left on private property are the responsibility of the county zoning office.

Ted Payne of the zoning office said his office takes in about six cars a week. Currently, anywhere from 80 to 100 are still left on the streets awaiting removal to the impoundment lot, Payne said.

Payne said that lack of money to repair cars is one of the main reasons that people leave them. He said that people can buy a second-hand car, often on its last legs, for a lower price than it would take to repair the former one. A new transmission system may cost $400, but another old car could cost only $250, Payne said.

Often a home mechanic will buy two rundown cars, set them in his yard and strip the parts of one car to fix up the other one, Payne said.

He remarked that most of the cars that he deals with are beyond repair. And many people do not want to spend money to have their car towed to the scrap heap. And because the price of scrap metal has declined, there are fewer companies willing to tow away a car because the tow is more expensive than the car's scrap value.

"The value of junk has decreased. There used to be freelance towing companies that would tow it for nothing. They could take it to the junkyard and get $40. Now a junk car is worth $12, so companies don't want to tow it," Payne said.

"The avenue for getting rid of them is not there like it used to be. The whole burden has fallen on the police department," Payne said.

The increase in the number of calls to pick up abandoned autos is a seasonal phenomenon.

"When it's midwinter and dark at five, people don't notice them. When it gets warm and people go outside, you tend to notice the condition of the property around you," Payne noted.

Abandoned cars are a chronic problem in the rest of Northern Virginia as well.

With the authorization of Fairfax police, towing companies in that county remove an average of 16,000 cars a year from the streets, according to police statistics. This includes cars that have been in accidents or whose owners have been involved in crimes, said a police spokesman.

In Alexandria, 500 unclaimed autos are in the impoundment lot at any time, said Charles Kenyon, chief of the police department's transportation section.

Kenyon said that even after a clean sweep of 50 square blocks, city workers can return in two weeks to find a new group of abandoned cars.

"You're talking to a person who feels he's in a sea of junk cars. You can't say that, well, this week there's no cars. You can't rest," Kenyon said.