A lawyer from Philadelphia has agreed to take over the Virginia Central Railway, a mile-long Fredericksburg line that was shut down last year by the collapse of a boxcar-leasing plan.

Attorney David Wasserstrom will assume operation of the Virginia Central from Railvest Inc., a Washington business that bought the route in 1975.

Wasserstrom, like Railvest, will use the Virginia Central's name on box cars to qualify for higher lease payments under complex federal regulations for rental of railroad rolling stock.

Railvest's car-leasing plan promised investors a tax credit two or three times their investment in the cars.

Details of Wasserstrom's plan to take over the railroad could not be obtained yesterday. Neither he nor former Railvest president Joseph Keating could be reached for comment.

The Philadelaphia attorney apparently will have to assume some of the Virginia Central's debts in order to get title to the railroad, which owns only a mile of mainline and a few sidings.

The railroad owns no freight cars of its own and leases its lone locomotive from a Washington doctor.

Since the Virginia Central suspended operations last summer, freight service to the railroad's customers has been provided by the Richmond, Fredericksburg & Potomac Railroad under orders of the Interstate Commerce Commission. The RF&P has been losing money running the route and is negotiating with Wasserstrom to handle freight operations for him, a spokesman said.

The Virginia Central is one of several short railroads that have been bought by rail-car leasing companies in recent years. Boxcars owned or leased by railroads qualify for rental fees 66 percent higher than cars not carrying the names of a railroad.