The Fairfax County Board of Supervisors, meeting for the last time today before its summer recess, is expected to endorse a one-year experiment to provide commuter rail service between Fredericksburg, Va., and Washington, according to county officials.

But a key unanswered question is: Where would funding for the plan, which would consist of one morning and one evening train each day and cost an estimated $1.2 million, come from?

Virginia Rep. Stan E. Parris (R) has asked the federal Urban Mass Transit Administration (UMTA) for $700,000 for the service, which would be operated by Amtrak on existing tracks and would include stops in Lorton, Springfield, Alexandria and Crystal City. Fares from commuters would generate about $400,000, according to officials.

UMTA, which is expected to rule on the request within the next two weeks, is likely to approve a grant, but not necessarily the full amount requested, officials say.

"We're optimistic about the funding," said Fairfax Supervisor Elaine McConnell, who said she plans to ask the county board to support the plan.

If UMTA does not approve a grant for the amount requested, Northern Virginia legislators may seek state funds. Fairfax, Prince William and Stafford counties, as well as the city of Fredericksburg, also may have to contribute funds to the program, according to county officials.

Under the proposal, Amtrak would supply a train for the service. On Oct. 31, Amtrak is scheduled to cancel a train, "The Virginian," that serves much of the same route as part of a run between Richmond and Boston. However, that same train could be used for the commuter rail program if the funding is approved.

Amtrak says it needs a commitment from Fairfax officials by Oct. 1 to pay for the cost of platforms, parking lots and other facilities, such as access roads, at commuter stations in Lorton and Springfield.

County officials say they don't yet know what it would cost to build those facilties. And they say that even if the board endorses the commuter rail service today, as expected, approval of any specific funding is unlikely until federal and state contributions are set.

If the one-year experiment is successful, Northern Virginia officials hope it will lead to a more extensive commuter rail service between Fredericksburg and Manassas to Washington's Union Station.

That plan, which would include four trains daily on each line, would cost about $7 million to $8 million to launch. Northern Virginia officials, recalling the push by some state legislators to eliminate state subsidies for Metro, say privately that funding from Richmond for a full-blown commuter rail program is doubtful.

Fairfax County Transportation Director Shiva K. Pant said the one-year experiment of limited daily service "could be a worthwhile expenditure" if it led to the expanded commuter rail plan later. He added, however, that the county must weigh the costs of the program against the number of people who would be served by it.

County officials are scheduled to look this week at possible commuter rail station sites near the Springfield Mall and Lorton, east of I-95.