Officials of Virginia, Maryland, the District of Columbia and the Army signed a new regional agreemant yesterday on how to share the Potomac River's water during drought, then a member of the Virginia State Water Control Board made a grudging admission.

"As a Southerner," said board vice chairman J. Leo Bourassa, "I've never seen a document that had so much Yankee trading in it."

While a tentative agreement among the parties was announced in early December, it was only in the last few days that lingering differences were smoothed out.

The agreement signed yesterday clears the way for Fairfax County to start tapping, the Potomac and for suburban Maryland to increase its present use in the time of drought.

Among those at yesterday's signing ceremony in a television recording studio at the Pentagon was Secretary of the Army Clifford L. Alexander Jr. But Virginia Gov. Mills E. Godwin signed the document in Richmond, and Maryland acting Gov. Blair Lee 111 signed in Annapolis.

Alexander, Godwin and Lee, in a "summit" meeting 2 1/2 months ago, committed themselves to resolving what had been a protracted and frequently acrimonious dispute. Despite the pledge - and the setting of a February deadline for agreement - the problems were enormous.

Positions had become polarized. On one side were Maryland and Virginia, wanting their share of drought-period water to increased as the populations of the Washington suburbs grew. On the other side was the Army Corps of Engineers, objecting that such a formula would gradually reduce the District's share of the water.

Before the summit, there was more name calling than negotiating. John F. Herrity, chairman of the Fairfax Board of Supervisors, denounced corps officials, calling them "colonels and general masquerading as politicians." The Virginia State Water Control Board voted to sue the corps.

Even at the summit meeting, which was supposed to bring a spirit of conciliation, the two governors reportedly laid out sharply worded positions. According to officials who attended the meeting, which was closed to the press and public, the governors stunned Alexander by informing him that a 1976 Maryland-Virginia agreement that the corps said was unfair to Washington had actually been drawn up by the corps.

Corps officials, in subsequent interviews, conceded that the disputed document was drafted within the corps, but said it had never reached high levels for approval.

After the summit, negotiations continued among officials beneath the governors and Alexander. There was, one party said, "a great deal of progress at the first meeting. Virginia was yielding on its original demand for a share of Potomac water as big as Maryland's or Washington's. The corps was yielding on its position, which actually froze out Virginia when drought had greatly reduced the flow of the river.

The second meeting, one party said, "started out as a disastrous disappointment. There were people there who hadn't attended the first meeting; they weren't part of the understandings that had been reached."

One of the sticking points was Bourassa's insistence that Virginia had rights, more than 100 years old, to take water out of the Potomac. Virginia would not yield on these so-called riparian rights, Bourassa said he told the other parties.

Actually the agreement signed yesterday does not mention such riparian rights in any of its crucial clauses. Bernhardt K. Wruble, the principal deputy general counsel under Alexander and one of the negotiates said the decision to oomit mention succeded because while it did not guarantee Virginia's riparian rights, it didn't take anything away from the state's calims.

Bourassa conceded that Virginia yielded on its original position of demanding the same share of drought water as Maryland and Washington, both of which depend on the Potomac more than Virginia.

As both Bourassa and Wruble said, the formula agreed upon gives Virginia - actually the Fairfax County Water Authority, which serves more than 600,000 Northern Virginians - probably all the water it would need even in times of severe drought.

The 23-page document, Wruble said, represents repeated refinements and alternatives to formulas that couldn't stand up to scrutiny from one side or the other. "Its a balanced agreement in which many compromises are reflected," Alexander said at yesterday's ceremony.

While Virginia yielded on its demand for an equal share, the District gave up some ground too. As time goes on, Virginia and Maryland's share will increase, but much more gradually than in the 1976 agreement signed by the states but rejected by the corps.

Furthermore the new agreement provided incentives for the District to buy into any new water supply projects undertaken by the Maryland or Northern Virginia suburbs.

All the parties agree that this provision will encourage development of a regional supply sustem.

One of the unsettled questions is who was responsible around the impasse that existed for almost the first 10 months of 1977. Rep. Herbert E. Harris 11 D-Va.) said he started the movement by inviting Alexander to his office and getting agreement to set a timetable for reaching agreement. Fairfax Board Chairman Herrity said he was the first to propose the summit meeting that marked the start of the eventually successful negotiations.

Yesterday's agreement removed the main obstacle to construction by Fairfax of an intake on the Loudoun County shoreline of the Potomac as a supplement to Fairfax's Occoquan Reservoir. But actual construction can't begin until the corps will not make a decision until some months after an environmental hearing on the project, scheduled for Jan. 23.

Suburban Marylamd will not be able to begin construction of its new in-take - larger than its present one - until that project also is approved.