They will descend on Richmond Monday, loaded with maps and freshly sharpened pencils, each bringing a different plan for redrawing the state's 140 precious House and Senate districts.

For a week or more, the halls of the state Capitol will sound like a seminar on mathematics, as General Assembly members bargain over census figures and exchange secret longings. It is a scene that will be reenacted in every statehouse in the union, but Virginia, because its 100 House members are up for election this fall, will be the first to tackle the job.

By the time the smoke from Virginia-grown tobacco has cleared, Northern Virginians may well find they have lost another battle to the more powerful -- and overwhelmingly Democratic -- delegation from Tidewater.

Based on census statistics, there seems little doubt that Northern Virginia is entitled to additional House representation. Those numbers show that Northern Virginia has been growing more quickly than any other area of the state, with a total population of more than 1.1 million in 1980.

That's a gain of more than 181,000 people since 1970 and, under current guidelines calling for one House member for every 53,463 people, Northern Virginia theoretically should gain three new delegates. Such a gain would give Northern Virginia 21 delegates, more than any other region in the state. g

But, as each of the 140 legislators who will meet here next week already knows, there's more to reapportionment than simple division.

It's going to be a test of mathematics versus political and regional alliances. And few of those who have watched the Assembly in action expect cut-and-dried census numbers to have the upper hand.

Northern Virginians -- Republican and Democratic -- say that this year, unlike 1971, the Washington suburbs will not yield a single disputed seat to Tidewater. "That's one thing the Northern Virginians are solid on," says Del. Elise B. Heinz, a Democrat, who faces the loss of her seat, shared by Arlington and Alexandria, because of the population changes. "They're not going to shortchange Northern Virginia."

But the reality of the Virginia legislature, with its premium on seniority, is that the smaller Tidewater region may be able to easily outmaneuver the Northern Virginians.

It's no coincidence that the key Privileges and Elections committees, which have the biggest say on redistricting, are headed by Tidewater legislators in both chambers. "Tidewater voters know how the seniority system works," says Del. David Brickley (D-Prince William) somewhat ruefully. "They just keep bringing back the same people year after year."

Today, Tidewater legislators chair 10 of 20 House committees and five of 11 Senate committees, as well as holding the majority leadership posts in both chambers.

By contrast, the ever-changing pool of voters in Northern Virginia has a habit of trading in its legislators for newer models. "I think sometimes we give people the impression that we're not real serious about politics because we turn over every few years," notes Del. Mary Marshall (D-Arlington).

That may explain why there is only one Northern Virginian among the ranks of committee chairmen -- Sen. Adelard L. Brault (D-Fairfax), who chairs the Senate Education and Health Committee -- and none in the top leadership positions.

It hasn't always been that way. In the mid-1970s, Northern Virginia seemed to be in control of the General Assembly. Then Alexandria voters defeated House Majority Leader James M. Thomson, a veteran legislator who was considered the delegation's most influential member. His defeat was followed in 1978 by the retirement of Fairfax senator Omer L. Hirst, who chaired the Senate Privileges and Elections Committee.

At the start of the 1980 session, the Northern Virginians suffered another setback when Brault was ousted as Senate majority leader.

If problems of seniority weren't enough, Northern Virginia's difficulties are often compounded by the inability of the delegation to work as a cohesive unit. The delegation the Washington suburbs sends to Richmond, unlike the largely united Democratic delegation from Tidewater, is split by a host of clashing goals and ideologies. In the past two legislative sessions, the delegation has been divided on such key issues as the gasoline tax to finance Metrorail and the repeal of the state sales tax on food.

While Arlington's delegation of Democrats is often championing liberal causes and tenants' rights, the Fairfax Republicans are more closely aligned with the interests of industry and development. And a couple of Fairfax Republicans who count themselves among the ranks of ultraconservatives, John Buckley and Lawrence Pratt, can seldom be depended on to vote with the delegation on any issue.

Given those factors, it's not surprising that the most optimistic people going to Richmond Monday will be coming up Interstate 64 from Tidewater instead of down Interstate 95 from Washington.