Investigators will get some clues to the case of the missing 115,400 Northern Virginians when area residents begin returning their 1980 census forms within the next few weeks.

Residents can expect to receive the census questionaires in their mail tomorrow, and U.S. Census officials say they hope the forms will be returned within two weeks.

The 115,400 Northern Virginians whom area governments hope to find, represent the difference between 1980 population estimates made by local governments and those made by the State of Virginia, which bases all its projections on figures from its official population estimator, the University of Virginia's Tayloe-Murphy Institute.

At stake are millions of grant dollars from more than 100 state and federal programs, grants based in part on population estimates. In arguing that Northern Virginia's population has been underestimated, Fairfax, Arlington, Alexandria and other local jurisdictions claim Tayloe-Murphy Institute methods which the state relies on are inadequate to count urban area residents. m

But the state and Tayloe-Murphy contend that counties and cities almost always overestimate their populations, and that since the 1970 census Northern Virginia has experienced a slower growth rate, and thus has a smaller population than local officials believe.

The state and local estimates are now 10 percent apart; however, projections for the year 2000 show a 32 percent difference, or close to half a million residents. Federal and state funds for highways, water, sewer and other long-range projects are all affected by such a huge swing in population projections.

The most dramatic difference of opinion is over the future of Arlington, Alexandria, Fairfax City and Falls Church, which the state predicts will lose a total of 21,300 residents during the next 20 years. But the Metropolitan Washington Council of Governments (COG) and its cooperative forecasting program estimates that the four jurisdictions are still growing and will gain 80,000 residents by the year 2000.

"The state's been making out like a bandit because it uses low figures," said Arlington Treasurer Bennie Fletcher, a sentiment echoed by COG and virtually all local jurisdictions.

Fairfax County and Alexandria appear to be the biggest losers in the numbers game.

"We're talking about $20 to $40 million in federal and state grants to Fairfax County, not counting state aid to schools," said Fairfax demographer David Sheatsky.

Sheatsky is particularly critical of Tayloe-Murphy for reyling heavily on school populations as indicators of population losses or gains. "And they don't have good figures on the number of kids in private and parochial schools," he adds, a contention Tayloe-Murphy officials say may be true.

Although Alexandria and Arlington may be closing schools because of sharp enrollment declines, officials in both areas claim that large numbers of single, divorced and elderly residents are moving in. And, officials add, both areas are undergoing building booms and registering increased numbers of voters.

In Fairfax, the most recent county population estimates, for 1977, show the county with 573,000 residents. However, Tayloe-Murphy's final 1977 estimates -- used as the basis for most current stage and federal grants -- show Fairfax with only 533,400 residents. That 40,000 difference grows to 56,000 in their 1980 population projections and to 176,000 in predictions for the year 2000.

In Alexandria, local officials predicted last year the city's 1980 population would be 121,000 (a figure since revised to 116,900). But the state projected Alexandria's 1980 city population at 104,500, which city officials say is absurdly low.

The city has been so upset at what it considers state underestimating that two years ago it considered asking the U.S. Census Bureau to do a mini-census. The idea was dropped because it would have cost $75,000 to $100,000, said the city's chief comprehensive planner George Colyer.

Several mini-censuses have been done recently in Virginia, in several small towns, in Richmond and surrounding Henrico and Chesterfield counties. In Richmond and Henrico, the Tayloe-Murphy estimates were less than 1 percent off. In Chesterfield, Tayloe-Murphy's estimates were 6 percent off, "but then county officials were 12 percent off," said Tayloe-Murphy's Julie Martin.

Alexandria did lose several thousand residents when the 2,100-unit Shirley-Duke apartment complex closed two years ago and more than half the 5,000 residents left the city.

Shirley-Duke will not be counted in the 1980 census this month, important for political redistricting purposes, although the project is expected to reopen in two years with more than 4,200 residents. Those residents eventually will be counted, however, when the state and city make their annual population estimates for state and federal aid programs.

Cities and counties can appeal the annual state estimates to the U.S. Census Bureau.

"We've filed appeals to the census every year for the past four or five years; almost all local jurisdictions have," said Fairfax County's Sheatsky. "But all appeals have been denied. In fact, the census has granted only one large city appeal in the nation, in Houston, where there had been an annexation."

COG's chief of data and forecasts, John McClain, predicts the 1980 census will prove local population estimates are closer to the truth than those of the state and Tayloe-Murphy.

"Their methods are not really as sophisticated as ours," said McClain. "We use the housing inventory and keep track of new housing and demolitions. They claim we don't keep track of demolitions but we do."

COG and the localities here figure population primarily by multiplying households by average household size, as determined by surveys.

Tayloe-Murphy says that method can be very accurate theoretically but, in reality, tends to exaggerate population. Tayloe-Murphy uses an average of three statistical methods, similar to the U.S. Census, that tabulates things like births, deaths, addresses on income tax returns and changes in school enrollments.