For the first time since the nation started counting noses in 1790, local governments are being given a chance this summer to look over U.S. Census figures before they're released officially.

Officials in the Washington area, like those in many parts of the country, generally don't like what they've seen so far, believing that there are more people in their jurisdiction than the census takers have found.

The Census Bureau acknowledges that the preliminary counts are low and says it will try to find the uncounted population if local officials point the way. They expect the complete counts to be higher -- though probably not by much -- when the official figures are issued starting next month.

"These counts aren't completely finished," said Ken Field, a public information officer for the Census Bureau. "We're doing our own review, too, and they're subject to change.

"Ten years ago we had more than a thousand lawsuits challenging the results.

We won almost all of them. But this time we want to eliminate [the confrontations]."

"We're not completely satisfied," said Marie Friedman, the official in the Montgomery County administrator's office who is in charge of the local census review. "We think we have the data to indicate there should be a higher count. . . . But certainly they're making a step in the right direction. It's not as complete a review as we had hoped for. But it helps."

The census figures are important. The final counts will be used for distributing about $50 billion a year in federal aid, a source of funds that local and state governments increasingly rely on.

The census figures also are used for apportioning seats in Congress and in state legislatures -- a task that the Supreme Court has ruled must be done strictly on the basis of one man-one vote.

The latest group of preliminary figures for the Washington area show major population losses since 1970 in Arlingtion, Alexandria, and Falls Church, Virginia's older inner suburbs, and major gains in Prince William and Loudoun counties, the newer suburbs that lie far beyond the Beltway.

Figures for Fairfax County were not yet available.

But preliminary figures issued earlier for Prince George's, Montgomery and other counties in Maryland show a similar pattern -- with older suburbs, like older cities, losing people, while new communities flourish on what used to be farmland.

So far the preliminary population figures for every local community, except Falls Church, are lower than its own population forecasters expected. But except for Alexandria, where there is an 18 percent discrepancy, the differences are not large.

The figures include:

Alexandria -- Population fell from 110,927 in 1970 to 100,593 this year -- a 9.3 percent decline. At the same time the number of housing units rose by 7,818. The census Bureau said average houshold per household to 2.07, apparently reflecting a loss of families with children that accounted for the population decline.

Arlington County -- The population loss here was 13.6 percent since 1970 -- down to 150,646 this year. Even so, the number of housing units in Arlington rose by 5.4 percent to 75,105. Average houshold size was exactly the same as Alexandria -- 2.07.

Falls Church -- The preliminary census figures put its population at 9,382, a loss of 12.9 percent during the 1970s.

Farther away from Washington, the pattern is sharply different:

Charles County -- Population surged by 43 percent to 68,428. The number of housing units increased considerably more, by 73 percent, indicating that even in the metropolitan fringe households are becoming smaller. Average size now is 3.35.

Loudoun County -- The county had the fastest growth rate in the metropolitan area -- a 55 percent increase that brought its population up to 57,624. The number of housing units in Loudoun rose by almost 75 percent.

Prince William County -- The preliminary census report says that population climbed during the decade to 142,199 -- an increase of 49.5 percent. pAlthough the housing stock almost doubled, average houshold size declined from 3.88 to 3.23.

Local planners had estimated that average household size was still about 3.6.

The preliminary figures are based on a considerable amount of work since April 1, the day of the nose count.

The first phase was carried out by mail. Forms were sent to every household the Census Bureau knew about from mailing lists and a preliminary canvass. In the Washington area about 82 percent of the households mailed back the forms.

Then about 4,000 census takers fanned out through the area trying to reach the others.

By early July, when the data was collected for the preliminary counts, the Census Bureau either had a form for every household or had knocked on each door four times, Census officials said. Lincoln Steigerwalt, a bureau official who helped plan the 1980 census, said the households where no on has replied yet have been grouped into two categories -- vacant "if we have good reason to believe they are that way" or unclassified "if the [census taker] has some doubt if it's vacant or occupied."

In the census takers' second sweep, which is going on now, Steigerwalt said all the vacant and unclassified units are being visited again, usually by a different census take than the one who went the first time.

In most of the area communities where preliminary figures have been released so far, the Census Bureau has found about as many housing units as local officials thought existed or slightly more. But a significant number of units still are unclassified -- ranging from about 4.5 percent or 10,500 units in Prince George's County, to about one percent or 745 units in Arlington.

Local officials also believe the vacancy rates that the preliminary figures show -- 4 to 6 percent -- are probably too high, and that more people will be found when the unclassified units are rechecked.

"I'll honestly admit I think we over-estimated household size," said Prince William planner James Gracie. "The census probably will find some more people out here but not as many as we thought there were.

"It looks like they did a good job of finding all the housing units," Gracie said. "But I think it's great that they're giving us a chance to check it out."