The 1920 census found for the first time that urban residents were a majority of the population.

Farm-state representatives, fully aware that House seats are reapportioned among the states every 10 years based on the census, charged that rural residents had been undercounted. They blocked reapportionment for a decade, but failed to win a constitutional amendment to bar counting of aliens, who lived mainly in northern cities.

Those debates have a familiar ring. The April 1, 1990, decennial census, seeking to count every resident in the country through questionnaires sent to 106 million houses and apartments, is 27 months away, with the Census Bureau required to report the count by Dec. 31, 1990, for House reapportionment purposes.Excluding Illegal Aliens

But fierce battles are under way on whether to adjust for alleged undercounts, particularly of blacks and Hispanics, and whether to exclude illegal aliens from the count. Currently, the bureau intends to do neither, but legislation or lawsuits could change its plans.

Political power and money are the overarching issues.

Kimball Brace, president of Election Data Services Inc., has projected that based on 1987 population figures and assuming the Census Bureau takes no steps in 1990 to adjust the undercount or to exclude illegal aliens from the count:Virginia, Arizona and Georgia will each gain one House seat compared with 1980, Texas and Florida will each gain three seats, and California will gain four. Michigan, New York, Ohio and Pennsylvania will each lose two seats, while Illinois, Iowa, Kansas, Massachusetts and West Virginia will each lose one.

However, an undercount adjustment or an exclusion of illegals would change these figures. Some states, such as New York, have a disproportionate number of blacks, Hispanics or illegals. And small alterations can have big impacts: in 1980, Indiana would have been allocated the 435th House seat (instead of New York) if its population had been 7,222 greater.School and Water Districts

In addition, within each state, the legislatures draw up the boundaries of each congressional district based on population in different communities, counties, neighborhoods and blocks. The boundaries of state legislature districts, water districts, school districts and the like are similarly drawn.

How the census allocates representation in turn helps determine which party will have more power. If the census found that predominantly Democratic New York City grew in population while the rest of the state lagged, the city could get a larger share of the state's congressional seats and state Assembly seats.

Moreover, from $33 billion to $50 billion a year in federal grants to states and localities is allocated according to population. New York City, in a 1980 suit that it lost a few weeks ago, claimed loss of up to $52 million a year in grants because blacks and Hispanics were under-

counted.

In the current disputes, spokesmen for minorities and some large cities want the Census Bureau to adjust its 1990 count to compensate for any undercount.

In 1980, according to the bureau, overall population was under-

counted by about 1 percent to 2 percent. (It made many estimates, but 1 to 2 percent are the figures usually cited.) Some of those not counted were legal residents who feared eviction or moved often; others were illegal aliens.

For blacks, however, the 1980 undercount is usually estimated at 5 or 6 percent, and for Hispanics a bit lower. Officials in cities like New York, Los Angeles and Detroit believe they will benefit from adjusting the undercount, and many observers believe an adjustment would help Democrats since the bulk of blacks and Hispanics live in areas that vote Democratic.

Technically, the issue is whether an accurate adjustment can be made. A National Academy of Sciences study panel and a number of Census Bureau experts who have studied the issue for years say it can.

Kirk Wolter, chief of the bureau's Statistical Research Division, believes the agency "could arrive at a single set of figures finally that would be better and more accurate than the original enumeration," providing accurate numbers for units as small as 300 to 500 households and in some cases possibly smaller.

American Statistical Association President Barbara Bailar, who recently left the Census Bureau as associate director for statistical standards, has said "we can do" an accurate adjustment.Some Express Doubts

Others are dubious. Charles Jones, the bureau's associate director in charge of the 1990 census, said that even if an acceptable adjustment is possible, he doubts it could be completed by Dec. 31, 1990, or even by April 1, 1991, in time to reapportion Congress and redistrict within states. "I don't think it can be done in time . . . . I'd feel comfortable having an extra six months but I'm not even sure of that."

For the Census Bureau, the major problem centers on adjustments for small areas, where the states and federal government need figures to draw up the boundaries of local units or to distribute money to counties, towns and school districts based on population. The larger the unit, the more accurate the adjustment. In small areas, an error of only a few people in an adjustment can produce worse figures than the original census count.

Rep. Mervyn Dymally (D-Calif.), chairman of the House subcommittee on census and population, has introduced a bill to force an adjustment, as has Sen. Daniel Patrick Moynihan (D-N.Y.).

In the view of Dymally aide TerriAnn Lowenthal, an adjustment would probably not shift more than one or two House seats from one state to another -- possibly California, Texas or Florida could gain a seat more than projected, New York might save one seat. Others believe Pennsylvania or Massachusetts might lose.

The administration, however, has turned down proposals to make an undercount adjustment. Undersecretary Robert Ortner of the Commerce Department, the Census Bureau's parent agency, declared Oct. 30, "The department does not intend to adjust the 1990 decennial count for purported undercount and overcount of population subgroups," adding, "We don't play with the numbers."

Brace and others said there is speculation that fear of Democratic gains was a factor in Commerce's decision. But, he noted, "There is no firm evidence."

However, Bailar resigned from the bureau last month -- in protest, according to sources in the statistical community, of the possibility that political factors had influenced the decision. She declined to discuss her reasons.

The other major dispute involves the counting of illegal aliens. Reps. Thomas E. Petri (R-Wis.), Barbara B. Kennelly (D-Conn.), Thomas J. Ridge (R-Pa.) and others want to bar such aliens from the 1990 count for the purpose of reapportionment. The bureau estimated that there were 3 million to 4 million illegal aliens residing in the United States on a regular basis in 1980, of whom 2 million were counted.

A Kennelly spokesman said that if illegal aliens were counted again, Connecticut and Pennsylvania were most likely to lose, while Texas, California and New York probably would benefit.

A Ridge-Kennelly bill introduced Dec. 18 also would force the bureau to include in the census count for purposes of reapportionment all U.S. service families overseas (up to 1 million people).

Roger Conner, who heads a group called the Federation for American Immigration Reform, said he doubts that framers of the Constitution wanted illegal aliens represented in Congress.

Conner said that to deduct illegal aliens, the bureau could include a census question asking people if they are citizens. This would show how many noncitizens had been counted in each jurisdiction.

The Census Bureau could then determine from Immigration and Naturalization Service records which of these noncitizens were permanent resident aliens legally in the United States who should not be excluded from the count, Conner said. The remaining figure would constitute the number of illegal aliens who had been counted, who could then be subtracted in apportioning seats.Constitutionality

Dymally contends excluding illegal aliens from the count is unconstitutional. The bureau agrees. "We count everyone except temporary residents. That's the way we read the Constitution," spokesman Jim Gorman said.

Bureau experts also believe INS records are inadequate for the calculations Conner has outlined. Beyond that, the bureau fears that a question on citizenship could imply the bureau is an immigration enforcement agency and scare many noncitizens into hiding or not answering -- including permanent resident aliens who are legally entitled to be here.

Most congressional observers give the Dymally undercount bill and the Petri, Ridge and Kennelly illegal aliens proposals little chance of enactment, because states that could lose from these bills would block them.

But New York and other jurisdictions may sue to force an under-

count adjustment. And regarding illegal aliens, Conner said, "We will file a lawsuit in a matter of weeks asking that only citizens and lawful permanent residents be counted."

After the last census, the Census Bureau estimated the 1980 under-

count, although it did not adjust the official count. One methodology, demographic analysis, starts with a base population figure from the last census, adds estimated immigration and births since then, and subtracts emigration and deaths.

By this method, the bureau concluded that the overall national undercount in 1980 ranged from 1 percent to 2.2 percent, and the black undercount from 5.6 percent to 6.5 percent.

A second method, permitting adjustment down to local levels, which demographic analysis cannot do, is a post-census survey. A survey of households is taken in some areas shortly after the census, and the results compared with the census findings for those areas. If the bureau did a 1990 adjustment, it would employ this method, using a 300,000-household sample.

"You find some in the second you didn't find in the first, some missing in the second you did find in the first," said Stephen Fienberg, dean of the College of Humanities and Social Sciences at Carnegie Mellon University, who favors adjusting for the undercount.

By comparing these results, an adjustment can be calculated for the sampled area and then projected to similar areas all over the country.

The bureau did such surveys after the 1980 census and ended with 12 different estimates of the 1980 undercount. They ranged from a national overcount of 1 percent for the population as a whole to a national undercount of 2.1 percent. For blacks, the estimates ranged from an undercount of 1.1 percent to an undercount of 7.8 percent; for Hispanics, from an undercount of zero to an undercount of 7.8 percent.

A problem with this method is error in matching the people from the original census with those in the sample for the same neighborhood. Names can be slightly different, for example.

A second problem is that no two areas are exactly alike. Errors are possible when extrapolating the results of the post-census survey from a sampled neighborhood to a similar neighborhood elsewhere.Compounding Inaccuracy?

Even a small error in matching the people or in projecting from one neighborhood to another can produce a result further from the truth than the original census count, said David Freedman, a professor of statistics at the University of California at Berkeley, who opposes adjustment.

"It's easy to get 90 percent accuracy," Freedman said, "but you have to get 99.9 percent accuracy" or you may end up with less valid figures, he said. "I don't think you can improve the count even at the state level."

However, on May 26, a National Academy of Sciences panel headed by Benjamin King of the Educational Testing Service declared that "census adjustment is technically feasible." It urged funds for a post-census survey.

Wolter said that in the analyses done after the 1980 census, a great deal of information needed to made adjustments -- as much as 9 percent -- had been missing, leading to the 12 diverse estimates, but since then, methods had been developed that could reduce missing data to 1 percent. Therefore, variations would be much less and a single set of figures could be worked out.

Jacob S. Siegel, a former bureau undercount expert now at Georgetown University, said an adjustment could probably improve the counts at the state level and perhaps in cities and counties of 100,000 or more. But estimates for small areas such as census tracts (about 4,000 people) or "thousands of government units with less than 10,000 people . . . are subject to such large error that adjustments may produce more errors than the original count."

There the matter rests; the experts disagree, the politicians disagree. It may be up to the courts to decide these fundamental issues.