The first numbers from the 2010 Census, to be released tomorrow, are the state population totals that have been the basis of the proportional division of seats in the House of Representatives since the nation’s early days. The number of House seats has been fixed at 435 since 1913, but there have been numerous tweaks in the methodology used to divide them up — and debate continues today.

The U.S. Constitution requires that a census be taken every 10 years in order to divide the House of Representatives “among the several States according to their respective numbers, counting the whole number of persons in each State,” except for slaves, who, until the late 1800s, were counted as three-fifths of a person, and certain Indians. Under federal law, the Census Bureau must deliver population totals to the president nine months after Census Day, which now means the deadline is Dec. 31. The reapportioned Congress will convene in 2013.

The first numbers for each state will include a total of residents, as well as an apportionment count that will also include any members of the military or federal employees overseas (and any dependents living with them) who can be allocated back to a particular state. In 2000, more than half a million Americans overseas were included in state apportionment counts. These overseas Americans also were included in the apportionment counts from the 1970 and 1990 censuses. (They won’t be included in the set of totals that are used to redistrict within states.)

For more than a century after the first census was taken in 1790, the number of House seats grew with the country, but the number has been fixed at 435 since 1913.

The Constitution requires that each state be allotted at least one representative, but does not provide a solution to the inevitable problem of how to avoid fractional allocations of representatives because districts do not cross state lines. Various methods have been tried, and since 1940, the remaining 385 seats have been doled out based on a formula called the “method of equal proportions.”

Under this method, after the first 50 seats have been distributed, the 51st seat is given to the state with the highest priority based on dividing its population by the geometric mean of its current and next House seats. The results for the subsequent seats are determined the same way.

As the Congressional Research Service points out in a recent paper, there remains debate as to whether this is the fairest method, but it was upheld by the U.S. Supreme Court in 1991 in a ruling on a lawsuit by Montana.

Other challenges to the apportionment process have questioned the method used to come up with population totals upon which apportionment is based. There have been at least two recent unsuccessful challenges to the inclusion of federal employees and members of the military who are stationed overseas.

In 1991, the state of Massachusetts sued unsuccessfully to overturn the apportionment process, arguing that it was improper to include overseas federal employees in the apportionment count. Massachusetts had lost a seat to Washington because that state benefited from a larger count of federal employees stationed overseas. Utah made a related argument in a lawsuit after the 2000 Census, stating that it would have gained one more seat if Mormon missionaries stationed overseas had been included, but it lost that case in federal court.

Other proposals have tried to exclude unauthorized immigrants (or all immigrants) from the census itself or from the population count used to apportion House seats. As the Congressional Research Service concludes in a paper about immigrants and the census, it appears that in order for this to happen, it would require an amendment to the Constitution, which now mandates “an actual enumeration” of “the whole number of persons” in the U.S.

For more of the latest developments on the 2010 census, read “Evaluating How Census 2010 Reached Hard-to-Count Groups,” a summary of a new GAO report that finds that the Census Bureau did a better job in 2010 than it had in 2000 reaching out to “hard-to-count” groups, such as minorities and renters, who are more likely to be missed by census-takers than other Americans. And find other related reports at All Things Census.