The way the U.S. House of Representatives is to be constituted is specified in Article 1, Section 2 of the U.S. Constitution.
U.S. Constitution (Article 1, Section 2)
The House of Representatives shall be composed of members chosen every second year by the people of the several states... No person shall be a representative who shall not have attained to the age of twenty-five years, and been seven years a citizen of the United States, and who shall not, when elected, be an inhabitant of that state in which he shall be chosen.
Representatives and direct taxes shall be apportioned among the several states which may be included within this Union, according to their respective numbers... The actual enumeration shall be made within three years after the first meeting of the Congress of the United States, and within every subsequent term of ten years in such manner as they shall by law direct. The number of representatives shall not exceed one for every thirty thousand, but each state shall have at least one representative; and until such enumeration shall be made, the state of New Hampshire shall be entitled to choose three, Massachusetts eight, Rhode Island and Providence Plantations one, Connecticut five, New-York six, New- Jersey four, Pennsylvania eight, Delaware one, Maryland six, Virginia ten, North-Carolina five, South-Carolina five, and Georgia three.
Over the years, there has been (and continues to be) many battles over apportionment of the U.S. House of Representatives.
1787 Constitution drafted by the Constitutional Convention
1790 First Census
1791 After much debate, Congress approved a bill for a 120 member House and Hamilton's method to apportion seats among the states. Hamilton's method won out over Jefferson's method. Hamilton's method was supported by the Federalists while Jefferson's method was supported by the Republicans.
1791 President Washington vetoes the above bill (first veto in US history!).
House, unable to override the veto, passed a new bill for a 105
member House and Jefferson's method to apportion seats among the
(This method was used until 1840.)
1822 Rep. William Lowndes (SC) proposed an apportionment method now known as the Lowndes method. It never passed.
1832 John Quincy Adams (former President and, at this time, a representative from Massachusetts) proposes the Adam's method for apportionment. It fails.
1832 Senator Daniel Webster (Mass) proposes Webster's method. It fails.
1832 Congress passes a bill that retains Jefferson's method but changes the size of the House to 240.
1842 Webster's method is adopted and the size of the House is reduced to 223.
1852 Rep. Samuel Vinton (Ohio) proposed a bill adopting Hamilton's method with a House size of 233. Congress passes this bill with a change to a House size of 234, a size for which Hamilton's and Webster's methods give the same apportionment.
1872 A very confusing year! First the House size was chosen to be 283 so that Hamilton's and Webster's methods would again agree. After much political infighting, 9 more seats were added and the final apportionment did not agree with either method.
1876 Rutherford B. Hayes became President based on the botched apportionment of 1872. The electoral college vote was 185 for Hayes and 184 for Tilden. Tilden would have won if the correct apportionment as required by law had been used.
1880 The Alabama Paradox surfaced as a major flaw of Hamilton's method.
1882 Concerns continued over the flaws in Hamilton's method. Congress passed a bill that kept Hamilton's method but changed the House size to 325 so that Hamilton's method gave the same apportionment as Webster's.
1901 The Census Bureau gave Congress tables showing apportionment based on Hamilton's method for all House sizes between 350 and 400.
1901 For all House sizes in this range (except for 357) Colorado would get 3 seats. For 357, Colorado would get 2 seats. Rep. Albert Hopkins (IL), chm of the House Committee on Apportionment, submitted a bill using a House size of 357--causing an uproar.
1901 Congress defeated Hopkin's bill and instead adopted Webster's method with a House size of 386.
1907 Oklahoma joined the union and the New States Paradox was discovered as a result.
1911 Webster's method was readopted with a House size of 433. A provision was made to give Arizona and New Mexico each 1 seat if they were admitted to the union.
1911 Joseph Hill (chief statistician of the Census Bureau) proposed the Huntington-Hill method.
1921 No reapportionment was done after the 1920 census IN DIRECT VIOLATION OF THE CONSTITUTION!
1931 Webster's method was adopted with a House size of 435.
1941 The Huntington-Hill method was adopted with a House size of 435
1990 The U.S. Census Bureau, for only the second time since 1900, allocated Defense Department overseas employees for apportionment purposes. This resulted in Massachusetts losing a seat to Washington. Massachusetts filed suit.
1992 Overruling a U. S. district court decision, the U. S. Supreme Court ruled against Massachusetts on technical grounds involving "the separation of powers and the unique constitutional position of the President." (The President is charged with calculating and transmitting the apportionment to Congress.)
1992 Montana challenged the constitutionality of the Huntington-Hill method (Montana v. US Dept. of Commerce). The Supreme Court upheld the method. Montana was upset because it lost a seat to Washington based on the results of the 1990 census.