WHEN THE NEW Congress was called to order last week, a biannual event took place: Another round in the game of amending the Constitution has begun.

Sen. Orrin Hatch (R-Utah), the incoming chairman of the Senate Judiciary subcommittee on constitutional amendments, already is hinting that his first priority will be an amendment outlawing racial quotas. Strom Thurmond (R-S.C.), the new chairman of the Senate Judiciary Committee, has promised an amendment limiting presidents to a single six-year term. And there certainly will be amendments intorduced to outlaw school busing for racial balance, to ban abortions and to restore prayer in public schools.

If any of these should survive the hearing process and be passed by both houses, they would go to the states for ratification, joining the pending Equal Rights Amendment and the D.C. Voting Rights Amendment. The Founding Fathers meant the process to be difficult. Of the more than 7,000 constitutional amendments proposed, just 26 have made it.

Even before the ink on the Constitution was dry, the cry went up for amendments. Twelve were quickly sent to the states for ratification. The 10 passed became the Bill of Rights, but the two that failed can be viewed with the perfect vision of history. One would have provided one congressman for every 50,000 persons, which means that today there would be more than 4,000 representatives. The other would have taken citizenship away from anyone accepting a title of nobility -- hardly a burning issue today.

Many of the amendments proposed since then, like some of today's proposals, were addressed to issues that no longer concern Americans. Here are only a few of the constitutional proposals -- some absurd, others just ahead of their time -- that have been dropped into the congressional hoppers in the past 191 years:

1789 -- Authorize Congress to establish a rule for the resettlement of the poor in the United States.

1809 -- Exculde government contractors from election to Congress.

1808 -- Choose presidents by lot from a list of retiring senators.

1808 -- Abolish the vice presidency.

1811 -- Prohibit the appointment to civil offices of relatives of senators and representatives.

1822 -- Devide the country into four presidential districts, with a president elected from each district.

1826 -- Limit the age of judges.

1828 -- Prevent dueling

1829 -- Apportion surplus federal money to the states.

1832 -- Establish a colony for "free people of color."

1848 -- Elect all postmasters.

1860 -- Establish two Senates, representing the North and the South, with all laws to be approved by both.

1864 -- Elect presidents alternately from free and slave states.

1869 -- Deny Chinese the right to vote.

1871 -- Establish an income tax.

1875 -- Limit presidents to one six-year term, then make them senators for life.

1876 -- Bar all ministers from federal office.

1881 -- Establish three vice presidents.

1884 -- Establish national marriage and divorce laws.

1890 -- Prohibit lotteries.

1892 -- Prohibit voting by aliens.

1893 -- Change name of the United States to the United States of the World.

1893 -- Establish a nationwide property tax.

1894 -- Limit Supreme Court justices to 10-year terms.

1894 -- Acknowledge God and the Christian religion.

1903 -- Give Congress the right to limit fortunes.

1904 -- Keep land equally divided among all people.

1907 -- Provide for a referendum on all amendments.

1913 -- Prohibit intermarriage between blacks and members of other races.

1914 -- Limit terms of all federal and state offices to 15 years.

1915 -- Provide that no war can be declared unless approved by voters in a majority of congressional districts.

1921 -- Empower Supreme Court to determine disability of presidents.

1929 -- Guanantee equal rights for men and women.

1936 -- Prevent representatives from taking compensation for services, speeches or debates.

1943 -- Maintain a balanced budget.

1963 -- Abolish the income tax.