Oyez! Oyez! Oyez! US Supreme Court is now in session

It's a monument to history, tradition, nostalgia. On its exterior, marble candelabra display carved panels with Justice holding sword and scales and the Three Fates weaving the thread of life.

Sixteen stately columns adorn the main entrance on the west. Above is incised ''Equal Justice Under Law.'' On the east side, more marble. Figures representing great lawgivers - Moses, Confucius, Solon - flanked by symbols typifying Means of Enforcing the Law, Tempering Justice With Mercy, Carrying on of Civilization, and Settlement of Disputes Between States.

Inside, solemn corridors and a museum of memorabilia. Then the focal point of this monument to justice - a spacious chamber of marble and mahogany. It's dignified, stately, but not pretentious. This is America's court of last resort. And, ostensibly, this is where ultimate justice is done.

Midmorning, at the stroke of 10, a sharp knock of a gavel and a marshal's chant commence the drama:

''Oyez! Oyez! Oyez! All persons having business before the Honorable, the Supreme Court of the United States, are now admonished to draw near and give their attention, for the Court is now sitting. God save the United States and this Honorable Court!''

A panel of black-robed wise men (and one wise woman) enters on cue and settles comfortably into ample leather-cushioned chairs slightly elevated above the assemblage of lawyers, government officials, reporters, and guests.

The chief justice, Warren Burger, slides into the center chair. On his right sits the senior associate justice. The second senior is on his left, and so on, alternating left and right by seniority.

Unlike other courts in the land, there is no jury. Plaintiffs and defendants are not called to the stand to be interrogated and cross-examined. Witnesses are nowhere to be seen.

All that has gone on before - in lower courts. In most cases, several lower courts. The issue is no longer the guilt or innocence of the defendant but the administration of the law and how it should be applied in a case.

Here it's only the lawyers who are in the spotlight. Each side has 30 minutes to present a case and submit to questions by the justices. For the counselor, it could be likened to taking orals for the doctor-of-law degree. The questions are often tough and penetrating. They come from all sides. But there is only one authoritative text that arguments must measure up to - the Constitution of the United States.

The cases are both civil and criminal. They range in subject from bankruptcy questions and monopolistic practices to police procedures in capital crimes and issues bearing on separation of church and state.

Justices mostly rely on what has gone on before. They often fall back on the reasoning of their famous predecessors. The chamber is filled with memories of former justices: John Jay and John Marshall, Louis D. Brandeis, Charles Evans Hughes, Felix Frankfurter, Oliver Wendell Holmes, and William Howard Taft.

Former Chief Justice Hughes called the workings of the court ''distinctly American in concept and function.'' French philosopher Alexis de Tocqueville concluded that ''a more imposing judicial power was never constituted by any people.''

The US Supreme Court has come a long way since Alexander Hamilton, in helping to frame it, saw it as the ''weakest'' branch of government. He opted for lifetime appointments to give justices lasting influence. Today some critics, mainly ultraconservatives, want to strip it of some of its power.

Starting as a tribunal of six, the court first convened in the Royal Exchange Building in New York City 194 years ago today, Feb. 1, 1790. It didn't hand down a formal opinion for three terms. Now nine-strong, the justices look at more than 5,000 cases a year; they hear arguments on 160 to 180 of them and write about 150 signed opinions a session.

This litigation explosion - today typical on all rungs of the US judicial ladder - has triggered calls for court reform from Chief Justice Burger and several of his colleagues. Among suggestions: an intermediate tribunal to screen cases before they reach the Supreme Court, and revised laws that would allow some litigation now mandated for high-court review to be resolved earlier in the judicial process. Congressional action would be needed for change.

Regardless, the court plugs on - hearing cases three days a week from October through June, debating constitutional principles behind closed doors in judicial conference, and dividing up the writing of opinions.

Through January of this term, the high tribunal has grabbed headlines by affirming the right of television viewers to make videotapes of programs for private use; confirming that the news media and the public have a right of access to the jury selection process; allowing $10 million in damages to the estate of celebrated nuclear plant worker Karen Silkwood to compensate for her exposure to radiation; and ruling that ''proportionality'' (comparing sentences for similar crimes where the death penalty has been decreed) need not be a factor in holding up executions.

Other, perhaps landmark, decisions are expected in the spring. They could involve the ''exclusionary rule,'' the time-honored practice of barring from trials police evidence that has been gathered in possible violation of defendants' rights; the granting of federal aid to students who attend private colleges that refuse to subscribe to antidiscrimination guidelines; and the church-state implications of erecting Christmas displays on municipal property.

Most scholars say that today's court, the so-called ''Burger court,'' carries a stamp of judicial activism as a result of landmark decisions on abortion, discrimination, and legislative authority. But unlike its predecessor, which was under the tutelage of Chief Justice Earl Warren, this court seems to lack a coherent social and political philosophy.

In a recent volume on the current court, Vincent Blasi, professor of civil liberties at Columbia Law School, describes it as having a ''rootless activism'' which encompasses a ''centrist philosophy - dominant, transcending most ideological divisions, but pragmatic in nature, lacking a central theme or any agenda.''

This ''centrist'' philosophy would seem to stem from what many see as the 2-4 -3 composition of the present court. On the liberal side are Justices William Brennan and Thurgood Marshall; in the center, Justices Byron White, Harry Blackmun, Lewis Powell Jr., and John Paul Stevens; and leaning to the right, Chief Justice Burger, William Rehnquist, and Sandra Day O'Connor.

Regardless of these generally accepted ideological stripes, rulings tend to be unpredictable. Coalitions form around specific issues and cases.

For instance, despite criticism of media excesses, the court has often been unanimous in affirming what it sees as clear-cut freedom of speech rights. And while a vocal minority on the left has won some support from the center for outlawing the death penalty as ''cruel and unusual punishment,'' the court as a whole has stopped short of such action.

Many judicial scholars feel that the high tribunal could well don unmistakably conservative colors if President Reagan is reelected and afforded a chance to realign the court. (One potential opponent, Sen. John Glenn of Ohio, is already staking this out as a campaign issue.)

Five of the justices are in their mid-70s and eligible for retirement. This group includes liberals Mr. Brennan and Mr. Marshall, while conservatives Mr. Rehnquist and Mrs. O'Connor are the youngest members of the court and likely to remain in office for years to come.