What kind of justices will the next United States president appoint to the Supreme Court? It is the kind of question that influences some voters. At present five of the nine justices are in their 70s and vacancies will probably occur. (The average president makes a couple of choices in a four-year term.) Jimmy Carter was the only full-term president who had no appointment. Mr. Nixon, by contrast, named four justices and all four of them are still on the court; they are Chief Justice Burger and Associate Justices Blackmun, Powell, and Rehnquist. That leaves five others; each was named by a different president: Brennan (Eisenhower); White (Kennedy); Marshall, the first black, (Johnson); Stevens (Ford); and O'Connor, the first woman (Reagan).
Students dispute how much a president's selection can influence the court's philosophy. It depends on personality and chance. Many justices have surprised the presidents who appointed them by showing their independence after being confirmed; the disappointed Theodore Roosevelt exclaimed after a decision by Oliver Wendell Holmes: ''I could carve a justice with more backbone out of a banana.''
Richard Nixon did much to politicize the court issue; he thought the court under Chief Justice Warren had become too ''liberal'' and promised in his election campaign to name judges ''who share my conservative philosophy.'' He made law and order an issue in 1968, he bought prime time on election eve 1970 to promise ''to give the peace forces more muscle to deal with the criminal forces'' and he had two appointees rejected by the Senate while a third voluntarily withdrew. What he was after, he affirmed, was ''judicial conservatives'' who shared his desire to defend ''the peace forces.''
At some times in its history the Supreme Court has acted as a kind of legislative body; it did so for a time when the conservative majority blocked the early New Deal. Later it gave way. The public wants a court of which it can be proud. Often it does not understand the technical niceties. But it knows the court is not just a court of law; it is the instrument under America's unique separation of powers that reconciles constitutional verities to the times we live in. It links past experience with future hopes. It demands people steeped in diverse fields, philosophers with vision.
There is always the difficulty that this philosophical bent will be overdone. Legal student Martin Shapiro, writing on ''The New American Political System'' in an essay in 1978 argued that the Warren court had become a ''super legislature.'' He asserted that in the past 25 years the court had initiated some ''five major policies.'' These, he said, affected school desegregation; legislative reapportionment; changes in the criminal justice system (including procedure in police searches and the ''exclusionary rule'' barring evidence illegally obtained); revision of obscenity laws and, revision of birth control and abortion laws. Many of the individual opinions, he claimed, state the author's policy preferences ''dressed up in cursory and pro forma legal argument.''
Some students don't think this a bad thing. John Peter Giraudo, of the University of California, declares, ''Most social reforms in the United States since the Second World War have been instituted by the judiciary.'' Certainly the Supreme Court often exercises directional guidance in social and political matters. It is sometimes hard to explain what holds the system together. How in a democratic society, asks Harvard's Alan M. Dershowitz, ''can nine unelected and politically nonresponsible men overrule the policy choices of state legislatures, Congress, popular referenda and presidents?'' Nobody can quite say. Why should judges have the last word, asks the professor, on such emotional issues as abortion, busing, pornography, and even national security? Like smoldering volcanoes, he observes, ''they erupt periodically, usually when the court is under attack for having rendered a particularly unpopular or controversial decision.''
Watching the black-robed court over the years in its tremendous Greek temple on Capitol Hill one is awed. The judges don't wear wigs like their British counterparts but the usher chants the medieval cry as they enter, ''Oh yez! Oh yez! Oh yez!'' Special circumstances always surround the court. Today the four Nixon judges are specially watched (they don't vote as a bloc despite their common origin). There is the item that a Democratic president hasn't named a justice since LBJ picked Thurgood Marshall in 1967. Another factor is the unusual number of family and social issues that are finding their emotional way to the court.
All in all, if President Reagan is reelected and makes the normal number of court appointments in the next four years his shadow could be lengthened over the land for a generation.