AFTER a weekend of extraordinary public hearings that left the charges of sexual harassment against Judge Clarence Thomas thoroughly aired, if not resolved, the Senate has acted. Judge Thomas will sit on the Supreme Court of the United States.Open-mindedness is a strength in a judge, a strength that Thomas claimed during his earlier confirmation process. Following the ordeal of the last few days, he ought to be immeasurably more open to such critical legal issues as the Fifth Amendment protection against self-incrimination, due process of law, equality of treatment under the law, the right to privacy, and, yes, sexual harassment. The nominee's chief area of strength, before the weekend's hearings, was character. He seemed a man of firm principles. Those credentials of character were impugned, however, by the harassment allegations. Surveys indicate that a majority of Americans are with the judge, having decided either that the charges were false, or that the judge has to be given the benefit of the doubt. Other millions of Americans are firmly convinced of the truth of the allegations against Thomas. Clarence Thomas is not the first person to join the court under a cloud. Justice Hugo Black, for example, was known to have been a member of the Ku Klux Klan. His record on the court, over more than three decades, dispelled the cloud. We hope Thomas can do the same. The nominee, the senators, the public - all have condemned the process by which the allegations were handled. But once Anita Hill made it clear she would drop her demand for anonymity, a full public airing was inevitable. And the proceedings themselves were fair, under the circumstances. All sides were heard, though the charged political emotions of committee members sometimes got out of hand. The proceedings were not, as one senator claimed, nonadversarial. It may not have been a "trial," but prosecutorial methods were much in evidence. The Judiciary Committee owes it to future nominees - and to those who step forward with potentially damaging evidence against them - to have a clearer set of rules governing the treatment of serious charges that threaten reputations. Senators owe it to themselves and the country to devise a clear set of principles by which future nominees are to be scrutinized, so that the ground rules are clearer and all know where confirmation hearings will probe. The Supreme Court of the United States, Justice Thomas included, now needs the support of the American people.