ELEANOR DUNHAM has a right to be furious. Her sister, Constance Mellon, was raped and murdered in her Alexandria town house in 1980. Frank Weston, the man who has been indicted for the killing -- and who has described the crime in detail to the police -- is sitting in a Pittsburgh jail awaiting sentencing for another murder committed in that city, for which he was convicted in 1981. He cannot be extradited to Virginia to stand trial in the Mellon case until he is sentenced for the other crime. What is holding it up? A judge who claims that he has a "mind-boggling" caseload and who, in four years, hasn't gotten around to sentencing Mr. Weston.

The Pittsburgh jurist, Court of Common Pleas Judge Henry R. Smith Jr., surely is busy and has a difficult, burdensome job. So does every other criminal court judge in the country. It is not an easy duty, particularly for thoughtful and humane judges who want to carry out the law while taking every prisoner's special circumstances into consideration. But the essence of a judge's responsibility is to make decisions. That is why he is on the bench. A jurist who cannot bring himself to keep up with the workload and make the hard decisions does not belong in this high position.

Pittsburgh is short of criminal court judges. Perhaps the city should have more, or perhaps the workload should be redistributed so that one judge would not have 113 convicted criminals awaiting sentencing, as Judge Smith does. Perhaps the higher courts of the state should exercise more supervision. The Pennsylvania Supreme Court ordered Judge Smith to sentence Frank Weston in September 1983 -- which was already 21/2 years after he was convicted -- and he has not yet done so. But at the very least, Judge Smith's backlog ought to be attacked directly. Days can be set aside for sentencing. Priorities can be assigned, with dangerous offenders and those wanted in other states given first attention.

With every passing day, murder charges become harder to prove. Witnesses die, move away or forget exact details of events. Physical evidence deteriorates or is misplaced. A case becomes less urgent in the minds of the police, the public and even, sometimes, the victim's family. Mrs. Dunham is determined to see that this does not happen in the case of the man who has been indicted for murdering her sister. She has every right to insist on prompt justice in Pittsburgh so that the Alexandria trial can proceed.