Archibald Cox, rectitude with a bow tie, came to town this week to instruct the Senate in its duties and to ask it do a difficult thing: to read the Stein report on Edwin Meese III, President Reagan's nominee for attorney general.

Cox, the former Watergate special prosecutor who is chairman of Common Cause, says he believes that if the senators read the report on Meese by independent counsel Jacob Stein, they would block Meese's appointment.

Cox knows that he will be heard as a voice from the past -- he is, at 72, "statutorily senile" at Harvard Law School. He understands that his opposition to the ultraconservative Meese will be seen as philosophical hostility. Nonetheless, he has asked to testify when Meese's name is resubmitted to the Senate.

At his news conference, Cox was treated to the withering local wisdom that Meese was, for practical purposes, confirmed on Nov. 6 when Reagan won. Cox did not disagree. He simply observed that the prospect of inevitable defeat is not an excuse for running away from a fight about principle.

The principle, he says, is that Meese has demonstrated a blindness to ethical and moral considerations that makes him unfit to be the nation's chief law-enforcement officer.

The Stein report, a 385-page examination of the circumstances under which five Californians -- all of whom helped Meese in financial matters -- ended up with federal jobs.

Stein's charge was to ascertain whether Meese should be indicted in any of the instances. He concluded that he should not. The report was hailed by the administration as an exoneration of Meese. Reagan called it "gratifying."

As far as Cox and Common Cause are concerned, the report is a sword, not a shield.

Of seven Senate Judiciary Committee members interviewed, only Sen. Howard M. Metzenbaum (D-Ohio), who asked questions that led Meese to ask for an independent investigation, has read it. The others say they intend to.

Cox, in tones as mild as the weather, held up the banner of excellence, which is seldom raised in the Reagan administration, which does not regard even indictability as a bar to service. Even if Meese were a legal scholar of some distinction, his indifference to an appearance of conflict of interest would disqualify him.

Republicans on the Judiciary Committee speak highly of Meese, who has often been short of cash but never of loyalty to Reagan.

Sen. Jeremiah Denton (R-Ala.) said, "I like him, and I like his wife.

Sen. John P. East (R-N.C.) said he finds Meese "a man of character and integrity and experience, who has the trust and confidence of the president."

Sen. Paul Laxalt (R-Nev.) said he sees "difficulties, but nothing insurmountable" from the Common Cause intervention. "People see him Meese as a decent guy who went through his baptism of fire pretty well."

Sen. Alan K. Simpson (R-Wyo.), who was once Cox's student and "will listen to him on anything," said he thinks that Meese's confirmation is a forgone conclusion. He doubts that Metzenbaum "wants to go through it all again."

He notes that the tiger on Metzenbaum's staff, Roy Meyers, who did the digging on Meese's financial transactions, has left the senator.

"When any guy with the papers moves on, all of us lose some of our powers," Simpson said. "I think Howard will be carrying a heavy burden. We have been through the anguish; we have all made our own judgments."

Simpson also said he thinks that Metzenbaum's role as a crusader has been hurt by the embarrassment he suffered over a $250,000 finder's fee that he received as a result of a phone call he made to expedite the sale of the Hay-Adams Hotel. A real estate board cleared him of wrongdoing, but in the clamor, he returned the money.

Metzenbaum says the flap is "irrelevant." He is preparing to question Meese again about additional details turned up in the Stein report.

Cox does not say that Meese's benefactors got their plums as a direct result. His point is that the man who would be attorney general must be a model of ethical sensitivity.

But the evidence is that the country has accepted Reagan's low standard for public servants.

It is not enough, Cox said, for an attorney general to be able to say, "I have been found not to be a crook."

Demoralized Democrats show no stomach for a rematch with Meese. They think it's another fight with Reagan that they are bound to lose.