To put Tuesday's Chicago mayoral election in context, it helps to remember a line from the 1968 Kerner report on race relations in America's cities.

"What white Americans have never fully understood--but what the Negro can never forget--is that white society is deeply implicated in the ghetto," said the report, commissioned by President Lyndon B. Johnson after the wave of urban violence in 1966-67. "White institutions created it, white institutions maintain it, and white society condones it."

Harold Washington came out of Chicago's South Side ghetto to win the mayor's office. The campaign that produced his narrow victory was the single most searing political event I have witnessed in this country since the chaotic year in which the Kerner Commission report was published.

The commission's finding that America was becoming "two societies, one black, one white--separate and unequal" was amply confirmed by the pattern of the vote that gave Washington his narrow victory over Republican nominee Bernard E. Epton. Black voters voted almost 100 percent for the black candidate. White voters voted more than 80 percent for the white candidate.

The gap of perceptions was even deeper. Reporting the last two weeks of the campaign, I was struck again and again by the mirror-image reversals of black and white attitudes.

Washington's candidacy was seen by fellow blacks as an affirmation of citizenship rights and responsibilities long denied them. "He is our John the Baptist," the Rev. B. Herbert Martin said last Saturday, "crying 'the Kingdom is at hand.'"

That same candidacy was seen by most whites as a threat of black domination, if not worse. A white woman Washington worker, wearing his button on her coat, was told by a passing Epton supporter, "He wins, you'll get raped."

In supporting Republican Epton, many of his prominent white backers said they were nobly setting aside their normal Democratic partisanship to save the city from a man who was chronically and occasionally criminally sloppy about paying his bills. "If a white candidate had his record," said defecting Democratic Alderman Roman Pucinski, "we'd run him out of town."

To blacks, the income tax charges that sent Washington briefly to jail a decade ago were themselves an expression of racism. Many of them cited a pillar of the Chicago bar, a nationally prominent white attorney, who acknowledged that he, too, had failed to file returns for two years--and was not disciplined by the bar association or prosecuted by the U.S. attorney.

"They say play by the rules," said a warmup speaker at one Washington campaign appearance, "but the rules aren't the same for us as for them."

But now the election is over, and the task of governing Chicago, a city with at least its share of economic and social problems, falls on Washington's broad shoulders.

The hunch here is that he is going to measure up to the task. Unlike Epton, a meek creature who would have been swallowed in two bites by the sharks on the city council, Washington is a tough and tested politician who can play the Chicago game on anyone's terms.

He is under no illusions about the size of the job he faces. Last October, when the possibility of his becoming mayor was no more than a gleam in a few dreamers' eyes, he laid out in the starkest terms for Leonard Downie of The Washington Post and me the fiscal and political barriers he would have to overcome to deliver on the expectations his own election would create. "It's more than a one-term task," he said.

And there is a basis for reconciliation. Many of the leaders of the Chicago business establishment rallied belatedly to Washington's cause, after sinking literally millions of dollars into the campaigns of Mayor Jane Byrne and Cook County State's Attorney Richard M. Daley, whose split of the white vote allowed Washington to win the Democratic nomination.

Key lawyers and executives showed up for Washington's general election fund-raiser and signed onto his transition planning team--recognizing in his leadership the best potential for pulling the city together to face its problems.

Reconciling the white ethnic voters will be a lot tougher. But there is a precedent. It can be found in Mr. Dooley's semi-fictional account of what happened in 1894, when "Bill O'Broyn," the Populist candidate for Senate, came to Finucane's Hall. There was such turmoil, said Finley Peter Dunne's imaginary commentator, that "the quartet stopped singin' and th' tinor wint out an' got a brick" to use on the "arnychist."

But "O'Broyn" turned them around with his speech, finally saying, "Disperse peaceably to ye'er homes. The hall is rinted be th' hour."

"An' thin," said Mr. Dooley, finishing the tale in a fashion Washington would understand, "he wint out with th' quartet chasin' him. He'd niglicted to pay f'r their warbles."