IN A HUGE commercial and industrial metropolis like Chicago or New York, the real job of a mayor is to exert a commanding discipline over the city's public life. Richard J. Daley did this in Chicago in the 31 years he was mayor. Harold Washington, after finally gaining a majority of the aldermen last year, was very much in command. That is why many Chicagoans who were never his supporters were made uneasy by his death yesterday.

Celebrated after his narrow victory in 1983 as Chicago's first black mayor, Mr. Washington insisted that he should be known as Chicago's first reform mayor. Mayor Daley spent much of his time filling places in city government with loyal members of his Democratic machine. Mayor Washington spent much time getting rid of what he regarded as incompetent hacks, with the aim of improving the delivery of government services. Chicagoans must judge whether he achieved this goal. But he did succeed in taking the edge off the racial hostility that made it almost impossible for him to campaign in many white neighborhoods in 1983; voting was still racially polarized when he ran for reelection in 1987, but there was less hatred in the air.

Harold Washington started off in South Side politics at 13 in 1935 and was a legislator from 1964 to 1983. He was no political innocent. He brought to his duties an impressive intellect and a useful cheerfulness. The question for Chicago is whether his interim successor, Alderman David Orr of the lakefront 49th Ward, or whomever the aldermen choose to succeed him, has big enough shoulders to take command as Mayors Daley and Washington did -- and those who served in between did no