Julian Bond, the nationally prominent Georgia legislator, once complained to a reporter that "white, liberal good-government types" were the scourage of black politicians.

Only partly in jest, he explained that whenever blacks got into political office and tried the same shenanigans as their white predecessors, the good-government types were there to blow the whistle.

A strain of that argument was heard here recently when Atlanta's Maynard Jackson, in his second term as the only black big-city mayor in the Deep South, confronted evidence that his black police chief, A. Reginald Eaves, had encouraged blacks to cheat on a police promotion exam and had engineered a cover-up of the affair.

"I must tell you," Jackson said after the release of a report outlining Eaves' alleged misdeeds, "that my job is greatly complicated by a most disturbing fact, the importance of which I have to consider.

"I know and everybody else knows we live in a city where for years white examinees were taken aside and tutored."

In fact, that's not true. While police in the past, according to reliable sources, were merely promoted over the handful of black police without any testing. But Jackson made his dislemma clear nonetheless.

Jackson, who early in his career as mayor enjoyed a mandate of support from blacks for whatever action he took, has dashed their expectations on several occasions.

Before his landslide reelection last fall (he polled more than 90 percent of the black vote and about a third of the white), Jackson fired a popular black administrator and broke the back of a municipal garbage strike by firing the strikers, most of whom were black.

Yet Atlanta's blacks up to now have maintained strong unity behind Jackson.After she was fired, the administrator, Emma Darnell, who had snarled the city's prrchasing a process by painstaking insistence on affirmative-action guarnatees ran against Jackson for mayor. She got less than 5 percent of the vote, despite having wide sympathy in the black community.

The custer of Eaves on Friday however, apparently marks the first real evidence of the beginning of some black backlash against Jackson, City hall insidere were explaining this weekend that the reason Jackson was fled for a week before taking action on Eaves was that a direct firing would have led to what would have amounted to a trial by the biracial city council - which Eaves might have won.

As it was, Jackson secured Eaves resignation, effective in June and suspended him until then.

The effect of Eaves' departure on Jackson's political future us hard to gange. Jackson has said he does not intend to run for a third term in 1981. He is reported to be interested in a Cabinet-level post or a diplomatic assignment in Africa.

Clearly, his chances at an administrative post would have been damaged by a refusal to deal with Eaves.