While blacks make up 47 percent of the population of this Mississippi capital city, they have about as much political clout as their slave ancestors, who built the white-columned city hall that commands the highest hill in town, black leaders say.

No black has been elected to city office here since 1912, when the city adopted a mayor-commission form of government elected at large. Nor did the balance of power change two weeks ago, when the white mayor fought off a slew of opponents, including Henry Kirksey, a black state legislator vying to become the first black mayor.

Kirksey, 65, didn't expect to win the election. Since 1960, white suburbs have been annexed three times, each time substantially diluting black voting strength just as it appeared blacks were about to become a majority. And each election, like this one, has been characterized by racial bloc voting and increasingly apathetic black voters.

"Many blacks in Jackson have just given up," Kirksey said as he watched the votes roll in and hope slip away in his campaign headquarters, a downtown warehouse littered with paper cups, chicken bones and broken dreams. "Blacks have never been able to elect anyone here in the past. So why should they bother to register and vote?"

Blacks have made substantial inroads invoting and achieving political power in Mississippi and across the Deep South since the 1965 Voting Rights Act banned literacy tests, poll taxes and other devices used to disqualify black voters in the Old South.

But black leaders and civil rights activists like Kirksey worry that white politicians of the New South will try to eliminate the gains through more subtle tactics if Congress fails to extend key provisions of the act when it comes up for renewal in August.

Already, they say, there is ample evidence of this in cities like Jackson and in counties and small towns across the South. Blacks are still denied a political voice in communities in which they make up a sizable chunk through at-large local elections, redistricting and annexing white suburbs to dilute minority voting strength.

One key provision of the Voting Rights Act that would expire is section 5, which requires six southern states, Alaska and parts of four other states -- all states with a history of discrimination -- to get Justice Department approval before changing election laws, a process known as pre-clearance. In 1976, the department objected to Jackson's annexation, which increased the city's tax base, because it diluted black voting strength in at-large elections. Still, residents of the annexed area were permitted to vote in 1977 municipal elections and all black candidates were defeated.

Again this month, in what some black leaders attacked as an "illegal election," the city allowed the largely white annexed areas to vote -- in spite of fresh Justice Department objections -- and all black candidates were defeated once more.

"The Voting Rights Act never guaranteed anyone the right to be elected," and city attorney Howard Ross, "just the right to express themselves at the ballot box. City hall is open five days a week and Saturdays upon request. We give ourselves a double hernia allowing everyone to register. And we'll put anyone in jail who tries to stop them. But don't cry to me if you don't register and vote. Even though that's easier than going to the store for a six-pack, that right is protected by the Voting Rights Act, too."

The city agreed, however, to keep the annexed areas' ballots separate, just in case those votes might tip the scales against a miniority candidate in a close race. White voters flocked to the polls, and Democratic Mayor Dale Danks, a lawyer who favors diamond pinky rings, won a second term handily, even carrying some black areas and the Jackson Country Club district of wealthy white Republicans, a "miracle" one city official attributed to racial fear of a black mayor.

In the final count, the annexed voters didn't matter, black turnout was low. Kirksey would have lost anyway, Ross said.

But local black leaders say Jackson's at-large elections, where minority candidates running citywide are routinely defeated through racial bloc voting, have all but numbed blacks to voting. The Justice Department is contemplating a lawsuit to force compliance with the Voting Rights Act.

To afford blacks a voice, the department had asked Jackson to adopt single-member districts, a notion the city threw out to its voters in a 1977 referendum. Whites voted against it, blacks voted for it. It was defeated. Kirksey then sued the city, challenging at-large elections.

Earlier this week, civil rights lawyers argued before the 5th U.S. Circuit Court of Appeals in New Orleans that Jackson's at-large voting was discriminatory in purpose and effect, the tougher standard the Supreme Court ordered as a test last year in a Mobile, Ala., voting rights case that was viewed as a setback by blacks in their decade-old drive to open up all-white governments across the South.

In the Jackson case, a Mississippi district judge had ruled earlier that Kirksey failed to show that city officials intended to discriminate when the at-large elections were set up in 1912. If the 5th Circuit reverses that decision and, as a remedy, orders single-member districts adopted, officials say the Justice Department will likely drop its objection to Jackson's annexation.

The Voting Rights Act applies tougher standards to cities than the court, and Congress must decide in the weeks ahead whether southern states have sufficiently atoned for past sins against blacks and won't repeat them if the extraordinary provisions are allowed to lapse. As a salve to southern egos, Congress could also decide to extend key provisions to the country as a whole, an option that would torpedo the law by swamping beleaguered Justice Department lawyers, civil rights adovocates say.

Under its provisions, a federal court or the Justice Department can order an election change if the proposed change would dilute minority voting. Section 5 also shifts the burden of proof from the victim of discrimination to the perpetrator, forcing a city like Jackson to request permission before it changes any election procedure that might hurt minority voters. Such a remedy was created to relieve victims of discrimination from forcing compliance through the courts, often a long and tortuous path.

Opponents of extending the law's key provisions, such as Sen. Strom Thurmond (R-S.C.) and many conservative Democrats in the South, object to pre-clearance as an insult to the South in an era devoid of the police dogs, fire hoses and violent intimidation used against those who helped blacks to register to vote in the '60s. Extension will depend on the congressional battle looming ahead, and Justice Department recommendations requested by President Reagan.

Rep. Henry J. Hyde (Ill.), ranking Republican on the House Judiciary subcommittee on civil and constitutional rights, has heard testimony from both sides, with civil rights groups and black leaders from the South arguing strongly for the extension. John Lewis, former director of the Voter Education Project, has called the act "the lifeblood of black political progress;" other civil rights leaders call it the most important civil rights legislation in history.

In Mississippi, civil rights groups credit the act with the dramatic increase in black voter registration -- from 6.7 percent of the voting age population in 1964 to 60 percent today. Yet, lawyers like Frank Parker, director of the Lawyer's Committee for Civil Rights Under Law, maintain that white politicians in Mississippi and throughout the South are still skirting the law.

The Mississippi legislature, for example, abandoned multi-member districts with at-large voting in heavily black areas only after the Justice Department objected and successfully sued to force compliance. More than a dozen Mississippi counties have tried to switch to at-large elections, but were blocked by similar objections under the act.

Rep. Hyde, an early foe of extending section 5, said in an interview that he has moderated his views as a result of subcommittee testimony and now favors extension. But Hyde wants to provide a way for certain jurisdictions in the South to be "able to get out of the penalty box" if they can show they have been "saintly" and not discriminated for a period of time.