In early editions of The Washington Post yesterday, the headline on a story about the campaign of attorney Carrington Williams for the Democratic nomination for the U.S. Senate in Virginia, erroneously said, Williams Va. Campaign Seen as 'Cerebral,' Futile." In later editions, the headline was corrected to read, "Williams Va. Campaign Follows Middle Of Road."

Carrington Williams, a tax specialist as a lawyer and for eight years as a member of the Virginia House of Delegates from Fairfax County, held a news conference on the national economy in the state Capitol in Richmond Tuesday.

As a candidate for the Democratic nomination to the U.S. Senate, Williams decried passage of the Humphrey-Hawkins guaranteed employment bill by the U.S. House and laid out his own proposals for stimulating the economy.

It was a detailed plan built around tax incentives for small businesses. It offers a sharp reduction in tax rates on small business profits that are reinvested in the business and a tax deduction on dividends paid to attract job-producing capital. It also would do away with tax benefits that encourage large corporations to acquire small ones.

Williams citied studies that detail the distress of small business in America and their importance to full employment.

It was a typically cerebral discussion of an important issue by Williams, and it got typically scant coverage by the press that is following the Democratic senate nominations race. Not even the Richmond Times-Dispatch, which routinely covers most candidate press conferences in Richmond, published a story on this one.

The next day, Williams shrugged off the fuzzy focus on issues in the contest and vowed to keep talking about them. "I can't run anything as deadly serious as a campaign for the United States Senate on nothing but smiles and handshakes," he said.

No one has ever accused Williams of taking such a superficial approach to public life. In interviews with party officials and campaign figures, he is described as "dedicated," "able" and "distinguished," but his changes of winning the nomination after months of vigorous campaigning are regarded by these political figures as only fair.

Williams himself said in an interview that he believes former state attorney general Andrew P. Miller has to be regarded as the front runner as Democrats prepare to choose state nominating convention delegates at city and county mass meetings on April 15.

However, he puts himself and state Sens. Clive L. DuVal II of Fairfax and Hunter B. Andrews of Hamption in a class of candidates that are close enough to Miller to win on a second or third ballot at the June 9-10 convention in Williamsburg. None of the candidates believes the nomination will be decided on the first ballot.

The other Democrats seeking the nomination to the seat being vacated by retiring Republican William L. Scott are former Fairfax County supervisors Rufus Phillips and Frederick A. Babson, Falls Church faminist Flora Crater and Norfolk City Council member Conoly Phillips.

Williams is among those Democratic candidates who are campaigning for a re-establishment of a moderate-conservative image for the state party after 10 years of ideological turmoil. During those 10 years, party regulars have polarized for and against populist former Lt. Gov. Henry E. Howell, who was decisively beaten in last year's gubernatorial election. With Howell's defeat, Virgina became the only state in the nation that has failed to elect a Democratic governor or senator in 10 years.

To turn this around, Williams said in an interview, "We've got to move back toward the middle of the road. At a joint appearance of candidates at a University of Virginia Law School forum last month he said:

"Where are a majority of the people of Virginia today? I'm convinced they are conservative on money issues and practical or moderate on most other issues. Therefore, I think that's where the pitch has to be made; and if you deviate much from that, you are going to be trouble. You cannot deviate to the right or to the left. We've got to get away from the factionalism that has divided us in the past. That's obvious."

Williams puts himself on the conservative side of economic issues. He said in the interview that he fears nomination of one of the Democratic candidates that favors Humphrey-Hawkins, a bill that would make the federal government employer of last resort for the jobless, would subject the nominee to a lethal fire from the Republican opponent in the fall.

On civil rights and most other non-fiscal issues, he has taken a progressive approach typical of Northern Virginia Democrats in the General Assembly. However, he said he would oppose renewal of the federal Voting Rights Act, a law that subjects Virginia elections to federal regulation because of past discrimination against black voters.

"I served on the House Privileges and Elections Committee for six years," he said, "and I know of no racial discrimination in Virginia in connection with regisration and elections."

The Democratic candidates also are split on this issue and again Williams said support of extension of the act would be lethal in a race with any of the Republican candidates next fall.

Virginia Democrats have rarely resorted to conventions to nominate statewide candidates, but for Williams, 58, this will be his second as a candidate. In 1971, he lost the Democratic nomination in a special election for lieutenant governor by five votes. His defeat came when former Gov. Mills E. Godwin, then a Democrat, threw his support to former Del. George Kostel of Clifton Forge. Howell, running as an independent, beat Kostel in the election.

In this race, Williams, like most of the Democratic candidates, is relying primarily on his own money to finance his preconvention race. He says he has put about $125,000 into the campaign.