One era closed and another began yesterday as the Federal Trade Commission announced the end of its ballyhooed probe of television advertising directed at children.

Hours later Reagan administration economist James C. Miller III became the agency's new chairman, taking the oath of office from Vice President George Bush.

The timing of the two events was not intentional. But perhaps no two occurrences better symbolized the end of the activist era of the FTC than the close of the "kidvid" matter -- a pet project of Miller's predecessor, former FTC Chairman Michael Pertschuk -- and Miller's formal arrival at the agency's Pennsylvania Avenue headquarters.

The commission staff threw in the towel on the "kidvid" probe six months ago, recommending that the agency abandon the project. A ban on advertising aimed at children "would have such a limited scope that it could not be an effective remedy," the FTC staff said at the time.

The language when the project began was different. "Never before has there been a a better opportunity to help change a system that permits children to be manipulated for private gain," said Peggy Charren, president of Action for Children's Television (ACT), in 1978 when the pressure on the FTC was at its zenith.

But the coalition of 46 health, education and other activist groups fighting for the matter was ultimately overwhelmed by the nation's changing mood toward regulation and a well-heeled coalition of candy, cereal and broadcasting interests.

The business lobby also put a roadblock in the case by charging that Pertschuk had prejudged the matter in speeches and interviews. Although a federal judge upheld the industry charge, Pertschuk was later cleared by an appeals court. He withdrew from the case because of the controversy.

The business opposition also convinced members of Congress during last year's bruising fight over the FTC's future that the children's advertising effort was misguided. The proceeding was suspended and never resumed.

"We're not surprised when the Reagan administration's middle name is deregulation," said Nancy Dietz, an ACT legal assistant, who said the group was considering a legal appeal of the FTC decision.

The case began in 1977 after ACT and the Center for Science in the Public Interest petitioned the FTC to take a look at television ads for children.

The FTC staff recommended that the FTC propose a ban on commercials aimed at children "too young to understand the selling purpose" of advertising, a ban on ads for highly sugared products aimed at viewers under the age of 12 and the establishment by advertisers of a fund to promote nutritional advice.

The current three-member FTC, minus Pertschuk and Miller, showed little stomach for the far-reaching goals sought by Charren's group. The goals, if achieved, would have changed the look of children's television.

"In short, the commission's review of the rulemaking record developed thus far clearly indicates that a major commitment of the commission's resources would be required to continue this proceeding, resources which would necessarily have to be diverted from other pressing enforcement priorities," the FTC said yesterday.

Miller has been a frequent critic of FTC activities. As chairman of the administration's FTC transition team, he proposed in a report for the White House that the commission "terminate all cases based on 'social theories' and consider guidelines to staff concerning future proposals."

Clearly, the "kidvid" case was based, in part, on social theory -- a concern for the health and welfare of the nation's children that went beyond the FTC's traditional role. But the case also helped win for the FTC the pundits' title of "national nanny," as critics suggested the agency was attempting to play parent for America's young.

The case may signal an end for the FTC effort, but ACT vows to continue to fight unfair children's advertising. "We will continue to work to reduce advertising time on children's television, and we will work to insure that cable television is a commercial-free alternative," Dietz said.