The potential for rapid change in automobile industry fortunes was emphasized yesterday as American Motors Corp. -- long the weakest of America's four manufacturers -- declared its first cash dividend in more than five years.

At the same time, Chrysler Corp's newly installed chairman and chief executive, Lee Iacocca, was at an unannounced meeting in Washington with Treasury Secretary G. William Miller. Iacocca, whose firm is projecting the largest 12-month net loss in business history during 1979, promised Miller a revised federal assistance proposal "within a reasonable time."

AMC's announcement yesterday came as that firm neared the end of a fiscal year which has included record earnings from operations.

Chairman Gerald Meyers said the dividend of 7 1/2 cents a share takes into account long-term capital needs of the company. ". . . We are confident that we can meet our objectives and also recognize the need of stockholders for a return on their investment," he added.

A payout of 7 1/2 cents a share quarterly, which will cost AMC $2.3 million for 30.4 million shares outstanding, will be distributed on a regular basis for a total of 30 cents a share per year. The initial payout will be distributed Nov. 13 to owners of record Oct. 9.

The last previous AMC payout was 10 cents a share, on Sept. 25, 1974.

Chrysler, meantime, dropped one shift from an assembly-plant making large cars and closed the plant for two weeks, to reduce inventories. About 2,000 production employes were laid off indefinitely -- increasing Chrysler's layoff total to about 30,000 and industry layoffs to 89,000.

The factory, Lynch Road in Detroit, began producing 1980 models -- Chrysler New Yorker and Newport, Dodge St. Regis, Plymouth Gran Fury -- a month ago. Ward's Automotive Reports said the company had a 91-day supply of the large Chryslers and a 94-day supply of the Dodges compared with a desired level of 60-day supplies.

With the layoff news as a backdrop, Iacocca dropped in for a surprise meeting with Miller. Early yesterday, Miller met with the Michigan congressional delegation and said he would meet with Iacocca "soon," but that no meeting was yet scheduled.

In mid-afternoon, Miller revealed he had met with Iacocca and that Chrysler would submit soon a revised plan for federal aid. In separate statements, Miller called the meeting "encouraging" while Chrysler said a new proposal will "be responsible" to Miller's call last weekend for a reduction in the company's plea for $1.2 billion of loan guarantees. No timetable was established.