Sam Zagoria was incorrectly identified in Thursday's editions of The Washington Post. He is director of the labor-management relations service sponsored by the U.S. Conference of Mayors.

Striking firefighters agreed to return to work in Dayton, Ohio, late yesterday after a three-day walkout during which angry citizens doused fires with garden hoses as firemen picketed for higher pay and less work.

The dispute - which reportedly resulted in the strikers getting much of what they had demanded 24 hours earlier - rekindled a debate that Calvin Coolidge thought he had ended 56 years ago.

"There is no right to strike against the public safety by anybody, anywhere, anytime," said the dour New Englander in breaking the Boston police strike of 1919 and putting himself on the road that untimately led from the Massachusetts Statehouse to the White House.

But the issue didn't die with Coolidge or with his era.

Militancy has been rising over the past decade among the nation's 12 million state and local government employees, who have found themselves on the losing end of municipal belt-tightening and have begun demanding the same collective-bargaining rights as private industry employees.

One result has been a push for national bargaining legislation to replace the hodgepodge of existing state bargaining laws - a push backed up by periodic waves of striked and accompanying publicity about piles of smelly garbage, unmanned draw-bridges and firemen picketing as houses burn.

The issue is complicated than a debate over Coolidge's maxim, however.

Many public employee unions, including the American Federation of State, County and Municipal Employees (AFSCME) and the International Association of Fire Fighters (IAFF), which represents the Dayton striker, say they would give up the right to strike in return for binding arbitration of bargaining disputes by an impartial third party.

Government officials, however, are increasingly reluctant to lose control of a power for which voters hold them responsibile - the power to raise and spend money - according to Sam Zagoria, labor-management specialist for the International City Management Association.

Moreover, union leaders such as IAFF President Howard W. McClennan say the strikes are occurring only because machinery such as arbitration does not exist to resolve disputes without worker walkouts.

But others, such as Rep. Frank Thompson (D-N.J.), the sponsor of legislation to extend collective-bargaining rights to public employees, say Dayton-type strikes hurt the cause.

"The members of [of Congress] get terribly upset when something like this happens," he said yesterday. "It seems every time legislation of this kind comes up, the sanitation men will go out or someone will refuse to pull up a bridge somewhere."

Available statistics indicate an increase in the number of public employee strikes this year, although officials warn that the figures may be inconclusive. The Bureau of Labor Statistics reports 113 governmental strikes through May of this year, compared with 85 for the same period last year.

The number of public employee striked rose during the late 1960s, tapered off during the wage-price controls period of the early 1970s, peaked in 1975 and fell off in 1976 - generally reflecting trends in private employment, a BLS official said.

It was the Dayton strike - the latest of 15 walkouts by firefighters in Ohio, Indiana and Illinois this summer - that brought the strike issue to the fore again.

There have been roughly the same number of firefighters' strikes this year as last but "they're getting longer and our guys are getting fed up," said Walt Lambert, research director for the IAFF. he predicted that strikes will spread next year to states in the Southeast which, like the three Midwestern states, have no bargaining laws.

Dayton was different because of the pictures, flashed across television screens and the front pages of newspapers, of firemen marching on picket lines while at least 25 buildings burned, with some of the blazes battled by residents wielding garden hoses.

No one was injured, but at least 12 families were left homeless, according to an Associated Press report. The 375 striking firemen, who send "phantom squads" to fires to see whether lives were being threatened, had pledged to fight only those fires jeopardizing lives.

According to wire reports, the Dayton firemen got a two-hour reduction in their 52-hour workweek, economic benefits amounting to more than $2,000 per worker over the next two years, extra days off and amnesty from repercussions for striking.

Asked what caused City Manager James Alloway to improve the city's offer, union leader Timothy Harker told the Associated Press: "All he had to do was look out his window last night and see all those fires burning."

As the strike ended, Dayton's police union was scheduled to meet to consider a walkout of its own against the trouble-plagued city of 241,000, which has been faced with a declining population, a busing controversy, an acute winter fuel shortage and a taxpayers' revolt that culminated last spring in voter rejection of a tax rate increase.

The prospect for national public employee bargaining legislation, one of the AFL-CIO's priority items, is doubtful, according to several labor and congressional sources.

A recent Supreme Court ruling against enforcement of federal minimum wage rules for state and local government workers casts doubt on the constitutionality of a federal law mandating collective bargaining for these same employees, and unions are divided over how to proceed.

"There's no question that the [Supreme Court] reversal took much of the steam of the push for a federal collective bargaining law," said William Hamilton, an AFSCME spokesman.

But Thompson said he may push for hearings on his bill later this year. The measure, which includes a right to strike, is considered likely to be amended to provide for impasse procedures such as arbitration.