A faint hope for early resolution of the Prince George's County public employes strike emerged yesterday when the two sides tentatively agreed to meet Friday with a federal mediator.

Despite this development, the union and County Executive Lawrence J. Hogan remained at bitter odds yesterday, the strike's second day, and there was sharp disagreement over the walkout's size and impact.

The meeting tentatively scheduled for Friday was the result of calls yesterday by the federal Mediation and Conciliation Service to Hogar and leaders of the 1,500-member union, sources said. Neither side would discuss the possible meeting, although both ackowleged they had been contacted. Meetings with the mediator would not necessarily signal resumption of negotiations.

As picketing workers again circled the Central Admisistrative Building in Upper Marlboro yesterday, Hogan broadcast a pep talk to nonstriking workers, boasting that only 10 percent were absent. "The health and safety of the citizens of this county," he said, "is being protected and will continue to be protected."

Later, Hogan's office issued figures showing that 714 of 1,574 workers were absent.

Leaders of the union, the American Federation of State, County and Employees (AFSCME,) stuck to claims that 90 percent of the work force was striking. "How can he say there's no impact," said Ernest Crofoot, the union's state representative. "Animal shelter's closed, no trucks going into the landfill and there aren't any guards at the jail."

The strike, which primarily involves clerical staff, landfill operators, road crews, jail guards and animal shelter workers, has caused varying degrees of inconvenience.

Police and fire protection are not affected by the strike. Besides the county jail, which was manned again yesterday by state troopers, county agencies hardest hit by the strike appeared to be the animal shelter in Forrestville and the Public Works Department. Garage repairs of county vehicles have nearly stopped, nine out of 10 private trash trucks honored the picket line at the county landfill in Upper Marlboro and pet owners were turned away by the animal shelter because of the skeleton staff there.

"The man there was by himself and almost in tears," said Joan King, who went to the shelter to find a missing pet. The shelter was closed and all animals were evacuated to the Montgomery County animal shelter in Rockville. a

But those were extreme examples. The county government had not collapsed, but police and department heads said the impact of the strike -- currently scattered throughout the government structure -- could grow the longer the strike is prolonged.

"It's the delays in service and the overwork that could prove unbearable," said one department head who asked not to be named.

The Consumer Protection Department whose staff has been cut by one-third, is asking many callers to file their grievances by mail. Five of six county consumer protection invistigators are striking and officials say response to claims will take longer than usual.

At the Department of Aging the eight buses that transport elderly residents to activity centers and stores sat idle in a county parking lot yesterday.

"I don't know what I'm going to do if this thing goes on" said Mary Rattler, 61, who remained in her Seat Pleasent home yesterday. "I'm living alone and looking at four walls . . ."

Officials emphasized, though that the 500 meals served daily to county senior citizens were provided yesterday despite the strike.

At the Central Administrative Building there were no long lines at counters in such departments as building and permits licenses and finance. Some officials speculated that many residents who would normally have done business there yesterday decided to stay away because of the strike.

For those who did appear there were delays. "We'll be with you soon as we can," a secretary advised one man who sat haunched in an office chair, briefcase sandwiched between his knees. "The strike, you know?" she said, waving her hand in the general direction of several empty desks.

One agency, the Department of Business Licenses, lost all five of its workers. An administrative assistant from the Department of Finance manned the office where, amid strains of radio soul music, he administered examinations to taxicab operators.

In public works, sources of vehicles -- backhoes, road graders and crew trucks -- used for road repair work sat on a Forrestville parking lot as pickets chanted outside a chain link fence.

Meanwhile, the 120 prison guards fired by Hogan after they walked off their jobs early Tuesday were ordered to appear in court today to explain why they should not be held in contempt for ignoring a court injunction.

State police troopers have replaced the guards at the jail, but state officials have told Hogan that the troopers will remain there only through the court hearing. Hogan has apparently decided to hire a priviate security firm to replact them. In the meantime, applicants for guard posts were screened and interviewed at the jail yesterday.

A possible confrontation between Hogan and the county's Fraternal Order of Police over using police officers as replacements for the guards was avoided yesterday when Police Chief John McHale rescinded the order after FOP leaders objected.

"Everything appears to be hunky-dory now," said FOP president Laney Hester after an FOP meeting yesterday. "We were not trained to act as guards, and the county executive now plans to use a private agency instead."