Prince George's County police entered the second day fo their slowdown yesterday while members of the County Council began wrestling wtih the question of whether to send the police-county contract dispute to binding arbitration, as the police union has requested.

Union President Lancey Hester said he thought participation in the slow down - which involves no enforcing traltic violations, parking regulations or making misdemeanor arrests - was 100 percent.

Police spokesman John Hoxie said, however, they way the slowdown was being conducted it was impossible to gauge its effectiveness. "We have no idea how many men are participating or to what extent," he said. "But Lancey has no way of knowing either."

In the Hyattsville police station yesterday, many officers reported for the 4 p.m. shift still wearing black bands across their badges in memory of Albert M. Claggett and James Brian Swart, the two officers who were killed early Monday morning. The officers' deaths policemen say, have increased the anger felt over stalled contract talks, dissatisfaction with working conditions and concern over what the police perceive as a lack of support by police and county administration.

As the men were read the routine memos of a Saturday roll call and assigned to the usual weekend duties, they were also given the word on how to comport themselves during the slowdown: "Don't hump it. Don't push yourselves."

"You've got to do something, because we don't want an injunction," the officers were told, but we're not doing anything that interferes with our safety."

"After each incident," Sgt. Bill Somnuk said after the roll-call was over, "we are going to come back to the station and write very extensive reports."

Normally, Somnuk said, police merely take notes after calls and save the laborious report process until after they are off duty. By taking time to write reports after each incidnet, his squad will reduce its time in the field by 35 percent to 40 percent, Somnuk said.

"I'm going to be living behind the Riverdale drive-in," shouted one officer. "Just park behind a shopping center," a nother officer explained to a friend. "You can't see anything back there."

Hester, president of the Fraternal Order of Police (FOP) said his offices were counting on community support to help influence the council to vote to submit the contract dispute between the police and the county to bind arbitration.

"I think the people of this community are on our side and we want them to remain that way," he said. "The way we're handling this, they will, I think, judging by the phone calls Kelly's office has beeb receiving, the people are on our side.

Senior Kelly aide John A. Lally conceded that Kelly's office had received numerous phone calls, but played down their importance.

"We've gotten phone calls from people supporting the police," he said."But a lot of them were from people with FOP ties and a lot of others were from people reacting sympathetically to the emotional situation of the past week."

"But I think Hester and his people may be misinterpreting the amount of support they would have when it came down to people deciding between more money for the police or less taxes for themselves. People want taxes down and Kelly knows it."

Lally reiterated Kelly's hard-line stance against binding arbitration. Kelly has cited a Harford County court ruling that says that a County Council may not give up the right to regulate taxes as the reason he does not think the country can be ordered to take a contract dispute to an arbitrator.

"If the council sent the contract to binding arbitration they would in effect be giving up their right to set the tax rate to a third party," Lally said. "We don't think they can do that."

Hester insisted that he still expects a favorable ruling from the council, although there were indications yesterday that the council would not grant the binding arbitration request.

Four council members said they were not sure, under the law, if the council had the authority to step into a contract dispute. Two others said if they did vote on the issue they would vote against sending the contract to binding arbitration.

Eight of the 11 council members are running for reelection on the same slate with Kelly. It did not appear likely yesterday that they would side with the police on the binding arbitration matter.