In the taut showdown between the police force and City Hall, underscored by the late-afternoon demonstrations, Officer Russell and many of his colleagues made it evident that they saw a multifaceted issue in simple terms.

He brushed aside the fact that the Mayor's offer was more generous than those accepted by other city unions. Police officers, he said, deserve better still. Don't talk to him about what teachers make: teachers dodge chalk and he dodges bullets.

He readily dismissed the fact that corruption charges had been filed against some of those bargaining for him as beside the point. To him, the point was a mathematical one: he was not paid enough.

He spoke of a fellow officer, one of the most admired in the precinct, who reluctantly left last month to join a force in Nassau County for a raise of $18,000 a year.

Throughout the city, officers on the beat yesterday spoke of a blanketing mood of gloom and bitter anger, one profound enough that some even suggested it was affecting the vigor with which they pursued criminals. Officer after officer said they felt that they had done what the Mayor asked of them in reducing crime, and then some, and now the Mayor had failed to reward officers adequately where they wanted it most -- in their paychecks.

In a demonstration of their discontent, half-hourlong protests were staged around 4 P.M. outside all 75 station houses to denounce the Mayor's actions. Clad in street clothes, officers marched while displaying signs proclaiming, ''We are the lowest paid Cops in the state'' and ''How much is a Cop's life worth?''

For the most part, the protests were fairly restrained, yet they attracted thousands of officers.

Chanting ''Zero percent can't pay the rent,'' ''Rudy must go'' and ''Rudy's a liar, set him on fire,'' about 75 officers marched before the 71st Precinct in Crown Heights, Brooklyn, in one of the more boisterous protests. Passing motorists honked in support, and even prisoners in a Correction Department bus offered upraised thumbs and banged on the barred windows to support those who had arrested them.