A policeman's lot is not a happy one, wrote W.S. Gilbert in 1879 ("The Pirates of Penzance"). Of course, it isn't much fun encountering the business end of a nightstick, either - especially when it's wielded by an unhappy constable.

You don't have to be a robber on parole, like Rodney King, to appreciate the horror of that videotaped police beating in Los Angeles earlier this month. To be sure, King was not returning home from choir practice when a gang of officers pulled him from his car, cracked their truncheons on his skull and kicked and pummeled him into submission. But what kind of misconduct deserves such a punishment?Those who direct attention to King's deficiencies have correctly identified a less-than-solid citizen; the main point, however, is that police brutality is an outrage, whether the victim is T.S. Eliot or Rodney King.

Unfortunately, TV news, in its customary way, has managed to distort this remarkable incident with daily reports on the impending resignation - or stubborn resistance, take your pick - of L.A. Police Chief Daryl Gates. This is the sort of ancillary "crisis" that distracts the public from the problem that matters.

In Los Angeles, as elsewhere, the problem is not Gates; it is the system he represents, and the violence it tolerates. Police brutality in Los Angeles will not disappear with Gates.

Nor is this largely a matter of race, as many believe and the videotape might suggest. Plenty of metropolitan police departments in America - in Detroit, in New York, in Washington and elsewhere - are headed by black chiefs and are comparably violent. My own memorable encounter with a truncheon-wielding Philadelphia cop - I had pulled over to the curb of a no-parking zone to ask him for directions - featured racial epithets and physical provocations. If anything, race tends largely to exacerbate the problem.

Of course, the sins of some police officers should not tarnish the many. As any public safety official would probably admit, people tend to go into police work for three basic reasons: There are those who wish to serve the community; there are those who are fascinated by the process of detection, and there are those who like to wear a uniform and swagger around the neighborhood. It's category three that tends to cause trouble - for everyone, including categories one and two.

Police work should also be understood in context. It seems obvious that even the most idealistic officer must suffer, at long last, from daily contact with the dregs of the earth. A steady diet of liars, wastrels, wife-beaters, prostitutes, thieves, con men, drug addicts, drunks, rapists and murderers cannot help but influence one's perspective on humanity. Frustration and revulsion must rage close to the surface; the law-abiding citizen may seem like an anomaly.

The glib, racist dialogue on the L.A. police radio was distressing to hear; but like surgeons, cops affect a kind of gallows humor to contend with their conditions.

Still, good things will happen in reaction to this episode. The police are just as vulnerable as the clergy or the press to excessive praise: Some self-examination will be good for the soul. The fact that a law-and-order president has expressed revulsion at this incident, and directed his attorney general to investigate brutality, is eloquent in itself. Police departments differ, and reflect their various communities, so patterns of abuse will vary around the nation.

If chiefs such as Gates learn anything from this episode, let us hope it is this: Trust, not fear, is the thread that binds the citizen to the constable, and we break it at our peril.