HE ARRIVED with the summer people. He was one of the new cops, posted to the beach for the season, and he walked into the luncheonette one day for lunch, sat down the way cops do, arranging the gun and the ticket book and all the other things they have to carry, and ordered lunch.

He ordered the special and a drink and then some ice cream and then coffee. When he finished he tipped his hat and went right out the door, leaving without paying. I went after him. Where I worked, there was no such thing as a free lunch.

We had our rules. The rule said a cop could have a free coffee or a free drink -- a coke or something. After that, he had to pay his own way, although this was not the rule everywhere. In some places, cops ate for free. They always rode the bus for free and parked where they wanted and they bought things like liquor at discounts other people could not get.

I bring this up now because the other day, Sunday, a policeman walked into the Roy Rogers restaurant on Wisconsin Avenue and went right to the front of the line. He took a malt and then went to the cashier, a girl wearing a cowgirl outfit topped by a red cowboy hat, and showed her the malt and then went right out the door. When last seen, he was heading north on Wisconsin in car number 64, one hand on the wheel, one holding a malt, a straw stuck in his mouth.

"Don't policemen have to pay for what they get?" asked a certain columnist whose son was even then eating his way through a cheeseburger.

"Not for drinks and things," responded the cashier.

"Drinks and things?"

"I mean, they don't have to pay for drinks. They have to pay for hamburgers and things."

This, then, is the freebie policy of Roy Rogers as stated by the girl in the cowgirl hat. It is, however, not the policy of the parent Marriott Corporation which says, officially and in writing, that giving anything to the police for free or at a discount is forbidden. This is a policy that makes a lot of sense to the people in the front office. You can bet it does not make a lot of sense to the people in the stores.

There is a view of the world you get if you have ever worked at night behind the counter of a fast-food place. There are nights when it seems that everyone who walks in has darting eyes and a bulge in his jacket.

There are nights when the fog rolls in tight, when people seem to loom up at you in the doorway, when cars approaching are nothing but fuzzy lights behind the window and the radio crackles with news of holdups and muggings and awful things that people do to other people for money.

These are the nights you can't wait for the beat cop to stop in. You want to give him a cup of coffee and you want him to stay and stay and stay. You ask about the wife and the kids, about good collars and precinct politics and collisions down the road you saw coming to work in the morning. It is like those secret nights of childhood when some awful fear gripped you and wanted your parents to stay and stay and stay -- wanted the light never to go out and the door never to close. Nights like that, you want a cop.

Anyway, it does not take a genius to figure out that a cop in a store is worth more than a cup-of-coffee's worth of protection, not to mention peace of mind. It is for this reason that the Southland Corp., the parent firm of the 7-Eleven Stores, figured out it was cheaper to offer free cups of coffee to cops than to hire private guards. 7-Eleven called these "courtesy cups," but the various police departments called them something else and forbade the acceptance of them. It is the general policy of most police departments to forbid such things.

No matter. It is done, probably done less now than in the past, but done still. It only gets controversial when some corporation makes it a matter of policy, turning what is supposed to pass for spontaneous generosity into a mini-bribe. This, after all, is what these things amount to. The free coffee and the like are offered not because the cops are valued as customers, like you and me, but because they are valued as cops -- men with guns.

But that is the whole point. If the cops are valued because they have guns they are feared for the same reason -- the gun and the badge. They are noticed. They stand out. Back in the days when that cop walked out on me without paying, we all noticed the way the world worked. Cops didn't pay for coffee, bus rides or newspapers and they could park where they wanted if they had notices on their dashboards saying they were cops. These were bad lessons for a kid and what it came down to was the belief that there two kinds of people who don't pay for things -- cops and crooks.

Car 64, come back. Some kids are waiting for you to pay.