Approaching The Towers Apartments from, say, the front, there is a sign directing maids and servicemen to the rear, and men are requested to wear jackets in the main lobby after 6 p.m. The Towers is that kind of place. The music of Chopin comes out of little ducts near the air conditioning vents.

But the problem is that the air conditioner itself is not working, and has not been for the past three weeks.

Contrary to the notion that the well-to-do would not know what to do in a situation like this, many of the 500 or so residents living at this exclusive, far Northwest Washington complex remain cool.

"I'm heading for the beach," said Carl Stear, a physician, revving up the engine of his Mercedes 450SEL. "Of course it's hot," he said gruffly. "That's why I'm going to the beach."

At 4 a.m. yesterday, as temperatures began to rise, one of eight glass doors leading into The Towers shattered. A nurse working at The Towers was injured by the broken glass.

"It was as hot as in the daytime," said one maintenance man. "The door just blew out."

"It wasn't that bad," said assistant manager Bernice Howison. "It 'twasn't the heat. The same thing happened last winter."

The air conditioning said property supervisor Col. W.W. Allen, should be back to normal today. Maintenance men, working at the complex - at 4201 Cathedral Ave., where apartments rent from $236 to $714 a month - have been at it for 24 hours a day, he said.

"About 85 per cent of the people are being very understanding," Mrs. Howison said. "But you always have a few hecklers - in any crowd."

One tenant, Carrie Johnson, is not happy. Swaying back and forth from the basement market past the complex's beauty shop, she continually examined the palm of her right hand.

"It's not unbearable heat," the 63-year-old woman said, her face grimaced as though in pain. "My palm. It's sweat. I can't say any more about it. If I did. I would say bad things - like hell and damnation."

Inside the Cheryl of the Towers Coiffures. Lillian Davidson complained about the breakdown that had hurt the beauty parlor business.

"It's just like they stepped out of a shower," she whispered. "Nobody wants to come in to get their hair done because it will fall down as soon as they step outside."

Rolls Royce's Cadillacs, Mercedes and other luxury cars continuously rolled from the underground garage yesterday - with many apparently fleeing the heat.

Those who could not get away soon enough were seen meandering through the glass-enclosed hallways, grumbling at statues of little, half naked Roman boys who appeared to be eating grapes and holding cloth around their waists.

To beat the heat, some residents are using portable fans. Many put on their bathing suits and head for the apartment's swimming pool.

"If something isn't done soon," one woman said, "I'll have to move in with my sister (who lives in another apartment building).

"It would happen on the hottest das of the year," complanined one man as he patted his forehead with one hand and steadied the walk of a companion with the other.

"Do you like this hat? I think I need a new hat," his companion replied.