The tropical air is thick these days with dark complaint. Mad dogs and Englishmen are howling across the water, each to each.

In Palm Beach, a town almost completely run by career dowagers of immense fortune and bejeweled hauteur, the arrival here Tuesday of the future king and queen of England is being greeted with a studied yawn. Some of those here who made their fortunes through industrial or marital guile refuse to cartwheel down Worth Avenue to the strains of "Hail Britannia" for the youthful scions of a shriveled empire.

Gregg Dodge, the widow of auto mogul Horace Dodge, announced to The Miami Herald recently that she would attend neither the afternoon polo match nor Armand Hammer's royal evening event at the Breakers Hotel. "That's the day I have my legs waxed," she said reasonably. Even "the Queen of Palm Beach," the redoubtable socialite Mary Sanford, has chosen to bolt the Breakers beano.

There is also a weird yelping across the bridge in the low-rent city of West Palm. At the dog track the other night no one seemed to care much about the royal arrival. John Caruso, who is 18, plum-cheeked and a maintenance worker in nearby Lake Worth, watched a pack of crazed greyhounds dart along the dirt. "No," he said absently. "I don't think people around here much care about England. And isn't the prince gonna play polo? I like the dogs better."

Caruso watched the handlers at the starting line stuff a half-dozen hounds into individual steel boxes before the race. He checked the odds on a couple of whey-faced canines named Swindle Critter and Mountain Wallop and marked his program. Once inside the cages the dogs started clawing and crying and bitching and moaning, until finally the mechanical "rabbit" came roaring around the rail and the announcer screamed "HERE COMES RUSTY!" and the dogs bolted their blind agony, screaming free in the night.

Yes, Charles and Diana (if one dare be so familiar) have no idea what they are getting into here. This is a far different sort of capital. The establishment is permanent, loaded and severe.

The fantasy island of Palm Beach pays no mind to Lord and Lady Rumplebottom, the Viscout Applethrottle or any such Anglo-titles. Old money talks and nobody, but nobody, walks. The local aristocracy does not accept visitors easily.

Every year from November to April the Breakers is the scene of one charitable ball after another: the Cancer Ball, the Red Cross Ball and, for the Retina Research Institute, the Eye Ball. "Diseases do better here than culture," said one uncharitable resident.

Those who run these affairs do not exactly bake up a few brownies and sweetmeats for a sale or raffle off a Chevette. Nothing so simple as that. These are all elaborate black- or white-tie events with lots of air-kissing, glad-handing and picture-taking. And a handful of Palm Beachers run them all.

Then came Armand Hammer, the 87-year-old peripatetic chairman of Occidental Petroleum. Hammer has been thick with the prince and princess ever since their wedding. He invited the royal couple to Tuesday's dinner in his honor, which is supposed to raise as much as $4 million for the modestly titled Armand Hammer United World College of the American West in the little mountain town of Las Vegas, N.M. Prince Charles is president of the council that runs the school.

Not a few Palm Beachers think Hammer is off on a mind-bending bit of presumption, indulging a massive ego trip and sucking the tax-free charity dollars out of the town before the "season" ever begins. Hammer donated $75,000 to the Palm Beach Community Chest as a good-will gesture to ease the initial whining, but there are still complaints and bruises along the gilded coast. The organizers say about 400 people will come, far below the original estimate. Fewer than 30 will be locals.

"When I first heard the name Armand Hammer I wondered if he had anything million mansions and $45,000 wedding gowns. There is a good deal of sex in Booth's book, some of it between married adults. Booth, a lithe blond Englishwoman, appears on the front and back of the novel's dust jacket wearing what seems to be an incredibly uncomfortable bathing suit.

The local bookstores are sold out.

"You know," says Booth, as Pulitzer makes herself a sandwich, "the book is doing fab-u-lous-ly. Sometimes the jacket gets a reaction, though. The other night I got a call and this fellow told me what magnificent breasts I had. I told him that I hoped it wasn't just a cheap obscene phone call. I told him I hoped he had at least bought the book."

Pulitzer giggles. "Palm Beach" is dedicated to her. Naturally.

The self-proclaimed "dynamic duo" of Palm Beach may not be terribly welcome in the parlors of the elite, but they hear what they hear.

Booth: "You know, I hear only almost no Palm Beachers will be at the ball. The whole thing has become a disaster. It's a nonevent."

Pulitzer: "It's power, don't you think?"

Booth: "Sure, power. Things here are very intricate and if someone like Armand Hammer comes in and disturbs it . . ."

Pulitzer: "Nobody can see beyond the power structure. Palm Beachers could have gotten behind this thing instead of climbing onto their high horse. It's all about ego."

Booth: "The people that live here have everything that money can buy. Huge fortunes, servants, homes everywhere. There are a lot of people here that have much bigger fortunes than the British royal family. But the one thing they aren't are princes and princesses. So they snub Charles and Diana and show their power that way. It's so small."

Visitor: "Tell me, what does a Palm Beach lady do all day?"

Pulitzer: "In West Palm they work, I can tell you that. I live there."

Booth: "In Palm Beach the ladies get up at about 9. Then they fiddle with the flowers, irritate the gardener, plan the meals for the day. Then it's time for lunch at the Epicurean. If you're still walking, maybe an hour of tennis at the Bath and Tennis Club or the Everglades.

"Then maybe you get your hair done at Domani's and your nails done at Armonds. The ladies love those long talons here. Sooner or later you go to Dr. Lawrence Robbins in Miami for a little plastic surgery. Everyone uses him.

"Then it's time for a rest. Maybe read the paper but nothing too, too heavy. And finally you dress and go out to one of the balls at the Breakers. That's the life."

Booth's book describes how young Lisa tries to fulfil her mother Mary-Ellen's dream of penetrating Palm Beach society. As poor Mary-Ellen dies in a fire, she tells her daughter what's what.

" 'I remember, mommy. I remember everything. Don't die. Mommy, please don't die.'

"Then in open defiance of her most fervent prayer, Mary-Ellen's back arched and her body contracted. Like a leaf carried on the wind, the message was borne on the sweet, dying air.

" 'Palm Beach . . . Lisa . . . it's only a bridge away . . ."

No newspaper in America reflects its community better than the Palm Beach Daily News, better known as The Shiny Sheet for its glossy paper stock. The average income of its readers is $250,000. More than half are millionaires.

And the readers get what they want: gossip columns, real estate and business news, ads for manservants and Lester Lanin's band, and dozens of pictures of Palm Beachers at charity balls. The best charity is anonymous charity, the Bible says, but in these parts The Shiny Sheet is the Good Book. There are other local papers, The Luxury Weekly among them, but none has the cachet of The Shiny Sheet.

"They read The Washington Post or The New York Times to get mad and they read us to get happy," said publisher Agnes Ash. "People take our coverage very personally. We get calls all the time from people asking us why they didn't print their picture. Well, honestly, it's usually because they blinked."

Were there world enough and time, Princess Diana, a legendary shopper, would have a blast on Worth Avenue, which makes Rodeo Drive in Beverly Hills look like your local mall. Martha's boutique specializes in ball gowns. They are selling a beaded Galanos frock for $18,000 and a pair of rhinestoned stockings for $18.

"That's not bad for a pair of stockings these days," said the saleswoman.

At Greenleaf & Crosby jewelers they sell 14-karat dolphins, butterflies and shoehorns. And at the Epicurean gourmet shop they bark: "May I tempt your palate with a digestive wheatmeal cookie from Fortnum & Mason?"

Worth Avenue is fairly choked with Rolls-Royces, Jaguars, Bentleys, Mercedes-Benzes. Students at Palm Beach Day School ride to their scholarly pursuits in Jensen Intercepters and spend weekends on their boats. The Boston Whaler is the preferred tub.

"Palm Beach is the top of the heap," Ash said. "Some people say Charles and Diana are not visiting the real America. They're really visiting the American Dream. You make your money and head for utopia."

Some made their money, took off for utopia and found utopia closed. There is a meanness to the place.

One church, Bethesda-by-the-Sea Episcopal, and two private clubs, the Everglades and Bath and Tennis, are centers of social life. Though nearly 30 percent of the island is Jewish during the winter season, no Jews belong to the key clubs. Many of the Jews who live here talk about how they were either scorned or thrown out of the clubs if a member dared bring them as guests.

The Kennedy family was rejected by the Everglades and B&T. Instead, they joined the "Jewish club," the Palm Beach Country Club.

The Miami Herald ran a three-part series last spring describing how the clubs work. Numerous members had no problem at all expressing in public their disdain for any pressures to reform. Ruth Fleitas, the wife of a former board member of B&T, said her club should not be compelled to admit anyone it didn't want to.

"I'm so sick and tired of Jews," Fleitas told The Herald. "They are the most prejudiced people on earth."

The Shiny Sheet recently printed a list of the "Super Rich" in Palm Beach, and a substantial number are Jewish, including Este'e Lauder, the Edgar Bronfmans and the Newhouses. Much of the Jewish community here lives in a section fondly known as the Gaza Strip.

"I'm friendly with publishing heir Si Newhouse, who is Jewish," said Pat Booth. "He's got a huge place here but he told me he won't come during the season because he knows he won't be invited anywhere."

The Palm Beach Polo and Country Club in Wellington, where the prince will play on Tuesday, does accept Jews.

Recently cartoonist Garry Trudeau ran a series of "Doonesbury" strips mocking Palm Beach for requiring nonresidents to carry ID cards.

"Oh, that was so terrible," said Mayor Yvelyne (Deedy) Marix. "He was trying to compare Palm Beach to South Africa and that's not fair. This is a wealthy community and it makes us sitting ducks for robberies, doesn't it? Those cards are for people who have access to hotel rooms and private houses. And most of the card holders are white! Is that so bad? I still believe we are the loveliest community in the world."

The prince and princess are unlikely to see a run-of-the-mill taxicab if they wander by Worth Avenue. Those who have no limo can walk to the limo stand and hire one.

Outside Gucci, Guy Cavalier stood on the sidewalk next to his royal blue Lincoln stretch. He kept his tie pinned to his shirt with a paper clip.

"The minimum rate is $3. That'll take you, oh, about three blocks. But limos are nice. Look at this beautiful place. Would you want to see some horrible yellow taxi with ads plastered all over it? The limo protects you from all that eye pollution.

"I'm telling you, I love Palm Beach. There's no crime. Everybody's happy. I live in West Palm, but it's better here. Palm Beach is heaven on earth. I'd love to live here."