ON A PERFECT 78-degree Florida winter afternoon, two men were basking between the ocean and the blue-tile pool at The Breakers Hotel in Palm Beach when one began telling the other about a wager he had won while aboard another friend's yacht.

"We went out for Sunday brunch and the afternoon football game," the man with the Rolex said. "Well, Doc starts bad-mouthing the Miami Dolphins and talking about the great undefeated Chicago Bears. Right off, someone says, 'Put your money where your mouth is,' so Doc says, 'Okay, I'll give you Miami and six.' Hell, all of us got in on that sucker bet and on Monday night, well, you saw the game."

The other man nodded: "Miami 38, Chicago 24."

"Right! The next Sunday, we get together on the yacht and Doc, he shows up with one dollar bills! That's right, one dollar bills! He must have lost at least a thousand, but he pays each of us one dollar bill at a time. Then, he announced that he's going to kill himself . . ."

The other man chuckled and almost spilled his Bloody Mary.

"We all go up on deck and old Doc takes off his shirt and all our wives egg him on and then, honest to God, he suddenly drops his pants and steps overboard."

Both men roared.

A few days later in Belle Glade, a rural town 40 miles west of Palm Beach, Teresa Jones returned from a corner store to her two-room apartment and her four children waiting for breakfast.

The apartment was a mess: A plastic pail filled with garbage sat inside by the door, unwashed clothes were scattered everywhere, pieces of tile were missing from the floor, exposing black adhesive that stuck to her children's bare feet. There was no stove or refrigerator in the $240-a-month apartment. The only furniture was an old sofa and a broken chair.

Four-month-old Starsha was curled up in a blanket on the sofa trying to sleep, but each time she dozed off, her 2-year-old brother, Jashae, tickled or pinched her. He was wearing a pair of unzipped brown pants damp with urine. The communal toilet is down the hall. Jacqueal, a shy 3-year-old, was chasing a cockroach with a broom. Antione, age 5, was staring out the apartment's cracked window.

Jones had bought four boxes of Cracker Jacks and Coca-Colas for breakfast. Jashae squealed and raced toward his mother when he saw the Cracker Jacks, almost knocking over his sister. Irritated, Jones grabbed a belt and struck him on his legs, then dragged him to the sofa: "Sit down and shut up. You quit that crying, you hear?" The boy sat still and crammed a handful of candied popcorn into his mouth.

PALM BEACH and Belle Glade share the same county, but little else. They represent American extremes of prosperity and poverty.

Palm Beach is a virtual oasis exclusively for the wealthy. The 14-mile golden isle off Florida's eastern shore is among the least stratified communities in America, according to a demographic study by the Alexandria-based Claritas Inc. The average island resident is 63 years old, white, college-educated, retired, Republican and worth more than $1 million.

Belle Glade also is an oasis, but of the poor. The squalid living conditions of migrant workers in this self-proclaimed "Winter Vegetable Capital of the World" were first exposed by Edward R. Murrow in the classic 1962 CBS documentary "Harvest of Shame." Little has changed.

A fourth of Belle Glade's 16,500 residents qualify for welfare. The average resident is 36 years old, black, is not registered to vote and dropped out of high school.

Each December, Palm Beach and Belle Glade celebrate a "Season."

In Palm Beach, the season is a time for the rich, many from the Northeast, to party. During a two-month period, the island's population swells from 12,500 to 40,000 as the wealthy congregate to play tennis, golf, croquet, shop at Gucci and Cartier on glittering Worth Avenue and attend nightly charity balls.

In Belle Glade, the season marks the start of harvest. More than 10,000 additional farm laborers, many brought from Jamaica by sugar cane growers, come to Belle Glade to compete for jobs "cuttin' cane" or picking lettuce, oranges, beans and radishes. Many of the workers eventually move north, passing through the orchards and vegetable fields in Virginia and Maryland. THE RICH

Paul Ilyinsky (pronounced Ill-e-in-ski) was born in a Rolls-Royce. His mother was attending an opera in London on Jan. 27, 1928, when the labor pains started. Ilyinsky arrived during the rush home.

Ilyinsky is president of the Palm Beach Town Council. He is a dashing man with a confident air and a voice so eloquent that it can make a simple zoning request sound grandiose.

Angelica Ilyinsky is a statuesque woman well regarded for her orchids, skill at canasta and shrewd political instincts. On a recent morning, it was Angelica Ilyinsky who intercepted an angry telephone call from one of Palm Beach's grandames. The woman had been issued a $50 ticket by police for taking her dog on its morning constitutional on the beach. Her dog, she charged, was being singled out unfairly for punishment. "I can assure you madame, that all dogs in Palm Beach are treated equally," Angelica Ilyinsky replied, defusing the caller's anger.

The Ilyinskys were born into wealth, just like most of their neighbors. Palm Beach remains an island where nearly everyone is someone and a person's name always carries a footnote: "Oh darling, you must meet Helen Boehm, head of the international Boehm procelain empire and owner of the Boehm polo team."

"Have you met Mercedes Kellogg, the wife of the cereal heir?"

"Oh! There's Janet Annenberg Hooker; she's the media heiress, you know, and sister of Walter Annenberg, former ambassador to the Court of St. James's."

Angelica's great-grandfather was Samuel H. Kauffmann, a founder of the defunct newspaper The Washington Star. Paul's father was Grand Duke Dimitri, of the House of Romanov, the last Imperial Russian family. His mother was the daughter of a wealthy Cincinnati industrialist.

The Ilyinskys live in a house worth approximately $2.7 million, filled with Russian heirlooms. They employ a live-in maid, a full-time captain for their 72-foot Burger yacht and also support Ilyinsky's childhood nanny, now 92 years old, who lives in Norway. They belong to the Bath and Tennis Club, which excludes Jews, according to two members,(there are no blacks living in Palm Beach) and is considered by many to be the most prestigious of the island's clubs.

Paul Ilyinsky's days are spent at city hall, aboard his yacht, at the club or tinkering with a huge model train layout that fills two rooms of his home. Angelica works at the public garden once a week, serves on several local advisory boards and plays cards each afternoon.

The Ilyinskys are proud of their pristine isle. It has been pictured unfairly in the past, both say, because of such highly publicized scandals as the divorce of publishing heir Herbert Pulitzer Jr. and his wife Roxanne. Most island residents are not much different, Paul Ilyinsky contends, from people living in places like Bethesda or McLean.

Agnes Ash, publisher of the Palm Beach Daily News and a 20-year veteran of island society-watching, agrees that there is probably no more or less scandalous behavior in Palm Beach than in any community. The difference, she says, is that the super rich can afford more outrageous scandals: "Decadence is expensive; it's hard to live a decadent life style on the cheap."

"The whole idea of this town," Ash continues, "is not to do anything too controversial because you are supposed to be having a vacation." That is why, Ash explains, Palm Beach's growing Jewish population doesn't fuss about discrimination at clubs.

This "resort attitude" also explains why golf carts have the right of way on island highways, why trash is collected five days a week at back doors, and why waiters, store clerks and even the Palm Beach police are embarrassingly polite. Palm Beach is supposed to be perfect. There is no hospital, nursing home or even a waste treatment plant on the island. The sewage, sick and infirm are sent to the mainland for treatment.

"Palm Beach is kind of a pre-heaven for the wealthy," Ash concludes.

The first party that Paul and Angelica Ilyinsky attended during December was a Christmas buffet and dance for town employes at a local mansion. The gala, however, didn't really qualify as one of Palm Beach's official social functions because none of the town employes live on the island or belong to its social set. The Ilyinskys would make their official debut the next night at a black-tie gala at the very same mansion but with a much different crowd.

Ilyinsky was the only town council member to attend and stay late at the town Christmas party. The couple mingled with the police officers and sanitation workers with the enthusiasm of hungry insurance agents. "God, I love these people," Paul Ilyinsky gasped between trips to tables. "Having them respect me is important to me."

Ilyinsky's father was a blue-blood, but not wealthy. Grand Duke Dimitri was booted out of Russia in 1916 by the Imperial family after he helped murder the infamous monk, Grigori Efimovich Rasputin. Ironically, the banishment saved Dimitri from slaughter during the Bolshevik revolution.

Paul Ilyinsky was raised by a nanny in France and then England while his parents traveled. "I didn't grow up thinking that I was better than anyone else," he explained. "I grew up being told constantly that I wasn't as good as anyone else because my father was a simple soldier who had married a very rich woman. And the truth was that I wasn't as good as many of my peers, and deep down, I knew that."

In 1937, his parents divorced and Ilyinsky was brought to the United States by his mother and enrolled in Woodbury Forest Preparatory School in Virginia. One morning, several senior students cornered him. "Are you really a Russian prince?" one demanded. Ilyinsky snapped to attention: "No, sir! I'm a Woodbury Forest cadet!"

"I craved to be like everyone else," Ilyinsky explains. "I wanted them to like me because I was a person, not because of my title."

When Ilyinsky was 16, he lied about his age and joined the Marines. The grunts called him "Ski" because no one could pronounce Ilyinsky. Paul Ilyinsky was finally just "one of the guys."

Palm Beach helped mold Angelica Ilyinsky as a child. "We were trained for the best colleges in America, but also were taught in school how to pour tea and host parties . . .." she recalls. "It was very much an elite life style."

Angelica Ilyinsky doesn't recall her childhood as particularly happy, especially when her parents divorced. "Believe me, just because you are born with money doesn't mean that you don't have to prove yourself to your peers when you are growing up. You do!"

A few weeks before high school graduation, Angelica Ilyinsky and two girlfriends were expelled for accepting an innocent car ride from three boys. It was something "proper Palm Beach ladies" didn't do. Her parents sent her to France for two years. She met Ilyinsky when she returned and attended a Palm Beach party. It was love at first sight, she says. Three months later, they eloped.

The newlyweds took a one-month honeymoon in Haiti. When they returned, Paul Ilyinsky opened a Palm Beach photography studio bankrolled by his mother. The couple bought a house next to the Pulitzers and before long the Ilyinskys' children were playing with Caroline and John-John Kennedy.

In the early 1960s, however, the Ilyinskys began thinking about leaving Palm Beach. "I don't think that Pauly and I would still be married if we had stayed in Palm Beach," recalls Angelica Ilyinsky. "Our friends were all getting divorced and we were afraid it was catching. People were bored. It wasn't a healthy environment for young couples."

There were other pressures. They felt they could no longer afford Palm Beach. "This is a dream world," says Angelica Ilyinsky. "We felt our children had to see what America was really all about. We wanted them to go to baseball games, to see poor people."

The Ilyinskys moved to Cincinnati where Paul went to work for his uncle, managing an office tower. They stayed 18 years, until their children were on their own. Then they hurried back "home" to Palm Beach and the life style they love.

Are the rich really different? Paul Ilyinsky finds the question irritating. "C'mon," he replies. "Okay. We are smarter.

"Look, I've made some money on my own, you know, a terrible lot of money, as a matter of fact. I did it because I was smart enough to hire smart people. That is the advantage, my friend. You can afford the best advice in the country when you are rich."

"People are people, but when you have money you know more people of influence," adds Angelica Ilyinsky. "They help you and you help them. You also know how to make the system work for you."

Do the rich bear more responsibility for the poor? "Of course," Angelica says. "But let's be blunt," says Paul Ilyinsky. "I'm not a good enough Christian to jeopardize my way of life, if you know what I mean. I'm certainly not going to give it all to charity." The Ilyinskys say they give $10,000 a year to charities.

"Rich people do have problems," she says. Insecurity: "You want the little people to like you for what your are, not for what you have." Control: "Our parents used their money to control us. All parents do. Listen, you pay a price for money in this world." The family fortune can take on a life of its own: Protecting the fortune is more important than protecting the family.

"But let's face it," says Paul Ilyinsky. "Given a choice, who wouldn't take life with wealth?" THE POOR

Shortly before 5 a.m. a dozen old school buses arrive at a dirt lot in an area of Belle Glade called the ghetto, a seven-block by seven-block section of town. Soon, farm laborers assemble. Each is black. Some wander between buses asking the drivers where they are going. The drivers reply: "Oranges," "Beans," "Grapefruit." Sometimes the workers ask how much the landowner will pay. Many drivers either don't know or won't say. The price will be set after the workers get to the fields. Pickers who don't like the pay must walk home.

Silina Franc,ois, a Haitian woman in her late forties, rose before the first buses arrived at the lot. She used a pair of pliers to turn the broken knob on her television set clockwise to a news program.

Her 19-year-old daughter, Alene, turned away from the noise, twisting on the living room couch.

"A. . .lene, A . . .lene, A . . .lene," Silina Franc,ois coaxed. The teen-ager stirred, and her mother left to catch a bus. It was up to Alene to make sure that her four brothers, younger sister and Carleen, Alene's 3-year-old daughter, made it to school.

By 7:30 a.m., the kids were up and gone. Alene put several handfuls of cooked rice and a piece of chicken into a plastic bag for her lunch and hurried down the street to meet her older sister, Macula.

"You got to get to the fields early," Alene explained, "or you will get stuck with the thinnest rows."

They arrived at the bean field by 8:30 a.m. and sat atop bushel baskets in front of the rows that they wanted. An hour later, the morning dew had dried and the string beans were ready to be picked. The workers would be paid $2 per bushel, the crew boss said.

Bernard Davis, a sack boy, came by. He was responsible for paying pickers once they filled a basket. He would pour the beans into a burlap bag that he would carry to a waiting truck. Davis was important because he decided when a basket was full. He could pay Alene once the beans in her basket reached the rim or he could demand that she pile them higher, making the basket hold as much as one-third more.

"Hey, you wanta go to a movie tonight?" Davis asked Alene.

"Naw."

"C'mon," he said, leaning close. "You is so pretty, girl. How about I come over tonight and we sit on your porch?"

Alene turned to her sister and said something in Creole.

"Hey, woman," Davis interrupted. "I told you not to speak that stuff in front of me. You talk American." He threw a bean at her. She threw one back. He reached out to grab her shoulder. She intercepted his hand.

"I want her to go with me this season and be my woman," he explained later. "But, ooh, she's a hard one. She says she won't go, but I'll get her."

There were no toilets in the field. Men relieved themselves where they worked. Women sometimes clustered together, taking turns behind their human circle. No one wants to leave their beans, Alene explained as she began picking. "Don't trust nobody to watch 'em."

It was hot. The crew boss had set up a jug of water in one corner. He had torn a soft-drink can in half to serve as a communal cup.

A middle-aged white man pulled his truck off the highway and approached Alene. "Hey, little girl, you wanta sell some beans? I'll give you $5."

Alene declined. Bernard Davis rushed over. "What's wrong with you, girl?" Davis asked Alene. "This man wants to give you $5 for a bushel. Do it."

"Tell 'em to pick his own," Alene snapped.

"You is crazy girl," an irritated Davis replied, as the white man moved on to another worker. He paid the woman $5 and carried the beans to his truck.

Alene had been afraid to sell the man her beans, she said later, because some landowners hire whites to buy produce from pickers. Then, they confiscate the worker's wages and kick them off the field.

When it was time for Davis to pick up Alene's next basket and pay her, he balked. "Not enough beans," he said. She added more, but he was unsatisfied.

It took Alene nearly four hours to pick five bushels. She received $10. That was all that she wanted to earn, she said, but she kept picking for another half-hour, this time filling a bucket that she had brought with her. Occasionally, she would look to see if the crew boss was watching. She would take the beans home and the family either would eat them or trade them with neighbors for produce that they had stolen.

Alene needed the $10 to finish paying for a Cabbage Patch doll for Carleen, she said. "I already got her one." Why was she buying another? "We can play with them together."

Alene was 11 when she came from Haiti to the United States with her mother. They cleaned houses in Miami at first, then a friend told them about Belle Glade. Alene went first. She was 14 and scared. "I'd heard that black Americans hated Haitians and killed 'em 'cause they said Haitians ate their cats and took their jobs." Her mother eventually joined Alene.

One by one, Silina Franc,ois paid to bring five more of her nine children to Belle Glade. None of the children's four different fathers support the family. Silina Franc,ois, who speaks little English, works six days each week to support it. She earns from $45 to $125 per day during the season.

Each member of the Franc,ois family is here on a temporary visa, although none plan to leave. They said they do not receive any federal assistance. Their income depends on Silina's pay. There are no safety nets. Silina gets no sick days, pays no Social Security, receives no benefits. No one but she knows how many days she works or how much she is paid. But it is better than Haiti, she says.

The family's largest monthly bill is its $500-per-month rent for a trailer located only one block from "Tiger Street," the Haitians' term for a red-light district. The eight family members and a cousin share the three-bedroom trailer.

A city study in 1980 found that 49 percent of Belle Glade's 6,000 dwellings were substandard and at least 16 percent were in such bad condition that they were "unfit for human habitation." Overcrowding and a lack of decent housing have created a slumlord's dream. Empty, dilapidated rooms rent for $65 per week. It is not unusual to find elderly farm workers living in abandoned migrant houses beside Highway 441 or in makeshift structures made of discarded wood, waxed cardboard and scrap metal.

Alene is effervescent when she returns home. Usually, she must study for night school, but not on Friday afternoons. She fixes her hair and joins other teen-age girls outside watching her brothers and other boys play football in the street.

Christine Franc,ois stands nearby, clapping her hands in time to a song that she and a friend sing:

"Mama's on the bottom,

"Daddy's on the top.

"Sister's on the corner,

"Selling fruit, cock, tail,

"Gonna Rock, rock, rock tonight.

"Gonna rock, rock, rock, tonight."

Kids learn about sex quickly here. The crowded living conditions make privacy difficult. Alene got pregnant at 16 by her first boyfriend. "My mamma, she was mad. She says the first one is okay 'cause anyone makes a mistake, but anymore and I be out of her house for good."

"Boys," Alene continues, "sweet talk until the baby comes, then they gone and treat you like a dog."

It is nearly 8 p.m. when Silina Franc,ois arrives home, carrying several large naval oranges. She is exhausted. Most of her children still are playing outside. All of the boys, except Patrick, age 17, have gone to a nearby video arcade. Patrick is a born-again Christian. He is waiting to go to church with his girlfriend.

"Two choices in Belle Glade," Patrick says. "Religion or rocks." It is a reference to tiny pieces of cocaine called "rocks" and sold on Tiger Street for $10 each. The drug is smashed and smoked in a marijuana reefer.

People are everywhere outside. Some haggle with the Arab merchants who sell cheap merchandise in stores that ring the ghetto. Other farm workers walk along Tiger Street. It is noisy there. Prostitutes beckon Jamaican workers who are standing on the balconies of a nearby dormitory. The price is "10 and 2" says Kelly Kline, an oddity in the ghetto because she is a white prostitute. Ten dollars goes to the hooker, Kline explains, and $2 rents the room. A prostitute can earn in a few hourswhat it takes Alene almost two days to make.

Alene stays outside the trailer talking to friends until late, then she comes inside to take care of Carleen and watch television.

It will be noisy all night long in the ghetto. Reggae. A child crying. Two men fighting.

Patrick and Alene don't think they are poor. "We have everything we need," Patrick says. "When it comes to money, if my mamma don't have it, we understand and we do without it."

Do they hate rich people?

"In America," Patrick says, "it's your duty and responsibility to try to get up there, at least up into the middle class, so when your kids grow up they will have a better living. Someday you could have some millionaires in your family if everyone works hard enough."

His remarks are similar to those made by workers in Palm Beach. "When I see the Rolls-Royces, I feel inspired," said Tracy Strickmane, a Palm Beach bartender.

"I think that every employe who works for Palm Beach secretly looks at this place and fantasizes that he or she will be part of it someday," Robert Moore, a building inspector, said. "It's the American dream . . . Work hard and you'll make it."

Few black Americans in Belle Glade believe that. "I would submit that the American black community in Belle Glade as a whole has a terrible emptiness in their lives," explained Sister Patricia Downs, a nun at the Haitian Catholic Center in Belle Glade. "They believe that this is the way it is and that is how it is going to be forever . . ."

Downs is concerned that young Haitians coming to American will fall into the same apathy if they stay in the Belle Glade ghetto. "In 20 years of working with black communities in other parts of the country," Downs continued, "I have never seen anything like it is here."

Alene still dreams, but not as big as she once did. "I'm not going to pick beans all my life," she says. "I'm going to get out of Belle Glade." She is unsure about how or when and, moments later, if she really wants to.

If she gets a diploma, a teacher has promised to help her apply at a college in Kansas. But she would have to leave Carleen behind. It could be worth it, Alene says, if she could meet a "man who wants to marry me. Belle Glade men don't marry."

She also could move to Delaware, she says. "A friend told me you can get $3.10 per hour working in chicken houses there."

But leaving Belle Glade frightens Alene. She understands how it works. "I don't know nothing about white people," she says at one point. "I don't see them unless they are a teacher or the boss man or the landlord. Blacks here say you should stay away from white people. Black and white don't mix. They say whites always lie."

Alene will wait until this picking season ends before deciding what she will do. "Staying another season," she says, "won't hurt nothing."