The sea captains who called at this island, on their way to India 300 years ago knew its interior as a place of ebony forests strewn with volcanic boulders and inhabited by wild creatures like that ill-fated cousin of the pigeon, the dodo.

But visitors passing beyond Mauritius' corona of gleaming white beaches lined with palm trees today find it blanketed in spindly stalks of sugar cane and crammed with almost a million people whose culture reflects the civilizations of three continents.

For Mauritius, 750 miles off the east coast of Africa, sugar and ethnic diversity are the legacies of being drawn into the orbit of European colonial empires and then spewed out, planted and populated, as an independent member of the United Nations 300 years later. Some islanders believe this experience has destined Mauritius -- in a stretch of the earth once called "the world's end" -- to share the fate of the extinct dodo.

"Islands are doomed," said Mauritian editor Percy McGaw. "All we have is sugar and man."

What is worse for Mauritius, it has too much of both. Its population is expanding at a rate that will see it double in 40 years.

Tiny shops and homes made of wooden planks or corrugated iron border almost every foot of the narrow roads that take you from one end of the island to the other in about 90 minutes. Bunches of bananas and pineapples hang from the rafters of shops, like the one owned by "B. Meetoo."

Indian women, saris tucked tight against their bodies, draw water from outdoor communal taps. If they are average Mauritians they will live to be 67 years old. Their husband's salaries, if they are average, will bring each member of the family the equivalent of about $800 a year in income.

Many of their husbands are among the 70,000 laborers in the sugar industry, the single largest employer on the island. As the world's 10th largest producer of sugar, Mauritius earns two-thirds of its foreign exchange and one-third of its gross domestic product from this commodity, which is already overabundant in a world turning to sugar substitutes.

Attempts to diversify Mauritius' agricultural sector have met with only limited success, partly because sugar is the crop that best resists the cyclones that periodically batter the island.

Slumping world sugar prices and rising oil prices left Mauritius in August 1979 with only enough foreign exchange for two weeks of imports. It turned to the International Monetary Fund for a loan of $98 million. In return it was forced to devalue its currency, which sent inflation at home soaring to near 40 percent.

With unemployment running at close to 13 percent of the work force and predictions that it may rise to 17 percent by the end of the year, it is easy to see what is the main preoccupation of the government.

"One out of three families has at least one member out of work, and this is not funny," said businessman Rene Seeyave.

In addition, free education to the university level has given Mauritians a 61 percent literacy rate and rising aspirations so that young people coming onto the labor market are not inclined to toil in the sugar-cane fields or even in the factories set up in a small, duty-free manufacturing zone.

All these factors help explain why such a big ado is made over the "event," as it is called here. That is when somebody gets a job overseas. It is the occasion for a press conference and front-page story, like last month when 62 Mauritians got construction jobs in Saudi Arabia.

They are the lucky ones, escapees from what often seems more like a ship of would-be emigrants permanently anchored at sea than a self-contained country.

"Everyone would leave in a day -- there would be nobody left -- if the U.S., Canada, Australia just opened their doors to us," said Lindsay Riviere, whose parents and relatives all emigrated to Australia eight years ago.

Mauritius' permanent connection to the rest of the world began when the Dutch briefly settled here in the 1600s. In 1715 the French came to what they called "Ile de France," decorating they tiny harbor town of Port Louis with their architecture. Mauritian courts still follow French legal traditions.

The British took Mauritius from the French in 1810 and governed it until independence in 1968.

Ties between Mauritius and its lost colonizer remain close. The prime minister, for example, still nominates Mauritians for the honor of British knighthood. However, not even Sir Seewoosagur Ramgoolam, the prime minister, can tell you offhand how many knights are roaming Mauritius' lush tropical countryside.

"But there must be quite a few," he said in his office. "To protect you," he added quickly, smiling.

Outside his office a few unarmed police officers stand around. They are there less for protection than to maintain some order in the pressing crowd of men who constantly wait hours, even days, to see "the old man," as he is called here by friend and foe.

Whatever people think of Ramgoolam's politics, his example of racial tolerance is given a large dose of credit for the island's record of only sporadic racial strife, despite its cultural diversity.

Indians, both Hindus and Moslems, make up 67 percent of the islanders. They are descendants of the indentured laborers brought to work in the sugar cane fields after slavery was abolished in 1833.

Roman Catholic creoles are the second-largest ethnic bloc, a mixture of the French planter stock and their African slaves.About 20,000 white Franco-Mauritians who still play a dominant role in the economy and a Chinese minority who run the commerce make up the rest of the population.

Apart from Ramgoolam's leadership, Mauritians say they have another reason for getting along with each other.

"We are so small. It's sea all around. There's no place to flee to," said Riviere.