Someone had the idea of feeding them breadfruit, a cheap and versatile plant about the size of a grapefruit. Unfortunately it only grew in Tahiti - almost exactly the opposite side of the planet.
The navy got the job of transporting a shipful of these plants, all potted and growing, from the one place to the other (why seeds alone would not have done I'm not sure) and to show how seriously they took the job they sent one of their smaller ships, the Bethia, (renamed 'Bounty' just for the occasion) and a junior officer, Lt William Bligh, though there must have been plenty of seasoned captains twiddling their thumbs in peacetime.
It seems the admiralty were uninspired by the whole mission, and my impression of Bligh is that he was a rather serious, earnest young officer; highly competent but a bit charmless, probably with a hankering to be given the chance to make his name. No doubt he saw this as his chance, while the Admiralty probably had a good giggle about it and made bets on whether his ship would even make it.
Bligh did make it but got there late thanks to an ambitious, and abortive, attempt to go by way of the notoriously stormy Cape Horn. This meant waiting around for months on Tahiti until the season was right again to transport the plants. In the meantime Bligh's crew were living it up in the tropical paradise, thanks largely to the attentions of the local young ladies, who evidently found their visitors as exotic as the sailors found them.
This is where Bligh fell down on the job. By failing to keep his crew occupied and disciplined, they ceased to be a crew and when it came time to leave it was no easy task getting them to become one again and Bligh was not really up to it. He couldn't inspire them so he had to shout and swear and bully. They did not react well to this.
After a few weeks they decided they had had enough and a large section of the crew mutinied. The leader of the rebellion was Fletcher Christian, a man who comes across as a rather vain and spoilt young aristocrat. Once a good friend of Bligh, his pride was probably wounded by being reduced to another of Bligh's sounding boards, and in front of the crew too.
Bligh and his loyal officers and crew were set adrift in one of the ship's rowing boats three thousand miles from the nearest European outpost, while Christian took the Bounty back to Tahiti with the goal of picking up their girlfriends and starting their own colony.
That plan did not go well. The local islands were all already populated by natives who did not take kindly to settlers so they had to go further afield, eventually fetching up on a remote rock called Pitcairn, where their descendants still live.
Bligh now came into his own, successfully dealing with hostile natives, all sorts of weather, food and water shortages, and even having to practically carry their boat across parts of the Great Barrier Reef, cutting their feet to bits on the coral, plus the occasional mishap such as accidentally setting fire to a whole island, finally arriving at a Dutch outpost on East Timor... all without the benefit of charts. The navigation was all down to Bligh's memory.
That was only half the battle. With only his good name as a British officer to trade with he had to get his crew back to England in stages, either hitching lifts on ships or getting his own built when none were available. Tragically, after surviving the epic open boat trip, several of the crew died of cholera in disease-ridden Jakarta.
A few bets might have been lost when Bligh finally got back to England. Tempers certainly were, and this time a real no-nonsense captain, Edward Edwards, was sent in an armed frigate, the Pandora, to find the mutineers and bring them back to be fairly tried then hung.
At Tahiti, he found several of Bligh's crew - a few bona-fide mutineers, but some loyal men who had stayed with the Bounty because the boat was full. Edwards didn't discriminate but had them all locked up in a wooden cage on the ship's open deck.
Edwards had less joy than Bligh at the Great Barrier Reef, though - the Pandora struck it and sank. Two of the Bounty men went down with it, while the survivors had to recreate Bligh's open boat voyage. The citizens of East Timor must have started to think this was some new extreme sport.
In a bitter twist of fate, two of Bligh's crew had sailed with Edwards to help identify the mutineers, and they had to endure the open boat voyage a second time.
Three mutineers were eventually hung.
Bligh was given another shot at the breadfruit mission, perhaps at the request of the gambling enthusiasts at the Admiralty. This time he succeeded. Depressingly though, he noted in his logs that the once pristine topical paradise of Tahiti was no longer unspoilt. Other European ships had called since the Bounty and many of the natives were going around in European clothes.
Even more sadly, the slaves in the West Indies didn't care for breadfruit and refused to eat the stuff.
As a footnote, the fate of the Bounty was a mystery for 25 years until Pitcairn was stumbled upon by an American ship. They found John Adams, last survivor of the Bounty and now patriarch of the colony, some native women and their offspring, including one Thursday October Christian, named after the day of his birth.
When the Americans informed them that their island was the other side of the international date line, the colonists corrected their calendars, and Thursday changed his name to Friday.