In a four-month test voyage from Portsmouth to Jamaica, H4 was found to be just 1 minute and 54 seconds out. And yet the Longitude Board refused to fully recognise Harrison's achievement and he never received the full amount of prize money he was owed.

The Association, meanwhile, still lay scattered beneath the Outer Gilstone, as she would for another 200 years. In 1963, Larn, then a Chief Petty Officer First Class in the Royal Navy, initiated the search for the wreck when he approached an admiral to ask if he could borrow a minesweeper. It took Larn and a team of divers from the Naval Air Command Sub Aqua Club (NACSAC) three years to find the Association, but on 4 July 1967 they discovered a bronze cannon and gold coins on the Gilstone Ledge.

In just six weeks, they raised several French cannons from the seabed – trophies from the War of the Spanish Succession (one of which they donated to the Valhalla Museum on Tresco) – along with gold and silver coins, pewter plates and a phenomenal assortment of artefacts, from buckles and buttons to candlesticks and combs.

Word quickly got out, though, and amateur salvagers descended on the Scillies. "Anybody with a diving cylinder and a bedroll turned up here," Larn told me. "There was nothing to stop anybody from looting the wreck of the Association after we left, and that's exactly what happened. Coins were so plentiful that people were paying for pints in the pub with them."

No official record was ever made of what was hauled out of the sea, and within months the findings were dispersed across the globe. A silver plate inscribed with Sir Cloudesley Shovell's coat of arms was sold to Rochester Town Hall where the admiral had served as local MP; artefacts from the wreck now decorate a pub in Penzance; and fragments of the ship's bell were auctioned off to private collectors in the United States.

A new mission to see Titanic