At the time the Endeavour — sailing under another name — is believed to have been scuttled, Captain Cook was still alive.
But the much-lauded explorer was on another ship, Discovery, on his third and final Pacific expedition which ended with his murder in Hawaii in 1779.
The Endeavour had been sold following Cook's triumphant 1768-1771 voyage to New Zealand and Australia's east coast with botanist Sir Joseph Banks aboard, and it vanished from naval records.
Kathy Abbass of the Rhode Island Marine Archaeology Project has led investigations into the fortunes of the sturdy Endeavour, which was hand-picked by Cook and went on to serve as a troop carrier.
Bought by an English private owner and renamed the Lord Sandwich, the Endeavour carried British troops to the US in the American Revolutionary war.
The Lord Sandwich then became a prison ship in Newport Harbour.
When Abbass was researching the 13 ships scuttled in a blockade of Narragansett Bay, Rhode Island to protect Newport from the French Fleet, she found a document which said the Lord Sandwich was Cook's Endeavour.
"In the [British national] archives in Greenwich, I found a document that was a transport manager's report which revealed where each of the ships was scuttled," Abbass told The Australian.
"It said there were five to the northwest of Goat Island and that the Lord Sandwich was one of them."
The Endeavour had been bought and renamed by shipowner John Wilkinson from Whitby, in northern England, the town in which the original ship was built as the collier called the Earl of Pembroke.
The ship was built from white oak, elm, pine in a flat-bottomed design which allowed her to sail in shallow waters and beached for cargo loading.
Divers including those from the Australian National Maritime Museum will have to look for the Endeavour's distinguishing features, among which are its length.
The Endeavour has a broad, flat bow, a square stern, and a long boxlike body with a deep hold.
Although only 29.7m long, it is a larger vessel than those among which it was scuttled.
"There is an 80 per cent chance we've got her now," Abbass said.
"The question is: which one is she, and how do you prove it?
"We know the Endeavour is more than 30 per cent bigger than the others … if we find all five and the other ships are much smaller, then it is likely that we've found her."
Marine archaeologist James Hunter is among four divers flying to Newport in September in the hope of finally solving the mystery of Cook's Endeavour.
A BRIEF HISTORY OF CAPTAIN COOK'S HMS ENDEAVOUR
• Launched in 1764 as a collier by the name of Earl of Pembroke
• Purchased by the navy in 1768 for a scientific mission to the Pacific Ocean to explore the seas of the 'unknown southern land', and renamed as His Majesty's Bark the Endeavour
• Departed Plymouth, England in August 1768, reaching Tahiti in time to observe the 1769 Transit of Venus across the Sun
• Sailed into uncharted ocean to the south, stopping at the Pacific islands of Huahine, Borabora, and Raiatea - all of which Cook claimed for Great Britain
• Ancored off New Zealand in September 1769
• Became the first ship to reach the east coast of Australia in April 1770, when Captain Cook first set foot in what is now known as Botany Bay
• Sailed north along the Australian coast, narrowly avoiding disaster after running aground on the Great Barrier Reef and being forced to beach for the sake of repairs
• Resumed westward journey on 26 December 1770, reaching the English port of Dover on 12 July after nearly three years at sea
• Was sold into private hands in 1775 and later renamed as Lord Sandwich
• Hired as a British troop transport during the American War of Independence and was scuttled in a blockade of Narragansett Bay, Rhode Island in 1778
