Scientists hopeful of finding 18th century ship 'the Endeavour' A replica of the Endeavour sits in Sydney's Darling Harbour as the centuries-long hunt for the remains of famed ship -- the vessel used by James Cook on a voyage of discovery to Australia and New Zealand -- could be nearing an end. Marine archaeologists from Australia and the United States said recently they believe they may have found the site where the vessel was scuttled off the east coast of the US in 1778.