Awarded to Captain [later Vice Admiral] William Bligh of The Bounty fame, the first was particularly poignant as it marked the eventual success of his mission to transport breadfruit from Tahiti to the West Indies - the journey he was originally undertaking when the mutiny struck and the breadfruit was thrown overboard.
As is now well known, having served aboard The Resolution as Sailing Master under Captain James Cook on his third epic voyage to the Pacific in 1776, Bligh returned to the Pacific in 1787 in command of The Bounty to transport breadfruit trees to the West Indies. The breadfruit was seen as an important and cheap source of nutrition for feeding the slave populations of the sugar plantations.
In 1789, the mutinous crew, led by Fletcher Christian, took over the ship and, cast adrift in a longboat with a company of 18 men, Bligh accomplished the feat of navigating his 22ft boat across 3600 nautical miles of the Pacific to safety in West Timor - without the help of any navigational equipment - in 47 days.
His reward on returning to London was a court martial for the loss of The Bounty, a charge from which he was honourably acquitted in October 1790.
Bligh's extreme tenacity became clear when he returned to Tahiti to complete his original commission in 1794, this time successfully taking breadfruit trees to the West Indies.
In recognition of this success, the Society for the Encouragement of Arts, Manufactures and Commerce, later the Royal Society of Arts, (founded in 1754 in Covent Garden in London) awarded him the Society's gold medal.
Offered with an estimate of Aus$50,000 (£30,000), it doubled that price at the sale on July 27 to sell at Aus$100,000 (£60,000) on behalf of his descendants.
The second medal was the Naval Gold Medal (1795) awarded to Bligh in 1797 for the defeat of the Dutch Fleet at Camperdown, in which the British captured a number of enemy ships without loss. It sold on estimate at Aus$200,000 (£120,000.
The buyer's premium was 16.5 per cent.
By Ivan Macquisten