1724- 83. He was born in Boston, Massachusetts, the second son of the Dutch born colonial administrator William Burnet FRS, and of his second wife Anna Mary Van Horne. Both his parents died at a young age and he was left in the care of an uncle.
Burnet joined the navy at New York as a 12 year-old boy aboard the Tartar 20, Captain Matthew Norris, and he was commissioned lieutenant on 20 August 1744. Having been promoted commander on 12 May 1756 he captained the sloop Happy with some distinction and bravery in the Seven Years War, taking the privateer Renard 14 on 18 February 1757 and effecting the significant capture of a Dutch vessel laden with timber and stores.
In recognition of his efforts Burnet was posted captain of the Cambridge 80 on 5 May 1757, and flying the broad pennant of Commodore John Moore he went out to the Leeward Islands station in June, taking part in the unsuccessful expedition to Martinique during January 1759, and in the brutal, badly conducted assault on Guadeloupe thereafter.
Following a short spell aboard the Bedford 64 in home waters, he removed to the Rochester 50 in early 1760, and after taking the privateer Subtile on 3 April he served under the orders of Commodore Robert Swanton in the reinforcements for the expedition to the St. Lawrence which set sail from England later that month. Thereafter rejoining the Leeward Islands fleet in the summer of 1761, he commanded the Rochester in Rear-Admiral George Brydges Rodney?s successful expedition against Martinique during the early part of 1762.
Burnet next commanded the Marlborough 70 in Admiral Sir George Pocock?s reduction of Havana in the summer of 1762. During the voyage home his ship was on the point of foundering when on 29 November her crew were rescued by the Antelope 50, Captain Thomas Graves, which was returning from Newfoundland. The abandoned Marlborough was then destroyed.
Burnet commissioned the new Boyne 70 during the Falklands Islands dispute of 1770, commanding her from October and going out to Jamaica in June 1771. After returning to England in 1772 she became a guardship at Plymouth, and he retained the command through to 1774.
At the beginning of 1779 he was appointed to the Prudent 64, serving with the Channel fleet in its August retreat from the allied armada, and later being sent with a squadron of frigates to protect the coast of Scotland from a rebel privateer squadron commanded by John Paul Jones. News soon reached him however that Jones had already defeated the British frigate Serapis on 23 September and had sailed for the Texel.
TThe Prudent was coppered at Plymouth during the winter, and in May 1780 sailed for North America with Rear-Admiral Thomas Graves? squadron. On 16 March 1781 Burnet commanded her at the Battle of Cape Henry, being in the thick of the action early on, and ending it with his ship much damaged and casualties of seven men killed and twenty-four wounded. Following a storm in July he was obliged to take the Prudent into New York for repairs and therefore missed the Battle of the Chesapeake in September. He did however take the privateer Boulonge on 23 July.
He removed to the Royal Oak 74 in the month of September for Graves? second fruitless visit to the Chesapeake, and although he did not sail with Rear-Admiral Sir Samuel Hood?s squadron to the Leeward Islands he later led the order of battle at the Battle of the Saintes on 12 April 1782. The French handled the Royal Oak roughly and his first lieutenant was one of eight men killed, although he did receive the surrender of the Glorieux 74.
Burnet returned to England as a passenger shortly after the action, and he did not see any further employment.
He died on 4 June 1783 in Plymouth.
Burnet had a son from a first marriage, Major-General John Burnet, and a daughter, Ann, born in 1765 to Mary Hinchley who he subsequently married on 25 October 1770. Following Burnet?s death she married a wealthy businessman, Thomas Rock.
He was regarded as a good officer, but was nevertheless one of several officers named by Lord Robert Manners as lacking character and ability as a sea officer.