Oval miniature (unfinished and here currently shown in monochrome) in watercolour and graphite on card, in a rectangular cream-coloured card mount and a gilt frame.

This is one of a number of unfinished miniatures by Smart that he did for engraving, in this case in Robert Bowyer's group print of the commanding officers of Admiral Adam Duncan's fleet at the Battle of Camperdown in 1797 (see PAJ2555). The National Portrait Gallery has others similar, including of Captain William Bligh, who commanded the 'Director' there. In all such cases, the engraver filled in the captain's uniform (1795-1812 pattern) based on Smart's light pencil outline, as shown here. Fairfax was born in Surrey on 8 March 1739, the son of a cavalry officer. He entered the navy in 1750 in the 'Centurion' under Augustus Keppel, in the Mediterranean, and then served in the 'Mars' and 'Garland' under Marriot Arbuthnot. He became lieutenant on 20 December 1757 in the 'Duke'. From 1758 to 1760 he was in the 'Eurus' in North America, serving on operations in the St Lawrence, then went on half pay until May 1778 except for three years in the 'Greyhound', 1766-69. In May 1778 he was promoted commander in the cutter 'Alert' in the fleet under Keppel. In June, in company with the 'Arethusa', 'Alert' captured the French lugger 'Coureur', at the same time as 'Arethusa' was beaten off in her famous fight with the 'Belle Poule'. In August 'Alert' was taken by the French 'Junon' (40 guns), and Fairfax became a prisoner for most of the remaining War of American Independence. In January 1782 he was promoted post captain, commanding the frigate 'Tartar' in the West Indies until the peace in 1783. In 1793 he was appointed to command the 'Sheerness' and then 'Repulse', to 1796. This was in the North Sea fleet, in which he then became flag-captain to Admiral Duncan in the 'Venerable' both during the 'great mutiny' crisis of early 1797 and then at the Battle of Camperdown on 11 October. His reward was a knighthood and he remained in command of 'Venerable' until 1798. In 1799 he was appointed a Colonel of Marines and he reached flag rank on 7 January 1801. Though then considered for command of the Baltic fleet, he did not serve again but advanced to Vice-Admiral of the White by seniority on 25 October 1809 and of the Red on 31 July 1810. Fairfax first married Hannah Spears of Burntisland, Fife, in 1767, but she died in 1770. In 1772 he remarried to Janet Margaret, daughter of Samuel Charters and cousin of Sir Samuel Greig, an admiral in the Russian service. They had four sons and two daughters, several of whom died young but the fourth and sole-surviving son, Henry, was created a baronet in 1836 in recognition of his father's services. One of the daughters, Mary (1780–1872), first married her cousin Samuel Greig the younger, a captain in the Russian navy, with whom she had two sons, but was widowed in 1807. She remarried in 1812 to another cousin, William Somerville, and they had two daughters but Mary's fame - both in Britain and abroad - today well eclipses her father's from her talents as a scientific writer and expositor of mathematics. While not as original as Lord Byron's mathematical daughter, Ada Lovelace (1815-52), she was her forerunner in this area, in which both are regarded as female pioneers. Her father, who is usually referred to by both his given names, settled in Burntisland, where he had property likely to have been inherited through his first wife. He died in Edinburgh on 7 November 1813.