Law officers edit

• Lord Advocate – William Grant of Prestongrange
• Solicitor General for Scotland – Patrick Haldane of Gleneagles, jointly with Alexander Hume

Judiciary edit

• Lord President of the Court of Session – Lord Arniston the Elder
• Lord Justice General – Lord Ilay
• Lord Justice Clerk – Lord Tinwald

• Robert Gordon's College, Aberdeen, opens.
• James Short's Gregorian telescope (38 cm (14″) aperture reflector), the world's largest at this date, is constructed.
• Approximate date – Alexander Stephen begins shipbuilding at Burghead on the Moray Firth, origin of Alexander Stephen and Sons.^[1]

• 7 January – Robert Anderson, literary editor (died 1803)
• 18 February – David Bogue, nonconformist leader (died 1825 in England)
• 27 May – George Hill, Church of Scotland minister and academic (died 1819)
• 15 July (bapt.) – Robert Jackson, military physician and surgeon (died 1827 in England)
• 5 September – Robert Fergusson, poet writing in Braid Scots (died 1774)
• 14 October – John Fraser, botanist (died 1811 in England)
• 3 December – Hew Whitefoord Dalrymple, British Army general and Governor of Gibraltar (died 1830 in England)
• 8 December – Lady Anne Barnard, née Lindsay, poet, ballad and travel writer (died 1825 in England)
• William Dunbar, merchant, plantation owner, naturalist, astronomer and explorer (died 1810 in the United States)
• Approximate date – George Robertson, topographical, agricultural and genealogical writer (died 1832)

• 5 March – Sir Alexander Reid, 2nd Baronet, laird and politician
• 3 May – John Willison, evangelical Church of Scotland minister and religious writer (born 1680)

• Timeline of Scottish history