Law officers edit

• Lord Advocate – Ilay Campbell; then Robert Dundas of Arniston
• Solicitor General for Scotland – Robert Dundas of Arniston; then Robert Blair

Judiciary edit

• Lord President of the Court of Session – Lord Glenlee until 27 September; then from 26 October Lord Succoth
• Lord Justice General – The Viscount Stormont
• Lord Justice Clerk – Lord Braxfield

• 10 July – Scottish explorer Alexander Mackenzie reaches the Mackenzie River delta in North America.
• November – foundation stone for Old College, University of Edinburgh, laid.
• December – steamboat experiments on the Forth and Clyde Canal by Patrick Miller of Dalswinton.
• The original lighthouses at Eilean Glas on Scalpay, Outer Hebrides, and Dennis Head Old Beacon on North Ronaldsay, Orkney, are completed by Thomas Smith.
• Robert Adam designs a new house at Newliston.
• Andrew Duncan delivers the first lectures on forensic medicine in Britain, at the University of Edinburgh.^[1]
• The Aberdeen Medico-Chirurgical Society is founded by James McGrigor and James Robertson.
• Robert Burns is appointed an exciseman.
• New pump room for St Bernard's Well, Stockbridge, Edinburgh, designed by painter Alexander Nasmyth.
• John Ainslie completes and publishes his 9-sheet map of Scotland.
• Flax mill established at Old Deer.
• Clyde Model Dockyard is established as a toyshop in Glasgow.

• 5 January – Thomas Pringle, writer, poet and abolitionist (died 1834)
• 28 February – David Duncan, Presbyterian minister (died 1829)
• 1 March – John Ramsay McCulloch, economist (died 1864 in London)
• 17 August – William Knox, poet and journalist (died 1825)
• 12 October – William Collins, publisher (died 1853)
• 30 October – Michael Scott, author (died 1835)
• 9 November – Robert Pearse Gillies, poet and writer (died 1858 in London)
• November – Peter Miller Cunningham, naval surgeon and pioneer in Australia (died 1864 in Greenwich)
• 3 December – Archibald Robertson, physician (died 1864 in Bristol)
• 20 December – William Burn, architect, pioneer of the Scottish Baronial style (died 1870)
• 23 December – George Douglas, 17th Earl of Morton, Tory politician (died 1858)
• Thomas Wright, prison visitor (died 1875 in Manchester)

• 17 March – Sir Charles Douglas, 1st Baronet, admiral (born 1727)
• 27 September – Thomas Miller, Lord Glenlee, judge and politician (born 1717)

• 9 October – the first recorded cricket century to be scored in Scotland is made by the Hon. Colonel Charles Lennox: he scores 136 not out.^[2]