Events from the year 1740 in Scotland.

• Secretary of State for Scotland: vacant

• 7 July – Adam Smith sets out from Scotland to take up a scholarship at Balliol College, Oxford.^[1]
• Hugh and Robert Tennent take over the Wellpark Brewery, originally known as the Drygate Brewery, in Glasgow.
• General George Wade is succeeded as Commander-in-chief in Scotland by Sir John Cope.
• The 43rd Highland Regiment of Foot (the 'Black Watch') first musters, at Aberfeldy.

• 28 March (bapt.) – James Small, inventor (died 1793)
• 15 July – Archibald Hamilton, 9th Duke of Hamilton (died 1819)
• 29 October – James Boswell, diarist and biographer of Samuel Johnson (died 1795)
• James Cannon, mathematician and a principal draftsman of the Pennsylvania Constitution of 1776 (died in 1782 in the United States)
• William Davidson, settler, lumberman, shipbuilder and politician in New Brunswick (died 1790 in Canada)
• William Smellie, master printer, naturalist, antiquary, editor and encyclopedist (died 1795)
• Christopher Wyvill, cleric, landowner and political reformer in England (died 1822)

• 2 February – John Simson, heterodox theologian (born 1668?)
• 22 May – John Boyle, 2nd Earl of Glasgow (born 1688)
• 8 September – William Bruce, 8th Earl of Kincardine

• 1 August – the patriotic song "Rule, Britannia!", with words by Scottish-born poet James Thomson, is first performed at Cliveden, the English country home of Frederick, Prince of Wales.^[2]

• Timeline of Scottish history