Events from the year 1878 in Scotland.

• 14 January – Alexander Graham Bell demonstrates the telephone to Queen Victoria.^[1]
• 15 March – restoration of the Scottish hierarchy of the Roman Catholic Church, carried out on the instructions of the newly appointed Pope Leo XIII.
• 31 May – the North British Railway's first Tay Bridge across the Firth of Tay is ceremonially opened, its engineer, Thomas Bouch, being made a burgess of Dundee. Designed in iron to replace a train ferry, it is the world's longest bridge at this date.^[2]
• 12 December – the iron-hulled full-rigged ship Falls of Clyde is launched at Russell & Company's yard at Port Glasgow for Wright and Breakenridge's Glasgow-based Falls Line. In 1968 she will be laid up as a museum ship in Honolulu.
• Sophia Jex-Blake sets up in practice in Edinburgh as the city's first woman doctor.
• The hydropathic establishment in Moffat is opened.
• Construction of forts on Inchkeith begins.
• West coast shipping operator David Hutcheson & Co. passes wholly to control of David MacBrayne.
• The sanitary porcelainware works at Barrhead that becomes part of Armitage Shanks is established.

• 20 January – Finlay Currie, actor (died 1968 in England)
• 23 March – Muirhead Bone, graphic artist (died 1953 in England)
• 12 April – Alex McDonald, footballer (died 1949)
• 24 July – Louisa Jordan, nurse (died 1915 in Serbia)
• 10 August – Louis Esson, poet and playwright (died 1943 in Australia)
• 14 December – James Greenlees, rugby union footballer, educationalist and soldier (died 1951)
• Robert Freeman, Baptist minister in the United States
• George Wittet, architect (died 1926 in Bombay)

• 26 January – Kirkpatrick Macmillan, inventor of the bicycle (born 1812)
• 19 February – George Paul Chalmers, painter (born 1833; died as the result of a street attack)
• 6 June – Robert Stirling, Church of Scotland minister and inventor of the Stirling engine (born 1790)
• 13 August – George Gilfillan, writer and poet (born 1813)
• 5 December – George Whyte-Melville, novelist and poet (born 1821)^[3]
• 31 December – James Matheson, Member of Parliament and co-founder of Jardine, Matheson & Co. (born 1796)

• July – William McGonagall journeys on foot from Dundee to Balmoral Castle over mountainous terrain and through a violent thunderstorm in a fruitless attempt to perform his verse before Queen Victoria.^[4]

• Timeline of Scottish history
• 1878 in Ireland