- John Hanning Speke and James Augustus Grant leave Zanzibar to search for source of the Nile .
- October 1 - The Battle Of The Volturno
- October 5 - Austria , Britain , France , Prussia and the Ottoman Empire form a commission to investigate causes of clashes between Maronite s and Druze s in Lebanon earlier in the year
- October 18 - the British general Lord Elgin - with protestations from the French - ordered his forces to set fire to the huge complex of Beijing 's Old Summer Palace , known as the Gardens of Perfect Brightness, which burned to the ground. It took 3,500 British troops to set the entire place ablaze and took three days to burn. Elgin justified the order as retaliation for the imprisonment, torture, and murder of several western prisoners of war, among them two British envoys who had been under protection of a flag of truce. The burning of the Gardens Of Perfect Brightness is still a very sensitive issue in China today.
- October 19 - New Māori revolt begins in New Zealand
- October 26 - Battle Of The Volturno . Garibaldi again defeats the Neapolitan forces, advancing on Gaeta , the last remaining Neapolitan strong-point.
- October 26 - Giuseppe Garibaldi gives Naples to the king Victor Emmanuel II .
- December 20 - South Carolina becomes the first state to secede from the Union.
- December 29 - The world's first ocean-going (all) iron-hulled and armoured Battleship , the (British) '' is launched.
- January 3 - Kato Takaaki , 24th Prime Minister Of Japan (d. 1926 )
- January 8 - Emma Booth , the fourth child of Willliam and Catherine Booth (d. 1903 )
- January 25 - Charles Curtis , Vice President Of The United States (d. 1936 )
- January 29 - William Jacob Baer , American painter (d. 1941 )
- January 29 - Anton Chekhov , Russian writer (d. 1904 )
- February 11 - Rachilde , French author (d. 1953 )
- February 25 - Sir William Ashley , economic historian (d. 1927 )
- February 29 - Herman Hollerith , American businessman and inventor (d. 1929 )
- March 2 - Susanna M. Salter , first woman mayor in the United States (d. 1961 )
- March 5 - Sam Thompson , baseball player (d. 1922 )
- March 13 - Hugo Wolf , Austrian composer (d. 1903 )
- March 19 - William Jennings Bryan , American politician (d. 1925 )
- March 22 - Alfred Ploetz , German physician, biologist, and eugenicist (d. 1940 )
- March 27 - Frank Frost Abbott , American classical scholar (d. 1924 )
- May 2 - Theodor Herzl , founder of modern political Zionism (d. 1904 )
- May 9 - J. M. Barrie , Scottish author (d. 1937 )
- May 20 - Eduard Buchner , German chemist, Nobel Prize laureate (d. 1917 )
- May 21 - Willem Einthoven , Dutch inventor, recipient of the Nobel Prize In Physiology Or Medicine (d. 1927 )
- May 25 - James McKeen Cattell , American psychologist (d. 1944 )
- May 29 - Isaac Albéniz , Spanish composer (d. 1909 )
- June 20 - Jack Worrall , Australian cricketer, footballer, and coach (d. 1937 )
- July 3 - Charlotte Perkins Gilman , American feminist (d. 1935 )
- July 7 - Gustav Mahler , Austrian composer (d. 1911 )
- July 19 - Lizzie Borden , American murder suspect (d. 1927 )
- August 3 - W.K. Dickson , Scottish inventor (d. 1935 )
- August 7 - Alan Leo , British astrologer (d. 1917 )
- August 16 - Jules Laforgue , French poet (d. 1887 ) hi
- September 5 - Andrew Volstead , American politician (d. 1947 )
- September 6 - Jane Addams , American social worker, recipient of the Nobel Peace Prize (d. 1935 )
- September 13 - John J. Pershing , American general (d. 1948 )
- November 1 - Boies Penrose , United States Senator from Pennsylvania (d. 1921 )
- November 6 - Ignacy Jan Paderewski , Polish pianist and composer (d. 1941 )
- November 23 - Billy The Kid , American gunfighter (d. 1881 )
- November 23 - Hjalmar Branting , Prime Minister Of Sweden , recipient of the Nobel Peace Prize (d. 1925 )
- December 4 - Charles De Broqueville , Belgian Prime Minister (d. 1940 )
- December 7 - Joseph Cook , sixth Prime Minister Of Australia (d. 1947 )
- December 15 - Niels Ryberg Finsen , Danish physician, recipient of the Nobel Prize In Physiology Or Medicine (d. 1904 )
- John Coughlin , American politician (d. 1938 )
- Frederick George Jackson , British Arctic explorer (d. 1938 )
- Albert Giraud , Belgian poet (d. 1929 )
- Lancelot Speed , British illustrator (d. 1931 )
- January 27 - János Bolyai , Hungarian mathematician (b. 1802 )
- January 27 - Thomas Brisbane , Scottish astronomer (b. 1883 )
- January 29 - Stephanie De Beauharnais , Grand Duchess of Baden (b. 1789 )
- February 20 - Henry Drummond , Canadian poet (b. 1851 )
- March 17 - Anna Jameson , German author
- March 25 - James Braid , Scottish surgeon (b. 1795 )
- May 12 - Sir Charles Barry , English architect (b. 1795 )
- May 16 - Anne Isabella Milbanke , wife of George Gordon Byron, 6th Baron Byron (b. 1792 )
- July 1 - Charles Goodyear , American inventor (b. 1800 )
- October 31 - Thomas Cochrane, 10th Earl Of Dundonald , British admiral (b. 1775 )
- December 14 - George Hamilton-Gordon , 4th earl of Aberdeen (b. 1784 )
- Dai Xi , Chinese painter (b. 1801 )
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