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- January 4 – The Fabian Society is founded in London.
- January 5 – Gilbert and Sullivan's Princess Ida has its première at the Savoy Theatre, London.
- January 18 – Dr. William Price attempts to cremate his dead baby son, Iesu Grist, in Wales. Later tried and acquitted on the grounds that cremation is not contrary to English law, he is thus able to carry out the ceremony (the first in the United Kingdom in modern times) on March 14, setting a legal precedent.
- February 1 – A New English Dictionary on historical principles, part 1, edited by James A. H. Murray, the first fascicle of what will become The Oxford English Dictionary, is published in England.
- February 5 – Derby County Football Club is founded in England.
- March 13 – The siege of Khartoum, Sudan begins (ends on January 26, 1885).
- April 20 – Pope Leo XIII publishes the encyclical Humanum genus, denouncing Freemasonry and certain liberal beliefs which he considers to be associated with it.
- April 22
- May 1 – The eight-hour workday is first proclaimed by the Federation of Organized Trades and Labor Unions in the United States. This date, called May Day or Labour Day, becomes a holiday recognized in almost every industrialized country.
- May 16 – Angelo Moriondo of Turin is granted a patent for an espresso machine.
- May 16 : Sweden's Finance Minister Robert Themptander becomes his country's Prime Minister (1884–88)
- June 4 – (May 23 O.S.) The future flag of Estonia is consecrated as the flag of the Estonian Students' Society.
- June 13 – LaMarcus Adna Thompson opens the "Gravity Pleasure Switchback Railway" at Coney Island, New York City.
- July 3 – The Dow Jones Transportation Average, consisting of eleven transportation-related companies: nine railroads and two non-rail companies (Western Union and Pacific Mail), was created. The index is the oldest stock index still in use.
- July 5 – Germany takes possession of Togoland.
- July 14 – German administration in Cameroon.
- July 23 – Today's Courier records the first tennis tournaments held on the grounds of Shrubland Hall, Leamington Spa, England.
- August 5 – The cornerstone for the Statue of Liberty is laid on Bedloe's Island in New York Harbor.
- August 10 – An earthquake measuring 5.5 Mfa (based on the felt area) affected a very large portion of the eastern United States. The shock had a maximum Mercalli intensity of VII (Very strong). Chimneys were toppled in New York, New Jersey, Connecticut, and Pennsylvania. Property damage was severe in Jamaica and Amityville in New York.
- August 22 – Sino-French War (for control of Tonkin) breaks out (continues to April 1885).
- August 23 – Sino-French War: Battle of Fuzhou: French Admiral Amédée Courbet's Far East Squadron virtually destroys China's Fujian Fleet.
- September 5 – Staten Island Academy is founded.
- September 15 –Medicine: The invention of local anesthesia by Karl Koller is made public at a medical congress in Heidelberg, Germany.
- October 6 – The United States Naval War College is established in Newport, Rhode Island.
- October 18 – The University of Wales, Bangor (UK) is founded.
- October 22
- November 1 – The Irish Gaelic Athletic Association is founded in Thurles, Ireland.
- November 2 – Timișoara is the first town of Europe with streets illuminated by electric light.
- November 4 – United States presidential election, 1884: Democratic Governor of New York Grover Cleveland defeats Republican James G. Blaine in a very close contest to win the first of his non-consecutive terms.
- November 15 – The Berlin Conference which regulates European colonisation and trade in Africa begins (ends February 26, 1885).
- December 1
- American Old West: Near Frisco, New Mexico, deputy sheriff Elfego Baca holds off a gang of 80 Texan cowboys who want to kill him for arresting cowboy Charles McCarthy (the cowboys were terrorizing the area's Hispanos and Baca was working against them).
- Porfirio Díaz returns as President of Mexico, an office he will hold until 1911.
- December 4 – Reformers in Korea who admire the Meiji Restoration in Japan stage the Gapsin Coup with Japan's help. China intervenes to rescue the king and help suppress the rebels.
- December 6 – The Washington Monument is completed in Washington, D.C., becoming the tallest structure in the world at this date.
- December 10
- December 16 – The World Cotton Centennial world's fair opens in New Orleans.
- The first Christian missionary arrives in Korea.
- Police training schools are established in every prefecture in Japan.
- The Yellow Crane Tower last burns in Wuhan.
- Parliamentarism is introduced in Norway.
- Scottish Plymouth Brethren missionary Frederick Stanley Arnot identifies the source of the Zambezi river, near Kalene Hill.
- The first ascent is made of Castle Mountain in the Canadian Rockies by geologist Arthur Philemon Coleman.
- The Stefan–Boltzmann law is reformulated by Ludwig Boltzmann.
- Mexican General Manuel Mondragón creates the Mondragón rifle, the world's first automatic rifle.
- The water hyacinth is introduced in the United States and quickly becomes an invasive species.
- Leicester City F.C. is formed as Leicester Fosse Football Club in England.
- Economic depression in the United States.
- January 2 – Ben-Zion Dinur, Russian-born Israeli educator, historian and politician (d. 1973)
- January 12
- January 13 – Sophie Tucker, Russian-born singer and comedian (d. 1966)
- January 20 – Charles Whittlesey, United States Army officer, commander of the "Lost Battalion" in World War I (d. 1921)
- January 21 – Roger Nash Baldwin, American social activist (d. 1981)
- January 23 – Ralph DePalma, Italian-born race car driver (d. 1956)
- January 24 – Thomas Blamey, Australian field marshal (d. 1951)
- January 26 – Roy Chapman Andrews, American explorer, adventurer, and naturalist (d. 1960)
- January 28 – Auguste Piccard, Swiss physicist, balloonist, and inventor (d. 1962)
- January 30 – Sōjin Kamiyama, Japanese actor in American silent films, (d. 1954)
- January 31 – Theodor Heuss, German politician and publicist (d. 1963)
- February 1 – Bradbury Robinson, who threw the first forward pass in American football history in 1906 (d. 1949)
- February 8 – Burt Mustin, American actor (d. 1977)
- February 10 – Frederick Hawksworth, GWR chief mechanical engineer (d. 1976)
- February 12
- February 13 – Alfred Carlton Gilbert, American athlete and inventor (d. 1961)
- February 16 – Robert J. Flaherty, American filmmaker (d. 1951)
- February 18 – Andrew Watson Myles, Canadian politician (d. 1970)
- February 22 – Lew Cody, American actor (d. 1934)
- February 26 – John Cyril Porte, Irish-born British flying boat pioneer (d. 1919)
- March 6 – R. Williams Parry, Welsh poet (d. 1956)
- March 13 – Sir Hugh Walpole, English novelist (d. 1941)
- March 17 – Alcide Nunez, American jazz musician (d. 1934)
- March 21 – George David Birkhoff, American mathematician (d. 1944)
- March 24 – Peter Debye, Dutch chemist, Nobel Prize laureate (d. 1966)
- March 25 – Georges Imbert, Alsatian chemist (d. 1950)
- March 26
- March 27 – James Cruze, American motion picture director (d. 1942)
- April 1 – Laurette Taylor, American stage actress (d. 1946)
- April 4 – Isoroku Yamamoto, Japanese naval commander (d. 1943)
- April 6 – Walter Huston, American actor (d. 1950)
- April 7 – Bronisław Malinowski, Polish anthropologist (d. 1942)
- April 12
- April 22 – Armas Launis, Finnish composer and ethnomusicologist (d. 1959)
- May 1 – Henry Norwest, Canadian World War I sniper (d. 1918)
- May 5 – Jean Decoux, French admiral, Governor-General of French Indochina (1940-1945) (d. 1963)
- May 8 – Harry S. Truman, 33rd President of the United States (d. 1972)
- May 10 – Olga Petrova, English-born actress (d. 1977)
- May 14 – Claude Dornier, German aircraft designer (d. 1969)
- May 20 – Leon Schlesinger, American producer and filmmaker (d. 1949)
- May 21 – Manuel Pérez y Curis, Uruguayan poet (d. 1920)
- May 23 – Corrado Gini, Italian statistician, demographer and sociologist (d. 1965)
- May 27 – Max Brod, Austrian author (d. 1968)
- May 28 – Edvard Beneš, Czechoslovak politician (d. 1948)
- May 30
- June 13
- June 18 – Édouard Daladier, Prime Minister of France (d. 1970)
- June 21 – Claude Auchinleck, British field marshal (d. 1981)
- June 23 – Cyclone Taylor, Canadian ice hockey player (d. 1979)
- June 30 – Franz Halder, German general (d. 1972)
- July 2 – Alfons Maria Jakob, German neurologist (d. 1931)
- July 12 – Amedeo Modigliani, Italian painter and sculptor (d. 1920)
- July 15 – Phraya Manopakorn Nititada, Thailand's first Prime Minister (d. 1948)
- July 18 – Alberto di Jorio, former head of the Vatican Bank and secretary of the 1958 conclave (d. 1979)
- July 19 – Maurice Nicoll, British psychiatrist (d. 1953)
- July 23 – Emil Jannings, Swiss-born German actor (d. 1950)
- July 27 – Kathleen Howard, Canadian/American opera singer & character actress (d. 1956)
- August 8 – Sara Teasdale, American poet (d. 1933)
- August 9 – John S. McCain, Sr., American admiral (d. 1945)
- August 10 – Robert G. Fowler, American pioneer aviator (d. 1966)
- August 10 – Panait Istrati, Romanian writer (d. 1935)
- August 15 – Mary Nash, American actress (d. 1976)
- August 20 – Rudolf Bultmann, German Lutheran theologian (d. 1976)
- August 23 – Will Cuppy, American humorist (d. 1949)
- August 27 – Harry Antrim, American actor (d. 1967)
- August 30 – Theodor Svedberg, Swedish chemist, Nobel Prize laureate (d. 1971)
- September 1 – Richard C. Saufley, American naval aviation pioneer (d. 1916)
- September 17 – Charles Tomlinson Griffes, American composer (d. 1920)
- September 24
- September 30 – Bessie Barriscale, American actress (d. 1965)
- October 7 – Major Harold Geiger, U.S. Army aviation pioneer (d. 1927)
- October 9 – Martin Johnson, American adventurer and documentary filmmaker (d. 1937)
- October 11
- October 16 – Rembrandt Bugatti, Italian sculptor (d. 1916)
- October 24 – Arthur S. Carpender, American admiral (d. 1960)
- October 28 – William Douglas Cook, founder of Eastwoodhill Arboretum and Pukeiti (New Zealand) (d. 1967)
- October 30 – Gengan Tonaki, Japan's oldest living man (d. 1997)
- November 4 – Harry Ferguson, Irish engineer and inventor (d. 1960)
- November 20
- November 22 – Syed Sulaiman Nadvi, Indian/Pakistani historian, biographer, littérateur and scholar of Islam (d. 1953)
- December 3
- December 25 – Evelyn Nesbit, American model & actress, (d. 1967)
- December 30 – Tojo Hideki, Prime Minister of Japan (d. 1948)
- December 31 – Stanley Forman Reed, Associate Justice of the Supreme Court of the United States (d. 1980)
- M. Louise Gross, American politician and lobbyist (d. 1951)
- Wyncie King, American illustrator (d. 1961)
- Richard Spikes, African American inventor (d. 1962)
- Catherine Schleimer-Kill, Luxemburgian women's rights activist (d. 1973)
- January 6 – Gregor Mendel, Czech geneticist (b. 1822)
- January 25 – Johann Gottfried Piefke, German conductor and composer (b. 1815)
- February 8 – Cetshwayo kaMpande, Zulu king (b. 1826)
- February 14
- February 26 – Emmanuel Félix de Wimpffen, French general (b. 1811)
- March 1 – Isaac Todhunter, English mathematician (b. 1820)
- March 13 – Leland Stanford, Jr., in memory of whom Stanford University was founded (b. 1868).
- March 19 – Elias Lönnrot, Finnish philologist and collector of traditional Finnish oral poetry (b. 1802).
- March 21 – Ezra Abbot, American Bible scholar (b. 1819)
- March 23 – Henry C. Lord, American railroad executive (b. 1824)
- March 28 – Prince Leopold, Duke of Albany, youngest son of Queen Victoria (b. 1853)
- April 4 – Marie Bashkirtseff, Russian artist (b. 1858)
- April 6 – Emanuel Geibel, poet and dramatist (b. 1815)
- April 24 – Marie Taglioni, ballerina (b. 1804)
- May 6 – Judah P. Benjamin, Cabinet officer of the Confederate States (b. 1811)
- May 12 – Bedřich Smetana, Czech composer (b. 1824)
- May 13 – Cyrus McCormick, American inventor (b. 1809)
- June 19 – Juan Bautista Alberdi, Argentine politician, writer and main Constitution promoter (b. 1810)
- June 21 – Alexander, Prince of Orange, Heir apparent to the Dutch throne (b. 1851)
- June 25 – Hans Rott, Austrian composer (b. 1858)
- July 1 – Allan Pinkerton, American detective (b. 1819)
- July 10 – Paul Morphy, American chess player (b. 1837)
- July 15
- August 9 – Annestine Beyer, Danish reform pedagogue (b. 1795)
- October 4 – Leona Florentino, Filipina poet (b. 1849)
- October 16 – Bernice Pauahi Bishop, Hawaiian ali‘i (b. 1831)
- October 18 – William VIII, Duke of Brunswick (b. 1806)
- November 16 – František Chvostek, Moravian physician (b. 1835)
- November 25 – Adolph Wilhelm Hermann Kolbe, German chemist (b. 1818)
- December 1 – William Swainson (lawyer), second, and last, Attorney-General of the Crown Colony of New Zealand (b. 1809)
- December 20 – Domenico Consolini, Roman Catholic Cardinal (b. 1806)
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- #33/256. Bollettino delle privative industriali del Regno d’Italia 2nd Series 15 (1884) pp. 635–655.
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- Disc 4 – 287920 Chichester Bell