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1885 (MDCCCLXXXV) was a common year starting on Thursday of the Gregorian calendar and a common year starting on Tuesday of the Julian calendar, the 1885th year of the Common Era (CE) and Anno Domini (AD) designations, the 885th year of the 2nd millennium, the 85th year of the 19th century, and the 6th year of the 1880s decade. As of the start of 1885, the Gregorian calendar was 12 days ahead of the Julian calendar, which remained in localized use until 1923.
- January 3–4 – Sino-French War – Battle of Núi Bop: French troops under General Oscar de Négrier defeat a numerically superior Qing Chinese force, in northern Vietnam.
- January 4 – The first successful appendectomy is performed by Dr. William W. Grant, on Mary Gartside.
- January 17 – Mahdist War in Sudan – Battle of Abu Klea: British troops defeat Mahdist forces.
- January 20 – American inventor LaMarcus Adna Thompson patents a roller coaster.
- January 24 – Irish rebels damage Westminster Hall and the Tower of London with dynamite.
- January 26 – Mahdist War in Sudan: Troops loyal to Mahdi Muhammad Ahmad conquer Khartoum; British commander Charles George Gordon is killed.
- February 5 – King Leopold II of Belgium establishes the Congo Free State, as a personal possession.
- February 7 – The play La vida alegre y muerte triste by dramatist José Echegaray opens.
- February 9 – The first Japanese arrive in Hawaii.
- February 16 – Charles Dow publishes the first edition of the Dow Jones Industrial Average. The index stood at a level of 62.76, and represented the dollar average of 14 stocks: 12 railroads and two leading American industries.
- February 21 – United States President Chester A. Arthur dedicates the Washington Monument.
- February 23
- February 26 – The final act of the Berlin Conference regulates European colonization and trade, in the scramble for Africa.
- February 28 – February concludes without having a full moon.
- March 3 – A subsidiary of the American Bell Telephone Company, American Telephone and Telegraph (AT&T), is incorporated in New York.
- March 4 – Grover Cleveland is sworn in, as the 22nd President of the United States.
- March 7 – The Roman Catholic Archdiocese of Madrid is founded.
- March 14 – Gilbert and Sullivan's comic opera The Mikado opens, at the Savoy Theatre in London.
- March 26
- March 30 – The Battle for Kushka triggers the Panjdeh Incident, which nearly gives rise to war between the British Empire and Russian Empire.
- March 31 – The United Kingdom establishes the Bechuanaland Protectorate.
- August 29 – Gottlieb Daimler is granted a German patent for the Daimler Reitwagen, regarded as the first motorcycle, which he has produced with Wilhelm Maybach.
- September 2 – The Rock Springs massacre occurs in Rock Springs, Wyoming; 150 white miners attack their Chinese coworkers, killing 28, wounding 15, and forcing several hundred more out of town.
- September 6 – Eastern Rumelia declares its union with Bulgaria, completing the Unification of Bulgaria.
- September 8 – Saint Thomas Academy is founded in Minnesota.
- September 12 – Arbroath FC defeats Bon Accord FC, 36-0, in the highest score ever in professional football.
- September 15 – A train wreck of the P. T. Barnum Circus kills giant elephant Jumbo, at St. Thomas, Ontario.
- September 18 – The union of Eastern Rumelia with Bulgaria is proclaimed at Plovdiv.
- September 30 – A British force abolishes the Boer republic of Stellaland, and adds it to British Bechuanaland.
- October 3 – Millwall F.C. is founded by workers on the Isle of Dogs in London, as Millwall Rovers.
- October 12 – The city of Fresno, California is incorporated.
- October 13 – The Georgia Institute of Technology is established in Atlanta, as the Georgia School of Technology.
- October 25 – Symphony No. 4 (Brahms) is premiered in Meiningen, Germany, with Johannes Brahms himself conducting it.
- November – The Third Anglo-Burmese War begins.
- November 7 – Canadian Pacific Railway: In Craigellachie, British Columbia, construction ends on a railway extending across Canada. Prime Minister Sir John A. Macdonald considers the project to be vital to Canada, due to the exponentially greater potential for military mobility.
- November 14–28 – Serbo-Bulgarian War: Serbia declares war against Bulgaria, but is defeated in the Battle of Slivnitsa on November 17–19.
- November 16 – Louis Riel, Canadian rebel leader of the Métis, is executed for high treason.
- December 1 – The U.S. Patent Office acknowledges this date as the day Dr Pepper is served for the very first time; the exact date of Dr. Pepper's invention is unknown.
- December 28 – 72 Indian lawyers, academics and journalists gather in Bombay, to form the Congress Party.
- Karl Benz produces the Benz Patent-Motorwagen, regarded as the first automobile (patented and publicly launched the following year).
- John Kemp Starley demonstrates the Rover safety bicycle, regarded as the first practical modern bicycle.
- Chile's Matrimony and Civil Registry laws come into effect.
- The Home Insurance Building in Chicago, designed by William Le Baron Jenney, is completed. With ten floors and a fireproof weight-bearing metal frame, it is regarded as the first skyscraper.
- Bicycle Playing Cards are first produced.
- The Soldiers' and Sailors' Families Association is established in the United Kingdom, to provide charitable assistance.
- Camp Dudley, the oldest continually running boys' camp in the United States, is founded.
- John Ormsby publishes his new English translation of Don Quixote, acclaimed as the most scholarly made up to that time. It will remain in print through the 20th Century.
- Michigan Technological University (originally Michigan Mining School) opens its doors for the first time, in the future Houghton County Fire Hall.
- Chuo Law College, as predecessor of Chuo University, founded in Kanda, Tokyo, Japan.
- BHP (Broken Hill Proprietary), a mining and natural gas product in worldwide, founded in New South Wales, Australia.
- Before November 1 – More than 24,000 Christians killed, 225 churches burnt, seventeen orphanages and ten convents destroyed in Cochinchina, now known as Vietnam.