1864 in science
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- August 29 – William Huggins is the first to take the spectrum of a planetary nebula when he analyzes NGC 6543.
- English botanist Richard Spruce completes a 15-year expedition to the Andes and Amazon Basin during which he has collected more than 30,000 plant specimens.
- August 20 – John Alexander Reina Newlands produces the first periodic table of the elements.
- Lothar Meyer develops an early version of the periodic table, with 28 elements organized by valence.
- Cato Maximilian Guldberg and Peter Waage, building on Claude Louis Berthollet's ideas, propose the law of mass action.
- Barbituric acid was first synthesized on November 27, 1864, by German chemist Adolf von Baeyer.
- Alfred Enneper publishes his parametrization of the Enneper surface in connection with minimal surface theory.
- December 8 – James Clerk Maxwell presents his paper A Dynamical Theory of the Electromagnetic Field to the Royal Society in London, treating light as an electromagnetic wave and presenting Maxwell's equations.
- February 17 – In the American Civil War, the tiny Confederate hand-propelled submarine H. L. Hunley sinks the USS Housatonic using a spar torpedo in Charleston Harbor, becoming the first submarine to sink an enemy ship (although the submarine and her crew of eight are also lost).
- December 8 – The Clifton Suspension Bridge across the Bristol Avon in England, designed by Isambard Kingdom Brunel and completed as a memorial to him, opens to traffic.
- Oriel Chambers, Liverpool, England, the world's first metal-framed glass curtain walled building, designed by Peter Ellis (architect), is built.
- Henry Roscoe and Robert Bunsen carry out what is reputed to be the first flashlight photography, using magnesium as a light source.
- Possible date – Siegfried Marcus builds the first motorized cart, in Vienna.
- The species Homo neanderthalensis is formally described by William King.
- The Central Park Zoo opens in New York City as a menagerie.
- January (prob. date) – George Washington Carver (died 1943), African American agricultural botanist.
- January 13 – Wilhelm Wien (died 1928), German physicist.
- March 12 – W. H. R. Rivers (died 1922), English psychiatrist.
- April 21 – Max Weber (died 1920), German sociologist.
- June 14 – Alois Alzheimer (died 1915), German neuroscientist.
- June 25 – Walther Nernst (died 1941), German chemist.
- June 22 – Hermann Minkowski (died 1909), Lithuanian-German mathematician.
- December 1 – Carsten Borchgrevink (died 1934), Norwegian Antarctic explorer.
- January 14 – Father Nicholas Callan (born 1799), physicist.
- March 21 – Luke Howard (born 1772), meteorologist and manufacturing chemist.
- May 3 – William Lobb (born 1809), plant collector.
- May 5 – Elizabeth Andrew Warren (born 1786), Cornish botanist and marine algolologist.
- November 23 – Friedrich Georg Wilhelm Struve (born 1793), astronomer.
- December 8 – George Boole (born 1815), mathematician.
- December 12 – John Fowler (born 1826), agricultural engineer.
- Kwok, Sun (2000). "History and overview". The Origin and Evolution of planetary Nebulae. Cambridge University Press. pp. 1–7. ISBN 0-521-62313-8. Retrieved 13 January 2012.
- Spruce, Richard (1884). "Hepaticae of the Amazon and the Andes of Peru and Ecuador". Transactions and Proceedings of the Botanical Society. Edinburgh. 15 (1–2).
- Spruce, Richard (1908). Wallace, Alfred Russel, ed. Notes of a botanist on the Amazon and the Andes... during the years 1849–1864. London: Macmillan.
- Pearson, Michael (2004). Richard Spruce: naturalist and explorer. Settle, Yorkshire: Hudson History. ISBN 1-903783-28-3.
- Newlands, John A. R. (1864-08-20). "On Relations Among the Equivalents". Chemical News. 10: 94–95. Archived from the original on 21 July 2011. Retrieved 2011-08-30.
- "Julius Lothar Meyer and Dmitri Ivanovich Mendeleev". Science History Institute. Retrieved 21 March 2018.
- Bowden, Mary Ellen (1997). "Julius Lothar Meyer and Dmitri Ivanovich Mendeleev". Chemical achievers : the human face of the chemical sciences. Philadelphia, PA: Chemical Heritage Foundation. pp. 59–63. ISBN 9780941901123.
- Guldberg, C. M.; Waage, P. (1864). "Studies Concerning Affinity". Forhandlinger i Videnskabs-Selskabet i Christiana: 35.
- Waage, P. (1864). "Experiments for Determining the Affinity Law". Forhandlinger i Videnskabs-Selskabet i Christiania: 92.
- Guldberg, C. M. (1864). "Concerning the Laws of Chemical Affinity". Forhandlinger i Videnskabs-Selskabet i Christiania: 111.
- Schaffer, Jeffrey P. Yosemite National Park (4th ed.). p. 48.
- Enneper, A. (1864). "Analytisch-geometrische Untersuchungen". Zeitschrift für mathematische Physik. 9: 96–125.
- Maxwell, J. Clerk (1865). "A dynamical theory of the electromagnetic field" (PDF). Philosophical Transactions of the Royal Society of London. 155: 459–512. doi:10.1098/rstl.1865.0008. Retrieved 2011-08-30.
- Chaffin, Tom (2008). The H. L. Hunley: the Secret Hope of the Confederacy. New York: Hill and Wang. ISBN 978-0-8090-9512-4.
- Penguin Pocket On This Day. Penguin Reference Library. 2006. ISBN 0-14-102715-0.
- "History". Oriel Chambers. Retrieved 2009-07-27.
- "Henry Roscoe (1833-1915): flashlight photography". Museum of Science and Industry (Manchester). 2007. Archived from the original on 2012-03-02. Retrieved 2011-11-17.