1871 in science
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- June 8–October 2 – Hayden Geological Survey of 1871 in the United States, including what will next year become the Yellowstone National Park. Between July 21–August 26, the first ever photographs of this region are taken by William Henry Jackson.
- November 17 – George Biddell Airy presents his discovery that astronomical aberration is independent of the local medium.
- James Clerk Maxwell makes public the thought experiment which will become known as Maxwell's demon in the philosophy of thermal and statistical physics, in his book Theory of Heat and establishes Maxwell relations, statements of equality among the second derivatives of the thermodynamic potentials with respect to different thermodynamic variables.
- John Strutt publishes his first papers on the theory of acoustic resonance and on the phenomenon now called Rayleigh scattering, explaining why the sky is blue.
Physiology and medicine
- Porphyria is first explained biochemically by Felix Hoppe-Seyler.
- Friedrich Trendelenburg describes the first successful elective human tracheotomy to be performed for the purpose of administering general anaesthesia.
- Institution of Electrical Engineers established in the United Kingdom as the Society of Telegraph Engineers.
- Souter Lighthouse in England is the first to use alternating current electricity.
- Ralph Hart Tweddell invents the portable hydraulic riveter, manufactured by Fielding & Platt of Gloucester in England.
- Cosmos: A Sketch of a Physical Description of the Universe by Alexander von Humboldt, covering a large number of topics in scientific exploration and invention.
- The Descent of Man and Selection in Relation to Sex by Charles Darwin, outlining his theory for man's origins and his theory of sexual selection, and including his first published use of the term evolution (published by John Murray in London, February 24).
- January 7 – Émile Borel (died 1956), French mathematician.
- February 15 – Martin Knudsen (died 1949), Danish physicist.
- May 19
- August 15 – Arthur Tansley (died 1955), English botanist and ecologist.
- August 19 – Orville Wright (died 1948), American pioneer aviator.
- August 30 – Ernest Rutherford (died 1937), New Zealand-born British physicist and laureate of the Nobel Prize in Physics.
- September 17 – Eivind Astrup (died 1895), Norwegian Arctic explorer.
- October 19 – Walter Bradford Cannon (died 1945), American physiologist.
- October 26 – Albert Stewart Meek (died 1943), English-born ornithologist.
- January 25 – Jeanne Villepreux-Power (born 1794), French marine biologist.
- March 18 – Augustus De Morgan (born 1806), British logician.
- April 8 – Francisco Javier Muñiz (born 1795), Argentine physician and paleontologist.
- April 16 – Johann Ritter von Oppolzer (born 1808), Austrian physician.
- June 9 – Anna Atkins (b. 1799), British botanist.
- May 11 – John Herschel (born 1792), English mathematician and astronomer.
- October 18 – Charles Babbage (born 1791), English mathematician and inventor of computing machines.
- December 8 – James Murray (born 1788), Irish physician.
- Airy, G.B. (1871). "On the Supposed Alteration in the Amount of Astronomical Aberration of Light, Produced by the Passage of the Light through a Considerable Thickness of Refracting Medium". Proceedings of the Royal Society. London. 20: 35–39. Bibcode:1871RSPS...20...35A. doi:10.1098/rspl.1871.0011. Retrieved 2015-01-03.
- Leff, Harvey S.; Rex, Andrew F., eds. (2002). Maxwell's Demon 2: Entropy, Classical and Quantum Information, Computing. CRC Press. p. 370. ISBN 0-7503-0759-5.
- Gavroglu, Kostas (2004). "Strutt, John William, third Baron Rayleigh (1842–1919)". Oxford Dictionary of National Biography. Oxford University Press. doi:10.1093/ref:odnb/36359. Retrieved 2011-11-03. (subscription or UK public library membership required)
- Hoppe-Seyler, F. (1871). "Das Hämatin". Tübinger Med-Chem Untersuch. 4: 523–33.
- Trendelenburg, F (1871). "Beiträge zu den Operationen an den Luftwegen" [Contributions to airways surgery]. Archiv für Klinische Chirurgie (in German). 12: 112–33.
- Hargrave, R. (1934). "Endotraheal Anesthesia in Surgery of the Head and Neck". Canadian Medical Association Journal. 30 (6): 633–7. PMC . PMID 20319535.
- Bain, J. A.; Spoerel, W. E. (1964). "Observation on the use of cuffed tracheqstomy tubes (with particular reference to the james tube)". Canadian Anaesthetists' Society Journal. 11 (6): 598–608. doi:10.1007/BF03004104. PMID 14232175.
- Wawersik, Juergen (1991). "History of Anesthesia in Germany". Journal of Clinical Anesthesia. 3 (3): 235–44. doi:10.1016/0952-8180(91)90167-L. PMID 1878238. Retrieved 2011-10-19.