1813 in science
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- April – William Charles Wells reads a paper to the Royal Society of London making the first clear statement about natural selection.
- Charles Waterton begins the process of turning his estate at Walton Hall, West Yorkshire, England, into what is, in effect, the world's first nature reserve.
- Mathieu Orfila publishes his groundbreaking Traité des poisons, formalizing the field of toxicology.
- Louis Jacques Thénard commences publication of his textbook Traité de chimie élémentaire, théorique et pratique in Paris.
- Edward Howard invents the enclosed vacuum pan for refining sugar.
- May 11 – Gregory Blaxland, William Lawson and William Wentworth leave on an expedition to cross the Blue Mountains (New South Wales).
- S. D. Poisson publishes Poisson's equation, his correction of Laplace's second order partial differential equation for potential.
- British engineer Peter Ewart supports the idea of the conservation of energy in his paper "On the measure of moving force".
- Henri de Saint-Simon publishes Physiologie sociale.
- March 1 – Sir Humphry Davy employs Michael Faraday as "chemical assistant" at the Royal Institution of Great Britain in London.
- January 19 – Henry Bessemer, English inventor (died 1898)
- February 18 – Karl Weltzien, Russian-born German inorganic chemist, an organizer of the Karlsruhe Congress (died 1870)
- March 19 – David Livingstone, Scottish missionary and explorer (died 1873)
- July 12 – Claude Bernard, French physiologist (died 1878)
- October 17 – Georg Büchner, Hessian-born writer and anatomist (died 1837).
- December 19 – Thomas Andrews, Irish chemist (died 1885)
- April 10 – Joseph Louis Lagrange, Piedmont-born mathematician (born 1736)
- April 19 – Benjamin Rush, Founding Father of the United States, chemist and physician (born 1746)
- April 27 – General Zebulon Pike, American explorer (born 1779)
- May – Johann Karl Wilhelm Illiger, German zoologist (born 1775)
- July 22 – George Shaw, English naturalist (born 1751)
- August 23 – Alexander Wilson, Scottish American ornithologist (born 1766)
- Published posthumously in 1818 in his Two Essays.
- Green, J. H. S. (1957). "William Charles Wells FRS (1757–1817)" (PDF). Nature. 179: 997–99. doi:10.1038/179997a0. Retrieved 2011-12-16.
- Darwin, Charles (1866). "Historical Sketch". On the Origin of Species by means of natural selection (4th & subsequent ed.). London: Murray.
[Wells] distinctly recognises the principle of natural selection, and this is the first recognition which has been indicated.
- Glass, Bentley; et al., eds. (1959). Forerunners of Darwin, 1745-1859. Baltimore: Johns Hopkins Press. p. 369.
- Blackburn, Julia (1989). Charles Waterton, 1782-1865: traveller and conservationist. London: The Bodley Head. pp. 52–9. ISBN 0-370-31248-1.
- Bertomeu-Sánchez, José Ramón; Nieto-Galan, Agustí, eds. (2006). Chemistry, Medicine and Crime: Mateu J. B. Orfila (1787–1853) and his times. Sagamore Beach, MA: Science History Publications. ISBN 0-88135-275-6.
- Bulletin de la société philomatique.