1851 in science
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- February – First public exhibition of a Foucault pendulum, at the Meridian of the Paris Observatory, demonstrating the Earth's rotation. A few weeks later Foucault installs one at the Panthéon.
- July 28 – Solar eclipse of July 28, 1851: Total solar eclipse. The first correctly exposed photograph, a daguerrotype, of the solar corona is made during the total phase of the eclipse by Berkowski at Koenigsberg Observatory in Prussia. Astronomers Robert Grant and William Swan (of the United Kingdom) and Karl Ludwig von Littrow (of Austria) observe this eclipse and determine that solar prominences are part of the Sun because the Moon is seen to cover and uncover them as it moves in front.
- October 24 – Ariel and Umbriel, moons of Uranus, are discovered by William Lassell.
- The William Brydone Jack Observatory is completed at Fredericton, New Brunswick.
- March – English sculptor Frederick Scott Archer makes public the wet plate collodion photographic process.
- Charles-Adolphe Wurtz produces compound ureas.
- The Royal Marsden is established as the Free Cancer Hospital by surgeon William Marsden in London, the world's first specialist cancer hospital.
- Hippolyte Fizeau carries out the Fizeau experiment to measure the relative speeds of light in moving water.
- November 13 – First protected submarine telegraph cable laid, across the English Channel.
- William Armstrong introduces the weight-loaded hydraulic accumulator.
- January 19 – Jacobus Kapteyn (died 1922), astronomer.
- March 16 – Martinus Beijerinck (died 1931), Dutch microbiologist and botanist.
- April 12 – E. Walter Maunder (died 1928), astronomer.
- July 8 – Arthur Evans (died 1941), archaeologist.
- July 20 – Arnold Pick (died 1924), neurologist.
- August 3 – George FitzGerald (died 1901), mathematician.
- January 27 – John James Audubon (born 1785), naturalist and illustrator.
- February 18 – Carl Gustav Jakob Jacobi (born 1804), mathematician.
- March 9 – Hans Christian Ørsted (born 1777), physicist.
- July 6 – Thomas Davenport (born 1802), electrical engineer.
- July 17 – John Farey (born 1791), mechanical engineer and technical writer.
- September 2 – William Nicol (born 1770), geologist.
- Tobin, William (2003). The Life and Science of Léon Foucault, the Man who Proved the Earth Rotates. Cambridge University Press. ISBN 0-521-80855-3.
- Schielicke, Reinhard; Wittmann, Axel D. (2005). "On the Berkowski daguerreotype (Königsberg, 1851 July 28): the first correctly-exposed photograph of the solar corona". Acta Historica Astronomiae. 25: 128–147. Bibcode:2005AcHA...25..128S.
- Littmann, Mark; Willcox, Ken; Espenak, Fred (1999). "Chronology of Discoveries about the Sun". MrEclipse.com. Retrieved 2012-06-06.
- Astronomical Journal 2(33):p. 70 (1851).
- The Chemist March 1851.
- Riemann, Bernhard (1867). Grundlagen für einen allgemeine Theorie der Functionen einer veränderlichen complexen Grösse [Basis for a general theory of functions of a variable complex quantity]. Göttingen (Germany): Adalbert Rente. pp. 8–9.
- Fizeau, H. (1851). "Sur les hypothèses relatives à l'éther lumineux". Comptes rendus de l'Académie des sciences. Paris. 33: 349–355.
- McNeill, Ian (1972). Hydraulic Power. London: Longman. ISBN 0-582-12797-1.