1808 in science
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- Barium, calcium, magnesium, and strontium isolated by Sir Humphry Davy.
- Joseph Louis Gay-Lussac formulates the law of combining volumes for gases.
- John Dalton begins publication of A New System of Chemical Philosophy, explaining his atomic theory of chemistry and including a list of atomic weights.
- Jöns Jakob Berzelius publishes Lärbok i Kemien in which he proposes modern chemical symbols and notation, and of the concept of relative atomic weight.
- French mathematician Christian Kramp introduces the notation n! in factorials.
- German mathematician Carl Friedrich Gauss publishes Theorematis arithmetici demonstratio nova, introducing Gauss's lemma in the third proof of quadratic reciprocity.
- Irish American mathematician Robert Adrain produces a formulation of the method of least squares.
- The early medical journal Bibliotek for Læger begins publication in Denmark.
- January 12 – Organizational meeting leading to creation of the Wernerian Natural History Society is held in Edinburgh.
- Alexander von Humboldt publishes his Ansichten der Natur.
- February 11 – Anthracite coal is first burned as fuel by Jesse Fell in Wilkes-Barre, Pennsylvania; the discovery leads to the use of coal as a key fuel source of the industrial revolution in the United States.
- August 24 – William Congreve patents the Congreve clock with a rolling ball regulator.
- Bryan Donkin patents a steel nib pen in England.
- Copley Medal: William Henry
- Joseph Louis Lagrange is appointed by Napoleon as a Grand Officer of the Legion of Honour and a Comte of the French Empire.
- February 29 – Hugh Falconer, Scottish-born geologist, botanist, paleontologist and paleoanthropologist (died 1865).
- July 8 – George Robert Gray, English zoologist (died 1872).
- July 25 – Johann Benedict Listing, German mathematician (died 1882).
- August 4 – Johann Ritter von Oppolzer, Austrian physician (died 1871).
- October 29 – Caterina Scarpellini, Italian astronomer (died 1873).
- November 6 – Friedrich Julius Richelot, German mathematician (died 1875).
- Anne Elizabeth Ball, Irish phycologist (died 1872).
- March 3 – Johan Christian Fabricius, Danish entomologist (born 1745).
- May 18 – Rev. Elijah Craig, American inventor of bourbon whiskey (birth date uncertain).
- October 21 - Maria Christina Bruhn, Swedish inventor (born 1732)
- December 24 – Thomas Beddoes, reforming English physician (born 1760).
- "December 6 Births". Today in Science History. Today in Science History. 2007. Retrieved 2007-03-12.
- "John Dalton". Science History Institute. Retrieved 20 March 2018.
- Bowden, Mary Ellen (1997). "John Dalton". Chemical achievers : the human face of the chemical sciences. Philadelphia, PA: Chemical Heritage Foundation. pp. 48–51, 53. ISBN 9780941901123.
- "Jöns Jakob Berzelius". Science History Institute. Retrieved 20 March 2018.
- Bowden, Mary Ellen (1997). "Jöns Jakob Berzelius". Chemical achievers : the human face of the chemical sciences. Philadelphia, PA: Chemical Heritage Foundation. pp. 26–28. ISBN 9780941901123.
- Elements d'arithmétique universelle. Higgins, Peter (2008), Number Story: From Counting to Cryptography, New York: Copernicus, p. 12, ISBN 978-1-84800-000-1
- Published in his own journal, The Analyst, or, Mathematical Museum 1(4), probably issued in 1809. Stigler, Stephen M. (2004). "Adrain, Robert (1775–1843)". Oxford Dictionary of National Biography. Oxford University Press. doi:10.1093/ref:odnb/172. Retrieved 2012-01-23. (subscription or UK public library membership required)
- "Wernerian Natural History Society". Scholarly Societies Project. Archived from the original on 2012-02-04. Retrieved 2012-01-09.
- Sweet, Jessie M. (1967). "The Wernerian Natural History Society in Edinburgh". Freiberger Forschungshefte, Reihe C. 223: 205–218.
- MacMillan, David M.; et al. (2000-10-15). "Oscillating Path ("Congreve") Rolling Ball Clocks". The Rolling Ball Web. Retrieved 2017-04-15.