1798 in science
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- Caroline Herschel's index and updating of Flamsteed's star catalogue is published by the Royal Society of London.
- The element beryllium is discovered by Louis Vauquelin as the oxide in beryl and in emeralds. Friedrich Wöhler and A. A. Bussy independently isolate the metal in 1828 by reacting potassium and beryllium chloride.
- Thomas Robert Malthus publishes the first edition of An Essay on the Principle of Population (anonymously) in London.
- Lagrange publishes his Résolution des équations numériques, including the method of approximating to the real roots of an equation by means of continued fractions.
- Edward Jenner publishes An Inquiry into the Causes and Effects of the Variolae Vaccinae.
- Charles Bell publishes A System of Dissection Explaining the Anatomy of the Human Body in collaboration with his brother John.
- Alexander Crichton publishes An inquiry into the nature and origin of mental derangement; comprehending a concise system of the physiology and pathology of the human mind and a history of the passions and their effects, including a description of a condition resembling the inattentive subtype of attention deficit hyperactivity disorder.
- John Dalton publishes "Extraordinary Facts Relating to the Vision of Colours", describing colour blindness for the first time in print.
- Philippe Pinel publishes Nosographie philosophique, ou méthode de l'analyse appliquée à la médecine, emphasising the importance of nosology (classification of diseases) to medicine. It goes through six editions in the next ten years.
- Samuel Thomas von Sömmerring publishes Tabula sceleti feminini in Frankfurt am Main, the first accurate representation of the female skeleton.
- Benjamin Thompson, Count Rumford, publishes An Experimental Enquiry Concerning the Source of the Heat which is Excited by Friction.
- The platypus is first discovered by Europeans.
- The Philosophical Magazine is initiated by Alexander Tilloch to cover the field of natural philosophy; it will still be published more than two centuries later.
- April 3 – Charles Wilkes, American navigator (died 1877)
- August 17 – Thomas Hodgkin, English physician (died 1866)
- September 19 – Caesar Hawkins, English surgeon (died 1884)
- November 4 – Karl Kreil, Austrian astronomer (died 1862)
- December 28 – Thomas Henderson, Scottish astronomer (died 1844)
- May 10 – George Vancouver, English explorer (born 1757)
- May 2 – Erland Samuel Bring, Swedish mathematician (born 1736)
- December 4 – Luigi Galvani, Italian physicist (born 1737)
- Ogilvie, Marilyn Bailey (1986). Women in Science: Antiquity through the Nineteenth Century. Cambridge, Massachusetts: MIT Press. pp. 97–98. ISBN 0-262-65038-X.
- Jacyna, L. S. (2004). "Bell, Sir Charles (1774–1842)". Oxford Dictionary of National Biography. Oxford University Press. doi:10.1093/ref:odnb/1999. Retrieved 2011-04-06. (subscription or UK public library membership required)
- Dalton, J. (1798). "Extraordinary facts relating to the vision of colours; with observations". Memoirs of the Literary and Philosophical Society of Manchester. 5: 28–45. The original lecture was delivered in 1794.
- Burke, James (1985). The Day the Universe Changed. London: BBC. p. 207. ISBN 0-563-20192-4.
- Burnett, John (2004). "Tilloch, Alexander (1759–1825)". Oxford Dictionary of National Biography. Oxford University Press. Retrieved 2010-02-17.