1775 in science
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- May 25 – Joseph Priestley's account of his isolation of oxygen in the form of a gas ("dephlogisticated air") is read to the Royal Society of London.
- Torbern Bergman's De attractionibus electivis ("A Dissertation on Elective Attractions") is published, containing the largest tables of chemical affinity ever published.
- July 30 – 3-year second voyage of James Cook completed, the first eastabout global circumnavigation, during which the Antarctic Circle has been crossed three times, Terra Australis shown to be a myth, and Larcum Kendall's K1 chronometer demonstrated to be a reliable timekeeper for the purpose of calculating longitude.
- English surgeon Percivall Pott finds the first occupational link to cancer, contributing to the science of epidemiology.
- German physician Melchior Adam Weikard anonymously publishes the textbook Der Philosophische Arzt including the earliest description of symptoms resembling attention deficit hyperactivity disorder.
- February 21 – La Specola, Florence's Museum of Zoology and Natural History, opens to the public.
- Johan Christian Fabricius publishes his Systema entomologiæ.
- Peter Forsskål's Descriptiones Animalium: Avium, amphiborum, insectorum, vermium quæ in itinere orientali (containing early observations on bird migration) and Flora Ægyptiaco-Arabica sive descriptiones plantarum quas per Ægyptum Inferiorem et Arabiam felicem detexit are published posthumously, edited by Carsten Niebuhr.
- James Watt's 1769 steam engine patent is extended to June 1800 by Act of Parliament of Great Britain and the first engines are built under it.
- Jacques-Constantin Périer operates a paddle steamer on the Seine, but it proves to be underpowered.
- Thomas Crapper patents a flush toilet in London.
- Edinburgh confectioner Charles Spalding devizes improvements to the diving bell, adding a system of balance-weights.
- Pierre-Simon Girard, age 74, invents a water turbine.
- December 30 – John Arnold takes out his first patent for improvements in the construction of marine chronometers in Britain, including the first for a compensation balance.
- January 22 – André-Marie Ampère, French physicist (died 1836)
- February 9 – Farkas Bolyai, Hungarian mathematician (died 1856)
- May 10 – William Phillips, English geologist (died 1828)
- July 23 – Étienne-Louis Malus, French physicist and mathematician] (died 1812)
- September 30 – Robert Adrain, Irish-born mathematician (died 1843)
- November 19 – Johann Karl Wilhelm Illiger, German entomologist and zoologist (died 1813)
- March 3 – Richard Dunthorne, English astronomer (born 1711)
- October 25 – Johan Maurits Mohr, Dutch astronomer (born 1716)
- Priestley, Joseph (1775). "An Account of Further Discoveries in Air". Philosophical Transactions of the Royal Society 65: 384–94. doi:10.1098/rstl.1775.0039. JSTOR 106209.
- "The University of Copenhagen – A Danish centre of learning since 1479". Københavns Universitet. Retrieved 2011-05-19.
- Scherer, F. M. (1965). "Invention and Innovation in the Watt-Boulton Steam-Engine Venture". Technology and Culture 6: 165–87. JSTOR 3101072.
- "The Invention of the Steam Engine: The Life of James Watt. Part 4: The Steam Engine Gains Popularity". About.com Inventors. Retrieved 2011-02-25.
- Spratt, H. Philip (1958). The Birth of the Steamboat. London. p. 35.
- "The Development of the Flushing Toilet – Detailed Chronology 1596 onwards". Stoke-on-Trent: Twyfords Bathrooms.
- Transactions of the Society Instituted at London for the Encouragement of Arts, Manufactures, and Commerce 1 (3rd ed.), Society of Arts, 1806, pp. 220–232, retrieved 2013-01-22
- No. 1113. Betts, Jonathan (2004). "Arnold, John (1735/6–1799)". Oxford Dictionary of National Biography. Oxford University Press. doi:10.1093/ref:odnb/677. Retrieved 2012-03-09. (subscription or UK public library membership required)