1784 in science
- September 10 – Edward Pigott identifies the variable star Eta Aquilae from York, England.
- October 19 – John Goodricke begins his observations of the variable star Delta Cephei from York.
- Publication of the Annals of Agriculture edited by Arthur Young begins in Great Britain.
- Peter Simon Pallas begins publication of Flora Rossica, the first Flora of Russia.
- L'Abbé René Just Haüy states the geometrical law of crystallization.
- Antoine Lavoisier pioneers stoichiometry.
- Cholesterol is isolated.
History of science
- Publication of David Bourgeois' Recherches sur l'art de voler, depuis la plus haute antiquité jusque'a ce jour in Paris, the earliest work on the history of flight.
- Carl Friedrich Gauss, at the age of seven, pioneers the field of summation with the formula summing 1:n as (n(n+1))/2.
- February 11 – Royal College of Surgeons in Ireland chartered.
- Madame du Coudray, pioneer of modern midwifery in France, retires.
- Benjamin Franklin makes the first known specific reference (in a letter) to the wearing of bifocal spectacles.
- John Hunter first describes the condition phlebitis.
- The first description of a Pterodactylus fossil is made by Cosimo Alessandro Collini, although he is unable to determine what kind of creature it is.
- January 15 – Henry Cavendish's paper to the Royal Society of London, Experiments on Air, reveals the composition of water.
- Jean-Paul Marat publishes Notions élémentaires d'optique (Elementary Notions of Optics)
- William Roy measures the baseline for the Anglo-French Survey (1784–1790) linking the observatories of Paris and Greenwich. The measurement is accurate to within a few inches in a distance of over 280,000 ft., an unprecedented accuracy for this time. Roy is awarded the Copley Medal in the following year.
- April 28 – James Watt receives a British patent for his parallel motion and other improvements to the steam engine.
- June 4 – Elizabeth Thible becomes the first woman passenger in a hot air balloon, at Lyon, France.
- August 21 – Joseph Bramah receives his first lock patent in London.
- Rev. Dr. Edmund Cartwright designs his first power loom in England.
- Henry Cort of Funtley, England, applies the coal-fired reverbatory furnace to the puddling process for conversion of cast to wrought iron.
- March 12 – William Buckland, English geologist and paleontologist (died 1856)
- June 17 – Andrew Crosse, English 'gentleman scientist', pioneer experimenter in electricity (died 1855)
- July 22 – Friedrich Bessel, German mathematician (died 1846)
- date unknown - Mary Anne Whitby, English scientist (died 1850)
- May 12 – Abraham Trembley, Swiss naturalist (born 1710)
- September 1 – Jean-François Séguier, French astronomer and botanist (born 1703)
- September 4 – César-François Cassini de Thury, French astronomer (born 1714)
- Haüy, René Just (1784). Essai d'une théorie sur la structure des crystaux. Paris: Gogué.
- The College of Optometrists. "The 'Inventor' of Bifocals?". Archived from the original on 13 June 2011. Retrieved 2011-06-21.
- Collini, C. A. (1784). "Sur quelques Zoolithes du Cabinet d'Histoire naturelle de S.A.S.E. Palatine & de Bavière, à Mannheim". Acta Theodoro-Palatinae Mannheim 5 Pars Physica: 58–103.
- Taquet, P.; Padian, K. (2004). "The earliest known restoration of a pterosaur and the philosophical origins of Cuvier's Ossemens Fossiles". Comptes Rendus Palevol. 3: 157–175. doi:10.1016/j.crpv.2004.02.002.
- Unwin, David M. (2006). The Pterosaurs: From Deep Time. New York: Pi Press. ISBN 0-13-146308-X.
- Cavendish, Henry (1784). "Experiments on Air". Philosophical Transactions of the Royal Society of London. 75: 372–384. doi:10.1098/rstl.1785.0023. JSTOR 106582.
- Roy, William (1785). "An Account of the Measurement of a Base on Hounslow-Heath". Philosophical Transactions of the Royal Society of London. 75: 385–480. doi:10.1098/rstl.1785.0024.
- No. 1432.
- Gazette d'Amsterdam 25 June 1784; Journal des sçavans November 1784 pp. 760-762.
- Gales, W. K. V. (1981). Ironworking. Princes Risborough: Shire. p. 8. ISBN 0-85263-546-X.