1843 in science

Astronomy

• March 11–14 – Eta Carinae flares to become the second brightest star.
• February 5–April 19 – "Great March Comet" observed.
• December 21 – The first total solar eclipse of Saros 139 occurs over southern Asia.
• Heinrich Schwabe reports a periodic change in the number of sunspots: they wax and wane in number according to a ten-year cycle.

Chemistry

• Jean-Baptiste Dumas names lactose.
• Carl Mosander discovers the chemical elements Terbium and Erbium.
• John J. Waterston produces an account of the kinetic theory of gases.
• Alfred Bird produces single-acting baking powder.

Mathematics

• September – Ada Lovelace translates and expands Menabrea’s notes on Charles Babbage's analytical engine, including an algorithm for calculating a sequence of Bernoulli numbers, regarded as the world's first computer program.
• October 16 – William Rowan Hamilton discovers the calculus of quaternions and deduces that they are non-commutative.
• Arthur Cayley and James Joseph Sylvester found the algebraic invariant theory.
• John T. Graves discovers the octonions.
• Pierre-Alphonse Laurent discovers and presents the Laurent expansion theorem.

Physics

• James Prescott Joule experimentally finds the mechanical equivalent of heat.
• Ohm's acoustic law is proposed by German physicist Georg Ohm.

Physiology and medicine

• April–May – English surgeon Benjamin Brodie extracts a coin lodged in the bronchus of engineer Isambard Kingdom Brunel using novel methods.
• British surgeon James Braid publishes Neurypnology: or the Rationale of Nervous Sleep, a key text in the history of hypnotism.
• Oliver Wendell Holmes Sr., argues that puerperal fever is spread by lack of hygiene in physicians.

Technology

• March 25 – Completion of the Thames Tunnel, the first bored underwater tunnel in the world.
• July 19 – Launch of, the first iron-hulled, propeller-driven ship to cross the Atlantic Ocean.
• November 21 – Thomas Hancock patents the vulcanisation of rubber using sulphur in the United Kingdom
• The steam powered rotary printing press is invented by Richard March Hoe in the United States.
• Robert Stirling and his brother James convert a steam engine at a Dundee factory to operate as a Stirling engine.
• The first public telegraph line in the United Kingdom is laid between Paddington and Slough.
• Approximate date – Euphonium invented.

Publications

• October – Anna Atkins begins publication of Photographs of British Algae: Cyanotype Impressions, a collection of contact printed cyanotype photograms of algae which forms the first book illustrated with photographic images.

Awards

• Copley Medal: Jean-Baptiste Dumas
• Wollaston Medal for Geology: Jean-Baptiste Elie de Beaumont; Pierre Armand Dufrenoy

Births

• January 13 – David Ferrier, Scottish neurologist.
• May 6 – G. K. Gilbert, American geologist.
• June 12 – David Gill, Scottish astronomer.
• June 23 – Paul Heinrich von Groth, German mineralogist.
• July 24 – William de Wiveleslie Abney, English astronomer.
• August 17 – Alexandre Lacassagne, French forensic scientist.
• November 30 - Martha Ripley, American physician.
• December 11 – Robert Koch, German physician, famous for the discovery of the tubercle bacillus and the cholera bacillus and for his development of Koch's postulates; awarded the Nobel Prize in Physiology or Medicine in 1905
• Adelaida Lukanina, Russian chemist.

Deaths

• July 25 – Charles Macintosh, Scottish inventor of a waterproof fabric.
• August 10 – Robert Adrain, Irish American mathematician.
• September 11 – Joseph Nicollet, French geographer, explorer, mathematician and astronomer.
• September 19 – Gaspard-Gustave Coriolis, French mathematician and discoverer of the Coriolis effect.
• September 30 – Richard Harlan, American zoologist.
• November 16 – Abraham Colles, Anglo-Irish surgeon.