1871 in science

Exploration

• June 8–October 2 – Hayden Geological Survey of 1871 in the United States, including what will next year become the Yellowstone National Park. Between July 21–August 26, the first ever photographs of this region are taken by William Henry Jackson.

  Physics

• November 17 – George Biddell Airy presents his discovery that astronomical aberration is independent of the local medium.
• James Clerk Maxwell makes public the thought experiment which will become known as Maxwell's demon in the philosophy of thermal and statistical physics, in his book Theory of Heat and establishes Maxwell relations, statements of equality among the second derivatives of the thermodynamic potentials with respect to different thermodynamic variables.
• John Strutt publishes his first papers on the theory of acoustic resonance and on the phenomenon now called Rayleigh scattering, explaining why the sky is blue.

  Physiology and medicine

• Porphyria is first explained biochemically by Felix Hoppe-Seyler.
• Friedrich Trendelenburg describes the first successful elective human tracheotomy to be performed for the purpose of administering general anaesthesia.
• Friedrich Miescher publishes his 1869 isolation of what will subsequently be called nucleic acid.

  Technology

• Institution of Electrical Engineers established in the United Kingdom as the Society of Telegraph Engineers.
• Souter Lighthouse in England is the first to use alternating current electricity.
• Ralph Hart Tweddell invents the portable hydraulic riveter, manufactured by Fielding & Platt of Gloucester in England.

  Publications

• Cosmos: A Sketch of a Physical Description of the Universe by Alexander von Humboldt, covering a large number of topics in scientific exploration and invention.
• The Descent of Man and Selection in Relation to Sex by Charles Darwin, outlining his theory for man's origins and his theory of sexual selection, and including his first published use of the term evolution.

  Awards

• Copley Medal: Julius Robert von Mayer
• Wollaston Medal for Geology: Andrew Ramsay

  Births

• January 7 – Émile Borel, French mathematician.
• February 15 – Martin Knudsen, Danish physicist.
• May 19
• * Walter Russell, American polymath.
• * Inez Whipple Wilder, American herpetologist and anatomist.
• August 15 – Arthur Tansley, English botanist and ecologist.
• August 19 – Orville Wright, American pioneer aviator.
• August 30 – Ernest Rutherford, New Zealand-born British physicist and laureate of the Nobel Prize in Physics.
• September 17 – Eivind Astrup, Norwegian Arctic explorer.
• October 19 – Walter Bradford Cannon, American physiologist.
• October 26 – Albert Stewart Meek, English-born ornithologist.

  Deaths

• January 25 - Jeanne Villepreux-Power, French marine biologist.
• March 18 – Augustus De Morgan, British logician.
• April 8 – Francisco Javier Muñiz, Argentine physician and paleontologist.
• April 16 – Johann Ritter von Oppolzer, Austrian physician.
• June 9 - Anna Atkins, British botanist.
• May 11 – John Herschel, English mathematician and astronomer.
• October 18 – Charles Babbage, English mathematician and inventor of computing machines.
• December 8 – James Murray, Irish physician.