1858 in science
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- In Luxor, Egypt, the Rhind papyrus is found (named for Alexander Henry Rhind, the discoverer); it is sometimes called the Ahmes papyrus for the scribe who wrote it around 1650 BC.
- Donati's Comet, the first comet to be photographed, is discovered by Giovanni Battista Donati on 2 June and remains visible for several months afterwards.
- William Herschel initiates fingerprinting as a means of identification, in Bengal.
- Rudolf Virchow publishes Die Cellularpathologie in ihrer Begründung auf physiologische und pathologische Gewebelehre: 20 Vorlesungen, gehalten während der Monate Februar, März und April 1858 im Pathologischen Institut zu Berlin.
- George Bentham's Handbook of the British flora is published. This will be in use (in editions edited by Joseph Dalton Hooker) for a century.
- Publication of Darwin's theory:
- June 18 – Charles Darwin receives papers from Alfred Russel Wallace setting out the latter's theory of natural selection which he forwards to Charles Lyell.
- July 1 – Darwin and Wallace's papers on their theories of evolution, On the Tendency of Species to form Varieties; and on the Perpetuation of Varieties and Species by Natural Means of Selection (submitted with the support of Lyell and Joseph Dalton Hooker) are read by John Joseph Bennett to a meeting of the Linnean Society of London. They are first published on August 20.
- February 13 – Richard Francis Burton and John Hanning Speke become the first Europeans to discover Lake Tanganyika.
- May 14 – Dr David Livingstone's 6-year Second Zambesi Expedition, under the patronage of the Royal Geographical Society, arrives at the African coast with the prefabricated iron paddle steamer Ma Robert.
- August 3 – John Hanning Speke discovers Lake Victoria, source of the River Nile.
- The Möbius strip is discovered independently by German mathematicians August Ferdinand Möbius and Johann Benedict Listing.
- Arthur Cayley publishes "A memoir on the theory of matrices", introducing the modern concept of the matrix in mathematics.
- August 2 – Medical Act 1858 passed "to Regulate the Qualifications of Practitioners in Medicine and Surgery" in the United Kingdom.
- First publication of Gray's Anatomy.
- Publication in London of Thomas B. Peacock's On Malformations, &c., of the Human Heart, with original cases which becomes a standard cardiology textbook.
- French pediatrician Eugène Bouchut develops a new technique for non-surgical orotracheal intubation to bypass laryngeal obstruction resulting from a diphtheria-related pseudomembrane.
- January 31 – I. K. Brunel's SS Great Eastern, the largest ship built to date, is launched on the River Thames using Tangye hydraulic rams.
- August – The first aerial photography is carried out by Nadar from a moored balloon in France using the collodion process.
- Hoffmann kiln patented in Germany by Friedrich Hoffmann for continuous production brickmaking.
- January 2 – Bernard Sachs (died 1944), American neurologist.
- January 9 – Elizabeth Gertrude Britton, née Knight (died 1934), American botanist.
- January 28 – Eugène Dubois (died 1940), Dutch paleoanthropologist.
- February 7 – Herman Frederik Carel ten Kate (died 1931), Dutch anthropologist.
- March 18 – Rudolf Diesel (died 1913), German mechanical engineer.
- April 23 – Max Planck (died 1947), German theoretical physicist.
- May 19 – Thomas Allinson (died 1918), English physician and dietetic reformer.
- August 11 – Christiaan Eijkman (died 1930), Dutch physiologist.
- August 19 – Ellen Willmott (died 1934), English horticulturist.
- August 27 – Giuseppe Peano (died 1932), Italian mathematician.
- October 4 – Mihajlo Idvorski Pupin (died 1935), Banat-born physicist.
- November 1 – Ludwig Struve (died 1920), Russian astronomer.
- November 30 – Jagadish Chandra Bose (died 1937), Bengali physicist.
- Laura Forster (died 1917), Australian physician.
- April 28 – Johannes Peter Müller (born 1801), German physiologist.
- June 10 – Robert Brown (born 1773), Scottish botanist.
- June 28 – Jane Marcet (born 1769), British popular science writer.
- November 8 – George Peacock (born 1791), English mathematician.
- December 16 – Richard Bright (born 1789), English physician.
- date unknown - Amelia Griffiths (born 1768), British phycologist.
- Herschel, William J. (1916). The Origin of Finger-Printing (PDF). Oxford University Press. ISBN 978-1-104-66225-7. Archived (PDF) from the original on 25 July 2011. Retrieved 11 August 2011.
- Penguin Pocket On This Day. Penguin Reference Library. 2006. ISBN 978-0-14-102715-9.
- "The Zambesi Expedition". Livingstone Online. Archived from the original on 2012-03-02. Retrieved 2011-08-26.
- Pickover, Clifford A. (2006). The Möbius Strip: Dr. August Möbius's Marvelous Band in Mathematics, Games, Literature, Art, Technology, and Cosmology. Thunder's Mouth Press. ISBN 978-1-56025-826-1.
- Herges, Rainer (2005). "Möbius, Escher, Bach – Das unendliche Band in Kunst und Wissenschaft". Naturwissenschaftliche Rundschau: 301–310. ISSN 0028-1050.
- Rodley, Chris, ed. (1997). Lynch on Lynch. London. p. 231.
- Philosophical Transactions of the Royal Society (London) 148 (1858). Repr. Cayley, Arthur (2009) . The Collected Mathematical Papers. Cambridge Library Collection – Mathematics. 2. Cambridge University Press. pp. 475–96. ISBN 978-1-108-00507-4. archive.
- Dieudonné, Jean, ed. (1978). "III". Abrégé d'histoire des mathématiques 1700-1900. 1. Paris: Hermann. p. 96.
- Crilly, Tony (2007). 50 Mathematical Ideas you really need to know. London: Quercus. p. 156. ISBN 978-1-84724-008-8.
- "Thomas Bevill Peacock (1812-1882), 19th Century Cardiologist". Journal of the American Medical Association. 203 (9): 801. 1968. doi:10.1001/jama.1968.03140090185016. Retrieved 2011-03-30.
- Bouchut, E. (1858). "D'une nouvelle méthode de traitement du croup par le tubage du larynx" [On a new method of treatment for croup by larynx intubation]. Bulletin de l'Académie Impériale de Médecine (in French). 23: 1160–2. Retrieved 2010-09-06.
- Trede K, Baldessarini RJ, Viguera AC, Bottero A (2009). "Treatise on insanity in pregnant, postpartum, and lactating women (1858) by Louis-Victor Marcé: a commentary". Harvard Review of Psychiatry. 17 (2): 157–65. doi:10.1080/10673220902891802. PMID 19373623.
- "ss Great Eastern". Brunel 200. 2006. Archived from the original on 2011-07-08. Retrieved 2011-06-29.
- "Brief history of aerial photography". www.findaerialphotography.com. 2007. Retrieved 2015-01-02.