View source for Gustav Kirchhoff

{{Short description|German physicist and mathematician (1824–1887)}}
{{Use dmy dates|date=February 2021}}
{{Infobox scientist
| name              = Gustav Kirchhoff
| image             = Gustav Robert Kirchhoff.jpg
| birth_name        = Gustav Robert Kirchhoff
| birth_date        = {{Birth date
|1824|03|12|df=yes}}
| birth_place       = [[Königsberg]], [[East Prussia]], [[Kingdom of Prussia]]
| death_date        = {{Death date and age|1887|10|17|1824|03|12|df=yes}}
| death_place       = [[Berlin]], [[German Empire]]
| resting_place     = [[Alter St.-Matthäus-Kirchhof]], Berlin
| alma_mater        = [[University of Königsberg]] ([[Dr. phil.]])
| known_for         = {{Indented plainlist|
* Discovery of [[caesium]] and [[rubidium]]
* [[Kirchhoff's diffraction formula]]
* [[Kirchhoff's circuit laws]]
* [[Kirchhoff's theorem]]
* [[Kirchhoff's law of thermal radiation]]}}
| spouses           = {{Indented plainlist|
* {{Marriage|Clara Richelot|1857|1869|end=died}}
* {{Marriage|Luise Brömmel|1872}}}}
| children          = 5
| awards            = {{Indented plainlist|
* [[Rumford Medal]] (1862)
* [[Cothenius Medal]] (1876)
* [[Matteucci Medal]] (1877)
* [[Davy Medal]] (1877)}}
| fields            = {{Flat list|
* [[Spectroscopy]]
* [[optics]]
* [[electromagnetism]]
* [[graph theory]]
* [[thermodynamics]]}}
| work_institutions = {{Indented plainlist|
* [[University of Berlin]] (1847–1850, 1875–1887)
* [[University of Breslau]] (1850–1854)
* [[University of Heidelberg]] (1854–1875)}}
| doctoral_advisor  = [[Franz Ernst Neumann]]
| notable_students  = {{Collapsible list|title={{Nobold|''See list''}}
 | [[Hermann Aron]]<ref name=MGP>{{Cite web|title=Gustav Kirchhoff|url=https://www.genealogy.math.ndsu.nodak.edu/id.php?id=46968|work=[[Mathematics Genealogy Project]]|publisher=North Dakota State University|access-date=2025-10-15}}</ref>
 | [[Ivan Borgman]]<ref name="Physics Tree">{{Cite web|title=Physics Tree - Gustav Robert Kirchhoff|url=https://academictree.org/physics/peopleinfo.php?pid=25612|website=academictree.org|access-date=2025-10-15}}</ref>
 | [[Siegfried Czapski]]<ref name="Physics Tree"/>
 | [[Loránd Eötvös]]<ref name=MGP/>
 | [[Heinrich Hertz]]<ref name="Physics Tree"/>
 | [[Heike Kamerlingh Onnes]]<ref name="Physics Tree"/>
 | [[Viktor Kirpichov]]<ref name=MGP/>
 | [[Johannes Knoblauch]]<ref name=MGP/>
 | [[Sofia Kovalevskaya]]<ref name="Physics Tree"/>
 | [[Gabriel Lippmann]]<ref name=MGP/>
 | [[Jacob Lüroth]]<ref name=MGP/>
 | [[Edward Leamington Nichols]]<ref name="Physics Tree"/>
 | [[Max Noether]]<ref name=MGP/>
 | [[Karol Olszewski]]<ref name="Physics Tree"/>
 | [[Max Planck]]<ref name="Physics Tree"/>
 | [[Ernst Schröder (mathematician)|Ernst Schröder]]<ref name=MGP/>
 | [[Arthur Schuster]]<ref name=MGP/>
 | [[August Witkowski]]<ref name="Physics Tree"/>
 | [[Heinrich Martin Weber]]<ref name=MGP/>
 | [[Arthur Williams Wright]]<ref name="Physics Tree"/>
}}
}}

'''Gustav Robert Kirchhoff''' ({{IPA|de|ˈgʊstaːf ˈʁoːbɛʁt ˈkɪʁçhɔf|lang}}; 12 March 1824 – 17 October 1887) was a German [[physicist]] and [[mathematician]] who contributed to the fundamental understanding of [[electrical circuit]]s, [[spectroscopy]], and the emission of [[black-body radiation]] by heated objects.<ref name="Marshall">{{cite journal |last1=Marshall |first1=James L. |last2=Marshall |first2=Virginia R. |title=  Rediscovery of the Elements: Mineral Waters and Spectroscopy |journal=The Hexagon |date=2008 |pages=42–48 |url=http://www.chem.unt.edu/~jimm/REDISCOVERY%207-09-2018/Hexagon%20Articles/bunsen%20and%20spectroscopy.pdf |access-date=31 December 2019}}</ref><ref>{{Cite book |url=https://books.google.com/books?id=8qHGRTC7h-MC&pg=PT79 |title=An Introduction to Electrical Science |last=Waygood |first=Adrian |date=19 June 2013 |publisher=Routledge |isbn=9781135071134 |language=en }}</ref> He coined the term ''[[black body]]'' in 1860.<ref>{{Cite book |last=Schmitz |first=Kenneth S. |title=Physical Chemistry |publisher=Elsevier |year=2018 |isbn=9780128005996 |pages=278}}</ref>

Several different sets of concepts are named "Kirchhoff's laws" after him, which include [[Kirchhoff's circuit laws]], [[Kirchhoff's law of thermal radiation]], [[Kirchhoff's diffraction formula]], and Kirchhoff's law of thermochemistry.

The [[Bunsen–Kirchhoff Award]] for spectroscopy is named after Kirchhoff and his colleague, [[Robert Bunsen]].

== Biography ==
Gustav Robert Kirchhoff was born on 12 March 1824 in [[Königsberg]], [[Prussia]], the son of Friedrich Kirchhoff, a lawyer, and Johanna Henriette Wittke.<ref>{{Cite book |url=https://books.google.com/books?id=SPU8BQAAQBAJ&pg=PA288 |title=Modern Thermodynamics: From Heat Engines to Dissipative Structures |last1=Kondepudi |first1=Dilip |last2=Prigogine |first2=Ilya |date=5 November 2014 |publisher=John Wiley & Sons |isbn=9781118698709 |pages=288 |language=en }}</ref> His family were [[Lutheranism|Lutherans]] in the [[Evangelical Church of Prussia]].

Kirchhoff studied at the [[University of Königsberg]], where he attended the mathematico-physical seminar directed by [[C. G. J. Jacobi]],<ref>{{cite book |title=The Biographical Encyclopedia of Astronomers |last=Hockey |first=Thomas |date=2009 |publisher=[[Springer Nature]] |isbn=978-0-387-31022-0 |access-date=22 August 2012 |chapter=Kirchhoff, Gustav Robert |chapter-url=http://www.springerreference.com/docs/html/chapterdbid/58778.html |title-link=The Biographical Encyclopedia of Astronomers }}</ref> [[Franz Ernst Neumann]], and [[Friedrich Julius Richelot]]. In 1845,  Kirchhoff formulated [[Kirchhoff's circuit laws|two circuit laws]],<ref>{{Cite web|last=Kirchhoff|first=S.|year=1845|title=Ueber den Durchgang eines elektrischen Stromes durch eine Ebene, insbesondere durch eine kreisförmige|url=https://zenodo.org/records/2422851|language=de|doi=10.1002/andp.18451400402}}</ref> which are now ubiquitous in [[electrical engineering]]. He completed this study as a seminar exercise; it later became his doctoral thesis, supervised by Neumann.

In 1847, Kirchhoff graduated from the University of Königsberg and became a ''[[Privatdozent]]'' (unsalaried lecturer) at the [[University of Berlin]], where he stayed until 1850 when he was offered a professorship at the [[University of Breslau]]. In 1854, he was called to the [[University of Heidelberg]], where he collaborated with [[Robert Bunsen]] in spectroscopic work. In 1875, Kirchhoff returned to Berlin, where he remained until his death in 1887.

In 1857, Kirchhoff married Clara Richelot, the daughter of his mathematics professor Richelot; the couple had five children. In 1872, after Clara's death in 1869, he married Luise Brömmel.<ref>{{cite web
 | url =http://www.kip.uni-heidelberg.de/oeffwiss/kirchhoff
 | title =Gustav Robert Kirchhoff – Dauerausstellung
 | publisher =Kirchhoff-Institute for Physics
 | access-date =18 March 2016
| quote =Am 16. August 1857 heiratete er Clara Richelot, die Tochter des Königsberger Mathematikers ... Frau Clara starb schon 1869. Im Dezember 1872 heiratete Kirchhoff Luise Brömmel. }}</ref>

Kirchhoff died on 17 October 1887 in [[Berlin]] at the age of 63. He is buried at [[Alter St.-Matthäus-Kirchhof]] in [[Schöneberg]], Berlin (just a few meters from the graves of the [[Brothers Grimm]]).

== Research ==
[[File:Bunsen-Kirchhoff.jpg|thumb|left|upright|Kirchhoff ''(left)'' and [[Robert Bunsen]], {{Circa|1850}}|alt= Black-and-white image of two middle-aged men, either one leaning with one elbow on a wooden column in the middle. Both wear long jackets, and the shorter man on the left has a beard.]] 

In 1857, Kirchhoff calculated that an electric signal in a [[electrical resistance|resistanceless]] wire travels along the wire at the [[speed of light]].<ref>
{{cite journal
 |last=Kirchhoff |first=Gustav
 |year=1857
 |title=On the motion of electricity in wires
 |journal=[[Philosophical Magazine]]
 |volume=13 |pages=393–412
 }}</ref><ref>{{cite journal
 |last1=Graneau |first1=Peter 
 |last2=Assis |first2=André Koch Torres 
 |title=Kirchhoff on the motion of electricity in conductors
 |url=http://www.ifi.unicamp.br/~assis/Apeiron-V19-p19-25%281994%29.pdf |archive-url=https://web.archive.org/web/20060108091219/http://www.ifi.unicamp.br/~assis/Apeiron-V19-p19-25(1994).pdf |archive-date=2006-01-08 |url-status=live
 |journal=Apeiron
 |volume=1
 |issue=19
 |date=1994
 |pages=19–25
}}</ref>

In 1859, Kirchhoff proposed [[Kirchhoff's law of thermal radiation|a law of thermal radiation]], and gave a proof in 1861. 

Together, Kirchhoff and Bunsen improved on [[Joseph von Fraunhofer]]'s 1814 [[spectroscopy|spectroscope]], which Kirchhoff used to pioneer the identification of the [[Sun#Composition|elements in the Sun]], showing in 1859 that the Sun contains [[sodium]]. Kirchhoff and Bunsen discovered [[caesium]] and [[rubidium]] in 1861.<ref name="Weeks">{{cite book |last1=Weeks |first1=Mary Elvira |title=The discovery of the elements |date=1956 |publisher=Journal of Chemical Education |location=Easton, PA |url=https://archive.org/details/discoveryoftheel002045mbp |edition=6th }}</ref>

Kirchhoff contributed greatly to the field of [[spectroscopy]] by formalizing three laws that describe the [[optical spectrum|spectral]] composition of [[light]] emitted by incandescent objects, building substantially on the discoveries of [[David Alter]] and [[Anders Jonas Ångström]]. In 1862, he was awarded the [[Rumford Medal]] "for his researches on the fixed lines of the solar spectrum, and on the inversion of the bright lines in the spectra of artificial light".{{efn|Kirchhoff's banker, on hearing that Kirchhoff had identified the elements present in the Sun, remarked "of what use is gold in the Sun if it cannot be brought to Earth?" Kirchhoff deposited his prize money (gold sovereigns) with the banker, saying "here is gold from the Sun."<ref>[[Isaac Asimov|Asimov, Isaac]], ''The Secret of the Universe'', Oxford University Press, 1992, p. 109</ref>}}

Kirchhoff also contributed to [[optics]], carefully solving the [[wave equation]] to provide a solid foundation for [[Huygens' principle]] (and correct it in the process).<ref>Baker, Bevan B.; and Copson, Edward T.; ''The Mathematical Theory of Huygens' Principle'', Oxford University Press, 1939, pp.{{nnbsp}}36–38.</ref><ref name=miller1991>Miller, David A. B.; "Huygens's wave propagation principle corrected", Optics Letters '''16''', 1370–1372, 1991</ref>

=== Kirchhoff's circuit laws ===
{{main|Kirchhoff's circuit laws}}
Kirchhoff's first law states that at any node in an electrical circuit where current can branch, the sum of the currents leaving the node is equal to the sum of the currents entering the node. The second law states that the algebraic sum of the potential drops along a closed circuit, taken in any direction of flow, is equal to zero.<ref>Corso di Fisicia 2 author Paul A .Tipler</ref>

=== Kirchhoff's three laws of spectroscopy ===
{{See also|History of spectroscopy}}
[[File:Kirchhof laws.svg|thumb|Visual depiction of Kirchhoff's laws of spectroscopy|alt=|left]]
#A solid, liquid, or dense gas excited to emit light will radiate at all wavelengths and thus produce a continuous spectrum.
#A low-density gas excited to emit light will do so at specific wavelengths, and this produces an [[emission spectrum]]. 
# If light composing a continuous spectrum passes through a cool, low-density gas, the result will be an absorption spectrum.

Kirchhoff did not know about the existence of [[energy level]]s in atoms. The existence of discrete spectral lines had been known since [[Fraunhofer lines|Fraunhofer]] discovered them in 1814. That the lines formed a discrete mathematical pattern was described by [[Johann Balmer]] in 1885. [[Joseph Larmor]] explained the splitting of the [[spectral line]]s in a [[magnetic field]] known as the [[Zeeman Effect]] by the oscillation of [[electron]]s.<ref>Buchwald, Jed Z.; and Warwick, Andrew; editors; ''Histories of the Electron: The Birth of Microphysics''</ref><ref>{{Citation |last=Larmor |first=Joseph |year=1897 |title=On a Dynamical Theory of the Electric and Luminiferous Medium, Part 3, Relations with material media |journal=Philosophical Transactions of the Royal Society |volume=190 |pages=205–300 |doi=10.1098/rsta.1897.0020|bibcode = 1897RSPTA.190..205L |title-link=s:Dynamical Theory of the Electric and Luminiferous Medium III |doi-access=free }}</ref> These discrete spectral lines were not explained as [[electron transition]]s until the [[Bohr model]] of the atom in 1913, which helped lead to [[quantum mechanics]].{{clear}}

=== Kirchhoff's law of thermal radiation ===
It was [[Kirchhoff's law of thermal radiation]] in which he proposed an unknown universal law for radiation that led [[Max Planck]] to the discovery of the quantum of action leading to [[quantum mechanics]].

=== Kirchhoff's law of thermochemistry ===
{{see also|Standard enthalpy of reaction#Variation with temperature or pressure}}
Kirchhoff showed in 1858 that, in [[thermochemistry]], the variation of the [[Standard enthalpy of reaction|heat of a chemical reaction]] is given by the difference in [[heat capacity]] between products and reactants:

:<math>\left(\frac{\partial \Delta H}{\partial T}\right)_p = \Delta C_p</math>.

Integration of this equation permits the evaluation of the heat of reaction at one temperature from measurements at another temperature.<ref>[[Keith J. Laidler|Laidler, Keith J.]]; and Meiser, J. H.; "Physical Chemistry", Benjamin/Cummings 1982, p. 62</ref><ref>[[Peter Atkins|Atkins, Peter]]; and de Paula, J.; "Atkins' Physical Chemistry", W. H. Freeman, 2006 (8th edition), p. 56</ref>

=== Kirchhoff's theorem in graph theory ===
Kirchhoff also worked in the mathematical field of [[graph theory]], in which he proved [[Kirchhoff's theorem|Kirchhoff's matrix tree theorem]].

== Recognition ==
=== Awards ===
{| class="wikitable"
! Year
! Organization
! Award
! Citation
! {{Reference column heading}}
|-
| 1862
| {{Flagicon|UKGBI}} [[Royal Society]]
| [[Rumford Medal]]
| "For his researches on the fixed lines of the solar spectrum, and on the inversion of the bright lines in the spectra of artificial light."
| <ref>{{Cite web|title=Rumford Medal|url=https://royalsociety.org/medals-and-prizes/rumford-medal/|website=royalsociety.org|access-date=2024-06-19}}</ref>
|-
| 1876
| {{Flagicon|German Empire}} [[German National Academy of Sciences Leopoldina|Leopoldina]]
| [[Cothenius Medal]]
|
| <ref>{{Cite web|title=Preisträger der Cothenius-Medaille von 1864 bis 1953|url=https://www.leopoldina.org/ueber-uns/auszeichnungen/medaillen/cothenius-medaille/historie-der-cothenius-medaille-1864-bis-1953|url-status=dead|website=www.leopoldina.org|language=de|archive-url=https://web.archive.org/web/20250223093331/https://www.leopoldina.org/ueber-uns/auszeichnungen/medaillen/cothenius-medaille/historie-der-cothenius-medaille-1864-bis-1953|archive-date=2025-02-23|access-date=2025-11-24}}</ref>
|-
| 1877
| {{Flagicon|Kingdom of Italy}} [[Accademia dei XL]]
| [[Matteucci Medal]]
|
| <ref>{{Cite web|title=Medaglie|url=https://www.accademiaxl.it/attivita/medaglie/|website=www.accademiaxl.it|language=it|access-date=2025-11-04}}</ref>
|-
| 1877
| {{Flagicon|UKGBI}} [[Royal Society]]
| [[Davy Medal]]{{Efn|Awarded jointly with [[Robert Bunsen]].}} 
| "For their researches & discoveries in spectrum analysis."
| <ref>{{Cite web|title=Davy Medal|url=https://royalsociety.org/medals-and-prizes/davy-medal/|url-status=live|website=royalsociety.org|archive-url=https://web.archive.org/web/20130728050634/http://royalsociety.org/awards/davy-medal/|archive-date=2013-07-28|access-date=2011-08-05}}</ref>
|}

=== Memberships ===
{| class="wikitable"
! Year
! Organization
! Type
! {{Reference column heading}}
|-
| 1864
| {{Flagicon|US|1863}} [[American Philosophical Society]]
| International Member
| <ref>{{Cite web|title=APS Member History|url=https://search.amphilsoc.org/memhist/search?creator=Gustav+R.+Kirchhoff&title=&subject=&subdiv=&mem=&year=&year-max=&dead=&keyword=&smode=advanced|url-status=live|website=search.amphilsoc.org|archive-url=https://web.archive.org/web/20241208011858/https://search.amphilsoc.org/memhist/search?creator=Gustav+R.+Kirchhoff&title=&subject=&subdiv=&mem=&year=&year-max=&dead=&keyword=&smode=advanced|archive-date=2024-12-08|access-date=2025-11-24}}</ref>
|-
| 1884
| {{Flagicon|Netherlands}} [[Royal Netherlands Academy of Arts and Sciences]]
| Foreign Member
| <ref>{{Cite web|title=G.R. Kirchhoff (1824 - 1887)|url=https://dwc.knaw.nl/biografie/biografisch-apparaat/pmknaw/?pagetype=authorDetail&aId=PE00001261|url-status=live|website=dwc.knaw.nl|archive-url=https://web.archive.org/web/20241215024223/https://dwc.knaw.nl/biografie/biografisch-apparaat/pmknaw/?pagetype=authorDetail&aId=PE00001261|archive-date=2024-12-15|access-date=2015-07-22 }}</ref>
|}

=== Orders ===
{| class="wikitable"
! Year
! Head of state
! Order
! {{Reference column heading}}
|-
| 1874
| {{Flagicon|German Empire}} [[Wilhelm I]]
| {{Lang|fr|[[Pour le Mérite]]}}
| <ref>{{Cite web|title=Gustav Robert  Kirchhoff|url=https://www.orden-pourlemerite.de/mitglieder/gustav-robert-kirchhoff|website=www.orden-pourlemerite.de|language=de|access-date=2026-01-20}}</ref>
|}

== Publications ==
* {{Cite book|title=Gesammelte Abhandlungen|volume=|publisher=Johann Ambrosius Barth|location=Leipzig|year=1882|language=de|url=https://gutenberg.beic.it/webclient/DeliveryManager?pid=11943571}}
* {{Cite book|title=Vorlesungen über Electricität und Magnetismus|volume=|publisher=Benedictus Gotthelf Teubner|location=Leipzig|year=1891|language=de|url=https://gutenberg.beic.it/webclient/DeliveryManager?pid=11946679}}
* ''Vorlesungen über mathematische Physik''. 4 vols., B. G. Teubner, Leipzig 1876–1894.
** Vol. 1: ''Mechanik''. 1. Auflage, B. G. Teubner, Leipzig 1876 ([http://archive.org/stream/vorlesungenberm02kircgoog#page/n7/mode/1up online]).
** Vol. 2: ''Mathematische Optik''. B. G. Teubner, Leipzig 1891 (Herausgegeben von Kurt Hensel, [http://archive.org/stream/vorlesungenberm01plangoog#page/n14/mode/1up online]).
** Vol. 3: ''Electricität und Magnetismus''. B. G. Teubner, Leipzig 1891 (Herausgegeben von Max Planck, [https://archive.thulb.uni-jena.de/hisbest/rsc/viewer/HisBest_derivate_00011231/KNT_63c_bild_Seite_002.tiff online]).
** Vol. 4: [https://books.google.com/books?id=t0QMSU3Q8FQC ''Theorie der Wärme'']. B. G. Teubner, Leipzig 1894, Herausgegeben von Max Planck<ref>{{cite journal |last=Merritt |first=Ernest |url=https://books.google.com/books?id=wx7OAAAAMAAJ&pg=PA73 |pages=73–75 |title=Review of ''Vorlesungen über mathematische Physik. Vol. IV. Theorie der Wärme'' by Gustav Kirchhoff, edited by Max Planck |journal=Physical Review |year=1895 |publisher=American Physical Society }}</ref>

== See also ==
* [[Circuit rank]]
* [[Computational aeroacoustics]]
* [[Atomic emission spectroscopy|Flame emission spectroscopy]]
* [[Spectroscope]]
* [[Kirchhoff Institute of Physics]]
* [[List of German inventors and discoverers]]

==Notes==
{{notelist}}

==References==
{{reflist}}

==Bibliography==
*{{cite journal |doi=10.1007/BF01558883 |title=Zur Erinnerung an Gustav Kirchhoff |date=1925 |last1=Warburg |first1=E. |journal=[[Die Naturwissenschaften]] |volume=13 |page=205 |bibcode = 1925NW.....13..205W |issue=11 |s2cid=30039558 }}
*{{cite journal |doi=10.1007/BF00625887 |title=Gustav Robert Kirchhoff (on the ninetieth anniversary of his death) |date=1977 |last1=Stepanov |first1=B. I. |journal=Journal of Applied Spectroscopy |volume=27 |page=1099 |bibcode=1977JApSp..27.1099S |issue=3 |s2cid=95181496 }}
*{{cite journal |doi=10.1088/0031-9120/4/6/304 |title=Kirchhoff-Gustav Robert 1824–1887 |date=1969 |last1=Everest |first1=A. S. |journal=[[Physics Education]] |volume=4 |page=341 |bibcode=1969PhyEd...4..341E |issue=6 |article-number=304 |s2cid=250765281 }}
*{{cite journal |first=Gustav |last=Kirchhoff |title=Ueber die Fraunhoferschen Linien |journal=[[Monatsberichte der Königliche Preussische Akademie der Wissenschaften zu Berlin]] |date=1860 |pages=662–665 |url=https://books.google.com/books?id=XDIXZiXWIuEC&pg=PA3}} [http://hdl.handle.net/2027/mdp.39015050939274 HathiTrust full text] {{ISBN|978-1-113-39933-5}}. Partial English translation available in [[Magie, William Francis]], ''A Source Book in Physics'' (1963). Cambridge: [[Harvard University Press]]. p.&nbsp;354-360.
*Kirchhoff, Gustav (1860). “IV. Ueber das Verhältniß zwischen dem Emissionsvermögen und dem Absorptionsvermögen der Körper für Wärme und Licht,” ''Annalen der Physik'' 185(2), 275–301. (coinage of term “blackbody”) [On the relationship between the emissivity and the absorptivity of bodies for heat and light]

== Further reading ==
* {{MathGenealogy|id=46968}}
* {{MacTutor Biography|id=Kirchhoff}}
* {{ScienceWorldBiography | urlname=Kirchhoff | title=Kirchhoff, Gustav (1824–1887)}}
* [[Klaus Hentschel]]: Gustav Robert Kirchhoff und seine Zusammenarbeit mit Robert Wilhelm Bunsen, in: Karl von Meyenn (Hrsg.) ''Die Grossen Physiker'', Munich: Beck, vol. 1 (1997), pp.&nbsp;416–430, 475–477, 532–534.
* [[Klaus Hentschel]]: [https://books.google.com/books?id=WceRw3sr-rQC ''Mapping the Spectrum. Techniques of Visual Representation in Research and Teaching''], Oxford: OUP, 2002.
* [http://www.ifi.unicamp.br/%7Eassis/Apeiron-V19-p19-25(1994).pdf Kirchhoff's 1857 paper on the speed of electrical signals in a wire]
*{{Wikisource-inline|list=
** {{Cite Americana|wstitle=Kirchhoff, Gustav Robert |short=x |noicon=x}}
** {{Cite NSRW|wstitle=Kirchhoff, Gustav Robert |short=x |noicon=x}}
** {{Cite EB1911|wstitle=Kirchhoff, Gustav Robert |short=x |noicon=x}}
** {{Cite NIE|wstitle=Kirchhoff, Gustav Robert|year=1905 |short=x |noicon=x}}
** {{Cite PSM|wstitle=Sketch of Gustav Robert Kirchhoff|volume=33|month-and-year=May 1888 |noicon=x}}
** {{Cite AmCyc|wstitle=Kirchhoff, Gustav Robert |short=x |noicon=x}}
}}

==External links==
*{{wikiquote-inline}}
*{{commons category-inline|Gustav Robert Kirchhoff}}
*[https://openlibrary.org/authors/OL4863835A Open Library]

{{Authority control}}

{{DEFAULTSORT:Kirchhoff, Gustav}}
[[Category:Gustav Kirchhoff| ]]
[[Category:1824 births]]
[[Category:1887 deaths]]
[[Category:German optical physicists]]
[[Category:19th-century German inventors]]
[[Category:Discoverers of chemical elements]]
[[Category:Scientists from Königsberg]]
[[Category:German spectroscopists]]
[[Category:German fluid dynamicists]]
[[Category:University of Königsberg alumni]]
[[Category:Academic staff of the University of Breslau]]
[[Category:Academic staff of Heidelberg University]]
[[Category:Academic staff of the Humboldt University of Berlin]]
[[Category:Honorary Fellows of the Royal Society of Edinburgh]]
[[Category:Foreign members of the Royal Society]]
[[Category:Foreign associates of the National Academy of Sciences]]
[[Category:Members of the Royal Netherlands Academy of Arts and Sciences]]
[[Category:Recipients of the Pour le Mérite (civil class)]]
[[Category:Physicists from the Kingdom of Prussia]]
[[Category:19th-century German physicists]]
[[Category:Rare earth scientists]]
[[Category:Fellows of the Royal Society of Edinburgh]]
[[Category:Recipients of the Matteucci Medal]]
[[Category:Members of the Göttingen Academy of Sciences and Humanities]]
[[Category:Recipients of the Cothenius Medal]]
[[Category:International members of the American Philosophical Society]]
[[Category:German fellows of the Royal Society]]