Search Results for Kirchhoff


  1. Gustav Kirchhoff (1824-1887)
    • Gustav Robert Kirchhoff .
    • Gustav Kirchhoff's father was Friedrich Kirchhoff, a law councillor in Konigsberg with a strong sense of duty to the Prussian state.
    • Kirchhoff was educated in Konigsberg where he entered the Albertus University of Konigsberg which had been founded in 1544 by Albert, the first duke of Prussia.
    • Kirchhoff attended the Neumann-Jacobi seminar from 1843 to 1846.
    • Now 1843 was the year in which Jacobi became unwell, so it was Neumann who influenced Kirchhoff in a very positive way.
    • Neumann's interests were at this time firmly in mathematical physics and, at the time Kirchhoff began to study at Konigsberg, Neumann had become interested in electrical induction.
    • In fact Neumann published the first of his two major papers on electrical induction in 1845 while Kirchhoff was studying with him.
    • Kirchhoff was taught mathematics at the University of Konigsberg by Friedrich Jules Richelot.
    • It was while he was studying with Neumann that Kirchhoff made his first outstanding research contribution which related to electrical currents.
    • Kirchhoff's laws, which he announced in 1845, allowed calculation of currents, voltages and resistances in electrical circuits with multiple loops, extending the work of Ohm.
    • Kirchhoff considered an electrical network consisting of circuits joined at nodes of the network and gave laws which reduce the calculation of the currents in each loop to the solution of algebraic equations.
    • Kirchhoff's laws followed from applying Ohm's law but the way in which he was able to generalise the results showed great mathematical skills.
    • At this stage Kirchhoff was unaware that Ohm's analogy between the flow of heat and the flow of electricity, which formed the accepted understanding of electrical currents at that time, led to an incorrect understanding of electrical currents.
    • Kirchhoff's work would, a couple of years later, lead to him to realise this error and to give a correct understanding of how the theory of electric currents and electrostatics should be combined.
    • The year 1847 was an eventful one for Kirchhoff.
    • Republican and socialist feelings meant that the monarchy was in trouble, but Kirchhoff was in a privileged position and was unaffected by events around him as he pressed forward with his career.
    • In the year that he arrived in Breslau, Kirchhoff solved a problem concerning the deformation of elastic plates.
    • Problems remained, however, which Kirchhoff solved using variational calculus.
    • While Kirchhoff was in Breslau he met Bunsen who spent the academic year 1851-52 there; the two becoming firm and lasting friends.
    • In 1854 Bunsen, who was working at Heidelberg, encouraged and supported Kirchhoff to move there.
    • Kirchhoff accepted the offer of an appointment as professor of physics and he began a fruitful collaboration with Bunsen.
    • Kirchhoff was not the only one working at the time on electric currents.
    • Wilhelm Weber and Rudolf Kohlrausch were also working on the nature of such currents and published similar results to that of Kirchhoff around 1857 on the velocity of a current in a highly conductive wire.
    • Kirchhoff and Weber both discovered that the velocity was independent of the nature of the wire and was almost exactly equal to the velocity of light.
    • Fundamental work by Kirchhoff on black body radiation (a term he introduced in 1862) was important in the development of quantum theory.
    • Kirchhoff was able to make his fundamental breakthrough by producing purer forms of substances than had been previously the case.
    • Kirchhoff and Bunsen went on to examine the spectrum of the sun in 1861 and were able to identify the chemical elements in the sun's atmosphere.
    • Kirchhoff is perhaps best known for being the first to explain the dark lines in the sun's spectrum as caused by absorption of particular wavelengths as the light passes through gases in the sun's atmosphere.
    • With Clara, his first wife, Kirchhoff had three sons and two daughters and he was left to bring them up on his own in 1869 when Clara died.
    • Kirchhoff had been made offers by other universities but he was happy in Heidelberg and turned down such offers.
    • In [',' L Rosenfeld, Biography in Dictionary of Scientific Biography (New York 1970-1990).','1] Rosenfeld sums up Kirchhoff's contribution:- .
    • Among the leading physicists of the nineteenth century, it was Kirchhoff whose temperament was best suited to this task.
    • The excellence of Kirchhoff as a teacher can be inferred from the printed text of his lectures (he managed to publish only those on mechanics, the others being edited posthumously).
    • Honours awarded to Gustav Kirchhoff .
    • 3.nLunar featuresnCrater Kirchhoff .
    • Kirchhoff Institute Heidelberg (In German) .
    • .

  2. Ernst Schröder (1841-1902)
    • He studied mathematics under Otto Hesse, physics under Gustav Kirchhoff and chemistry under Robert Bunsen.
    • Heidelberg was an exciting place at this time with Kirchhoff and Bunsen making fundamental advances analysing the spectrum of elements.
    • Both Kirchhoff and Bunsen had been students of Hesse.
    • Hesse had been a professor at Konigsberg before being appointed to Heidelberg and Kirchhoff and Bunsen had both been his students at Konigsberg.
    • Franz Neumann had been the professor of physics at Konigsberg at that time and had also taught Kirchhoff and Bunsen.

  3. Max Planck (1858-1947)
    • It was customary for German students to move between universities at this time and indeed Planck moved to study at the University of Berlin from October 1877 where his teachers included Weierstrass, Helmholtz and Kirchhoff.
    • He later wrote that he admired Kirchhoff greatly but found him dry and monotonous as a teacher.
    • After the death of Kirchhoff in October 1887, the University of Berlin looked for a world leading physicist to replace him and to become a colleague of Helmholtz.
    • After Gustav Kirchhoff has shown that the state of the heat radiation which takes place in a cavity bounded by any emitting and absorbing material at uniform temperature is totally independent of the nature of the material, a universal function was demonstrated which was dependent only on temperature and wavelength, but not in any way on the properties of the material.

  4. Georg Zehfuss biography
    • This dissertation was examined by Otto Hesse and Gustav Kirchhoff; Hesse evaluated the three mathematical parts of the dissertation while Kirchhoff evaluated the one part related to physics.
    • Kirchhoff also praised the physics section which was on the theory of thermodynamics.
    • His application included recommendations from many mathematicians including Ludwig Christian Wiener, Ferdinand Minding, Osip Ivanovich Somov, Oskar Schlomilch, Otto Hesse, Gustav Kirchhoff and Richard Dedekind.

  5. Heinrich Hertz (1857-1894)
    • At Berlin he studied under Helmholtz and Kirchhoff.
    • However he was also asked to go to Berlin as a replacement for Kirchhoff.
    • In mechanics Hertz followed Kirchhoff and considered only length, time and mass as the fundamental entities, force being a derived concept.

  6. Bevan Braithwaite Baker biography
    • Kirchhoff's famous formula is first derived from the formula of Helmholtz and then proved directly.
    • It is pointed out that to extend the theorem of Kirchhoff to the space outside a closed surface it is necessary to prescribe the asymptotic behaviour of the wave-functions under consideration.
    • The analogue of Kirchhoff's formula, due to Volterra, is derived and an interesting account is given of a method, devised by Marcel Riesz and based on the theory of fractional integration, which provides a powerful method of solving initial value problems for equations like the wave equation.

  7. Leo Königsberger (1837-1921)
    • While a professor in Heidelberg he had married Sophie Beral-Kappel (1848-1923) on 13 August 1873 in Baden-Baden with Bunsen and Kirchhoff as witnesses; they had two children one son Johann and one daughter Ani.
    • However, he felt that he had a duty to his wife to improve his situation so, with great sadness at leaving his friends and colleagues Bunsen and Kirchhoff, he accepted.
    • His work on differential equations was, however, also influenced by the applications which interested Bunsen, Kirchhoff and Helmholtz, with whom he was close friends in Heidelberg.

  8. Walter Gröbli biography
    • Probably encouraged by Weber and Schwarz, Grobli went to Berlin to hear Kirchhoff, Helmholtz, Kummer and Weierstrass in 1875.
    • In Berlin he caused a stir by solving the prize problem on vortex motion posed by Kirchhoff.
    • The thesis was cited a number of times in the late 19th century, by G R Kirchhoff, D N Goryachev and H Lamb for example.

  9. Otto Hesse (1811-1874)
    • These doctoral include Gustav Kirchhoff and Carl Neumann at Konigsberg, but he also lectured to several other students there who would go on to become exceptional mathematicians including Siegfried Aronhold, Alfred Clebsch and Rudolph Lipschitz.
    • In 1855 Hesse was appointed as an ordinary professor at Halle, but he only held this post for one year since when he was offered the chair at Heidelberg, to succeed Ferdinand Schweins, he was eager to accept and join his former students Kirchhoff and Bunsen there.

  10. Lóránd Eötvös (1848-1919)
    • He terminated his law studies in 1867 and went to study at Heidelberg where he was taught by Kirchhoff, Helmholtz and Bunsen.
    • Kirchhoff taught him the importance of accurate measurements.

  11. Edward Copson biography
    • Kirchhoff's famous formula is first derived from the formula of Helmholtz and then proved directly.
    • .The analogue of Kirchhoff's formula, due to Volterra, is derived and an interesting account is given of a method, devised by Marcel Riesz and based on the theory of fractional integration, which provides a powerful method of solving initial value problems for equations like the wave equation.

  12. Hermann von Helmholtz (1821-1894)
    • Kirchhoff was the other main candidate and because he was considered a superior teacher to Helmholtz he was offered the post.
    • However, when Kirchhoff decided not to accept Helmholtz was in a strong position.

  13. Julius Plücker (1801-1868)
    • He anticipated Kirchhoff and Bunsen in indicating that spectral lines were characteristic for each chemical substance.
    • made many important discoveries in spectroscopy, anticipating the German chemist Robert Bunsen and the German physicist Gustav R Kirchhoff, who later announced that spectral lines were characteristic for each chemical substance.

  14. Heinrich Weber (1842-1913)
    • These included Gustav Kirchhoff (appointed to Heidelberg in 1854), Robert Bunsen (appointed to Heidelberg in 1852), Hermann von Helmholtz (appointed to Heidelberg in 1858), Otto Hesse (appointed to Heidelberg in 1856), and Moritz Cantor (appointed to Heidelberg in 1853).
    • In [',' P Roquette, Heinrich Weber, David Hilbert and Konigsberg, Hilbert Seminar, State University of Kaliningrad, Svedlogorsk (1 June 1992).','15] Peter Roquette examines why Weber went to Konigsberg for his postgraduate study and notes that three of his teachers at Heidelberg, Hesse, Kirchhoff and Helmholtz, came from Konigsberg:- .

  15. F F P Bisacre biography
    • The reason for this depends upon the fact that the Huygens-Kirchhoff integrals for the electric and magnetic vectors have different cosine factors which have the same value only in the case of ordinary reflection.
    • In §2 an extension of the Huygens-Kirchhoff integrals bringing in a second approximation is given.

  16. Carl Runge (1856-1927)
    • He had not found the lectures on mathematical physics given by Kirchhoff and by Helmholtz particularly attractive.

  17. Kurt Hensel (1861-1941)
    • Among his teachers were Lipschitz, Weierstrass, Borchardt, Kirchhoff, Helmholtz and Kronecker.

  18. Giuseppe Basso biography
    • In addition to important papers on optics and other branches of mathematical physics including magnetism, Basso wrote a number of important obituaries including those of Victor Regnault (1810-1878), Gustav Robert Kirchhoff, Rudolf Clausius, Gilberto Govi (1825-1889) Wilhelm Weber, James Prescott Joule (1818-1889), and Enrico Betti.

  19. John Henry Michell biography
    • Earlier attacks on the problem, even by Helmholtz and Kirchhoff, had yielded only the solutions of a few special cases not of the highest importance.

  20. Joseph Keller biography
    • This surface integral is similar to one obtained from the usual Kirchhoff diffraction theory.

  21. Gösta Mittag-Leffler (1846-1927)
    • Hardly ever was there such a brilliant collection of distinguished mathematicians: Weierstrass, Kummer, Kronecker, Helmholtz, Kirchhoff, Borchardt etc.

  22. Jacob Lüroth (1844-1910)
    • Between the years 1863 and 1865 he was a student at the University of Heidelberg where he attended lectures by Otto Hesse and Gustav Kirchhoff and was advised by them on topics for research.

  23. Sofia Kovalevskaya (1850-1891)
    • Professor Konigsberger, the eminent chemist Kirchhoff, ..

  24. Julius König (1849-1913)
    • Feeling now that he wanted to follow a course in the natural sciences, although still retaining his medical interests, he went to Heidelberg which had an excellent reputation for science with famous men such as Bunsen, Kirchhoff and Helmholtz on the teaching staff.

  25. Eduard Heine (1821-1881)
    • He took part in the Konigsberg mathematical semiar which was also attended by Aronhold, Kirchhoff, and Seidel.

  26. Carl Friedrich Gauss (1777-1855)
    • They discovered Kirchhoff's laws, as well as building a primitive telegraph device which could send messages over a distance of 5000 ft.

  27. Giacinto Morera biography
    • Finally we note that he improved the proof of the Kirchhoff formula for the Huygens principle.

  28. Georg Simon Ohm (1789-1854)
    • A detailed study of the conceptual framework used by Ohm in formulating Ohm's law is given in [',' T Archibald, Tension and potential from Ohm to Kirchhoff, Centaurus 31 (2) (1988), 141-163.','6].

  29. Ludwig Boltzmann biography
    • In these places he studied under Bunsen, Kirchhoff and Helmholtz.

  30. Claude Berge biography
    • Graph Theory has its origin in a great number of old problems (in the work of Euler, Kirchhoff et al.) and in recent years its range has become vastly greater.

  31. Oskar Bolza biography
    • He studied under two leading physicist, namely Helmholtz and Kirchhoff, from 1876 to 1878.

  32. Mór Réthy biography
    • The second part of his bursary was spent at Heidelberg University, where Kirchhoff, Konigsberger and Schering assured him lifelong mental munition.

  33. Elwin Christoffel biography
    • If mathematical physicists are also taken into account then Butzer and Feher believe that Christoffel would have to be compared with Green, Hamilton, Sylvester, Helmholtz, Cayley, Kirchhoff, Maxwell, Beltrami, Lie, Boltzmann, Poincare and Fredholm.

  34. Heinrich Friedrich Weber biography
    • Afterwards he continued to do research, under Kirchhoff, but he earned his living as a private teacher in the house of the German politician August Dennig in Pforzheim.

  35. J Willard Gibbs (1839-1903)
    • In Heidelberg he was influenced by Kirchhoff and Helmholtz.

  36. Franz Neumann (1798-1895)
    • One such student was Kirchhoff who attended the Neumann-Jacobi seminar from 1843 to 1846.

  37. Ernst Fiedler biography
    • In 1882 he moved to Berlin, where he attended lectures by Kummer, Kirchhoff, Helmholtz and Weierstrass in particular.

  38. Max Noether (1844-1921)
    • At Heidelberg he was taught by Jacob Luroth who was awarded a doctorate in 1865, but mainly he was influenced by Gustav Kirchhoff who was the professor of physics.

  39. George Stokes (1819-1903)
    • However when Kirchhoff later published this explanation, Stokes disclaimed any prior discovery.

  40. Sergei Alekseevich Chaplygin biography
    • Chaplygin gave a geometric interpretation of those cases of the movement of a body in a liquid that had earlier been studied from a purely analytic standpoint by the German scientists Clebsch and Kirchhoff, as well as by the Russian scientist Steklov.

History Topics

  1. Quantum mechanics history

  2. Classical light
    • In 1860 Bunsen and Kirchhoff observed dark lines in the spectrum of a light source passed though burning substances.

Societies etc

  1. National Academy of Sciences
    • Physicists: Professor R Clausius of the University of Bonn; Baron H von Helmholtz, professor in the University of Berlin; Professor Robert Kirchhoff of the University of Berlin; Professor G G Stokes of the University of Cambridge, England; and Sir William Thomson, professor in the University of Glasgow.


  1. Kirchhoff
    • Gustav Robert Kirchhoff .

  2. Fellow of the Royal Society
    • Gustav R Kirchhoff 1875 .

  3. Lunar features
    • (W) (L) Kirchhoff .

  4. Fellows of the RSE
    • Gustav Robert Kirchhoff1868More infoMacTutor biography .

  5. Fellows of the RSE
    • Gustav Robert Kirchhoff1868More infoMacTutor biography .

  6. Lunar features
    • Kirchhoff .


  1. References for Gustav Kirchhoff
    • References for Gustav Kirchhoff .
    • .
    • L Boltzmann, Gustav Robert Kirchhoff, Populare Schriften (Leipzig, 1905).
    • T Archibald, Tension and potential from Ohm to Kirchhoff, Centaurus 31 (2) (1988), 141-163.
    • E H Dill, Kirchhoff's theory of rods, Arch.
    • N P Khomenko and T M Vyvrot, Euler and Kirchhoff - initiators of the main directions in graph theory (Russian) I : On the history of the mathematical sciences 'Naukova Dumka' (Kiev, 1984), 63-69, 168.
    • N P Khomenko and T M Vyvrot, Euler and Kirchhoff - initiators of the main directions in graph theory (Russian) II : Sketches on the history of mathematical physics 'Naukova Dumka' (Kiev, 1985), 28-34, 183.

  2. References for Georg Simon Ohm
    • T Archibald, Tension and potential from Ohm to Kirchhoff, Centaurus 31 (2) (1988), 141-163.

  3. References for Leonhard Euler
    • N P Khomenko and T M Vyvrot, Euler and Kirchhoff - initiators of the main directions in graph theory II (Russian), in Sketches on the history of mathematical physics 'Naukova Dumka' (Kiev, 1985), 28-34.

Additional material

  1. Ahrens book of quotes
    • Gustav Kirchhoff.
    • Gustav Kirchhoff.
    • Kirchhoff's claim that the science of mechanics purely describes naturally occurring motion has been repeated excessively.
    • Kirchhoff did not fundamentally change classical mechanics; his reformation was purely a formal one.
    • Hertz however went much further, but while most authors later adopted Kirchhoff's manner of representation, even if not completely his beliefs, I have never yet seen someone following the path Hertz started, despite the frequent praise it receives.
    • Gustav Kirchhoff.

  2. Max Planck: 'Quantum Theory
    • Gustav Kirchhoff showed that, in a space bounded by bodies at equal temperatures, but of arbitrary emissive and absorptive powers, the nature of the heat of radiation is completely independent of the nature of the bodies.
    • According to Kirchhoff's theorem, this must be independent of the constitution of the body.
    • If a number of such oscillators be placed in a space enclosed by reflecting walls, they will exchange energy one with another by taking up or emitting electro-magnetic waves, analogous with a sound source and resonators, until finally stationary black radiation, so-called, obtains in the enclosure according to Kirchhoff's law.

  3. Michell Twisted Rings
    • Beyond its obvious importance as a natural philosophy question and its application in engineering problems, the problem of twisted elastic rings and related instability of elastic materials has gained some renewed interest in science largely due to the realization that Kirchhoff models for elastic rods are suitable models for the study of macromolecules such as DNA molecules [C J Benham, An elastic model of the large structure of duplex DNA (1979); C J Benham, Geometry and mechanics of DNA superhelicity (1983); A Vologodskii, Topology and Physics of Circular DNA (1992); R S Manning, J H Maddocks and J D Kahn, A continuum rod model of sequence-dependent DNA structure (1996)] but also plants [W K Silk, On the curving and twining of stems (1989); A Goriely and M Tabor, Spontaneous helix-hand reversal and tendril perversion in climbing plants (1998)] and microbial filaments [R E Goldstein, A Goriely, G Hubber and C Wolgemuth, Bistable helices (2000)].
    • His paper is clear and concise and a good example of applied mechanics at his best, a well-formulated problem of interest solved elegantly by direct analysis of Kirchhoff equations.
    • The connection with Zajac's work was only realized years later by Coleman, Tobias, Olson, and collaborators in a series of papers [B D Coleman, E H Dill, M Lembo, Z Lu and I Tobias, On the dynamics of rods in the theory of Kirchhoff and Clebsch (1993); I Tobias and W K Olson, The effect of intrinsic curvature on supercoiling - Predictions of elasticity theory (1993); Y Yang, I Tobias and W K Olson, Finite element analysis of DNA supercoiling (1993)].

  4. Max Planck and the quanta of energy
    • Since Gustav Kirchhoff has shown that the state of the heat radiation which takes place in a cavity bounded by any emitting and absorbing substances of uniform temperature is entirely independent upon the nature of the substances, a universal function was demonstrated which was dependent only upon temperature and wavelength, but in no way upon the properties of any substance.
    • According to Kirchhoff's Law, this would have to prove independent of the nature of the body.
    • If a number of such Hertzian oscillators are set up within a cavity surrounded by a sphere of reflecting walls, then by analogy with audio oscillators and resonators, energy will be exchanged between them by the output and absorption of electromagnetic waves, and finally stationary radiation corresponding to Kirchhoff's Law, the so-called black-body radiation, should be set up within the cavity.

  5. Horace Lamb addresses the British Association in 1904
    • It is noteworthy, however, that the development of the modern German school of mathematical physics, represented by Helmholtz and Kirchhoff, in linear succession to Franz Neumann, ran in many respects closely parallel to the work of Stokes and his followers.
    • It would, however, be going too far to claim this tendency as the exclusive characteristic of English physicists; for example, the elastic investigations of Green and Stokes have their parallel in the independent though later work of Kirchhoff; and the beautiful theory of dynamical systems with latent motion which we owe to Lord Kelvin stands in a very similar relation to the work of Helmholtz and Hertz.
    • A zealous, or overzealous, mathematician might indeed make out something of a case if he were to contend that, after all, the greatest work of such men as Stokes, Kirchhoff, and Maxwell was mathematical rather than experimental in its complexion.

  6. Andrew Forsyth addresses the British Association in 1905, Part 2
    • When the wonderful school of French physicists, composed of Monge, Sadi Carnot, Fourier, Poisson, Poinsot, Ampere, and Fresnel (to mention only some names), together with Gauss, Kirchhoff, and von Helmholtz in Germany, and Ivory, Green, Stokes, Maxwell, and others in England, applied their mathematics to various branches of physics, for the most part its development was that of an ancillary subject.

  7. Ahrens publications
    • Uber das Gleichungssystem einer Kirchhoff'schen galvanischen Stromverzweigung, Math.

  8. Felix Klein on intuition
    • It seems to me, therefore, that Kirchhoff makes a mistake when he says in his Spectral Analyse that absorption takes place only when there is an exact coincidence between the wave-lengths.

  9. Basso publications
    • In commemorazione di Gustavo Roberto Kirchhoff, Atti Acc.

  10. Horace Lamb addresses the British Association in 1904, Part 2
    • The changed point of view is often associated with the publication of Kirchhoff's lectures on Mechanics in 1876, where it is laid down in the opening sentence that the problem of Mechanics is to describe the motions which occur in Nature completely and in the simplest manner.

  11. Craig books
    • The names of Euler, Lagrange and Laplace in the last century, and of Helmholtz, Stokes, Thomson, Rayleigh and Kirchhoff in this, stand out predominantly as those that have done the most to advance the theory to its present position.


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Astronomy section

  1. The Reaches of the Milky Way
    • In the 1860's, Kirchhoff and Bunsen performed rigorous experiments and discovered that the lines were associated with chemical elements, which meant we could determine the chemical composition of the sun.

  2. List of astronomers

  3. List of astronomers
    • Kirchhoff, Gustav Robert .

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