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The Second Physicist pp 205–239Cite as

Kirchhoff, Clausius, Weber, and Connectedness

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Part of the book series: Archimedes ((ARIM,volume 48))

Abstract

Following major discoveries in electricity and electromagnetism in the early nineteenth century, electrical research underwent a strong, combined experimental and theoretical development through the second half of the century. Nearly all of the leading physicists in Germany worked extensively in the subject. In this chapter, we take up Weber’s continuing research in electrodynamics, culminating in a comprehensive theory of physics, and Clausius’s new fundamental law of electrodynamics. The mechanical theory of heat continued to be of wide interest to German physicists. We follow Clausius’s ongoing work on the subject, now directed to the molecular motions responsible for heat. We also take up Kirchhoff’s research on the mechanical theory of heat together with his work on elasticity theory. All of these examples of work illustrate the growing theoretical connectedness of physics. We look at the university positions in which Weber, Clausius, and Kirchhoff carried out their theoretical researches.

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Notes

  1. 1.

    Emil Warburg, “Zur Erinnerung an Gustav Kirchhoff,” Naturwiss. 13 (1925): 205–12, on 207.

  2. 2.

    Jolly to Baden Ministry of the Interior, 12 June 1846.

  3. 3.

    Ibid.

  4. 4.

    Heidelberg U. Curator to Baden Ministry of the Interior, 1 August 1846, Bad. GLA, 235/3135.

  5. 5.

    Jolly to Baden Ministry of the Interior, 12 June 1846.

  6. 6.

    Heidelberg U. Curator to Baden Ministry of the Interior, 24 September 1846, Bad. GLA, 235/3135.

  7. 7.

    Jolly’s appointment, 28 September 1846, Bad. GLA, 235/3135. His new salary as ordinary professor was 1000 florins. Jolly Personalakte, Heidelberg UA, III, 5b, Nr. 233.

  8. 8.

    Heidelberg U. Curator to Baden Ministry of the Interior, 24 September 1846. D. R., “Jolly,” 808. C. Voit, “Philipp Johann Gustav von Jolly,” Sitzungsber. bay. Akad. 15 (1885): 119–36, on 123–24.

  9. 9.

    Dean of Heidelberg U. Philosophical Faculty Bunsen to Baden Ministry of the Interior, 26 July 1854, Bad. GLA, 235/3135.

  10. 10.

    Bunsen to Baden Ministry of the Interior, 26 July 1854. The philosophical faculty’s explanation may have had an ulterior motive. The three professors who were dismissed, in respectful terms, as textbook writers were Wilhelm Eisenlohr, Johann Müller, and Heinrich Buff. The first two were employees of the state of Baden, at Karlsruhe Polytechnic and at Freiburg University, respectively, and the third was a colleague and relative of Liebig’s at Giessen, to whom Jolly was beholden for a recommendation to Munich University and for whom Jolly was trying to secure a Heidelberg position. The faculty’s explanation appears designed to counteract, on the one hand, the state’s possible intention to fill the Heidelberg position cheaply by promoting one of the two physicists at the other Baden institutions of higher learning and, on the other hand, to prevent Jolly from bringing about Buff’s appointment. Jolly’s relationship to Liebig in this connection can be seen in Jolly’s letter to Liebig, 19 February 1854, Liebigiana, Bay. STB, 58 (Jolly, Philipp v.) Nr. 3.

  11. 11.

    Weber to Bunsen, 12 March 1854, Bad. GLA, 235/3135.

  12. 12.

    Weber to Bunsen, 12 March 1854; Neumann to Bunsen, 20 March 1854; Ettingshausen to Bunsen, 14 March 1854, Bad. GLA, 235/3135. Dean of Heidelberg U. Philosophical Faculty Bunsen to Baden Ministry of the Interior, 26 July 1854. Bad. GLA, 235/3135.

  13. 13.

    As extraordinary professor at Breslau, Kirchhoff got a salary of 1050 florins; as ordinary professor at Heidelberg, he got 1600 florins plus another 400 florins for housing. Kirchhoff Personalakte, Heidelberg UA, III, 5b, Nr. 244. Letter from Kirchhoff to his brother Carl, 18 October 1854, quoted in Warburg, “Kirchhoff,” 208. When Neumann recommended Kirchhoff for the Heidelberg professorship, he wrote to Bunsen that he was sorry to see Kirchhoff leave a Prussian university, Breslau, but he wanted the “freer scientific activity” of Heidelberg for Kirchhoff because at Breslau he worked with difficulty under Frankenheim. Neumann to Bunsen, 20 March 1854, Bad. GLA, 235/3135.

  14. 14.

    Kirchhoff to his brother Carl, 18 October 1854; Bunsen to Baden Ministry of the Interior, 26 July 1854.

  15. 15.

    Robert Helmholtz, “A Memoir of Gustav Robert Kirchhoff,” trans. J. de Perott, Annual Report of the … Smithsonian Institution … to July,1889, 1890, 527–40, on 529.

  16. 16.

    Reinhard Riese, Die Hochschule auf dem Wege zum wissenschaftlichen Grossbetrieb. Die Universität Heidelberg und das badische Hochschulwesen 1860–1914, vol. 19 of Industrielle Welt, Schriftenreihe des Arbeitskreises für moderne Sozialgeschichte, ed. Werner Conze (Stuttgart: Ernst Klett, 1977), 88–90, 194–96. By Kirchhoff’s time, the presumed intellectual unity of the philosophical faculty was widely disputed and debated. The Staatswissenschaften, in the 1860s, were the first to separate off at Heidelberg. In 1890, at the initiative of the natural scientists, and after inquiring about Tübingen, Strassburg, and Leipzig, at which a division of the philosophical faculty had already occurred, the Heidelberg natural sciences and mathematics faculty also separated off (90). In 1900, the Heidelberg mathematical-physical seminar divided; in light of the impending call of a professor for mathematical physics, the natural sciences and mathematics faculty wanted Heidelberg, like other universities, to “divide completely the mathematical and physical seminar.” (“Prodecan,” Pfizer to Heidelberg U. Senate, 25 January 1900, Bad. GLA, 235/3228).

  17. 17.

    By the wording of the proposal for a mathematical-physical seminar—the request for “official” recognition—it sounds as if an unofficial seminar may have been in existence. Kirchhoff and Königsberger’s proposal to “Excellency,” 14 April 1869, Bad. GLA, 235/3228.

  18. 18.

    Kirchhoff and Königsberger’s annual report on the seminar for the academic year 1869–70, Bad. GLA, 235/3228. The rigid procedure followed in Kirchhoff’s seminar was observed firsthand by Arthur Schuster, The Progress of Physics During 33 Years (1875–1908) (Cambridge: Cambridge University Press, 1911), 13–14.

  19. 19.

    Kirchhoff gave the 6-h lecture course on experimental physics and supervised practical work in the laboratory. He also offered a 3-h survey course on theoretical physics, which treated mainly mechanics in the “wider sense” and concluded with the mechanical theory of heat. In addition, he gave a 1-h course on separate branches of theoretical physics such as the “mechanics of elastic and fluid bodies” and the “theory of heat and electricity.” In the summer semester of 1870, for the first time, Kirchhoff’s “physical seminar” was listed among the courses of the philosophical faculty. From then on, he offered in alternate semesters his seminar and his 3-h theoretical physics course. His teaching of theoretical physics was supplemented by that of the Prviatdocent Friedrich Eisenlohr, who regularly offered a course in his specialty, theoretical optics, in addition to courses on mechanics, potential theory, and other mathematical subjects. (Anzeige der Vorlesungen … auf der Grossherzoglich Badischen Ruprecht-Carolinischen Universität zu Heidelberg, the published list of courses offered each semester at Heidelberg; Friedrich Pockels, “Gustav Robert Kirchhoff,” In Heidelberger Professoren aus dem 19. Jahrhundert [Heidelberg: C. Winter, 1903], vol. 2, 243–63, on 248; Wilhelm Lorey, Das Studium der Mathematik an den deutschen Universitäten seit Anfang des 19. Jahrhunderts [Leipzig and Berlin: B. G. Teubner, 1916], 72–73).

  20. 20.

    Leo Königsberger, Mein Leben (Heidelberg: Carl Winters, 1919), 101; Schuster, Progress of Physics, 14.

  21. 21.

    Kirchhoff’s laboratory and lectures attracted not only gifted German physicists such as Eilhard Wiedemann and E. Bessel-Hagen but also many gifted foreign physicists such as Boltzmann and Victor von Lang from Austria, Gabriel Lipmann from France, H. Kamerlingh Onnes from Holland, and Schuster from Britain.

  22. 22.

    Robert Helmholtz, “Kirchhoff,” 528. The volume Kirchhoff edited himself, Gesammelte Abhandlungen (Leipzig, 1882), runs to 641 pages; the posthumous volume edited by Ludwig Boltzmann, Nachtrag to Kirchhoff’s Gesammelte Abhandlungen (Leipzig, 1891), runs to 137.

  23. 23.

    Woldemar Voigt, “Zum Gedächtniss von G. Kirchhoff,” Abh. Ges. Wiss. Göttingen 35 (1888): 3–10, on 6.

  24. 24.

    Gustav Kirchhoff, “Ueber das Gleichgewicht und die Bewegung einer elastischen Scheibe,” Journ. f. d. reine u. angewandte Math. 40 (1850): 51–88, in Ges. Abh., 237–79; “Ueber das Gleichgewicht und die Bewegung eines unendlich dünnen elastischen Stabes,” Journ. f. d. reine u. angewandte Math. 56 (1858): 285–313, in Ges. Abh., 285–316. Kirchhoff’s 1850 and 1858 papers are closely related, but they have some important differences; Kirchhoff remarked that the first paper could be developed in a stronger way by following the method of the second (Ges. Abh., 311).

  25. 25.

    Isaac Todhunter, A History of the Theory of Elasticity and of the Strength of Materials from Galilei to the Present Time, vol. 2, Saint-Venant to Lord Kelvin, pt. 2 (Cambridge, 1893), 54. Kirchhoff’s 1858 paper—his “most important” elasticity paper, according to Todhunter (68)—was judged by William Thomson and P. G. Tait, Natural Philosophy, pt. 2 §609, as the “first thoroughly general investigation of the equations of equilibrium and motion of an elastic wire.”

  26. 26.

    Kirchhoff, “Ueber die Schwingungen,” 279–80.

  27. 27.

    In his 1850 paper, Kirchhoff’s variational equation reads 0 = δP − KδΩ, expressing the equality of the moments of the external force and of the internal elastic forces for the equilibrium state. Here P is the moment of the external forces, K is a constant, and Ω is a volume integral of a homogenous function of the main dilations. His 1858 paper proceeds from a similar variational equation. Earlier George Green had given the equation but had not expressed it in terms of principal dilations (Todhunter, Elasticity, 41, 56; Kirchhoff, “Ueber das Gleichgewicht und die Bewegung eines … Stabes,” 295).

  28. 28.

    This is Todhunter’s comment on Kirchhoff’s solution for the vibrations of the plate, which he expressed as “doubly-infinite series of functions akin to Bessel’s functions” (Todhunter, Elasticity, 45, 43).

  29. 29.

    Todhunter, Elasticity, 45; Gustav Kirchhoff, “Ueber die Schwingungen einer kreisförmigen elastischen Scheibe,” Ann. 81 (1850): 258–64, in Ges. Abh., 279–85; “Ueber das Verhältniss der Quercontraction zur Längendilatation bei Stäben von federhartem Stahl,” Ann. 108 (1859): 369–92, in Ges. Abh., 316–39.

  30. 30.

    Todhunter, Elasticity, 45.

  31. 31.

    Todhunter, Elasticity, 46–47. Measurements of the radii of the circular nodes belonging to the different tones on glass and metal plates agreed in an “excellent way” with each other and—generally accurate to two places—with the values calculated from Kirchhoff’s theory (Kirchhoff, “Ueber die Schwingungen,” 285).

  32. 32.

    Kirchhoff, “Verhältniss,” 316–17, 338.

  33. 33.

    Todhunter, Elasticity, 39.

  34. 34.

    Todhunter says that Kirchhoff gave too much emphasis to Poisson’s error. He evidently had no criticism of Poisson’s method; their differences had to do with the degree of “fitness” attributed to the elastic plates. Thomson and Tait “practically reconciled Poisson and Kirchhoff” (Elasticity, 40).

  35. 35.

    Todhunter, Elasticity, 40.

  36. 36.

    Gustav Kirchhoff, “Ueber die Anwendbarkeit der Formeln für die Intensitäten der galvanischen Strőme in einem Systeme linearer Leiter auf Systeme, die zum Theil aus nicht linearen Leitern bestehen,” Ann. 75 (1848): 189, in Ges. Abh., 33–48; Edmund Whittaker, A History of the Theories of Aether and Electricity, vol. 1, The Classical Theories (New York: Harper & Brothers, 1960), 224.

  37. 37.

    Ludwig Boltzmann, Gustav Robert Kirchhoff (Leipzig, 1888); repr. in Populäre Schriften (Leipzig: J. A. Barth, 1905), 22; Gustav Kirchhoff, “Ueber die Bewegung der Elektricität in Drähten,” Ann. 100 (1857): 193–217, in Ges. Abh., 131–54; “Ueber die Bewegung der Elektricität in Leitern,” Ann. 102 (1857): 529–44, in Ges. Abh., 154–68; Wilhelm Weber, “Elektrodynamische Maassbestimmungen insbesondere über elektrische Schwingungen,” Abh. sächs. Ges. Wiss. 6 (1864): 571–716, repr. in Werke, vol. 4, Galvanismus und Elektrodynamik, zweiter Theil, ed. Heinrich Weber (Berlin, 1894), 105–241, on 157; Leon Rosenfeld, “The Velocity of Light and the Evolution of Electrodynamics,” Nuovo Cimento, supplement to vol. 4 (1957): 1630–69, on 1635, 1640, attributes Kirchhoff’s failure to develop the analogy between light and electricity to his phenomenology. Kirchhoff’s avoidance of risky physical hypotheses would have made it difficult for him to anticipate a physical basis for the coincidence of the two velocities (Darrigol, Electrodynamics, 71–73).

  38. 38.

    Gustav Kirchhoff, “Ueber einen Satz der mechanischen Wärmetheorie und einige Anwendungen desselben,” Ann. 103 (1858): 177–206, in Ges. Abh., 454–82; Pockels, “Kirchhoff,” 250–51.

  39. 39.

    According to Boltzmann, Kirchhoff’s first flint glass prism, which he obtained in 1857, had been polished by Fraunhofer, an example of a connection between research by one of our physicists and excellent German instrument makers (Boltzmann, Kirchhoff, 4). Gustav Kirchhoff and Robert Bunsen, “Chemische Analyse durch Spectralbeobachtungen,” Ann. 110 [1860]: 160–89; in Ges. Abh., 598–625. Bunsen told Wilhelm Ostwald the history of the discovery of spectrum analysis, which Ostwald reported in the “Anmerkungen,” 71–72, appended to his edition of Chemische Analyse durch Spectralbeobachtungen von G. Kirchhoff und R. Bunsen (1860), vol. 72 of Ostwald’s Klassiker der exakten Wissenschaften (Leipzig, 1895). William McGucken, Nineteenth-Century Spectroscopy (Baltimore: Johns Hopkins University Press, 1969), 26–28, 34, 50. Daniel M. Siegel, “Balfour Stewart and Gustav Robert Kirchhoff: Two Independent Approaches to ‘Kirchhoff’s Radiation Law,’” Isis 67 (1976): 565–600, on 568–69. Pockels, “Kirchhoff,” 252–53.

  40. 40.

    Henry Roscoe, “Gedenkrede auf Bunsen,” in Gesammelte Abhandlungen von Robert Bunsen, ed. Wilhelm Ostwald and M. Bodenstein (Leipzig: W. Engelmann, 1904), vol. 1, xv–lix, on xxxiv.

  41. 41.

    Gustav Kirchhoff, “Ueber den Zusammenhang zwischen Emission und Absorption von Licht und Wärme,” Monatsber. preuss. Akad. (1859), 783–87; in Ges. Abh., 566–71, on 567, 569–70. Kirchhoff’s understanding of absorption and emission was reached independently and at about the same time by Balfour Stewart, resulting in a priority dispute. Siegel, “Balfour Stewart and Gustav Robert Kirchhoff.” Gustav Kirchhoff, “Zur Geschichte der Spectral-Analyse und der Analyse der Sonnenatmosphäre,” Ann. 118 [1863]: 94–111; in Ges. Abh., 625–41.

  42. 42.

    Gustav Kirchhoff, “Ueber das Verhältniss zwischen dem Emissionsvermögen und dem Absorptionsvermögen der Körper für Wärme und Licht,” Ann. 109 (1860), 275–301; in Ges. Abh., 571–98, on 571–73.

  43. 43.

    Kirchhoff, “Ueber das Verhältniss,” 573–74; Pockels, “Kirchhoff,” 256–57.

  44. 44.

    Kirchhoff defined the “emissive power” E of a body in terms of the kinetic energy it transfers to the ether through heat rays of a given polarization: the intensity of the rays emitted by the body in the wavelength interval λ to λ + dλ in a unit of time is E dλ. He defined the “absorptive power” A of the body as the ratio of the intensity of the absorbed rays to that of the incident rays. Whereas E or A individually depends not only on wavelength but also on the polarization, on the geometry of the slits used in observing the emission and absorption, and on the condition of the body, the ratio E/A is the same for all bodies for a given temperature and for rays of a given wavelength (Kirchhoff, “Ueber das Verhältniss,” 574, 592).

  45. 45.

    Leon Rosenfeld, “Kirchhoff, Gustav Robert,” DSB 7 (1973): 379–83, on 382.

  46. 46.

    Voigt, “Kirchhoff,” 8–9.

  47. 47.

    Kirchhoff, “Ueber das Verhältniss,” 597–98; Pockels, “Kirchhoff,” 257.

  48. 48.

    Rosenfeld, “Kirchhoff,” 382.

  49. 49.

    McGucken, Spectroscopy, 35; Voigt, “Kirchhoff,” 8. Boltzmann, Kirchhoff, 4.

  50. 50.

    Gottfried Guggenbühl, “Geschichte der Eidgenössischen Technischen Hochschule in Zürich,” in Eidgenössische Technische Hochschule 1855–1955 (Zurich: Buchverlag der Neuen Zürcher Zeitung, 1955), 3–260, on 19, 35, 68; Zurich ETH, 100 Jahre Eidgenössische Technische Hochschule. Sonderheft der Schweizerischen Hochschulzeitung, 28 (Zürich: Verlag Lecmann, 1955), 46; Studer to Kern, 12 June 1855, A. Schweiz. Sch., Zurich.

  51. 51.

    Albrecht Mousson to (presumably) Kern, 30 August 1855; Kohlrausch to Kern, 23 January 1855; “Ausszug aus dem Protokoll der 112. Sitzung der schweizerischen Bundesrathes” to “Schulrath der polytechnischen Schule, in Zürich,” 24 August 1855; A. Schweiz. Sch., Zurich.

  52. 52.

    Weber to Kern, 1 January 1855.

  53. 53.

    Weber to Kern, 9 May 1855, A. Schweiz. Sch., Zurich. Kohlrausch to Kern, 23 January and 12 February 1855; Weber to Kern, 1 January 1855; Studer to Kern, 30 May 1855; A. Schweiz. Sch., Zurich.

  54. 54.

    Weber to Kern, 1 January 1855; Poggendorff to Brunner, 18 May 1855; A. Schweiz. Sch., Zurich. “Auszug aus dem Protokoll,” 24 August 1855.

  55. 55.

    Weber to Kern, 9 May 1855.

  56. 56.

    Georg Sidler to Kern, 31 March 1855, A. Schweiz. Sch., Zurich.

  57. 57.

    Rudolph Clausius, “Ueber das mechanische Aequivalent einer elektrischen Entladung und die dabei stattfindende Erwärmung des Leitungsdrahtes,” Ann. 86 (1852): 365, 371.

  58. 58.

    Clausius to Würzburg University Senate, 18 May 1867, Clausius Acte, Würzburg UA, Nt. 404.

  59. 59.

    Mousson, also writing for Clausius, to the President of the Swiss Education Council, 16 November 1857, A. Schweiz. Sch., Zurich.

  60. 60.

    Mousson to President of the Swiss Education Council, 16 November 1857; Clausius and Mousson, “Bericht über die physikalische Sammlung der polytechnischen Schule 1857,” 20 January 1858.

  61. 61.

    Mousson, writing also for Clausius, “Jahresbericht über die physikalische Sammlung des schweizerischen Polytechnikums für das Jahr 1864,” 4 January 1865.

  62. 62.

    Clausius and Mousson, “Bericht über die physikalische Sammlung des schweizerischen Polytechnikums 1861,” 6 January 1862; Ferdinand Rosenberger, Die Geschichte der Physik, vol. 3, Geschichte der Physik in den letzten hundert Jahren (Braunschweig, 1890; repr. Hildesheim: G. Olms, 1965), 473; “Bericht über die physikalische Sammlung der polytechnischen Schule für das Jahr 1858,” 11 January 1859.

  63. 63.

    Rudolph Clausius, “Ueber die Art der Bewegung, welche wir Wärme nennen,” Ann. 100 (1857): 353–80. This and later writings by Clausius on the kinetic theory are discussed in Stephen G. Brush, The Kind of Motion We Call Heat: A History of the Kinetic Theory of Gases in the 19th Century, vol. 1, Physics and the Atomists (Amsterdam and New York: North-Holland, 1976), 168–82; Edward E. Daub, “Rudolf Clausius and the Nineteenth Century Theory of Heat” (Ph.D. diss., University of Wisconsin-Madison, 1966); and “Atomism and Thermodynamics,” Isis 58 (1967): 293–303; Elizabeth Wolfe Garber, “Maxwell, Clausius and Gibbs: Aspects of the Development of Kinetic Theory and Thermodynamics” (Ph.D. diss., Case Institute of Technology, 1966); and “Clausius and Maxwell’s Kinetic Theory of Gases,” HSPS 2 (1970): 299–319; Martin J. Klein, “Gibbs on Clausius,“HSPS 1 (1969): 127–49; Peter M. Harman, Energy, Force, and Matter: The Conceptual Development of Nineteenth-Century Physics (Cambridge: Cambridge University Press, 1982),128.

  64. 64.

    Rudolph Clausius, “Ueber die mittlere Länge der Wege, welche bei der Molecularbewegung gasförmiger Körper von den einzelnen Molecülen zurückgelegt werden; nebst einigen anderen Bemerkungen über die mechanische Wärmetheorie,” Ann. 105 (1858): 239–58.

  65. 65.

    Quoted in Daub, “Rudolf Clausius,” 127.

  66. 66.

    Harman, Energy, Force, and Matter, 131, 133.

  67. 67.

    Riecke, “Clausius,” 17, 20–22.

  68. 68.

    Klein, “Gibbs on Clausius,” 148; Daub, “Rudolf Clausius,” 142–43; Garber, “Clausius and Maxwell’s Kinetic Theory,” 307–9, 317; Brush, Motion We Call Heat, vol. 1, 181–82; Harman, Energy, Force, and Matter, 138–41.

  69. 69.

    Rudolph Clausius, Abhandlungen über die mechanische Wärmetheorie. Erste Abtheilung (Braunschweig, 1864). Quotations from “Vorrede,” v–x. The second revised edition is entitled Die mechanische Wärmetheorie, vol. 1, Entwickelung der Theorie, soweit sie sich aus den beiden Hauptsätzen ableiten lässt, nebst Anwendungen (Braunschweig, 1876). Quotations from the preface to the English translation of the second edition by W. R. Browne, The Mechanical Theory of Heat (London, 1879), vii–viii.

  70. 70.

    Rudolph Clausius, Ueber das Wesen der Wärme, verglichen mit Licht und Schall (Zurich, 1857). Quotations on 29, 31.

  71. 71.

    Verzeichniss der Vorlesungen ... Würzburg. Würzburg U. Senate to Bavarian Ministry of the Interior (draft), 13 January 1869, Clausius Personalakte, Würzburg UA, Nr. 404. Bavarian Ministry of the Interior to Würzburg U. Senate, 14 March and 23 March 1867; Clausius to Würzburg U. Senate, 18 May 1867; Würzburg University sent it to the Bavarian Ministry of the Interior, 5 October 1868; Würzburg U. Senate to Bavarian Ministry of the Interior (draft), 13 January 1869.

  72. 72.

    Draft of the report by the mathematics and natural sciences section of the Bonn U. Philosophical faculty on a successor in physics to Plücker, July 1868, Plücker Personalakte, Bonn UA. Also there, “Separatvotum als Erwiderung auf dasjenige des Herrn Professor Lipschitz von 13ten Juli 1868,” 14 July 1868.

  73. 73.

    Draft of Lipschitz’s report on the same question, July 1868, Plücker Personalakte, Bonn UA.

  74. 74.

    Bonn U. faculty report in July 1868, “Separatvotum” of 14 July 1868, and Lipschitz’s separate vote, 13 July 1868. After Plücker’s death, Lipschitz had written to Helmholtz to ask him if he wanted to move to physics and to come to Bonn. On learning that Helmholtz did, Lipschitz proposed to the Bonn philosophical faculty that they place Helmholtz first on the list of candidates for the physics chair. Neumann supported Lipschitz’s efforts to bring Helmholtz to Bonn, and Lipschitz reported to Neumann that the government had done “everything in its power” to get him. Lipschitz to Neumann, 14 June 1868 and 15 January 1869, Neumann Papers, Göttingen UB, Ms. Dept. Since Helmholtz had already told the Bonn philosophical faculty of his willingness to come, their doubts about his availability appear to have reflected more their disinclination than their poor chance of getting him. Helmholtz declined the call in the end because he felt that the Prussian ministry of culture was trifling with him. Helmholtz to Carl Ludwig, 27 January 1869, quoted in Königsberger, Helmholtz 2: 118–19.

  75. 75.

    Kirchhoff for that reason was never placed on the list of candidates at Bonn. Lipschitz to Neumann, 14 June 1868.

  76. 76.

    Faculty reports cited above. Also Lipschitz to Neumann, 14 June 1868; in this letter, Lipschitz mentioned that he also suggested Meyer as a candidate, but the Bonn faculty rejected him, as it initially did Clausius, for not being an experimental physicist. The Bonn faculty did not count Clausius’s current, brief tenure as Würzburg’s physics professor or his earlier co-directorship of the physics institute at Zurich.

  77. 77.

    Mathematics and natural sciences section of Bonn U. Philosophical Faculty to “Prodecan” Knoodt, 9 July 1868, and its “Separatvotum” in reply to Lipschitz, 14 July 1868, Plücker Personalakte, Bonn UA.

  78. 78.

    Clausius to Bonn U. Curator Beseler, 12 March 1869, and documents giving details of Clausius’s appointment, Clausius Personalakte, Bonn UA.

  79. 79.

    Ketteler to Dean of the Bonn U. Philosophical Faculty H. von Sybel, 27 June 1870, Ketteler Personalakte, Bonn UA. Ketteler’s next publication was “of a more mathematical and critical nature,” according to Clausius, who also said that Ketteler was “longing” for a physical cabinet. Clausius’s recommendation of Ketteler for a position at the Karlsruhe Polytechnic, 29 October 1870, Bad. GLA, 448/2355.

  80. 80.

    Clausius to Bonn U. Curator Beseler, 12 March 1869, Clausius Personalakte, Bonn UA.

  81. 81.

    For his first semester at Bonn, in the summer of 1869, Clausius originally intended to teach “optics, electricity, and magnetism treated experimentally, 5 hours per week” and “heat theory treated mathematically, 4 hours per week.” He changed his schedule to an elementary public 2-h lecture course on the mechanical heat theory, a 2-h lecture course on elasticity theory and the theory of elastic oscillations treated mathematically, and the 5-h experimental lecture course he had proposed before. Clausius to Bonn U. Curator Beseler, 27 and 29 January 1869, Clausius Personalakte, Bonn UA.

  82. 82.

    Heinrich Konen, “Das physikalische Institut,” in Geschichte der Rheinischen Friedrich-Wilhelm-Universität zu Bonn am Rhein, by Bonn University, ed. A. Dyroff (Bonn: F. Cohen, 1933), vol. 2, 348–49. Clausius improved the budget in 1871 and 1873; with extraordinary grants, he bought, for example, a goniometer, an air pump, a microscope, and various electric and magnetic apparatus.

  83. 83.

    Barbara Jaeckel and Wolfgang Paul, “Die Entwicklung der Physik in Bonn in 1818–1968,” in 150 Jahre Rheinische Friedrich-Wilhelms-Universität zu Bonn 1818–1968 (Bonn: H. Bouvier, Ludwig Röhrscheid, 1970), 91–100, on 93. Konen, “ Das physikalische Institut,” 349. Hertz to his parents, 5 April 1889, quoted in Heinrich Hertz, Erinnerungen, Briefe, Tagebücher, ed. M. Hertz and Charles Süsskind, 2nd rev. ed. (San Francisco: San Francisco Press, 1977), 288.

  84. 84.

    Clausius to Bonn U. Curator Beseler, 24 December 1871, Clausius Personalakte, Bonn UA.

  85. 85.

    Clausius to Beseler, 24 December 1871. Konen, “Das physikalische Institut,” 349.

  86. 86.

    Lipschitz to Bonn U. Curator, 12 May 1883, Clausius Personalakte, Bonn UA. Clausius’s salary was 2700 thaler, the equivalent of 8100 marks; after his call to Göttingen, his salary was raised to 9000 marks.

  87. 87.

    Rudolf Clausius, “Upon the New Conception of Electrodynamic Phenomena Suggested by Gauss,” Philosophical Magazine 37 (1869): 445–56, on 445, 456. Clausius did not consider Gauss’s law because it did not conserve energy.

  88. 88.

    In 1879 Clausius reworked his electrical researches to include electrodynamic phenomena in Die mechanische Behandlung der Elektricität (Braunschweig, 1879), which he presented as the second volume of Die mechanische Wärmetheorie. This work contained, for example, his theories of dielectrics, electrolytic conduction, thermoelectricity, and his fundamental theory of electrodynamics. Eduard Riecke, “Rudolf Clausius,” Abh. Ges. Wiss. Göttingen 35 (1888): appendix, 1–39, on 24. Walter Kaufmann, “Physik,” Naturwiss. 7 (1919): 542–48, on 546. Rudolph Clausius, “Ueber ein neues Grundgesetz der Elektrodynamik,” Sitzungsber. Niederrhein. Ges. (1875): 306–9; translated as “On a New Fundamental Law of Electrodynamics,” Philosophical Magazine 1 (1876): 69–71.

  89. 89.

    The dynamic part of Clausius’s potential is:

    $$ \mathrm{V}=\frac{kee^{\prime }}{r}\left(\frac{dxdx^{\prime }}{dtdt}+\frac{dydy^{\prime }}{dtdt}+\frac{dzdz^{\prime }}{dtdt}\right), $$

    where k is is a contant depending on units, e and e′ are electric masses, r their separation, and dx/dt, dy/dt, dz./dt and dx′/dt, dy′/dt, dz′/dt their absolute velocities. If ε is the angle between the absolute velocities v and v′, the potential acquires the simpler form: V=(kee′/r) vv′ cos ε. Upon applying his law to the interaction of two current elements, Clausius arrived at the same force that the mathematician Hermann Grassmann had published many years before, “Neue Theorie der Elektrodynamik,” Ann. 64 (1845): 1–18; in light of their “entirely different” starting points, Clausius considered their agreement an “encouraging corroboration.” Clausius, Die mechanische Behandlung der Electricität (Braunschweig, 1879), 227–81, on 276–77.

  90. 90.

    Clausius, “On a New Fundamental Law,” 69; “Ueber das Verhalten des elektrodynamischen Grundgesetzes zum Princip von der Erhaltung der Energie und über eine noch weitere Vereinfachung des ersteren,” Sitzungsber. Niederrhein. Ges. (1876): 18–22, translated as “On the Bearing of the Fundamental Law of Electrodynamics toward the Principle of the Conservation of Energy, and on a Further Simplification of the Former,” Philosophical Magazine 1 (1876): 218–21, on 218–19. Clausius applied the new law and responded to criticism of it in Die mechanische Behandlung der Electricität, chaps. 10 and 11.

  91. 91.

    Specifically, Clausius required that the expressions agree with the laws for closed currents and the energy principle and with the internal theoretical criteria of simplicity and generality. This is a general method in theoretical physics. Forty years after Clausius, Einstein looked for the simplest equations that the principles of general relativity allowed, reducing the role of ad hoc assumptions (“What is the Theory of Relativity,” 1919, in Ideas and Opinions [New York: Dell, 1973], 222–27, on 223).

  92. 92.

    Rudolph Clausius, Ueber den Zusammenhang zwischen den grossen Agentien der Natur, Rectoratsantritt, 18 October 1884 (Bonn, 1885), 20–27.

  93. 93.

    Grete Ronge, “Die Züricher Jahre des Physikers Rudolf Clausius,” Gesnerus 12 (1955): 73–108, on 82.

  94. 94.

    Weber to Göttingen U. Curator, 29 December 1866, Göttingen UA, 4/Vh/10.

  95. 95.

    Weber to Göttingen U. Curator, 18 October 1866, Göttingen UA, 4/Vh/21.

  96. 96.

    Kohlrausch was offered the ordinary professorship for mathematics and physics at the agricultural academy in Hohenheim. As a counteroffer, Weber proposed that Kohlrausch be given an extraordinary professorship carrying a small salary in addition to his assistantship. Silcher to Kohlrausch, 24 January 1867; Weber to Göttingen U. Curator, 29 January 1867; Kohlrausch Personalakte, Göttingen UA, 4/V b/156.

  97. 97.

    Weber to an official, 17 June 1870, STPK, Darmst. Coll. 1912.236.

  98. 98.

    Weber to Göttingen U. Curator, 29 January and 15 February 1867; Prussian Minister of Culture von Mühler to Kohlrausch, 19 February 1867; Kohlrausch Personalakte, Göttingen UA, 4/V b/156.

  99. 99.

    Göttingen U. Curator von Warnstedt to Prussian Minister of Culture von Mühler, 20 February 1869 and 18 June and 2 July 1870; Kohlrausch to Göttingen U. Curator, 23 July 1870; Kohlrausch Personalakte, Göttingen UA, 4/V b/156. Weber to an official, 17 June 1870.

  100. 100.

    Weber to Richard Dedekind, 10 August 1870, Dedekind Papers, Göttingen UB, Ms. Dept.

  101. 101.

    Weber asked the government to try to hire the Berlin extraordinary professor Quincke, who, he supposed, might be looking for a job elsewhere after Helmholtz’s move to Berlin. The government replied that there was no money to appoint someone to Kohlrausch’s “professorship.” Göttingen U. Curator to Prussian Minister of Culture von Mühler, 9 September 1870, Göttingen UA, 4/Vh/21.

  102. 102.

    Weber to Göttingen U. Curator, 7 October 1870, Göttingen UA, 4/Vh/21.

  103. 103.

    Göttingen U. Philosophical Faculty to Göttingen U. Curator, 29 June 1871; Weber to Curator, 6 February 1873; Riecke’s appointment to extraordinary professor, 26 February 1873; Göttingen U. Curator von Warnstedt to Prussian Ministry of Culture, 25 April 1876; Ministry to Warnstedt, 9 September 1876; Riecke Personalakte, Göttingen UA, 4/V b/173. Weber to Curator, 4 December 1873; Warnstedt to Prussian Minister of Culture Falk, 5 December 1873; Weber Personalakte, Göttingen UA, 4/V b/95a.

  104. 104.

    Weber to Dedekind, 20 October 1876, Dedekind Papers, Göttingen UB, Ms. Dept.

  105. 105.

    Weber to Göttingen U. Curator von Warnstedt, 26 October 1873; Warnstedt to Prussian Minister of Culture Falk, 29 October and 5 December 1873; Weber Personalakte, Göttingen UA, 4/V b/95a. In productivity, Eduard Riecke lived up to Weber’s example. Although his method of research was predominantly theoretical, he regularly did experiments, usually to make measurements using theory as a guide. Woldemar Voigt, “Eduard Riecke als Physiker,” Phys. Zs. 16 (1915): 219–21, on 219; Emil Wiechert, “Eduard Riecke,” Gött. Nachr. (1916): 45–56, on 47–48. Both Riecke’s research and his handling of the physics institute were praised by Weber, Listing, and the rest of the Göttingen science professors when they recommended his promotion to ordinary professor. Göttingen U. Curator to Prussian Ministry of Culture, 6 September 1881, Riecke Personalakte, Göttingen UA, 4/V b/173. The minister warned the Göttingen curator that Prussia would not support three physics professors at Göttingen, so that if Riecke were made professor he would have to replace Weber. The curator replied that Weber, who had given up hope of getting Friedrich Kohlrausch as his successor, wanted to be replaced by Riecke and that no one could now take it away from him in any case. So in December 1881 Riecke formally succeeded Weber. Prussian Minister of Culture Gossler to Göttingen U. Curator von Warnstedt, 4 November 1881; Warnstedt to Gossler, 8 November 1881; Minister to Warnstedt, 14 December 1881; Riecke Personalakte, Göttingen UA, 4/V b/173. Riecke’s salary was 3500 marks—raised by 1000 marks in 1883 and another 2000 marks in 1886—plus 540 marks for rent.

  106. 106.

    Edmund Hoppe, Geschichte der Elektrizität (Leipzig, 1884), 511–12; Eduard Riecke, “Wilhelm Weber,” Abh. Ges. Wiss. Göttingen 38 (1892): 1–44, on 26–27. Whittaker, Aether and Electricity, vol. 1, 206.

  107. 107.

    Wilhelm Weber, “Ueber einen einfachen Ausspruch des allgemeinen Grundgesetzes der elektrischen Wirkung,” Ann. 136 (1869): 485–89; “Elektrodynamische Maassbestimmungen insbesondere über das Princip der Erhaltung der Energie,” Abh. sächs Ges. d. Wiss. 10 (1871): 1–61; repr. in Wilhelm Weber’s Werke, vol. 4, Galvanismus und Elektrodynamik, zweiter Theil, ed. Heinrich Weber (Berlin, 1894), 243–46 and 247–99.

  108. 108.

    Weber, “Elektrodynamische Maassbestimmungen insbesondere über das Princip der Erhaltung der Energie,” 254–55, 296–99.

  109. 109.

    K. H. Wiederkehr, Wilhelm Eduard Weber. Erforscher der Wellenbewegung und der Elektrizität 1804–1891, vol. 32 of Grosse Naturforscher (Stuttgart: Wissenschaftliche Verlagsgesellschaft, 1967), 106.

  110. 110.

    Wilhelm Weber, “Elektrodynamische Maassbestimmungen insbesondere über die Energie der Wechselwirkung,” Abh. sächs. Ges. d. Wiss. 11 (1878): 641–96; repr. in Werke, vol. 4, pt. 2, 361–412, on 394–95; “Elektrodynamische Maassbestimmungen insbesondere über den Zusammenhang des elektrischen Grundgesetzes mit dem Gravitationsgesetze,” handwritten manuscript, published posthumously in 1894 in Werke, vol. 4, pt. 2, 479–525, on 479–81. Weber’s biographer writes of Weber’s enduring “vision that all natural phenomena are governed by a single law: his fundamental law of electric action” (Wiederkehr, Weber, 181). Weber referred his law of interaction to more fundamental features of nature. He showed that the interaction between pairs of particles was completely determined by the principle of the conservation of energy, suitably formulated, and by the law of electrostatic interaction, which for him had the requisite simplicity of a fundamental law. He saw his accomplishment as reducing his general law of interaction to a “theorem,” a deductive consequence of what was truly fundamental. His method here was similar to Clausius’s; see note 91 above. Wilhelm Weber, “Ueber das Aequivalent lebendiger Kräfte,” Ann., Jubelband (1874): 199–213; “Ueber die Bewegungen der Elektricität in Körpern von molekularer Konstitution,” Ann. 156 (1875): 1–61; repr. in Werke, vol. 4, pt. 2, pp. 300–311 and 312–57; “Elektrodynamische Maassbestimmungen insbesondere über die Energie der Wechselwirkung,” 372.

  111. 111.

    Wilhelm Weber and Friedrich Zöllner, “Ueber Einrichtungen zum Gebrauch absoluter Maasse in der Elektrodynamik mit praktischer Anwendung,” Verh. Sächs. Ges. Wiss. 32 (1880): 77–143; repr. in Werke, vol. 4, pt. 2, 420–76.

  112. 112.

    Wilhelm Weber, “Ueber Construction des Bohnenberger’schen Reversionspendels zur Bestimmung der Pendellänge für eine bestimmte Schwingungsdauer im Verhältnis zu einem gegebenen Längenmaass,” Verh. Sächs. Ges. Wiss.(1883); reprinted in Ann. 22 (1884): 439–49.

  113. 113.

    Darrigol, Electrodynamics, 214.

  114. 114.

    Wilhelm Wien, “Ziele und Methoden der theoretischen Physik,” Jahrbuch der Radioaktivität und Elektronik 12 (1915): 241–59, on 245.

  115. 115.

    Weber to Bunsen, 12 March 1854, Bad. GLA, 235/3135.

  116. 116.

    Leipzig University Philosophical Faculty to Saxon Ministry of Culture and Public Education, undated draft, ca. 1869, Wiedemann’s Personalakte, Leipzig UA, PA 1060, Bl. 5–8.

  117. 117.

    Wien, “Ziele und Methoden,” 259.

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Jungnickel, C., McCormmach, R. (2017). Kirchhoff, Clausius, Weber, and Connectedness. In: The Second Physicist. Archimedes, vol 48. Springer, Cham. https://doi.org/10.1007/978-3-319-49565-1_9

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