Abstract
In the middle decades of the nineteenth century, a career in physics in Germany usually meant the career of a university physics professor. Within German universities, opportunities for doing research in physics increased, while outside them, independent physics research became nearly impossible, and industrial physics laboratories had not yet taken its place. Developments in physical research led to changes in physics instruction, raising it to the level of professional training. Physics professors could claim that it was not only desirable but necessary for their teaching that they also carry out research, and that they were therefore entitled to be furnished by the state with means for research. To reach the latter stage took most of the period covered by this book. More than any other development in the 1830s, research in Earth magnetism set physics on a new course, and methods of mathematics and measuring physics that were introduced then were important for theoretical physics for the rest of the century.
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Notes
- 1.
Gauss mentioned the practical uses of Earth magnetism in his “Einleitung” to the Resultate aus den Beobachtungen des magnetischen Vereins im Jahre 1836, 3–12, repr. in Carl Friedrich Gauss, Werke, ed. Königliche Gesellschaft der Wissenschaften zu Göttingen, vol. 5, (n.p., 1877), 345-51, on 350.
- 2.
A. Galle, “Über die geodätischen Arbeiten von Gauss,” in Gauss, Werke, vol. 11, pt. 2, 1st treatise (Berlin and Göttingen: Springer, 1924), 16, 27, 38, 47–48, to cite only a few references to the interests of the different German states in the surveying and triangulation projects. The participating astronomers frequently referred to in this connection, aside from Gauss, were F. W. Bessel, J. G. F. Bohnenberger, Johann Franz Encke, Bernhard August von Lindenau, Wilhelm Olbers, Johann Georg Soldner, and Franz Xaver von Zach. E. Weis, “Bayerns Beitrag zur Wissenschaftsentwicklung im 19. und 20. Jahrhundert,” in Handbuch der bayerischen Geschichte, vol. 4, pt. 2, Das neue Bayern 1800–1970, ed. Max Spindler (Munich: C. H. Beck, 1975), 1034–88, on 1043; Günter D. Roth, Joseph von Fraunhofer, Handwerker–Forscher–Akademiemitglied 1787–1826 (Stuttgart: Wissenschaftliche Verlagsgesellschaft, 1976), 31–37, 65, 70.
- 3.
Roth, Fraunhofer, 31–32, 45–46, 71–73; Weis, “Bayerns Beitrag,” 1042. An inventory of the old astronomical observatory in Göttingen dating from 1788 lists eight instruments from English instrument makers among a total of eleven, including a “Newtonian reflecting telescope by Herschel” and two telescopes by Dollond. Gauss used Dollond’s instruments, but his main work in practical astronomy at Göttingen did not begin until after he had acquired from Reichenbach the new instruments that he would like to have bought from the English instrument maker Ramsden had it been possible, but which he was now getting from Ramsden’s student. Martin Brendel, “Über die astronomischen Arbeiten von Gauss,” in Gauss, Werke, vol. 11, pt. 2, 3rd treatise (Berlin and Göttingen: Springer, 1929), 46–49, 55–56. Reichenbach was sent to study in England at the expense of the Bavarian government. Weis, “Bayerns Beitrag,” 1037–38.
- 4.
Gauss to Göttingen U. Curator, 29 January 1833, Göttingen UA, 4/V f/48.
- 5.
Alexander von Humboldt, Briefe zwischen A. v. Humboldt und Gauss. Zum hundertjährigen Geburtstage von Gauss am 30. April 1877, ed. Karl Bruhns (Leipzig, 1877), 24. Humboldt’s letter to Gauss containing the remark is dated 17 February 1833.
- 6.
See, for example, the advice Gauss gave to Weber in 1844, in Clemens Schaefer, “Über Gauss’ physikalische Arbeiten (Magnetismus, Elektrodynamik, Optik),” In Carl Friedrich Gauss’s Werke, 2nd treatise in vol. 11, pt. 2 (Berlin and Göttingen: Springer 1929), 118–19.
- 7.
Gauss to H. C. Schumacher, 3 March 1832, in Schaefer, “Über Gauss’ physikalische Arbeiten,” 30.
- 8.
In S. D. Poisson, “Mémoire sur la distribution de l’électricité à la surface des corps conducteurs,” Mémoires de l’Institut, année 1811 (Paris, 1812), 1: “It is not sufficient for maintaining a constant electric state in an electrified conducting body that the internal border surface of the free electricity at the surface of the conductor be an equilibrium surface, but it is also required that this electricity does not exert any attraction or repulsion at any point in the internal space.” Gauss now pointed out that the second condition, namely, that the resultant force at every point in the internal enclosed space be zero, is already contained in the first, if the attraction and repulsion take place according to the inverse-square force law. Quoted in Schaefer, “Über Gauss’ physikalische Arbeiten,” 99–100. Schaefer also quotes Gauss’s letter to Encke, 18 August 1832 (13–14), and to Bessel, 31 December 1831 (100), on this work.
- 9.
Schaefer, “Über Gauss’ physikalische Arbeiten,” 14.
- 10.
Carl Friedrich Gauss. “Allgemeine Theorie des Erdmagnetismus,” Resultate … 1838, repr. in Gauss, Werke, vol. 5, 119–75, on 122–26.
- 11.
For the case in which the agents are continuously distributed, Gauss replaced the sum by an integral. He derived the standard equations for the potential in the absence of, and in the presence of, sources k:
$$ \frac{ d dV}{d{ x}^2}+\frac{ d dV}{d{ y}^2}+\frac{ d dV}{d{ z}^2}=0,\mathrm{and}\ \frac{ d dV}{d{ x}^2}+\frac{ d dV}{d{ y}^2}+\frac{ d dV}{d{ z}^2}=-4\pi k. $$Gauss, “Allgemeine Lehrsätzte in Beziehung auf die im verkehrten des Quadrats der Entfernung wirkenden Anziehungs- und Abstossungs-Kräfte,” Resultate…1839, repr. in Gauss, Werke, vol. 5, 195–242, on 199–200. Gauss read the paper on 9 March 1840. Limited uses of the potential long antedated Gauss’s general, rigorous theory of the potential. In the late eighteenth century, Lagrange and Laplace wrote the components of the gravitational attraction as the partial differential quotients of a certain function. In the early nineteenth century, this way of expressing forces was extended by Poisson and others to electricity and magnetism (Morris Kline, Mathematical Thought from Ancient to Modern Times [New York: Oxford University Press, 1972], 681–82). Before Gauss, some of the theorems on the potential had already been derived by George Green in 1828, but Green’s work remained unnoticed until after Gauss’s had attracted wide interest in the subject. It was resurrected in 1846 by William Thomson. It was only made readily accessible to a German audience through its publication in Crelle’s Journal in 1850–1854. For this reason it was largely on the basis of Gauss’s work that potential theory was developed in Germany into an “independent mathematical discipline” of importance to mathematicians and physicists alike (Albert Wangerin’s “Anmerkungen” to the repr. of Gauss’s “Allgemeine Lehrsätze,” ed. A. Wangerin as vol. 2 of Ostwald’s Klassiker der exakten Wissenschaften [Leipzig, 1889], 51–60, on 52).
- 12.
Gauss to Göttingen U. Curator, 29 January 1833.
- 13.
The unit of magnetic quantity is that which acts on another unit of magnetic quantity at unit distance with unit moving force. Poisson had expressed the intensity of Earth magnetism by the force with which a unit magnetic quantity acts on a second unit, but because his unit of magnetic quantity was arbitrary, he did not have an absolute system (Ernst Dorn’s “Anmerkungen” to Gauss’s “Intensitas vis magneticae terrestris,” trans. and repr. as Die Intensität der erdmagnetischen Kraft auf absolutes Maass zurückgeführt [1832], ed. E. Dorn, Ostwald’s Klassiker der exakten Wissenschaften [Leipzig, 1894], vol. 53, 50–62, on 54). Schaefer notes that although Poisson did not have an absolute system in Gauss’s sense, his method produced values for Earth-magnetic force that are independent of the magnetic state of the needles used, and in that sense he too had “absolute measures.” Schaefer, “Über Gauss’ physikalische Arbeiten,” 25.
- 14.
Dorn, “Anmerkungen,” 50; Ferdinand Rosenberger, Die Geschichte der Physik, vol. 3, Geschichte der Physik in den letzten hundert Jahren (Braunschweig, 1890; repr. Hildesheim: G. Olms, 1965), 302. In the course of the nineteenth century, opinions on the possibility of expressing all physical laws in absolute units varied. The early promise of the universal applicability of absolute units led to their overvaluation, as physicists later recognized: chemistry, heat, radiation, and even electricity and magnetism required a fourth fundamental unit (Dorn, 52).
- 15.
Hermann von Helmholtz, Vorlesungen über die Theorie der Wärme, ed. Franz Richarz (Leipzig: J. A. Barth, 1903), 32. Dorn, “Anmerkungen,” 50; Ferdinand Rosenberger, Die Geschichte der Physik, vol. 3, Geschichte der Physik in den letzten hundert Jahren (Braunschweig, 1890; repr. Hildesheim: G. Olms, 1965), 302.
- 16.
Gauss to Olbers, 2 August 1832, in Wilhelm Obers, Wilhelm Obers, sein Leben und seine Werke. Briefwechsel zwischen Olbers und Gauss, ed. C. Schilling, vol. 2, pt. 2 (Berlin: J. Springer, 1909), 588.
- 17.
Gauss to Olbers, 18 February 1832, in Briefwechsel zwischen Olbers und Gauss, 584–85.
- 18.
Gauss to Olbers, 2 August 1832, in Briefwechsel zwischen Olbers und Gauss, 587.
- 19.
Gauss to Göttingen U. Curator, 29 January 1833. Also Gauss to Olbers, 2 August 1832, in Briefwechsel zwischen Olbers und Gauss, 587; Schaefer, “Über Gauss’ physikalische Arbeiten,” 28; and Gauss to Encke, 18 August and 25 December 1832, in Schaefer, 31.
- 20.
Gauss to Olbers, 2 August 1832, in Briefwechsel zwischen Olbers und Gauss, 588.
- 21.
Weber to Göttingen U. Curator, 15 December 1832, and Göttingen U. Curator to Weber, 17 January 1833, Göttingen UA, 4/V h/16.
- 22.
Weber to Göttingen U. Curator, 12 August 1834, Göttingen UA, 4/V h/16.
- 23.
Gauss to Göttingen U. Curator, 29 January 1833.
- 24.
Gauss, “Einleitung,” 349.
- 25.
Gauss, “Einleitung,” 350–51. Carl Friedrich Gauss, “Ein neues Hülfsmittel für die magnetischen Beobachtungen,” in Göttingische gelehrte Anzeigen, 30 October 1837, 1721–28, repr. in Werke, vol. 5, 352–56, on 352.
- 26.
Gauss, “Ein neues Hülfsmittel,” vol. 5, 353. “Über ein neues, zunächst zur unmittelbaren Beobachtung der Veränderungen in der Intensität des horizontalen Theils des Erdmagnetismus bestimmtes Instrument,” Resultate … 1837, 1–19, repr. in Werke, vol. 5, 357–73, on 358. The lecture to the Göttingen Scientific Society on which this paper is based was given on 19 September 1837. The subject is the “bifilar” magnetometer.
- 27.
Gauss, “Über ein neues … Instrument,” 361.
- 28.
Gauss to Olbers, 2 September 1837, in Briefwechsel zwischen Olbers und Gauss, 649.
- 29.
Gauss to Olbers, 2 September 1837, in Briefwechsel zwischen Olbers und Gauss, 649–50.
- 30.
Gauss to Gerling, 28 October 1832, quoted in Schaefer, “Über Gauss’ physikalische Arbeiten,” 104.
- 31.
Gauss, “Intensitas vis magneticae terrestris,” 301.
- 32.
Schaefer, “Über Gauss’ physikalische Arbeiten,” 104. Later Gauss did exacting galvanic measurements. By coiling a great length of wire around the magnetic bar and passing a current through it, he converted the bifilar magnetometer into a sensitive galvanometer; the weakest galvanic force deflected the twenty-five pound bar significantly. With the galvanometer, he measured frictional and thermoelectric currents as well as battery currents (Christoph Stähelin, “Wilhelm Weber in seiner allgemeinen Bedeutung für die Entwicklung und die Fortschritte der messenden und experimentirenden Naturforschung,” in J. C. F. Zöllner, Principien einer elektrodynamischen Theorie der Materie, vol. 1, Abhandlungen zur atomistischen Theorie der Elektrodynamik [Leipzig, 1876], xcix–cxxiv, on c–ci, cxi).
- 33.
Weber to Göttingen U. Curator, 15 December 1832.
- 34.
Gauss to Göttingen U. Curator, 29 January 1833; Gauss to Schumacher, 21 March 1833, in Schaefer, “Über Gauss’ physikalische Arbeiten,” 127.
- 35.
Gauss, “Fortsetzung,” 531–32.
- 36.
Carl Friedrich Gauss, “Erdmagnetismus und Magnetometer,” Schumacher’s Jahrbuch für 1836, 1–47, reprinted in Werke, vol. 5, 315–44, on 336.
- 37.
Weber to Edward Sabine, 20 February 1845, in Wilhelm Weber, Werke, vol. 2, Magnetismus, ed. Eduard Riecke (Berlin, 1892), 274–76.
- 38.
Göttingen U. Curator to Gauss (with a copy of the letter to Weber), 5 May 1834, authorizing the transfer, Göttingen UA, 4/V h/16. Carl Friedrich Gauss, “Eine Fortsetzung der am 9. August 1834 gegebenen Nachricht,” Göttingische gelehrte Anzeigen, 7 March 1835, 345–57, repr. in Werke, vol. 5, 528–36, on 529–30.
- 39.
Müller to Hoppenstedt, 17 May 1838.
- 40.
Weber to Karl von Richthofen, 9 April 1841, Göttingen UB, Ms. Dept., Phil. 182.
- 41.
Weber to Sabine, 20 February 1845.
- 42.
The term “Gaussian” was applied to Kirchhoff’s work, for example.
- 43.
Weber to Richthofen, 9 April 1841.
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Jungnickel, C., McCormmach, R. (2017). Promoting a New Physics: Earth Magnetism at Göttingen. In: The Second Physicist. Archimedes, vol 48. Springer, Cham. https://doi.org/10.1007/978-3-319-49565-1_4
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