The Language of Physics pp 137-167 | Cite as

# On the Margins: Experimental Physics and Mathematics in the German States, 1790–1830

## Abstract

Paris was not the only site for the practice and development of mathematics and experimental philosophy around the turn of the nineteenth century.^{1} Throughout the eighteenth century, in Britain and the German States, experimental philosophers and mathematicians built their own traditions, interacting with, but not over-whelmed by, the research of the French. After 1800 the achievements of French experimentalists and mathematicians intruded into those traditions and began to change them. These intrusions reoriented research problems and the terms of their solution by both experimentalists and mathematicians. At the same time and on a broad scale, British and German societies went through metamorphoses. In the German states, the invasion and occupation of the Rhineland by the French accelerated these changes. Experiences in the Napoleonic wars added to the structural, economic translocations already affecting Britain.

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- 1.Although this narrative focuses on events and changes in Britain and the German States, other sites in Europe continued their own traditions in the study of nature and interacted with those states. Among the more important in this period are those of Sweden and Denmark. Physics in the United States does not enter this account until physics became a profession and only in the person of Josiah Willard Gibbs. American physics had its own distinct social history. However, the pervasive “baconianism” that Robert Bruce,
*The Launching of Modern American Science, 1846–1876*(New York: Alfred Knopf, 1987) Prologue, found so dismal was not so different from the standards of Europe of similar eras.Google Scholar - 2a.The fragmented intellectual and social character of this era has been detailed by David Knight, “German Science in the Romantic Period, 1781–1831,” in
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*State, Society, University*. Kees Gispen supports this view in his explanation of the place of engineers in German society in the nineteenth century. Kees Gispen,*New Profession, Old Order: Engineers in German Society, 1815–1914*(Cambridge: Cambridge University Press, 1989) chap. 1. One can challenge his ideas on the commitments of all academics later in the century to the notions of social hierarchy he claims they accepted. Hermann von Helmholtz’s son Richard became an engineer, a career he followed with the encouragement of his father. Helmholtz also understood the economic need for research institutions for industry, part of the justification for the establishment of the Physikalisch-Technische-Reichanstalt.Google Scholar - 38a.See David Cahan,
*An Institute for an Empire: The Physikalisch-Technische-Reichanstalt, 1871–1918*(Cambridge: Cambridge University Press, 1989).Google Scholar - 39.McClelland
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*Hist. Stud. Phy. Sci*. 3 (1971): 137–182, 148–149.Google Scholar - 42.Functional theories of the scientist do not bring us any closer to a solution of this dilemma. See, Joseph Ben-David,
*The Scientist’s Role in Society: A Comparative Study*(Englewood Cliffs NJ: Prentice-Hall, 1971). The concept of role simply leads to a narrative of events, not an interpretation of those events.Google Scholar - 44.See
*Die Mathematischen Wissenschaften*, Felix Klein ed. (Leipzig: Teubner, 1914). Volumes included in the series covered the teaching of mathematics in Germany, its philosophy and the nature of mathematics as a science. The history volumes,*Vorlesungen über Geschichte der Mathematik*, M. Cantor, ed. (Leipzig: Barth, 1894–1907) 4 vols., was a collection of essays by mathematicians on various aspects of the history of mathematics. This older historiography of mathematics is discussed in Dirk Struik, “The Historiography of Mathematics from Proclus to Cantor,”*NTM*17 (1980): 1–22.MathSciNetMATHGoogle Scholar - 45.On this see H. N. Jahnke,
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*Social History of Nineteenth-Century Mathematics*, Mehrtens, Bos, and Schneider, eds. 257–280. This collection also includes a bibliography on the subject. On the early nineteenth century, see Mehrtens, “German Scientific Renaissance in Mathematics,” in*Social and Epistemological Problems*, Jahnke and Otte, eds.Google Scholar - 48.Gert Schubring has argued that mathematicians used
*Wissenschaftideologie*to create the modern German mathematical profession. See Gert Schubring, “The Conception of Pure Mathematics as an Instrument in the Professionalization of Mathematics,” in*Social History*, Mehrtens Bos and Schneider, eds. 111–134.Google Scholar - 49a.This interpretation clearly diverges from that of Jungnickel and McCormmach
*Intellectual Mastery*, vol. 1, who accept as physics much of what was mathematics in the early nineteenth century. While they recognize the importance of French mathematical physics, they do not explore what that discipline was, or, how the Germans understood that discipline. They also do not define what they mean by the discipline whose history they are narrating, that is, theoretical physics. On this last point, see also Cahan, “Pride and Prejudice in the History of Physics: The German Speaking World, 1740–1945,”*Hist. Stud. Phys. Sci.*19 (1988): 173–191Google Scholar - 49b.Pearce Williams, “Review of
*Intellectual Mastery of Nature*,”*Hist. Math.*15 (1988): 389–392.CrossRefGoogle Scholar - 50.There are numerous references to Fourier in Ohm’s mathematical paper on galvanic electricity. See Kenneth Caneva, “Ohm, Georg Simon,”
*Dict. Sci. Bio*. vol. 10, 186–194, 188.Google Scholar - 51a.See John L. McKnight, “Laboratory Notebooks of G. S. Ohm: A Case Study in Experimental Method,”
*Amer. J. Phys*. 35 (1967): 110–114, 111–112.ADSCrossRefGoogle Scholar - 51b.John L. McKnight The first paper in which this comparative measure of resistance appears is Ohm, “Vorläufige Anzeige des Gesetzes, nach welchem Metalle die Contact-Electricität leiten,”
*J. für Chem. Phy*. 44 (1825): 110–118Google Scholar - 51c.John L. McKnight “Vorläufige Anzeige des Gesetzes, nach welchem Metalle die Contact-Electricität leiten,” reprinted in
*Ann. Phy*. 4 (1825): 79–88Google Scholar - 51d.Ohm,
*Gesammelte Abhandlungen*, E. Lommel ed., (Leipzig: Barth, 1892), 1–8.Google Scholar - 52e.Ohm described experiments comparing the conductivity of several metals and ordering them with respect to their conductivity in Ohm, “Über Leitungsfähigkeit der Metalle für Elektricität,”
*J. Chem. Phy*. 44 (1825): 245–247, reprinted Ohm,*Abh*., 9–10. He argued with the work of Becquerel and Barlow on conductivity in Ohm, “Über Electricitätsleiter,” same journal and volume, 370–373, reprinted Ohm, Abh. 11–13.Google Scholar - 52.The mathematical manipulation appeared in Ohm, “Vorläufige.” The linear form of his law appeared in Ohm, “Bestimmung des Gesetzes, nach welchem Metalle die Contactelektricität leiten, nebst einem Entwürfe zu einer Theorie des Voltaischen Apparate und des Schweiggerischen Mutliplicators,”
*J. Chem. Phy*. 46(1826): 137–166, reprinted Ohm,*Abh*., 14–36,25.Google Scholar - 53a.Ohm,
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*Scientific Memoirs, selected from the Transactions of Foreign Academies and Learned Societies and from Foreign Journals*, Richard Taylor, ed. vol. 2 (New York: Johnson Reprint of 1841 edition, 1966), 401–506, that closely follows the German edition. The geometrical analogy appears on pps., 405–416.Google Scholar - 54a.It is best to keep in mind that in the 1820s, while one can connect electrostatic and galvanic phenomena, they were kept separate, even seen as two kinds of electricity. See Thomas Archibald, “Tension and Potential, Ohm to Kirchhoff,”
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*Scientific Memoirs*, 451. This equation appeared in Fourier*Analytical Theory of Heat*, 88. The differentials are partial differentials. See also Bernard L. Pourprix, “La mathématisation des phénomènes galvaniques par G. S. Ohm (1815–1817),”*Rev. Hist. Sci*. 42 (1989): 139–154, on the mathematical aspects of Ohm’s work.MathSciNetGoogle Scholar - 60.Jungnickel and McCormmach,
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*Abh. der Math.-Phy. Cl. König. Bayerische Akad. Sci*. 7 (1853): 43–149, 267–370, reprinted Ohm,*Abh*., 665–855.Google Scholar - 65.Initial reactions to Ohm’s law were to his experiments. In 1831 Fechner carried out an extensive series of experiments to test Ohm’s experimental results that were in turn criticized by Ohm. Fechner,
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*Die Entstehung des Mathematiklehrerberufs im 19 Jahrhunderts*(Basel: Beltz Verlag, 1983) and Jahnke and Otte, “Origins of the Program of the ‘Arithmetization of Mathematics’,” and Gert Schubring, “The Conception of Pure Mathematics,” in*Social History*, Mehrtens, Bos and Schneider, eds. 21–49 and 111–134 respectively.Google Scholar - 75.Schubring, “Mathematics and Teacher Training: Plans for a Polytechnic in Berlin,”
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