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.

## Keywords

Mathematical Physic Nineteenth Century Experimental Physic Early Nineteenth Century German State## Preview

Unable to display preview. Download preview PDF.

## References

- 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
*The Emergence*, Crosland, ed. 161–178, Barry S. Gower, “Speculation in Physics: The History and Practice of Naturphilosophie,”*Studies Hist. Phil. Sci.*3(1973): 301–356.CrossRefGoogle Scholar - 2b.For recent studies on Romanticism and science, see
*Romanticism and the Sciences*, Cunningham and Jardine, eds. (Cambridge: Cambridge University Press, 1990)Google Scholar - 2c.
*Romanticism and Science in Europe*(1790–1840), Stefano Possi and Mauritz Bossi, eds. (Dordrecht: Kluwer Academic, 1994).Google Scholar - 2d.For a useful survey of the literature, see Trevor Levere, “Romanticism, Natural Philosophy, and the Sciences: A Review and Bibliographical Essay,”
*Persp. Sci.*4 (1996): 463–488.Google Scholar - 3.For a full discussion on these points, see C. E. McClelland,
*State, Society and University in Germany, 1700–1914*(New York: Cambridge University Press, 1980).Google Scholar - 4.Frederick Gregory, “Kant’s Influence on Natural Scientists in the German Romantic Period,” in
*New Trends in the History of Science*, R. P. W. Visser, H. J. M. Bos and C. Palm, eds. Proceedings of a Conference at the University of Utrecht, 1986 (Amsterdam: Rodopi, 1989), 53–66. See also Michael Heidelberger, “Some Patterns of Change in the Baconian Sciences in Early Nineteenth-Century Germany,” in*Epistemological and Social Problems*, Jahnke and Otte, eds. 3–18.Google Scholar - 6a.See Michael Friedman, “Kant on Concepts and Intuition in the Mathematical Science,”
*Synthese*, 84 (1990): 213–257MathSciNetMATHGoogle Scholar - 6b.and Friedman,
*Kant and the Exact Sciences*, (Cambridge MA.: Harvard University Press, 1992)Google Scholar - 6c.Friedman
*Kant’s Philosophy of Mathematics*, Carl J. Posy, ed. (Dordrecht: Kluwer Academic, 1992).Google Scholar - 7.See S. R. Morgan, “Schelling and the Origins of his Naturphilosophie,” in
*Romanticism and the Sciences*, Cunningham and Jardine, 25, Gregory,“Kant, Schelling and the Administration of Science in the Romantic Era,”*Osiris*, 5 (1989): 17–35. See Knight, “German Science,” on the reasons for the rejection of Kant by Schelling, the leading philosopher in the Naturphilosophie group.CrossRefGoogle Scholar - 8.For an overview of the varied versions of, and ways in which, Naturphilosophie was used as explanation in physics, see Keith Caneva,
*Mayer*, chap. 3. See also Gregory, “Romantic Kantianism and the End of the Newtonian Dream in Chemistry,”*Arch. Int. Hist. Sci.*34 (1984): 108–123.Google Scholar - 9.See letter from Oersted to Weiss, 12 May, 1829, Oersted,
*Correspondance avec divers savants*, M. C. Harding, ed. and trans. (Copenhagen: H. Aschenhoug and Co., 1920), 280–289, 285.Google Scholar - 10a.Oersted,
*Correspondance*(Hildesheim: Gerstenberg, 1981), 22.Google Scholar - 10b.Walter Kaiser,
*Theorien der Electrodynamik im Neunzehnten Jahrhundert*(Hildesheim: Gerstenberg, 1981), 22.Google Scholar - 11.See Poggendorff, “Vorwort,”
*Ann. Phy*. 1 (1824): vii.Google Scholar - 12a.See See Gower, “Speculation in Physics,”
*Stud. Romant*. 9 (1970): 193–215CrossRefGoogle Scholar - 12b.Gregory, “Influence,” for general discussions of the influence of Naturphilosophie on physics.
*Stud. Romant*. 9 (1970): 193–215CrossRefGoogle Scholar - 12c.H. A. M. Snelders, “Romanticism and Naturphilosophie and the inorganic natural Sciences, 1797–1840: An Introductory Survey,”
*Stud. Romant*. 9 (1970): 193–215, argues that Naturphilosophie “deeply” influenced scientific life in Germany.CrossRefGoogle Scholar - 12d.See also Snelders, “Point Atomism in nineteenth-century Germany,”
*Janus*, 58 (1971): 194–200. See also Walter D. Wetzeis, “Johann Wilhelm Ritter: Romantic Physics in Germany,” in*Romanticism*, Cunningham and Jardine, eds. 199–212.Google Scholar - 14a.For Goethe’s work on light and opposition to Naturphilosophie see Keld Nielsen, “Another Kind of Light: The Work of T. J. Seebeck and his Collaboration with Goethe,”
*Hist. Stud. Phys. Sci.*20 (1989): 107–178Google Scholar - 14b.For Goethe’s work on light and opposition to Naturphilosophie see Keld Nielsen, “Another Kind of Light: The Work of T. J. Seebeck and his Collaboration with Goethe,”
*Hist. Stud. Phys. Sci.*21 (1991): 317–397.Google Scholar - 14c.See also H. D. Irmscher, “Goethe und Herder im Wechselspiel von Attraction und Repulsion,”
*Goethe Jahrbuch*, 106 (1989): 22–52.Google Scholar - 15a.Gren, “Vorrede,”
*J. der Phys*. 1 (1790): 137.ADSGoogle Scholar - 15b.See also Dieter B. Hermann,
*Die Entste- hung der Astronomischen Fachschriften in Deutschland, 1798–1821*(Berlin: Archenhold-Sternwarte, 1972), 137. Thomas H. Broman, “J. C. Reil and the “Journalization” of Physiology,” in*The Literary Structure of Scientific Argument*, Dear, ed. 13–42, establishes the same pattern of publication, news and reprinted materials, in the early years of the*Archiv für die Physiologie*, although in other ways it represented a break with earlier medical journals.Google Scholar - 16.Hans Schimank, “Ludwig Wilhelm Gilbert und die Anfange der ‘Annalen der Physik’,”
*Sudhoff’s Archive*, 47 (1963): 360–372.Google Scholar - 18a.Johann Karl Fischer,
*Geschichte der Physik*,(New York: Burt Franklin reprint of the Göttingen edition of 1805)Google Scholar - 18b.J. D. Reuss,
*Repertorium Commentationum et Societatibus Litterariis Editarum*(New York: Burt Franklin reprint of the Göttingen edition of 1805) 6 vols., vol. 4 Physics.Google Scholar - 19.Quoted from C. H. Pfaff, a chemist, in Kenneth Caneva, “From Galvanism to Electrodynamics. The Transformation of German Physics and its Social Context,”
*Hist. Stud. Phys. Sci*. 9 (1978): 63–159, 86.Google Scholar - 20.See Caneva, “Galvanism to Electrodynamics,” for some of these reactions to French mathematical physics.Google Scholar
- 21a.Heidelberger, “Some Patterns of Change,” in
*Epistemological and Social Problems*, Jahnke and Otte eds., 3–18, argues that in this era no mathematics was possible in physics. For Seebeck and Fries see, Nielsen, “Other Kind of Light. Part I,” 162–163 and “Part II,” 341–343. For Fries on mathematics see, F. Gregory, “Neo-Kantian Foundations for Geometry in the German Romantic Period,”*Hist. Math*. 10 (1983): 184–201MathSciNetCrossRefMATHGoogle Scholar - 21b.F. Gregory “Die Kritik von J. F. Fries an Schelling’s Naturphilosophie,”
*Sudhofff’s Archive*, 67 (1983): 145–157.Google Scholar - 21c.See also Fries,
*Abteilung 3. Schriften zur angewandte Philosophie II Naturphilosophie und Naturwissenschaft*(Darmstadt: Scientia Verlag Aalen, 1979 reprint) 5 volsGoogle Scholar - 21f.Gert König and Lutz Geldsetzerintrod.,
*Abteilung 3. Schriften zur angewandte Philosophie II Naturphilosophie und Naturwissenschaft*(Darmstadt: Scientia Verlag Aalen, 1979 reprint) vol. 1.Google Scholar - 22.See also Jungnickel and McCormmach,
*Intellectual Mastery of Nature*, vol.1, 44–45.Google Scholar - 24.For other examples see Fritz Krafft, “Der Weg von den Physiken zur Physik an den deutschen Universitäten,”
*Ber Wissen*. 1(1978): 123–167.CrossRefGoogle Scholar - 26.This is of course the traditional historiography of the German university reform. F. Paulsen,
*The German Universities and University Study*, Frank Thilly, trans. (New York: Charles Scribner, 1906) is the most obvious example of this genre. For a recent example see Elinor S. Shaffer, “Romantic Philosophy and the Organization of Disciplines: the Founding of the University of Berlin,” in*Romanticism*, Cunningham and Jardine, eds. 37–54. One can add to this numerous histories of specific universities across Germany published in the late nineteenth and early twentieth centuries.Google Scholar - 27.Paul R. Sweet,
*Wilhelm von Humboldt: A Biography*2 vols., (Columbus OH.: Ohio State University Press, 1980), gives ample evidence that Humboldt was only happy as a private citizen. He shed public offices as soon as possible.Google Scholar - 28.For details of these and other limitations, see McClelland,
*State, Society and University in Germany*, 122–132.Google Scholar - 29.An example of this was Seebeck’s attempts to obtain a university post and the reasons for his difficulties in doing so. See Nielson, “A Different Kind of Light, Part II.” Ohm suffered similar difficulties.Google Scholar
- 30.We shall examine France in the nineteenth century in chapter IX. See also Laudan, “Ideas and Organization,” for a case of active organization without intellectual redirection.Google Scholar
- 31.For a discussion of the problems of social constructivism, see Stephen Cole,
*Making Science: Between Nature and Society*(Cambridge MA.: Harvard University Press, 1992).Google Scholar - 32.Elizabeth Garber and Fred Weinstein, “History of Science as Social History,” in
*Advances in Psychoanalytic Sociology*, Rabow and Platt, eds. (Malabar FL.: Krieger Pub., 1987), 279–298.Google Scholar - 33.Alexander Busch,
*Geschichte des Privatdocenten*(Göttingen: Abhandlungen zur Soziologie, 5 (1959)) for this Marxist interpretation. This and other interpretations of the development of the universities in the German states are outlined in McClelland,*State, Society and the University, chap. 1*.Google Scholar - 35.Rudolph Stichweh,
*Zur Entstehung des modernen Systems wissenschaftlicher Disziplinen: Physik in Deutschland, 1740–1890*(Frankfurt am Main: Suhrkamp, 1984.)Google Scholar - 36.R. Steven Turner,
*The Prussian University and the Research Imperative, 1806–1848*, unpublished PhD dissertation, 1973.Google Scholar - 38a.McClelland
*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
*State, Society, University*, p. 112, who finds Wilhelm von Humboldt’s rhetoric a nostalgic recollection of his years of freedom as a student at Halle then Göttingen. See also Robert S. Leventhal, “The Emergence of Philological Discourse in the German States, 1790–1810,”*Isis*, 77(1986): 243–260.CrossRefGoogle Scholar - 40.See William Clarke, “On the Dialectical Origins of the Research Seminar,”
*Hist. Sci*. 27 (1989): 111–139, offers a more complex description of the origins of the nineteenth-century seminar over a long time period.Google Scholar - 41.See R. Steven Turner, “The Growth of Professorial Research in Prussia, 1818 to 1848-Causes and Context,”
*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,
*Mathematik und Bildung in der Humboldtschen Reform*(Göttingen: Vandenhoek und Ruprecht, 1990.)MATHGoogle Scholar - 46a.On this see, Lewis Pyenson,
*Neohumanism and the Persistence of Pure Mathematics in Wilhelmian Germany*(Philadelphia: American Philosophical Society, 1983)MATHGoogle Scholar - 46b.David E. Rowe, “Klein, Hubert and the Göttingen Mathematical Tradition,”
*Osiris*5 (1989): 186–213.MathSciNetCrossRefMATHGoogle Scholar - 47.On the problems and excitement of this approach, see Herbert Mehrtens, “The Social History of Mathematics,” in
*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,
*Die galvanische Kette, mathematisch bearbeitet*(Berlin, 1827)Google Scholar - 53b.Ohm, Abh., 61–186, translated as Ohm, “The Galvanic Circuit, Investigated Mathematically,” in
*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,”
*Centaurus*, 31 (1988): 141–163 on the development of the concept.MathSciNetADSCrossRefMATHGoogle Scholar - 54b.Gustav Robert Kirchhoff, “Über eine Ableitung der Ohm’sehe Gesetze, welche sich an die Theorie der Elektrostatik anschliesst,”
*Ann. Phy*. 76 (1849): 506–513ADSCrossRefGoogle Scholar - 51c.translated as, Kirchhoff, “Ohm’s law and Electrostatics,”
*Phil. Mag*. 37 (1850): 463–468, drew Ohm’s work and electrostatics together.Google Scholar - 55.Ohm, “Galvanic Circuit,”
*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,
*Intellectual Mastery*vol. 1, see Ohm’s purposes as physical because Ohm did not test for the convergence of the series he was using. His model, Fourier, did not either. By contemporary standards both were doing mathematics.Google Scholar - 61a.Ohm, “Nachträge zu seiner mathematischen Bearbeitung der galvanischen Kette,”
*Archive für die gesammte Naturlehre*14 (1828): 475–493.Google Scholar - 61b.The physical explanation appeared in Ohm, “Nachweisung eines Überganges von dem Gesetze der Elektricitätsver-breitung zu dem Spannung,”
*Archive für die gesammte Naturlehre*17 (1829): 1–25.Google Scholar - 62.See Ohm, “Zur Theorie der galvanischen Kette,”
*J. Chem. Phy*. 67 (1833): 341–354, reprinted in Ohm,*Abh*., 560–572.Google Scholar - 63a.See Ohm, “Über die Definition des Tons, nebst daran geknüpfter Theorie der Sirene und ähnlicher tonbildender Vorrichtungen,”
*Ann. Phy*. 59 (1843): 513–565, reprinted Ohm,*Abh*., 587–633ADSCrossRefGoogle Scholar - 63b.Ohm, “Erklärungen in einaxigen Krystallplatten zwischen geradlinig polarischtem Lichte wahrnehmbaren Interferenz-Erscheinungen in mathematischer Form mitgetheilt,”
*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,
*Maassbestimmungen über die galvanische Kette*(Leipzig: F. A. Brockhaus, 1831). Fechner was followed over the century by many others. For the fate of Ohm’s Law see Caneva, “From Galvanism to Electrodynamics.”Google Scholar - 66.See Kathryn M. Olesko,
*Physics as a Calling: Discipline and Practice in the Königsberg Seminar for Physics*(Ithaca NY: Cornell University Press, 1991), chap. 2 for a discussion of Bessel’s analysis of the second-pendulum, and Neumann’s use of Bessel’s approach in the analysis of experimental data.Google Scholar - 67a.The experimental methods were developed in Franz Ernst Neumann,
*Beitrage zur Krystallonomie*(Berlin: 1823).Google Scholar - 67b.Neumann published one paper on crystal symmetry before his dissertation, Neumann, “Über das Crystallsystem des Axinits,”
*Ann. Phy.*4 (1825): 63–76. Neumann’s dissertation was published as, “De tactionibus atque intersectionibus circulorum et in piano et in sphaera sitorum, sphaerarum atque conorum ex eodem vertice pergentium commentatio geometrica,”*Isis*, (1826): cols., 349–369, 468–489, see Franz Ernst Neumann,*Gesammelte Werke*, M. Krafft, E. R. Neumann, H. Steinmatz and A. Wangerin, eds. 3 vols. (Leipzig: B. G. Teubner, 1906–1928), vol. 1. In these papers Neumann displayed his ability to visualize relationships in space that is so apparent in his work in optics and electromagnetic induction.ADSCrossRefGoogle Scholar - 68.Olesko,
*Physics as a Calling*, 123. Olesko is the latest to note this. See Woldemann Voigt, “Gedächtnissrede,” in Neumann,*Gesammelte Werke*vol. 1, 3–19. The quotation is from Fourier,*Analytical Theory*, 6.Google Scholar - 69.Luise Neumann,
*Franz Neumann Erinnerungs blatter von seiner Tochter*(Leipzig: F. S. B. Mohr, 1904), 226. Also quoted in Olesko,*Physics as a Calling*, 129.Google Scholar - 71a.See Wolfgang Eccarius, “Der Techniker und Mathematiker August Leopold Crelle (1780–1855) und sein Beitrag zur Förderung und Entwicklung der Mathematik im Deutschland des 19 Jahrhunderts,”
*NTM*, 12 (1975): 38–49MathSciNetMATHGoogle Scholar - 71b.See Wolfgang Eccarius “Zur Gründungsgeschichte des Journals für reine und angewandte Mathematik,”
*NTM*, 14 (1977): 8–28.MathSciNetMATHGoogle Scholar - 72a.See Gert Schubring,
*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,”
*Hist. Stud. Phys. Sci*. 12 (1981): 161–194, 174.Google Scholar - 76.Crelle defended the “purity” of mechanics in Crelle,
*Encyklopädie deutsche Darstellung der Theorie der Zahlen*(Berlin: 1845), vol. 1, iii-iv. See also Schubring, “Mathematics and Teacher Training,” 178.Google Scholar - 78a.K.-R. Biermann, “Über die Förderung deutscher Mathematiker durch Alexander von Humboldt,” in
*Alexander von Humboldt: Gedenkschrift zur 100 Wiederkehr seines Todestages*(Berlin: Akademie Verlag, 1959) 83–160, p. 88.Google Scholar - 78b.See also Biermann,“Der Briefwechsel zwischen Alexander von Humboldt und G. J. Jacobi über die Entdeckung des Neptun,”
*NTM*, 6 (1969): 61–67.MathSciNetMATHGoogle Scholar - 79.See
*Briefwechsel zwischen C. G. J. Jacobi und M. H. Jacobi*, W. Ahrens, ed. (Leipzig: B. G. Teubner, 1907) 22.Google Scholar - 82.Muncke, “Physik,” in
*Physikalisches Wörterbuch*11 vois (Leipzig: Schweikert, 1825–1845) vol. 7 (1833): 493–573, 510–511. His effort to distinguish theoretical and experimental physics appear on pages 503–504.Google Scholar - 84.Poggendorff, “Vorwort,”
*Ann. Phy*. 1 (1824): vii.Google Scholar - 85.See Jungnickel and McCormmach,
*Intellectual Mastery*, vol. 1, chap. 5 for some of the details of the types of articles published during the 1840s. Their comments on the content of this, and other journals in chapter 2 are based on the assumption that “mathematical physics” was physics in the 1820s. The overlap in coverage between Poggendorff’s and Crelle’s journal in their account is left unexplained.Google Scholar