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Zöllner’s Universe

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Abstract

The idea that space is not Euclidean by necessity, and that there are other kinds of “curved” spaces, diffused slowly to the physical and astronomical sciences. Until Einstein’s general theory of relativity, only a handful of astronomers contemplated a connection between non-Euclidean geometry and real space. One of them, the German astrophysicist Johann Carl Friedrich Zöllner (1834–1882), suggested in 1872 a remarkable cosmological model describing a finite universe in closed space. I examine Zöllner’s little-known contribution to cosmology and also his even more unorthodox speculations of a four-dimensional space including both physical and spiritual phenomena. I provide an overview of Zöllner’s scientific work, of his status in the German scientific community, and of the controversies caused by his polemical style of science. Zöllner’s cosmology was effectively forgotten, but there is no reason why it should remain an unwritten chapter in the history of science.

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Notes

  1. According to Jaki, Zöllner’s considerations “constituted a remarkable anticipation of the idea of a finite and oscillating universe”; see Jaki, The Paradox of Olbers’ Paradox (ref. 3), p. 160. However, this is to read too much into the essay. Zöllner’s universe was static, and he nowhere indicated that the curvature of space varied periodically in time, such as Alexander Friedmann, in the very different context of general relativity cosmology, would do fifty years later.

  2. Ptolemaic astronomy was essentially two-dimensional, while the Copernican version allowed astronomers to determine the relative distances of the planets and in this sense to provide the universe with a depth-dimension.

  3. Moles argues that Nietzsche’s doctrine of the eternal cosmic recurrence should be seen on the background of Riemannian geometry. His conclusion that “Zöllner’s influence on Nietzsche is apparent” is questionable, given its lack of documentary evidence; see Moles, “Nietzsche’s Eternal Recurrence” (ref. 61), p. 27.

References

  1. The scholarly literature on Zöllner is limited. For a biography with selections of his correspondence, see Felix Koerber, Karl Friedrich Zöllner: Ein deutsches Gelehrtenleben (Berlin: Hermann Paetel, 1899). A more modern biography is Dieter B. Herrmann, Karl Friedrich Zöllner (Leipzig: B.G. Teubner, 1982), published on the occasion of the centenary of Zöllner’s death. See also idem, “Zöllner, Johann Karl Friedrich,” in Charles Coulston Gillispie, ed., Dictionary of Scientific Biography 14 (1976), pp. 627–630. For the local and cultural context, see Christoph Meinel, Karl Friedrich Zöllner und die Wissenschaftskultur der Gründerzeit (Berlin: Sigma, 1991).

  2. Examples of the latter are Max Jammer, Concepts of Space: The History of Theories of Space in Physics (Cambridge, Mass.: Harvard University Press, 1954), pp. 179–180; republished (New York: Dover Publications, 1993), pp. 181–182, and C.J. Scriba and P. Schreiber, 5000 Jahre Geometrie: Geschichte, Kulturen, Menschen (Berlin, Heidelberg, New York: Springer, 2005), p. 427.

  3. The significance of Zöllner’s discussion was first pointed out by Stanley L. Jaki, The Paradox of Olbers’ Paradox: A Case History of Scientific Thought (New York: Herder and Herder, 1969), pp. 158–164; see also Helge Kragh, “Geometry and Astronomy: Pre-Einstein Speculations of Non-Euclidean Space,” ArXiv:1205.4909v2 [physics.hist-ph] (2012), esp. pp. 20–34.

  4. J.C.F. Zöllner, Grundzüge einer allgemeinen Photometrie des Himmels (Berlin: Mitscher & Röstell, 1861). On Zöllner’s instrument and its use in astronomy, see A. Pannekoek, A History of Astronomy (London: Allen & Unwin and New York: Interscience Publishers, 1961), pp. 385–387; D.B. Herrmann and D. Hoffmann, “Astrofotometrie und Lichttechnik in der 2. Hälfte des 19. Jahrhunderts,” NTM: Schriftenreihe für Geschichte der Naturwissenschaften, Technik und Medizin 13 (1976), 94–104, esp. 96–98; Klaus Staubermann, “The Trouble with the Instrument: Zöllner’s Photometer,” Journal for the History of Astronomy 31 (2000), 323–338; C. Serken and K.B. Staubermann, ed., Karl Friedrich Zöllner and the historical dimension of astronomical photometry: A collection of papers on the History of Photometry (Brussels: VUB University Press, 2000), which includes on pp. 162–178 a bibliography of Zöllner’s publications.

  5. F. Zöllner, “Ueber eine neue Art von Pseudoskopie und ihre Beziehungen zu den von Plateau und Oppel beschrieben Bewegungsphänomenen,” Annalen der Physik und Chemie 110 (1860), 500–523 + Taf. VIII, No. 4.

  6. J.C.F. Zöllner, Photometrische Untersuchungen mit besonderer Rücksicht auf die physische Beschaffenheit der Himmelskörper (Leipzig: Wilhelm Engelmann, 1865).

  7. Jürgen Hamel, “Karl Friedrich Zöllners Tätigkeit als Hochschullehrer an der Universität Leipzig: Ein Beitrag zur Geschichte der Institutionalisierung der Astrophysik,” NTM 20 (1983), 35–43.

  8. Zöllner, Photometrische Untersuchungen (ref. 6), pp. 315–316. On the rise of astrophysics, see Joann Eisberg, “Solar Science and Astrophysics,” in Mary Jo Nye, ed., The Cambridge History of Science. Vol. 5. The Modern Physical and Mathematical Sciences (Cambridge: Cambridge University Press, 2003), pp. 505–521.

  9. Obituary notice in Monthly Notices of the Royal Astronomical Society 43 (1883), 185.

  10. H. Vogel, “Spectralanalytische Untersuchungen an der Sonne,” Astronomische Nachrichten 78 (1872), columns 248–250, on 249; trans. as “Results of the Spectra Analytical Observations at Bothkamp Observatory,” in A.J. Meadows, Early Solar Physics (Oxford: Pergamon Press, 1970), pp. 121–124, on p. 123.

  11. F. Zöllner, “Ueber eine neue Methode zur Messung anziehender und abstossende Kräfte,” Ann. Phys. u. Chem. 30 (1873), 131–134; reprinted in Friedrich Zöllner, Wissenschaftliche Abhandlungen. Vierter Band (Leipzig: L. Staackmann, 1881), pp. 313–316.

  12. F. Zöllner, “On the Temperature and Physical Constitution of the Sun,” Philosophical Magazine 40 (1870), 313–327; ibid. 46 (1873), 290–304; reprinted as “Ueber die Temperatur und physische Beschaffenheit der Sonne,” Erste Abhandlung, in Friedrich Zöllner, Wissenschaftliche Abhandlungen. Vierter Band (ref. 11), pp. 184–207; idem, Zweite Abhandlung, ibid., pp. 241–279.

  13. Pierre-Marie Robitaille, “A Thermodynamic History of the Solar Constitution—II: The Theory of a Gaseous Sun and Jeans’ Failed Liquid Alternative,” Progress in Physics 3 (2011), 41–59, esp. 44.

  14. Zöllner, Photometrische Untersuchungen (ref. 6), p. 240. Jean-Louis Tassoul and Monique Tassoul, A Concise History of Solar and Stellar Physics (Princeton and Oxford: Princeton University Press, 2004), p. 85; David DeVorkin, “Stellar evolution and the origin of the Hertzsprung-Russell diagram,” in Owen Gingerich, ed., Astrophysics and twentieth-century astronomy to 1950: Part A (Cambridge: Cambridge University Press, 1984), pp. 90–108, esp. p. 92.

  15. H.C. Vogel, “Spektralanalytische Mittheilungen,” Astro. Nach. 84 (1874), columns 113–124.

  16. F. Zöllner, “Ueber die Stabilität kosmischer Massen und die physische Beschaffenheit der Cometen,” Berichte über die Verhandlungen der königlich Sächsischen Gesellschaft der Wissenschaften zu Leipzig, Mathematisch-Physische Classe 23 (1871), 174–257; reprinted in Friedrich Zöllner, Wissenschaftliche Abhandlungen. Zweiter Band. Zweiter Theil (Leipzig: L. Staackmann, 1878), pp. 597–679. Johann Carl Friedrich Zöllner, Über die Natur der Cometen. Beiträge zur Geschichte und Theorie der Erkenntniss (Leipzig: Wilhelm Engelmann, 1872), pp. 75–162. For a contemporary review of theories of comets, including Zöllner’s, see W. Zenker, “Ueber die physikalischen Verhältnisse und die Entwickelung der Cometen,” Astro. Nach. 79 (1872), columns 273–326.

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  17. K.F. Zöllner, “Ueber die physische Beschaffenheit der Cometen,” Astro. Nach. 86 (1875), columns 257–306; ibid. 87 (1876), columns 273–340. W. Zenker, “Ueber einige Punkte der von mir aufgestellten Cometen-Theorie,” ibid. 84 (1874), columns 103–112.

  18. On Zöllner’s and Bredikhin’s contributions to cometary science, see Tofigh Heidarzadeh, A History of Physical Theories of Comets, From Aristotle to Whipple (New York: Springer, 2008), pp. 225–228. On Bredikhin, see A.M. Finkelstein and Yu.D. Medvedev, “The First Russian Astrophysicist,” Herald of the Russian Academy of Sciences 76 (2006), 571–576.

  19. On Weber’s electrodynamics, see Christa Jungnickel and Russell McCormmach, Intellectual Mastery of Nature. Theoretical Physics from Ohm to Einstein. Vol. 1. The Torch of Mathematics 18001870 (Chicago and London: The University of Chicago Press, 1986), pp. 139–152, and Olivier Darrigol, Electrodynamics from Ampère to Einstein (Oxford: Oxford University Press, 2000), pp. 54–76.

  20. A.K.T. Assis, “On the first electromagnetic measurement of the velocity of light by W. Weber and R. Kohlrausch,” in Fabio Bevilacqua and Enrico Antonio Gianetto, ed., Volta and the History of Electricity (Milan: Hoepli, 2003), pp. 267–286, which includes an English translation of the Weber-Kohlrausch paper.

  21. L. Rosenfeld, “The Velocity of Light and the Evolution of Electrodynamics,” Nuovo Cimento, Supplemento 4 (1956), 1630–1669, esp. 1644–1667; reprinted in Selected Papers of Léon Rosenfeld, edited by Robert S. Cohen and John J. Stachel (Dordrecht, Boston, London: D. Reidel, 1979), pp. 134–177, esp. pp. 148–174.

  22. Zöllner, Natur der Cometen (ref. 16), p. lii. Ferdinand Rosenberger, Die Geschichte der Physik. Vol. III. Geschichte der Physik in den letzten hundert Jahren (Braunschweig: Vieweg und Sohn, 1890; reprinted Hildesheim: Georg Ohms Verlagsbuchhandlung, 1965), pp. 582–584.

  23. Zöllner, Natur der Cometen (ref. 16), p. 334. Zöllner elaborated his version of Weber’s theory in later publications: F. Zöllner, “Über die physikalischen Beziehungen zwischen hydrodynamischen und elektrodynamischen Erscheinungen,” Ann. Phys. u. Chem. 158 (1876), 497–539; Johann Carl Friedrich Zöllner, Principien einer elektrodynamischen Theorie der Materie. Erster Band. I. Buch (Leipzig: Wilhelm Engelmann, 1876); Friedrich Zöllner, Erklärung der universellen Gravitation aus den statischen Wirkungen der Elektrizität und die allgemeine Bedeutung des Weberschen Gesetzes (Leipzig: L. Staackmann, 1882).

  24. H.-J. Treder, “Eddingtons Zahlen, Einstein’s Kriterium und Rydbergs rationelles Dimensionssystem,” Astro. Nach. 302 (1981), 115–125.

  25. O.F. Mossotti, Sur les Forces qui Régissent la Constitution intérieure des Corps, etc. (Turin: De l’Imprémerie Royale, 1836). Zöllner included a complete reprint of Mossotti’s work in his Erklärung der universellen Gravitation (ref. 23), pp. 83–112.

  26. H.A. Lorentz, “Beschouwingen over de zwaartekrach,” Koninklijke Akademie van Wetenschappen te Amsterdam Verslag van de gewone Vergaderingen der Wis- en Naturkundige Afdeeling 8 (1900), 603–620, on 612; trans. as “Considérations sur la pesanteur,” Archives Néerlandaises des Sciences Exactes et Naturelles 7 (1902), 325–342, on 333; reprinted in Collected Papers. Vol. 5 (The Hague: M. Nijhoff, 1937), pp. 198–215, on p. 207.

  27. Zöllner, Natur der Cometen (ref. 16), p. 334. W. Scheibner, “Ueber die formale Bedeutung des Hamiltonschen Princips und das Weber’sche Gesetz,” Ber. Verhand. k. Säch. Gesell. Wissen. Leipzig, Math.-Phys. Classe 49 (1897), 578–601. Several other physicists and astronomers applied similar reasoning in attempts to explain the Mercury anomaly. See N.T. Roseveare, Mercury’s perihelion. From Le Verrier to Einstein (Oxford: Clarendon Press, 1982), pp. 121–129.

  28. Aspects of the Zöllner scandal are covered in Meinel, Karl Friedrich Zöllner (ref. 1), pp. 17–35; Robin Small, “Nietzsche, Zöllner, and the Fourth Dimension,” Archiv für Geschichte der Philosophie 76 (1994), 278–301; and David Cahan, “Anti-Helmholtz, Anti-Zöllner, Anti-Dühring: The Freedom of Science in Germany during the 1870s,” in Lorenz Krüger, ed., Universalgenie Helmholtz: Rückblick nach 100 Jahren (Berlin: Akademie Verlag, 1994), pp. 330–344, esp. pp. 331–336.

  29. Clausius to Tyndall, April 4, 1872, quoted in Cahan, “Anti-Helmholtz” (ref. 28), p. 334. Clausius and Zöllner later became involved in a dispute concerning Weber’s electrodynamics; see R. Clausius, “Erwiderung auf die von Zöllner gegen meine elektrodynamischen Betrachtungen erhobenen Einwände,” Ann. Phys. u. Chem. 2 (1877), 118–130.

  30. [H. von Helmholtz,] “Helmholtz on the Use and Abuse of the Deductive Method in Physical Science,” Nature 11 (1875), 211–212, on 212. This was a translation of Helmholtz’s preface made by the English chemist Alexander Crum Brown. Tait offered his low opinion of Zöllner in P.G. Tait, “Zöllner’s Scientific Papers,” Nature 17 (1878), 420–422. On the Zöllner-Helmholtz dispute, see Jed Z. Buchwald, “Electrodynamics in Context: Object States, Laboratory Practice, and Anti-Romanticism,” in David Cahan, ed., Hermann von Helmholtz and the Foundations of Nineteenth-Century Science (Berkeley, Los Angeles, London: University of California Press, 1993), pp. 334–373.

  31. Zöllner, “Ueber die Endlichkeit der Materie im unendlichen Raume,” in Natur der Cometen (ref. 16), pp. 299–312.

  32. The history of the paradox named after Heinrich Wilhelm Olbers is detailed in Jaki, The Paradox of Olbers’ Paradox (ref. 3), and Edward Harrison, Darkness at Night: A Riddle of the Universe (Cambridge, Mass.: Harvard University Press, 1987). Harrison refers to Zöllner’s solution of Olbers’ paradox on p. 173, but mistakenly dates it to 1883.

  33. Nikolai Ivanovich Lobachevsky, “Neue Anfangsgründe der Geometrie mit einer vollstãndigen Theorie der Parallellinien,” in Nikolaj Iwanowitsch Lobatschefskij: Zwei geometrische Abhandlungen, trans. by Friedrich Engel (Leipzig: B.G. Teubner, 1898), pp. 67–235; Jeremy Gray, Worlds Out of Nothing: A Course in the History of Geometry in the 19th Century (London: Springer-Verlag, 2007), pp. 113–122.

  34. Zöllner, Natur der Cometen (ref. 16), p. 312.

  35. Bernhard Riemann, “On the Hypotheses which Lie at the Bases of Geometry,” Nature 8 (1873), 14–17, 36–37, on 36.

  36. Zöllner, Natur der Cometen (ref. 16), p. 308.

  37. Richard A. Proctor, The Universe of Suns: Presenting Researches into and New Views respecting the Constitution of the Heavens (London: Longmans, Green & Co., 1878), as quoted in Jaki, The Paradox of Olbers’ Paradox (ref. 3), p. 183. See also Helge S. Kragh, Entropic Creation: Religious Contexts of Thermodynamics and Cosmology (Aldershot: Ashgate, 2008), pp. 109–110.

  38. Zöllner, Natur der Cometen (ref. 16), pp. 304–305.

  39. For a discussion of these ideas, see Kragh, Entropic Creation (ref. 37). pp. 23–46.

  40. Zöllner, Natur der Cometen (ref. 16), pp. 308–309.

  41. R. Clausius, “On the Second Fundamental Theorem of the Mechanical Theory of Heat,” Phil. Mag. 35 (1868), 405–419, on 417. For ideas of a cyclic universe ca. 1850–1920 and references to the literature, see Kragh, Entropic Creation (ref. 37), pp. 103–191.

  42. Zöllner, Natur der Cometen (ref. 16), p. 311. As early as 1848, John Herschel had considered the same objection, but without drawing the conclusion that the universe must be finite; see Jaki, The Paradox of Olbers’ Paradox (ref. 3), pp. 147–149.

  43. Zöllner, Natur der Cometen (ref. 16), pp. 339–341, on p. 339. See also H. Leihkauf, “K.F. Zöllner und der physikalische Raum,” NTM 20 (1983), 29–33.

  44. Fiedler to Zöllner, February 14, 1878, in Koerber, Karl Friedrich Zöllner (ref. 1), pp. 85–87, on p. 87.

  45. W.K. Clifford, “On the Space-Theory of Matter,” Proceedings of the Cambridge Philosophical Society 2 (1876), 157–158. Clifford’s vision of a geometrization of physics is analyzed by Ruth Farwell and Christopher Knee, “The End of the Absolute: A Nineteenth-Century Contribution to General Relativity,” Studies in History and Philosophy of Science 21 (1990), 91–121.

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  47. J. Lense, “Das Newtonsche Gesetz in nichteuklidischen Räumen,” Astro. Nach. 205 (1917), columns 241–248.

  48. Robert K. DeKosky, “William Crookes and the Fourth State of Matter,” Isis 67 (1976), 36–60. On Crookes’ and other Victorian scientists’ interest in spiritualism, see Janet Oppenheim, The other world: Spiritualism and psychical research in England, 18501914 (Cambridge: Cambridge University Press, 1985), and William H. Brock, William Crookes (18321919) and the Commercialization of Science (Aldershot: Ashgate, 2008).

  49. J.C. Friedrich Zöllner, “On Space of Four Dimensions,” The Quarterly Journal of Science 8 (1878), 227–237. Corinna Treitel, A Science for the Soul: Occultism and the Genesis of the German Modern (Baltimore and London: The Johns Hopkins University Press, 2004), pp. 3–7; Klaus B. Staubermann, “Tying the knot: skill, judgement and authority in the 1870s Leipzig spiritistic experiments,” British Journal for the History of Science 34 (2001), 67–79.

  50. Michael Heidelberger, Nature from Within: Gustav Theodor Fechner and His Psychophysical Worldview. Translated by Cynthia Klohr (Pittsburgh: University of Pittsburgh Press, 2004), p. 68. Hans G. Fellner and William F. Lindgren, “Gustav Theodor Fechner: Pioneer of the Fourth Dimension,” The Mathematical Intelligencer 33 (2011), 126–137.

  51. Friedrich Zöllner, Die Transcendentale Physik und die sogenannte Philosophie. Eine Deutsche Antwort auf einesogenannte wissenschaftliche Frage,” Wissenschaftliche Abhandlungen. III. Band (Leipzig: L. Staackmann, 1879).

  52. Johann Carl Friedrich Zöllner, Transcendental Physics: An Account of Experimental Investigations from the Scientific Treatises. Translated from the German, with a Preface and Appendices, by Charles Carleton Massey (Boston: Colby & Rich, 1881).

  53. Ibid., p. 37. Wayne H. Stromberg, “Helmholtz and Zoellner: Nineteenth-Century Empiricism, Spiritism, and the Theory of Space Perception,” Journal of the History of the Behavioral Sciences 25 (1989), 371–383.

  54. Zöllner, Transcendental Physics (ref. 52), p. 95. Moritz Wirth, Herrn Professor Zöllners Experimente mit dem amerikanischen Medium Herrn Slade und seine Hypothese intelligenter vierdimensionaler Wesen (Leipzig: Oswald Mutze, 1882).

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  56. Farwell and Knee, “The End of the Absolute” (ref. 45), p. 112.

  57. Zöllner, Principien einer elektrodynamischen Theorie (ref. 23), p. lxxix.

  58. Ibid.

  59. Wilhelm Meyer, Kraft und Stoff im Universum und die Ziele der astronomischen Wissenschaft (Basel: Schweighauserische Verlagsbuchhandlung, 1878), p. 11.

  60. A.E. Haas, “Ist die Welt in Raum und Zeit unendlich?” Archiv für systematische Philosophie 18 (1912), 167–184, esp. 172.

  61. Small, “Nietzsche, Zöllner, and the Fourth Dimension,” (ref. 28). Alistair Moles, “Nietzsche’s Eternal Recurrence as Riemannian Cosmology,” International Studies in Philosophy 21 (1989), 21–35, on 22.

  62. E. Budde, Zur Kosmologie der Gegenwart. Bemerkungen zu J.C.F. Zöllner’s Buch Ueber die Natur der Kometen (Bonn: Eduard Weber’s Buchhandlung, 1872), p. 16.

  63. Hans Vaihinger, “Der gegenwärtige Stand des kosmologischen Problemes,” Philosophische Monatshefte 11 (1875), 193–219, on 216.

  64. W. Wundt, “Ueber das kosmologische Problem,” Vierteljahrschrift für wissenschaftliche Philosophie 1 (1875), 80–136, on 81.

  65. Ibid., p. 115.

  66. Ibid., p. 119.

  67. K. Lasswitz, “Ein Beitrag zum kosmologischen Problem und zur Feststellung des Unendlichkeitsbegriffes,” ibid. 1 (1877), 329–360, followed by Wundt’s reply, “Einige Bemerkungen zu vorstehender Abhandlung,” ibid., 361–365. Zöllner did not respond to either Budde, Vaihinger, Wundt, or Lasswitz.

  68. Kragh, Entropic Creation (ref. 37), pp. 118–127. Helge Kragh, “Pierre Duhem, Entropy, and Christian Faith,” Physics in Perspective 10 (2008), 379–395.

  69. P. Angelo Secchi, Die Sterne. Grundzüge der Astronomie der Fixsterne (Leipzig: F.A. Brockhaus, 1878), p. 331.

  70. Constantin Gutberlet, Die neue Raumtheorie (Mainz: Franz Kirchheim, 1882), pp. 50–67; Konstantin Gutberlet, Der Cosmos. Sein Ursprung und seine Entwickelung (Paderborn: Ferdinand Schöningh, 1908), p. 54.

  71. Koerber, Karl Friedrich Zöllner (ref. 1). Herrmann, Karl Friedrich Zöllner (ref. 1), p. 52, briefly discusses “Zöllner’s cosmos.”

  72. For example, it was not listed in Royal Society’s exhaustive Catalogue of Scientific Papers 18001900 (Cambridge: Cambridge University Press, 1909–1912) and also not in George Bruce Halsted, “Bibliography of Hyper-Space and Non-Euclidean Geometry,” American Journal of Mathematics 1 (1878), 261–276. However, Zöllner’s essay was included in Duncan McL.Y. Sommerville, Bibliography of Non-Euclidean Geometry Including the Theory of Parallels, the Foundations of Geometry and the Space of n Dimensions (London: Harrison and Sons, 1911).

  73. Die Fortschritte der Physik im Jahre 1872 28 (1877), 945–962.

  74. S. Newcomb, Popular Astronomy (New York: Harper & Brothers, 1878), p. 505.

  75. For these and other contributions, see Kragh, “Geometry and Astronomy” (ref. 3), esp. pp. 36–61.

  76. Otto Struve and Velta Zebergs, Astronomy of the 20th Century (New York and London: Macmillan, 1962), pp. 362–367.

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I thank Roger H. Stuewer for carefully editing my article, improving its references, and suggesting new figures.

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Correspondence to Helge Kragh.

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Helge Kragh is Professor of History of Science at the Centre for Science Studies, Aarhus University, Aarhus, Denmark. His main research interests are in post-1850 developments in physics, chemistry, and cosmology.

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Kragh, H. Zöllner’s Universe. Phys. Perspect. 14, 392–420 (2012). https://doi.org/10.1007/s00016-012-0099-4

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