Abstract
With this discussion of research published in the Annalen der Physik we approach the close of J. C. Poggendorff’s long editorship. By 1874, his fiftieth anniversary, he had brought out 150 volumes. Poggendorff’s Annalen, the customary form of its citation, had become synonymous with German physics. Inevitably, work by German authors came to occupy more space in the Annalen and work by foreign authors less. Inevitably too, it would seem, work came to be increasingly physical, as work in chemistry, especially in organic chemistry, was channeled to other specialized journals. Even as the work submitted to the journal was restricted, it increased in quantity, and Poggendorff took to bringing out supplementary volumes from time to time. Toward the end of his editorship, he began a regular series, the Beiblätter, for brief reports of recent work not appearing in the Annalen. What was new in the Annalen in 1869–1871 was the extent to which German physicists now drew on German sources of theoretical work, especially Clausius’s, Kirchhoff’s, and Helmholtz’s.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsNotes
- 1.
The volumes Poggendorff brought out over these many years included nearly nine thousand papers and notices by over two thousand authors. Each year he published works by about thirty new authors. The numerical measure of his achievement was given in the Jubelband for Poggendorff’s fiftieth anniversary by W. Baretin, “Ein Rückblick,” Ann. (1874): ix–xiv, on xii–xiii. We again make the Annalen the principal source of our survey.
- 2.
W. Baretin, “Johann Christian Poggendorff,” Ann. 160 (1877): v–xxiv, on xi.
- 3.
The physicist J. F. Benzenberg reported that on his trip to Paris in 1815, he found that L. W. Gilbert’s Annalen was not to be had at the Institut’s library and that although it was at the Royal Library, its pages were uncut. In his Ueber die Daltonsche Theorie (Düsseldorf, 1830), preface.
- 4.
Baretin, “Poggendorff,” xii. Poggendorff’s successor, Gustav Wiedemann, spoke of theory and experiment having been joined in the Annalen. Wiedemann, “Vorwort,” Ann. 39 (1890): i–iv.
- 5.
Emil Frommel, Johann Christian Poggendorff (Berlin, 1877), 67.
- 6.
The total number of papers in the Annalen from each of those countries follows in that order: Austria-Hungary, Switzerland, and Holland.
- 7.
For part of 1869–1871, Kundt and Friedrich Kohlrausch were in Zurich, accounting for a good share of the substantial contribution from Switzerland to the Annalen.
- 8.
The other countries represented in the Annalen were Britain, Denmark, Sweden, (Western) Russia, France, Italy, and Belgium. Of physics published in the New World and elsewhere, Poggendorff took no notice in 1869–1871. In one of these years he published a series of brief papers sent to him from Argentina by a young, world-traveling physicist from Berlin, who was an assistant to Magnus.
- 9.
In order of the number of pages they published in the Annalen in 1869–1871, the nineteen institute directors were: Wilhelm von Bezold (Munich), Adolph Wüllner (Bonn and Aachen), Wilhelm Hittorf (Münster), Eugen Lommel (Erlangen), O. E. Meyer (Breslau), Gustav Magnus (Berlin), Rudolph Clausius (Würzburg and Bonn), August Kundt (Würzburg), J. B. Listing (Göttingen), Eduard Reusch (Tübingen), Wilhelm Beetz (Munich), Heinrich Buff (Giessen), Johann Müller (Freiburg), Hermann Knoblauch (Halle), Heinrich Weber (Braunschweig), Gustav Kirchhoff (Heidelberg), Franz Melde (Marburg), Heinrich Wilhelm Dove (Berlin), and Wilhelm Weber (Göttingen). Dove, who was ordinary professor of physics at Berlin and director of the Prussian state meteorological institute, is included in this list because he took charge temporarily of the Berlin University physics institute for a year after Magnus’s death in 1870. University institute directors who did not publish in the Annalen in 1869–1871 were: Ottokar von Freilitzsch (Greifswald), Karl Snell (Jena), Gustav Karsten (Kiel), Franz Neumann (Königsberg), Wilhelm Hankel (Leipzig), and Philipp Jolly (Munich); Rostock University did not have a physics professor. With the exception of Hankel, they published either no articles in any physics journals or at most an occasional article elsewhere. Hankel published thermoelectric studies of crystals regularly in the Abhandlungen of the Saxon Society of Sciences; from 1876, he republished this material in the Annalen.
- 10.
The Annalen authors who were not institute directors were mostly recent graduates, and their theoretical competence expressed the current understanding of what a properly trained physicist should know. For physicists just beginning about 1870, theoretical physics would provide increasing opportunities, and through their teaching or research or both, most of them would be closely associated with theoretical physics in their subsequent careers. Of the three extraordinary professors of physics publishing in the Annalen in 1869–1871—Friedrich Kohlrausch, Georg Quincke, and Karl Zöppritz—the latter two taught mathematical physics in their academic positions at that time. Of the—at least—eight Privatdocenten who published in the Annalen in these years, most had close connections with theory. Wilhelm Feussner was at Marburg, where he would teach theoretical physics for 50 years, from 1880 as extraordinary professor and from 1908 as ordinary honorary professor. Friedrich Narr was at Munich, where he would teach the subject, from 1886 as extraordinary professor, to the end of his career. Eduard Ketteler was at Bonn, where as extraordinary professor he would teach the subject from 1872 to 1889, nearly the end of his career. Leonhard Sohncke at Königsberg and Emil Warburg at Berlin would both teach theoretical physics (Warburg as extraordinary professor for the subject), and although their teaching responsibility would be experimental physics over most of their careers, they were associated with theoretical physics in their research: Sohncke as a developer of Franz Neumann’s direction in theoretical crystal physics, and Warburg as one of the most theoretically capable German experimental physicists. Hermann Herwig had only a brief academic career (he died in his thirties, while professor of physics at Darmstadt); his dissertation at Göttingen had been on mathematics, and his subsequent work in experimental physics showed theoretical interest. Richard Rühlmann did not continue in an academic career but became a gymnasium teacher of physics and mathematics. Emil Budde did not continue either, but he managed to do research all the same, much of which, like his first paper in the Annalen in 1870, was purely theoretical. Of the—at least—six students or assistants who published in the Annalen in 1869–1871, only two had academic careers. Paul Glan, a Berlin graduate in 1870 and after that an assistant to Helmholtz, went on to teach theoretical physics at Berlin as Privatdocent from 1875 to the end of his life. Eduard Riecke, a Göttingen graduate in 1871, became assistant and Privatdocent the same year; then and during appointments as extraordinary professor in 1873 and ordinary professor of experimental physics in 1881, he regularly gave lectures on theoretical physics until Woldemar Voigt was brought to Göttingen. His research was primarily theoretical throughout his career.
- 11.
Poggendorff’s and Riess’s publications in the Annalen compare in volume with those of the two most prolific institute directors, Bezold and Wüllner.
- 12.
Papers by chemistry teachers took up one fifth as much space in the Annalen as those by physics teachers, and papers by teachers of crystallography, mineralogy, and geology together took up one third as much space. Physiologists were well represented; less well represented were astrophysicists, mathematicians, physicians, and pharmacists. All told, the contributions to the Annalen from teachers outside of physics took up two thirds as much space as contributions from teachers within physics.
- 13.
Despite the recognized connections of mathematics and physics, only two academic mathematicians published in the Annalen in 1869–1871, and they published only one article each on mechanics, a topic that belonged as much to mathematics as to physics. Mathematicians had their own journals and did not need the Annalen, the journal that physicists increasingly regarded as their own.
- 14.
Overzier, vol. 139, 651–60, on 660. Because we refer to a large number of papers published in the Annalen, in the remainder of this chapter we use this highly abbreviated form of citation: author’s last name, volume number, page numbers. The journal, unless otherwise specified, is always the Annalen, and the volumes all fall within the 3 years, 1869–1871.
- 15.
Hittorf, vol. 136, 1–31, 197–234, on 223.
- 16.
Lommel, vol. 143, 26–51, 568–85, on 30–34.
- 17.
For example, Kundt on the variation of the index of refraction with wavelength (vol. 142,163–71), and O. E. Meyer on the variation of the constant of the internal friction of air with temperature and, possibly, with pressure (vol. 143, 14–26). Kirchhoff studied theoretically the variation of the constant of the magnetization of iron with the intensity of the magnetizing force (supplementary vol. 5, 1–15).
- 18.
For example, Bezold on “electric dust figures” (vol. 140, 145–59) and on “Lichtenberg figures” (vol. 144, 337–63, 526–50), and Melde and Kundt on “sound figures” (Melde, vol. 139, 485–93; Kundt, vol. 137, 456–70, vol. 140, 297–305).
- 19.
For example, Magnus on radiant heat (vol. 139, 431–57, 582–93), Kundt on anomalous dispersion (vol. 142, 163–71), and Lommel on the relation of chlorophyll to light (vol. 143, 568–85).
- 20.
For example, the phenomena of galvanic arcs, fluorescence, and induced magnetism by, respectively, Bezold (vol. 140, 552–60), Lommel (vol. 143, 26–51), and Kirchhoff (supplementary vol. 5, 1–15).
- 21.
Wilhelm Weber called attention to a property of his fundamental law of electric action (vol. 136, 485–89), Bezold to analogies between the laws of photometry and the laws of gravitational attraction (vol. 141, 91–94), and Clausius to the mechanical principles underlying the second fundamental law of heat theory (vol. 142, 433–61).
- 22.
Clausius, vol. 141, 124–30; vol. 142, 433–61.
- 23.
Clausius’s work led Ludwig Boltzmann to publish a priority claim in the Annalen (vol. 143, 211–30). This was one of many papers by Boltzmann in the Annalen in these years, all in response to papers by others published there. He worked in Austria and published most of his researches there. The Stettin secondary school teacher Robert Most provoked Boltzmann by his “simple proof” of the second law of heat theory, which he regarded as “simpler” than the first law (vol. 136, 140–43). Boltzmann pointed out that Most assumed at the start that dQ/T is a complete differential, so it was “naturally not hard” for him to prove the second law (vol. 137, 495). What Most regarded as clear about his proof Boltzmann regarded as simply wrong (vol. 140, 635–44).
- 24.
As, for example, Bezold did in connection with his study of electrical condensers (vol. 137, 223–47. Clausius responded (vol. 139, 276–81).
- 25.
Johann Müller, vol. 144, 333–34.
- 26.
Hoh, vol. 138, 496.
- 27.
Oppel, vol. 144, 307–9.
- 28.
Poggendorff, vol. 139, 510–11.
- 29.
Friedrich Kohlrausch, vol. 136, 618–25, on 625; Poggendorff, vol. 141, 161–205, on 203; Johann Müller, vol. 136, 154–56.
- 30.
Wüllner, vol. 137, 337–61, on 347–48.
- 31.
Buff, vol. 137, 497–517, on 497.
- 32.
Magnus was criticized for making a statement that had no empirical basis but was simply a generalization from the theory of gases. Knoblauch, vol. 139, 150–57, on 152–53.
- 33.
For example, the theory of a vibrating string based on the analysis of a volume element of the string rather than on molecular forces (Reinhold Hoppe, vol. 140, 263–71); and the theory of induced magnetism based on the analysis of volume and surface elements of the magnetized body (Kirchhoff, supplementary vol. 5, 1–15).
- 34.
Drawing on Gauss’s method, J. Stahl had recently derived the fundamental equations of capillarity. According to Boltzmann, Stahl’s derivation shared the defect of Gauss’s method, which is to compute finite sums by integrating over all pairs of molecules. This procedure assumes that each molecule contributes a vanishingly small part of the sum, regardless of how far it is from any given molecules. Since it is likely that the contribution of a neighboring molecule is finite, Boltzmann reasoned, the use of the integral calculus is not justified here, and he showed how to develop capillary theory using only finite sums and replacing the integration symbol ∫ by the symbol Σ (vol. 141, 582–90).
- 35.
Lommel explained that he was using “molecule” in the “chemical sense”: a group of atoms characterized by their nature, number, and relative positions (vol. 143, 568–85, on 573); Budde proceeded from the understanding that the “molecule” of most simple gases consists of two atoms (vol. 144, 213–19).
- 36.
As set out by Gustav Hansemann (vol. 144, 82–108).
- 37.
Jochmann attributed the departure of Cauchy’s reflection theory from observations on reflection and refraction in thin metal sheets to “molecular” properties of the metal surface, which affect the optical constants (supplementary vol. 5, 620–35, on 632–33).
- 38.
For example, in a theoretical investigation of the “internal constitution of gases” (Hansemann, vol. 144, 82–108).
- 39.
Heinrich Schröder went on to say that it was premature to explain the action of a gas on solids or liquids by molecular motions, so that for now he had to renounce the highest task of physics (supplementary vol. 5, 87–115, on 114–15).
- 40.
Paul du Bois-Reymond, vol. 139, 262–75, on 267.
- 41.
Lüdtge, vol. 139, 620–28, on 620.
- 42.
Ketteler, vol. 140, 1–53, 177–219, on 200; Lommel, vol. 143, 26–51; Sellmeyer, vol. 143, 272–82; Glan, vol. 141, 58–83.
- 43.
Hansemann, vol. 144, 82–108; Recknagel, supplementary vol. 5, 563–91; Narr, vol. 142, 123–58.
- 44.
Clausius’s central concept of disgregation was related to molecular arrangements (Budde, vol. 141, 426–32).
- 45.
Faraday’s concept of charge as a peculiar molecular position was introduced (Knochenhauer, vol. 138, 11–26, 214–30).
- 46.
Quincke determined that for glass, silver, water, and several other substances, the radius of action of molecular forces is a very small but non-vanishing length, of the order of 0.000050 mm, or approximately one-tenth the average wavelength of light (vol. 137, 402–14, on 413); Robert Lüdtge accepted this result (vol. 139, 620–28, on 620).
- 47.
Boltzmann and Toepler determined that the width of an air particle’s vibration at the limits of hearing is about one-tenth of the wavelength of green light, showing how astonishingly sensitive the organ of hearing is (vol. 141, 321–52, on 349–52).
- 48.
Listing, vol. 136, 467–72.
- 49.
Ibid., 473–79.
- 50.
Schneebeli explained that although the laws of collision had been known since the seventeenth century, the actual process of collision remained “rather mystical” owing to the short duration of collisions. With a new method, he determined the time of collision of steel cylinders and spheres; for a cylinder colliding with a fixed bar, the time was 0.00019 s (vol. 143, 239–50).
- 51.
From Britain, William Huggins reported to the Annalen his attempt to determine the very small amount of heat the earth receives from individual stars, using an apparatus consisting of a sensitive galvanometer and various thermopiles (vol. 138, 45–48).
- 52.
From Graz, Boltzmann and August Toepler sent the Annalen an experimental investigation of sound vibrations using a new optical stroboscopic method. They determined the mechanical work per second done by the air on the ear at the limits of hearing to be 1/3,000,000,000 kilogram-meter (vol. 141, 321–52, on 352).
- 53.
Wilhelm Weber’s law (vol. 136, 485–89). Examples of theories developed in terms of potentials are Bezold’s in electricity (vol. 137, 223–47) and photometry (vol. 141, 91–94) and Kirchhoff’s in magnetism (supplementary vol. 5, 1–15).
- 54.
For example, Clausius, vol. 142, 433–61, on 449; Boltzmann, vol. 143, 211–30, on 220, 228.
- 55.
In Cauchy’s theories of reflection (Jochmann, vol. 136, 561–88) and of dispersion (Ketteler, vol. 140, 1–53, 177–219); in Fresnel’s formulas for reflection for light intensity (Kurz, vol. 141, 312–17), and his hypothesis of ether drag (Ketteler, vol. 144, 109–27, 287–300, 363–75, 550–63).
- 56.
In Poisson’s theories of acoustics (Kundt, vol. 137, 456–70), of capillarity (Quincke, vol. 139, 1–89; J. Stahl, vol. 139, 239–61), of elasticity (Heinrich Schneebeli, who was Kundt’s student in Switzerland, vol. 140, 598–621), of pendulum motion (O. E. Meyer, vol. 142, 481–524), of magnetism (Kirchhoff, supplementary vol. 5, 1–15), of Earth temperature (Fröhlich, vol. 140, 647–52), and (if the Journal für die reine und angewandte Mathematik is included here) of heat (Lorberg, vol. 71, 53–90) and of hydrodynamics (O. E. Meyer, vol. 73, 31–68).
- 57.
For Laplace’s theory of capillarity (J. Stahl, vol. 139, 239–61; Quincke, vol. 139, 1–89), but also for his electrodynamics (Hittorf, vol. 136, 1–31, 197–234).
- 58.
Young’s theory of capillarity (Quincke, vol. 139, 1–89; Paul du Bois-Reymond, vol. 139, 262–75), Faraday’s theory of charges (Knochenhauer, vol. 138, 11–26, 214–30), Stokes’s theory of frictional fluids (Warburg, vol. 139, 89–104; vol. 140, 367–79), Green’s and Stokes’s theories of pendulum motion (O. E. Meyer, vol. 142, 481–524), and Maxwell’s theories of colors (J. J. Müller, vol. 139, 411–31, 593–613) and electromagnetism (Kirchhoff, supplementary vol. 5, 1–15).
- 59.
Paul du Bois-Reymond, vol. 139, 262–75; J. Stahl, vol. 139, 239–61; Boltzmann, vol. 141, 582–90.
- 60.
Wilhelm Weber’s work on waves (Quincke, vol. 139, 1–89; Kundt, vol. 140, 297–305; Matthiessen, vol. 141, 375–93), on sound (Warburg, vol. 136, 89–102; vol. 137, 632–40; vol. 139, 89–104; J. J. Müller, vol. 140, 305–8), and on electrodynamics (Wilhelm Weber, vol. 136, 485–89, calling attention to a publication of his in the Annalen on electrodynamics over 20 years before).
- 61.
Franz Neumann’s theoretical work entered German physics in oblique ways in 1869–1871. He had long before stopped publishing, but his work was used and cited even in cases where he had not published it himself. August Kurz cited an actual, if old, publication of 1834 on crystallography (vol. 141, 312–17), but Emil Jochmann found Neumann’s formula for metallic reflection in a Swiss publication by Heinrich Wild, who had studied for a while with Neumann, and in an abstract. Jochmann thought that no derivation or statement of the suppositions of Neumann’s formula had been published, and he assumed that they rested on the supposition of Neumann’s other optical work, which is that the ether has the same density but different elasticity in different media (vol. 136, 561–88). Quincke, who also had studied with Neumann, stated a capillary law governing the spread of one fluid over another, which he thought Neumann was the first to express (vol. 139, 1–89). Paul du Bois-Reymond, who had spent some time with Neumann, called this law the “third principal law of capillarity” and supposed that the only place it was published was in his own dissertation in 1859 (vol. 139, 262–75). Riecke tested Neumann’s law for the magnetism of an ellipsoid but gave no reference to any publication on it by Neumann (vol. 141, 453–56).
- 62.
On Kirchhoff’s work in acoustics (Seebeck, vol. 139, 104–32), in heat (Wüllner, vol. 137, 337–61; Magnus, vol. 139, 431–57, 582–93; Lommel, vol. 143, 26–51), in hydrodynamics (Paul du Bois-Reymond, vol. 139, 262–75), in elasticity (Adolf Seebeck, vol. 139, 104–32; Schneebeli, vol. 140, 598–621), and in electricity (Knochenhauer, supplementary vol. 5, 146–66).
- 63.
Budde, vol. 141, 426–32; vol. 144, 213–19; Narr, vol. 142, 123–58; Hansemann, vol. 144, 82–108; Bezold, vol. 137, 223–47; Recknagel, supplementary vol. 5, 563–91.
- 64.
Clausius, vol. 141, 124–30; vol. 142, 433–61.
- 65.
For example, Riemann’s work in electricity (Bezold, vol. 137, 223–47) and in geometry (J. J. Müller, vol. 139, 411–31, 593–613), Krönig’s in kinetic theory (Hansemann, vol. 144, 82–108; Recknagel, supplementary vol. 5, 563–91) and Carl Neumann’s in optics (Ketteler, vol. 140, 1–53, 177–219) and in electrodynamics (Wilhelm Weber, vol. 136, 485–89). If the Journal für die reine und angewandte Mathematik is included here, Jochmann’s and Lorberg’s recent work in electrodynamics enters (Helmholtz, vol. 72, 57–129).
- 66.
On Helmholtz’s work in acoustics (Warburg, vol. 139, 89–104; Adolf Seebeck, vol. 139, 104–32; Sondhauss, vol. 140, 53–76, 219–41; Glan, vol. 141, 58–83; Lommel, vol. 143, 26–51; Boltzmann and Toepler, vol. 141, 321–52) in hydrodynamics (Warburg, vol. 140, 367–79; Paul du Bois-Reymond, vol. 139, 262–75), in color theory and in geometry (J. J Müller, vol. 139, 411–31, 593–613), and in galvanism (Bernstein, vol. 142. 54–88).
- 67.
Bezold, vol. 144, 337–63, 526–50, on 535.
- 68.
The full title of the Prussian Academy of Sciences’ proceedings is Monatsberichte der königlich preussischen Akademie der Wissenschaften zu Berlin.
- 69.
The full title of the Bavarian Academy’s proceedings is Sitzungsberichte der königlich bayerischen Akademie der Wissenschaften zu München.
- 70.
Bezold, vol. 138, 554–60.
- 71.
Pfaundler, vol. 144, 428–38.
- 72.
Carl Neumann published a number of brief notices in his new journal, the Mathematische Annalen, but only one substantial work in mathematical physics, which had to do with crystal optics (vol. 1, 325–58). Karl Von der Mühll published a mathematical physics paper there (vol. 2, 643–49), as did his Giessen colleague Alexander Brill (vol. 1, 225–52).
- 73.
Clausius and Bezold published brief notes in the Zeitschrift, and Lommel published an “elementary presentation” of some mathematical methods. Boltzmann published a paper on Ampère’s law that was unusual for its length and its experimental nature; but it was a republication of a paper in the Sitzungsber. Wiener Akad. the year before.
- 74.
Relaxing the restrictions that the body does not rotate around its axis and that its axis remains parallel to a fixed plane, Kirchhoff showed that the problem could still be solved, though this more general motion leads to elliptical integrals (Journal 71, 237–62).
- 75.
Kirchhoff, Journal 70, 289–98.
- 76.
Boltzmann relaxed Kirchhoff’s assumption of the circular cross section of the rings (Journal 73, 111–34). Lorberg relaxed Kirchhoff’s assumption that the electricity in the conductor is not acted on by outside forces (Journal 71, 53–90). Helmholtz’s general potential reduces to Neumann’s when one current is closed (Journal 72, 57–129).
- 77.
The ten-year index volumes of the Annalen show this. Half of the topics with entries taking up an entire column or more in the index are electrical, with light and heat far behind. This measure applies alike to the indices for the 10 years centering on 1860 and for the 10 years centering on 1870.
- 78.
Physicists still struggled with the question of whether in a light wave the oscillation of the ether is in the plane of polarization or normal to it. See Jochmann, vol. 136, 561–88.
- 79.
The Berlin secondary school teacher K. H. Schellbach showed his experiments to Quincke, Poggendorff, and Magnus; the latter evidently made them known to the young physicists working with him (vol. 139, 670–72).
- 80.
Kirchhoff, Ann., supplementary vol. 5, 1–15.
- 81.
Kirchhoff, Journal 71, 263–73. Kirchhoff studied two rings with infinitely small, circular cross sections placed in an infinite, frictionless, incompressible fluid. By using familiar assumptions about the motion of the fluid, he showed that the kinetic energy of the fluid has the same form as the potential of Ampère’s law for the electrodynamic interaction of two electrical currents. The rings exert “apparent,” or pressure, forces on one another that are the same as the forces that would act if electric currents were to flow through the rings.
- 82.
Boltzmann pointed out that Kirchhoff’s conclusion about the formal identity of apparent fluid forces and Ampèrian forces is not generally valid, and he devoted considerable discussion to the electrical side of the analogy (Journal 73: 111–34).
- 83.
Helmholtz, Journal 72, 57–129; repr. in Hermann von Helmholtz, Wissenschaftliche Abhandlungen (Leipzig, 1882–1895) vol. 1, 545–628, discussion on 556–58.
- 84.
Helmholtz, Wiss. Abh., vol. 1, 557.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2017 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Jungnickel, C., McCormmach, R. (2017). Physical Research in the Annalen and Other Journals Around 1870. In: The Second Physicist. Archimedes, vol 48. Springer, Cham. https://doi.org/10.1007/978-3-319-49565-1_10
Download citation
DOI: https://doi.org/10.1007/978-3-319-49565-1_10
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-49564-4
Online ISBN: 978-3-319-49565-1
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)