# Drude, Paul Karl Ludwig

# Drude, Paul Karl Ludwig

(*b*. Brunswick, Germany, 12 July 1863; *d*. Berlin, Germany, 5 July 1906)

*physics*.

Drude was the son of a medical doctor in Brunswick. He attended the local Gymnasium and then went on to study at the University of Göttingen. His original ambition was to become a mathematician, and he studied mathematics, first at Göttingen and then at Freiburg and Berlin. In his sixth semester he returned to Göttingen, where he came under the influence of W. Voigt and as a result began to study theoretical physics. Drude’s dissertation, under Voigt’s direction, was a purely theoretical treatment of the equations governing the reflection and refraction of light at the boundaries of absorbing crystals.

Drude worked with Voigt at Göttingen until 1894. He then moved to Leipzig where he pursued both theoretical and practical researches on the propagation of electromagnetic waves and wireless telegraphy, as well as continuing his work on physical optics. His interest in the physical determinants of optical constants led him toward an attempt to correlate and account for the optical, electrical, thermal, and chemical properties of substances. Drude’s interest in these problems was stimulated by his own growing conviction, based on studies begun in 1888, that Maxwell’s electromagnetic theory was superior to the older mechanical view of light. This conviction led him to publish *Physik des Äthers* (1894), one of the first German books to base explanations of electrical and optical effects on Maxwell’s theory. By 1898 Drude had begun to consider these matters within the structure of the theory of electrons; indeed, he thereby laid the foundation for understanding such phenomena as conduction in metals, thermal conductivity, and optical properties of metals as interactions of the electrical charges of substances with their environment.

In 1894 Drude married Emilie Regelsberger, the daughter of a Göttingen jurist. With the death of Wiedemann in 1889, he assumed the editorship of *Annalen der Physik*, the most prestigious of physics journals. In 1901, shortly after the publication of his *Lehrbuch der Optik*, Drude moved to Giessen where he became director of the Institute of Physics.

In Giessen, where he remained until 1905, Drude continued his work in optics and the electron theory. Having declined other appointments, it was only with some reluctance that he answered the call to Berlin to take over directorship of the physics institute. Almost immediately after Drude assumed this position, the size of the institute’s staff was enlarged by a third in order to meet the demands of the increase of both the theoretical and the practical work that he brought with him. He died suddenly and unexpectedly within a year of moving to Berlin.

Drude’s chief contributions fall into two categories: his early work in physical optics, in which he concentrated on the relationship between the physical properties and the optical characteristics of crystals, and his later work, in which he attempted to explain both physical and optical properties in a unified theory. In both phases theory and experiment were carefully interwoven; the transition in Drude’s orientation is closely correlated with his change from a mechanical to an electromagnetic view of optical phenomena.

Drude may be considered the intellectual descendant of Franz Neumann—the first of Germany’s great theoretical physicists, who developed a mechanical theory of light propagation based on the work of Fresnel and closely related to Fresnel’s own theory. It was a mechanical theory which assumed that light oscillations were of a mechanical-elastic nature, transmitted through an ether conceived of as an elastic solid. Neumann’s theory had its counterparts in England and France but was distinguished by the power and rigor of the mathematical analysis and by the assumption that the density of the ether is the same in all bodies. This leads to the conclusion that the displacement of ether particles in a plane polarized ray is in the plane of polarization. (The Fresnel theory assumed that the elasticity of the ether was the same in all bodies, leading to the conclusion that the displacement of ether particles is perpendicular to the plane of polarization.) Neumann was not only a theoretical physicist. At Königsberg he worked both in the physics department and the department of mineralogy. It was quite natural then that he should do extensive work on the optical properties of crystals. His laboratory was well equipped to investigate the structure of crystals and their elastic properties. Voigt, whose work continued that of Neumann, was particularly interested in magneto-and electro-optics. Drude’s dissertation was a direct offshoot of Voigt’s work. Voigt then set him the problem of checking his work in the laboratory, using crystals of bournonite. The experimental difficulties were great, and Drude almost immediately realized that the optical constants of such crystals were not independent of the state of the crystal’s surface. He discovered that the index of refraction and the coefficient of reflection of a crystal changed steadily from the time it was freshly cleaved. With characteristic care and thoroughness Drude then undertook a reexamination of the optical constants of a wide variety of absorbing substances, making measurements as difficult and exacting as those of the original experiments. When he was finished the optical constants of a wide variety of substances were known to an accuracy hitherto unthinkable.

This work occupied Drude from 1887 to 1891. During this period, too, he first became interested in Maxwell’s work in electrodynamics, stimulated by Hertz’s detection of electromagnetic radiation. Maxwell’s treatise of 1873 was translated into German in 1882; but Maxwell’s views were not widely accepted. The mechanical view of light propagation still held sway, and it had been under the influence of that theory that Drude had been working.

Drude did not become an immediate convert to the electromagnetic point of view. In 1888 he began an intensive four-year study, first immersing himself in the electromagnetic point of view, then reexamining the mechanical theory of light. He did not feel obliged to reject the mechanical theory which—although it presented some difficulty, especially in regard to the propagation of transverse waves through an elastic medium—had served so well.

Finally Drude took a phenomenological approach, attempting to remove nonessential elements from the mechanical formulation of optics. He argued that the differential equations and the imposed boundary conditions must be retained while assumptions about the mechanical nature of light waves and the elasticity of the ether were extraneous. He published the fruits of his investigation in a paper entitled “In wie weit genügen die bisherigen Lichttheorien den Anforderungen der praktischen Physik?” (1892). In this paper Drude pointed out that if the investigator restricted himself to differential equations and necessary boundary conditions, which he designated as the “explanation system” (*Erklärungssystem*), the mechanical and electromagnetic theories were equivalent. For example, to transform the mechanical view to the electromagnetic view, instead of such terms as “density,” “elasticity,” and “velocity of the ether,” one needed only to substitute “magnetic permeability,” “dielectric constant,” and “magnetic field strength.” Drude’s paper was much in the spirit of Hertz’s own assertions about Maxwell’s theory—that the Maxwell theory should be considered as Maxwell differential equations.

Drude gradually took up the electromagnetic view-point. In another paper of 1892, “Ueber magnetiooptische Erscheinungen,” he developed a system of equations directly from Maxwell’s equations to account for Kerr’s discovery that the reflectivity of magnetic substances (iron, cobalt, and nickel) is influenced by the state of magnetization and for Kundt’s observation that the plane of polarization of light is rotated in passing through thin plates of these substances. Although the ease with which Maxwell’s theory allowed such work to be done was important to Drude, he did not yet advocate one theory to the exclusion of the other. Rather, for another two years he lectured at Göttingen on the Maxwell theory; these lectures led to the publication of his first book, *Die Physik des Äthers* (1894). As a result of the heuristic effect that Maxwell’s theory had on his own work between 1894 and 1898, Drude became an advocate of the electromagnetic view.

With his move to Leipzig, Drude’s work on physical constants and his work on electromagnetic radiation began to merge into one set of coherent concerns. Drude had already hinted in some of his published work that by using the electromagnetic theory one might be able to explain electrical and optical properties of matter as the interaction of electromagnetic fields with electrical charges contained within the body. The publication of Lorentz’ electron theory between 1892 and 1895 undoubtedly spurred him in that direction.

Shortly after arriving at Leipzig in 1894, Drude undertook further investigations on the relationship between optical and electrical constants and the constitution of substances. Using seventy to eighty centimeters radiation, he measured coefficients of absorption in a wide variety of solutions and compared these to coefficients of conductivity for the same solutions. According to Maxwellian theory, a close correlation should have existed between electrical conductivity and absorption of light—the higher the conductivity, the greater should be the absorption. Drude found, however, that this was not always the case. For example, the absorption coefficients of amyl alcohol and copper salt solutions might be the same, whereas the conductivity of the copper salt solution might be thousands of times greater than the conductivity of the alcohol. By careful and controlled experimentation, Drude found that, in fact, a whole class of substances absorbed seventy-five centimeters electromagnetic radiation—quite independent of their coefficient of conductivity when it was measured by direct current methods. The same substances also exhibited a marked deviation from expected values of their dielectric constants and also exhibited anomalous dispersion. Drude was able to demonstrate that selective absorption of seventy-five centimeters radiation was directly related to the chemical structure of substances and that it was the hydroxyl radical (OH) that was responsible. Thus he developed a new practical analytic tool for chemists.

The problem presented some theoretical difficulties. The obvious explanation for selective absorption would have to be based on the hypothesis that it represented a resonance phenomenon with the natural period of the molecular constituents of the substance; this suggested to Drude that the natural period at the atomic level was not independent of the particular molecular arrangement since a much higher resonance frequency would be expected of independent considerations.

The organization of Drude’s *Lehrbuch der Optik* (1900) reflects his own approach to problems in optics. The first half of the book is devoted almost exclusively to the phenomena and to their mathematical characterization. Then, after a brief outline of the mechanical and electromagnetic theories, Drude gives what he considers to be the advantages of the electromagnetic theory: first, transverse waves are a direct consequence of Maxwell’s conception of electromagnetic interaction; second, special boundary conditions are not required in the electromagnetic theory for radiation in the optical region of the spectrum; and third, the velocity of light can be determined directly from electromagnetic experiments. “In fact,” Drude wrote, “it is an epoch-making advance in natural science when in this way two originally distinct fields of investigation, like optics and electricity, are brought into relations which can be made the subject of quantitative measurements” (*The Theory of Optics*, C. R. Mann and R. A. Millikan, trans., 2nd ed. [New York, 1959], p. 261).

Drude’s move to Giessen thus occurred at a time when he was intent on understanding the optical, thermal, and electrical properties of metals by application of the electron theory. Drude was not the only person interested in such a practical application of the electron theory. Both J. J. Thomson and E. Riecke made substantial though different contributions. In the theory developed by Drude every metal contains a large number of free electrons, which he treated as a gas, the electrons having an average kinetic energy equal to the average kinetic energy of the atoms and molecules of the substance. The essential difference between conductors and nonconductors was that nonconductors contained relatively few free electrons. In early versions of his theory, Drude assumed that both positive and negative electrons were part of the “gas” but in a later simplification assumed that only negative electrons were mobile. Using the temperature of the substance as an index of the average kinetic energy of the particles in the electron gas, the velocity of the electrons should be enormous if it were not for the very small mean free path—due, mainly, to collisions with atomic centers.

Consider a neutral conductor, not under the influence of an electric force. Since the motion of the electron gas is perfectly random, there should be no net charge created at any point and no net transfer of electricity from one point to another. Under the influence of an electric field, however, there should be an increase in the average velocity of electrons in one direction and a decrease in their average velocity in the opposite direction. Such a situation would constitute an electric current whose intensity should be theoretically calculable. Drude arrived at the result that the electrical conductivity would be given by

where *e* is the charge on a single electron, *N* is the number of electrons per unit volume, *l* is the mean free path, *m* is the mass of the electron, and *u* is the average velocity of the electrons. Since the electrons are treated as a gas, the average kinetic energy of the gas should be proportional to the absolute temperature. The coefficient of conductivity may thus be expressed as absolute temperature:

where *T* is the temperature and α is a universal constant.

The power of Drude’s analysis lies in that when one turns to different phenomena, such as thermal conductivity, the analysis is similar. Suppose the ends of a metal bar be maintained at different temperatures. The conduction of heat in the metal is due to collisions between the free electrons. The mean free path, however, is determined as before by collisions with essentially stationary metal atoms. Based on these assumptions, the coefficient of thermal conductivity for a substance is given by

Drude used a scheme of this type to account for such things as thermoelectric and magnetoelectric effects. While agreement with experimental results was never perfect, it was usually within the right order of magnitude. For example, the ratio of Drude’s values for the thermal and electrical conductivity of a substance is proportional to the absolute temperature:

Since α and *e* are both universal constants, Drude would have predicted that the ratio of thermal to electric conductivity at a given temperature was the same for all metals. Although this is not precisely true it is a good approximation to what was known to be the case experimentally.

Drude did not make these researches serially; typically, he had several different research projects in progress at the same time—in addition to lecturing, directing doctoral students, heading the various physical institutes, and editing the *Annalen der Physik*. Drude carried this diverse and taxing load with grace and performed his duties with characteristic thoroughness.

Drude died a week after he had written the foreword to the second edition of his *Lehrbuch der Optik* and six days after he had given his inaugural speech at the Berlin Academy—a speech in which he sketched plans for future research.

## BIBLIOGRAPHY

I. Original Works. Drude’s writings include “Ueber die Gesetze der Reflexion und Brechung des Lichtes an der Grenze absorbierende Kristalle,” in *Annalen der Physik*, **32** (1887), 584–625; “Beobachtungen über die Reflexion des Lichtes am Antimonglanz,” *ibid*., **34** (1888), 489–531; “Ueber Oberflächenschichten,” in *Göttingen Nachrichten* (1888), pp. 275–299; and *Annalen der Physik*, **36** (1889), 532–560, 865–897; “Bestimmung der optischen Konstanten der Metalle,” *ibid*., **39** (1890), 481–554; “Ueber die Reflexion und Brechung ebener Lichtwellen beim Durchgang durch eine mit Oberflächenschichten behaftete planparallele Platte,” *ibid*., **43** (1891), 126–157; “In wie weit genügen die bisherigen Lichttheorien den Anforderungen der praktischen Physik?,” in *Göttingen Nachrichten* (1892), pp. 366–412.

“Ueber magnetiooptische Erscheinungen,” in *Annalen der Physik*, **46** (1892), 353–422; “Ueber die Phasenänderung des Lichtes bei der Reflexion an Metallen,” *ibid*., **50** (1893), 595–624, and **51** (1894), 77–104; “Zum Studium des elektrischen Resonators,” in *Göttingen Nachrichten* (1894), pp. 189–223, and *Annalen der Physik*, **53** (1894), 721–768; *Physik des Äthers auf elektro-magnetischer Grundlage* (Stuttgart, 1894); “Die Natur des Lichtes,” “Theorie des Lichtes für durchsichtige Medien,” “Theorie der anomalen Dispersion,” “Doppelbrechnung,” “Uebergang des Lichtes über die Grenze zweier Medien,” “Rotationspolarisation,” “Gesetze der Lichtbewegung für absorbierende Medien,” and “Polarisation des gebeugten Lichtes,” in *Winkelmanns**Handbuch der Physik*, II, pt. 1, “Optik,” (Breslau, 1894), 623–840; “Untersuchungen über die elektrische Dispersion,” in *Annalen der Physik*, **54** (1894), 352–370.

“Der elektrische Berchungsexponent von Wasser und wässerigen Lösungen,” in *Berichte. Sächsische Akademie der Wissenschaften*. Math.-phys. Kl., **48** (1896), 315–360, and *Annalen der Physik*, **59** (1896), 17–63; “Elektrische Anomalie und chemische Konstitution,” in *Berichte. Sächsische Akademie der Wissenschaften*. Math.-phys. Klasse, **48** (1896), 431–435, and *Annalen der Physik*, **60** (1897), 500–509; “Neuer physikalischer Beitrag zur Konstitutionsbestimmung,” in *Chemische Berichte*, **30** (1897), 930–965; “Ueber Messung der Dielektrizitätskonstanten kleiner Substanzmengen vermittelst elektrischer Drahtwellen,” in *Berichte. Sächsische Akademie der Wissenschaften*. Math.-phys. Klasse, **48** (1896), 583–612; “Theorie der anomalen elektrischen Dispersion,” in *Annalen der Physik*, **64** (1898), 131–158; “Zur Elektronentheorie. I,” *ibid*., **1** (1900), 566–613; “Zur Elektronentheorie. II,” *ibid*., **3** (1900), 369–402; *Lehrbuch der Optik* (Leipzig, 1900, 1906), C. R. Mann and R. A. Millikan, trans., as *The Theory of Optics* (Chicago, 1902; repr. New York, 1959).

“Zur Elektronentheorie. III,” in *Annalen der Physik*, **7** (1902), 687–692; “Zur Konstruktion von Teslatransformatoren,” *ibid*., **9** (1902), 293–610; “Elektrische Eigenschaften und Eigenschwingungen von Drahtspulen mit angehängten geraden Drähten oder Metallplatten,” *ibid*., **11** (1903), 957–995; “Ueber induktive Erregung zweier elektrischer Schwingungskreise mit Anwendung auf Perioden- und Dämpfungsmessung, Teslatransformatoren und drahtlos Telegraphie,” *ibid*., **13** (1904), 512–561; “Optische Eigenschaften und Elektronen-Theorie. I,” *ibid*., **14** (1904), 677–726; “Optische Eigenschaften und Elektronen- Theorie. II,” *ibid*., 936–961; and “Die Natur des Lichtes,” “Theorie des Lichtes für durchsichtige, ruhende Medien,” “Doppelbrechung,” “Uebergang des Lichtes über die Grenze zweier Medien,” “Die Gesetze der Lichtbewegung für absorbierende Medien,” “Theorie der Dispersion,” “Rotationspolarisation,” and “Theorie des Lichtes für bewegte Körper,” all in *Winkelmanns Handbuch der Physik*, vol. VI (2nd ed., Breslau, 1906).

II. Secondary Literature. On Drude and his work see also M. Plank, “Paul Drude,” in *Verhandlungen der Deutschen physikalischen Gesellschaft*, **8** (1906), 599–630; F. Richarz and W. König, *Zur Erinnerung an Paul Drude* (Giessen, 1906); and W. Voigt, “Paul Drude,” in *Physikalische Zeitschrift*, **7** (1906), 481–482.

Stanley Goldberg

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