# Lorenz, Ludwig Valentin

# Lorenz, Ludwig Valentin

(*b.* Elsinore, Denmark, 18 January 1829; *d.* Copenhagen, Denmark, 9 June 1891)

*physics.*

Lorenz, a civil engineer by training, graduated from the Technical University of Denmark in Copenhagen; he taught at the Danish Military Academy and at a teacher’s training college in Copenhagen. During the last years of his life he was financially supported by the Carlsberg Foundation to such an extent that he could devote all his time to research.

Lorenz was an eminent physicist, although the content and range of his achievements were not fully recognized by his contemporaries. This lack of recognition was due mainly to his great difficulties in presenting his ideas and mathematical calculations in intelligible form, but it was also due to his publishing some of his important papers only in Danish.

Lorenz’ researches in physics, mainly optics and heat and electricity conductivities of metals, were carried out with equal emphasis on theoretical and experimental methods. The basis Of his research in optics was the propagation of light waves conceptualized in terms of the theory of elasticity. Finally, however, he was convinced of the incompatibility of the boundary conditions of the theory of elasticity with FresneFs formulas for reflection and refraction; he then concentrated his efforts on finding a phenom-enological description of the propagation of light waves instead of speculating on the nature of light. Independently of the Irish physicist Macculiagh, he showed in 1863 that the partial differential equation for the light vector u should be (in modern notation)

where the phase velocity *a* is a constant that is characteristic for the homogeneous optical medium under consideration. He als gave the correct boundary conditions for the light vector when it is passing from one medium to another.

Lorenz then showed that if *a* is not considered as a constant but as a periodic function of space, his wave equation led to the theory of double refraction; where periods of a are small in comparison with the wavelength. This theory, by use of the same mathematical technique, has again been used recently.

A further remarkable result of Lorenz’ optical researches on the basis of his fundamental wave equation was the well-known formula (Lorentz-Lorenz formula) for the refraction constant , according to which

where *n*_{∞} is the index of refraction for an infinite wavelength and *v* is the specific volume. He also showed that for a mixture

where is the index *i* refers to the components of the mixture. His first paper on the refraction constant, in which he also gave an experimental verification of his formula in the case of water, dates from 1869. In 1870 H. A. Lorentz arrived at the same result, independently of Lorenz.

In 1890, Lorenz published in *Det kongelige danske Videnskabemes Selskab Skrifter* a paper on the diffraction of plane waves by a transparent sphere, again using his fundamental wave equation with the relevant boundary conditions; he thereby anticipated later calculations by Mie and Debye. Unfortunately, this very important paper was published only in Danish, and thus it had no influence on later developments.

This paper contains the first determination of the number of molecules in a given volume of air, based upon the scattering of sunlight in the atmosphere. It is the first fairly accurate estimation of the order of magnitude of Avogadro’s number, usually ascribed to Lord Rayleigh, who published it in 1899, nine years after the publication of Lorenz’ paper and independently of Lorenz.

Most impressive of all Lorenz’ achievements in optics is his electromagnetic theory of light, developed in a relatively unknown paper of 1867, two years after Maxwell’s famous paper on the same subject. At that time Lorenz did not know Maxwell’s theory, and his own approach was quite different. Lorenz’ electromagnetic theory of light can be described briefly as an interpretation of the light vector as the current density vector in a medium obeying Ohm’s law. This paper contains the fundamental equations for the vector potential and the scalar potential or —for the first time—the corresponding retarded potentials expressed in terms of the current density vector and the electrical charge density. The concept of retarded potentials had already been introduced in an earlier paper by Lorenz in connection with research on the theory of elasticity. He found that the differential equation for the current density vector was the same as his fundamental wave equation for the light vector, completed with a term which explains the absorption of light in conducting media, and that his theory led to the correct value for the velocity of light.

Lorenz, most important contribution in heat and electricity conductivities of metals was the Lorenz law, according to which the ratio between the conductivities of heat and electricity is proportional to the absolute temperature, where the constant of proportionality is the same for all metals. It had already been shown by R. Franz, who worked with Wiedemann, that this ratio is the same for all metals at the same temperature; and Lorenz then proved, through very accurate measurements of the two conductivities at 0° C. and 100° C. that this ratio is proportional to the absolute temperature.

It is characteristic of Lorenz’ mastery of both theoretical and experimental methods that when, in the determination of the conductivity of heat, he encountered the problem of the cooling of a body by the air through heat convection, he solved the problem by calculations based on Navier’s and Stokes’s equations of hydrodynamics. It is a very difficult problem in mathematical physics, but he succeeded in solving it by using quite modern methods of similarity. Having finished his calculations, he found them confirmed by experiments.

In the determination of the specific conductivities for electricity, Lorenz used an absolute method of his own invention, which later was applied by himself and others, such as Rayleigh, to fix the international unit of resistance, the ohm.

In an unpublished paper of great interest, Lorenz developed a complete theory of currents in telephone cables, showing that the attenuation of the current along the cable can be reduced by increasing the inductance per unit of length. He therefore proposed the use of cables wound with a covering of soft iron, an idea also proposed by Heaviside, independently of Lorenz, that later was taken up by the Danish electrotechnician C. E. Krarup. This improvement is now known as continuous loading.

Lorenz was also deeply interested in problems of pure mathematics, such as the distribution of prime numbers; but here he encountered severe criticism from Danish mathematicians, who did not appreciate the undoubted lightness—if not recklessness—with which he applied the methods of mathematics. It is, however, probable that there also are problems of interest in some of his mathematical works.

Lorenz’s contemporaries in the scientific circles of Copenhagen no doubt realized that he was an eminent scientist, and by the standard of his time his work was well supported. But although he was much respected, few understood what he actually did. This lack of deeper understanding, combined with his own tendency to isolation and his rather polemical attitude toward some of his colleagues, made him a somewhat lonely philosopher.

## BIBLIOGRAPHY

Lorenz’ writings were brought together in *Oeuvres scientifiques de L. Lorenz*, 2 vols,, revised and annotated by H. Valentiner (Copenhagen, 1898-1904).

Secondary literature includes Kirstine Meyer, in *Dansk Biografisk Leksikon*, XIII (Copenhagen, 1937), 464-469; and Mogens Pihl, *Der Physiker L. V, Lorenz* (Copenhagen, 1939); and “The Scientific Achievements of L. V. Lorenz,” in E. C. Jordan, ed., *Electromagnetic Theory and Antennas, I* (New York, 1963), xxi-xxx.

Mogens Pihl

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