# Sohncke, Leonhard

# SOHNCKE, LEONHARD

(*b*. Halle, Germany, 22 February 1842; *d*. Munich, Germany, 1 November 1897)

*crystallography, physics, meteorology*.

Sohncke’s chief scientific contribution was the extension of the lattice theory of Bravais to arrive at sixty-five of the 230 possible space groups.

Sohncke’s father was professor of mathematics at the University of Halle and was known for his translation into German of Chasles’s *Aperçu historique sur l’origine et la dévelopement des méthodes en géométrie*. Sohncke was thus stimulated to study mathematics. He received his early education at the Gymnasium in Halle and then pursued mathematics and physics at the University of Halle and then at the University of Königsberg. There, Franz Neumann, professor of mineralogy and physics, influenced Sohncke greatly and urged him to direct his attention toward theoretical physics, Sohncke received his doctorate in 1866 and taught for a brief period in the Gymnasium in Königsberg before becoming *Privatdozent* at the university.

In 1871, on the recommendation of Kirchhoff, Sohncke was called as professor of physics to the Technische Hochschule in Karlsruhe. In 1883 he moved to the University of Jena in the same capacity, and in 1886 he became professor of physics at the Technische Hochschule in Munich, where he remained until his death. Sohncke acquired a reputation as a fine teacher and instructed many young physicists who later attained success. He also won prominence in educational circles because of his campaign, while in Munich, to break the monopoly held in secondary education by the Gymnasiums and to aid the Realschulen in reaching parity with them.

Early in his career Sohncke was concerned primarily with pure mathematics, particularly series; and he published several short papers in mathematical journals. In the mid-1870’s, however, he turned his attention to the internal symmetry of crystals. Working under Neumann at Königsberg, Sohncke had become aware of this field and knew of the previous work of Bravais in determining the fourteen types of space lattices and the thirty-two symmetry classes. He had also followed the investigations of Camille Jordan in group theory. During his research, Sohncke discovered that Hessel in 1830, had anticipated the work of Bravais; and Sohncke saw to it in his later publications that Hessel’s contribution was recognized.

The fourteen Bravais lattices accounted for only seven of the thirty-two classes of external symmetry. In studying internal symmetry, Sohncke realized that previous investigators had looked upon internal symmetry from a completely external orientation. They had imposed, as a condition of symmetry, translational equivalence; and Sohncke saw that this restriction was not justifiable. Inasmuch as symmetry is defined as the equivalence of it configurations, it is of no consequence whether the direction of one’s view has been altered in being transported from one point to another within an object. Thus Sohncke insisted that the view of th system of points is the same from every point and that it need not be a parallel view.

Sohnncke eventyally arrived at sixty-five different spatial arrangements of points, introducing two new symmetry elements: the screw axis, in which a rotation around an axis is combined with a translation of the system along the axis; and the glide plane, in which the reflection in a mirror plane is combined with a similar translation without rotation along the axis. (Using only simple translation, Bravais had arrived at fourteen lattices.) Sohncke, however, failed to consider two additional symmetry elements of the thirty-two classes of external symmetry: rotation-reflection and rotation-inversion axes. Their inclusion by Fyodorov and almost simultaneously by Arthur Schoenflies and William Barlow in the late 1880’s added the additional 165 space groups. Sohncke published his results in his major work. *Die Entwicklung einer Theorie der Krystallstruktur* (1879). He also made models from cigar boxes to demonstrate his derived space groups; and while in Munich, where he became a close friend of the crystallographer Groth, he extended his study of crystal physics.

When Sohncke accepted his post at Karlsruhe he simultaneously took over the direction and administration of the network of meteorological stations in the province of Baden. He also became editor of *the Juhresbericht über die Beobachtungsergebnisse der Badischen meteorologischen Stationen*, and in order to popularize meteorology he published *Über Stürme und Sturmwarnungen* (1875). He also wrote several articles on temperature changes in humid, rising streams of air; the derivation of the formula for barometric height; and the green rays of the sunset. Further, he proposed a theory of the presence of electricity in thunderstorms. Sohncke further conducted research in optics. He determined the thickness of a drop of oil when placed on water after having diffused on its surface.

While in Munich, Sohncke became particularly interested in the flight of aerial balloons, and he directed the activities of a society that encouraged this activity. He organized a number of ascents, and as a reward for his efforts the group named one of its balloons “Sohncke.”

## BIBLIOGRAPHY

I. Original Works. Sohncke’s chief publications are *Über Stürme and Sturmwanungen* (Berlin, 1875); *Die Entwicklung einer Theorie der Krystallstrukter* (Leipzig, 1879); *Über Wellenbewegung* (Berlin, 1881): and *Gemein Verständliche aus dem Gebiete der Physik* (Jena, 1892), his last publication. He also published more than forty articles in scientific journnals.

II. Secondary Literature. See S. Günther, “Leonhard Sohncke,” in *Allgemeine Deutsche Biographie* LIV, 377–379; F. Erk, “Leonhard Sohncke,” in *Meteorologische Zeitschrift*, **15** (1898). 81–84; and “Leonhard Sohncke,” in *Akademie der Wissenschaften (München), Sitzunggsberichten***28** (1898), 440–449.

John G. Burke

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