(1842 – 1897)
Sohncke's was the son of a university mathematician, and was introduced at an early age to the study. During his studies at the University of Königsberg, F. Neumann introduced him to the studies of mineralogy and crystallography. In 1866, he received his Ph.D. in physics. He was appointed to a position at the Technische Hochschule in Karlsruhe. In 1883, Sohncke accepted a similar position at the University of Jena, and in 1886 he became professor of physics at the Technische Hochschule in Münich, where he remained until his death. By several accounts, Sohncke was an outstanding teacher, who inspired his students in their studies. He was also interested in the flight of Arial balloons, and administrated a Münich society that encouraged this activity.
Biographical references: ADB: 54, 377-9. DBA: I 1192, 357-363; II 1233, 105-109. DSB: 12, 511-2 [by J.G. Burke]. Meteorologische Zeitschrift: 15 (1898), 81-4. Poggendorff: 3, 1263-4 & 4, 1412. WBI. World Who's Who in Science: 1576.
1. German, 1879.
Entwickelung | Einer | Theorie Der Krystallstruktur | Von | Dr. Leonhard Sohncke, | Ord. Professor Der Physik Am Polytechnikum Zu Karlsruhe. | [ornament] | Mit 55 Holzschnitten Im Text Und 5 Lithogr. Tafeln. | Leipzig, | Druck Und Verlag Von B.G. Teubner. | 1879.
8°: a4 1-158 164; 128l.; [i]-viii, -247,  p., 5 folding plates.
Contents: [i-ii], Title page, verso "Das Recht der Uebersetzung wird vorbehalten."; [iii]-v, "Vorwort."- dated March 1879.; [vi], "Angabe der Stellen, wo folgende theils neue, theils nicht | allgemein bekannte Benennungen erklärt sind."; [vii]-viii, "Inhalt."; , "Abschnitt I. | Vorbereitende Betrachtungen."; , Blank.; -60, Text.; , "Abschnitt II. | Konstruktion der regelmässigen allseitig | unendlichen Punksysteme."; , Blank.; -180, Text.; , "Abschnitt III. | Prüfung der Theorie an der Erfahrung."; , Blank.; -247, Text.; [1 pg], "Erklärung der Tafeln."; [At end], 5 folding plates.
Very scarce. A major contribution to crystallography was Entwicklung einer Theorie der Krystallstruktur, which derived the extension of the lattice theory of Auguste Bravaisto arrive at sixty-five of the 230 possible space groups. The fourteen Bravais lattices described only seven of the possible thirty-two classes of external symmetry. Just how the chemical atoms were arranged within the unit cells formed by the space lattice remained a matter of speculation, however. In his studies of internal symmetry, Sohncke realized that previous investigators had looked upon internal symmetry from a completely external orientation. They had imposed, as a condition of their symmetry, translational equivalence, and Sohncke saw that this restriction was not justifiable. Inasmuch as symmetry is defined as the equivalence of internal 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 the system of points is the same from every point and that it need not be a parallel view.
Sohncke eventually arrived at sixty-six different spatial arrangements of points by introducing two new symmetry elements (this number was reduced in 1888 to 65 when two of the elements were shown to be equivalent). The first was the screw axis, in which a rotation around an axis is combined with a translation of the system along the axis. The second was the glide plane, in which the reflection in a mirror plane is combined with a similar translation without rotation along the axis. However, Sohncke failed to consider two additional symmetry elements of the thirty-two classes of external symmetry: rotation-reflection and rotation-inversion axes. Their inclusion by Evgraf Stepanovich Fyodorov and almost simultaneously by Arthur Schoenflies and William Barlow in the late 1880's added the additional 165 space groups, for the actual total of 230 space groups. It was Sohncke's work as published in Die Entwicklung einer Theorie der Krystallstruktur that placed these later researchers on the correct path.
Bibliographical references: Burckhardt, Symmetrie der Kristalle, 1988: 65-72. Burke, Origins of the Science of Crystals, 1966: 171-72. Dana's 7th (Bibliography): 81. DSB: 12, 511-12 [by J.G. Burke]. Lima-de-Faria, Historical Atlas of Crystallography, 1990: 48-49..