PROF. BAUMHAUER discusses the symmetry of crystals in accordance with recent views, and employs the axes of symmetry to distinguish the classes. Weiss and Mohs first recognised that crystals fell into seven groups depending on the relative lengths and inclinations of the crystallographic axes. The older school of crystallo-graphers, following the lead of Naumann, commenced with the class of highest symmetry in each system, and derived the remainder by removing elements of symmetry. The logical method, as was pointed out by Gadolin, is to start with the class of lowest symmetry and add elements of symmetry until the most complicated class is reached. Each class is, in reality, quite independent of any other, even if in the same system. Groth adopted this view in the last edition of his “Physikalische Krystallographie,” and rejecting all ideas of hemihedrism, introduced a nomenclature which has been here employed by Prof. Baumhauer. He, however, differs from the Munich professor, but joins Schönflies in dividing the thirty-two classes into groups depending on the axes of symmetry present. This method splits up the monoclinic system, two classes of which join the rhombic system to form the digonal group (i.e. the group with at least one axis of two-fold symmetry), whilst the third, which possesses a plane of symmetry only, remains by itself in the monogonal group. The triclinic class, according to the author, forms the anaxial group; Schönflies, on the other hand, splits it up and gives the holohedral class to the digonal group, and the other to the monogonal group. The latter arrangement is certainly more logical, though there is something to be said for Prof. Baumhauer's objection that a “2-zählige Spiegelachse” being in any direction, and therefore not necessarily parallel to a crystallographically possible edge, cannot be said to exist. The author follows Schönflies in placing the classes represented by phenacite and calcite respectively in the hexagonal group, whereas Groth includes them in the trigonal group. These two groups, however, might well be regarded as one.