The modern classification of crystals into thirty-two groups is a highly important addition to our knowledge of the subject of crystallography, as well as a valuable contribution to the field of natural science. We are indebted to many investigators for the development o£ this classification, chief among whom are Hessel, Bravais, Moebius, Gadolin, Curie, Fedorow, and Schoenflies. While Hessel was the originator of the classification, his work, unfortunately, was long neglected, and it was not until Gadolin, Schoenflies, and others had given independent developments of the subject, that crystallographers came to recognize the importance of their work.
While the classification of crystals into thirty-two groups rests on a sound and philosophical basis, it is probable that many have found its presentation, especially to elementary students, attended by certain difficulties, chief among which are the multiplicity of the types of symmetry of the thirty-two groups and the consequent lack of . . .