CRYSTAL CLASSES. No less than thirty-two crystal classes are called for by the mathematical theory which is based on the study of the proper ties of crystals. The edifice of crystal knowledge is one of the best founded in theory of any in the realm of physical science. Believing the origin of crystal structure aid shape to lie in the grouping of the molecular, crystallographers set themselves the task of determining how many arrangements of points in space were possible if certain assumptions were made in accordance with properties known to be common to all crys tals. It was found that thirty-two, and only that number, were possible, and, as regarded their symmetry, twenty-three corresponded ex actly to the twenty-three kinds of crystal sym metry then known. It is the best possible proof of the general correctness of the theory that in the next eight years representatives were dis covered among crystals of six of the nine remain ing classes of crystal structure, and none were found not in correspondence with the classifica tion. The thirty-two classes, known or possible,
of crystal synnnetry fall into six larger groups called 'crystal systems,' though some authors prefer to subdivide one of the systems. making the number seven. Crystal faces being described and named in terms of their directions, i.e. the relative intercepts which they make upon a system of coordinate axes, crystal systems are determined by the kinds of coordinate axes which are suited to the symmetry and which will allow of the simplest calculations. The six systems are known as (1) triclinic, which in cludes two classes; (2) monoclinic. which in chides three classes; (3) orthorhombic, which includes three classes; (4) tetragonal. with seven classes: (5) hexagonal, with two divisions —the trignnal, seven classes; and hexagonal, live classes; and (G) isometric, which has five classes.