It is truly curious how frequently the perfect number, seven, is endowed with exceptional importance with regard to natural phenomena. The seven orders of spectra, the seven notes of the musical octave, and the seven chemical elements, together with the seven vertical groups to which by their periodic repetition they give rise, of the “period” of Mendeléeff’s classification of the elements, will at once come to mind as cases in point. This proverbial importance of the number seven is once again illustrated in regard to the systems of symmetry or styles of architecture displayed by crystals. For there are seven such systems of crystal symmetry, each distinguished by its own specific elements of symmetry. It is only within recent years that we have come to appreciate what are the real elements of symmetry. For although there are but seven systems, there are no less than thirty-two classes of crystals, and these were formerly grouped under six systems, on lines which have since proved to be purely arbitrary and not founded on any truly scientific basis. It was supposed that those classes in any system which did not exhibit all the faces possible to the system owed this lack of development to the suppression of one-half or three-quarters of the possible number, and such classes were consequently called “hemihedral” and “tetartohedral” respectively. As in the higher systems of symmetry there were usually two or more ways in which a particular proportionate suppression of faces could occur, it happened that several classes, and not merely three—holohedral (possessing the full number of faces), hemihedral, and tetartohedral—constituted each of these systems. Thanks largely to the genius of Victor von Lang, who was formerly with us in England at the Mineral Department of the British Museum, and to his successor there, Nevil Story Maskelyne, we have at last a much more scientific basis for our classification of crystals, and one which is in complete harmony with the now perfected theory of possible homogeneous structures. Victor von Lang showed that the true elements of symmetry are planes of symmetry and axes of symmetry. A crystal possessing a plane of symmetry is symmetrical on both sides of that plane, both as regards the number of the faces and their precise angular disposition with respect to one another. It is quite possible, and even the usual case, that the relative development of the faces, that is their actual sizes, may prevent the symmetry from being at first apparent; but when we come to measure the angles between the faces, by use of the reflecting goniometer, and to plot their positions out on the surface of a sphere, or on a plane representation of the latter on paper, the exceedingly useful “stereographic projection,” we at once perceive the symmetry perfectly plainly. [Illustration: FIG. 15.—Crystal of Potassium Nickel Sulphate. ] [Illustration: