PLATE X.
Fig. 37.—Piz Palü and Snow-field of the Pers Glacier, from the Diavolezza Pass, Upper Engadine.
(From a Photograph by the author.)
The water flowers of Fig. 35 remind one very much of snow crystals, two of which, re-engraved from the wonderfully careful drawings of the late Mr Glaisher, are represented in Fig. 36, Plate IX. They all exhibit the symmetry of the hexagonal prism, which is equally a form of the trigonal system as it is of the hexagonal system. The snow crystals, being formed from water vapour condensed in the cold upper layers of the atmosphere, appear more or less as skeleton crystals, owing to the rarity of the semi-gaseous material condensed, compared with the extent of the space in which the crystallisation occurs. Indeed the exquisite tracery of these snow crystals appears to afford a visual proof of the existence of the trigonal-hexagonal space-lattice as the framework of the crystal structure of ice. When one considers the countless numbers of such beautiful gems of nature’s handiwork massed together on an extensive snow-field of the higher Alps—such as that of the Piz Palü in the Upper Engadine, shown in Fig. 37, Plate X., as seen from the Diavolezza Pass—produced in the pure air of the higher regions of the atmosphere, and frequently seen by the early morning climber lying uninjured in all their beauty on the surface of the snow-field, one is lost in amazement at the prodigality displayed in the broadcast distribution of such peerless gems.
CHAPTER V
HOW CRYSTALS ARE DESCRIBED. THE SIMPLE LAW LIMITING THE NUMBER OF POSSIBLE FORMS.
The most wonderful of all the laws relating to crystals is the one already briefly referred to which limits and regulates the possible positions of faces, within the lines of symmetry which have been indicated in the last chapter. Having laid down the rules of symmetry, it might be thought that any planes which obey these laws, as regards their mode of repetition about the planes and axes of symmetry, would be possible. But as a matter of fact this is not so, only a very few planes inclined at certain definite angles, repeated in accordance with the symmetry, being ever found actually developed. The reason for this is of far-reaching importance, for it reveals to us the certainty that a crystal is a homogeneous structure composed of definite structural units of tangible size, probably the chemical molecules, built up on the plan of one of the fourteen space-lattices made known to us by Bravais, and to be referred to more fully in Chapter VIII. In order to render this fundamental law comprehensible, it will be essential to explain in a few simple words how the crystallographer identifies and labels the numerous faces on a crystal, in short, how he describes a crystal, in a manner which shall be understood immediately by everybody who has studied the very simple rules of the convention.
It is a matter of common knowledge that the mathematical geometrician defines the position of any point in space with reference to three planes, which in the simplest case are all mutually at right angles to each other like the faces of a cube, and which intersect in three rectangular axes a, b, c, the third c being the vertical axis, b the lateral one, and a the front-and-back axis. The distances of the point from the three reference planes, as measured by the lengths of the three lines drawn from the point to the planes parallel to the three axes of intersection, at once gives him what he calls the “co-ordinates” of the point, which absolutely define its position. In the same way we can imagine three axes drawn within the crystal, by which not only the position of any point on any face of the crystal may be located, but which may be used more simply still to fix the position of the face itself. The directions chosen as those of the three axes are the edges of intersection of three of the best developed faces.
If there are three such faces inclined at right angles they would be chosen in preference to all others, as they would certainly prove to be faces of prime significance as regards the symmetry of the crystal. If there are no such rectangularly inclined faces developed on the crystal, then the three best developed faces nearest to 90° to each other are chosen, the two factors of nearness to rectangularity and excellence of development being simultaneously borne in mind in making the choice of axial planes, and discretion used.
Fig. 38.—The Cube and its Three Equal Rectangular Axes.
