related to those not in that plane. In the simpler cases the arrangement of molecules is rectangular; in the remaining cases oblique either in one or two
In order to simplify the explanation and conception of the complicated phenomena which crystals exhibit, an hypothesis has been invented which is an excellent instance of the Descriptive Hypotheses before mentioned (p. 522). Crystallographers imagine that there are within each crystal certain axes, or lines of direction, by the comparative length and the mutual inclination of which the nature of the crystal is determined. In one class of crystals there are three such axes lying in one plane, and a fourth perpendicular to that plane; but in all the other classes there are imagined to be only three axes. Now these axes can be varied in three ways as regards length: they may be (1) all equal, or (2) two equal and one unequal, or (3) all unequal. They may also be varied in four ways as regards direction: (1) they may be all at right angles to each other; (2) two axes may be oblique to each other and at right angles to the third; (3) two axes may be at right angles to each other and the third oblique to both; (4) the three axes may be all oblique. Now, if all the variations as regards length were combined with those regarding direction, it would seem to be possible to have twelve classes of crystals in all, the enumeration being then logically and geometrically complete. But as a matter of empirical observation, many of these classes are not found to occur, oblique axes being seldom or never equal. There remain seven recognised classes of crystals, but even of these one class is not positively known to be represented in nature.
The first class of crystals is defined by possessing three equal rectangular axes, and equal elasticity in all directions. The primary or simple form of the crystals is the cube, but by the removal of the corners of the cube by planes variously inclined to the axes, we have the regular octohedron, the dodecahedron, and various combinations of these forms. Now it is a law of this class of crystals that as each axis is exactly like each other axis, every modification of any corner of a crystal must be repeated symmetrically with regard to the other axes; thus the forms produced are symmetrical or regular, and the class is called the Regular System of crystals. It includes a great variety of substances, some of them being elements, such as carbon in the form of diamond, others more or less complex compounds, such as rock-salt, potassium iodide and bromide, the several kinds of alum, fluor-spar, iron bisulphide, garnet, spinelle, &c. No correlation then is apparent between the form of crystallisation and the chemical composition. But what we have to notice is that the physical properties of the crystallised substances with regard to light, heat, electricity, &c., are closely similar. Light and heat undulations, wherever they enter a crystal of the regular system, spread with equal rapidity in all directions, just as they would in a uniform fluid. Crystals of the regular system accordingly do not in any case exhibit the phenomena of double refraction, unless by mechanical compression we alter the conditions of elasticity. These crystals, again, expand equally in all directions when heated, and if we could cut a sufficiently large plate from a cubical crystal, and examine the sound vibrations of which it is capable, we should find that they indicated an equal elasticity in every direction. Thus we see that a great number of important properties are correlated with that of crystallisation in the regular system, and as soon as we know that the primary form of a substance is the cube, we are able to infer with approximate certainty that it possesses