all these properties. The class of regular crystals is then an eminently natural class, one disclosing many general laws connecting together the physical and mechanical properties of the substances classified.
In the second class of crystals, called the dimetric, square prismatic, or pyramidal system, there are also three axes at right angles to each other; two of the axes are equal, but the third or principal axis is unequal, being either greater or less than either of the other two. In such crystals accordingly the elasticity and other properties are alike in all directions perpendicular to the principal axis, but vary in all other directions. If a point within a crystal of this system be heated, the heat spreads with equal rapidity in planes perpendicular to the principal axis, but more or less rapidly in the direction of this axis, so that the isothermal surface is an ellipsoid of revolution round that axis.
Nearly the same statement may be made concerning the third or hexagonal or rhombohedral system of crystals, in which there are three axes lying in one plane and meeting at angles of 60°, while the fourth axis is perpendicular to the other three. The hexagonal prism and rhombohedron are the commonest forms assumed by crystals of this system, and in ice, quartz, and calc-spar, we have abundance of beautiful specimens of the various shapes produced by the modification of the primitive form. Calc-spar alone is said to crystallise in at least 700 varieties of form. Now of all the crystals belonging both to this and the dimetric class, we know that a ray of light passing in the direction of the principal axis will be refracted singly as in a crystal of the regular system; but in every other direction the light will suffer double refraction being separated into two rays, one of which obeys the ordinary law of refraction, but the other a much more complicated law. The other physical properties vary in an analogous manner. Thus calc-spar expands by heat in the direction of the principal axis, but contracts a little in directions perpendicular to it. So closely are the physical properties correlated that Mitscherlich, having observed the law of expansion in calc-spar, was enabled to predict that the double refracting power of the substance would be decreased by a rise of temperature, as was proved by experiment to be the case.
In the fourth system, called the trimetric, rhombic, or right prismatic system, there are three axes, at right angles, but all unequal in length. It may be asserted in general terms that the mechanical properties vary in such crystals in every direction, and heat spreads so that the isothermal surface is an ellipsoid with three unequal axes.
In the remaining three classes, called the monoclinic, diclinic, and triclinic, the axes are more or less oblique, and at the same time unequal. The complication of phenomena is therefore greatly increased, and it need only be stated that there are always two directions in which a ray is singly refracted, but that in all other directions double refraction takes place. The conduction of heat is unequal in all directions, the isothermal surface being an ellipsoid of three unequal axes. The relations of such crystals to other phenomena are often very complicated, and hardly yet reduced to law. Some crystals, called pyro-electric, manifest vitreous electricity at some points of their surface, and resinous electricity at other points when rising in temperature, the character of the electricity being changed when the temperature sinks again. This production of electricity is believed to be connected with the hemihedral character of the crystals exhibiting it. The crystalline structure of a substance again influences its magnetic behaviour, the general law being that the direction in which the molecules of a crystal are most approximated tends to place itself axially or equatorially between the poles of