vertical or principal axis is often much longer or shorter in this group, but the other two are always equal and lie in the horizontal plane, at right angles to each other, and at right angles to the vertical axis.

The fourth system, the rhombic—or orthorhombic, or prismatic, or trimetric—has, like the tetragonal, three axes; but in this case, none of them are equal, though the two lateral axes are at right angles to each other, and to the vertical axis, which may vary in length, more so even than the other two.

The fifth, the monoclinic—or clinorhombic, monosymmetric, or oblique—system, has also three axes, all of them unequal. The two lateral axes are at right angles to each other, but the principal or vertical axis, which passes through the point of intersection of the two lateral axes, is only at right angles to one of them.

In the sixth and last system, the triclinic—or anorthic, or asymmetric—the axes are again three, but in this case, none of them are equal and none at right angles.

It is difficult to explain these various systems without drawings, and the foregoing may seem unnecessarily technical. It is, however, essential that these particulars should be clearly stated in order thoroughly to understand how stones, especially uncut stones, are classified. These various groups must also be referred to when dealing with the action of light and other matters, for in one or other of them most stones are placed, notwithstanding great differences in hue and character; thus all stones exhibiting the same crystalline structure as the diamond are placed in the same group. Further, when the methods of testing come to be dealt with, it will be seen that these particulars of grouping form a certain means of testing stones and of distinguishing spurious from real. For if a stone is offered as a real gem (the true stone being known to lie in the highest or cubic system), it follows that should examination prove the stone to be in the sixth system, then, no matter how coloured or cut, no matter how perfect the imitation, the test of its crystalline structure stamps it readily as false beyond all shadow of doubt—for as we have seen, no human means have as yet been forthcoming by which the crystals can be changed in form, only in arrangement, for a diamond crystal is a diamond crystal, be it in a large mass, like the brightest and largest gem so far discovered—the great Cullinan diamond—or the tiniest grain of microscopic diamond-dust, and so on with all precious stones. So that in future references, to avoid repetition, these groups will be referred to as group 1, 2, and so on, as detailed here.

CHAPTER IV.

PHYSICAL PROPERTIES.

B—Cleavage.

By cleavage is meant the manner in which minerals separate or split off with regularity. The difference between a break or fracture and a "cleave," is that the former may be anywhere throughout the substance of the broken body, with an extremely remote chance of another fracture being identical in form, whereas in the latter, when a body is "cleaved," the fractured part is more readily severed, and usually takes a similar if not an actually identical form in the divided surface of each piece severed. Thus we find a piece of wood may be "broken" or "chopped" when fractured across the grain, no two fractured edges being alike; but, strictly speaking, we only "cleave" wood when we "split" it with the grain, or, in scientific language, along the line of cleavage, and then we find many pieces with their divided surfaces identical. So that when wood is "broken," or "chopped," we obtain pieces of any width or thickness, with no manner of regularity of fracture, but when "cleaved," we obtain strips which are often perfectly parallel, that is, of equal thickness throughout their whole length, and of such uniformity of surface that it is difficult or even impossible to distinguish one strip from another. Advantage is taken of these lines of cleavage to procure long and extremely thin even strips from trees of the willow variety for such trades as basket-making.

The same effect is seen in house-coal, which may easily be split the way of the grain (on the lines of cleavage), but is much more difficult and requires greater force to break across the grain. Rocks also show distinct lines of cleavage, and are more readily split one way than another, the line of cleavage or stratum of break being at any angle and not necessarily parallel to its bed. A striking example of this is seen in slate, which may be split in plates, or laminæ, with great facility, though this property is the result of the pressure to which the rock has been for ages subjected, which has caused a change in the molecules, rather than by "cleavage" as the term is strictly understood, and as existing in minerals. Mica is also another example of laminated cleavage, for given care, and a thin, fine knife to divide the plates, this mineral may be "cleaved" to such remarkably thin sheets as to be unable to sustain the most delicate touch without shattering.

These are well-known examples of simple cleavage, in one definite direction, though in many instances there are several forms and directions of cleavage, but even in these there is generally one part or line in and on which cleavage will take place much more readily than on the others, these planes or lines also showing different properties and angular characters, which, no matter how much fractured, always remain the same. It is this "cleavage" which causes a crystal to reproduce itself exactly, as explained in the last chapter, showing its parent form, shape and characteristics with microscopic perfection, but more and more in miniature as its size is reduced.

This may clearly be seen by taking a very small quantity of such a substance as chlorate of potash. If a crystal of this is examined under a magnifying glass till its crystalline form and structure are familiar, and it is then placed in a test-tube and gently heated, cleavage will at once be evident. With a little crackling, the chlorate splits itself into many crystals along its chief lines of cleavage (called the cleavage planes), every one of which crystals showing under the microscope the identical form and characteristics of the larger crystal from which it came.

The cleavage of minerals must, therefore, be considered as a part of their crystalline structure, since this is caused by cleavage, so that both cleavage and crystalline structure should be considered together. Thus we see that given an unchangeable crystal with cleavage planes evident, it is possible easily to reproduce the same form over and over again by splitting, whereas by simply breaking, the form of the crystal would be lost; just as a rhomb of Iceland spar might be sawn or broken across the middle and its form lost, although this would really be more apparent than real, since it would be an alteration in the mass and not in the shape of each individual crystal. And given further cleavage, by time or a sudden breaking down, even the mass, as mass, would eventually become split into smaller but perfect rhombs.

Much skill is, therefore, required in cutting and fashioning a precious stone, otherwise the gem may be ruined at the onset, for it will only divide along its lines of cleavage, and any mistake in deciding upon these, would "break," not "split" the stone, and destroy the beauty of its crystalline structure. An example of this was specially seen in the great Cullinan diamond, the splitting of which was perhaps the most thrilling moment in the history of precious stones.