The third of the six systems enumerated above, the tetragonal--or the quadratic, square prismatic, dimetric, or pyramidal--system has three axes like the cubic, but, in this case, though they are all at right angles, two only of them are equal, the third, consequently, unequal. The 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.