ular--there are, as we have seen, three axes, all at right angles,
all of them being equal.

The second, the hexagonal system--called also the rhombohedral--is
different from the others in having four axes, three of them equal and
in one plane and all at 120 deg. to each other; the fourth axis is not
always equal to these three. It may be, and often is, longer or shorter.
It passes through the intersecting point of the three others, and is
perpendicular or at right angles to them.

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 t