PRECIOUS STONES. 47
figure;
such a form would be a regular octahedron. If we could bore through
such an octahedron from one of its corners to the diametrically
opposite corner in the case of each of the three pairs of such corners,
all the bore holes would pass through one point at the centre. On
measuring the length of the holes they would be found all equal, and
each one would be at right angles to the other two holes. Imaginary
lines might be drawn down the centre of each hole; we should then have
three lines of equal length, passing through a common point, and
inclined to one another at 90°. Such imaginary lines would represent
the "axes" of the crystal of Fluor Spar. It would be noticed that each
of the faces of the octahedron met the three lines at points equally
distant from the centre of the crystal; the lengths thus cut off would
be the " intercepts " on the axes. If other faces of the crystal were
examined and the angles they made with one another measured, and from
these angles the points where these faces would cut the axes were
calculated, it would be found that the intercepts could be expressed
in whole numbers; for instance, a face might cut one axis at a unit
distance from the centre, and each of the other two at twice this
distance: the relation is always a simple one.
An
examination of all the known crystallised bodies reveals the fact that
their crystals can be placed in one of six classes, known as the six "
crystallographic systems." They are known as the cubic, hexagonal,
tetragonal, rhombic, monosymmetric or monoclinic, and the triclinic. We
may think of them all with regard to the relation of their axes.
The
system to which the above example belongs is the cubic; in it there are
three axes, all at right angles, and all of equal length.
The hexagonal system has three equal axes inclined to
