onsidered as modifications of a
few simple plans. The best way to understand the relation of one crystal
to another is to look upon every crystal as having its faces and angles
arranged in definite fashion about certain imaginary lines drawn
through the crystal. These lines are called axes, and bear much the same
relation to a crystal as do the axis and parallels of latitude and
longitude to the earth and a geographical study of it. All crystals can
be referred to one of six simple plans or systems, which have their axes
as shown in the following drawings.

The names and characteristics of these systems are as follows:

1. Isometric or regular system (Fig. 46). Three equal axes, all at right
angles.

[Illustration: Fig. 46]

2. Tetragonal system (Fig. 47). Two equal axes and one of different
length, all at right angles to each other.

[Illustration: Fig. 47]

3. Orthorhombic system (Fig. 48). Three unequal axes, all at right
angles to each other.

[Illustration: Fig. 48]

4. Monoclinic system (Fig. 49). Two axes at right angles, and a third at
right angles to one of these, but inclined to the other.

[Illustration: Fig. 49]

5. Triclinic system (Fig. 50). Three axes, all inclined to each other.

[Illustration: Fig. 50]

6. Hexagonal system (Fig. 51). Three equal axes in the same plane
intersecting at angles of 60 deg., and a fourth at right angles to all of
these.

[Illustration: Fig. 51]

Every crystal can be imagined to have its faces and angles arranged in a
definite way around one of these systems of axes. A cube, for instance,
is referred to Plan 1, an axis ending in the center of each face; while
in a regular octohedron an axis ends in each solid angle. These forms
are shown in Fig. 46. It will be seen that both of these figures belong
to the same system, though they are very different in appearance. In the
same way, many geometric forms may be derived from each of the systems,
and the light lines about the axes in the drawings show two of the
simplest forms of each of the systems.

In general a given substance always crystallizes in the same system, and
two corresponding faces of each crystal of it always make the same angle
with each other. A few substances, of which sulphur is an example,
crystallize in two different systems, and the crystals differ in such
physical properties as melting point and density. Such substances are
said to be _dimorphous_.

EXERCISES

1. (a) Would the same a