250 
ELEMENTARY CHEMICAL MICROSCOPY 
It appears probable that only chemical elements and their 
definite compounds form crystals. 
Crystals may form when a solid phase separates from a liquid. 
The liquid may be either a solution or a molten mass. Crystals 
may also form from vapors on cooling. 
The bounding polygons of a crystal are called faces, all of 
which are symmetrically placed with reference to systems of 
imaginary lines termed axes. 
The angles formed by the meeting of these bounding polygons 
are called interfacial angles, which may be acute, right or obtuse, 
and are never reentrant. 
A study of the interfacial angles of chemical compounds is of 
the utmost importance, since these angles are constant for a 
compound, in the case of similar faces, no matter what its 
origin. 
Crystals are classified into six systems according to their sym¬ 
metry. A plane of symmetry is any plane which passed through 
a crystal will divide it into two parts, one-half being the mirror 
image of the other. 
The six different systems (so-called), to which crystal forms 
may be referred, differing from one another by the varying of 
the symmetry of the crystals, are also often, but less correctly, 
defined as differing by variations in the relation of the axes. 
It has been proved by Groth that there can be only four kinds 
of axes of symmetry — twofold (binary), threefold (ternary), 
fourfold (quatenary) and sixfold (senary). The equivalent faces 
become coincident through revolutions of i8o degrees, 120 
degrees, 90 degrees and 60 degrees respectively. In crystallog¬ 
raphy, by symmetry is always meant symmetry of direction, not 
of actual form or position. It follows, therefore, from the above 
facts, that the crystal angles are constant, definite and character¬ 
istic for each crystal form, and for each substance thus crystalliz¬ 
ing, and that substances may often be identified by the measure¬ 
ment of their crystal angles, 
Slow chemical replacement processes sometimes cause more 
or less complete changes in the composition of a substance with¬ 
out affording an opportunity for an accompanying change in 
