1 68 ELEMENTARY CHEMICAL MICROSCOPY 



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 

 symmetry. 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. 



Crystal axes are usually designated by the letters, a, b, c, of 

 which the c axis is always the vertical, a the forward and back, 

 and b the right and left. 



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 (quartenary) and sixfold (senary) . The equivalent faces 

 become coincident through revolutions of 180 degrees, 120 de- 

 grees, 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 crys- 

 tallizing, and that substances may often be identified by the 

 measurement 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 



