37^: 



C. K. SWARTZ PROPOSED CLASSIFICATION OF CRYSTALS 



historically developed. It is, therefore, that which is accepted in the fol- 

 lowing discussion. 



Types of symmetry. — Symmetry may be defined as the repetition of 

 similar parts and properties in a crystal. It may be produced in two 

 fundamental ways : 



I. By rotation about an axis, termed symmetry by rotation. 



II. By reflection about a plane or planes, termed symmetry by reflec- 

 tion. 



A third type (III) is produced by the combination of simultaneous 

 rotation and reflection by which points, in rotating, oscillate alternately 

 from upper to lower positions in a crystal, and vice versa. Such an axis 

 may be termed an axis of combined rotation and reflection, or, more sim- 

 ply, an alternating axis. It may be considered a combined axis and plane 

 normal to it. This is the "zusammengesetzte" symmetry of Fedorow. 



TTe will now consider classes which develop in each type of symmetry. 



e 6.— Axial 



Figuee 7. — Polyaxial 



Figubb S. — Ortnoaxial 



Figube 9. — Repetition of 



Figube 10.— Hedral 



class. 



class. 



class. 



singular axis by oblique 

 plane of symmetry. 



class. 



Development of groups and classes of crystals. 



I. Symmetry by rotation. Botation may be about one axis or many 



axes. 



1. Rotation about one axis — Axial class* (figure 6). 



Rotation may occur about one axis, producing crystals having 

 a single axis of symmetry. The axis may have periods of 2, 3, 4. 

 6 only, according to the law of the Rationality of Parameters, pro- 

 ducing four groups of crystals. ( See table, page 377, for summary. ) 



All these crystals have one axis of symmetry and are singly 

 terminated. The name suggested for this class is Axial (axon = 

 an axis). 



2. Rotation about many axes — Polyaxial class (figure 7). 



Rotation may occur about many axes, producing crystals con- 

 taining many axes of symmetry. Two possibilities are presented": 



a. A singular axis is present. Its periods may be 2, 3, 4, 6, according 

 to the law of the Rationality of Parameters. The number of the 

 lateral axes equals period of singular axis. 



I). No singular axis is present. There are three equal axes whose 

 periods are 2 or 4. 



* This class may also be termed Monaxial instead of Axial, since it has only one axis 

 of symmetry and all of its crystals are singly terminated. 



