

380 C. K. SWARTZ PROPOSED CLASSIFICATION OF CRYSTALS 



An examination of the above table shows that the seven classes fall into 

 pairs of two members each, which differ in that the axial have single and 

 the hedral double faces in the general form (mPn). Thus in the Ortho- 

 axial class we have third order pyramids, and in the Orthohedral class 

 di-pyramids ; the third order rhombohedron of the Amebaxial class corre- 

 sponds to the hexagonal scalenohedron of the Amebahedral class having 

 faces in pairs, etcetera. There is, however, no hedral class corresponding 

 to the Polyaxial class, which thus stands alone. 



LARGER DIVISIONS OF CRYSTALS 



In addition to the systems and classes, the above development shows 

 (see plates I and II) that certain larger divisions occur, expressing the 

 fundamental geometrical and physical properties of crystals. These 

 major divisions are three in number. We here term them the Isometric, 

 Dimetric, and Trimetric divisions respectively. 



Isometric division. — This comprises all crystals having no singular 

 direction. Their crystallagraphic axes have hence one unit of length. 

 Their optical properties are alike in all directions and their elasticity fig- 

 ure is a sphere. 



Dimetric division. — This comprises crystals having one singular direc- 

 tion. Their crystallographic axes have hence two units of length. They 

 are optically uniaxial. Their elasticity figure is an ellipsoid. 



Trimetric division. — This comprises crystals having three or more sin- 

 gular directions; hence their crystallographic axes have three units of 

 length. They are optically biaxial. Their elasticity figure is the tri- 

 axial ellipsoid of Fresnel. 



These divisions correspond to and express the fundamental physical and 

 geometrical properties of crystals. They are the same as those developed 

 by Hessel, although expressed in other terms. We are thus led by the 

 preceding development to divisions representing the larger geometrical 

 and physical units in crystals. 



INTEGRITY OF THE SEVEN CLASSES OF CRYSTALS 



The foregoing discussion shows that the seven classes of symmetry are 

 well defined and natural units each containing forms having a single type 

 of symmetry. This conclusion is supported by the following consider- 

 ations : 



1. Their development, already sketched, shows this fact. 



2. It is also shown by the fact that the members of one class possess 

 common geometrical properties. Thus the Scalenohedral group of the 

 Hexagonal system, the Scalenohedral group of the Tetragonal system, 

 and the Hextetrahedral group of the Isometric system are members of one 



