378 C. K. SWARTZ PROPOSED CLASSIFICATION OP CRYSTALS 



The remaining two- and one-fold groups might have been classified into 

 two- and one-fold systems respectively. They have, however, been divided 

 according to the number of fixed directions of symmetry (determining 

 the number of their rectangular directions), as follows: 



5. Possessing three fixed directions of symmetry — Orthorhombic sys- 

 tem. 



6. Possessing one or two fixed directions of symmetry — Monoclinic 

 system. 



7. Possessing no fixed direction of symmetry — Triclinic system. 



The various systems are thus seen to spring from the above develop- 

 ment. 



The members of one system and one class constitute a group of crystals. 

 The relations of the various classes and systems are shown in plates I and 

 II. 4 The first plate shows the general form (mPn) in each group; the 

 second the spherical projections of the symmetry of each group. The 

 character of the symmetry of each class is illustrated in the first vertical 

 column. 



CHARACTERISTICS OF THE SEVEN CLASSES 



The characteristics of the seven classes may be exhibited by arranging 

 them in a slightly different manner from that in which they were devel- 

 oped. They are seen to comprise two distinct types — (I) axial, (II) 

 hedral. 



I. Axial classes. 



The axial classes have pyramids produced by rotation. They are char- 

 acterized by the fact that the faces of the general form (mPn) are single, 

 never in pairs, about the axis of rotation. They develop first, second, 

 and third order forms, the latter being both right- and left-handed. 



1. The Axial class contains singly terminated pyramids possessing a single 



axis of symmetry. The other axial classes consist of two such 

 pyramids joined base to base. This may be done in three ways. 

 The faces of the upper pyramid may be 



2. Directly over those of the lower pyramid — Orthoaxial class; 



3. Obliquely over those of the lower pyramid, being rotated either to the 



right or the left hand, producing right- and left-handed forms — ■ 

 Poly axial class; 



4. Alternating with those of the lower pyramid (the faces of the upper 



pyramid being over the edges of lower pyramid) — Amebaxial class. 



II. Hedral classes. 



The hedral classes, on the contrary, have pyramids produced by reflec- 

 tion about vertical planes of symmetry (as usually held). The faces of 

 the general form (mPn) hence occur in pairs about these planes, produc- 

 ing di-forms (di-pyramids, scalenohedra, etcetera). 



4 The monoclinic crystals are drawn with axis of symmetry vertical to show their rela- 

 tions better to crystals of other systems. 



