394 C. K. SWARTZ PROPOSED CLASSIFICATION OF CRYSTALS 



Schoenflies proposes a two-fold classification of the thirty-two groups 

 so developed : 42 



I. Into divisions based on the period and character of the principal 

 axis of symmetry comprising Isometric, Hexagonal, Tetragonal, Trigonal, 

 Digonal, and Monogonal divisions. 



II. Into the ordinarily accepted seven systems, essentially as in the 

 classification of Gadolin. His work, which is of great importance, closes 

 with a highly suggestive discussion of the inner structure of crystals. 



Miers. — It remains to make reference to the classification introduced 

 by H. A. Miers in the year 1902 in his work on Mineralogy. 43 He recog- 

 nizes the close relations which exist among a number of the groups of 

 crystals, giving them analogous names. He classifies a large number of 

 the groups into the four divisions recognized by Hessel and designates 

 them in a somewhat analogous manner, prefixing the syllable di (dou- 

 ble = Hessers zweifach) to the name of the system for groups having 

 crystal faces in pairs. He does not, however, apply the same classifica- 

 tion to all systems of crystals. His divisions are exhibited in the follow- 

 ing table, 44 in which the larger grouping is numbered and arranged by 

 the writer. Miers does not present the larger grouping here given. 



I. No axis of symmetry. 



1. Asymmetric. 



2. Center of symmetry. 



3. Plane of symmetry. 



II. Possessing a principal axis of symmetry. 



1. Polar (hemimorphic) J ^ , " 



\ Double (di). 



2. Alternating i Single - 



1 Double (di). 



3. Holoaxial (many axes) ] Single. 



4. Equatorial (borizontal plane of symmetry) j Sm S le - 



1 Double (di). 

 III. With equal axes (Isometric). 



1. Polar (hemimorphic three-fold axes) I ^ ingle - 



' Double (di). 



2. Holoaxial (many axes, four-fold) -} Single. 



3. Central (center of symmetry) ( Sm S Ie - 



(Double (di). 



RELATION OF THE DIVISIONS PROPOSED TO THOSE OF PRECEDING AUTHORS 



The relation of the author's results to those obtained by the various 

 investigators is shown in the following tables, the first giving the larger 

 divisions and the second the subordinate groups as developed by the dif- 

 ferent authors : 



42 Ibid., pp. 110, 125-131. 



43 Mineralogy. MacMillan and Company, 1902. 

 «* Ibid., p. 280. 



