392 C. K. SWARTZ PROPOSED CLASSIFICATION OF CRYSTALS 



one group (the Tetragonal trisplienoidal group) is missing in Bravais' 

 table. 33 



Fedorow. — Fedorow contributed a highly important discussion in 1885, 

 entitled "Elementen der Lehren von den Figuren." 34 His work, unfor- 

 tunately, is in the Eussian language, so that it did not at once gain the 

 wide attention of which it was worthy. 



Fedorow gives a brief outline of his results in an article published in 

 Zeitschrift fur Kryst. in 1892. 35 He states that his results are almost 

 identical with those of Schoennies, though obtained by different methods. 

 He develops the thirty-two crystal groups in four major divisions, as fol- 

 lows : 36 



I. With principal axis. 



1. Hexagonal and Trigonal divisions. 



2. Tetragonal division. 



3. Division possessing two- and one-fold periods (including Ortho- 



rhornbic, Monoclinic, and Triclinic systems). 

 II. Without principal axis (Isometric). 



The subdivisions of these types are shown in table II, page 396. 



Fedorow introduces the conception of a combined axis and plane of 

 symmetry (zusammengesetzte sjnrimetrie) to produce the type of crystals 

 frequently termed sphenoidal (alternating). 



Minnig 'erode. — B. Minnigerode discussed all possible sym metrical fig- 

 ures in a brief article in the Neues Jahrbuch for 1887. 37 He develops 

 symmetrical assemblages, which he terms groups, by the method of de- 

 terminants, and finally restricts the forms arrived at to those possessing 

 the periods possible in crystals. The divisions of crystals found by him 

 are the following : 38 



I. Derivatives of Octohedral group (Isometric system). Groups 1-5. 

 II. Derivatives of Dihedral group. 



1. Possessing six- or three-fold period (Hexagonal system). 



a. Six-fold axis. Groups 6-10. 



&. Three-fold axis and center of symmetry = six-fold period. 



Groups 11-12. 

 c. Three-fold axis and center of symmetry = three-fold period. 



Groups 13-17. 



2. Possessing four-fold period, or two-fold period and center of sym- 



metry = four-fold period (Tetragonal system). 

 a. Four-fold period. Groups 18-22. 



33 Ibid., p. 454. 

 84 St. Petersburg, 1885. 

 35 Vol. 20, 1892, pp. 25-75. 



38 See synopsis by Scboenflies, Krystall Systeme und Krystall Structur, 1891, p. 104. 

 37 Untersucbung iiber die symmetriscbe Verbaltnisse der Krystalle. Neues Jabrb. fur 

 Min. Geol. und Pal. Beilage, bd. v, 1887, pp. 145-166. 

 « Ibid., pp. 157-164. 



