WORK OF CURIE AND OF FEDOROW 391 



Gadolin's discussion is so full and clear that for a time the origination 

 of the entire conception of the thirty-two groups of crystals seems to have 

 been attributed to him rather than to Hessel, whose work was generally 

 neglected. While superior to Hessel in clearness and brevity, his work is 

 much less extended. Moreover, he does not call attention either to the 

 seven types of axes or to the large and philosophical grouping of that 

 author. 



Curie. — In the year 1884 P. Curie published two papers 30 in the Bulle- 

 tin of the Mineralogical Society of France upon symmetrical figures. 



Curie develops all possible forms of symmetrical figures, of which he 

 recognizes nine types and twenty-four subtypes. 31 He then considers the 

 possible crystallographic forms which possess the periods 1, 2, 3, 4, 6. He 

 finds that they are restricted to five of his types and eleven subtypes shown 

 in the following table : 32 



III. Cubic (Isometric). 



1. No planes of symmetry. 



2. Planes of symmetry. 



IV. Tetrahedral (Isometric). 



1. No planes of symmetry. 



2. Planes and axes of symmetry coincident. 



3. Planes and axes of symmetry alternate. 



V. Forms possessing a double principal axis (that is, containing many axes). 



1. No planes of symmetry. 



2. Planes and axes of symmetry coincident. 



3. Planes and axes of symmetry alternate. 



VI. Forms possessing an inverse axis (that is, containing one axis only). 



1. No planes of symmetry. 



2. Planes of symmetry normal to axis. 



3. Alternating planes of symmetry normal to axis. 



4. Planes of symmetry parallel to axis. 



IX. Forms possessing no repetition (that is, containing no axis). 



1. No axis. 



2. Center of symmetry. 



3. Plane of symmetry. 



The different periods of the axes of symmetry in the above divisions 

 give rise to thirty-two groups of symmetry possible in crystals, which are 

 precisely the same as those found by the earlier investigators. 



Curie's discussion is devoted to the geometric rather than to the crys- 

 tallographic aspects of the subject. He calls attention to the fact that 



30 Sur les questions d'ordre. Bulletin de la SociSte* Mineralogie de France, vol. 7, 1884, 

 pp. 89-118. 



Sur la Symetrie, ibid., pp. 418-457. 



31 Ibid., p. 450, where a table is given. 



32 Bulletin de la Societe" Mineralogie de France, table, p. 450. Tbe subdivisions are 

 found in the discussion, pp. 444-449. 



