THE ATOMIC VIEW OF NATURE. 



443 



centres, or to lines, called axes, or to planes of sym- 

 metry. 1 French and German investigators have deduced 

 in different ways the different possible forms of sym- 

 metry, and have shown that in all thirty-two different 

 forms of symmetry or groups are geometrically possible. 

 These thirty-two fundamental groups of crystals can be 

 gathered up into six classes or types, according to the 

 different systems of crystallographic axes or the number 

 of planes of symmetry belonging to them. 2 



1 The question may be raised, 

 to what extent crystallography is 

 obliged to assume a molecular 

 structure of matter, or what sup- 

 port does the atomic view receive 

 from it ? On this point see Ost- 

 wald's ' Allgemeine Chemie,' vol. i. 

 p. 855, &c. The geometrical forms 

 of crystals can either be derived 

 from elementary polyhedra, as Haiiy 

 attempted to do by his " molecules 

 integrantes " and his theory of 

 decrescences, space being in this 

 system considered as continuously 

 filled ; or the elementary particles 

 may be considered to consist of 

 meshes of points geometrically ar- 

 ranged in the corners of a primitive 

 figure in three dimensions ; or ele- 

 mentary spheres or ellipsoids may 

 be supposed to be piled on each 

 other likecannon-balls. The two lat- 

 ter systems assume vacant spaces ; 

 the first view refers the crystalline 

 shape to some primitive crystal, and, 

 therefore, does not explain it. It 

 has accordingly been said that " the 

 structure of crystals is one of the 

 principal supports of the molecular 

 theory. In assuming continuous 

 matter without at least points 

 which are geometrically or kine- 

 matically distinct, the anisotropic 

 structure of crystals is quite un- 

 thinkable" (Lehmann, 'Molecular- 

 physik,' vol. ii. p. 376). This view 

 does not agree with what Ostwald 



says ('Allgemeine Chemie,' vol. i. p. 

 868) ; he considers that the struc- 

 ture of crystals affords no proof 

 for the molecular constitution of 

 matter, as the data of elasticity 

 by no means necessarily require 

 a molecular arrangement, but for- 

 mally can be ascribed as easily to 

 continuous matter. " Nevertheless 

 the molecular view has the advan- 

 tage of greater evidence, and leads 

 to the same results with much 

 greater simplicity, and hence more 

 convincingly." It seems, however, 

 that if chemical facts and physical 

 theory force upon us the atomic 

 view, crystallographic phenomena 

 force us to complete it by some 

 conception of geometrical arrange- 

 ments. 



- This purely geometrical treat- 

 ment was introduced by Bravais 

 in his ' Etudes crystallograph- 

 iques' (1851), the much earlier 

 work of Hessel (' Krystallometrie,' 

 1831) having been forgotten. It 

 was further developed by L. Sohnke 

 (' Entwickelung der Theorie der 

 Krystallstructur, ' 1879), and com- 

 pleted by Curie (1884) and Min- 

 nigerode (1886). A concise sum- 

 mary will be found in Liebisch, 

 ' Physikalische Krystallographie, ' 

 Leipzig, 1891, pp. 3 to 50 ; also 

 Groth, ' Physikalische Krystallo- 

 graphie,' Leipzig, 1895, p. 324, 

 &c. 



