133 



1>< li.xliral arrangement; that is all. The specific character of tin- 

 crystal-structure lies in the fact that all atoms of the same kind 

 an ri|ui\;il ( ut for the architecture of the crystal, and that for tin- 

 nit liaim-al equilibrium finally reached therein, the total action of 

 t at h atom is as if it were an autonomical individual. Atoms of 

 di lit rent kinds can moreover always be grouped together so as 

 to form complexes which, similarly and infinitely repeated in an 

 absolutely regular and periodical way, according to the special sym- 

 nu try-properties of the whole structure, will fill up space to 

 produce the remarkable masterpiece of nature, that we call a crystal. 



However it is exactly this very general character of the theory 

 which makes its application to concrete cases rather difficult. The 

 whole number of symmetrical arrangements thus found amounts 

 to no less than two hundred and thirty, the symmetry of which can 

 be grouped in the same 32 classes as we have previously found to 

 be possible for crystals (Chapter V). 



A considerable number of possible structures belongs therefore 

 to each of these 32 classes; and as for the explanation of physical 

 phenomena the precise arrangement of the constitutive atoms is 

 the point of interest which this general theory leaves totally out of 

 consideration, the chance of its successful application for the purpose 

 of explaining crystallographical and crystallophysical phenomena 

 cannot be said to be very hopeful .But this general and, from a 

 mathematical point of view, highly finished theory certainly remains 

 of interest, as being the final and exhaustive solution of the special 

 mathematical problem concerning the regular arrangement in dis- 

 continuous and homogeneous systems. 



14. In the preceding paragraphs we repeatedly had occasion 

 to point out that the most general properties of space-lattices and of 

 regular structures, were just those, by which also crystals are cha- 

 racterised. Crystalline matter behaves in many respects as a physical 

 medium of continuous structure ; but for a number of physical pheno- 

 mena, as for instance with respect to its cohesion-, and growM-pheno- 

 mena, with respect to its influence on a thin pencil of Ron t gen-rays 

 travelling through it, etc., it exhibits an undeniable discontinuous cha- 

 racter. The validity of Hauy's law for space-lattices, the correspon- 

 dence of the values for the periods of eventually occurring symmetry- 

 axes in regular systems of the kinds mentioned above, and the circum- 

 stance that all possible regular structures as deduced in the modern 

 structure-theories belong exactly to the same 32 classes to which 





