129 



*6; ;6; :6; 



' ' 



Solmcke's theory shows therefore in this respect an analogous 

 li< icncy to that of Bravais, if used for the explanation of such 

 ht r symmetrical crystal-structures, although its deficiency has 

 significance, and is not so strongly marked, as that of 

 view. Therefore Sohncke's theory must certainly be 

 msidered to be a real progress in comparison with that of the 

 itter, although the problem mentioned above has evidently not 



got its most general solution by it. 



12. Before finishing these considerations of Sohncke's regular 

 rstems, we may remark here that the theory can be extended 

 to cases in which the constitutive repeats of the tridimensional 

 ittern are no longer of the same kind, but of different character, 

 [f a definite number of such Sohnckian systems, which all possess 

 le same and parallel translations, but which are neither congruent 

 lor need be built up by the same 

 irticles, be suitably placed the one 

 ito the other, such an interpenetra- 

 tion can lead to a complex, materially 

 leterogeneous system, the foundation 

 >t which is a space-lattice which is 

 laracterised by the translations just 

 lentioned. 



As an instance of this, a section 

 )f such a periodical pattern has been 

 ^presented in fig. 116. It is deduced 

 rom the pattern of fig. 113 in such a way that a motif of an other kind 

 placed every time at the centre of each hexagonal group of fig. 

 r ij. The fundamental features of the regular systems are evidently 

 Dreserved in this new arrangement too, and Sohncke has, for in- 

 stance, proposed systems of this kind to explain the crystal-structure 

 )f complex molecular compounds like salt-hydrates, etc. Moreover 

 ic was able to give a rational explanation in this way of the occur- 

 ;nce of some tetartohedral and hemimorphic crystals, which could not 

 be explained by means of the original, unextended theory of his. 



Another example of two such interpenetrating systema built up 

 from two different motifs, is the pattern shown in fig. 117. Here the 

 symmetry of the whole pattern is evidently the same as of each 

 of its motifs, these having the same tetragonal symmetry. 



The extended theory of Sohncke can be used succesfully for 

 the explanation of the structure of crystalline chemical compounds, 



9 



.* .* 



Fig. 116. 



