194 



teristic of crystalline matter, do not necessarily possess the perfect 

 homogeneity involved by Hessel's and Bravais' theories 1 ). Its 

 constituting and identical molecules are therefore not always parallel 

 to each other, but they may have different orientations in space, 

 depending on the special symmetry of the crystalline substance. 

 In very numerous cases it is built up from lower symmetrical masses 

 according to the general laws of twin-formation. 



The fact that it is just those space-lattices whose dimensions are such 

 as to make them appear to possess an approximate symmetry, which 

 show most conclusively, that tendency to aggregate into apparently 

 higher symmetrical complexes whose twinning-elements correspond 

 with the approximate symmetry-elements of these simulated higher 

 symmetrical complexes, was certainly first recognised in its general 

 significance by Mallard. But from this to his later views, that all 

 space-lattices should really be pseudo-cubic 2 ), or that all higher 

 symmetrical crystals should only be pseudo-symmetrical aggrega- 

 tions of submicroscopical lamellae of lower symmetry, -- is a long 

 way. A rational proof of these views cannot at present be given, and 

 as such these hypotheses have no immediate value for our knowledge 

 in its present state. But even if we leave these views aside, it can 

 only be once more emphasised, that the idea of lamellar aggregation 

 has been, and in future will prove, a very successful one in the expla- 

 nation of a great number of the most interesting phenomena in the 

 science of inorganic matter. 



13. In this and the preceding chapters we were able to compare 

 on several occasions the specific symmetry of objects in inanimate 

 and in living nature. As strikingly different features of the sym- 

 metry-properties revealed in both domains we must chiefly bear in 

 mind two important facts: 1) the occurrence in living nature of 

 symmetry-axes which are characterised by irrational values of the 

 cosines of their periods K ; and 2) the much higher symmetry of the 



1) J.Beckenkamp, Statische und Kinetische Krystalltheorien /, p. 194. (1913). 



2) E. Mallard, Bull, de la Soc. Miner. 7. 349. (1884); 9. 54, 123. (1886). 

 F. Wallerant, ibidem, 24. 159. (1901). 



This theory however has in recent times got a new support, although in somewhat 

 modified form, by the dynamical views of J. Stark. According to this investigator, 

 rock-salt for instance would be built up by three submicroscopical systems of tetra- 

 gonal-hemimorphic symmetry. They form a quasi-homogeneous complex of appa- 

 rently holohedral cubic symmetry. Similar ideas are found in a paper of Becken- 

 kamp (Cf.: J. Stark, Jahrbuch f. Radioaktiv. und Elektronik. 12. 280. (1915). 



