178 



bohedra just mentioned (fig. 1400). The angles of these extinction- 

 directions with the diagonal of each rhombohedron-face will in 

 these three cases be respectively: 46, or 11, or 24. 



The mimetic form thus obtained is therefore now an apparent 

 rhombohedron, which however itself is again pseudo-cubic. Two 

 such pseudo-cubic simulative forms may now combine into pene- 

 tration-twins, with either their pseudo-trigonal axis c as twin-axis, 

 or, rarely, with the face (1011) as twinning-plane. 



In the first case we may have the complex of fig. i^ob, which, 

 by a suitable development of its bordering faces, finally obtains 

 the simulative form of the regular rhombic-dodecahedron (fig. 1400), 

 sometimes in combination with a subordinate form representing an 

 apparent octahedron. 



6. The case of chabazite is very instructive in so far as it illu- 

 strates how strongly the tendency of the original lower symmetrical 

 individual to similate a higher symmetry, is exhibited. The triclinic 

 individual has the latent predisposition in its space-lattice to imitate 

 a trigonal symmetry; but it has also the capacity of simulating a 

 yet higher symmetry, namely that of a cubic crystal. Now repeated 

 twinning is made use of, first, to reach the already false position 

 of a mimetic, pseudo-trigonal individual; but, as it were, not satis- 

 fied with this success, it again combines and recombines, until finally 

 the deceptive form of the higher symmetrical cubic rhombic- 

 dodecahedron is reached. 



The result in all such cases is one of the same kind: the pseudo- 

 symmetrical crystal finally approaches more closely, by repeated 

 combination of individuals of its own species, to the higher symmetry, 

 to which the predisposition is a part of its special internal structure, 

 and of which the single individual is only a defective representative. 



This strong tendency to strive at higher perfection by aggregation 

 is one of the most remarkable facts in inorganic matter; it is a 

 "struggle for higher symmetry", by the aid, as it were, of the 

 most primitive form of "communism". Just as union into well- 

 governed states gives a greater stability of life to human creatures, 

 and is the necessary condition for their speedy and regular progress, 

 so the aggregation of imperfectly shaped crystals into higher sym- 

 metrical complexes, is probably a way of reaching a higher degree 

 of mechanical stability. 



7. It was such facts as these, that have led Mallard since 

 1876 to his most suggestive explanation of a number of optical 





