188 



completely, it is true, but in any case very nearly, with the space- 

 lattice in its original position. 



If, therefore, such layers of molecular dimensions are successively 

 subjected to all symmetrical operations which correspond to the 

 presence of one or more symmetry-elements of apparent symmetry 

 in the space-lattice under consideration, a complex pseudosymmetri- 

 cal crystal may be formed, exhibiting rotatory power or not, accor- 

 ding to the way in which the superimposed layers are arranged. *) 



As the cross-laid lamellae become thinner, and their compound 

 twinning and mutual penetration more perfect, the mimetic crystals 

 will approach more closely to a true higher symmetrical individual; 

 and if the dimensions of the crossed lamellae become submicros- 

 copically small, the crystal is no longer distinguishable from a homo- 

 geneous one by any existing physical means. Mallard then says, 

 that the substance under consideration is dimorphic; the symmetry 

 of both polymorphic forms being that of the composing lamellae 

 on the one hand, and that of the higher symmetrical individual 

 now obtained on the other. The higher symmetrical modification 

 thus appears as an extremely perfect and regular aggregate of sub- 

 microscopical individuals of the lower symmetrical form, -- in an 

 analogous way to that, in which the mixed-crystals are built up from 

 their isomorphous components by the intercalation of alternating 

 layers of molecular dimensions. 2 ) The suggestive idea of Mallard, 

 therefore, should have the great advantage of reuniting under the 

 same point of view three different phenomena exhibited by crystals : 

 their optical rotatory power, their optical anomalies, and their eventual 

 polymorphism. They should all be explained by the repeated twinning 

 of pseudosymmetrical space-lattices and their combination into 

 aggregates of apparently higher symmetry 3 ) . 



J ) If, for instance, the angle between the consecutive lamellae be 90 or 180, 

 no rotation of the plane of polarisation of the emergent rays will occur. 



2 ) See, however, in this respect: L. Vegard and H. Schjelderup, Phys. Zeits., 

 18, 93, (1917). 



3 ) That this explanation of "polymorphism" cannot always hold, is evident, 

 as has already been recognised by Mallard himself. The mere difference in specific 

 weight between the two modifications, as it is observed frequently, cannot be plau- 

 sibly explained by his theory. However, there is a certain number of substances 

 which behave just as Mallard's view demands. At present these substances are 

 classified as those, which are really pseudosymmetrical, to distinguish them from 

 those in which true dimorphism occurs. Cf.: P. Groth, Einleitung in die Chemische 

 Krystallogvaphie, (1904), p. 4 7; G. Wyrouboff, Bull, de la Soc. Min6r., 29, 

 335, (1906); F. Wallerant, ibid., 24, 159, (1901); 27, 184, (1904). 



