100 



deformation in the direction of the binary axes of a quartz-crystal, 

 suddenly disappears as soon as a temperature of 580 C. is reached l ), 

 because the /3-quartz stable at temperatures above 575 C. has a 

 higher symmetry than the ordinary trigonal- trapezohedral quartz- 

 modification (^-quartz), while the symmetry of the primary cause 

 producing the effect remains the same in both cases. 



That such phenomena can really occur in a crystalline medium 

 which has the symmetry of a sub-group of that group to which 

 the proper symmetry of the phenomenon under investigation 

 belongs, is elucidated by the fact that the symmetry of a crystalline 

 medium is in reality a minimum symmetry, namely the lowest degree 

 of symmetry, beneath which the symmetry of any physical pheno- 

 menon observed in the crystal can never sink. Somewhat different 

 is the case, when phenomena can be produced in the crystal under 

 all circumstances, as e. g. luminous radiation. In truth, their sym- 

 metry appears to be much higher than that attributed to the medium 

 itself according to its cohesion and molecular structure, i. e. than 

 that of the "crystal-class", to which it belongs. In such cases the 

 possibility of the occurrence of the said phenomenon (here: radia- 

 tion), is not dependent, properly speaking, on the special nature of 

 the medium, and the latter can therefore not be looked upon as 

 to be a real physical "cause" of the phenomenon under consideration. 

 These higher symmetries of the phenomena observed are such, 

 that certain symmetry-elements which are characteristic of thes 

 phenomena under all circumstances, are added to those of the 

 crystal-class to which the crystal belongs. 



13. As an illustration of this we wish to consider the symmetry 

 which a crystal will manifest with respect to the diffraction of 

 Ron t gen-rays, if a planparallel plate cut from it in some known 

 direction is traversed by a narrow pencil of such rays perpendicular 

 to its surface. This highly important phenomenon was discovered 

 by Von Laue 2 ) some years ago, and has since been studied by 

 several investigators in different ways, and with particular success 



*) A. Perrier, Archiv. des Sciences phys. et natur. Geneve, 41, 493, (1916). 

 Indeed, it is commonly assumed that the ^3-form of quartz, stable above 575 C, 

 belongs to the hexagonal-trapezohedral class (D$). In that case the binary 

 axes do not possess a "polarity" any longer, as they do in the ordinary a-quartz 

 with its principal axis of odd period. (Cf. also: page 39, and fig. 34 and 35 

 respectively) . 



2 ) M. Von Laue, Friedrich and Knipping, Sitz. Bayr. Akad. d. Wiss. Miin- 

 chen, (1912), p. 303. 



