242 E. T. Wherry — Amphisymmetric Crystals. 



ment, exert attractions in gyroidal fashion. In general, 

 it is to be inferred that the methods here grouped as 

 chemical may bring out, not the actual symmetry of the 

 crystal structure or of the atoms as they stand, but sym- 

 metry latent in those atoms. 



The recognition that the various methods of bringing 

 out hidden symmetry differ in significance, as above out- 

 lined, makes it possible to replace arbitrariness by ration- 

 ality in the choice of symmetry class. If it is desired to 

 base the classification of a crystal on its actual structure 

 or point system, then the physical methods, which bring 

 out the symmetry of that structure, should be depended 

 upon as indicating the class. If, on the other hand, the 

 purpose is to study atomic forces, then the indications of 

 the chemical methods, which bring out the latent sym- 

 metry of the atoms or molecules, may be followed. X-ray 

 workers need consider in general only the structural sym- 

 metry, but chemists may be interested more in the latent 

 symmetry relations. 



In the alkali halides pyro-electricity, polarized light, 

 and X-rays' all agree in indicating the structure to be 

 cubic holosymmetric, and they should in general be so 

 classified. On the other hand, etch-figures show that the 

 constituent atoms have latent gyroidal symmetry, so that 

 in any application of the properties of the halides to 

 working out the features of alkali metal or halogen atoms, 

 they may be assigned to the cubic-gyroidal class. The 

 statements concerning amphisymmetric substances in cur- 

 rent crystallography books are accordingly inadequate. 

 Groth in his "Chemische Krystallographie " states that 

 potassium chloride is "Kubisch (pentagonikositetrahe- 

 drisch)," i.e., cubic (gyroidal). A better statement 

 would be : " Cubic ; structurally holosymmetric ; latently 

 gyroidal" (or, if class numbers are preferred, "structur- 

 ally of class 32, latently 29"). To cite an entirely differ- 

 ent example, Dana in his "System of Mineralogy" 

 describes scheelite, calcium tungstate, as "Tetragonal; 

 with pyramidal hemihedrism. ' ' In this case neither 

 pyroelectricity nor polarization-plane rotation could 

 occur, so that this statement represents all that could be 

 ascertained about the mineral at the time. However, the 

 "hemihedrism" (or merosymmetry) is shown only by 

 rare faces, probably produced by films of impurities, and 



