238 E. T. Wherry — Amphisymmetric Crystals. 



developed, a crystal may seem more symmetrical than it 

 really is (pseudo-symmetry). Accordingly, when differ- 

 ent methods have indicated different classes (amphisym- 

 metry) it has been customary to select as typical that 

 possessing the lesser degree of symmetry. For example, 

 the alkali halides show consistently, when studied by the 

 methods of group A, cubic holosymmetry (Class 32) ; yet, 

 just because those of group B yield forms with the lower 

 cubic gyroidal symmetry (Class 29), this series of com- 

 pounds is assigned by practically all crystallographers to 

 the latter class. On the other hand, in diamond the 

 methods of group A indicate cubic holosymmetry (32), 

 those of B hextetrahedral (31). In this case some 

 crystallographers follow the same rule as with the halides, 

 and assign diamond to the class of lower symmetry, while 

 others equally arbitrarily assign it to the higher. 



As long as crystallography was of little interest to any- 

 one working in other sciences, the fact that symmetry 

 classes were at times selected arbitrarily does not appear 

 to have attracted any particular attention ; but after Laue 

 thought of passing X-rays through crystals and his 

 striking results led physicists to read up on crystallog- 

 raphy, considerable perplexity began to be registered. 3 

 Thus the Braggs in "X-Rays and Crystal Structure/ f 

 p. 157, say: 



"This structure [worked out by X-rays] lias holohedral sym- 

 metry. If the copper and oxygen atoms have these exact geo- 

 metrical positions, the crystal of cuprite ought to exhibit holohe- 

 dral symmetry. Instead of this, certain uncommon forms of the 

 costal show that its symmetry is in reality holoaxial [Class 29]. 

 If this holoaxial symmetry corresponded to a large distortion . . . 

 it is probable that the spectra would show the influence of this 

 distortion .... On the other hand the c^stallographic evidence 



3 Since the submission of this paper for publication, Wyckoff (This 

 Journal, 3: 177, 1922) has brought out the difficulty in a striking way. He 

 urges further study of the crystallography of ammonium chloride (and 

 inf erentially of other halides) . It is shown in the .present contribution that 

 what is needed is a more discriminating interpretation of existing data ; the 

 ' ' crystallographic information ' ' supposed to point " to an enantiomorphic 

 hemihedry ' ' does not do anything of the sort, but merely shows that the 

 atoms when set free from the crystal structure exhibit some enantiomorphic 

 features, which their electron arrangement necessitates in any case. Ammo- 

 nium chloride, one of the 15 members of the sodium chloride group tabulated 

 below, is structurally holosymmetric and only latently gyroidal (enantio- 

 morphic) . Compare also footnote 6, below. 



