180 R. W. G. Wypkoff — Crystallp graphic and 



multiple of 96. In other words, the number of atoms of 

 nitrogen and of chlorine in a nnit cube must be 96 or some 

 submultiple thereof. Neither 64 nor 27 are such submul- 

 tiples so that it must be concluded that either one or eight 

 molecules of ammonium chloride are associated with the 

 unit cube. These two groups of possible arrangements 

 are most readily studied with the aid of table l. 5 It will 

 be observed that there is no space group isomorphous 

 with (the enantiomorphic hemihedry) having special 

 cases which permit the placing of one molecule of ammo- 

 nium chloride within the unit. All possible arrangements 

 for the atoms of ammonium chloride that will have the 

 desired symmetry are as follows : 



(2) From O 4 : 



N- c\c\c\' iin* i(U • nii« m- 331. 313. 133 

 . UUU, -2 2"U, 2 U 2"? U 2"2> 4?i) U 4 J 444) 444' 



CI • 1 1 1 • f)()l. • 0^0 • J-00, ' 333 • u=£ • -L 3 -! • 3 11 

 Vyi • 222? uu 2 ) VJ 2 U 5 2 WU ) 444) 444) 444) 444* 



H : Thirty-two points one of which is uuu. 



(3) From O 8 : 



N: 000; Ofi; JOf; fiO; J#; f|i; *»; Uh 



Cl:Ui; iiO; Oil; |§|; A; |o}; f|u; 8».; 



H: Two groups of 16 equivalent positions obtained by 



assigning two different values of u to groups of points one of which 



is uuu. 



(4) From O 1 : 



Eight equivalent positions: 

 uuu/ uuu/ uuu/ uuu/ uuu/ uuu/ uuu/ uuu. 

 N: At t( = u 

 CI : At u = w 3 , 



H: At u = u 3 , and at 24 other positions which may 

 be chosen in various ways. 



(5) From O 2 : 



Eight equivalent positions: 



uuu; uuu; uuu; uuu/ | — u^—u^—u/ 



H-i,i— u ,u+i; |— w,w+i,w+i; 

 u-\-^,u-j-^—u. 



N: At u = u l9 

 CI: At u = w 3 , 



H: At u = u 3 and at 24 other points which can be 

 chosen in several ways. 



5 This table and the discussion. which follows is based upon material con- 

 tained in a book entitled "An Analytical Expression of the Theory of 

 Space Groups," as yet unpublished. A similar table will be found in 

 P. Niggli, Geometrische Krystallographie des Discontinuums, p. 410. 



