Structure of Zinc Bromate Hexahydrate. 191 



associated with the unit cube, the manner of arrange- 

 ment of the atoms of zinc bromate hexahydrate is defi- 

 nitely determined to be as follows : 



Zinc atoms : Arrangement 4b, 



000: U0; OH; £0£. 



Bromine atoms : Arrangement 8h, 



uuu; u+i, | — u, it: u. it4-£, i—u; |— v, u, U + -J-; 

 uiiu: i — u y w+ij u; u, $ — v.. u + i; u+i, u, 4 — u. 



Bromate oxygen atoms : General positions, 



xyz; x+±, l—y, z: x, y+i, \—z; \—x, y, z+\; 

 zxy; z, x+±, $—y; \—z, x, y+i; z-\-\ % \— as, y; 

 yzx; % — y, z, « + £; y+k, \—z, x; y, z+$, i—x; 

 xyz; i—x, y+$, z; x, -k—y, z+i; x+l, y, \—z; 

 zxy; z y \—x, y+i: z+i, k, i— y; %—z, •x'+i, V: 

 yzx; y + %, z, ±—x; \—y, z + \, x; y, \—z, x+\. 



Water oxygen atoms : General positions with different 

 values of x, y and z. 



Hydrogen atoms : Two sets of general positions. The 

 coordinates and terminology are taken from the writer's 

 book entitled "An Analytical Representation of the 

 Theory of Space Groups" which is shortly to be pub- 

 lished by the Carnegie Institution of Washington. 



An inspection of the special cases of the space group 

 T h 6 shows that the arrangement outlined above is the 

 only reasonable one for the atoms of zinc bromate hexa- 

 hydrate, since any other would string out sets of eight 

 equivalent atoms along the body diagonals of the unit 

 cube. Though it is impossible at the present time to 

 obtain the positions of other than the zinc atoms, it is 

 probable that the value of u, the parameter defining the 

 bromine atoms, is in the neighborhood of -} and that the 

 values of x, y and z for the bromate oxygen atoms are 

 such as to cluster these atoms more or less closely about 

 the bromine atoms. It will also be observed that the 

 groups of atoms constituting the water molecules cannot 

 be unequally distributed between the metal atoms and the 

 bromate groups, but must all be related in exactly the 

 same manner to the zinc atoms (or to the bromate 

 groups). This distribution is in accord with that found 



Am. Jour. Sci. — Fifth Series, Vol. IV, No. 21. — September, 1fl22. 

 13 



