486 wherry: classes of crystals 



on this substance with X-rays have yielded contradictory re- 

 sults; Vegard^ interpreted his data as indicating a sphenoidal 

 arrangement of the oxygen atoms, while WilUams^" worked out 

 a trapezohedral configuration of the structure-unit, the structure 

 as a whole being holohedral. The second view seems on the 

 whole the most reasonable, so the crystalUzation of rutile, as 

 well as of cassiterite and zircon, which belong to the same group, 

 should probably be stated as: 



System, tetragonal; structure, holohedral; structure-unit, 

 trapezohedral. 



The structure of sulfur has not been fully worked out by 

 X-rays, as it shows a peculiar abnormahty in the spacing of the 

 planes in the direction of the vertical crystal axis. No assign- 

 ment of the structure-unit to a special symmetry class is pos- 

 sible, but it may be pointed out that the habit of the crystals of 

 this substance is sometimes decidedly bisphenoidal, whereas the 

 remaining properties are holohedral, which indicates a relation 

 similar to that shown by the other substances here considered. 



Manganite has not been studied by X-rays at all, and it pos- 

 sesses metalhc properties to such an extent that neither electric 

 polarity nor optical rotatory power can be observed. But a 

 bisphenoidal distribution of faces has been observed on crystals 

 of it from many localities, and crystals altered to pyrolusite 

 from Virginia recently studied by the writer^i show in addition 

 hemimorphism along the right-left crystal axis b. The hemi- 

 morphism in this case appears to be merely a result of difference 

 in rate of growth, since the forms observed at both ends have 

 essentially the same symbols, and moreover, etching figures on 

 this mineral exhibit holohedral symmetry. It may therefore 

 be suggested that in manganite the structure-unit possess some 

 hemihedral feature not present in the structure as a whole, and 

 this finds expression in the peculiarities observed in the distri- 

 bution of faces. 



The evidence collected in this paper appears to justify the 

 conclusion that both the symmetry of the space-lattice as a 



9 Phil. Mag. VI, 32:90. 1916. 



1° Proc. Royal Soc. A. 93: 418. 1917. 



11 To be described shortly in collaboration with Prof. Thomas L. Watson. 



