128 



Mr. H. A. Miers on the 



faces. They vary from the habit of fig. 4, in which the cube 

 predominates, to the similar combination of octahedral habit 

 in which the cube-faces are comparatively small, crystals of 

 cubic habit being most common. The dodecahedron-faces d 

 often enter into the combination, as is shown in fig. 5, which 

 represents a third distinct habit characterized by the pre- 

 dominance of the hemihedral form x. The only other form 

 observed on these crystals is {2 1 1}. The cube, octahedron, 

 and dodecahedron planes are bright and even, while the faces 

 x are bright, but slightly rounded and uneven ; they are 

 roughly striated parallel to their intersections with the octa- 

 hedron, and sometimes parallel to the most remote of the three 

 nearest cube-faces. 



The angles, measured and calculated, are as follows : — 



Observed. 



Calculated. 



Mean. 



No. of 

 edges. 



Limits. 



a?=(986J. 



x =(875). 



(100):*=47° 30 



18 



46° 39 — 48 22 



48° 0-7 



47 4-7 



(010): ^=53 43 



18 



52 34 — 55 49 



53 308 



53 255 



(001) : *=63 58 



18 



62 45 — 64 53 



63 308 



64 48-6 



(111):*= 9 23 



11 



8 54 — 10 49 



9 14-5 



10 356 



The best measurements obtained for a single face x to the 

 three cube-faces were 47° 50', 53° 20', 64° 4'. 



The position of the faces x in the figures shows that they 

 afford an example of the hemihedrism which has been described 

 in the text-books of Crystallography * from the time of Mohs 

 as trapezohedral or gyroidal, and as a theoretically possible 

 though hitherto unobserved mode of hemihedrism in the 

 Cubic System. Within the last three years, however, it has 

 been discovered as occurring on one, and has been suggested 

 for another, artificial salt. 



If alternate faces of the complete 48-faced figure be sup- 

 pressed, two half- forms are obtained for which the cubic and 

 dodecahedral planes are no longer planes of symmetry. It 

 was made clear by Mohs f that these two half-forms are 

 enantiomorphous, and may therefore be distinguished as right 



* Groth, Physikalische Krystallographie, 1876, p. 221 ; Mallard, Traite 

 de Crystallographie, 1879, i. p. 88 (Ilemiedrie holoaxe) ; Liebisch, 

 Geometrische Krystallographie, 1881, p. 246 (7 {hkl}). 



f Mohs, Gi-undriss der Mineraioyie, i. 1822, p. 170. 



