TKTRAGONAL SYSTEM 81 



and character of the solvent, ,i> well as upon the crystal 

 form etched; but, however produced, if produced under like con- 

 ditions, the etch figures on all faces of any one form will be alike 

 aiul conform to the symmetry of the face. Etch figures are there- 

 fore one of the most reliable means of determining the symmetry of 

 any crystal face, and often decide the type to which a crystalline 

 compound will belong when the crystal forms or combination of 

 forms fail, and when the most general or distinctive form of the 

 type is absent. Nickel sulphate, NiS0 4 , 6 H 2 O, has been placed in 

 the tetragonal holoaxial type from the symmetry of its etch figures 

 alone, while the most general or distinctive form of this type, the 

 tetragonal trapezohedron, has never been observed on any crystal, 

 and from the combination of forms alone it might belong to type 

 27, ditetragonal equatorial, or to type 24, the tetragonal equatorial. 

 As an illustration of the method of determining the symmetry of 

 apparently holohedral hemihedrons, Fig. 146 a represents the seven 

 tetragonal prisms of the first order, with diagrammatic etch figures on 

 each, conforming to the symmetry of the face in each of these seven 

 possible prisms in the tetragonal system. The planes of sym- 

 metry where they cross the prism face are represented by dotted 

 lines and where they cross the etch figure by a white line. In 27, 

 the ditetragonal type, the prism face is symmetrical to two planes 

 of symmetry, the vertical and equatorial planes and a center of 

 symmetry. The shape of the etch figures on this face a, as indi- 

 cated, must be symmetrical to planes parallel to these two planes 

 and an axis of symmetry ; furthermore, when the etch figure a is 

 revolved 90 about the vertical axis c, it must become congruent 

 with the etch figures, as a', on the adjacent prism face of the same 

 form. If all these conditions are fulfilled, then the prism is of 

 type 27. 



In type 26, the ditetragonal alternating, where the prism face is 

 crossed by the vertical plane of symmetry only and the equatorial 

 plane of symmetry is absent, the etch figures will be of a different 

 shape, as represented, from those on the prism of type 27. They 

 will be without an axis of symmetry, but will be symmetrical to 

 the vertical plane ; and when revolved 90 around the vertical 

 axis c and reflected over the equatorial plane, they will become 

 congruent with the etch figures, as a, on the adjacent prism face. 



In this type an axis of digonal symmetry ends in the edge ; the 

 etch figure a, if revolved around this axis 180, will be congruent 

 with a'. They are oppositely oriented on adjacent faces. 



