STRUCTURE OF QUARTZ 149 



such figures can never lead to a symmetrical whole. So 

 the crystalline form too of this salt is a rhombic form 

 made unsymmetric by the presence of the semi-pyramids, 

 in front, above on the left, below on the right ; behind, 

 above on the right, below on the left. Though the external 

 form in such cases does not always show the absence of 

 internal symmetry, other indications of the asymmetry are 

 present as erosion figures 1 . 



If the molecule is symmetrical, still the arrangement in 

 the crystal may lead to an unsymmetrical whole, as is the 

 case, e.g., with quartz (SiO 2 ), 

 whose molecular constitution is /\""f\~""?\ 



, i , C / W \/ \ 



symmetrical, as appears from 

 its triatomicity, as well as from 

 its inactivity in the fused state. 

 Just for this case, Sohncke 2 

 worked out a crystalline struc- 

 ture that gives an account of the 

 enantiomorphic and therefore asymmetric reflected image 

 forms of quartz, and the opposite and equal optical activity 

 associated with them. Assume first three spatial gratings, 

 in which the particles are arranged 

 according to the trigonal prism 



(Fig. 32), interlaced as in Fig. 33, Q Q 



in which they are projected on j g* 



the base of the prism ; point i 



requires a rotation of 120 about Q 2< m 3 ^ 

 an axis passing normally through ^ 



the centre of the triangle 1,2,3, an( l O. 



a displacement along the latter, ^ 



to come into the position of point 2 ; Fi q 



the latter, a similar screw move- 

 ment, to become 3 ; finally, a repetition of the movement gives 

 a fourth point, whose projection, however, coincides with 

 that of i. If then we draw a circle through the projections 



1 See the discussion Trube, Walden, Berl. Ber. 29. 1692, 2447 ; 30. 98, 288. 



2 Groth, Physik. Krystallographiej 1894, p. 262. 



