64 



Fig. 74. 



Scheelite. 



the crystalforms are reproduced of scheelite: CaWO^, (C^f), and of 



apatite: Cal(PO^, (C^); these figures show 



the respective symmetries comparatively clearly. 



Of course the heteropolar character of the prin- 

 cipal axis has here disappeared; and from the 



figures reproduced, it is obvious that the poly- 



hedra under consideration really possess a 



symmetry-centre . 



The symmetry of the group C H 2 is very often 



met with in the case of crystalline substances: 



all so-called monoclinic substances, the number 



of which is extremely great, belong to this 



group, as far as they are holohedral. 



Commonly the horizontal plane of symmetry is placed vertically 



in figures of this kind, so that the 

 binary axis will now have a horizon- 

 direction. This custom is followed 

 also in the accompanying drawing 

 (fig. 76), which represents a crystal of 

 amphibole : 



p Ca(Mg,Fe)(Si0 3 ) 2 + q MgAl 2 Si0 6 

 in various proportions p and q. 



9. The remaining groups of the 

 second order yet to be dealt with, 

 are related to the dihedron-groups 



D n or to the endospherical groups T, K, and P respectively. 

 Let us start with those which are related to D n , and which, 



therefore, have a homopolar principal axis A n and n binary axes 



situated in a plane perpendicular 



to A n , being either homopolar, but 



of two different sets, or heteropolar 



and of the same set (p. 39). 



We must now add either reflections 



S, or an inversion / to the groups D n ; 



in every case the whole system of axes 



of D n must coincide with itself by 



the operations corresponding to the 



symmetry-elements added. Therefore, 



the following cases must be taken into account: the added plane 



of reflection may be either horizontal : S H , or vertical : S v , and in the 



Fig. 75. 



Apatite. 



Fig. 76. 

 Amphibole. 



