< I;YST.\I.I.<M;I;AIMIY 



15 



' Alternating axis. In Fig. 18, if any point a is revolved around 

 an :i\is oo', <)0 J , to a position a', then reflected over the plane bb', 

 to a position a", becoming congru- 

 ent, and so on four times in one 

 complete revolution, then oo' is a 

 tetragonal alternating axis. If the 

 crystal becomes congruent by ro- 

 tation and reflection six times in 

 :!<'.( i . then the 'axis is a hexagonal 

 alternating axis; in all such cases 

 the plane of reflection is not a plane 

 of symmetry in the crystal. Di- 

 gonal or trigonal alternating axes 

 are not possible. 



Center of symmetry. In Fig. 19, 



FIG. 18. Axis of Alternating Sym- 

 metry : Chalcopyrite. 



if from any point a, a line be drawn to o, the center, and ex- 

 tended an equal distance in the same direction beyond the center, 



when o is a center of symmetry it 

 will meet a point a', similarly lo- 

 cated. The face abc will be re- 

 peated at a'b'c', and all crystals 

 having a center of symmetry will be 

 bounded by pairs of parallel faces. 

 \/Crystallographical axes. In or- 

 der that crystal faces may be located 

 in space, their relations mathe- 

 matically calculated, their angles 

 measured, at the same time furnish- 

 ing a concise, accurate, and con- 

 venient form of expressing all their 

 relations, crystal faces are referred 

 to imaginary lines drawn through 

 the crystal and known as the crystallographical axes. These axes 

 are, as in analytical geometry, generally three (in one system four) 

 intersecting at a common point within the crystal, the origin. 

 The length and inclination of the axes will vary with the system 

 to be represented. The direction through the crystal is always so 

 chosen as to give the simplest relation possible, which is deter- 

 mined by the symmetry that is present. Where there are axes 

 of symmetry present, the axes of highest symmetry are chosen as 

 cry-tallo^raphical axes. Where axes of symmetry are absent the 



Flu. 19. Axinite, showing a Cen- 

 ter of Symmetry. 



