CRYSTALS UNDER THE MICROSCOPE 181 



TETRAGONAL SYSTEM. 



Two equal horizontal crystallographic axes at right angles to each other and to 

 the vertical. Vertical or c-axis either longer or shorter than the other two. c-axis 

 is one of fourfold symmetry. Each horizontal axis is one of twofold symmetry. 



Interaxes (lines) bisecting the interaxial angles between a- and b-axes may also 

 serve as subordinate axes of symmetry. 



Cleavage, rectangular. 



Uniaxial. 



Optic axis coincident with c-axis. Hence in one position isotropic; in other two, 

 parallel extinction. 



Crystals four-sided or eight-sided or lath-shaped or six-sided. Four- or eight- 

 sided crystals isotropic (seen on end). Crystals lying on their side give parallel 

 extinction. 



Interference figure: symmetrical cross with concentric rings. 



Index of refraction, e in direction parallel to optic axis; index in the plane 

 normal to the optic axis. 



HEXAGONAL SYSTEM. 



Vertical or c-axis is at right angles to the three horizontal axes at their point 

 of intersection. Horizontal axes intersect at angles of 60. c-axis may be longer 

 or shorter than the horizontal and is an axis of sixfold symmetry. Each hori- 

 zontal axis is one of twofold symmetry. 



Interaxes may serve as subordinate axes of symmetry. 



Cleavage lines usually intersect at angles of 60. 



Uniaxial. 



Optic axis coincident with c-axis. 



Crystals three-sided or six-sided, or long rectangles showing three faces. Three- 

 angled and six-angled forms usually isotropic (seen endwise). Long crystals 

 lying on their sides exhibit parallel extinction. 



Interference figure: symmetrical black cross with concentric spectrum colored 

 rings. Tetartohedral crystals are circular polarizing. 



Indices of refraction have same relations as in tetragonal system. 



ORTHORHOMBIC SYSTEM. 



Three axes at right angles to each other, of unequal length. Each axis is one 

 of twofold symmetry. Any axis may be made the vertical. 



Cleavage in direction of diametral planes. 



Biaxial. 



Optic axes: since any crystallographic axis according to convenience may be 

 made the c-axis no relationship may be formulated between the optic and crys- 

 tallographic axes. 



Extinction parallel 1 in all three positions of the crystals. 



Three indices of refraction, least index in direction of greatest elasticity, greatest 

 index in direction of least elasticity. 



MONOCLINIC SYSTEM. 



Three axes of unequal length. The a-axis and c-axis are oblique to each other. 

 The b-axis is perpendicular to the other two at their point of intersection. The 

 b-axis is an axis of twofold symmetry. 



1 In biaxial crystals complete extinction is obtained only with monochromatic 

 light. 



