264 



PRINCIPLES OF CRYSTALLOGRAPHY. 



Fu).38 



the planes of the axes appear roimd the normal to the plate, (second 

 crystallographic axes, o Y, bisecting,) dispersed in the shape of a fan, 

 (Fig. 38.) 



3. Oethorhombic system. — Three unequal planes of symmetry at 



right angles to each other. Every plane 

 of symmetry must coincide with a prin- 

 cipal section ; here the position of the 

 princii)al optical section is completely 

 determined, and only the value and po- 

 sition of the axes of elasticity are unde- 

 termined. In most cases the similar 

 principal sections of all colors coincide, 

 as also do the axes of elasticity «, 6, c. 



The image of the axes, according to the former suppositions, is sym- 

 metrical with regard to the two black beams; it appeals also in white 

 light, similar to Fig. 34, bat in this case the black ellipses are replaced 

 with color. The principal optical section is not dispersive ; the optical 

 axes, however, are ; that is, the angle of the axes is different for different 

 colors, as in both the previous systems. 



4. Khombohedric system. — Three tautogonal and similar planes of 

 symmetry, inclined at an angle of GCP. Every one of these must be a 

 principal section of the ellipsoid; this is only possible if all these zones 

 belonging to the section of the ellipsoid are equal to each other; that is, 

 it is an ellipsoid of rotation ; the principal section perpendicular to the 

 plane of symmetry is a circle; the axis of the zone of symmetry is the 

 optical axis of all the colors. Here, as we have already mentioned, two 

 cases are possible, positive or negative crystals, according as & = c or 

 a = &. 



If we again make the supposition that the similar axes of elasticity 

 coincide for all colors, we get, as the image of a plate cut iierpendicular 

 to the optical axis between two crossed polarizers, a black cross with 

 concentric colored rings, (Fig. 39.) 



5. Tetragonal system. — Five planes of symmetry, four of which 

 l'ig.2>9. are inclined 45° to each other, every alternate one 



being similar, the fifth perpendicular to the four 

 others. 



A principal optical section is parallel to this 

 last, as the hypotlietical plane of symmetry 01. 

 All its perpendicular ellipsoid sections must be 

 equal to each other, because in this zone four 

 planes of symmetry exist, all of which must be 



principal sections of the ellipsoid. The tetragonal system, therefore, is 



optically exactly like the rhombohedral. 

 G. Hexagonal system. — Seven planes of symmetry, six tautogonal 



inclined 30°, every alternate three similar, one perpendicular to them. 



This last, taken as a principal section, makes, as in the two previous 



