262 



PRINCIPLES OF CRYSTALLOGRAPHY. 



as soon as its direction of vibration coincides with that of the analyzer 

 and polarizer. 



In order to observe the absorption, we have only, when the plate is in 

 the position of darkness, to take away the analyzer or the polarizer. In 

 this case only the color corresponding to the one direction of vibration 

 of the plate appears. This occurrence thus shows itself entirely analo- 

 gous to the previous one. 



It is at once clear that a plate i^erpendicular to an optical axis ap- 

 pears dark in every position of the crossed polarizers. Eespecting the 

 relations of a plate with parallel sides between polarizers in a cone of 

 monochromatic light, we only remark that optical axes are shown by a 

 system of very nearly concentric rings, through whose center a dark, 

 straight or hyperbolic beam, or a dark cross, appears. The appearance 

 of these in white light will be described for some of the systems. 



§ 4. — Optical Eelations in each Crystalline System. 



As has already been mentioned above, the position of the principal 

 optical section and the value of the axes of elasticity are difl'erent for 

 different colors. A coincidence takes place only in the case of the exist- 

 ence of one or more planes of symmetry, because such a one must 

 always be a i)rincipal optical section, 



1. Triclinic system. — No plane of symmetry. The position of the 

 ellipsoid of polarization for the different colors cannot be determined a 

 2)r'wri; the axes of elasticity are inclined to the axes of the crystal; all 

 the principal optical sections are dispersed, that is, have a different po- 

 sition for every color. In general, the dispersion of the principal section, 

 both here and in the following crystalline systems, is small, and seldom 

 goes beyond one or two degrees. The appearances of color in plane 

 plates with parallel sides, which allow the optical axes to be distin- 

 guished, are in monochromatic light as follows: A plate perpendicular 

 to the bisectrix shows, when the polarizers are crossed, a black cross, 

 (Fig. 34,) upon one arm of which the elliptical rings of the optical axes 



F/g.3/j.. 



appear surrounded by lemniscates if the principal axes of the plate co- 

 incide with those of the polarizer; when hyperbolae (Fig. 35) pass 

 through the rings of the axes, the principal sections of the plate are 

 inclined 45^ to the polarizer; in white light the rings of some colors 



