260 



PRINCIPLES OF CRYSTALLOGRAPHY. 



If a crystal has a plane of symmetry, it must coincide with a princi- 

 pal section of the ellipsoid for every color, because an ellipsoid with 

 three axes is symmetrical only in its principal sections ; this coincidence 

 must not, however, occur in the same principal section for every color; 

 thus, for red light, h c, and for blue light, ac, may fall in the plane of sym- 

 metry. If two axes of elasticity of the same ellipsoid are equal, their 

 principal section will be a circle, and the two axes become reduced to one ; 

 if, tor instance, the third axis of elasticity is perpendicular to this principal 

 section, the ellipsoid is an ellipsoid of rotation. The sections of such 

 an ellipsoid, with a plane, are either perpendicular to the optical axis, 

 section a circle, no double refraction, direction of vibration undeter- 

 mined ; or parallel to the optical axis, section an ellipse, one axis of which 

 is the optical axis, the other has a constant value, which is that of the 

 axis of elasticity originating in the circle ; or inclined to the optical axis, 

 section an ellipse, whose axes are inclined to the optical axes. Ellipsoids 

 with a single axis are of two kinds, lengthened or flattened, according as — 



h = c 



the optical axis ; negative crystal, (Fig. 31.) 



a = h ; _f the optical axis ; positive crystal, (Fig. 32.) 



n-y.3J. 



Ficj.SZ. 



If all three of the axes of elasticity of the ellipsoid are equal to each 

 other, it becomes a sphere ; every section by a plane will be a circle : all 

 the axes of such a circle will be equal to each other. Such a crystal is 

 mouorefiingent, and has no determined direction of vibration, that is to 

 say, the direction of vibration of the beam of light entering the crystal 

 remains the same. 



As has been already mentioned above, the relations of absorption in 

 the whole crystal can be determined if they are given for the three axes 

 of elasticity. If we construct an ellipsoid from the three principal ab- 

 sorption-constants (for a determined color) as axes, we find, exactly as 

 in the ellipsoid of polarization, the amount of absorption for a given 

 direction in the crystal by i^assing a normal plane and determining the 

 axes of the elliijse- section so produced. 



