320 POLARISATION. 



propagating the waves of light in the different directions of space 

 with unequal velocity. That is to say, this propagating power 

 readies its maximum in a certain direction, and its minimum in a 

 direction at right angles ; between these two di- 

 rections the regular transitions lie. If we suppose 

 that from a given point within the substance lines 

 are drawn (Fig. 178), representing the relative 

 conducting power in the corresponding directions, 

 the terminal points of these lines will lie in a 

 surface of ellipsoidal form, of which the given 

 point is the centre. This is the so-called surface 

 FIG. 178. of elasticity or ellipsoid of elasticity. 1 The 

 geometrical axes of this ellipsoid, which are 

 termed axes of elasticity, coincide with the axes of the crystals when 

 the latter are rectangular, but deviate more or less from them in 

 oblique-angled systems. In monoclinic crystal-forms the devia- 

 tion, however, occurs only in the plane which divides them into 

 two symmetrical halves. 



In crystals with one principal axis and equal sub-axes, to which 

 the tetragonal, hexagonal, and rhomboidal forms belong, the con- 

 ducting power is equal in all directions when perpendicular to 

 the principal axis, and greatest or least when parallel to it ; the 

 ellipsoid of elasticity here represents a surface of revolution, whose 

 axis coincides with the principal axis of the crystal. On the other 

 Jiand, in crystals with three unequal axes, such as the rhombic, 

 monoclinic, and triclinic systems, the geometrical axes of the surface 

 jof elasticity are also unequal, hence the latter is an ellipsoid with 

 .a major, a mean, and a minor axis. 



1 Strictly speaking, the surface of elasticity, as Fresnel determined ana- 

 lytically, is not an ellipsoid, but a surface of the fourth order, whose 

 jcquation, with regard to rectangular axes, is 



(-5 4. x"- + y 2 ) 2 = 2 x- -f l~ y*~ + c 2 z\ 



'The diametral sections through these surfaces are, however, approximately 

 .ellipses, and in two particular positions circles as in the ellipsoid. The same 

 also is true for the surface of elasticity of pressure, according to Neumann. In 

 mathematical Optics the ellipsoid, being far easier to manipulate than the 

 ,real surface of elasticity, is hence mada the basis fer further calculations. 



For the following considerations a definite assumption as to the form of the 

 : surface of elasticity is not at all necessary. It is sufficient to know that its 

 : sectional surfaces are, in general, oval figures with two unequal axes, and in 

 itwo special cases circles. 



