324 



POLARISATION. 



through the mean axis or are parallel to it. Their inclination to 

 the axis a is determined by the ratio a:l:c, and we get 



8 denoting the angle of inclination in question. The normals of the 

 circular sections i.e., the lines which cut them perpendicularly 

 therefore lie in the plane of the major and the minor axes ; they 

 intersect the former at angles which are the complementary of 8 

 to 90. 



We will endeavour to demonstrate these relations by a diagram. 

 Let a a (Fig. 181) be the major, and c c the minor axis ; the mean 



FIG. 181. 



FIG. 182. 



axis, which is perpendicular to the surface of the paper, appears 

 therefore at b as a point. Let the two circular sections be k k and 

 k' k' ; they are also perpendicular to the surface of the paper, and 

 are consequently seen as lines which form right angles with the 

 normals o o and o o'. 



The optical action of double-refracting substances is connected 

 with these properties of the ellipsoid of elasticity, as follows : 

 If P Q (Fig. 182) is a piece of double-refracting substance with any 

 known ellipsoid of elasticity, its action upon the pencil of parallel 

 rays a b is dependent only upon the ratios of elasticity in a plane 

 -/' n perpendicular to the direction of the rays, and is consequently 

 determined by the ellipse which represents the diametrical section 

 of the ellipsoid parallel to that plane. If, therefore, we suppose 

 any given object rotating under the Microscope, so that its 

 ellipsoid of elasticity (Fig. 183) gradually assumes all possible 

 inclinations to the rays of light incident from below, then the 

 effect which it produces is determined for each position by the 

 sectional surface m b n I, which is parallel to the plane of the 



