PHENOMENA IN RELATION TO THE ELLIPSOID OF ELASTICITY. 329 



The axial directions of the effective ellipses of elasticity remain 

 altogether unchanged if the rotation takes place round a prin- 

 cipal axis of the ellipsoid situated in the plane of the field of view ; 

 on the other hand, they suffer a continuous alteration if any other 

 diameter or an inclined axis forms the axis of revolution. The 

 approximate process of this change is determined through the known 

 or easily constructed sectional surfaces, which become effective after 

 a rotation of 90. 



There is no difficulty, therefore, from what has been stated above, 

 in approximately determining the position of the axis of the ellipse 

 of elasticity for any inclination of our ellipsoid, and in defining, as far 

 as necessary, the changes with regard to position and excentricity 

 which take place during revolution. The planes of polarisation of 

 the two systems of waves are, however, also given with the axial 

 position ; and with the excentricity the difference of phase, which 

 they attain in a medium of given thickness, also rises and falls. 

 The difference of phase, as is well known, involves interference 

 colour, and thus we arrive at the conclusion that the optical action of 

 a doicblc-refracting medium, whose ellipsoid of elasticity is given, may be 

 pre-determined for any given direction of the penetrating rays of light* 



We have intentionally combined the above explanations with the 

 general case that the three axes of the ellipsoid of elasticity 

 are unequal, since the special cases which may be imagined are 

 contained in them. It may be not quite superfluous, in addition 

 to what has been stated above, to briefly mention these special 

 cases. If we suppose, first, that the difference between the mean 

 and the minor axes of the ellipsoid gradually diminishes and 

 at length becomes nil, then the two circular sections approach 

 nearer and nearer to the plane of these axes, since the angles- 

 they make with this plane become more and more acute, and at 

 length coincide with it. The two optic axes consequently move 

 in an opposite direction ; when they have reached the major 

 axis of the ellipsoid they coincide and form a single axis. The 

 refracting medium becomes, therefore, optically uniaxial and posi- 

 tive, since it was also positive in a biaxial state before the axial 

 angle was 0, in accordance with the above-given definition. If, on 

 the other hand, we suppose the mean axis to become gradually 

 equal to the major axis, then the optic axes at last coincide 

 with the minor axis of the ellipsoid, and the negatively biaxial 

 medium becomes negatively uniaxial. 



