322 POLARISATION. 



since in the compressed glass the attraction of the molecules 

 increases with their mutual approximation, and the repulsion 

 of the atmosphere always keeps it in equilibrium, it must be 

 assumed that the density of the air undergoes a change through 

 the compression in a manner similar to that of the substance. But 

 with the density of the air the velocity of propagation of the light 

 is also changed ; and even if we leave unexplained how this 

 alteration is effected, it is nevertheless apparent that the resulting 

 ellipsoid exhibits the optical properties of the compressed glass 

 in a manner analogous to the surface of elasticity of the crystals. 



There is, moreover, no difficulty in demonstrating experiment- 

 ally the agreement for all the different cases imaginable. If the 

 glass is compressed or expanded in one direction only, it acts 

 as a crystal with one principal axis, which lies in the direction of 

 the active force ; the surface of elasticity is an ellipsoid of revo- 

 lution. If we then apply perpendicularly to the first a second force 

 unequal to it, the ellipsoid of revolution is changed into another 

 having three unequal axes; the glass now acts as a crystal 

 without a principal axis. We may then state generally, that a 

 parallelepiped of glass may always be so compressed that its 

 optical action corresponds to a given positive or negative crystal 

 with one or two axes. 



The manner in which the atmospheric density acts upon the 

 motion of light is, in general, explained by the above-determined 

 relations. But a definite formulation of the precise correspondence 

 has not yet been found. Those relations are not sufficient to con- 

 struct the ellipsoid of elasticity in a given medium with known 

 optical properties, as far as they are determimtble by observation ; 

 this can be done only on assumptions which are derived from the 

 tJieory of the propagation of light, and must therefore not be con- 

 fused with facts such as direct observation furnishes. The undu- 

 latory theory in its present form assumes that the velocity of pro- 

 pagation of light is dependent merely upon the composition of the 

 atmosphere in the direction of the vibrations, but not in the direc- 

 tion of the rays. The ellipsoid of elasticity is hence so constructed, 

 that its diameters, which are parallel to the directions of vibration 

 of any rays, correspond to the velocities (calculated from the refrac- 

 tive indices) with which those rays traverse the crystalline medium. 

 It appears therefore flattened like the globe in positive uniaxial 

 crystals, and oval in negative uniaxial crystals. 



