170 The Aether as an Elastic Solia. 



a maximum in an equatorial direction, its amplitude being, in 

 fact, proportional to the sine of the polar distance. The polar 

 line must, by considerations of symmetry, be the line of the 

 incident vibration. Thus we see that none of the light scattered 

 in the ^-direction can come from that constituent of the incident 

 light which vibrates parallel to the o>axis ; so the light observed 

 in this direction must consist of vibrations parallel to the 2-axis. 

 But we have seen that the plane of polarization of the scattered 

 light is the plane of xy ; and therefore the vibration is at right 

 angles to the plane of polarization.* 



The phenomena of diffraction and of polarization by scatter- 

 ing thus agreed in confirming the result arrived at in Fresnel's 

 and Green's theory of reflexion. The chief difficulty in accepting 

 it arose in connexion with the optics of crystals. As we have 

 seen, Green and Cauchy were unable to reconcile the hypothesis 

 of aethereal vibrations at right angles to the plane of polariza- 

 tion with the correct formulae of crystal-optics, at any rate so 

 long as the aether within crystals was supposed to be free from 

 initial stress. The underlying reason for this can be readily 

 seen. In a crystal, where the elasticity is different in different 

 directions, the resistance to distortion depends solely on the 

 orientation of the plane of distortion, which in the case of light 

 is the plane through the directions of propagation and vibration. 

 Now it is known that for light propagated parallel to one of the 

 axes of elasticity of a crystal, the velocity of propagation 

 depends only on the plane of polarization of the light, being the 

 same whichever of the two axes lying in that plane is the 

 direction of propagation. Comparing these results, we see that 

 the plane of polarization must be the plane of distortion, and 

 therefore the vibrations of the aether-particles must be executed 

 parallel to the plane of polarization.f 



* The theory of polarization by small particles was afterwards investigated by 

 Lord Rayleigh, Phil. Mag. xli(187l). 



fin Fresnel's theory of crystal-optics, in which the aether-vibrations are at 

 right angles to the plane of polarization, the velocity of propagation depends only 

 on the direction of vibration, not on the plane through this and the direction of 

 transmission. 



