152 The Aether as an Elastic Solid. 



Fresnel, that the vibrations are executed at right angles to the 

 plane of polarization, and that the optical differences between 

 media are due to the different densities of aether within them. 



It now remained for Green to discuss the case in which the 

 incident light is polarized at right angles to the plane of inci- 

 dence, so that the motion of the aethereal particles is parallel to 

 the intersection of the plane of incidence with the front of the 

 wave. In this case it is impossible to satisfy all the six 

 boundary-conditions without assuming that longitudinal vibra- 

 tions are generated by the act of reflexion. Taking the plane 

 of incidence to be the plane of yz, and the interface to be the 

 plane of xy, the incident wave may be represented by the 

 equations 



6 = A + lz 



where, if i denote the angle of incidence, we have 



I = . / cos i t m = - / sin i. 

 \n Mn 



There will be a transverse reflected wave, 



and a transverse refracted wave, 



y); e z = - C f(t + 1& + my), 



where, since the velocity of transverse waves in the second 

 medium is v/W/oz, we can determine ^ from the equation 



^f^.&j 



n 



there will also be a longitudinal reflected wave, 



8 9 



e y = D -f(t -\z + my); e z = D -f(t - \z + my), 



