288 Mr. J. J. Thomson on 



city is less for 2000 reversals a second than when the dis- 

 placement is not reversed. It would be interesting, however, 

 to see whether, with the rate of reversal obtainable in a labo- 

 ratory, the specific inductive capacity altered more quickly 

 with the rate of reversal the greater the refractive index of the 

 medium. 



The boundary conditions will enable us to determine the 

 intensities of the refracted and reflected rays produced by a 

 ray of plane-polarized light incident on a reflecting surface. 

 According to Maxwell's theory, the electric displacement is 

 perpendicular to the plane of polarization, the magnetic dis- 

 placement is in the plane of polarization, and both these dis- 

 placements are perpendicular to the direction of propagation 

 of the ray. 



Let us calculate, first, the intensities for the reflected and 

 refracted ray for light polarized perpendicular to the plane of 

 incidence. 



Let 



o^sin — (vt— e), a 2 sin — (vt— e), a 3 sm^-j(v f t—e) 

 AAA 



be the electric displacements perpendicular to the incident 

 ray P, the reflected ray P 0', and the refracted ray P 0", 

 respectively ; then since we suppose p, q, r all zero, by equa- 

 tion (5) the magnetic displacements perpendicular to the 

 plane of incidence will be respectively 



4-7T . 27T / A v 47T . 2-7T , , >. 



axsin— (vt—ej, -— ^ — a 2 sm-zr-{vt—e)j 



4tt . 2tt / , v 

 for the incident, reflected, and refracted rays, where K 1? K 2 are 



