BAD CONDUCTORS. 619 



Eliminating the functions F", G", and H" between these three 

 equations, we get 



/ 2 m* n* 



(27) - + - + -- = 0. 



This is an equation of the same form as that which determines 

 the velocity of propagation of light in double refracting media. 

 For a given direction it gives two velocities corresponding to two 

 distinct waves which move in the same direction. If the wave, 

 for instance, is perpendicular to the x axis, we have ;/z = 0, = 0, 

 and the values of the velocity are b and c. 



636. If the medium is symmetrical in reference to one axis 

 (for instance, the x axis), the two velocities b and c are equal, and 

 equation (27) reduces to 



/2( V 2 _ P)* + (L - /2)(V 2 - 2 )(V 2 - 2 ) = 0. 



For a wave perpendicular to the axis, /= i ; there is then only 

 one velocity of propagation, V = , whatever be the direction of 

 the electrical and magnetic disturbances in the plane of the wave. 

 If the wave is parallel to the axis, /=0, and we have two velocities 

 of propagation, V = a, and V = . The wave which is propagated 

 with the velocity ^, has the character of the ordinary wave in 

 optical phenomena, and corresponds to an electrical disturbance 

 perpendicular to the axis. As this wave is polarized in the plane 

 of the axis and of the ray, we see that the plane of polarization 

 of the light is perpendicular to the plane of the electrical dis- 

 turbance. 



637. BAD CONDUCTORS. Let us suppose that the medium is 

 an imperfect insulator, and is isotropic, and that the effects of 

 displacement and of conductivity are of the same order. The 

 energy is then partially transformed into heat, and the wave which 

 is propagated is gradually weaker. 



Let us consider a plane wave perpendicular to the z axis, the 

 disturbance being parallel to the x axis. Equations (15) give then 



BF **F 2> 2 F 

 (28) 47ir + K = . 



It W W 

 The integral is a function of the form 



F = e~ pz cos (nt qz) , 



