Mr. J. Larmor. [^ a } r 14-. 



The value of KI in electromagnetic units is very small, the square of 

 the reciprocal of the velocity of light in the medium ; so that there 

 are, broadly, two classes of media, (i) , conductors in which KI is 

 neglected, (ii) insulators in which UiV\w\ are zero. The equations of 

 propagation for each case are involved in, the above equations. 



Propagation in Dielectric Media. 



The simplest and most important case of this generalised theory, 

 as displacement currents in conductors are negligible, is that of 

 dielectrics. 



In the first place, .we may consider the propagation of V. We 

 have 



\dx dy dz 



Now 



L+ + = fl^+*! + *F 

 4 ^ dy * dz J / U dy ^dz 



r dt 



dV 

 ~dt 



t 2 TT (PV d 



Therefore _ V <V = _-_ 



1-hEi .. (FV-' 1 , f ,,<?V, 

 a.d, finally, -g- v-V = _ __ v J v't> -^ ^, 



n wnich is a function of'r. 



This equation determines the mode of propagation of V. It repre- 

 sents wave-motion of a complicated character which may be analysed 

 most easily by applying the equation to the case of a plane wave with 

 the displacement at right angles to its front. There are two com- 

 paratively simple cases. 



(i.) If vV = '! = A + Br~', the equation becomes 



K, dt- 



which represents wave propagation with velocity depending on the 

 wave-length, and therefore involving dispersion. 



