138 Mr. 0. Heaviside on Electromagnetic Waves, and the 



become K, c become S, Airg become R, and fj, become L, 

 when making the application to the possible problem ; whilst, 

 when dealing with a real conducting dielectric, g has to 

 be zero. 



Required the solutions of (28) and (29) due to any initial 

 states E and H , when s is not zero. Using the notation 

 and transformations of (25), (or direct from (2G), (27)), we 

 produce 





dE. , , TT 



. . (40) 



which 





• • (41) 



with the same equation for E^ 



The complete solution maybe thus described. Let, at time 

 2 = 0, there be H = H through the small distance a at the 

 origin. This immediately splits into two plane waves of half 

 the amplitude, which travel to right and left respectively at 

 speed v, attenuating as they progress, so that at time t later, 

 when they are at distances +vt from the origin, their ampli- 

 tudes equal ^^ (42) 



with corresponding E's, viz. 



|pH e-" and — £/*i'IT e-»', . . . (43) 



on the right and left sides respectively. These extend 



through the distance a. Between them is a diffused dis- 

 turbance, given by 



H ~^W(« + sW? ( * a - , * a), }< • • • (**) 

 E "-*i£(-sW^-^}. • • • w 



in which v 2 t 2 > z 2 . 



In a similar manner, suppose initially E = F through 

 distance a at the origin. Then, at time t later, we have two 

 plane strata of depth a at distance vt to right and left respec- 

 tively, in which 



E = p o e-^=± y urH, (46) 



the + sign to be used in the right-hand stratum, the — in 

 the left. And, between them, the diffused disturbance 



