522 The Electromagnetic Theory of Light [CH. xvni 



satisfied by each of the six quantities X, Y, Z, a, ft, 7, reduces for a wave of 

 frequency p to 



1 *^u + V*u = 0.. ...(569). 



L> " 



For a conducting medium, replacing K by K -\ : , we find that the 



1J}T 



differential equation becomes 



(^-^) + V-u-0 ..................... (570). 



For a plane wave propagated in a direction which, for simplicity, we shall 

 suppose to be that of the axis of x, the solution will be 



where (a + W= __ ..................... (572). 



Kestoring the time-factor e ipt , the solution (571) becomes 



the negative sign in the ambiguity being taken so as to give propagation 

 parallel to the positive axis of x. Clearly this solution represents the propa- 

 gation of waves having velocity p//3 and wave-length X given by /3 = 27r/X, 

 the amplitude of these waves falling off with a modulus of decay a per unit 

 length. From equation (572) we obtain, on equating imaginary parts, 



so that, in terms of the wave-length X and frequency p, the modulus of decay 

 is given by 



= # ................................. (573). 



We see at once that for a good conductor a is large. Thus good 

 conductors are necessarily bad transmitters of light, so that transparent 

 substances (e.g. glass) are necessarily good insulators. The converse of thia 

 statement is not true opaque substances are not necessarily good conduc- 

 tors, for other agencies, which have not been taken into account in the 

 present analysis, may interfere with the transmission of light. 



601. Let us form an estimate of the magnitude of a by substituting 

 approximate numerical values in equation (573). For a wave of yellow light 

 in silver or copper we may take in c.G.s. units (remembering that r as given 

 on p. 331 is measured in practical units), 



j = 3xl0 15 , ^=1, X = 6xlO- 5 , 

 T = 1-6 x 10~ 6 ohms = 1-6 x 10 3 (electromag.), 

 from which we obtain a = 11 x 10 8 . 



