﻿Theory of the Optical Properties of Metals. 669 



We therefore conclude that 



ip(l — a A) 1 — a A 



or again 



which is the fundamental equation of the theory in its most 

 general form. 

 If we write 



G*-«b)» = i + jA^ 



so that yu- aud tc would be the refractive index and absorp- 

 tion coefficient respectively of the metal if the free electrons 

 were extracted, and if also we can separate C into real and 

 imaginary parts in the form 



= 0, + »c„ 



then we may conclude that 



fX 2 — k 2 = Hq 2 — icj + 



a 



p(l-aA)' 

 whilst 



The whole question thus turns on the determination of C 

 and its separation into real and imaginary parts. We have 

 above given the most general form for C obtainable on the 

 basis of the present theory, but it is probably too complicated 

 to be of any assistance in the present instance, and we must 

 have resort to the first approximation furnished by the 

 analysis for stationary waves. In fact, if the velocities of 

 the greater majority of the electrons are considerably smaller 

 than the velocity of propagation of radiation in the medium, 

 we may write with a sufficient approximation even for 

 progressive waves 



3??l V 7T 3 J , [pirn ' 







* This separation is not correct since A is also complex ; but it i* 

 probably sufficient in any real case to take A in the terms in C with its 

 real value alone. 



