Theory of the Optical Properties of Metals. 441 



so that 



~ ±7re 2 L 



.— r 00 i+-! 



and 



771V rf] --1' 



oo 1,4 



3m<f 2 Jo !+(£*/ 



,-^-t- = 1 + a(j^iJ? r - 1) , 

 1 — a A 



kirpeH 



a=- - 



then it is easily verified that ^ 



If we are dealing with light of a period somewhat removed 

 from the proper periods of the free vibrations of the resonance 

 electrons, there will be no absorption due to these, and thus 

 & r =0 and the formulae reduce to 



Poo 4 * 



2 47T^lN(l + a/^l) 



= Mr 2 r~i V 



3m</ s 2 

 , 27r* 2 / m N (1 + a/xT^I) /y 7 f " o- 1+ V~ J ^cr 



3mp ? 1+s Jo 1 + (#>■)* 



These are the general results of the more detailed theory. 

 If we use <r for the conductivity for steady currents, and 

 fjL ro the value of fi r when p = 0, then the last equation may be 

 written in the form 



I <7 S ~ 



+ o -< 



*e 



da 



•A> i+ 



4 



-1 



2 



da 





i-i-«(^. 2 -i) go r <r i+ ^ e "v - 



'>C !+ *> 



It is obvious that the present investigation does not 

 materially affect the general comparison of the theoretical 



