Dispersion of Metals. 665 



the Laplacian operator. A wave-train advancing in the 

 x direction with a velocity Y may be specified by 



where p is the frequency and i — ^/ — 1. With the aid of 

 this, the equation of condition becomes 



C 2 „ , .4:rCV 



V J p 



Since the real part of the ratio C/V is by definition the 

 index of refraction (n), we set (7Y = n(l + ^) *, and hence 

 we have 



n 2 (l- f c 2 + 2i f c) = K + i A ^°' . . . . (1) 



p v ' 



The significance of uk, l)ecomes evident on substituting the 

 value of V in the equation of the wave-train, which then 

 becomes 



E v = E e c e V° ; 



Hence n/c is seen to be of the nature of an extinction or 

 absorption coefficient. 



Now in equation (1) it is to be observed that the values of 

 K and a contemplated are those operative for currents of 

 the frequency of those set up by the incident wave-train. 

 If we use the (constant) values for them given by experi- 

 ments with steady currents, ihe equation yields, on equaling 

 the imaginary and real terms of each side, 



n 2 K= and ?i 2 (l — k 2 )=T£, 



relations, which as has been many times pointed out, are far 

 from being experimentally confirmed. And in view of the 

 enormous frequency of the currents which accompany light- 

 waves, it is not surprising that such discrepancies should 

 present themselves. If, however, K and a can be expressed 

 as functions of the frequency, then equation (1) will yield 

 dispersion formulae with which the results of experiment can 

 be compared. Such expressions for K and a have been 

 obtained by several investigators, proceeding from the 

 general hypotheses of the electron theory. The formulae 

 thus obtained for K involve, however, too many undetermined 

 constants to allow of a satisfactory evaluation with the ex- 

 perimental data at our command. Hence it seems best for 



* Drude's notation. 



