Dispersion of Metals. 6fi7 



unable, however, to confirm his values for the numerical 

 coefficients in the expansions, but find them as given above. 

 If we had made use of the average velocity of the electrons 

 instead of assuming the Maxwellian distribution, we should 

 have been led to the expression 



a = <T 



.pm<r Q 



J--M V 2 



±Se~ 



1 + 



p' z m' 2 a^ 



NV 



the real part of which is the formula given by Schuster and 

 Jeans. It is included here for the sake of a comparison of 

 the results of the two hypotheses as to the electronic 

 velocities. 



If now we write S] and S 2 for the two series in equation (4) 

 and substitute the value of a in equation (1), we obtain, on 

 separating the real and imaginary parts, 



n~/c= 9 Si, ('-)) 



p 6 nr<T 



and 



» 2 (l-/t 2 )=K- 4w ^ NgS S 2 , .... (6) 



in which, in the first terms of each series the value of a is 

 quoted from equation (3). Equation (6) differs from that 

 given by Nicholson (loc. cit.) in that the second term on the 

 right-hand side is ir times as great *. lam unable, however, 

 to find any error in the formula as given above. 



The hypothesis of equal velocities for the electrons yields 

 on similar treatment, 



. 2ttC 2 NV/ ttX" 1 



n 2 K=— — (1+ — 



jrvrcTQ \ 4a/ 



and 



Thus, neglecting the correction terms, the values of n 2 K 

 are, on this hypothesis, 7r/4 times as great as those given by 

 the assumption of the Maxwellian distribution, while to the 

 same approximation the values of n 2 (l — k 2 ) are the same on 

 both hypotheses. Now Nicholson, owing to the absence of 

 the factor ir in equation (6), of course finds that the value of 

 K-fn 2 (/e 2 — 1) on the equal velocity hypothesis is ir times as 



* In addition there are minor differences in the values of the numerical 

 coefficients in Sx and S 2 . 



