282 Mr. Gr. H. Livens : Influence of Density on Position 

 We have thus the value for K or /j?(l—ifc) 2 j viz. 



1 v* 

 1— a 2,— 



Lorentz has considered this formula for jjl at parts of the 

 spectrum where the absorption is negligible, that is between 

 the spectrum lines. Natanson has extended Lorentz's results 

 for similar cases, and applied the theory to a large number 

 of practical cases. I propose to consider the formula more 

 particularly in the neighbourhood of a line in the spectrum 

 of the substance under consideration, where the absorption 

 is no longer negligible. 



We consider the formula near the absorption band deter- 

 mined by the natural free period n = n Q of a group of electrons. 

 Let Ni be the number of electrons per unit volume with this 

 period as the natural one. As we are dealing with the 

 region near n — n only, we put n = « + f and neglect high 

 powers of f, and thus 



pi= — m 1 2« f + ih 1 n . 



We adopt the notation 



and . v e 2 



A=2, 



k — inn 2 ' 



2 referring to all the electrons not included in N x . 



Adopting all the approximations usual to this theory, as 

 set out in Prof. Voigt's book, we get 



n . W1 , 1 A(-2wof+m f w ) + p 1 



whence _ 1 P\rin 



^"2[(l-aA)2^ + a/> 1 ] 2 + (l-aA)VV* 



This agrees with the usual formula obtained if we put a = 0. 

 Moreover, for the gas A is small and we can write 



M - 1 n ' n ° pi 



2.„/2' 



2(2w f + «pi) 2 -f n 2 n 



The last approximation merely means that each spectrum 

 line is, as far as its position and intensity are concerned, 



