of Emission and Absorption Lines in a Gas-Spectrum. 283 



practically independent of the other lines in the same 

 spectrum. 



The centre of the band, the place of maximum absorption, 

 occurs at the position 



api 



*~ 2n - 



The maximum value of the absorption coefficient is 



Z n n 



The positions in the spectrum where the intensity is one 

 half its maximum value are given by 



? 2n ± 2 * 



The first of these results is really the only one which 

 differs essentially from that given in the usual theory. The 

 position of the absorption band does not actually correspond 

 to the natural period n = n of the group of electrons con- 

 cerned, but is displaced from this position through a distance 



f = — ~-^, measured on the frequency scale. Now 



N x e 2 „_ N /*Y 



Thus pi is proportional to the density of the electrons of the 

 Nx group. This is assumed to be proportional to the ordinary 

 density of the gas. 



We have thus shown that the spectrum line is displaced 

 from its absolute position given by n = n . The displacement 

 is towards the red end of the spectrum (greater wave-length 

 or smaller frequency), and is directly proportional to the 

 density of the gas. It is different for different lines, being 

 proportional to the density of the electrons which give rise 

 to each line. 



§ 6. The inverse Zeeman effect. — I have applied the fore- 

 going principles to the theory of the simple Zeeman effect, 

 and to a simple case of Voigt's theory of the complicated 

 effect. 



The algebraical work is much the same as that just given, 

 and I shall content myself with quoting results as the method 

 of obtaining them is now obvious. 



Under the action of an external magnetic field H the 



