of Emission and Absorption Lines in a Gas-Spectrum. 281 



Thus for the propagation of this wave-train to be possible in 

 the medium we must have 



Now in the general case K is imaginary, and it is then that 

 q is imaginary and absorption results. Suppose 



where //, and k are real ; the exponential factor is then 



e c £ ^ c) . 

 We see that — ) is the velocity of the disturbance in the 



medium, and therefore jjl is the ordinary index of refraction 

 of the medium. The absorption is determined by (f^fc), 

 which may be called the index of absorption. We have now 



and this is the important relation. We know K and can 

 thus determine fi and /jlk, and from the latter deduce all the 

 circumstances of the absorption. We shall now proceed to 

 a detailed discussion of this relation in the several cases. 



§ 5. Absorption in the neighbourhood of a line in the spectrum. 

 — The method pursued in this and the following paragraphs 

 follows very closely that given by Voigt in his book 

 ' Magneto- und Electro-Optik,' and I refer the reader to 

 that book for a fuller discussion of the algebraical processes 

 involved. 



We first discuss the ordinary absorption phenomenon 

 without the action of an external magnetic field. The 

 frequency of the incident disturbance being n we have for 

 the typical electron 



(k + ihn — mn 2 )x = <?(E 2 + aP z ), 



and two similar equations ; say 



px=e{E x +aP x ). 



Now eliminate the single electron by adding up per unit 

 volume over all the electrons in a differential element of 

 volume, obtaining the polarization as a statistical sum 



p p 



