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^ 3. How anomalous refraction and anomalous scattering act in 

 producing dispersion lines. 



It appears from the above remarks that the distribution of the 

 intensity in a dispersion line is determined by two darkening laws 

 which, it is true, depend on local circumstances (dimensions and 

 shape of the source of light, condition of the medium, etc.), and 

 to that extent are unknown, but which we do know will change 

 with loave-length in accordance with the functions (1) and (2). We 

 shall first deal with the share which irregular refraction, and there- 

 after with the share which molecular scattering has in the formation 

 of dispersion lines. 



A. Imaginary pure )-e/raction lines. 



Imagine a selectively absorbing gaseous mixture, lacking the 

 faculty of molecular scattering, but with many irregular gradients 

 of density; let a beam of white light travel through that medium, 

 and attention be confined to a small part of the spectrum where 

 only one characteristic frequency, i.e. one ideally sharp absorption 

 line, is in evidence. 



If the said line were absent, the mixture would, in this narrow 

 range of wave-lenghts, show a refracting power jj, — 1 varying only 

 very slowly with A, but to this will now be added the anomalous 

 refracting power fj, — 1 of the constituent producing the absorption 

 line, thus determining the resultant refracting power: 



« - 1 = (n, - 1) + («, - 1). 



The term (n, — 1) will, as a rule, preserve the same (generally 

 positive) sign throughout the region considered, whereas {7l^ — 1) is 

 negative on the violet side of the line, positive on the red side. 

 Light on the violet side of a line will be called F-light, on the red 

 side 7?-light. All effects of refraction in a gaseous mixture are, 

 therefore, on an average greater for /j!-light than for T'^-light, because 

 they depend on (n — 1)' or on the absolute value of n — 1, i.e. on 

 I (71,-1) + (n— 1)1 . 



Fig. \a shows the course of n, — 1 and jij — 1 each separately ; 

 Fig. 2rt gives n — 1 = (», — 1) -\- {n^ — 1); in Fig. 3rt is represented 

 the course of \n — {\z=z\{n, — 1) -\- {n^ — l)j which determines the 

 distribution of the light in our "refraction line". 



The sharp absorption line will thus be enveloped in an asymme- 

 tric refraction line, whose "centre of gravity" is displaced towards 

 the red if n^ — 1 has the positive sign. 



(The general displacement of the Fraunhofer lines towards the 



22* 



