337 



II. ThK REr.ATION BETWEEN AVIDTH AND MÜTÜAI- INFLUENCE IN 

 DISPERSION LINKS AND IN FrAUNHOFER LINES. 



In this chapter formulae will be deduced expressing the connection 

 between mutual influence and width of dispersion lines. If Frauidiofer 

 lines are in the main dispersion lines, it will (hus be possible, starting 

 from daia concerning the widening of the lines in the spectrum of 

 the sun's limb, to derive values for the probable increase of the 

 mutual influence in passing from the centre to the limb. We may 

 then compare these theoretical results with the data obtained from 

 observations regarding limb-centre displacements of Fraunliofer lines. 



The i-espective shares which irregular refraction and molecular 

 scattering may have in (he production of the lines will again be 

 treated separately. 



^ J . Refraction lines in the spectrum of the centre of the solar disk. 



The distribution of the luminosity in a refraction line depends on 

 the values of \n — 1|^ ƒ(/.). We owe to Roschdestwensky ') the most 

 accurate measurements concerning the form of this function. He 

 found that in region of the two yellow sodium lines Sellmeier's formula: 



a.X' a, A' 



represents the observations almost exactly. We shall suppose this 

 formula to be applicable to the cases we are considering. 



If the difference between A, and .^, is rather considerable and if 

 we only pay attention to the surroundings of one of the lines, we 

 may unite the latter two terms of (1) into a single, nearly constant 

 refracting power (?;„ — 1), and moreover put A -f- A, ^ 2 ^. The 



expression thus simplifies itself, if we write ^' for — ^, to: 



« ^ = A3r + ^"~^^ ^^^ 



The intensity at any place in the spectrum depends on the absolute 

 value \n — 1]. On either side of the absorption line we mark the 

 values of )■ where n — 1 ^ ± // (cf. Fig. 5), H being provisionally 

 an arbitrary constant. These places in the spectrum will be called 

 the "//-boundaries" of the dispersion line; their distance (to be 



') Roschdestwensky, Anomale Dispersion im Natriumdampf. Ann. d. Phys. 

 39, 307, 1912. 



