138 



^ 4. The above lias boen known for a long time and has been 

 repeated here as an introdnction only to some fnrlher considerations. 

 These will be limited to lines in the visible and the ultraviolet 

 spectrum, i.e. to lines which in all probability are due to vibrations 

 of negative electrons. 



We shall also conline ourselves to such problems as may be treated 

 without going deeply into the mechanism of the absorption. There are 

 good grounds for this resti'iction, for it must be owned that in many 

 cases we are very uncertain about the true nature of the phenomenon. 



In the case of a vibrating electron there is always a resistance of 

 one kind, viz. the force that is represented by 



6;rc' 

 if V is the velocity. For harmonic vibrations we may write for it 



so that it proves to be proportional to the velocity and opposite to 

 it. If this "radiation resistance", as it may appropriately be called, 

 because it is intimately connected with the radiation issuing from 

 the particle, is the only one, we must substitute in the above for- 

 mulae for the coefticient g the value 



Replacing here n by ?;„ we deduce from form. (7) 

 ÖJtA^c» 3 

 « = — — = 7-Ï ^^^« • 



Now i\^?./, the number of vibrating electrons in a "cubic wave- 

 length" will have in many cases a high value. Hence, on our 

 present assumption, a would be very great and for rays of frequency 

 n„ the weakening would be considerable even over a distance of 

 one wave-length only. Indeed, one tinds for the exponent in (9) 



- 2h,l, --= - ^/6^' (12) 



It must be remarked here that in the case now under consider- 

 ation, we cannot speak of true "absorption", i.e. of transformation 

 of the vibrations into irregular heat motion, but only of a "scattering" 

 of the light by the vibrating electrons, so that h may properly be 

 called the "index of extinction". 



Formula (11) leads to a very small value for the width of the 

 dark line. Indeed, using (lOj and replacing n by n^ in (11), we 

 easily liiid for the width measured by the difference of wave-length 



