139 



between the borders 



e'M„^„ 



QjTc^R 



{R radius of the electron) for tlie (electromagnetic) mass m. 

 Now we have 



R=l,2b . 10-13 cm, 

 so that for 5 = 10 



A;1= 12.10-1-^ cm = 0,0012 ALT., ..... (13) 



This is a very small width indeed. 



We shall soon see however that equations (12) and (13) appl^y 

 to the ideal case onlj of molecules having no velocity of translation. 

 In reality, on account of the heat motion of the molecules a "line 

 of extinction" will be much broader than is given by (13) and less 

 strong at the middle than wo should infer from (12). 



One remark more has to be made about the radiation resistance. 

 Though the extinction to which it gives rise, quickly decresases as 

 the frequency n deviates more and more from the frequency «„, 

 yet in the case of thick layers of gas it remains observable at a 

 considerable distance trom n^. We may suppose e.g. that in the case 

 of atmospheric air, ti„ belongs to a point in the ultraviolet. Now, if 

 for light in the visible spectrum, we calculate the extinction corre- 

 sponding to the coefficient (/j, we find exactly the well known 

 formula of Rayleigh which agrees in a satisfactory way with obser- 

 vations. 



§ 5. As the radiation resistance does not give rise to any true 

 absorption, we must look for another explanation of this pheno- 

 menon. We can hardly think of a real friction or viscosity, but we 

 may suppose that the vibrations of the electrons which are excited 

 by the incident light cannot go on regularly for a long time, but 

 are disturbed over and over again by collisions or impacts which 

 convert them into irregular heat motion. It can be shown ') that 

 this leads to the same effect as a frictional resistance and that the 



1) H. A. LoRENTZ, The absorption and emission lines of gaseous bodies, Proc. 

 Amsterdam Acad. 8 (1905), p. 591. 



