J 41 



With ;. 3=6.10-5 cm, /— 9,4.10-6 ^m, ?i = 4,93.10* cm/sec, and 

 the above value of E, the ratio becomes 



^=172. 



Now, we found in § 3 tliat, at a rather large distance from 7i„ , 

 the index of absorption is proportional toy. Our calculation therefore 

 shows that the collisions would cause an extinction 172 times stronger 

 than that to which the radiation resistance gives rise. As the latter 

 leads to Rayleigh's formula which has been confirmed by the obser- 

 vations, we must conclude that the effect of the collisions is much 

 less than we supposed it to be. Thus, when light is propagated in 

 air the electric moment which is excited in a molecule must remain 

 nearly unclianged in direction and magnitude during an impact. 



Of course, notwitlistanding this, it may very well be that in the 

 neighbourhood of n„ and under special circumstances the collisions 

 disturb the vibrations. Recently Stark has given good reasons for 

 supposing that the electric field round a charged particle changes 

 the vibrations of a neighbouring molecule in such a way that a 

 broadening of the spectral line is brought about. 



§ 6. It has often been remarked that, according to Doppler's 

 principle, the molecular motion must give rise to a broadening of the 

 spectral lines. We shall tirst consider this effect for the case of an 

 emission line, on the assumption that there are no other causes for a 

 broadening. 



Let «(,, the frequency of the vibrations within the molecules, be 

 the same for all the particles and let S. denote the component of the 

 velocity of a molecule along a line directed towards the observer, 

 I being positive when the molecule approaches the observer, and 

 negative in the opposite case. Then the observed frequency is given by 



n = n„(l+i). 



The change in frequency expressed in terms of »„, i.e. the fraction 



which also represents the ratio of the change of wave-length to 

 ^0, is therefore given by 



a> — - (15) 



c 



Let us further write iV for the number of molecules per unit of 

 volume and u^ for the mean square of their velocity. Then we find 



