143 



^ 7. We shall now pass on to consider the iiithieiice of mole- 

 cular motion on an absorption line. We shall suppose that there is 

 a radiation resistance only, or at any rate that there are only 



u 

 resistances whose coefficients g are much smaller than mn„ - so 



that, acting by themselves, they would produce a much smaller 

 width than the one we calculated in § 6. Cases of somewhat 

 greater density are hereby excluded. 



The problem is easily solved if, after having grouped the mole- 

 cules according to their velocity of translation, we substitute for 

 each group a proper value of n„ in the expression for the electric 

 moment and then take the sum over all the groups in the way 

 shown in equation (3). 



Let § be the velocity of translation of a molecule in the direction 

 of the beam of light and let one of the groups contain particles with 

 velocities between § and § -|- '^s- 1» (3) we must then replace N 

 by (16) or (17). Further it is clear that the particles in question will 



resonate with ligiit of the frecjueacy /«(, I 1 H — J = «„ (1 + '") '" "'^ 



same way as they would with light of the frequency ;/, if they 

 had no velocity of translation. We therefore write ?*„ (J -|- w) instead 

 of ?*,,. We shall also put 



« = «„(1 +r) (19) 



so that 1' determines the ditference between the frequency of the inci- 

 dent light and n„, and we shall coJitlne ourselves to small values 

 of V, as we may do in the case of narrow lines. Then, for small 

 values of to, the only ones for which (J 7) has an appreciable mag- 

 nitude, we may write 



K(l + a>)]=— «' = 2«„>-r). 



Moreover, since n will differ very little from n„ we may in the 

 term ing I'eplace n by ?i„ and consider ^ as a constant, though in 

 reality this coefticient may depend on ?i (as ^i does according to (11)). 



Putting further 



9 



we find 



= k (20) 



+ «=.... 



dm 



1( ys Nee' i — - 

 2k 2,3t mun^'J 



— v-\-ik 

 or, if we introduce 



