Refractivity and Atomic Interaction. 119 



Broadening of Absorption Bands. — We have assumed from 

 the beginning that the distances between the atoms, or rather 

 between the centres l9 2 , etc., are fixed. Our differential 

 equations, however, will continue to be approximately valid if 

 these distances are slightly oscillating between certain ex- 

 treme values, in other words *, it the i£'s are considered as 

 (comparatively) slowly variable parameters. To fix the ideas, 

 let us suppose that the " friction," to be taken account of in 

 the equations of motion of the dispersive particles in the 

 neighbourhood of the free periods, is very small. Then, if 

 the distance R were rigorously constant, the corresponding 

 absorption bands, at \ 1? A 2 as well as at X' (and V), would 

 be very sharp " lines." If, however, the distance oscillates 

 between R and R-f 8R, then the new absorption line will 

 oscillate between A/ and V f 8\' } and will appear, therefore, 

 as a band of breadth oV. In the simplest case of two equal 

 atoms this breadth will be, by (31), and assuming SR to be 

 a small fraction of R, 



and if R differs but little from R 



ej 



*— 5S-S ^ 



that is, proportional to the cube of \ f itself. Thus the 

 broadening of the absorption band due to oscillations of R 

 would be much greater in the red than in the violet region. 

 This seems to harmonize with general experience. Of 

 course, the bands would, independently of these oscilla- 

 tions, become broader and less sharp with increasing 

 " friction " or "extinction/' which, according to Lorentz, 

 is due chiefly to the collisions of the molecules. It is well 

 known that the extinction due to radiation or re-emission of 

 energy alone has been found much too small to account for 

 the absorption phenomena that are actually observed in 

 many cases. It is for this reason that Lorentz (' Theory 

 of Electrons/ pp. 141-112) has taken account of the collisions 

 of molecules. But, as Lorentz himself admits, the collisions, 

 say, in gaseous bodies, are not sufficiently frequent to ex- 

 plain the observed breadth of the absorption bands. Under 



* And without entering into the dynamics of the centres as mass- 

 points. 



