624 Mr. G. H. Livens on the Influence of Physical 



quote the results there deduced. The equation of motion o£ 

 the typical electron of mass m and charge e was taken in the 

 form 



mx 4- hx + hx — e(E x + aP x )j 



where, E^ is the .^-component of the electric force and P x that 

 of the polarization intensity. It was then found in the usual 

 way that the absorption coefficient for light of a frequency 

 (^o + f) was 



, 1 Pi^W 



/ " t 2 [ (1 - aA) 2nof + a Pl ] 2 + (1 - aA; W»i' 8 ' 



where, if N x is the number of electrons with the natural free 

 period n = n , 



' m m 



and 



A=2 



k — mn 2 ' 



this sum being taken over all the electrons per unit volume 

 which have not the natural free period n = n . 



From this we deduce at once that the maximum absorption 

 is of amount 



uh- 1 Pi (\\ 



* 2~rc V(l-«A) J ' { } 



and occurs not in the position f = (n = n ) but displaced 

 towards the red end of the spectrum through a distance 

 given by 



g 2(1 -oAK 



Now consider for simplicity the case when the spectrum 

 of the dissolved substance consists only of a single line corre- 

 sponding to the frequency n = n , and that this line does not 

 occur in the absorption spectrum. The value of A then 

 arises entirely from the electrons in the solvent. Moreover, 

 if fju is the index of refraction of the solvent for the particular 

 light of frequency n = n , then 



2 1 i A 



-o 



1-aA 

 1 



+ 



a 1 — a A 



Thus an increase in //, arises mainly from an increase in 

 the term 1/(1 — aA), That is, an increase in fi corresponds 



