Absorption and Fluorescence. 427 



these stages is characterized by its power of absorbing light 

 rays of definite wave-length, and consequently when only 

 one absorption band is shown, as in the case of pyridine, 

 only one stage in the opening up is present, and we are 

 therefore only concerned with the equilibrium between the 

 closed fields and the fields when opened up to one only of 

 the possible stages. It is obvious, from the fact that the 

 absorptive power increases with dilution, that the solvent 

 increases the amount of the opened up stage present. The 

 mass-action law as usually conceived does not therefore hold 

 good, since if b is the fraction of the molecules opened up r 



the mass-action law leads to the relation r = constant* 



1 — 6 



In other words, the fraction opened up, and therefore k, 

 should be independent of the concentration. On the other 

 hand, an increase in the mass of the solvent increases the 

 relative number of opened-up molecules in the equilibrium 

 up to a constant value when the solvent has opened up the 

 maximum possible for that solvent. If / be the fraction of 

 that maximum which exists at any given concentration, it is 

 clear that f must lie between at V = (infinitely large 

 concentration) and 1 at V = 20 (infinitely small concen- 

 tration), and, further, that / is some function of the con- 

 centration. The simplest possible relation connecting/ with 

 the mass of the solvent under the given conditions 



/=!■ 



-aV 



where a is a constant characteristic of the substance and the- 

 solvent used. It is a justifiable assumption to make that 

 the absorptive power (k) is proportional to the concentration 

 of the opened up stage, and we may therefore put 



/= 



K' 



where K is the maximum and constant value of k in the 

 given solvent. We thus have 



k 



whence 

 and 



- = 1 — e- aY 

 K * ' 



rv— k v 



K 



i K xr 



