544 SCIENCE PROGRESS 



molecules. With increasing concentration, on the other hand, 

 although the number of fluorogenes is greater the fluorescence 

 diminishes also, because of the diminution in the fluorescent 

 power, which, according to Perrin, finally approximates to zero. 

 On this basis the existence of the optimum concentration can 

 be accounted for. 



Perrin considers the following case. Let us suppose that a 

 layer of the fluorescent solution of concentration c possesses a 

 thickness d cm. If I is the intensity of the incident exciting 

 light, the intensity / of the light which has penetrated to a 

 distance x from the first exposed face may be written thus 



I e- aCX 



where a is the coefficient of absorption of the solution for the 

 exciting light. The intensity of fluorescence emitted by a very 

 thin slice of the solution at the position x is then given by : 



IoPe- aCX cdx 



and the intensity of this slice as observed across the face of 

 incidence is : 



I Q Pe- acx cdxe- pcx = I Pe-( a + ® cx cdx 



where (3 is the coefficient of absorption of the solution for the 

 fluorescent light. On integrating from zero to d we obtain for 

 the total observed fluorescent intensity the expression : 



a + /3 ' jr ^ 1 e ) 



The variable portion of this expression is the product of two 

 positive factors of which one is the fluorescent power, P, the 

 other involving the absorption effects, (i — e~ (a + ficd ). The 

 latter factor increases steadily as the concentration increases. 

 If P steadily diminishes as concentration increases there will 

 be a certain concentration for which the fluorescent intensity 

 will be a maximum. 



Photometric measurements made by Lepine show that 

 beyond a certain dilution the fluorescence of a given mass 

 remains constant — that is, the fluorescent power reaches a 

 finite limit. This is the same as saying that beyond a certain 

 dilution the chance of destruction of a fluorogene molecule 

 remains constant. The chance of destruction diminishes 



