PHENOMENA OF PHOSPHORESCENCE. 20Q 



If we put 



p=~ri, m 2 = p() 2 = p and - = -aTp = A 2 



()- T" a/ T -1 T 



A 7 A^o t - r o 

 Writing pi for the average value of p between o and / 



i _ ,dN ka Jt ' 



N= I=-k = -- 



i api a/ / /. \ -s 



A^o r 



\N T ) 



i c x & 



Pl= - I pj/, -J (pit) =p 



t 7 o a/ 



Although we are unable to determine p and pi as functions of / it is clear 

 that both will decrease as t increases. It is clear also that the change will 

 become less rapid as the decay proceeds, and that both p and pi will sooner 

 or latter become nearly constant. When /~* is plotted against / we shall 

 therefore obtain a curve which is concave downward and which finally 

 becomes a straight line. In other words, the decay curve will agree in 

 form with the curves determined by experiment. 



The effect upon the decay curve of an irregular distribution of the active 

 substance may be illustrated by the following simple case : Let the active 

 material be uniformly distributed, except that small regions occasionally 

 occur where the concentration is abnormally large. The whole volume 

 may thus be divided into two parts, V\ and v 2 . The distribution of the 

 active material is uniform throughout each part, but the concentration in 

 vi is different from that in z> 2 . When the substance is excited to phosphores- 

 cence the ionic concentration will also differ in the two regions. Let the 

 number of ions per cubic centimeter at the end of excitation be ii\ in the 

 volume v\ and 2 in the volume i> 2 . Throughout the region v x the intensity 

 of the light emitted per cubic centimeter will be 



ak 

 t = 



(i/m+aty 



and the total intensity at any instant due to this part of the whole mass 

 will be 



1_ (i/i+a/)~ 2 

 The light emitted by the volume v 2 is given by the similar expression 



akvi 

 (i/w 2 +a/) 2 



