2l6 STUDIES IN LUMINESCENCE. 



Since we have usually plotted the reciprocal square root of the intensity 

 of phosphorescence, it will be convenient to use the same procedure here. 



i/Vj> -t=L= e im '(i/ Wo +a/) 

 , / i/wo+a/ 



i/V/ 2 = 



i/VS- 



V[^T^?oM(l-" W, )j 



i/wo+a< 



v pa[i 4*0 knpo/m k<?o; m e~ mt \ 



Replacing certain groups of constant terms by single letters for brevity, 

 these expressions may be written 



i/y/T^A^'ii/no+at) 



i/np+at 

 ^Ao-Boe- 1 



I/V7 



2 : 



i/V/ 3 = 



i/np+at 

 ^Az-Bze- 



If a curve is plotted for i/V 7i in accordance with the above equation it 

 Is found to be of the type shown in Fig. 190 for 7 = 0. The curve for 1/ V fo 

 and i/V Ii is concave upward during the early stages of decay, becoming 

 practically straight when / is so large as to make e~ mt inappreciable. 



No decay curves corresponding to either of these types has been observed. 

 It must be remembered, however, that the effects of absorption, diffusion, 

 and irregular distribution have been neglected in the present discussion. 

 It is probable that one or more of these sources of disturbance are present, 

 in which case the theoretical decay curves would be modified in such a way 

 as to make them correspond more nearly with the curves actually observed. 

 If m is large, for example, the curve for 7 2 - ' will be straight except in the 

 immediate neighborhood of t = o. Irregularities in the distribution of the 

 active substance would then produce a deviation from linearity, as previ- 

 ously discussed. It appears probable that the observed facts, in the cases 

 of phosphorescence thus far studied, are best explained in this way. It is 

 interesting to note, however, that curves may be obtained as the result of 

 ionic grouping which agree very closely with the experimental curves, even 

 on the assumption of a uniform distribution of the active material. If, for 

 example, 7\ and 7 2 both contribute to the phosphorescence, while 1 3 is zero 

 or negligible 



(7) I/V7= i/no+a/ 



<A+Be~ mt 



where 



\po~\- J B = pia<pu p-2.a 



