PHENOMENA OF PHOSPHORESCENCE. 205 



curve are to be explained in some manner which does not involve the 

 assumption of two bands at all. While it may prove of interest at some 

 later time to develop the theory along the lines suggested by the first of 

 these alternatives, the present discussion will be based upon the acceptance 

 of the second, and we shall consider in what ways the form of the decay 

 curve, as well as certain other peculiarities of phosphorescence, may be 

 explained in substances possessing only one band in the phosphorescence 

 spectrum. 



ABSORPTION EFFECTS. 



If a homogeneous substance possessing only one band in its phosphores- 

 cence spectrum is uniformly excited throughout, and if the light emitted 

 by the interior portions suffers no diminution by absorption before reaching 

 the surface, then according to the dissociation theory here considered the 

 decay of phosphorescence will be in accordance with the law 



V/ 



These conditions, however, can never be exactly attained. The exciting 

 light must be absorbed to some extent, for otherwise no energy would be 

 available to produce phosphorescence. The excitation will therefore be 

 greatest at the surface, and will diminish, at a rate determined by the 

 absorbing power of the material, as we pass to points within. Since the 

 ions are in consequence more numerous in the surface layers, and since 

 the number of recombinations per second, which determines the intensity 

 of phosphorescence, is proportional to the square of the number of ions, 

 it is clear that the light emitted during the early stages of decay will come 

 chiefly from the surface. As decay proceeds, however, the relatively high 

 rate of recombination at points where n is large will cause a rapid approach 

 to uniformity of ionic concentration, and the part contributed to the total 

 light by the interior of the mass will become increasingly important. At 

 first the intensity of phosphorescence is approximately proportional to 

 Vian' 2 , where V\ is the volume of the surface layer that is chiefly effective. 

 Later, when the light from the interior becomes comparable in intensity 

 with that from the surface, the phosphorescence will be approximately 

 proportional to Voari 1 , where Vo">Vi. In terms of the total number of 

 ions, N, the two intensities will thus be approximately proportional to 

 a/ V\ N 2 and a/ F 2 A 2 . So far as the slant of the decay curve is concerned 

 this is equivalent to a decrease in the coefficient of recombination and will 

 result in making the curve concave toward the axis of /. Absorption of 

 the emitted light will complicate the phenomena but will not modify the 

 general result. The effect of absorption is therefore to produce a change 

 in the form of the decay curve which is at least in the right direction to 

 account for the observed deviation from linearity. 



In discussing the effect of absorption in detail we shall assume that both 

 the exciting light and the emitted light suffer absorption, the two coefficients 

 of absorption being /3 and ",' respectively. At any depth x below the sur- 

 face the intensity of the exciting light will be 



E=E e- fix 



