220 STUDIES IN LUMINESCENCE. 



in the intensity of phosphorescence results. The rate of decrease of 

 course depends upon the intensity of the active rays. 



If the infra-red rays are allowed to act for a short time and are then 

 cut off, the condition of the phosphorescent substance will differ in two 

 respects from that which it would have reached during ordinary decay: 

 (i) the number of favorable groups is less than it would have been with- 

 out the action of the longer waves; (2) the number of free ions is, at least 

 to some extent, in excess of the normal. After the infra-red rays have 

 ceased to act, however, the free ions will soon form groups again, either 

 favorable or unfavorable, and the decay curve will quickly return to the 

 standard form. But the number of favorable groups will be less than if 

 the infra-red rays had not acted. The effect of exposure to the longer 

 waves is simply to bring the substance quickly into the same condition that 

 it would ordinarily acquire only after a much longer period of decay. The 

 theory here discussed is thus seen to be in agreement with the experimental 

 results recorded in Chapter V. 



It seems probable that in some substances certain rays, presumably 

 in the infra-red, may have the effect of breaking down the unfavorable 

 as well as the favorable groups. In such cases exposure to these rays 

 would probably bring about an increase in the brilliancy of phosphores- 

 cence instead of a decrease. This is the case with certain of the phospho- 

 rescent sulphides. The same effect would be produced in substances where 

 the recombination of a free positive ion gives out more light than that of an 

 attached ion, i. e., where pi> Pz. 



In cases like that of Sidot blende the form of the decay curve as modified 

 by exposure to infra-red rays may be determined as follows : 



We shall assume that the rate at which favorable groups are broken 

 down is proportional to the intensity of the active rays I r and the number 

 of favorable groups present (\pn). We therefore have 



(8) - (\[>n) = a\f/n- Ripn ki<pn 



at 



where R is proportional to I r . 



The destructive effect of the infra-red is so great, even for rays of small 

 intensity, while k\ is so small, that the last term knpn may in general be 

 neglected. It is only in the case of exposure to very weak rays, or with 

 substances which show the infra-red effect in small intensity, that the 

 omission of this term will lead to appreciable errors. Equation (8) there- 

 fore becomes 



,dn dip , dip . , d\p , 



Y , -r , = ayri- + n , = a\pn- Rwn , =R4> 



dt dt dt dn 



(9) ^ = ^i 



-Rt 



where / is reckoned from the time when exposure to the infra-red rays begins. 

 If we take / as the time that has elapsed since the end of excitation we have 



4 / = 4 /i e- R{l - h) 



