PHENOMENA OF PHOSPHORESCENCE- 221 



where /i is the time at which the longer waves begin to act and i/'i is the 

 value of \p at this time. 



To determine the number of free positive ions pit after the infra-red rays 

 begin to act we have the equation 



(<pn) = a.<pn~-\-R\pn k<pn 

 at 



dn dip dip . . 



^t:+ y. =<paw t +n- = a<pn- + R^n k 2 <pn 

 at at dt 



f t +k 2 <p = R + = R + 1 e- R ^ 

 do) <p=<p 1 e- k -+ 1 ^-e- R - 



K2 K 



An interesting special case, corresponding to the experimental condi- 

 tions in much of our work with Sidot blende, is that in which the exposure 

 to infra-red rays begins at once when excitation ceases, i. c, ti = o. In this 

 case 



<Px = <Po ^1 = ^0 <p=<Poe~ kit +^-(e- m -e- ktt ) ^ = ^,e~ Rl 



K2 R 



I = p 1 a<pn-+p2a^n- = (A 1 e- Rl +B l c- k2t )n- 

 where 



2 p / Rfn \ 



Ai = p2(i2\(/o- hi = pia 1 [<po- -J 



K2 R \ k 2 RJ 



For the special case where p\(x.\ = P2&2, 



i i/m-\-at 



7) = 



V/ I ^o k 



Vk 2 -R V k 2 -RJ 



C2~ J^ \ K2 



If the infra-red rays are intense so that R/kz is large 

 i i/no + at 



Vl ^hfo/R e~ Rt + (^! + to)e- kil 

 and in the extreme case where R may be treated as infinite 



i i/no+at 



This gives a curve having the same form as the observational curve shown 

 in Fig. 72. The data of Fig. 70 will be found to give a curve of the same 

 form for i/V /', but the curve has been plotted only in the case of Fig. 72. 



At high temperatures the increased activity of the molecular movements 

 will tend to prevent the formation of groups, or rather to destroy the 

 groups almost as quickly as they are formed. All those phenomena that 

 depend upon the existence of groups will therefore become less prominent 



