Mechanics of Luminosity . 381 



about the limiting condition, an increase in the duration pro- 

 duces an increase in the number of transformed molecules. 

 The evolution of light dependent upon the transformation of 

 molecules B into molecules A will therefore last longer. 



We have thus an exactly analogous case to dissociation 

 under the influence of heat, which appears to come to an end 

 at a definite condition of equilibrium, the condition of which 

 is that the number of molecules decomposed is equal to the 

 number of molecules formed. As an increase and decrease of 

 incident light act upon phosphorescent substances, so a rise 

 and fall in temperature act in this case. We may therefore 

 apply the conclusions which hold good in the phenomena of 

 dissociation to our case. 



The results of experiment agree with these theoretical 

 conclusions, and in the first case the way in which the expe- 

 rimental results run. 



If x is the quantity of the modification B in the unit of 

 volume, the equation holds good, 



•_ dx _ 



at 



where i is the brightness, and a and c are constants, c gives 

 the brightness produced by the transformation of the quantity 

 1 in the unit time, whilst a, cceteris paribus, determines the 

 rapidity of the transformation. 



By integration we obtain x = Ce~ at , where C is an inte- 

 gration-constant, which is proportional to the initial intensity. 

 It is itself dependent upon the number of molecules of A which 

 are, upon the whole, transformed into B at the time t = ; then 



the brightness must therefore vary according to an exponen- 

 tial function, which is nearly the case. 



The quantity acG denotes the brightness existing at the 

 time £ = 0. For two different series of experiments only the 

 constant C changes, and assumes perhaps the values Cj and 2 . 

 The ratio of the intensities i 1 and i 2 , at any equal times t, is 

 therefore 



%i __ Ci ac _ 



i 2 C 2 ac ' 



consequently equal to that at the time zero, and therefore 

 constant. 



If we observe at any time for two series of experiments 

 brightnesses which have the ratio p? : 1, then in the first case 



