Mechanics of Luminosity. 159 



first, that the body is continuously excited ; and, secondly, 

 that at any time the exciting cause is removed, and then the 

 body, left to itself, gradually radiates its store of luminous 

 energy. 



A. If the body is continuously excited we may use the 

 equation 



di={<f>^bi\dt (1) 



The change of intensity di which occurs in the element of 

 time dt is equal to the change of intensity cj> dt produced by 

 the external cause, diminished by the change of intensity bidt 

 in consequence of radiation, where we assume that the decrease 

 in intensity is proportional to the intensity existing at the 

 moment *. 



b is, as follows from the equation, the reciprocal value of 

 the time in which the unit of intensity is radiated if the radi- 

 ating body is maintained at unit brightness. The decrease in 

 brightness may be produced both by radiation and by internal 

 absorption. 



The function </> is essentially different according to the mode 

 of excitation. 



For phenomena of photo-luminescence we may assume that 

 </> = AJ, i. e. that <£ is proportional to the intensity J of the 

 incident light, A is the reciprocal value of the time neces- 

 sary for unit intensity to be excited by incident intensity 1. 

 We may also say that A expresses how large a fraction of 

 the incident intensity is converted into excited intensity in 

 unit time. Then 



di=(AJ — bi)dt. 



Hence, if C is a constant, 



If 2 = 0, for * = 0, then C = AJ, and 



i=^-(l-e-v) (2) 



If we make some other assumption for the relationship be- 

 tween the decrease in intensity di and the intensity i, equa- 



* This equation holds good in the first instance for the coininimicated 

 and radiated intensities ; but if we assume that the radiated intensity is 

 proportional to the luminous energy existing at the moment, it may 

 further be applied without alteration to the intensities of the luminous 

 motions. 



