Theory of the Flicker Photometer. 297 



3. Critical Frequency-Illumination Relations with Super- 

 posed Steady and Flickering Illuminations. 



Before leaving the equations developed to indicate the 

 sensibility of the flicker photometer, it is of interest to note 

 that they show as well the behaviour, on our theory, of a 

 flickering illumination superposed on a steady one. Thus 

 equation (4), while developed to represent the case of two 

 dovetailed flickering illuminations of unequal intensity, 

 represents as well the case of a steady illumination, of the 

 value of the lesser illumination, upon which is superposed 

 a fluctuating illumination of the amplitude of the difference 

 of the two illuminations. 



What will be the behaviour of a fluctuating illumination 

 of this character as the illumination is varied ? So far as 

 the authors are aware this case has not been studied experi- 

 mentally. We obtain an answer by combining equations (4) 

 and (5), which give 



I . , 1,-Ll 2 



[alogI A + fc]. ... (6) 



_^+log^j 



[log*]* 



The most striking characteristic of this expression is 

 evident upon inspection, namely that each different ratio of 

 steady to flickering light calls for a different slope (coefficient 

 of log I A ) in the critical frequency-log I plot. 



We may calculate the critical frequency-log I lines as 

 follows : — 



Let experimental values of co be taken at two illuminations 

 for the ordinary experimental case of 12 = 0. Assume a 

 value for 8. From this a and h may be obtained, which 

 constitute all the data necessary. 



In fig. 3 are shown, first, an experimental critical fre- 

 quency-log I line, for the case of I 2 = 0, obtained with an 

 abrupt transition disk, then the corresponding line as calcu- 

 lated for a ratio of ~ of *8, for three values of 8. Finally 



1 . . Io 



are shown lines obtained by experiment for ratios of y- of 



*83 and ''5 6. It will be noted that in their most novel 

 characteristic — the variation of slope — the experimental 

 lines verify the prophesy of theory. 



As in the matter of sensibility, the correspondence between 

 theory and experiment is not quantitatively all that could 



