Theory of the Flicker Photometer, 715 



critical frequency, will yield a resultant uniform impression. 

 In the case represented by fig. 4, an increase of the average 

 value of curve " " will ultimately give a uniform sensation. 

 In the case represented by fig. 5 an increase in the range of 

 fluctuation (decrease in heat capacity of filament) of " A " 

 would give a uniform condition. In short (in every part of 

 the diagram fig. 1, except where the straight lines cross) 

 neither a choice of equal brightness nor of equal critical 

 frequency points for two colours will eliminate flicker. If 

 this reasoning is correct the flicker photometer indicates 

 equality at some point between these two where the 

 instantaneous summation of brightness of the two compared 

 colours is a constant. This condition is shown in fig. 6. 

 It is our problem now to determine this intermediate 

 point. 



3. Mathematical Development. 



We make first the fundamental assumption that the bright- 

 nesses of colours may be added arithmetically. To this we 

 add the following three plausible assumptions, namely : — 



1. That the " diffusivity " of the retinal " transmitter " is 

 a function not of speed of alternation, but of brightness. 



2. That the disappearance of flicker occurs when the ratio 

 of maximum to minimum of the fluctuating impression has a 

 certain value. This is the Weber-Fechner law. It is here 

 assumed that this law is a characteristic of sensation, and 

 that the Fechner fraction is perceptible independent of the 

 duration of the impression. This means that we assume the 

 ultimate receiver has a negligible capacity. The whole 

 system under consideration is similar to a fluctuating light- 

 source illuminating a thermocouple whose temperature 

 changes are indicated on an oscillograph whose deflexions 

 cannot be read to less than a certain small value. 



3. That the point of equality on a flicker photometer does 

 not depend upon the speed. This is in agreement with ex- 

 periment, which shows that the only effect of change of 

 speed above a certain necessary minimum value is to decrease 

 the sensibility. 



Aided by these three assumptions it is possible to determine 

 from the illumination-critical frequency relationship the 

 diffusivity as a function of illumination, and then to use the 

 diffusivity values to plot the fluctuation of the impression 

 under a given stimulus, finally selecting those relative values 

 of brightness for any chosen colours which shall make flicker 

 disappear upon alternation one with the other. 



3 A 2 



