Theory of the Flicker Photometer. 721 



the K's are equal. This is in conformity with the experi- 

 mental work which indicates a condition of close approxima- 

 tion of the equality of brightness mean of several observers 

 with their flicker photometer mean. Above this point the 

 various crossed lines cling rather closely and approach 

 parallelism with the original straight ones. (At go they 

 are all together again.) The experimental curves and the 

 calculated ones agree so closely in character that the ex- 

 perimentally indicated equality point within the range of the 

 experimental work appears to be borne out. But this cross- 

 ing point is not necessary to the theory, whose essential 

 characteristic is that it shows the flicker photometer values 

 to be asymptotic at high illumination to the equal brightness 

 ones. The formula used for calculation, when closely studied, 

 shows that for low values of I the values to be used are 

 determined more by approximation to similar contour (K), 

 at higher values by approximation to equal brightness (I), 

 notwithstanding the fact that the straight lines (fig. 7) are 

 rapidly diverging. 



A point of extreme importance may be noted here : 



The increasing approximation of the flicker photometer 

 criterion to the equal brightness criterion as the illumination 

 increases, is not dependent on the (experimentally established) 

 different slopes of the log I-critical frequency lines for 

 different colours, nor on the choice of any particular expres- 

 sion for the mode of transmission of the stimuli, such as the 

 Fourier equation. It is a necessary consequence of applying 

 our fundamental assumptions to any relationship between 

 brightness and critical frequency in which critical frequency 

 changes proportionately less rapidly than the brightness. 



The previous conclusion drawn by one of the writers that 

 the equality of brightness and flicker photometer approach 

 each other at high illuminations is thus exactly in accord 

 with the present theory. 



The experimental results obtained with small photometric 

 fields are interpreted on the present hypothesis as indicating 

 the diffusivities for different colours to vary less from each 

 other at the fovea. The fact that at about 25-metre candles 

 the luminosity curves obtained with all field sizes coincide, 

 is evidence that at this illumination the flicker photometer 

 has practically reached the condition where it measures 

 brightness to within the errors of reading. 



The experimental curves for extreme red and green show 

 a bend back toward each other. This may be experimental 

 error, since the theory indicates a condition of practical 

 parallelism. A ready explanation is furnished, however, by 



