308 Messrs. H. B. Ives and E. F. Kingsbury on the 



the two illuminations. It is to be noted, also, that besides 

 using only the first two terms of the complete expansion, 

 we have made the simplest possible assumption as to the 

 relation between the diffusivity and the amount of light 

 entering the eye. We have as well assumed the Fechner 

 fraction to be the same, no matter what the shape of the 

 transmitted impression. It may very well be that in place 

 of the constant 8 some function of the angular opening 

 should be used. Whether these various possible explana- 

 tions of this discrepancy are sufficient we have not been 

 able to establish. It appears probable to us that, in the 

 simplified form of the theory as worked out, differences 

 actually existing in the slopes of these lines have been much 

 exaggerated. This is a point which can be settled only by 

 the complete solution of the equation from which oj is 

 obtained. We suggest that this might be obtained experi- 

 mentally by studying the conduction of heat through slabs 

 of various thicknesses, the heat being applied periodically 

 in a manner to imitate the intermittent exposures here 

 studied. 



In spite of the apparent disagreement between theory and 

 experiment on this one point, we think it may be claimed 

 that the theory does give the principal facts in a sufficiently 

 striking manner to warrant its being considered as sub- 

 stantially correct. We have felt justified in using it in the 

 remainder of this paper, with the sole caution of confining 

 ourselves to illumination values at which its indications are 

 close to the experimental data. 



With regard to the newly discovered behaviour of the eye 

 at low illuminations toward various angular openings, we 

 suggest that it would be an interesting experiment to make 

 measurements with various openings on a totally colour-blind 

 observer. If the behaviour of the eye toward blue lioht 

 which has become colourless at low illuminations is similar 

 to that of the totally colour-blind eye at normal illumina- 

 tions, as appears established from various researches, then 

 it is to be expected that with such eyes critical frequency 

 will 



(1) be independent of the illumination ; 



(2) depend upon the opening of the sector, and will 



decrease as the sector opening is increased. 



Von Kries and Uhthoff * have made critical frequency 



* " Ueber die Wahrnehimmg des Flimmercs durcli normale und durcli 

 total farbenblinde Personen," Von Kries, Zeit. fur Psych, und Phys. der 

 Sinnesorgane, vol. xxxii. p. 113 (1903). 



