Contributions to the Study of " Flicker" 353 



certain sector only, reflects the yellow light to the eye, the rest of 

 the disc being of a perfect black. Let the disc be rotating very 

 slowly : then, as the yellow sector passes before the eye, it will 

 appear as bright as possible under the giren illumination, i.e., it will 

 appear of no less bright a yellow than it would, if the whole disc 

 were yellow, i.e., the stimulus given to the part of the retina on 

 which its image rests, is the maximum possible to this yellow, under 

 this particular and constant illumination. Now, suppose the rate of 

 rotation to be raised until flicker has just vanished, no part of the disc 

 now looks so bright as the sector did at first, and since the final 

 brightness of the disc varies directly as the width of the yellow 

 sector (this is the fundamental assumption on which all the colour 

 equations rest, and is verified by experiments described later), then, 

 when the flicker has vanished, the effective stimulus at any point of the 

 retina is to the original and maximum stimulus as the angle of the yellow 

 sector is to the angle of the whole disc, i.e., 360, the illumination being 

 constant throughout. 



Moreover, since the mere increase in the rate of rotation has no 

 effect whatever on the real width and brightness of the yellow 

 sector, but only diminishes the time during which its stimulus is 

 applied to the retina, and diminishes, in the same ratio, the time the 

 black sector takes to pass (and the more rapid passage of the black 

 sector must, considered alone, tend to increase the brightness of the 

 disc), whilst it (the increase in rate of rotation) increases to the same 

 extent 'the number of stimuli applied to the retina per second, and 

 the number of transits of the black sector ; it follows, since the final 

 apparent brightness of the disc is less than if it were all yellow, 

 that the yelloiv sector requires a finite time in order to produce its maxi- 

 mum effect, and the same argument applies to any colour. This 

 conclusion is in complete accordance with the results of other 

 experimentalists. 



But this is not all that these considerations prove : for since the 

 increase in speed of rotation diminishes in the same ratio both the 

 time the image of the yellow sector takes to pass over a point on the 

 retina, and also the time the image of the black sector takes to pass 

 (i.e., the time the sensation evoked by the yellow sector must neces- 

 sarily last undiminished, if there is to be no flicker), the increased 

 speed would have no effect whatever on the flicker except to multiply 

 the number of times it occurred per second, if it were not that a 

 weaker stimulus has a longer " last " (using the word " last " to 

 mean the duration of the sensation undiminished, after the stimulus 

 has been withdrawn). This is a second proof of the principle 

 established in a different way earlier in the present paper (p. 351). 



Experiments were next made to measure directly the apparent 

 brightness of rotating flickerlcss discs, and to find an expression for 



