354 Mr. T. C. Port or. 



the effect of successive equal increments to the bright sector. The 

 method used was to measure the distances from a movable source of 

 light, of the rotating disc, and of a fixed disc, of the same colour as 

 the bright sector of the rotating disc, when the brightness of the 

 two discs appeared equal. It was found that for illuminations about 

 the same as those used in the other experiments recorded in this 

 paper, the law which connects the apparent brightness with the 

 width of the bright sector is that enunciated before, i.e., that a 

 flickerless half-and-half disc appears half as bright as the fixed and 

 wholly white or coloured disc, at any rate within the errors of 

 experiment which, however, in this part of the research were not 

 inconsiderable. When the width of the white or coloured sector 

 was increased in steps of 10 at a time, the increment of the 

 apparent brightness in the flickerless disc followed, within the errors 

 of experiment, the series 1/0, 1/1, 1/2, 1/3, 1/4, &c., as it should ; and 

 since these fractions express the ratio between the increase of 

 stimulus caused at any stage by an additional 10 of coloured 

 sector, and the stimulus already existing before its addition, it follows 

 that we can, with the help of the principles established already, 

 predict how the rate of rotation for the disappearance of flicker must 

 vary with the growth of the white or coloured sector. We should 

 expect the first few additions of the 10 to produce the most marked 

 alteration (a rise, as we already know) in the rate of rotation neces- 

 sary for the disappearance of flicker, since the diminution in the 

 amount of the black sector is trifling in comparison with its total 

 width. Towards the final additions of 10, we shall reach a stage 

 when the effect of the increment of 10 of white or colour is almost 

 negligible in comparison with the total width of the white or 

 coloured sector, but just at this time, the relative diminution of the 

 black sector will be most rapidly increasing, and in order that 

 flicker may only just be invisible, the rate of rotation must 

 be considerably diminished, and this diminution will bear to the 

 total velocity almost the ratio the diminution of the black sector 

 (10) bears to its total width ; but not exactly this ratio, for since 

 the effective stimulus is still increasing, though the increase is small 

 compared with its total magnitude, and since this implies apart 

 from any effect of change in the width of the black sector that the 

 rate of rotation must be raised for the flicker to vanish, it follows 

 that the rate of rotation will not diminish at so rapid a pace as the 

 shrinkage of the black sector's width would demand, if it alone had 

 to be considered. So far, therefore, the " flicker " curve (for a disc 

 with a growing white or coloured sector, the angle of the bright 

 sector being measured on the axis of Y, and the speed of rotation on 

 the axis of X) will be, on the whole, symmetrical with respect to the 

 straight line passing through the point on the axis of Y correspond 



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