314 



Mr. T. C. Porter. 



[May 14. 



the black sector affects the flicker curves (such as those given in fig. 3 

 of the present paper), and perhaps the simplest way to make this 

 plain, is to take a numerical example : suppose then that the amount 

 of white light reflected from 360° of black is equal to that reflected 

 from 24° of the white cardboard from which the disc is made ; then, 

 if the angular breadth of the white sector is, say, 60°, the total 

 amount of white light reflected from the remaining 300° of black will 

 be equal to the light reflected from 22° of white, and this light is dis- 

 tributed evenly throughout the black. 



Now if this disc is made to rotate until it becomes flickerless, its 

 luminosity or albedo will be rightly expressed as that of a mixture of 

 60° + 22° = 82° of white, and 278° of absolute black, and if a second 

 disc were made with a white sector of 82°, and an absolutely black 

 sector of 278°, this second disc, when flickerless, would appear of 

 the same brightness as the other disc of 60° white, and 300° imperfect 

 black, but — and this is the point of the illustration — the flicker does 

 not just vanish at the same speed of rotation for the two discs, — for 

 flicker depends essentially upon contrast, and' the contrast between the 

 white and absolute black is greater than between the same white and 

 imperfect black. Let the whiteness or albedo of the white cardboard be 

 expressed numerically by 100, then the flicker in the case of the first 

 disc is produced by the contrast between the 60° sector of white of 

 albedo 100, and the 300° sector of what is really dark grey, albedo 7*3. 

 Thus 7*3 of the white sector's brightness will contribute nothing to the 

 flicker, for the disc may be regarded as being of the albedo 7*3 all 

 over, there being added, where the white sector is, an additional 

 albedo, not of 100, but of 100 - 7'3 = 92'7. In order, therefore, that 

 flicker may vanish on a disc of 60° white, and 300° of absolute black, 

 at the same rate of rotation as for a disc of 60° white and 300° of the 

 imperfect black already mentioned, we must lessen the contrast 

 between the white and black of the first disc by reducing the albedo 

 of its white sector in the ratio of 92*7 : 100, and this can be done 

 experimentally by altering the distance of the rotating sector from the 

 source of light. Now the effect of altering the distance of the disc 

 from the source of illumination is shown by the curves of fig. 4, and 

 since the greater the distance from the source of illumination the 

 further the curve lies to the left in this figure, we see that the effect of 

 the imperfection of blackness in the black sector of the rotating disc 

 is to shift its curve further to the left than it would lie if the black 

 were perfect, and thus, as is evident from the figure, to make it of a 

 rather flatter form than it would otherwise be : it is also evident that 

 unless the amount of light reflected by the black sector is large, the 

 shift in the curve is small, and the difference in form very slight. 



(2.) The rate of rotation at which flicker appears just to vanish, 

 depends, amongst other things, on the distance of the observer from 



