1877.] 



Phenomena connected with Vision. 



491 



states that the time which elapses between intermittent luminous 

 impressions without producing discontinuity of sensation varies as the 

 square root of their luminous intensities ; but Helmholtz seems to regard 

 the statement as doubtful *. 



Herman says that the time required to perceive an impression varies 

 in arithmetical progression when the intensity of the stimulus increases 

 in geometrical progression, but does not give his authority. M. Del- 

 boeuf t, making experiments with revolving disks, neglected the rate of 

 rotation, and states that no difference occurs in the results whether it is 

 rapid or comparatively slow. 



I made a series of experiments with revolving disks similar to those 

 made by MM. Delboeuf and Plateau. A white card disk, 6 inches in 

 diameter, is set into rapid rotation by clockwork. A portion of a sector 

 of the disk is blackened, so that a grey ring appears during rotation : by 

 reducing the breadth of this sector until the ring was no longer visible, 

 and making the experiment by artificial light, I found that the breadth 

 of the sector at the time of disappearance varies as the distance of the 

 source of light, and that by varying the rate of rotation in the inverse 

 ratio' of the distance of the light the ring remains just invisible. 



I find that a disk with a portion of a sector, occupying -g-J-o of its 

 circumference, blackened, gives no grey ring with a single candle to 

 illuminate it 10 feet from it when it revolves from 5 to 6 times in a 

 second, but by halving the distance of the. candle it must revolve from 

 10 to 12 times in a second before the ring entirely disappears. A 

 white sector on a black disk obeys the same law, but must occupy only 

 ToW circumference of the disk with the same illumination. 



I have concluded that when the grey ring ceases to appear the rotation 

 is sufficiently rapid to cause the sector to occupy the same space for too 

 short a time for it to be seen. With a dull light a white streak on a 

 black surface must occupy the same position for about goVo ^ second 

 to be seen at all ; but the time varies inversely as the square root of the 

 illumination. A black spot upon a white ground must rotate much 

 more slowly to be seen. In this case we have to deal with the duration 

 of an exceedingly faint after image — that of the white surface — during 

 the passage of the black spot. The rate of rotation necessary to 

 obliterate the effect of the black spot varies also inversely as the distance 

 of the illuminating source. 



3. On the Relation of the foregoing Ohservations to Fechners laiv. 



A very simple modification of Eechner's convention with regard to 

 sensations and their relation to stimuli will make the foregoing observa- 

 tions accord entirely with his law, and would further change the arbitrary 

 measure of sensation in Eechner's formula into an equivalent measure of 



^ Helmholtz, Phys. Optique. 

 t Bulletin Belgique, 1872. 



