MIDDLE SPEED

Intensities.123456789
First Subject.810911109978
1011131310111098
1010111198877
101111141012899
10111011997107
1111111310109107
Second Subject.10911111281178
1214131415141099
10141313121111109
11141313131212109
1311131412121099
13121314121211119
Third Subject.710913109978
812121312101087
711101011101088
911131112101188
91111101091097
911121211101088
Average.9 15⁄16 11 1⁄3 11 1⁄2 12 5⁄18 11 1⁄9 10 1⁄3 9 7⁄8 8 5⁄8 8 1⁄9
Mean Error, .075 in.

The low-speed measurements show the same general tendencies except that the curvature is smaller with this speed when the faintest lights were used than with any of the others. The maximum curvature is also less and occurs with a more intense light than with the middle speed. These modifications offer no special difficulties. Since the light moves slowly, although the centre of the image, which is reënforced by induced excitation from the ends, does appear in consciousness in time ahead of the rest of the image, yet it does not appear so far in advance of the rest of the figure in space as it would if the light moved with a higher speed. While the same difference in brightness between the centre and the ends of the image should make one part appear in consciousness just as far ahead of the rest in time with this speed as with any other, yet since the speed is slow it would not appear to be so far ahead in space. The fact that the maximum amount of apparent curvature is less would also be explained in the same manner.

When the high and middle speeds were used the results were surprisingly consistent and the variations between the observers not very great. With the low speed the individual differences are very much more prominent. Uncertainties and variations between observers and between different observations of the same observer became greater and greater as the intensity of the light decreased. One seemed to be approaching the lower limit of induction, below which, even if the spreading of light stimuli through the retina took place at all, it was to such a slight extent that it made no very marked difference in the appearance of the moving image. Individual differences are very great in this respect. For instance, my own average measurement was 15⁄64 in. of curvature for the image produced when a light of the lowest intensity moved at the lowest speed. Mr. Vaughan's measurements averaged 30⁄64 in., a measurement of just twice as much for the same light at the same speed.

So far there has been given only a general view of what happens when an oblong moving image appears convexly curved. It may be well to consider the different causes which determine a certain curvature of the image and see how they are related.

As we have seen, the curvature is a function of the difference in intensity of various excitations between the centre and the ends of the retinal area excited. This difference is modified both by the objective intensity of the light and by the speed at which the light moves. Its efficiency to produce curvature is also modified by both these factors, since it requires a certain small amount of time for the irradiation to take place. If this time is not given by the too rapid passage of the image over a certain part of the retina, the difference in intensity will be lessened and the curvature therefore be decreased. On the other hand, if the figure moves too slowly, although this difference in intensity may be as great as possible for the brightness of the light which is acting, yet the curvature may be lessened on account of the fact that, although the centre of the image does appear ahead of the ends in time, yet it does not appear so far ahead of the ends of the image in space as it would if the same difference in intensity were present and the image moved more rapidly.

It will be remembered that the intensity of the centre of the figure owes its increase to reënforcement by excitation irradiating from the surrounding points. It seems only reasonable to suppose that this added intensity due to irradiation does not increase without limit, or with exactly the required ratio to produce a curvature of the front of the image which becomes continuously greater as the intensity of the light increases, indefinitely.

If this be so, then, at a certain brightness, the difference in intensity between the ends and the centre of the image will have reached a maximum, and a further increase in brightness of the light will not serve to increase the apparent curvature of the image, but rather to decrease it.

COLOR IRRADIATION

The color of the image has a decided influence upon the amount of perceived curvature, independently of the intensity.

The following experiments were performed with lights of different colors, in order to investigate the relations between the kinds and amounts of irradiation of the different colors by comparing the amounts of the curvatures obtained. We encountered a good deal of difficulty in fixing upon a proper method of comparison between the different colors. Finally it was decided to use such intensities of light as would give a maximum amount of curvature with each of the four primary colors, to measure this amount in each case, and also to measure the amount obtained when the intensity of the light was greater and less than that required to give the maximum.

It was found that very different objective intensities of light were required to give a maximum amount of curvature with the different colors. The colored images were obtained by placing colored pieces of glass in a frame which stood before the source of light. The intensity of the light could be regulated by interposing or taking away pieces of ground glass which rested in the frame between the light and the colored glass.

The red glass gave a nearly saturated color, but its place in the spectrum was rather nearer the orange than I could have wished. It was a thick piece of glass and absorbed a great deal of light. A 32-candle-power light with four pieces of ground glass in front of it gave a maximum curve for most observers.

The yellow gave a very well-saturated color with light from the incandescent lamps which we used. The glass was thinner and absorbed less light than the red. A 32-candle-power lamp with three pieces of ground glass usually gave the maximum.

Two 32-candle-power lamps and one of 24-candle-power were required with the green.

The green glass was not quite so saturated in color as the red or yellow. It was a slightly yellowish green. Red and yellow rays were visible through it to some extent when it was examined through the spectroscope. It absorbed somewhat less light than the red and decidedly more than the yellow. The maximum curvature was obtained when the source of light was screened with four pieces of ground glass.

The blue glass was a bluish violet, very heavy, and absorbed a great deal of light; it allowed many red and violet rays to pass through. It was necessary to use with this glass two 32-candle-power lamps and one 100-candle-power. When the combined light of these lamps was reduced by interposing three thicknesses of ground glass, the maximum curvature was observed. The light which then appeared, however, seemed of greater intensity than any other which gave a maximum.

The curvature of the white light was measured again in order to compare it with the colored lights. This was necessary, since the work was done with a different set of subjects and the former work showed individual variations. An 8-candle-power light was used as before. This, reduced by four pieces of ground glass, gave the maximum in most cases.

The following curves and tables show the average of the observations of four subjects. In the table the figures under the columns numbered 1 and 2 represent the amount of curvature perceived when the intensity of light was greater than that required to give a maximum under 4 and 5, when the light was not strong enough to produce a maximum of curvature. The columns numbered 3 represent the greatest amount of curvature perceptible with each color.

The curves shown in the diagram represent these measurements plotted out.