In the problem of brightness constancy, Gelb, A., Kardos, L., Koffka, K. and others emphasized the importance of factors such as the configuration and the articulation in the visual field, especially the relation of the brightness of a particular region to that of its adjacent region. On the other hand, Wallach, H. who repeated Gelb's experiment advanced what he called the proportional law, showing that dependence of perceived colors on the ratio of stimulus intensities accounts for the constancy of achromatic colors under varying illumination.In the present study, the role of the light intensities of the background was investigated with especial reference to Wallach's proportional law. The achromaticcolors were used for this purpose.Stimuli-Each stimulus consisted of a disk and a ring that surrounded it and formed its background (Fig. 2 and 4). The intensity of each of these two regions could be varied independently. The experiments were conducted in a dark room, two pairs of disk and ring were observed successively by using the binocular method, and the apparent brightnesses of both disks were compared with each other.In Experiment I and II, it was observed that Wallach's proportional law depends upon the interaction between the light intensity of the disk and that of the ring, in other words, upon the contrast effect of the ring upon the apparent brightness of the disk. We may say, that the law becomes valid under the condition in which the contrast effect prevails, that is, when the intensity of the ring is lighter than that of the disk, but it does not when the contrast effect is difficult to appear (the ring being darker than the disk) (Fig. 3 and 5).In Experiment III and IV, it was found that the degree of brightness constancy of the disk depends upon the conditions in which the disk adjoins a lighter ring or a darker ring than itself (Fig. 6, 7, 8 and 9). The degree of brightness constancy is greater under the condition, when the disk has a lighter ring than itself, i.e., when the contrast effect of the ring is stronger. On the other hand, when the disk has a darker ring than itself, i.e., when the contrast effect of the ring is weaker, the degree of brightness constancy is smaller. Such results will lead to the conclusion that the existence of a lighter background is the most important factor in brightness constancy. These findings agree fairly well with the results of the investigation by Leibowitz, H. (14).Moreover, in so far as our experimental conditions are concerned, is may be said that the importance of the factor of the contrast effect of the background should increase in relation to the degree of figuredness of the particular region and the modes of appearance of their colors. On the other hand, it seems that one of the factors upon which the degree of figuredness depends, is the phenomenal gradient of the brightness between the particular region and its background brought out by contrast.