The opposite is true for color sensations. They, too, are numerous, perhaps a million. But it is easy to group them into a system which permits us to understand their interrelations. The relations between the various colors are so simple that they can be symbolically represented by a geometrical figure, a double pyramid with a four-cornered base, like the one in figure 14. The vertical axis represents the visual sensations which are colorless, arrayed so that the brightest white is at one end, the darkest black at the other, the various grays between. The base of the pyramids, which is not perpendicular to the axis, but slanting, represents the series of colors of [Illustration: FIG. 14.--COLOR PYRAMID.] the spectrum plus the non-spectral purples, between red and violet, all arranged in an orderly manner around the axis. The nearer we approach the axis, the less saturated, that is, the more whitish, or grayish, or blackish are the colors represented. The most saturated colors are therefore represented by the peripheral line of the base. The base is slanted because the most saturated colors are not all of the same brightness (meaning by this term exclusively lightness as opposed to darkness). The saturated yellow is much brighter than the saturated blue and must therefore be located here, symbolically, nearer the point of white than of black, while blue must be located nearer the point of black than of white. The figure shows clearly that it is impossible to deviate from the peculiar brightness of each saturated color without diminishing the saturation, for we cannot move up or down from any point of the peripheral line of the base and yet remain within the double pyramid, without approaching the axis. But if our starting point is a color of less than the maximum of saturation, we may change the brightness within certain limits without changing the saturation, for we may then, to a certain extent, move up and down parallel to the axis. Some have represented the color system by a double cone, using as common base a circle. But a four-cornered base represents an additional fact of experience which is lost sight of in the circular plane. The four colors red, green, blue, and yellow possess this property: that any one of them is entirely dissimilar in color tone to any of the other three, while any given color other than these must resemble just two of these. No other four or any other number of colors can be found which fulfill exactly these conditions. In order to represent this fact symbolically, we ought to give the colors red, green, blue, and yellow distinguished places in the periphery of the basal plane, and this can be done most easily by choosing as a base a four-cornered plane.