18. If we neglect the somewhat different position of the maximal saturation of the various colors in the line of brightness, the relation that exists between sensations of chromatic brightness and those of pure, or achromatic, brightness, by virtue of the gradual transition of colors into white on the one hand, and into black on the other, may be represented in the simplest manner as follows. First, we may represent the system of pure color-tones, that is, of the colors at their maximal saturation, by a circle, as above. Then we may draw through the centre of this circle, perpendicular to its plane, the straight line of pure brightness, in such a way that where it cuts the plane of the circular surface, it represents the sensation of pure brightness corresponding to the minimum of saturation for the colors with which we started. In like manner, the other color-circles for increasing and decreasing grades of brightness, may be arranged perpendicularly along this line, above and below the circle of greatest saturation. But the decreasing saturation of the colors in these latter circles must be expressed in the shortening of their radii; just as in the first circle, the shorter the distance from the centre, the less the saturation. These radii grow continually shorter, until finally, at the two extremities of the line, the circles disappear entirely. This corresponds to the fact that for every color the maximum of brightness corresponds to the sensation white, while its minimum corresponds to black [ 2 ]
19. The whole system of sensations of chromatic brightness may, accordingly, be most simply represented by a spherical surface whose equator represents the system of pure color-tones, or colors of greatest saturation, while the two poles correspond to white and black, the extremities of the sensations of chromatic brightness. Of course, any other geometrical figure with similar attributes, as, for example, two cones with a common base and apexes pointing in different directions, would serve the same purpose. The only thing essential for the representation, is the gradual transition to white and black, and the corresponding decrease in the variety of the color-tones, which finds its expression in the continual decrease in the length of the radii of the color-circles. Now, as above shown, the system of saturations corresponding to a particular sensation of pure brightness, may be represented by a circular surface which contains all the sensations of light belonging to one grade of brightness.
When we unite grades of saturation and brightness to a single system, the total system of light sensations may be represented by a solid sphere. The equator is the system of pure color-tones; the polar axis is the system of pure brightnesses; the surface represents the system of chromatic brightnesses, and, finally, every circular plane perpendicular to the polar axis, corresponds to a system of saturations of equal brightness.
This representation by means of a sphere is indeed arbitrary, in the sense that any other solid figure with analogous attributes may be chosen in its place; still, it presents to view the psychological fact that the total system of light sensations is a closed continuity of three dimensions. The three-dimensional character of the system arises from the fact that every concrete sensation of light has three determinants: color-tone, saturation, and brightness. Pure, or achromatic, brightness and pure, or saturated, colors are to be regarded as the two extreme cases in the series of saturations. The closed form of the system comes from the circular character of the color-line, on the one hand, and, on the other, from the termination of the system of chromatic brightness in the extremes of pure brightness. A special characteristic of the system is that only the changes in the two dimensions, or those of color-tones and saturations, are pure variations in quality, while every movement in the third dimension, or that of brightness, is at once a modification of both quality and intensity. As a consequence of this circumstance, the whole three-dimensional system is required to represent the qualities of light-sensations, but it includes also the intensities of these sensations.
20. Certain principal senses are prominent in this system, because we use them as points of reference for the arrangement of all the others. These are, white and black, in the achromatic series, and the four principal colors, red, yellow, green, and blue, in the chromatic. Only these six sensations have clearly distinguished names in the early development of language. All other sensations are then named eiher with reference to these or with modifications of the names themselves. Thus, we regard grey as a stage in the achromatic series lying between white and black, We designate the different grades of saturation according to their brightness, as whitish or blackish, light or dark color-tones; an we generally choose compound names for the colors between the four principal ones, as, for example, purple-red, orange-yellow, yellow-green, etc. These all show their relatively late origin by their ver composition.