Sensations of achromatic light, when considered alone, form a complex system of one dimension, which extends, like the tonal line, between two limiting qualities. The sensations in the neighborhood of one of these limits we call black; in the neighborhood of the other white, while between the two we insert grey in its different shades (dark grey, grey, and light grey). This one-dimensional system of achromatic sensations differs from that of tones in being at once a system of quality and of intensity for every qualitative change in the direction from black to white is seen at the same time as an increase in intensity, an every qualitative change in the direction from white to black is seen as a decrease intensity. Each point in the series, which thus has a definite quality and intensity, is called a degree of brightness of the achromatic sensations. The whole system may, accordingly, be designated as the sensations of pure brightness. The use of the word "pure" indicates the absence of all sensations of color. The system of pure brightness is absolutely one-dimensional for, both the variations in quality and those in intensity belong to one and the same dimension. It differs essentially, in this respect, from the tonal line, in which each point is merely a degree of quality, and has also a whole series of gradations in intensity. Simple tone-sensations thus form a two-dimensional continuity so soon as we take into account both determinants, quality and intensity, while the system of pure brightness is always one-dimensional, even when we attend to both determinants.
The whole system may, therefore, be regarded as a continuous series of grades of brightness, in which the lower grades are designated black so far as quality is concerned, and weak in point of intensity, while the higher grades are called white and strong.
15 . Sensations of color also form a one-dimensional system when their qualities alone are taken into account. Unlike the system of sensations of pure brightness, this system returns upon itself from whatever point we start, for at first, after leaving a given quality, we pass gradually to a quality that shows the greatest difference, and going still further we find that the qualitative differences become smaller again, until finally we reach the starting point once more. The color-spectrum obtained by refracting sunlight through a prism, or that seen in the rainbow, shows this characteristic, though not completely. If in these cases we start from the red end of the spectrum, we come first to orange, then to yellow, yellow- green, green-blue, blue, indigo-blue, and finally to violet which is more like red than any of the other colors except orange, which lies next to red.
The line of colors in the spectrum does not return quite to its starting-point, because it does not contain all of colors that we have in sensation. Purple-red shades, which can be obtained by the objective mixture of red and violet rays, are wanting in the spectrum. Only when we fill out the spectral series with them, is the system of actual color-sensations complete, and then the system is a closed circle. This characteristic is not to be attributed to the circumstance that the spectrum actually presents for our observation a series returning nearly to its beginning. The same order of sensations can be found by arranging according to their subjective relationship, colored objects presented in any irregular order. Even children who have never observed attentively a solar spectrum or a rainbow, and can, therefore, begin the series with any other color just as well as with red, always arrange them in the same order.
The system of pure colors is, then, to be defined as one-dimensional.
It does not extend in a straight line, however, but returns upon itself. Its simplest geometrical representation would be a circle . From a given point in this system we pass, when the sensation is gradually varied, first to sensations, then to those most markedly different, and finally to others similar to the first quality, but in the opposite direction.
Every color must, accordingly, be related to one other particular color as a maximum of difference in sensation. This color may be called the opposite color, and in the representation of the color-system by a circle, two opposite colors are to be placed at the two extremities of the same diameter. Thus, for example, purple-red and green, yellow and blue, light green and violet, are opposite colors, that is, colors which exhibit the greatest qualitative differences.
The quality determined by the position of a sensation in the color-system, in distinction to other qualitative determinations, is called color-tone, a figurative name borrowed from tonal sensations. In this sense the simple names of colors; such as red, orange, yellow, etc., denote merely color tones. The color-circle is a representation of the system of color-tones abstracted from all the other attributes belonging to the sensations. In reality, every color-sensation has two other attributes, one we call its saturation, the other its brightness. Saturation is peculiar to chromatic sensations, while brightness belongs to achromatic sensations as well.
