(31) This clue is found in the union of these three qualities by measured scales in a _color sphere and color tree_.[10] The equator of the sphere[11] may be divided into ten parts, and serve as the scale of hue, marked R, YR, Y, GY, G, BG, B, PB, P, and RP. Its vertical axis may be divided into ten parts to serve as the scale of value, numbered from black (0) to white (10). Any perpendicular to the neutral axis is a scale of chroma. On the plane of the equator this scale is numbered 1, 2, 3, 4, 5, from the centre to the surface. [Illustration: Fig. 3.] [Footnote 10: See Color Tree in paragraph 14.] [Footnote 11: Unaware that the spherical arrangement had been used years before, I devised a double tetrahedron to classify colors, while a student of painting in 1879. It now appears that the sphere was common property with psychologists, having been described by Runge in 1810. Earlier still, Lambert had suggested a pyramidal form. Both are based on the erroneous assumption that red, yellow, and blue are primary sensations, and also fail to place these hues in a just scale of luminosity. My twirling color solid and its completer development in the present model have always made prominent the artistic feeling for color value. It differs in this and in other ways from previous systems, and is fortunate in possessing new apparatus to measure the degree of hue, value, and chroma.] (32) This chroma scale may be raised or lowered to any level of value, always remaining perpendicular to the axis, and serving to measure the chroma of every hue at every level of value. The fact that some colors exceed others to such an extent as to carry them out beyond the sphere is proved by measuring instruments, but the fact is a new one to many persons. (Figs. 2 and 3.) [Illustration: Fig. 2. (See Fig. 20) The Color Tree] (33) For this reason the COLOR TREE is a completer model than the sphere, although the simplicity of the latter makes it best for a child’s comprehension. (34) The color tree is made by taking the vertical axis of the sphere, which carries a scale of value, for the trunk. The branches are at right angles to the trunk; and, as in the sphere, they carry the scale of chroma. Colored balls on the branches tell their Hue. In order to show the MAXIMA of color, each branch is attached to the trunk (or neutral axis) at a level demanded by its value,--the yellow nearest white at the top, then the green, red, blue, and purple branches, approaching black in the order of their lower values. It will be remembered that the chroma of the sphere ceased with 5 at the equator. The color tree prolongs this through 6, 7, 8, and 9. The branch ends carry colored balls, representing the most powerful red, yellow, green, blue, and purple pigments which we now possess, and could be lengthened, should stronger chromas be discovered.[12] [Footnote 12: See Plate I.]