[Illustration: Fig. 5.] +A color sphere can be used to unite the three dimensions of hue, value, and chroma.+ (12) Having used the familiar structure of the orange as a help in classifying colors, let us substitute a geometric solid, like a sphere,[4] and make use of geographical terms. The north pole is white. The south pole is black. The equator is a circuit of middle reds, yellows, greens, blues, and purples. Parallels above the equator describe this circuit in lighter values, and parallels below trace it in darker values. The vertical axis joining black and white is a neutral scale of gray values, while perpendiculars to it (like a pin thrust into the orange) are scales of chroma. Thus our color notions may be brought into an orderly relation by the color sphere. Any color describes its light and strength by its location in the solid or on the surface, and is named by its place in the combined scales of hue, value, and chroma. [Footnote 4: See frontispiece.] +Two dimensions fail to describe a color.+ (13) Much of the popular misunderstanding of color is caused by ignorance of these three dimensions or by an attempt to make two dimensions do the work of three. (14) Flat diagrams showing hues and values, but omitting to define chromas, are as incomplete as would be a map of Switzerland with the mountains left out, or a harbor chart without indications of the depth of water. We find by aid of the measuring instruments that pigments are very unequal in this third dimension,--chroma,--producing mountains and valleys on the color sphere, so that, when the color system is worked out in pigments and charted, some colors must be traced well out beyond the spherical surface (paragraphs 125-127). Indeed, a COLOR TREE[5] is needed to display by the unequal levels and lengths of its branches the individuality of pigment colors. But, whatever solid or figure is used to illustrate color relations, it must combine the three scales of hue, value, and chroma, and these definite scales furnish a name for every color based upon its intrinsic qualities, and free from terms purloined in other sensations, or caught from the fluctuating colors of natural objects. [Footnote 5: For description of the Color Tree see paragraphs 33 and 34.] +How this system describes the spectrum.+ (15) The solar spectrum and rainbow are the most stimulating color experiences with which we are acquainted. Can they be described by this solid system? (16) The lightest part of the spectrum is a narrow field of greenish yellow, grading into darker red on one side and into darker green upon the other, followed by still darker blue and purple. Upon the sphere the values of these spectral colors trace a path high up on the yellow section, near white, and slanting downward across the red and green sections, which are traversed near the level of the equator, it goes on to cross the blue and purple well down toward black.