es of all sections unite in a
scale of gray from black to white, no matter what hue each contains.

The curved outside of each section shows its particular hue graded from
black to white; and, should the section be cut at right angles to the
thin edge, it would show the third dimension,--chroma,--for the color is
graded evenly from the surface to neutral gray. A pin stuck in at any
point traces the third dimension.

[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