between white and black,--that is, on the equator of the sphere,--so
that a middle red will be written R 5/, suggesting the steps 6, 7, 8,
and 9 which are above the equator, while steps 4, 3, 2, and 1 are below.
It is well to show only three values of a color at first; for instance,
the middle value contrasted with a light and a dark one. These are
written R 3/, R 5/, R 7/. Soon he perceives and can imitate finer
differences, and the red scale may be written entire, as R 1/, R 2/,
R 3/, R 4/, R 5/, R 6/, R 7/, R 8/, R 9/, with black as 0 and white
as 10.

(42) _Chroma-difference is the third_ and most subtle color quality. The
child is already unconsciously familiar with the middle chroma of red,
having had the enamels of MIDDLE COLOR always in view, and the red
enamel is to be contrasted with the strongest and weakest red chromas
obtainable. These he writes R /1, R /5, R /9, seeing that this describes
the chromas of red, but leaves out its values. R 5/1, R 5/5, R 5/9, is
the complete statement, showing that, while both hue and value are
unchanged, the chroma passes from grayish red to middle red (enamel
first learned) and out to the strongest red in the chroma scale obtained
by vermilion.

(43) It may be long before he can imitate the intervening steps of
chroma, many children finding it difficult to express more than five
steps of the chroma scale, although easily making ten steps of value and
from twenty to thirty-five steps of hue. This interesting feature is of
psychologic value, and has been followed in the color tree and color
sphere.

+Does such a scientific scheme leave any outlet for feeling
and personal expression of beauty?+

(44) Lest this exact attitude in color study should seem inartistic,
compared with the free and almost chaotic methods in use, let it be said
that the stage thus far outlined is frankly disciplinary. It is somewhat
dry and unattractive, just as the early musical training is fatiguing
without inventive exercises. The child should be encouraged at each step
to exercise his fancy.

(45) Instead of cramping his outlook upon nature, it widens his grasp of
color, and stores the memory with finer differences, supplying more
material by which to express his sense of coloristic beauty.

(46) Color harmony, as now treated, is a purely personal affair,
difficult to refer to any clear principles or definite laws. The very
terms by which it seeks expression are borrowed from music, and sugg