It has been shown that the neutral centre of the system is a balancing point for all colors, that a line through this centre finds opposite colors which balance and complement each other; and we are now ready to make a practical application, carrying out these ideal relations of color as far as pigments will permit in a color sphere[27] (Fig. 16).
[Footnote 27: Patented Jan. 9, 1900.]
(103) The materials are quite simple. First a colorless globe, mounted so as to spin freely on its axis. Then a measured scale of value, specially devised for this purpose, obtained by the daylight photometer.[28] Next a set of carefully chosen pigments, whose reasonable permanence has been tested by long use, and which are prepared so that they will not glisten when spread on the surface of the globe, but give a uniformly mat surface. A gla.s.s palette, palette knife, and some fine brushes complete the list.
[Footnote 28: See paragraph 65.]
(104) Here is a list of the paints arranged in pairs to represent the five sets of opposite hues described in Chapter III., paragraphs 61-63:--
_Color Pairs._ _Pigments Used._ _Chemical Nature._
Red and Venetian red. Calcined native earth.
Blue-green. Viridian and Cobalt. Chromium sesquioxide.
Yellow and Raw Sienna. Native earth.
Purple-blue. Ultramarine. Artificial product.
Green and Emerald green. a.r.s.enate of copper.
Red-purple. Purple madder. Extract of the madder plant.
Blue and Cobalt. Oxide of cobalt with alumina.
Yellow-red. Orange cadmium. Sulphide of cadmium.
Purple and Madder and cobalt. See each pigment above.
Green-yellow. Emerald green See each pigment above.
and Sienna.
(105) These paints have various degrees of hue, value, and chroma, but can be tempered by additions of the neutrals, zinc white and ivory black, until each is brought to a middle value and tested on the value scale. After each pair has been thus balanced, they are painted in their appropriate s.p.a.ces on the globe, forming an equator of balanced hues.
[Ill.u.s.tration: Fig. 17.]
(106) The method of proving this balance has already been suggested in Chapter IV., paragraph 93. It consists of an ingenious implement devised by Clerk-Maxwell, which gives us a result of mixing colors without the chemical risks of letting them come in contact, and also measures accurately the quant.i.ty of each which is used (Fig. 17).
(107) This is called a Maxwell disc, and is nothing more than a circle of firm cardboard, pierced with a central hole to fit the spindle of a rotary motor, and with a radial slit from rim to centre, so that another disc may be slid over the first to cover any desired fraction of its surface. Let us paint one of these discs with Venetian red and the other with viridian and cobalt, the first pair in the list of pigments to be used on the globe.
(108) Having dried these two discs, one is combined with the other on the motor shaft so that each color occupies half the circle. As soon as the motor starts, the two colors are no longer distinguished, and rapid rotation melts them so perfectly that the eye sees a new color, due to their mixture on the retina. This new color is a reddish gray, showing that the red is more chromatic than the blue-green. But by stopping the motor and sliding the green disc to cover more of the red one, there comes a point where rotation melts them into a perfectly neutral gray.
No hint of either hue remains, and the pair is said to balance.
(109) Since this balance has been obtained by _unequal areas_ of the two pigments, it must compensate for a lack of equal chroma in the hues (see paragraphs 76, 77); and, to measure this inequality, a slightly larger disc, with decimal divisions on its rim, is placed back of the two painted ones. If this scale shows the red as occupying 3? parts of the area, while blue-green occupies 6? parts, then the blue-green must be only half as chromatic as the red, since it takes twice as much to produce the balance.
(110) The red is then grayed (diminished in chroma by additions of a middle gray) until it can occupy half the circle, with blue-green on the remaining half, and still produce neutrality when mixed by rotation.
Each disc now reads 5 on the decimal scale. Lest the graying of red should have disturbed its value, it is again tested on the photometric scale, and reads 4.7, showing it has been slightly darkened by the graying process. A little white is therefore added until its value is restored to 5.
(111) The two opposites are now completely balanced, for they are equal in value (5), equal in chroma (5), and have proved their equality as complements by uniting in equal areas to form a neutral mixture. It only remains to apply them in their proper position on the sphere.
(112) A band is traced around the equator, divided in ten equal s.p.a.ces, and lettered R, YR, Y, GY, G, BG, B, PB, P, and RP (see Fig. 18). This balanced red and blue-green are applied with the brush to s.p.a.ces marked R and BG, care being taken to fill, but not to overstep the bounds, and the color laid absolutely flat, that no unevenness of value or chroma may disturb the balance.
(113) The next pair, represented by Raw Sienna and Ultramarine, is similarly brought to middle value, balanced by equal areas on the Maxwell discs, and, when correct in each quality, is painted in the s.p.a.ces Y and PB. Emerald Green and Purple Madder, which form the next pigment pair, are similarly tempered, proved, and applied, followed by the two remaining pairs, until the equator of the globe presents its ten equal steps of middle hues.
+An equator of ten balanced hues.+
(114) Now comes the total test of this circuit of balanced hues by rotation of the sphere. As it gains speed, the colors flash less and less, and finally melt into a middle gray of perfect neutrality. Had it failed to produce this gray and shown a tinge of any hue still persisting, we should say that the persistent hue was in excess, or, conversely, that its opposite hue was deficient in chroma, and failed to preserve its share in the balance.
[Ill.u.s.tration: Fig. 18.]
(115) For instance, had rotation discovered the persistence of reddish gray, it would have proved the red too strong, or its opposite, blue-green, too weak, and we should have been forced to retrace our steps, applying a correction until neutrality was established by the rotation test.
(116) This is the practical demonstration of the a.s.sertion (Chapter I., paragraph 8) that a _color has three dimensions which can be measured_.
Each of these ten middle hues has proved its right to a definite place on the color globe by its measurements of value and chroma. Being of equal chroma, all are equidistant from the neutral centre, and, being equal in value, all are equally removed from the poles. If the warm hues (red and yellow) or the cool hues (blue and green) were in excess, the rotation test of the sphere would fail to produce grayness, and so detect its lack of balance.[29]
[Footnote 29: Such a test would have exposed the excess of warm color in the schemes of Runge and Chevreul, as shown in the Appendix to this chapter.]
+A chromatic tuning fork.+
(117) The five princ.i.p.al steps in this color equator are made in permanent enamel and carefully safeguarded, so that, if the pigments painted on the globe should change or become soiled, it could be at once detected and set right. These five are middle red (so called because midway between white and black, as well as midway between our strongest red and the neutral centre), middle yellow, middle green, middle blue, and middle purple. They may be called the CHROMATIC TUNING FORK, for they serve to establish the pitch of colors, as the musical tuning fork preserves the pitch of sounds.
+Completion of a pigment color sphere.+
(118) When the chromatic tuning fork has thus been obtained, the completion of the globe is only a matter of patience, for the same method can be applied at any level in the scale of value, and a new circuit of balanced hues made to conform with its position between the poles of white and black.
[Ill.u.s.tration: Fig. 19.]
(119) The surface above and below the equatorial band is set off by parallels to match the photometric scale, making nine bands or value zones in all, of which the equator is fifth, the black pole being 0 and the white pole 10.
(120) Ten meridians carry the equatorial hues across all these value zones and trace the gradation of each hue through a complete scale from black to white, marked by their values, as shown in paragraph 68. Thus the red scale is R1, R2, R3, R4, R5 (middle red), R6, R7, R8, and R9, and similarly with each of the other hues. When the circle of hues corresponding to each level has been applied and tested, the entire surface of the globe is spread with a logical system of color scales, and the eye gratified with regular sequences which move by measured steps in each direction.
(121) Each meridian traces a scale of value for the hue in which it lies. Each parallel traces a scale of hue for the value at whose level it is drawn. Any oblique path across these scales traces a regular sequence, each step combining change of hue with a change of value and chroma. The more this path approaches the vertical, the less are its changes of hue and the more its changes of value and chroma; while, the nearer it comes to the horizontal, the less are its changes of value and chroma, while the greater become its changes of hue. Of these two oblique paths the first may be called that of a Luminist, or painter like Rembrandt, whose canvases present great contrasts of light and shade, while the second is that of the Colorist, such as t.i.tian, whose work shows great fulness of hues without the violent extremes of white and black.
+Total balance of the sphere tested by rotation on any desired axis.+
(122) Not only does the mount of the color sphere permit its rotation on the vertical axis (white-black), but it is so hung that it may be spun on the ends of any desired axis, as, for instance, that joining our first color pair, red and blue-green. With this pair as poles of rotation, a new equator is traced through all the values of purple on one side and of green-yellow on the other, which the rotation test melts in a perfect balance of middle gray, proving the correctness of these values. In the same way it may be hung and tested on successive axes, until the total balance of the entire spherical series is proved.
(123) But this color system does not cease with the colors spread on the surface of a globe.[30] The first ill.u.s.tration of an orange filled with color was chosen for the purpose of stimulating the imagination to follow a surface color inward to the neutral axis by regular decrease of chroma. A slice at any level of the solid, as at value 8 (Fig. 10), shows each hue of that level pa.s.sing by even steps of increasing grayness to the neutral gray N8 of the axis. In the case of red at this level, it is easily described by the notation R 8/3, R 8/2, R 8/1, of which the initial and upper numerals do not change, but the lower numeral traces loss of chroma by 3, 2, and 1 to the neutral axis.
[Footnote 30: No color is excluded from this system, but the excess and inequalities of pigment chroma are traced in the Color Atlas.]
(124) And there are stronger chromas of red outside the surface, which can be written R 8/4, R 8/5, R 8/6, etc. Indeed, our color measurements discover such differences of chroma in the various pigments used, that the color tree referred to in paragraphs 34, 35, is necessary to bring before the eye their maximum chromas, most of which are well outside the spherical sh.e.l.l and at various levels of value. One way to describe the color sphere is to suggest that a color tree, the intervals between whose irregular branches are filled with appropriate color, can be placed in a turning lathe and turned down until the color maxima are removed, thus producing a color solid no larger than the chroma of its weakest pigment (Fig. 2).
+Charts of the color solid.+
(125) Thus it becomes evident that, while the color sphere is a valuable help to the child in conceiving color relations, in uniting the three scales of color measure, and in furnishing with its mount an excellent test of the theory of color balance, yet it is always restricted to the chroma of its weakest color, the surplus chromas of all other colors being thought of as enormous mountains built out at various levels to reach the maxima of our pigments.
(126) The complete color solid is, therefore, of irregular shape, with mountains and valleys, corresponding to the inequalities of pigments. To display these inequalities to the eye, we must prepare cross sections or charts of the solid, some horizontal, some vertical, and others oblique.