Chapter XVIII: Section II

_Of Diagrams designed to Represent and Define Colours and their Modifications._

130. Various contrivances have been proposed under the titles of Tables, Scales, Colour-Circles, Chromatometers, &c., for representing either by numbers or a rational nomenclature, colours and their modifications. They are generally founded on these three propositions:—1. There are three primary colours. 2. Equal portions of these colours being mixed, produce pure secondary colours. 3. Equal portions of the three primary colours produce black.

131. But we know of no substance which exhibits pure colour; that is, which reflects only one kind of coloured rays, whether pure red, pure yellow, or pure blue. And since it is impossible to procure pure colouring matters, how can it be said that orange, green, and violet are composed of two simple colours mixed in equal proportions? Or that black consists of a mixture of equal parts of three simple colours?

These chromatic tables, &c., point out mixtures which do not produce the results deducible from the principles on which they are said to be based.

132. But most of the blue, red, and yellow colours with which we are acquainted, give, by their binary compounds, violet, green, and orange inferior in brilliancy to the natural violet, green and orange colours of objects. This result would be explained by admitting that colours mixed two by two, reflect at least two kinds of coloured rays; and that where there is any mixture of colours which reflect separately red, yellow, and blue, there is produced a certain amount of black which reduces the brilliancy of the mixture.

133. Conformably with this view, the violet, green, and orange colours which result from a mixture of coloured matters, are most brilliant when the respective colours of these materials approach each other. For example, a mixture of blue and red inclines more to violet than a mixture of blue and yellow inclines to green, and that of red and yellow inclines still more to orange.

134. In order to represent all the modifications that I have called _tones_ and _hues_ of colours, as well as the relations which exist between those that are complementary to each other, I have devised the following diagram (Plate 7). From a centre, _c_, I describe two circumferences, _y_ Y. I divide each of these by means of three rays, _c a_, _c b_, _c d_, into arcs of 120 degrees each. I divide the portion of each ray comprised between the two circles _y_ Y into twenty parts, which represent as many tones of the colours red, yellow, and blue.

135. In each of the scales of these three colours there is one tone, which, when pure, represents the colour of the scale to which it relates. I therefore call it the _normal tone of that scale_. If we represent a unit of surface _s_, entirely covered by the pigment which reflects the normal colour, and if we suppose that this colouring matter is equally distributed over the surface _a_ 1, we shall represent the tones superior to the normal tone by the unit of surface covered with 1 of the normal colour, plus the quantities of black increasing with the number of tones; and we shall represent the inferior tones by the unit of surface covered with a fraction of the quantity 1, constituting the normal tone, mixed with (——) quantities of black, as the tone has a less elevated number. If the tone 15 of the red scale be the normal tone, the normal tone of the yellow scale will have a lower number, while the normal tone of the blue scale will have a higher number. This depends upon the unequal lightness of the colours.

136. If each arc of 120° be divided into two of 60° and if radii pass through the points of division, beginning at _y_, there will be represented twenty tones of the orange, green, and violet scales, the colours at the extremities of each diameter being complementary to one another. Each arc of 60° might be divided into arcs of 30°, and thus would be obtained radii representing twenty tones of scales, which I shall call orange-red, orange-yellow, greenish-yellow, greenish-blue, bluish-violet, and violet-red.

137. By dividing each arc into five, for example, by means of five radii, which I divide into twenty parts each, beginning at the circumference _y_, I shall obtain sixty new scales.

138. Beginning with red, I designate them as follows:—

_a_ Red _e_ Yellow _i_ Blue
1 Red 1 Yellow 1 Blue
2 Red 2 Yellow 2 Blue
3 Red 3 Yellow 3 Blue
4 Red 4 Yellow 4 Blue
5 Red 5 Yellow 5 Blue
139. _b_ Red-orange _f_ Yellow-green _k_ Blue-violet
1 Red-orange 1 Yellow-green 1 Blue-violet
2 Red-orange 2 Yellow-green 2 Blue-violet
3 Red-orange 3 Yellow-green 3 Blue-violet
4 Red-orange 4 Yellow-green 4 Blue-violet
5 Red-orange 5 Yellow-green 5 Blue-violet
140. _c_ Orange _g_ Green _l_ Violet
1 Orange 1 Green 1 Violet
2 Orange 2 Green 2 Violet
3 Orange 3 Green 3 Violet
4 Orange 4 Green 4 Violet
5 Orange 5 Green 5 Violet
141. _d_ Orange-yellow _h_ Green-blue _m_ Violet-red
1 Orange-yellow 1 Green-blue 1 Violet-red
2 Orange-yellow 2 Green-blue 2 Violet-red
3 Orange-yellow 3 Green-blue 3 Violet-red
4 Orange-yellow 4 Green-blue 4 Violet-red
5 Orange-yellow 5 Green-blue 5 Violet-red

I attach no importance to this nomenclature; I employ it only as the simplest to distinguish the seventy-two scales just described. The number may be increased indefinitely, by inserting as many as we choose between the above.

142. Let us now represent the gradations of each colour in the scales of the circle by the addition to it of black, progressively increasing till it becomes pure black. Imagine a quadrant whose radius is equal to that of the circle, and arranged so as to turn upon an axis perpendicular to the plane of the circle. Divide this quadrant, 1st, by concentric arcs _y yʹ_, which coincide with the circles denoted by the same letters; 2nd, by ten radii, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. Divide each of these radii into twenty parts, representing twenty tones, corresponding to the tones of the scales represented on the circle.

143. I suppose that the tenth radius comprises the gradations of normal black, covering the half-circle described by the movement of the quadrant upon its axis; this black mixed in decreasing quantities, with increasing quantities of white, gives the twenty tones of normal grey, and ends by being lost in the white situated above the tone 1. I suppose, further, that the normal tone of each of the scales taken upon each of the radii of the quadrant 1, 2, 3, 4, 5, 6, 7, 8, 9, is formed of the mixture of black with the colour of any of the scales that the circle contains, and in such a proportion that the normal tone 15 of that scale is represented by the unit of surface covered with 1, or ¹⁰/₁₀ of red.

144. The tone 15 of the scale of the

1st Radius = ⁹/₁₀ of Red + ¹/₁₀ of Black.
2nd ” = ⁸/₁₀ ” + ²/₁₀ ”
3rd ” = ⁷/₁₀ ” + ³/₁₀ ”
4th ” = ⁶/₁₀ ” + ⁴/₁₀ ”
5th ” = ⁵/₁₀ ” + ⁵/₁₀ ”
6th ” = ⁴/₁₀ ” + ⁶/₁₀ ”
7th ” = ³/₁₀ ” + ⁷/₁₀ ”
8th ” = ²/₁₀ ” + ⁸/₁₀ ”
9th ” = ¹/₁₀ ” + ⁹/₁₀ ”

These proportions relate to the effect of the mixtures upon the eye, and not to the material quantity of the red and black substances.

145. We see then—1. That each of these _tones_, 15, composed of colour and black, reduced by white and deepened by black, gives a scale of twenty tones, so much the more broken as they are nearer the scale of normal black. 2. That the quadrant by its movement upon the axis of the circle, represents the scales of every colour except red, broken by black. These broken scales are equidistant, and are formed of equidistant tones. 3. That all the colours are thus contained in a circle, whose plan comprehends the pure colours; the central space, black; and the intermediate space the pure colours, broken by the various proportions of black.

146. The diagram, as just described, thus represents the lowering of pure colours by white, and their gradation by black; their modifications by their mutual mixtures, the modification of hues, and the modification of breaking. We will presently inquire into the possibility of realizing it by means of coloured materials.

147. We have presumed—1. That the normal tone of each of the scales is as pure as possible. 2. That the tones bearing the same number in all the scales,—both those of the pure colours and those of the broken colours,—are, to the sight, of equal depth. 3. That if three tones, of the same number, be taken in three consecutive scales, the tone of the intermediate scale is the mean between the colours of the extreme scales. It is thus easy to explain the modifications of a pure colour commencing with its normal tone.

148. These modifications are so produced that—1. _The Pure Colour never leaves its Scale._—The modification is in the direction of the radius of the circle—proceeding from the normal tone towards the centre, it gains white; while proceeding from the normal tone towards the circumference, it gains black.

149. 2. _The Pure Colour leaves its Scale by the addition of Black._—In this case the various scales comprised in the quadrant perpendicular to the circle, begin at the normal tone of one of the pure scales of the circle with which the quadrant coincides. This normal tone, resulting from a quantity of colour represented by unity, covering a unit of surface _s_, the normal tones of the quadrant result from the mixture of black and a fraction of unity of the colour. These mixtures constitute broken colours, each covering a unit of surface _s_, and are of the same depth as the normal tone of the pure colour. The fraction of the quantity of colour is, in the broken normal tones, so much less, as the scales, to which these tones belong, approximate to the vertical axis of the semicircle.

Besides, each normal tone of the scales of the quadrant is modified, like the normal tones of the scales of the circle, by increasing quantities of white towards the centre, and of increasing quantities of black towards the circumference.

150. 3. _A Pure Colour is modified by the addition of another Pure Colour._—In this case hues are formed so much more resembling each other, as the quantities of the second colour are smaller. These modifications are made circularly, so that the tones retain their numbers. Thus admitting, with painters and dyers, that there are only three primary colours, and that by combining these two by two, we obtain all the pure complex colours; and by combining them in threes, all the broken colours; we find that it is possible to represent by this hypothesis, all the modifications of colours.

151. Another advantage of this construction is that of giving to all artists who may make applications of the law of simple contrast, the complementaries of all the pure colours; since the colours of the circular plan which are found at the extremities of the same diameter are complementary to each other. For example, not only are red and green, blue and orange, yellow and violet on the same diameter, but it is so with orange-red and bluish-green, and yellowish-green and violet-red; of red No. 1 and of green No. 1; so that all the colours opposed to each other are mutually complementary.

152. The complementary of a colour contiguous to another being once known, it is easy, according to the principles of combination, to determine the modification that the second must receive from the first; since this modification is the result of the mixture of the complementary with the contiguous colour. In fact, if there is no difficulty when the result is that of the non-complementary mixture with a simple colour, red, yellow, and blue, with a binary colour, orange, green, violet (using the language of painters, 76), there is no greater difficulty when the result is that of the mixture of two binary colours. For, the complementary being much less intense than the colour with which it is mixed, the result will be found by subtracting from the last binary colour the portion of its simple colour, which with the complementary forms white, or in other words, neutralises it.

153. _Examples._—1. Orange being added as a complementary to green, neutralises a portion of its blue, and consequently makes it appear less blue or more yellow.

2. Orange being added as complementary to violet, neutralises a portion of its blue, and consequently makes it appear less blue or more red.

3. Green being added as complementary to violet, neutralises a portion of its red, and consequently makes it appear less red or more blue.

154. These three examples are easily explained by subtracting from the binary colour a portion of its simple colour which is identical with that contiguous to it. Thus:—

1. Blue subtracted from Green, makes it appear more Yellow.
2. Blue ” ” Violet ” ” Red.
3. Red ” ” Violet ” ” Blue.

155. To put the diagram into practice we must adopt invariable types of colour, either in the solar spectrum, or in polarized light, or coloured rings, or colours developed in a constant manner, by any process whatever; then imitate them with the utmost fidelity, by means of colouring matters which should be applied to the circular plan of our chromatic diagram.

These types must be sufficiently numerous to reproduce the principal colours, in order that a practised eye may without difficulty insert all the tones of the same scale and all the hues of which types are wanting. In fact the diagram thus established, should present terms so near that the various colours of the natural bodies might be referred to them.

156. 1. _That it represents all the Modifications resulting from the Mixture of Colours._—Thus any colour lowered by white and deepened with black may, retaining its place in the scale, give rise to an infinite variety of tones; infinite, inasmuch as an unlimited number may be inserted from tone 1 to tone 20.

157. 2. Pure colours, by their mutual modifications, may produce an infinite variety of hues; for between two adjacent hues we may insert as many as we desire.

158. 3. The normal tone of a pure colour represented by a quantity equal to 1, covering the unit of surface, is the commencement of the normal tones and scales proceeding towards black; these normal tones being represented by black and a quantity of colour less than unity, constituting the mixtures which cover a unit of surface s, and colour it of a tone which has the same number as the normal tone of the pure scale to which it relates. It is understood that in proceeding from this tone to the corresponding tone of normal black, we may insert an unlimited number of mixtures of colour and black.

159. The modifications of colours, thus indicated by the diagram, render it extremely easy to understand the definitions given above (123) of the words, scales, tones, hues, pure and broken colours.

160. 2. _It affords the means of knowing the complementaries of every colour, since the names written at the two extremities of any one diameter indicate the colours complementary to each other._

161. EXAMPLES.—_a._ Suppose it be required to know the mutual influence of _blue and yellow_; at one extremity of a diameter we read the word _blue_, and at its opposite end, the word _orange_; showing that blue tends to give orange to yellow. Again, at the end of another diameter we read the word yellow, and at its opposite, the word violet; by which we see that yellow tends to give violet to blue.

162. _b._ Suppose _green and blue_ be contiguous; at one extremity of a diameter we read the word green, and at its opposite end, red; showing that green tending to give red to blue, must render it more violet. Again, at one end of a diameter we read the word blue, and at its opposite end, orange. But what arises from the mixture of green and orange? The orange will tend to neutralize its complementary, blue, in the green; and as it is always too feeble to neutralize all the blue, its influence will be limited to neutralizing a portion of it; whence it results that green, contiguous to blue, will appear more yellow than it really is.

163. _c._ Let _green and yellow_ be contiguous, we shall see in like manner that the green, by imparting red to the yellow, will render it orange; and that violet, the complementary of yellow, by neutralizing some yellow in the green, will make the green appear bluer, or less yellow.

164. 3. _A third advantage of this diagram, which distinguishes it from other chromatic diagrams, is, that it affords the preceding advantages, without being coloured._

165. 4. _A fourth advantage is that of its manifesting to all artists who use coloured materials of a definite size, especially the workers of tapestry, carpets and the like, the relation of number which must exist between the tones of the various scales which they work together._