The eye is quiet, and the mind soothed and complacent, when colours are opposed to each other in equivalent proportions chromatically, or in such proportions as neutralize their individual activities. This is perfect harmony, or union of colours. But the eye and the mind are agreeably moved, also, when the mathematical proportions of opposed or conjoined colours are such as to produce agreeable combinations to sense; and this is the occasion of the variety of harmony, and the powers of composition in colouring. Thus colours in the abstract are a mere variation of relations of the same thing. Black and white are the same colour; and, since colours are mere relations, if there were only one colour in the world there would be no colour at all, but only light and shade, however strange, offensive, or paradoxical such assertions may appear.

The neutralizing powers of colours, called compensating, have also been improperly denominated antipathies, since they are the foundation of all harmony and agreement in colours; too much of any colour in a painting being invariably reconciled to the eye by the due introduction of its opposite or equivalent, either in the way of compounding, by glazing or mingling, or by contrast, in the first manner with neutralizing and subdued effect, and in the last with heightened effect and brilliancy, - in the one case by overpowering the colour, in the other by overpowering the organ; while in each the equilibrium, or due subordination of colours, is restored. It is not sufficient, however, that the artist is informed what colours neutralize and contrast, if he remain unacquainted with their various powers in these respects. If he imagine them of equal force, he will be led into errors in practice, from which nothing but a fine eye and repeated attempts can relieve him; but, if he know beforehand the powers with which colours act on and harmonize each other, the eye and the mind will go in concert with the hand, and save him much disappointment and loss of time, to say nothing of the advantage and gratification of such foreknowledge in realizing their beauties with intention.

We have been enabled to demonstrate the proportional powers of colours numerically, as given in our Scale of Chromatic Equivalents, by means of the Metrochrome,* whereby it is ascertained that certain proportions of the primary colours, which reduced to their simplest terms are as 3 yellow, 5 red, and 8 blue, of equal intensities, neutralize each other, integrally, as 16; consequently, red 5 is equivalent to green 11, yellow 3 to 13 purple, and blue 8 to 8 orange. The intermediate proportions all round the scale may be obtained by adding any number thereon to that preceding or following it, and the like compounded number diametrically opposite it will be its proportional for the colours on the same diameter. Some of these may be reduced to simpler terms: thus the equal proportionals 8, to both which the two ends of the needle, or index, point on the scale, are as unity, 1 = 1, (the simplest of all ratios, that of equality; and its colours are orange and blue), literally the points of extreme hot and cold, which are, so to call them, the poles of harmony in colouring. This result is accidental, but it is a coincidence which evinces the truth of our process, and singularly comports with the rule of harmony in painting which has been founded on sense or feeling, and requires that equality or balance of warm and cool colouring in a picture, upon which tone so essentially depends.*

* For the principle and mechanism by which we have effected this, see Chap. xxvi. Exp. 27. 4 to. edit.

These are the only two contrasting colours which, like black and white, are equal powers: all other contrasts are perfect only when one of the antagonist colours predominates, according to the proportions marked upon the scale. A line diagonally across the needle, or index, indicates the positions of the scale at which colours become most advancing and most retiring; and a like line perpendicularly across the scale points out all the middle colours. These three lines divide the entire scale into equal portions throughout.

* This balance and insensible union of hues and shades in painting, and of tones in music, the Greeks denominated by the same term, tonos. "Tandem se ars ipsa distinxit, et invenit lumen atque umbras, differentia colomm alterna vice sese excitante: postea decnde adjectus est splendor, alius hic quam lumen; quern, quia inter hoc et umbram esset, appellaverunt On The Relations And Harmony Of Colours 6 says Pliny, 1. xxxv. c. 5.

Again, by the Scale of Chromatic Equivalents may be determined the proportions in which any three colours neutralize and harmonize each other: thus, as 3, 5, and 8, are these proportions of the primaries, yellow, red, and blue, so 8, 11, and 13, are those of the secondaries, orange, green, and purple. For the more readily finding the proportions of any three harmonizing colours on the scale, it is graduated all round, and divided into three equal parts, which are each subdivided into 32 degrees, numbered accordingly on the outward edge of the scale, and trisecting it all round, so that each colour of the scheme with its two harmonics are indicated by the same number, and the numbers corresponding on the inward edge shew their proportions. In like manner may be found the proportions of six or nine harmonizing colours, etc. By causing this external circle of figures to move round the scale, it may be made to indicate the proportions of any number and variety of hues which harmonize; but this is unimportant for practice. This scheme is also a key to the whole science of nature in the painting of flowers, and it coincides therewith that the archetype of all floreal forms is triadic, consisting of the involution of triangles variously irradiated; the numbers of their rays or leaves being invariably 3, 4, or 5, or multiples thereof; - of which only by the bye.*

* See Exp. xxviii.