CHAPTER XIV.

Complementary Colours--Complementary Pigment Colours--Measurement of Complementary Colours.

We are now in a position to enter into the question of complementary colours, which is one of supreme interest to artists. A complementary colour, in its strictest sense, may be described as the colour which, combined with the colour whose complement is required, makes up white. In this definition we have three characteristics to take into account, viz. hue and luminosity, and dilution with white light. As an example of what we mean we refer to an experiment which was made and described at page 125. It was said that if the violet slit was placed in a certain position in the blue of the spectrum, it was possible to move the green slit into a part of the yellow, so that the two colours when mixed together would form white. In that case the blue is complementary to the yellow, and the yellow to the blue, so long as the intensities are those which make up white light. Again, if it requires the light coming through the three slits to make up white light, be it the white of the electric light or that of gaslight, we can obtain the complementary colour of the light issuing through any one of them by covering that slit up. Thus suppose the slits to be in the normal position the complementary colour of the red is a green-blue, formed by the mixture of the violet and green rays, the complementary colour of the green is a purple, formed by the mixture of the red and the violet light, whilst the complementary colour of the violet is greenish yellow, formed by the mixture of the red and green rays. It will be evident that as the intensities of the three rays respectively will be different according as the white light matched is the electric light or gaslight, the complementary colours in the former will be different in hue and intensity to those in the latter.

Fig. 38.--Chromatic Circle.

Another couple of striking experiments which the writer devised to show these colours can be made with the colour patch apparatus, and on the same principle as that used for obtaining the intensity of the rays reflected from pigments, and transmitted through coloured transparent bodies. Instead of the small slit with a right-angled prism in front to deflect the beam from the top spectrum, where two spectra are produced (see Fig. 16, p. 95), a single spectrum is used, with a right-angled prism of such a size that it deflects half of it, which is again reflected on to the screen by a mirror, and through a lens to form a second patch of equal size as the undeflected beam. A rod can be so placed in the path of the beams that two coloured stripes are formed, together with a white stripe caused by their overlapping. The two coloured stripes are complementary one to the other. By moving the prism along the spectrum various coloured stripes can be formed, in some cases one being much less luminous than the other, and yet they are complementary. If instead of the large right-angled prism a smaller one be used, the complementary colour due to a small part of the spectrum can be shown in the same manner.

It is customary to show the complementary colours diagrammatically by what is known as the chromatic circle. Roughly it is drawn as in the above figure (Fig. 38). The three colours, red, green and blue, which are taken for primary colours, are placed at 120° apart in a circle, and lines drawn from them through the centre, at which white is supposed to be situated. Where these lines cut the circumference is placed the complementary colour. Other colours can be placed round the circle with their complementary colours opposite, and so a fairly complete diagram of the spectrum can be made. But it must be remembered that this is really of no scientific value, as it conveys no idea of the luminosity of the spectrum colours, nor of the quantities which have to be mixed together to form the complementaries. Such a circle is, however, convenient as a sort of _memoria technica_, and can be filled up according to the fancy of the observer.

The following are pairs of most carefully selected complementary colours of pigments, as adopted by Professor Church.

_Complementaries._ _Pigments._

{Red Madder red or crimson vermilion. { and {Green blue Viridian, the emerald oxide of chromium with a little cobalt.

{Orange Cadmium yellow, of full orange hue. { and {Greenish blue Cobalt green.

{Orange yellow Cadmium yellow, or deep chrome. { and {Turquoise C[oe]rulium, or cobalt blue, with a little emerald green.

{Yellow Lemon yellow, pale chrome, or aureolin. { and {Blue Ultramarine from lapis-lazuli.

{Greenish yellow Aureolin with a little viridian. { and {Violet blue French ultramarine.

{Green yellow Lemon yellow, with some emerald green. { and {Violet French ultramarine with madder carmine.

{Yellowish green Lemon yellow with much emerald green. { and {Purplish violet Madder carmine with French ultramarine.

{Green Emerald green with lemon yellow. { and {Purple Madder carmine with French ultramarine.

{Emerald green Emerald green alone. { and {Reddish purple Madder carmine with a little French ultramarine.

As these pairs of pigments are complementary, it follows that if rotated together in proper proportions, they should make a grey which will be indistinguishable from a grey formed by rotating black and white sectors together. (See chap. XV.)

It will probably happen that a good deal more of one of the pairs of the colours is required in the disc than of the other, and supposing that the two are each used of the full brightness which the pigments are capable of giving, it follows that in a diagram where equal areas are filled with the pigments as complementary, some means must be adopted to give the true depth of tone to each. The mixture of white will heighten the luminosity of either, or the admixture of black will lower it, but often alters the hue.

One of the most beautiful methods of observing complementary colours is by means of the polarization of light, which we need not describe in detail. What is known as Brücke's schistoscope is perhaps one of the most convenient. Dove's Iceland spar prism is also useful, when two pigments have to be worked on to paper, so as to be complementary. The two squares of pigmented paper are placed side by side, and two images of each are formed. One image of one colour can be caused to overlap the second of the other, and if the two when superposed appear of a grey they are complementary one to the other. If too much of one colour appears, it must be toned down till the grey is formed. This is a very simple piece of apparatus, and for experiments with pigments will be found to be very handy. When the right tint of each is secured in this manner, a further test may be made by making the pigmented surfaces into sectors, and rotating them together, when if the double-image prism gives correct results, the angular aperture of the sectors should be 180° each, to match a grey produced by a mixture by rotation of black and white.

We have already shown how the complementaries of the spectrum colours can be found; the question is can we find the complementaries of pigments by the spectrum? There is one very self-evident way. We can place the three slits in the spectrum as given in chapter IX., and match in intensity the white light of the reflected beam, and note the apertures of the slits. We must then in the reflected beam place the pigment whose complementary colour is required, and match its colour with the light from the three slits, keeping, for the sake of convenience, the white light falling on the pigmented surface of unaltered intensity, and again note the apertures. If we deduct the last measures from the first, the difference of aperture will give the complementary colour. Thus it was found that with slits in a certain position in the spectrum, to make white light the following apertures in hundredths of a millimetre were required:

{ Red 165 (1) { Green 60 { Violet 100

Emerald green was placed in the patch and was matched by the light from the three slits, when it was found that it required

{ Red 4 (2) { Green 35 { Violet 25

Deducting one from the other we get as the complementary colour,

{ Red 125 (3) { Green 25 { Violet 75

This is a complementary colour, but like the green itself it is mixed with white light; but we can easily deduce what is the simplest complementary colour; for we have only to deduct the possible white light from the second measure. Now evidently the greatest amount of white light is when the whole of the green is taken as forming part of it, with the proper proportions of red and violet, and these we can obtain by taking the proportions of the colours in (1); therefore deduct--

{ Red 69 (4) { Green 25 { Violet 41·5

and this would leave as the complementary colour without any admixture of white--

(5) { Red 56 { Violet 33·5

which is a purple as would be expected.

Now to give the same dilution of white to the complementary that the emerald green has, we must take away from the emerald green all the white mixed with it, and add that quantity to the complementary. The white in the emerald green can be found by treating the whole of the red as going to form the white; we then have from (1)--

{ Red 40 (6) { Green 14·4 { Violet 24

Deducting these from (2), we find that the colour of emerald green, less the white light, is 20·6 of green mixed with 1 of violet. To find the proper dilution of the complementary colour we must add the above proportions of the three colours, and as our final result we find the complementary colour, of equal impurity, is a mixture of--

{ Red 96 (7) { Green 14·4 { Violet 57·5

The slits may be set at these apertures and a colour patch thrown on the screen, and we shall find it of a delicate pink. The truth of this can be seen by using a double-image prism to view the pigmented surface, illuminated by the same white light as that in which it was measured, and the colour patch on the screen by its side. The two colours may be caused to overlap, when it will be seen that white is produced.

Another example was an orange pigment, and this we will work out in the form of colour equation. The same mixture gave white, viz.:

165 R + 60 G + 100 V = W 165 R + 42 G = O

Therefore the complementary colour, which is

W - O = 18 G + 100 V,

or a dark-blue colour. In this case there was apparently no white light reflected from the orange. It was slightly glossy, and as polarized light was used for the reflected beam, it was probably somewhat quenched; but what is more probable is that the green contains some violet as well as red, for the reasons given in chapter XI. The reason we have been particular in showing to what extent complementary colours must be diluted with white to the same proportion that the colour itself is diluted, will be apparent if considered for a moment. A deep brown is in reality orange, much degraded in tone, and can be produced as a colour patch on the screen if a bright orange pigment be placed in the reflected beam of the colour patch, and the light nearly shut off by the rotating sectors. Now the same complementary colour will be found for both, but if we were to use the bright complementary colour which we obtained with the orange for the brown, and endeavoured to obtain a white with it by means of the double-image prism we should fail, as the complementary colour would predominate. Complementary colours can always be formed by a mixture of only two rays, and although the overlapping images may form white, yet when the two are placed side by side, it often will be found that the complementary, unless diluted with white, is evidently too dark to be satisfactory, but the luminosity may be increased by adding white to it, as any amount of white may be added to the mixture of the two rays which form the complementary, and of course white will still be formed with the original colour. It is thus quite feasible to give the complementary the same luminosity as the latter by adding white light to it. Like the colour itself, the complementary colour can always be expressed either by a single ray of the spectrum, or by white light from which a single ray is deducted. (See chapter XIII.)