? _Z_ + _x"X_" + "_W_ = ?_wW_ _Z_ = (?_w_ - ")_W_ - _x"X"_
which again is the colour expressed in terms of white light less the complementary colour. We have thus arrived at the very simple deduction that the hue and luminosity of any colour, however compounded, may be registered by a reference to white light and a single ray of the spectrum.
In practice this dominant ray is very easy to find. Suppose we wish to determine numerically the colour of a signal-green gla.s.s in the electric light, we should proceed as follows--
The colour patch apparatus (described in chapter IV.) is employed, and the coloured gla.s.s is placed between the silvered mirror which reflects the beam already reflected from the first surface of the first prism of the spectrum apparatus, and the screen, and a square image of that surface of the prism showing the tint of the gla.s.s is formed on the screen by means of the lens. Touching this image is a square patch of white light formed by the re-combination of the spectrum by means of another lens. An opaque slide containing an adjustable slit is moved across the spectrum in the manner described in the chapter referred to until the colour of this last patch is approximately the same hue as that of the gla.s.s.
In the path of the reflected beam, but between the prism and the silvered mirror, is inserted a piece of plain gla.s.s which can be made to reflect part of the beam into the spectrum patch of light, a square patch of the white light being formed by means of a third lens. We thus have monochromatic light mixed with white light. The requisite intensity of the added white light can be adjusted by means of the rotating sectors, as described in the same chapter, which open and close at will during rotation, and the total luminosity of the mixed beams can be altered by this, together with the adjustable slit in the slide. The slit may probably have to be moved in the spectrum to make the hue of these mixed lights the same as that of the gla.s.s, but by trial the position of the ray whose colour when diluted with white makes the match is readily found. The position of the slit in the spectrum is noted, as also the aperture of the sectors. The relative luminosities of the beam reflected from the plain gla.s.s mirror and of the coloured ray is next measured by placing a rod in the path of the two beams, and equalizing by the sectors the luminosity of the shadows which are illuminated, the one by the spectral ray, and the other by the white light. When the sector aperture is noted the registration is complete, as far as hue is concerned, but the luminosity of the ray transmitted through the gla.s.s should be compared with that of the reflected beam, and then the luminosity is also recorded.
Should the colour of a pigment be in question, the ray reflected from the silvered mirror is made to fall on the pigmented surface and the same procedure adopted.
If a purple gla.s.s (say) has to be registered, we proceed in a slightly different manner. The patch of coloured light pa.s.sing through the purple gla.s.s is superposed over the spectrum patch, and the slit in the slide is moved till a ray is found which will make white light when superposed on the colour of the gla.s.s. The luminosities of this white light, of the reflected beam, and of the spectral colour are compared "inter se," and there are then sufficient data with which to make numerical registration.
Coloured gla.s.ses to be used at night with oil or gas, or pigments to be viewed by these lights, must be registered in these lights. As the spectrum colours are always the same, it is convenient to use the electric light spectrum, and the only alteration in the apparatus is to use two gas-lights to illuminate two square apertures, in front of one of which the gla.s.s whose colour has to be measured is placed. The images of these apertures are thrown on the screen, the coloured image touching the square image of the spectral colour patch, and the naked image over the latter. The same determinations are gone through as those just described.
The following are the determinations of some gla.s.ses-- +-------------+----------+-------------------------+ | | | |Percentage | | | | |of Luminosity| | | Wave- | | of Light | | Gla.s.ses |lengths of|Percentage | Transmitted | | Measured. | Dominant | of White | through | | | Ray. | Light. | the Gla.s.s. | +-------------+----------+-----------+-------------+ | Ruby | 6220 | 2 | 131 | | Canary | 5850 | 26 | 820 | | Bottle Green| 5510 | 31 | 106 | | No. 1 Signal| | | | | Green | 4925 | 32 | 69 | | No. 2 Signal| | | | | Green | 5100 | 61 | 194 | | Cobalt | 4675 | 42 | 375 | +-------------+----------+-----------+-------------+
The following are determinations of some coloured pigments--
+--------------+------------+----------+---------------+ | | | | Percentage | | | |Percentage|of Luminosity, | | |Wave-lengths| of | White | | Coloured |of Dominant | White | Paper | | Papers. | Ray. | Light. | being 100. | +--------------+------------+----------+---------------+ |Vermilion | 6100 | 25 | 148 | |Emerald Green | 5220 | 590 | 227 | |French Ultra- | | | | | marine Blue | 4720 | 610 | 44 | |Brown Paper | 5940 | 500 | 250 | | " " | 5870 | 670 | 195 | |Orange | 5915 | 40 | 625 | |Chrome Yellow | 5835 | 260 | 777 | |Blue Green | 5005 | 425 | 148 | |Eosin Dye | 6400 | 720 | 447 | |(Sporting | | | | | Times) | | | | |Cobalt | 4820 | 555 | 145 | +--------------+------------+----------+---------------+
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 circ.u.mference 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 quant.i.ties 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 Crulium, 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 Brucke"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 415
and this would leave as the complementary colour without any admixture of white--
(5) { Red 56 { Violet 335
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 quant.i.ty 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)--