CHAPTER XIII.

Match of Compound Colours with Simple Colours--All Colours reduced to Numbers--Method of matching a Colour with a Spectrum Colour and White Light.

If we place the solution of bichromate of potassium in front of the slit of the collimator, we shall see that on producing a spectrum on the screen, all rays from the red to the yellow-green pass; hence bichromate of potash transmits a colour which is a compound colour.

It has been shown that this orange colour and the spectral yellow can be matched by mixing the simple colours of red and green together; but it will be instructive to see if a simple colour in the spectrum itself can be found which can match such a compound colour as that of the bichromate.

If we place the bichromate in the reflected beam of the colour patch apparatus and illuminate one shadow cast by the rod with the light transmitted by it, and pass a slit along the spectrum, to produce monochromatic light, with which the other shadow of the rod is illuminated, a position will be found near the orange sodium line "D," where the two colours apparently match in every respect; when the intensities of the two illuminated shadows are equalized as before by the rotating sectors. In the same way by filling the part of the square with the pigment on which the shadow illuminated by the reflected beam falls, we can see if we can match emerald green, cyanine blue, and other coloured pigments.

It will often be--more often than not--necessary, however, to dilute the spectrum colour thrown on the white half of the patch with a trace of white light. By reference to our previous experiments we arrive at what may appear an unlooked-for result, that _no matter what the colour_ may be, we can refer it to one ray of the spectrum, together with a percentage of added white light. It is worthy of remark, that the place in the spectrum where the simple and the compound colours match, varies according to the kind of light with which the pigment is illuminated. This we can show in a very simple way.

To persons who are totally colour-blind to one sensation, viz. the green or the red, the matching of a compound colour with a simple one in the spectrum should possess no difficulties. Taking the trichromic theory of three sensations for the normal-eyed person, it is evident that only the following classes of sensations are possible in the normal-eyed, the green colour-blind and the red colour-blind--

Normal-eye. Green colour-blind. Red colour-blind.

Red Red --

Green -- Green.

Violet Violet Violet.

Mixtures of red -- -- and green

Mixtures of red Mixtures of red -- and violet and violet

Mixtures of green Mixtures of green and violet and violet.

Mixtures of red, -- green and violet

If we take as a type of colour-blindness the green colour-blind person, we see that every colour in the spectrum must be either pure red or violet, or else these colours mixed with more or less white light, since these two sensations when excited in certain proportions give the sensation of white. At one place, which is commonly called the neutral point, the proportions of the two colours are such that the impression there given is only white; hence it follows that, between this neutral point and each end of the spectrum, the rays are mixtures of violet and white, or red and white, the dilution of the colours varying from no white to all white. As every compound colour must be a mixture of the same two colours in certain proportions, it follows that the green colour-blind person can match every compound colour with some one ray of the spectrum, and that every colour must to him be either red or violet, diluted with different proportions of white light.

In the same way, a person who is colour-blind to the red can also match any colour with a single spectrum colour, and he will see it as green or violet diluted with more or less white light. This can be readily understood, but it is not quite so plain how any colour sensation felt by the normal eye can be referred to the spectrum.

If we take three rays in the spectrum--one in the red between C and the red Lithium line which we will call _R_, another in the green between F and _b_ which we will call _G_, and a third in the violet near G but on the _H_ side of it, and which we may call _V_--then by varying their intensities (which is equivalent to varying the luminosities) and mixing them, we can give the same impression to the eye that any compound colour gives; and that any intermediate simple spectrum colour gives, if very slightly diluted with white light. With these same three colours, but in different proportions, we can also give the impression of white light to the eye. The intermediate spectrum colours between the green and the violet rays selected when slightly diluted are imitated by mixing these rays together in different proportions, and similarly those lying between the red and the green by mixing together these rays in different proportions--and there is some ray present in the spectrum which, when very slightly diluted with white light, has the same colorific effect on the eye as the mixtures of the pairs _v_ and _b_, and _G_ and _R_, in any proportions whatever.

Let the luminosities of the rays _R, G_ and _V_, which give the impression of white light, be _a_, _b_ and _c_ units respectively, and _p_, _q_ and _r_ those which give that of the colour which has to be registered and reproduced. We then get the following equations--where _W_ is white, _w_ its luminosity, _Z_ the colour, and _z_ its luminosity--

_aR_ + _bG_ + _cV_ = _wW_--(i.); _pR_ + _qG_ + _rV_ = _zZ_--(ii.);

Then evidently--

(_a_ + _b_ + _c_) = _w_; and (_p_ + _q_ + _r_) = _z_.

Let _p_ = [Alpha]_a_, _q_ = [Beta]_b_, _r_ = [Gamma]_c_,

Then we may write (ii.) as--

[Alpha]_aR_ + [Beta]_bG_ + [Gamma]_cV_ = _zZ_--(iii.).

Now either [Alpha], [Beta], or [Gamma] must be smaller than the other two. As an example, if [Alpha] be the smallest, we multiply (i.) by [Alpha] when we get--

[Alpha]_aR_ + [Alpha]_bG_ + [Alpha]_cV_= [Alpha]_wW_--(iv.)

Subtracting (iv.) from (iii.) and we get--

([Beta]-[Alpha])_bG_ + ([Gamma]-[Alpha])_cV_ = _zZ_ - [Alpha]_wW_.

Now it has already been stated that between _V_ and _G_ there is some ray which gives the same sensation of colour, mixed with a very small quantity of white light, as the above mixture of _V_ and _G_--let us call it _X_ and its luminosity _x_ [_x_ being evidently equal to ([Beta]-[Alpha])_b_ + ([Gamma]-[Alpha])_c_], and [Mu] the luminosity of the small quantity of white added.

We then get _zZ_ = _xX_ + ([Mu] + [Alpha]) _W_.

Here we have the colour _Z_ in terms of a single ray, and of white light.

This same holds good when in (ii.) [Gamma] is smaller than [Alpha] and [Beta]; but it does not do so should it happen that [Beta] is the smallest, for there is no part of the spectrum which contains simple colours giving the same sensation to the eye as mixtures of red and blue. There is, however, a very simple way in which the registration of such a colour (which it must be remarked must be of a purple tone) can be effected. It can be fixed by its complementary. To do this we must add to (ii.) a certain amount of _R_ and _V_, which will make the whole white. Thus, suppose in (iii.) [Alpha] to be larger than [Gamma] and [Gamma] than [Beta], then we must add PhphPhi Pi mu [Phi]_bG_ + [Theta]_cV_ and we have

[Alpha]_aR_ + ([Beta] + [Phi])_bG_ + ([Gamma] + [Theta])_cV_ = _nW_ = _Z_ + [Phi]_bG_ + [Theta]_cV_; but ([Beta] + [Phi]), and ([Gamma] + [Theta]) each equal [Alpha] Therefore _n_ = [Alpha]_w_. Therefore _Z_ + [Phi]_bG_ + [Theta]_cV_= [Alpha]_wW_.

Now between _V_ and _G_ in the spectrum there is some single colour which gives the sensation of the mixture of _G_ and _V_. Let it be _X_´ with luminosity _x_´, together with white whose luminosity is [Mu]´, which must equal ([Phi]_b_ + [Theta]_c_).

Therefore _Z_ + _x´X_´ + [Mu]´_W_ = [Alpha]_wW_ _Z_ = ([Alpha]_w_ - [Mu]´)_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 glass in the electric light, we should proceed as follows--

The colour patch apparatus (described in chapter IV.) is employed, and the coloured glass 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 glass 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 glass.

In the path of the reflected beam, but between the prism and the silvered mirror, is inserted a piece of plain glass 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 glass, 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 glass 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 glass 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 glass (say) has to be registered, we proceed in a slightly different manner. The patch of coloured light passing through the purple glass 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 glass. 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 glasses 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 glass 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 glasses-- +-------------+----------+-------------------------+ | | | |Percentage | | | | |of Luminosity| | | Wave- | | of Light | | Glasses |lengths of|Percentage | Transmitted | | Measured. | Dominant | of White | through | | | Ray. | Light. | the Glass. | +-------------+----------+-----------+-------------+ | Ruby | 6220 | 2 | 13·1 | | Canary | 5850 | 26 | 82·0 | | Bottle Green| 5510 | 31 | 10·6 | | No. 1 Signal| | | | | Green | 4925 | 32 | 6·9 | | No. 2 Signal| | | | | Green | 5100 | 61 | 19·4 | | Cobalt | 4675 | 42 | 3·75 | +-------------+----------+-----------+-------------+

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 | 2·5 | 14·8 | |Emerald Green | 5220 | 59·0 | 22·7 | |French Ultra- | | | | | marine Blue | 4720 | 61·0 | 4·4 | |Brown Paper | 5940 | 50·0 | 25·0 | | " " | 5870 | 67·0 | 19·5 | |Orange | 5915 | 4·0 | 62·5 | |Chrome Yellow | 5835 | 26·0 | 77·7 | |Blue Green | 5005 | 42·5 | 14·8 | |Eosin Dye | 6400 | 72·0 | 44·7 | |(Sporting | | | | | Times) | | | | |Cobalt | 4820 | 55·5 | 14·5 | +--------------+------------+----------+---------------+