By taking a large number of colour equations, Knig, who works in Helmholtz's laboratory, has derived what he considers curves of the three fundamental sensations in a normal-eyed person, and also those of the colour-blind. It may be said that with the colour-blind only two of the fundamental sensations are seen, and therefore only two curves are found, and that these agree in the main with some two of the curves of the three belonging to the normal-eyed.

Fig. 36. Maxwell's Colour-box.

Maxwell was the first to make a definite piece of apparatus for the purpose of obtaining colour equations, and we reproduce from his paper in the _Philosophical Transactions_ of the Royal Society for 18--, a somewhat modified diagram of it.

This apparatus is often known as Maxwell's colour-box, and is in fact a spectroscope reversed. With a collimator and prisms we form a spectrum on the focusing-screen of the camera (Fig. 6), by light coming through the slit, and we can obtain light on the distant screen, a patch of any colour, by placing in the spectrum slits as given at Fig. 30. If we were to illuminate the slits so placed with white light, and look through the slit of the collimator, we should see the front surface of the first prism illuminated by the mixture of the colours which would, when the light illuminated the collimator slit, have formed one colour patch on the screen. In Maxwell's apparatus, the slits S1, S2, S3 are illuminated by the light reflected from a white card C, placed in the sunshine, the rays pa.s.sing through them fall on two prisms P1, P2, are reflected back again through these prisms by a concave mirror M3, are received on another mirror M, and fall at E on to the eye. At A is an aperture in the box, letting through white light on to a mirror M1, which reflects it through a lens L on to M2, which again reflects it on to M, and so to the eye at E. Thus at E an image of the prisms, and an image of the aperture are seen, and the white light of the latter can be compared with the mixture of the colours formed by the prism pa.s.sing through S1, S2, and S3.

Suppose we have one slit S1, the white light will be decomposed by the prisms, and will be seen at E as light of the same colour as would be seen at S1, if the light were sent from E to S1, and so with the other slits. Thus when two or three of the slits are uncovered, the light falling on the eye at E will be a mixture of two or three colours.

There are two drawbacks to the mode of illumination used, one being that the quality of sunlight varies, and therefore colour equations will not be accurately comparable one with the other; and the second is that the light reflected from the card is not absolutely the same in all directions, and it cannot be perpendicularly placed to each of the rays which strike the prisms, after pa.s.sing through the different slits. This latter is a small objection, and is not of much account, but the first drawback is a more serious one.

Fig. 37.--Maxwell's Curves of Colour Sensations.

With this apparatus, then, Maxwell formed his colour equations, but he fixed as the colours which may be called his standard colours, portions of the spectrum which are certainly not pure, and hence he got curves which are not as perfect as those of Knig.

It will be seen, for instance, that his red and violet curves do not overlap, but touch each other near E. Were this true, the green colour-blind person should see a dark s.p.a.ce in the spectrum, since the green sensation is missing in such eyes. As a matter of fact the luminosity of the spectrum is very considerable to such a person at this point.

It will also be seen that some of his curves are negative curves lying below the base. This shows that the three standard colours he took are somewhat wrong. The dotted curve gives the combination of his three sensations at every point, and should be the luminosity curve; but owing to his having taken empirically certain standards of luminosity for his three colours, it does not represent the truth, as may be seen on comparison with Fig. 11, page 79.

It must be recollected that since Maxwell's observations the subject has been largely experimented upon, and naturally improved appliances and greater knowledge have enabled more nearly correct views to be entertained regarding it.

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 pota.s.sium 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 pa.s.s; 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 pa.s.s 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 cla.s.ses 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_ = ?_a_, _q_ = _b_, _r_ = ?_c_,

Then we may write (ii.) as--

?_aR_ + _bG_ + ?_cV_ = _zZ_--(iii.).

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

?_aR_ + ?_bG_ + ?_cV_= ?_wW_--(iv.)

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

(-?)_bG_ + (?-?)_cV_ = _zZ_ - ?_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 quant.i.ty 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 (-?)_b_ + (?-?)_c_], and the luminosity of the small quant.i.ty of white added.

We then get _zZ_ = _xX_ + ( + ?) _W_.

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

This same holds good when in (ii.) ? is smaller than ? and ; but it does not do so should it happen that 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.) ? to be larger than ? and ? than , then we must add ?_bG_ + ?_cV_ and we have

?_aR_ + ( + ?)_bG_ + (? + ?)_cV_ = _nW_ = _Z_ + ?_bG_ + ?_cV_; but ( + ?), and (? + ?) each equal ? ? _n_ = ?_w_.

? _Z_ + ?_bG_ + ?_cV_= ?_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 ', which must equal (?_b_ + ?_c_).