CHAPTER XII.

Formation of Colour Equations--K[oe]nig's Curves--Maxwell's Apparatus and Curves.

The plan of obtaining colour equations will by this time have become fairly evident. And we may as well illustrate it by equations obtained with the apparatus we have been using in our previous experiments. Let us suppose we have an individual who is desirous of having his eye-sight for colour tested, and that we have the slide with the three slits _in situ_. It will be found that when we alter their width and form white light with them, matching in purity the white light of the reflected beam, that we shall have to reduce the intensity of the latter very considerably, by means of the rotating sectors. The aperture may sometimes be as small as 4°, and at other times perhaps somewhere between 4° and 5°. Now the variation in aperture between 4°, and say 4·7, is very considerable, but it is highly probable that the latter might be estimated as 4·6, since only degrees are marked on the sectors. It therefore becomes essential to use a less brilliant reflected beam for the comparison, and this is secured by using as a mirror a plain unsilvered glass. What before read 4 will perhaps read 60, and 4·7 will be 70-1/2, whilst 4·6 would be 69, a difference easily read. We can now commence operations. Let us then place the red slit at say (35) of the scale, the green at (28), and the violet at (17), and make white light of the same intensity by altering the apertures of the slits. Let us do the same with the slits at (34), (28), and (17), instead of at (35), (28), and (17); and again make white light, and similarly with the slits at (35), (28), and (18); and let the following be the results--

(1) 20(35) + 60(28) + 40(17) = 100 W (2) 10(34) + 55(28) + 40(17) = 100 W (3) 20(35) + 59(28) + 10(18) = 100 W

Subtracting (1) from (2) we get--

10(34) = 20(35) + 5(28) or (34) = 2(35) + 1/4(28)

which means that the colour sensation at (34) is made up of two parts of the sensation of (35), together with 1/4 part of the sensation of (28).

In the same way we find that the colour sensation of (18) is made up of the sensations of (17) and (28).

(18) = 4(17) + 1/10(28).

In this way all the different colour sensations can be referred to the sensations which we may happen to consider as best representing the fundamental sensations. What these are is a matter still unsettled; though from the equations formed by colour-blind people, who only require really two colours to form equations, their places are approximately known; evidently as before said, the ray in the spectrum which the green colour-blind person sees as white light, is that where to the normal eye the green fundamental sensation is purest, being free from predominance of either of the other two sensations, and might be taken as a standard colour. Now if our luminosity curve is correct, and if the sum of the luminosities of each colour separately is equal to the luminosity of the colours when mixed (which we have shown to be the case in chapter VII.), it follows that the correctness of the measures can be checked by using the widths of the slits as multipliers of the luminosities. These luminosities can then be added together, and they should equal in luminosity the white light with which the comparison was made. The results can be compared together by reducing the equations to the same standard of white light.

The following is a set of observations which bear this out.

The red and violet slits in this case were kept at 35 and 17·8 on the scale, and the position of the green slit altered.

+--------------+-----------+-------------+--------------+ | Position of |Aperture of| Luminosity | Sum of the | | Slits. | Slits. | of Colour. | Luminosity | +---+-----+----+---+---+---+----+----+---+ of each | | | | | | | | | | | Colour | | R | G | V | R | G | V | R | G | V |multiplied by | | | | | | | | | | |the Aperture. | +---+-----+----+---+---+---+----+----+---+--------------+ |35 |28·5 |17·8|115| 38|112|18·1|73 |·65| 4930 | |35 |28·0 |17·8|119| 45|100|18·1|61·5|·65| 4989 | |35 |27·75|17·8|122| 52| 85|18·1|52 |·65| 4960 | |35 |27·35|17·8|125| 65| 74|18·1|40 |·65| 4907 | |35 |27·0 |17·8|128| 78| 67|18·1|33·2|·65| 4954 | |35 |26·3 |17·8|133|125| 40|18·1|20·3|·65| 4987 | |35 |26·0 |17·8|134|150| 10|18·1|16·7|·65| 4952 | |35 |25·85|17·8|135|170| 0|18·1|15·0|·65| 4993 | | | | | | | | | | +--------------+ | | | | | | | | | Mean 4959 | +---+-----+----+---+---+---+----+----+------------------+

The red slit was at a point in the spectrum between C and the red lithium line, and excited probably the fundamental sensation of red alone. The violet slit was close to G, and probably in this case the fundamental sensation of violet was almost excited alone. With the green slit the reverse was the case, all three fundamental sensations being excited. At 26·3 the green sensation was probably the fundamental sensation mixed with white light alone, as at that point the green blind person saw white light in the spectrum, on the red side of it there being what he describes as a warm colour, and on the violet side a cold colour.

An inspection of the table will show how very closely the sum of the luminosities agree amongst themselves, the white light formed by them in each case being of equal intensities. It must be recollected that white light is not necessary to form colour equations; colours may be mixed to form any other colour, which may be taken as a standard. This is often useful in the case of the light between the violet and the blue, where the luminosities are small compared with the luminosity in the green, yellow, and red.

Fig. 35.--K[oe]nig's Curves of Colour Sensations.

By taking a large number of colour equations, K[oe]nig, 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 passing 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 passing 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 passing 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 K[oe]nig.

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 space 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.