CHAPTER XII._Colour Measurement and Mixture

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.

+--------------+-----------+-------------+--------------+

+---+-----+----+---+---+---+----+----+---+ of each |

| R | G | V | R | G | V | R | G | V |multiplied by |

+---+-----+----+---+---+---+----+----+---+--------------+

|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 |

| | | | | | | | | +--------------+

+---+-----+----+---+---+---+----+----+------------------+

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.