CHAPTER XIII._Colour Measurement and Mixture

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--

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

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

| Ruby | 6220 | 2 | 13·1 |

| Canary | 5850 | 26 | 82·0 |

| Bottle Green| 5510 | 31 | 10·6 |

| Green | 4925 | 32 | 6·9 |

| Green | 5100 | 61 | 19·4 |

| Cobalt | 4675 | 42 | 3·75 |

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

The following are determinations of some coloured pigments--

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

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

|Vermilion | 6100 | 2·5 | 14·8 |

|Emerald Green | 5220 | 59·0 | 22·7 |

| 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 |

|Cobalt | 4820 | 55·5 | 14·5 |

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