CHAPTER VIII._Colour Measurement and Mixture

Methods of Measuring the Intensity of the Different Colours of the

Spectrum, reflected from Pigmented Surfaces--Templates for the Spectrum.

Fig. 14.--Measurement of the Intensity of Rays reflected from white and

coloured surfaces.

We will now proceed to demonstrate how we can measure the amount of

spectral light reflected by different pigments. Let us take a strip of

card painted with a paste of vermilion, leaving half the breadth white;

and similarly one with emerald green. If we place the first in the

spectrum so that half its breadth falls on the red, and the other half

on the white card, we shall see that apparently the red and orange rays

are undiminished in intensity by reflection from the vermilion, but that

in the green and beyond but very little of the spectrum is reflected.

With the emerald green placed similarly in the spectrum, the red rays

will be found to be absorbed, but in the green rays the full intensity

of colour is found, fading off in the blue. What we now have to do is

to find a method of comparing the intensities of the different rays

reflected from the pigments, with those from the white surface. We will

commence with the second of the two methods which the writer devised

with this object, and then describe the first, which is more complex.

Suppose we have, say a card disc three inches in diameter, painted with

the pigment whose reflective power has to be measured, and place it on a

rotating apparatus with black and white sectors of say five inches

diameter, and capable of overlapping so as to show different proportions

of black to white (see Fig. 42). If we throw a colour patch (shown in

Fig. 14 as the area inside the dotted square) on the combination of

black and white, and at the same time on the pigmented disc, it is

probable that either one or other will be the brighter. By moving the

slit along the spectrum it is evident, however, that a colour can be

found which is equally reflected from them both whilst rotating. Take as

an example the sectors as set at two parts white, to one part black, the

centre disc being vermilion, the slit is moved along the spectrum until

such a point is reached that the colour reflected from the ring and the

disc appears of the same brightness, for it must be recollected that

they cannot differ in hue, as the light is monochromatic. It will be

found that the place where they match in brightness is in the red, the

exact position being fixed by the scale at the back of the slide. Taking

the proportion of black to white as three to one, the match will be

found to take place in the orange. Increasing the proportion of black

more and more, a point will be reached where the reflection takes place

uniformly along the blue end of the spectrum, this will be from the

green to the end of the violet. By sufficiently increasing the number of

matches made, a curve of reflection can be made showing the exact

proportion of each ray of the spectrum that is reflected. The uniform

reflection along the blue end of the spectrum shows that a certain

amount of white light is reflected from the pigment.

Next taking the emerald green disc, if we adopt the same procedure it

will be found that for some shades of the ring there are two places in

the spectrum from which the colours reflected give the same brightness.

By plotting curves in exactly the same way as that shown for the curve

of luminosity at page 78, substituting for the open aperture of the

sector the angular value of the white used, we can show graphically the

correct reflection for each part of the spectrum. Sometimes three places

in the spectrum will be read, as giving equal reflections from the

coloured disc and the grey ring.

The accompanying figures show the results obtained for reflection from

vermilion, emerald green, and French blue, after having made a

correction for the white by adding the amount which the black reflects.

The scale is that of the prismatic spectrum employed. On page 46 we

stated that a white surface could be made to appear darker than a black

surface, by illuminating the latter and cutting off the light from the

former. By placing the black surface in place of one of the coloured

ones, as shown in page 82, the luminosity of the black surface can be

ascertained. In this case it was found that almost exactly 5% of the

white light from the crater of the positive pole was reflected. In the

table the original measures are shown, and also the corrected measures,

and for convenience sake the intensity of every ray throughout the

length of the spectrum reflected from white, has been taken as 100. The

position of the reference lines on the scale (Fig. 15) are as follows--

Fig. 15.--Intensity of Rays reflected from Vermilion, Emerald Green, and

French Ultramarine.

B=101, C=96·25, D=89, E=79·9, F=71·5, G=53·5.

VERMILION.

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

| White Sectors. | |

+-----------------------------------|Reading of |

|--------------+ Black. | 100. | |

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

| 10 | 350 | 27·5 | 7·65 | 71-1/2 |

| 20 | 340 | 37·0 | 10·15 | 84 |

| 30 | 330 | 46·5 | 12·95 | 86·2 |

| 50 | 310 | 65·5 | 18·10 | 88·0 |

| 70 | 290 | 84·5 | 23·50 | 88·7 |

| 90 | 270 | 103·5 | 29·7 | 89·5 |

| 120 | 240 | 132·0 | 37·2 | 90·3 |

| 150 | 210 | 160·5 | 45·0 | 91 |

| 180 | 180 | 189·0 | 52·5 | 91·6 |

| 210 | 150 | 217·5 | 60·2 | 92·5 |

| 220 | 140 | 227·0 | 63·2 | 93·5 |

| 230 | 130 | 236·5 | 66·2 | 94·5 |

| 240 | 120 | 246·0 | 68·5 | 96 |

| 230 | 130 | 236·5 | 66·2 | 97·7 |

| 210 | 150 | 217·5 | 60·2 |100·0 |

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

EMERALD GREEN.

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

| White Sectors | |

+------------------+--------------------+ Reading of |

+--------+---------|rected For| White | Scale. |

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

| 10 | 350 | 27·5 | 7·65 | 50 |

| 20 | 340 | 37·0 | 10·15 | 54 |

| 30 | 330 | 46·5 | 12·95 | 55 |

| 50 | 310 | 65·5 | 18·10 | 57·5 |

| 70 | 290 | 84·5 | 23·5 | 60·0 |

| 90 | 270 | 103·5 | 29·7 | 63·5 |

| 110 | 250 | 122·5 | 34·7 | 65·5 |

| 130 | 230 | 141·5 | 39·5 | 67·5 |

| 150 | 210 | 160·5 | 45·0 | 68·5 |

| 170 | 190 | 179·5 | 50·0 | 71 |

| 190 | 170 | 195·5 | 54·7 | 73·5 |

| 210 | 150 | 217·5 | 60·2 | 75·0 |

| 220 | 140 | 227 | 63·2 | 76 |

| 220 | 140 | 227 | 63·2 | 78 |

| 210 | 150 | 217·5 | 60·2 | 80 |

| 190 | 170 | 198·5 | 54·7 | 82 |

| 170 | 190 | 179·5 | 50·0 | 83 |

| 150 | 210 | 160·5 | 45·0 | 84 |

| 130 | 230 | 141·5 | 39·5 | 85 |

| 110 | 250 | 122·5 | 34·7 | 86·5 |

| 90 | 270 | 103·5 | 29·7 | 87·5 |

| 70 | 290 | 84·5 | 23·5 | 88·5 |

| 50 | 310 | 65·5 | 18·10 | 90·0 |

| 30 | 330 | 46·5 | 12·95 | 92 |

| 20 | 340 | 37·0 | 10·15 | 94 |

| 10 | 350 | 27·5 | 7·65 | 98 |

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

FRENCH ULTRAMARINE BLUE.

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

| White Sectors. | |

+-----------------+-----------+-----------+ Reading of |

+--------+--------+ corrected | White | Scale. |

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

| 0 | 360 | 18·0 | 5·0 | 84 |

| 10 | 350 | 27·5 | 7·65 | 80 |

| 20 | 340 | 37·0 | 10·15 | 77 |

| 30 | 330 | 46·5 | 12·95 | 75 |

| 40 | 320 | 56·0 | 15·6 | 74 |

| 60 | 300 | 75·0 | 20·7 | 72·5 |

| 80 | 280 | 94·0 | 25·5 | 70·5 |

| 100 | 260 | 113·0 | 32·5 | 68 |

| 120 | 240 | 132·0 | 37·2 | 66·5 |

| 140 | 220 | 151·0 | 42·3 | 62·5 |

| 160 | 200 | 170·0 | 47·4 | 59·5 |

| 170 | 190 | 179·5 | 50·0 | 55 |

| 160 | 200 | 170·0 | 47·4 | 51 |

| 140 | 220 | 151·0 | 42·3 | 46 |

| 0 | 360 | 18·0 | 5·0 | 95 |

| 10 | 350 | 27·5 | 7·65 | 98 |

| 20 | 340 | 37·0 | 10·15 | 99 |

| 30 | 330 | 46·5 | 12·95 | 110 |

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

These three measurements have been given in full, since they will be

useful for reference when other experiments are described.

Fig. 16.--Method of obtaining two Patches of identical Colour.

When we have to measure the colour transmitted through coloured bodies,

we have to adopt a slightly different plan, which is extremely accurate.

The first thing necessary is to make some arrangement whereby two beams

of identical colour--that is, of the same wave-length--reach the screen,

one of which passes through the transparent body to be measured, and the

other unabsorbed. If we in addition have some means of equalizing the

intensity of the two beams, we can then tell the amount cut off by the

body through which one beam passes. The method that would be first

thought of would be to use two spectra, from two sources of light; but

should we adopt that plan there would be no guarantee that the spectra

would not vary in intensity from time to time. The point then that had

to be aimed at was to form two spectra from the same source of light,

and with the same beam that passes through the slit of the collimator.

Here we are helped by the property of Iceland spar, which is able to

split up a ray into two divergent rays. By placing what is called a

double-image prism of Iceland spar at the end of the collimator, we get

two divergent beams of light falling on the prisms, and by turning the

double-image prism we are able to obtain two spectra on the screen of

the camera one above the other, and if the slit of the slide be

sufficiently long two beams would issue through it of identical colour,

and separated from one another by a dark space, the breadth of which

depends on the length of the slit of the collimator. It is to be

observed that by this arrangement we have exactly what we require: a

light from one source passes through the same slit, is decomposed by the

same prisms, and as the beams diverge in a plane passing through the

slit of the collimator, the length of spectrum is the same. The problem

to solve is how to utilize these two spectra now we have got them. We

can make the light from the top spectrum pass through the coloured body

by the following artifice. Let us place a right-angled prism in front of

the top slit, reflecting say the beam to the right, and after it has

travelled a certain distance, catch it by another right-angled prism,

and thus reflect it on to the screen. Already in the path of the ray,

issuing through the slit from the bottom spectrum, the lens L4 is

placed, forming a square patch on the screen. By placing a similar lens

in the path of the other ray after reflection from the second

right-angled prism, we can superpose a second patch of the same colour

over the first patch, and by putting a rod in the path of the two beams

we can have as before two shadows side by side, but this time each

illuminated by the same colour. One shadow will be more strongly

illuminated than the other, owing to the different intensities of beams

into which the double-image prism splits up the primary ray. The two,

however, can be equalized by placing a rotating apparatus in the path of

one of the beams. When equalized the sector is read off, and tells us

how much brighter one spectrum is than the other. Thus suppose in the

direct beam the sectors had to be closed to an angle of 80°, to effect

this, the bottom spectrum would be 180/80, or 2·25 times brighter than

the bottom spectrum. It should be noted that as the two spectra are

formed by the identical quality of light, this same ratio will hold good

throughout their length. If it does not, it shows that the double-image

prism is not in adjustment, and that the same rays are not coming

through the slit in the slide, and it must be rotated till the readings

throughout are the same. One of the most sensitive tests for adjustment

is to form a patch with orange light, when the slightest deviation from

adjustment will be seen by the two patches differing in hue.

We can now place the coloured transparent object in the path of the beam

which is most convenient, and by again equalizing the shadows, measure

the amount it cuts off; this we can do for any ray we choose. As both

right-angled prisms can be attached to the card or slide which moves

across the spectrum, nothing besides the card need be moved. In the

following diagram we have the proportion of rays transmitted by the

three different glasses, red, green, and blue, in terms of the

unabsorbed spectrum. Take for instance on the scale of the spectrum the

number 11. The curve shows that at that particular part of the spectrum

which lies in the blue, the blue glass only allowed 4/100 or 1/25 of the

ray to pass, whilst the green glass allowed 10/100 or 1/10 to pass. So

at scale No. 4 in the orange, through the blue only 2% was transmitted,

through the green glass 4%, and through the red 20%.

Fig. 17.--Absorption by Red, Blue, and Green Glasses.

Fig. 18.--Light reflected from Metallic Surfaces.

Fig. 19.--1. Vermilion 2. Carmine. 3. Mercuric Iodide. 4. Indian Red.

From such curves as these we can readily derive the luminosity curves of

the spectrum, after the white light has passed through the coloured

object. All we have to do is to alter the ordinates of the luminosity

curve of white light in the proportion to the intensities of the rays

before and after passing through the object. It will be seen that when

the luminosity curve of the spectrum of _any_ source is known, this

method holds good.

Fig. 20.--1. Gamboge. 2. Indian Yellow. 3. Cadmium Yellow. 4. Yellow

Ochre.

The intensity of the different rays of the spectrum reflected from

metallic surfaces can also be measured, if for the first or second

right-angled prism a small piece of the metal is substituted, using it

as a reflecting surface, as can also the rays reflected from any surface

which is bright and polished. In Fig. 18 the dotted curves show the

_luminosity_ of the spectrum reflected from the different metals, curve

V being that of white light. These curves are derived by reducing the

ordinates of curve V proportionately to the intensity curves. Thus at 49

brass reflects 77% of the light, and the luminosity of the white is 80.

The luminosity of the light from the brass is therefore 77/100 of 80,

or 61. This shows the method which is adopted, of deducing luminosities

from intensities.

Fig. 21.--1. Emerald Green. 2. Chromous Oxide. 3. Terre Verte.

The light reflected from pigments can also be measured by the same plan.

The procedure adopted is that carried out when measuring their

luminosities, viz. to cause the ray from one spectrum to fall on a strip

of a white surface, and that from the other on a strip of the coloured

surface (see page 82). This is a more convenient method than that just

described, when the coloured surface is small. The annexed figures

(Figs. 19, 20, 21, 22) show the results obtained from various pigments.

Fig. 22.--1. Indigo. 2. Antwerp Blue. 3. Cobalt. 4. French Ultramarine.

Fig. 23.--Method of obtaining a Colour Template.

From curves such as these we are able to produce the colour of the

pigment on the screen from the spectrum itself. This is a useful proof

of the truth of the measurements made. To do this we must mark off on a

card (Fig. 23) the absolute scale of the spectrum along the radius of a

circle, and draw circles at the various points of the scale from its

centre. From the same centre we must draw lines at angles to the fixed

radius corresponding to the various apertures of the sectors required at

the various points of the scale to measure the light reflected from a

pigment. Where each radial line cuts the circle drawn through the

particular point of the scale to which its angle has reference, gives us

points which joined give a curved figure. Such a figure, when cut out

and rotated in front of the spectrum in the proper position (as for

instance by making the D sodium line correspond with that on the scale),

will cut off exactly the same proportion of each colour that the pigment

absorbs. The spectrum, when recombined, should give a patch of the exact

colour of that measured. The spectrum must be made narrow, as the

template is only theoretically correct for a spectrum of the width of a

line, as can be readily seen.

Templates like these will always enable any colour to be reproduced on

the screen, and if the light be used for the spectrum in which the

colour has to be viewed, be it sunlight, gaslight, starlight--whatever

light it is--the colour obtained will be that which the pigment would

reflect if it were viewed in that light.

The identity of the colour produced on the screen by this plan with that

measured, can be readily seen by placing the latter in the reflected

beam of white light alongside the coloured patch formed on the white

surface.

Fig. 24.--Template of Carmine.

In Fig. 24 we have a mask or template of carmine, which was used for

determining if the measurements were right. The black fingerlike-looking

space on the right was the amount of red reflected light, and the other

that of the blue and violet; scarcely any light at all was reflected

from the green part of the spectrum.

Fig. 26.--Absorption of transmitted and reflected Light by Prussian Blue

and Carmine.

On page 108 we have given the diagram of the luminosity of the spectrum

in reference to a standard white light. It will bring this luminosity

more home if, in a similar manner to that described above, we make a

template of this curve (Fig. 25). We can place a narrow slit

horizontally in front of the condensing lens of the optical lantern, and

throw an image of it on to the screen. If in close contact with this

slit we rotate the template, we shall have on the screen a graduated

strip of white light, giving in black and white the apparent luminosity

of the spectrum as seen by the eye.

Fig. 25.--Template of Luminosity of White Light.

It has been stated in chapter V., that it is generally immaterial

whether a pigment is in contact with the paper or away from it, so long

as the light passes through the pigment. The above figure (Fig. 26)

shows the truth of this assertion. I. and II. are the curves taken of

the light transmitted by Prussian blue and carmine respectively, and

III. and IV., from the light reflected from these colours on paper.

Fig. 27.--Collimator for comparing the intensity of two sources of

Light.

To measure the difference in the intensities of the rays of different

sources of light we can use a spectroscopic arrangement with two slits

(S) (Fig. 27) placed in a line at right angles to the axis of the

collimator. One slit is a little below the other, the rays being

reflected to the collimating lens L, by means of two right-angled prisms

P, and two spectra are formed, one above the other. By placing the

rotating sectors in front of one of the sources, the intensities of the

different parts of the spectrum can be equalized and measured.

Fig. 28.--Spectrum Intensities of Sunlight, Gaslight, and Blue Sky.

The curves for the annexed figure (Fig. 28) were derived from measures

taken in this manner. If the rays of a May-day sun are taken at 100, it

will be seen what a rapid diminution there is in the green and the blue

rays in gaslight. Gaslight only possesses about 20% of the green rays,

whilst of the violet hardly 5%. On the other hand the light which comes

to us from the sky shows a very marked falling off in the yellow and red

rays. A very easy experiment will convince us of the difference in

colour between skylight and gaslight. If we let a beam of daylight fall

on a sheet of paper at the end of a blackened box, and cast a shadow

with a rod by such a beam, and then bring a lighted candle or gas-flame

so that it casts another shadow of the rod alongside, one shadow will be

illuminated by the artificial light, and the other by the daylight. The

difference in colour will be most marked: the blue of the latter light

and the yellow of the former being intensified by the contrast (see page

198).

Fig. 29.--Comparison of Sun and Sky Lights.

By a little trouble the blue light from the sky may be compared with

sunlight. A beam of light B (Fig. 29) is reflected by a silvered glass

mirror from the blue sky into the box HH, at the end of which is a

screen E. Another mirror A, which is preferably of plain glass, reflects

light from the sun on to a second unsilvered mirror G (shown in the

figure as a prism), which again reflects it on to the screen, and each

of these lights casts a shadow from the rod D; K are rotating sectors to

diminish the sunlight, and we can make two equally bright shadows

alongside one another. The bluer colour of the sky will be very

evident.