Luminosity of the Spectrum to Normal-eyed and Colour-blind
Persons--Method of determining the Luminosity of Pigments--Addition
of one Luminosity to another.
The determination of the luminosity of a coloured object, as compared
with a colourless surface illuminated by the same light, is the
determination of the second colour constant. We will first take the pure
spectrum colours, and show how their luminosity or relative brightness
can be determined. Viewing a spectrum on the screen, there is not much
doubt that in the yellow there is the greatest brightness, and that the
brightness diminishes both towards the violet and red. Towards the
latter the luminosity gradient is evidently more rapid than towards the
former. This being the case, it is evident that, except at the brightest
part there are always two rays, one on each side of the yellow, which
must be equally luminous. If the spectrum be recombined to form a white
patch upon the screen, and the slide with the slit be passed through
it, patches of equal area of the different colours will successively
appear; but the yellow patch will be the brightest patch. If the patch
formed by the reflected beam be superposed over the colour patch, and
the rod be interposed, we get a coloured stripe alongside a white
stripe, and by placing our rotating sectors in the path of the reflected
beam, the brightness of the latter can be diminished at pleasure.
Suppose the sectors be set at 45°, which will diminish the reflected
beam to one-quarter of its normal intensity, we shall find some place in
the spectrum, between the yellow and the red, where the white stripe is
evidently less bright than the coloured stripe, and by a slight shift
towards the yellow, another place will be found where it is more bright.
Between these two points there must be some place where the brightness
to the eye is the same. This can be very readily found by moving the
slit rapidly backwards and forwards between these two places of "too
dark" and "too light," and by making the path the slit has to travel
less and less, a spot is finally arrived at which gives equal
luminosities. The position that the slit occupies is noted on the scale
behind the slide, as is also the opening of the sectors, in this case
45°. As there is another position in the spectrum between the yellow and
the violet, which is of the same intensity, this must be found in the
same manner, and be similarly noted. In the same way the luminosities of
colours in the spectrum, equivalent to the white light passing through
other apertures of sectors, can be found, and the results may then be
plotted in the form of a curve. This is done by making the scale of the
spectrum the base of the curve, and setting up at each position the
measure of the angular aperture of the sector which was used to give the
equal luminosity or brightness to the white. By joining the ends of
these ordinates by lines a curve is formed, which represents graphically
the luminosity of the spectrum to the observer. In Fig. 11 the maximum
luminosity was taken as 100, and the other ordinates reduced to that
scale. The outside curve of the figure was plotted from observations
made by the writer, who has colour vision which may be considered to be
normal, as it coincides with observations made by the majority of
persons. The inner curve requires a little explanation, though it will
be better understood when the theory of colour vision has been touched
upon.
Fig. 11.--Luminosity Curve of the Spectrum of the Positive Pole of the
Electric Light.
The observer in this case was colour-blind to the red, that is, he had
no perception of red objects as red, but only distinguished them by the
other colours which were mixed with the red. This being premised, we
should naturally expect that his perception of the spectrum would be
shortened, and this the observations fully prove. If it happened that
his perceptions of all other colours were equally acute with a
normal-eyed person, then his illumination value of the part of the
spectrum occupied by the violet and green ought to be the same as that
of the latter. The diagram shows that it is so, and the amount of red
present in each colour to the normal-eyed observer is shown by the
deficiency curve, which was obtained by subtracting the ordinates of
colour-blind curve from those of the normal curve. There are other
persons who are defective in the perception of green, and they again
give a different luminosity curve for the spectrum. These variations in
the perception of the luminosity of the different colours are very
interesting from a physiological point of view, and this mode of
measuring is a very good test as to defective colour vision. We shall
allude to the subject of colour-blindness in a subsequent chapter.
The following are the luminosities for the colours fixed by the
principal lines of the solar spectrum, and for the red and blue lines of
lithium, to which reference has already been made.
+----------------------------------------------------+
| | | Luminosity. |
| | |-------------------+
| Line. | Colour. | Normal | Red |
| | | Eye. | Colour |
| | | | Blind. |
+---------------+----------------+--------+----------+
| A | Very dark Red | -- | -- |
| B | Red (Crimson) | 1·0 | 0 |
| Red Lithium | Red (Crimson) | 8·5 | ·5 |
| C | Red (Scarlet) | 20·6 | 2·1 |
| D | Orange | 98·5 | 53·0 |
| E | Green | 50·0 | 49·0 |
| F | Blue Green | 7·0 | 7·0 |
| Blue Lithium | Blue | 1·9 | 1·9 |
| G | Violet | ·6 | ·6 |
| H | Faint Lavender | -- | -- |
+----------------------------------------------------+
The failure of the red colour-blind person to perceive red is very well
shown from this table. It will for instance be noticed that he perceives
about one-tenth of the light at C which the normal-eyed person
perceives.
A modification of this plan can be employed for measuring the luminosity
of the spectrum, and it is _excessively_ useful, because we can adapt it
to the measurement of colours other than these simple ones. In the plan
already explained it was the colour in the patch that was altered, to
get an equal luminosity with a certain luminosity of white light. In the
modified plan the luminosity of the white light is altered, for the
luminosity of the shadow illuminated by the reflected beam can be
altered rapidly at will by opening or closing the apertures of the
sectors whilst it is rotating. The slit in the slide is placed in the
spectrum at any desired point, and the aperture of the sectors altered
till equal luminosities are secured. The readings by this plan are very
accurate, and give the same results as obtained by the previous method
employed.
It must be remembered that we have so far dealt with colours which are
spectrum colours, and which are intense because they are colours
produced by the spectrum of an intensely bright source of light. By an
artifice we can deduce from this curve the luminosity curve of the
spectrum of any other source of light. If by any means we can compare,
_inter se_, the intensity of the same rays in two different sources of
light, one being the electric light, we can evidently from the above
figure deduce the luminosity curve of the spectrum of the other source
of light (see p. 109).
We can now show how we can adapt the last method to the measurement of
the luminosity of the light reflected from pigments.
Fig. 12.--Rectangles of White and Vermilion.
Fig. 13.--Arrangement for measuring the Luminosities of Pigments.
Suppose the luminosity of a vermilion-coloured surface had to be
compared with a white surface when both were illuminated, say by
gaslight, the following procedure is adopted. A rectangular space is cut
out of black paper (Fig. 12) of a size such that its side is rather less
than twice the breadth of the rod used to cast a shadow: a convenient
size is about one inch broad by three-quarters of an inch in height.
One-half of the aperture is filled with a white surface, and the other
half with the vermilion-coloured surface. The light L (Fig. 13)
illuminates the whole, and the rod R, a little over half an inch in
breadth, is placed in such a position that it casts a shadow on the
white surface, the edge of the shadow being placed accurately at the
junction of the vermilion and white surface. A flat silvered mirror M is
placed at such a distance and at such an angle that the light it
reflects casts a second shadow on the vermilion surface. Between R and
L are placed the rotating sectors A. The white strip is caused to be
evidently too dark and then too light by altering the aperture of the
sectors, and an oscillation of diminishing extent is rapidly made till
the two shadows appear equally luminous. A white screen is next
substituted for the vermilion and again a comparison made. The mean of
the two sets of readings of angular apertures gives the relative value
of the two luminosities. It must be stated, however, that any diffused
light which might be in the room would relatively illuminate the white
surface more than the coloured one. To obviate this the receiving screen
is placed in a box, in the front of which a narrow aperture is cut just
wide enough to allow the two beams to reach the screen. An aperture is
also cut at the front angle of the box, through which the observer can
see the screen. When this apparatus is adopted, its efficiency is seen
from the fact that when the apertures of the rotating sectors are closed
the shadow on the white surface appears quite black, which it would not
have done had there been diffused light in any measurable quantity
present within the box. The box, it may be stated, is blackened inside,
and is used in a darkened room. The mirror arrangement is useful, as any
variation in the direct light also shows itself in the reflected light.
Instead of gaslight, reflected skylight or sunlight can be employed by
very obvious artifices, in some cases a gaslight taking the place of the
reflected beam. When we wish to measure luminosities in our standard
light, viz. the light emitted from the crater of the positive pole of
the arc-light, all we have to do is to place the pigment in the white
patch of the recombined spectrum, and illuminate the white surface by
the reflected beam, using of course the rod to cast shadows, as just
described. The rotating sectors must be placed in either one beam or the
other, according to the luminosity of the pigment.
The luminosities of the following colours were taken by the above
method, and subsequently we shall have to use their values.
Electric Light.
White 100
Vermilion 36
Emerald Green 30
Ultramarine 4·4
Orange 39·1
Black 3·4
Black (different surface) 5·1
Suppose we have two or more colours of the spectrum whose luminosities
have been found, the question immediately arises, as to whether, when
these two colours are combined, the luminosity of the compound colour is
the sum of the luminosities of each separately. Thus suppose we have a
slide with two slits placed in the spectrum, and form a colour patch of
the mixture of the two colours and measure its luminosity, and then
measure the luminosity of the patch first when one slit is covered up,
and then the other. Will the sum of the two latter luminosities be equal
to the measure of the luminosity of the compounded colour patch? One
would naturally assume that it would, but the physicist is bound not to
make any assumptions which are not capable of proof; and the truth or
otherwise is perfectly easy to ascertain, by employing the method of
measurement last indicated. Let us get our answer from such an
experiment.
+-------------+---------------+
| Colours | Observed |
| Measured. | Luminosity. |
+-------------+---------------+
| R | 203·0 |
| G | 38·5 |
| V | 8·5 |
| (R + G) | 242 |
| (G + V) | 45 |
| (R + V) | 214 |
| (R + G + V) | 250 |
+-------------+---------------+
Three apertures were employed, one in the red, another in the green, and
the third in the violet, and the luminosity was taken of each
separately, next two together, and then all three combined, with the
results given above.
The accuracy of the measurements will perhaps be best shown by adding
the single colours together, the pairs and the single colours, and
comparing these values with that obtained when the three colours were
combined. When the pairs are shown they will be placed in brackets; thus
(R + G) means that the luminosity of the compound colour made by red and
green are being considered.
R + G + V = 250·0
(R + G) + V = 250·5
(R + V) + G = 252·5
(G + V) + R = 248·0
(R + G + V) = 250·0
The mean of the first four is 250·25, which is only 1/10% different from
the value of 250 obtained from the measurement of (R + G + V) combined.
Other measures fully bore out the fact that the luminosity of the mixed
light is equal to the sum of the luminosities of its components. It is
true that we have here only been dealing with spectrum colours, but we
shall see when we come to deal with the mixture of colours reflected
from pigments that the same law is universally true.
It will be proved by and by that a mixture of three colours, and
sometimes of only two colours, be they of the spectrum or of pigments,
can produce the impression of white light. If then we measure all the
components but one, and also the white light produced by all, then the
luminosity of the remaining component can be obtained by deducting the
first measures from the last. For instance, red, green and violet were
mixed to form white light. The luminosity of the white being taken as
100, the red and violet were measured and found to have a luminosity of
44·5 and 3 respectively. This should give the green as having a
luminosity of 52·5. The green was measured and found to be 53, whilst a
measurement of the red and green together gave a luminosity of 96·5
instead of 97.