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In this case there is nothing to prove the existence of more than one
sensation in vision.

In those photographic pictures in which there is only one tint of which
the different intensities correspond to the different degrees of illumination of the
object, we have another illustration of an optical effect depending on one variable
only.

2. Now, suppose that different kinds of light are emanating from different
sources, but that each of these sources gives out perfectly homogeneous light,
then there will be two things on which the nature of each ray will depend : —
(1) its intensity or brightness ; (2) its hue, which may be estimated by its
position in the spectrum, and measured by its wave length.

If we take a rectangular plane, and illuminate it with the different kinds
of homogeneous light, the intensity at any point being proportional to its hori-
zontal distance along the plane, and its wave length being proportional to its
height above the foot of the plane, then the plane will display every possible
variety of homogeneous light, and will furnish an instance of an optical effect
depending on two variables.



THE THEORY OF COLOURS IN RELATION TO COLOUR-BLINDNESS.



121



3. Now, let us take the case of nature. We find that colours differ not
only in intensity and Ime, but also in tint ; that is, they are more or less pure.
We might arrange the varieties of each colour along a line, which should begin
with the homogeneous colour as seen in the spectrum, and pass through all
gradations of tint, so as to become continually purer, and terminate in white.

We have, therefore, three elements in our sensation of colour, each of which
may vary independently. For distinctness sake I have spoken of intensity, hue,
and tint ; but if any other three independent qualities had been chosen, the
one set might have been expressed in terms of the other, and the results identified.

The theory which I adopt assumes the existence of three elementary sen-
sations, by the combination of which all the actual sensations of colour are
produced. It will be shewn that it is not necessary to specify any given colours
as typical of these sensations. Young has called them red, green, and violet ; but
any other three colours might have been chosen, provided that white resulted
from their combination in proper proportions.

Before going farther I would observe, that the important part of the theoiy
is not that three elements enter into our sensation of colour, but that there are
only three. Optically, there are as many elements in the composition of a ray
of light as there are different kinds of light in its spectrum; and, therefore,
strictly speaking, its nature depends on an infinite number of independent
variables.

I now go on to the geometrical form into which the theory may be thrown.
Let it be granted that the three pure sensations corre-
spond to the colours red, green, and violet, and that we
can estimate the intensity of each of these sensations
numerically.

Let V, r, g be the angular points of a triangle, and
conceive the three sensations as having their positions at
these points. If we find the numerical measure of the
red, green, and violet parts of the sensation of a given
colour, and then place weights proportional to these parts

at r, g, and v, and find the centre of gravity of the three weights by the
ordinary process, that point will be the position of the given colour, and the
numerical measure of its intensity will be the sum of the tliree primitive
sensations.

In this way, every possible colour may have its position and intensity

VOL. I. 16




122 THE THEORY OF COLOURS IN RELATION TO COLOUR-BLINDNESS.

ascertained; and it is easy to see that when two compound colours are com-
bined, their centre of gravity is the position of the new colour.

The idea of this geometrical method of investigating colours is to be found
in Newton's Opticks (Book I., Part 2, Prop. 6), but I am not aware that it has
been ever employed in practice, except in the reduction of the experiments
which I have just made. The accuracy of the method depends entirely on the
truth of the theory of three sensations, and therefore its success is a testimony
in favour of that theory.

Every possible colour must be included within the triangle rgv. White
will be foimd at some point, w, within the triangle. If lines be drawn through
w to any point, the colour at that point will vary in hue according to the
angular position of the line drawn to w, and the purity of the tint will depend
on the length of that line.

Though the homogeneous rays of the prismatic spectrum are absolutely pure
in themselves, yet they do not give rise to the "pure sensations" of which we
are speaking. Every ray of the spectrum gives rise to all three sensations,
though in different proportions ; hence the position of the colours of the spectrum
is not at the boundary of the triangle, but in some curve C R Y G B V
considerably within the triangle. The nature of this curve is not yet determined,
but may form the subject of a future investigation *.

All natural colours must be within this curve, and all ordinary pigments
do in fact lie very much within it. The experiments on the colours of the
spectrum which I have made are not brought to the same degree of accuracy as
those on coloured papers. I therefore proceed at once to describe the mode of
making those experiments which I have found most simple and convenient.

The coloured paper is cut into the form of discs, each with a small hole

in the centre, and divided along a radius, so as to admit ^ ^

of several of them being placed on the same axis, so that C^^ J

part of each is exposed. By slipping one disc over another,

we can expose any given portion of each colour. These >^ — ~^
j:«^« „i J „ ^:^.^.^^ j. j.^^i.^4. ,'4.; ^v ( <=> )




discs are placed on a little top or teetotum, consisting of \^ y

a flat disc of tin-plate and a vertical axis of ivory. This

axis passes through the centre of the discs, and the quantity of each colour exposed

is measured by a graduation on the rim of the disc, which is divided into 100 parts.

* [See the author's Memoir in the Philosophical Transactions, 1860, on the Theory o£ Compound
Colours, and on the relations of the Colours of the Spectrum.]



THE THEORY OF COLOURS IN RELATION TO COLOUR-BLINDNESS. 123

By spinning the top, each colour is presented to the eye for a time pro-
portional to the angle of the sector exposed, and I have found by independent
experiments, that the colour produced by fast spinning is identical with that
produced by causing the light of the different colours to fall on the retina at
once.

By properly arranging the discs, any given colour may be imitated and
afterwards registered by the graduation on the rim of the top. The principal
use of the top is to obtain colour-equations. These are got by producing, by
two different combinations of colours, the same mixed tint. For this purpose
there is another set of discs, half the diameter of the others, which lie above
them, and by which the second combination of colours is formed.

The two combinations being close together, may be accurately compared, and
when they are made sensibly identical, the proportions of the different colours
in each is registered, and the results equated.

These equations in the case of ordinary vision, are always between four
colours, not including black.

From them, by a very simple rule, the different colours and compounds have
their places assigned on the triangle of colours. The rule for finding the position
is this : — Assume any three points as the positions of your three standard colours,
whatever they are ; then form an equation between the three standard colours,
the given colour and black, by arranging these colours on the inner and outer
circles so as to produce an identity when spun. Bring the given colour to the
left-hand side of the equation, and the three standard colours to the right hand,
leaving out black, then the position of the given colour is the centre of gravity
of three masses, whose weights are as the number of degrees of each of the
standard colours, taken positive or negative, as the case may be.

In this way the triangle of colours may be constructed by scale and compass
from experiments on ordinary vision. I now proceed to state the results of
experiments on Colour-Blind vision.

If we find two combinations of colours which appear identical to a Colour-
Blind person, and mark their positions on the triangle of colours, then the
straight line passing through these points will pass through all points corre-
sponding to other colours, which, to such a person, appear identical-with the first
two.

We may in the same way find other lines passing through the series of

IG— 2




124 THE THEORY OF COLOURS IN RELATION TO COLOUR-BLINDNESS.

colours wMch appear alike to the Colour-Blind. All these
lines either pass through one point or are parallel, ac-
cording to the standard colours which we have assumed,
and the other arbitrary assumptions we may have made.
Knowing this law of Colour-Blind vision, we may predict
any number of equations which will be true for eyes
having this defect.

The mathematical expression of the difference between
Colour-BUnd and ordinary vision is, that colour to the
former is a function of two independent variables, but to an ordinary eye, of
three ; and that the relation of the two kinds of vision is not arbitrary, but
indicates the absence of a determinate sensation, depending perhaps upon some
undiscovered structure or organic arrangement, which forms one-third of the
apparatus by which we receive sensations of colour.

Suppose the absent structure to be that which is brought most into play
when red light falls on our eyes, then to the Colour-Blind red light will be
visible only so far as it affects the other two sensations, say of blue and
green. It will, therefore, appear to them much less bright than to us, and will
excite a sensation not distinguishable from that of a bluish-green light.

I cannot at present recover the results of all my ^periments ; but I recollect
that the neutral colours for a Colour-Blind person may be produced by com-
bining 6 degrees of ultramarine with 94 of vermiUon, or 60 of emerald-green
with 40 of ultramarine. The first of these, I suppose to represent to our eyes
the kind of red which belongs to the red sensation. It excites the other two
sensations, and is, therefore, visible to the Colour-BHnd, but it appears very
dark to them and of no definite colour. I therefore suspect that one of the
three sensations in perfect vision will be found to correspond to a red of the
same hue, but of much greater purity of tint. Of the nature of the other two,
I can say nothing definite, except that one must correspond to a blue, and the
other to a green, verging to yellow.

I hope that what I have written may help you in any way in your
experiments. I have' put down many things simply to indicate a way of thinking
about colours which belongs to this theory of triple sensation. We are indebted
to Newton for the original design ; to Young for the suggestion of the means
of working it out; to Prof. Forbes'' for a scientific history of its application

*Phil. Mag. 1848.



THE THEORY OF COLOURS IN RELATION TO COLOUR-BLINDNESS. 125

to practice; to Helmholtz for a rigorous examination of the facts on which it
rests; and to Prof Graasman (in the Phil. Mag, for 1852), for an admirable
theoretical exposition of the subject. The colours given in Hay's Nomenclature
of Colours are illustrations of a similar theory applied to mixtures of pigments,
but the results are often different from those in which the colours are combined
by the eye alone. I hope soon to have results with pigments compared with
those given by the prismatic spectrum, and then, perhaps, some more definite
results may be obtained. Yours truly,

J. C. MAXWELL.



Edinburgh, 4tli Jan. 1855.



[From the Transactions of the Royal Society of Edinburgh, Vol xxi. Part ii.]



VII. Experiments on Colour, as perceived hy the Eye, with remarks on Colour-
Blindness. Communicated by Dr Gregory.

The object of tbe following communication is to describe a method by
which every variety of visible colour may be exhibited to the eye m such a
form as to admit of accurate comparison ; to shew how experiments so made
may be registered numerically; and to deduce from these numerical results
certain laws of vision.

The different tints are produced by means of a combination of discs of paper,
painted with the pigments commonly used in the arts, and arranged round an
axis, so that a sector of any required angular magnitude of each colour may be
exposed. "When this system of discs is set in rapid rotation, the sectors of
the different colours become indistinguishable, and the whole appears of one uni-
form tint. The resultant tints of two different combinations of colours may be
compared by using a second set of discs of a smaller si^e, and placing these over
the centre of the first set, so as to leave the outer portion of the larger discs
exposed. The resultant tint of the first combination will then appear in a ring
round that of the second, and may be very carefully compared with it.

The form in which the experiment is most manageable is that of the com-
mon top. An axis, of which the lower extremity is conical, carries a circular
plate, which serves as a support for the discs of coloured paper. The circumfer-
ence of this plate is divided into 100 equal parts, for the purpose of ascertainmg
the proportions of the different colours which form the combination. When the
discs have been properly arranged, the upper part of the axis is screwed down,
so as to prevent any alteration in the proportions of the colours.

The instrument used in the first series of experiments (at Cambridge, in
November, 1854) was constructed by myself, with coloured papers procured from



EXPERIMENTS ON COLOUR, AS PERCEIVED BY THE EYE.



127



Mr D. R Hay. The experiments made in the present year were with the
improved top made by Mr J. M. Bryson, Edinburgh, and coloured papers pre-
pared by Mr T. Purdie, with the unmixed pigments used in the arts. A number
of Mr Bryson's tops, with Mr Purdie's coloured papers has been prepared, so as
to afford different observers the means of testing and comparing results inde-
pendently obtained.

The colour used for Mr Purdie's papers were —



Vermilion


V


Ultramarine


U


Emerald Green


EG


Carmine .


C


Prussian Blue .


PB


Brunswick Green


BG


Red Lead


RL


Verditer Blue .


VB


Mixture of Ultramarine




Orange Orpiment


00






and Chrome


uc


Orange Chrome


OC










Chrome Yellow


CY










Gamboge


Gam










Pale Chrome .


PC


Ivory Black .
Snow White .


Bk
SW







White Paper (Pirie, Aberdeen),

The colours in the first column are reds, oranges, and yellows; those in
the second, blues ; and those in the third, greens. Vermilion, ultramarine, and
emerald green, seem the best colours to adopt in referring the rest to a uniform
standard. They are therefore put at the head of the Hst, as types of three
convenient divisions of colour, red, blue, and green.

It may be asked, why some variety of yellow was not chosen in place of
green, which is commonly placed among the secondary colours, while yellow
ranks as a primary? The reason for this deviation from the received system is,
that the colours on the discs do not represent primary colours at all, but are
simply specimens of different kinds of paint, and the choice of these was deter-
mined solely by the power of forming the requisite variety of combinations. Now,
if red, blue, and yellow, had been adopted, there would have been a difficulty
in forming green by any compound of blue and yellow, while the yellow formed
by vermilion and emerald green is tolerably distinct. This will be more clearly
perceived after the experiments have been discussed, by referring to the diagram.

As an example of the method of experimenting, let us endeavour to form a
neutral gray by the combination of vermilion, ultramarine, and emerald green.
The most perfect results are obtained by two persons acting in concert., when



128 EXPERIMENTS ON COLOUR, AS PERCEIVED BY THE EYE.

the operator arranges the colours and spins the top, leaving the eye of the
observer free from the distracting effect of the bright colours of the papers when
at rest.

After placing discs of these three colours on the circular plate of the top,
and smaller discs of white and black above them, the operator must spin the
top, and demand the opinion of the observer respecting the relation of the
outer ring to the inner circle. He will be told that the outer circle is too
red, too blue, or too green, as the case may be, and that the inner one is too
light or too dark, as compared with the outer. The arrangement must then be
changed, so as to render the resultant tint of the outer and inner circles more
nearly alike. Sometimes the observer will see the inner circle tinted with the
complementary colour of the outer one. In this case the operator must interpret
the observation with respect to the outer circle, as the inner circle contains only
black and white.

By a little experience the operator will learn how to put his questions, and
how to interpret their answers. The observer should not look at the coloured
papers, nor be told the proportions of the colours during the experiments.
When these adjustments have been properly made, the resultant tints of the
outer and inner circles ought to be perfectly indistinguishable, when the top
has a sufficient velocity of rotation. The number of divisions occupied by the
different colours must then be read off on the edge of the plate, and registered
in the form of an equation. Thus, in the preceding experiment we have ver-
milion, ultramarine, and emerald green outside, and black and white inside. The
numbers, as given by an experiment on the 6th March 1855, in dayhght without
sun, are —

•37 V + -27 U + '36 EG = -28 SW+-72 Bk (1).

The method of treating these equations will be given when we come to the
theoretical view of the subject.

In this way we have formed a neutral gray by the combination of the
three standard colours. We may also form neutral grays of different intensities
by the combination of vermilion and ultramarine with the other greens, and thus
obtain the quantities of each necessary to neutralize a given quantity of the
proposed green. By substituting for each standard colour in succession one of the
colours which stand under it, we may obtain equations, each of which contains
two standard colours, and one of the remaining colours.



EXPERIMENTS ON COLOUR, AS PERCEIVED BY THE EYE. 129

Thus, in the case of pale chrome, we have, from the same set of experiments,
•34 PC + -55U + -12 EG = '37 SW + -63Bk (2).

"We may also make experiments in which the resultiag tint is not a neutral
gray, but a decided colour. Thus we may combine ultramarine, pale chrome, and
black, so as to produce a tint identical with that of a compound of vermilion
and emerald-green. Experiments of this sort are more difficult, both from the
inability of the observer to express the difference which he detects in two tints
which have, perhaps, the same hue and intensity, but differ in purity ; and also
from the complementary colours which are produced in the eye after gazing too
long at the colours to be compared.

The best method of arriving at a result in the case before us, is to render
the hue of the red and green combination something like that of the yellow, to
reduce the purity of the yellow by the admixture of blue, and to diminish its
intensity by the addition of black. These operations must be repeated and
adjusted, till the two tints are not merely varieties of the same colour, but
absolutely the same. An experiment made 5th March gives —

•39 PC-I - 21 U + -40 Bk = ^59 V-f41 EG (3).

That these experiments are really evidence relating to the constitution of the
eye, and not mere comparisons of two things which are in themselves identical,
may be shewn by observing these resultant tints through coloured glasses, or by
using gas-light instead of day-light. The tints which before appeared identical
will now be manifestly different, and will require alteration, to reduce them to
equality.

Thus, in the case of carmine, we have by day-light,

•44 C-h-22 JJ + 'U EG= •I? SW-f-^83 Bk,
while by gas-light (Edinburgh)

•47 C-l-^08 U-1-^45 EG = ^25 SW-|-^75 Bk,
which shews that the yellowing effect of the gas-light teUs more on the white
than on the combination of colours. If we examine the two resulting tints
which appeared identical in experiment (3), observing the whirling discs througli
a blue glass, the combination of yellow, blue, and black, appears redder than- the
other, while through a yellow glass, the red and green mixture appears redder.
So also a red glass makes the first side of the equation too dark, and a green
glass makes it too light.

VOL. I. 17



130 EXPERIMENTS ON COLOUR, AS PERCEIVED BY THE EYE.

The apparent identity of the tints in these experiments is therefore not real,
but a consequence of a determinate constitution of the eye, and hence arises
the importance of the results, as indicating the laws of human vision.

The first result which is worthy of notice is, that the equations, as observed
by different persons of ordinary vision, agree in a remarkable manner. If care
be taken to secure the same kind of light in all the experiments, the equations,
as determined by two independent observers, will seldom shew a difference of
more than three divisions in any part of the equation containing the bright
standard colours. As the duller colours are less active in changing the resultant
tint, their true proportions cannot be so well ascertained. The accuracy of vision
of each observer may be tested by repeating the same experiment at different
times, and comparing the equations so found.

Experiments of this kind, made at Cambridge in November 1854, shew that
of ten observers, the best were accurate to within 1^ division, and agreed
within 1 division of the mean of all ; and the worst contradicted themselves to
the extent of 6 degrees, but still were never more than 4 or 5 from the mean
of all the observations.

We are thus led to conclude —

1st. That the human eye is capable of estimating the likeness of colours
with a precision which in some cases is very great.

2nd. That the judgment thus formed is determined, not by the real identity
of the colours, but by a cause residing in the eye of the observer.

3rd. That the eyes of different observers vary in accuracy, but agree with
each other so nearly as to leave no doubt that the law of colour-vision is
identical for all ordinary eyes.



Investigation of the Law of the Perception of Colour.

Before proceeding to the deduction of the elementary laws of the perception
of colour from the numerical results previously obtained, it will be desirable
to point out some general features of the experiments which indicate the form
which these laws must assume.

Betuming to experiment (1), in which a neutral gray was produced from
red, blue, and green, we may observe, that, while the adjustments were incom-



EXPERIMENTS ON COLOUR, AS PERCEIVED BY THE EYE. 131

plete, the difference of the tints could be detected only by one circle appearing
more red, more green, or more blue than the other, or by being lighter or
darker, that is, having an excess or defect of all the three colours together.
Hence it appears that the nature of a colour may be considered as dependent
on three things, as, for instance, redness, blueness, and greenness. This is con-
firmed by the fact that any tint may be imitated by mixing red, blue, and
green alone, provided that tint does not exceed a certain brilliancy.

Another way of shewing that colour depends on three things is by con-
sidering how two tints, say two lilacs, may differ. In the first place, one may
be lighter or darker than the other, that is, the tints may differ in shade.
Secondly, one may be more blue or more red than the other, that is, they may
differ in hue. Thirdly, one may be more or less decided in its colour ; it may vary
fi*om purity on the one hand, to neutrality on the other. This is sometimes
expressed by saying that they may differ in tint.

Thus, in shade, hue, and tint, wo have another mode of reducing the
elements of colour to three. It will be shewn that these two methods of con-



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