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sidering colour may be deduced one from the other, and are capable of exact
numerical comparison.

On a Geographical Method of Exhibiting the Relations of Colours.

The method which exhibits to the eye most clearly the results of this theory
of the three elements of colour, is that which supposes each colour to be repre-
sented by a point in space, whose distances from three co-ordinate planes are
proportional to the three elements of colour. But as any method by which the
operations are confined to a plane is preferable to one recLuiring space of three
dimensions, we shall only consider for the present that which has been adopted
for convenience, founded on Newton's Circle of colours and Mayer and Young's

Vermilion, ultramarine, and emerald-green, being taken (for convenience) as
standard colours, are conceived to be represented by three points, taken (for con-
venience) at the angles of an equilateral triangle. Any colour compounded of
these three is to be represented by a point found by conceiving masses propor-
tional to the several components of the colour placed at their respective angular
points, and taking the centre of gravity of the three masses. In this way, each



colour will indicate by its position the proportions of the elements of which it is
composed. The total intensity of the colour is to be measured by the whole
number of divisions of V, U, and EG, of which it is composed. This may be
indicated by a number or coefficient appended to the name of the colour, by
which the number of divisions it occupies must be multiplied to obtain its mass
in calculating the results of new combinations.

This will be best explained by an example on the diagram (No. 1). We
have, by experiment (l),

•37 Y+-27 U + -36 EG= -28 SW4- 72 Bk.

To find the position of the resultant neutral tint, we must conceive a mass
of -37 at V, of -27 at U, and of '36 at EG, and find the centre of gravity.
This may be done by taking the line UV, and dividing it in the proportion of
•37 to ^27 at the point a, where

aV : aU :: ^27 : '37.

Then, joining a with EG, divide the joining line in W in the proportion of ^36
to ("37 + "27), W will be the position of the neutral tint required, which is not
white, but 0*28 of white, diluted with 0^72 of black, which has hardly any effect
whatever, except in decreasing the amount of the other colour. The total in-
tensity of our white paper will be represented by oi = 3'57; so that, whenever
white enters into an equation, the number of divisions must be multiplied by
the coefficient 3-57 before any true results can be obtained.

We may take, as the next example, the method of representing the relation
of pale chrome to the standard colours on our diagram, by making use of ex-
periment (2), in which pale chrome, ultramarine, and emerald-green, produced a
neutral gray. The resulting equation was

•33PC + -55U + -12EG = -37SW + -63Bk (2).

In order to obtain the total intensity of white, we must multiply the
number of divisions, -37, by the proper coefficient, which is 3*57. The result is
1-32, which therefore measures the total intensity on both sides of the equation.

Subtracting the intensity of •55U + -12EG, or '67 from 1-32, we obtain '65
as the corrected value of -33 PC. It will be convenient to use these corrected
values of the different colours, taking care to distinguish them by small initials
instead of capitals.


Equation (2) then becomes

•65 pc + -55 U + -12 EG = 1 -32 w.

Hence pc must be situated at a point such that w is the centre of gravity
of •65pc + -55U + '12EG.

To find it, we begin by determining ^ the centre of gravity of -55 U + '12EG,
then, joining /8w, the point we are seeking must lie at a certain distance on
the other side of w from c This distance may be found from the proportion,

•65 : (-55 + -12) :: ^ : w pc,
which determines the position of pc. The proper coefficient, by which the ob-
served vakies of PC must be corrected, is ^, or 1-97.

We have thus determined the position and coefficient of a colour by a single
experiment, in which it was made to produce a neutral tint along with two of
the standard colours. As this may be done with every possible colour, the
method is applicable wherever we can obtain a disc of the proposed colour. In
this way the diagram (No. l) has been laid down from observations made in
daylight, by a good eye of the ordinary type.

It has been observed that experiments, in which the resultant tint is neutral,
are more accurate than those in which the resulting tint has a decided colour,
as in experiment (3), owing to the effects of accidental colours produced in the
eye in the latter case. These experiments, however, may be repeated till a
very good mean result has been obtained.

But since the elements of every colour have been already fixed by our
previous observations and calculations, the agreement of these results with those
calculated from the diagram forms a test of the correctness of our method.

By experiment (No. 3), made at the same time with (l) and (2), we have
•39PC + -2lU + -40Bk = -59V + -4lEG (3).

Now, joining XJ with pc, and V with EG, the only common point is that
at which they cross, namely y.

Measuring the parts of the line V EG, we find them in the proportion of
•58 V and "42 EG = 1*00 7.

Similarly, the line U pc is divided in the proportion
78 pc and •22U=r00y.



But -78 pc must be divided by 1-97, to reduce it to PC, as was previously
explained. The result of calculation is, therefore,

•39 PC + -22 U + -39 Bk = -58 V + "42 EG,
the black being introduced simply to fill up the circle.

This result differs very little from that of experiment (3), and it must be
recollected that these are single experiments, made independently of theory, and
chosen at random.

Experiments made at Cambridge, with all the combinations of five colours,
shew that theory agrees with calculation always within 0-012 of the whole,
and sometimes within 0*002. By the repetition of these experiments at the
numerous opportunities which present themselves, the accuracy of the results
may be rendered still greater. As it is, I am not aware that the judgments
of the human eye with respect to colour have been supposed capable of so
severe a test.

Further consideration of the Diagram of Colours.

We have seen how the composition of any tint, in terms of our three
standard colours, determines its position on the diagram and its proper coefficient.
In the same way, the result of mixing any other colours, situated at other
points of the diagram, is to be found by taking the centre of gravity of their
reduced masses, as was done in the last calculation (experiment 3).

We have now to turn our attention to the general aspect of the diagram.

The standard colours, V, U, and EG, occupy the angles of an equilateral
triangle, and the rest are arranged in the order in which they participate in
red, blue, and green, the neutral tint being at the point w within the triangle.
If we now draw lines through w to the different colours ranged round it, we
shall find that, if we pass from one line to another in the order in which they
lie from red to green, and through blue back again to red, the order will be —

Carmine .
Vermilion .
Red Lead .
Oi-ange Orpiment
Orange Chrome
Chrome Yellow
Gramboge .



Pale Chrome


Mixed Green (U C)


Brunswick Green


Emerald Green .


Verditer Blue .


Prussian Blue .





It may be easily seen that this arrangement of the colours corresponds to
that of the prismatic spectrum ; the only difference being that the spectrum
is deficient in those fine purples which lie between ultramarine and vermilion,
and which are easily produced by mixture. The experiments necessary for deter-
mining the exact relation of this list to the lines in the spectrum are not yet

If we examine the colours represented by different points in one of these
lines through w, we shall find the purest and most decided colours at its outer
extremity, and the faint tints approaching to neutrality nearer to w.

If we also study the coefficients attached to each colour, we shall find that
the brighter and more luminous colours have higher numbers for their coefficients
than those which are dark.

In this way, the qualities which we have already distinguished as hue, tint,
and shade, are represented on the diagram by angular position with respect to ir,
distance from w, and coefficient; and the relation between the two methods of
reducing the elements of colour to three becomes a matter of geometry.

Theory of the Perception of Colour.

Opticians have long been divided on this point ; those who trusted to
popular notions and their own impressions adopting some theory of three primary
colours, while those who studied the phenomena of light itself proved that no
such theory could explain the constitution of the spectrum. Newton, who was
the first to demonstrate the actual existence of a series of kinds of light,
countless in number, yet all perfectly distinct, was also the first to propound
a method of calculating the effect of the mixture of various coloured light ;
and this method was substantially the same as that which we have just
verified. It is true, that the directions which he gives for the construction
of his circle of colours are somewhat arbitrary, being probably only intended
as an indication of the general nature of the method, but the method itself
is mathematically reducible to the theory of three elements of the colour-

♦ See Note III. For a confirmation of Newton's analysis of Light, see Helmholtz, Pogg. Ann,
1852; and Phil. Mag. 1852, Part ii.


Youno", who made the next great step in the establishment of the theory
of light, seems also to have been the first to follow out the necessary conse-
quences of Newton's suggestion on the mixture of colours. He saw that, since
this tripUcity has no foundation in the theory of light, its cause must be looked
for in the constitution of the eye; and, by one of those bold assumptions
which sometimes express the result of speculation better than any cautious
trains of reasoning, he attributed it to the existence of three distinct modes
of sensation in the retina, each of which he supposed to be produced in different
deo-rees by the different rays. These three elementary effects, according to his
view, correspond to the three sensations of red, green, and violet, and would
separately convey to the sensorium the sensation of a red, a green, and a violet
picture ; so that by the superposition of these pictures, the actual variegated
world is represented*.

In order fully to understand Young's theory, the function which he
attributes to each system of nerves must be carefully borne in mind. Each nerve
acts, not, as some have thought, by conveying to the mind the knowledge of the
length of an undulation of light, or of its periodic time, but simply by being
Quore or less affected by the rays which fall on it. The sensation of each
elementary nerve is capable only of increase and diminution, and of no other
change. We must also observe, that the nerves corresponding to the red
sensation are affected chiefly by the red rays, but in some degree also by those
of every other part of the spectrum ; just as red glass transmits red rays freely,
but also suffers those of other colours to pass in smaller quantity.

This theory of colour may be illustrated by a supposed case taken from
the art of photography. Let it be required to ascertain the colours of a land-
scape, by means of impressions taken on a preparation equally sensitive to rays of
every colour.

Let a plate of red glass be placed before the camera, and an impression
taken. The positive of this will be transparent wherever the red light has been
abundant in the landscape, and opaque where it has been wanting. Let it now
be put in a magic lantern, along with the red glass, and a red picture will be
thrown on the screen.

Let this operation be repeated with a green and a violet glass, and, by

* Young's Lectures, p. 345, Kelland's Edition. See also Helmholtz's statement of Young's Theory,
in his Paper referred to in Note I. ; and Herschel's LigJU, Art. 518.


means of three magic lanterns, let the three images be superimposed on the
screen. The colour of any point on the screen will then depend on that of the
corresponding point of the landscape; and, by properly adjusting the intensities
of the lights, &c., a complete copy of the landscape, as far as visible colour is
concerned, will be thrown on the screen. The only apparent difference will be,
that the copy will be more subdued, or less pure in tint, than the original.
Here, however, we have the process performed twice — first on the screen, and
then on the retina.

This illustration will shew how the functions which Young attributes to the
three systems of nerves may be imitated by optical apparatus. It is therefore
unnecessary to search for any direct connection between the lengths of the
undulations of the various rays of light and the sensations as felt by us, as
the threefold partition of the properties of light may be effected by physical
means. The remarkable correspondence between the results of experiments on
different individuals would indicate some anatomical contrivance identical in all.
As there is little hope of detecting it by dissection, we may be content at
present with any subsidary evidence which we may possess. Such evidence is
furnished by those individuals who have the defect of vision which was
described by Dalton, and which is a variety of that which Dr G. Wilson has
lately investigated, under the name of Colour-Blindness.

Testimony of the Colour- Blind with respect to Colour.

Dr George Wilson has described a great number of cases of colour-
bhndness, some of which involve a general indistinctness in the appreciation
of colour, while in others, the errors of judgment are plainly more numerous
in those colours which approach to red and green, than among those which
approach to blue and yellow. In these more definite cases of colour-blindness,
the phenomena can be tolerably well accoimted for by the hypothesis of an
insensibility to red light; and this is, to a certain extent, confirmed by the
fact, that red objects appear to these eyes decidedly more obscure than to
ordinary eyes. But by experiments made with the pure spectrum, it appears
that though the red appears much more obscure than other colours, it is not
wholly invisible, and, what is more curious, resembles the green more than
any other colour. The spectrum to them appears faintly luminous in the red;

VOL. L 18


bright yellow from orange to yellow, bright but not coloured from yellow-
green to blue, and then strongly coloured in the extreme blue and violet,
after which it seems to approach the neutral obscure tint of the red. It is
not easy to see why an insensibihty to red rays should deprive the green
rays, which have no optical connection with them, of their distinctive appearance.
The phenomena seem rather to lead to the conclusion that it is the red
serisation which is wanting, that is, that supposed system of nerves which is
affected in various degrees by all light, but chiefly by red. We have fortunately
the means of testing this hypothesis by numerical results.

Of the subjects of my experiments at Cambridge, four were decided cases
of colour-bHndness. Of these two, namely, Mr E. and Mr S., were not
suflficiently critical in their observations to afford any results consistent within
10 divisions of the colour-top. The remaining two, Mr N. and Mr X., were
as consistent in their observations as any persons of ordinary vision can be,
while the results shewed all the more clearly how completely their sensations
must differ from ours.

The method of experimenting was the same as that adopted with ordinary
eyes, except that in these cases the operator can hardly influence the result
by yielding to his own impressions, as he has no perception whatever of the
similarity of the two tints as seen by the observer. The questions which he
must ask are two, Which circle appears most blue or yellow ? Which appears
lightest and which darkest ? By means of the answers to these questions he
must adjust the resulting tints to equality in these respects as it appears to
the observer, and then ascertain that these tints now present no difference of
colour whatever to his eyes. The equations thus obtained do not require five
colours including black, but four only. For instance, the mean of several obser-
vations gives —

•19 G+'05 B + -76 Bk=100R (4).

[In these experiments R, B, G, Y, stand for red, blue, green, and yellow
papers prepared by Mr D. R. Hay. I am not certain that they are identical
with his standard colours, but I beUeve so. Their relation to vermihon, ultra-
marine, and emerald-green is given in diagram (1). Their relations to each other
are very accurately given in diagram (2).]

It appears, then, that the dark blue-green of the left side of the equation
is equivalent to the full red of the right side.


Hence, if we divide the line BG in the proportion 19 to 5 at the point y8,
and join R)8, the tint at ^ will differ from that at R (to the colour-blind)
only in being more brilliant in the proportion of 100 to 24, and all inter-
mediate tints on the line R^ will appear to them of the same hue, but
of intermediate intensities.

Now, if we take a point D, so that RD is to R^ in the proportion of
24 to 100 — 24, or 76, the tint of D, if producible, should be invisible to
the colour-blind. D, therefore, represents the pure sensation which is unknown
to the colour-blind, and the addition of this sensation to any others cannot
alter it in their estimation. It is for them equivalent to black.

Hence, if we draw lines through D in different directions, the colours
belonging to any line ought to differ only in intensity as seen by them, so
that one of them may be reduced to the other by the addition of black
only. If we draw DW and produce it, all colours on the upper side of DW
will be varieties of blue, and those on the under side varieties of yellow, so
that the line DW is a boundary line between their two kinds of colour, blue
and yellow being the names by which they call them.

The accuracy of this theory will be evident from the comparison of the
experiments which I had an opportunity of making on Mr N. and Mr X. with
each other, and with measurements taken from the diagram No. 2, which was
constructed from the observations of ordinary eyes only, the point D alone
being ascertained from a series of observations by Mr N.

Taking the point y, between R and B, it appears, by measurement of the
lines Ry and By, that y corresponds to

•07 B + -93R.

By measurement of Wy and Dy, and correction by means of the coeflScient
of W, and caUing D black in the colour-blind language, y corresponds to

•105 W-f895 Bk.

By measurement -93 R+ '07 B = ^105 W + •sgs Bk 1

By observation N. & X. together "94 R-f -06 B = •lO W-f-^90 Bk I (5).

By X. alone -93 R-h-07 B = -10 W + -90 Bk J

The agreement here is as near as can be expected.




By a similar calculation with respect to the point 8, between B and G,

By measurement -43 B + -57 G = -335 W + *665 Bk 1

Observed by N. and X '41 B + '59 G = '34 W + -66 Bk I (6).

By X. alone -42 B + -58 G = -32 W + -68 Bk J

We may also observe, that the line GD crosses RY. At the point of inter-
section we have —

By calculation '87 B + 'IS Y = -34 G + -66 Bk

Observed by N. and X -86 R + -14 Y = -40 G + 'GO Bk

X •84R + '16 Y=-31 G + '69 Bk

X -QOR + 'IO Y = -27 G + 73Bk


Here observations are at variance, owing to the decided colours produced
affecting the state of the retina, but the mean agrees well with calculation.

Drawing the line BY, we find that it cuts lines through D drawn to every
colour. Hence all colours appear to the colour-blind as if composed of blue
and yellow. By measurement on the diagram, we find for red

Measured -138 Y+-123 B + 749 Bk = 100 R'

Observed by N..., -15 Y + 'll B-1 - 74 Bk = 100RJ- (8).

X....-13 Y + 'll B + -76 Bk = 100R


For green we have in the same way —

Measured 705 Y + -295 B = '95 G + -05 Bkl

Observed by N.... 70 Y + -30 B = -86 G + -14 Bk i ....
X.... 70 Y+-30 B = '83 G+-17BkJ

For white —

Measured '407 Y + -593 B = '326 W + "674 Bk

Observed by N.... -40 Y+-60 B = -33 W+-67 Bk
X.... -44 Y+-56 B=-33 W+-67 Bk

The accuracy of these results shews that, whether the hypothesis of the
want of one element out of three necessary to perfect vision be actually true
or not, it affords a most trustworthy foundation on which to build a theory
of colour-blindness, as it expresses completely the observed facts of the case.
They also furnish us with a datum for our theory of perfect vision, namely,
the point D, which points out the exact nature of the colour-sensation, which
must be added to the colour-blind eye to render it perfect. I am not aware


of any method of determining by a legitimate process the nature of the other
two sensations, although Young's reasons for adopting something like green and
violet appear to me worthy of attention.

The only remaining subject to which I would call the attention of the
Society is the effect of coloured glasses on the colour-blind. Although they can-
not distinguish reds and greens from varieties of gray, the transparency of red
and green glasses for those kinds of light is very different. Hence, after finding
a case such as that in equation (4), in which a red and a green appear iden-
tical, on looking through a red glass they see the red clearly and the green
obscurely, while through a green glass the red appears dark and the green light.

By furnishing Mr X. with a red and a green glass, which he could dis-
tinguish only by their shape, I enabled him to make judgments in previously
doubtful cases of colour with perfect certainty. I have since had a pair of
spectacles constructed with one eye-glass red and the other greeiL These Mr X.
intends to use for a length of time, and he hopes to acquire the habit of discri-
minating red from green tints by their different effects on his two eyes. Though
he can never acquire our sensation of red, he may then discern for himself what
things are red, and the mental process may become so familiar to him as to act
unconsciously like a new sense.

In one experiment, after looking at a bright light, with a red glass over one
eye and a green over the other, the two tints in experiment (4) appeared to him
altered, so that the outer circle was lighter according to one eye, and the inner
according to the other. As far as I could ascertain, it appeared as if the eye
which had used the red glass saw the red circle brightest. This result, which
seems at variance with what might be expected, I have had no opportunity of

This paper is already longer than was originally intended For further
information I would refer the reader to Newton's Optich, Book i. Part ii., to
Young's Lectures on Natural Philosophy, page 345, to Mr D. R. Hay's works on
Colours, and to Professor Forbes on the "Classification of Colours" (Phil. Mag.,
March, 1849).

The most remarkable paper on the subject is that of M. Helmholtz, in the
Philosophical Magazine for 1852, in which he discusses the different theories of
primary colours, and describes his method of mixing the colours of the spectrum.
An examination of the results of M. Helmholtz with reference to the theory


of three elements of colour, by Professor Grassmann, is translated in the Phil.
Mag., April, 1854.

References to authors on colour-blindness are given in Dr G. Wilson's papers
on that subject. A valuable Letter of Sir J. F. W. Herschel to Dalton on his
peculiarity of vision, is to be found in the Life of Dalton by Dr Henry.

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