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reducing dichromic observations. The three standard colours will be referred to
as (104), (88), and (68), these being the positions of the red, green, and blue on
the scale of the new instrument.

Mr James Simpson, formerly student of Natural Philosophy in my class, has
ftimished me with thirty-three observations taken in good sunlight. Ten of
these were between the two standard colours, and give the following result : —

337 (88) + 33-1 (68) = W (1).

The mean errors of these observations were as follows : —

Error of (88) = 2-5; of (68) = 2-3; of (88) + (68) = 4'8 ; of (88)-(68) = 1-3.

The fact that the mean error of the sum was so much greater than the mean
error of the difference indicates that in this case, as in all others that I have
examined, observations of equality of tint can be depended on much more than
observations of equality of illumination or brightness.

From six observations of my own, made at the same time, I have deduced
the " trichromic " equation

22-6 (104)4-26 (88) + 37-4 (68) = W (2).

If we suppose that the light which reached the organ of vision was the
same in both cases, we may combine these equations by subtraction, and so find
22-6(104)-77(88) + 4-3(68) = i> (3),

where D is that colour, the absence of the sensation of which constitutes the
defect of the dichromic eye. The sensation which I have in addition to
those of the dichromic eye is therefore similar to the full red (104), but
different from it, in that the red (104) has 7'7 of green (88) in it which must
be removed, and 4*3 of blue (68) substituted. This agrees pretty well with the
colour which Mr Pole* describes as neutral to him, though crimson to others.
It must be remembered, however, that different persons of ordinary vision require
different proportions of the standard colours, probably owing to differences in the
absorptive powers of the media of the eye, and that the above equation (2), if
observed by K., would have been

23(104) + 32(88) + 3l(68) = W (4).

♦ Philosophical Transactions, 1859, Part I. p. 329.

ON THE THEORY OF COMPOUND COLOURS.

439

and the value of D, as deduced from these observers, would have been

23(104)- 17 (88)- ri (68) = Z) (5),

in which the defective sensation is much nearer to the red of the spectrum. It
is probably a colour to which the extreme red of the spectrum tends, and
which differs from the extreme red only in not containing that small proportion
of "yellow" light which renders it visible to the colour-blind.

From other observations by Mr Simpson the following results have been
deduced : —

Table a.

(88.)

(68.)

(99-2 + ) =

337

1-9

31-3(96) =

33-7

2-1

28 (92) =

33-7

1-4

33-7(88) =

33-7

54-7(84) =

33-7

6-1

71 (82) =

33-7

15-1

99 (80) =

33-7

33-1

70 (78) =

15-7

33-1

56 (76) =

5-7

331

36 (72) =

- 0-3

33-1

33-1(68) =

33-1

40 (64) =

0-2

33-1

55-5(60) =

1-7

33-1

(57-) =

- 0-3

33-1

(88.)

(68.)

100(96) =

108

7

100(92) =

120

6

100(88) =

100

100(84) =

61

11

100(82) =

47

21

100(80) =

34

33

100(78) =

22

47

100(76) =

10

59

100(72) =

- 1

92

100(68) =

100

100(64) =

83

100(60) =

3

60

In the Table on the left side (99*2 + ) means the whole of the spectrum beyond
(99'2) on the scale, and (57-) means the whole beyond (57) on the scale. The
position of the fixed lines with reference to the scale was as follows : —

A, 116; a, 112; B, 110; C, 106; D, 98-3; E, 88; F, 79; G, 61; H, 44.

The values of the standard colours in different parts of the spectrum are given
on the right side of the above Table, and are represented by the cai-ves of
fig. 9, Plate VII. p. 444, where the left-hand curve represents the intensity
of the "yellow" element, and the right-hand curve that of the "blue" element
of colour as it appears to the colour-blind.

The appearance of the spectrum to the colour-blind is as follows: —
From A to E the colour is pure " yellow " very faint up to D, and
reaching a maximum between D and E. From E to one-third beyond F towards

440 ON THE THEORY OF COMPOUND COLOURS.

G the colour is mixed, varying from " yellow " to " blue," and becoming neutral
or "white" at a point near F. In this part of the spectrum, the total inten-
sity, as given by the dotted line, is decidedly less than on either side of it, and
near the line F, the retina close to the "yellow spot" is less sensible to light
than the parts further from the axis of the eye. This peculiarity of the light
near F is even more marked in the colour-blind than in the ordinary eye.
Beyond F the " blue " element comes to a maximum between F and G, and
then diminishes towards H ; the spectrum from this maximum to the end being
pure "blue."

In fig. 10, Plate VII. p. 444, these results are represented in a different
manner. The point D, corresponding to the sensation wanting in the colour-blind,
is taken as the origin of coordinates, the "yellow" element of colour is represented
by distances measured horizontally to the right from D, and the "blue" element
by distances measured vertically from the horizontal line through D. The
numerals indicate the different colours of the spectrum according to the scale
shewn in fig. 9, and the coordinates of each point indicate the composition of
the corresponding colour. The triangle of colours is reduced, in the case of
dichromic vision, to a straight line "B" "Y," and the proportions of "blue"
and "yellow" in each colour are indicated by the ratios in which this line is
cut by the line from D passing through the position of that colour.

The results given above were all obtained with the light of white paper,
placed in clear simshine. I have obtained similar results, when the sun was
hidden, by using the light of uniformly illuminated clouds, but I do not consider
these observations suflficiently free from disturbing circumstances to be employed
in calculation. It is easy, however, by means of such observations, to verify the
most remarkable phenomena of colour-blindness, as for instance, that the colours
from red to green appear to differ only in brightness, and that the brightness
may be made identical by changing the width of the slit; that the colour
near F is a neutral tint, and that the eye in viewing it sees a dark spot in
the direction of the axis of vision ; that the colours beyond are all blue of
different intensities, and that any "blue" may be combined with any "yellow"
in such proportions as to form "white." These results I have verified by the
observations of another colour-blind gentleman, who did not obtain sunlight for
bis observations; and as I have now the means of carrying the requisite
apparatus easily, I hope to meet with other colour-blind observers, and to obtain
their observations under more favourable circumstances.

ON THE THEORY OF COMPOUND COLOURS. 441

On the Comparison of Colour-blind with ordinary Vision by means of Observations

with Coloured Papers.

In March 1859 I obtained a set of observations by Mr Simpson, of the
relations between six coloured papers as seen by him. The experiments were
made with the colour-top in the manner described in my paper in the Trans-
actions of the Royal Society of Edinburgh, Vol. xxi. pt. 2, p. 286; and the
colour-equations were arranged so as to be equated to zero, as in those given
in the Philosophical Magazine, July, 1857. The colours were — Vermilion (V),
ultramarine (U), emerald-green (G), ivory-black (B), snow-white (W), and pale
chrome-yellow (Y). These six colours afford fifteen colour-blind equations, since
four colours enter into each equation. Fourteen of these were observed by
Mr Simpson, and from these I deduced three equations, giving the relation of
the three standards (V), (U), (G) to the other colours, according to his kind of
vision. From these three equations I then deduced fifteen equations, admitting
of comparison with the observed equations, and necessarily consistent in
themselves.

The comparison of these equations furnishes a test of the truth of the theory
that the colour-blind see by means of two colour-sensations, and that therefore
eveiy colour may be expressed in terms of two given colours, just as in ordinary
vision it may be expressed in terms of three given colours. The one set of
equations are each the result of a single observation ; the other set are deduced
from three equations in accordance with this theory, and the two sets agree to
within an average error = 2*1.

Table b.

V.

U.

G.

B.

W.

Y.

1.

Observed . .

-100

+ 45

+ 22

+ 33 =0.

Calculated .

-100

+ 37-5

+ 26-5

+ 36 =0.

2.

Observed . .

+ 58

-69

-31

-42 =0.

Calculated .

+ 58-3

-67-3

-32-7

+ 41-7 = 0.

3.

Observed . .

+ 32

-100

+ 12

+ 56 =0.

Calculated .

+ 32-3

-100

+ 8-3

+ 59-4 = 0.

4.

Observed . .

+ 38

- 89

-11

+ 62 =0.

Calculated .

+ 40

- 85

-15

+ 60 =0.

5.

Observed . .

+ 32

+ 68

-60

-40

-0.

Calculated .

+ 34

+ 66

-63-5

-36-5

=0.

442 ON THE THEORY OF COMPOUND COLOURS.

Table b (continued).

V.

U.

G.

B.

W.

Y.

6.

Observed . .

.-100

+ 82

+ 5

+ 13 =0.

Calculated .

.-100

+ 83-9

+ 4-5

+ 11-6 = 0.

7.

Observed . .

.+ 47

-

100

+ 22

+ 31 = 0.

Calculated .

.+ 44-7

-

100

+ 24-5

+ 30-8 = 0.

8.

Observed . .

.-100

+

20

+ 77

+ 3 =0.

Calculated .

.-100

+

17

+ 77-5

+ 5-5=0.

9.

Not Observed

Calculated .

.+ 96

-

31

-69

+ 4

=0.

10.

Observed . .

.- 70

+ 53

-30

+ 47 =0.

Calculated .

.- 73-5

+ 53

-26-5

+ 47 =0.

11.

Observed . .

.-100

+ 8

+ 71

+ 21 =0.

Calculated .

.-100

+ 8

+ 74-5

+ 17-5 = 0.

12.

Observed . .

.+ 85

+ 15

-88

-12

=0.

Calculated .

.+ 86

+ 14

-88-5

-11-5

=0.

13.

Observed . .

.- 20

+ 39

_

80

+ 61 =0.

Calculated .

.- 19

+ 40

-

81

+ 60 =0.

14.

Observed . .

.- 66

+ 30

+

70

-34

=0.

Calculated .

.- 70

+ 27

+

73

-30

=0.

15.

Observed . .

. + 100

- 2

_

27

-71

=0.

Calculated .

.+ 96

+ 4

-

24

-76

=0.

But, axjcording to our theory, colour-blind vision is not only dichromic, but
the two elements of colour are identical with two of the three elements of
colour as seen by the ordinary eye ; so that it differs from ordinary vision
only in not perceiving a particular colour, the relation of which to known colours
may be numerically defined. This colour may be expressed under the form

aV + 6U + cG = D (16),

where V, U, and G are the standard colours used in the experiments, and D is
the colour which is visible to the ordinary eye, but invisible to the colour-
blind. If we know the value of D, we may always change an ordinary colour-
equation into a colour-blind equation by subtracting from it nD (n being chosen
so that one of the standard colours is eliminated), and adding n of black.

In September 1856 I deduced, from thirty-six observations of my own, the
chromatic relations of the same set of six coloured papers. These observations,
with a comparison of them with the trichromic theory of vision, are to be
found in the Philosophical Magazine for July 1857. The relations of the

ON THE THEORY OF COMPOUND COLOURS. 443

six colours may be deduced from two equations, of which the most convenient

form is

V. U. G. B. W. Y.

+ 397 +2G-6 +337 -227 -77-3 =0 (17).

-62-4 +18-6 -37-6 +457 +357 = (18).

The value of D, as deduced from a comparison of these equations with the
colour-blind equations, is

1-198 V + 0-078U-0-276G = D (19).

By making D the same thing as black (B), and eliminating W and Y
respectively from the two ordinary colour-equations by means of D, we obtain
three colour-blind equations, calculated from the ordinary equations and con-
sistent with them, supposing that the colour (D) is black to the colour-blind.

The following Table is a comparison of the colour-bhnd equations deduced
from Mr Simpson's observations alone, with those deduced from my observations
and the value of D.

Table

C.

V.

u.

G.

B.

w.

Y.

(15) Calculated

. +96

+ 4

-24

-76

By (19) . . .

. +93-9

+ 6-1

-21-7

-78-3

(U) Calculated

. -70

+ 27

+ 73

-30

By (17) and (19)

. -70

+ 27-2

-72-8

-30

(13) Calculated

. -19

+ 40

-81

+ 60

By (18) and (19)

. -13-6

+ 38-5

-86-4

+ 61-5

The average error here is 1*9, smaller than the average error of the indi-
vidual colour-blind observations, shewing that the theory of colour-blindness being
the want of a certain colour-sensation which is one of the three ordinary colour-
sensations, agrees with observation to within the limits of error.

In fig. 11, Plate VII. p. 444, I have laid down the chromatic relations of these
colours according to Newton's method. V (vermilion), U (ultramarine), and G
(emerald-green) are assumed as standard colours, and placed at the angles of
an equilateral triangle. The position of W (white) and Y (pale chrome-yellow)
with respect to these are laid down from equations (17) and (18), deduced
from my own observations. The positions of the defective colour, of white, and
of yellow, as deduced from Mr Simpson's equations alone, are given at " c7,"
"w" and "y." The positions of these points, as deduced from a combination

444 ON THE THEORY OF COMPOUND COLOURS.

»

of these equations with my o\7n, are given at "D," *'W," and "Y." The
difference of these positions from those of "c?," "w;," and "3/," shews the amount
of discrepancy between observation and theory.

It will be observed that D is situated near V (vermilion), but that a line
from D to W cuts UV at C near to V. D is therefore a red colour, not
scarlet, but further from yellow. It may be called crimson, and may be imitated
by a mixture of 86 vermiHon and 14 ultramarine. This compound colour will be
of the same hue as D ; but since C hes between D and W, C must be
regarded as D diluted with a certain amount of white ; and therefore D must
be imagined to be like C in hue, but without the intermixture of white which
is unavoidable in actual pigments, and which reduces the purity of the tint.

Lines drawn from D through "W" and "Y," the colour-blind positions of
white and yeUow, pass through W and Y, their positions in ordinary vision.
The reason why they do not coincide with W and Y, is that the white and
yeUow papers are much brighter than the colours corresponding to the points
W and Y of the triangle V, U, G; and therefore lines from D, which represent
them in intensity as well as in quality, must be longer than DW and DY in
the proportion of their brightness.

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VOL. I. PLATE VII. (II)

[Lecture at the Royal Institution of Great Britain. May 17, 1861.]

XXII. On the Theory of Three Primary Colours.

The speaker commenced by shewing that our power of vision depends
entirely on our being able to distinguish the intensity and quality of colours.
The forms of visible objects are indicated to us only by differences in colour
or brightness between them and surrounding objects. To classify and arrange
these colours, to ascertain the physical conditions on which the dijfferences of
coloured rays depend, and to trace, as far as we are able, the physiological
process by which these different rays excite in us various sensations of colour,
we must avail ourselves of the united experience of paintei-s, opticians, and
physiologists. The speaker then proceeded to state the results obtained by these
three classes of inquirers, to explain their apparent inconsistency by means of
Young's Theory of Primary Colours, and to describe the tests to which he had
subjected that theory.

Painters have studied the relations of colours, in order to imitate them by
means of pigments. As there are only a limited number of coloured substances
adapted for painting, while the number of tints in nature is infinite, painters
are obliged to produce the tints they require by mixing their pigments in
proper proportions. This leads them to regard these tints as actually com-
pounded of other colours, corresponding to the pure pigments in the mixture.
It is found, that by using three pigments only, we can produce all colours
lying within certain limits of intensity and purity. For instance, if we take
carmine (red), chrome yellow, and ultramarine (blue), we get by mixing the
carmine and the chrome, all varieties of orange, passing through scarlet to
crimson on the one side, and to yeUow on the other; by mixing chrome and
ultramarine we get all hues of green; and by mixing ultramarine with carmine,
we get all hues of purple, from violet to mauve and crimson. Now these are
all the strong colours that we ever see or can imagine : all others are like

446 ON THE THEORY OF THREE PRIMARY COLOURS.

these, only less pure in tint. Our three colours can be mixed so as to form
a neutral grey; and if this grey be mixed with any of the hues produced by
mixing two colours only, all the tints of that hue will be exhibited, from the
pure colour to neutral grey. If we could assume that the colour of a mixture
of different kinds of paint is a true mixture of the colours of the pigments,
and in the same proportion, then an analysis of colour might be made with
the same ease as a chemical analysis of a mixture of substances.

The colour of a mixture of pigments, however, is often very different from
a true mixture of the colours of the pure pigments. It is found to depend on
the size of the particles, a finely ground pigment producing more effect than
one coarsely ground. It has also been shewn by Professor Helmholtz, that when
light falls on a mixture of pigments, part of it is acted on by one pigment
only, and part of it by another ; while a third portion is acted on by both pig-
ments in succession before it is sent back to the eye. The two parts reflected
directly from the pure pigments enter the eye together, and form a true mixture
of colours ; but the third portion, which has suffered absorption from both
pigments, is often so considerable as to give its own character to the resulting
tint. This is the explanation of the green tint produced by mixing most blue
and yellow pigments.

In studying the mixture of colours, we must avoid these sources of error,
either by mixing the rays of light themselves, or by combining the impressions
of colours within the eye by the rotation of coloured papers on a disc.

White light, according to Newton, consists of a great number of different kinds
of coloured light which can be separated by a prism. Newton divided these
into seven classes, but we now recognize many thousand distinct kinds of light
in the spectrum, none of which can be shewn to be a compound of more
elementary rays. If we accept the theory that light is an undulation, then,
as there are undulations of every different period from the one end of the
spectrum to the other, there are an infinite number of possible kinds of Hght,
no one of which can be regarded as compounded of any others.

Physical optics does not lead us to any theory of three primary colours,
but leaves us in possession of an infinite number of pure rays with an infinitely
more infinite number of compound beams of Hght, each containing any propor-
tions of any number of the pure rays.

These beams of light, passing through the transparent parts of the eye, fall

ON THE THEORY OF THREE PRIMARY COLOURS. 447

on a sensitive membrane, and we become aware of various colours. We know
that the colour we see depends on the nature of the light; but the opticians
say there are an infinite number of kinds of light ; while the painters, and all
who pay attention to what they see, tell us that they can account for all
actual colours by supposing them mixtures of three primary colours.

The speaker then next drew attention to the physiological difficulties in
accounting for the perception of colour. Some have supposed that the different
kinds of light are distinguished by the time of their vibration. There are
about 447 billions of vibrations of red light in a second; and 577 billions of
vibrations of green light in the same time. It is certainly not by any mental
process of which we are conscious that we distinguish between these infini-
tesimal portions of time, and it is difficult to conceive any mechanism by which
the vibrations could be counted so that we should become conscious of the
results, especially when many rays of different periods of vibration act on the
same part of the eye at once.

Besides, all the evidence we have on the nature of nervous action goes
to prove that whatever be the nature of the agent which excites a nerve, the
sensation will differ only in being more or less acute. By acting on a nerve
in various ways, we may produce the faintest sensation or the most violent
pain ; but if the intensity of the sensation is the same, its quality must be
the same.

Now, we may perceive by our eyes a faint red light which may be made
stronger and stronger till our eyes are dazzled. We may then perform the
same experiment with a green light or a blue light. We shall thus see that
our sensation of colour may differ in other ways, besides in being stronger or
fainter. The sensation of colour, therefore, cannot be due to one nerve only.

The speaker then proceeded to state the theory of Dr Thomas Young, as
the only theory which completely reconciles these difficulties in accounting for
the perception of colour.

Young supposes that the eye is provided with three distinct sets of nervous
fibres, each set extending over the whole sensitive surface of the eye. Each
of these three systems of nerves, when excited, gives us a different sensation.
One of them, which gives us the sensation we call red, is excited most by
the red rays, but also by the orange and yellow, and slightly by the violet ;
another is acted on by the green rays, but also by the orange and yellow and
part of the blue; while the third is acted on by the blue and violet rays.

448 ON THE THEORY OF THREE PRIMARY COLOURS.

If we could excite one of these sets of nerves without acting on the
others, we should have the pure sensation corresponding to that set of nerves.
This would be truly a primary colour, whether the nerve were excited by pure
or by compound light, or even by the action of pressure or disease.

If such experiments could be made, we should be able to see the primary-
colours separately, and to describe their appearance by reference to the scale
of colours in the spectrum.

But we have no direct consciousness of the contrivances of our own bodies,
and we never feel any sensation which is not infinitely complex, so that we
can never know directly how many sensations are combined when we see a
colour. Still less can we isolate one or more sensations by artificial means, so
that in general when a ray enters the eye, though it should be one of the
pure rays of the spectrum, it may excite more than one of the three sets of
nerves, and thus produce a compound sensation.

The terms simple and compound, therefore, as applied to colour-sensation,
have by no means the same meaning as they have when appHed to a ray of
light.

The speaker then stated some of the consequences of Young's theory, and
described the tests to which he had subjected it: —

1st. There are three primary colours.

2nd. Every colour is either a primary colour, or a mixture of primary
colours.

3rd. Four colours may always be arranged in one of two ways. Either
one of them is a mixture of the other three, or a mixture of two of them

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