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of Y and Z were 27 and 37, and their positions (44) and (68) ; and that the
illumination produced by these slits was exactly equal, in my estimation as an
observer, to the constant white W.

ON THE THEORY OF COMPOUND COLOURS. 427

The position of 'the slit A" was then shifted from (24) to (28), and when
the proper adjustments were made, I found a second colour-equation of this form —
Oct. 18, J. 16 (28) + 21 (44) + 37 (68) = W (14).

Subtracting one equation from the other and remembering that the figures in
brackets are merely symbols of position, not of magnitude, we find

16(28) = 18-5 (24) + 6(44) (15),

shewing that (28) can be made up of (24) and (44), in the proportion of IS'o
to 6.

In this way, by combining each colour with two standard colours, we may
produce a white equal to the constant white. The red and yellow colours from
(20) to (32) must be combined with green and blue, the greens from (36) to (52)
with red and blue, and the blues from (56) to (80) with red and green.

The following is a specimen of an actual series of observations made in this
way by another observer (K.) : —

Table III.

Oct. 13, 1859. Observer (K.).

(X) {Y) {Z)

18|(24) + 32^(44) + 32 (68) = W*
17|(24) + 32|(44) + 63 (80) = W.

18 (24) + 32|(44) + 35 (72) = W.

19 (24) + 32 (44) + 31|(68) = W*

19 (24) + 30|(44) + 35 (64) = W.

20 (24) + 23 (44) + 39 (60) = W.

21 (24) + 14 (44) + 58 (56) = W.

22 (24) + 62 (52) + 11 (68) = W.

22 (24) + 42 (48) + 29|(68) = W.

19 (24) + 31|(44) + 33 (68) = W*.

16 (24) + 28 (40) + 32^(68) = W.
6 (24) + 27 (36) + 32^(68) = W.

23 (32)+ 11|(44) + 821(68) = W.

17 (28) + 26 (44) + 32^(68) = W.

20 (24) + 33|(44) + 32|(68) = W».
46 (20) + 33 (44) + 30 (68) = W.

The equations marked with an asterisk (*') are those which involve the
three standard colours, and since every other equation must be compared with
them, they must be often repeated.

428 ON THE THEORY OF COMPOUND COLOURS.

The following Table contains the means of' four sets of observations by the
same observer (K.) : —

Table IV. (K.)

44-3 (20) + 31 -0 (44) + 27-7 (68) = W.
16-1 (28) + 25-6 (44) + 30-6 (68) = W.
22-0 (32) + 12-1 (44) + 30-6 (68) = W.
6-4 (24) + 25-2 (36) + 31 -3 (68) = W.
15-3 (24) + 26 -0 (40) + 307 (68) = W.
19-8 (24) + 35-0 (46) + 30-2 (68) = W.
21-2 (24) + 41 -4 (48) ^ 27-0 (68) = W.
22-0 (24) + 62-0 (52) + 13-0 (68) = W.
21 -7 (24) + 10-4 (44) + 61 -7 (56) = W.
20-5 (24) + 23-7 (44) + 40-5 (60) = W.
19-7 (24) + 30-3 (44) + 33-7 (64) = W.
18-0 (24) + 31-2 (44) + 32-3 (72) = W.
17-5 (24) + 30-7 (44) + 44-0 (76) = W.
18-3 (24) + 33-2 (44) + 63-7 (80) = W.

§ VIII. Detet-mination of the Average Error in Observations of different kinds.

In order to estimate the degree of accuracy of these observations, I have
taken the differences between the values of the three standard colours as
originally observed, and their means as given by the above Table. The sum
of all the errors of the red (24) from the means, was 31 '1, and the number
of observations was 42, which gives the average error 74.

The sum of errors in green (44) was 48-0, and the number of observa-
tions 31, giving a mean error 1-55.

The sum of the errors in blue (68) was 46-9, and the number of observa-
tions 35, giving a mean error 1*16.

It appears therefore that in the observations generally, the average error
does not exceed 1*5 ; and therefore the results, if confirmed by several obser-
vations, may safely be trusted to that degree of accuracy.

The equation between the three standard colours was repeatedly observed,
in order to detect any alteration in the character of the light, or any other
change of condition which would prevent the observations from being comparable
with one another; and also because this equation is used in the reduction of

(R)= -54

(G-B)=-99
(B-R)=-85
(R-G)=-86

G + B) = 2-67

(G + B) = 2-31
(B + R) = l-59
(R + G) = l-57

VG'4.B' =

(G) = l-22

JB' + R'

(B) = M5

jR' + ii'-

(R +

sfR' + G

' + B^=l-76

ON THE THEORY OF COMPOUND COLOURS. 429

all the others, and therefore requires to be carefully observed. There are twenty
observations of this equation, the mean of which gives

18-6(24) + 31'4(44) + 30-5(68) = W* (16)

as the standard equation.

We may use the twenty observations of this equation as a means of
determining the relations between the errors in the diflferent colours, and thus
of estimating the accuracy of the observer in distinguishing colours.

The following Table gives the result of these operations, where R stands
for (24), G for (44), and B for (68):—

Table V. — Mean Errors in the Standard Equation.

1-26
1-33

The first column gives the mean difference between the observed value of
each of the colours and the mean of all the observations. The second column
shews the average error of the observed differences between the values of the
standards, from the mean value of those differences. The third column shews
the average error of the sums of two standards, from the mean of such sums.
The fourth column gives the square root of the sum of the squares of the
quantities in the first column. I have also given the average error of the
sum of R, G and B, from its mean value, and the value of ^R^ + G' + B'.

It appears from the first column that the red is more accurately observed
than the green and blue.

§ IX. Relative Accuracy in Observations of Colour and of Brightness.

If the errors in the different colours occun^ed perfectly independent of each
other, then the probable mean error in the sum or difference of any two colours
would be the square root of the sum of their squares, as given in the fourth
column. It will be seen, however, that the number in the second column is
always less, and that in the third always greater, than that in the fourth ;
shewing that the errors are not independent of each other, but that positive
errors in any colour coincide more often with positive than with negative errors

430 ON THE THEORY OF COMPOUND COLOURS.

in another colour. Now the hue of the resultant depends on the ratios of the
components, while its brightness depends on their sum. Since, therefore, the
difference of two colours is always more accurately observed than their sum,
variations of colour are more easily detected than variations in brightness, and
the eye appears to be a more accurate judge of the identity of colour of the
two parts of the field than of their equal illumiiiation. The same conclusion may
be drawn from the value of the mean error of the sum of the three standards,
which is 2-67, while the square root of the sum of the squares of the errors
is 176.

§ X. Reduction of the Observations.

By eliminating W from the equations of page 428 by means of the standard
equation, we obtain equations involving each of the fourteen selected colours of
the spectrum, along with the three standard colours; and by transposing the
selected colour to one side of the equation, we obtain its value in terms of
the three standards. If any of the terms of these equations are negative, the
equation has no physical interpretation as it stands, but by transposing the
negative term to the other side it becomes positive, and then the equation may
be verified.

The following Table contains the values of the fourteen selected tints in
terms of the standards. To avoid repetition, the symbols of the standard colours
are placed at the head of each colunm.

Table

VI.

Observer (K,).

(24.)

(44.)

(68.)

44-3(20) =

18-6

+ 0-4

+ 2-8

16-1(28) =

18-6

+ 5-8

- 01

22-0(32) =

18-6

+ 19-3

- 01

25-2(36) =

12-2

+ 31-4

- 0-8

26-0(40) =

3-3

+ 31-4

- 0-2

35-0(46) =

- 1-2

+ 31-4

+ 0-3

41-4(48) =

- 2-6

+ 31-4

+ 3-5

62-0(52) =

- 3-4

+ 31-4

+ 17-5

61-7(56) =

- 3-1

+ 21-0

+ 30-5

40-5(60) =

- 1-9

+ 7-7

+ 30-5

33-7(64) =

- 11

+ M

+ 30-5

32-3(72) =

+ 0-6

+ 0-2

+ 30-5

44-0(76) =

+ 1-1

+ 0-7

+ 30-5

63-7(80) =

+ 0-3

- 1-8

+ 30-6

ON THE THEORY OF COMPOUND COLOURS. 431

From these equations we may lay down a chart of the spectrum on Newton's
diagram by the following method : — Take any three points, A, B, C, and let A
represent the standard colour (24), B (44), and C (68). Then, to find the position
of any other colour, say (20), divide AC in P so that (18'6) ^P= (28) PC, and
then divide BP in Q so that (IS'G + 2-8) P^ = (0-4) (?P. At the point Q the
colour corresponding to (20) must be placed. In this way the diagram of fig. 4,
Plate VI., p. 444, has been constructed from the observations of all the colours.

§ XL Tlie Spectrum as laid down on Newton's Diagram.

The curve on which these points lie has this striking feature, that two
portions of it are nearly, if not quite, straight lines. One of these portions
extends from (24) to (46), and the other from (48) to (64). The colour (20)
and those beyond (64), are not far from the line joining (24) and (68). The
spectrum, therefore, as exhibited in Newton's diagram, forms two sides of a
triangle, with doubtful fi-agments of the third side. Now if three colours in
Newton's diagram lie in a straight line, the middle one is a compound of the
two others. Hence all the colours of the spectrum may be compounded of
those which lie at the angles of this triangle. These correspond to the following
colours : —

Table VII.

Scale.

Wave-length.

Index

in water.

Wave-length
in water.

R

Scarlet .

. 24

2328

1-332

1-747

G

Green . .

. 46f

1914

1-334

1-435

B

Blue . .

. 64i

1717

1-3.39

1-282

All the other colours of the spectrum may be produced by combinations of
these; and since all natural colours are compounded of the colours of the spec-
trum, they may be compounded of these three primary colours. I have strong
reason to believe that these are the three primary colours corresponding to three
modes of sensation in the organ of vision, on which the whole system of colour,
as seen by the normal eye, depends.

§ XII. Results found hy a second Observer.

"We may now consider the results of three series of observations made by
myself (J.) as observer, in order to determine the relation of one observer to

432

ON THE THEORY OF COMPOUND COLOURS.

another in the perception of colour. The standard colours are connected by the
following equation, as determined by six observations : —

18-l(24) + 27-5(44) + 37(68) = W* (17).

The average errors in these observations were —

Table VIII.

R, -28
G, -83
B, -16

G + B, -83
B + R, -42

R + G, -95

G - B, -83
B-R, -28
R-G, -72

R + G + B, -95

shewing that in this case, also, the power of distinguishing colour is more to be
depended on than that of distinguishing degrees of illumination.

The average error in the other observations from the means was '64 for red,
76 for green, and 1*02 for blue.

Table IX.

Observations by

J., October

1859.

(24.)

(44.)

(68.)

44-3(20)= 18-1

- 2-5

+ 2-3

16-0(28)= 18-1

+ 6-2

- 0-7

21-5(32)= 18-1

+ 25-2

- 0-7

19-3(36)= 8-1

+ 27-5

- 0-3

20-7(40)= 2-1

+ 27-5

- 0-5

52-3(48) = - 1-4

+ 27-5

^10-7

95-0(52) = - 2-4

+ 27-5

+ 37-0

51-7(56) = - 2-2

+ 4-8

+ 37-0

37-2(60) = - 1-2

+ 0-8

+ 370

36-7(64) = - 0-2

+ 0-8

+ 37-0

350(72) = + 0-6

- 0-2

+ 37-0

400(76) = + 0-9

+ 0-5

+ 37-0

51-0(80) = + 1-1

+ 0-5

+ 37-0

§ XIII. Comparison of Results hy Newton's Diagram.

The relations of the colours, as given by these observations, are laid down
in fig. 5, Plate VI., p. 444. It appears from this diagram, that the positions of
the colours lie nearly in a straight line from (24) to (44), and from (48) to (60).
The colours beyond (60) are crowded together, as in the other diagram, and
the observations are not yet suflaciently accurate to distinguish their relative
positions accurately. The coloiir (20) at the red end of the spectrum is further

ON THE THEORY OF COMPOUND COLOURS. 433

from tlie line joining (24) and (68) than in the other diagram, but I have not
obtained satisfactory observations of these extreme colours. It will be observed
that (32), (36), and (40) are placed further to the right in fig. 5 than in fig. 4,
shewing that the second observer (J.) sees more green in these colours than
the first (K.), also that (48), (52), (56), and (60) are much further up in fig. 5,
shewing that to the second observer they appear more blue and less green.
These differences were well seen in making an observation. When the instru-
ment was adjusted to suit the first observer (K.), then, if the selected colour
were (32), (36), or (40), the second (J.), on looking into the instrument, saw it
too green ; but if (48), (52), (56), or (60) were the selected colour, then, if right
to the first observer, it appeared too blue to the second. If the instrument
were adjusted to suit the second observer, then, in the first case, the other saw
red, and in the second green ; shewing that there was a real difference in the
eyes of these two individuals, producing constant and measurable differences in
the apparent colour of objects.

§ XIV. Comparison hy Curves of Intensity of the Primaries.

Figs. 6 and 7, Plate VI. p. 444, are intended to indicate the intensities of
the three standard colours at different points of the spectrum. The curve marked
(R) indicates the intensity of the red or (24), (G) that of green or (44), and (B)
that of blue or (68). The curve marked (S) has its ordinates equal to the
sum of the ordinates of the other three curves. The intensities are found by
dividing every colour-equation by the coefficient of the colour on the left-hand
side. Fig. 6 represents the results of observations by K., and fig. 7 represents
those of J. It will be observed that the ordinates in fig. 7 are smaller between
(48) and (56) than in fig. 6. This indicates the feeble intensity of certain kinds
of light as seen by the eyes of J., which made it impossible to get observations
of the colour (52) at all without making the slit so wide as to include all
between (48) and (56).

This blindness of my eyes to the parts of the spectrum between the fixed
lines E and F appears to be confined to the region surrounding the axis of
vision, as the field of view, when adjusted for my eyes looking directly at the
colour, is decidedly out of adjustment when I view it by indirect vision, turning
the axis of my eye towards some other point. The prism then appears greener

434 ON THE THEORY OF COMPOUND COLOURS.

and brighter than the mirror, shewing that the parts of my eye at a" distance
from the axis are more sensitive to this blue-green light than the parts close
to the axis.

It is to be noticed that this insensibility is not to all light of a green
or blue colour, but to Hght of a definite refrangibility. If I had a species of
colour-blindness rendering me totally or partially insensible to that element of
colour which most nearly corresponds with the light in question, then the light
from the mirror, as well as that from the prism, would appear to me deficient
in that colour, and I should still consider them chromatically identical ; or if
there were any difierence, it would be the same for ail colours nearly the same
in appearance, such as those just beyond the line F, which appear to me quite
bright.

We must also observe that the peculiarity is confined to a certain portion
of the retina, which is known to be of a yellow colour, and which is the seat
of several ocular phenomena observed by Purkinje and Wheatstone, and of the
sheaf or brushes seen by Haidinger in polarized light ; and also that though,
of the two observers whose results are given here, one is much more affected
with this peculiarity than the other, both are less sensible to the light between
E and F than to that on either side; and other observers, whose results are
not here given, confirm this.

§ XV. Explanation of the Differences between the two Observers.

I think, therefore, that the yellow spot at the foramen centrale of Soemmering
will be found to be the cause of this phenomenon, and that it absorbs the rays
between E and F, and would, if placed in the path of the incident light,
produce a corresponding dark band in the spectrum formed by a prism.

The reason why white light does not appear yellow in consequence, is that
this absorbing action is constant, and we reckon as white the mean of all the
colours we are accustomed to see. This may be proved by wearing spectacles
of any strong colour for some time, when we shall find that we judge white
objects to be white, in spite of the rays which enter the eye being coloured.

Now ordinary white light is a mixture of all kinds of light, including that
between E and F, which is partially absorbed. If, therefore, we compound an
artificial white containing the absorbed ray as one of its three components, it

ON THE THEORY OF COMPOUND COLOURS. 435

will be much more altered by the absorption than the ordinary light, which
contains many rays of nearly the same colour, which are not absorbed. On the
other hand, if the artificial light do not contain the absorbed ray, it will be
less altered than the ordinary light which contains it. Hence the greater the
absorption the less green will those colours appear which are near the absorbed
part, such as (48), (52), (56), and the more green will the colours appear which
are not near it, such a^ (32), (36), (40). And these are the chief differences
between fig. 4 and fig. 5.

I first observed this peculiarity of my eyes when observing the spectrum
formed by a very long vertical slit. I saw an elongated dark spot running up
and down in the blue, as if confined in a groove, and following the motion
of the eye as it moved up or down the spectrum, but refusing to pass out
of the blue into other colours. By increasing the breadth of the spectrum, the
dark portion was found to correspond to the foramen centrale, and to be visible
only when the eye is turned towards the blue-green between E and F. The
spot may be well seen by first looking at a yellow paper, and then at a blue
one, when the spot will be distinctly seen for a short time, but it soon dis-
appears when the eye gets accustomed to the blue*.

I have been the more careful in stating this peculiarity of my eyes, as I
have reason to believe that it affects most persons, especially those who can see
Haidinger's brushes easily. Such persons, in comparing their vision with that
of others, may be led to think themselves affected with partial colour-blindness,
whereas their colour-vision may be of the ordinary kind, but the rays which
reach their sense of sight may be more or less altered in their proportions by
passing through the media of the eye. . The existence of real, though partial
colour-blindness will make itself apparent, in a series of observations, by the
discrepancy between the observed values and the means being greater in certain
colours than in others.

§ XVI. General Conclusions.

Neither of the observers whose results are given here shew any indications
of colour-blindness, and when the differences arising from the absorption of the
rays between E and F are put out of account, they agree in proving that there
are three colours in the spectrum, red, green, and blue, by the mixtures of

* See the Report of tlie British Association for 1856, p. 12.

436 ON THE THEORY OF COMPOUND COLOURS.

which colours chromatically identical with the other colours of the spectrum
may be produced. The exact position of the red and blue is not yet ascer-
tained; that of the green is ^ from E towards F.

The orange and yellow of the spectrum are chromatically equivalent to
mixtures of red and green. They are neither richer nor paler than the corre-
sponding mixtures, and the only difference is that the mixture may be resolved
by a prism, whereas the colour in the spectrum cannot be so resolved. This
result seems to put an end to the pretension of yellow to be considered a
primary element of colour.

In the same way the colours from the primary green to blue are chro-
matically identical with mixtures of these ; and the extreme ends of the spectrum
are probably equivalent to mixtures of red and blue, but they are so feeble
in illumination that experiments on the same plan with the rest can give no
result, but they must be examined by some special method. When observations
have been obtained from a greater number of individuals, including those whose
vision is dichromatic, the chart of the spectrum may be laid down independently
of accidental differences, and a more complete discussion of the laws of the
sensation of colour attempted.

POSTSCRIPT.

[Keceived May 8,— Read May 24, I860.]

Since sending the above paper to the Royal Society, I have obtained
some observations of the colour of the spectrum by persons whose vision is
"dichromic," and who are therefore said to be " colour-bhnd."

The instrument used in making these observations was similar in principle
to that formerly described, except that, in order to render it portable, the rays
are reflected back through the prisms, nearly in their original direction ; thus
rendering one of the limbs of the instrument unnecessary, and allowing the
other to be shortened considerably on account of the greater angular dispersion.
The principle of reflecting light, so as to pass twice through the same prism,
was employed by me in an instrument for combining colours made in 1856,
and a reflecting instrument for observing the spectrum has been constructed
independently by M. Porro.

ON THE THEORY OF COMPOUND COLOURS. 437

Light from a sheet of paper illuminated by sunlight is admitted at the slits
X, Y, Z (fig. 8, Plate VIL p. 444), falls on the prisms P and F (angles = 45"),
then on a concave silvered glass, S, radius 34 inches. The light, after reflexion,
passes again through the prisms R and P, and is reflected by a small mirror,
e, to the slit E, where the eye is placed to receive the light compounded of
the colours corresponding to the positions and breadths of the slits X, Y, and Z.

At the same time, another portion of the light from the illuminated paper
enters the instrument at BC, is reflected at the mirror M, passes through the
lens L, is reflected at the mirror M', passes close to the edge of the prism P,
and is reflected along with the coloured light at e, to the eye-slit at E.

In this way the compound colour is compared with a constant white light
in optical juxtaposition with it. The mirror M is made of silvered glass, that
at M' is made of glass roughened and blackened at the back, to reduce the
intensity of the constant light to a convenient value for the experiments.

This instrument gives a spectrum in which the lines are very distinct,
and the length of the spectrum from A to H is, 3-6 mches. The outside
measure of the box is 3 feet 6 inches, by 11 inches by 4 inches, and it can
be carried about, and set up in any position, without readjustment. It was
made by Messrs Smith and Ramage of Aberdeen.

In obtaining observations from colour-blind persons, two sHts only are
required to produce a mixture chromatically equivalent to white; and at one
point of the spectrum the colour of the pure rays appears identical with white.
This point is near the line F, a little on the less refrangible side. From this
point to the more refrangible end of the spectrum appears to them "blue."
The colours on the less refrangible side appear to them all of the same quahty,
but of different degrees of brightness; and when any of them are made
sufficiently bright, they are called "yellow." It is convenient to use the term
"yellow" in speaking of the colours from red to green inclusive, since it will
be found that a dichromic person in speaking of red, green, orange, and brown,
refers to different degrees of brightness or purity of a single colour, and not
to different colours perceived by him. This colour we may agree to call
"yellow," though it is not probable that the sensation of it is like that of
yellow as perceived by us.

Of the three standard colours which I formerly assumed, the red appears
to them "yellow," but so feeble that there is not enough in the whole red
division of the spectrum to form an equivalent to make up the standard white.

438 ON THE THEORY OF COMPOUND COLOURS.

The green at E appears a good "yellow," and the blue at f from F towards
G appears a good "blue." I have therefore taken these as standard colours for

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