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I had intended to describe some experiments on the propriety of the method
of mixino- colours by rotation, which might serve as an extension of Mr Swan's
experiments on instantaneous impressions on the eye. These, together with the
explanation of some phenomena which seem to be at variance with the theory of
vision here adopted, must be deferred for the present. On some future occasion,
I hope to be able to connect these simple experiments on the colours of pigments
with others in which the pure hues of the spectrum are used. I have already
constructed a model of apparatus for this purpose, and the results obtained are
sufficiently remarkable to encourage perseverance.

Note I.
On different Methods of Exhibiting the Mixtures of Colours.

(1) Mechanical Mixture of Coloured Powders.
By grinding coloured powders together, the differently- coloured particles may
be so intermingled that the eye cannot distinguish the colours of the separate
powders, but receives the impression of a uniform tint, depending on the nature
and proportions of the pigments used. In this way, Newton mixed the powders
of orpiment, purple, bise, and viride ceris, so as to form a gray, which, in sun-
light, resembled white paper in the shade. (Newton's Opticks, Book i. Part n.,
Exp. XV.) This method of mixture, besides being adopted by all painters, has
been employed by optical writers as a means of obtaining numerical results.
The specimens of such mixtures given by B. R. Hay in his works on Colour,
and the experiments of Professor J. D. Forbes on the same subject, shew the
importance of the method as a means of classifying colours. There are two
objections, however, to this method of exhibiting colours to the eye. When
two powders of unequal fineness are mixed, the particles of the finer powder
cover over those of the coarser, so as to produce more than their due effect
in influencing the resultant tint. For instance, a small quantity of lamp-black.


mixed with a large quantity of chalk, will produce a mixture which is nearly
black. Although the powders generally used are not so different in this respect
as lamp-black and chalk, the results of mixing given weights of any coloured
powders must be greatly modified by the mode in which these powders have
been prepared.

Again, the light which reaches the eye from the surface of the mixed pow-
ders consists partly of light which has fallen on one of the substances mixed
without being modified by the other, and partly of light which, by repeated
reflection or transmission, has been acted on by both substances. The colour of
these rays will not be a mixture of those of the substances, but will be the
result of the absorption due to both substances successively. Thus, a mixture of
yellow and blue produces a neutral tint tending towards red, but the remainder
of white light, after passing through both, is green; and this green is generally
sufficiently powerful to overpower the reddish gray due to the separate colours
of the substances mixed. This curious result has been ably investigated by
Professor Helmholtz of Konigsberg, in his Memoir on the Theory of Compound
Colours, a translation of which may be found in the Annals of Philosophy for
1852, Part 2.

(2) Mixture of differently-coloured Beams of Light by Superposition

on an Opaque Screen.
When we can obtain light of sufficient intensity, this method produces the
most beautiful results. The best series of experiments of this kind are to be
found in Newton's Opticks, Book i. Part ii. The different arrangements for
mixing the rays of the spectrum on a screen, as described by Newton, form
a very complete system of combinations of lenses and prisms, by which almost
every possible modification of coloured light may be produced. The principal
objections to the use of this method are— (1) The difficulty of obtaining a con-
stant supply of uniformly intense light; (2) The uncertainty of the effect of
the position of the screen with respect to the incident beams and the eye of
the observer; (3) The possible change in the colour of the incident light due
to the fluorescence of the substance of the screen. Professor Stokes haa found
that many substances, when illuminated by homogeneous light of one refrangi-
bility, become themselves luminous, so as to emit light of lower refrangibility.
This phenomenon must be carefully attended to when screens are used to exhibit


(3) Union of Coloured Beams hy a Piism so as to form one Beam.

The mode of viewing the beam of light directly, without first throwing it
on a screen, was not much used by the older experimenters, but it possesses
the advantage of saving much light, and admits of examining the rays before
they have been stopped in any way. In Newton's 11th proposition of the 2nd
Book, an experiment is described, in which a beam is analysed by a prism,
concentrated by a lens, and recombined by another prism, so as to form a beam
of white light similar to the incident beam. By stopping the coloured rays at
the lens, any proposed combination may be made to pass into the emergent
beam, where it may be received directly by the eye, or on a screen, at pleasure.

The experiments of Helmholtz on the colours of the spectrum were made
with the ordinary apparatus for directly viewing the pure spectrum, two oblique
slits crossing one another being employed to admit the light instead of one
vertical sht. Two pure spectra were then seen crossing each other, and so
exhibiting at once a large number of combinations. The proportions of these
combinations were altered by varying the inclination of the slits to the plane of
lefraction, and in this way a number of very remarkable results were obtained, —
for which see his Memoir, before referred to.

In experiments of the same kind made by myself in August 1852 (inde-
pendently of M. Helmholtz), I used a combination of three moveable vertical
slits to admit the light, instead of two cross shts, and observed the compound
ray through a slit made in a screen on which the pure spectrum is formed.
In this way a considerable field of view was filled with the mixed light, and
might be compared with another part of the field illuminated by light proceeding
from a second system of slits, placed below the first set. The general character
of the results agreed with those of M. Helmholtz. The chief difficulties seemed
to arise from the defects of the optical apparatus of my own eye, which ren-
dered apparent the compound nature of the light, by analysing it as a prism
or an ordinary lens would do, whenever the lights mixed differed much in


(4) Union of two beams by means of a transparent surface, which reflects
the first and transmits the second.

The simplest experiment of this kind is described by M. Helmholtz. He
places two coloured wafers on a table, and then, taking a piece of transparent
glass, he places it between them, so that the reflected image of one apparently
coincides with the other as seen through the glaas. The colours are thus mixed,
and, by varying the angle of reflection, the relative intensities of the reflected
and transmitted beams may be varied at pleasure.

In an instrument constructed by myself for photometrical purposes two re-
flecting plates were used. They were placed in a square tube, so as to polarize
the incident light, which entered through holes in the sides of the tubes, and
was reflected in the direction of the axis. In this way two beams oppositely
polarized were mixed, either of which could be coloured in any way by coloured
glasses placed over the holes in the tube. By means of a Nicol's prism placed
at the end of the tube, the relative intensities of the two colours as they
entered the eye could be altered at pleasure.

(5) Union of two coloured beams by means of a doubly -refracting Prism.

I am not aware that this method has been tried, although the opposite
polarization of the emergent rays is favourable to the variation of the experiment.

(6) Successive presentation of the different Colours to the Retina.

It has long been known, that light does not produce its full effect on the
eye at once, and that the effect, when produced, remains visible for some time
after the light has ceased to act. In the case of the rotating disc, the various
colours become indistinguishable, and the disc appears of a imiform tint, which
is in some sense the resultant of the colours so blended. This method of com-
bining colours has been used since the time of Newton, to exhibit the results
of theory. The experiments of Professor J. D. Forbes, which I witnessed in
1849, first encouraged me to think that the laws of this kind of mixture might
be discovered by special experiments. After repeating the well-known experiment
in which a series of colours representing those of the spectrum are combined

VOL. I. ^^


to form gray, Professor Forbes endeavoured to form a neutral tint, by the
combination of three colours only. For this purpose, he combined the three
so-called primary colours, red, blue, and yellow, but the resulting tint could
not be rendered neutral by any combination of these colours ; and the reason
was found to be, that blue and yellow do not make green, but a pinkish tint,
when neither prevails in the combination. It was plain, that no addition of
red to this, could produce a neutral tint.

This result of mixing blue and yellow was, I beUeve, not previously known.
It directly contradicted the received theory of colours, and seemed to be at
variance with the fact, that the same blue and yellow paint, when ground
together, do make green. Several experiments were proposed by Professor Forbes,
in order to eliminate the effect of motion, but he was not then able to under-
take them. One of these consisted in viewing alternate stripes of blue and
yellow, with a telescope out of focus. I have tried this, and find the resultant
tint pink as before*. I also found that the beams of light coloured by trans-
mission through blue and yellow glasses appeared pink, when mixed on a screen,
while a beam of light, after passing through both glasses, appeared green. By
the help of the theory of absorption, given by Herschelf, I made out the
complete explanation of this phenomenon. Those of pigments were, I think, first
explained by Helmholtz in the manner above referred to J.

It may still be asked, whether the effect of successive presentation to the
eye is identical with that of simultaneous presentation, for if there is any action
of the one kind of light on the other, it can take place only in the case of
vsimultaneous presentation. An experiment tending to settle this point is recorded
by Newton (Book i. Part ii., Exp. 10). He used a comb with large teeth to
intercept various rays of the spectrum. When it was moved slowly, the various
colours could be perceived, but when the speed was increased the result was
perfect whiteness. For another form of this experiment, see Newton's Sixth
Letter to Oldenburg (Horsley's Edition, Vol. iv., page 335).

In order more fully to satisfy myself on this subject, I took a disc in
which were cut a number of sUts, so as to divide it into spokes. In a plane,
net-rly passing through the axis of this disc, I placed a blue glass, so that one

* See however Encyc. Metropolitana, Art. "Light," section 502. t lb. sect. 516.

X I have lately seen a passage in Moigno's Cosmos, stating that M. Plateau, in 1819, had obtained
jjray by whirling together gamboge and Prussian blue. Correspondance Math, et Phys. de M. Quet«let,
Vol. v., p. 221.


half of the disc might be seen by transmitted light — blue, and the other by
reflected light — white. In the course of the reflected light I placed a yellow
glass, and in this way I had two nearly coincident images of the slits, one
yellow and one blue. By turning the disc slowly, I observed that in some
parts the yellow slits and the blue slits appeared to pass over the field alter-
nately, while in others they appeared superimposed, so as to produce alternately
their mixture, which was pale pink, and complete darkness. As long as the
disc moved slowly I could perceive this, but when the speed became great, the
whole field appeared uniformly coloured pink, so that those parts in which the
colours were seen successively were indistinguishable from those in which they
were presented together to the eye.

Another form in which the experiment may be tried requires only the
colour-top above described. The disc should be covered with alternate sectors
of any two colours, say red and green, disposed alternately in four quadrants.
By placing a piece of glass above the top, in the plane of the axis, we make
the image of one half seen by reflection coincide with that of the other seen
by transmission. It wiU then be seen that, in the diameters of the top which
are parallel and perpendicular to the plane of reflection, the transmitted green
coincides with the reflected green, and the transmitted red with the reflected
red, so that the result is always either pure red or pure green. But in the
diameters intermediate to these, the transmitted red coincides with the reflected
green, and vice versa, so that the pure colours are never seen, but only their
mixtures. As long as the top is spun slowly, these parts of the disc will
appear more steady in colour than those in which the greatest alternations
take place ; but when the speed is sufficiently increased, the disc appears per-
fectly uniform in colour. From these experiments it appears, that the apparent
mixture of colours is not due to a mechanical superposition of vibrations, or
to any mutual action of the mixed rays, but to some cause residing in the
constitution of the apparatus of vision.

(7) Presentation of the Colours to he mixed one to each Eye.

This method is said not to succeed with some people ; but I have always
found that the mixture of colours was perfect, although it was difficult to con-
ceive the objects seen by the two eyes as identical. In using the spectacles,



of which one eye is green and the other red, I have found, when looking at
an arrangement of green and red papers, that some looked metallic and others
transparent. This arises from the very different relations of brightness of the
two colours as seen by each eye through the spectacles, which suggests the false
conclusion, that these differences are the result of reflection from a polished
surface, or of light transmitted through a clear one.

Note IT.

Results of Experiments with Mr Hay's Papers at Cambridge, November, 1854.

The mean of ten observations made by six observers gave

•449 E+-299 G + -252 B=-224 W+776 Bk (l).

■696 R+-304 G = '181 B + -327 Y + '492 Bk (2).

These two equations served to determine the positions of white and yellow
in diagram No. 2. The coeflScient of W is 4*447, and that of yellow 2'506.

From these data we may deduce three other equations, either by calcu-
lation, or by measurement on the diagram (No. 2).

Eliminating green from the equations, we find

•565 B + -435 Y = -307 E. + -304 W + -389 Bk (3).

The mean of three observations by three different observers gives

•573 B-f477 Y = ^313 E + ^297 W + -390Bk.
Errors of calculation - '008 B + ^008 Y - '006 K + ^007 W - •OOl Bk.

The point on the diagram to which this equation corresponds is the intersec-
tion of the lines BY and RW, and the resultant tint is a pinkish-gray.

Eliminating red from the equations, we obtain
Calculation "533 B-fl50 G-f317 Y = ^337 W-f -663 Bk"

By 10 observations -537 B-l- '146 G-h ^317 Y= -337 W-f '663 Bk ■ (4).

Errors -'004 -f- -004 — — —

Eliminating blue •660 R-f340 G = -218 Y + -108 W-f '682 Bkl

By 5 observations ^672 R-f '328 G = "224 Y+ '094 W-f672 Bk i (5).

Errors -'012 -f012 -•006 -f014 -f008 I


Note III.

On the Tlicory of Compound Colours.

Newton's theorem on the mixture of colours is to be found in his Opticks,
Book I., Part ii., Prop. vi.

In a mixtiu'e of primary colours^ the quantity and quality of each being
gicen, to know the colour of the compound.

He divides the circumference of a circle into parts proportional to the seven
musical intervals, in accordance with his opinion of the divisions of the spectrum.
He then conceives the colours of the spectrum arranged round the circle, and at
the centre of gravity of each of the seven arcs he places a little circle, the
area of which represents the number of rays of the corresponding colour which
enter into the given mixture. He takes the centre of gravity of all these circles
to represent the colour formed by the mixture. The hue is determined by
drawing a line through the centre of the circle and this point to the circum-
ference. The position of this line points out the colour of the spectrum which
the mixture most resembles, and the distance of the resultant tint from the
centre determines the fulness of its colour.

Newton, by this construction (for which he gives no reasons), plainly shews
that he considered it possible to find a place within his circle for every possible
colour, and that the entire nature of any compound colour may be known from
its place in the circle. It will be seen that the same colour may be compounded
from the colours of the spectrum in an infinite variety of ways. The apparent
identity of all these mixtures, which are optically different, as may be shewn by
the prism, implies some law of vision not explicitly stated by Newton. This
law, if Newton's method be true, must be that which I have endeavoured to
establish, namely, the threefold nature of sensible colour.

With respect to Newton's construction, we now know that the proportions
of the colours of the spectrum vary with the nature of the refracting medium.
The only absolute index of the kind of light is the time of its vibration. The
length of its vibration depends on the medium in which it is ; and if any pro-
portions are to be sought among the wave-lengths of the colours, they must
be determined for those tissues of the eye in which their physical effects are


supposed to terminate. It may be remarked, *that the apparent colour of the
spectrum changes most rapidly at three points, which lie respectively in the
yellow, between blue and green, and between violet and blue. The wave-lengths
of the corresponding rays in 'water are in the proportions of three geometric
means between 1 and 2 very nearly. This result, however, is not to be con-
sidered established, unless confirmed by better observations than mine.

The only safe method of completing Newton's construction is by an exami-
nation of the colours of the spectrum and their mixtures, and subsequent
calculation by the method used in the experiments with coloured papers. In
this way I hope to determine the relative positions in the colour-diagram of
every ray of the spectrum, and its relative intensity in the solar light. The
spectrum will then form a curve not necessarily circular or even re-entrant, and
its peculiarities so ascertained may form the foundation of a more complete
theory of the colour-sensation.

On the relation of the pure rays of the Spectrum to the three assumed Elementary


If we place the three elementary colour-sensations (which we may call, after
Young, red, green, and violet) at the angles of a triangle, all colours which
the eye can possibly perceive (whether by the action of light, or by pressure,
disease, or imagination) must be somewhere within this triangle, those which lie
farthest from the centre being the fullest and purest colours. Hence the colours
which lie at the middle of the sides are the purest of their kind which the
eye can see, although not so pure as the elementary sensations.

It is natural to suppose that the pure red, green, and violet rays of the
spectrum produce the sensations which bear their names in the highest purity.
But from this supposition it would follow that the yellow, composed of the red
and green of the spectrum, would be the most intense yellow possible, while
it is the result of experiment, that the yellow of the spectrum itself is much
more full in colour. Hence the sensations produced by the pure red and green
rays of the spectrum are not the pure sensations of our theory. Newton has
remarked, that no two colours of the spectrum produce, when mixed, a colour
equal in fulness to the intermediate colour. The colours of the spectrum are
all more intense than any compound ones. Purple is the only colour which


must be produced by combination. The experiments of Helmholtz lead to the
same conclusion ; and hence it would appear that we can find no part of the
spectrum which produces a pure sensation.

An additional, though less satisfactory evidence of this, is supplied by the
observation of the colours of the spectrum when excessively bright. They then
appear to lose their peculiar colour, and to merge into pure whiteness. This
is probably due to the want of capacity of the organ to take in so strong an
impression ; one sensation becomes first saturated, and the other two speedily
follow it, the final efiect being simple brightness.

From these facte I would conclude, that every ray of the spectrum is capable
of producing all three pure sensations, though in different degrees. The curve,
therefore, which we have supposed to represent the spectrum will be quite within
the triangle of colour. All natural or artificial colours, being compounded of
the colours of the spectrum, must lie within this curve, and, therefore, the colours
corresponding to those parts of the triangle beyond this curve must be for ever
unknown to us. The determination of the exact nature of the pure sensations,
or of their relation to ordinary colours, is therefore impossible, unless we can
prevent them from interfering with each other as they do. It may be possible
to experience sensations more pure than those directly produced by the spec-
trum, by first exhausting the sensibility to one colour by protracted gazing, and
then suddenly turning to its opposite. But if, as I suspect, colour-blindness be
due to the absence of one of these sensations, then the point D in diagram (2),
which indicates their absent sensation, indicates also our pure sensation, which
we may call red, but which we can never experience, because all kinds of
light excite the other sensations.

Newton has stated one objection to his theory, as follows: — "Also, if only
two of the pnmanj colours, which in tJw circle are opposite to one another, be
mixed in an equal proportion, the point Z" (the resultant tint) "shall fall upon
the centre " (neutral tint) ; " and yet the colour compounded of these two shcdl
not he p>erfectly white, hut some faint anonymous colour. For I could never yet, by
mixing only two primary colours, produce a perfect ivhite" This is confirmed by
the experiments of Helmholtz ; who, however, has succeeded better with some
pairs of colours than with others.

In. my experiments on the spectrum, I came to the same result ; but It
appeared to me that the very peculiar appearance of the neutral tints produced


was owing to some opticjal effect taking place in the transparent part of the
eye on the mixture of two rays of very different refrangibility. Most eyes are
by no means achromatic, so that the images of objects illuminated with mixed
light of this kind appear divided into two different colours; and even when
there is no distinct object, the mixtures become in some degree analysed, so as
to present a very strange, and certainly "anonymous" appearance.

Additional Note on the more recent experiments of M. Helmholtz*.

In his former memoir on the Theory of Compound Colours f, M. Helmholtz
arrived at the conclusion that only one pair of homogeneous colours, orange-
yellow and indigo-blue, were strictly complementary. This result was shewn by
Professor Grassmann| to be at variance with Newton's theory of compound
colours ; and although the reasoning was founded on intuitive rather than
experimental truths, it pointed out the tests by which Newton's theory must
be verified or overthrown. In applying these tests, M. Helmholtz made use of

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