The large numbers marked with an asterisk were obtained by placing the rotating sectors in front of the white reflected beam.

The light of D had to be reduced to 14 before it was extinguished; therefore to extinguish the original light of this colour in the spectrum would require 180/14, or 129 times the intensity of the white light of the reflected beam. With the E light it would take 180/22, or 82 times the white light to extinguish it, and so on. If we tabulate the results in this manner, and take the white light necessary to extinguish the D light empirically as 985, which is its percentage luminosity in the spectrum of the electric light, we can then compare the extinguishing factor with the luminosity in each case.

+------------+-------------------------------------------+ | | | White required| | | |White required| to extinguish | Luminosity | | Colour. | to Extinguish| the Spectrum, | of | | | the Spectrum.|with 50 as That| Spectrum. | | | | required at E.| | |------------+--------------+---------------+------------+ |near line B | 6 | 39 | 49 | | C | 32 | 195 | 206 | | D | 129 | 78 | 985 | | E | 82 | 50 | 50 | | F | 12 | 75 | 75 | | G | 087 | 56 | 6 | +--------------------------------------------------------+

The very close resemblance between the last two columns indicates that the same luminosity of white light is necessary to extinguish the same luminosity of most colours, within the limits of observation that is to say. Indeed the method of extinction was a plan which Draper and Vierordt essayed, but the results, tabulated from experiments made by them with the apparatus they employed, give a curve of intensity very unlike that given in Chapter VII. In these experiments the luminosity of the orange light corresponding to the D line coming through the slit was measured, and it was found to be 375/180 of the white light. Now according to the last table but one 14/180 of this light was extinguished by the full white light, consequently 375/180 14/180, or 1/62 of the orange light was extinguished by the white light. In other words, if white light be sixty-two times brighter than the orange light, the colour of the latter when the two are mixed will be invisible. The extinction of all colours requires somewhat more light than this, and a calculation shows that the extinction of every colour is effected by white light, which is seventy-five times brighter than the colour. Artists are well aware that a pale wash of a pigment may be washed over drawing paper, and when dry is invisible to the eye. The above experiments fully account for it.

The other experiment which was to be tried was to see how much white light could be extinguished by a colour. There are several ways by which this can be effected. For instance we may superpose a white dot on the colour patch by placing a card, in which a circular hole is cut, in the reflected beam near the prism, from which the reflection takes place; or by putting a black circular disc of small dimensions pasted on a gla.s.s in the same position, by which means the white light is superposed over the whole of the colour patch, with the exception of what, when the colour is cut off, is a black spot; or again by placing a rod to shade half the patch from the white light, but leaving the whole of it exposed to the coloured beam. All these methods have been tried, and it appears that the size of the piece of the patch over which the white light is thrown may have some effect on the resulting curve, but of one thing there is evidence, viz. that a great deal more white light can be mixed unperceived with orange light, than can be with the green, blue, or violet. From one experiment it was found that 1/36 part of white light of the same luminosity as the orange could be mixed with the orange and not be perceived; but that with the green light at E 1/90 would just be visible, whilst at F in the blue-green the 1/120 could be distinguished.

Looking at these results, and applying them in elucidating the experiments in which it was attempted, but without success, to match the intermediate colours between violet and green (of which the light at F is a case in point), by mixing them together, unless white light were added to the simple colour; and the success of the other experiment, in which orange light could be obtained of the same hue as that at D by a mixture of the red and green, it will be noticed that 33 times more white light can be added to the orange than to the green light at F, without its perception. The white light produced by the mixture in the first case might well show when mixed with the green, but might pa.s.s wholly unperceived when mixed with the orange.

CHAPTER XI.

Primary Colours--Molecular Swings--Colour Sensations--Sensations absent in the Colour-blind.

For some purposes it is advantageous to show experiments before indicating the deductions from them which may lead to a theory. Those described in Chapter IX. will enable us to treat the theory of colour perception from a standpoint of some advantage. How is it that the combination of three colours suffices to form white, or to match any colours we wish, be they spectrum colours to which a little white is added, or the colours of pigments? The most plausible theory that can be advanced is that it is only necessary for the eye to be furnished with a three-colour-perceiving apparatus to give the impression of every colour, and yet this would be somewhat difficult to believe had we not had the experiments narrated in that chapter before us. We should have almost expected some machinery in the eye to exist, which would answer to the rhythmic swing of the rays of every wave-length which together make up white light. But now we have to stand face to face with the results of experiment, and we find that at the most only three colours are necessary to make up white light, and that from these three spectrum colours we can form any others, with the limitation already mentioned, when some simple colours are in question.

We must here digress for a moment, and notice the fact that from our experiments we have derived the three primary colours as they are called, viz. red, violet, and green; the definition of a primary colour being that it cannot be formed by the mixture of any other colours. We have ascertained that yellow and blue make white. It is therefore evident that blue, yellow, and red cannot be primary colours, since two of them form white; and we have moreover shown that yellow can be made from green and red; hence it might be fair to a.s.sume that the three primary colours are red, green, and blue. But blue, when mixed with a very small percentage of white light, can be made by green and violet.

Hence, in the white light formed by the two colours yellow and blue, we have the first made by green and red, and the second by green and violet; hence the three colours which really make the white light are red, green, and violet. The approximate positions of these three colours in the spectrum are those already indicated; though, as we shall presently see, it is highly improbable that any person whose eyes are what are called normal, has ever experienced the fundamental green sensation.

The fact that red, yellow, and blue cannot be primary colours has been mentioned, as even now it is sometimes taught that they are so. As long as the theory of colour princ.i.p.ally lay with artists there was reasonable ground for their a.s.sumption, since they worked with impure colours, viz. those of pigments; and as we shall see later on the truth of the a.s.sumption agreed with such experiments as they would make. When, however, the question was taken up by the physicist with more exact methods of experimenting, and with pure colours, the falsity of the old triad was soon capable of proof.

To return from our digression: how it is that three mixed colours can give the sensation of white light is at first sight hard to understand; but a reference to the action of light on a photographic salt helps us in some degree. In the case of a sensitive salt, such as the bromo-iodide of silver, we find that a chemical decomposition is caused by the violet end of the spectrum, and is only feebly affected by any other part, though with prolonged exposure even the red will cause it.

The annexed figure (Fig. 33) gives the idea of the relative action of different parts of this violet portion.

Fig. 33.--Curve of Sensitiveness of Silver Bromo-iodide.

The height of the curve shows the relative effects produced. Now this curve is not symmetrical, but has a maximum effect nearer to the violet end of the spectrum than to the red. The atomic composition of the silver bromo-iodide is probably two atoms of silver and one of bromine and one of iodine oscillating together, and we can conceive of some one atom, the period of whose swings in its molecule is isochronous with some wave-length of light. Further, we can conceive that, like a pendulum whose vibrations are increased in magnitude by well-timed blows, the swing of the atom is also increased, and that eventually it gets beyond the sphere of the attraction of its parent molecule, leaves it, and is attracted to some neighbouring molecule of different const.i.tution, and that thus a chemical change is induced. This we can conceive, but how can other waves, which are not isochronous with the rhythmic swing of the atoms, alter the composition of the molecule? If we have an impulse given to a pendulum exactly timed with the period of oscillation, there is no doubt that the swing is increased. If we have one nearly in accord, it will be found that though the swings are not increased in amplitude so greatly as when there is perfect accord, yet an increased swing is given, and as exact accord is removed further and further, so the increase in the swing of the pendulum gets smaller and smaller. In somewhat the same manner it is possible that many series of waves, differing in wave-length, and therefore in periods of oscillation, may be capable of increasing the amplitude of a swing, and with the photographic salt this probably occurs, with the result which we see in the above figure. Suppose in the eye we have three such sensitive pendulums which are capable of responding to the beats of waves of light, it requires no great imagination to see that one such pendulum will respond not only to that wave of light which is isochronous with it, but also with waves shorter and longer than that particular wave. The same pendulum indeed may respond to the whole of the visible spectrum, but when far off from the maximum the response would be very small indeed. We may therefore a.s.sume that though each pendulum may have its maximum increase of oscillation at one part of the spectrum, yet at other parts not only it alone answers to the beating of the waves, but that the other pendulums are also affected by the same, and thus the whole spectrum is recognized by the swings more or less long, of either one, two, or of all three.

To Thomas Young is usually attributed the three-colour theory, though it seems to have been promulgated in an incomplete state some time before; Clark-Maxwell and Helmholtz revived it in later years, and it is usually known as the Young-Helmholtz theory. It should be remarked that the three fundamental colour sensations are not of necessity the same sensations as are given by the three primary colours, as we shall see further on. The following figure (Fig. 34) is taken from Helmholtz's physiological optics, as diagrammatic of the three sensations.

Fig. 34.--Curves of Colour Sensations.

To this diagram there is an objection, in one respect, viz. that it gives the same luminosity-value to the blue of the spectrum as it does to the red and green. It has been seen that if we call the luminosity of the yellow 100, that of the blue is about 5. The objection does not hold if it is remembered that the three maxima of impressions are taken as equal. If the ordinates were increased, so that the maxima were of the same height as that of the photographic curve, the resemblance between them and this last would be very marked. It will be noticed that each of the three colour sensations is not only excited by a limited portion of the spectrum, but by all of it, the height of the curves being a measure of their response.

Now a.s.suming that this is the case, since a certain degree of stimulation given simultaneously to the three sensations causes an integral sensation of white light, it follows that the colour perceived in every part of the spectrum is due to the excess of stimulation of either one or two of the fundamental sensations, together with the sensation of white light. If this diagram were correct, at no point in the spectrum is one fundamental sensation excited alone, but we believe that the diagram obtained by Knig (Fig. 35), from colour equations (which will be explained in our next chapter), is more exact, and that it is probable that in the extreme violet and extreme red of the spectrum the only sensations which are stimulated are the violet and red respectively. Our measures in the red and violet of the spectrum make it appear that each of the two sensations can be perceived unaccompanied by any others, and the fact that the red colour blind person perceives a shortened spectrum in the red end, is a further proof of this deduction, so far as the red is concerned.

The colour which the fundamental green sensation excites in the normal eye has probably never been seen, nor can be seen. This is due to the fact that all three sensations overlap in the green; that is, that the pendulum which answers to the green colour in the spectrum also affects, but with much less energy, the other two pendulums, which respond to the red and violet sensations.

The word pendulum has been used advisedly, for it may equally as well apply to a molecular aggregation as to one which is visible and measurable. Without entering into the physiological structure of the eye, we may say that it has usually been a.s.sumed that the pendulums are the ends of nerves which vibrate with the waves of light; but this seems rather doubtful. Gross matter, such as these ends are, compared with the molecules of which they are built up, cannot, as a rule, vibrate with waves of light, and there seems to be no reason why there should be an exception in the case of the eye. It seems much more probable that a chemical decomposition takes place in some substance attached to them, and where such decomposition takes place electricity of some kind must be produced. In other sensations of the body the nerves act as telegraph wires, carrying messages to the brain, and it is not improbable that the nerves of the eye are employed in somewhat the same manner. Professor Dewar has shown that when light acts on an extirpated eye, a current of electricity does traverse the nerves, and of such an amount that it can be shown to a large audience. This experiment is not, however, conclusive, as the effect may be mistaken for the cause. This idea, however, is only hypothetical, as is indeed the hypothesis of the mechanical action of light on the gross matter of which the rods and cones attached to the retina are composed.

We have in a previous chapter stated that there are some eyes in which the sensation of some colour is altogether absent, and in others in which it is more or less deficient. Thus some eyes appear to be lacking wholly in the sensation of red, others of green, and some very few of violet; and there have been cases known in which two sensations, the red and violet, have been totally absent. In the first case, where the sensation of red is entirely absent, what is known to the normal-eyed as white can be matched with a mixture of blue and green, and there is a place in the spectrum that is recognized as white. Similarly white can be matched by a green blind person with a mixture of red and blue.

To those who may be curious to see the colour which red and green blind persons would call white, a very simple means is at hand to demonstrate it. Using the colour patch apparatus with the three slits inserted in the slide, and in the positions we have indicated in the violet, green, and red, and forming white light for ourselves on the screen, if we cover up the red slit entirely we shall have a patch of sea-green colour, which a red blind person would call white; and if we cover the green slit, uncovering of course the red, we shall have a brilliant purple, which to a green blind person would be white. They both would call white what the normal-eyed person sees as white, for the simple reason that either the red or the green mixed with the remaining colours would be unperceived. The examination of colour-blind people is of prime importance for testing any theory of colour vision. For instance, if it were a.s.serted that the fundamental sensations did not overlap as shown in the diagram above, then it would follow that at some place in the spectrum there would be a dark point. If they do overlap, it must follow that both for the red and for the green colour blind person there must be some place in the spectrum where what is white light to them is produced.

Colour-blind people were tested with the colour apparatus. The reflected beam and the colour patch were made to cast shadows as before, and the rotating sectors placed in the path of the former. A slide with one slit was pa.s.sed across the spectrum, and the position noted where it was said that the two shadows were illuminated with white light; to the normal-eyed person one shadow of course appeared illuminated with the sea-green colour, or bluish green, according as the observer was red or green colour blind. The ray in the spectrum which to the red colour blind is white, has a wave-length of about 4900, and that for the green colour blind a wave-length of 5020, which corresponds to the position in which we usually place the green slit when a normal-eyed person is making colour matches.

It may be further remarked, that if the maxima of all the three colour sensations are taken, as in the diagram, as of equal value, that the place in the spectrum where the white light is perceived by the colour-blind is where the two sensations are of equal strength, that is, where the two curves cut one another, and are of equal height. By obtaining the proportions of the different colours with colour-blind persons which make up what to them is white light, the curves for the two sensations can be worked out in the form of simple equations.

The experiments carried out with colour-blind people are of the most interesting character, and a good deal remains to be done with the data already obtained from them.

To the popular mind a colour-blind person is usually thought a strange creature, and it is a matter of wonderment, if not of amus.e.m.e.nt, that they cannot distinguish between the red of cherries and the leaves of the cherry tree. The physicist, studying the theory of colour, views the matter quite differently, and he looks upon an intelligent observer of this cla.s.s as a boon. It may be remarked that both the red-blind and the green-blind persons would be unable to distinguish between the cherries and the leaves. The red-blind person would see the cherries as green, as also the leaves; whilst the green-blind person would see both as red.

Without regarding form it is probable that the red-blind would see the leaves as a bright green, whilst the green-blind would see them as darker red than the cherries. Failure to distinguish between the two is more likely to occur with the green of leaves, and the red of such fruits as cherries, since the former contains a marked proportion of red in it, and the latter a small proportion of green.

One highly-educated gentleman was led to know his deficiency in colour sense, by hearing a companion on a tour going into raptures over a sunset. He saw but little difference between it and that to be seen at midday. Testing his vision it appeared that he was totally blind to the sensation of green, and that white and purple would consequently be mistaken by him for one another. The crimson on the clouds, illuminated by the setting sun, would appear to him as only slightly different to the white clouds which he would see at midday; in fact he would be always seeing what to us would be a sunset. For this gentleman to mix spectrum colours to match others would evidently be no guide to normal-eyed persons.

We believe that amongst us in our daily life we have many persons who are blind to some colour, but who are not aware of it, or if they are aware of it, hide their defect as far as possible. That some are ignorant of it to a late period of their life we know.

We have said that there are cases in which persons are only defective in colour perceptions, and not wanting in them altogether. The former are more common than the latter, and to the experimenter are by no means so interesting. They are only alluded to here to indicate that there are degrees in the defectiveness of eyes to colour. One point which must be remembered here is that all colour production for registration by the mixture of three colours is delusive, unless the eye of the operator is tested for its colour sense.

CHAPTER XII.

Formation of Colour Equations--Knig's Curves--Maxwell's Apparatus and Curves.

The plan of obtaining colour equations will by this time have become fairly evident. And we may as well ill.u.s.trate it by equations obtained with the apparatus we have been using in our previous experiments. Let us suppose we have an individual who is desirous of having his eye-sight for colour tested, and that we have the slide with the three slits _in situ_. It will be found that when we alter their width and form white light with them, matching in purity the white light of the reflected beam, that we shall have to reduce the intensity of the latter very considerably, by means of the rotating sectors. The aperture may sometimes be as small as 4, and at other times perhaps somewhere between 4 and 5. Now the variation in aperture between 4, and say 47, is very considerable, but it is highly probable that the latter might be estimated as 46, since only degrees are marked on the sectors. It therefore becomes essential to use a less brilliant reflected beam for the comparison, and this is secured by using as a mirror a plain unsilvered gla.s.s. What before read 4 will perhaps read 60, and 47 will be 70-1/2, whilst 46 would be 69, a difference easily read. We can now commence operations. Let us then place the red slit at say (35) of the scale, the green at (28), and the violet at (17), and make white light of the same intensity by altering the apertures of the slits. Let us do the same with the slits at (34), (28), and (17), instead of at (35), (28), and (17); and again make white light, and similarly with the slits at (35), (28), and (18); and let the following be the results--

(1) 20(35) + 60(28) + 40(17) = 100 W (2) 10(34) + 55(28) + 40(17) = 100 W (3) 20(35) + 59(28) + 10(18) = 100 W

Subtracting (1) from (2) we get--

10(34) = 20(35) + 5(28) or (34) = 2(35) + 1/4(28)

which means that the colour sensation at (34) is made up of two parts of the sensation of (35), together with 1/4 part of the sensation of (28).

In the same way we find that the colour sensation of (18) is made up of the sensations of (17) and (28).

(18) = 4(17) + 1/10(28).

In this way all the different colour sensations can be referred to the sensations which we may happen to consider as best representing the fundamental sensations. What these are is a matter still unsettled; though from the equations formed by colour-blind people, who only require really two colours to form equations, their places are approximately known; evidently as before said, the ray in the spectrum which the green colour-blind person sees as white light, is that where to the normal eye the green fundamental sensation is purest, being free from predominance of either of the other two sensations, and might be taken as a standard colour. Now if our luminosity curve is correct, and if the sum of the luminosities of each colour separately is equal to the luminosity of the colours when mixed (which we have shown to be the case in chapter VII.), it follows that the correctness of the measures can be checked by using the widths of the slits as multipliers of the luminosities. These luminosities can then be added together, and they should equal in luminosity the white light with which the comparison was made. The results can be compared together by reducing the equations to the same standard of white light.

The following is a set of observations which bear this out.

The red and violet slits in this case were kept at 35 and 178 on the scale, and the position of the green slit altered.

+--------------+-----------+-------------+--------------+ | Position of |Aperture of| Luminosity | Sum of the | | Slits. | Slits. | of Colour. | Luminosity | +---+-----+----+---+---+---+----+----+---+ of each | | | | | | | | | | | Colour | | R | G | V | R | G | V | R | G | V |multiplied by | | | | | | | | | | |the Aperture. | +---+-----+----+---+---+---+----+----+---+--------------+ |35 |285 |178|115| 38|112|181|73 |65| 4930 | |35 |280 |178|119| 45|100|181|615|65| 4989 | |35 |2775|178|122| 52| 85|181|52 |65| 4960 | |35 |2735|178|125| 65| 74|181|40 |65| 4907 | |35 |270 |178|128| 78| 67|181|332|65| 4954 | |35 |263 |178|133|125| 40|181|203|65| 4987 | |35 |260 |178|134|150| 10|181|167|65| 4952 | |35 |2585|178|135|170| 0|181|150|65| 4993 | | | | | | | | | | +--------------+ | | | | | | | | | Mean 4959 | +---+-----+----+---+---+---+----+----+------------------+

The red slit was at a point in the spectrum between C and the red lithium line, and excited probably the fundamental sensation of red alone. The violet slit was close to G, and probably in this case the fundamental sensation of violet was almost excited alone. With the green slit the reverse was the case, all three fundamental sensations being excited. At 263 the green sensation was probably the fundamental sensation mixed with white light alone, as at that point the green blind person saw white light in the spectrum, on the red side of it there being what he describes as a warm colour, and on the violet side a cold colour.

An inspection of the table will show how very closely the sum of the luminosities agree amongst themselves, the white light formed by them in each case being of equal intensities. It must be recollected that white light is not necessary to form colour equations; colours may be mixed to form any other colour, which may be taken as a standard. This is often useful in the case of the light between the violet and the blue, where the luminosities are small compared with the luminosity in the green, yellow, and red.

Fig. 35.--Knig's Curves of Colour Sensations.