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COLOUR-PATCH APPARATUS.

THE ROMANCE OF SCIENCE.

COLOUR MEASUREMENT

AND

MIXTURE.

With Numerous Illustrations.

BY

CAPTAIN W. de W. ABNEY, c.b., r.e., d.c.l., f.r.s.

PUBLISHED UNDER THE DIRECTION OF THE COMMITTEE
OF GENERAL LITERATURE AND EDUCATION APPOINTED BY THE
SOCIETY FOR PROMOTING CHRISTIAN KNOWLEDGE.

SOCIETY FOR PROMOTING CHRISTIAN KNOWLEDGE.
LONDON: NORTHUMBERLAND AVENUE, W.C.;
43, QUEEN VICTORIA STREET, E.C.
BRIGHTON: 135, NORTH STREET.
NEW YORK: E. & J. B. YOUNG & CO.
1891.

PREFACE.

Some ten years ago there were three measurements of the spectrum which I set myself to carry out; the last two, at all events, involving new methods of experimenting. The three measurements were: (1st) The heating effect; (2nd) the luminosity; and (3rd) the chemical effect on various salts, of the different rays of the spectrum. The task is now completed, and it was in carrying out the second part of it that General Festing, who joined me in the research, and myself were led into a wider study of colour than at first intended, as the apparatus we devised enabled us to carry out experiments which, whilst difficult under ordinary circumstances, became easy to make. On two occasions, at the invitation of the Society of Arts, I have delivered a short course of lectures on the subject of Colour, and naturally I chose to treat it from the point of view of our own methods of experimenting; and these lectures, expanded and modified, form the basis of the present volume.

As a treatise it must necessarily be incomplete, as it scarcely touches on the history of the subject—a part which must always be of deep interest. The solely physiological aspect of colour has also been scarcely dealt with; that part which the physicist can submit to measurement being that which alone was practicable under the circumstances.

W. de W. Abney.

South Kensington,
1st May, 1891.

CONTENTS.

[CHAPTER I.]

Sources of Light—Reflected Light—Reflection from Roughened Surfaces—Colour Constants p. 11

[CHAPTER II.]

A Standard of Light—Formation of the Spectrum by Prisms and by the Diffraction Grating—Wave-lengths of the principal Fraunhofer Line—Position of Colours in the Spectrum p. 17

[CHAPTER III.]

The Visible and Invisible Parts of the Spectrum—Methods for showing the Existence of the Invisible Portions—Phosphorescence—Photography of the Dark Rays—Thermo-Electric Currents p. 30

[CHAPTER IV.]

Description of Colour Patch Apparatus—Rotating Sectors—Method of making a Scale for the Spectrum p. 41

[CHAPTER V.]

Absorption of the Spectrum—Analysis of Colour—Vibrations of Rays—Absorption by Pigments—Phosphorescence—Interference p. 51

[CHAPTER VI.]

Scattered Light—Sunset Colours—Law of the Scattering by Fine Particles—Sunset Clouds—Luminosities of Sunlight at different Altitudes of the Sun p. 62

[CHAPTER VII.]

Luminosity of the Spectrum to Normal-eyed and Colour-blind Persons—Method of determining the Luminosity of Pigments—Addition of one Luminosity to another p. 76

[CHAPTER VIII.]

Methods of Measuring the Intensity of the Different Colours of the Spectrum, reflected from Pigmented Surfaces—Templates for the Spectrum p. 88

[CHAPTER IX.]

Colour Mixtures—Yellow Spot in the Eye—Comparison of Different Lights—Simple Colours by Mixing Simple Colours—Yellow and Blue from White p. 112

[CHAPTER X.]

Extinction of Colour by White Light—Extinction of White Light by Colour p. 126

[CHAPTER XI.]

Primary Colours—Molecular Swings—Colour Sensations—Sensations absent in the Colour-blind p. 133

[CHAPTER XII.]

Formation of Colour Equations—Kœnig's Curves—Maxwell's Apparatus and Curves p. 147

[CHAPTER XIII.]

Match of Compound Colours with Simple Colours—All Colours reduced to Numbers—Method of Matching a Colour with a Spectrum Colour and White Light p. 156

[CHAPTER XIV.]

Complementary Colours—Complementary Pigment Colours—Measurement of Complementary Colours p. 167

[CHAPTER XV.]

Persistence of Images on the Retina—The Use of Coloured Discs p. 179

[CHAPTER XVI.]

Contrast Colours—Measurement of Contrast Colours—Fatigue of the Eye—After-Images p. 196

LIST OF ILLUSTRATIONS.

COLOUR MEASUREMENT

AND

MIXTURE.

CHAPTER I.

Sources of Light—Reflected Light—Reflection from Roughened Surfaces—Colour Constants.

There is nothing, perhaps, in our everyday life which appeals more to the mind than colour, yet so accustomed are the generality of mankind to its influence that but few stop to inquire the "why and wherefore" of its existence, or its cause. To those few, however, there is a source of endless and boundless enjoyment in its study; for in the realms of physical and physiological science there is perhaps no other subject in which experiments give results so fascinating and often so beautiful. Although its serious study must be undertaken with a clear mind, a good eye, and a fair supply of patience, yet a general idea of the subject may be grasped by those who are possessed of but ordinary intelligence.

Colour phenomena are encountered nearly every day of one's life, and the fact that they are so frequently met with, prevents that attention to them, or even their remark. Who amongst us, for instance, has noticed the existence of what are called positive and negative after images, after looking at some strongly illuminated object, or would have gauged the fact that a certain portion of the nervous system can be fatigued by a colour, and give rise to images of its complementary, had not an enterprising advertiser, who manufactures a household necessary, drawn attention to it in a manner that could not be misunderstood.

If on an autumn afternoon we pass through a garden whilst it is still perfectly light, we can notice the gorgeous colouring of the flowers, and appreciate with the eyes the beauty of each tint. As evening comes on the tints darken, the darkest-coloured flowers begin to lose their colour, and only the brightest strike the eye. When night still further closes in every colour goes, though the outlines of the flowers may still be distinguished; and it would not be impossible, in some parts, to see a tiny speck of pale light upon the ground amongst them. This speck of light we should know from experience to be the light from a glow-worm. Why is it that we lose the colour of the flowers and recognize the tiny light from this small worm? The reason for the one is that in order for objects which are not self-luminous to be seen at all, light must fall on them and illuminate them, and the light which they reflect may be coloured if they possess the qualities to reflect coloured light. The glow-worm's light is seen, not because it does not emit light in the day-time, but because the eye, being limited in sensitiveness, is unable to distinguish it when it is flooded with the light of day. The glow-worm, however, is self-luminous, as is shown by the fact that it emits light in the dark, the light itself being slightly coloured if compared with that of day. That a candle-flame or the sun is self-luminous is an axiom, and need not be philosophised upon; but what must be impressed on the reader is, that though an object which requires to be illuminated to be seen, is not self-luminous, yet when illuminated it does in fact become a source of illumination to the eye, although the light is only light reflected from its surface. It is a point worth remembering that the rougher the surface of an object, the brighter to the eye it will be. That is, a coloured object when polished will be a bad secondary source of illumination, as the light incident upon it will be very nearly reflected from the surface, according to the ordinary laws of reflection; but if it be roughened it will become a much better source, as the roughnesses, though obeying the laws of reflection, will reflect light in every direction. A good example of this is an ordinary sheet of glass. Light from a source falling on its surface is scarcely reflected in any direction except in that determined by the ordinary laws of reflection, and it will be scarcely visible to the eye. Grind its surface, however, and the innumerable facets caused by the grinding will reflect light back to the eye in whatever position it be placed, and will thus be distinctly seen.

We may here premise that even the roughest surface will reflect a greater percentage—varying greatly according to the nature of the surface—of light in the direction which it would do if it were a smooth surface than in any other; and in taking measurements of the light irregularly reflected from a rough surface, this fact must be borne in mind.

Not only must we know how colour is produced, but we must also be able to refer it to some standard which shall be readily reproduced, and which shall be unalterable. There are two variable factors which have to be taken into account in colour experiments: the first is the quality of light which illuminates the object, and the second is the sensitiveness of the eye which perceives it, as light is only a sensation which is recognized by the brain through the medium of the eye. We shall, as we go on, see that different qualities of light may cause objects to appear of different hues, and further that eyes may vary in perceptive power, to an extent of which the large majority of people are not aware. Hence it becomes necessary as far as possible to eliminate these variables.

The task which we have set ourselves to perform then, is first to find a suitable light for experimental work, and next to endeavour to refer colour to an eye which has no abnormal defects. This being accomplished, we have then to find means to measure the different constants which are involved in colour, and to refer the measurements to some standard. Colour constants are three, viz. hue, luminosity, and purity; and it will be seen that if these three are determined, the measurement of the colour is complete.

Perhaps the meaning of these terms may require to be explained. The hue of a colour is what in common parlance is often called the colour. Thus we talk of rose, violet, magenta, emerald green, and so on, but for measuring purposes the hue had best be referred to the spectrum colours as a standard (the means of doing so will be shortly explained), for they are simple colours, which can be expressed by numbers. Compound colours, which it may be said are invariably to be found in nature, being mixtures of simple colours, can be just as readily referred to the spectrum. By the luminosity of a colour we mean its brightness, the standard of reference being the brightness of a white surface when illuminated by the same white light. By the purity of a colour we mean its freedom from admixture with white light. An example of different degrees of purity will be found in washes of water-colours of different tenuity. Thus if we wash a sheet of paper with a light tint of carmine, the whiteness of the paper is not obliterated; if we pass another wash over it the whiteness of the paper is lessened, and so on. The lightest tint is that which is most lacking in purity.

CHAPTER II.

A Standard Light—Formation of the Spectrum by Prisms and by the Diffraction Grating—Wave-lengths of the principal Fraunhofer Line—Position of Colours in the Spectrum.

As we have to turn to the spectrum for pure and simple colours, from which we may produce any compound colour we may wish to deal with, we will first consider the light with which we shall form it. A spectrum may be produced from any source of light, such as sunlight, limelight, the electric light, gaslight, or incandescence electric light, as also from incandescent vapours, or gases; but it is only a solid which is, or is rendered incandescent, that will give us a continuous spectrum, as it is called, that is, a spectrum which is unbroken by gaps of non-luminosity, or sudden change of brightness, throughout its length.

Fig. 1.—Spectrum of Sunlight.

The great desideratum for the study of colour is a light which not only gives a practically continuous spectrum, but one which is produced by the radiation of matter which is black when cold, and which can be kept at a constantly high temperature. We have purposely said "black" in the sentence above, since it is believed that differently coloured bodies, when heated to equal temperatures, might not give the same relative intensities to the different parts of the spectrum, the variation being dependent on the colour of the heated body. A black body must always give the same visible spectrum when heated to the same temperature. The spectrum of sunlight ([Fig. 1]) is not continuous, as we find it crossed by an innumerable number of fine lines of varying breadth and blackness. This want of continuity would not be fatal to its adoption were it possible to use it outside the limits of our atmosphere, as then, unless the temperature of the sun itself changed, the spectrum produced would be invariable; but unfortunately the relative brightness or luminosity of the different parts of the spectrum varies from day to day, and hour to hour, according to the height of the sun above the horizon (see [Chap. VI].); and its integral brightness varies according to the clearness of the sky. It is evident then, that, as a reference light, sunlight is most unsuitable, so we may dismiss it from our possible standards.

Fig. 2.—The Carbon Poles of an Electric Light.

By the process of elimination we may arrive at the light upon which we can rely, for the purpose we have in view, viz. the production of a spectrum of moderate size, and sufficiently bright to be well viewed when projected upon a screen. For some purposes, as for instance in becoming acquainted with the general character of the spectrum, a feebler light, such as gaslight, or light from electrical glow lamps, may be employed, since the spectrum may be viewed directly by the eye without the intervention of a screen. They have two drawbacks for our object: one being the want of general intensity, and the other the feeble luminosity of blue and violet rays in their spectrum (see [page 110]). The limelight we can also dismiss for want of steadiness. Its whiteness and luminosity varies according to the oxygen playing on the lime cylinder, rendering the relative intensities of the different parts of the spectrum so erratic as to make it unreliable. This leaves the (electric) arc-light as the only one which is really available. Remember how the arc-light is produced. A current of electricity passes between the ends of two thick black carbon rods, or poles as they are called, through an air space of small interval, and the passage of the current renders the tips of these rods white-hot ([Fig. 2]). The centre of the end of one pole, called the positive pole, where a crater-like depression is formed, is the part which attains the whitest heat, and its temperature seems to be constant, and to be that of the volatilization of carbon. Numerous experiments have been made by the writer, and he has found that the light emitted by this crater in the positive pole is, within the limits of the error of observation, always of the same whiteness, and consequently gives a spectrum which is unvarying in the proportionate intensities of the different colours. When the experiments made to determine the luminosity of the spectrum are described, the method of ascertaining this will be readily understood.

In the spectrum produced by this light there are two places in the violet where there are bands of violet lines slightly brighter than the general spectrum. They are principally due to the light emitted from the incandescent vapour of carbon, which is volatilized and plays between the two poles (see [Fig. 2]); but as these bands are of but small visual intensity, and situated towards the limit of the visible spectrum, they do not interfere with eye-measures of colours, though they do, to a certain extent, to the analysis of radiation by photography. If we throw the positive pole a little behind the negative pole we can, however, considerably mitigate this evil. We can separate the carbon rods to such a degree that the white-hot crater faces the observer, and a good deal of the arc is hidden. This is well seen in the figure.

We have now described the light we have adopted, and the reasons for adopting it; and having obtained our light, we can now consider by what plan we shall form our spectrum. There are two ways open to us—one by glass prisms, and the other by a diffraction grating. Glass prisms separate white light, or indeed any light, into its components, from the fact that the refraction of each coloured ray differs from every other. Thus the red rays are least refracted, and the violet the most, and the yellow, green and blue are intermediate between them, being placed in the order of least refrangibility. Between these there is of course every shade of simple colour, one melting into the other. In order to form a pure and bright spectrum with prisms, in a room of limited dimensions, we have to use certain auxiliary apparatus which are not positively essential, though convenient. The real essentials to form a spectrum are a narrow slit, a glass prism, with perfectly plane faces, and a lens. If this be the only apparatus available, the slit must be placed at a long distance from the prism, the beam of light must pass through the slit on to the prism, and the lens must be placed at such a distance from the slit that it forms a sharp image on a screen. When the light passes through the prism, the screen will have to be rotated in the arc of a circle, so that its distance from the slit measured along the line of the ray to the prism, and from the prism to the screen, is the same as it would be without the intervening prism. An apparatus of this description is not convenient, however, as it requires much more space than is often available. If a lens be placed between the slit and the prism, at exactly its focal length from the former, the light entering the slit will, after passage through the lens, emerge as parallel rays, that is, they will emerge as they would do if the slit were placed at an infinite distance from the observer.

The focal length of this collimating lens need not be greater than twelve to eighteen inches, so that the great space required by the cruder apparatus is very much curtailed. The lens and slit are mounted one at each end of a tube of the necessary length, and are thus handy to use.

Instead of one prism two or three may be used, giving an angular dispersion of the spectrum two or three times respectively greater than that which would be given by only one prism; consequently to obtain a given length of spectrum with the increased dispersion, the focal length of the lens used to focus the image on the screen may be diminished.

The drawback to the use of prisms is that the dispersion of the red end of the spectrum is much less than that of the blue end, and is apt to give a false impression as to the relative luminosities of, and length of spectrum occupied by, the different colours. In some text-books it is told us that the diffraction grating gives us a dispersion which is in exact relation to the wave-length. This is not true, however, as it can only give one small portion in such relationship, and that only when it is specially set for the purpose. The subject of diffraction is one into which it would be foreign to our purpose to wander. We may say that for measures such as we shall make, it is handier to employ prisms, as the prismatic spectrum is more intense than the diffraction spectrum. This can be readily understood when we consider the subject even superficially. If we throw a beam of light on a grating which contains perhaps some 14,000 parallel lines in the space of one inch in width, the lines being ruled on a plane and bright metallic surface, and receive the reflected beam on a screen, the appearance that is presented is a white central spot, together with six or seven spectra of gradually diminishing brightness on each side of it, all except the first pair overlapping one another. That these different spectra do exist can be readily shown by placing in the beam a piece of red glass, when symmetrical pairs of the red part of the spectrum will be found, one of each pair being on opposite sides of what will now be the central red spot. Half the light falling on the grating is concentrated in this central spot, and the remaining half goes to form the spectra; the pair nearest the central spot being the brightest. We thus are drawn to the conclusion that at the outside we can only have less than one-quarter of the incident light to form the brightest spectrum we can use. With two good prisms we use at last three-fourths of the incident light, so that for the same length of spectrum we can get at least three times the average brightness that we should get were we to employ a diffraction grating.

We must now refresh the reader's memory with a few simple facts about light, in order that our meaning may be clear when we speak of rays of different wave-lengths. Every colour in the spectrum has a different wave-length, and it is owing to this difference in wave-length that we are able to separate them by refraction, or diffraction, and to isolate them. Light, or indeed any radiation, is caused by a rhythmic oscillation of the impalpable medium which we, for want of a better term, call ether, and the distance between two of these waves which are in the same phase is called the wave-length of the particular radiation. The extent of the oscillation is called the amplitude, which when squared is in effect a measure of the intensity of the radiation. Thus at sea the distance between the crests of two waves is the wave-length, and the height from trough to crest the amplitude; and the intensity, or power of doing work, of two waves of the same wave-lengths but of different heights, is as the square of their heights. Thus, if the height of one were one unit, and of the other two units, the latter could do four times more work than the former. The waves of radiation which give the sensation of colour in the spectrum vary in length, not perhaps to the extent that might be imagined, considering the great difference that is perceived by the eye, but still they are markedly different. The fact that the spectrum of sunlight is not continuous, but is broken up by innumerable fine lines, has already been alluded to. The position of these lines is always the same, as regards the colour in which they are situated, and is absolutely fixed directly we know their wave-length; hence if we know the wave-lengths of these lines, we can refer the colour in which they lie to them. Now some lines of the solar-spectrum are blacker and consequently more marked than others, and instead of referring the colours to the finer lines, we can refer them to the distance they are from one or more of these darker lines, where these latter are absolutely fixed; in fact they act as mile-stones on a road.

In the red we have three lines in the solar spectrum, which for sake of easy reference are called A, B and C; in the orange we have a line called D, in the green a line called E, in the blue F, in the violet G, and in the extreme violet H. These lines are our fiducial lines, and all colours can be referred to them. The following are the wave-lengths of these lines, on the scale of 1/10,000,000 of a millimetre as a unit

When the spectrum is produced by prisms the intervals between these lines are not proportional to the wave-lengths, and consequently if we measure the distance of a ray in the spectrum from two of these lines, we have to resort to calculation, or to a graphically drawn curve, to ascertain its wave-length. For the purpose of experiments in colour the graphic curve from which the wave-length can immediately be read off is sufficient. The following diagram ([Fig. 3]) shows how this can be done.

The names and range of the principal colours which are seen in the spectrum has been a matter of some controversy. Professor Rood has, however, made observations which may be accepted as correct with a moderately bright spectrum. If the spectrum be divided into 1000 parts between A in the red, and H, the limit of the violet, he makes the following table of colours.

Fig. 3.—Curve for converting the Prismatic Spectrum into Wave-lengths.

In the above scale (Fig. 3) A = 0, B = 74·0, C = 112·7, D = 220·3, E = 363·1, F = 493·2, G = 753·6, H = 1000.

These are the main subdivisions of colour, but it must be recollected that one melts into the other. When the spectrum is very bright the colours tend to alter in hue; thus the orange becomes paler, and the yellow whiter, and the blue paler. On the other hand, if the spectrum be diminished in brightness the tendency is for the colours to change in the opposite direction. Thus the yellow almost disappears and becomes of a green hue, whilst the orange becomes redder, and the spectrum itself becomes shorter to the eye than before.

Let us strictly guard ourselves, however, from the criticism that all eyes see not alike. Suffice it to say that the above table is correct for the ordinary or normal eye, and does not necessarily apply to those who have defective vision as regards colour sensation.

CHAPTER III.

The Visible and Invisible Parts of the Spectrum—Methods for showing the Existence of the Invisible Portions—Phosphorescence—Photography of the Dark Rays—Thermo-Electric Currents.

We are apt to forget, when looking at the spectrum, that what the eye sees is not all that is to be found in the prismatic analysis of light. The spectrum, it must be recollected, is not limited to those rays which the eye perceives. There are rays both beyond the extreme violet and below the extreme red, which exist and which exercise a marked effect on the world's economy. Thus, rays beyond the violet are those which with the violet and the blue rays principally affect vegetation, enabling certain chemical changes to take place which are necessary for its growth and health; whilst the rays below the red are those possessing the greatest amount of energy, and if they fall upon bodies which absorb them, as very nearly all bodies do to a certain extent, they heat them. The warmth we feel from sunlight is principally due to the dark rays which lie below the red of the spectrum.

The existence of both kinds of these dark rays may be demonstrated in a very simple manner by the effect that they produce on certain bodies. For instance, there is a yellow dye with which cheap ribbon is dyed, which if placed in the spectrum and beyond the violet causes a visible prolongation of the spectrum. The light in the newly-seen and once invisible part of the spectrum is yellow, the colour of the ribbon itself. In fact, the whole of that part of the spectrum, which on the white screen is seen as blue and violet, becomes yellow, the red and green remaining unchanged. This change in colour is due to fluorescence, a phenomenon of light which Sir G. Stokes found was caused by an alteration in the lengths of the waves of light when reflected from certain bodies. It is not meant to imply by this that the wave-length of any ray falling on a body can be altered by reflection, but only that the body itself on which the rays fall emits rays of light which are not of the same wave-length as those which fall upon it. Now it is a fact that the rays that lie beyond the violet, and which are ordinarily invisible, are shorter than the violet rays, and that these are shorter than the yellow rays. It follows therefore that when, what we may now call, the ultra-violet rays fall on the yellow dyed ribbon, the waves emitted by it are so lengthened that they appear yellow to the eye instead of dark, violet, or blue.

We can also brush a solution of quinine on the screen, and immediately the place where the ultra-violet rays fall is illuminated by a violet light. We do not see the ultra-violet rays themselves, but only the rays of increased wave-length, which are emitted by their effect on the sulphate of quinine. Common machine oil as used for engines also emits greenish rays when excited by the ultra-violet rays, and a very beautiful colour it is. Fluorescence then is one means of demonstrating the existence of the ultra-violet rays—or Ritter's rays as they were formerly called, after their discoverer—in a very simple manner. The method of rendering the effects of the infra-red rays visible to the eye is also interesting. All, or at all events most, of our readers have seen Balmain's luminous paint. A glass or card coated with this substance, which is essentially a sulphide of calcium, when exposed to the light of the sun, or of the electric arc, and then taken into comparative darkness, is seen to shine with a peculiar violet-coloured light. If when thus excited we place it in a bright spectrum for some little time, we shall find on shutting off the light that where the ultra-violet and blue fell on it, the violet light is intenser than the light of the main part of the screen; where the yellow fell there is neither increase or diminution in brightness; but that in the red it becomes darker, and also beyond the limit of the visible spectrum, indicating the existence of rays beyond, which through their greater length have not the power of affecting the eye. If the spectrum be shut off, however, very soon after it falls on the plate, it has been asserted that the red and infra-red rays have increased the brightness of that particular part of the plate on which they fell. At first these two observations seem to contradict one another; they do not in reality. We may expose a tablet of Balmain's paint to light, and place a heated iron in contact with the back of the plate; we shall then find that the iron produces a bright image of its surface on a less bright background. This bright image will gradually fade away, and the same space will eventually become dark compared with the rest of the plate. The reason of this is clear. When light excites the paint a certain amount of energy is poured into it, which it radiates out slowly as light. When the hot iron is placed in contact with it, the heat causes the light to radiate more rapidly, and consequently with greater intensity, at the part where its surface touches, and the energy of that particular portion becomes used up. When the energy of radiation of this part becomes less than that of the rest of the tablet, its light must of necessity be of less brightness than that of the background, with which the heated iron has had no contact. For this reason the image of the iron subsequently appears dark. We shall see presently, and as before stated, that the principal heating effect of the spectrum lies in the red and infra-red, and it is owing to the heating of the paint by these rays that the image might be at first slightly brighter than the background, and subsequently darker.

There is another way in which the existence of both the ultra-violet and infra-red rays can be demonstrated, and that is by means of photography. If we place an ordinary photographic plate in the spectrum and develop it, we shall find that besides being affected by the blue and violet rays, it is also affected by the rays beyond the violet, the energy of these rays being capable of causing a decomposition of the sensitive silver salt. If quartz prisms and lenses be used, and the electric light be the source of illumination, the ultra-violet spectrum will extend to an enormous extent. A more difficult, but perhaps even more interesting means of illustrating the existence of the infra-red rays, and first due to the writer, can be made by means of photography. It is possible to prepare a photographic plate with bromide of silver, which is so molecularly arranged that it becomes capable of being decomposed not only by the violet and blue rays, but also by the red rays, and by those rays which have wave-lengths of nearly three times that of the red rays. It would be inappropriate to enter into a description of the method of the preparation of these plates. Those who are curious as to it will find a description in the Bakerian lecture published in the Philosophical Transactions of the Royal Society for 1881. With plates so prepared it has been found possible to obtain impressions in the dark with the rays coming from a black object, heated to only a black heat.

That these dark rays possess greater energy or capacity for doing work of some kind than any other rays of the spectrum, can be shown by means of a linear thermopile (Fig. 4), if it be so arranged as to allow only a narrow vertical slice of light to reach its face.

Fig. 4.—The Thermopile.

The principle of the thermopile we need not describe in detail. Suffice it to say that the heating of the soldered junctions of two dissimilar metals (there are ten pairs of antimony and bismuth in the above instrument) produces a feeble current of electricity, which, however, is sufficient to cause a deflection to the suspended needle of a delicate galvanometer. To the needle is attached a mirror weighing a fraction of a grain, and the deflections are made visible by the reflection from it of a beam of light issuing from a fixed point along a scale. The greater the heating of the junctions of the thermopile, within limits which in these cases are never exceeded, the greater is the current produced, and consequently the greater is the deflection of the mirror-bearing needle, and of the beam of light along the scale. In order to get a comparative measure of the energies of the different rays, it is necessary that they should be completely absorbed. Now the junctions themselves of the pile being metal, and therefore more or less bright, will not absorb completely, but if they be coated with a fine layer of lamp-black, the rays falling on the pile will be absorbed by this substance, and their absorption will cause a rise in temperature in it, and the heat will be communicated to the thermopile.

If we make a bright spectrum, and one not too long, say three inches in length, and pass the linear thermopile through its length, we shall find that when the galvanometer is attached, the galvanometer needle will be differently deflected in its various parts. The deflection will be almost insensible in the violet, but sensible in the blue, rather more in the green, still more in the yellow, and it will further increase in the red. When, however, the slit of the thermopile is placed beyond the limit of the visible spectrum, the deflection enormously increases, and will increase till a position is reached as far below the red as the yellow is above it. After this maximum is reached, by moving the pile still further from the red, the galvanometer needle will travel towards its zero, and finally all deflection will cease. At this point we may suppose we have reached the limit of the spectrum, but if rock-salt prisms and lenses be used, the limit will be increased. What the real limit of the spectrum is, is at present unknown; Mr. Langley with his bolometer, and rock-salt prisms, an instrument more sensitive than the thermopile, must have nearly reached it.

Fig. 5.—Heating effect of different Sources of Radiation.

The above figure is a graphic representation of the heating effect of the spectrum of the electric light, sunlight, and the incandescence electric light, on the lamp-black coating of the thermopile, as shown by the galvanometer. The vast difference between the heating effect of the visible rays of the first two sources compared with the last is clearly indicated.

Since every ray may be taken as totally absorbed, the heating of the lamp-black is a measure of the energy or the capacity of performing work of some description, which they possess. Waves of the sea do work when they beat against the shore, and they do work when they lift a vessel. If we notice a ship at anchor we shall find that behind the vessel and towards the shore the waves are lowered in height or amplitude; the energy which they have expended in raising the vessel of necessity causes this lowering. In the same way the waves of light, after falling on matter whose molecules or atoms are swinging in unison with them, are destroyed, and the energy is spent in either decomposing the matter into a simpler form at first—though the subsequent form may be more complex—or in raising its temperature. As lamp-black or carbon is in its simplest form, the only work done upon it by the energy of radiation is the raising of its temperature, and it is for this reason that this material is so excellent for covering the junctions of the pile. The eye evidently does not absorb all rays, since only a limited part of the spectrum is visible, and it would be useless to take a measure of the heating effect of lamp-black for the visible part of the spectrum as a measure of its luminosity, since the latter fades off in the red—the very place in which the heat curve rises rapidly.

CHAPTER IV.

Description of Colour Patch Apparatus—Rotating Sectors—Method of making a Scale for the Spectrum.

Before proceeding further we must describe somewhat in detail two or three pieces of apparatus to be used in the experiments we shall make.

The first piece was devised by the writer a few years ago, and has got rid of several objections which existed in older pieces of apparatus. It is not only useful for lecture purposes, but also for careful laboratory work. The ordinary lecture apparatus for throwing a spectrum on the screen is of too crude a form to be effective for the purpose we have in view; the purity of the colours seen on the screen is more than doubtful, and this alone unfits it for our experiments. If we want to form a pure spectrum we must have a narrow slit, prisms with true, flat surfaces, and lenses of proper curvature. As a rule the ordinary lecture apparatus for forming the spectrum lacks all of these requisites.

Fig. 6.—Colour Patch Apparatus.

The accompanying diagram (Fig. 6) will give an idea of the apparatus we shall employ. On the usual slit S₁ of a collimator C is thrown, by means of a condensing lens L₁, a beam of light, which emanates from the intensely white-hot carbon positive pole of the electric light. The focus is so adjusted that an image of the crater is formed on the slit. The collimating lens L₂ is filled by this beam, and the rays issue parallel to one another and fall on the prisms P₁ and P₂, which disperse them. The dispersed beam falls on a corrected photographic lens L₃, attached to a camera in the ordinary way. It is of slightly larger diameter than the height of the prisms, and a spectrum is formed on the focusing-screen D, which is slewed at a slight angle with the perpendicular to the axis of the lens L₃. This is necessary, because the focus of the least refrangible or red rays is longer than that of the more refrangible or blue rays. By slewing the focusing-screen as shown, a very good general focus for every ray may be obtained. When the focusing-screen is removed, the rays form a confused patch of parti-coloured light on a white screen F, placed some four feet off the camera. The rays, however, can be collected by a lens L₄, of about two feet focus, placed near the position of the focusing-screen, and slightly askew. This forms an image on the screen of the near surface of the last prism P₂; and if correctly adjusted, the rectangular patch of light should be pure and without any fringes of colour. The card D slides into the grooves which ordinarily take the dark slide. In it will be seen a slit S₂, the utility of which will be explained later on.

We shall usually require a second patch of white light, with which to compare the first patch. Now, although the light from the positive pole of the carbons is uniform in quality, it sometimes varies in quantity, as it is difficult to keep its image always in exactly the centre of the slit. If we can take one part of the light coming through the slit to form the spectrum, and another part to form the second patch of white light, then the brightness of the two will vary together. At first sight this might appear difficult to attain; but advantage is taken of the fact that from the first surface of the first prism P₁ a certain amount of light is reflected. Placing a lens L₅, and a mirror G, in the path of this reflected beam, another square patch of light can be thrown on the same screen as that on which the first is thrown, and this second patch may be made of the same size as the first patch, if the lens L₅ be of suitable focus, and it can be superposed over the first patch if required; or, as is useful in some cases, the two patches may be placed side by side, just touching each other.

We are thus able to secure two square white patches upon the screen F, one from the re-combination of the spectrum, and one from the reflected beam. If a rod be placed in the path of these two beams when they are superposed, each beam will throw a shadow of the rod upon the screen. The shadow cast by the integrated spectrum will be illuminated by the reflected beam, and the shadow cast by the latter will be illuminated by the former. In fact we have an ordinary Rumford photometer, and the two shadows may be caused to touch one another by moving the rod towards or from the screen. When the illumination of the two shadows by the white light is equal, the whole should appear as one unbroken gray patch. To prevent confusion to the eye a black mask is placed on the screen F with a square aperture cut out of it, on which the two shadows are caused to fall. If it be desired to diminish the brightness of either patch, it can be accomplished by the introduction of rotating sectors M, which can be opened and closed at pleasure during rotation, in the path of one or other of the beams.

Fig. 7.—Rotating Sectors.

The annexed figure (Fig. 7) is a bird's-eye view of the instrument. A A are two sectors, one of which is capable of closing the open aperture by means of a lever arrangement C, which moves a sleeve in which is fixed a pin working in a screw groove, which allows the aperture in the sectors to be opened and closed at pleasure during their revolution; D is an electro-motor causing the sectors to rotate. To show its efficiency, if two strips of paper, one coated with lamp-black and the other white, are placed side by side on the screen, and if one shadow from the rod falls on the white strip, and the other shadow on the black strip of paper, and the rotating sectors are interposed in the path of the light illuminating the shadow cast on the white strip, the aperture of the sectors can be closed till the white paper appears absolutely blacker than the black paper. White thus becomes darker than lamp-black, owing to the want of illumination. This is an interesting experiment, and we shall see its bearings as we proceed, as it indicates that even lamp-black reflects a certain amount of white or other light.

Having thus explained the main part of the apparatus with which we shall work, we can go on and show how monochromatic light of any degree of purity can be produced on the screen. If the slit in the cardboard slide D be passed through the spectrum when it has been focused on the focusing-screen, only one small strip of practically monochromatic light will reach the screen, and instead of the white patch on the screen we shall have a succession of coloured patches, the colour varying according to the position the slit occupies in the spectrum. It should be noted that the purity of the colour depends on two things—the narrowness of the slit S₁ of the collimator, and of the slit S₂ in the card. If two slits be cut in the card D, we shall have two coloured patches overlapping one another, and if the reflected beam falls on the same space we shall have a mixture of coloured light with white light, and either the coloured light or the white light can be reduced in brightness by the introduction of the rotating sectors. If the rod be introduced in the path of the rays we shall have two shadows cast, one illuminated with coloured light, monochromatic or compound, and the other with white light, and these can be placed side by side, and surrounded by the black mask as before described.

Fig. 8.—Spectrum of Sodium Lithium and Carbon.

There is one other part of the apparatus which may be mentioned, and that is the indicator, which tells us what part of the spectrum is passing through the slit. Just outside the camera, and in a line with the focusing-screen, is a clip carrying a vertical needle. A small beam of light passes outside the prism P₁; this is caught by a mirror attached to the side of the apparatus, and is reflected so as to cast a shadow of the needle on to the back of the card D, on which a carefully divided scale of twentieths of an inch is drawn. To fix the position of the slit the poles of the electric light are brushed over with a solution of the carbonates of sodium and lithium in hydrochloric acid, and the image of the arc is thrown on the slit. This gets rid of the continuous spectrum, and only the bright lines due to the incandescent vapours appear on the focusing-screen (Fig. 8). Amongst other lines we have the red and blue lines due to the vapour of lithium; the orange, yellow (D), and green lines of sodium, together with the violet lines of calcium (these last due to the impurities of the carbons forming the poles). These lines are caused successively to fall on the centre of the slit by moving the card D, which for the nonce is covered with a piece of ground glass, and the position of the shadow of the needle-point on the scale is registered for each. A further check can be made by taking a photograph of these lines, or of the solar spectrum, and having fixed accurately on the scale any one of these lines already named, the position of the others on the scale may be ascertained by measurement from the photograph. Now the wave-lengths of these bright lines have been most accurately ascertained, in fact as accurately as the dark lines in the solar spectrum. Thus the scale on the card is a means of localizing the colour passing through the slit or slits. Should more than one slit be used in the spectrum the positions of each can be determined in exactly the same way. The most tedious part of the whole experimental arrangement with this apparatus is what may be called the scaling of the spectrum.

A fairly large spectrum may be formed upon the screen without altering any arrangement of the apparatus, when it has been adjusted to form colour patches. If a lens L₆ (see [Fig. 6]) of short focus be placed in front of L₄ (the big combining lens), an enlarged spectrum will be thrown upon the screen F, and if slits be placed in the spectrum the images of their apertures are formed by the respective coloured rays passing through them, so that the colours which are combined in the patch can be immediately seen.

CHAPTER V.

Absorption of the Spectrum—Analysis of Colour—Vibrations of Rays—Absorption by Pigments—Phosphorescence—Interference.

We must now briefly consider what is the origin, or at all events the cause, of the colour which we see in objects. It is not proposed to enter into this by any means minutely, but only sufficiently to enable us to understand the subject which is to be brought before you. What for instance is the cause of the colour of this green solution of chlorophyll, which is an extract of cabbage leaves? If we place it in the front of the spectrum apparatus and throw the spectrum on the screen, we find that while there is a certain amount of blue transmitted, the green is strong, and there are red bands left, but a good deal of the spectrum is totally absorbed. Forming a colour patch of this absorption spectrum on the screen, we see that it is the same colour as the chlorophyll solution, and of this we can judge more accurately by using the reflected beam, and placing the rod in position to cast shadows. (The light of the reflected beam is that of the light entering the slit.) The colour then of the chlorophyll is due to the absence of certain colours from the spectrum of white light. When white light passes through it, the material absorbs, or filters out, some of the coloured rays, and allows others to pass more or less unaffected, and it is the re-combination of these last which makes up the colour of the chlorophyll. We have a green dye which to the eye is very similar in colour to chlorophyll, but putting a solution of it in front of the spectrum, we see that it cuts off different rays to the latter. It would be quite possible to mistake one green for the other, but directly we analyze the white light which has filtered through each by means of the spectrum, we at once see that they differ. Hence the spectrum enables the eye to discriminate by analysis what it would otherwise be unable to do. Any coloured solution or transparent body may be analyzed in the same way, and, as we shall see subsequently, the intensity of every ray after passing through it can be accurately compared with the original incident light. There are some cases, indeed the majority of cases, in which the colour transmitted through a small thickness of the material is different to that transmitted through a greater thickness. For instance, a weak solution of litmus in water is blue when a thin layer is examined, and red when it is a thicker or more concentrated layer. Bichromate of potash is more ruddy as the thickness increases. This can be readily understood by a reference to the law of absorption. Suppose we have a thin layer of a liquid which gives a purple colour when two simple colours, red and blue, pass through it, and that this thin layer cuts off one-quarter of the red and one-half of the blue incident on it, another layer of equal thickness will cut off another quarter of the three-quarters of red passing through the first layer, and half of the one-half left of the blue; we shall thus have nine-sixteenths of the red passing and only a quarter of the blue. With a third layer we shall have twenty-seven sixty-fourths of red and only one-eighth of blue left, showing that as the thickness of the liquid is increased the blue rapidly disappears, leaving the red the dominant colour. Now what is true of two simple colours is equally true of any number of them, where the rates of absorption differ from one another, and what is true for a solution is true for a transparent solid. In some opaque bodies, such as rocks, the reflected colour often differs slightly from that of the same when they are cut into thin and polished slices, through which the light can pass. The reason is that when opaque, light penetrates to a very small distance through the surface, and is reflected back, whilst in these layers the colour has to struggle through more coloured matter, and emerges of a different hue.

The question why substances transmit some rays and quench others, brings us into the domain of molecular physics. Of all branches of physical science this is perhaps the most fascinating and the most speculative, yet it is one which is being built up on the solid foundations of experiment and mathematics, till it has attained an importance which the questions depending on it fully warrants. We have to picture to ourselves, in the case in point, molecules, and the atoms composing them, of a size which no microscope can bring to view, vibrating in certain definite periods which are similar to the periods of oscillation of the waves of light. At page 26 we have given the lengths of some of the waves which give the sensation of coloured light. Now as light, of whatever colour it may be, is practically transmitted with the same velocity through air which has the same density throughout, it follows that the number of vibrations per second of each ray can be obtained by dividing the velocity of light in any medium by the wave-length. The following table gives roughly the number of vibrations per second of the ether giving rise to the colours fixed by the dark solar lines.

If we endeavour to gauge what this rate of oscillation means we shall scarcely be able to realize it, even by a comparison with some physically measurable rate of vibration. A tuning-fork, for instance, giving the middle C, vibrates 528 times per second. Compare this with the number of vibrations of the waves of light, and we still are as far as ever from realizing it, yet the velocity of light, and the lengths of the different waves have been accurately determined; the latter, although the much smaller quantity, with even greater accuracy than the first. These rates of vibration must therefore be—cannot help being—at all events approximately true. This being so, we know that some of the atoms of the molecules at least, and perhaps in some cases the molecules themselves, are vibrating at the same rate as those waves of light, which they refuse to allow to pass. If we have a child's swing beginning to oscillate, we know that it is only by well-timed blows that the extent of the swing is permanently increased, and the energy exerted by the person who gives the well-timed blow is expended on producing the increased amplitude. In the same way if the rate of vibration of a wave of light is in accord with that of a molecule or atom, the amplitude or swing of the atom or molecule is increased, and the energy of the wave and therefore its amplitude is totally or partially destroyed; and as the amplitude is a function of the intensity of the light, the ray fails to be seen at all, or else is diminished in brightness.

In what way the atoms vibrate where more than one ray is absorbed is still a matter of speculation, but no doubt as experimental methods are more fully developed, and mathematicians investigate the results of such experiments, we shall be able to form a picture of the vibrations themselves. At page 137 a speculation as to the reason why solids or liquids can absorb more waves of light than one which are adjacent to each other is put forward, but it does not deal with the absorptions which occupy various parts of the spectrum. Again, too, we have the fact that the energy absorbed by these atoms and molecules from the waves of light, must show itself as work done on them—it may be as heat or as chemical action. We shall see by and by that in some cases, no doubt, at least a part is expended in the latter form of work.

Perhaps this mode of looking at the question of colour in objects may make the subject more interesting to the reader than it at first appears to be deserving. The whole subject is one which enlarges the faculty of making mental pictures, and this is one of the most useful forms of scientific education.

But how can we distinguish between pigments which to the eye are apparently the same? If we dye paper with the green dye referred to, we can place it in the spectrum, and we shall see that the dye reflects differently to the white paper. In fact we shall find that it refuses to reflect in those parts of the spectrum which the transparent solution refused to transmit. So long as the light passes through the dye-stuff, it is indifferent, as regards the colour produced, whether the colouring matter be at a distance from the paper or whether the latter be dyed with it, as we can see at once. If we place the solution of the dye in the reflected beam of the apparatus and form a patch on the screen, and alongside throw the patch of white light from the integrated or recombined spectrum upon the dyed paper, it will be found that the two colours are alike; that is, the green-coloured light on the white paper, or the white light on the green paper are the same. Similarly we may experiment on other dyes, such as magenta, log-wood, &c., and we shall see that like results are obtained. It should be said, however, that when the paper is dyed with the colouring matter a small quantity of white light will be reflected from the surface of the paper itself. We may now say that the general colour is given to a body by its refusal to transmit or reflect, more or less completely, certain rays of the spectrum. Should the solvent form a compound with the dye, perhaps this would not be absolutely true, but in the large majority of cases the statement is correct. When we have bodies which are also fluorescent, this statement would also have to be modified, but we need not consider these for the present.

Another source of colour in objects, though very rarely met with, and which for our object we need not stay to explain in detail, is the interference of light. Such is seen in soap-bubbles. Briefly it may be said that the colours are due to rays of light reflected from the inner surface of the film, which quench other rays of light of the same wave-length reflected from the outer surface. If two series of waves of the same wave-length are going in the same direction and from the same source, each of which has the same intensity as the other, that is, having the same amplitude, and it happens that the one series is exactly half a wave-length behind the other, then the crest of one wave in the first series will fill up the trough of the other in the second series, and no motion would result, and this lack of motion means darkness, since it is the wave motion which gives the sensation of light. If then we have white light falling on two reflecting surfaces, such as the front and back of a soap-film, part of the light will be reflected from each, and if the film be of such a thickness that the latter reflects light exactly ½ wave-length, 3/2 or 5/2 wave-length, &c., of some colour behind the former, the colour due to that particular wave-length will be absent from the reflected white light, and instead of white light we shall have coloured light, due to the combination of all the colours less this colour, which is quenched.

A very pretty experiment to make is to throw the image of a soap film on the screen, and to watch the change in the colours of the film. Their brilliancy increases as the film becomes thinner, and the bands, which first appear close to each other, separate, and then we see a large expanse of changing colour. A soap solution should be made according to almost any of the published formulæ, and a piece of flat card be dipped in it, and be drawn across a ring of wire some inch in diameter, or—what the writer prefers best—the stop of a photographic lens. A film will form and fill the aperture. The ring or stop may be placed vertically in a clamp, and a beam of light caused to fall at an angle of about 45 degrees on to the film. If a lens be placed in the path of the reflected beam to form an image of the aperture, the colours which the film shows can be exhibited to an audience, if the diameter of the image be made four or five feet. Instead of this large image, a small image may be thrown on the slit of the spectroscope, by using a lens of a greater focal length, and if the beam be so directed that it falls on the axis of the collimator, a very fairly bright spectrum may be also thrown on the screen. The appearance of the spectrum is somewhat like that shown in the above diagram (Fig. 9).

Fig. 9.—Interference Bands.

If we take a horizontal line across the spectrum, we shall see what particular colours are missing from the reflected light which falls on the part of the slit corresponding to that line. The colours of some objects, such as of the opal, and the lovely colouring of some feathers are due to interference of light. The partial scattering of different rays by small particles will also cause light to be coloured, as we shall see in the experiments we shall make to imitate the colour of sunlight at various altitudes of the sun. We may, however, take it as a rule that the colour of objects is produced by the greater or less absorption of some rays, and the reflection in the case of opaque bodies, or the transmission, in the case of transparent bodies, of the remainder.

CHAPTER VI.

Scattered Light—Sunset Colours—Law of the Scattering by Fine Particles—Sunset Clouds—Luminosities of Sunlight at different Altitudes of the Sun.

It is probable that we should be able to ascertain approximately the true colour of sunlight (if we may talk of the colour of white light) if we could collect all the light from a cloudless sky, and condense it on a patch of sunlight thrown on a screen. For skylight is, after all, only a portion of the light of the sun, scattered from small particles in the atmosphere, part of the light being scattered into space, and part to our earth. The small particles of water and dust—and when we say small we mean small when measured on the same scale as we measure the lengths of waves of light—differentiate between waves of different lengths, and scatter the blue rays more than the green, and the green than the red; consequently what the sun lacks in blue and green is to be found in the light of the sky. The effect that small water particles have upon light passing through them can be very well seen in the streets of London at night, when the atmosphere is at all foggy. Gaslights at the far end of a street appear to become ruby red and dim, and half-way down only orange, but brighter, whilst close to they are of the ordinary yellow colour, and of normal brightness. When no fog is present the gas-lights in the distance and close to are of the same colour and brightness, showing that their change in appearance is simply due to the misty atmosphere intervening between them and the observer. We can imitate the light from the sun, after its passage through various thicknesses of atmosphere, in a very perfect manner in the lecture-room, using the electric light as a source. A condensing lens is put in front of the lamp, and in front of that a circular aperture in a plate. Beyond that again is a lens which throws an enlarged image of the aperture on the screen, which we may call our mock sun. If we place a trough of glass, in which is a dilute solution of hyposulphite of soda, carefully filtered from motes as far as possible, in front of the aperture, we have an image of the aperture unaffected by the insertion of the solution. The white disc on the screen will, as we have said before, be a close approximation to sunlight on a May-day about noon, when the sky is clear. By dropping into the trough a little dilute hydrochloric acid, a change will be found to come over the light of the mock sun; a pale yellow colour will spread over its surface, and this will give way to an orange tint, and at the same time its brightness will diminish. Gradually the orange will give place to red, the luminosity will be very small, being of the same hue as that seen in the sun when viewed through a London fog. Finally the last trace of red will so mingle with the scattered white light that the image will disappear, and then the experiment is over.

If we track the cause of this change of colour in our artificial sun, we shall find that it is due to minute particles of sulphur separating out from the solution of hyposulphite, and the longer the time that elapses the more turbid the dilute solution will become. This experiment exemplifies the action of small particles on light. Examining the trough it will be found that whilst the light which passes through the solution principally loses blue rays, the light which is scattered from the sides is almost cerulean in blue, and can well be compared with the light from the sky. We can analyze the transmitted light very readily by focusing the beam from the positive pole of the electric light on to the slit of our colour apparatus, and placing the lens L₆ ([Fig. 6]) in position to form the large spectrum on the screen. We can also show the colour of the light which goes to form the spectrum, by sending the patch of light reflected from the first surface of the first prism just above it. We thus have the spectrum and the light forming the spectrum to compare with one another. Using this apparatus and inserting the trough of dilute hyposulphite in the beam, the spectrum is of the character usually seen with the electric light; but on dropping the dilute hydrochloric acid into the solution the same hues fall on the slit of the spectroscope which fell upon the screen to form the mock sun, and the spectrum is seen to change as the light changes from white to yellow, and from yellow to red. First the violet will disappear, the blue and the green being dimmed, the former most however; then the blue will vanish to the eye, the green becoming still less luminous, and the yellow also fading; the green and yellow will successively disappear, leaving finally on the screen a red band alone, which will be a near match to the colour of the unanalyzed light, as may be seen by comparing it with the adjacent patch formed from the reflected beam.

We have here a proof that the succession of phenomena is caused by a scattering of the shorter wave-lengths of light, and that the shorter the waves are the more they are scattered. It has been found theoretically by Lord Rayleigh that the scattering takes place in inverse proportion to the fourth power of the wave-length; thus, if two wave-lengths, which may be waves in the green and violet, are in the proportion of three to four, the former will be scattered as 1/3⁴ to 1/4⁴, or as 256 to 81, which is approximately as three to one. Consequently if the green in passing through a certain thickness of a turbid medium loses one-half the violet in passing through the same thickness will lose five-sixths of its luminosity. The inverse fourth powers of the following wave-lengths, which are within the limits of the whole visible spectrum, are shown below.

Supposing λ7000 by the scattering of small particles loses one-tenth of its luminosity, then λ6000 would have ·454 of its original brightness; λ5000, ·234; and λ4000, ·095; that is, whilst λ7000 would lose one-tenth only of its luminosity, λ4000 in the violet would retain not quite one-hundredth of its brightness.

During the years 1885, 1886, and 1887, the writer measured the luminosity of the solar spectrum at different times of the year, and at different hours of the day (see Phil. Trans. 1887: "Transmission of Sunlight through the Earth's Atmosphere"), and from the results he found that the smallest coefficient of scattering for one atmosphere at sea-level for each wave-length was ·0013, when λ⁻⁴ was for convenience sake multiplied by 10¹⁷ (thus λ6000⁻⁴ on this scale was 77·2), and that the mean was ·0017.

The following table shows the loss of light for the rays denoted by the principal lines given at page 26, using this last coefficient for different air thicknesses. This is equivalent to giving the intensity of the rays of sunlight when the sun is at different altitudes.

The sun traverses the following thicknesses of atmosphere when it is at the angles shown above the horizon.

Fig. 10.—Absorption of Rays by the Atmosphere.

It traverses thirty-two atmospheres when it is very nearly setting. Bougier and Forbes have calculated that the extreme thickness of the

atmosphere, traversed by its light when the sun is on the horizon, is approximately 35½ atmospheres. The absorption shown by 32 atmospheres will therefore be very close to that which would be observed at sunset on an ordinary day, and it will be seen that practically all rays have been scattered from the light, except the red, and a little bit of the orange.

As to the luminosity of the sun at these different altitudes, we can easily find it by reducing the luminosity curve of the sun at some known altitude by the factors in the table just given, for as many wave-lengths as we please, and thus construct another curve. The area of the figure thus obtained would be a measure of the total luminosity on the same scale as the area of the luminosity curve from which it was derived.

The following are the approximate luminosities of the sun when the light shines

It will thus be seen that the sun is 420 times less bright just at sunset than it is if it were to shine directly overhead, and about 350 times brighter than it is for a winter sun in a cloudless and mistless sky at twelve o'clock, for the altitude of the sun in our latitude is about 30° at that time, and corresponds with a thickness of two atmospheres, through which the sun has to shine. We all know that to look at the sun at any time near noon in a cloudless sky dazzles the eyes, but that near sunset it may be looked at with impunity. The reduction in luminosity explains this fact.

The distribution of the scattering particles in the atmosphere is very far from regular. As we ascend, the particles get more sparse, as is shown by the less scattering that takes place of the blue rays compared with the red. Thus at an altitude of some 8000 feet the mean coefficient of scattering is about ·0003, instead of ·0017, which it is at sea-level. It must be recollected that there is only about three-fourths of the air above us at 8000 feet, and it is less dense. There will therefore be a diminution of particles not only because there is less air, but because the air itself is less capable of keeping them in suspension. Up to 3000 or 4000 feet there is no very great marked difference in the scattering of light, as observations carried on during five years have shown; but above that the scattering rapidly diminishes, and at 20,000 feet it must be very small indeed, if the diminution increases as rapidly as has been found it does at the altitude of 8000 feet.

We must repeat once more that the blue of the sky is principally if not entirely due to the presence of these particles, the rays scattered by them, which are principally the blue rays, being reflected back from them, giving the sensation of blue which we know as sky-blue. The greater the number of these fine particles that are encountered by sunlight, the greater the scattering will be, and the bluer the sky. It is more than probable that the blue sky of Italy, so proverbial for being beautiful, is due to this cause, since from its geographical position the small particles of water must be very abundant there.

Carrying this argument further, we should expect that as we mount higher the blue would become more fully mixed with the darkness of space, and this Alpine travellers will tell you is the case. At heights of 12,000 feet or more, on a clear day, the sky seems almost black, and it is no uncommon thing to see this admirably rendered in photographs of Alpine scenery when taken at a height. Many of the late Mr. Donkin's photographs show this in great perfection, as also Signor Sella's.

Before quitting this subject we may call attention not only to the colour of the sun itself at sunset, but also to the colouring of the sky which accompanies the sun as it sinks. This colouring is often different to the colour that the sun itself assumes; but we can easily show that the effects so wonderfully beautiful are entirely dependent on this scattering of light by these small intervening particles in the air. We often see a ruddy sun, and perhaps nearly in the zenith, or even further away from the sun, clouds of a beautiful crimson hue, lying on a sky which appears almost pea-green, whilst nearer to the sun the sky is a brilliant orange, which artists imitate with cadmium yellow. Let us fix our attention first on the crimson cloud. The clouds of which the colouring is so gorgeous are often not 1000 feet above us, and were we to be at that altitude we should see the sun not quite so ruddy as we see it from the earth, and the cloud would consequently be illuminated by the sun with a more orange tint; but the light reflected from the cloud to our eyes has to pass through, say 1000 feet of dense atmosphere, and thus the total atmosphere that the light traverses in the latter case is always greater than the air thickness through which the direct light from the sun has to pass; hence more orange is cut off, and the light reflected from the cloud is redder. This red, however, will not account for the brilliant crimson and purples which we so often see. It has to be remembered that not sunlight alone illumines the cloud, but also the blue light of the sky. The feebler the intensity of the red, the more will the blue of the sky be felt in the mixture of light which reaches our eyes, and consequently we may have any tint ranging from crimson to purple, since red and blue make these hues, according to the proportions in which they are mixed.

Now let us see how we get the brilliant orange of the sky itself. When the evening is perfectly clear and free from mist and cloud, the orange in the sky is very feeble, showing that the intensity depends upon their presence. Now a look at the table will show that the sun is very close to the horizon when it becomes ruddy under normal conditions; but that when the light traverses a thickness of eight atmospheres, the blue and violet, and most of the green, are absent, leaving a light of yellowish colour. To traverse eight atmospheres the light has only to come from a point some eight degrees above the horizon. When the sun is near the horizon, it sends its rays not only to us and over us, but in every direction; and an eye placed some few thousand feet above the earth would see the sun almost of its midday colour, for sunset colours of the gorgeous character that we see at sea-level are almost absent at high altitudes. If a cloud or mist were at such an altitude the sunlight would strike it, and whilst only a small portion would be selectively scattered, owing to the general grossness of the particles, the major part would be reflected back to our eyes, and come from an altitude of over eight to ten degrees, and would therefore, after traversing the intervening atmosphere, reach us as the orange-coloured light of which we have just spoken. The clouds which are orange when near the sun, are usually higher than those which are simultaneously red or purple. The pea-green colour of the sky is often due to contrast, for the contrast colour to red is green, and this would make the blue of the sky appear decidedly greener. Sometimes, however, it is due to an absolute mixture of the blue of the sky and the orange light which illuminates the same haze. In the high Alps it is no uncommon occurrence for the snow-clad mountains to be tipped with the same crimson we have described as colouring the clouds, and this is usually just after sunset, when the sun has sunk so low beneath the horizon that the light has to traverse a greater thickness of dense air, and consequently to pass through a larger number of small particles than it has when just above the horizon. In this case the red of the sunlight mixes with blue light of the sky, and gives us the crimson tints. The deeper and richer tints of the clouds just after sunset are also due to the same cause, the thickness of air traversed being greater.

It is worth while to pause a moment and think what extraordinary sensual pleasure the presence of the small scattering particles floating in the air causes us; that without them the colouring which impresses itself upon us so strongly would have been a blank, and that artists would have to rely upon form principally to convey their feelings of art. Indeed without these particles there would probably be no sky, and objects would appear of the same hard definition as do the mountains in the atmosphereless moon. They would be only directly illuminated by sunlight, and their shadows by the light reflected from the surrounding bright surfaces.

CHAPTER VII.

Luminosity of the Spectrum to Normal-eyed and Colour-blind Persons—Method of determining the Luminosity of Pigments—Addition of one Luminosity to another.

The determination of the luminosity of a coloured object, as compared with a colourless surface illuminated by the same light, is the determination of the second colour constant. We will first take the pure spectrum colours, and show how their luminosity or relative brightness can be determined. Viewing a spectrum on the screen, there is not much doubt that in the yellow there is the greatest brightness, and that the brightness diminishes both towards the violet and red. Towards the latter the luminosity gradient is evidently more rapid than towards the former. This being the case, it is evident that, except at the brightest part there are always two rays, one on each side of the yellow, which must be equally luminous. If the spectrum be recombined to form a white patch upon the screen, and the slide with the slit be passed through it, patches of equal area of the different colours will successively appear; but the yellow patch will be the brightest patch. If the patch formed by the reflected beam be superposed over the colour patch, and the rod be interposed, we get a coloured stripe alongside a white stripe, and by placing our rotating sectors in the path of the reflected beam, the brightness of the latter can be diminished at pleasure. Suppose the sectors be set at 45°, which will diminish the reflected beam to one-quarter of its normal intensity, we shall find some place in the spectrum, between the yellow and the red, where the white stripe is evidently less bright than the coloured stripe, and by a slight shift towards the yellow, another place will be found where it is more bright. Between these two points there must be some place where the brightness to the eye is the same. This can be very readily found by moving the slit rapidly backwards and forwards between these two places of "too dark" and "too light," and by making the path the slit has to travel less and less, a spot is finally arrived at which gives equal luminosities. The position that the slit occupies is noted on the scale behind the slide, as is also the opening of the sectors, in this case 45°. As there is another position in the spectrum between the yellow and the violet, which is of the same intensity, this must be found in the same manner, and be similarly noted. In the same way the luminosities of colours in the spectrum, equivalent to the white light passing through other apertures of sectors, can be found, and the results may then be plotted in the form of a curve. This is done by making the scale of the spectrum the base of the curve, and setting up at each position the measure of the angular aperture of the sector which was used to give the equal luminosity or brightness to the white. By joining the ends of these ordinates by lines a curve is formed, which represents graphically the luminosity of the spectrum to the observer. In Fig. 11 the maximum luminosity was taken as 100, and the other ordinates reduced to that scale. The outside curve of the figure was plotted from observations made by the writer, who has colour vision which may be considered to be normal, as it coincides with observations made by the majority of persons. The inner curve requires a little explanation, though it will be better understood when the theory of colour vision has been touched upon.

Fig. 11.—Luminosity Curve of the Spectrum of the Positive Pole of the Electric Light.

The observer in this case was colour-blind to the red, that is, he had no perception of red objects as red, but only distinguished them by the other colours which were mixed with the red. This being premised, we should naturally expect that his perception of the spectrum would be shortened, and this the observations fully prove. If it happened that his perceptions of all other colours were equally acute with a normal-eyed person, then his illumination value of the part of the spectrum occupied by the violet and green ought to be the same as that of the latter. The diagram shows that it is so, and the amount of red present in each colour to the normal-eyed observer is shown by the deficiency curve, which was obtained by subtracting the ordinates of colour-blind curve from those of the normal curve. There are other persons who are defective in the perception of green, and they again give a different luminosity curve for the spectrum. These variations in the perception of the luminosity of the different colours are very interesting from a physiological point of view, and this mode of measuring is a very good test as to defective colour vision. We shall allude to the subject of colour-blindness in a subsequent chapter.

The following are the luminosities for the colours fixed by the principal lines of the solar spectrum, and for the red and blue lines of lithium, to which reference has already been made.

The failure of the red colour-blind person to perceive red is very well shown from this table. It will for instance be noticed that he perceives about one-tenth of the light at C which the normal-eyed person perceives.

A modification of this plan can be employed for measuring the luminosity of the spectrum, and it is excessively useful, because we can adapt it to the measurement of colours other than these simple ones. In the plan already explained it was the colour in the patch that was altered, to get an equal luminosity with a certain luminosity of white light. In the modified plan the luminosity of the white light is altered, for the luminosity of the shadow illuminated by the reflected beam can be altered rapidly at will by opening or closing the apertures of the sectors whilst it is rotating. The slit in the slide is placed in the spectrum at any desired point, and the aperture of the sectors altered till equal luminosities are secured. The readings by this plan are very accurate, and give the same results as obtained by the previous method employed.

It must be remembered that we have so far dealt with colours which are spectrum colours, and which are intense because they are colours produced by the spectrum of an intensely bright source of light. By an artifice we can deduce from this curve the luminosity curve of the spectrum of any other source of light. If by any means we can compare, inter se, the intensity of the same rays in two different sources of light, one being the electric light, we can evidently from the above figure deduce the luminosity curve of the spectrum of the other source of light (see [p. 109]).

We can now show how we can adapt the last method to the measurement of the luminosity of the light reflected from pigments.

Fig. 12.—Rectangles of White and Vermilion.

Fig. 13.—Arrangement for measuring the Luminosities of Pigments.

Suppose the luminosity of a vermilion-coloured surface had to be compared with a white surface when both were illuminated, say by gaslight, the following procedure is adopted. A rectangular space is cut out of black paper (Fig. 12) of a size such that its side is rather less than twice the breadth of the rod used to cast a shadow: a convenient size is about one inch broad by three-quarters of an inch in height. One-half of the aperture is filled with a white surface, and the other half with the vermilion-coloured surface. The light L (Fig. 13) illuminates the whole, and the rod R, a little over half an inch in breadth, is placed in such a position that it casts a shadow on the white surface, the edge of the shadow being placed accurately at the junction of the vermilion and white surface. A flat silvered mirror M is placed at such a distance and at such an angle that the light it reflects casts a second shadow on the vermilion surface. Between R and L are placed the rotating sectors A. The white strip is caused to be evidently too dark and then too light by altering the aperture of the sectors, and an oscillation of diminishing extent is rapidly made till the two shadows appear equally luminous. A white screen is next substituted for the vermilion and again a comparison made. The mean of the two sets of readings of angular apertures gives the relative value of the two luminosities. It must be stated, however, that any diffused light which might be in the room would relatively illuminate the white surface more than the coloured one. To obviate this the receiving screen is placed in a box, in the front of which a narrow aperture is cut just wide enough to allow the two beams to reach the screen. An aperture is also cut at the front angle of the box, through which the observer can see the screen. When this apparatus is adopted, its efficiency is seen from the fact that when the apertures of the rotating sectors are closed the shadow on the white surface appears quite black, which it would not have done had there been diffused light in any measurable quantity present within the box. The box, it may be stated, is blackened inside, and is used in a darkened room. The mirror arrangement is useful, as any variation in the direct light also shows itself in the reflected light. Instead of gaslight, reflected skylight or sunlight can be employed by very obvious artifices, in some cases a gaslight taking the place of the reflected beam. When we wish to measure luminosities in our standard light, viz. the light emitted from the crater of the positive pole of the arc-light, all we have to do is to place the pigment in the white patch of the recombined spectrum, and illuminate the white surface by the reflected beam, using of course the rod to cast shadows, as just described. The rotating sectors must be placed in either one beam or the other, according to the luminosity of the pigment.

The luminosities of the following colours were taken by the above method, and subsequently we shall have to use their values.

Suppose we have two or more colours of the spectrum whose luminosities have been found, the question immediately arises, as to whether, when these two colours are combined, the luminosity of the compound colour is the sum of the luminosities of each separately. Thus suppose we have a slide with two slits placed in the spectrum, and form a colour patch of the mixture of the two colours and measure its luminosity, and then measure the luminosity of the patch first when one slit is covered up, and then the other. Will the sum of the two latter luminosities be equal to the measure of the luminosity of the compounded colour patch? One would naturally assume that it would, but the physicist is bound not to make any assumptions which are not capable of proof; and the truth or otherwise is perfectly easy to ascertain, by employing the method of measurement last indicated. Let us get our answer from such an experiment.

Three apertures were employed, one in the red, another in the green, and the third in the violet, and the luminosity was taken of each separately, next two together, and then all three combined, with the results given above.

The accuracy of the measurements will perhaps be best shown by adding the single colours together, the pairs and the single colours, and comparing these values with that obtained when the three colours were combined. When the pairs are shown they will be placed in brackets; thus (R + G) means that the luminosity of the compound colour made by red and green are being considered.

The mean of the first four is 250·25, which is only 1/10% different from the value of 250 obtained from the measurement of (R + G + V) combined. Other measures fully bore out the fact that the luminosity of the mixed light is equal to the sum of the luminosities of its components. It is true that we have here only been dealing with spectrum colours, but we shall see when we come to deal with the mixture of colours reflected from pigments that the same law is universally true.

It will be proved by and by that a mixture of three colours, and sometimes of only two colours, be they of the spectrum or of pigments, can produce the impression of white light. If then we measure all the components but one, and also the white light produced by all, then the luminosity of the remaining component can be obtained by deducting the first measures from the last. For instance, red, green and violet were mixed to form white light. The luminosity of the white being taken as 100, the red and violet were measured and found to have a luminosity of 44·5 and 3 respectively. This should give the green as having a luminosity of 52·5. The green was measured and found to be 53, whilst a measurement of the red and green together gave a luminosity of 96·5 instead of 97.

CHAPTER VIII.

Methods of Measuring the Intensity of the Different Colours of the Spectrum, reflected from Pigmented Surfaces—Templates for the Spectrum.

Fig. 14.—Measurement of the Intensity of Rays reflected from white and coloured surfaces.

We will now proceed to demonstrate how we can measure the amount of spectral light reflected by different pigments. Let us take a strip of card painted with a paste of vermilion, leaving half the breadth white; and similarly one with emerald green. If we place the first in the spectrum so that half its breadth falls on the red, and the other half on the white card, we shall see that apparently the red and orange rays are undiminished in intensity by reflection from the vermilion, but that in the green and beyond but very little of the spectrum is reflected. With the emerald green placed similarly in the spectrum, the red rays will be found to be absorbed, but in the green rays the full intensity of colour is found, fading off in the blue. What we now have to do is to find a method of comparing the intensities of the different rays reflected from the pigments, with those from the white surface. We will commence with the second of the two methods which the writer devised with this object, and then describe the first, which is more complex. Suppose we have, say a card disc three inches in diameter, painted with the pigment whose reflective power has to be measured, and place it on a rotating apparatus with black and white sectors of say five inches diameter, and capable of overlapping so as to show different proportions of black to white (see [Fig. 42]). If we throw a colour patch (shown in [Fig. 14] as the area inside the dotted square) on the combination of black and white, and at the same time on the pigmented disc, it is probable that either one or other will be the brighter. By moving the slit along the spectrum it is evident, however, that a colour can be found which is equally reflected from them both whilst rotating. Take as an example the sectors as set at two parts white, to one part black, the centre disc being vermilion, the slit is moved along the spectrum until such a point is reached that the colour reflected from the ring and the disc appears of the same brightness, for it must be recollected that they cannot differ in hue, as the light is monochromatic. It will be found that the place where they match in brightness is in the red, the exact position being fixed by the scale at the back of the slide. Taking the proportion of black to white as three to one, the match will be found to take place in the orange. Increasing the proportion of black more and more, a point will be reached where the reflection takes place uniformly along the blue end of the spectrum, this will be from the green to the end of the violet. By sufficiently increasing the number of matches made, a curve of reflection can be made showing the exact proportion of each ray of the spectrum that is reflected. The uniform reflection along the blue end of the spectrum shows that a certain amount of white light is reflected from the pigment.

Next taking the emerald green disc, if we adopt the same procedure it will be found that for some shades of the ring there are two places in the spectrum from which the colours reflected give the same brightness. By plotting curves in exactly the same way as that shown for the curve of luminosity at page 78, substituting for the open aperture of the sector the angular value of the white used, we can show graphically the correct reflection for each part of the spectrum. Sometimes three places in the spectrum will be read, as giving equal reflections from the coloured disc and the grey ring.

The accompanying figures show the results obtained for reflection from vermilion, emerald green, and French blue, after having made a correction for the white by adding the amount which the black reflects.

The scale is that of the prismatic spectrum employed. On page 46 we stated that a white surface could be made to appear darker than a black surface, by illuminating the latter and cutting off the light from the former. By placing the black surface in place of one of the coloured ones, as shown in page 82, the luminosity of the black surface can be ascertained. In this case it was found that almost exactly 5% of the white light from the crater of the positive pole was reflected.In the table the original measures are shown, and also the corrected measures, and for convenience sake the intensity of every ray throughout the length of the spectrum reflected from white, has been taken as 100. The position of the reference lines on the scale (Fig. 15) are as follows—

Fig. 15.—Intensity of Rays reflected from Vermilion, Emerald Green, and French Ultramarine.

B=101, C=96·25, D=89, E=79·9, F=71·5, G=53·5.

VERMILION.

EMERALD GREEN.

FRENCH ULTRAMARINE BLUE.

These three measurements have been given in full, since they will be useful for reference when other experiments are described.

Fig. 16.—Method of obtaining two Patches of identical Colour.

When we have to measure the colour transmitted through coloured bodies, we have to adopt a slightly different plan, which is extremely accurate. The first thing necessary is to make some arrangement whereby two beams of identical colour—that is, of the same wave-length—reach the screen, one of which passes through the transparent body to be measured, and the other unabsorbed. If we in addition have some means of equalizing the intensity of the two beams, we can then tell the amount cut off by the body through which one beam passes. The method that would be first thought of would be to use two spectra, from two sources of light; but should we adopt that plan there would be no guarantee that the spectra would not vary in intensity from time to time. The point then that had to be aimed at was to form two spectra from the same source of light, and with the same beam that passes through the slit of the collimator. Here we are helped by the property of Iceland spar, which is able to split up a ray into two divergent rays. By placing what is called a double-image prism of Iceland spar at the end of the collimator, we get two divergent beams of light falling on the prisms, and by turning the double-image prism we are able to obtain two spectra on the screen of the camera one above the other, and if the slit of the slide be sufficiently long two beams would issue through it of identical colour, and separated from one another by a dark space, the breadth of which depends on the length of the slit of the collimator. It is to be observed that by this arrangement we have exactly what we require: a light from one source passes through the same slit, is decomposed by the same prisms, and as the beams diverge in a plane passing through the slit of the collimator, the length of spectrum is the same. The problem to solve is how to utilize these two spectra now we have got them. We can make the light from the top spectrum pass through the coloured body by the following artifice. Let us place a right-angled prism in front of the top slit, reflecting say the beam to the right, and after it has travelled a certain distance, catch it by another right-angled prism, and thus reflect it on to the screen. Already in the path of the ray, issuing through the slit from the bottom spectrum, the lens L₄ is placed, forming a square patch on the screen. By placing a similar lens in the path of the other ray after reflection from the second right-angled prism, we can superpose a second patch of the same colour over the first patch, and by putting a rod in the path of the two beams we can have as before two shadows side by side, but this time each illuminated by the same colour. One shadow will be more strongly illuminated than the other, owing to the different intensities of beams into which the double-image prism splits up the primary ray. The two, however, can be equalized by placing a rotating apparatus in the path of one of the beams. When equalized the sector is read off, and tells us how much brighter one spectrum is than the other. Thus suppose in the direct beam the sectors had to be closed to an angle of 80°, to effect this, the bottom spectrum would be 180/80, or 2·25 times brighter than the bottom spectrum. It should be noted that as the two spectra are formed by the identical quality of light, this same ratio will hold good throughout their length. If it does not, it shows that the double-image prism is not in adjustment, and that the same rays are not coming through the slit in the slide, and it must be rotated till the readings throughout are the same. One of the most sensitive tests for adjustment is to form a patch with orange light, when the slightest deviation from adjustment will be seen by the two patches differing in hue.

We can now place the coloured transparent object in the path of the beam which is most convenient, and by again equalizing the shadows, measure the amount it cuts off; this we can do for any ray we choose. As both right-angled prisms can be attached to the card or slide which moves across the spectrum, nothing besides the card need be moved. In the following diagram we have the proportion of rays transmitted by the three different glasses, red, green, and blue, in terms of the unabsorbed spectrum. Take for instance on the scale of the spectrum the number 11. The curve shows that at that particular part of the spectrum which lies in the blue, the blue glass only allowed 4/100 or 1/25 of the ray to pass, whilst the green glass allowed 10/100 or 1/10 to pass. So at scale No. 4 in the orange, through the blue only 2% was transmitted, through the green glass 4%, and through the red 20%.

Fig. 17.—Absorption by Red, Blue, and Green Glasses.

Fig. 18.—Light reflected from Metallic Surfaces.

1. Vermilion 2. Carmine. 3. Mercuric Iodide. 4. Indian Red.
Fig. 19.

From such curves as these we can readily derive the luminosity curves of the spectrum, after the white light has passed through the coloured object. All we have to do is to alter the ordinates of the luminosity curve of white light in the proportion to the intensities of the rays before and after passing through the object. It will be seen that when the luminosity curve of the spectrum of any source is known, this method holds good.

1. Gamboge. 2. Indian Yellow. 3. Cadmium Yellow. 4. Yellow Ochre.
Fig. 20.

The intensity of the different rays of the spectrum reflected from metallic surfaces can also be measured, if for the first or second right-angled prism a small piece of the metal is substituted, using it as a reflecting surface, as can also the rays reflected from any surface which is bright and polished. In [Fig. 18] the dotted curves show the luminosity of the spectrum reflected from the different metals, curve V being that of white light. These curves are derived by reducing the ordinates of curve V proportionately to the intensity curves. Thus at 49 brass reflects 77% of the light, and the luminosity of the white is 80. The luminosity of the light from the brass is therefore 77/100 of 80, or 61. This shows the method which is adopted, of deducing luminosities from intensities.

1. Emerald Green. 2. Chromous Oxide. 3. Terre Verte. Fig. 21.

The light reflected from pigments can also be measured by the same plan. The procedure adopted is that carried out when measuring their luminosities, viz. to cause the ray from one spectrum to fall on a strip of a white surface, and that from the other on a strip of the coloured surface (see [page 82]). This is a more convenient method than that just described, when the coloured surface is small. The annexed figures (Figs. 19, 20, 21, 22) show the results obtained from various pigments.

1. Indigo. 2. Antwerp Blue. 3. Cobalt. 4. French Ultramarine. Fig. 22.

Fig. 23.—Method of obtaining a Colour Template.

From curves such as these we are able to produce the colour of the pigment on the screen from the spectrum itself. This is a useful proof of the truth of the measurements made. To do this we must mark off on a card (Fig. 23) the absolute scale of the spectrum along the radius of a circle, and draw circles at the various points of the scale from its centre. From the same centre we must draw lines at angles to the fixed radius corresponding to the various apertures of the sectors required at the various points of the scale to measure the light reflected from a pigment. Where each radial line cuts the circle drawn through the particular point of the scale to which its angle has reference, gives us points which joined give a curved figure. Such a figure, when cut out and rotated in front of the spectrum in the proper position (as for instance by making the D sodium line correspond with that on the scale), will cut off exactly the same proportion of each colour that the pigment absorbs. The spectrum, when recombined, should give a patch of the exact colour of that measured. The spectrum must be made narrow, as the template is only theoretically correct for a spectrum of the width of a line, as can be readily seen.

Templates like these will always enable any colour to be reproduced on the screen, and if the light be used for the spectrum in which the colour has to be viewed, be it sunlight, gaslight, starlight—whatever light it is—the colour obtained will be that which the pigment would reflect if it were viewed in that light.

The identity of the colour produced on the screen by this plan with that measured, can be readily seen by placing the latter in the reflected beam of white light alongside the coloured patch formed on the white surface.

Fig. 24.—Template of Carmine.

In Fig. 24 we have a mask or template of carmine, which was used for determining if the measurements were right. The black fingerlike-looking space on the right was the amount of red reflected light, and the other that of the blue and violet; scarcely any light at all was reflected from the green part of the spectrum.

Fig. 26.—Absorption of transmitted and reflected Light by Prussian Blue and Carmine.

On page 108 we have given the diagram of the luminosity of the spectrum in reference to a standard white light. It will bring this luminosity more home if, in a similar manner to that described above, we make a template of this curve ([Fig. 25]). We can place a narrow slit horizontally in front of the condensing lens of the optical lantern, and throw an image of it on to the screen. If in close contact with this slit we rotate the template, we shall have on the screen a graduated strip of white light, giving in black and white the apparent luminosity of the spectrum as seen by the eye.

Fig. 25.—Template of Luminosity of White Light.

It has been stated in chapter V., that it is generally immaterial whether a pigment is in contact with the paper or away from it, so long as the light passes through the pigment. The above figure ([Fig. 26]) shows the truth of this assertion. I. and II. are the curves taken of the light transmitted by Prussian blue and carmine respectively, and III. and IV., from the light reflected from these colours on paper.

Fig. 27.—Collimator for comparing the intensity of two sources of Light.

To measure the difference in the intensities of the rays of different sources of light we can use a spectroscopic arrangement with two slits (S) (Fig. 27) placed in a line at right angles to the axis of the collimator. One slit is a little below the other, the rays being reflected to the collimating lens L, by means of two right-angled prisms P, and two spectra are formed, one above the other. By placing the rotating sectors in front of one of the sources, the intensities of the different parts of the spectrum can be equalized and measured.

Fig. 28.—Spectrum Intensities of Sunlight, Gaslight, and Blue Sky.

The curves for the annexed figure (Fig. 28) were derived from measures taken in this manner. If the rays of a May-day sun are taken at 100, it will be seen what a rapid diminution there is in the green and the blue rays in gaslight. Gaslight only possesses about 20% of the green rays, whilst of the violet hardly 5%. On the other hand the light which comes to us from the sky shows a very marked falling off in the yellow and red rays. A very easy experiment will convince us of the difference in colour between skylight and gaslight. If we let a beam of daylight fall on a sheet of paper at the end of a blackened box, and cast a shadow with a rod by such a beam, and then bring a lighted candle or gas-flame so that it casts another shadow of the rod alongside, one shadow will be illuminated by the artificial light, and the other by the daylight. The difference in colour will be most marked: the blue of the latter light and the yellow of the former being intensified by the contrast (see [page 198]).

Fig. 29.—Comparison of Sun and Sky Lights.

By a little trouble the blue light from the sky may be compared with sunlight. A beam of light B (Fig. 29) is reflected by a silvered glass mirror from the blue sky into the box HH, at the end of which is a screen E. Another mirror A, which is preferably of plain glass, reflects light from the sun on to a second unsilvered mirror G (shown in the figure as a prism), which again reflects it on to the screen, and each of these lights casts a shadow from the rod D; K are rotating sectors to diminish the sunlight, and we can make two equally bright shadows alongside one another. The bluer colour of the sky will be very evident.

CHAPTER IX.

Colour Mixtures—Yellow Spot in the Eye—Comparison of Different Lights—Simple Colours by mixing Simple Colours—Yellow and Blue form White.

The colour of an object in nature, without exception we might almost say, is due, not to one simple spectrum colour, or even to a mixture of two or three of them, but to the whole of white light, from which bands of colour are more or less abstracted, the absorption taking place over a considerable portion or portions of the spectrum. Notwithstanding this we shall now experimentally show that every colour can be formed by the simple admixture of not more than three simple colours, if they be rightly chosen, and from this we shall make a deduction regarding vision itself. We are in a position to obtain three simple colours by means of a slide containing three slits. Now for our purpose we require that the three slits can be placed in any part of the spectrum, and that they can be narrowed or widened at pleasure. Instead of a card the writer uses a metal slide, as shown in Fig. 30.

Fig. 30.—Slide with slits to be used in the Spectrum.

It will be seen that the three slits can be closed or opened from the centre by a parallel motion. They also slide in a couple of grooves, so that they can be moved along the frame into any position. The position they occupy is indicated by a scale engraved on the front of the slide. Behind the grooves in which the slits move are another pair of grooves, into which small pieces of card CCCC can slide, and thus close the apertures between the slits. By this arrangement all rays except those coming through the slits themselves are cut off. The metal frame fits on to an outer wooden frame, which slides in the grooves used with the card in the apparatus as already described. It is convenient always to keep the scale on the back of this wooden slide in the same position as regards the shadow of the needle-point used for registering the position, and to move the slits along their grooves when a change in position is required. Using these three slits three different colours can be thrown on the same square patch on the screen.

A very crucial experiment is to see if we can make white light by the admixture of three colours, for if this can be done it almost follows that any colour can be formed. We must use the colour patch apparatus, and begin with placing one slit in the violet near the line G, another between E and F, and a third between B and C of the solar spectrum, and fill up the gaps between them with cards as shown in the figure. For our present purpose it is better to make the colour patch and the white patch touch each other, not using the rod, as by this means we avoid fringes of colour. We shall find that the aperture of the slits can be so altered that we can produce a perfect match with the white reflected light. By placing the rotating sectors in front of the reflected beam we can reduce its intensity, so that the two patches are equally bright. By a tapering wedge we can measure the width of the slits, and thus get the proportions of these three different colours which must be used to give the white. This is a sample of the method that we employ when we match any other colour. Suppose, for instance, it be wished to measure the colour of a solution of bichromate of potash; it is placed in the path of the reflected light, and we have an orange strip of light which we have to match. In this case it will be found that the slit in the blue has to be closed entirely, and only the green and red slits opened. The intensities of the two lights are equalized by the rotating sectors as before. So again with a solution of permanganate of potash. In this instance no green light will be required (or if any of it but a trifle), and the colour of the permanganate will be formed by the rays coming through the blue and red slits.

This plan is a very useful one for measuring all kinds of transparent colours in terms of three rays. The method of finding the intensity of any ray of the spectrum transmitted by any such medium has already been explained. The latter has one advantage over the former, in that the measurements by it are exact, whatever source of light be used to form the spectrum. By the method now described this is not the case. For instance, the colour of permanganate of potash may be matched in the electric light with the red and blue slits. If the limelight were substituted for the electric light, it would be found that the slits would require other apertures, not proportional to those already formed, to match the colour of this substance.