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.

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.

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.

Normal Eye.  Red Colour Blind.
A Very dark Red 
B Red (Crimson) 1·0   0
Red Lithium Red (Crimson)   8·5     ·5
C Red (Scarlet)   20·6   2·1
D Orange   98·5   53·0
E Green   50·0   49·0
F Blue Green     7·0   7·0
Blue Lithium Blue   1·9   1·9
G Violet     ·6     ·6
H Faint Lavender   —   —

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.

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.

Electric Light.
White 100
Vermilion   36
Emerald Green   30
Ultramarine     4·4
Orange   39·1
Black     4
" (different surface)    5·1

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.

Colours Measured.Observed Luminosity.
R 203·0
G   38·5
V     8·5
(R + G)242
(G + V)  45
(R + V)214
(R + G + V)250

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.

R + G + V =250·0
(R + G) + V =250·5
(R + V) + G =252·5
(G + V) + R =248·0
(R + G + V)=250·0

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.