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 gla.s.s 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 gla.s.s, 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 subst.i.tuted 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.

Fig. 31.--Screen on which to match Gamboge.

If we wish to register the tint of any pigment, we have to slightly alter our mode of procedure. Suppose, for instance, we wish to register the colour of gamboge. In such a case we paint a small bit of card (Fig.

31) with the pigment, and divide the white s.p.a.ce on which the colour patches are thrown into two parts, and cover one-half with the pigmented card, leaving the other half white. The reflected beam illuminates the pigment, and the spectrum patch the white. The widths of the three slits are then altered till the two tints agree, and the brightness matched by means of the rotating sectors.

There are certain sad and aesthetic colours which it might be considered cannot be matched by a mixture of three colours. A brown colour, or "eau de nil," might appear to come out of the range of matching. These colours, however, can be matched in precisely the same manner as the brighter colours are matched. Thus a brown pigment will be found to require red and a little green, and a trifle of blue; and the only difference between it and a brighter shade of the same colour, is that more total light has to be cut off from it to give the sombreness. A sad colour only means a pigment or dye which reflects but little light, and if that be so it can naturally be matched by using but very small quant.i.ties of the compounding colours.

There is one curious phenomenon to which attention may be called in this matching, which is worthy of remark. The match will be found to differ according as the patches are compared from a distance of a couple of feet, or from a considerable distance. More green will be required in the latter case than in the former. If matched at a distance of about six feet, and the eyes be then turned so that the edge of the patch falls on their centres, it will be noticed that the colour mixture appears of a green hue. This last experiment indicates that the retina is not equally sensitive for all colours throughout its area.

Physiologists tell us that what is known as the yellow spot occupies a central position in the retina, and that it absorbs a part of the spectrum lying in the green. Now when the eyes are close to the patch, its image occupies a considerable part of the retina, and the colour is compounded as it were of the colour as seen on the yellow spot, and of that beyond it, for the yellow spot will take in an image of from six to eight degrees in angular measurement. When viewed at a distance we have the image of the patch falling almost entirely on the yellow spot, and hence a greater quant.i.ty of green is required, as it has to make up the deficiency caused by the absorption. When the eyes are turned a little on one side the image falls on the outside of the yellow spot, and the patch illuminated by the mixed light appears green, compared with the patch illuminated with the white reflected beam.

It is thus evident that when colour matches have to be made, the distance of the eye from the screen should always be stated, as also the dimensions of the patches viewed. It may be fairly asked why, if the half patch illuminated by the mixed colours appears greener when the eye is turned, the other should not equally do so. This is a very fair question to ask. It must be remembered that one strip is illuminated with white light, in which every coloured ray of light is compounded, whilst in the other only three rays are blended. The green ray chosen happens to be taken from that part of the spectrum which is absorbed by the yellow spot; but all of the green rays of the spectrum are not so much absorbed, hence in ordinary white light, in which all the green rays are present, only a small percentage of the total green in the spectrum is absorbed, compared with that absorbed from the single green ray with which the match is made. No doubt both patches are really greener when the eye receives the impression of their images outside the yellow spot, but one is much greener than the other, and it is thus _comparatively_ green. It is possible to make a match with some colours with a blue-green in which the phenomenon described does not appear; but in cases where a match has to be made with colours in which but little blue is required, it would be impossible to make it, owing to the blue existent in such a green-blue ray.

We will now return to our compounding of three colours to make white.

Why have we chosen the positions of the slits which we did in the spectrum for its formation? Would not other positions answer as well?

Let us give our answer by experiment. Let us move the slit which is now in the green towards the red; we shall find that as we do so--and keeping the blue slit of the same width--that we shall have to close the red slit, and alter the aperture of the green slit itself. If we reason on this point we shall be forced to the conclusion that the green slit lets through more red light of some description, as less red from the red slit is required to make the match. If we move the green slit almost into the yellowish green, we shall find that the red slit has to be entirely closed, and that white light is formed of the two colours, yellowish green and violet. This shows us that the yellowish green colour here used is formed by a mixture of the red and green rays which pa.s.sed through the two slits in their original positions. If we replace the slits in these positions and close the violet slit, we are at once able to verify it.

If we again form white light with the slits in their original positions, and move the green slit towards the blue, we shall find that, keeping the red slit at a constant aperture, the blue slit will have to be closed, and the green slit altered in width. The necessity of lessening the aperture of the blue slit shows that there is a certain amount of blue light coming through the green slit. At one point, when the slit has travelled into the blue-green, the blue slit may be entirely closed, and white light be formed of this and the red, showing that the blue-green colour is composed of the same proportions of blue and green which pa.s.sed through the blue and green slits in their original position. The positions chosen were arrived at by the writer from experiments made in this manner, moving first one slit and then the others, and the position of the green slit was confirmed by a consideration of the neutral point which exists in a green colour-blind person's spectrum.

The method of mixing three colours together gives us a means of imitating all kinds of white light, as it does of coloured light. At page 110 we have already given a diagram of the relative amounts of spectrum colours in sunlight, skylight and gaslight. If we by any means throw a patch of the light which we wish to match on the patch formed by the colour patch apparatus, and interpose the rod, we can measure the apertures of the three slits, and thus arrive at the relative proportions of each colour present. In an experiment carried out, sunlight, the electric arc-light, and gaslight were compared in this manner. The following are the results, the red being near the C line, the green near the E line, and the violet near the G line of the solar spectrum.

+--------+-----------+----------+-----------+-----------+ | | Sunlight. | Electric | Gaslight. | Skylight. | |--------+-----------+----------+-----------+-----------+ | Red | 100 | 100 | 100 | 100 | | Green | 193 | 203 | 95 | 256 | | Violet | 228 | 250 | 27 | 760 | +--------+-----------+----------+-----------+-----------+

Now from the above it might seem that as three simple spectrum colours will give us the colour of any pigment, that therefore two colours ought to give us the same colour as any intermediate simple colours in the spectrum which lie between them; for instance, that the simple blue-green ought to be obtained by mixing spectral green and spectral violet together. This can be ascertained with a single colour patch apparatus, by cutting a slit in the card that fills up the aperture between the two adjustable slits, and deflecting the beam transmitted through it by a right-angled prism, and back on to the screen through another similar prism, as described in chapter VIII. It is more convenient, however, to use a duplicate apparatus precisely similar to the first, with the exception that no collimator is required, placing them side by side, and mirrors making the reflected beam from the first traverse the second set of prisms. There will be a reflected beam from the second apparatus, which can be utilized in the same way as was that from the first apparatus, and the two spectra will vary together in brightness, as will also the new reflected beam, since they all are formed by the light coming through one slit. A patch of the colour intermediate between the two is thrown on the screen from the second apparatus, and the second patch from the first apparatus overlaps it. A rod placed in the usual manner throws two shadows, which are illuminated by the two different beams. If blue-green be a colour it is wished to match, it will be found that no matter in what part of the violet and green the slits are placed, no match can be effected. But if some very small quant.i.ty of red light be mixed with simple blue-green, that then a colour identical in every respect as regards the eye can be obtained from the violet and green of the first apparatus. It must be remembered that a mixture of red, green and violet form white, and that they are mixed in definite proportions. No matter how feeble in intensity the white may be, the same proportions will still obtain. In the above experiment, as the blue-green must contain violet and green, the small quant.i.ty of red must combine with the proper proportion of violet and green, and will form white light, so that the match is obtained by the residues of the violet and green mixed with the small quant.i.ty of white light, of which the red is the indicator.

We can test the truth of this argument in a very simple way. If we add to the colour with which the match has to be made a small quant.i.ty of white light from the reflected beam, cutting off more or less by the rotating sectors, we can get the exact hue of the impure blue-green made by the mixture of the colours coming through the two slits; and further we shall find that the amount of white added corresponds with the amount of red which would be required when the components of the white light in the terms of the three colours are taken into account. For spectrum colours between the violet and the green it may therefore safely be said that no match can be effected by the mixture of violet and green light; but that it always gives the intermediate colour diluted with white light. For colours between the green and the red of the spectrum, a very close, if indeed not an exact match, can be made with the red and green slits, without the addition of white.

If we take from the second apparatus light from above the position of the violet slit in the first apparatus, that is, nearer the limit of visibility, it will be found that a match is made, for at all events a very considerable way with the violet slit alone, by merely reducing the aperture, thus showing that the colour is the same, only less intense.

In the same way it will be seen that the rays coming from any point between the lower limit of the spectrum to a little below the C line are identical in colour.

As we have arrived at the fact that in colour mixtures of violet and green, white light is to be found in the colour produced, it follows that either the violet or the green, or both, must themselves contain some small proportion of white. It might perhaps be said that violet is really a mixture of red and blue, and hence the white in the mixture with the green; but if in the first apparatus we place one slit in the purest blue we can find, and the other in the red, and throw a violet patch on the screen from the second apparatus, we shall be unable to form the same hue of violet by any means; it will always be diluted with white. Now as the very blue we are using, if matched as above by green and violet, requires white light to be added to it, and as to match the violet with the same blue and red, white light has also to be added to it, it follows that the violet must be freer from white light at all events than the blue.

There is one other experiment that must be mentioned before leaving for a time this part of our subject, viz. the formation of white by a mixture of yellow and blue. If one of the slits be placed in the yellow of the spectrum, a position will be found in the blue where, if a second slit be placed, and the apertures are adjusted, an absolute match with the reflected white of the apparatus can be secured. This experiment will be referred to later on, when considering the question of primary colours.

The above experiments have a great bearing on the theory of colour vision, and should be considered very carefully in connection with the shortened spectrum which we have shown exists when red colour-blind people are observing its luminosity.

There is one point to be recollected in relation to the mixtures of the three or two different colours which make white light. If different coloured pigments be illuminated by the "made" white light, they will not appear of the same hues, as a rule, as when viewed by ordinary white light. They will vary not only in colour, but in brightness. This might be expected when the spectral light which they reflect is taken into account.

CHAPTER X.

Extinction of Colour by White Light--Extinction of White Light by Colour.

In the last chapter we have shown the impossibility of matching the hue of the simple colours between the violet and the green, unless a certain and appreciable quant.i.ty of white light be added to them. We will now turn to a phase of colour measurement which will materially help us to see why, in some cases, the addition of white light to the simple spectrum colours, between the red and green, does not appear necessary in order to make a match with a mixture of red and green.

We will ask ourselves two questions: one is, whether any colour, and if so how much, can be added to white without appearing to the eye? and the other, if any, and if so how much, white light can be added to a colour without its being perceived?

Perhaps one of the readiest methods of explaining exactly what we mean is by a rotating disc. Suppose we have a red disc, of nine or ten inches in diameter, and at every one inch from the centre paste on it a white wafer about one-eighth of an inch in diameter, and cause it to rapidly rotate. On examination we shall find that pink rings will be formed by the combination of the white and red near the centre, but that towards the margins no rings will be visible, owing of course to more red being combined with the same amount of white. This shows that the eye is only sensitive to a certain degree, and cannot distinguish a very small diminution in colour purity. The intensity of the light has something to do with the number of these pink rings which are visible, as may readily be tested in a room. If the rotating disc be placed near a window, and the number of rings visible be counted, a different number will be visible when it is placed in a dark corner. A kindred experiment is to place red circular wafers upon a white disc, and note the rings visible.

This gives the sensitiveness of the eye for the diminution in intensity at the other end of the scale. It will be found that there is a marked difference between the two.

Fig. 32.--Diaphragm in front of Prism.

It is more instructive if we experiment with pure colours, and so we must resort to our colour patch apparatus described in Fig. 6. If a small circular aperture about quarter of an inch in diameter be cut in a card, and placed in front of the prism nearest the camera lens (Fig.

32), the colour patch, instead of being an image of the face of the prism, will be an image of the circular hole, and when the slit is pa.s.sed through the spectrum we shall have a coloured spot on the screen, on which we can superpose a patch of white light from the reflected beam. There are two ways in which we can reduce the intensity of the spot, by narrowing the slit through which the spectral ray pa.s.ses or by placing the rotating sectors in front of the coloured beam. This last, perhaps, is the readiest plan, as it only involves the reading of the sector. We can then diminish the intensity of the coloured spot to such a degree that by its dilution with white light it will entirely disappear. It will be found that red disappears at a different aperture of sector to that required for the green, and the green to that for the blue.

From our previous experiments in chapter VII. we know the luminosity of the spectrum to the eye, and it will be of interest to see what relation the luminosity at which the spots of different colour disappear, when they are so diluted with white light, bear to the total luminosity of these rays.

In a set of measurements made it was found that the reduced angular apertures required for the colours indicated by the following were:

B required 300* of aperture.

C " 56 "

D " 14 "

E " 22 "

F " 150 "

G " 2100* "