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the coloured portions of the spectrum will be seen alike, and may be represented by that colour of the normalsighted which corresponds to the centre of this coloured portion. It is obvious that no difference will be seen in colour between the various portions of the coloured band, because if a person is not able to see any difference between yellow and blue, it is evident that he will not see any difference between red and orange. What are the two colours seen when the whole of the gray has disappeared ? As I have shown, the colour will be represented by that colour which in the normal-sighted corresponds to the centre of each of the two colours. According to the theory, these centre points ought to correspond to the centres of the two halves of the physical colour series. The two colours should be complementary to each other, It is evident that these complementaries must be those which are closest to each other as far as the spectrum is concerned. The complementaries which are adjacent to each other are yellow and blue.

These colours are the yellow and blue, having the wave-lengths 2120 and 1781 respectively, the ratio of the wave-lengths being 1.190. These two colours should meet between the blue and the green.

The next step will be the formation of another point of difference at the centre of the series; that is to say, there will be three definite points of difference instead of two. These three points of difference will be the centres of the terminal psycho-physical units, and the centre of the spectrum; that is to say, the three points will be the centres of the red, green, and violet, of the spectrum.

It will be noticed in a psycho-physical colour series, in which a person is able to see three colours, that the two points of greatest difference will be between the points of difference of a person who is only able to see two colours and the ends of the spectrum, because his approximate units are smaller. Taking, for convenience, the centre point of an approximate unit as representing that unit, it will be noticed, that as more colours are seen, these points are gradually moved towards the ends of the spectrum. In the normal-sighted, therefore, the two colours presenting the greatest contrast are the red and violet.

There are many persons who, whilst admitting readily enough that the three points of greatest difference in the spectrum are the red, green, and violet, would object to red and violet being the two points of greatest difference. It is evident enough, in the series of discs, that the largest disc presents the greatest contrast to the smallest one; and, in the sound series, it is evident that the deepest bass notes form the greatest contrast to the highest treble, provided that both are heard distinctly. There are several reasons why violet should not, at first sight, appear the colour most strongly contrasting with red. The most important reason is, that very few of the violets met with in nature are pure—that is, the object is found to reflect some of the red rays in addition. If we compare monochromatic strips of spectral colour we shall see that true violet presents the greatest possible contrast to red. The difference is admirably illustrated by using the terms warm and cold, which artists have applied to these colours. Again, when violet is contrasted with blue the former does acquire a reddish tinge, which is due to the effects of simultaneous contrast. It is of the greatest importance that when one colour is being considered, the others should be excluded.

The other reason for not regarding red and violet as the most dissimilar colours, is that violet is regarded by most persons as a mixture of red and blue. But red and blue do not make violet, as will be seen by mixing the

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pure spectral colours. Red and blue make a purple, which plainly shows the element of red. Violet is a colder colour than blue, and, instead of being a transition colour between blue and red, it is more unlike red than blue. Let the reader look at spectral violet, and he will be unable to detect any red element whatever. This shows that colours must be looked at as forming a series, not a circle. As red and violet, and red and blue can be combined we have a double series, one consisting of the spectral colours, and the other consisting of hues of purple. Those who look at colour from a scientific standpoint, regard the complementary of any colour as that which contrasts most strongly with it. It will be found, on referring to the chapter on the physiological phenomena of colour, that this is not the case.

Another point for consideration is : Shall we take the end members of the series as the points of comparison ? In looking at the series of discs to which I have referred, we should naturally take Nos. 1 and 20 as forming the greatest contrast. But this would only be on account of the knowledge we possess that No. 20 is the largest disc, and No. 1 the smallest. For all practical purposes, No. 19 presents quite as great a contrast to No. 1 as No. 20 does. If we cannot distinguish any difference between members of a series, as far as we are concerned, they may be considered to be exactly alike.

It is evident that there is an absolute psycho-physical unit at each end of the colour series, represented by the spectrum. I have defined an absolute psycho-physical unit as a portion of a physical series, in which it is impossible to see any difference between the members of the series, even under the most favourable circumstances, and with the most careful comparison. Then, not only the end member of the series, but any one of the members, included in the absolute psycho-physical unit, might be taken to represent the unit, without in any way affecting the result. In addition to there being an absolute psycho-physical colour unit at each end of the spectrum, there is an approximate colour unit, and these are the colours red and violet. As an approximate colour unit consists of a portion of a physical series, the members ineluded being not easily distinguished from each other, and so much alike as to be called by the same name, cæteris paribus, the central point of this unit will be that which is most representative of the colour. If any portion of the unit presented any marked difference in intensity, it is probable that the most intense portion would be selected.

Having shown how the psycho-physical colour series appears with three approximate psycho-physical colour units, we must consider where the fourth point of difference would be situated. As I have stated in the last chapter, if the units of a physical series differ from those adjacent to them in a proportional manner, the fourth and fifth points of difference will appear at the same time, and be situated at points midway between the centre and ends of the series. The units of the light series do not differ in a proportional manner if we are to regard the wave theory of light as the correct one. Therefore, in the psychophysical colour series the fourth point of difference will appear before the fifth, and be situated at the point of greatest difference. The waves of light at the red end of the spectrum are larger than those at the violet end, and, therefore, the fourth point of difference will appear at a point midway between the red and the centre of the green, namely, the yellow. An example with smaller numbers will show why the fourth point of difference should appear on the red side of the green. Let us suppose that we have a series of vibrating members, the vibrations being from 5 per second for the lowest member, to 105 per second for the highest member. There will be much more difference between the first and second member of the series than between the last member, and the one just before it. In the first case there will be a difference of }, in the second case 104, a very much smaller fraction. The fifth point of difference will appear midway between the violet and the centre of the green. The sixth point of difference will appear on the red side of the fourth point of difference. There will then be two points of difference between the red and the centre of the green, namely, orange and yellow. It is evident that when orange is seen, the fourth point of difference—namely, yellow-will appear to have moved more towards the green, the fourth point of difference now being a combination of the two, namely, orange-yellow. This can be seen to take place if a spectroscope be arranged so that no orange is seen. A spectrum of this kind can be obtained with a fine slit; on slightly widening the slit so that more light is admitted the orange will be seen, and the yellow will appear to change its position and move towards the green. The seventh point of difference will appear between the green and the violet; that is to say, there will be two points of difference, or colours seen, between the green and the violet, instead of one. It is not necessary to consider the extension of the series any further, because I have not met with a person who could see more than seven colours in the spectrum. The series could be extended ad infinitum, the extra point of difference being put first on the red side of the green, then on the violet side.

I have now discussed the theory of psycho-physical perception in its application to colour. I have shown what we should expect from this theory in its relation to colour-blindness. The question is: Are these predictions

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