According to the Young-Helmholtz theory of vision it is supposed that each set of nerves, the red say, transmits the sensation of red to the brain, whatever the manner in which they may have been stimulated. Thus the red nerves are affected not only by red light but also, to a smaller extent, by light of other wave-lengths; the impression produced on the brain is, however, always that of red light.

It has been found possible, by studying the colour sensations of normal-eyed and of colour-blind persons, to draw three curves showing the sensitiveness of the three primary sets of nerves to stimulation by light of different wave-lengths. Such a curve is shown in Fig. 377, and

The above theory as to three sets of colour nerves accounts satisfactorily for the abnormal colour sensations of colour-blind persons. Thus a colour-blind person is one in which one (very rarely two) of the sets of colour nerves is missing. Thus a red colour-blind person is one in which the red nerves are insensitive. Hence such a person will only possess the violet and green sensations, and it will at once be perceived why the luminosity curve (Fig. 375) obtained by such an observer falls so much below the normal at the red end of the spectrum, for there the green and violet sensations are very weak.

In the case of a green colour-blind person, the green sensation is absent, and hence the curves in Fig. 377 show that for blue light, about half-way between E and F, the two remaining sensations are equally stimulated. Now equal stimulation of all three sensations corresponds, in the normal eye, to white, and in the green colour-blind, in the same way, equal stimulation of the violet and red sensations also corresponds to the sensation produced by white. Hence when blue light enters the eye of a green colour-blind person the impression produced is the same as that produced by white light. This fact is brought out very clearly if such a colour-blind person is shown a spectrum, for he will say that he sees red at one end and violet at the other, with a white band between.

399. Complementary Colours. -Two colours are said to be complementary when, if combined, they produce the sensation of white.

The complementary colours of the spectrum colours can be obtained by stopping the light of any given wave-length by means of an opaque rod and allowing the remaining colours to be combined by the lens L (Fig. 374) on the screen at B. Then the colour seen at B will be the complementary of that which is removed from the spectrum by the interposition of the rod.

Since not only all the spectrum colours, but also the three primary colours taken in their proper proportions, produce the sensation of white, if one of the slits is closed the colour produced by the mixture of the remaining two will be complementary to the missing colour.

It is not necessary that either of the two complementaries should be a compound colour, for if a slit be placed in the blue near F, and another in the yellow between D and C, the mixture of the two simple colours transmitted will produce the sensation of white, and hence these two colours are complementary. The reason for the production of the sensation of white by the mixture of the above two colours can be seen by a study of the curves in Fig. 377. For it will be seen that the sum of the ordinates of the red and green curves, where cut by the dotted lines F, 1, 2, 3 and 4, 5, 6, are each equal to the ordinate, F3, of the violet curve. Hence the combined effect of these two lights is to excite all three primary sensations to an equal extent, that is, to produce the sensation of white.

Although a mixture of blue and yellow light produces the sensation of white, it is otherwise if we mix blue and yellow pigments, for in this case the result is a pigment which, when illuminated by white light, produces the sensation of green. The reason for this is that in the case of pigments the light which reaches the eye is white light which has been deprived of some of its components by absorption within the pigment. Thus a blue pigment will absorb all the colours except the blue and green, while a yellow pigment will absorb all but the red, yellow, and green. Now suppose we have a mixture of fine yellow and blue pigment particles illuminated by white light, the blue particles will absorb all the components of the white light except the blue and green, but will transmit these two colours. The yellow particles will absorb the blue but will also transmit the green. Thus all the components of the white light will be absorbed, by one or other of the two kinds of particles, except the green, and hence all the light which is transmitted or reflected from the pigment will be green. The truth of this explanation can be proved by painting a card with yellow pigment and holding it in a beam of light which has passed through a blue solution. Blue and green light will now fall on the yellow pigment, and of this the blue will be absorbed and the green will be reflected, so that the card appears green. In the same way a card painted blue, when illuminated by light obtained by passing white light through a yellow solution, will also

appear green, for of the incident yellow and green light the yellow will be absorbed by the pigment.

Experiments with pigments led to the conclusion that red, yellow, and blue were the three primary colours, for the red pigment will absorb the green which is transmitted by the other two, and so a neutral tint is produced. Thus when using pigments to examine the phenomena of colour great care must be taken, for in no case are pigment colours, even approximately, monochromatic; and it must always be remembered that the colour of a pigment is obtained by the absorption of light of certain wave-lengths from the incident light.

CHAPTER X

POLARISATION AND DOUBLE REFRACTION

400. Light transmitted by Tourmaline-Polarisation.-We have supposed that light is due to a wave-motion in the ether, but have not yet considered whether the waves are longitudinal, such as is the case with sound-waves, or are transverse, i.e. whether the displacement, whatever its nature may be, which causes the sensation of light (and also, of course, of radiant heat) takes place normally to the wave-front or parallel to the wave-front. This question can be answered at once by means of an experiment made with two crystals of tourmaline.

If we take a slice of a crystal of tourmaline cut parallel to the crystallographic axis, and pass a ray of light through it, part of the light will pass through, and will, with most specimens of tourmaline, be coloured greenish owing to selective absorption within the crystal, otherwise to the eye the character of the light appears unaltered, and remains of the same intensity if the tourmaline plate is rotated. If the light which has passed through one tourmaline plate is allowed to fall on another, placed with its axis parallel to the first, the light will pass through the two; the only visible effect will be to slightly darken the greenish tint, the intensity being very slightly diminished by the second plate. If, however, the second plate is gradually rotated round an axis parallel to the light, so that the axes of the two crystals are inclined at a finite angle to one another, the intensity of the transmitted light will gradually diminish, till, when the axes are at right angles, none of the light which has passed through the first plate will pass through the second.

Hence the light which has passed through a plate of tourmaline has acquired properties which it did not before possess, in that it can no longer pass through a second plate of that substance when this plate is turned so that its axis is perpendicular to the axis of the first plate.

In order to see to what conclusions this experiment leads, let us consider an analogous problem. If we have a stretched string, we have seen that it is capable of two distinct modes of vibration, namely, a longitudinal vibration, in which the particles of the string move backwards and forwards in the direction of the length of the string, and a transverse vibration, in which the particles move in planes perpendicular to the length of the string. In the case of the string vibrating longi

tudinally, the appearance of the string is the same on all sides, ie. it remains stretched straight between its extremities. When it is vibrating transversely, however, its appearance is ordinarily different on different sides, since it vibrates in a single plane. Hence a string vibrating transversely has definite sides, so that, to define its motion with reference to the surrounding medium, we must state the plane, passing through the undisturbed position of the string, in which the vibration takes place. Another kind of transverse vibration of which a string is capable is that in which each particle describes a circle in a plane at right angles to the undisturbed position of the string. Suppose, then, that we cause a string to vibrate in this manner by attaching one end to a hook fixed at a little way from the centre of a rapidly rotating disc A (Fig. 378). The string

will appear to swell out into something like the shape shown by the dotted lines. If now the string is passed through a narrow vertical slit D, since the motion of the string can then only take place up and down this slit, beyond D the

motion will consist of transverse vibrations executed in a plane passing through the undisturbed position of the string and the slit, and by rotating the slit the plane in which the vibrations are taking place will also be rotated. Next, if a second slit is placed at F, and this slit is parallel to the first, the motion of the string, being parallel to this slit, will be unaffected. If, however, the first slit remaining vertical, the second slit F is turned out of the vertical, it will begin to interfere with the vibration of the cord, and when it is horizontal it will no longer allow any of the motion of the cord, which is in a vertical plane, to pass, and hence the portion of the cord between the second slit and B will remain

at rest.

The experiment with the crossed tourmalines gives just such a result as the above, and so we conclude that the reason the light will not pass through the second tourmaline, when the axes are at right angles, is that during its passage through the first the light vibrations have acquired sides, or, in other words, they now occur in one plane, so that they are stopped by the second tourmaline, just as the transverse vibrations of the cord are stopped by the second slit after they have been confined to one plane by the first.

Since no such action could take place with the cord vibrating longitudinally, we conclude that the light vibrations are transverse.

Ordinary light, then, consists of transverse vibrations, and since when a single tourmaline is used the intensity of the transmitted light does not change as the tourmaline turns, the vibrations must take place