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one another, and cancelling or supplementing one another, as the case may be. The effect is, however, different for different wave-lengths, so that while rays of certain wavelength cancel one another, those of another wave-length are allowed to pass, and by this means we have often a magnificent display of colour.

E

D

A

B

FIG. 105.

C

327. Objection to the preceding Explanation. -The oscillation of a vibrating particle has been compared to that of a pendulum. Now if the displacement of the pendulum from its lowest point A (Fig. 105) be doubled, or if A C = 2 A B, we have, by a well-known proposition in geometry (provided the displacements are small), A E = 4 A D; that is to say, the pendulum vibrating through the arc B A falls from B to A through a vertical distance D A, while that vibrating through the arc C A 2 B A falls from C to A through a vertical distance equal to 4 D A. Now the energy of the oscillation is represented by the vertical distance through which the pendulum falls; hence we see that if we double the amplitude of a vibration we increase its energy four times.

Suppose, now, we have two similar waves moving in the same direction, as in Fig. 106.

We have said that they will supplement one another, and form one wave of double the amplitude, as in the figure; but by doubling the amplitude of the oscillation, shall we not increase the energy four times, as in the case of the pendulum, which represents oscillatory movements generally?

FIG. 106.

=

Can we therefore, consistently with the laws of the conservation of energy, imagine two rays of unit energy to unite so as to form one ray of which the energy is four units?

Let us now consider two rays that are travelling in the same direction, but so that the crest of the one fits into the hollow of the other.

U

The result, as we have seen, will be a destruction of motion. Now suppose that each of the waves represents unit of energy. Can we, consistently with the laws of the conservation of energy, imagine two rays of unit energy to unite so as to have their energy entirely cancelled?

We reply, that if either of these two phenomena occurred alone, the laws of energy would present a formidable obstacle to this conception of light. Thus, if two rays of unit energy were to unite into one ray, having an energy equal to four units, without any other compensation; or if two rays of unit energy were to cancel one another without any other compensation, we might justly imagine that the laws of energy had been broken.

The case is, however, completely altered if we bear in mind that the two phenomena always occur together; that is to say, if we have two rays of unit energy combining into a ray of energy equal to four units, we have at the same time, and side by side with it, other two rays of unit energy cancelling each other.

There is thus, on the whole, neither a creation nor a destruction of energy, but merely a displacement, and thus the apparent objection to the undulatory theory derived from the laws of energy is entirely removed.

328. Alteration of Wave-length by Motion of Radiating Body. The reader may have noticed when in a railway station, that if an engine approaches the station at a rapid rate, and whistles at the same time, the note is different as it approaches the station and as it recedes on the other side, being shriller in the first case than in the second.

The reason of this is very obvious, if we bear in mind that the whistle consists in a number of impulses that are rapidly communicated to the air one after another by the engine, and that the note or wave-length consists in the distance between one such impulse and the next. When the engine is approaching the station it gives an impulse to the air, which impulse is propagated in the air towards the station with the usual velocity of sound. But the engine has already advanced some distance in the same direction before it gives

the next impulse, therefore the distance between the two impulses will be less than if the engine were at rest, and the note will therefore be shriller.

On the other hand, when the engine is leaving the station, it gives an impulse to the air, which impulse is propagated to the station with the usual velocity, but the engine has already moved some distance in the contrary direction before it gives the next impulse, and the consequence is that the distance between two impulses will now be greater than if the engine were at rest; that is to say, the sound will be more grave.

Thus, when a sounding body is rapidly approaching the ear its note is rendered more acute, while if it be receding from the ear its note becomes more grave; we might therefore expect that when a luminous body is approaching the eye, there will be a general decrease in the wave-length of its light, and that when it is receding from the eye there will be a general increase of wave-length. But in order that this change may be perceptible, the rate of approach or recession of the body must bear a sensible proportion to the velocity of light; in other words, the body must be moving at the rate of at least several miles per second. Now, it is only in the heavenly bodies that we can look for such velocities. Let us therefore suppose that we have brought upon the slit of our spectroscope the image of a star or planet, in the spectrum of which there is an absorption band corresponding to the double line D. If this star be not in motion either towards or from the eye, the position in the spectrum of these absorption lines should agree precisely with that of the bright lines formed by burning incandescent sodium before the slit of the spectroscope ; but if the star be moving towards the eye, these absorption lines ought to be slightly displaced towards the most refrangible end of the spectrum, which is that of smallest wave-length. In like manner, if the star be receding from the eye, the absorption lines ought to be displaced towards the red or least refrangible portion of the spectrum. Mr. Huggins has by this means been able to make out the proper motion of several

stars in a direction to and from the eye; and more recently Mr. Lockyer has been able by the same means to detect violent convection currents in the sun's atmosphere (Art. 226).

LESSON XXXV.-POLARIZATION OF LIGHT. CONNEXION BETWEEN RADIANT ENERGY AND THE OTHER FORMS OF ENERGY.

329. It thus appears that we have strong evidence in favour of the undulatory theory of light, but we do not yet know of what particular kind of wave motion a ray of light consists. It may either consist of transversal vibrations (Art. 134), in which the direction of displacement is perpendicular to that of the wave motion, as in a wavelet produced by throwing a stone into water, or of vibrations in the direction of the wave motion similar to those of sound.

It will easily be seen that there is a very marked difference between these two kinds of vibrations. Let us, for the sake of illustration, take a long string, extending horizontally between two points, and strike it rapidly with a vertical stroke, we shall then perceive a wave consisting of a vertical displacement propagated rapidly from one end to the other of the string. Let us now strike it on one side with a horizontal stroke, and we shall see a similar wave consisting of a horizontal displacement propagated rapidly in the same direction.

In both cases the displacement is perpendicular to the direction of motion, but the one is in a horizontal and the other in a vertical plane. A transversal undulation is thus capable of assuming a particular side, or bias, or direction.

Now in a wave of condensation and rarefaction, such as that of sound, there is evidently no capability of assuming a particular side or bias of this kind. This is expressed by saying that a transversal wave is capable of polarization, while a wave of condensation and rarefaction is incapable of it.

330. Next suppose that we strike the string of which we have spoken with a vertical stroke, and that we likewise make it to pass between the vertical plates of a frame (Fig. 107), it is clear that these vertical plates will not prevent the vibration taking place; we may, in fact, place a great number of such frames in the path of the wave without interfering with its progress. If, however, we place another frame with horizontal plates (Fig. 108), so as to have

one plate on each side of the vibrating string, it is evident that the arrangement will now tend to check the vertical undulation; and if we have a great many such frames, even although the string does not when at rest touch the plates, yet the progress of a vertical wave may be completely checked thereby.

FIG. 107.

Suppose now that we cause a horizontal wave to pass along the string. This wave will be stopped by the frame with vertical plates, or the same which allowed a vertical wave

to pass, while it will be unaffected by the frame with horizontal plates, or the same which stopped a vertical wave; in fine, the one frame will stop the vertical wave and the other the horizontal. Now suppose that a mixture of vertical and horizontal waves are being propagated along the string; if we insert in their path a series of frames with horizontal plates we shall obstruct the vertical parts or components of these waves, and if we insert frames with vertical plates we shall stop the horizontal components, and if we insert both kinds of frames we shall stop all motion.

FIG. 108.

331. Polarization by Tourmaline.-A similar phenomenon takes place in rays of light. A ray of ordinary sunlight, proceeding, let us say, in a horizontal line, would seem to consist of transversal waves, and not waves of condensation and rarefaction; but there would be as many vibrations in one plane as in another-in fact the rays would consist of an impartial mixture of horizontal and vertical vibrations,

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