Fig. 1. Shots or Disturbances with Momentum from a Moving Gun.
But now let the receiver be moving at same pace as the gun, as when two grappled ships are firing into each other. The motion of the target carries the point Y forward, and the shot A leaves it at Z, because Z is carried to where Y was. So in that case the marker looking along Z A will see the gun, not as it was when firing, but as it is at the present moment; and he will see likewise the row of shots making straight for him. This is like an observer looking at a terrestrial object. Motion of the earth does not disturb ordinary vision.
Fig. 2 shows as nearly the same sort of thing as possible for the case of emitted waves. The tube is a source emitting a succession of disturbances without momentum. A B C D may be thought of as horizontally flying birds, or as crests of waves, or as self-swimming torpedoes; or they may even be thought of as bullets, if the gun stands still every time it fires, and only moves between whiles.
Fig. 2. Waves or Disturbances without Momentum from a Moving Source. The line A B C D is now neither the line of fire nor the line of aim: it is simply the locus of disturbances emitted from the successive positions 1 2 3 4.
A stationary target will be penetrated in the direction A Y, and this line will point out the correct position of the source when the received disturbance started. If the target moves, a disturbance entering at A may leave it at Z, or at any other point according to its rate of motion; the line Z A does not point to the original position of the source, and so there will be aberration when the target moves. Otherwise there would be none.
Fig. 3. Beam from a Revolving Lighthouse. Now Fig. 2 also represents a parallel beam of light travelling from a moving source, and entering a telescope or the eye of an observer. The beam lies along A B C D, but this is not the direction of vision. The direction of vision, to a stationary observer, is determined not by the locus of successive waves, but by the path of each wave. A ray may be defined as the path of a labelled disturbance. The line of vision is Y A 1, and coincides with the line of aim; which in the projectile case (Fig. 1) it did not.
The case of a revolving lighthouse, emitting long parallel beams of light and brandishing them rapidly round, is rather interesting. Fig. 3 may assist the thinking out of this case. Successive disturbances A, B, C, D, lie along a spiral curve, the spiral of Archimedes; and this is the shape of the beams, as seen illuminating the dust particles, though the pitch of the spiral is too gigantic to be distinguished from a straight line. At first sight it might seem as if an eye looking along those curved beams would see the lighthouse slightly out of its true position; but it is not so. The true rays or actual paths of each disturbance are truly radial; they do not coincide with the apparent beam. An eye looking at the source will not look tangentially along the beam, but will look along A S, and will see the source in its true position. It would be otherwise for the case of projectiles from a revolving turret.
Thus, neither translation of star nor rotation of sun can affect direction. There is no aberration so long as the receiver is stationary.
But what about a wind, or streaming of the medium past source and receiver, both stationary? Look at Fig. 1 again. Suppose a row of stationary cannon firing shots, which get blown by a cross wind along the slant 1 A Y (neglecting the curvature of path which would really exist): still the hole in the target fixes the gun's true position, the marker looking along Y A sees the gun which fired the shot. There is no true deviation from the point of view of the receiver, provided the drift is uniform everywhere, although the shots are blown aside and the target is not hit by the particular gun aimed at it.
With a moving cannon combined with an opposing wind, Fig. 1 would become very like Fig. 2.
(N.B.-The actual case, even without complication of spinning, etc., but merely with the curved path caused by steady wind-pressure, is not so simple, and there would really be an aberration or apparent displacement of the source towards the wind's eye: an apparent exaggeration of the effect of wind shown in the diagram.)
In Fig. 2 the result of a wind is much the same, though the details are rather different. The medium is supposed to be drifting downwards, across the field. The source may be taken as stationary at S. The horizontal arrows show the direction of waves in the medium; the dotted slant line shows their resultant direction. A wave centre drifts from D to 1 in the same time as the disturbance reaches A, travelling down the slant line D A. The angle between dotted and full lines is the angle between ray and wave-normal. Now, if the motion of the medium inside the receiver is the same as it is outside, the wave will pass straight on along the slant to Z, and the true direction of the source is fixed. But if the medium inside the target or telescope is stationary, the wave will cease to drift as soon as it gets inside, under cover as it were; it will proceed along the path it has been really pursuing in the medium all the time, and make its exit at Y. In this latter case-of different motion of the medium inside and outside the telescope-the apparent direction, such as Y A, is not the true direction of the source. The ray is in fact bent where it enters the differently-moving medium (as shown in Fig. 4).
Fig. 4. Ray through a Moving Stratum. A slower moving stratum bends an oblique ray, slanting with the motion, in the same direction as if it were a denser medium. A quicker stratum bends it oppositely. If a medium is both denser and quicker moving, it is possible for the two bendings to be equal and opposite, and thus for a ray to go on straight. Parenthetically I may say that this is precisely what happens, on Fresnel's theory, down the axis of a water-filled telescope exposed to the general terrestrial ether drift.
In a moving medium waves do not advance in their normal direction, they advance slantways. The direction of their advance is properly called a ray. The ray does not coincide with the wave-normal in a moving medium.
Fig. 5. Successive Wave Fronts in a Moving Medium. All this is well shown in Fig. 5.
S is a stationary source emitting successive waves, which drift as spheres to the right. The wave which has reached M has its centre at C, and C M is its normal; but the disturbance, M, has really travelled along S M, which is therefore the ray. It has advanced as a wave from S to P, and has drifted from P to M. Disturbances subsequently emitted are found along the ray, precisely as in Fig. 2. A stationary telescope receiving the light will point straight at S. A mirror, M, intended to reflect the light straight back must be set normal to the ray, not tangential to the wave front.
The diagram also equally represents the case of a moving source in a stationary medium. The source, starting at C, has moved to S, emitting waves as it went; which waves, as emitted, spread out as simple spheres from the then position of source as centre. Wave-normal and ray now coincide: S M is not a ray, but only the locus of successive disturbances. A stationary telescope would look not at S, but along M C to a point where the source was when it emitted the wave M; a moving telescope, if moving at same rate as source, will look at S. Hence S M is sometimes called the apparent ray. The angle S M C is the aberration angle, which in Chap. X we denote by e.
Fig. 6 shows normal reflexion for the case of a moving medium. The mirror M reflects light received from S1, to a point S2,-just in time to catch the source there if that is moving with the medium.
Parenthetically I may say that the time taken on the double journey, S1 M S2, when the medium is moving, is not quite the same as the double journey S M S, when all is stationary; and that this is the principle of Michelson's great experiment; which must be referred to later.
Fig. 6. Normal Reflexion in Moving Medium.
The angle M S X is the angle ? in the theory of Michelson's experiment described in Chapter IV. The ether stream we speak of is always to be considered merely as one relative to matter. Absolute velocity of matter means velocity through the ether-which is stationary. If there were no such physical standard of rest as the ether-if all motion were relative to matter alone-then the contention of Copernicus and Galileo would have had no real meaning.
CHAPTER IV
Table of Contents EXPERIMENTS ON THE ETHER
Table of Contents We have arrived at this: that a uniform ether stream all through space causes no aberration, no error in fixing direction. It blows the waves along, but it does not disturb the line of vision.
Stellar aberration exists, but it depends on motion of observer, and on motion of observer only. Etherial motion has no effect upon it; and when the observer is stationary with respect to object, as he is when using a terrestrial telescope, there is no aberration at all.
Surveying operations are not rendered the least inaccurate by the existence of a universal etherial drift; and they therefore afford no means of detecting it.
But observe that everything depends on the ether's motion being uniform everywhere, inside as well as outside the...
