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]).
