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.)
Public-domain text, read in full here on John Shaqi.
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