INFLUENCE OF MOTION ON VARIOUS PHENOMENA
Notwithstanding its genuine physical nature and properties, the ether
is singularly intangible and inaccessible to our senses, and
accordingly is a subject on which it is extremely difficult to try
experiments. Many have been the attempts to detect some phenomena
depending on its motion relative to the earth. The earth is travelling
round the sun at the rate of 19 miles a second, and although this is
slow compared with light--being in fact just about 1/10,000th of the
speed of light,--yet it would seem feasible to observe some
modification of optical phenomena due to this motion through the
ether.
And one such phenomenon is indeed known, namely, the stellar
aberration discovered by Bradley in 1729. The position of objects not
on the earth, and not connected with the solar system, is apparently
altered by an amount comparable to one part in ten thousand, by the
earth's motion; that is to say, the apparent place of a star is
shifted from its true place by an angle 1/10,000th of a "radian,"[3]
or about 20 seconds of arc.
This is called Astronomical Aberration, and is extremely well known.
But a number of other problems open out in connexion with it, and on
these it is desirable to enter into detail. For if the ether is
stationary while the earth is flying through it--at a speed vastly
faster than any cannon ball, as much faster than a cannon ball as an
express train is faster than a saunter on foot--it is for all
practical purposes the same as if the earth were stationary and the
ether streaming past it with this immense velocity, in the opposite
direction. And some consequence of such a drift might at first sight
certainly be expected. It might, for instance, seem doubtful whether
terrestrial surveying operations can be conducted, with the extreme
accuracy expected of them, without some allowance for the violent rush
of the light-conveying medium past and through the theodolite of the
observer.
Let us therefore consider the whole subject further.
ABERRATION.
Everybody knows that to shoot a bird on the wing you must aim in front
of it. Every one will readily admit that to hit a squatting rabbit
from a moving train you must aim behind it.
These are examples of what may be called "aberration" from the
sender's point of view, from the point of view of the source. And the
aberration, or needful divergence between the point aimed at and the
thing hit has opposite sign in the two cases--the case when receiver
is moving, and the case when source is moving. Hence, if both be
moving, it is possible for the two aberrations to neutralise each
other. So to hit a rabbit running alongside the train you must aim
straight at it.
If there were no air that is all simple enough. But every rifleman
knows to his cost that though he fixes both himself and his target
tightly to the ground, so as to destroy all aberration proper, yet a
current of air is very competent to introduce a kind of spurious
aberration of its own, which may be called windage; and that he must
not aim at the target if he wants to hit it, but must aim a little in
the eye of the wind.
So much from the shooter's point of view. Now attend to the point of
view of the target.
Consider it made of soft enough material to be completely penetrated
by the bullet, leaving a longish hole wherever struck. A person behind
the target, whom we may call a marker, by applying his eye to the hole
immediately after the hit, may be able to look through it at the
shooter, and thereby to spot the successful man. I know that this is
not precisely the function of an ordinary marker, but it is more
complete than his ordinary function. All he does usually is to signal
an impersonal hit; some one else has to record the identity of the
shooter. I am rather assuming a volley of shots, and that the marker
has to allocate the hits to their respective sources by means of the
holes made in the target.
Well, will he do it correctly? Assuming, of course, that he can do so
if everything is stationary, and ignoring all curvature of path,
whether vertical or horizontal curvature. If you think it over you
will perceive that a wind will not prevent his doing it correctly; the
line of hole will point to the shooter along the path of his bullet,
though it will not point along his line of aim. Also, if the shots are
fired from a moving ship, the line of hole in a stationary target will
point to the position the gun occupied at the instant the shot was
fired, though it may have moved since then. In neither of these cases
(moving medium and moving source) will there be any error.
But if the _target_ is in motion, on an armoured train for instance,
then the marker will be at fault. The hole will not point to the man
who fired the shot, but to an individual ahead of him. _The source
will appear to be displaced in the direction of the observer's
motion._ This is common aberration. It is the simplest thing in the
world. The easiest illustration of it is that when you run through a
vertical shower, you tilt your umbrella forward; or, if you have not
got one, the drops hit you in the face; more accurately, your face as
you run forward hits the drops. So the shower appears to come from a
cloud ahead of you, instead of from one overhead.
We have thus three motions to consider, that of the source, of the
receiver, and of the medium; and, of these, only motion of receiver is
able to cause an aberrational error in fixing the position of the
source.
So far we have attended to the case of projectiles, with the object of
leading up to light. But light does not consist of projectiles, it
consists of waves; and with waves matters are a little different.
Waves crawl through a medium at their own definite pace; they cannot
be _flung_ forwards or sideways by a moving source; they do not move
by reason of an initial momentum which they are gradually expending,
as shots do; their motion is more analogous to that of a bird or other
self-propelling animal, than it is to that of a shot. The motion of a
wave in a moving medium may be likened to that of a rowing-boat on a
river. It crawls forward with the water, and it drifts with the water;
its resultant motion is compounded of the two, but it has nothing to
do with the motion of its source. A shot from a passing steamer
retains the motion of the steamer as well as that given it by the
powder. It is projected therefore in a slant direction. But a boat
lowered from the side of a passing steamer, and rowing off, retains
none of the motion of its source; it is not projected, it is
self-propelled. That is like the case of a wave.
The diagram illustrates the difference. Fig. 1 shows a moving cannon
or machine-gun, moving with the arrow, and firing a succession of
shots which share the motion of the cannon as well as their own, and
so travel slant. The shot fired from position 1 has reached A, that
fired from position 2 has reached B, and that fired from position 3
has reached C, by the time the fourth shot is fired at D. The line A B
C D is a prolongation of the axis of the gun; it is the line of aim,
but it is not the line of fire; all the shots are travelling aslant
this line, as shown by the arrows. There are thus two directions to be
distinguished. There is the row of successive shots, and there is the
path of any one shot. These two directions enclose an angle. It may be
called an aberration angle, because it is due to the motion of the
source, but it need not give rise to any aberration. True direction
may still be perceived from the point of view of the receiver.
To prove this let us attend to what is happening at the target. The
first shot is supposed to be entering at A, and if the target is
stationary will leave it at Y. A marker looking along Y A will see the
position whence the shot was fired. This may be likened to a
stationary observer looking at a moving star. He sees it where and as
it was when the light started on its long journey. He does not see its
present position, but there is no reason why he should. He does not
see its physical state or anything as it is now. He sees it as it was
when it sent the information which he has just received. There is no
aberration caused by motion of source.
[Illustration: 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.
[Illustration: 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.
[Illustration: 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).
[Illustration: 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.
[Illustration: 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 ε.
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.
[Illustration: FIG. 6. Normal Reflexion in Moving Medium.
The angle M S X is the angle θ 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.
FOOTNOTE:
[3] _Radian_ is the name given by Prof. James Thomson to a unit angle
of circular measure, an angle whose arc equals its radius, or about
57°.