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 pa.s.s 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).

[Ill.u.s.tration: 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.

[Ill.u.s.tration: 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.

[Ill.u.s.tration: 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.

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.

CHAPTER IV

EXPERIMENTS ON THE ETHER

We have arrived at this: that a uniform ether stream all through s.p.a.ce 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 telescope, and along the whole path of the ray. If stationary anywhere it must be stationary altogether: there must be no boundary between stationary and moving ether, no plane of slip, no quicker motion even in some regions than in others. For (referring back to the remarks preceding Fig. 4) if the ether in receiver is stagnant while outside it is moving, a wave which has advanced and drifted as far as the telescope will cease to drift as soon as it gets inside, but will advance simply along the wave-normal. And in general, at the boundary of any such change of motion a ray will be bent, and an observer looking along the ray will see the source not in its true position, not even in the apparent position appropriate to his own motion, but lagging behind that position.

Such an aberration as this, a lag or negative aberration, has never yet been observed; but if there is any slip between layers of ether, if the earth carries any ether with it, or if the ether, being in motion at all, is not equally in motion everywhere throughout every transparent substance, then such a lag or negative aberration must occur, in precise proportion to the amount of the carriage of ether by moving bodies (_cf._ p. 61).

On the other hand, if the ether behaves as a perfectly frictionless inviscid fluid, or if for any other reason there is no rub between it and moving matter, so that the earth carries no ether with it at all, then all rays will be straight, aberration will have its simple and well-known value, and we shall be living in a virtual ether stream of nineteen miles a second, by reason of the orbital motion of the earth.

It may be difficult to imagine that a great ma.s.s like the earth can rush at this tremendous pace through a medium without disturbing it.

It is not possible for an ordinary sphere in an ordinary fluid. At the surface of such a sphere there is a viscous drag, and a spinning motion diffuses out thence through the fluid, so that the energy of the moving body is gradually dissipated. The persistence of terrestrial and planetary motions shows that etherial viscosity, if existent, is small; or at least that the amount of energy thus got rid of is a very small fraction of the whole. But there is nothing to show that an appreciable layer of ether may not adhere to the earth and travel with it, even though the force acting on it be but small.

This, then, is the question before us:--

_Does the earth drag some ether with it? or does it slip through the ether with perfect freedom?_ (Never mind the earth's atmosphere; the part it plays is known and not important.)

In other words, is the ether wholly or partially stagnant near the earth, or is it streaming past us with the opposite of the full terrestrial velocity of nineteen miles a second? Surely if we are living in an ether stream of this rapidity we ought to be able to detect some evidence of its existence.[4]

It is not so easy a thing to detect as you would imagine. We have seen that it produces no deviation or error in direction. Neither does it cause any change of colour or Doppler effect; that is, no shift of lines in spectrum. No steady wind can affect pitch, simply because it cannot blow waves to your ear more quickly than they are emitted. It hurries them along, but it lengthens them in the same proportion, and the result is that they arrive at the proper frequency. The precise effects of motion on pitch are summarised in the following table:--

_Changes of Frequency due to Motion._

Source approaching shortens waves.

Receiver approaching alters relative velocity.

Medium flowing alters both wave-length and velocity in exactly compensatory manner.

What other phenomena may possibly result from motion? Here is a list:--

_Phenomena resulting from Motion._

(1) Change or apparent change in direction; observed by telescope, and called aberration.

(2) Change or apparent change in frequency; observed by spectroscope, and called Doppler effect.

(3) Change or apparent change in time of journey; observed by lag of phase or shift of interference fringes.

(4) Change or apparent change in intensity; observed by energy received by thermopile.

What we have arrived at so far is the following:--

Motion of either source or receiver can alter frequency; motion of receiver can alter apparent direction; motion of the medium can do neither.

But the question must be asked, can it not hurry a wave so as to make it arrive out of phase with another wave arriving by a different path, and thus produce or modify interference effects?

Or again, may it not carry the waves down stream more plentifully than up stream, and thus act on a pair of thermopiles, arranged fore and aft at equal distances from a source, with unequal intensity?