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 likewisethe 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.2shows 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 thecorrect 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.2also 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 brandishingthem rapidly round, is rather interesting. Fig.3may 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.1again. 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 fromthe 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.1would 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.2the 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 wavesin 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, thewave 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 pursuingin the mediumall 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 thereforethe 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 theapparentray. The angle S M C is the aberration angle, which in Chap.Xwe denote by ε.
Fig.6shows 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, S1M S2, when the medium is moving, is not quite the same as the doublejourney 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 θ in the theory of Michelson's experiment described in ChapterIV.
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.
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 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 evenin 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 mass 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?
And once more, perhaps the laws of reflection and refraction in a moving medium are not the same as they are if it be at rest. Then, moreover, there is double refraction, colours of thin plates and thick plates, polarisation angle, rotation of the plane of polarisation; all sorts of optical phenomena that need consideration.
It may have to be admitted, perhaps, that in empty space the effect of an ether drift is difficult to detect, but will not the presence of dense matter—especially the passage through dense transparent matter—make the detection easier? So a great number of questions arise, all of which have been, from time to time, seriously discussed.
Interference.
As an instance of such discussion, consider No. 3 of the phenomena tabulated above. I expect that every reader understands interference, but I may just briefly say that two similar sets of waves "interfere" whenever and wherever the crests of one set coincide with and obliterate the troughs of the other set. Light advances in any given direction when crests in that direction are able to remain crests, and troughs to remain troughs. But if we contrive to split a beam of light into two halves, to send them round by different paths, and make them meet again, there is no guarantee that crest will meet crest and trough trough; it may be just the other way in some places, and wherever that opposition of phase occurs there, there will be local obliteration or "interference." Two reunited half-beams of light may thus produce local stripes of darkness, and these stripes are called interference bands.
It is not to be supposed that there is anydestructionof light, or any dissipation of energy: it is merely a case of redistribution.
The bright parts are brighter just in proportion as the dark parts are darker. The screen is illuminated in stripes and no longer uniformly, but its total illumination is the same as if there were no interference.
Projection of Interference Bands.
It is not easy to project these interference bands on a screen so as to make them visible to an audience,—partly because the bands or stripes of darkness are exceedingly narrow; indeed I had not previously seen the experiment attempted. But by means of what I call an interference kaleidoscope, consisting of two mirrors set at an angle with a third semi-transparent mirror between them, it is possible to get the bands remarkably clear and bright, so that they can readily be projected: and I showed these at a lecture to the Royal Institution of Great Britain in 1892.
Each mirror is mounted on a tripod with adjustable screw feet, which stand on a thick iron slab, which again rests on hollow india-rubber balls. Looking down on the mirrors the plan is as in the diagram Fig.7, which indicates sufficiently the geometry of the arrangement, and shows that the two half-beams, into which the semi-transparent plate divides the light, will each travel round the same contour A B C in opposite directions, and will then reunite and travel together towards the point of the arrow. A parallel beam from an electric lantern, when thus treated, depicts bright and broad interference bands on a screen. And the arrangement is very little sensitive to disturbance, becausethe paths of the two halves of the beam are identical, and because of the mounting. A piece of good glass can be interposed without disturbance, and the table can be struck a heavy blow without confusing the bands.
Fig. 7. Plan of Interference Kaleidoscope with three mirrors.The arrow-feather ray is bifurcated at A by a semi-transparent mirror of thinly-silvered glass; and the two halves reunite along the arrow-head after traversing a triangular contour A B C in opposite directions. The simple geometrical relations which permit this are sufficiently indicated in the figure. The arrangement would suit Fizeau's experiment.
The only regular and orderly way of causing a shift of the bands is to accelerate one half of thebeam and to retard the other half, by moving a transparent substance along the contour. For instance, let the sides of the triangle A B C, or one of them, consist of a tube of water in which a rapid stream is maintained; then the stream has a chance of accelerating one half the beam, and retarding the other half, thereby shifting the fringes from their normal position by a measurable amount. This is the experiment made in 1859 by Fizeau. (Appendix3.)
Now that most interesting and important, and I think now well-known, experiment of Fizeau proves quite simply and definitely that if light be sent along a stream of water, travelling inside the water as a transparent medium, it will go quicker with the current than against it.
You may say that is only natural; a wind assists sound one way and retards it the opposite way. Yes, but then sound travels in air; and wind is a bodily transfer of air; hence, of course, it gives the sound a ride. Whereas light does not really travel in water, but always in ether; and it is by no means obvious whether a stream of water can help or hinder it. Experiment decides, however, and answers in the affirmative. It helps it along with just about half the speed of the water; not with the whole speed, which is curious and important, and really means that the moving water has no effect whatever on the ether of space, though we must defer explaining how this comes about.Suffice for present purposes the fact that the velocity of light inside moving water, and therefore presumably inside all transparent matter, is altered to some extent by motion of that matter.
Fig. 8. Hoek's arrangement.The light from source S is reflected so as to travel half through stagnant water and half through air on its direct journey, the path being inverted on the return journey, after which it enters the eye.
Does not this fact afford an easy way of detecting a motion of the earth through the ether? Every vessel of stagnant water is really travelling along through the ether at the rate of nineteen miles a second. Send a beam of light through it one way, and it will be hurried; its velocity, instead of being 140,000 miles a second, will be 140,009 miles. Send a beam of light the other way, and its velocity will be 139,991; just as much less. Bring these two beams together; surely some of their wave-lengths will interfere. M. Hoek, Astronomer at Utrecht, tried the experiment in this very form; here is a diagram of his apparatus (Fig.8). Babinet had tried another form of the experiment previously. Hoek expected to see interference bands, from the twohalf-beams which had traversed the water, one in the direction of the earth's motion and the other against it. But no interference bands were seen. The experiment gave a negative result.
Fig. 9. Arrangement of Mascart and Jamin.A modification of Fig.8, with the beam split definitely into two halves by reflexion from a thick glass plate and reunited before observation. The two half-beams go through stagnant water in opposite directions.
An experiment, however, in which nothing is seen is never a very satisfactory form of a negative experiment; it is, as Mascart calls it, "doubly negative," and we require some guarantee that the conditions were right for seeing what might really have been in some sort there. Hence Mascart and Jamin's modification of the experiment is preferable (Fig.9). The thing now looked for is a shift of already existing interference bands, when the above apparatus is turned so as to have different aspects with respect to the earth's motion; but no shift was seen.
Interference methods all fail to display any trace of relative motion between earth and ether.
Try other phenomena then. Try refraction. The index of refraction of glass is known to depend on the ratio of the speed of light outside, to the speed inside, the glass. If then the ether be streaming through glass, the velocity of light will be different inside according as it travels with the stream or against it, and so the index of refraction may be different. Arago was the first to try this experiment by placing an achromatic prism in front of a telescope on a mural circle, and observing the deviation it produced on stars.
Observe that it was anachromaticprism, treating all wave-lengths alike; he looked at thedeviatedimage of a star, not at itsdispersedimage or spectrum,—else he might have detected the change-of-frequency-effect due to motion of source or receiver first actually seen by Sir W. Huggins. I do not think Arago would have seen it, because I do not suppose his arrangements were delicate enough for that very small effect; but there is no error in the conception of his experiment, as Prof. Mascart has inadvertently suggested there was.
Then Maxwell repeated the attempt in a much more powerful manner, a method which could have detected a very minute effect indeed, and Mascart has also repeated it in a simple form. All are absolutely negative.
Well, then, what about aberration? If one looks through a moving stratum, say a spinning glass disk, there ought to be a shift caused by the motion (see Fig.4). That particular experiment has not been tried, but I entertain no doubt about its result, though a high speed and considerable thickness of glass or other medium would be necessary to produce even a microscopic apparent displacement of objects seen through it.
But the speed of the earth is available, and the whole length of a telescope tube may be filled with water; surely that is enough to displace rays of light appreciably.
Sir George Airy tried it at Greenwich on a star, with an appropriate zenith-sector full of water. Stars were seen through the water-telescope precisely as through an air telescope. A negative result again! (The theory is fully dealt with in ChapterXand Appendix3.)
Stellar observations, however, are unnecessarily difficult. Fresnel had pointed out that a terrestrial source of light would do just as well. He had also (being a man of exceeding genius) predicted that nothing would happen. Hoek has now tried it in a perfect manner and nothing did happen.
But these facts are not at all disconcerting; they are just what ought to be anticipated, in the light of true theory. The absence of all effect caused by stagnant dense matter inserted in the path of a beam of light, that is of dense transparent matter not artificially moved with reference to the earth—or rather with reference to source and receiver—is explicable on Fresnel's theory concerning the behaviour of ether inside matter.
If the index of refraction of the matter is called μ, that means that the speed of light inside it is1/μth of the speed outside or in vacuo. And that is only another way of saying that the virtual etherial density inside it is represented by μ², since the velocity of waves is inversely as the square root of the density of the medium which conveys them;—the elasticity being reckoned as constant, and the same inside as out.
But then if the ether is incompressible its density must really be constant,—so how can it be denser inside matter than it is outside? The answer is that presumably the ether is not really extra dense, but is, as it were,loadedby the matter. The atoms of matter, or the constituent electrons, must be presumed to be shaken by the passage of the waves of light, as they obviously are in fluorescent substances; and accordingly the speed of propagation will be lessened by the extra loading which the waves encounter. It is not a real increase of density, but a virtual increase, which is really due to the addition of a certain fraction of material inertia to the inertia of the ether itself. The density of ether outside being 1, and that of the loaded ether inside being μ², the effect of theload is expressible as μ²−1, while the free ether is the same inside as out.
Suppose now that the matter is moved along. The extra loading, being part of the matter, of course travels with it, and thereby affects the speed of light to the extent of the load,—that is to say, by an amount proportional to μ²−1 as contrasted with μ².
This is Fresnel's predicted ratio (μ²−1): μ², or 1 −1/μ²; and in Fizeau's experiment with running water—especially as repeated later, with modern accuracy, by Michelson—this represents exactly the amount of observed effect upon the light.
But if, instead of running water, stagnant water is used—that is stationary with respect to the earth, though still moving violently through the ether—then the (μ²−1) effect of the load will be fixed to the matter, and can produce no extra or motile effect. The only part that could produce an effect of that kind would be the free ether, of density 1. But then this—on the above view—is absolutely stationary, not being carried along by the earth at all; hence this can give no effect either. Consequently the whole effect of an ether-drift past the earth is zero, on optical experiments, according to the theory of Fresnel; and that is exactly what all the experiments just described have confirmed.
Since then Prof. Mascart, with great pertinacity, has attacked the phenomena of thick plates,Newton's rings, double refraction, and the rotatory phenomenon of quartz; but he has found absolutely nothing attributable to a stream of ether past the earth.
The only positive result ever supposed to be attained was in a very difficult polarisation observation by Fizeau in 1859. Unless this has been repeated, it is safest to ignore it; but I believe that Lord Rayleigh has repeated it, and obtained a negative result.
Fizeau also suggested, but did not attempt, what seems an easier experiment, with fore and aft thermopiles and a source between them, to observe the drift of a medium by its convection of energy; but arguments based on the law of exchanges[5]tend to show, and do show as I think, that a probable alteration of radiating power due to motion through a medium would just compensate the effect otherwise to be expected.
We may summarise most of these statements as follows:—
I may say, then, that not a single optical phenomenon is able to show the existence of an ether stream near the earth. All optics go on precisely as if the ether were stagnant with respect to the earth.
Well, then, perhaps itisstagnant. The experiments I have quoted do not prove that it is so. They are equally consistent with its perfect freedom and with its absolute stagnation; though they are not consistent with any intermediate position. Certainly, if the ether were stagnant nothing could be simpler than their explanation.
The only phenomena then difficult to explain would be those depending on light coming from distant regions through all the layers of more or less dragged ether. The theory of astronomical aberration would be seriously complicated; in its present form it would be upset (p.45). But it is never wise to control facts by a theory; it is better to invent some experiment that will give a different result in stagnant and in free ether. None of those experiments so far described are really discriminative. They are, as I say, consistent with either hypothesis, though not very obviously so.
Fig. 10. The course of the light and of the two half-beams in Michelson's most famous experiment.The light is split at A, one half sent towards B and back, the other half to C and back. Compare with Fig.7.
Michelson Experiment.
Mr. Michelson, however, of the United States, invented a plan that looked as if it really would discriminate; and, after overcoming many difficulties, he carried it out. It is described in thePhilosophical Magazinefor 1887.
Michelson's famous experiment consists in looking for interference between two half-beams of light, of which one has been sent to and froacrossthe line of ether drift, and the other has been sent to and froalongthe line of ether drift.
A semi-transparent mirror set at 45° is employed to split the beam, and a pair of normal and ordinary mirrors, set perpendicular to the two half-beams, are employed to return them back whence they came, so that they can enter the eye through an observing telescope.
It differs essentially from the interference kaleidoscope, Fig.7, inasmuch as there is now no luminous path B C, and no contour enclosed by the light. Each half-beam goes to and fro on its own path, and these paths, instead of being coincident, are widely separate,—one North and South, for instance, and the other East and West.
Under these conditions the bands are much more tremulous than they were in the arrangement of Fig.7, and are subject to every kind of disturbance. The apparatus has to be excessively steady, and no fluctuation even of temperature must be permitted in the path of either beam. To secure this, the source, the mirrors, and the observing telescope, were all mounted upon a massive stone slab; and this was floated in a bath of mercury.
The slab could then be slowly turned round, so that sometimes the path A B and sometimes the path A C lay approximately along or athwart the direction of the earth's motion in space.
And inasmuch as the motion along would take a little longer than the motion across, though everything else was accurately the same, some shift of the interference bands might be expected as the slab rotated.
But whereas in all the experiments previously described the effect looked for was a first-order effect, of magnitude one in ten or twenty thousand,—depending, that is to say, on the first power of the ratio of speed of earth to speed of light,—the effect now to be expected depends on thesquareof that same ratio, and therefore cannot be greater, even in the most favourable circumstances, than 1 part in a hundred million.
It is easy to realise therefore that it is an exceptionally difficult experiment, and that it required both skill and pertinacity to perform it successfully.
That it is an exceptionally difficult experiment will be realised when I say that it would fail in conclusiveness unless one part in 400 millions could be clearly detected.
Mr. Michelson reckons that by his latest arrangement he could see 1 in 4000 millions if it existed (which is equivalent to detecting an error of1/1000of an inch in a length of 60 miles); but he sawnothing. Everything behaved precisely as if the ether was stagnant; as if the earth carried with it all the ether in its immediate neighbourhood. And that was his conclusion.
Theory of Michelson Experiment.
The theory of the Michelson experiment can be expressed thus: its optical diagram being the same as is expressed geometrically in Fig.6.
If a relatively fixed source and receiver move through the ether with velocityu, such thatu/v=α the aberration constant; then the time of any to and fro journey S M, inclined at angle θ to the direction of the drift, is increased, above what it would be if there were no drift, in the ratio
√(1 − α² sin² θ)/1 − α²
This follows from merely geometrical considerations.
Hence if a ray is split, and half sent so that θ=0 while the other half is sent so that θ=90 (as in Fig.10), the one will lag behind the other by a distance ½α² times the distance travelled; which, though very small, may be a perceptible fraction of a wave-length, and therefore may cause a perceptible shift of the bands.
But when the experiment is properly performed, no such shift is observed.
The experiment thus seems to prove that there is no motion through the ether at all, that there is no etherial drift past the earth, that the ether immediately in contact with the earth is stagnant—or that the earth to that extent carries all neighbouring ether with it.
If we wish to evade this conclusion, there is no easy way of doing so. For it depends on no doubtful properties of transparent substances, but on the straightforward fundamental principle underlying all such simple facts as that—It takes longer to row a certain distance and back, up and down stream, than it does to row the same distance in still water; or that it takes longer to run up and down a hill, than to run the same distance laid out flat; or that it costs more to buy a certain number of oranges at three a penny and an equal number at two a penny than it does to buy the whole lot at five for twopence.
Hence, although there may besomeway of getting round Mr. Michelson's experiment, there is no obvious way; and if the true conclusion be not that the ether near the earth is stagnant, it must lead to some other important and unknown fact.
That fact has now come clearly to light. It was first suggested by the late Professor G.F. FitzGerald, of Trinity College Dublin, while sitting in my study at Liverpool and discussing the matter with me. The suggestion bore the impressof truth from the first. It independently occurred also to Professor H.A. Lorentz, of Leiden, into whose theory it completely fits, and who has brilliantly worked it into his system. It may be explained briefly thus:—
Electric charges in motion constitute an electric current. Similar charges repel each other, but currents in the same direction attract. Consequently two similar charges moving in parallel lines will repel each other less than if stationary,—less also than if moving one after the other in the same line. Likewise two opposite charges, a fixed distance apart, attract each other less when moving side by side, than when chasing each other. The modification of the static force, thus caused, depends on the squared ratio of their joint speed to the velocity of light.Atoms of matter are charged; and cohesion is a residual electric attraction (see end of Appendix1). So when a block of matter is moving through the ether of space its cohesive forces across the line of motion are diminished, and consequently in that direction it expands, by an amount proportioned to the square of aberration magnitude.A light journey, to and fro, across the path of a relatively moving medium is slightly quicker than the same journey, to and fro, along (see p.64). But if the journeys are planned or set out on a block of matter, they do not remain quite the same when it is conveyed through space: the journey across the direction of motion becomes longer than the other journey, as we have just seen. And the extra distance compensates or neutralises the extra speed; so that light takes the same time for both.
Electric charges in motion constitute an electric current. Similar charges repel each other, but currents in the same direction attract. Consequently two similar charges moving in parallel lines will repel each other less than if stationary,—less also than if moving one after the other in the same line. Likewise two opposite charges, a fixed distance apart, attract each other less when moving side by side, than when chasing each other. The modification of the static force, thus caused, depends on the squared ratio of their joint speed to the velocity of light.
Atoms of matter are charged; and cohesion is a residual electric attraction (see end of Appendix1). So when a block of matter is moving through the ether of space its cohesive forces across the line of motion are diminished, and consequently in that direction it expands, by an amount proportioned to the square of aberration magnitude.
A light journey, to and fro, across the path of a relatively moving medium is slightly quicker than the same journey, to and fro, along (see p.64). But if the journeys are planned or set out on a block of matter, they do not remain quite the same when it is conveyed through space: the journey across the direction of motion becomes longer than the other journey, as we have just seen. And the extra distance compensates or neutralises the extra speed; so that light takes the same time for both.
Thebalance of evidence at this stage seems to incline in the sense that there is no ether drift, that the ether near the earth is stagnant, that the earth carries all or the greater part of the neighbouring ether with it,—a view which, if true, must singularly complicate the theory of ordinary astronomical aberration: as is explained at the beginning of the last chapter.
But now put the question another way.Canmatter carry neighbouring ether with it when it moves? Abandon the earth altogether; its motion is very quick, but too uncontrollable, and it always gives negative results. Take a lump of matter that you can deal with, and see if it pulls any ether along.
That is the experiment which I set myself to perform, and which in the course of the years 1891-97 I performed. It may be thus described in essence:—
Take a steel disk, or rather a couple of large steel disks a yard in diameter clamped together witha space between. Mount the system on a vertical axis, and spin it like a teetotum as fast as it will stand without flying to pieces. Then take a parallel beam of light, split it into two by a semi-transparent mirror, M, a piece of glass silvered so thinly that it lets half the light through and reflects the other half, somewhat as in Fig.7; and send the two halves of this split beam round and round in opposite directions in the space between the disks. They may thus travel a distance of 20 or 30 or 40 feet. Ultimately they are allowed to meet and enter a telescope. If they have gone quite identical distances they need not interfere, but usually the distances will differ by a hundred-thousandth of an inch or so, which is quite enough to bring about interference.
The mirrors which reflect the light round and round between the disks are shown in Fig.11. If they form an accurate square the last two images will coincide, but if the mirrors are the least inclined to one another at any unaliquot part of 360° the last image splits into two, as in the kaleidoscope is well known, and the interference bands may be regarded as resulting from those two sources. The central white band bisects normally the distance between them, and their amount of separation determines the width of the bands. There are many interesting optical details here, but I shall not go into them.