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Title: The Ether of Space
Author: Lodge, Oliver, Sir, 1851-1940
Language: English
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*** Start of this LibraryBlog Digital Book "The Ether of Space" ***
HARPER'S LIBRARY _of_ LIVING THOUGHT
[Illustration: HARPER'S LIBRARY _of_ LIVING THOUGHT]
"Wie Alles sich zum Ganzen webt
Eins in dem andern wirkt und lebt!"
THE ETHER
OF
SPACE
BY
SIR OLIVER
LODGE, F.R.S.
HARPER &
BROTHERS
LONDON & NEW YORK
[Illustration: FIG. 15. View of Ether machine complete and in action.
(See Chapter V, and figs. 12 and 13.)
_Frontispiece_]
THE ETHER OF
SPACE
BY
SIR OLIVER LODGE, F.R.S.
_D. Sc. Lond., Hon. D. Sc. Oxon. et Vict._
_LL.D. St. Andrews, Glasgow, and Aberdeen_
_Vice-President of the Institution of Electrical Engineers_
_Rumford Medallist of the Royal Society_
_Ex-President of the Physical Society of London_
_Late Professor of Physics in the University College of Liverpool_
_Honorary Member of the American Philosophical Society of Philadelphia;
of the Manchester Philosophical Society; of the Batavian_
_Society of Rotterdam; and of the Academy of Sciences of Bologna_
_Principal of the University of Birmingham_
ILLUSTRATED
LONDON AND NEW YORK
HARPER & BROTHERS
45 ALBEMARLE STREET, W.
1909
_Copyright, 1909, by Harper & Brothers
All rights reserved_
PREFACE
Investigation of the nature and properties of the Ether of Space has
long been for me the most fascinating branch of Physics, and I welcome
the opportunity of attempting to make generally known the conclusions
to which I have so far been led on this great and perhaps
inexhaustible subject.
OLIVER LODGE.
UNIVERSITY OF BIRMINGHAM,
_March, 1909_.
TO THE FOUNDERS OF
UNIVERSITY COLLEGE, LIVERPOOL,
ESPECIALLY TO THOSE BEARING THE NAMES
OF RATHBONE AND OF HOLT
THIS BOOK IS INSCRIBED
CONTENTS
CHAPTER PAGE
INTRODUCTION. GENERAL AND HISTORICAL xi
I. THE LUMINIFEROUS ETHER AND THE
MODERN THEORY OF LIGHT 1
II. THE INTERSTELLAR ETHER AS A CONNECTING
MEDIUM 13
III. INFLUENCE OF MOTION ON VARIOUS
PHENOMENA 29
IV. EXPERIMENTS ON THE ETHER 44
V. SPECIAL EXPERIMENT ON ETHERIAL
VISCOSITY 67
VI. ETHERIAL DENSITY 80
VII. FURTHER EXPLANATIONS CONCERNING
THE DENSITY AND ENERGY OF THE ETHER 87
VIII. ETHER AND MATTER 98
IX. STRENGTH OF THE ETHER 115
X. GENERAL THEORY OF ABERRATION 127
APPENDIX 1. ON GRAVITY AND ETHERIAL
TENSION 143
APPENDIX 2. CALCULATIONS IN CONNEXION
WITH ETHER DENSITY 146
APPENDIX 3. FRESNEL'S LAW A SPECIAL CASE
OF A UNIVERSAL POTENTIAL FUNCTION 152
LIST OF ILLUSTRATIONS
FIG.
_Illustrations of Aberration._
1. Cannon shots 35
2. Boats or Waves 36
3. Lighthouse beams 37
4. Ray through a moving stratum 40
5. Wave-fronts in moving medium 41
6. Normal reflexion in moving medium 43
_Experiments on Ether drift._
7. Interference Kaleidoscope 51
8. Hoek's experiment 53
9. Experiment of Mascart and Jamin 54
10. Diagram of Michelson's experiment 61
_Illustrations of Ether Machine_ (Lodge).
11. Diagram of course of light 69
12. General view of whirling part of Ether Machine 72
13. General view of optical frame 73
14. Drawing of optical details 74
15. View of Ether Machine in action _Frontispiece_
16. Appearance of interference bands and micrometer wires 76
17. Iron mass for magnetisation 77
18. Appearance of bands 76
19. Arrangement for electrification 78
INTRODUCTION
"Ether or Æther (αιθηρ probably from αιθω I burn,) a material
substance of a more subtle kind than visible bodies, supposed to exist
in those parts of space which are apparently empty."
So begins the article "Ether," written for the ninth edition of the
_Encyclopædia Britannica_, by James Clerk Maxwell.
The derivation of the word seems to indicate some connexion in men's
minds with the idea of Fire: the other three "elements," Earth, Water,
Air, representing the solid, liquid, and gaseous conditions of
ordinary matter respectively. The name Æther suggests a far more
subtle or penetrating and ultra-material kind of substance.
Newton employs the term for the medium which fills space--not only
space which appears to be empty, but space also which appears to be
full; for the luminiferous ether must undoubtedly penetrate between
the atoms--must exist in the pores so to speak--of every transparent
substance, else light could not travel through it. The following is an
extract from Newton's surmises concerning this medium:--
"Qu. 18. If in two large tall cylindrical Vessels of Glass
inverted, two little Thermometers be suspended so as not to
touch the Vessels, and the Air be drawn out of one of these
Vessels, and these Vessels thus prepared be carried out of a
cold place into a warm one; the Thermometer _in vacuo_ will
grow warm as much and almost as soon as the Thermometer which
is not _in vacuo_. And when the vessels are carried back into
the cold place, the Thermometer _in vacuo_ will grow cold
almost as soon as the other Thermometer. Is not the Heat of the
warm Room conveyed through the Vacuum by the Vibrations of a
much subtiler Medium than Air, which after the Air was drawn
out remained in the Vacuum? And is not this Medium the same
with that Medium by which Light is [transmitted], and by whose
Vibrations Light communicates Heat to Bodies?... And do not
the Vibrations of this Medium in hot Bodies contribute to the
intenseness and duration of their Heat? And do not hot Bodies
communicate their Heat to contiguous cold ones by the
Vibrations of this Medium propagated from them into the cold
ones? And is not this Medium exceedingly more rare and subtile
than the Air, and exceedingly more elastic and active? And doth
it not readily pervade all bodies? And is it not (by its
elastic force) expanded through all the Heavens?"
"Qu. 22. May not Planets and Comets, and all gross Bodies,
perform their motions more freely, and with less resistance in
this Æthereal Medium than in any Fluid, which fills all Space
adequately without leaving any Pores, and by consequence is much
denser than Quick-silver and Gold? And may not its resistance be
so small, as to be inconsiderable? For instance; if this _Æther_
(for so I will call it) should be supposed 700000 times more
elastic than our Air, and above 700000 times more rare; its
resistance would be above 600000000 times less than that of
Water. And so small a resistance would scarce make any sensible
alteration in the Motions of the Planets in ten thousand Years."
That the ether, if there be such a thing in space, can pass readily
into or through matter is often held proven by tilting a mercury
barometer; when the mercury rises to fill the transparent vacuum.
Everything points to its universal permeance, if it exist at all.
But these, after all, are antique thoughts. Electric and Magnetic
information has led us beyond them into a region of greater certainty
and knowledge; so that now I am able to advocate a view of the Ether
which makes it not only uniformly present and all-pervading, but also
massive and substantial beyond conception. It is turning out to be by
far the most substantial thing--perhaps the only substantial thing--in
the material universe. Compared to ether the densest matter, such as
lead or gold, is a filmy gossamer structure; like a comet's tail or a
milky way, or like a salt in very dilute solution.
To lead up to and justify the idea of the reality and substantiality,
and vast though as yet largely unrecognised importance, of the Ether
of Space, the following chapters have been written. Some of them
represent the expanded notes of lectures which have been given in
various places--chiefly the Royal Institution; while the first chapter
represents a lecture before the Ashmolean Society of the University of
Oxford in June, 1889. One chapter (viz. Chap. II) has already been
printed as part of an appendix to the third edition of _Modern Views
of Electricity_, as well as in the _Fortnightly_ and _North American
Reviews_; but no other chapters have yet been published, though parts
appear in more elaborate form in Proceedings or Transactions of
learned societies.
The problem of the constitution of the Ether, and of the way in which
portions of it are modified to form the atoms or other constituent
units of ordinary matter, has not yet been solved. Much work has been
done in this direction by various mathematicians, but much more
remains to be done. And until it is done, some scepticism is
reasonable--perhaps laudable. Meanwhile there are few physicists who
will dissent from Clerk Maxwell's penultimate sentence in the article
"Ether" of which the beginning has already been quoted:--
"Whatever difficulties we may have in forming a consistent idea
of the constitution of the æther, there can be no doubt that
the interplanetary and interstellar spaces are not empty, but
are occupied by a material substance or body, which is
certainly the largest, and probably the most uniform body of
which we have any knowledge."
THE ETHER OF SPACE
CHAPTER I
THE LUMINIFEROUS ETHER AND THE MODERN THEORY OF LIGHT
The oldest and best known function for an ether is the conveyance of
light, and hence the name "luminiferous" was applied to it; though at
the present day many more functions are known, and more will almost
certainly be discovered.
To begin with it is best to learn what we can, concerning the
properties of the Interstellar Ether, from the phenomena of Light.
For now wellnigh a century we have had a wave theory of light; and a
wave theory of light is quite certainly true. It is directly
demonstrable that light consists of waves of some kind or other, and
that these waves travel at a certain well-known velocity,--achieving a
distance equal to seven times the circumference of the earth every
second; from New York to London and back in the thirtieth part of a
second; and taking only eight minutes on the journey from the sun to
the earth. This propagation in time of an undulatory disturbance
necessarily involves a medium. If waves setting out from the sun exist
in space eight minutes before striking our eyes, there must
necessarily be in space some medium in which they exist and which
conveys them. Waves we cannot have, unless they be waves in something.
No ordinary matter is competent to transmit waves at anything like the
speed of light: the rate at which _matter_ conveys waves is the
velocity of sound,--a speed comparable to one-millionth of the speed
of light. Hence the luminiferous medium must be a special kind of
substance; and it is called the ether. The _luminiferous_ ether it
used to be called, because the conveyance of light was all it was then
known to be capable of; but now that it is known to do a variety of
other things also, the qualifying adjective may be dropped. But,
inasmuch as the term 'ether' is also applied to a familiar organic
compound, we may distinguish the ultra-material luminiferous medium by
calling it the Ether of Space.
Wave-motion in ether, light certainly is; but what does one mean by
the term wave? The popular notion is, I suppose, of something heaving
up and down, or perhaps of something breaking on a shore. But if you
ask a mathematician what he means by a wave, he will probably reply
that the most general wave is such a function of _x_ and _y_ and _t_
as to satisfy the differential equation
d²y/dt² = v² d²y/dx²;
while the simplest wave is
y = a sin (x-vt).
And he might possibly refuse to give any other answer.
And in refusing to give any other answer than this, or its equivalent
in ordinary words, he is entirely justified; that _is_ what is meant
by the term wave, and nothing less general would be all-inclusive.
Translated into ordinary English the phrase signifies, with accuracy
and comprehensive completeness, the full details of "a disturbance
periodic both in space and time." Anything thus doubly periodic is a
wave; and all waves--whether in air as sound waves, or in ether as
light waves, or on the surface of water as ocean waves--can be
comprehended in the definition.
What properties are essential to a medium capable of transmitting
wave-motion? Roughly we may say two: _elasticity_ and _inertia_.
Elasticity in some form, or some equivalent of it,--in order to be
able to store up energy and effect recoil; inertia,--in order to
enable the disturbed substance to overshoot the mark and oscillate
beyond its place of equilibrium to and fro. Any medium possessing
these two properties can transmit waves, and unless a medium possesses
these properties in some form or other, or some equivalent for them,
it may be said with moderate security to be incompetent to transmit
waves. But if we make this latter statement one must be prepared to
extend to the terms elasticity and inertia their very largest and
broadest signification, so as to include any possible kind of
restoring force, and any possible kind of persistence of motion,
respectively.
These matters may be illustrated in many ways, but perhaps a simple
loaded lath, or spring, in a vice will serve well enough. Pull it to
one side, and its elasticity tends to make it recoil; let it go, and
its inertia causes it to overshoot its normal position. That is what
inertia is,--power of overshooting a mark, or, more accurately, power
of moving for a time even against driving force,--power to rush
uphill. Both causes together make it swing to and fro till its energy
is exhausted. This is a disturbance simply periodic in time. A regular
series of such springs, set at equal intervals and started vibrating
at regular intervals of time one after the other, would be periodic in
space too; and so they would, in disconnected fashion, typify a wave.
A series of pendulums will do just as well, and if set swinging in
orderly fashion will furnish at once an example and an appearance of
wave motion, which the most casual observer must recognise as such.
The row of springs obviously possesses elasticity and inertia; and any
wave-transmitting medium must similarly possess some form of
elasticity and some form of inertia.
But now proceed to ask what is this Ether which in the case of light
is thus vibrating? What corresponds to the elastic displacement and
recoil of the spring or pendulum? What corresponds to the inertia
whereby it overshoots its mark? Do we know these properties in the
ether in any other way?
The answer, given first by Clerk Maxwell, and now reiterated and
insisted on by experiments performed in every important laboratory in
the world, is:--
The elastic displacement corresponds to electrostatic
charge,--roughly speaking, to electricity.
The inertia corresponds to magnetism.
This is the basis of the modern electromagnetic theory of light.
Let me attempt to illustrate the meaning of this statement, by
reviewing some fundamental electrical facts in the light of these
analogies:--
The old and familiar operation of charging a Leyden jar--the storing
up of energy in a strained dielectric--any electrostatic charging
whatever is quite analogous to the drawing aside of our flexible
spring. It is making use of the elasticity of the ether to produce a
tendency to recoil. Letting go the spring is analogous to permitting a
discharge of the jar--permitting the strained dielectric to recover
itself--the electrostatic disturbance to subside.
In nearly all the experiments of electrostatics etherial elasticity is
manifest.
Next consider inertia. How would one illustrate the fact that water,
for instance, possesses inertia--the power of persisting in motion
against obstacles--the power of possessing kinetic energy? The most
direct way would be, to take a stream of water and try suddenly to
stop it. Open a water tap freely and then suddenly shut it. The
impetus or momentum of the stopped water makes itself manifest by a
violent shock to the pipe, with which everybody must be familiar. This
momentum of water is utilised by engineers in the "water-ram."
A precisely analogous experiment in Electricity is what Faraday called
"the extra current." Send a current through a coil of wire round a
piece of iron, or take any other arrangement for developing powerful
magnetism, and then suddenly stop the current by breaking the circuit.
A violent flash occurs, if the stoppage is sudden enough, a flash
which means the bursting of the insulating air partition by the
accumulated electromagnetic momentum. The scientific name for this
electrical inertia is "self-induction."
Briefly we may say that nearly all electromagnetic experiments
illustrate the fact of etherial inertia.
Now return to consider what happens when a charged conductor (say a
Leyden jar) is discharged. The recoil of the strained dielectric
causes a current, the inertia of this current causes it to overshoot
the mark, and for an instant the charge of the jar is reversed; the
current now flows backwards and charges the jar up as at first; back
again flows the current; and so on, charging and reversing the charge,
with rapid oscillations, until the energy is all dissipated into heat.
The operation is precisely analogous to the release of a strained
spring, or to the plucking of a stretched string.
But the discharging body, thus thrown into strong electrical
vibration, is imbedded in the all-pervading ether; and we have just
seen that the ether possesses the two properties requisite for the
generation and transmission of waves, viz.: elasticity, and inertia or
density; hence just as a tuning fork vibrating in air excites aërial
waves, or sound, so a discharging Leyden jar in ether excites etherial
waves, or light.
Etherial waves can therefore be actually produced by direct electrical
means. I discharge here a jar, and the room is for an instant filled
with light. With light, I say, though you can see nothing. You can
see and hear the spark indeed--but that is a mere secondary
disturbance we can for the present ignore--I do not mean any secondary
disturbance. I mean the true etherial waves emitted by the electric
oscillation going on in the neighbourhood of the recoiling dielectric.
You pull aside the prong of a tuning fork and let it go: vibration
follows and sound is produced. You charge a Leyden jar and let it
discharge: vibration follows and light is excited.
It is light, just as good as any other light. It travels at the same
pace, it is reflected and refracted according to the same laws; every
experiment known to optics can be performed with this etherial
radiation electrically produced,--and yet you cannot see it. Why not?
For no fault of the light, the fault (if there be a fault) is in the
eye. The retina is incompetent to respond to these vibrations--they
are too slow. The vibrations set up when this large jar is discharged
are from a hundred thousand to a million per second, but that is too
slow for the retina. It responds only to vibrations between 400
billion and 700 billion per second. The vibrations are too quick for
the ear, which responds only to vibrations between 40 and 40,000 per
second. Between the highest audible and the lowest visible vibrations
there has been hitherto a great gap, which these electric oscillations
go far to fill up. There has been a great gap simply because we have
no intermediate sense organ to detect rates of vibration between
40,000 and 400,000,000,000,000 per second. It was therefore an
unexplored territory. Waves have been there all the time in any
quantity, but we have not thought about them nor attended to them.
It happens that I have myself succeeded in getting electric
oscillations so slow as to be audible,--the lowest I had got in 1889
were 125 per second, and for some way above this the sparks emit a
musical note; but no one has yet succeeded in directly making electric
oscillations which are visible,--though indirectly every one does it
when they light a candle.
It is easy, however, to have an electric oscillator which vibrates 300
million times a second, and emits etherial waves a yard long. The
whole range of vibrations between musical tones and some thousand
million per second, is now filled up.
With the large condensers and self-inductances employed in modern
cable telegraphy, it is easy to get a series of beautifully regular
and gradually damped electric oscillations, with a period of two or
three seconds, recorded by an ordinary signalling instrument or siphon
recorder.
These electromagnetic waves in space have been known on the side of
theory ever since 1865, but interest in them was immensely quickened
by the discovery of a receiver or detector for them. The great though
simple discovery by Hertz, in 1888, of an "electric eye," as Lord
Kelvin called it, made experiments on these waves for the first time
easy or even possible. From that time onward we possessed a sort of
artificial sense organ for their appreciation,--an electric
arrangement which can virtually "see" these intermediate rates of
vibration.
Since then Branly discovered that metallic powder could be used as an
extraordinarily sensitive detector; and on the basis of this
discovery, the 'coherer' was employed by me for distant signalling by
means of electric or etheric waves; until now when many other
detectors are available in the various systems of wireless telegraphy.
With these Hertzian waves all manner of optical experiments can be
performed. They can be reflected by plain sheets of metal,
concentrated by parabolic reflectors, refracted by prisms, and
concentrated by lenses. I have made, for instance, a large lens of
pitch, weighing over three hundredweight, for concentrating them to a
focus.[1] They can be made to show the phenomenon of interference, and
thus have their wave-length accurately measured. They are stopped by
all conductors, and transmitted by all insulators. Metals are opaque;
but even imperfect insulators, such as wood or stone, are strikingly
transparent; and waves may be received in one room from a source in
another, the door between the two being shut.
The real nature of metallic opacity and of transparency has long been
clear in Maxwell's theory of light, and these electrically produced
waves only illustrate and bring home the well-known facts. The
experiments of Hertz are, in fact, the apotheosis of Maxwell's theory.
* * * * *
Thus, then, in every way, Clerk Maxwell's brilliant perception or
mathematical deduction, in 1865, of the real nature of light is
abundantly justified; and for the first time we have a true theory of
light,--no longer based upon analogy with sound, nor upon the supposed
properties of some hypothetical jelly or elastic solid, but capable of
being treated upon a substantial basis of its own, in alliance with
the sciences of Electricity and of Magnetism.
Light is an electromagnetic disturbance of the ether. Optics is a
branch of electricity. Outstanding problems in optics are being
rapidly solved, now that we have the means of definitely exciting
light with a full perception of what we are doing, and of the precise
mode of its vibration.
It remains to find out how to shorten down the waves--to hurry up the
vibration until the light becomes visible. Nothing is wanted but
quicker modes of vibration. Smaller oscillators must be used--very
much smaller--oscillators not much bigger than molecules. In all
probability--one may almost say certainly--ordinary light is the
result of electric oscillation in the molecules or atoms of hot
bodies, or sometimes of bodies not hot--as in the phenomenon of
phosphorescence.
The direct generation of _visible_ light by electric means, so soon as
we have learnt how to attain the necessary frequency of vibration,
will have most important practical consequences; and that matter is
initially dealt with in a section on the Manufacture of Light, § 149,
in Chapter XIV of _Modern Views of Electricity_. But here we abandon
further consideration of this aspect of our great subject.
FOOTNOTE:
[1] See Lodge and Howard, _Philosophical Magazine_ for July, 1889. See
also _Phil. Mag._, August, 1888, page 229.
CHAPTER II
THE INTERSTELLAR ETHER AS A CONNECTING MEDIUM
So far I have given a general idea of the present condition of the
wave theory of light, both from its theoretical and from its
experimental sides. The waves of light are not anything mechanical or
material, but are something electrical and magnetic--they are in fact
electrical disturbances periodic in space and time, and travelling
with a known and tremendous speed through the ether of space. Their
very existence depends upon the ether, and their speed of propagation
is its best known and most certain quantitative property.
A statement of this kind does not even initially express a tithe of
our knowledge on the subject; nor does our knowledge exhaust any large
part of the region of discoverable fact; but the statement above made
may be regarded as certain, although the absence of mechanics or
ordinary dynamics about it removes it, or seems to remove it, from the
category of the historically soundest and best worked department of
Physical Science, viz. that explored by the Newtonian method. Though
in truth there is every reason to suppose that we should have had
Newton with us in these modern developments.
There is, I believe, a general tendency to underrate the certainty of
some of the convictions to which natural philosophers have gradually,
in the course of their study of nature, been impelled; more especially
when those convictions have reference to something intangible and
occult. The existence of a continuous space-filling medium, for
instance, is probably regarded by most educated people as a more or
less fanciful hypothesis, a figment of the scientific imagination,--a
mode of collating and welding together a certain number of observed
facts, but not in any physical sense a reality, as water and air are
realities.
I am speaking purely physically. There may be another point of view
from which all material reality can be denied, but with those
questions physics proper has nothing to do; it accepts the evidence of
the senses, regarding them as the tools or instruments wherewith man
may hope to understand one definite aspect of the universe; and it
leaves to philosophers, equipped from a different armoury, the other
aspects which the material universe may--nay, must--possess.
By a physical "explanation" is meant a clear statement of a fact or
law in terms of something with which daily life has made us familiar.
We are all chiefly familiar, from our youth up, with two apparently
simple things, _motion_ and _force_. We have a direct sense for both
these things. We do not understand them in any deep way, probably we
do not understand them at all, but we are accustomed to them. Motion
and force are our primary objects of experience and consciousness; and
in terms of them all other less familiar occurrences may conceivably
be stated and grasped. Whenever a thing can be so clearly and
definitely stated, it is said to be explained, or understood; we are
said to have "a dynamical theory" of it. Anything short of this may be
a provisional or partial theory, an explanation of the less known in
terms of the more known, but Motion and Force are postulated in
physics as the completely known: and no attempt is made to press the
terms of an explanation further than that. A dynamical theory is
recognised as being at once necessary and sufficient.
Now, it must be admitted at once that of very few things have we at
present such a dynamical explanation. We have no such explanation of
matter, for instance, or of gravitation, or of electricity, or ether,
or light. It is always conceivable that of some such things no purely
dynamical explanation will ever be forthcoming, because something more
than motion and force may perhaps be essentially involved. Still,
physics is bound to push the search for an explanation to its
furthest limits; and so long as it does not hoodwink itself by
vagueness and mere phrases--a feebleness against which its leaders are
mightily and sometimes cruelly on their guard, preferring to risk the
rejection of worthy ideas rather than permit a semi-acceptance of
anything fanciful and obscure--so long as it vigorously probes all
phenomena within its reach, seeking to reduce the physical aspect of
them to terms of motion and force,--so long it must be upon a safe
track. And, by its failure to deal with certain phenomena, it will
learn--it already begins to suspect, its leaders must long have
surmised--the existence of some third, as yet unknown, category, by
incorporating which the physics of the future may rise to higher
flights and an enlarged scope.
I have said that the things of which we are permanently conscious are
motion and force, but there is a third thing which we have likewise
been all our lives in contact with, and which we know even more
primarily, though perhaps we are so immersed in it that our knowledge
realises itself later,--viz. life and mind. I do not now pretend to
define these terms, or to speculate as to whether the things they
denote are essentially one and not two. They _exist_, in the sense in
which we permit ourselves to use that word, and they are not yet
incorporated into physics. Till they are, they may remain more or less
vague; but how or when they can be incorporated, is not for me even
to conjecture.
Still, it is open to a physicist to state how the universe appears to
him, in its broad character and physical aspect. If I were to make the
attempt I should find it necessary for the sake of clearness to begin
with the simplest and most fundamental ideas; in order to illustrate,
by facts and notions in universal knowledge, the kind of process which
essentially occurs in connection with the formation of higher and less
familiar conceptions,--in regions where the common information of the
race is so slight as to be useless.
_Primary Acquaintance with the External World._
Beginning with our most fundamental sense I should sketch the matter
thus:--
We have muscles and can move. I cannot analyse motion,--I doubt if the
attempt is wise,--it is a simple immediate act of perception, a direct
sense of free unresisted muscular action. We may indeed move without
feeling it, and that teaches us nothing, but we may move so as to feel
it, and this teaches us much, and leads to our first scientific
inference, viz. _space_; that is, simply, room to move about. We might
have had a sense of being jammed into a full or tight-packed universe;
but we have not: we feel it to be a spacious one.
Of course we do not stop at this baldness of inference: our educated
faculty leads us to realise the existence of space far beyond the
possibility of direct sensation; and, further, by means of the direct
appreciation of _speed_ in connection with motion,--of uniform and
variable speed,--we become able to formulate the idea of "time," or
uniformity of sequence; and we attain other more complex
notions--acceleration and the like--upon a consideration of which we
need not now enter.
But our muscular sense is not limited to the perception of free
motion: we constantly find it restricted or forcibly resisted. This
"muscular action impeded" is another direct sense, that of "_force_";
and attempts to analyse it into anything simpler than itself have
hitherto resulted only in confusion. By "force" is meant primarily
muscular action not accompanied by motion. Our sense of this teaches
us that space, though roomy, is not empty: it gives us our second
scientific inference--what we call "matter."
Again we do not stop at this bare inference. By another sense, that of
pain, or mere sensation, we discriminate between masses of matter in
apparently intimate relation with ourselves, and other or foreign
lumps of matter; and we use the first portion as a measure of the
extent of the second. The human body is our standard of size. We
proceed also to subdivide our idea of matter,--according to the
varieties of resistance with which it appeals to our muscular
sense,--into four different states, or "elements" as the ancients
called them; viz. the solid, the liquid, the gaseous, and the
etherial. The resistance experienced when we encounter one or other of
these forms of material existence varies from something very
impressive--the solid,--through something nearly impalpable--the
gaseous,--up to something entirely imaginative, fanciful, or
inferential, viz. the ether.
The ether does not in any way affect our sense of touch (i.e. of
force); it does not resist motion in the slightest degree. Not only
can our bodies move through it, but much larger bodies, planets and
comets, can rush through it at what we are pleased to call a
prodigious speed (being far greater than that of an athlete) without
showing the least sign of friction. I myself, indeed, have designed
and carried out a series of delicate experiments to see whether a
whirling mass of iron could to the smallest extent grip the ether and
carry it round, with so much as a thousandth part of its own velocity.
These shall be described further on, but meanwhile the result arrived
at is distinct. The answer is, no; I cannot find a trace of mechanical
connection between matter and ether, of the kind known as viscosity or
friction.
Why, then, if it is so impalpable, should we assert its existence? May
it not be a mere fanciful speculation, to be extruded from physics as
soon as possible? If we were limited for our knowledge of matter to
our sense of touch, the question would never even have presented
itself; we should have been simply ignorant of the ether, as ignorant
as we are of any life or mind in the universe not associated with some
kind of material body. But our senses have attained a higher stage of
development than that. We are conscious of matter by means other than
its resisting force. Matter acts on one small portion of our body in a
totally different way, and we are said to _taste_ it. Even from a
distance it is able to fling off small particles of itself sufficient
to affect another delicate sense. Or again, if it is vibrating with an
appropriate frequency, another part of our body responds; and the
universe is discovered to be not silent but eloquent to those who have
ears to hear. Are there any more discoveries to be made? Yes; and
already some have been made. All the senses hitherto mentioned speak
to us of the presence of ordinary matter,--gross matter, as it is
sometimes called,--though when appealing to our sense of smell, and
more especially to a dog's sense of smell, it is not very gross;
still, with the senses hitherto enumerated we should never have become
aware of the ether. A stroke of lightning might have smitten our
bodies back into their inorganic constituents, or a torpedo-fish might
have inflicted on us a strange kind of torment; but from these violent
tutors we should have learnt little more than a schoolboy learns from
the once ever-ready cane.
But it so happens that the whole surface of our skin is sensitive in
yet another way, and a small portion of it is astoundingly and
beautifully sensitive, to an impression of an altogether different
character--one not necessarily associated with any form of ordinary
matter--one that will occur equally well through space from which all
solid, liquid, or gaseous matter has been removed. Hold your hand near
a fire, put your face in the sunshine, and what is it you feel? You
are now conscious of something not arriving by ordinary matter at all.
You are now as directly conscious as you can be of the etherial
medium. True the process is not very direct. You cannot apprehend the
ether as you can matter, by touching or tasting or even smelling it;
but the process is analogous to the kind of perception we might get of
ordinary matter if we had the sense of hearing alone. It is something
akin to _vibrations in the ether_ that our skin and our eyes feel.
It may be rightly asserted that it is not the etherial disturbances
themselves, but other disturbances excited by them in our tissues,
that our heat nerves feel; and the same assertion can be made for our
more highly-developed and specialised sight nerves. All nerves must
feel what is occurring next door to them, and can directly feel
nothing else; but the "radiation," the cause which excited these
disturbances, travelled through the ether,--not through any otherwise
known material substance.
It should be a commonplace to rehearse how we know this. Briefly,
thus: Radiation conspicuously comes to us from the sun. If any free or
ordinary matter exists in the intervening space, it must be an
exceedingly rare gas. In other words, it must consist of scattered
particles of matter, some big enough to be called lumps, some so small
as to be merely atoms, but each with a considerable gap between it and
its neighbour. Such isolated particles are absolutely incompetent to
transmit light. And, parenthetically, I may say that no form of
ordinary matter, solid, liquid, or gaseous, is competent to transmit a
thing travelling with the speed and subject to the known laws of
light. For the conveyance of radiation or light all ordinary matter is
not only incompetent, but hopelessly and absurdly incompetent. If this
radiation is a thing transmitted by anything at all, it must be by
something _sui generis_.
But it is transmitted,--for it takes time on the journey, travelling
at a well-known and definite speed; and it is a quivering or periodic
disturbance, falling under the general category of wave-motion.
Nothing is more certain than that. No physicist disputes it. Newton
himself, who is commonly and truly asserted to have promulgated a
rival theory, felt the necessity of an etherial medium, and knew that
light consisted essentially of waves.
_Sight._
A small digression here, to avoid any possible confusion due to the
fact that I have purposely associated together temperature nerves and
sight nerves. They are admittedly not the same, but they are alike in
this, that they both afford evidence of radiation; and, were we blind,
we might still know a good deal about the sun, and if our temperature
nerves were immensely increased in delicacy (not all over, for that
would be merely painful, but in some protected region), we might even
learn about the moon, planets, and stars. In fact, an eye, consisting
of a pupil (preferably a lens) and a sunken cavity lined with a
surface sensitive to heat, could readily be imagined, and might be
somewhat singularly effective. It would be more than a light recorder,
it could detect all the etherial quiverings caused by surrounding
objects, and hence would see perfectly well in what we call "the
dark." But it would probably see far too much for convenience, since
it would necessarily be affected by every kind of radiation in simple
proportion to its energy; unless, indeed, it were provided with a
supply of screens with suitably selected absorbing powers. But
whatever might be the advantage or disadvantage of such a sense-organ,
we as yet do not possess one. Our eye does not act by detecting heat;
in other words, it is not affected by the whole range of etherial
quiverings, but only by a very minute and apparently insignificant
portion. It wholly ignores the ether waves whose frequency is
comparable with that of sound; and, for thirty or forty octaves above
this, nothing about us responds; but high up, in a range of vibration
of the inconceivably high pitch of four to seven hundred million
million per second--a range which extremely few accessible bodies are
able to emit, and which it requires some knowledge and skill
artificially to produce--to those waves the eye is acutely,
surpassingly, and most intelligently sensitive.
This little fragment of total radiation is in itself trivial and
negligible. Were it not for men, and glow-worms, and a few other forms
of life, hardly any of it would ever occur, on such a moderate-sized
lump of matter as the earth. Except for an occasional volcano, or a
flash of lightning, only gigantic bodies like the sun and stars have
energy enough to produce these higher flute-like notes; and they do it
by sheer main force and violence--the violence of their gravitative
energy--producing not only these, but every other kind of radiation
also. Glow-worms, so far as I know, alone have learnt the secret of
emitting the physiologically useful waves, and none others.
_Why_ these waves are physiologically useful--why they are what is
called "light," while other kinds of radiation are "dark," is a
question to be asked, but, at present, only tentatively answered. The
answer must ultimately be given by the Physiologist; for the
distinction between light and non-light can only be stated in terms of
the eye, and its peculiar specialised sensitiveness; but a hint may be
given him by the Physicist. The etherial waves which affect the eye
and the photographic plate are of a size not wholly incomparable with
that of the atoms of matter. When a physical phenomenon is concerned
with the ultimate atoms of matter, it is often relegated at present to
the field of knowledge summarised under the head of Chemistry. Sight
is probably a chemical sense. The retina may contain complex
aggregations of atoms, shaken asunder by the incident light
vibrations, and rapidly built up again by the living tissues in which
they live; the nerve-endings meanwhile appreciating them in their
temporarily dissociated condition. A vague speculation! Not to be
further countenanced except as a working hypothesis leading to
examination of fact; but, nevertheless, the direction in which the
thoughts of some physicists are tending--a direction towards which
many recently discovered experimental facts point.[2]
_Gravitation and Cohesion._
It would take too long to do more than suggest
some other functions for which a continuous medium of communication is
necessary. We shall argue in Chapter VIII that technical action at a
distance is impossible. A body can only act immediately on what it is
in contact with; it must be by the action of contiguous
particles,--that is, practically, through a continuous medium, that
force can be transmitted across space. Radiation is not the only thing
the earth feels from the sun; there is in addition its gigantic
gravitative pull, _a force or tension more than what a million million
steel rods_, _each seventeen feet in diameter_, _could stand_ (_see_
Chap. IX). What mechanism transmits this gigantic force? Again, take a
steel bar itself: when violently stretched, with how great tenacity
its parts cling together! Yet its particles are not in absolute
contact, they are only virtually attached to each other by means of
the universal connecting medium--the ether,--a medium that must be
competent to transmit the greatest stresses which our knowledge of
gravitation and of cohesion shows us to exist.
_Electricity and Magnetism._
Hitherto I have mainly confined myself to the perception of the ether
by our ancient sense of radiation, whereby we detect its subtle and
delicate quiverings. But we are growing a new sense; not perhaps an
actual sense-organ, though not so very unlike a new sense-organ,
though the portions of matter which go to make the organ are not
associated with our bodies by the usual links of pain and disease;
they are more analogous to artificial teeth or mechanical limbs, and
can be bought at an instrument-maker's.
Electroscopes, galvanometers, telephones--delicate instruments these;
not yet eclipsing our sense-organs of flesh, but in a few cases coming
within measurable distance of their surprising sensitiveness. And with
these what do we do? Can we smell the ether, or touch it, or what is
the closest analogy? Perhaps there is no useful analogy; but
nevertheless we deal with it, and that closely. Not yet do we fully
realise what we are doing. Not yet have we any dynamical theory of
electric currents, of static charges, and of magnetism. Not yet,
indeed, have we any dynamical theory of light. In fact, the ether has
not yet been brought under the domain of simple mechanics--it has not
yet been reduced to motion and force: and that probably because the
_force_ aspect of it has been so singularly elusive that it is a
question whether we ought to think of it as material at all. No, it is
apart from mechanics at present. Conceivably it may remain apart; and
our first additional category, wherewith the foundations of physics
must some day be enlarged, may turn out to be an etherial one. And
some such inclusion may have to be made before we can attempt to annex
vital or mental processes. Perhaps they will all come in together.
Howsoever these things be, this is the kind of meaning lurking in the
phrase that we do not yet know what electricity or what the ether is.
We have as yet no dynamical explanation of either of them; but the
past century has taught us what seems to their student an overwhelming
quantity of facts about them. And when the present century, or the
century after, lets us deeper into their secrets, and into the secrets
of some other phenomena now in course of being rationally
investigated, I feel as if it would be no merely material prospect
that will be opening on our view, but some glimpse into a region of
the universe which Science has never entered yet, but which has been
sought from far, and perhaps blindly apprehended, by painter and poet,
by philosopher and saint.
_Note on the Spelling of Ethereal._
The usual word "ethereal" suggests something unsubstantial, and
is so used in poetry; but for the prosaic treatment of Physics
it is unsuitable, and etheric has occasionally been used
instead. No just derivation can be given for such an adjective,
however; and I have been accustomed simply to spell etherial
with an _i_ when no poetic meaning was intended. This
alternative spelling is not incorrect; but Milton uses the
variant "ethereous," in a sense suggestive of something strong
and substantial (_Par. Lost_, vi, 473). Either word, therefore,
can be employed to replace "ethereal" in physics: and in
succeeding chapters one or other of these is for the most part
employed.
FOOTNOTE:
[2] Cf. sections 157A, 143, 187, and chap. xvi., of my _Modern Views
of Electricity_.
CHAPTER III
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°.
CHAPTER IV
EXPERIMENTS ON THE ETHER
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 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 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 any _destruction_ of 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, because
the 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.
[Illustration: 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 the beam 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.
(Appendix 3.)
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.
[Illustration: 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 two half-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.
[Illustration: 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 an _achromatic_ prism, treating all wave-lengths
alike; he looked at the _deviated_ image of a star, not at its
_dispersed_ image 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 Chapter X and
Appendix 3.)
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 is 1/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, _loaded_ by 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 the load 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:--
_Summary._
{ A real and apparent change of wave-length.
{
Source alone { A real but not apparent error in direction.
moving produces {
{ No lag of phase or change of intensity,
{ except that appropriate
{ to altered wave-length.
{ No change of frequency.
Medium alone { No error in direction.
moving, or { A real lag of phase, but undetectable
source and receiver { without control over the
moving { medium.
together, produces { A change of intensity corresponding
{ to different distance,
{ but compensated by change
{ of radiating power.
{ An apparent change of wave-length.
{ An apparent error in direction.
Receiver alone { No change of phase or of intensity,
moving produces { except that appropriate
{ to different virtual
{ velocity of light.
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 it _is_ stagnant. 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.
[Illustration: 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 the
_Philosophical Magazine_ for 1887.
Michelson's famous experiment consists in looking for interference
between two half-beams of light, of which one has been sent to and fro
_across_ the line of ether drift, and the other has been sent to and
fro _along_ the 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 the _square_ of 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
of 1/1000 of an inch in a length of 60 miles); but he saw nothing.
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
velocity _u_, such that u/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-α²sin²θ) / (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 be _some_ way 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 impress of 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 Appendix 1). 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.
FOOTNOTES:
[4] The word "stationary" is ambiguous. I propose to use "stagnant,"
as meaning stationary with respect to the earth, i.e. as opposed to
stationary in _space_.
[5] Lord Rayleigh, _Nature_, March 25, 1892.
CHAPTER V
SPECIAL EXPERIMENT ON ETHERIAL VISCOSITY
The balance 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. _Can_ matter 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 with a 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.
[Illustration: FIG. 11. Diagrammatic Plan of Optical Frame for Ether
Machine; with Steel Disks, one yard in diameter, inside the frame. The
actual apparatus is shown in Figs. 13 and 14 and Fig. 12.
M is a semi-transparent mirror, reflecting half an incident
beam and transmitting the other half. The two half-beams each
go three times round the square contour, in opposite
directions, and then reunite. It is an extension of the idea of
Fig. 7.]
The thing to observe is whether the motion of the disks is able to
replace a bright band by a dark one, or vice versa. If it does, it
means that one of the half-beams, viz. that which is travelling in the
same direction as the disks, is helped on a trifle, equivalent to a
shortening of journey by some quarter millionth of an inch or so in
the whole length of 30 feet; while the other half-beam, viz. that
travelling against the motion of the disks, is retarded, or its path
virtually lengthened, by the same amount.
If this acceleration and retardation actually occurs, waves which did
not interfere on meeting before the disks moved, will interfere now;
for one will arrive at the common goal half a length behind the other.
Now a gradual change of bright space to dark, and vice versa, shows
itself, to an observer looking at the bands, as a gradual change of
position of the bright stripes, or a shift of the bands. A shift of
the bands, and especially of the middle white band, which is much more
stable than the others, is what we look for. The middle band is, or
should be, free from the "concertina"-like motion which is liable to
infect the others.
At first I saw plenty of shift. In the first experiment the bands
sailed across the field as the disks got up speed until the crosswire
had traversed a band and a half. The conditions were such that had the
ether whirled at the full speed of the disks I should have seen a
shift of three bands. It looked very much as if the light was helped
along at half the speed of the moving matter, just as it is inside
water.
On stopping the disks the bands returned to their old position. On
starting them again in the opposite direction, the bands ought to have
shifted the other way too, if the effect was genuine; but they did
not; they went the same way as before.
The shift was therefore wholly spurious; it was caused by the
centrifugal force of the blast of air thrown off from the moving
disks. The mirrors and frame had to be protected from this. Many other
small changes had to be made, and gradually the spurious shifts have
been reduced and reduced, largely by the skill and patience of my
assistant, Mr. Benjamin Davies, until presently there was barely a
trace of them.
But the experiment is not an easy one. Not only does the blast exert
pressure, but at high speeds the churning of the air makes it quite
hot. Moreover, the tremor of the whirling machine, in which from four
to nine horse-power is sometimes being expended, is but too liable to
communicate itself to the optical part of the apparatus. Of course
elaborate precautions are taken against this. Although the two parts,
the mechanical and the optical, are so close together, their supports
are entirely independent. But they have to rest on the same earth, and
hence communicated tremors are not absent. They are the cause of most
of the slight residual trouble.
The whole experiment is described in fairly full detail in the
_Philosophical Transactions of the Royal Society_ for 1893 and 1897.
And there also are described some further modifications whereby the
whirling disks are electrified--likewise without optical effect, and
are also magnetised; or rather a great iron mass, strongly magnetised
by a current, is used to replace the steel disks.
The effect was always zero, however, when spurious results were
eliminated; and it is clear that at no practicable speed does either
electrification or magnetisation confer upon matter any appreciable
viscous grip upon the ether. Atoms _must_ be able to throw it into
vibration, if they are oscillating or revolving at sufficient speed;
otherwise they would not emit light or any kind of radiation; but in
no case do they appear to drag it along, or to meet with resistance in
any uniform motion through it. Only their acceleration is effectual.
In the light of Larmor's electron theory, we know now that
acceleration of atoms, or rather of a charge upon an atom, necessarily
generates radiation, proportional in amount to the _square_ of the
acceleration--whether that be tangential or normal. There is no
theoretical reason for assuming any influence on uniform velocity. And
even the influence on acceleration is exceedingly small under ordinary
circumstances. Only during the violence of collision are ether waves
freely excited. The present experiment, however, has nothing to do
with acceleration: it is a test of viscosity. An acceleration term
exists in motion through even a perfect fluid.
[Illustration: FIG. 12. General view of whirling part of Ether
machine, with pair of steel disks, and motor. _To face page 72._]
[Illustration: FIG. 13. General view of optical framework--sustaining
mirrors, telescope, and collimator--to surround the disks of the Ether
machine. Compare fig. 11. _To face page 73_.]
The conclusion at which I arrived in 1892 and 1893 is thus expressed
(p. 777 of vol. 184 _Philosophical Transactions of the Royal
Society_): "I feel confident either that the ether between the
disks is quite unaffected by their motion, or, if affected at all, by
something less than the thousandth part. At the same time, so far as
rigorous proof is concerned, I should prefer to assert that _the
velocity of light between two steel plates moving together in their
own plane an inch apart is not increased or diminished by so much as
the 1/200th part of their velocity_."
That was the conclusion in 1893; but since then observations have been
continued, and it is now quite safe to change the 1/200th into
1/1000th. The spin was sometimes continued for three hours to see if
an effect developed with time; and many other precautions were taken,
as briefly narrated in the _Philosophical Transactions_ for 1897.
The following illustrations give an idea of the apparatus employed.
Fig. 12 shows a photograph of the whirling machine before being bolted
down to its stone pier; with the pair of disks at top ready to be
whirled by an armature on the shaft, which is supplied with a current
sometimes of nine horse-power. The armature winding was of low
resistance, and was specially braced, so as to give high speed without
flying out, and without generating too much back-E M F. The
ampere-meter and volt-meter and the carbon rheostat (in armature
circuit), for regulating the speed, are plainly seen. The smooth
pulley on the shaft is for applying a brake. The small disk above it
is perforated to act as a siren for estimation of speed; but other
arrangements for this purpose were subsequently added. The two large
disks at top were of the best circular-saw steel; they are somewhat
thicker at middle than at edge, and are strongly bolted up between
iron cheeks, which are attached to the shaft. The lower end of the
shaft is a step-bearing of hardened steel in a vessel of oil. The
upper collar is elastic, so as to allow for a steadying teetotum
action at high speeds.
Fig. 13 is a photograph of the optical square, which was ultimately to
be placed in position surrounding the disks. The slit and collimator
are shown; the micrometer end of the observing telescope is out of the
picture.
The mirrors on the sides of the square are accurately plane; they are
adjustable on geometric principles, and are pressed against their
bearings by strong spiral springs. They were made by Hilger.
A drawing of the arrangement is given in Fig. 14, and here the double
micrometer eye-piece is visible.
In Fig. 15 the whole apparatus is shown mounted. The whirling machine
strongly bolted down to a stone pier independent of the floor; the
optical frame independently supported by a gallows frame from other
piers. The centrifugal mercury speed-indicator is visible in front,
and Mr. Davies is regulating the speed. At the back is seen a
boiler-plate screen for the observer with his eye at the telescope.
(See Frontispiece.)
[Illustration: _Lodge_
_Phil. Trans. 1893. A. Plate 31._
The mirror frame is pivoted on a vertical axis here Horizontal
axis of frame Mode of mounting the semi-transparent mirror M so
as to give altitude and azimuth movement to the reflected beam
Details of brass plate supporting fourth mirror front, side and
back views Back view shows the three slots in which the ends of
the supporting screws rest giving a fine adjustment, the plate
being supported by three rigid pushes and three elastic pulls.
FIG. 14 Plan of optical frame with steel disk in position, and
glazed drum to isolate them from the frame. G represents one of
the panes of optical glass. Supports of telescope and collimator
also shewn, and part of the fixing of the four mirrors 1.2.3.4.,
three of them let into recesses in the wooden frame, each mirror
held by a brass plate supported by three finely cut screws
against which it is pressed by the spring-bolts shewn M is the
semi-transparent mirror West, Newman lith FIG. 14.
_To face page 74._]
The expense of the apparatus was borne by my friend the late George
Holt, shipowner, of Liverpool.
Fig. 16 exhibits something like the appearance seen in the eye-piece,
with the interference bands on each side of the middle band, and with
the micrometer wires set in position--each moved by an independent
micrometer head. The straight vertical wire was usually set in the
centre of the middle white band, and the =X= wire on the yellow of the
first coloured band on one side or the other.
The method of observation now consists in setting a wire of the
micrometer accurately in the centre of the middle band, while another
wire is usually set on the first band to the left. Then the micrometer
heads are read, and the setting repeated once or twice to see how
closely and dependably they can be set in the same position. Then we
begin to spin the disks, and when they are going at some high speed,
measured by a siren note and in other ways, the micrometer wires are
reset and read--reset several times and read each time. Then the disks
are stopped and more readings are taken. Then their motion is
reversed, the wires set and read again; and finally the motion is once
more stopped and another set of readings taken. By this means the
absolute shift of middle band, and its relative interpretation in
terms of wave-length, are simultaneously obtained; for the distance
from the one wire to the other, which is often two revolutions of a
micrometer head, represents a whole wave-length shift.
In the best experiments I do still often see something like a fiftieth
of a band shift; but it is caused by residual spurious causes, for it
repeats itself with sufficient accuracy in the same direction when the
disks are spun the other way round.
Of real reversible shift, due to motion of the ether, I see nothing. I
do not believe the ether moves. It does not move at a five-hundredth
part of the speed of the steel disks. Further experience confirms and
strengthens this estimate, and my conclusion is that such things as
circular saws, flywheels, railway trains, and all ordinary masses of
matter do not appreciably carry the ether with them. Their motion does
not seem to disturb it in the least.
The presumption is that the same is true for the earth; but the earth
is a big body,--it is conceivable that so great a mass may be able to
act when a small mass would fail. I would not like to be too sure
about the earth--at least not on a strictly experimental basis. What I
do feel sure of is that if moving matter disturbs ether in its
neighbourhood at all, it does so by some minute action, comparable in
amount perhaps to gravitation, and possibly by means of the same
property as that to which gravitation is due--not by anything that
can fairly be likened to etherial viscosity. So far as experiment has
gone, our conclusion is that the viscosity or fluid friction of the
ether is zero. And that is an entirely reasonable conclusion.
[Illustration: FIG. 16. Approximate appearance of the interference
bands and micrometer wires as seen in the eye-piece of the telescope
of the Ether machine.]
[Illustration: FIG. 18. Appearance of the interference bands in the
channel of the iron spheroid. They were reflected in the upper iron as
shown.]
_To face page 76._
Oblate spheroid for Whirling Machine.
[Illustration: FIG. 17. Section of oblate spheroid of soft iron for
whirling machine, showing arrangement for winding central core with
wire so as to be able to magnetise it strongly while spinning inside
the optical frame.]
_To face page 77._
MAGNETISATION.
For testing the effect of magnetism, an oblate spheroid was made of
specially selected soft iron, 3 feet in diameter, weighing nearly a
ton. Its section is shown in Fig. 17. It had an annular channel or
groove, half an inch wide and 1 foot deep, round the bottom of which
was wound a kilometre of insulated wire to a depth of 4½ inches;
the terminals of which were brought out to sliding contacts on the
shaft, so that the whole could be very highly magnetised while it was
spinning. Everything was arranged so as to be symmetrical about the
central axis.
To the coil of wire, whose resistance was 30 ohms, 110 volts was
ordinarily, and 220 volts exceptionally, applied. The magnetic field
with 110 volts was about 1800 c.g.s., on the average, all over the
main region through which the beam of light circulated.
This light-bearing space, or gap in the magnetic circuit, was only
half an inch wide; and accordingly in the eye-piece the iron surfaces
could be seen, above and below, as well as the interference bands in
the luminous gap. The whole appearance is depicted in Fig. 18.
ELECTRIFICATION.
For the electrification experiment, a third and insulated disk was
clamped between the two steel disks and kept electrified to sparking
tension. The arrangement is shown diagrammatically on a smaller scale
in Fig. 19.
[Illustration: FIG. 19. Arrangement for electrifying a third or middle
steel disk to sparking potential while spinning.]
The electrification test was exceptionally easy to apply, by
connecting the insulated charging pin to a Voss machine in action:
because when the disks were spinning and the bands in good condition,
the electrification could be instantaneously applied, taken off,
reversed, or whatever was desired; and the effect of the sudden
lowering of potential by sparks passing between the revolving plates
could be exactly looked for.
The conclusion of my second _Philosophical Transactions_ paper--that
of 1897--is that _neither an electric nor a magnetic transverse field
confers viscosity upon the ether, nor enables moving matter to grip
and move it rotationally_.
QUESTION OF A POSSIBLE LONGITUDINAL MAGNETIC DRIFT.
Later I tried a longitudinal magnetic field also; arranging a series
of four large electric bobbins or long coils along the sides of a
square inscribed at 45° in the optical square, Figs. 11 and 13; so
that the light went along their axes.
The details of this experiment have been only partially recorded, but
the salient points are to be found stated in the _Philosophical
Magazine_ for April, 1907, pages 495-500.
The result was again negative; that is to say, a magnetic field causes
no perceptible acceleration in a beam of light sent along the lines of
force. The extra velocity that could have been observed would have
been 1/9th of a millimetre per second, or 16 miles per hour, for each
C.G.S. unit of field intensity.
Another mode of expressing the result is that the difference of
magnetic potential applied, namely, a drop of two million C.G.S. units
of magnetic potential, does not hurry light along it by so much as
1/50th part of a wave-length.
There may be reasons for supposing that some much slower drift or
conveyance than this is really caused in the ether by a magnetic
field; but if so, the ether must be regarded as so excessively dense
that the amount of such a drift for any practicable magnetic field
seems almost hopelessly beyond experimental means of detection.
CHAPTER VI
ETHERIAL DENSITY
This leads us to enter upon the question of whether it is possible to
determine with any approach to accuracy the actual density or
massiveness of the ether of space, compared with those forms of matter
to which our senses have made us accustomed.
The arguments on which an estimate may be made of the density or
massiveness of the ether as compared with that of matter depend on the
following considerations, the validity of which again is dependent
upon an electrical theory of matter. In this theory, or working
hypothesis, an assumption has to be made: but it is one for which
there is a large amount of justification, and the reasons for it are
given in many books,--among others in my book on _Electrons_, and
likewise at the end of the new edition of _Modern Views of
Electricity_, also in my _Romanes Lecture_, published by the Clarendon
Press in 1903. Put briefly, the assumption is that matter is composed,
in some way or other, of electrons; which again must be considered to
be essentially peculiarities, or singularities, or definite
structures, in the ether itself. Indeed, a consideration of electrons
alone is sufficient for the argument, provided it be admitted that
they have the mass which experiment shows them to possess, and the
size which electrical theory deduces for them: the basis of the
idea--which, indeed, is now experimentally proved--being that their
inertia is due to their self-induction,--i.e. to the magnetic field
with which they must be surrounded as long as they are in motion.
The mass, or inertia, of an electron is comparable to the thousandth
part of that of the atom of hydrogen. Its linear dimension, let us say
its diameter, is comparable to the one-hundred-thousandth part of what
is commonly known as molecular or atomic dimension; which itself is
the ten-millionth part of a millimetre.
Hence, the mass and the bulk of an electron being known, its density
is determined, provided we can assume that its mass is all dependent
on what is contained within its periphery. But that last assumption is
one that quite definitely cannot be made: its mass is for the most
part outside itself, and has to be calculated by magnetic
considerations. (See Appendix 2.)
These details are gone into in my paper in the _Philosophical
Magazine_ for April, 1907, and in Chapter XVII of _Modern Views of
Electricity_. But without repeating arguments here, it will suffice
to say that although the estimates may be made in various ways,
differing entirely from each other, yet the resulting differences are
only slight; the calculated densities come out all of the same order
of magnitude, namely, something comparable to 10¹² C.G.S.
units,--that is to say, a million million grammes per cubic
centimetre, or, in other words, a thousand tons to the cubic
millimetre.
But, throughout, we have seen reason to assert that the ether is
incompressible; arguments for this are given in _Modern Views of
Electricity_, Chapter I. And, indeed, the fundamental medium filling
all space, if there be such, _must_, in my judgment, be ultimately
incompressible; otherwise it would be composed of parts, and we should
have to seek for something still more fundamental to fill the
interstices.
The ether being incompressible, and an electron being supposed
composed simply and solely of ether, it follows that it cannot be
either a condensation or a rarefaction of that material, but must be
some singularity of structure, or some portion otherwise
differentiated. It might, for instance, be something analogous to a
vortex ring, differentiated kinetically, i.e. by reason of its
rotational motion, from the remainder of the ether; or it might be
differentiated statically, and be something which would have to be
called a strain-centre or a region of twist, or something which cannot
be very clearly at present imagined with any security; though various
suggestions have been made in that direction.
The simplest plan for us is to think of it somewhat as we think of a
knot on a piece of string. The knot differs in no respect from the
rest of the string, except in its tied-up structure; it is of the same
density with the rest, and yet it is differentiated from the rest;
and, in order to cease to be a knot, would have to be untied--a
process which as yet we have not learned how to apply to an electron.
If ever such a procedure becomes possible, then electrons will thereby
be resolved into the general body of the undifferentiated ether of
space,--that part which is independent of what we call "matter."
The important notion for present purposes is merely this: that the
density of the undifferentiated or simple ether, and the density of
the tied-up or be-knotted or otherwise modified ether constituting an
electron, are one and the same. Hence the argument above given, at
least when properly worked out, tends to establish the etherial
density as of the order 10¹² times that of water.
There ought to be nothing surprising (though I admit that there is
something very surprising) in such an estimate; inasmuch as many
converging lines of argument tend to show that ordinary matter is a
very porous or gossamer-like substance, with interspaces great as
compared with the spaces actually occupied by the nuclei which
constitute it. Our conception of matter, if it is to be composed of
electrons, is necessarily rather like the conception of a solar
system, or rather of a milky way; where there are innumerable dots
here and there, with great interspaces between. So that the average
density of the whole of the dots or material particles taken
together,--that is to say, their aggregate mass compared with the
space they occupy,--is excessively small.
In the vast extent of the Cosmos, as a whole, the small bulk of actual
matter, compared with the volume of empty space, is striking--as we
shall show directly; and now on the small scale, among the atoms of
matter, we find the conditions to be similar. Even what we call the
densest material is of extraordinarily insignificant massiveness as
compared with the unmodified ether which occupies by far the greater
proportion of its bulk.
When we speak of the density of _matter_, we are really though not
consciously expressing the group-density of the modified ether which
constitutes matter,--not estimated per unit, but per aggregate; just
as we might estimate the group or average density of a cloud or mist.
Reckoned per unit, a cloud has the density of water; reckoned per
aggregate, it is an impalpable filmy structure of hardly any density
at all. So it is with a cobweb, so perhaps it is with a comet's tail,
so also with the Milky Way, with the cosmos,--and, as it now turns
out, with ordinary matter itself.
For consider the average density of the material cosmos. It comes out
almost incredibly small. In other words, the amount of matter in
space, compared with the volume of space it occupies, is almost
infinitesimal. Lord Kelvin argues that ultimately it must be really
infinitesimal (_Philosophical Magazine_, Aug., 1901, and Jan., 1902),
that is to say that the volume of space is infinitely greater than the
total bulk of matter which it contains. Otherwise the combined force
of gravity--or at least the aggregate gravitational potential--on
which the velocity generated in material bodies ultimately depends,
would be far greater than observation shows it to be.
The whole visible universe, within a parallax of 1/1000 second of arc,
is estimated by Lord Kelvin as the equivalent of a thousand million of
our suns; and this amount of matter, distributed as it is, would have
an average density of 1·6 × 10⁻²³ grammes per c.c. It is noteworthy
how exceedingly small is this average or aggregate density of matter
in the visible region of space. The estimated density of 10⁻²³
c.g.s. means that the visible cosmos is as much rarer than a "vacuum"
of a hundred millionths of an atmosphere, as that vacuum is itself
rarer than lead.
It is because we have reason to assert that any ordinary mass of
matter consists, like the cosmos, of separated particles, with great
intervening distances in proportion to their size, that we are able to
maintain that the aggregate density of ordinary stuff, such as water
or lead, is very small compared with the continuous medium in which
they exist, and of which all particles are supposed to be really
composed. So that lead is to the ether, as regards density, very much
as the "vacuum" above spoken of is to lead. The fundamental medium
itself must be of uniform density everywhere, whether materialised or
free.
CHAPTER VII
FURTHER EXPLANATIONS CONCERNING THE DENSITY AND ENERGY OF THE ETHER
A reader may suppose that in speaking of the immense density or
massiveness of ether, and the absurdly small density or specific
gravity of gross matter by comparison, I intend to signify that matter
is a _rarefaction_ of the ether. That, however, is not my intention.
The view I advocate is that the ether is a perfect _continuum_, an
absolute _plenum_, and that therefore no rarefaction is possible. The
ether inside matter is just as dense as the ether outside, and no
denser. A material unit--say an electron--is only a peculiarity or
singularity of some kind in the ether itself, which is of perfectly
uniform density everywhere. What we "sense" as matter is an aggregate
or grouping of an enormous number of such units.
How then can we say that matter is millions of times rarer or less
substantial than the ether of which it is essentially composed? Those
who feel any difficulty here, should bethink themselves of what they
mean by the average or aggregate density of any discontinuous system,
such as a powder, or a gas, or a precipitate, or a snowstorm, or a
cloud, or a milky way.
If it be urged that it is unfair to compare an obviously discrete
assemblage like the stars, with an apparently continuous substance
like air or lead,--the answer is that it is entirely and accurately
fair; since air, and every other known form of matter, is essentially
an aggregate of particles, and since it is always their average
density that we mean. We do not even know for certain their individual
atomic density.
The phrase "specific gravity or density of a powder" is ambiguous. It
may mean the specific gravity of the dry powder as it lies, like snow;
or it may mean the specific gravity of the particles of which it is
composed, like ice.
So also with regard to the density of matter, we might mean the
density of the fundamental material of which its units are made--which
would be ether; or we might, and in practice do, mean the density of
the aggregate lump which we can see and handle; that is to say, of
water or iron or lead, as the case may be.
In saying that the density of matter is small,--I mean, of course, in
the last, the usual, sense. In saying that the density of ether is
great,--I mean that the actual stuff of which these highly porous
aggregates are composed is of immense, of wellnigh incredible,
density. It is only another way of saying that the ultimate units of
matter are few and far between--i.e. that they are excessively small
as compared with the distances between them; just as the planets of
the solar system, or worlds in the sky, are few and far between,--the
intervening distances being enormous as compared with the portions of
space actually occupied by lumps of matter.
It may be noted that it is not unreasonable to argue that the density
of a _continuum_ is necessarily greater than the density of any
disconnected aggregate: certainly of any assemblage whose particles
are actually composed of the material of the _continuum_. Because the
former is "all there," everywhere, without break or intermittence of
any kind; while the latter has gaps in it,--it is here, and there, but
not everywhere.
Indeed, this very argument was used long ago by that notable genius
Robert Hooke, and I quote a passage which Professor Poynting has
discovered in his collected posthumous works and kindly copied out for
me:--
"As for _matter_, that I conceive in its essence to be
immutable, and its essence being expatiation determinate, it
cannot be altered in its quantity, either by condensation or
rarefaction; that is, there cannot be more or less of that
power or reality, whatever it be, within the same expatiation
or content; but every equal expatiation contains, is filled, or
is an equal quantity of _materia_; and the densest or
heaviest, or most powerful body in the world contains no more
materia than that which we conceive to be the rarest, thinnest,
lightest, or least powerful body of all; as gold for instance,
and _æther_, or the substance that fills the cavity of an
exhausted vessel, or cavity of the glass of a barometer above
the quicksilver. Nay, as I shall afterwards prove, this cavity
is more full, or a more dense body of æther, in the common
sense or acceptation of the word, than gold is of gold, bulk
for bulk; and that because the one, viz. the mass of æther, is
all æther: but the mass of gold, which we conceive, is not all
gold; but there is an intermixture, and that vastly more than
is commonly supposed, of æther with it; so that vacuity, as it
is commonly thought, or erroneously supposed, is a more dense
body than the gold as gold. But if we consider the whole
content of the one with that of the other, within the same or
equal quantity of expatiation, then are they both equally
containing the _materia_ or body."--[_From the Posthumous Works
of Robert Hooke, M.D., F.R.S., 1705, pp. 171-2_ (_as copied in
Memoir of Dalton, by Angus Smith_).]
Newton's contemporaries did not excel in power of clear expression, as
he himself did; but Professor Poynting interprets this singular
attempt at utterance thus:--"All space is filled with equally dense
_materia_. Gold fills only a small fraction of the space assigned to
it, and yet has a big mass. How much greater must be the total mass
filling that space."
The tacit assumption here made is that the particles of the aggregate
are all composed of one and the same continuous substance,
--practically that matter is made of ether; and that assumption, in
Hooke's day, must have been only a speculation. But it is the kind of
speculation which time is justifying, it is the kind of truth which we
all feel to be in process of establishment now.[6]
We do not depend on that sort of argument, however; what we depend on
is experimental measure of the mass, and mathematical estimate of the
volume, of the electron. For calculation shows that however the mass
be accounted for--whether electrostatically or magnetically, or
hydrodynamically--the estimate of ratio of mass to effective volume
can differ only in a numerical coefficient, and cannot differ as
regards order of magnitude. The only way out of this conclusion would
be the discovery that the negative electron is not the real or the
main matter-unit, but is only a subsidiary ingredient; whereas the
main mass is the more bulky positive charge. That last hypothesis
however is at present too vague to be useful. Moreover, the mass of
such a charge would in that case be unexplained, and would need a
further step; which would probably land us in much the same sort of
etherial density as is involved in the estimate which I have based on
the more familiar and tractable negative electron. (See Appendix 2.)
It may be said why assume any finite density for the ether at all? Why
not assume that, as it is infinitely continuous, so it is infinitely
dense--whatever that may mean--and that all its properties are
infinite? This might be possible were it not for the velocity of
light. By transmitting waves at a finite and measurable speed, the
ether has given itself away, and has let in all the possibilities of
calculation and numerical statement. Its properties are thereby
exhibited as essentially finite--however infinite the whole extent of
it may turn out to be. Parenthetically we may remark that
"gravitation" has not yet exhibited any similar kind of finite
property; and that is why we know so little about it.
ETHERIAL ENERGY.
Instead then of saying that the density of the ether is great, the
clearest mode of expression is to say that the density of matter is
small. Just as we can say that the density of the visible cosmos is
small, although in individual lumps its density is comparable to that
of iron or rock.
At the risk of repetition, I have explained this over again, because
it is a matter on which confusion may easily arise. The really
important thing about ether is not so much its density, considered in
itself, as the energy which that density necessarily involves, on any
kinetic theory of its elasticity. For it is not impossible--however
hopeless it may seem now--that a modicum of that energy may some day
be partially utilised.
Lord Kelvin's incipient kinetic theory of elasticity is a complicated
matter, and I will only briefly enter upon it. But before doing so, I
want to remove an objection which is sometimes felt, as to the fluid
and easily permeable character of a medium of this great
density,--that is to say, as to the absence of friction or
viscosity--the absence of resistance to bodies moving through it. As a
matter of fact there is no necessary connexion whatever between
density and viscosity.
'Density' and 'Viscosity' are entirely different things; and, if there
is no fluid friction, a fluid may have any density you please without
interposing any obstacle to constant velocity. To _acceleration_ it
does indeed oppose an obstacle, but that appears as essentially a part
of the inertia or massiveness of the moving body. It contributes to
its momentum; and, if the fluid is everywhere present, it is
impossible to discriminate between, or to treat separately, that part
of the inertia which belongs to the fluid displaced, and that part
which belongs to the body moving through it,--except by theory.
As for the elasticity of the ether, that is ascertainable at once from
the speed at which it transmits waves. That speed--the velocity of
light--is accurately known, 3 × 10¹⁰ centimetres per second. And
the ratio of the elasticity or rigidity to the density is equal to the
square of this speed;--that is to say, the elasticity must be 9 ×
10²⁰ times the density; or, in other words, 10³³ C.G.S. units.
That is an immediate consequence of the estimate of density and the
fact of the velocity of light; and if the density is admitted, the
other cannot be contested.
But we must go on to ask, To what is this rigidity due? If the ether
does not consist of parts, and if it is fluid, how can it possess the
rigidity appropriate to a solid, so as to transmit transverse waves?
To answer this we must fall back upon Lord Kelvin's kinetic theory of
elasticity:--that it must be due to rotational motion--intimate
fine-grained motion throughout the whole etherial region--motion not
of the nature of locomotion, but circulation in closed curves,
returning upon itself,--vortex motion of a kind far more finely
grained than any waves of light or any atomic or even electronic
structure.
Now if the elasticity of any medium is to be thus explained
kinetically, it follows, as a necessary consequence, that the speed
of this internal motion must be comparable to the speed of wave
propagation;--that is to say that the internal squirming circulation,
to which every part of the ether is subject, must be carried on with a
velocity of the same order of magnitude as the velocity of light.
This is the theory then,--this theory of elasticity as dependent on
motion,--which, in combination with the estimate of density, makes the
internal energy of the ether so gigantic. For in every cubic
millimetre of space we have, according to this view, a mass equivalent
to what, if it were matter, we should call a thousand tons,
circulating internally, every part of it, with a velocity comparable
to the velocity of light, and therefore containing--stored away in
that small region of space--an amount of energy of the order 10²⁹
ergs, or, what is the same thing, 3 × 10¹¹ kilowatt centuries;
which is otherwise expressible as equal to the energy of a million
horse-power station working continuously for forty million years.
SUMMARISED BRIEF STATEMENTS CONCERNING THE ETHER
_(As communicated by the author to the British Association at
Leicester, 1907)._
1. The theory that an electric charge must possess the equivalent of
inertia was clearly established by J.J. Thomson in the _Philosophical
Magazine_ for April, 1881.
2. The discovery of masses smaller than atoms was made experimentally
by J.J. Thomson, and communicated to Section A at Dover in 1899.
3. The thesis that the corpuscles so discovered consisted wholly of
electric charges was sustained by many people, and was clinched by the
experiments of Kaufmann in 1902.
4. The concentration of the ionic charge, required to give the
observed corpuscular inertia, can be easily calculated; and
consequently the size of the electric nucleus, or electron, is known.
5. The old perception that a magnetic field is kinetic has been
developed by Kelvin, Heaviside, FitzGerald, Hicks, and Larmor, most of
whom have treated it as a flow along magnetic lines; though it may
also, perhaps equally well, be regarded as a flow perpendicular to
them and along the Poynting vector. The former doctrine is sustained
by Larmor, as in accordance with the principle of Least Action, and
with the absolutely stationary character of the ether as a whole; the
latter view appears to be more consistent with the theories of J.J.
Thomson.
6. A charge in motion is well known to be surrounded by a magnetic
field; and the energy of the motion can be expressed in terms of the
energy of this concomitant field,--which again must be accounted as
the kinetic energy of ethereous flow.
7. Putting these things together, and considering the ether as
essentially incompressible--on the strength of the Cavendish electric
experiment, the facts of gravitation, and the general idea of a
connecting continuous medium--the author reckons that to deal with the
ether dynamically it must be treated as having a density of the order
10¹² grammes per cubic centimetre. (See Appendix 2.)
8. The existence of transverse waves in the interior of a fluid can
only be explained on gyrostatic principles, i.e. by the kinetic or
rotational elasticity of Lord Kelvin. And the internal circulatory
speed of the intrinsic motion of such a fluid must be comparable with
the velocity with which such waves are transmitted.
9. Putting these things together, it follows that the intrinsic or
constitutional vortex energy of the ether must be of the order 10³³
ergs per cubic centimetre.
_Conclusion._--Thus every cubic millimetre of the universal ether of
space must possess the equivalent of a thousand tons, and every part
of it must be squirming internally with the velocity of light.
FOOTNOTE:
[6] It does not seem to have been noticed that in Query 22, quoted in
the Introduction to the present book, Newton seems to throw out a
curious hint in this same direction,--though he immediately abandons
it again. He does not appear to have carefully _edited_ his queries;
probably they were published posthumously.
CHAPTER VIII
ETHER AND MATTER
THE MECHANICAL NECESSITY FOR A CONTINUOUS
MEDIUM FILLING SPACE
In this chapter I propose to summarise in simple and consecutive form
most of the arguments already used. Thirty years ago Clerk Maxwell
gave to the Royal Institution of Great Britain a remarkable address on
"Action at a Distance." It is reported in the Journal R.I., Vol. VII,
and to it I would direct attention. Most natural philosophers hold,
and have held, that action at a distance across empty space is
impossible; in other words, that matter cannot act where it is not,
but only where it is. The question "Where is it?" is a further
question that may demand attention and require more than a superficial
answer. For it can be argued on the hydrodynamic or vortex theory of
matter, as well as on the electrical theory, that every atom of matter
has a universal though nearly infinitesimal prevalence, and extends
everywhere; since there is no definite sharp boundary or limiting
periphery to the region disturbed by its existence. The lines of force
of an isolated electric charge extend throughout illimitable space.
And though a charge of opposite sign will curve and concentrate them,
yet it is possible to deal with both charges, by the method of
superposition, as if they each existed separately without the other.
In that case, therefore, however far they reach, such nuclei clearly
exert no "action at a distance" in the technical sense.
Some philosophers have reason to suppose that mind can act directly on
mind without intervening mechanism,--and sometimes that has been
spoken of as genuine action at a distance; but no proper conception or
physical model can be made of such a process, nor is it clear that
"space" and "distance" have any particular meaning in the region of
psychology. The links between mind and mind may be something quite
other than physical proximity; and in denying action at a distance
across empty space I am not denying telepathy or other activities of a
non-physical kind. For although brain disturbance is certainly
physical, and is an essential concomitant of mental action whether of
the sending or receiving variety, yet we know from the case of heat
that a material movement can be excited in one place at the expense of
corresponding movement in another, without any similar kind of
transmission or material connexion between the two places: the thing
that travels across vacuum is not heat.
In all cases where physical motion is involved, however, I would have
a medium sought for. It may not be matter, but it must be something;
there must be a connecting link of some kind, or the transference
cannot occur. There can be no attraction across really empty space.
And even when a material link exists, so that the connexion is
obvious, the explanation is not complete; for when the mechanism of
attraction is understood, it will be found that a body really only
moves because it is pushed by something from behind. The essential
force in nature is the _vis a tergo_. So when we have found the
"traces," or discovered the connecting thread, we still run up against
the word "cohesion"; and we ought to be exercised in our minds as to
its ultimate meaning. Why the whole of a rod should follow, when one
end is pulled, is a matter requiring explanation; and the only
explanation that can be given involves, in some form or other, a
continuous medium connecting the discrete and separated particles or
atoms of matter.
When a steel spring is bent or distorted, what is it that is really
strained? Not the atoms--the atoms are only displaced; it is the
connecting links that are strained--the connecting medium--the ether.
Distortion of a spring is really distortion of the ether. All stress
exists in the ether. Matter can only be moved. Contact does not exist
between the atoms of matter as we know them; it is doubtful if a
piece of matter ever touches another piece, any more than a comet
touches the sun when it appears to rebound from it; but the atoms are
connected, as the comet and the sun are connected, by a continuous
_plenum_ without break or discontinuity of any kind. Matter acts on
matter only through the ether. But whether matter is a thing utterly
distinct and separate from the ether, or whether it is a specifically
modified portion of it--modified in such a way as to be susceptible of
locomotion and yet continuous with all the rest of the ether, which
can be said to extend everywhere far beyond the bounds of the modified
and tangible portion--are questions demanding, and I may say in
process of receiving, answers.
Every such answer involves some view of the universal and possibly
infinite uniform omnipresent connecting medium, the Ether of space.
It has been said, somewhat sarcastically, that the ether was made in
England. The statement is only an exaggeration of the truth. I might
even urge that it has been largely constructed in the Royal
Institution; for, I will summarise now the chief lines of evidence on
which its existence is believed in, and our knowledge of it is based.
First of all, Newton recognised the need of a medium for explaining
gravitation. In his "Optical Queries" he shows that if the pressure of
this medium is less in the neighbourhood of dense bodies than at
great distances from them, dense bodies will be driven towards each
other; and that if the diminution of pressure is inversely as the
distance from the dense body, the law of force will be the inverse
square law of gravitation.
All that is required, therefore, to explain gravity, is a diminution
of pressure, or increase of tension, caused by the formation of a
matter unit--that is to say of an electron or corpuscle. And although
we do not yet know what an electron is--whether it be a strain centre,
or what kind of singularity in the ether it may be--there is no
difficulty in supposing that a slight, almost infinitesimal, strain or
attempted rarefaction should be produced in the ether whenever an
electron comes into being--to be relaxed again only on its resolution
and destruction. Strictly speaking it is not a real _strain_, but only
a "stress"; since there can be no actual _yield_, but only a pull or
tension, extending in all directions towards infinity.
The tension required per unit of matter is almost ludicrously small,
and yet in the aggregate, near such a body as a planet, it becomes
enormous.
The force with which the moon is held in its orbit would be great
enough to tear asunder a steel rod four hundred miles thick, with a
tenacity of 30 tons per square inch; so that if the moon and earth
were connected by steel instead of by gravity, a forest of pillars
would be necessary to whirl the system once a month round their
common centre of gravity. Such a force necessarily implies enormous
tension or pressure in the medium. Maxwell calculates that the
gravitational stress near the earth, which we must suppose to exist in
the invisible medium, is 3000 times greater than what the strongest
steel could stand; and near the sun it should be 2500 times as great
as that.
The question has arisen in my mind, whether, if the whole sensible
universe--estimated by Lord Kelvin as equivalent to about a thousand
million suns--were all concentrated in one body of specifiable
density,[7] the stress would not be so great as to produce a tendency
towards etherial disruption; which would result in a disintegrating
explosion, and a scattering of the particles once more as an enormous
nebula and other fragments into the depths of space. For the tension
would be a maximum in the interior of such a mass; and, if it rose to
the value 10³³ dynes per square centimetre, something would have to
happen. I do not suppose that this can be the reason, but one would
think there must be _some_ reason, for the scattered condition of
gravitative matter.
Too little is known, however, about the mechanism of gravitation to
enable us to adduce it as the strongest argument in support of the
existence of an ether. The oldest valid and conclusive requisition of
an ethereous medium depends on the wave theory of light, one of the
founders of which was the Royal Institution Professor of Natural
Philosophy at the beginning of last century, Dr. Thomas Young.
No ordinary matter is capable of transmitting the undulations or
tremors that we call light. The speed at which they go, the kind of
undulation, and the facility with which they go through vacuum, forbid
this.
So clearly and universally has it been perceived that waves must be
waves of something--something distinct from ordinary matter--that Lord
Salisbury, in his presidential address to the British Association at
Oxford, criticised the ether as little more than a nominative case to
the verb to undulate. It is truly _that_, though it is also truly more
than that; but to illustrate that luminiferous aspect of it, I will
quote a paragraph from the lecture of Clerk Maxwell's to which I have
already referred:--
"The vast interplanetary and interstellar regions will no longer be
regarded as waste places in the universe, which the Creator has not
seen fit to fill with the symbols of the manifold order of His
kingdom. We shall find them to be already full of this wonderful
medium; so full, that no human power can remove it from the smallest
portion of space, or produce the slightest flaw in its infinite
continuity. It extends unbroken from star to star; and when a molecule
of hydrogen vibrates in the dog-star, the medium receives the impulses
of these vibrations, and after carrying them in its immense bosom for
several years, delivers them, in due course, regular order, and full
tale, into the spectroscope of Mr. Huggins, at Tulse Hill."
This will suffice to emphasise the fact that the eye is truly an
etherial sense-organ--the only one which we possess, the only mode by
which the ether is enabled to appeal to us; and that the detection of
tremors in this medium--the perception of the direction in which they
go, and some inference as to the quality of the object which has
emitted them--cover all that we mean by "sight" and "seeing."
I pass then to another function, the electric and magnetic phenomena
displayed by the ether; and on this I will only permit myself a very
short quotation from the writings of Faraday, whose whole life may be
said to have been directed towards a better understanding of these
ethereous phenomena. Indeed the statue in the entrance hall of the
Royal Institution, Albemarle Street, may be considered as the statue
of the discoverer of the electric and magnetic properties of the Ether
of space.
Faraday conjectured that the same medium which is concerned in the
propagation of light might also be the agent in electromagnetic
phenomena. "For my own part," he says, "considering the relation of a
vacuum to the magnetic force, and the general character of magnetic
phenomena external to the magnet, I am much more inclined to the
notion that in the transmission of the force there is such an action,
external to the magnet, than that the effects are merely attraction
and repulsion at a distance. Such an action may be a function of the
æther; for it is not unlikely that, if there be an æther, it should
have other uses than simply the conveyance of radiation."
This conjecture has been amply strengthened by subsequent
investigations.
One more function is now being discovered; the ether is being found to
constitute matter--an immensely interesting topic, on which there are
many active workers at the present time. I will make a brief quotation
from Professor Sir J.J. Thomson, where he summarises the conclusion
which we all see looming before us, though it has not yet been
completely attained, and would not by all be similarly expressed:--
"The _whole_ mass of any body is just the mass of ether surrounding
the body which is carried along by the Faraday tubes associated with
the atoms of the body. In fact, all mass is mass of the ether; all
momentum, momentum of the ether; and all kinetic energy, kinetic
energy of the ether. This view, it should be said, requires the
density of the ether to be immensely greater than that of any known
substance."
Yes, far denser--so dense that matter by comparison is like gossamer,
or a filmy imperceptible mist, or a milky way. Not unreal or
unimportant,--a cobweb is not unreal, nor to certain creatures is it
unimportant, but it cannot be said to be massive or dense; and matter,
even platinum, is not dense when compared with the ether. Not till
last year, however, did I realise what the density of the ether must
really be,[8] compared with that modification of it which appeals to
our senses as matter, and which for that reason engrosses our
attention.
Is there any other function possessed by the ether, which, though not
yet discovered, may lie within the bounds of possibility for future
discovery? I believe there is, but it is too speculative to refer to,
beyond saying that it has been urged as probable by the authors of
_The Unseen Universe_, and has been thus tentatively referred to by
Clerk Maxwell:--
"Whether this vast homogeneous expanse of isotropic matter is fitted
not only to be a medium of physical interaction between distant
bodies, and to fulfil other physical functions of which, perhaps, we
have as yet no conception, but also ... to constitute the material
organism of beings exercising functions of life and mind as high or
higher than ours are at present--is a question far transcending the
limits of physical speculation."
And there for the present I leave that aspect of the subject.
_Ether and Matter._
I shall now attempt to illustrate some relations between ether and
matter.
The question is often asked, is ether material? This is largely a
question of words and convenience. Undoubtedly, the ether belongs to
the material or physical universe, but it is not ordinary matter. I
should prefer to say it is not "matter" at all. It may be the
substance or substratum or material of which matter is composed, but
it would be confusing and inconvenient not to be able to discriminate
between matter on the one hand, and ether on the other. If you tie a
knot on a bit of string, the knot is composed of string, but the
string is not composed of knots. If you have a smoke or vortex-ring in
the air, the vortex-ring is made of air, but the atmosphere is not a
vortex-ring; and it would be only confusing to say that it was.
The essential distinction between matter and ether is that matter
_moves_, in the sense that it has the property of locomotion and can
effect impact and bombardment; while ether is _strained_, and has the
property of exerting stress and recoil. All potential energy exists in
the ether. It may vibrate, and it may rotate, but as regards
locomotion it is stationary--the most stationary body we know:
absolutely stationary, so to speak; our standard of rest.
All that we ourselves can effect, in the material universe, is to
alter the motion and configuration of masses of matter; we can move
matter, by our muscles, and that is all we can do directly: everything
else is indirect.
But now comes the question, how is it possible for matter to be
composed of ether? How is it possible for a solid to be made out of
fluid? A solid possesses the properties of rigidity, impenetrability,
elasticity, and such-like; how can these be imitated by a perfect
fluid such as the ether must be?
The answer is, they can be imitated by a _fluid in motion_; a
statement which we make with confidence as the result of a great part
of Lord Kelvin's work.
It may be illustrated by a few experiments.
A wheel of spokes, transparent or permeable when stationary, becomes
opaque when revolving, so that a ball thrown against it does not go
through, but rebounds. The motion only affects permeability to matter;
transparency to light is unaffected.
A silk cord hanging from a pulley becomes rigid and viscous when put
into rapid motion; and pulses or waves which may be generated on the
cord travel along it with a speed equal to its own velocity, whatever
that velocity may be, so that they appear to stand still. This is a
genuine case of kinetic rigidity; and the fact that the
wave-transmission velocity is equal to the rotatory speed of the
material, is typical and important,--for in all cases of kinetic
elasticity these two velocities are of the same order of magnitude.
A flexible chain, set spinning, can stand up on end while the motion
continues.
A jet of water at sufficient speed can be struck with a hammer, and
resists being cut with a sword.
A spinning disk of paper becomes elastic like flexible metal, and can
act like a circular saw. Sir William White tells me that in naval
construction steel plates are cut by a rapidly revolving disk of soft
iron.
A vortex-ring, ejected from an elliptical orifice, oscillates about
the stable circular form, as an india-rubber ring would do; thus
furnishing a beautiful example of kinetic elasticity, and showing us
clearly a fluid displaying some of the properties of a solid.
A still further example is Lord Kelvin's model of a spring balance,
made of nothing but rigid bodies in spinning motion.[9] This
arrangement utilises the processional movement of balanced
gyrostats--concealed in a case and supporting a book--to imitate the
behaviour of a spiral spring, if it were used to support the same
book.
If the ether can be set spinning, therefore, we may have some hope of
making it imitate the properties of matter, or even of constructing
matter by its aid. But _how_ are we to spin the ether? Matter alone
seems to have no grip of it. As already described, I have spun steel
disks, a yard in diameter, 4000 times a minute, have sent light round
and round between them, and tested carefully for the slightest effect
on the ether. Not the slightest effect was perceptible. We cannot spin
ether mechanically.
But we can vibrate it electrically; and every source of radiation does
that. An electrical charge, in sufficiently rapid vibration, is the
only source of ether-waves that we know; and if an electric charge is
suddenly stopped, it generates the pulses known as X-rays, as the
result of the collision. Not speed, but sudden change of speed, is the
necessary condition for generating waves in the ether by electricity.
We can also infer some kind of rotary motion in the ether; though we
have no such obvious means of detecting the spin as is furnished by
vision for detecting some kinds of vibration. Rotation is supposed to
exist whenever we put a charge into the neighbourhood of a magnetic
pole. Round the line joining the two, the ether is spinning like a
top. I do not say it is spinning fast: that is a question of its
density; it is in fact spinning with excessive slowness, but it is
spinning with a definite moment of momentum. J.J. Thomson's theory
makes its moment of momentum exactly equal to _e m_, the product of
_charge_ and _pole_; the charge being measured electrostatically and
the pole magnetically.
How can this be shown experimentally? Suppose we had a spinning top
enclosed in a case, so that the spin was unrecognisable by ordinary
means--it could be detected by its gyrostatic behaviour to force. If
allowed to "precess" it will respond by moving perpendicularly to a
deflecting force. So it is with the charge and the magnetic pole. Try
to move the charge suddenly, and it immediately sets off at right
angles. A moving charge is a current, and the pole and the current try
to revolve round one another;--a fact which may be regarded as
exhibiting a true gyrostatic action due to the otherwise
unrecognisable etherial spin. The fact of such magnetic rotation was
discovered by Faraday.
I know that it is usually worked out in another way, in terms of lines
of force and the rest of the circuit; but I am thinking of a current
as a stream of projected charges; and no one way of regarding such a
matter is likely to exhaust the truth, or to exclude other modes which
are equally valid. Anyhow, in whatever way it is regarded, it is an
example of the three rectangular vectors.
The three vectors at right angles to each other, which may be labelled
Current, Magnetism, and Motion respectively, or more generally E, H,
and V, represent the quite fundamental relation between ether and
matter, and constitute the link between Electricity, Magnetism, and
Mechanics. Where any two of these are present, the third is a
necessary consequence. This principle is the basis of all dynamos, of
electric motors, of light, of telegraphy, and of most other things.
Indeed, it is a question whether it does not underlie everything that
we know in the whole of the physical sciences; and whether it is not
the basis of our conception of the three dimensions of space.
Lastly, we have the fundamental property of matter called _inertia_,
which can, to a certain extent, be explained electromagnetically,
provided the ethereous density is granted as of the order 10¹²
grammes per cubic centimetre. The elasticity of the ether would then
have to be of the order 10³³ c.g.s.; and if this is due to
intrinsic turbulence, the speed of the whirling or rotational
elasticity must be of the same order as the velocity of light. This
follows hydrodynamically; in the same sort of way as the speed at
which a pulse travels on a flexible running endless cord, whose
tension is entirely due to the centrifugal force of the motion, is
precisely equal to the velocity of the cord itself. And so, on our
present view, the intrinsic energy of constitution of the ether is
incredibly and portentously great; every cubic millimetre of space
possessing what, if it were matter, would be a mass of a thousand
tons, and an energy equivalent to the output of a million-horse-power
station for 40 million years.
The universe we are living in is an extraordinary one; and our
investigation of it has only just begun. We know that matter has a
psychical significance, since it can constitute _brain_, which links
together the physical and the psychical worlds. If any one thinks that
the ether, with all its massiveness and energy, has probably no
psychical significance, I find myself unable to agree with him.
FOOTNOTES:
[7] On doing the arithmetic, however, I find the necessary
concentration absurdly great, showing that such a mass is quite
insufficient. (See Appendix 1.)
[8] See Lodge, _Philosophical Magazine_, April, 1907. Also Appendix 2
below.
[9] Address to Section A of British Association at Montreal, 1884.
CHAPTER IX
STRENGTH OF THE ETHER
To show that the ether cannot be the slight and rarefied substance
which at one time, and indeed until quite lately, it was thought to
be, it is useful to remember that not only has it to be the vehicle of
light and the medium of all electric and magnetic influence, but also
that it has to transmit the tremendous forces of gravitation.
Among small bodies gravitational forces are slight, and are altogether
exceeded by magnetic and electric or chemical forces. Indeed
gravitational attraction between bodies of a certain smallness can be
more than counterbalanced even by the pressure which their mutual
radiation exerts--almost infinitesimal though that is;--so that as a
matter of fact, small enough bodies of any warmth will repel each
other unless they are in an enclosure of constant temperature, i.e.
unless the radiation pressure upon them is uniform all round.
The size at which radiation repulsion over-balances gravitational
attraction, for equal spheres, depends on the temperature of the
spheres and on their density; but at the ordinary temperature to
which we are accustomed, say 60° Fahrenheit or thereabouts, equality
between the two forces will obtain for two wooden spheres in space if
each is about a foot in diameter; according to Professor Poynting's
data (_Philosophical Transactions_, Vol. 202, p. 541). For smaller or
hotter bodies, radiation repulsion overpowers mutual gravitation; and
it increases with the fourth power of their absolute temperature. The
gravitational attractive force between particles is exceedingly small;
and that between two atoms or two electrons is negligibly small, even
though they be within molecular distance of each other.
For instance, two atoms of, say, gold, at molecular distance, attract
each other gravitationally with a force of the order
γ (10⁻²² x 10⁻²²) / (10⁻⁸)² =
10⁻⁴⁴ / 10⁻¹⁶ x 10⁻⁷ = 10⁻³⁵ dyne;
which would cause no perceptible acceleration at all.
The gravitational attraction of two electrons at the same distance is
the forty-thousand-millionth part of this, and so one would think must
be entirely negligible. And yet it is to the aggregate attraction of
myriads of such bodies that the resultant force of attraction is
due;--a force which is felt over millions of miles. The force is not
only felt indeed, but must be reckoned as one of prodigious magnitude.
When dealing with bodies of astronomical size, the force of
gravitation overpowers all other forces; and all electric and magnetic
attractions sink by comparison into insignificance.
These immense forces must be transmitted by the ether, and it is
instructive to consider their amount.
SOME ASTRONOMICAL FORCES WHICH THE ETHER HAS TO TRANSMIT.
_Arithmetical Calculation of the Pull of the Earth on the Moon._
The mass of the earth is 6000 trillion (6 × 10²¹) tons. The mass of
the moon is 1/80th that of the earth. Terrestrial gravity at the
moon's distance (which is 60 earth radii) must be reduced in the ratio
1:60²; that is, it must be 1/3600th of what it is here.
Consequently the pull of the earth on the moon is
6 × 10²¹ / 80 × 3600 tons weight.
A pillar of steel which could transmit this force, provided it could
sustain a tension of 40 tons to the square inch, would have a diameter
of about 400 miles; as stated in the text, page 102.
If this force were to be transmitted by a forest of weightless pillars
each a square foot in cross-section, with a tension of 30 tons to the
square inch throughout, there would have to be 5 million million of
them.
_Arithmetical Calculation of the Pull of the Sun on the Earth._
The mass of the earth is 6 × 10²¹ tons. The intensity of solar
gravity at the sun's surface is 25 times ordinary terrestrial gravity.
At the earth's distance, which is nearly 200 solar radii, solar
gravity will be reduced in the ratio of 1:200 squared.
Hence the force exerted by the sun on the earth is
(25 × 6 × 10²¹)/(200)² tons weight.
That is to say, it is approximately equal to the weight of 37 ×
10¹⁷ ordinary tons upon the earth's surface.
Now steel may readily be found which can stand a load of 37 tons to
every square inch of cross-section. The cross-section of a bar of such
steel, competent to transmit the sun's pull to the earth, would
therefore have to be
10¹⁷ square inches,
or say 700 × 10¹² square feet.
And this is equivalent to a million million round rods or pillars each
30 feet in diameter.
Hence the statement in the text (page 26) is well within the mark.
_The Pull of the Earth on the Sun._
The pull of the earth on the sun is, of course, equal and opposite to
the pull of the sun on the earth, which has just been calculated; but
it furnishes another mode of arriving at the result, and may be
regarded as involving simpler data--i.e. data more generally known.
All we need say is the following:--
The mass of the Sun is 316,000 times that of the Earth.
The mean distance of the sun is, say, 23,000 earth radii.
Hence the weight or pull of the sun by the earth is
316000/(23000)² × 6 × 10²¹ tons weight.
In other words, it is approximately equal to the ordinary commercial
weight of 36 × 10¹⁷ tons, as already calculated.
_The Centripetal Force acting on the Earth._
Yet another method of calculating the sun's pull is to express it in
terms of the centrifugal force of the earth; namely, its mass,
multiplied by the square of its angular velocity, multiplied by the
radius of its orbit;--that is to say,
F = M (2φ/T)² r
where T is the length of a year.
The process of evaluating this is instructive, owing to the
manipulation of units which it involves:--
F = 6 x 10²¹ tons x (4φ² x 92 x 10⁶ miles)/(365¼ days)²
which of course is a mass multiplied by an acceleration. The
acceleration is--
(40 x 92 x 10⁶)/133300 x (24)² miles per hour per hour
= (3680 x 10⁶ x 5280)/133300 x 576 x (3600)² feet per sec. per sec.
= (115 x 5280)/133300 x 576 x 12·96 feet per sec. per sec.
= g/1640
Hence the Force of attraction is that which, applied to the earth's
mass, produces in it an acceleration equal to the 1/1640th part of
what ordinary terrestrial gravity can produce in falling bodies; or
F = 6 × 10²¹ tons × g/1640
= 6/1640 x 10²¹ tons weight;
which is the ordinary weight of 37 × 10¹⁷ tons, as before.
The slight numerical discrepancy between the above results is of
course due to the approximate character of the data selected, which
are taken in round numbers as quite sufficient for purposes of
illustration.
If we imagine the force applied to the earth by a forest of round
rods, one for every square foot of the earth's surface--i.e. of the
projected earth's hemisphere or area of equatorial plane,--the force
transmitted by each would have to be 2700 tons; and therefore, if of
30-ton steel, they would each have to be eleven inches in diameter, or
nearly in contact, all over the earth.
_Pull of a Planet on the Earth._
While we are on the subject, it seems interesting to record the fact
that the pull of any planet on the earth, even Neptune, distant though
it is, is still a gigantic force. The pull of Neptune is 1/20,000th of
the sun's pull: i.e. it is 18 billion tons weight.
_Pull of a Star on the Earth._
On the other hand, the pull of a fixed star, like Sirius--say a star,
for example, which is 20 times the mass of the sun and 24 light years
distant--is comparatively very small.
It is easily found by dividing 20 times the sun's pull by the squared
ratio of 24 years to 8 minutes; and it comes out as 30 million tons
weight.
Such a force is able to produce no perceptible effect. The
acceleration it causes in the earth and the whole solar system, at its
present speed through space, is only able to curve the path with a
radius of curvature of length thirty thousand times the distance of
the star.
_Force required to hold together the Components of some Double Stars._
But it is not to be supposed that the transmission of any of these
forces gives the ether the slightest trouble, or strains it to
anywhere near the limits of its capacity. Such forces must be
transmitted with perfect ease, for there are plenty of cases where the
force of gravitation is vastly greater than that. In the case of
double stars, for instance, two suns are whirling round each other;
and some of them are whirling remarkably fast. In such cases the force
holding the components together must be enormous.
Perhaps the most striking case, for which we have substantially
accurate data, is the star ββ Aurigæ; which, during the general
spectroscopic survey of the heavens undertaken by Professor Pickering
of Harvard, in connexion with the Draper Memorial, was discovered to
show a spectrum with the lines some days double and alternate days
single. Clearly it must consist of a pair of luminous objects
revolving in a plane approximately containing the line of vision; the
revolution being completed every four days. For the lines will then be
optically displaced by the motion, during part of the orbit--those of
the advancing body to the right, those of the receding body to the
left,--while in that part of the orbit which lies athwart the
direction of vision, the spectrum lines will return to their proper
places,--opening out again to a maximum, in the opposite direction, at
the next quadrant.
The amount of displacement can be roughly estimated, enabling us to
calculate the speed with which the sources of light were moving.
Professor Pickering, in a brief statement in _Nature_, Vol. XLI, page
403, 1889, says that the velocity amounts to about 150 miles per
second, and that it is roughly the same for both components.
Taking these data:--
Equality and uniformity of speeds,
150 miles per second each,
Period 4 days,
we have all the data necessary to determine the masses; and likewise
the gravitative pull between them. For the star must consist of two
equal bodies, revolving about a common centre of gravity midway
between them, in nearly circular orbits.
The speed and period together easily give the radius of the circular
orbit as about 8 million miles.
Equating centrifugal and centripetal forces
mv² / r = γ m² / (2r)²
and comparing the value of 4r³ / T² so obtained with the r³ /
T² of the earth, we find the mass of each body must be about 30,000
times that of the earth, or about 1/10th that of the sun.
* * * * *
(This is treating them as spheres, though they must really be pulled
into decidedly prolate shapes. Indeed it may seem surprising that the
further portions can keep up with the nearer portions as they revolve.
If they are of something like solar density their diameter will be
comparable to half a million miles, and the natural periods of their
near and far portions will differ in the ratio (17/16)^{3/2} = 1·1
approximately. Tenacity could not hold the parts together, but
gravitational coherence would.)
* * * * *
This, however, is a digression. Let us continue the calculation of the
gravitative pull.
We have masses of 3 × 10⁴ × 6 × 10²¹ tons, revolving with
angular velocity 2π ÷ 4 days, in a circle of radius 8 × 10⁶ miles.
Consequently the centripetal acceleration is 4 π² × 8 × 10⁶ / 16
miles per day per day; which comes out 32 / 2·2 ft. per sec. per sec.,
or nearly half ordinary terrestrial gravity.
Consequently the pull between the two components of the double star ß
Aurigæ is
_g_ / 2.2 × 18 × 10²⁵ tons,
or equal to the weight of
80 × 10²⁴ tons on the earth,
which is more than twenty million times as great as is the pull
between the earth and our sun.
* * * * *
Simple calculations such as these could have been made at any time;
there is nothing novel about them, as there is about the estimate of
the ether's density and vast intrinsic energy, in Chapters VI and VII.
But then there is nothing hypothetical or uncertain about them either;
they are certain and definite: whereas it may be thought there is
something doubtful about the newer contentions which involve
consideration of the mass and size of electrons and of the uniform and
incompressible character of etherial constitution. Even the idea of
"massiveness" as applied to the ether involves an element of
uncertainty, or of figurativeness; because until we know more about
ether's peculiar nature (if it is peculiar), we have to deal with it
in accordance with material analogies, and must specify its
massiveness as that which would have to be possessed by it if it
fulfilled its functions and yet were anything like ordinary matter. It
cannot really _be_ ordinary matter, because ordinary matter is
definitely differentiated from it, and is presumably composed of it;
but the inertia of ordinary matter, however it be electrically or
magnetically explained, must in the last resort depend on something
parentally akin to inertia in the fundamental substance which fills
space. And this it is which we have attempted in Chapters VI and VII
to evaluate and to express in the soberest terms possible.
CHAPTER X
GENERAL THEORY OF ABERRATION
In Chapter III the subject of Aberration was treated in a simple and
geometrical manner, but it is now time to deal with it more generally.
And to do this compactly I must be content in the greater part of this
chapter to appeal chiefly to physicists.
The following general statements concerning aberration can be made:--
1. A ray of light in clear space is straight, whatever the motion of
the medium, unless eddies exist; in other words, no irrotational
disturbance of ether can deflect a ray.
2. But if the observer is in motion, the apparent ray will not be the
true ray, and his line of vision will not truly indicate the direction
of an object.
3. In a stationary ether the ray coincides with wave-normal. In a
moving ether the ray and wave-normal enclose an aberration angle ε,
such that sin ε = v/V, the ratio of the ether speed to the light
speed.
4. In all cases the line of vision depends on motion of the observer,
and on that alone. If the observer is stationary, his line of vision
is a ray. If he moves at the same rate as the ether, his line of
vision is a wave-normal.
5. Line of vision depends not at all on the motion of the ether, so
long as it has a velocity-potential. Hence if this condition is
satisfied the theory of aberration is quite simple.
_General Statement as to Negative Results in the Subject._
It is noteworthy that almost all the observations which have been made
with negative results as to the effect of the Earth's orbital motion
on the ether are equally consistent with complete connexion and
complete independence between ether and matter. If there is complete
connexion, the ether near the earth is relatively stagnant, and
negative terrestrial results are natural. If there is complete
independence, the ether is either absolutely stationary or has a
velocity-potential, and the negative results are, as has been shown,
thereby explained. Direct experiment on the subject of etherial
viscosity proves that that is either really or approximately zero, and
substantiates the "independence" explanation.
_Definition of a Ray._
A ray signifies the path of a definite or identical portion of
radiation energy--the direction of energy-flux. In other words, it
may be considered as the path of a labelled disturbance; for it is
some special feature which enables an eye to fix direction: it is that
which determines the line of collimation of a telescope.
Now in order that a disturbance from A may reach B, it is necessary
that adjacent elements of a wave front at A shall arrive at B in the
same phase; hence the path by which a disturbance travels must satisfy
this condition from point to point. This condition will be satisfied
if the time of journey down a ray and down all infinitesimally
differing paths is the same.
The equation to a ray is therefore contained in the statement that the
time taken by light to traverse it is a minimum; or
∫{A,B} ds/V = minimum
If the medium, instead of being stationary, is drifting with the
velocity _v_, at angle θ to the ray, we must substitute for V the
modified velocity V cos ε + _v_ cos θ; and so the function that has to
be a minimum, in order to give the path of a ray in a moving medium,
is
Time of
journey = ∫{A,B} ds / V(cos ε + α cos θ)
= ∫{A,B} (V cos ε - v cos θ) / (V²(1-α²)) ds = minimum
where α is the ratio v/V.
_Path of Ray, and Time of Journey, through an Irrotationally Moving
Medium._
Writing a velocity-potential φ in the above equation to a ray, that is
putting
v cos θ = dφ/ds,
and ignoring possible variations in the minute correction factor
1-α² between the points A and B, it becomes
Time of
journey = ∫{A,B} cos ε / (1 - α²) · ds/V - (φβ - φα) / V²( 1-α²)
= minimum.
Now the second term depends only on end points, and therefore has no
effect on path. The first term contains only the second power of
aberration magnitude; and hence it has much the same value as if
everything were stationary. A ray that was straight, will remain
straight in spite of motion. Whatever shape it had, that it will
retain.
Only cos ε, and variations in α², can produce any effect on path;
and effects so produced must be very small, since the value of cos ε
is
√ (1 - α²sin²θ).
A second-order effect on direction may therefore be produced by
irrotational motion, but not a first-order effect. A similar statement
applies to the time of journey round any closed periphery.
_Michelson's Experiment._
We conclude, therefore, that general etherial drift does not affect
either the path of a ray, or the time of its journey to and fro, or
round a complete contour, to any important extent. But that taking
second-order quantities into account, the time of going to and fro in
any direction inclined at angle θ to a constant drift is, from the
above expression,
T₁ + T₂ = 2T cos ε / (1-α²) = √(1 - α²sin²θ) / (1 - α²) × 2T,
where 2 T is the ordinary time of the double journey without any
drift.
Hence some slight modification of interference effects by reason of
drift would seem to be possible; since the time of a to-and-fro
light-journey depends subordinately on the inclination of ray to
drift.
The above expression applies to Michelson's remarkable experiment[10]
of sending a split beam to and fro, half along and half across the
line of the earth's motion; and is, in fact, a theory of it. There
ought to be an effect due to the difference between θ = 0 and θ = 90°.
But none can be detected. Hence, either something else happens, or the
ether near the earth is dragged with it so as not to stream through
our instruments.
_Alternative Explanation._
But if the ether is dragged along near moving matter, it behaves like
a viscous fluid, and all idea of a velocity-potential must be
abandoned. This would complicate the theory of aberration (pp. 45 and
61), and moreover is dead against the experimental evidence described
in Chapter V.
The negative result of Mr. Michelson's is, however, explicable in
another way,--namely, by the FitzGerald-Lorentz theory that the linear
dimensions of bodies are a function of their motion through the ether.
And such an effect it is reasonable to expect; since, if cohesion
forces are electrical, they must be affected by motion, to a known and
calculable amount, depending on the square of the ratio of the speed
to the velocity of light. (See end of Chap. IV.)
The theory of Professor H.A. Lorentz, accordingly, shows that the
shape of Michelson's stone supporting block will be distorted by the
motion; its dimensions across and along the line of ether drift being
affected differently. And the amount of the change will be such as
precisely to compensate and neutralise the optical effect of motion
which might otherwise be perceived. This theory is now generally
accepted.
It is this neutralising or compensatory effect,--which acts equally on
to-and-fro motion of light, to-and-fro motion of electric currents,
and on the shape of material bodies,--that renders any positive result
in experiments on ether-drift so difficult or impossible to obtain; so
that, in spite of the speed with which we are rushing through space,
no perceptible influence is felt on either electrical or optical
phenomena, except those which are due to relative motion of source and
observer.
_Some Details in the Theory of the Doppler Effect, or Effect of Motion
on Dispersion by Prism or Grating._
When light is analysed by a prism or grating into a spectrum, the
course of each ray is deflected--refracted or diffracted--by an amount
corresponding to its frequency of vibration or wave-length.
Motion of the medium, so long as it is steady, affects neither
frequency nor wave-length, and accordingly is without influence on the
result. It produces no Doppler effect except when waxing or waning.
Motion of the source alone crowds the waves together on the advancing
side and spreads them out on the receding side. An observer therefore
whom the source is approaching receives shorter waves, and one from
whom the source is receding receives longer waves, than normal. At any
fixed point waves will arrive, therefore, with modified frequency.
So long as a source is stationary the wave-lengths emitted are quite
normal, but motion of an observer may change the frequency with which
they are _received_, in an obvious way; they are swept up faster if
the receiver is approaching, they have a stern chase if it is
receding.
All this is familiar, and was geometrically illustrated in Chapter
III, but there are some minor and rather curious details which are
worthy of brief consideration.
_Grating Theory._
For suppose a 'grating' is used to analyse the light. Its effect can
depend on nothing kinetic; it must be regulated by the merely
geometric width of the ruled spaces on it. Consequently it can only
directly apprehend wave-lengths, not frequencies.
In the case of a moving _source_, therefore, when the wave-length is
really changed, a grating will appreciate the fact, and will show a
true Doppler effect. But in the case of a moving _observer_, when all
the waves received are of normal length, though swept up with abnormal
frequency, the grating must still indicate wave-length alone, and
accordingly will show no true Doppler effect.
But inasmuch as the telescope or line of vision is inclined at the
angle of dispersion to the direction of the incident ray, ordinary
aberration must come in, as it always does when an observer moves
athwart his line of vision; and so there will be a spurious or
apparent Doppler effect due to common aberration. That is to say a
spectrum line will not be seen in its true place, but will appear to
be shifted by an amount almost exactly imitative of a real Doppler
effect--the imitation being correct up to the second order of
aberration magnitude. The slight outstanding difference between them
is calculated in my _Philosophical Transactions_ paper, 1893, page
787. It is too small to observe.
It is not an important matter, but as it is rather troublesome to work
out the diffraction observed by a grating advancing towards the source
of light, it may be as well to record the result here.
The following are the diffracted rays which require attention,--with
the inclination of each to the grating-normal specified:--
The diffracted ray if all were stationary, θ₀;
The real diffracted ray when grating is advancing, φ;
The ray as perceived, allowing for aberration, θ;
The equivalent diffracted ray if all were stationary and the wave-length
really shortened, θ₁.
As an auxiliary we use the aberration angle ε, such that sin ε = α sin
θ, where α = v/V.
Among these four angles the following relations hold; so that, given one
of them, all are known.
{ θ = φ - ε
{ sin θ₁ = (1 - α) sin θ₀
{ sin φ = (1 - α vers φ) sin θ₀
Whence θ and θ₁ are very nearly but not absolutely the same. θ₁ is
the ray observed by an instrument depending primarily on frequency,
like a prism; θ is the ray observed by an instrument depending
primarily on wave-length, like a grating.
_Prism Theory._
Now let a prism be used to analyse the light; its dispersive power is
in most theories held to depend directly upon frequency--i.e. upon a
time relation between the period of a light vibration and the period
of an atomic or electronic revolution or other harmonic excursion.
Let us say, therefore, that prismatic dispersion directly indicates
frequency. It cannot depend upon wave-length, for the wave-length
inside different substances is different, and though refractive index
corresponds to this, dispersive power does not.
In the case of a prism, therefore, no distinction can be drawn between
motion of source and motion of receiver; for in both cases the
frequency with which the waves are received will be altered,--either
because they are really shorter, though arriving at normal speed, or
because they are swept up faster, although of normal length.
_Achromatic Prism._
It must be noticed that the observation of Doppler effect by a prism
depends entirely on dispersion; i.e. on waves of different length
being affected differently. But prisms can be constructed whose
dispersion is corrected and neutralised. Such achromatic prisms, if
perfectly achromatic, will treat waves of all sizes alike; and,
accordingly, the shortening of the waves from a moving source will not
produce any effect. Achromatic prisms will therefore behave to
terrestrial and to extra-terrestrial sources, i.e. to relatively
stationary and relatively moving sources, in the same way.
This must be recollected in connexion with several of the negative
results rightly obtained by some observers; such as Arago, for
instance, who applied an achromatic prism to a star which the earth
was approaching, without observing any effect. A Doppler effect should
have been observed by a dispersive prism, but not by an achromatic
one: for the refractive index of a substance is not affected by any
motion of the earth.
It is not reasonable to expect that refractive index would be
affected, since it depends in simple geometrical fashion on retarded
velocity, i.e. on optical etherial loading or apparent extra internal
density.
An achromatic _grating_, however, is (rashly speaking) an
impossibility.
EFFECT OF TRANSPARENT MATTER.
But when a ray is travelling through transparent matter, will not
motion of that matter affect its course?
If the matter is moved relatively to source and receiver, as in
Fizeau's experiment with running water, most certainly it will; to the
full effect of the loading or extra or travelling density, (μ²-1),
compared with the total density μ².
This fraction of the velocity of the material medium must directly
influence the velocity of light, for the waves will be conveyed in the
sense of the material motion _u_, with the additional speed
u(μ²-1)/μ². (See also Appendix 3.)
But if the transparent matter through which the light is going is
stationary with respect to source and receiver--only sharing with them
the general planetary motion, i.e. being subject to the opposite
all-pervading ether drift,--then no influence due to the drift can be
experienced; for the free ether of space behaves just as it would if
the matter were not there. This can be shown more elaborately by the
following calculation.
_Optical Effect of Ether Drift through Dense Stationary Bodies._
The calculation of the lag in phase caused by Fresnel's etherial
motion may proceed thus:--A dense slab of thickness _z_, which would
naturally be traversed with the velocity V/μ, is traversed with the
velocity (V/μ) cos ε + (v/μ²) cos θ; where _v_ is the relative
velocity of the ether in its neighbourhood; whence the time of journey
through it is
(μz) / V(cos ε + (α/μ) cos θ), instead of μz/V,
So the equivalent air thickness, instead of being (μ - 1)z, is
μz / (cos ε + (α/μ) cos θ) - z =
( (μ cos ε - α cos θ) / (1 - α/μ)² - 1 )z,
or, to the first order of minutiæ,
(μ - 1)z - αz cos θ;
θ being the angle between ray and ether drift inside the medium.
So the extra equivalent air layer _due to the motion_ is approximately
±α z cos θ, a quantity independent of μ.
Hence, no plan for detecting this first-order effect of motion is in
any way assisted by the use of dense stationary substances; their
extra ether, being stationary, does not affect the lag caused by
motion, except indeed in the second order of small quantities, as
shown above.
Direct experiments made by Hoek,[11] and by Mascart, on the effect of
introducing tubes of water into the path of half-beams of light, are
in entire accord with this negative conclusion.
Thus, then, we find that no general motion of the entire medium can be
detected by changes in direction, or in frequency, or in phase; for on
none of them has it any appreciable (i.e. first-order) effect, even
when assisted by dense matter.
* * * * *
Another mode of stating the matter is to say that the behaviour of
ether inside matter is such as to enable a potential-function,
∫ μ²v cosθ ds,
to exist throughout all transparent space, so far as motion of ether
alone is concerned. (See Appendix 3.)
The existence of this potential function readily accounts for the
absence of all effect on direction due to the general drift of the
medium, whether in the presence of dense matter (such as water-filled
telescopes) or otherwise. Whatever may be the path of a ray by reason
of reflexion or refraction in a stationary ether, it is precisely the
same in a moving one if this condition is satisfied, although the
wave-normals and wave-fronts are definitely shifted.
However matter affects or loads the ether inside it, it cannot on this
theory be said either to hold it still, or to carry it with it. The
general ether stream must remain unaffected, not only near, but inside
matter, if rays are to retain precisely the same course as if it were
relatively stationary.
But it must be understood that the etherial motion here contemplated
is the _general drift of the entire medium_; or its correlative, the
uniform motion of all the matter concerned. There is nothing to be
said against aberration effects being producible or modifiable by
motion of _parts_ of the medium, or by the artificial motion of
transparent bodies and other partitioned-off regions. _Artificial_
motion of matter may readily alter both the time of journey and the
path of a ray, for it has no potential conditions to satisfy; it may
easily describe a closed contour, and may take part in conveying
light.
But I must repeat that this conveyance of light by moving matter is an
effect due to the material load only; it represents no disturbance of
the ether of space. Fresnel's law, in fact, definitely means that
moving transparent matter does _not_ appreciably disturb the ether of
space. Direct experiment, as recorded in Chapter V, shows that close
to rapidly-moving opaque matter there is no disturbance either.
I regard the non-disturbance of the ether of space by moving matter as
established.
FOOTNOTES:
[10] _Philosophical Magazine_, Dec., 1887.
[11] _Archives Néerlandaises_ (1869), Vol. IV, p. 443, or _Nature_,
Vol XXVI, p. 500. Also Chapter IV above.
SUMMARY.
The estimates of this book, and of _Modern Views of Electricity_, are
that the ether of space is a continuous, incompressible, stationary,
fundamental substance or perfect fluid, with what is equivalent to an
inertia-coefficient of 10¹² grammes per c.c.; that _matter_ is
composed of modified and electrified specks, or minute structures of
ether, which are amenable to mechanical as well as to electrical force
and add to the optical or electric density of the medium; and that
elastic-rigidity and all potential energy are due to excessively
fine-grained etherial circulation, with an intrinsic kinetic energy of
the order 10³³ ergs per cubic centimetre.
APPENDIX 1
ON GRAVITY AND ETHERIAL TENSION
In the arithmetical examples of Chapter IX we reckon merely the force
between two bodies; but the Newtonian tension mentioned in Chapter
VIII does not signify that force, but rather a certain condition or
state of the medium, to variations in which, from place to place, the
force is due. This Newtonian tension is a much greater quantity than
the force to which it gives rise; and, moreover, it exists at every
point of space, instead of being integrated all through an attracted
body.
It rises to a maximum value near the surface of any spherical mass;
and if the radius be R and the gravitational intensity is _g_, the
tension at the surface is T₀ = gR. At any distance _r_, further
away, the tension is T = gR²/r.
This follows at once thus:--
Stating the law of gravitation as F = γmm´/r², the meaning here
adopted for etherial tension at the surface of the earth is
T = ∫{R,∞} γE/r² dr = γE/R;
so that the ordinary intensity of gravity is
g = -dT/dR = γE/R² = 4/3πργR.
Accordingly, near the surface of a planet the tension is T₀ = gR, or
for different planets is proportional to ρR².
The velocity of free fall from infinity to such a planet is √(2T₀);
the velocity of free fall from circumference to centre, assuming
uniform distribution of density, is √(T₀); and from infinity to
centre it is √(3T₀).
Expanding all this into words:--
The etherial tension near the earth's surface, required to explain
gravity by its rate of variation, is of the order 6 × 10¹¹ c.g.s.
units. The tension near the sun is 2500 times as great (p. 103). With
different spheres in general, it is proportional to the density and to
the superficial area. Hence, near a bullet one inch in diameter, it is
of the order 10⁻⁶; and near an atom or an electron about 10⁻²¹ c.g.s.
If ever the tension rose to equal the constitutional elasticity or
intrinsic kinetic energy of the ether,--which we have seen is 10³³
dynes per square centimetre (or ergs per c.c.) or 10²² tons weight
per square millimetre,--it seems likely that something would give way.
But no known mass of matter is able to cause anything like such a
tension.
A smaller aggregate of matter would be able to generate the velocity
of light in bodies falling towards it from a great distance; and it
may be doubted whether any mass so great as to be able to do even that
can exist in one lump.
In order to set up a tension equal to what is here suspected of being
a critical, or presumably disruptive, stress in the ether [10³³
c.g.s.], a globe of the density of the earth would have to have a
radius of eight light years. In order to generate a velocity of free
fall under gravity equal to the velocity of light, a globe of the
earth's density would have to be equal in radius to the distance of
the earth from the sun, or say 26,000 times the earth's radius. If the
density were less, the superficial area would have to be increased in
proportion, so as to keep ρ R² constant.
The whole visible universe within a parallax of 1/1000 second of arc,
estimated by Lord Kelvin as the equivalent of 10⁹ suns, would be
quite incompetent to raise etherial tension to the critical point
10³³ c.g.s. unless it were concentrated to an absurd degree; but it
could generate the velocity of light with a density comparable to that
of water, if _mass_ were constant.
If the average density of the above visible universe (which may be
taken as 1.6 × 10⁻²³ grammes per c.c.) continued without limit, a
disruptive tension of the ether would be reached when the radius was
comparable to 10¹³ light years; and the velocity of light would be
generated by it when the radius was 10⁷ light years. But
heterogeneity would enable these values to be reached _more_ easily.
_Gravitation_ is thus supposed to be the result of a mechanical
tension inherently, and perhaps instantaneously, set up throughout
space whenever the etherial structure called an electric charge comes
into existence; the tension being directly proportional to the square
of the charge and inversely as its linear dimensions. _Cohesion_ is
quite different, and is due to a residual electrical attraction
between groups of neutral molecules across molecular distances: a
variant or modification of chemical affinity.
APPENDIX 2
CALCULATIONS IN CONNEXION WITH ETHER DENSITY
Just as the rigidity of the ether is of a purely electric character,
and is not felt mechanically--since mechanically it is perfectly
fluid,--so its density is likewise of an electromagnetic character,
and again is not felt mechanically, because it cannot be moved by
mechanical means. It is by far the most stationary body in existence;
though it is endowed with high intrinsic energy of local movement,
analogous to turbulence, conferring on it gyrostatic properties.
Optically, its rigidity and density are both felt, since optical
disturbances are essentially electromotive. Matter loads the ether
optically, in accordance with the recognised fraction (μ²-1) / μ²;
and this loading, being part and parcel of the _matter_, of course
travels with it. It is the only part amenable to mechanical force.
The mechanical density of matter is a very small portion of the
etherial density; whereas the optical or electrical density of
matter--being really that of ether affected by the intrinsic or
constitutional electricity of matter--is not so small. The relative
optical virtual density of the ether inside matter is measured by
μ²; but it may be really a defect of elasticity, at least in
non-magnetic materials.
Electrical and optical effects depend upon _e_. Mechanical or inertia
effects depend upon e². Electric charges can load the ether
optically, quite appreciably; but as regards mechanical loading, the
densest matter known is trivial and gossamer-like compared with the
unmodified ether in the same space.
_Massiveness of the Ether deduced from Electrical Principles._
Each electron, moving like a sphere through a fluid, has a certain
mass associated with it; dependent on its size, and, at very high
speeds, on its velocity also.
If we treat the electron merely as a sphere moving through a perfect
liquid, its behaviour is exactly as if its mass were increased by half
that of the fluid displaced and the surrounding fluid were
annihilated.
Ether being incompressible, the density of fluid inside and outside an
electron must be the same. So, dealing with it in this simplest
fashion, the resultant inertia is half as great again as that of the
volume of fluid corresponding to the electron: that is to say the
effective mass is 2πρα³, where ρ is the uniform density. If an
electron is of some other shape than a sphere, then the numerical part
is modified, but remains of the same order of magnitude, so long as
there are no sharp edges.
* * * * *
If, however, we consider the moving electron as generating circular
lines of magnetic induction, by reason of some rotational property of
the ether, and if we attribute all the magnetic inertia to the
magnetic whirl thus caused round its path,--provisionally treating
this whirl as an actual circulation of fluid excited by the
locomotion,--then we shall proceed thus:--
Let a spherical electron _e_ of radius _a_ be flying at moderate speed
_u_, so that the magnetic field at any point, _rθ_, outside, is
H = eu sinθ / r²,
and the energy per unit volume everywhere is μH²/8π.
But a magnetic field has been thought of by many mathematicians as a
circulation of fluid along the lines of magnetic induction--which are
always closed curves--at some unknown velocity _w_.
So consider the energy per unit volume anywhere: it can be represented
by the equivalent expressions
½ρw² = μH²/8π = μ/8π · e²u²sin²θ / r²;
wherefore
w/u = √(μ/4πρ) · e sinθ / r².
The velocity of the hypothetical circulation must be a maximum at the
equator of the sphere, where r=a and θ=90; so, calling this _w₀_,
w₀/u = √(μ/4πρ) e / a²,
and
w/w₀ = a² sinθ / r²;
wherefore the major part of the circulation is limited to a region not
far removed from the surface of the electron.
The energy of this motion is
½ρ ∫{0,π} ∫{a,∞} w² · 2π r sin θ · rdθ · dr,
whence, substituting the above value of _w_, the energy comes out
equal to 4/3 πρa³ w₀².
Comparing this with a mass moving with speed _u_,
m = 8/3 πρa³(w₀/u)².
This agrees with the simple hydrodynamic estimate of effective inertia
if w₀ = ½√3·u; that is to say, if the whirl in contact
with the equator of the sphere is of the same order of magnitude as
the velocity of the sphere.
Now for the real relation between _w₀_ and _u_ we must make a
hypothesis. If the two are considered equal, the effectively disturbed
mass comes out as twice that of the bulk of the electron. If _w₀_ is
smaller than _u_, then the mass of the effectively disturbed fluid is
less even than the bulk of an electron; and in that case the estimate
of the fluid-density ρ must be _exaggerated_ in order to supply the
required energy. It is difficult to suppose the equatorial circulation
_w₀_ _greater_ than _u_, since it is generated by it; and it is most
reasonable to treat them both as of the same order of magnitude. So,
taking them as equal,
e = a² √(4πρ/μ)
and m = twice the spherical mass.
Hence all the estimates of the effective inertia of an electron are of
the same order of magnitude, being all comparable with that of a mass
of ether equal to the electron in bulk. But the linear dimension of an
electron is 10⁻¹³ centimetre diameter, and its mass is of the order
10⁻²⁷ gram. Consequently the density of its material must be of the
order 10¹² grams per cubic centimetre.
This, truly, is enormous, but any reduction in the estimate of the
circulation-speed, below that of an electron, would only go to
increase it. And, since electrons move sometimes at a speed not far
below that of light, we cannot be accused of under-estimating the
probable velocity of magnetic spin by treating it as of the same order
of magnitude, at the bounding surface of the electron, as its own
speed: a relation suggested, though not enforced, by gyrostatic
analogies.
_Some Consequences of this Great Density._
The amplitude of a wave of light, in a place where it is most intense,
namely near the sun where its energy amounts to 2 ergs per c.c., comes
out only about 10⁻¹⁷ of the wave-length. The maximum tangential
stress called out by such strain is of the order 10¹¹ atmospheres.
The hypothetical luminous circulation-velocity, conferring momentum on
a wave-front, in accordance with Poynting's investigation, comes out
10⁻²² cm. per sec. These calculations are given in the concluding
chapter of the new edition of _Modern Views of Electricity_.
The supposed magnetic etherial drift, along the axis of a solenoid or
other magnetic field, if it exist, is comparable to ·003 centim. per
sec., or 4 inches an hour, for a field of intensity 12,000 c.g.s.
But it is not to be supposed that this hypothetical velocity is slow
everywhere. Close to an electron the speed of magnetic drift is
comparable to the locomotion-velocity of the electron itself, and may
therefore rise to something near the speed of light; say 1/30th of
that speed: but in spite of that, at a distance of only 1 millimetre
away, it is reduced to practical stagnation, being less than a
millimicron per century.
In any solenoid, the ampere-turns per linear inch furnish a measure of
the speed of the supposed magnetic circulation along the axis--no
matter what the material of the core may be--in millimicrons per sec.
[1 micron = 10⁻⁶ metre; 1 millimicron is 10⁻⁹ metre =
10⁻⁷ centimetre, or a millionth of a millimetre.]
To get up an etherial speed of 1 centimetre per second--such as might
be detected experimentally by refined optical appliances, through its
effect in accelerating or retarding the speed of light sent along the
lines of magnetic force,--would need a solenoid of great length, round
every centimetre of which 1000 amperes circulated 3000 times. That is
to say, a long field of four million c.g.s. units of intensity.
In other words, any streaming along magnetic lines of force, such as
could account for the energy of a magnetic field, must be comparable,
in centimetres per second, to one four-millionth of the number of
c.g.s. units of intensity in the magnetic field.
APPENDIX 3
FRESNEL'S LAW A SPECIAL CASE OF A UNIVERSAL POTENTIAL FUNCTION
The modern view of Fresnel's Law may be worded thus:--
Inside a region occupied by matter, in addition to the universal ether
of space, are certain modified or electrified specks, which build up
the material atoms. These charged particles, when they move, have
specific inertia, due to the magnetic field surrounding each of them.
And by reason of this property, and as a consequence of their
discontinuity, they virtually increase the optical density of the
ether of space, acting in analogy with weights distributed along a
flexible cord. Thus they reduce the velocity of light in the ratio of
the refractive index μ:1, and therefore may be taken as increasing the
virtual density of the ether in the ratio 1:μ².
That is to say, their loading makes the ether behave to optical waves
as if--being a homogeneous medium without these discontinuous
loads--it had a density μ² times that which it has in space outside
matter. Calling the density outside 1, the extra density inside must
be μ²-1, so as to make up the total to μ².
The μ²-1 portion is that which we call "matter," and this portion
is readily susceptible to locomotion, being subject to--that is,
accelerated by--mechanical force. The free portion of normal density 1
is absolutely stationary as regards locomotion, whether it be inside
or outside a region occupied by ordinary matter, for it is not
amenable to either mechanical or electric forces. They are transmitted
by it, but never terminate upon it; except, indeed, at the peculiar
structure called a wave-front, which simulates some of the properties
of matter.
(If free or unmodified ether can ever be moved at all, it must be by
means of a magnetic field; along the lines of which it has, in several
theories, been supposed to circulate. Even this, however, is not real
locomotion.)
Fizeau tested that straightforward consequence of this theory which is
known as Fresnel's Law, and ascertained by experiment that a beam of
light was accelerated or retarded by a stream of water, according as
it travelled with or against the stream. And he found the magnitude of
the effect precisely in accordance with the ratio of the locomotive
portion of the ether to the whole,--the fraction (μ²-1)/μ² of
the speed of the water being added to or subtracted from the velocity
of light, when a beam was sent down or up the stream.
But even if another mode of expression be adopted, the result to be
anticipated from this experiment would be the same.
For instead of saying that a modified portion of the ether is moving
with the full velocity of the body while the rest is stationary, it is
permissible for some purposes to treat the whole internal ether as
moving with a fraction of the velocity of the body.
On this method of statement the ether outside a moving body is still
absolutely stationary, but, as the body advances, ether may be
thought of as continually condensing in front, and, as it were,
evaporating behind; while, inside, it is streaming through the body in
its condensed condition at a pace such that what is equivalent to the
normal quantity of ether in space may remain absolutely stationary. To
this end its speed backwards relative to the body must be u/μ²
and accordingly its speed forward in space must be u(1-1/μ²).
For consider a slab of matter moving flatways with velocity _u_; let
its internal etherial density be μ², and let the external ether of
density 1 be stationary. Let the forward speed of the internal ether
through space be _xu_, so that a beam of light therein would be
hurried forward with this velocity. Then consider two imaginary
parallel planes moving with the slab, one in advance of it and the
other inside it, and express the fact that the amount of ether between
those two planes must continue constant. The amount streaming
relatively backwards through the first plane as it moves will be
measured by _u_ times the external density, while the amount similarly
streaming backwards through the second plane will be (u-xu) times
the internal density. But this latter amount must equal the former
amount. In other words,
u×1 must equal (u-xu) × μ².
Consequently _x_ comes out x = (μ²-1)/μ²; which is Fresnel's
incontrovertible law for the convective effect of moving transparent
matter on light inside it.
The whole subject, however, may be treated more generally, and for
every direction of the ray, on the lines of Chapter X, thus:--
Inside a transparent body light travels at a speed V/μ; and the ether,
which outside drifts at velocity _v_, making an angle θ with the ray,
inside may be drifting with velocity _v´_ and angle θ´.
Hence the equation to a ray inside such matter is
T´ = ∫ ds / ((V/μ) cos ε´ + v´ cos θ´) = min.,
where sin ε´/sin θ´ = v´/(V/μ) = α´.
This may be written
T´ = ∫ cos ε´ ds / (V/μ (1-α´²)) - ∫ v´ cos θ´ ds / (V²/μ² (1-α´²));
the second term alone involves the first power of the motion, and
assuming that μ²v´ cos θ´ = dφ´/ds, and treating α´ as a
quantity too small for its possible variations to need attention, the
expression becomes
T´ = μT cos ε´ / (1 - α´²) - (φ´B - φ´A) / (V²(1 - α´²)),
T being the time of travel through the same space when empty. Now, if
the time of journey and course of ray, however they be affected by the
dense body, are not to be _more_ affected by reason of etherial drift
through it than if it were so much empty space, it is necessary that
the difference of potential between two points A and B should be the
same whether the space between is filled with dense matter or not (or,
say, whether the ray-path is taken through or outside a portion of
dense medium). In other words (calling φ the outside and φ´ the inside
potential function), in order to secure that T´ shall not differ from
μT by anything depending on the first power of motion, it is necessary
that φ´B-φ´A shall equal φB-φA: i.e. that the potential inside and
outside matter shall be the same up to a constant, or that
μ²v´ cos θ´ = v cos θ; which for the case of drift along a ray is
precisely Fresnel's hypothesis.
Another way of putting the matter is to say that to the first power of
drift velocity
T´ = μ T - ∫ (μ² v´ cos θ´ - v cos θ) ds/V²,
and that the second or disturbing term must vanish.
Hence Fresnel's hypothesis as to the behaviour of ether inside matter
is equivalent to the assumption that a potential function,
∫ μ² v cos θ ds , exists throughout all transparent space, so far
as motion of ether alone is concerned.
Given that condition, no first-order interference effect due to drift
can be obtained from stationary matter by sending rays round any kind
of closed contour; nor can the path of a ray be altered by etherial
drift through any stationary matter. Hence filling a telescope tube
with water cannot modify the observed amount of stellar aberration.
The equation to a ray in transparent matter moving with velocity _u_
in a direction φ, and subject to an independent ether drift of speed
_v_ in direction θ, is
∫ ds / (V/μ cos ε + v/μ² cos θ + u[1 - (1/μ²)] cos φ) = const.
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Transcriber's Notes
Parentheses have been added to mathematical equations for
clarity and correctness. Letters representing mathematical
variables are not marked as italic when this would impair
clarity in expressions and equations.
The lower and upper limits of definite integrals are indicated
by curly brackets, e.g. ∫{0,π}...dθ represents a definite
integral with values of θ ranging from 0 to π.
The caret character ^ is used in the expression (17/16)^{3/2}
to signify raising the fraction 17/16 to the power 3/2. Other
exponents are represented using superscripted numerals, e.g. x².
Italic text is denoted by _underscores_ and bold text by
=equal signs=.
Obvious punctuation and spelling errors and inconsistent
hyphenation have been repaired.
In ambiguous cases, the text has been left as it appears in
the original book.
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