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CORNELL
UNIVERSITY LIBRARY

Cornell University Library
QC 171.S45
V.2
Electrodynamic wave-theory of physical f
3 1924 012 325 399 ...
^NINTCOINU.S-i

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ELECTRODYNAMIC WAVE-THEORY OF
PHYSICAL FORCES
VOLUME II
NEW THEORY OF THE AETHER
Definitely establishing
The Cause of Universal Gravitation, Magnetism, Electrodynamic Action, Molecular, Atomic and Explosive Forces, etc., including a notable improvement in the Foundations of the Wave-Theory of Light, and discovery of the Cause of Acoustic Attraction and Repulsion, which is
especially suitable for illustrating the invisible
Processes of Gravitational Attraction. In Seven Mathematical Memoirs Reprinted from the Astronomische
— Nachrichten, 1920 1922; to which are added two Mathematical
Memoirs on the Earth, and one on the Sun and Variable Stars.
By
T.J.J. SEE,
A. M., Lt. M., Sc. M. (Missou.); A. M., Ph. D. (Berol.);
Professor of Mathematics, U. S. Navy, Formerly in Charge of the 26-Inch Equatorial Telescope of the U. S. Naval Observatory, Washington, D. C, More Recently in Charge of the U. S. Naval Observatory, Mare Island, California.
— O Qedg del ysw/j.^TQet Plato.
1922.
Astronomische Nachrichten, Kiel.
I. Hermann, Paris. Thos. P. Nichols & Son Co., Lynn, Mass., U. S. A. Wheldon & Wesley, London.

IT-

DEDICATED TO MY BELOVED WIFE
FRANCES GRAVES SEE
WHOSE STEADFAST SUPPORT MADE POSSIBLE THE COMPLETION
AND SUITABLE PUBLICATION OF THESE DISCOVERIES IN THE
NEW THEORY OF THE AETHER.

n "Eti Toi'pvv, e'^T], Tcdfifieyd

elvai avTo, xal fj^idg otxelv Tovg

li'^XQi' ^HqaxXsioiv arriXmv and Wdaidog ev OjjuixQm tivI fiioqCw, coc neQ

negl z^Xfia iivQfirixuq fj /SatQaxovg, tcsqI ttjv S-dXazTav olxovvrac,

xal aXXovg dXXox)-i noXXovq iv noXXolci, toiovtoii; tonoig olxslv.

elvav yaQ navTa^i] neql T'qv yijv noXXd xozXa xal navcodund xal

Tag ld£ag xal id /j,eya^rjj «V a '^vvsQ^vrjxivai to %s vdwQ xal ttJv

ofiCxXriv xal top d^qa. avTrjV Si Tijv y-ijv xa-d-aqdv ev xa-d-aqco

xelad-ai Tfo ovoavw, iv w nif) Igti, rd darga, dv drj ald-fqa

ovofid'Qsiv Tovg noXXovg zcSv negl rd ToiavTa siwd-OTdov X^ysiv. ov

drj vnooTdd-fiiriv Tavia elvai. xal ivQ^slv del elg rd xolXa ttJc yijg.

IJXaTwv, OaCdiav, 109.

I believe that the earth is vety vast, and that we who dwell

in the region extending from the river Phasis to the Pillars of

Heracles inhabit a small portion only about the sea, like ants

or frogs about a marsh, and that there are other inhabitants of

many other like places; for everywhere on the face of the earth

there are hollows of various forms, and sizes, into which the

water and the mist and the lower air collect. But the true earth

— is pure and situated in the pure heaven

there are the stars

also; and it is the heaven which is commonly spoken of by us

as the Aether, and of which our own earth is the sediment

— gathering in the hollows beneath.

Plato, Phaedo, 109.

Introduction.

— During the past six years several of the most venerable Scientific Societies in Europe have been

considerably occupied with the Theory of Relativity,

without, however, taking the usual philosophic

precaution to inquire whether such a theory is at all. necessary to our understanding of the Physical Universe. The introduction of unnecessary complications into our processes of Scientific Thought always

has been viewed as an evil, great in proportion as it is indefensible.

Thus in his Rules of Philosophy (Principia, Lib. Ill) Newton lays down the following as the

First Rule:
„We are to admit no more causes of natural things than such as are both true and

sufficient to explain their appearances".

„To this purpose the philosophers say that Nature does nothing in vain, and more is in vain

when less will serve; for Nature is pleased with simplicity, and affects not the pomp of superfluous causes".

— Accordingly, whilst many investigators were debating the mystical Theory of Relativity,

with

Four-dimensional Time-Space manifolds, Geodetic Curves, the Curvature of Space, and similar devices
— for adding hopeless complexity to our geometrical and physical conceptions, I took refuge in Newton'^
rule of maximum simplicity, and developed the New Kinetic Theory of the Aether, which showed

that the Theory of Relativity is entirely devoid of physical foundation.

In fact, early in the year 1914, I entered upon the development of The Electrodynamic Wave-

Theory of Physical Forces, in the hope of illuminating the unsolved problem of the Cause of Universal Gravitation. Now that eight years have elapsed, and the memoirs of these two volumes are

published, it may interest the reader to learn that in November, 1914, when the present researches were

— still in a primitive stage, I sent the first outline of them to the Royal Society,

in the belief that any

definite light on the Cause of Universal Gravitation, which Sir Isaac Newton had not been able to

obtain, ought first to be communicated to that illustrious Society.

At that time, however, the War was very disturbing to European investigators. And if my

preliminary Paper was studied attentively by the Referees of the Royal Society, it is probable that they

— did not understand it,

possibly because several of the leading physicists in England already were

proposing to do away with the Aether. Yet, whatever cause operated to obscure the start which had

been made, it is a fact that fifteen months elapsed before any report from the Royal Society was made

to me (May, 1916). Meanwhile my researches had been renewed and much extended, and in due time

were published under the title: Electrodynamic Wave-Theory of Physical Forces, vol.1. Quarto,

171 pages, Boston, London, Paris, 1917.
This was, however, only the first part of the New Theory of Physical Forces, and the

subject therefore has been extended and greatly improved during the past four years. These later

discoveries in the Kinetic Theory of the Aether, which the Editor of the Astron. Nachrichten

has done me the honor to publish in that celebrated Journal, 1920-22, already are widely known to the

Scientific Public.
Perhaps it may not be inappropriate to point out also the failure of the Royal Astronomical Society and several more of the oldest Scientific Societies in Europe. Sagacious observers have regretfully remarked how they have wasted both time and precious resources in fruitless speculations on the mysticism of the Theory of Relativity, with no other result than to confuse the public mind.

(v)

VI

In view of the definite results here brought forth, the student of sound Physical Science may

— find it interesting to contrast the barren discussion of the abandoned Theory of Relativity

based

on the inadmissible Gerber formula, equation (1) below, now clearly shown to violate the Conservation
— of Energy, with the Kinetic Theory of the Aether, which has led to the Cause of Universal

Gravitation, and the Wave-Theory of the various Physical Forces. Thus it occurs to me that it would be a convenience to many investigators if these Memoirs

were collected into a volume. Accordingly, with the kind permission of the learned Editor, Professor
Dr. H. Kobold, I am enabled to offer to investigators the Second Volume of the Electr odynamic Wave-Theory of Physical Forces, 1922.

Although these Memoirs have been published serially only a short time, it appears that they

have awakened no ordinary interest among investigators who are inclined to examine the Physical Causes underlying the Phenomena of Nature. Until this fundamental work is carried much further than has

yet been done, we shall not be able to make satisfactory progress in dealing with even the simpler

natural phenomena.

— And as for the more intricate phenomena, the methods of research heretofore in use,

based

so largely on undiscerning if not blind empiricism, thus utterly ignoring the physical properties which

Transcendental Physics always was capable of correctly assigning to the Aether as a Monatomic Gas

— 689321600000 more elastic than Air in proportion to its density,

were of course hopelessly inadequate.

The first prerequisite of progress was therefore a valid Kinetic Theory of the Aether, deduced di-

rectly from observed phenomena, and thus capable of furnishing a secure foundation for the Science

of Dynamics.

The strange proposal recently made in certain quarters to do away with the Aether, is of course

inadmissible and indefensible, because the elementary principles of Mechanics show us that there must

be a Medium pulling towards the Sun, to overcome the centrifugal force of a planet's orbital motion,

with Tension equivalent to the breaking strength of millions of immense cables of the strongest steel.

Such an unauthorized proposal merely illustrates the need of profounder researches into the foundations

of Natural Philosophy. The physical necessity for the Medium was so fully recognized by Newton and

by Maxwell that to the competent investigator it requires no defense.

In his letter to Bentley, Febr. 25, 1692-93, Sir Isaac Newton remarks: „That gravity should be

innate, inherent and essential to matter, so that one body may act upon another at a distance through

a vacuum, without the mediation of anything else, by and through which their action and force may be conveyed from one to another, is to me so great an absurdity, that I believe no man who has in philo-

sophical matters a competent faculty of thinking can ever fall into it. Gravity must be caused by an

agent acting constantly according to certain laws; but whether this agent be material or immaterial, I
have left to the consideration of my readers." In Newton's discussion the Aether evidently is taken to
be immaterial, which conforms to modern views in Physical Science.

In his Account of Sir Isaac Newton's Philosophical Discoveries, London, 1748, p. Ill,
Maclaurin says:

„He (Newton) has plainly signified that he thought that those powers (of Gravitation) arose from
the impulses of a subtile Aetherial Medium that is diffused over the Universe, and penetrates the
pores of grosser bodies. It appears from his letters to Mr. Boyle that this was his opinion early; and if he did not publish it sooner, it proceeded from hence only, that he found he was not able, from experiment and observation, to give a satisfactory account of this medium and the manner of its operation in producing the chief phenomena of Nature."

What Sir Isaac Newton ascribed to the Impulses of a subtile aetherial medium, we now define
as Waves; and in the New Theory of the Aether, we make known the manner of the operation of
— — these wave-impulses in producing the chief phenomena of Nature. The leading objection to the Theory
of Gravitation, in Newton's time, that it introduced into philosophy occult qualities, no longer will hold
in our day, because wave-impulses in the Aether are universally recognized by modern Physical Science.

:
vu

In the Preface to the Second Edition of Newton's Principia, 1713, his celebrated pupil Coates combats the reasoning of that time as follows:

„But shall gravity therefore be called an occult Cause, and thrown out of philosophy, because
the Cause of Gravity is occult and not yet discovered?" . . . „Some there are who say that gravity is
praeternatural, and call it a perpetual miracle. Therefore they would have it rejected, because praeter-

natural causes have no place in Physics."

In view of such reasoning, we can well understand the statement of Voltaire, that although the great Newton outlived the publication of the Principia by more than forty years, yet at the end of that

time he had not over twenty followers outside of England. Indeed, since Newton had clearly shown

the nature of the planetary forces, and the laws they obey, and the beautiful Science of Celestical

— Mechanics was thus developed for two centuries

only to be contradicted recently, by the strange

— claim that „Gravity is not a force, but a property of Space" (De Sitter, Monthly Notices, Oct. 1916,

p. 702)

we may more justly regard it as a miracle that any progress can be made and sustained in

Physical Science as recently cultivated.

The difficulty of making progress would be much less than it is, but for the state of confusion

which has arisen in Physics from certain mystical speculations, now at length recognized to be both

vague and chimerical. For example, there can be no defense for a Theory based on Gerber's formula

for the Potential (Zeitschrift fur Mathematische Physik, Band XLIII, 1898, p. 93-104),

„

k-mm'

k^mm'i 2 dr 3 /dr\'

1

,,

i_l^V

r

[

c dt c-\dt

( c dt)

which contradicts the great principle of the Conservation of Energy. For this formula differs from the Potential of Weber's Law, long ago shown by Maxwell to be valid and conformable to the Conservation of Energy (cf. Maxwell's Treatise on Electricity and Magnetism, section 856). This Weber
Potential is:

and therefore essentially different from the Gerber formula. Accordingly, since it conforms to the Con-

servation of Energy, the Weber Potential alpne is admissible in a valid physical theory of the Universe.

Incidentally it may be noted that the Weber Potential corresponds to a wave-field, and thus points to

the Electrodynamic Wave-Theory of Physical Forces.
Recently the writer was asked by an astronomer how he came to take up the New Theory of

the Aether. The answer was that such hopeless confusion existed in this vital subject that a valid

clearing up of the foundations was necessary to our progress; and as others had not been able to carry

it out, the labor finally was devolved upon the present author. It will therefore be allowable to trace
a few features of this progress which appear to me somewhat remarkable.

In view of the many researches heretofore carried out in the theory of wave-motion, it will

always seem very extraordinary that earlier investigators were not led to the simple relationship between

the mean velocity (») of the Corpuscle of a Monatomic Gas and the Velocity (V) of a wave in the Gas,

AN namely (cf.

5079, p. 234)

V=^/,7tV.

(3)

Yet in reaching this Theorem it was not sufficient merely to notice the geometrical ratio theoretically existing between the paths of oscillating particles describing a semi -circumference while the wave traverses the diameter, which is 72?^: on the contrary, it was deemed necessary, as a physical pre-
caution, to confirm the ratio from the best experimental data of six actual gases, with the following
results:

Vlll

IX

there exists a greater degree of rarefaction, or the consequence of the impulsive force

of some fluid medium."

This is a good summary of Newton's conception that the Aether is heterogeneous, which we now

establish by definite mathematical and physical demonstration, (AN 5044), showing that in tri-dimensional

space waves propagated or reflected from the particles of matter necessarily produce such outward in-

= = A crease of density, a vr, owing to the law of Amplitude

k/r, with the central force /== k^/r^.

Accordingly, the Potential of Gravitation (Oeuvres Completes de Laplace, Tome X, p. 348)

y

~

rrr

a dx dy dz

J J J V{x- x'y+if-yy+iz-zf

~

r r radxdydz
JJJ r

,

,

varies as the reciprocal of the Aether Density, as centrally thinned out by wave-action. The Potential

is thus shown to be an accumulated state of stress incident to the triple integration for

the superposed Wave-Amplitudes of the various Atoms, Ai^=ki/ri.

Comformably to Newton's impression, Arago points out that the Aether tends to move towards

the planetary bodies, yet under the increased amplitudes of the receding waves encountered towards

— move these centres, it is so churned up or thinned out, that it does not really

only exerts a steady

stress in that direction, thus yielding an energy flux or gravitative force proportional to the energy of
= the vibrating Aetherons and therefore proportional to the square of the Amplitude A^ k^/r^. The only — way to decrease this central stress is to remove the matter of the planet on which the waves depend,

the motion of the Aetherons in Collision with the Atoms in some way generating the receding waves, or

renewing them from the incoming waves already existing and incessantly propagated from the other

bodies of the Universe. The infinitude of vibrating Atoms in each of an infinite system of bodies renders

the wave-field infinitely complex; but from any one planetary mass, the receding waves pursue paths of

Least Action, and the state of the central gravitative stress therefore is perpetual.

It will always appear wonderful to investigators that the brilliant Maxwell should have made the

unaccountable slip of imagining Gravitation due to a pressure in the direction of the force, and an equal

AN tension at right angles thereto (cf.

5048, p. 163-164). It appears that prior to the publication of these

Papers, English physicists never questioned Maxwell's erroneous assumption; and thus they handed down

his errors for half a century, when the truth of the matter could have been noticed and verified by any

good student of Mechanics. For Maxwell's postulated stresses were dynamically impossible; and although

the learned Professor Minchin of Oxford, in 1886, found that they would not explain Gravitation, he

did not suspect the error underlying them, nor remove it.

The learned Editors of Maxwell's Scientific Papers, in the two imposing volumes published

by the University of Cambridge, 1890, equally failed to notice what was required to balance the centri-

— fugal force,

as simply and clearly explained by Huyghens and Newton over two centuries before.

The mischief thus done came in time to be spread over the entire world, and vividly illustrates the perversion of thought which may arise from the slip of a great authority. The slowness of our progress

under these circumstances is less remarkable than it might seem at first sight. Looking to the future, for valid and simple conceptions of the Cause underlying Gravitation, we

consider the new explanation of Acoustic Attraction (AN 5130, p. 342) to be especially suitable for disclosing vividly the unseen wave-processes operating from star to star, in straight line minimum paths, throughout the immensity of the heavens. This wave-field of Gravitation is dealt with more fully in the Sixth Paper, and fully illustrated by plates admitting of one interpretation and only one. Thus we establish the Cause of Universal Gravitation by necessary and sufficient conditions. The proof therefore is

absolute and always will remain incontestable (AN 5140, p. 95-127).

It appears that the discovery of the Cause of Gravitation now rests on six classes of phenomena:

1.

The Fluctuations of the Moon's Mean Motion, Dec. 10,

AN 1916, (cf.

5048, p. 159).

2. The New and Direct explanation of Acoustic Attraction, in which the wave-process is rendered

AN visible to the eye, 1916, (AN 5130, p. 341-42,

5140, p. 98-100, plate 7).

3. The Proof of the Cause of the Distortion of the Equipotential Surfaces, about two equal Stars, 1917, at length somewhat more fully developed in the Sixth Paper, 1921, (AN 5140, p. 95-127).

4. Majorana's Physical Experiments on the Absorption of Gravitational Wave-Action by a layer

AN of Mercury, 1919, (cf. Philosophical Magazine for May, 1920, also

5079, p. 301-302).

5. The experiments by Dr. Chas. F. Brush of Cleveland, Ohio, (Proc. Am. Philos. Society,

— Philadelphia, vol. LX, no. 2, Jan. 1922) showing that under conditions otherwise identical the Earth's at-

traction exerts a different grip on pendulums of different metals

a Bismuth, pendulum gaining rapidly

on one of Zinc. In discussing the Kinetic Theory of Gravitation Dr. Brush adopts the view that the

energy of the Aether is in wave- form, in other words, the Wave-Theory.

6. It has long been recognized that Earth Currents, Aurorae, etc., recur periodically with certain

Solar disturbances. The writer has now (Sept., 1921) obtained a new and direct proof that Aether waves

upwards of 2400 meters in length are continually received upon the Earth from commotions in the Sun.

These are long enough to pass through the solid body of the Earth with but slight refraction, dispersion

and absorption. And as wireless waves of corresponding length are bent around the globe by the re-

AN sistance of this solid body, (cf.

5044, p. 71), we thus have observational proof that Gravitational waves,

such as are modified by our globe to produce the Fluctuation of the Moon's motion, do really exist,

and can be experimentally studied in Radio-telegraphy.

Accordingly our. present proof that the Cause of Gravitation is to be found in Wave-Action is most ample: and we may safely predict that further investigation will only confirm the results indicated

by the sextuple proof above cited.

The Wave-Theory of Magnetism outlined in the Third Paper is treated with greater rigor in the Seventh Paper. The Harmonic Law there developed definitely connects the Magnetism of the Earth with

Universal Gravitation. Extending Gauss' method for calculating the amount of Magnetism in the Earth,

we compute the amount of Magnetism in the Sun! It appears that Magnetic Action is conveyed not in

right lines, like Gravitation, but along the Curved Lines of Magnetic Force; and thus the new Law

of Nature very appropriately becomes a geometric tribute to the memory of the great mathematician Gaussl

AN In the Fourth Paper,

5085, will be found the Correction of a fundamental difficulty in the Wave-

Theory of Light which has stood for a full century. Poisson's Geometrical Theory of the nature of the

vibrations in the Aether is fully confirmed, and harmonized with the most refined optical phenomena.

^ = The longitudinal component in Light is shown to be utterly insensible to observation,

I : (66420- 10*),

AN (cf.

5085, p. 427-428, footnote). The removal of this longstanding difficulty in the Wave-Theory of

Light, and its harmonization with the Theory of Sound, as Poisson always held should be possible, is

a triumph of no ordinary character.

Attention should be called to the simple explanation of the Michelson-Morley experiment of 1887,

by means of the Kinetic Theory of the Aether, (AN 5048, p. 181-183). No change is required in the

dimensions of moving bodies, and such assumptions as Fitzgerald's Hypothesis are shown to be un-

authorized. As the Aetherons move with the velocity of 471000 kms the state of the wave-field is

instantly adjusted to any state of steady motion; and thus there is no such thing as the Earth

moving through the Aether. At all times the Earth carries its wave-field with it, adjusted to perfect

Kinetic equilibrium; and thus the Michelson experiment is perfectly explained, without any Theory of

Relativity whatever. The outstanding motion of Mercury's perihelion is explained by an absorption of

wave-energy, like that noticed in Majorana's experiments, and harmonizing still better since Grossmann

has shown, (AN 5115), that the outstanding motion is less than 43", between 29" and 38" per century,

AN with 14:'5 still to be deduced for the propagation in time, according to Weber's Law (cf.

5048, p. 137).

Accordingly, in the Second Paper, (AN 5048), we show that the whole Theory of Relativity is a foundation laid in Quicksand. A discerning investigator who has studied this new aspect of the Kinetic

Theory of the Aether, with the resulting abandonment of the Theory of Relativity, could now say

with Laplace, in dealing with another matter: „I have no use for this Hypothesis".

XI

In removing the mystery of the Michelson- Morley experiment, without the hypothesis of the

Earth moving through the Aether, and therefore without Relativity, we solve at the same stroke of the

pen the historical difficulty of the Aberration. The solution of the difficulty of the Aberration is simply

AN the parallelogram of motions, and thus as clear as any theorem in Geometry (cf.

5048, p. 183).

The problem of the density of the Aether is found to be capable of direct and simple solution

by the following process. It is fully established by precise Laboratory experiments that Hydrogen propagates Sound four times faster than Oxygen, which is a gas 16 times denser. The Cause of the rapid velocity of Sound in Hydrogen is therefore the lightness and high molecular velocity of the molecules

of that gas.
Now the Aether propagates wave motion 217839 times faster than Hydrogen, when the latter

is corrected for a Monatomic constitution. Therefore Hydrogen is (217839)^ times denser than Aether,

or the Aether has 1 : 47453880000 of the density of Hydrogen, making the Aether's absolute density

AN 1888.15-10-18 (cf.

5079, p. 236).

The argument here developed from exact experimental data in the Theory of Sound thus settles

the question, without raising any other perplexing problem. For just as the four times slower propagation
of wave motion in Oxygen, compared to Hydrogen, indicates that the Oxygen is 16 times heavier; so also

the Hydrogen must be held to be (217839)^ denser than Aether, which propagates waves 217839 times faster. In view of the simplicity of this reasoning, it is strange that the Aether should have been spoken
of by certain electronists as 2000 million times denser than lead! No such result is authorized by the laws of experimental Physics; and all such inference is as mischievious as it is contrary to our Common Sense.
Out of this New Theory of the Aether, in which each body carries with it a wave- field, requiring adjustment every time the velocity changes, has grown a new theory of Inertia, Momentum etc. The
adjustment of the wave-field is treated of briefly at the end of the Third Paper, (AN 5079, p. 299); and as it explains Inertia, Momentum, etc., it is especially worthy of the attention of natural philosophers.
In the Fifth and Sixth Papers we have dealt with Molecular and Atomic Forces. These Forces are traced to short waves in the Aether, by an argument from the theory of Physical Continuity which will be found difficult to evade. If wave-action be the Cause of one of these forces, it will also be found to be the active agency in the others. Thus we have been able to throw much light on the secret of Capillarity and of Vital Forces, and have worked out the source of the awful power noticed in Explosive
Forces, and in the mysterious forces of Chemical Affinity and of Cohesion which bind together the
Molecules of an Elastic Solid. This view is strikingly confirmed in a recent development of the New
Theory of the Aether, 2"'' Postscript to the Sixth Paper, and is so notable that I forbear to enter into

elaborate comment.
But we may point out that the Sextuple Integral defining the Molecular Strength or power of resistance of a solid body to molecular displacement is given the form

i2= CUr^-hr^+k)dr+cY^-Jds=\^-^+kr+C^^-s.

(^)---(5)

As the integration is to be extended from r^ to ri, and over the whole of this range the functions are both finite and continuous, we may subdivide the range into parts for the entire region of stability, r^ to r^, thus:

a

-r 7- -hkr-hC

(6)

5

4

Now we see by the accompanying (see p.xii) Fig. a, from the 2"'' Postscript to the Sixth Paper that
some of these areas are positive, as in the whole region between r^ and r^. These positive areas correspond
to the accumulation of attractive forces. When the molecular distances accord with this region, and
the oscillations do not carry the particles beyond the range r^-r^, the wave action only binds the molecules more solidly together. This is a state of entire stability, as in typical elastic solids such as Stone,
Steel, Diamond, etc.

Xll

But if the parts of the molecules come into

close contact and so oscillate as to range from r4 to r^,

repulsive forces begin to assert themselves quite powerfully; yet the stability may be secure, at least until
— a distance r, smaller than r^ is approached, at which

the repulsive forces rapidly become infinite.

This region of excessively close contact, r^-r-^,

is the danger zone, because the repulsive forces in-
crease asymptotically. Thus when the molecule has

its parts suddenly rearranged, and they come into such

close contact, the stability it dissolved and the reaction

gives a wide oscillation beyond r^, so that evaporation

or an explosion may follow. Such sudden outbursts may occur from waves of Heat, or the waves of an electric current, or when the Atomic Structure of cer-

Fig. a. Illustration of the curve of molecular forces 8 Wldr=f,
the unessential parts outside the limits fi-r^ being indicated by pointed lines.

— tain molecules is geometrically rearranged, thus breaking down in becoming more compact. The reaction
incident to this sudden exertion of repulsive forces yields of course a tendency to a violent explosion

the degree of violence depending on the closeness of the contact in the molecular rearrangement.
As the explosive force increases asymptotically at small distance, we see that the most terrific concentration of power resides in certain atomic and molecular structures. This power comes from the

Aether itself, as already explained in paragraph (iii) of Section 5, of the Sixth Paper. Yet the evaluation of the Sextuple Integral for i2, in the Z""* Postscript, has given us a better grasp of the extreme power
of Molecular and Atomic Forces, because we see from the Curves why the integration, giving the ex-

plosive action, rapidly becomes infinite.
Viewing the Aethereal Medium in its larger aspects, chiefly as the vehicle for propagation of

waves, it appears surprising that heretofore only three authors have investigated the elastic constant:

1. Newton, Optics, 1721, p. 326

e= 490000000000.

= 2. Sir John Herschel, Familiar Lectures, 1867, p. 282 e 1148000000000.

AN 3. See,

5044, p. 62

£= 689321600000.

In this Elastic Constant of the Aether rests the power of the stresses exerted through this medium

in the form of Physical Forces; and the interactions of the waves in traversing the various bodies give
them their molecular and other physical properties. Maxwell had developed the Theory of the Medium

to an enormous extent in electrical and magnetic phenomena; and he even concluded that the forces

observed in Nature are due to stresses in the Aether. But owing to his premature death at 48 years of
age he had not formulated any modus operandi as to how such stresses could arise in the Medium,
= nor studied the Elastic Constant of the Aether, s 689321600000.
Accordingly we have labored to extend and to improve the work of Newton and of Maxwell,
and endeavored to give a working theory of the chief Forces observed in Nature.

In conclusion it only remains to call attention to the two Memoirs on the Earth, and especially the Memoir on the Sun and Variable Stars. This latter investigation is so very remarkable that it can scarcely fail to be of the widest interest. It is not often that one can bring to light the true physical cause of so many great mysteries of three centuries since the age of Kepler and Galileol

The author's most grateful acknowledgements are due above all to Mrs. See, for the loyal support of an unfailing faith in the outcome of this very extensive investigation ; to Professor Dr. H. Kobold, for his indefatigable labor and care in supervising the publication, admidst many difficulties ; to Mr. W. S. Trankle, who has aided so greatly in completing the work, between the numerous engagements of the public service.

Starlight on Loutre, Montgomery City, Missouri, 1922 May 8.

T.J.J. See.

:

Abdruck aus den Astr. Nachr. Nr. 5044

— (Band 2H

April 1920)

New Theory of the Aether By T. y. y. See.

(First Paper.)

I. The Medium of the Aether is necessary for
Jeonveying Physical Action .across Space.
A superfine medium associated' with the stars and with
the light of day, known as the Aether [Aidt'jQ), has been universally recognized since the time oi Homer (Iliad, XV, 20,
and XVI. 365). During the last three centuries the greatest natural philosophers and mathematicians, from Huyghens, JSfewton, and Euler to Maxwell, Lord Kelvin and Poincari, have regarded this aetherial medium as a necessary condition for the action of physical forces across space. In his Me''.eanique Celeste 4-54 1> 1896, 7zwcra»(/ expresses the general opinion thus:

»Les theories les plus recentes de la physique donnent -lieu de croixe que les attractions des corps celestes ne peuvent Be transmettre a distance que par I'intermediaire d'un milieu,
sans doute I'ether. Mais on ne connait rien encore sur ce mode de transmission. II parait probable que le meme milieu sert de vehicule a des actions electriques ou electromagnetiques«.

Notwithstanding the very secure foundation for a valid theory of the aether erected by the labors of the most eminent iSeometers and natural philosophers since the age of Newtqn, a strange tendency has arisen within recent years, for abandoning the aether as an unnecessary hypothesis. Whether this reactionary tendency is based upon adequate grasp of
the geornetrical ^nd physical considerations involved may be doubted by the more experienced natural philosophers of today. At any rate we leave this to the judgement of those investigators who follow the argument here developed.

In their treatise on Magnetism and Electricity, London, igi2. Brooks and Poyser, who were inspired by the electronic Aleories emanating from Cambridge, express themselves thus

»In this book, we have implicitly assumed the existence

rf a medium, which is the seat of the phenomena denoted

by the terms electric and magnetic lines of force. It may,
however, be mentioned that at the present moment the various

questions associated with the ether give rise to problems of

great complexity and difficulty. The experimental knowledge

acquired during the last twenty years, taken in conjunction

'with recently acquired knowledge regarding the .electron'

and the constitution of matter, leads to apparently irrecon-

— cilable results, and the real nature of the ether

if it

— exists at all in the old sense of the word

must be regarded

:as absolutely unknown. For instance, if the ether is in-

compressible, as it is usually assumed to be, we are driven, by one line of argument, to the conclusion that it is 2000

jmillion times denser ^) than lead and possesses enormous
energy of internal motion. On the other hand, if it is compressible, it may be much rarer than the rarest gas. There

I
is no intrinsic difficulty in either view, but at present
no method is known by which we may hope to discriminate between them. The whole subject of the ether
is in that state of uncertainty and apparent confusion, which
in other branches of science has usually preceded some great advance in knowledge*.

Such an attitude as the above, by physicists of recognized authoritative connections, is confusing enough; but an even more bewildering doctrine has been put forth by Eiitstem, and quite widely adopted in England, though it generally is rejected in America. The english observers of; the total
solar eclipse of May 29, 1919, found some evidei^ces of a
deflection of the light of stars by the field of the sun, but it was by no means conclusive, and the weakness of the whole Theory of Relativity was impressively pointed out by
'Dr. Silberstein, (Observatory, November 1919, p. 396-7), who showed that Einstein'?, theory will not account for the refinement of moving perihelia, and would even permit a planet or comet to move in a straight line, under the gravitative

action of the sun. In view of these facts Dr. Silberstein justly says that the Einstein theory stands or falls by the Evershed and St John spectral observations, which are ample, yet do not confirm the theory.

In an interview at Chicago, Dec. 19, 1919, Professor A. A. Michelson, the eminent authority on light, openly rejects Einstein's, theory, because it does away with the idea of light traveling by means of vibrations in the aether which is supposed to fill all space, t Einstein thinks there is no such thing
as aether«, remarked Michelson. »He does not attempt to

account for the transmission of light, but holds that the aether

should be thrown overboard*

In view of the confusion of thought introduced by

the electronists, on the one hand, and by the Einstein pure

— mathematicians, on the other,

both extremes leading to

ideas not appropriate to the facts, which Dr. Whewell, History

— of the Inductive Sciences, 1847, I.8i, showed was the cause
of the failure of the physical sciences among the greeks

it seems highly important to enter upon an account of certain

unpublished researches on the aether made by the present

writer during the past six years, omitting so far as possible the results already available in volume I of the Electrodynamic
Wave-Theory of Physical Forces, Boston, London and Paris,

1917.
And first we shall show that the aether is necessary
for holding the planets in their orbits, from the established law of the centrifugal force. This centrifugal motion must
be counteracted, otherwise a planet can not be made to
curve the path at every point and thus revolve in a Keplerian

ellipse with the sun in the focus.

^) In a future paper a conclusive criterion will be given for rejecting this claim of a large density for tlie aether.

:

5044

52

It is well known that the centrifugal force is given

by the expression,

f =z mv^lo

(i)

m where is the revolving mass, v is the instantaneous velocity,

and q the radius of curvature of the orbit. As the planetary

orbits and the orbit of the moon are not far from circular,

we may with sufficient approximation calculate the centrifugal

force for circular orbits. In the case of the earth's attraction

for the moon, it suffices to take the earth's weight in metric tons, the moon's mass == 1/81.45, and the distance of the

rtioon 60 terrestrial radii, so that the weight at the earth's

surface is to be reduced by the divisor 3600. Then, as

gravity balances this centrifugal force, we have for the at-

traction of the earth on the moon

/= (s.9S6292Xio")/(8i. 45x3600)
= 20.3137 X lo^'' metric tons.

(2)

This enormous tension would require for its support the

full breaking strength of a weightless solid circular column of

= steel 645 kms in diameter, when the steel has the tensile

strength of over 30 metric tons to the square inch

6.4

sq. cms, and such a small bar of steel would thus about lift

a modern battleship of the largest type. The tensile strength

of the above single column, 645 kms in diameter, would be equivalent to about 5000000000000 columns of such

= weightless steel, each of one square foot cross section, g2 2
sq. cms, or about one such column to each area 16x16

256 sq. feet of a hemispherical cross section of the earth. So much for the stresses which control the moon's motion.

But the gravitational attraction of the sun upon the

earth is very much more powerful than that of the moon. ,
The attraction of the sun upon the earth is of course equal

to that of the earth upon the sun, which is easily seen to be
/= 332750/(23445)^x5. 956292X10"

3.60572X10^^ metric tons

(3)

where the number 332750 represents the sun's mass, in units of the earth's mass, and 23445 is the sun's mean distance,

in units of the earths radius.

This attraction of the sun on the earth is equivalent
to the tensile strength of 1 000000000000 weightless cir-

cular pillars of steel, like that discussed above, but each

having a diameter of 30 feet, about 9 metres. This is

equivalent to the tensile strength of a forest of weightless

steel pillars, each 11 inches or 28 cms in diameter, on

each square foot of a hemispherical cross section of the earth;

so that the surface of the globe would be almost covered

with these cables of steel.

Such calculations of the enormous gravitative power
of the heavenly bodies were first brought to my attention

by Professor Joseph Ficklin, of the University of Missouri,
about },?> years ago, and have never been overlooked in my subsequent studies of the cause of gravitation. Now with

these concrete figures before us, we see that the cause as-

signed for gravitation must be adequate to sustain these tre-

mendous forces, miraculously pulling like stupendous cables

of steel,, imagined as weightless as spider webs, yet stretched

to the utmost limits of their tensile strength across the

celestial spaces, for holding the planets in their orbits.

Accordingly Einsteini, proposal to do away with the

aether is chiefly remarkable for the lack of understanding of

the physical universe which it displays. Sir /s-ff^t -^' "'j'

himself denounced those who believed action could oc(^

across

empty

space

as

not

having

a

competent

faculty
|

thinking in philosophical matters. In his letter to Benn

1692-3, Febr. 25, he says: »That gravity should be innate, mherent and essentj
to matter, so that one body may act upon another at|
distance through a vacuum, without the mediation of anythj]
else, by and through which their action and force may conveyed from one to another, is to me so great an absurd that I believe no man who has in philosophical matter competent faculty of thinking, can ever fall into it. Gra
must be caused by an agent acting constantly according
certain laws; but whether this agent be material or immateri:
I have left to the consideration of my readers*.
In a paragraph cited below, Maclaurin tells us t

Newto?! held gravitation to be due to impulses of the aethi
but could not make out exactly how they arose; and f passage shows that Newton did not regard this medium aj';

ordinary material.
a) It is shown below that the elasticity of the aeth is 689321600000 times greater than that of our air in p portion to its density: it has therefore enormous power contraction, if any natural process be at work to cause

to collapse.
b) It is shown in the Electrodynamic Wave-Theory I Phys. Fore. I, 19 17, that between any two sources, as t sun and earth, the waves so interpenetrate, with rotatio: in opposite directions, as to decrease the stress and cau; collapse of the medium between the sun and the earth; a this therefore develops an enormous tension, with njaximu] stress in the right line between the bodies, while beyo: them there is corresponding increase of stress and thus external pressure also overcoming the effects of the centi

fugal force, and compelling the pldnet to follow the Kepleri

ellipse about the sun in the focus.

c) It is shown in section 7 below, that the potential

is simply an expression for the total accumulated stresS(*l-1

due to the waves from all the individual atoms of a body, ^

each wave following the law of amplitude,

;

= A klr

(I

and giving an element of force, as in gravitatipn,

, }.

Accordingly we see that Laplace's, definition of the potential,
1782, points directly to the wave-theory:

d) Therefore it is natural to hold that gravitation
a wave phenomenon in the. aether, and to dismiss all oth
I hypotheses as not fulfilling conditions essentia] to a tri
physical cause. This wave-theory oi gravitation will give
new ground for the deflection oi the light of stars when tl
paths, of their rays pass through the gravitational field
the sun, as indicated in the eclipse of May 29, and reporte
at the meetings of the Royal Society and. Royal Astronomic;
Society, Nov. 6, 1919, e) It will be shown below that both the density an
rigidity of the aether increases as we go outward from th
sun, according to the laws

53

5044

54

= D vr E=.v'r.

'

,(7)

Accordingly the velocity of the waves remains approximately

constant, (Electrodynamic Wave -Theory of Physical Forces

;l.'i4-i57, 1917)

V= = CV.{ElD) CV[v'rlvr).

(8)

But experience alone can determine whether this condition

holds with geometrical rigor, or whether along the actual path,

containing :dififuse coronal matter, the stationary condition,

= (5jd. o

(9)

may not lead to a sm^H deflection of the original path of light.

f) Such an increase of density in the aether, as we

recede from the sun was suspected by Newton in ,

172 1,

(3"* edition of Optics, p. 325). It is of authentic record that

Newton hAi&yeA gravitation arises from the impulses of a

subtile aethereal medium, but he»was not able, from ex-

periment and observation, to give a satisfactory account of

this mediiAn, and the manner of its operation, in producing

the chief phenomena of nature*, [Maclaurin, Account of

TV^z^z/wz's ^.Philqsophical Discoveries, London, 1748, p. in),

and thus he left the problem of the. cause of gravitation to

future investigators.

g) The observed deflection of the rays of stars passing near the sun, amounting to about i''7 5, may be most naturally explained by the action of the gravitational and mag^ netic wave -fields, under the influence of coronal matter, varying as the inverse fourth power of distance, and the arrangement of the density and rigidity of the aether, near the sun. An arc of i" at the sun's mean distance corresponds to an absolute space of 725 kms, i''7S to 1269 krns. In the presence of the sun's strong gravitational and magnetic fields, and the magnetized faint coronal matter pervading that wave-

agitated region, - it is probable that a central refraction or

deflection of the light, of this magnitude, somewhat analogous

to

an

unsymmetrical Z^ifwa«-effect, may be. anticipated. '

The

rotation of .the beam of polarized light by magnetism, in

Faraday's experiment of 1845, would lead us to expect some

action in the sun's coronal wave-field.

h) As Einstein's predicted displacement of the spectral
lines towards the red coiild not be confirmed by Evershed
and Stjohn, who had ample telescopic pbwer to make this
shift-effect at least 50 times the probable error of their measures, it cannot be presumed that the deflection of starlight passing near the sun is a confirmation of a purely
mathematical theory. The deflection of the light must rather

be explained by the physical propsrties of the aether, interspersed with faint coronal matter, varying as the inverse fourth power of the distance, in the region of intense wave-

agitation about the sun. -i) At the joint meeting of the Royal Society and Royal
Astronomical Society, Nov. 6, 1919, no one attempted to answer the weighty objections brought forward .by Dr. Silberstiin, who had made a careful study of Einstein's theory, and thus pointed out the bizarre conclusions drawn by some pure mathematicians who are prone to forget that the de-
,
flection of starlight near the sun is as purely a physical problem as the refraction of light in the earth's atmosphere.
Now the sun's deflection of light is similar to refraction, but

— very miriute,

half of it being o"87S, as against 2000" in

our atmosphere, or about 2300 times smaller.

j)

Since,

according

to

the

report

of the

observers of ;

the eclipse of May 29, 1919, this minute deflection disappears,

when the sun moves out of the path of the light from the

stars lying behind it, such a temporary, effect cannot properly

be attributed to » a warp of space*, but only to the refractive
action of the sun's envelope.. When Newton observed the

refraction of light by a prism' he had no thought of attributing

the effect tp »a warp of space«; and one cannot but reflec^
how fortunate it is that the physical theory of astronomical

refraction was perfected by Newton, Laplace and Bessel before

such confusing terms as »fourth- dimension -time -spice-

manifolds*, were introduced into science. . k) It cannot be held that Einstein's theory enlightens

us on the motion of mercury's perihelion, because af least

half a dozen explanations, some of them approved by Newton,

Hall, Newcomb and Seeliger, are already known; and another

simple one, involving no mysticisrtf and no rash assumptions,

but following from definitely established physical laws, will

be brought oufc in the present investigation.

2. New Law of the Density and Rigidity of
theAether. To deduce the law of the wave amplitude (4) in tri-
dimensional space, we proceed as follows. The displacement of any particle of a medium due -to wave motion, of a given wave length, is independent of the periodic time, and since

the oscillatory orbits of the particles are described in equal

times, under continuous' flow of the waves, these "orbits will

be proportional to the displacements or other homologous,

lines pertaining to the. periodic paths of the particles. Let
m the velocities of the' moving particles be v, and their mass;

then their kinptic energies will be represented by ^l^m v^.

In the spherical expansion. of the aether waves, there will

be no loss of energy in free space ; hence on two successive

sphere surfaces of thickness Ar^ the energies are equal,' so.

that we have: 47rr' V.

^,

.1

\nr- ^]iin v''^

(ip);

The kinetic energy of the vibratirig molecules varies

inversely as the square of the, distance. But the velocity varies also as .the ampUtude, in simple harmonic motion: therefore, for the, amplitudes A' and A"j corresponding to the radii r' and r", we have by taking the sqtiare root in

equation (10)

/ == A.',

m, -.A"

'

r",r

,

:

= = A" A'r'lr" //'>"

I

\

, (11)

,(12)

Accordingly.' the amplitude or side displacement becomes,

= A klr.

And

V = Mir =

(13)

= + lll{alV\[x-x'Y^[y-y'Y [z-z'Y\\iixAy^z (14)

which is the law of the potential first used by Laplace in ,1782. Thus it appears that if there be aether waves propagated Outwardly from any molecule of matter, the amplitude, or.maxirtium displacement of the oscillating particles of the aether, will vary inversely as the radius of the spherical wave-surface.

!

«

55

5044

56

A partial development somewhat like this is given in

certain treatises on physics, such as Wullner's, Experimental

Physik, 1.784, and Mitchie's, Elements of Wave Motion, p. 11, but no importance is attached to the result, as in my Electrodynamic Wave-Theory of Physical Forces, 1.14-157, 1Q17.

A = So accurately is this true, that when I brought this simple

formula for the wave amplitude,

kjr, before the Aca-

demy of Sciences of St. Louis, in a public address, Sept. 21,

1 9 17, great surprise at the simplicity of the formula was expressed by such experienced investigators as Professor F. E.

Nipher, and President E. A. Engler. Thus it is necessary to

develop the subject a little more fully in the present paper,

since no adequate discussion of the problem appears to be

available in existing works on physical science.

Let us now consider the arrangement of the density

of the aether about the sun.

i) Suppose we consider carefully the amplitude of the

waves from the sun in any solar spectral line, such as that

of sodium, V- It is evident that if we disregard all other

radiations, and fix attention upon this sodium light alone,

then as the wave amplitude varies inversely as the distance

from the sun's centre, this amplitude of our vibrations con-

stituting sodium light will be 219 times greater at the sun's
— surface than at the surface of the earth since the earth's

mean distance is 219 solar radii.

2) Similar reasoning will hold for the waves of light of the spectrum of such elements as strontium, barium, boron,

calcium, hydrogen, carbon, iron, nickel, cobalt, copper, ti-

A = tanium, etc. Thus all the light waves of all elements conform

to the law :

kjr.

3) All these chemical elements also radiate heat waves
which follow the same law of amplitude. And for both light

and heat the above law holds rigorously true. If there be

any other type of waves in the aether, the same law will

hold for these undulations also.
4) Now magnetism and gravitation have been referred
to electrodynamic waves, in the author's work on physical

A = forces, 19 1 7. If these waves exist, they also will follow the

same law

kjr; and that they do exist is shown by a

variety of phenomena, which admit of no other interpretation.

For example, the electrodynamic action of a current of elec-

tricity is due to waves: thus arise electrical forces: also mag-

netic forces, gravitational forces, etc.

5) Gravitation admits of no other explanation, while on this explanation we have an immediate insight into the

fluctuations of the moon's mean motion, which so long proved utterly bewildering to astronomers. And there must be not

only a cause of gravitation, but a simple one, harmonizing

with electrodynamic action, in the generation of electrical
forces, magnetic forces, etc. The electrodynamic wave-theory

alone fulfills this necessary and sufficient condition, for the

following special reason.

6) The aether is shown to have an elastic power 689 321 600000 times greater than that of our air in proportion to its density. Hence it will have practically, unlimited

power of contraction, and thus be able to generate the

stupendous forces required for holding the planets and stars

in their orbits.

7) But this will be possible only if the aether is
arranged according to the law of density (S= vr; which

A = in turn will follow if electrodynamic waves recede from the

sun, having amplitudes

k/r. For the amplitudes in-

creasing towards the sun's centre insures a decrease of density

of the aether about that centre, owing to the increasing wave-

agitation near the sun's surface.

8) Now all these mutual arrangements, favorable to

the wave-theory, would not exist, unless that theory repre-

sented a law of nature. Because not only are all facts of

the aether harmonized, but also all the forces brought under

the principles of the conservation of energy,' and of least

action. Thus nature not only acts simply, but also by the

most uniform processes throughout all space. It is not there-

fore admissible to hold any theory of the aether other than

that it is an infinite aeolotropic elastic solid, with the density

arranged about the heavenly bodies to increase directly with

A = the distance. And the wave amplitudes varying inversely as

the radius,

kjr, supports this theory, by geometrical

considerations, which exclude every other theory of the

medium for the interpretation of the forces operating through-

out the physical universe.

g) In the course of the article Aether (Encyclopedia

= Britannica, Qth. ed., 1877), Maxwell calculates the density

as ^

1.07X10""'^'', thus implying homogeneity, and speaks

of this medium as »a vast homogeneous expanse of isotropic

matter.
But it is obvious on reflection that this medium cannot

be homogeneous ^) ; for in that case there would be no stresses in the medium for generating the forces which govern the mutual interaction of bodies throughout space. The mutual

actions between bodies is an observed fact. In motion the

bodies are everywhere found to describe ellipses, parabolas

or hyperbolas about one another. Nothing but forces, due to

tension between the bodies, and increase of pressure beyond

them, could possibly produce this remarkable power for

holding the planets in their orbits.

10) Thus forces imply waves, and waves lead to forces, when the mutually interpenetrating waves are so directed as to undo one another, and cause the collapse of the medium in the right line between the bodies. As the gravitational forces are of enormous intensity, it follows that the elastic power of the aether has to be tremendous, in order to generate
the forces actually observed.

1 1) Accordii)gly, the existence of forces implies stresses

in the aether : the stresses imply waves : the waves imply

= heterogeneous density in the medium, which must vary with

' the radius from any mass according to the law a

vr.

There is no other view of the aether which can be held.

Homogeneity of density would imply no stresses ; no stresses would imply no forces; no forces would imply an inert

universe; which is contrary to observation and thus wholly

inadmissible.

') In the Baltimore Lectures, 1904, p. 265, under date of Nov. 16, 1899, Lord Kelvin says: »We have strong reason to believe that
the density of ether is constant throughout interplanetary and interstellar space'. This error is very widespread, and its persistence shipwrecks
physical research

57

5044

58

12) The aether is therefore arranged about the sun with

= the density foirowing the law, a

vr, which results from

A = wave-agitations having amplitudes,

kjr The energy of

the forces generated by these waves is proportional to the

square of the amplitude, and therefore we have for the force,

/-^V

(is)

which explains all the pbserved effects of gravitation, mag-

netism, etc.
13) Now quite aside from the simplicity and continuity

of the process of reasoning here outlined, it remains a fact

that the wave-theory is adequate to explain all the observed

phenomena of nature. The simple law of density of the aether here imagined may therefore be admitted to really

pervade the universe. So far from being homogeneous, the

aether is really very heterogeneous. Indeed, it is a gas,

— behaving as an elastic solid

an infinite aeolotropic elastic

— = solid

fulfilling the law of density, d

vr, and of wave

A = amplitude,

kjr, and therefore yielding forces following

f ^ the law,

k'^jr^, as required by Newton in 172 1, for

explaining the cause of universal gravitation.

At the earth the density of the aether is 2ig times

what it is at the sun's surface, because the earth's mean

distance is 219 times the solar radius. But Newton s, formula

for the velocity,

v= CV\EJD]

(r6)

would give a change of velocity if the density alone increased,

E while the elasticity

remained constant.

Now the v^ocity of light across the planetary spaces

was originally found by Rdmer, 1675, from the eclipses of

Jupiter's satellites, and subsequently confirmed by the elaborate

researches of Delambre, on the motions of these satellites

(cf. C. d. T. 1788, and Astronomic Theorique et Pratique,

1814). By discussing a thousand eclipses of the i^' satellite

Delambre fixed the constant of aberration at 20^255, while

Michelsons velocity of light, near 300 000 kms., and the

solar parallax SfSo makes the aberration about 20^48.
V Thus is about the same for the aether acros^ the

diameter of the earth's orbit, and for the aether of the terres-

trial atmosphere, in which the velocity has been investigated experimentally by Cornu, Michelson, Newcomb and others.

Fig. I.

Diagram showing graphically the decrease of the density of the aether towards the sun, o\ving to the asymptotic increase in wave amplitude.

Accordingly, this observational fact requires us to hold

E that

increases in about the same ratio a's D, so that our

V law of for the heavenly spaces becomes,

V= CV[v'rlvr)

(17)

E and therefore ^= v' r. Thus both the elasticity and rigidity

of the aether increase directly as the radius from the sun,

or other heavenly bodies.

The reason for this remarkable law is this: namely,

the viscosity of a gas depends upon th^ friction of the mole-

cules projected from one layer of gas into the adjacent layer,

and vice versa. In the case of the aether the viscosity

becomes rigidity. And with the increase of >the density of

the aether particles there should be more molecules projected

into the adjacent layers mutually, by the ordinary kinetic

exchange, in strict proportion to the density. Thus the

rigidity of the aether increases directly as the density, as in

the stbove formula.

It may be noted that by the formula of Newton, an

increase of the density by the factor 2ig, without change

in E, would lead to a reduced velocity of only about V15'''
of the original. No such enormous difference, in the velpcity

of light as determined by observations of Jupiter's satellites,

and that found by terrestrial experiments, is admissible; and

thus the above law of rigidity of the aether is approximately

verified by the comparison of celestial and terrestrial obser-

vations. But a more exact test of the value of V, from

eclipse observations of Jupiter's satellites, taken as directly

as possible across the diameter of the earth's orbit, for com-

parison with the experimental value found by Michelson, is

highly desirable.

3. The Relation between the Mean Molecular Velocity of a Gas and that of a Wave transmitted in such a Medium.

The Philosophical Magazine for June and September, 1877, contains two important articles on the theory of gases by Dr. 5. Tolver Preston, and also notes on the conclusions

then reached by the celebrated Professor y. Clerk Maxwell,
with whom Preston was in correspondence. In the first of

these papers, p. 452, § ig, Preston reaches- the following remarkable conclusion : »That the velocity of propagation of a wave (such as a wave of sound) in a gas is solely determined

by, and proportional to, the velocity of the molecules of the

gas; that this velocity of propagation of the wave is not affected

by density, pressure, or by the specific gravity of a gasj or by

anything else excepting the velocity of its molecules*.

In the second Postscript, p. 453, Preston states Maxwell's conclusion as follows:
» Professor Clerk Maxwell, to whom this paper was communicated, and who has taken a kindly interest in the subject,

has worked out mathematically the velocity for a wave or impulse propagated by a system of particles moving among

each other according to the conditions of equilibrium in-

— vestigated in the first part of this paper

the diameter of

the particles being assumed so small as to be negligible compared with their mean distance, and the particles being

further assumed spherical, so that there is no movement of

rotation developed- at the encounters (which would involve

loss of velocity)*.

59

5044

6o

» Under these premises, the velocity of the wave was

found to be Ys 1^5 (or 0.745) into the mean velocity of the particles. In most gases the velocity of sound is slightly

less than this. This is referable to the movements of rotation

developed at the encounters of the molecules (which cal-

culably would delay the wave to a certain extent). In vapour

of mercury, according to the determinations of Kundt and

Warburg, the velocity of sound is exactly ^/g "I/5 into the

molecular velocity*. ,

According to these announcements, the corpuscles of

= the aether, viewed as a monatomic gas, should have a mean

F molecular velocity of 3/ v's •

1.34 F, where F =:

A 3Xioi''cms, the velocity of light.

conclusicfti of such

great importance, which received the approval of the lumi-

nous mind 6f Maxwell, is entitled to profound attention.

Thus I have had it before me for some five years, but only

undertook the mathematical verification and physical test of
this Preston- Maxwell theorem quite recently'; and, as my
results differ slightly from those of Freston and Maxwell, I will give the process of test and verification employed.
In order to confirm this theory I have compared the observed velocity of sound for the four leading gases which are best determined, with their mean molecular velocities, and firjd the following indications of experiment, without regard to the Preston- Maxwell theory. In the experimental data there remains a little uncertainty. For the older values of V and k^ the table yields for the corrected ratio a mean
of 1.64, which is 0.07 above the theoretical value of 1.57. The newer data, preferred by Jeans, Dynamical Theory of
Gases, 2°*^ edition 1916, p. 9-13 1, give a- mean value of
1.57, though the discordance between the results for the individual gases is somewhat increased.

Gas

:

:

6i

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62

operations of the physical universe. Moreover, since light, heat, chemical affinity, etc., have long been referred to such waves in the aether, the more general electrodynamic wavetheory thus gives complete continuity to our theories of physics, thereby confirming the: correlation of all natural
forces, and giving new physical grounds for the doctrine of
the conservation of energy.

In the closing paragraph to his celebrated Treatise on Electricity and Magnetism, 1873, Maxwell justly says that »'whenever energy is transmitted from one body to another in time, ther^ must be a medium or substance in which the energy exists after it leaves one body and before it reaches the other*. This also points to wave action, such as Gauss was considering in 1835, and of which Weber gave the fundamental law in 1846, Newton's \a.^ of 1686 beiftg a special case corresponding to circular orbits.

In the Principia, Lib. 2, Prop. 48, Sir Isaac Newton

deduces the formula for the velocity of waves or pulses

propagated in an elastic medium, such as waves of sound

in the air,

y ^= CV{£/£>) .

This is now written
F= V{{i^/ia/n)-ii+at)}
_= 33 1-76 m 1/(1-1-0.003665/)

(18)
,

where t is the temperature; o: is a coefficient, 0.003665;

= = ^

acceleration of. gravity, 98 1 cm; A

normal barometric

= D pressure, ,76 cm; cr

13.6, density of Mercury;

.=== the

density of air, 0.001293; ^"d A ^1.4050 (cf: Wiillner's

Experimental Physik, S-SS^) is the ratio of the specific heat of air under constant pressure to that under constant volume,,

introduced^ by> Laplace for harmonizing Newton s, theoretical

formula with the observed velocity of sound in air.

In many investigations it is "possible to determine the
velocity with which waves are propagated, but it is not always" possible to determine independently the elasticity or density
of the medium -^ we can only find the ratio EJD. This is
partly true of thp aether, for-example, which transmits light waves or electrodynamic waves with the speed of 300000 kms -per second, but gives no process of fixitig the elasticity of
this medium except by an independent calculatiori of the density, which, however; may be made by the process first used by Lord Kelvin in 1854, (Baltimore Lectures, 1904, p. 261-263), and afterwards adopted hy Maxwell, Scientific
Papers, 2.767.

In section 5 below we find, by the process here de-

= scribed,, that at the sun's surface the density of the aether

is ^

^Xio'"-^* and the rigidity 1800. Using these con-

stants 'm_ Newton's formula, we tnay verify the observed velocity

of wave propagation

V^ == 'l^{n/D)

l/{ 1800/(2 X io~^^)} ^= 30 000 000 000 cms'
3X,io^°, the velocity of light.

To compare a perfect monatomic gas like the aether with diatomic gases like the air, we use the formula for the
velocity of sound

V= = V{{s-/tG/B)-k-{i-i-at)]

= l/[(9. 808X0. 76X 13. 59/0. ooi293).(i. 405) (i-Ha/)]

= 331.8m 1/(1-1-0.003665/) at /° C.

(19)

This shows that the velocity of light is 904268 times swifter

than sound. Squaring this number, and dividing, the result

by .

1. 666/1. 405

=^

1. 18624

we, get

the

immense

number

689 32 1 6000Q0; which shows how much the elasticity of the

aether, regarded as a monatomic gas, exceeds that of the air

in proportion to its density^). In the Optics, 3"'^ edition, 17 21,
p. 326, Newton makes this number 490000000000, which
is 7'i per cent correct.

In view of this excessive elasticity of the aether, in proportion to its very small density, compared to that of air,
we can understand the almost inconceivable velocity of light. It is also necessary to bear in mind this enormous elasticity in order to understand why the aether is practically incom-
pressible. When a wave begins to be generated, the distur-
bance is propagated away so rapidly that the wave amplitude necessarily is small compared to the wave length. In the calculations of section 5 we have taken the wave length as 101.23 times its amplitude, which Maxwell, Lord Kelvin and Larmor consider a safe basis in all numerical determinations.
The incompressibility of the aether is due to the very high mean velocity of the aether corpuscles, 47 12 39 kms per second, and their enormously long free path, 572959 kms: which makes the medium behave as an elastic solid for quick
acting forces, but enables the corpuscles to hiove out of the
way of the swiftest planets with a 10000-fold, greater speed. Owing to its enormous elasticity, the aether instantly adjusts itself to any state of steady motion, and thus this medium offers no resistance whatever to uniform celestial motions..

This circumstance fully explains a grave difficulty which has been felt from the age of Newton, and hitherto appeared

utterly bewildering to natural philosophers. In connection

with such extraordinary physical conditions in the medium,

it may^ be useful to recall an account of the interior con-

stitution of the sun given by Professor Newcomb in the En-

cyclopedia Americana, 1904:

»Yet another unknown factor is the temperature of the -

interior, . . it may be 1 000000 degrees. As the highest

temperature which it is possible to produce artificially pro-

bably does not amount to 10 000 degrees, it is impossible to

say what effect such a temperature would have upon matter.

Thus we have two opposing causes, the one an inconceivable

degree of heat, such that were matter exposed to it on the

surface of the earth, it would explode with a power to which

nothing within our experience can be compared, and a

pressure thousands of times any we can produce, tending to

condense and solidify this-intensely heated matter. One thing

which we can say with confidence as to the effect of these

causes

is

that

no

chemical combinations ,

can

take

place

in

matter so circumstanced. The distinction between liquid and

gaseous matter is lost' under such conditions. 'Whether, the

central portions are compressed into a solid, or remain liquid;,

it is impossible to say.«'

'-) In his thoughtful Familiar Lectures, on Scientific .Subjects, 1867, p. 282, Sir John Herschel- ^<i^% this figure as i 148000000000; but he omits altogether the ratio 1.66 which applies to the aether as a monatomic gas. This correction is verified both by theory and by observation on such monatomic gases as Mercuryvapor, Helium, Argon, Krypton, Neon, Xenon.

63

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64

In the writer's Researches on the Physical Constitution and Rigidity of the Heavenly Bodies, 1904-5, he reached the conclusion that the confined solar matter must necessarily be gaseous, though acquiring the property of a highly rigid solid under the enormous pressure and high ten\perature to which the matter is subjected. In fact it was found by calculation that the layers of the sun's globe have an average
rigidity of over 2000 times that of steel, (AN 4104, equa-
tion 22, p. 384), while the average rigidity of the matter, accumulated with increasing density in the interior layers,
may be 6000 times that of Nickel steel (AN 4104, equa-
tion 38, p. 392).
Such a globe must be viewed as bursting internally with pent up explosive energy, yet kept in equilibrium by the accumulating pressure of the surrounding layers: the confined matter is gaseous, yet rigid to the highest degree, and in such confinement must have the property of a solid of enormous rigidity.
Now the rigidity of the aether is variable with the
radius vector drawn to the sun's centre, but generally less than that of solids such as glass, which is about lo*^^. Yet with such liigh elasticity, due to the enormous molecular velocity 471239 kms, we see that it cannot be rent or cracked, as Lord Kelvin once suggested, (Popular Lectures and Addresses, 1. 33 6), by any forces at work in nature. The only artificial forces yet found capable of setting up waves in the aether were the extremely quick explosions of dynamite used by Professor Francis E. Nipher of St. Louis.
5. Table pf the Physical Constants of the Aether.
The general method employed for detfermining the
physical constants of the aether is' based on the process for calculating the mechanical value of a cubic mile of sunlight devised by Lord Kelvin, 1854, and first published in the Transactions of the Royal Society of Edinburgh, (cf. » Mechanical Energies of the Solar System*, 1854, and Baltimore Lectures, 1904, p. 261-265). This method was adopted and somewhat improved by Maxwell, 1875, ii^ '^^ Article Aether,
Ency. Brit. 9'*" ed. Some further improvements have been
introduced by the present writer, especially in those constants of the kinetic theory of the aether, which were never calculated by Kelvin or Maxwell. These are due entirely to the recent investigations, and are here outlined for the first time.
We adopt the constant of solar radiation recently found
by Bigelow, namely, 3.98 ca., 19 19. (Supplement No. I to the Treatises on the atmospheres of the sun and the earth. Four fundamental formulas for discussing the observations
made with various types of pyrheliometers, F. H. Bigelow,
John Wiley & Sons Inc., New York, 19 19, p. 4). A certain factor in the kinetic theory of the energy
of the aether waves coming from the sun was taken by Lord Kelvin as between Y2 ^ind i, (Baltimore Lectures, p. 263, § 5), and by Maxwell as 72- Working out the problem somewhat more fully than Lord Kelvin has done, thus taking account of the inclinations of all the wave elements in plane, circularly and elliptically polarized light, I find that this
,
factor for the total energy should be a little greater than one half, namely:

= 2/JT

0.63662.

o

Accordingly we thus arrive at the following

Table of Constants of the Aether:

1. 2.

Constant of solar radiation, found by Bigelow from ob-

R = servations,

3.98 fa.

= Assumed ratio of amplitude to wave length AJl

3.

j/ioi.23, which is nearly the same as was used by

= Maxwell, so that Ap

271/101.23 == 1/16.115.

= Energy per cubic centimetre at the sun's surface

= (0.63662)^ F^^/)^ 4-41455 ergs.

= = 4. Greatest tangential stress per sq. cm at the sun's surface

Q V^'(Ap)

111.1713 dynes.

5. 6.

Coefficient of rigidity of the aether:

= = at the sun's surface

q V^

1800,

.;

= at the earth's surface 219^ F^

394200.

•*;

= Density of the aether at the sun's surface q

2Xio~^*.;i

^ 7. Density of the aether at the earth's surface q' = 438X10"^*.

21Q0

Mean velocity of the aetheron, v == 47 123900000 cms.

= Molecular weight of the aetheron, [ff

i)

= 15.56X10-12

Average length of mean free path, at the sun's surface,
^= 572959 kms.

Number of corpuscular collisions per second, at the

C^ sun's surface,

0.82246.

= Radius of aether corpuscle

3.346X10— '^'^, or 1/4005

of the radius of a Hydrogen molecule.

The radius of a molecule of Hydrogen is taken as 1. 34X10"*, and the density assumed equal. In computing
the molecular weight of the aetheron in 9 above, we disregard the so-called ,Electrical mass' because Professor Sir y. y. Thomson, (Electricity and Magnetism, 4* ed., 1909, p. 521), and Crowther, (Molecular Physics, 19 14, p. 70), and other authorities, admit that this ,Electrical mass' resides in the aethereal medium itself, which we are investigating. This subject will be more fully discussed in a future paper.
It may be noticed that the aether gas, is endowed with enormously high molecular velocities and excessively long range of mean free path, so that the highly elastic aether
is very different from .the ordinary terrestrial gases. This is forcibly brought out in the following table; yet the similarity with the other gases is also notable, even for such an extreme
case as the aether. It is this enormous mean molecular velocity and the long free path which causes the aether to
vibrate as an elastic solid for rapidly acting forces, but easily gives way to slow motions. It is worthy of notice that the
particles of the aether move out of the way ten thousand times more rapidly than the swiftest planets revolve in their orbits.
The constants for the tables assembled below were drawn originally from.O. E. Meyer's Kinetic Theory of Gases, but in the final revision I have adopted the mean of the values cited by yeans, Kinetic Theory of Gases, 2""^ ed. 19 16.

6s

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66

Table for Comparing the Physical Properties of the Aether with well known Terrestrial Gases.

Gas

67

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68

past each other. In this way, the experiments on diffusion have given us the viscosity of air and other gases.

The mean free path, for example, follows quite accu-

rately the law.

i^^^^i^^

(20)

where x is the viscosity of the gas, and v the mean velocity of the molecule in cms per second, and q the absolute density.

It is important to notice that in the case of the aether,
viscosity passes into rigidity, by a process of reasoning fully explained in Daniell'i, Principles of Physics, ^^ ed., i8gs, p. 227. In calculating the mean free path of the aetheron, we use the rigidity of the aether at the solar surface, 1800, because both the density and rigidity of the aether vary with

the distance firom the sun, as already explained in section 2:

/= Thus for the aetheron the mean free path is

57 2959kms.

It is a fundamental doctrine in the kinetic theory of gases that all gases have an equal number of molecules in unit volume, under like conditions of temperature and pressure; but it is not yet possible to decide on the absolute value of this number, different estimates being indicated by various eminent
authorities: iV^^igXio^^ [Maxwell], iV^= rooo X lo^* [Crbokes], i\^ == 6000X 10^^ [Kelvin).

About all we can say is that the number of molecules

in a cubic centimetre of gas at the ordinary temperature and pressure probably is not smaller than that assigned by Maxwell,
7\^=igXio^^, the latest determination being 27X10^^ (cf.
Crowther, Molecular Physics, Phila., 1914, p. 3).

Using the value for the aether,

m v^ :^ 47 I 239000

= and for Hydrogen, »i

1859 m

'

we have by the principle first enunciated by Maxwell (Scient.

Pap. 2.365), that »on the average every molecule great or

small will have the same energy of motion*, the equation:

which 'gives

V2'«i?'i^= ^Um^^'i

iiii =;«i(i859 *))7(47 1 239000)^= 15.56232 X 10"^^.

(21) (22)

Thus it follows that an aetheron has a mass of 15.56 millionths of a millionth of the mass of a Hydrogen molecule. This is equivalent to 2.7389X10"^ of an electron, or about one

thirty-six millionth of an electron.

If we take the density of the aetheron as equal to that

of the Hydrogen molecule, we find by calculation that the

radius of the aetheron is equivalent to
= r 1/4005. 36-iy

(23)

or one four-thousand-and-fifth of the radius of a Hydrogen molecule. This explains why the aether so readily penetrates all bodies, even the most solid. It makes the size of an aetheron to a molecule of Hydrogen as a globe two miles in diameter is to the earth. Between masses as large as our terrestrial globe or larger, globes two miles in diameter would freely penetrate in great numbers, even if the larger globes were in contact, which of course is not the case with any solid or liquid, and still less is this true of a gas, in which the molecules are separated by distances relatively immense in comparison with the diameters of the molecules.

If the molecule of Hydrogen be taken to have a radius of I.34X^o~'^ that of the aetheron becomes
^= = 1.34X10-74°°° 3-346 Xio-^^ nearly. (24)

To form a convenient picture of the small size of the aetheron compared/to the Hydrogen molecule, we may recall
the trifling height of a mountain a mile high compared^ to the immense radius of the earth. If other molecules be larger than Hydrogen, as is generally supposed to be true, then the aetheron will be a small globe of the size of a moderate
mountain peak loooo feet high; so that the various molecules
will resemble Venus and the earth, Uranus and Neptune, Jupiter

and Saturn.

•

'

.

To fix upon a more familiar everyday image of this

world structure, we may imagine a box filled with large
oranges, and the finest dust, like that of lime, or smoke

from a cigar, penetrating the relatively vast spaces between

the.oranges, which however should not be in contact, but

in rapid motion.'

If

now

the

cigar

smoke, or '

the

particles

of lime dust, be imagined to have stupendous velocity, flying hither and thither with inconceivable speed, and thus moving

with; the

utmost

freedom

in

the

open

spaces betweeii the ,

oranges, as well as outside of them, we shall have a very

goocj image of the behavior of the aether in respect to matter:

The aether not only penetrates all matter freely,- but
even waves in it pass through all physical bodies, with only the hindrance incident to. refraction and dispersion such as
we see in light. The refraction is due to the unequal resistance offered by matter to the advance of the wave front,
and the dispersion to unequal resistance to various wave lengths. Shorter waves encounter relatively more resistance, because their oscillations are more rapid,' and thus the aether

yields and adapts itself less easily to the resisting molecules in the path of the waves, when the waves are short, and the changes, due to their advance, extremely rapid.

7. The geometrical and physical significance
of the potential.
In the Memoires of the Paris Academy of Sciences for
1782, p. 113, Laplace introduces the use of the analytical
expression since known as the potential, from the designation first used in 1828 by the English mathematician George Green (Essay on the application of mathematical analysis to the theories of electricity and magnetism, Nottingham, 1828). The potential is defined thus:
V = Mir = = JJJ{'^/^[(*-^')'-^(>-/)'+(^-^')']}d^cbdz. (25)
This expression has come into the most extensive use in all the physical sciences, and been of the highest service in the
mathematical theory of gravitational attraction, magnetism, electrodynamic action, and also in theory of static electricity.
But it is very remarkable that up .to the present time an expression of such universal use has not been given a clear geometrical or physical interpretation. The difficult} doubtless arose originally from beliefs like that expressed b} Laplace, in the opening paragraph of the Mdc. eel. I, 1799 that the »nature of force is now and always will be unknown*

*) jfoule's value of molecular velocity of Hydrogen, which makes the aetheron perhaps a little too large.

:

:

:

69

5044

JO

= In the state of darkness, relative to the invisible aethereal since the element of mass dm

adxdydz can be made so '

medium, existing at the close of the iS'*" century, Laplace
doubtless considered it sufficient to deal with expressions

small as to apply to every single particle or atom.
V At first sight the mere fact that the potential as thus

which give the forces acting on the planets, without inquiring defitied follows the law of wave amplitude in tridimensional

into, the geometrical nature and physical mechanism involved space strikingly suggests that the wave-theory represents the

in the generation of these forces, which were then believed order of nature. To find out by exact calculation what is

to lie beyond the reach of the investigator.

the probability of such a coincidence occurring by mere

After the development of Faraday's Experimental Researches in Electricity, and Maxwell's mathematical interpretation of these results, very- different views came to be entertained by geometers and natural philosophers. Yet it

chance, we may proceed as follows.
Taking the expressions for two independent the amplitude and the potential, we have
A=y = klx, = = V y M/x.

curves, (27)

was only the developments brought out in the »Electrod. Wave-Theory of Phys. Forc.<<, which seemed to justify definite expectations of. forming clear geometrical and physical' conceptions of the mechanism involved in the action of the magnetic and the planetary forces across space. Recently

It will be noticed that they belong to the same geometrical

— species

both being rectangular hyperbolas referred to their

— asymptote.s

and can be made identical throughout,, from'

= ^ == o to X 00, by introducing a summation 2, such

— that 2^ M.

these conceptions have been verified and extended, and

Accordingly it appears that by the mere variation of

= ^ therefore we shall here attempt to give a geometripaL-and a parameter the curves are made to coincide rigorously, point

physical, interpretation of the potential which so long proved by point, from x ,0 to x

c)o. Therefore the chances

bewildering to the physical mathematician.
In the »Electrod. Wave-Theory of Phys. Forc.«, 1Q17, p. 134, it is pointed- out that if waves be the basis of physical action across space, then the amplitude of such waves when propagated spherically and without resistance, in tridimensional

= = against such a rigorous coincidence accidentally occurring ,

throughout infinite space, x

o to x

00, becomes in-

finity to one, or,

00
C=Jdx = oo

(28)

o

space, will be given by the equation

= A

k\r .

and thus its actual occurrence points unmistakably to. a true (26) law of nature.

In an address to the Academy of Sciences of St. Louis, Sept.- 2 1, 1917, I gave this simple formula and pointed out its geometrical and physical significance. Professors F. E. Nipher, E. A. Engler and other physicists were present and showed great interest in the results announced, from which it would appear that this law had Jargely or entirely escaped
the notice of earlier investigators.
Now by comparing this expression (26) with that in
(25) above, we notice that the wave amplitude has the same form as the potential defined by Laplace in 1782. The question thus arises : Can the coincidence in form be due
to chance, or is the potential in fact an analytical expression for the total aether stress due to the superposition of waves from all the atoms, each of the waves being of the average wave amplitude, appropriate to the coordina.tes in the field
of force about an attracting mass? To get at the truth in this interesting inquiry, we notice that Laplace's formula of
1782 integrates the mass of every particle of the attracting body, divided by its distance, which corresponds to a summation of the effects due to the superposed wave amplitudes and thus increases directly as the mass, each set of waves
superposed from the atoms in any element a Ax&y Azlr,^
being independent - of all the rest, but the triple integral including the accumulated wave action of the whole mass
= V Mjr ==

It seems therefore certain and incontestible that the potential represents geometrically and physically the totalaccumulated stress due to the whole mass under the average wave amplitude of the field about the attmcting body in question.
It is to be noticed also that physically our definition of the potential confirms this conclusion'. In free space there is no cause to alter the spherical distribution of the waves, as they expand with 'increase of r. But in or near the shadows
,
of the earth, as shown in the »Electrod. Wave-Theory of Phys. Forc.«, a circular refraction of .the sun's waves will necessarily occur. The sun's potential varies, even at a constant distance, near the shadow of the earth; and owing to -this refraction, fluctuations of the moon's motion should
arise near the time of, lunar eclipses, as fully explained in this work of 19 17. This circular refraction of the electrodynamic wayes in passihg t'hrough the earth's mass changes the potential or total accumulated stress due to the integration of the waves from all the atoms, under the average w^ve amplitude and distribution of the waves in the space near the shadow of the earth: and therefore also the sun's forces acting on the moon.
Partially released from the sun's control, by the interposition of the body of the earth, with its refractions of the
sun's wave-field, the moon tends to fly the tangent while traversing the region of the shadow cone, and thus arise the fluctuations of the moon's mean motion, connected with

^lll{alV{[x-x'Y^[y-y'Y+[z~z'Y\]AxAy^z. (25) lunar eclipses, which long perplexed Laplace, Hansen, Newcomb,

The elements under the integral signs represent the ' individual potentials of every partick, and thus the potential increases directly as the mass whose wave-effects are integrated. This conforms rigorously to our conceptions of the Newtomaxi law of attraction, and involves no approximation,

Hill, Brown and other astronomers.
8. Explanation of the Propagation of the Wireless Waves around the Earth.
In the unpublished manuscript sent by the writer to the Royal Society in November, 19 14, which was the first

71

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72

outline of the »Electrod. Wave-Theory of Phys. Forc.« the following figure was used to illustrate the propagation of wireless waves around the earth.

Fig. z.

Illustration of the refraction of 'the wireless wave about the earth, and of light in a prism, owing to slower propagation of waves in dense masses.

It is a sufficient explanation of this figure to say that it corresponds exactly with' the propagation of light through
a glass prism, as shown in the figure of the prism above. The wireless waves travel faster in air than through the solid earth. The enormous elasticity of the aether, as set forth in section 4, prevents bodily rupture of the medium; and this secures continuity of the wave front, by beriding the surface backward near the globe, to correspond to the slower propagation in that dense mass. The retardation of the waves propagated straight through the earth causes the wave front to be bent and held back near the curved surface of the earth, and thus the wireless wave is refracted around the earth by the much greater resistance encountered in that
solid mass.
The correct theory of the bending of the wireless wave about the globe is thus the same as that of a ray of light by a prism, as sHown in the accompanying figure. The speed in the air is 4, but in the glass only 3, and thus there is a bending of the wave front through the angle. 6 when the light enters the glass, and also when it leaves the glass, as
long recognized by physical investigators.
The explanation of the refraction of light in a prism is directly confirmed by Foucaulf% celebrated experiment on the relative velocity of light in air and in water, (Annales de Chim. et de Phys. Ser. 3, t. 41, 1854), which has always been recognized as a crucial test of the wave theory of light, and which finally led to the total rejection of the emission theory.
The simplicity of the above explanation of the propa-
gation of wireless waves about the globe is thus remarkable.
But it is also confirmed experimentally by observations made by officers of the American Navy, upon wireless waves sent from Mare Island to San Diego, California, and received by submarines lying on the bed of the sea, through a depth of some 30 metres of sea water. In some experiments with the receiving apparatus underground the same effect was observed.

It appears that the earth also conducts the signals, so that
wireless apparatus may be installed and used in deep mines, which would enormously increase the power of signalling in
case of accidents interrupting communication by the shafts
and tunnels, It is probable, however, that the irregularity in the
structure and conducting power of the earth's strata would, somewhat handicap such iinderground signalling, yet not prevent the successful development of the method of signalling through the earth to the limited depths at which miners work.
- The problem of explaining the propagation of wireless
waves about the earth has hitherto challenged the ingenuity of the foremost mathematicians. It has been unsuccessfully
attacked by Professor H. M. Mac'donald (Proc. Roy. Soc. 1903 and Phil. Trans, igio). Lord Rayleigh and Prof. H. Poincaiii\
(Proc. Roy. Soc. 1903). See aXso.Foincard's Lectures of 1908 (La Lumiere filectrique, vol. 4, 2"^ series, Nov. 28, Dec. 5, 12, 19, 1908, especially p. 323). Professor A. Sommerfdd (Ann. der Phys., vol. 28, p. 665, 1909) has shown that a surface wave should exist; and Professor J. W. Nicholson (in the Phil. Mag., March, April, May, 1910) has dealt with certain problems of the exponential factor of the wave amplitude, but none of these eminent mathematicians arrived at any satisfactory theory of wave propagation about the globe.
In his well known work on the Principles of Electric'; Wave Telegraphy and Telephony, London, 3"^ editiori, 19 16, p. 826-851, Professor J. A. Fleming gives a full and accurate account of the difficulty experienced by these and other
mathematicians. In this revised edition of 1916, Fleming gives the following: » General conclusions as to the mode of propagation of long electric waves round the earth «.
»Summing up the conclusions so far reached by radiotelegraphists we may say tfiat the effect produced by a radiotelegraphic transmitter at a great distance, say 2000 or 6000 miles over the surface of, the earth, is a complex one in which several different actions play a part«.
» There is, first, a propagation through the aether of a true space electromagnetic wave which is difiracted round
the earth. The extent to which this contributes to the whole
effect is,' perhaps, greater than was formerly supposed, but
is yet an undetermined quantity. Some mathematicians are now inclined to attribute to it the major portion of the transmission by day«.
»Then in the next place there is undoubtedly a contribution made to the effect by waves which have suffered a refraction equivalent to a reflection by ionized air at high altitudes, and a very small effect due to the decrease in refractive index of air as we ascend upwards*.
» These causes tend to make the ray follow round the curvature of the earth and so assist as it were diffraction. It is to this variable ionic refraction that we must attribute the diurnal and annual variations in signal strength, and also the greater signalling distance by night as well as the irregularities attending the transition times of sunrise and sunset«.
»Then in addition we may inquire how far any contribution is made by a surface wave of the type investigated by Sommerfeld, which is equivalent to an electric wave pro-
pagated through or along the earth «.

'

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74

»It has been definitely proved that we can receive signals from stations hundreds of miles away without any high receiving aerial, but merely by connecting one terminal of the receiving circuit to earth, and the other terminal to any large well -insulated mass of metal, whether inside or outside of a house does not matter*.

If I understand the difficulties so lucidly outlined by Fleming, they will be found to have proceeded from the

inadequate theory of • the aether heretofore in use, the dis-
cussion being based upon diffraction around the earth, instead of upon refraction and dispersion within the denser mass of the earth, and thus a bending of the wave front.

This will sufficiently justify this quotation, since it is essential

that the difficulties heretofore encountered should be autho-
ritatively described. The reader can then judge aS to whether a simpler and more practicable solution of this problem has

been obtained.

As to the feebleness of wireless transmission by day,

I have reached the settled conviction that it results from
the magnetic wave field of the sun. When this storm of

waves fills our air by day, the wireless waves have great

— difficulty in getting through,

just as any system of regular

water waves in a lake, used for signalling across it, would

be almost lost in distinctness, owing to the surface chui;ning

of the lake under the violence of a wind storm. The trans-

mission is more difficult with the distance, and, after a certain

distance, entirely fails. At night the sun's magnetic wave field

is largely absent, and thus wireless transmission is much better.

It only remains to add that the celebrated argument of Cauchy, to the effect that refractive' dispersion of light

necessarily implies a granular structure in the transparent matter, is equally valid for showing that the aethereal mediurn itself is corpuscular. In his Popular Lectures and Addresses
1. 190, Lord Kelvin has modified Cauchy 1. theory of refractive dispersiori in his usual lucid manner. It is believed that the considerations adduced in this paper will render the arguments of both Cauchy and Kelvin sornewhat more definite and

interesting.

When the aetheron is so small, and moving so rapidly,
the generation and propagation of waves in the aether is intelligible. The refractive dispersion, by the resistance to the waves from the much larger molecules of ordinary matter, is easily understood; and thus refractive dispersion implies
in common matter, coarser granules than those of the mediurn
itself, but yet points to the moving aetherons as easily deranged by the resistance of the waves dispersed.
~
It will be shown hereafter that resistance soon changes the form of the wave, and causes it to break up into two distinct parts, the larger having increased amplitude, and shorter length, hence encountering more resistance than the original wave. It is certain therefore that we not only have retardation in the propagation through the earth, but also dispersion of the fragmentary waves, and absorption of some
of their .energy as heat.

9. Outlines of the Wave-Theory of Magnetism, with explanation ofthe mechanism of Attraction

and Repulsion.

For the sake of completeness the present investigation

requires a brief notice ofthe cause of attraction and repulsion

in magnets, and in electrodynamic action, as first outlined

in the vol. i, Electrod. Wave-Theory of Phys. Fore, 1917. Accordingly we begin with magnetism, which the celebrated

English physicist Maxwell had been so long engaged upon,

but had--failed to solve at the timeof his death 40 years ago.

The accompanying figure from the work of 1917 will

illustrate to the eye, the essential character of a magnet, as

A conceived in the wave -theory, of physical' forcfes.

large

magnet A is exhibited in the same field with two smaller

magnets, B. In the first case unlike poles are presented, and

we have mutual attraction. In the second case the poles

presented are like, with the well known result of mutual

repulsion. But how does this attraction and repulsion come

about?. What mechanism is involved, and in what medium .
does it work? Obviously the medium is the aether, because

an electric current produces a magnet from a piece of steel

wound in a solenoid, and because also the electrodynamic

action of a current travels with the ve-

locity of light, as was first inferred by

Maxwell, and afterwards proved by ex-

periment.

a) In the case of attraction, it will

o -o.--T>

/<> Q '/

Q'-
.

.,jj.

be seen that the waves from the small

B '"^f^gvi''''

have the elements ofthe aether

rotating in the opposite direction to the

l»»TBI.i.|»». i. ijg„-.,

rotations in the more fully outlined waves
from the magnet A. The plane waves
A from are to be imagined, for the sake

of simplicity, in the central plarje, or

equator, and travelling away with the ve-

— locity of light,

for the reason just as-

signed in electrodynamic action, by which

magnets are produced.

f^^iS^Srfi^ '/ Plane W«vo Morton I(/,

As shown graphically by the curve traced just above the heavy waves in the

figure, the amplitude of these receding

theory of magnetic attraction and repulsion. waves decreases according to the law:

.

,'

75

5044

76

= A kjr

(29)

and as the force due to -svave action is- siiown, in works on

physics, to be proportional to the square of the ampHtude,

^72/2 we have for the force': f=Plr^

1

\'

(30)

which is the form of law for gravitation, magnetism, and' all similar forces of nature obeying the law of the inverse squares.

B Now let the waves from magnet interpenetrate the

waves from magnet A, It will be seen that at every point

of space the rotations of the elements of the two sets of

waves are exactly opposite: the result is that the rotations
B from magnet undo as far as possible the opposite rotatit)ns

from. magnet A. Accordingly the stresses in the medium due

A to rotations of the aether, in the field between

and B,

and also beyond A and B, are reduced : the medium is thus

everywhere less agitated than before, and shrinks, so as to

A collapse or contract between

and B. But a collapse of

the aether is equivalent to a contraction, and thus the two

bodies attract as if held together by a stretched mass of

India rubber. This is a simple and direct explanation of

attraction. Nothing is postulated except waves like those

known to exist in light and heaj, but here seen to be ex-

actly parallel and somewhat differently 'directed from those

of light and heat, which usually have their planes tilted in

haphazard fashion.

B) The cause of' repulsion is similar to that of at-

traction, but in this case the poles presented are like; and

if we examine the above diagram, we discover that when

the waves from magnet B, 2°'' case, interpenetrate the waves

from magnet A, the rotations at every point will be con-

formable and in the same direction. The medium therefore

at every point is more agitated than before. The amplitudes

of the disturbed waves are thereby increased, and hence

there

is

an

increase of stress; '

and under the elasticity of

the aether the result, is an expansion, of the medium, which
.

gives

a

miitual

repulsion

of

the

two bodies. '

This is a simple explanation of repulsion, and it had

never been worked out prior to the researches published by

the writer in, igiy. Maxwell waS unable to conceive of any

mechanism for the explanation of attraction and repulsion

- of' magnets, though he found that mathematical stresses of a certain type, yielding tension along the lines of force and

pressure at right angles thereto, thus dynamically equivalent

to, those outlined above, would account for the phenomena

of magnetism.

It is true that Maxwell believed that there are rotations

around the Faraday lines of force, as Lord Kelvin had also

rendered probable as early as 1856; but neither A'^&m nor

Maxwell had seen that this would arise from the type of

waves here outlined, though Faraday'^ experiment of 1845,

on the rotation of the plane of a beam of polarized light,

— when passed along the line of force, through a dense,

— medium such as lead glass,

should have suggested the

'correct theory of the magnetic, waves to Kelvin and Maxwell,
as it did to me in ig 16.

As Maxwell was unable to unlock the Secret of mag-

netism, with both attraction and repulsion, it will not greatly

surprise us to learn that he was utterly bewildered by the

mystery of gravitation, and could not make a successful attack

upon this most difficult problem. In fact no considerable progress as to the cause of

gravitation has been made by other investigators since the time of Newton. As the subject of 'gravitation is immense, we must not enter upon it here, except to say that the evidence

is most conclusive that it is a wave-phenomenon, closely allied

to that of magrietism-, but differing from magnetism which

- has a parallel arrangement of the atoms and what Airy calls
(Treatise on Magnetism, 1870, p. 10) a duaHty of powers

— two poles

while gravitation is a central action only, owing

to the haphazard arrangement of the planes of the atoms.
It 'is well known that about 1822 Ampere first made

electro-magnets out of common steel, by means of an electric

current sent through a solenoid. The way in which the wire

IS wound about the bar' being magnetized suggests, and, in

fact, proves that the wire bearing the current has a wave-field

about it. There is proof that the waves are flat in the planes

through the axis of the wire: this conception harmonizes' all.,;:

the known phenomena of magnetism, in relation to electro-

dynamic action, and also harmonizes Ampire'% theory of ele-

mentary electric currents about the atoms with the waVe-theory

of magnetism above set forth. ; The wave-theory of magnetism explains all the phe^ •';

nomena of terrestrial magnetism, in relation to the periodic

influences of ,the sun and moon, such as magnetic storms,

earth. currents, the auror-a, and the semi-diurnal magnetic tide

depending on the moon, of which ho other explanation is

known. For the dependence of magnetic storms on sunspots

consult a paper by the author, in the Bulletin Society Astr.

de France, November, igi8.

There has been such' a bewildering confusion of thought

connected with the whole subject of physical action across ,

• space that it is necessary to bear ii> mind clearly the fun-

damental principles of natural philosophy. In the well knoWn

article on attraction, (Scientific Papers, vol. 2.487), Maxwell

points out that in the Optical Que'ries included in the third

edition of the Optics, 17 21, Newton shows that if the pressure

of the aether^al medium is less in the neighborhood of dense

bodies than at great distances from them dense bodies will

be drawn towards each other, and if the diminution of

pressure is inversely as the distance from the dense body,

the law will be that of gravitation. Maxwell considers that ,
Newton's conception rests largely on the idea of hydrostatic

pressure, as in incompressible liquids. But we have shown that
the' amplitude of the waves, A =:kjr, with forces f^k^lr^,

fulfills the condition which ^Newton held to be essential.

10. Integration of the General Differential

Equations of an Elastic Solid, *hich applies to the
Aether, when this Medium is viewed as an Infinite

Aeolotropic Elastic Solid propagating Waves.;

m As is usual in the theory of an elastic solid, let

denote

a

function
'

of

the

bulk

modulus k,

and

of the

rigidity «,

«"=1^ that

+ ni^k ^l^n.,

(31)

— Then k =^ m '^j^n, and this bulk modulus measures the

elastic force called out by, or .the elastic resistance against,

change of volume. On the other hand the »compressibility« ^

is measured by

= i/^ il{m-^Un)

(3 =

:

.

:

n

5044

78

Let «, /J, ;' be the component displacements experienced by a particle, so that when undisturbed the coordinates are x, y, z, and when disturbed x-^a, y-^fi, z-hy. Then a strain of any magnitude is specified by six elements:

A
B = (|)'*(|+0'*(87)'

da 8a Vy Oz

M
\^ d^y-^' ):dz

8^/9^
dy \dz

_~da(<da

dz \ Ox

J dz dx

Oz

) dx

(33)

''da

\8«

) dy dy

dx ^dy

dx dv

All particles in an unstrained state, which life on a spherical surface: rx'== ^I'+Vi'+^i'
will, in a strained state,- lie on an ellipsoidal surface

(34)-

(3S)
P Accordingly, if the external forces at (x y n) along the axes of x, y, 1 be X, y, Z, per unit of mass, and the

internal stresses be.:

dpxx
dx

dpyx dy

= dpz j dxdy dz
dz

dF
(
dx

dU dT
I dx dydz dy dz

dpxy
dx
d5££
dx

dpyy
dy
dy

— = ) d* djv d2

dJ7
(

dz

dx dy

dS_
\ dxdy dz
dz

= A dpz. - j dxdy dz
dz

/dT dS_ ±r:

'

\ dx dy dz

\dx

'
dy dz

{^(^)

Then the equilibrium of all the forces, internal and external, leads to the following equation

(dpxx \ dx

dpja dy

dpzx dz

= = qX

\
\

dxdy

dz

dU ('d^.
\
dx

dT

H

' qX j dx dy dz

dy dz

o

i ^Pxy

= = dpzj, qY]\ dxdydz

dU ('

d(2

l

dS_
" qY) dx dydz

o

\ dx

dy

dz

dx dy dz

( dpxz
\dx

d^
dy

= dT dpzz

\

A

qZ -

I d^cdjf d^

I

dz

dx

dS
h

^ " qZ ) da;djv dz

o-.

dy d^

(37)

These are the general equations of equilibrium of an elastic solid, when subjected to strain by any system of

m = forces, internal and external. For an isotropic solidj the equations become much simplified. Using

k-^^J^n, as in {31), we find the well

known formulae for an elastic solid, of density q per unit volume, (cf. Thomson and Tait, Treatise on Natural Philosophy,

edition 1883, § 6g8)

d (da

da; V8x

:

79

5044

8o

an infinite elastic solid (cf. Cambridge and Dublin Mathe-

matical Journal, 1848).

It may be noted that the density of an isotropic solid,

which does not vary with the coordinates {x,y,z), is expressed

by the ratio,
= Q [(wH-«) vM]/(dX/da:+dy/dj'+dZ/d^)'.

(43)

But by Foisson's equation we have

^'^V-^^ng^o q=~V'^Vl4n

(44)

or

e=- -(i/47r)(92F/8a:2-H92^/9/-t-92f7822). (45)

By comparing (43) and (45), we find'^that if a mass

of density,

= ^

i/[47r(OT-+-« -.I-"-!-----!--—)

46)

.

\ d^

djc

ds /

be distributed throughout space, we may conclude that its

potential at [x, y, z) will be identical with the

the elastic solid substance

= d

9a/9;c+9/J/9j/-i-9;'/9^.

dilatation of (47)

For if we divide (42) by [m-i-n), and subtract from it the first of (44), we get:

= V- 6-^[AXlAx-^dYlAy-h&ZlAz)l{m+n) -h
— V^f^— 47T? o

(48)

which gives

= V^(d— V) o

(49)

if

= — dXldx-^dYldy-^dZldz 47iq'{m->t-n)

o

ISoJ

or the density is defined by the expression:
= Q jlUn{m+n)]-{dXldx^dYldy^dZldz) . (51)

This specifies the density throughout space of the infinite isotropic solid, that of the finite solid body in (41) being

unity per unit of volume.
R To reach Lord Kelvins result most directly, we let

= denote the resultant of the forces, X, Y, ,Z, at any point

[x, y, z], at the distance r

V[x^-^y^-\-z^) from the oriigin,

whether discontinuous and vanishing in all points outside

some finite closed surface, or continuous and vanishing, at all

infinitely distant points with sufficient convergency to make

Rr converge to o as r increases to 00. Then the con-

vergency of Xr, Yr, Zr to zero, when r is infinite, clearly;

F=o makes

for all infinitely distant points. Accordingly,-

if 5 be any closed surface round the origin of coordinates, '

everywhere infinitely distant from it, the function ((5— V] is

= = V zero for all points of it, and satisfies the equation V" (d— V).

o for all points within it. Therefore d

throughout ,

the infinite isotropic solid.
Z Now let X', Y', Z' denote the values of X, Y, at any

point [x,y, ^), and by a triple integration throughout all space,

V we shall have for the potential

or dilatation 6:

-+-OD -HOO -4-00

= — (J

i/[47i:(ot-i-«)],-J
— —J 00 00

^{dX'ldx^-^Ay'ldy'-^AZ'lAz')lV[[x-x'Y-^{y-y'Y-h{z-z'Y]-dx'dy'ds'.
00

(-52)

For the element of the mass is

p =i= i/[47r (ot-h«)] • (dX/d^'-t-dy/dy-HdZ'/dz')

(53)

and- the mutual distances of the elements of mass filling the element of space dx dy dz is

r^V[[x-x'Y+[y~yY+{^-z'Y]-

" •,,(54)'

These expressions may be, rendered more convenient by integrating by parts, and noticing the prescribed con-

dition of convergence, according to which when x' is infinite,

' ,

-+-00 -4-00

= J ^X'jV[[x-x'Y+[y-y'Y+{^-z'Y]-Ay'dz' o

155)

— -00 CX3

And, therefore, for the three components of finite value, resolved along the coordinate axes, ' and integrated throughout

'

all space, we have:

-t- 00 -t- 00 -1-00

' d=ilUn[m+n)]-^ J .^ [X {x-x')+ Y' {y-y')+Z' [z-z')]l V[[x-x'YHy-y'Y'+{^- e'Y]-Ax' dy' dz' .

(56)

— -co cso ^00

U = = w-¥W We may integrate each of the equations (38) in the same way, for a, /J, y respectively.

displacements is:

a ^= u-\-

• ^ v-hV

y

The result for these

W where u, v, w, U, V,

(57)
denote the potentials at [x, y, z) of distributions of matter through all space of densities respectively

(m/4TTn]Sd/dx

{m/47tn)dd/dy

{m/4nn)dd/dz

Xj^nn

Yj^nn Zj^nn.

(58)

In other words the functions are such that throughout all space

...; :^<:

= = = = ^^u-h{m/fi) dS/dx o '^/'U-hX/n o

V^v-h{m/n] dd/dy o ^^V^YJn o

= = \'-w^{mln) dd/dz o V" W-hZjn o .

(S9)

Z Accordingly, if X", Y", Z" denote the values oi X, Y, for a point [x", y", z"), we find

-hoo H-CO -hoo

= + a

(i/47r«)J
—-CXD

—J00

^ {m-dd"ldxf'
00

X")IV[[x-x"Y+{y-y"Y+{z-z"Y]-dx/' dy" dz"

-f- 00 -h 00 -f- 00

= + + fi [ilAnn)l J l[fn-^d"ldy"+Y")IV[[x-x"Y {y~y"Y [z-z"Y]-dx"dy"dz"

(60)

00 00 00

-hoo -+-00 -t-oo

= r

(i/4/r«)J
-00

—J00

^[m-dS"ldz"+Z")IV[[x-x"Y+[y-y"Y+[z~z"Y]-dx"dy"dz"
00

:

:

.

8i

5044

82

By substituting for <J" its value in (56), we obtain expressions for a, /S, y depending' on the sums of a sextuple

—00 integral and a triple integral, the integrations having to be performed from

to -Hoo:

Iff 47in

I

r r r x'{x"—x') ¥'{/'-

-.')

dx' d/ dz'-hX" dx" dy" dz''

J J Ax 47r \m +n)J

[{x"-xr (y - -/)'-+- (2" -^')A^2Y]I,

V[(x-x')''+(y-y')^

Iff 47tn Iff 47Tn

X'{x"-x')-+-Y'[y"—y')-

•T7jff dy 4TC \m

+ + [[x"-x'Y [y"-y'Y \

V[[x-x'Y-^{y-y'Y-\-{z-z'\

y •X' {x"-xf)-+- {y"~y')-hZ'{z"-

j j +n)j dz \_47T (m

[{x"-x'Y-^{y"-y'Y -{z"-z'Y]'l'

Viix-x'Y'^'.y-y'Y-^i^-^'Y]

dx' dy' dz'-t- Y"\ dx" dy" dz" (6ry
dx' dy' dz'- -Z" \dx"dy"dz".

Lord Kelvin shows how to simplify these sextuple integrals, and obtains the following general solution for the

displacements produced by any distribution of force through an infinite elastic solid filling all space (limits of integration
as before —00 and -t-00):

2 (2/«-l-3«) X'

2 4Tin\m-

/// V[[x-c 'Y+{y-yY+[^-^r] —d m [[x- -x')'^+[y-y'Y^[si-z'Y]

X'(x-x')-hY'{y-y')-hZ'

^l dx'dy'dz'

=

r -3«;

dx [{x-

-{y-y'Y ,-z'Y]''' J

-«

J J 24nn[m-\-n) J

\/[{x-x'Y-h{y-y'Y-^{z-z'Y] d_ X'[x-x'Y Y'iy-

-Z'{z~z')]

(6.

-m[{x-.x'Y-^{y-y'Y-^{

^Uy

dx' dy' dz'
[{x~x'Y- -(y-y'YM^-^n'' i

=
/ 24nn \m-

JSS

2 (2m-\~ ^n) Z'
V[[x-x'Y+[y-y'Y- -[z-z'Y]
— — m[[x x')'^+{y—y']

d_ X'[x-

Y'[y- )-hZ'(z-~z']

^ dz [[x—x'Y-i-{y—y'Y'^{z' »'121»/.

dx' dy' dz'

This wjiole investigation is based upon the integration

of the general equations for an infinite isotropic elastic solid

which implies' that the density throughout all space shall be

equal to q as defined by (46).

•

Z Lord Kelvin's definition of X, Y,

as any arbitrary

functions whatever of [x, y, z), either discontinuous and vanishing at all points outside some finite closed surface, or

continuous and variishing at all infinitely distant points with

= sufficient convergency to make the product of their resultant
Ji V(X^-i- Y^-hZ^), by the distance
r= viix-x^Y-^iy-yy-^i^-^T]

namely Kr, converge to zero as r approaches infinity, implies

that the density ma!y vary through changes in the differential

elements

= dX/dx-hdYJdy-hdZ/dz y^W

(63)

as shown below. But no other changes than those in ^^JV, the Laplacian

operation on the potential can occur; and even this is chiefly at the boundaries of solid bodies. Accordingly it becomes advisable to investigate these possible changes a little more

closely.

12. Geometrical and Physical Conditions which

the Forces generated must satisfy.

Suppose X, Y, Z to denote the components of the forces

dm^ acting on an element of the soli'd

qdx dy dz, temporarily

imagined to be fluid at [x, y, z), reckoned per unit of the
mass. Then the difference of the pressures on the two faces

dydz of the rectangular parallelopiped of the .fluid is

6y dz {dpjdx) dx

(64)

and this fluid element will be in equilibrium when the

following equations are satisfied

dy dz (d^j/djc) dx—XSx 6y dz

dz dx (dp/dy) dy — Ydx dy dz

— = dx dy {dp/dz) dz Z dx dy dz

o

;

(6S)

which give the necessary and sufficient condition for the

equihbrium of any fluid mass:

= = X Apjdx

dpjdy Y

.

= dp/dz

Z .

(66)

From these equations we obtain immediately

= dp == dp/dx-dx-^r dp/dy -dy-hdpjdz-dz giXdx-i-Ydy-hZdz) .

(67)

This equation shows that Xdx-h Ydy-i-Zdz is the completed

differential of a function p (x,y,z) of three independent va-
riables, or may be made so by a factor. Physically this is

equivalent to concluding that the pressure in the fluid is along

the lines of force, and thus a series of surfaces exists which cuts

the lines of force at right angles. If the forces belong to
a conservative system, say when a gravitational mass has

attained a state of internal equilibrium, as in the theory of the

figures of the heavenly bodies, no factor is required to render

the differential complete, and we may put

Xdx-i-Ydy-+-Zdz= -dV

(68)

or by (67)

= d^3 -QdV.

(69)

This expression shows that the pressure p is constant over

the equipotential surfaces,
= Q -dp/dV

(70)

and the density also is a function of the potential V. This condition arises when the density of the body is uniform,

over the equipotential surfaces, for the distribution of force

:

:

5044

84

— to which the components {F, Q, R) belong

corresponding

to a homogeneous elastic solid, or a mass of incompressible

liquid held in a rigid vessel, with the density so distributed

as to 'be in equilibrium. The second equation of (67) is

satisfied by this condition, and we have,
= AXJAx+AYldy+dZldz \/^W

(71)

Accordingly by (42) we have the original equation of an

elastic solid

+? «) V-^+V^ff'= o

(72)

^ — which is satisfied by the assumption d

lV/{m-i-n).

The Aether as an Infinite Elastic Solid.

Hence if this analysis applies to the aether, as an infinite elastic solid,, the density of the medium must be arranged so as to give a potential augmenting about each
mass of' matter embedded in it, as shown in my Dynamical
Theory of Globular Clusters, 19 12. This latter condition of
the potential is described analytically as follows

^///, ^ T Q dx dv dz T/[(;c-;c')^-t-(j'-j'r+(^p?]

f'dm , ,
j ^"^

and the inference, from Dynamical Theory, that the potential

is greater towards the centres of matter, finds obvious physical

illustration in the accumulated arrangement of globular clusters,

with the starlight increasing in brightness till it attains a

perfect blaze near the centre, in such splendid globular clusters
as 47 Tucani and w Centauri.
This increase in potential towards the centres occupied

by matter can only be attributed to centripetal stresses in the aether: the medium is thus filled with waves receding from these masses, and the density in the agitated medium is inversely as the wave amplitude or directly as the radius (cf Electrod. Wave-Theory of Phys. Fore. 1. 134, 157-8, 1917).

Since the dilatation
= d da/dx-hd/S/dj-hdy/dz

(74)

is required to fulfil the equation
VHd-V) = a*)

(7S)

F where

is the potential, we see at once that the dilatation

throughout the aether is similar to the potential. The potential

is merely an expression for the total accumulated stress based

= A on average amplitude of the waves,

kjr, and the density

/= = a=vr, and the attractive force

P/r^ i^ V/dr^ —Mjr^-

This proves the Electrod. Wave-Theory of Phys. Fore, to

represent the true order of nature.
Accordingly, we have the following table for the dis-

placement or wave amplitude, density, potential and force:

Displacement or amplitude A

= Density of the aether a vr,

= ^ Potential

V Mjr

V==8=A.

k/r /--
i/k :dV/dr=-M/r

Since the direction of the force always is central, and the waves react .towards the origin at the centre of gravity, we conclude from this whole investigation:

I. That the aether behaves as an infinite aeolotropic elastic solid, with displacements everywhere identical with the electrodynamic wave amplitude d and also identical with

the potential V. This gives a geometrical and physical sig-

nificance to

the

potential,

which

hitherto has been entirely .

lacking, and long proved bewildering to the geometer and

the natural philosopher.

2. If this were not true, the general equations for an infinite elastic solid could not have been integrated by Lord Kelvin as outlined above (cf. Cambridge and Dublin Mathematical Journal, 1848). But as this celebrated geometer effected such an integration for the general equations ' of an infinite isotropic elastic solid, without giving a physical inter-
pretation to the solution found, we see that Lord Kelvin'i mathematical genius builded better than he knew, and natural

philosophers are now enabled for the first time to interpret
physically one of the sublimest results in the whole range

of mathematical science.

Newton surmised that if the density of the aether varied

directly as the distance from the centre, it would press towards the centre so as to develop the force of gravitation. Maxwell holds that Newton conceived this action as analogous to

A = hydrostatic pressure, but we have shown that the reaction of

the waves with amplitudes

kjr produces this arrangemeiiit

of density and would generate an effect similar to mere

hydrostatic pressure (cf Electrod. Wave-Theory of Phys. Fore.,

I-I34, 1917)-

Why the Forces between the Sun and Planets
Operate in Right Lines: Weierstrassian Theory of the Resulting Least Action.

«) Imagine, waves propagated from the sun and earth
as shown in the accompanying diagram: and lePthe velocities
of the mutually interpenetrating waves from the centres ^
E and be V^ and V^.

Fig. 4.

Illustration of the interpenetration of waves between the sun and
earth, which gives maximum tension along the line SE, where
the interpenetration is with double the velocity of light.

The problem arises as to the effect of the relative inter-

penetration of the waves, the velocities V-^ and V^ being

equal, but the amplitude and direction of propagation different'^

at every point of space.

r

= *) By referring to fig. I, section 2, we see the physical meaning of this equation: the aether has dilatation, ^

V, near, the sun,

owing td the increasing amplitude of the waves. This dilatation and decreased density of the medium exists about every star and planet.

:

.

5044

86

/S) It is obvious that between the bodies in the right

line S£, we shall have for the relative velocity of the wave

interpenetration

= S}. ^: y^-^ y^

2V

(76)

But on either side of the line SjE the value of Hi will be less than in that line, where iil becomes a maximum, double the velocity of light. For the two radii vectores q^ and q, meet at an angle /, and the relative velocity of the interpenetration in general will be

i2>= F1+F2COS/.

(77)

;') It is only between the bodies in the line S-E that
cos/= I, and the velocity of the relative interpenetration

/^. = is a maximum. When the radii vectores meet at right angles,

the angle

90°, and cos/= o, so that i3;

V^, only,

or V2 only, as the case may be. If the angle / exceeds qo°,

the addition in (77) becomes negative, and the value of Hi
is less than V^, or V^ separately. And when cos/= 180°,

the addition gives O- =: Vi— V^ ^^ o .

(78)

d) From this reasoning it follows .that:

i) If the medium contracts owing to the mutual interpene-

tration of waves, the contraction will be a maximum in

SE the right line

where i2,- is a maximum.

1= b) The contraction will be zero when

180°, and thus

the tension in the medium is wholly between the bodies,

or on' either side of the line connecting them. It is zero

5£ in the line

prolonged, but as the waves here superpose,,

the pressure or stress will increase externally.

e) This accords with experience in gravitational, mag-

netic, and electrodynamic forces, etc. And.^as. the theoryof

least

action

is

recognized

to

hold

generally

in

nature, this ,

geometrical plan of the contraction of the medium, under

mutual wave interpenetration, must be held to conform to

the rigorous criterion of least action or maximum wave inter-;

penetration. This function attains the maximum with least

action

of

the

forces

thereby

developed ;

and according to the

geometrical methods of Weierstrass, this points to a rigorous

mathematical law.

f) It is not accidental that the mutual wave inter-

penetration should be a maximum between the bodies, in the

SE \\n& SE, a minimum in the line

prolonged. For as the

aether is under an elastic power of 698321600000 times

greater than that of air in proportion to its density, the
medium will always contract to the maximum extent possible,

and thus pull in the right line connecting the' two bodies SE.

Hence if the postulated waves exist, the waves superposed

being accumulated with the mass, they will fully explain the

stupendous gravitational forces which govern the motions of

the planets.

ri) That the waves exist is obvious from several con-
siderations :
a) Forces can only result from maximum tension in the line SE, and this implies interpenetration of waves ; for
no other cause could produce this effect, whereas waves certainly would do so. b) Waves also make gravitational forces conform to other physical forces, according to the recognized law of con-

servation of energy,
c) When a kriown general cause exists, it must be held to be the true cause, in default of any other known cause.
d) The probability is infinity to one that no cause other
than a true one could fulfill all the geometrical conditions of gravitational forces without resting on the true laws

of nature.

6) As the wave-theory harmonized all gravitational phenomena under the recognized criteria of least action, and without the introduction of any mystical hypothesis, it must, from geometrical and physical laws, be held to represent the
true order of nature.

In closing this first paper it remains to add that the

second paper will deal with, the Fourier solutions of the j;ele-

brated- equation oi Poisson (Traite de Mdcanique, 2.697, 1833).

= d^ (DlAf a- V'®

O [x, y, z, t)

® where

is a scalar quantity, and a Ihe velocity of wave

propagation. This applies to wave motion in normal gases,

the aether, and an elastic solid. As the aether is a gas, but

under such elastic forces, that it behaves as an elastic solid

for quick acting forces, and is of infinite extent, while on

the other hand Lord Kelvin's, integration of the general equa-

tions of an infinite elastic solid likewise confirms this con-'

elusion, the deductions thus brought out will establish the

wave-theory with the required geometrical rigor. The out-

standing motion of the perihelion of Mercury, and of the

lunar perigee, together with the lunar fluctuations, under the

Newtonian law, as generalized by Weber in 1846,; will har-

monize every known celestial phenomena without the intro-

duction of any mystical hypothesis.

In the third and fourth papers I hope to give a simplified view of certain outstanding electrical problems and of Michelson and Lodger's experiments, and throw a very unexpected, but searching light on the nature of molecular forces. Thus the several fields covered will lead us to apply the wave-theory to such varied phenomena of nature, that it may not be without interest to both the geometer and the

natural philosopher.
I am indebted to Mr. W. S. Trankle, for efficient aid
in completing these researches.

Starlight on Loutre, Montgomery City, Missouri 19^0 Jan. 14.

T. y. y. ^if^.

Am Zusatz.

25. April sandte Herr Prof. See telegraphisch folgende Nachricht: »Have discovered from wave

theory new method for determining density of aether, only advance since Lord Kelvin's method 1854. Now find density

472X10^-'^ against 438X10"^^ by Kelvin's, method. See.'-'-

•

Abdruck aus den Asir. Nachr. Nr. 5048

— (Band 211.

Juni 1Q20.)

I. Gravitational Action propagated with the Velocity of Light.
In the first paper on the New Theory of .the Aether,
AN 5044, we have showii that the existence of this medium
is a necessary condition for conveying physical action from one body to another across the celestial spaces, and have given the elements of the kinetic theory of the aether -gas as the subtile vehicle of energy. Maxwell had a very clear
conception- of this medium 47 years ago, when he pointed
out, in the closing paragraph of the celebrated Treatise on Electricity and Magnetism, 1873, vol.11, p. 493, that * whenever energy is transmitted from one body to another in time there
must be a medium or substance in which the energy exists after it leaves one body and before it reaches the other«.
No better description can be given of the aether, as the vehicle of energy, than that just quoted.. And since
Maxivell says that the energy must exist in the medium, after it has left one bo.dy, but before it has reached the other, owing to the propagation in time, we see that this energy obviously must be conveyed through the agency of waves travelling with the velocity of light, just as radiant heat from the sun and electrodynamic action travel with the same velocity, 300000 kms per second.

From the celebrated letter oi Gauss \o Weber, March 19, 1845, [.Gauss, Werke 5-629) we learn that as early as 1835 Gaztss looked upon physical action across space as conveyed

^in time, and was trying to formulate a law of this action,

but put it aside temporarily, .and only recurred to it when

Weber had formulated his fundamental electrodynamical law,

published in 1846:

= + /

[mm'lr'^) { r -(i^^) (dr/d/)- (2;-/^2) dV/d^^} ^

(j)

The first term of this formula is Newton's law of gravitation,

1686, whilst the other terms take account of the effects of
m induction in the relative motion of the two bodies and m'.
The minor terms thus give the energy effects of the velocity

and acceleration or change of velocity, under wave action,

in the direction of the radius vector, as required by the

present author's Electrodynamic Wave-Theory of Phys. Fore,

vol. I, 1917.

In the work here cited (p. 143-149) I have calculated

the eff'ects of Weber's law upon the progressive movement of

the perihelia, periplaneta, and periastra of the best known

bodies of the solar system and of the sidereal universe. The

6^ tabulated

is the progression of the orbital perihelia in

a Julian century, owing to the propagation of gravitation

with the velocity of light.

Progression of Perihelia in a Julian Century, Weber's Law.

Planets
Mercury

i4"Sii

Satellites
V Jupiter:

4*233655

Venus

2.9125

I

1. 8212385

The Earth

1.2964

II

1-14345°

Mars

0.45619

III

0-715544

Jupiter

0.02 104

IV

0.40508

Saturn

0.0046 13

VI

0.068685

Uranus

0.00080395

VII

0.064658

Neptune
Satellites

0.00026 I 5

VIII
IX

0.034681 0.034128

The iSIoon (Earth) 0.00637

Saturn : Mimas

1.2403

Phobos (Mars)

o,.o2 65 I

Enceladus 0.966394

Deimos »

0.0 1 1098

Tethys 0.78066

Ariel (Uranus)

0.18439

Dione

Umbriel »'
Titariia »

0-13 23 s 0.080504

Oberon - »

0.060339

:

:

«

139

5048

140

above effect of Weber's law removes i4"5 of the total amount^),

leaving outstanding about 2%"i instead of the 43" assumed in Einstein's, Theory of Relativity. The outstanding 2 8"5 can be explained by the transformation and absorption of wave energy from the atoms on the opposite side of the sun,

yielding a law of attraction of the very form approved by Newton in the Principia, 1687:

/ == ;;i,„'/^20000001046 _

(2)

This explanation of the motion of Mercury's perihelion is more fully discussed below. Such a result was long ago

anticipated by Newton, and in 1894 carefully examined and proposed by ffall, and subsequently used by Newcomb and^

Seeliger. It therefore has the sanction of the most eminent
astronomers, and as it rests upon a known physical cause, it

involves no vague and chimerical reasoning such as underlies

Einstein's mystical Theory of Relativity.

Towards the end of this paper, we develop a new view

of the experiments of Michelson and Morley, 1887, and of

Sir Oliver Lodge, 1891-97, which results from the kinetic

theory of the aether, originally outlined by Newton, 1721, approved \yY Maxwell &r\AS. Tolver Preston, 1877, and recently developed by the present writer, as shown in the first paper.

This new view of the chief physical experiments on which the theory of relativity so largely rests may well claim the attention of natural philosophers. As bearing on the same

question we treat carefully of the outstanding rnotions of the perihelion of Mercury and of the lunar perigee; and show that neither phenomena lends the slightest support to non-

Newtonian mechanics.

In fact, although the theory of relativity has occupied
much space in scientific literature, and many treatises, memoirs,

and other papers have appeared on the subject, it is impossible

for a careful observer to escape the conviction that the whole

development heretofore brought out is false and misleading,
— — a veritable foundation laid on quicksand and that some

day philosophers will wonder that such an improvised ab-
surdity ever became current among men. Among the most

pernicious of these temporary doctrines is FitzGerald's hypo-

thesis, which under the kinetic theory of the aether is wholly

untenable.
A considerable number of persons are much impressed

.with the admissibility of any doctrine which becomes current among contemporaries, yet. the study of the history of science shows that truth is neither dependent upon popularity, nor discovered by majorities, but by the few individuals who think carefully and frequently in complete isolation, and who thus

attain superior vision into the deeper mysteries of nature. In promulgating his new System of the World, 1543,
Copernicus describes his reasoning in daring to depart from

the opinion of the majority:
»Though I know«, he says, »that the thoughts of a

philosopher do not depend on the judgment of the many,

his study being to seek out truth in all things as far as that
is permitted by God to human reason: yet when I considered*.

he adds, »how absurd my doctrine would appear, I long hesitated whether I should publish my book, or whether it
were not better to follow the example of the Pythagoreans
and others, who delivered their doctrines only by tradition

and to friends*.

2. The Effect of Resistance is to break up Long

Waves into Shorter Ones and actually to increase the

Amplitude of the Principal Cotnponent, as noticed

in Breakers at the Sea Shore.

In his celebrated work on Tides and Waves, Ency-

clopedia Metropolitana, 1845, Sir George Airy obtained one

of the most comprehensive and useful theories of wave motion

ever developed. Airy's theory has the advantage of being

intensely practical, because it applies to wave motion in a canal,

water being the chief liquid found upon the earth, and nearly

incompressible. The formula for the periodic time of the

^ waves is ^,

(2^;^/^) (^4"-^/^+ i)/(^4'i^A_ i) .

(3)

It may be shown analytically that when the wave length is shortened, as by resistance to the movement of the fluid,

the exponential expression ^4'^'^' increases, and thus the amplitude increases^). This change has been much discussed in various treatises and memoirs, and we shall not attempt to add to it here, except in the practical application of the

result to physical problems.
Now Airy finds (art. 201-2 10). the following theoretical
curves for the breaking up of water waves in rivers, considered as straight canals, with smooth banks. After explaining his

analysis of these theoretical waves in water. Airy interprets

the results as follows

»(2oi). To represent to the eye the form of the wave produced by the combination of the two terms, we have constructed the curve in figure q. The horizontal line represents the level line of the mean height of water: the elevation

or depression of the curve represents (on an enormously exaggerated scale) the elevation or depression above the mean
height, given by the expression above. The value of x' is
supposed to increase from the left to the right : on which supposition the quantity mvt—mx', representing the phase of the wave, diminishes from the left to the right [fnvt being

constant).*
»(202.) To exhibit to the eye the law of the ascent
and descent of the surface of the water at different points
of the canal, the figures 10, 11, 12, and 13 are constructed. The first of these is intended for the point where the canal communicates with the sea : the others for points successively more and more distant from the sea. The horizontal line
— is used as a measure of time, or rather of phase mvt mx':
in which, for each station, x' is constant: the elevation or depression of the corresponding point of the curve represents the corresponding elevation or depression of the water above
its mean height, as given by the expression above. »An inspection of these diagrams will suggest the,
following remarks

— ') In the Monthly Notices for April, 1917, p. 504, Dr. Silberstein treats at some length of the Einstein calculations, based on Gerber's
formula (Zeitschr. Math. Phys. 43.93-104, 1898) in which for the Newtonian potential Mir is put Jflr{i i/c-drldtY, and concludes: "As far as T can understand from fefrey's investigation, (MN 77.1 12- 11 8), it would rather alleviate the astronomer's difficulties if the sun by itself gave
only a part of these 43 seconds." Accordingly this is all the more reason for adopting Weber's law, though I reached it from a different point of view. *) This increase of amplitude will prove of high importance in the new theory of molecular forces, to be dealt with in a future paper.

«

141

5048

142

9. -13.
14. 15.

Airy's graphical illustration of the breaking up of waves under resistance. The canals considered are connected with the sea and of uniform width.

= Theoretical form of tide-wave in a shallow river, to second approximation, mx

= ^ ^ ^ mx

471

second station, mx

8t

third station.

o, first station, the sea;

= ^ Theoretical tidal curves for different stations on the river. lo

= ^ 12

third, 13

fourth station.

first station at mouth of river, 11

second,

Theoretical form of tide- wave in a shallow river to third approximation with large tide. The same with small tide.

»(2 03.) When the wave leaves the open sea, its front
slope and its rear slope are equal in leligth, and similar in form. But as it advances in the canal, its front slope becomes short and steep, and its rear slope becomes long and gentle. In advancing still further, this remarkable change takes place in the rear slope : it is not so steep in the middle as in the upper and the lower parts: at length it becomes horizontal at the middle : and, finally, slopes the opposite way, forming in fact two waves (figure g).*
»(204.) At the station near the sea (see figure 10), the time occupied by the rise of the water is equal to the time occupied by the descent: at a station more removed from the sea (figure 11) the rise occupies a shorter time than the descent: the rise is steady and rapid throughout, but the descent begins rapid, then becomes more gentle, then becomes rapid again: at stations still farther from the sea (figures 12 and 13) the descent, after having begun rapid, is absolutely checked, or is even changed for a rise, to ^hich another rapid descent succeeds : in this case there will be at that station two unequal tides corresponding to one tide at the mouth of the canal.
This numerical and practical discussion by Airy, with curves for illustrating the results is more satisfactory than any purely theoretical analysis of the effects of resistance, and thus all we need to do is to point out, that, just as water waves in canals degenerate and break up into partial waves, under the action of a variable resistance, depending on the depth of the water, and its distance up the river from the sea : so also in the aether, the long waves encounter resistance which progressively is more and more disintegrating on their existence, kinetic stability, and continuity. Ac-
cordingly we may be sure that long waves in the aether
will undergo corresponding changes by disintegration into shorter waves, and that the chief component will have increased amplitude.
There are various physical illustrations of this effect
which may be cited, as when the sun's radiation impinges on the earth, and the longer invisible infra-red rays, so much
studied hy Langky, pass into heat waves of shorter wave length.

Again, in our electric stoves and heaters, the electric current, made up of very long waves, first develops heat, so that the resisting wire acquires a dull glow, then a red heat, and finally becomes incandescent, with light of shorter and shorter wave length the longer the action continues. The transition here sketched is therefore known to be a reality in dealing with the transformation of electric energy into heat and light, under conditions observed daily 'in every part
of the world.
The analogies here cited are so obvious and familiar to us in the changes noticed when waves pass into breakers at the sea shore, that it seems impossible to deny the validity of the conclusion above drawn from every day experience, and fortified by the profound researches on tides and waves produced by one of the greatest mathematicians and natural
philosophers of the past age.
To those who hesitate at the contrast between water and aether, we point out that it is true that water is heavy
and inert, and sluggish in its movements, whereas the aether is excessively rare, with density at the earth's mean distance equal to 438X10"^*, and having an enormous elastic power, 68g 321 600000 times greater than that of our air in proportion to its density. Thus the light and electric waves in the aether travel 902000 times faster than sound waves in the air, and about 200000 times faster than sound in water at 30° C, which travels 4.54 times faster than in air, owing to the high incompressibility of the water.
There is thus tnuch diff'erence between the speed of waves in the aether and in water, even if the dense water, like the rare aether, be highly incompressible. But notwithstanding this difference, due chiefly to the extreme rarity of the aether, water being in comparison, with aether 2 2 8Xio-'-^ times denser, there is a substantial physical basis for comparison of the actions in the two media.
Our reasoning therefore is not speculative or hypothetical, but purely practical, since it rests upon facts definitely determined by experience, anH verified by careful observations of recognized phenomena of the physical universe.

:

s

:

143

5048

144

In order to bring out the practical bearing of the wave-

theory upon the motion of the perihelion of Mercury, and

the lunar fluctuations, discussed below, we notice that as long

ago as 1901, Professor Planck of Berlin supposed that in all

matter there were a great number of »resonators« of every

possible period (Ann. d. Physik, 4.556, 1901). Thus matter would receive and emit vibrations of all possible periods, as

postulated in the Electr. Wave-Theory of Phys. Fore. 1.85-88,

9 1

7 1

.

The lunar fluctuations occur where the sun's gravita-

tional waves have to traverse the solid mass of the earth,

and thus the action on the moon is decreased near the time

of lunar eclipses; and the moon partially released from the

sun's control, thus tends to fly the tangent. This gives rise
to disturbances in the mean motion which Neivcomb declared to be the most enigmatical phenomenon presented by the

celestial motions.

Now the lunar theorists were unable to find the perio-

dicities required to explain the lunar fluctuations, until I
discovered the obstructing cause at work, near the shadow of the earth, to modify the sun's gravitative action on the moon.

If this explanation of the fluctuations of the moon be

conceded, a similar cause will have to be admitted to act on the planet Mercury, which renders our sun gravitationally

unsymmetrical or lopsided, as if a small part of the matter on the opposite side of the sun were removed, or ineffective, owing to the interposition of the sun's huge globe in the

path of gravitational action. In other words, owing to re-

fraction, dispersion, absorption, large masses of matter exercise

a slight screening effect.

Jl

Fig. 2.

Illustrating the absorption and circular refraction of some of the waves from part of the matter in the side of. the sun opposite to Mercury, as if parts of the Sun's niass had been removed, and the globe thus rendered slightly lopsided. Compare also Fig. 3, in section 5 below.

Mercury therefore is less attracted than if the strict

law of inverse squares established by Newton held, and thus

we have the feebler law of force explained below:

/ = =3 ,„,„'/^2.ooooooio4.i

i/^o.ooooooioiej [nim'lr'') (

(^^

whence arises the hitherto unexplained progression of Mer-

cury's perihelion, by 28''44 per century, which has proved so bewildering to geoiiieters and astronomers ever since Leverrier

discovered the difference in 1859.

This explanation is very much simpler than any heretofore offered, and as it harmonizes the motion of Mercury

with the motion of the moon, under well established physical laws, without introducing any vague and chimerical hypotheses, it would seem difficult to deny its essential physical truth.

3. Explanation of the outstanding Motion of the Perihelion of Mercury, based on the Electrodynamic Wave-Th"eory of Physical Forces.
Aside from the investigation of the amount of the outstanding motion of Mercury's perihelion, by Leveiricr, 1859, and by Newcomb, 188 1, duly noted below, we cite the following researches as offering various explanations of the phenomenon :
1. Untersuchungen iiber die Bewegung des Planeten Merkur, and other notices of researches by Dr. Jl Bauschinger,
AN 109.32.
2. tJber die Bewegung des Merkurperihels, by P. Harzer,
AN 127.81, 1891. Harzer investigates the effects of unequal
moments of inertia of the sun about polar and equatorial axes, and of the matter in the corona, and finds these hypotheses
admissible.
3. A Suggestion in the Theory of Mercury, by A. Hall,
AJ 14.49, 1894. Hall adopts the suggestion oi Newton that the law is not exactly that of the inverse squares, and puts
/=;„;,//^2.00000016^
(5)
4. Hypothesis, that gravitation towards the sun is not exactly as the inverse square of the distance, Astronomical
Constants, p. ii8, by S. Newcomb, 1895. Newcomb adopts
Hall's, hypothesis, with very slight modification

/=,«^2'/r2<'000001574,

(g)

5. Uber die empirischen Glieder in der Theorie der Bewegung der Planeten Merkur, Venus, Erde und Mars. VJS 41.234-240, by H. Seeliger.
Das Zodiakallicht und die empirischen Glieder in der Bewegung der inneren Planeten. Sitz.-Ber. d. Kgl. Akad. d. Wiss. zu Miinchen, 36.595-622, by H. Seeliger.

Seeliger

assumes the .

matter

of the zodiacal

light

to be

distributed in two ellipsoids, an outer one and an inner one,

which will effect Mercury's perihelion, as observed, without

disturbing the other planets. He gets a very perfect agreement

with observations, fully as good as that supplied by Einstein fi

theory, without the vagueness of relativity. Seeliger'?, chief

results are

Seeliger'

= Mercury e dn = sinzdft = d/

-i-8"64 H-o.6i -1-0.38

Seeliger'i theory applies equally well to Venus, the Earth and Mars.

6. A Memoir on the outstanding anomalies of the
celestial motions, by Professor E. W. Brown, Amer. Journ. of Science, 29, in which various hypotheses, including the effects of the magnetic fields of the earth, sun and moon, are examined and rejected. See also Report of British Association for 19 14, for Prof. Brown's Address to Section A, p. 31 1-32 1.
7. Einstein's General Theory of Relativity, 1916, in which this author uses the value (JcT =: -1-43", and deduces the term of Gerber'% formula:

V=[Mlr)[i-xlc-ArlAt)-'-

(7)

required to be added to the law of gravitation to make this

= difference between theory and observation disappear. By using

the value 6^

+43" per century, and deducing a very

exact agreement based on this difference, instead of the

«

:

:

145

5048

146

difference 28*44, which results from Weber's, law, Einstein adds to the improbability of his theorj'.
It has long been remarked that among the outstanding
motions of the solar system recognized by astronomers during the past sixty years, and of which geometers have sought a valid explanation, none is more justly celebrated than the excessive/progression of the perihelion of Mercury, announced
bv Leverrier to the Paris Academy of Sciences, Sept. 12, 1859, (CR 49.379)-
Leverrier' s, announcement of an outstanding motion of 38" per century in Mercury's perihelion seemed to find almost immediate confirmation in Dr. Lescarbaulfs supposed observation of an intra-mercurial planet named Vulcan; and this anomaly therefore was made the basis for the provisional elements assigned to the new planet.
If on the one hand later observational researches, during many total solar ecHpses, have shown no signs of an intramercurial planet, it may be noticed, on the other, that the
fullest confirmation of Leverrier's analysis of the planetary motions, 1859, has been obtained by later investigators,
especially by Newcomb, who used all the observations of the transit of Mercury from 1677 to 1881, and deduced an outstanding motion in excess of that found by Leverrier, namely about 43" per century. (Astron. Pap. of the Amer.
Ephem.,' 1.367-484, 1881.) Accordingly, Leverrier spoke conservatively in the
original announcement of his discovery, when he said »The necessity of an increase iri the secular motion
of the perihelion of Mercury results exclusively from the transits of the planet over the disc of the sun. The exactitude of these observations is beyond doubt.
The anomalous motion of Mercury's perihelion thus established by Leverrier and Xewcomb, has been widely discussed in natural philosophy, and in fact combined with the Michehon- Morley experiment of 1887, for laying the foundation of a Theory of Relativity, on which already many
treatises have appeared, without, however, thus constituting
a simple and consistent physical doctrine which commands
universal assent.
There are, I think, grave reasons for doubting the whole Theory of Relativity, as now developed, on grounds which will be more fully outlined in treating of the Michehon- Morley experiment. For the present it must suffice to allude to the unsatisfactory theory resulting from Leverrier^ discovery of an outstanding motion in Mercury's perihelion, and the growth in natural philosophy of a doctrine which many regard as both vague and chimerical.
In 1894, Prof Asaph Hall of Washington outlined a new view of the anomalous motion of Mercury's perihelion (at 14.49), based on the hypothesis that for some unknown reason the Newtonian law of the inverse squares might not be strictly correct.
Already in 1686, while preparing the Principia, (Lib. I, sect. IX), Sir Isaac Newton had considered such a possible modification of the law of attraction; and even included some computations, in which he assumes that the central force departs a little from the inverse square of the distances.
Newton found that the perihelia would move forward under such a modification of the law of attraction (Lib. I,

sect. IX, Prop. XLV, Prop. XXXI, cor. I), but considered the

observed approximate fixity of the planetary perihelia a strong

proof of the accuracy of the law of the inverse squares. His

final view evidently is expressed in the General Scholium to

the Principia, 17 13, where he says that in receding from the

sun gravitation » decreases accurately in the duplicate pro-

portion of the distances as far as the orb of Saturn, as

evidently appears from the quiescence of the aphelia of the

planets; nay, and even to the remotest aphelia of the comets,

if these aphelia also are quiescent*.

In the Mecanique Celeste, 1799, Laplace likewise con-

cluded that the law of gravitation holds accurately for the

satellites as well as for the planets, (Liv. II, ch. I, § 6). In
Liv. XVI, chap. IV, however, Laplace investigated more fully

the effect on certain terms of the flioon's motion of some

assumed changes in the Newtonian law of attraction, but

from his remarks it is evident' that he did not consider it

probable that there is a departure from the strict law of the

inverse squares.

Thus, up to the time of Leverrier''!, researches on the

motion of Mercury, 1859, there were no well established deviations from the Newtonian law which might be made

the basis of observational inquiry, so as to serve as a crucial

test of the accuracy of that law.

In his paper of 1894, however. Professor Asaph Hall

sagaciously remarks

»If the Newtonian law of attraction is not a rigorous law

of nature, or if it is modified slightly under certain conditions,
probably this lack of rigor would become apparent first among

the swiftly moving bodies of our solar system, such as our

moon and the planet Mercury* (AJ 14.49). Our moon indeed does not move so swiftly, but owing

to its great proximity to the earth and the eclipse records'

extending over nearly 3000 years, the motion is very ac-

— curately known,

both by observation and by theoretical

— research and calculation,

so that the smallest disturbances

may become sensible to observation (cf. Electr. Wave-Theory

of Phys. Fore, 1. 113, 1917), which doubtless is the chief point Prof Hall had in view.

That Leverrier'% researches on the motion of Mercury,

1859, set in motion several hew lines of inquiry of great theoretical importance is shown by two investigations de-

veloped within the next fifteen years.

1. The researches of Tisserand on the motion of a

planet under fF^^^r's electrodynamic law, communicated to

the Paris Academy of Sciences, Sept. 30, 1872, by the eminent geometer Bertrand, who had inspired these investigations.

2. The problem proposed in 1873 by Bertrand to the

Paris Academy of Sciences, (CR 84), to find the closed curve

R = O described by a planet when the forces have the form of an

unknown function

{x,y) of two independent variables

X and y, and the differential equations of motion are

= = - m-A^-xJAt'

-Ji-xjr m-A'^ylAt"^

R-yjr (8)

R it being required to find the function

whatever be the

initial values of the coordinates x^, y^, and of the components

of the velocity

= x^' =- (d^/d/)o ' j'o'

(dj)'/d/)o .

(9)

The solution of this problem showed that this function

:

«

.

:

:

:

147

5048

148

R ^ always takes the form

m r", where m is the mass of

the planet, and r the radius vector.

It was Bertrand's theoretical improvement in the treatment of Newton's problem of a moving perihelion which led

to Hall's hypothesis of 1894, for explaining the excess in

the motion of the periheHon of Mercury. Since Hall's hypo-

thesis has been further developed by the writer's recent

researches in the Electr. Wave -Theory of Phys. Fore, it is

necessary to treat bf these successive steps for attaining an

Electrodynamic Theory of the motion of Mercury's perihelion.

(i). Bertrand' s so\n\.\on oi Newton's "pxdhltm of finding

the central force for a moving perihelion. As propoS)ed to the Academy of Sciences, in 1873, Bertrand's prdble.xn reads (CR 77)
»We consider a planet attracted by the sun under a

force of which the intensity depends only on the distance.
We suppose known this one fact: that the planet describes

a closed curve, whatever be the magnitude and direction of

We its velocity.

"have to find the law of attraction from this

single datum.

Bertrand remarks that as the force is central, the motion takes place in a plane through the centre of the sun, and

Kepler's law of equal areas in equal times holds true. If

^ the force have the form

^^ ffir"

(10)

it is found that there result just two formulae

i?2 =^ '"/''^
Rx= mr

(11) (12)

And these are the only two laws of attraction which permit

a planet to describe a closed curve, whatever be the initial

data (the velocity being nevertheless below a certain limit).

And if we suppose the attraction zero at an infinite distance,

there remains only one formula (11), or the law oi Newton,

which could thus be deduced from the sole fact of obser-

vation : that any planet whatever describes a closed curve,

without our being able to know the nature of this curve

(cf. Tisserand's Mecanique Celeste, 1. 48, 1889).

Resuming Newtoris problem of a moving perihelion,
© Bertrand derives a perfectly general formula 'for the arc

swept over by the planetary radius vector between the mini-
mum value ifx) and the maximum value (^2)
0= [7r/l/(«-H3)]x

[l+V24(«-l)(«+2)[('-2-n)/(^2+'-l)

(13)

— He remarks that when r^ r^ tends towards zero, we

have in the limit the Theorem of Newton, 1686:

= Lim©

7r/"l/(«-i-3)

(14)

which applies to an orbit almost circular described by a

planet under the influence of a central force proportional to

a power of the distance.

If for the motion of a planet around the sun, we take

n= — R = with Newton,

2,

mjr^, the relation (14) gives

Q = n, which is rigorous. Thus it only remains to find

— what will happen when we modify slightly the exponent 2

= — in the Newtonian law of gravitation. If, for example, we supposed n

2.001, it follows

that we should have:

lim

^ == jtj V[i —0.00 1 )

n (i-f- Y2°-°°i -<-•••)
180" 24"

s'

USJ

or a progression of the apsis line at each revolution of 10 48 ,

which is so large a quantity as to be totally inconsistent with

observation. Without further examination of the effects of

changing the exponent in Newton's law (cf. Principia, Lib. I,

Prop. XLV), we recognize that the change in the exponent

must be extremely small. This case has been considered by

Prof. Asaph Hall, who has applied the hypothesis to the

motions of the planets and of our moon.

f ^ (2) Hall's hypothesis of 1894, that the law of attrac-

tion may he =^ mm'lr'^'^'' , where j'

0.00000016. In

— A.J. No. 319, June 3, 1894, Prof. Asaph Hall remarks that
on applying Bertrand's formula to the case of Mercury

with Newcomb's value of the outstanding motion of the peri-

— heHon, or 43" per century

he finds that the perihelion

would move as the observations indicate by taking
«= — 2.00000016

(16)

the difference of the expo"hent from the law of Newton being

= V 0.00000016.

'

The change in the law of attraction required for pro-

ducing this progression of the line of apsides is therefore
very minute. If we use Weber's law, as in the author's Elect.

Wave-Theory of Phys. Fore, and Newcomb's value of the out-

= standing motion of Mercury's perihelion (Astr. Pap. of the
Amer. Ephem. 1. 473); namely, dc7 42^95, we shall obtain an outstanding motion of 2 8''44 per century, which is to be

accounted for by modification of the exponent in the law

of attraction.
(3) Law of attraction indicated by the outstanding motion of Mercury's perihelion. As the motion of Mercury's

perihelion offers the principal difficulty in modern celestial

mechanics, we take the law of attraction to have the form

f=mm'lr^+'

= [fJe^loo

+28^44

(i?)

and determine v by the condition that the outstanding cen-

tennial motion of the perihelion shall be -H 28^44. If the perihelion shifts 28"44 in 100 years, it will shift
0^2844 in one year; and as there are 4.1521 revolutions

of this planet in a year, the shift will be o;'o684956 in a

single revolution, and therefore, ©"0342 47 8 in a half re-

volution of Mercury.

By Bertrand's formula (13) above, we notice that when

the orbit is considerably eccentric, as in the case of the planet

Mercury, the term depending on [{r2---ri)j[r2-^r-i)Y == e'^

becomes sensible. In fact in this formula depends on the

products of two series as follows
= n/V{n-i-^)x

+ {i+V24(«-i)(« 2)[(r2-ri)/(r2+ri)]2H
= Tt/V(i-v)-{i-h^/2i(3-^v)ve^-\

}

}

=^ n{i+y,p+%v'+- }{i-^y^ve^+^/,,v'e'} (18)

= + 7r{ 1+^(1/2 V8^^)-

(19)

Accordingly, our equation of condition is:

+ [l+»^(V2 V8^^)+---}
= 180° o' 0^0342478 =^ 648000^0342478.

(20)

As the coefficient of the term involving p in the case
+ of Mercury becomes (V2 V8f^) =0.5052839, we find from

(20) by calculation that

= v 0.0000001045977

(21)

:

:,

149

5048

ISO

And the modified Newtonian law becomes:
/ = ,;2;«'/^2.0000001046_

,

J^^)

Applying this law of attraction (22) to the eight prin-

cipal planets of the solar system we have the following table

of centennial progressions for their perihelia:

Mercury Venus The Earth Mars

28*44 11. 1341
6.8496 3-6418

Jupiter Saturn
Uranus Neptune

0^577448 0.2325307 0.0815288 0.0415681

The progression of the perihelia here calculated from the modified Newtonian law are not contradicted by any known phenomena. The exact position of the periheHon of Venus is not well defined by observations, owing to the

great circularity of the orbit; and some slight uncertainty

also attaches to the position of the perihelia of the earth
and of Mars.

It will be seen that the change made in the Newtonian

law is exceedingly minute. For the change in the exponent

the ratio is

^Uv -= 1046/20000000060= 1/19120459

(23)

a little less than one nineteen-millionth of the whole. Such

an infinitesimal alteration in the resulting attractive force

would give no sensible effect in a single revolution, but as
the change 6^ accumulates with the.lapse of time, it finally
becomes very sensible, and we are obliged to take account

of the secular progression of the perihelion.

This cumulative effect is very similar to the alteration
in the moon's mean longitude which results from the secular acceleration of the moon's mean motion, first explained by
Laplace in 1787, under forces which are insensible for short intervals, but by continuing for long ages in the same direction, finally become sensible and have to be calculated in
the formation of tables of the moon designed for use over many centuries.

4. The Modification of the Newtonian Law
indicated by the outstanding Difference between the observed and Calculated Motions of the Lunar Perigee.
Just as the motion of Mercury's perihelion is the chief means for. throwing light on the form of the law of attraction for the planets of the solar system, so also the motion of the lunar perigee affords the best criterion for the form of the law of attraction operating on the motion of the satellites.
As the subject has been but little discussed heretofore, we
shall briefly outline the results of astronomical research on this interesting problem.

In the Monthly Notices of the Royal Astronomical Society 74-396, 19 14, Prof. E. W. Brown gives the anriual motion of the lunar perigee depending on the ellipticity of

the earth as follows:

^ {diH/dt)^

-l-6;'4i, for an oblateness of 1:296.3. (24)

He adds that for an oblateness of 1:297, the value would

be reduced by the factor

— (1/297 0.00 1 7 34): (1/296. 3 -0.001734)

(25)

and become:

{da/dt)i =: -i-6:'38 .

(26)

From these data it follows that the annual motion of

= the lunar perigee for an oblateness of i :.2g8.3 would be

(8cT/8/),

-t-6:'32.

(27)

The above values by Brown, as thus reduced to an

oblateness of i : 298.3, are confirmed by the part of the

motion of the lunar perigee depending on the ellipticity of

the earth's figure calculated by Dr. Hill, in his supplement

= io Delaunay's Theory of the Moon's Motion, Astron. Pap. 3.334,

namely:

(8oj/9/),

-h6:'82 .

(28)

This value, however, refers to Hill's oblateness of

I : 287.71, and must be reduced to correspond to the ob-

lateness of I : 298.3; which leads to a result differing only

o'oi from that found by Brown and cited above. Hill's

value for this reduced elHpticity of the earth therefore is

= (8c7/8/),

+6:'33.

(29)

Hence we conclude that this value of the annual per-

turbation of the lunar perigee depending on the eUipticity

of the figure of the earth is very accurately known. The

difference in these two authorities would be only 0^0124

per annum, or i"24 in a century, which is below the limit

of determination in the present state of science.
Prof. E.W.Brown also gives data to show (MN 75.514),
that when the theoretical secular acceleration of the perigee

is determined with the highest accuracy, it is 16" per century

smaller than the observed centennial motion of the perigee.

This is for an ellipticity of the earth of i : 297. By changing

the ellipticity to i : 294 Broivn reduces this value from 16"

to 3'; and by taking an ellipticity of i : 293.7, the outstanding

difference entirely vanishes.

Such a large value of the oblateness, however, seems

to be quite inadmissible; and thus on calculating the excess

in the actual motion of the perigee over the theoretical motion,

for an oblateness of 1:298.3, I'find it to be 2if9, or say

22" per century. If we admit this ellipticity of the earth ^),
— — which is decisively indicated by the four best methods

namely

i) Pendulum observations of gravity, as discussed by Helmert

and the U. S. Coast Survey,

2) Geodetic measurements of arcs on the earth's surface, 3) The lunar inequality in latitude, 4) The fluid-theory of the earth, isostasy and Laplace & law

of density;

then it will follow incontestibly that the moon has an

outstanding motion of its perigee of about 22" per century,

almost exactly one half the outstanding motion observed

in the perihelion of Mercury.

To form a better idea ofthe accuracy heretofore attained

in these calculations, of the centennial motions of the lunar

perigee, we recall the results of Hansen and Brown:

Observed

— O Calculated Diff.

C

Authority

[dn7/d4o= 14643560" 14643404" +I56'^T81'4!';.'"34T''

+ [dsT/d4o= 14643520" 14643504"

,e"^'-'"""'^^fl^^'

, ') In the writer's "Determination of the oblateness of the terrestrial spheroid", begun in 1904, but not yet published, this question las been carefully examined, and the value I : 298.3 shown to be the most probable of the various values heretofore proposed.

151

5048

152

As above pointed out, the difiference of 16° per century

here indicated by J^rown's calculation of the theoretical motion

of the perigee becomes 22" when the elKpticity of the earth

is reduced to i : 298.3.

It is also to be noticed that the observed centennial

motion of the lunar perigee used by Hansen is 40" larger

than that used by Brown. It would seem that very little

doubt could attach to the increased accuracy of Brown's

observed motion, though owing to the fluctuations in the

mean longitude the value 14643520" for the observed cen-

tennial motion of the perigee may yet admit of some im-

provement, if any of the observational equations should prove

to be vitiated by this troublesome cause.

Indeed, it is a little difficult to understand why feo

considerable a difference as 40" per century should exist in

the observed centennial motion of the perigee used by two

such very modern authorities as Hansen and Broivn. For

the position of the perigee is given with considerable accuracy

from the eclipse records of the Greeks, and the calculations

of Hipparchis and Ptolemy; and as about 226 revolutions

of the perigee would occur in 2000 years, the motion of

the perigee ought to be quite accurately fixed by the eclipse

records of the Greek astronomers. The above difference of

40" per century, increasing as the square of the time, in

20 centuries would accumulate to 16000", nearly four and

a half degrees, or about nine times the diameter of the moon.

The difference of 100'' between the above calculated

centennial motions of the perigee is less striking than it

otherwise would appear, but such differences warn us not

to overrate the accuracy attained.

It seems remarkable that the eclipse records of the

Greeks would leave the position of the perigee open to so

much uncertainty. Besides, in the modern observations of the

moon since 1750,- which are quite accurate, an uncertainty

of even 20" per century, or an accumulated difference of

5 7"8, in the interval of 170 years, ought not to exist. Still more intolerable is the difference of iisl'6, based on the

difference of 40" per century! But Hansen was unaware of

the fluctuations in the moon's mean longitude; and as the

fluctuations affect the node as well as the longitude, it may

also have vitiated sensibly his calculation of the observed

centennial motion of the perigee.

It is worthy of notice that Hansen's outstanding diffe-

rence between the observed and calculated centennial motion

— = O of the lunar perigee is

C -(-156"; while Brown's values

— = make this difference O C

+22". The mean of these

— = O two values is C

+89".

Now, in default of definite knowledge it is not quite

safe to assume that Hansen's values are wholly wrong, and

Brown's entirely right, notwithstanding the preeminence of

the latter's exhaustive researches in the lunar theory. Both

investigators may be somewhat in error, for one reason or

another, or for several reasons combined. Thus, apparently the

safest thing is to assume that the truth lies between -Hi 5 6",

as found by Hansen, and -1-22", which results from Brown's
calculations. And as we do not know what weights should

be assigned to these extreme- values, we can only take the

= simple mean of the two outstanding motions of the perigee,

and thus we have: [(807/8/)^]^^

+89".

(30)

It is to be observed also that in our researches on

the outstanding motions of Mercury's perihelion, we found

the exponent of Newton's law should be modified from 2 to

= 2-i->', where x'

0.0000001046.

To calculate the resulting outstanding motion for the

lunar perigee we notice, in the' first place, that the effect of

the time of propagation of gravitation by Weber's law, as

= shown in the table of section I above, is almost insensible,

(3c7

0*00637 per century. Thus we need consider only

the effect of the exponential change for a body having a

mean motion 3.219763 times greater than that of Mercury.

And since the unexplained motion of Mercury's perihelion

is 2 8"44, we get for the corresponding motion of the lunar

perigee
= [(8WH}oo=+28:'44X3.2i9763 +9i-S7. (0--C) (31)

This calculated value is so very near the mean of the

values found by Hansen and Broiun as to appear worthy of

— = O attention. If for example, Hansen's value

C

-+-156"'

0= — were 65" too large, leaving

-+-91", while Brown's

— 0= were as much too small, yielding O

2 2"-t-65"== -f-87",

the two values would be quite reconciled. And since Hansen

and Brown disagree as to the value of the observed centennial

motion of the perigee to the astonishing extent of 40", the

possibility of such unknown errors in their several results is

not to be wholly excluded. Accordingly, for some hitherto unsuspected reason,

Hansen's value of the observed centennial motion

perigee may be substantially correct, namely:

= [(8n7/8/),]oo

-+-14643560".

of the (32)

In this case, it would suffice to assume an error of 18" per century in Brown's calculated motion of the perigee.

Unfortunately Prof. Brown even proposed to adopt an

oblateness of the earth of i : 293.7, as if to avoid a modification of the form of the Newtonian law ^) ; and hence it seems not wholly improbable that an error of 18" per century
in the calculated centennial motion of the perigee may have been introduced, through some step based upon the tacit assumption of the strict rigor of the Newtonian law.
Under the circumstances, since Hansen's value of the outstanding residual in the centennial motion of the perigee apparently was obtained without prejudice, it should not be rejected, till Brown's values are independently tested and found to be not only the more accurate, but also wholly free from possible prejudice due to assumed rigor in the Newtonian law, or other systematic cause which might thus
unexpectedly creep in.

Under the present circumstances, it follows that if the

= outstanding residual in the centennial motion of the perigee

be [(5cj/8^)j]p(,

-)-pi»j7 the exponent of the law of attrac-

tion for the moon would be the same as that for the planet

Mercury, namely: f ^^ jj^jj^'l^i.wowQ\^\&

(

\

= ') In his address to the British Association in Australia, 1914 p. 316, Brown estimates that the exponent in the Newtonian law does

not differ from 2 by a fraction greater than i : 400000000

0.0000000025 ;

but

the

present

discussion

shows

that

this prediction

probably

overrates the accuracy we are justified in claiming, from 10 to 42 times.

:

153

5048

154

In conclusion, it would appear from this investigation
that the change in the exponent for the law of attraction may be the same for the moon and for Mercury. But if future

researches should develop a smaller difference in the observed and calculated centennial motions of the lunar perigee, such

as 2 2" per century, which seems to be the minimnm value now admissible; then there would be a smaller value of v

in the exponent of the modified law of Newton. The value
22' per century leads to a value about one-fourth of that

found for the planet Mercury, as may be seen from the

following considerations.

= The moon makes 1336. 85126 revolutions in a century,

and therefore: i I'/iSSS.Ss 126

o!'oo82283 ig the amount

of this secular progression of the perigee in half a lunation.

The equation of condition;

^ B "= n{\ -i-Ya'^"^ • • • }

JT {1-1-0.0082283/648000}

therefore gives v == 0.000000025396.

(34)

But although there can be no assurance that this modi-

fication of the exponent for the earth would be the same as for

— the sun

the earth being so different in density, size, and

— physical constitution from the sun yet at present apparently

we are not justified in using this smaller value, because in

the existing state of our knowledge there are no definite

grounds to authorize it.

Accordingly for the sake of simplicity and uniformity the value of v applied to the motion of the perihelion of Mercury is preferable also for the motion of the lunar perigee.

5. Outline of the Cause of the Fluctuations of
the Moon's Mean Motion.

In the Electrodynamic Wave-Theory of Physical Forces, vol. I., 19 1 7, it is shown that the previously unexplained fluctuations of the moon's mean motion, discovered by Ne.tOcomb in 1909, after a study of the moon's motion extending over more than forty years, (1867— 1909), is due to the refraction, dispersion, and perhaps absorption of the sun's gravitational waves in passing through the solid globe of the earth. The result is a slight decrease in the sun's gravitative action upon the moon when near the shadow of our globe in space, by which, near the time of Lunar eclipses, the moon is slightly released from the sun's control, and in the tendency to »fiy
the tangent*, has certain long period disturbances introduced
into its mean motion. An attempt to find such disturbances in the motion
of the, moon depending on the 18 -year period, had been made by Dr. K. F. Bottlinger, in a crowned prize Inaugural
Dissertation, at the University of Munich, Die Gravitations^ theorie und die Bewegung des Mondes, (Freiburg i.B., 1912). Bottlinger .deduced some evidence of an 18-year period, but in the case of the longer disturbances (61.7006 years, and 2 77-59 years respectively) he was not able to find the slightest indications of the required periods; so that in his address on the moon's motion at the meeting of the British Association in Australia, 1914, p.319, Prof. .£. ^. j9r(7z^« spoke as follows
»The shading of gravitation by interposing matter, e. g. at the time of eclipses, has been examined by Bottlinger. For one reason alone, I believe this is very doubtful. It is difficult

to see how new periodicities can be produced; the periods
should be combinations of those already present in the moon's
motion. The sixty to seventy years fluctuation stands out in

this respect, because its period is not anywhere near any

period present in the moon's motion or any probable com-

bination of the moon's periods. Indeed Dr. Bottlinger'' 1, curve shows this: there is no trace of the fluctuation*.
From this citation it is evident that Bottlinger not only had not convinced Brown of the reality of the fluctuations depending on the interposition of our globe in the path of the sun's gravitative action, but also that Brown felt that

an explanation of the 60-year and 275-year periods in the

observed fluctuation could not be based on the theory of

gravitational disturbances depending on the known cycles of

tlie moon's motion, in relation to the eclipse periodicities.

Notwithstanding this confidence of Professor Brown,

resulting from his great experience in the lunar theory, I was fortunate enough to discover such long period inequalities

in the moon's motion, bearing the closest analogy to. the

forces acting in the great inequality of Jupiter and Saturn,

of which the physical cause was discovered by Laplace in

— 1785,

after Euler and Lagrange had searched in vain for

the mystery underlying the celebrated 900-year inequality

of these great planets.

Without attempting to give a detailed account of these

researches in the lunar theory, we shall endeavor to outline

briefly the leading points, because this advance of 1917 bears

very directly, on the wave-theory, above applied to the motion

of the perihelion of Mercury and of the lunar perigee.

It is shown from an extension of Maxwell's, theory of

circular refraction in the eye of a fish (Cambridge and Dublin

Math. Journal, vol. XI), that a similar circular refraction of
gravitational waves occurs when the path of these waves is

through the solid mass of the earth. For in the earth, as

in the eye of the fish, the concentric shells are each of

uniform density, but with the density increasing from layer

to layer towards the centre. Thus a circular refraction of

the sun's gravitational waves will occur in propagation through

the globe of the earth, and also of the moon's gravitational

waves in passing through the same globe, owing to the concentric layers of which it is made up. The accompanying

figure 3 (pag. 156) illustrates the refraction of the sun's waves in passing through the earth.
By virtue of this circular refraction of the gravitational

waves in passing through the globe of the earth, it, follows

that^ the mutual interpenetration of the waves from the sun
and moon are not the same when the earth interposes its

solid mass in their path of action. The result is a weakening of the sun's gravitative action

on the moon; and, when our satellite is thus partially released

from the sun's control, it tends to »fly the tangent«, as near

the time of lunar eclipses. The outcome is a series of disturbances in the moon's mean longitude depending on the

motions of the perigee and node of the lunar orbit, with

respect to the Saros or eclipse cycle.

The principal eclipse cycles, incessantly repeated in

the theory of the moon's motion, are the following^):

') Cf. Electrod. Wave-Theory of Phys. Fore, l.ibi-102.

155

5048

156

= 1. The Saros, made up of 223 synodic months 6585.32 days, discovered by the Chaldeans and used at Babylon for predicting the return of eclipses, in con-

junction with the eclipse year of 346.62 days.

2. The eclipse year of 346.62 days, the average

time of the sun in passing around the heavens from

the moon's node and returning to the same node again

as it retrogrades under the sun's disturbing action in
18.6 years. Nineteen of these eclipse years make

6585.78 days, almost exactly equal to the cycle of the Saros given above, which is 6585.32 days.
The difference in these two periods is only 0.46

of a day, and therefore after 18 Julian years 10.82 days

(o'?46 less than ig eclipse years) the Saros of eclipses

is very nearly repeated, except that the location on the terrestrial globe is o"?32 =^ 7''4o"48^ further west in

longitude.

= 3. The nodical or draconitic month made up

of 2jl2i2-22: and thus 242 X27'?2i222

6585'?357.

"Tliis again is of almost the same length as the 223

synodic months and ig eclipse years defined in paragraphs I and 2 above.

Fig. 3

= 4. The anomalistic month made up of 2 7'?5 546o;
and thus 23qX27'?5546o 6585'?549. Accordingly, after 223 months the moon not only returns very closely to its original

Refraction of the sun's gravitational waves in passing through . the earth's 'mass, by which the moon is slightly released from the sun's control near the time of lunar eclipses.

position in respect to the sun and node, but also in respect

to the line of apsides of the moon's orbit; so that the pertur-

— = = bations near perigee, during the interval of the difference in

these two cycles, 6585'?549 6585432

0422Q

5''2g"?8

are so small as to modify but very slightly the return of the

cycle of eclipses composing the Saros.

Accordingly, these four fundamental lunar cycles recur

in the following periods:
1. The Saros ===223 synodic months
2. 19 eclipse years of 3 2 6'?62 each

^ 6585'?3 2 = 6585.78

3. 4.

242 nodical or draconitic months of

= 27'?2i222 each

6585.357

= 239 anomalistic months of 27^55460 each

6585.549

= Now the Saros

6585'?32 :^ 18 Julian years 10.82

days, or 18.0293 sidereal years of 365'?2563582 {ifansen).

And according to JVezson the period of the circulation of the

lunar perigee is 8.855 years. In the 10''' edition of his (3ut-

^oM , lines of Astronomy, 1869, p. 472, S\t

Ifersc/ie/ uses the

= period 3232^575343

8.85031 Juhan years,. which is only

slightly -different from the value cited above.

Accordingly, the forward motion of the perigee will

carry it twice around the heavens in 17.71 years, while the

node revolves in the retrograde direction in 18.6 years. Thus
^ if we call Q, the yearly motion of the node, and the cor-

responding motion of the perigee, we have

= = j; -i9?35484 = ta= -H4o?655o

360718.6 , 36078.855.

l3SJ

From the above data, it follows that the node will retro-

= grade through 360° in 18.6 years, but in the same time the
lunar perigee will progress through an angle of 7 56? 183 7 2o''-i-36?i83; so that after an interval of 18.6 years the perigee is displaced forward by 36? 183 in respect to the

restored node.

Fig. 4.

-7

—

<^o

Illustration of the progress of the moon's perigee

in respect to the node, in the 61.7-year fluctuation.

(i) Determination of the period of the 60 -year ^Vlc-
tuation.

It is very easily shown that owing to the relative

magnitudes of these direct and retrograde revolutions the

angular conjunctions will tend to recur in the regions of 360°,

240°, 120°, like the actual conjunctions of the planets Jupiter

and Saturn in the theory of the celebrated 900-year ine-

quality which was first theoretically explained by Laplace in

the year 1785. Here, too, as in the theory of Jupiter and

Saturn, the conjunction lines move forward. The amount of

= the displacement is 36?! 83 in 18.6 years; and in 3.31648

such periods, 3.3 1648 X r8. 6 years

61.7006 years, the

angular conjunction which started out at the angle 360° will

revolve forward through 120°, and the cycle of angular con-

junctions at all three points will begin over again, exactly

as in the great inequality of Jupiter and Saturn. This leads

157

5048

58

at once to the second long inequality in tHe moon's mean motion, which, without suspecting the cause, Newcomb estimated at » 60 years,, more or less«. His judgment of the period was surprisingly accurate; and as he concluded that the coefficient might be about 3^0, here again his value
could be adopted.

(2) Determination of the period of the great fluctuation

in 277.590 years.

In the case of the great fluctuation in the moon's mean motion, of which Newcotnb estimated the period at about

275 years, the calculation of the period is somewhat similar to that just cited, but also somewhat different. It is physically obvious that the modification of the sun's gravitation in passing through the body of the earth will depend on

the relative shifting of the line of angular conjunctions

node-perigee.
Now it is easily found by calculation that the angles

of the node-perigee are in angular conjunction, on a line ii?67o in advance of the original conjunction, after an

interval of 17.9971 years. For in this time the perigee pro-

gresses over an- arc of 47r-l- 1 i?67o, and the nqde retrogrades over an arc of 2 71— i i?67o, and meet exactly at the

conjunction line specified.
The problem thus arises to find the Interval in which

this secular displacement of the angular conjunction line will

complete the cycle in the moon's motion due to the reduction

of gravitation near the shadow of the earth. In each period of 17.9971 years, the node retrogrades through the angle in in respect to the shifting mean position of the perigee, and'

in the same interval the perigee progresses through the double of this angle, 45T, in respect to the retrograding mean node;

so that on the average their opposite motions amount to iin

in IT .qg-j i years.
As the physical effect of the reduction of gravity near

the shadow of the earth is the same whether the shifting

conjunction line node-perigee refer to ascending or descending

node, we perceive that this advancing conjunction line need

only sweep over the angle tt to give the required interval

for completing the cycle due to the changes of gravitation

near the shadow of the earth.

= Now i8o°/ii?67o

15.422,

= interval of 15.422 X 17.997 1 years

and _ therefore in an 277.590 years, the

cycle of- the changes of gravitation near the shadow of the

earth will be complete.

This is the period of the great fluctuation in the moon's
mean longitude which Newcomb estimated at 275 years, from the modern observations, and used in calculating the secular

acceleration from the eclipse records extending over 2 600 years

since the era of the Babylonians.

The diagram in Fig. 5 presents to the eye a continuous representation of the changes in node (outside circle) and

perigee (inside circle) during 18 years. At the end of 18 years

they both are in conjunction at i, near the original line of

conjunction, 360°, but ii?67o further forward. In each of

these periods of 18 years the nodes turn to every part of

the heavens, so that eclipses occur all around the earth's
orbit, with the earth and moon at all possible distances from

the sun. In this interval the lunar perigee revolves twice,
and the node once; so that the effectof the progression of

the perigee goes through symmetrical phases in respect to the earth's orbit in 18 years, as shown by the above diagram.

Fig. 5. Illustration of the progress of both node and perigee for producing the moon's great fluctuation in 277. 59. years.

This diagram also illustrates the secular progress of

the line node-perigee, the restoration to parallelism in this

conjunction line, advancing by ii?67o every 17.9971 years,

and requiring 277.590 years for completing the full cycle

of a semi-circumference.
We may express this result also by observing that

physically the decrease of gravitation near the shadow of

the earth will take place with equal effect whether the eclipse

be near the ascending or the descending node; and this

decrease will always correspondingly affect the moon's mean

= longitude. Therefore, the 18-year movement of node-perigee

conjunction line over the arcs i, 2, 3 • • •«, where n

15.422'

at 180°, will comprise all possible combinations of the con-

junction line node-perigee for modification of the sun's gravity

on the moon when near the shadow of the earth.

(3) Determination of the 18-year period of the Saros

cycle.

The Saros cycle is so well known that we need scarcely

= add that a minor disturbance in the moon's mean longitude

will recur in this period of 6585.32 days

18.0293 years.

In this period the symmetrical eclipse cycle of 223 lunations

is complete and the eclipses begin to repeat themselves, with

the moon very near the same relative position with respect

to the sun and node, and also with respect to the line of

apsides or perigee. This Saros cycle of the Chaldeans gives

rise to a minor disturbance in the moon's mean longitude,

with period of 18.0293 years, and a coefficient of about I'o.

It is the smallest of the moon's sensible fluctuations, yet

indicated by the researches of Newcomb and Bottlinger, and

illustrated graphically by the accompanying Fig. 6 (p. 159).

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5048

i6o

i6i

5048

162

in addition to the mystical one offered by Einstein, which
is devoid of physical basis ^and finally the natural and simple explanation based on the wave -theory, and outlined above
in section 3.
On the other hand, the lunar fluctuations, which are
vastly more complicated than the motion of Mercury's perihelion, admit of but -a single known explanation, namely, that discovered by the present writer in 19 16. It is therefore with some reason that the, most experienced physical mathematician at Cambridge wrote me, Jan. 28, 1917:
»1 wish the perihelion of Mercury could be resolved similarly (to the new work on the lunar fluctuations). Otherwise we have an unlimited number of ingenious kinds of relativity on our hands; which will be remarkable for self-
contradiction of the principle that everything is relative*.

It is just such confusioti as this that I have labored
to get rid of, and now my theory of the motion of Mercury's

perihelion is found to conform to the wave-theory, and to

correspond to the ideas of Newton, 1686, that the law of

gravitation in certain cases differs a little from the exact law

— of the inverse squares

the difference being explained by

the wave-theory, and the nature of the aether.

6. Gravitational Action is propagated by Stresses due to Waves in the Aether, but MaxweU's conception that the Stress is based on Pressure in the Direction of the Line of Force and on an equal Tension in all directions at tight angles thereto
is not admissible.

From the electrod. wave-theory of gravitation, outlined

in the writer's work of 1Q17, it follows that gravitation is

propagated by stresses in the aether due to the interpene-

tration of waves, and the action across space therefore travels

with the velocity of light. This mode of action is already

outlined also in the first paper on the new theory of the

AN aether,

5044. Forty-seven years ago in the celebrated

Treatise on Electricity and Magnetism, 1873, '^ol. i. Chap. V, §§ 103-116, Maxwell gave a remarkable theorem for the

stresses between two electrically charged material systems,

as producible by a distribution of stress over closed surfaces

about these systems.

He takes two electrical systems, namely, Ei, with

volume density q^, of the element whose coordinates are

*i> yii ^1 ; s^nd similarly for the other system, E^, Q^, Xo, y^, «2-
Then the x-oomponent of the force acting on the element of

.£1, owing to the repulsion of the element of E^, will be:

dX — =^ Qi Q2 {xi X2)/r^ • d*i dji d^ij dx^ dj/2 d^g

^2= (.^l-*2)^-|-(j>'l-J)'2)^-|-(%'-22)^

(36)

^^^ J J JJ J J(^i —^2)/f^'QiQ2dxi d ri dzidx2 dj/j dz^

This is as in the theory of action at a distance, and
the integrals will not be altered by extending the limits
from —00 to -4- 00.

Maxwell then proceeds to remark (§ 105) that if the action of E^ on E^ is effected, not by direct action at a distance, but by means of a distribution of stress in a medium extending continuously from E^, to E^, it is manifest that if we knew the stress at every point of any closed surface s which completely separates E^ from E^, we shall be able to determine completely the mechanical action of E^, on E-^^. Accordingly, he concludes that if it is possible to account for the action of E^, on E^ by means of a distribution of stress in the intervening medium, it must be possible to
express this action in the form of surface integrals extending over the surface s, which completely separates one system from the other.
Maxwell then develops the solution at some length, and after obtaining the required mathematical expressions, (§§ 105-110), remarks (§ in): »I have not been able to make the next step, namely to account by mechanical con-
siderations for .these stresses in the dielectric. I therefore leave the theory at this point.*
It can be shown that the action of waves, flat in planes normal to the Hnes of force will explain the mechanical difficulties here noted by Maxwell. For in his work on Matter, Aether and Motion, Boston, 1894, Prof. A. E. Dolbear describes an experiment of the following kind :
»If a dozen disks five or six inches in diameter are set loosely an inch apart upon a spindle a foot long, so that
they may be rotated fast, yet left free to move longitudinally upon the spindle, they will all crowd up close together, as the pressure is less between them than outside. If one can
imagine the spindle to be flexible and the ends brought opposite each other while rotating, it will be seen that the ends would exhibit an apparent attraction for each other, and if free to approach, would close up, thus making a
vortex ring with the sections of disks. If the axis of the disks were shrinkable, the whole thing would contract to a
minimum size that would ' be determined by the rapidity of the rotary movement, in which case not only would it be plain why the ring form was maintained, but why the diameter of the ring as a whole should shrink. So long as it rotated it would keep up a stress in the air about it. So far
as the experimental evidence goes, it appears that a vortex
ring in the air exhibits the phenomenon in question.* The behavior of the flexible spindle in this experiment
is analogous to that of the lines of force, which Faraday long ago observed had a notable tendency to shorten themselves. The gaseous medium of the air between the disks is thinned out, by the effect of the centrifugal force, just as the aether itself is near a magnet, owing to the rotations ') of the wave elements about the lines of force. Hence the lines of force tend to shorten themselves, as Faraday observed in his experiments with magnets and electric currents.
In view of this experiment it is not remarkable therefore that the lapse of time has confirmed MaxwelV's, stresses

We ')

hold the lines of force to be filaments of the aethereal vortices, due to rotations of the wave elements, as the waves recede

from a magnet. If Am be the element of aethereal mass in rotation, and the z-axis coincide with the axis of the magnet, the angular momentum
= — •of an element in the plane of the magnetic equator will be: .4 ^&m{yAxlAt x-iyjAi). This momentum of masses of aether S dw, about

the axis of the line of force, tends to beat back the aether in the equatorial plane, and causes it to press in on the two ends, parallel to the
z-axis. Hence we see the inevitable tendency of the lines of force to shorten themselves. Cf. Maxwell, On Physical Lines of Force, 1862,

Scientific Papers, Vol. i, p. 508.

:

:

i63

5048

164

for electrical action, yet shown on the other hand that the stresses conceived by him for gravitation are invalid, because in this latter case he conceived the pressure to be in the

direction of the lines of force.

MaxweU'i, conclusion as to gravitation is announced in the article Attraction (Scientific papers, vol. 2, p. 489): »To account for such a force (gravitation) by means of stress in an intervening medium, on the plan adopted for electric and magnetic forces, we must assume a stress of an opposite kind
from that already mentioned. We must suppose that there
is a pressure in the direction of the lines of force, combined

with a tension in all directions at right angles to the lines

of force. Such a state of stress would, no doubt, account

We for the observed effects of gravitation.

have not, however,

been able hitherto to imagine any physical cause for such

a state of stress.*

It seems remarkable that Maxwell himself should not
have seen the error underlying this reasoning. When we
whirl a stone by a string, it is the tension of the cord which holds the stone in its circular path, thus overcoming the

centrifugal force. If the string breaks, the stone goes flying
away, alonpthe tangent to the instantaneous path at the moment \^'eTi the tension of the string is released.

Innumerable examples of this central tension or pulling, necessary to overcome centrifugal force, should have occurred to Maxwell, as perfectly analogous to the forces which hold the planets in their orbits.

It was seven years after the death of Maxwell (i St g)
before the mathematical test required to overthrow the validity
of his 'gravitational stresses was given by Prof. George M.
Minchin in his Treatise on Statics, Oxford, 1886, Vol. II, pp. 448-455. Minchin calculates the Maxwellian gravita-

P tional stress intensities at any point

and finds the com-

ponents to be

= = C= A -R^ISny B E^jSny

Ji'^IZny

(37)

E where is the resultant force intensity, and y t^^ gravitation
constant. These expressions show that the three principal
A stresses are equal. The component along the line of force,
is, by Maxwell's hypothesis, a pressure, and the other two

components are tensions.

Apparently Prof. Minchin never seriously suspected the fallacy underlying Maxwell's assumption, that pressure in the
medium along the radius vector of a planet could make its
orbit curve about the sun, where in fact a tension, corresponding to the full breaking strength of stupendous cables of steel, is required to be exerted for holding a planet in its elliptical path. The nature of the curvature of the elliptic orbit was established by Kepler from the observations of Tycho, 1609, and first explained by Newton from the law of

gravitation, 1687.

After a very learned discussion, Prof. Minchin only

reaches the conclusion that since on trial, the mathematical
conditions specified by the stress analysis are not fulfilled,
— »either gravitation is not propagated by the Maxwellian

stress, or the aether is not of the nature of a solid body.«

• This is a good historical example of a false premise, on which much ingenious mathematical effort was spent,,

without detecting the physical error underlying the hypothesis. It will forcibly remind natural philosophers of Einstein'^ bizarre proposal to do away with the aether, without sub-
stituting any medium or substance in the planetary spaces'

which might exert contractile power for holding the planets,

and stars in their orbits.

It is scarcely necessary to add that if the signs of

Maxwell's stresses given above be changed, sO' as to give a component of tension in the line of force, and two equal pressures at right

angles thereto, thus

= = A B -^Ji^lSny -Ji^Sur

C= -R^ISny

(38)

gravitational phenomena would be explained.

Fig. 8.

Illustration of the development of stress between the sun and earth, owing to the interpenetration of the waves, rotating in opposite directions, from these two independent wave-fields, thus causing a tendency to collapse, in the medium between the two bodies, which furnishes the tension required to hold the planets in their orbits.

In the Electrod. wave -theory of Phys. Forces, 1917, pp. 131-133, will be found an explanation of why the aether tends to contract between any two bodies, as the sun and earth. This may be made a little more obvious by the following diagram, in which each body is shown surrounded by a wavefield, the aether near either -body being so agitated by the waves from its own atoms as to be of less density towards either centre than in the remoter spaces between the masses.
We are to conceive the waves from either
centre, by interpenetrating with those from the other centre, undoing the wave stress, depending on the other mass, and thus causing a constant tendency of the aether to collapse, which
results in pulling with maximum tension along
the right line connecting the two bodies.

:

:

:

::

165

5048

i66

This gives us a very simple and direct grasp of the mechanism underlying the planetary forces, which is not very different from those operative in electricity and magnetism,

except for the essentially haphazard arrangement of the planes

of the atoms in the heavenly bodies. These bodies are only

— slightly magnetic,

this power depending on the lining up

of a srriall fraction of their atoms, in planes which are mutually

parallel, as in common, magnets; while the great mass of the

atoms are tilted haphazard. The resulting action yields the

central force called gravity, instead of the duality of powers

noted by Airy (Treatise on Magnetism, 1870, p. 10) for the

magnetic attraction directed towards two poles.

= d® dO/Sx-dx-hdW/dydy-hdW/ds-dz

^^^'

d0 being an exact differential, to which Poisson (Traite de
Mecanique, 1833, Tome II, p. 697) and Cauchy have given so much attention, in the period immediately preceding and

following the development oi Fourier' & analysis, (1807-182 i). This method finally appeared in the celebrated Theorie Ana-

lytique de la Chaleur, 182 i. Besides the above reference to

Foisson's Mechanics, we cite the important memoirs indicated

below ^).

+ = Foisson usually treats his differential equation in the form

820/8^2_^2(92Q)/a^2^_g20/9^2 922>/a^2)

^

7. Sextuple Integration, under Fourier's Theorem,

for solving Foisson's Partial Differential Equation

82(p/8^2-_^2y2Q) fo rthevelocity- potential, in amedium

like the aether, capable of freely propagating waves.

We consider the partial differential equation for the

velocity-potential

in wave motion

Thus
three

O is any solution of the equation (39), which involves
variable coordinates, x, y, z, atid the time, /.
By a well known form of Fourier's theorem we have:

-f-00 -l-OO
= P.{x) i/2n-^ J/^-^)^V(-i).^(g).d5dA. (40)
— 00 — 00

— And as this will apply to the several variables, we get by three successive integrations between the limits 00 and -1-00
= + 0^n{x,y,z,i)=^ ( i/87r3) JJJJJJ,^l/(-0.i3( J, ^,C,^)-d§di?dUAd;(td^. A (^-x) X {^-y) (.^i^-z) v. (41)

If now we substitute the derivatives of this result in (39), observing by the form of A, in (41), that we have

upon actual derivation:

= (32/8^2^.82^9^2+82/8^2) ,^l/(-i) ,^l/(-i) (_p_^2_„2)

(^3^

we have for the solution of the original equation involving the four variables

= d^(D/dt^-aHd^<D/dx'^-{-d^O/dy^-hd^(D/dz^)

o

O = = = Q{x,y,z,t)

{'ilZn'^)llllll /'^<-'^^'-{^''l'dt''-^a'{r^-^l,''-^v'')\9.[t,riX,t)-d%dridldldiidv

o

(43)

~oo (limits of integration

and +00). This equation will be satisfied, if i3 (J, »/, X>, i) is determined so as to satisfy the equation:

+ = ^•'9.{t,riX,t)l-dfi+a^[l''+l>,'' v'')9.(t,7iX,t)

0.

(44)

We therefore integrate this differential equation, and in place of arbitrary constants, we introduce arbitrary func-

tions y^i and i//i of J, ri, "Q- Accordingly our solutions yield the following particular integrals

= 9.[-%,riX,t]^eB^'^^-'^'vA%,ri,l) S2(l V. ^, ^)

^~^''^^~'^
^Piil V. i)

= F {P+f^'+v'Y" .

(45)

If now we substitute the first of these in (41), and include the integration factor i/Stt^ in the arbitrary function,
we have (limits of integration —00 and +00):

= ® =- n{x,y;z,t)

JJJJJp(^+^^')^(- ')^Pi(g,^,C)-d?d^dCdAdf.d,^.

(46)

This is a particular integral of equation (41), and the second value in (45) would lead to an identical result,

as may be proved by actual substitution. Thus it only remains to complete the solution from

Let

= dydx^-hd^dy^-i-dydz^ y/

=t

e^

so as to reduce the given equation to the symbolical form:

®— = — ® [^/D(D i)] «^^-

o

= where 8/89 D. Then the transformation:

^ = O

^— 6.8j(/8e

S^/S/

such

particular

solutions.
(47) (48) (49)

will give:

— / [^/D(D- .i)],29.^

(S°)

© which is of the same form as the equation for

in (48).

') I. Fourier. Oeuvres de Fourier, Tomes I et II, publiees suos les auspices du Ministere de I'lnstruction Publique par les soins de
Gaston Darboiix, Paris, i888.'
2. Poisson: a) Memoire sur la Theorie des Ondes, Dec. 18, 1815; M^m. de I'Acad., T. I.
b) Memoire sur I'lntegration de quelques equations lineaires aux- differences partielles, e;t particulierement de I'equation generale du mouvement des fluides ^lastiques. Juill. 19, 1819, Mem. de I'Acad., T. III.
c) Memoire sur le Mouvement de Deux Fluides l^lastiques Superposes. Mars 24, 1823, Mem. de I'Acad., T. X. - d) Memoire sur I'^^quilibre et le Mouvement des Corps ijlastiques. Avril 14, 1828, Mem. de I'Acad., T. VIII.
e) Memoire sur I'Equilibre des Fluides. Nov. 24, 1828, Mem. de I'Acad., T. IX. f) Memoire sur la Propagation du Mouvement dans les Milieux Elastiques. Oct. 11, 1830, M^m. de I'Acad., T. X, g) Memoire sur I'J^quilibre et le Mouvement des Corps Crystallises. Oct. 28, 1839, M^m. de I'Acad.j T. XVIII. 3. Cauchy: a) Theorie de la Propagation des Ondes a la surface d'un Fluid Pesant d'une Profondeur Indefinie, 1815.
b) Sur I'lntegration d'Equations Lineaires. Exercises d' Analyse et de Physique Math^matique, T. I, p. 53. ci Sur la Transformation et la Reduction des Integrales Generales d'un Systeme d'Equations Lineaires aux differences
<''•
partielles, ibid. p. 178.

:

:

167

5048

i68

It thus follows that / admits of expression in the form (46), and therefore by merely changing the arbitrary

—00 function, we have (limits of integration

and -hoo):

= - X

Sr{x,y, z, f)

8/8/ SSS^S^ ,(^+^/'') Vi- . y/, (l^, C) • d? di} d^ d^ d^ d^

151)

To get the complete integral from these independent particular integrals (46) and (51), we add the two solutions

multiplied by arbitrary constants, (cf. Hattendorffi edition of Riemann% Partielle Differentialgleichungen, 1882, p. 100),

—00 +00 which may be included under the sextuple integral signs (limits of integration

and

:

-C2I

I52i

= mill Z^^^'^')!^^-')- y^i(?, n, n-d?d, dU^d/*dr

+8/8/ llllll /^+^^') 1^(- ') • nh [I, n>

d? dri dC d;i dft d^ .

These sextuple integrals admit of reduction to double integrals leading to a form of solution originally obtained by Poisson\ but Cauchy has made this reduction by means

Accordingly, at the time 4

there

/=oo
are
1=1

(53)
:oo of

of a trigonometrical transformation. The only essential precaution to be taken is to avoid processes by which the functions to be integrated become infinite within the limits.

The above equation belongs to the general form

= ^© 92(D/8/2

(54)

^ where

is a function of the derivatives with respect to the

these concentric wave surfaces, all moving with the velocity c, which is the velocity of light. But the time / also flows on,

= and if there be i intervals, the summation ^, i

00 will

2=1

yield for the double integration of intervals and wave?:

coordinates 9/8jc, 8/8j)/, 9/8z. For all such equations the

method above outlined furnishes directly a solution expressed

by sextuple integrals, which are reducible to the Poisson-

A Cauchy double integrals, if

is homogeneous and of the

z= I /^ I
which corresponds to all the points in an infinite plane.

second degree, as in the case of a sphere surface, with radius

increasing uniformly with the time

= ^2-i-y-(-^2

f2/2

(ss)

where c is the parameter representing the velocity of light.

As was long ago pointed out by Fourier, Poisson and
Cauchy, integrals of this type are peculiarly appropriate for

Imagine another system of coordinates (?/, rji, ^i), with

its origin at the centre of gravity of mi {^htTju, ^h,^i), to which the moving waves are referred at i times, so that for the n

bodies we have:

For the Bodies.

For the Waves emitted.

Wl (xi,J'i,Zi,/i)

the expression of those disturbances involving the transmission of energy in a medium, as in the steady flow of waves, whether

W22 [x2,y-i,Z2,ti)
m^ (••«3iJ>'3,^S,4)

m — ['ihi— h.i, rihi—rihi, ^hi t,hi, h)

(56)

of sound, light, heat or electrodynamic action. These wave disturbances are propagated through the medium in question

mn [Xn,yn, Zn, h)

— mn {^I„i—^hi, 'TjI^i ^Iu, ^I„i—^hi, ti) .

with a finite velocity, and unless the waves are regularly renewed the original disturbance leaves no trace behind when it has passed by; so that the upkeep of the energy flow involves periodic renewal of disturbances for maintaining the steady flow of waves. In his Theorie Analytique de la Chaleur, 182 I, ./^(?z^rzVr continually emphasizes the incessant movement
of heat.
Solution of Poissons equation for the velocity-
potential O in wave motion from n bodies.

Let there be n bodies emitting waves : wzi with coordinates [xi, }\, Zu t-j) surrounded at the instant t^ by an
infinite series of wave surfaces, which for simplicity we may
suppose to be spherical

x-^^-^yi'+Zi_^-Ci^ti^= o

— = Xi'^-\-y<i'^'^Z2'^ Ci^t-i^

o

= Then, -from the preceding investigation it will follow

that the solution of Poisson's. equation d^0/di^

a^y^fl) for

the velocity-potential

and transmission of energy of wave

motion, in the case of in bodies will be similar to that already

found for a single wave centre, except that as the waves from

the several bodies are everywhere superposed, the velocity-

0„ potentials ®i, 02, 0^-

from' the several centres must be

=added together to get the total effect, 0i-h02-h0g-\

h ©„

0, when the waves from the n bodies mutually interpene-

trate, giving maximum tension in the right lines which connect

the bodies in pairs, and maximum pressure in the prolongation

of these lines beyond the inasses.

= Accordingly, if we introduce the amplitude of the waves
from each mass, Aii kuj V[hi^-^riii^-^lu^) and retain the

amplitude /-^-^-^'^'')y(—

for deteriorating wave changes,

XI'

= ' /, 2

o.

under resistance, we shall find for the general solution the

—00 expression (all integrations between the limits

and -+-00):

= ®«, [mn] llllllKil !/[(?/„- %u

= + 0u{mi) 0.2,{m2)-+-0^,[7n^)-^

(»„, (;«„)

57;

Q [^i-Ui?] -Mn+^nKh) l/(- 0. ?p-„( J„^ ^„_ . dj„ d^„ dCn dl„ dfl„ dv,

U iWi- ^hi)-]-e^-^>'^'^nKf^) V(- 0.. yj„Cs„, nn,

• dS„d^„ dl^ndlndllndVn-

:

:

:

.

:

169

5048

I/O

This solution of Foisson's equation for" the velocity-

O potential

is well calculated to show the complexity of the

problem of explaining the forces which govern the operations

of the physical universe. The velocity-potential is essentially

a function of the elasticity in a gas, condensation alternating

with rarefaction, by which wave motion once generated is maintained at all points of space, and at velocities suitable to the elasticity and density of the medium at these points. Thus wherever waves penetrate the velocity -potential rhust

also exist.

And we see not 'only that the domain penetrated by

the waves

includes

all

space,

from

minus

infinity to ,

plus

infinity, in a sextuple integration, which corresponds to an

integration connecting every point of space with every other

point; but also that it must be continuous, that is, repeated

for every pair of points two and two.

The -waves from the individual atoms are infinitely more complex still, and in fact cannot be given except by
an integral like the foregoing, infinitely extended. This infinite integral could be written out analytically, yet its contemplation would aid us but little in grasping the infinitely
complex phenomena of nature.

In practice it suffices to remember that from every body an infinitely complex system of waves goes forth, to interpenetrate and combine with the like infinitely complex wave systems going forth from all other bodies. The summation of all these disturbances is an infinite intjegral pf the eifects of small commotions, the final result of which is the system of forces operating throughout the physical universe.

In thePrincipia (Lib. Ill, Props.VI-VIII and Prop. XXIV) Sir Isaac Newton points out how the gravitative force due to one- body may penetrate into the regions occupied by any other body or system, just as if the other body or system did not exist; so that each body or system acts independently
of the others, yet the final effect is a combination of the separate efi'ects. Gravitation, therefore, is an interpenetrating
— power just such an influence as would arise from waves
propagated from the several centres, and extending throughout all parts of the system of the world.

8. Geometrical Conditions fulfilled by the
Velocity-potential®, expressions for the molecular velocity and condensation at any distance from the source of disturbance, with an indication of the energy due to the waves of various lengths observed in nature.
The .solution of the problem of vibrating cords runs back to Daniel Bernoulli and D'Alembert, but the method of analysis was generalized by Lagrange, and Poisson has greatly improved the theory for application to all classes of waves. The energy in the wave function depends on three coordinates, it, «r, and the time /,,,because when a distur-
J)/,
bance ^originates in a medium it spreads in all directions.

sometimes at rates depending on the wave conductivity along

certain axes, but always at a rate defined by the time/.

* If the medium be gaseous, as in the kinetic theory of
the aether, ©must be the velocity-potential ^). Accordingly,

we outline the equations of such a medium:

— ® d 0)

®/8x 8

da; -+- f/j/8j. • dj' -+- 9 /Ss • d^

+ ^= uAx-^v Ay w Az

= = u doldx 'v'= dw/dy w 8®/8c

(s^)

where w u, v, are the component velocities.
The general equation of equilibrium is:

= = whence X=dvldx Y d v/dy' Z d V/dz .

^^"^^

= Now put J(i/^) dp

P; and we have the well known

relations

= = ( I /e) 8//9^.

SF/c>x

0/q) dpjdy

= {i/Q)Sp/dz dFldz

dpjdy

= + + y-j^ dO/dt-^y,[{dW/dx)^ {d(D/dyY {d(D/dzY] .

And the equation of continuity
+ = + dQ/dt^d/dx[Q-d0/dx) d/dy(Q-da)/dy) d/dz{Q-d0/ds) o.

60 (61)
(62)

For an incompressible fluid the second expression in

(62) vanishes:
+ = d^CD/dx^+d^e/dy^ d^Wfdz^ o .

(63)

But the aether is not incompressible, and this equation there-

fore does not apply to any gaseous medium.

In general the exact form of the wave surface cannot

be defined, owing to changes in the density and elasticity

of the bodies penetrated by. the advance of the wave front.

If the medium 'be symmetrical in, respect to three axes at

right angles, as in the case of certain Crystals, then the wave

surface,, from a disturbance at the centre of such a mass,

will pass, from the spherical form:
= x^-hy^^z^-c^f' o

(64)

and take the form of an ellipsoid Of three unequal axes

x^/a^-hy^/fi^-^zyr' c' f

(65)

where the axes a, /J, ;' denote the conductivities along the

ct= axes of the ellipsoid, and

i, at any stage of the progress

with the -wave surface in the form of the ellipsoid:

x^/a^+yy/S^-hzyr^ == I .

(66)

It follows therefore that the problem of wave motion

involves the solution of Poisson % equation

= Z-^Ol^f

«-''(82a)/8^2+8-'®/8/-H82(Z)/8^2)

(67)"

where a is the velocity of the wave propagation (cf. Poisson,

Traite de Mecanique, 1833, tome II, p. 663—720; or Lord

Rayleigh'i Theory of Sound, vol. II, chapter XIII).

w Let u, V,

be the component velocities parallel to

the axes Ox, Oy, Oz of an element of mass dm, at the in-

stant t, so that,

= X— a:'

J«d/ y-y' ^= ^'I'dl

^ — z s' ^wdt.

(68)

= ') If for any part of an elastic fluid mass A^ == uAx-^vdy+wiz

o be a perfect differential at. one moment, it will remain so

= for all subsequent time. When <& is siiigle valued, the integral round any closed circuit vanishes, I d<I>

o. This is- the irrotational condition

=0 of hydrodynamics. Hence, with condensations and rarefactions alternating, and of equal intensity, in wave motion, the above condition I d"!"

* = is met by the plane wave

/4 cos[2ic/X-(x—a^)], which is typical of the velocity-potential in general.

:

.

.

:

:

:

171

5048

172

If we neglect the squares of the velocities dW/dx,

= O dojdy, dO/dz, and put z/

o, w =^ o,

will become a

function of x and t only
= 820/8^2 ^2 820/8^2 = = O ii[x,t) Acoi[2nlX-[x-at)\^).

The solution obviously is an' undulation of flat wavelets
parallel to the axis of x, traveling with velocity a.

Let f be the velocity in the direction

vector, so that the resultant

= t,

V{u^-^V^-i-W^)

of the

radius (70)

then since for spherical disturbances

= x^-hy'^-\-z^ r'^ xdx-hydy-^zdz == rdr

= = = u

t, x/r

V

Zy/r w

t, z/r

^~w£—g£i-

= = udx-\-vdy-\-wdz l^dr ^ dO/dr

= d(D/dx ==d(D/dr-x/r d(D/dy d(D/dr-y/r

= dojdz dO/dr-z/r.

(70
(72) (73)

Differentiating a second time, we have
= d^W/dx^ d^0/dr^-x''/r^-hd0/dr-{y^-hz^)/r^

d^ai/dy-i =d^0/dr'^-yyr^-i-d(D/dr-(z^-i-x^)/r'*

= 82(0/822

d^OJdr^- z'^/>''^-^d0/dr-(x^-i-y'')/r'^ .

(74)

By means of these values, Poisson's equation,

= 82a)/8/2 a^d-^'m/dx^-^-d^O/dy^-hd^O/dz'^)

becomes

= d^cp/df^ aHdi0/dr^-h2/r-dW/dr)

(75)

This is the same as
= d^rO/dt^ a^d^rW/dr^)

(76)

the complete integral of which is
r(D =/{y-hat)-hF(r — ai)
/ where and J^ are two arbitrary functions.

(77)

= By extending his analysis (Traite de Mdcanique, 1833,

X vol. II, p. 706) Poisson shows that since

dOjdr, we have

= I ilr.f[at-r)-hilr'-f{at-r) = s ijar-f'[at—r)

(78)

Accordingly, Poisson concludes that at a great distance

from the centre of this disturbance we may neglect the

second terms of the values of t^, which are divided by r\

in comparison with the first, which are divided by r. Thus for

the whole duration of the movement we get for the conden-

sation or dilatation 5

= ^

'Qja .

(79)

By equation (78), therefore, the velocity of the mole" cules in a gaseous medium decreases inversely as r, just as

in the amplitudes of the waves postulated in the kinetic
theory of the aether. The condensation or dilatation .y varies
as the velocity in the direction of the radius vector, which itself varies inversely as r; and also inversely as a, the velocity

of wave propagation. Accordingly, for a highly elastic medium, s is small, and decreases very rapidly; which confirms

our view that the amplitudes of the aether waves are very minute, and decrease inversely as r in receding from the sun.

In finishing this paper, Febr. 19, 1920, I am surprised
to notice Poisson % sagacious remark (p. 706): »La vitesse propre des molecules d'air decroitra alors en raison inverse

A = de /-« : which affords an unexpected verification of the writer's

formula for the amplitudes of the aether waves,

kjr,

also derived from the kinetic theory, but by a different

process. It thus appears that Poisson had such a result for

the waves of sound 87 years ago, and its neglect for nearly

a century is remarkable.
As Lord Rayleigh points out in his Theory of Sound, 2°'' edition, 1896, vol. II, p. 16: the rate at which energy is
transmitted across unit area of a plane parallel to the front
of a progressive wave may be regarded as the mechanical
measure of the intensity of the radi'ktion. This is the basis
of Lord Kelvin's celebrated paper of 1854, »On the possible
density of the luminiferous medium, and on the mechanical
value of a cubic mile of sunlight*, (Trans. Roy. Soc, Edinburgh, 1854), which we have used, in our first paper on the new theory of the aether, for calculating the density of this medium.

The energy transmitted, in the direction of the three coordinate

O axes,

being taken successively as a function of x (and t),

= = y (and t), z (and /) only, is given by the approximate equations:

320/8^2

^2 . 820/8^2 82®/8/2

«2 . 82(J,/8j,2

= 82a)/8/2

«2. 82(0/822

(8c)

which are expressed in (75) above.

In case the gravitational wave transmission occurs within

= a mass of density q, we have Poisson's equation for the potential

d^^VJdx^-^'d^Vldy-'+'d^Vl^z^+ATt Q

o

(81)

instead of the equation of Laplace

= d-^V/dx^-hd^V/dy^-i-d^V/clz^

o.

(82)

And thus within an elastic solid the equation (80) would

= become 82®/8^2

a^.[^^(D/^x^-^-^^0/^y^-^-^^0/^z^-^-4^TQ) (83)

which is of the form adopted by Riemann, for the induction of electric currents, in the memoir presented to the Royal Society of Gottingen in 1858, but subsequently withdrawn, and after the death of the author, published in Poggendorff's Annalen I31. 237-263, 1867.

This investigation o{ Riemann was examined by Clausius (Poggendorff^'s Annalen 135.612) who doubts the validity of the mathematical processes for the phenomenon of electric induction, chiefly on the ground that the hypothesis that potential is propagated like light, does not lead either to the law of Weber or to the other laws of electrodynamics.

In our Electrod. Wave-Theory of Phys. Fore, however,

V = it is not held that potential is propagated like light; on the

contrary that the potential is a function

f[x,y,z,^, is

fixed in space, yet depends on the total accumulated stress

due to wave amplitudes of all the matter involved. Hence this

criticism is not valid against the wave-theory here dealt with.

= Moreover, we use Poisson's equation for the potential,
S7^V-^4TCQ o, only within solid masses, Laplace's equation
V^^^ o applying to all free space. Thus we adopt a
transition between^ these two equations at the boundary of any mass of matter, as long recognized by geometers and
natural philosophers.

The physical meaning of the transition is the sharp difference in velocity of propagation for all aether waves at

') Lord Rayleigh, Theory of Sound, vol. II, p. 15-16, a""* edition, 1896.

:

173

5048

174

the boundary of a mass of matter; and moreover the decrease

in total accurmilated stress due to the aether waves from all

the atoms, as the moving point J>(x,y,z) enters the body of

— density q, and leaves behind a part of the mass,

the aether

waves coming from the atoms of this shell from all directions

just balancing in a homogeneous sphere. But whatever the

law of density or form of the body, there is a change in

the sum of the second differentials of the potential at the

boundary of the body, from Laplace's to Foisson's, equation

Fig. 9.

Curve of the potential function V, showing its asymptotic decrease with the distance, and the tendency to an asymptotic increase towards the centre; but owing to finite dimensions of the mass, a gradual decline to zero.

This difference between Laplace's equation of the po-

tential for free space, and Foisson's corresponding equation

for space filled with matter of density q, owing to the inter-

vention of boundary conditions, is distinctly favorable to the

We wave-theory of physical forces.

therefore presented the

^ treatment of the wave equation of Foisson S'^0/di'^

(jr^yag)

for free space, by the general method of integration based

on Fourier's theorem.

This solution will hold for waves of any initial wave

length, propagated with the velocity of light, from n bodies,

in all parts of space, and everywhere mutually interpenetrating
so as to generate maximum tension in the right lines con-

necting the n bodies in pairs, in accordance with the observed

phenomena of universal gravitation.

If the solution will hold for separate bodies, from which

spherical waves are emitted, it obviously will hold also for

separate vibrating particles, within a single body; but here

the mathematical difficulty is increased, by virtue of the

unequal conductivity which heterogeneous solid bodies offer

to wave propagation; so that the expression of the effects

of the waves from the atoms would be infinitely complex.

Yet the above equation (57) gives the approximate representation of the propagation of wave energy from atoms,

which may be useful in certain problems of molecular physics.

The solution in (57) already involves an infinitely

complex integration, repeated «-times for the n bodies of the

universe. To include the initial waves of all possible lengths,

= = we should have to integrate this complex expression for (P

between the limitsi A

o; A

co, involving all possible

^ periodicities, the number of which is: «

[^/^]>.=o •

Now, according to the researches of Prof. Flanck on

E thermodynamic radiation, the energy

of wave length X

is given by the rather complex expression
= Ex^l {klFTl)l{e^l^^'^'^-i)-?.nFTl-^Al

(84)

which admits of integration within certain limits.

F T In this formula,

and

are the gas -constant and

= absolute temperature, k

V hV,

being the velocity of light,

= and h is Flanck's new constant, h

6.55 X io~^' ergs sees,

= so that if the wave frequency be j', A

Vjv and

= = x klRTl hvJFT.

(85)

And Flanck's fundamental equation for the quantum

= of energy of v frequency is e

fiv .

(86)

= By the use of Planck's formula therefore ^^dA 87rJ?rA-* [*/(«*- i)]dA.

(87)

This integration, to take account of the various wave lengths, could be carried out, but the subject is iii too primitive a condition to be undertaken at present.

9. A Definite Criterion for deciding between
the Great and Small Densities claimed for the Aether.

In Section I of the first paper on the new theory of the aether, we have cited the claim put forward by certain

electronists, that, on the hypothesis of incompressibility^ the aether has a density 2000 million times that of lead. In his Aether of Space, 1909, p. 91-105, Sir Oliver Lodge finds froni electrical theory that the density of the aether is 10^^,

a million million times that of water. It is only fair to point out that as the aether transmits
waves, as in light, heat, magnetism, electrodynamic action, and radio telegraphy, of the most varied length, and of

various amplitudes, it is not conceivable that it should be

incompressible, so that the dilatation is zero in the equation:

= = 8

da/dx-hdji/dy-i-dyjdz

o

'
(88)

where a, fi, y, are the displacements, and

by equation (63). For this would make the wave velocity infinite, which is contrary to observation. Accordingly,_whilst the aether is highly incompressible, owing to the enormous velocity of the aetherons, and the resulting kinetic elasticity, this medium certainly is not incompressible.
In the article Aether, Encyclopedia Britannica, ii'^'ed.,
igii, Prof. Sir Joseph Larmor is more poised and cautious
than the writers previously cited, but his faith in the older
theories is so shaken, that he intimates that the ratio of the amplitude of the waves to the wave length,' taken by Maxwell and Kelvin at about io~^, may be enormously overestimated. Larmor adds: »It is not impossible that the coefficient of
ultimate inertia of the aether is greater than the coefficient of inertia (of a different kind) of any existing substance*; which
shows his tendency to an abandonment of the older theory, under the teachings of the electron theorists.
It thus appears that the excessively small density, found
by Kelvin and Maxwell, namely, about lo""^*, or my own value at the earth's mean distance 438X10^^^ is opposed
by the modern teaching in favor of an enormous density, about 10^'^, as stated by Sir Oliver Lodge. The difference

175

5048

I 76

between the two results presents an en6rmous contrast, name!)'

the almost unlimited factor:

F- 10 with the value of Kelvin and Maxwell; , ,

==

0.0023

X

,80'-
10

wi--t.h.

.-. See'i

value.

(89)

Accordingly, progress is nearly impossible with this irre-
concilable difference of opinion among the learned. Brooks and Poyser, as representatives of the opinion of the electronists, state: »There is no intrinsic difficulty in either view, but at present (19 12) no method is known by which we may hope
to discriminate between them.«
The present writer has therefore labored to develop a
criterion for the rejection of one of tTiese competing values, which would leave the other in possession of the field. Besides the ''above criticism, that the finite velocity of wave propagation excludes the incoropressibility of the medium, I have given in the Observatory, Nov. 19 18, p. 411— 412, a brief discussion of the consequence of the intolerable disagreement in the values of the •aether density.
A simple calculation has enabled me to exclude Lodge'i
density as wholly inadmissible, because if true the energy of the waves from the sun'falling upon a single square centimetre of the earth's surface would be able to yaporize the
entire terrestrial globe in less than one minute of time, when ' we use Bigeloiu'% value of the constant of solar radiation, arid
Kelvin and Maxwell's density.
The mass of the earth is 5956292000000000000000
metric tons. If we take the average specific heat of the globe at 0.2, and the vaporizing point of its average matter at 3000° C, the total amount of heat required to reduce it to
— — vapour the interior being assumed to be without heat

Now if any good ground can be adduced for decreasing

the ratio of the amplitude to the wave-length, I am willing

— — to consider such a modification in the belief of the most

eminent physicists,

such as Kelvin, Maxwell, Larmor

but it should be pointed out that to make the reconciliation

of the extreme values complfete, the ratio of the amplitude

to the wave- length will have to be lowered by the enormous

factor

'

p^ ,0^30

(g2)

so that AlX now taken at io~^, would become

= ^'A Io-3^

(93)

The difficulty of this extreme step is so great that I

dismiss it as quite inadmissible. Until new evidence, resting

on ground more secure than mere assumption, is available

it must be held that Sir Oliver Lodge's attempt to reply to

this criticism completely breaks down. For even if we took

= All

10-=, or .4/1= 10-''

(94)

— which are values looo or loooo times more extreme than

appealed to the experienced judgements of Lord Kelvin, Max-

— ivell and Lannor,

the required factor would scarcely be

reduced in a sensible degree; and practical experience in

physical science certainly would not justify us in exceeding

the limit of lo"''

As a final argument against the electrical theory,

assigning the aether a density of 2000 million times that of
= lead (namely: i 1.352 X 2000000000 22704000000000
times that of water!), we may recall the fainiliar experience

of a man swimming in water. Here the swimmer is immersed

in an inert liquid of about the same density as his body;

would be

H = 5.g56292X lo--'- (0.2 X 3000) X 1 000000 calories,

= = 6X 5.956292 X 10^"

3.6 X 10^", nearly.

(90)

yet to move about a strong exertion is required of the most, powerful muscles, completely under the control of the will.
If the liquid had the density of quicksilver, the swim-

Now Bigelow\\'^\\\t of the solar constant is 3.98 cal. mer would scarcely sink down to his boot-tops, and his
per minute, or 0.0663 cal. per second; and, as Lodge's value muscles would be altogether too feeble to displace such an

of the density of the aether is about 10^° that above cited

from Kelvin sxiA. Maxwell, and 0.0023X10'*'' times my own

value,^ we have for the effect of such an increase in density

the raising of the solar radiation by the factor lo'"':
= H=^ 0.0663X 10'" 6.63X 10^^, Kelvin 2.ud Maxwell

or ZT^^ (0.0663X0. oo23)x 10^", with Sees value

(9^

inert and heavy liquid, if he were required to move through it: yet he could walk over such a magma, by great effort, analogous to that required when we walk in very yielding
volcanic ashes.
Now the density of mercury (13.6) is a little greater than that of lead (11.352), but the moment we consider an

The first of these values would vaporize the earth in' aether 2000000000 times denser than lead, we perceive the

54 seconds of time, the second in 0.277 of a day. But in nature this vaporization does not occur, and thus we conclude that the density of the aether stands at a value near that
fixed by Kelvin and Maxwell many years ago, but slightly improved in the writer's new theory of the aether.
In the Observatory, for Dec, igi8, p. 446, Sir Oliver
Lodge has attempted to reply to my criticism by pointing
out that the energy of the solar radiation depends on the amplitude of the wave, compared to the wave length, which with Kelvin and Maxwell I took at io~^, a value pronounced by Sir Joseph Larmor (in the article Aether, p. 292) »a very safe limit*. Lodge also adds: »many facts have suggested that the amplitude of the most brilliant light is exceedingly small compared with its wave length*.

culmination of absurdity 1 Even if it penetrated all bodies
quite perfectly, and gave equal pressure on all sides, still some displacement of the particles would be required when we move about in it, as in the case of water displaced by a swimn^ier. Obviously no living physical body would be capable of displacing such a dense medium; and we see that even the strongest stars, planets and comets would be dispersed to atoms under the changing resistance such a medium would interpose to their variously accelerated motions. The electrical theory assigning the aether a density
22704000000000 greater than that of water is therefore
the best possible illustration of a physical Reductio ad Ab-
surdum, and we know that either some premise or some

:

;

177

5048

178

link in the chain of reasoning eventually will not bear in-

vestigation ").

In the article Aether, Encyclopedia Britannica, ii'*'ed.,

19 1 1, Prof. %vs: Joseph Larmor concludes that we must treat the aether as a plenum. Under the influence of electrical theory,

he even speaks as if the aether were not molecular. In dis-

— cussing the transparency of the celestial spaces,

to which

much attention was given by Cheseux and Olbers, W. Herschei

— and W. Struve

(cf. Etudes d'Astron. stelL, St. Pdtersbourg,

1847) — Larmor first recalls the well known transparency

of space shown by astronomical research, and then adds

»If the aether were itself Constituted of discrete mole,

cules, on the model of material bodies^ such transparency

We would not be conceivable.

must be content to treat the

aether as a plenum, which places it in a class by itself; and

we thus recognize that it may behave very differently from

— matter, though in some manner consistent with itself,

a

remark which is fundamental in the modern theory:*

The first part of this reasoning apparently implies that

the aether is not molecular, at least »on the model of ma.terial bodies«. This may be correct in part, because no one

would suppose the aether to be made up of complex mole-

cules, underlaid by a finer medium, such as the aether is to
the more complex masses of common matter. On the other

hand there is not the smallest objection to an aethereal medium made up of spherical perfectly elastic monatomic

elements, so called aetherons, having a diameter of I:4oo5'^

of a hydrogen molecule, and a mass of 15.56 millionths pf a millionth of such a molecule, such as we show do really exist.

As no finer medium would underly such a monatomic

aether, it coiild not dissipate the energy of wave motion,

»on the model of material bodies*, and thus it would fulfill

Larmor's condition of a plenum. This would give such an

excessively fine monatomic molecular structure that the me-

dium would penetrate all material bodies, but waves in such

an aether would be very noticeably retarded in solid or liquid bodies, and much less so in gases, in accordance with

physical experience.

That the aether must necessarily be molecular Tollows

at once from our every day experience with such granular bodies as fine gravel, grains of corn, sand, shot or mustard

seed. If we fill a glass vessel with such coarse granular masses, and insert the fingers or any solid body, such as a rod, into the granules, we perceive that they are thrust aside to make way for the hand or solid rod. If we fill the vessel
with water, oil, alcohol, ether, or any similar liquid, our experience in such displacement is the same. The liquid is visibly thrust aside and this holds even when the molecular structure is relatively so fine that a drop of water might be

magnified to the dimensions of the earth without exhibiting

— the molecules of larger size than footballs,

as shown

by Lord Kelvin in his well kiiown researches on the size

of atoms.

But it will be said that the aether penetrates all bodies,

and thus we cannot sensibly displace it, as we can water,

We oil, alcohol or ether.

reply that it is -perfectly true that

the aether penetrates freely all bodies, even the dense and'

highly elastic or rigid masses of the earth, sun and stars,

almost as if their molecular structure were absent: yet we

learn from the phenomena of refraction and diffraction in

our laboratories, that light waves in the aether are very

perceptibly retarded in their motions through transparent
bodies; and in our investigation of celestial phenomena, we find from the investigation of the motion of the moon that

the sun's gravitational 'waves, though of such length as to pass through the earth, are yet sensibly Refracted; and perhaps

dispersed or partially absorbed at the time of total eclipses

— of the moon,

whence arises the fluctuations of the moon's

mean motion established by Newcomb in 1909, and explained

by the present writer in 19 16, (cf. Electrod. Wave-Theory

of Phys. Forces, vol. i).

From these considerations it appears that we have both

terrestrial and celestial evidence that the aether is molecular, but of such excessively fine grained structure that no

finer "rnedium whatever underlies it: thiis it penetrates all

bodies freely, under an elastic power, or expansive tendency,

68932 1600000, tirries greater than our atmosphere exhibits in proportion to its density, as more fully shown in the first

paper, sect. 4.

10. The Kinetic Theory of the Aether accords with the Views o{ Newton, 1721, and oi Maxwell, 1877.
In order to further illuminate the above discussion we may recall the earlier though little known views of Newton and Maxwell, on the physical constitution of the aether.
a) Views of Sir Zr««(:iVi'2<'2'^z, Treatise on Optics, 3''''ed.,
172 I, p. 325 et seq. ^)
»Qu. 20. Doth not this Aethereal Medium in passing out of Water, Crystal, and other compact and dense Bodies, into empty Spaces, grow .denser and denser by degrees,, and by that means refract the Rays of Light not in a point, but by bending them gradually in curve, lines? And doth not the gradual condensation of this Medium extend to some distance from the Bodies, and thereby cause the Inflexions of the Rays of Light, which pass by the edges of dense Bodies, at some distance from the Bodies-?«
»Qu. 21. Is not this Medium much rarer within the
dense Bodies of the Sun, Stars, Planets and. Comets, than in
the empty celestial Spaces between them? And in passing from them to great distances, doth it not grow denser and denser

') In the Optics, 1 721, pp. 342-3, Netvion discusses the very problem here treated of in the fbllowing manner: "The resistance of

water arises principally and almost entirely from the vis inertiae of its matter; and by consequence, if the heavens were as dense as water,

they would not have much less, resistance than water; if as dense as quick-silver, they would not have much less resistance than quick-silver

if absolutely dense, or full of matter without any vacuum, let the matter be never so subtile and fluid, they would have a greater resistance

A than quick-silver.

solid globe in such a medium would lose above half its motion in moving three times the length of its diameter, and a

globe not solid (such as are the planets) would be retarded sooner. And therefore to make way for the regular and lasting motions of the

planets and comets, it's necessary to empty the heavens of all matter, except perhaps some very thin vapours, stea,ms or effluvia, arising from
the atmospheres of the earth, planets and comets, and from such an exceedingly rare aethereal medium as we described above. A dense fluid

can be of no use for explaining the phaenomena of nature, the motions of the planets and comets being better explain'd without it."

'') Quoted at length, because (his edition is very inaccessible to the modern reader.

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perpetually, and thereby cause the gravity of those great Bodies toward one another, and of their parts towards the Bodies; every Body endeavouring to go from the denser parts of the Medium towards the rarer ? For if this Medium be rarer within the Sun's Body than at its surface, and rarer there than at the hundredth part of an inch from its Body and rarer there than at the fiftieth part of an inch from its Body, and rarer there than at the Orb of Saturn; I see no reason why the increase of density should stop anywhere, and not rather be continued through all distances from the
Sun to Saturn, and beyond. And though this Increase of density may at great distances be exceeding slow, yet if the elastick force of this medium be exceeding great, it may suffice to impel Bodies from the denser parts of the Medium towards the rarer, with all that power which we call Gravity. And that the elastick force of this Medium is exceeding great, may be gathered from the swiftness of its Vibrations. Sounds move about 1140 English feet in a Second Minute of Time, and in seven or eight Minutes of Time they move about one
hundred English Miles. Light moves from the Sun to us in about seven or eight Minutes' of Time, which distance is ^bout 70000000 English Miles, supposing the horizontal
Parallax of the Sun to be about 12". And the Vibrations or Pulses of this Medium that they may cause the alternate
Fits of easy Transmission and easy Reflexion, must be swifter than Light, and by consequence above 700000 times swifter
than Sounds. And therefore the elastick force of this Medium, in proportion to its density, must be above 700000 times 700000 (that is above 490000000000) times greater than
the elastic force of the Air in proportion to its density.
For the Velocities of the Pulses of elastic Mediums are in a sub-duplicate Ratio of the Elasticities and the Rarities of the Mediums taken together.*
»As Attraction is stronger in small Magnets than in great ones in proportion to their bulk, and Gravity is greater in the surfaces of small Planets than in those of- great ones in proportion to their bulk, and small Bodies are agitated much more by electric attraction than great ones; so the smallness of the Rays of Light may contribute very much to the power of the Agent by which they are refracted.
And so if any one should suppose that Aether (like our Air) may contain Particles which endeavour to recede from one another (for I do not know what this Aether is) and that
its Particles are exceedingly smaller than those of Air, or
even than those of Light: The exceeding smallness of its Particles may contribute to the greatness of the force by which those Particles may recede from one another, and thereby make that Medium exceedingly more rare and elastick than Air, and by consequence exceedingly less able to resist the motions of Projectiles, and exceedingly more abl6 to press upon gross Bodies, by endeavouring to expand itself.
»Qu. 22. May not Planets and Comets, and all gross
Bodies, perform their Motions more freely, and with less resistance in the Aethereal Medium than in any Fluid, which fills all Space adequately without leaving any Pores, and by consequence is much denser than Quick-silver or Gold ? For instance; If this Aether (for so I will call it) should be supposed 700000 times more elastic than our Air, and 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.*

In Newton' % views above quoted, Qu. 20, dating from

172 1, it will be noticed that he not only held the aether

= to be a superfine gas, of enormous elasticity, but also cal-
culated this elastic power to be ^7 490000000000 times

greater than that of air in proportion to its density. By the

= most careful calculations that can be made today, we find
this relative elastic power to be «<? 689321600000; which

shows that the value found by Newton two centuries ago was

— 7 I percent correct,

a wonderfully accurate result, even for

so incomparable a geometer as Newton\

His remarks in Qu. 22 have been raisconstructed by Sir (9/zwr Z^4fr (Introduction to his » Aether of Space «, 1909), in an effort to make it appear that Newton held the aether to have a large density, but the context shows the miscon-
struction involved in this claim. When Newton says that

there is "less resistance (to the planets) in the aethereal
medium than in any fluid which fills all space adequately without leaving any pores, and by consequence is much denser than quick-silver or gold?«, he means that the aether is very

fine grained, more so than any material fluid like quick-silver
or gold, which has pores. He thus held the aether to be

so fine grained that it could truly act as a plenum, yet as-
signed this medium excessively small density. »Maynotits

resistance be so small as to be inconsiderable ? For instance

If this aether (for so I will call it) should be supposed 700000

times more elastic than our air, and above 700000. times

— more rare«

which shows clearly that Newton's value of

the density of the aether is

= = a Y7 0.ooi293><Cio~^ 0.000000001849 (95}

= ^ that of water == i, or c

1/700000, that of air

i.

b) Views of Maxwell, 1877.
In the article Aether, Encyclopedia Britannica, 9'*^ ed.^ p. 572, 1878, Maxwell speaks as follows regarding the molecular constitution of the aether: »Mr. i". Tolver Preston (Phil. Mag., Sept. and Nov., 1877) has supposed that the aether is like a gas whose molecules very rarely interfere with each other, so that their mean path is far greater than any pla-
netary distances. He has not investigated the properties of such a medium with any degree of completeness, but it is easy to see that we might form a theory in which the mole-
cules never interfere with each other's motion of translation^ but travel in all directions with the velocity of light; and if we further suppose that vibrating bodies have the power of impressing on these molecules some vector property (such as rotation about an axis) which does not interfere with their motion of translation, and which is then carried along by the molecules, and if the alternation of the average value of this vector for all the molecules within an element of volume be the process which we call light, then the equations which express this average will be of the same form as that which expresses the displacement in the ordinary theory.
Accordingly it will be seen that the present paper is a development of the reasoning sketchtd by Newton, 1721,,
and again briefly outlined by Maxwell in 1877.

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The vector property, such as rotation about an axis, which Maxwell supposes might be impressed on the aether molecules, will be furnished by the wave motion in the aether, when the waves are taken to be flat in the planes of the equators of ordinary atoms. This is shown in the theory of magnetism outlined in the first paper, and will be treated of more fully in the third paper, in connection with a correction to the fundamental conceptions of the wave -theory
of light.
II. Under the Kinetic Theory of the Aether Michelsori% Celebrated Experiment of 1887 should yield a Negative Result. New Theory of Stellar Aberration based on the Motion of Light relatively to the moving Earth.
In. tke Philosophical Magazine for ,1887, Prof Michelson describes the famous experiment which he devised to detect the effect of a supposed aether drift past the earth, due to an assumed effect of the earth's orbital motion. In this experiment a beam of light, from a terrestrial source, is split into two parts, one of which is sent to and fro across the line of the supposed aether drift, while the other is 'sent along the line of the aether drift.
A semi-transparent mirror set at a 45° angle 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 the half beams whence they came, thus enabling them to enter the observer's eye through a telescope.
W\ N
/' // f/ / /

The path of the light, from a terrestrial source, is thus made parallel and perpendicular to the direction of the earth's orbital motion ; and the two half beams mutually interchanged for observation of the relative displacement of the
interference fringes.
In his work on Light Waves and their Uses, 1903, p. 158, Michelson sums up his experience thus:
»It was found that there was no displacement of the interference fringes, so that the result of the experiment was negative and would, therefore, show that there still is a dif-
ficulty in the theory itself; and this difficulty, I may say,
has not been satisfactorily explained*.

By the reasoning given below, in describing Fitzgerald^^

= hypothesis, sect. 12, it is shown that the effect sought is

very small, depending on the square of vjc

i/ioooo, the

ratio of the velocity of the earth in its orbit to the velocity

of light, and thus of the order of i : 100 000 000. But

Michelson estimates that by his improved apparatus he could
see fringe displacements of i part in 4000000000 if they

existed; and thus the precision of the apparatus exceeded the

magnitude of the fringe displacement sought by forty fold.

On repeated trial, under favorable conditions, everything
behaved exactly as if the aet"her were stagnant. Michelson therefore suspected the difficulty to be in the theory itself;
and we shall now examine into this question, to see if any
ground for this impression can be found.

Owing to the translatory motion of the earth, we may

change the fixed Newtonian coordinates to correspond to

uniform motion in the direction of the x-axis:

= = ^ x'

— X vt y'

y z' == z f

t

(96)

= At the initial epoch t

o, we may equate these coor-

dinates to zero, and our transformations, owing to the motion

of the earth, become:
ai [X- vt)

= y 3^y^

= g'

CiZi.

(97)

Since the velocity of light is the same in reference to

^ = the fixed and moveable systems of coordinates, at the instant

t

f

o, we get for identities of the spherical wave sur-

.

faces propagated from the moving source of light

= x^^y^-^z'^ c'^e

= x'^-hy'^-^z'-^

c^ f^

(98)-

where c is the velocity of light.

Fig. 10.

Illustration of the paths of the split beam of light in Michelson'i experiment of 1887, one part traveling along the direction of
the earth's orbital motion, the other at right angles thereto.

The apparatus was mounted on a stone support about 4 feet square, and one foot thick, and this stone in turn mounted on a circular disk of wood which floated in a tank of mercury. The resistance to rotation of the floating disk is very small, and a slight pressure on the circumference
enables the observer to turn it around in say five minutes, with practically no oscillation.

Under the kinetic theory any heavenly body carries an
electrodynamic wave-field about its Centre of figure, in perfect
kinetic equilibrium. The amplitude of the waves and therefore the density of the aether is arranged as shown in the accompanying diagram (p. 183), where the two stars may have the independent motions indicated by the vectors. The motion of either star automatically carries with it that star's own
wavefield, and each field is independent of the other, just as the field of light waves emitted by any star is independent of that propagated from any other star. Hence owing to the earth's orbital motion we have the phenomenon of stellar aberration, as if the aether were really stagnant, because the wave -field has no motion relatively to the earth, though the earth itself moves, and thus generates the aberration,
as follows:

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wave-field in kinetic equilibrium, moves with the earth, and the gravitational potential depends on the integration of all these wavelets
between the limits —00 to -Hoo.
Thus the triple integral for the potential' corresponds to a trebly infinite system of wavelets due to stresses decreasing with the distance, yet superposed at. all points of space, but the potential for any body itself is finite,
as in the theory of action at a distance.

./

<

Xdx djf dz

(99)

Some of the individual wave surfaces

from any one particle become,-

Fig. 1 1 .' Illustration of the proper motion of two stars which carry with them con-
centric wave-fields in perfect kinetic equilibrium, just as they carry their
spheres of gravitational influence due to these waves. There is thus no such thing as a motion of the aether past the earth, in the sense imagined by Young, 1803, who compared the aether, supposed to be streaming
through the earth, to the wind blowing through the tops of trees.

x"^-hy"''-

r9

2^2= f2/-2.

The light from a distant star travels independently of the motion of Jhe earth and of its moving aether wave-field. Hence to take account of the earth's forward motion, in respect to space, we may imagine the parallel rays of light from the star to be given a backward motion Si identical
with the forward motion of the earth, £/. This is the true motion of the light relatively to the moving earth, and by this simple device, stellar aberration is perfectly explained.
The light actually comes from the direction ^5, and a refractive medium in the path will have no effect whatever.

= The individual wave surfaces have a common and

parallel displacement in space,, v

dsldt

30 kins, owing

to. the orbital motion of the earth.

Yet the stress of the aether, in kinetic equilibrium, is

determined by the compounding of the effects of the waves

emanating from the earth. This fixes the density and rigidity

of the aether, which is arranged symmetrically about the

vibrating particles of the globe. Accordingly, under the

kinetic theory, the aether is stagnant in respect to the moving

earth, precisely as found by Michelsop in his celebrated

experiment of 1887.

Hence no theory but the kinetic theory, with the par-

ticles moving 1.57 times faster than light, can be admitted. This follows at once from our investigation of the enormous

elasticity of the aether, which gives the physical cause of
the observed velocity of 300000 kms per second, for the

Fig. 12.

A direct and simple explanation of the phenomenon
of stellar aberration, based on the motion of light relatively to the moving earth.

rThe reasoning o^ KUnkerfues, about the refractive index of the medium in which the light penetrates, does not deal -with the motion of the light relatively to the moving earth,
and thus has no bearing on the subject. And likewise Airy^
observational experiment, with the zenith telescope tube 36 inches long, filled with water (Greenwich Observations, 187 i,
p. 1-16), is misapplied ingenuity^). The negative results obtained by these authorities is proof of the correctness of the
simple view here set forth.
Accordingly, just as each star carries its own wave-field
with it, so also, each particle of vibrating matter in the earth, sends out its system of spherical waves, and the whole

wave motions constituting light and electricity.

Thus it only remains to state clearly the kinetic hypothesis underlying the wave-theory of physical forces, naraelyr
We conceive all atoms of matter to receive and to emi.t waves,
without regard to the motion of these atoms relatively to other atoms, just as we know the stars emit their typical spectral lines in spite of their proper motions in space.

Accordingly, as the Aether corpuscles have the enormous

velocity of 471000 kms per second, this medium is taken to

^ be in kinetic equilibrium about the moving earth, which will

secure the law of density a

v r, and of wave amplitude

A == k/r. For the .aether has an elasticity 689321600000

times greater than that of our air in proportion to its density,

and if any lack of perfect kinetic equilibrium existed, it

would

disappear

from the '

aethereal

envelope of the earth

') Though I have examined many authorities I can find no satisfactory explanation of the aberration. They are all confused, by some

such reasoning as the following, from Michehoji's Light Waves and their Uses, 1903, p. 151; »The objection to this explanation [Bradley's)

was, however, raised that if this angle (so'.'s) were the ratio of the velocity of the earth in its orbit to the velocity of light, and if we filled

a telescope with water, in which the velocity of light is known to be only three-fourths of what it is in air, it would take one and one-third

.times as long for the light to pass from the center of the objective to the cross-wires, and hence we ought to observe, not the actual angle,

A of aberration, but one which should, be one-third greater. The experiment was actually tried.

telescope was filled with water, and obser-

vations on various stars were continued throughout the greater part of the year, with the result that almost exactly the same value was found

for the angle of aberration.

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in an infinite!}' small fraction of a second, owing to the
mean velocity of the aetherons being 47 1000 kms per second.
12. Sir Oliver Lodged Experiments for detecting the Viscosity of the Aether, 1891-97, and Fitzgerald'^ Hypothesis of a contraction of the dimensions of bodies in the direction of their motion.
.In the Philosophical Transactions, 1893-97, Sir Oliver Lodge describes elaborate experiments with revolving steel disks, about a meter in diameter, which he had spun with the highest possible speed, in close proximity to a split beam of light, arranged as in Michelson's experiment of 1887, in the hope of discovering a relative displacement of the fringes, due to viscosity of the aether. The experiment was well conceived, and executed with great skill, but it failed to give the smallest indication of a displaicement such as viscosity of the aether would be supposed to yield. The results were entirely negative, and Lodge, like Mickelson, could only conclude that the aether behaves as if it were absolutely stagnant-
Let us now consider why the negative results oi Mickelson and Lodge follow, if the aether be a kinetic medium such as Newton, Maxwell and Dr. ^. Tolver Preston conceived it to be, and such as we have found it to be by exact calculations.
If the aether be corpuscular, the particles having a
velocity 1.57 times that of light, it is obvious that it will adjust itself instantly to any state of steady motion, and that
this kinetic equilibrium will be obtained more rapidly than
even the propagation of light. And when Sir Oliver Lodge's
moving disk is revol-^ing steadily, the aether will act as if it were absolutely stagnant.

Fig. 13.

Illustration of Sir Olive?- Lodge's, apparatus for effecting a displacement pf the aether, owing to viscosity, by the rapid rotation
of disks of steel, near which a split beam of light is passed.

Hence the conclusion reached by Sir Oliver Lodge
(Aether of Space, p. 82), as to the revolving disk experiments,
was natural enough and quite justified in the premises, when he declared: »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. 1 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 neigh-

borhood 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

And viscosity or fluid friction of the ether is zero.

that is

an entirely reasonable conclusion.*

In view of our theory of a kinetic medium, we may

now go further than Fresnel, Mickelson and Sir Oliver Lodge,

and declare that as the corpuscular aether, readjusts itself

instantly to any state of steady motion, it follows that the

motion of the earth can in no way disturb it. There is

planetary induction indeed, from the wave-effect due to the

relative motion of the sun and earth, but this is observable

only

by magnetic

instruments,

and not ,

by

means

of

other

apparatus used in physical experiments.

If, as is definitely proved by calculation, the aether
has an elasticity 689321600000 times greater than that of-

our air in proportion to its density, it is obvious that it not only penetrates all bodies, but even the- electrodynamic waves
in the aether may traverse the body of the terrestrialglobe

with only a small resistance, giving merely refraction, dispersion, and perhaps absorption, of part of the energy, as we have shown iri the theory of the lunar fluctuations (Electrod. Wave-Theory of Phys. Fore, vol. I, 1917). , It not only follows that this adjustment of the aether to any state of steady motion

will occur, but also that no power in the universe could

prevent such, a kinetic adjustment, in theall-pervading medium,

under the above stupendous elastic power which it exerts

against itself. "It is thereby .rendered almost incompressible,
the waves traveling with a velocity of 300000 kms per second.

The physical meaning of such rapid propagation of.
waves is this: When a wave begins to be generated, the
disturbance speeds away very rapidly, so that the- movement

is not cyclicly complete until a wave length X has been

traversed.. . As the amplitude a is very small, compared to /.,

— — as Lord Kelvin, Maxwell and Larmor have shown,

it

follows that the aether is nearly incompressible, though the

density at the sun's surface is only

^ (T

^.oX io~^* .

These last considerations also show why we cannot

disturb the aether by revolving. disk experiuients. Accordingly it is not remarkable that Prof F. E: Nipker, of St. Louis,

has ^succeeded in disturbing the aether only by means of

explosions of dynamite, an explosive of enormous power and

excessively quick action. ' This not only shows the futiliiV

of viscosity "experiments, with comparatively slow, steady
motions, as when the revolving disks, a meter in diaineter, make 66 rotations in a second -^j, but also confirms the

m _') This is only i 12356195 of the velocity of the aetheron, 471239000 per second.

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extremely rapid readjustment of the aether when disturbed. Therefore it follows that our theory of a kinetic medium,
with the particles traveling 1.57 times faster than light, is in accordance with all the established facts of observation.

After giving a summary of all the known effects (Aether of Space, p. 62-63), Lodge concludes that the aether behaves
under experiment as if it were stagnant with respect to the
earth. »Well then, perhaps it is stagnant. The experiments 1 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 aether were stagnant nothing could be simpler than their explanation.

The new theory of the aether as a kinetic medium

gives the stagnant quality sought by Michelson and Lodge, yet it preserves the »perfect freedom* with which the ex-

periments are consistent.

Accordingly, the aether being a perfectly elastic cor-

puscular medium, always adjusting its internal stresses with

— at least the velocity of light

the individual particles having

— a velocity of 1.57 times greater yet,

it follows that around

a body moving with uniform velocity there could be exerted

no sustained forces, impressed or acting upon the atoms, to alter the linear dimensions of the uniformly moving body; and hence we reject Fifzgerald'% hypothesis as altogether

misleading.
i^/fe,f<'ra/flf's 'Hypothesis, that the linear dimensions of bodies are altered by motion relative to the aether, superfluous and misleading.

In Nature for June 16, 1892, Sir Oliver Lodge mentions

a conversation with the late Prof. Geo. F. Fitzgerald, (cf. also

Lodges Aether of Space, igog, p. 68) to the effect that the dimensions of material bodies are slightly altered when they are in motion relative to the aether. The negative result of

the Michelson- Morley exYttnxae-ni of 1887 was the occasion

which called forth Fitzgerald's hypothesis.
V If be the velocity of the earth's orbital motion, c the
velocity of light, / the length of path traversed by the beam

of light divided in Michelson's experiment; then, one of the two portions of a split beam of light should make its journey

in less time than the other by the interval V^ljc^, if the

aether itself be motionless, as Michelson supposed. This difference, however, would be compensated if the arm of

the apparatus pointed in the direction of the earth's motion
were shorter than the other by an amount Y2 V^ljc"^, which would follow if the linear dimensions of moving bodies are

contracted in the direction of their motion in the ratio of
(i-V,FV) to !.

Now for the earth the ratio in question is:
= = F/c 3okm/sec: 300000 km/sec i/ioooo (loi)

and the square

== V'^jc'^ i/i 00000000

(102)

— which shows that the alteration in dimensions

namely

6l={^l,V^'lc']l

(,03)

is only one two hundredth millionth. (The minuteness of this hypothetical observed effect would make detection by experiment extremely difficult, even if a valid method could be devised. But let us consider, on other grounds, whether

such an alteration in dimensions is' consistent with sound
physical laws.
By this hypothesis of Fitzgerald, the end-on-dimensions of a moving body is shortened

Fig. 14.

Illustration of Fitzgerald's liypothesis that the
dimensions of a body, moving freely, uniformly, and without constraint, is decreased in the di-
rection of the motion.

as shown in the figure. This hypothetical change is not

— postulated for the starting of a body in motion

where

its figure might be changed in overcoming inertia, when

— the forward velocity is being developed

but for a body

already in uniform rectilinear motion, and thus so far as is

known subjected to no strain of its linear dimensions.

Newton's first law of motion (Principia, Lib. I, Axioms)

is: »Every body perseveres in its state of rest, or of uniform

motion in a right line,, unless it is compelled to change that

state by forces impressed thereon.

» Projectiles persevere in their motions, so far as they

are not retarded by the resistance of the air, or impelled

A downwards by the force of gravity.

top, whose parts by

their cohesion are perpetually drawn aside from rectilinear

motions, does not cease its rotation, otherwise than as it

is retarded by the air. The greater bodies of the planets

and comets, meeting with less resistance in more free spaces,

preserve their motions both progressive and circular for a

much longer time.«

If these axioms were obvious to Sir Isaac Newton, it

will no doubt be equally obvious to us that a body may

— have its dimensions altered in acquiring a velocity,

as

— when a ball is struck by a bat

yet the elasticity of the

body will immediately assert itself, so that the figure will

oscillate about its mean or undisturbed form; and after a

cert^n time the original figure will become restored. And

thereafter there will be no permanent change of figure. This

is. a fact of universal experience, and may be verified ex-

perimentally 'in our laboratories by all manner of actual

measurements.

The most careful physical experiments show that bodies

placed under constraint, tend very rapidly to restore their

figures of equilibrium. Accordingly it follows that bodies

having uniform motion of long duration in any direction,

could not undergo changes of figure, in virtue of uniform

motion, without physical constraint, which in turn would call

forth the power of restitution, at the instant of release. Hence in uniform unrestrained motion no alteration in' the

figure of equilibrium appropriate to a state of rest would be possible, and Fitzgerald's contraction hypothesis is contrary

to the order of Nature.

In concluding this second paper, it is scarcely necessary to point out that prior to the development of the kinetic theory
of the aether, experiments like those made by Michelson and Morley and Sir Oliver Lodge led to the idea of a stagnant.

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aether. There are indeed profound reasons why the aether

should

act

as if it ,

were

absolutely

stagnant,

whereas

the

particles really .

move

1.57 times

faster

than

Hght,

and

thus

the medium instantly adjusts itself to any state of steady

motion, whatever it may be; because the motion of the

aetheron is 10000 fold.fastej than that of our swiftest planets,

and over two millions of times faster than any steady

artificial motions which we can make experimentally, as in.

the researches of Sir Oliver Lodge with rapidly revolving

disks of steel.

On the old hypotheses the Michelson-Morley experiment

of 1887 was admirably adapted to detect the effect of the

earth's motion through the aether. Little did these eminent

experimenters - dream that the earth carried its wave-field of

— aether with it,

aU infinitely extended and adjusted in

perfect kinetic equilibrium. This wave-field has decreased

density towards the centre, in virtue of the increased amplitudes of the waves emanating from the atoms, and thus is truly stagnant about the moving earth in respect of waves of light from distant stars, in the phenomenon of aberration.

Accordingly, whether the components of the split beam of light, from a terrestrial source, as used by Michelson, travel

in the. direction of the earth's orbital motion, or at right .
angles thereto, no shift of the fringes is theoretically possible,

because of the perfect kinetic equilibrium of the wave-field

of the aether about the earth and extending away from it

indefinitely;.

For similar reasons Fitzgerald' % hypothesis rests on a

false premise, and only beclouds the reasoning in this difficult subject. The fundamental condition required for real

progress is a valid kinetic theory of the aether, such as
Newton first outlined two hundred years ago, and Maxwell

approved in 1877, but left very incomplete, owing to the

premature death of this great mathematician.

Since the difficulties connected with the motion of the

perihelion of Mercury and of the lunar perigee, as well as

the lunar fluctuations, which Newcomb pronounced the most

enigmatical

phenomena presented

by the celestial '

motions,

are fully overcome, without any mystical doctrine such as

Einstein introduces, it is evident that the whole theory of

relativity, as heretofore developed, is shaken to its founda-

tions, and will no longer deserve the serious consideration

of natural philosophers.

For several years experienced investigators in all parts

of the world have wondered at the strange sight presented

by British men of science in unjustifiably abandoning the

established natural philosophy of Newton, and hastily em-

bracing the untenable speculations of Einstein when the facts
of observation themselves are insecurely established.
And as for the overdrawn statement of Prof. Sir J. J.
Thomson, President of the Royal Society, that the supposed larger value of the solar deflection of light indicated by the
eclipse observations of May 2g, .1919, »is,the most important
result obtained in connection with the theory of gravitation •imch- Newton'^ day, and it- is fitting that it should be announced at a meeting. of the society' so closely connected with him«, it suffices to call attention to the unfortunate
impression thus conveyed to investigators, who remember on the one hand the historical fact that the Royal Society in 1686 refused to publish 1) Newton's Principia, and thus it had to be issued at the private expense of Dr. Edmund Halley (cf Brewster's Life oi Newton, 2 vols., 1855), and on the other. hand the vast development and perfection of the theory of gravitation since made by Euler, Clairault, Lagrange, Laplace, Poisson, Bessel, Gauss, Hansen, Leverrier, 'Airy, Delaunay, Adams, Tisserand, Gylden, Hill, Newcomb, Foincard, Darwin, and several eminent geometers still living.
In contradistinction to the singular spectacle thus pre-
sented in the Royal Society, it is a relief to find a much more cautious attitude in the Monthly Notices for Nov;, 19 19, p. 23, where Prof. Newall gives good reasons for rejecting
Einstein's theory of the deflection of Hgbt in the sun's field, in favor of optical refraction.
In the Nineteenth Century Magazine, for Dec, 19 19, Sir Oliver Lodge likewise is skeptical; for he reasons that if we accept Einstein's theory in its entirety,' »the death knell of the aether will seem to -have, been sounded, strangely
efficient properties will be attributed to emptiness, and theories of light and of gravitation will have come into being unintelligible on ordinary dynamical principles*. Such protests would indicate that the" Newtonian philosophy still has. some supporters in England, but apparently they are not
aware of the real strength of their cause, as now brought to light in the New Theory of the Aether.
Accordingly, in view of the comprehensive results al-
ready reached in the New Theory of the Aether, the 'defenders
of the Newtonian mechanics could hardly wish for a more complete triumph. And it is gratifying to realize that it is based upon the original conceptions of Sir Lsaac Newton himself, after the simple and elegant theory of this great philosopher had been almost completely abandoned by his countrymen.
I am indebted to my young friend Mr. E. L. Middleton,
for valuable assistance in the completion of this investiga.tion.

Starlight on Loutre, Montgomery City, Missouri, 1920 Febr. 19.

T. J. J. See.

') The well known delay of 14 years (1807-1821) in the publication oi Fourier' % mathematical researches on the theory of heat seems

— to place the Paris Academy of Sciences in an equally unfortunate light. In the Eloge Historique of Fourier delivered by Arago, blame is

placed on the commissioners of the Academy

Lagrange, Laplace and Legendre '— for poisoning the pleasure of Fourier's, triumph, which

Lord Keivin has also criticized. As no commissioners could be more competent than the three geometers just cited, history often is witness

to the weaknesses of the highest acadtemies of sciences; and hence, in his very original Researches in the Lunar Theory, 1877, Dr. G. W. Hill

had recourse to private publication, which probably was better than the fate accorded to Newton and Fourier.

1

,

Abdruck aus den Astr. Nachr. Nr. 5079.

— (Band 2 12.

Dezember 1920.)

New Theory of the Aether. By T. J. J. See.

(Third Paper.) (With 3 Plates.)

I. Two Remarkable Theorems on the Physical the aether based on an extension of recognized processes

Constitution of the Aether.

in the theory of sound. As the only method for attacking

In the year i q i o Professor E. T. Whittaker published, under the auspices of the Dublin University Press, a valuable » History of the Theories of Aether and Electricity* from

the problem of the density of the aether heretofore known is that invented by Lord Kelvin in 1854, this new method will prove extremely useful as an independent check on the

the age of Descartes to the close of the ig'*" century. The numerical values attained in these recondite researches; and title of this useful treatise and the general usage of science be found the more valuable because it is absolutely decisive

recognizes that there is some connection between aether against the doctrine of a large density for the aether, which

and electricity, yet in spite of the great learning shown in Whittaker'% work, the nature of that connection remains profoundly obscure, and the modern investigator therefore labors in vain to obtain any clear light upon the subject.
If we could prove, for example, that an electric current is nothing but a series of waves of a certain type propagated in the aether along and from the wire which bears the current, and also connect these waves with magnetism and light, by an extension of the reasoning thus laid down, it would add so much to our understanding of the processes under-

has recently exerted in science an influence both baneful

and bewildering.

(i) The new theorem v,= ^j^n V, connecting the mean

molecular velocity of a monatomic gas with the velocity of wave-

propagation, by means of half the Archimedean number, exactly

confirmed by observation in case of oxygen and nitrous oxide.

Since finishing the first paper on the New Theory of

the Aether, Jan. 14, 1920, I have had occasion to discuss

the new theorem

= v y^_nV

(i)

lying the unseen operations of the physical universe, as to connecting the mean molecular velocity of a monatomic gas

be worthy of almost any effort. Indeed, it would be worth and the velocity of wave-propagation, by means of half the

hazarding any chance offered by the conscientious contem- Archimedean number n, with the celebrated English physiplation of known phenomena. And thus I venture to add cist Sir Oliver Lodge, on the occasion of a public address

some considerations, which, without exhausting the subject, at San Francisco, April 11, 1920. And as Sir Oliver Lodge may open a new field to those who have the independence, kindly showed a great interest in this theorem, regarded it

practical energy and firm resolution to ptlrsue pioneer paths as very important, and urged me to extend the use of the

in science. These untrodden paths alone offer the hope of theorem, I have searched for other gases to which it might

'important discoveries in the physical universe.

be accurately applied,

And first we must confirm a new and important theo-

The observed data given in the following supplemen-

rem on the velocity of wave-progagation in monatomic gases, tary table are taken from IViillner's, Experimental-Physik

announced in the first paper, and also make known a new Band i, p. 804, and were accidentally overlooked in the pre-
and very remarkable method for determining the density of paration of my earlier table.

Gas
Oxygen, O Nitrous-Oxide, NO2

F(Air

^ 0.9524 [Dulong] = 0.7865 [Dulong]

316.2 m
281.

V observed
461.0 m
393-0

rnolecular wt.
32.0 44.0

»/,r(observed) r'/v-V(kJk2

1.402 I-29S

.458
398

5893 5858

V The last column gives the observed ratio vj

as cor all of which are of comparatively simple molecular consti!

rected for a monatomic constitution, or

= vlV-V[hlk,) i.z&

(2)

which verifies with great accuracy the use of half the Archi-

medean number n, in the theorem,

= V

V l/jTT

connecting the mean molecular velocity with that of wavepropagation in monatomic gases.

tution, we may regard it as fully established by experiment
that such a physical law governs the motions of waves in monatomic gases, and that the velocity of wave motion is
solely dependent upon the mean velocity of the molecules.
But in addition to the argument thus built up, for ahigh wave velocity, where- we have a rare gas of enormous
molecular velocity, we may use the observed velocity of
wave-propagation generally to throw light upon the molecular

As this theorem is now minutely verified for the six weights of all gases whatsoever. In the reference above given

best determined gases, namely:

to M'ullner's Experimental-Physik, Band i, p. 804, we find

1. Air

4. Carbon dioxide CO-^

that the velocity of sound in hydrogen was found by Dulong

2. Hydrogen

5. Oxygen

3. Carbon monoxide CO 6. Nitrous oxide NO^

to be 3.8123 times that in air, and by Regnault, 3.801 times
that in air. The mean of the two values is 3.80665. Now

!35

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236

the velocity of sound in oxygen found by Dulong was 0.9524 times that in air; and on multiplying this by 4, we get 3.8096 for the theoretical velocity of sound in hydrogen.
But since oxygen is supposed to have only 15.98 times the molecular weight of hydrogen, we should use the square root of this number, or 3.9975, instead of 4, for the multiplier, which gives 3.8072; an almost exact agreement with
the mean of the velocities of sound in hydrogen found by Dulong and Regnault.
It follows, from these considerations, that the velocity of wave motion in similar gases varies inversely as the square
roots of their densities. The fourfold increase in the velocity of sound in hydrogen compared to that in oxygen gives us a definite law which may be applied directly to all comparable gases, and even to monatomic gases by the use of
the faktor V[h\k:^.
(ii) New method for determining the density of the
aether from the velocity of light and electric waves compared to that of sound in terrestrial gases.
Up to the present time only one general method has
been available for calculating the density of the aether, namely, that devised by Lord Kelvin for determining the mechanical value of a cubic mile of sunlight, and first published in the Transactions of the Royal Society of Edinburgh for May, 1854 (cf. Baltimore Lectures, 1904, p. 260). This method was somewhat improved by the subsequent researches of Lord Kelvin, Maxtvell, and the present writer,
as duly set forth in the first paper on the New Theory of the Aether (AN 5044, 211.49), yet the principle underlying
it remains largely unchanged.
As it would be very desirable to have a second independent method for determining the density of the aether, I have held in mind this great desideratum while occupied with the researches on the wave-theory, and finally it occurred
to me to attack the problem from the point of view of the velocity of sound in gases. For we have now shown that
the aether is a gas, with particles traveling 1.57 times swifter than light; and this general, theory is again confirmed by the discussion above given for waves of sound in oxygen and nitrous oxide.
Owing to its extreme rarity, the aether is the one absolutely perfect gas of the universe; and we may even use
the velocity of light in the aether to calculate the density of this medium. It will be shown, especially in the fourth
paper, that there is much less difference between the waves of sound and light than we have long believed. In his luminous but neglected memoir of 1830, the celebrated French geometer Poisson, showed and thrice repeated, in spite of the earlier repeated objections oi Fresnel, that in elastic media
the motions of the molecules, at a great distance from the source of disturbance, are always normal to the wave front,
as in the theory of sound. And we shall show later how optical and magnetic phenomena are to be reconciled with
this incontestible result of Poisson's, analysis.
From the data given in the first paper on the New
Theory of the Aether it follows that the velocity of light is 904268 times swifter than that of sound in air. As sound

in hydrogen has a velocity 3.80665 times greater than in

air, this is equivalent to 237550 times the velocity of sound

in hydrogen. But hydrogen is a biatomic gas with the ratio

= k^

1. 40 1, while aether is monatomic, with the ratio

= ki

1.666; and therefore to reduce the motion in hydrogen

to the basis of a monatomic gas, we have to divide this

number by V[kilh)'r= 1.090477, which leads to the num-

ber 217839. This is the ratio of the velocity of light in a

monatomic aether to that of sound in a hypothetical mona-

tomic hydrogen, yet with density 0.0000896.

This result is based on the wave theory of sound as

given by Sir Isaac Newton in the Principia, 1686 (Lib. II,

Prop. XLVIII), which was corrected by Laplace in 18 16

(cf. Mecanique Celeste, T. V. Liv. XII, p. 96, and Ann. Phys.

et Chim., T. Ill, p. 288), to take account of the augmentation

of speed due, to the ratio of the specific heat of a gas under

constant pressure to that under constant volume. As above

used the formula for the propagation of sound is further

corrected to take account of the increase in velocity in a

monatomic gas, first inferred theoretically by Clausius about

sixty years ago, but since verified experimentally for mercury

vapor, argon, helium, neon, xenon, and krypton. The formula

thus becomes for aether and hydrogen, as reduced

monatomic elasticity:

= = VxlV.

V{£xa2/£,ai)

217839.

to a (3)

= Under identical physical conditions at the surface

earth, .£1

£2, and thus

= = K1/F2

l/(o-2/(ri)

217839

of the

or

= = = = ^1

^l"/f^2^

CzM

(217839)^ 47453880000 (4)

which is the density of hydrogen in units of that of aether.

To get the density of water in units of that of aether,

we take

= = ^Vg

7V"i/o. 0000896

529619000000000.

(5)

Accordingly the absolute density of the aether at the earth's surface becomes:

i/i\^2 == (r== 1888.15 -lo-is.

(6)

•

It should be noted that Lord Kelvin's method of 1854,

which we used in the first paper on the New Theory of the

Aether, is not strictly valid, because although it gives the

density at the earth's mean distance, in units of the assumed

density at the sun, this latter value itself cannot be found

by Kelvin's method, because of the decrease in the aether

density near the earth, not heretofore taken account of.

Let (Ts be the density at the neutral distance, Qg, where

the sun's gravitational intensity is just equal to that of the

earth. Then, since at the solar surface the mean gravity is

AN 27-86555 times terrestrial gravity (cf.

3992), we have:

27-86555/(219)2= 1/^32

(7)

= where Qg

distance at which solar and terrestrial gravity

= will just balance. This gives by calculation Qs

'
41.4868

terrestrial radii, about V3 of the moons distance. The

following table gives the results of similar calculations for

the absolute density of the aether at the surfaces of the sun

and principal planets of the solar system.

237

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238

Table

«

239

5079

240

tlieoretical value of wave propagation from the use of the
ratio V[kijki). And if the velocity of the wave-propagation be observed in both cases, and we desire to determine the relative density of one of the gases, we may effect this as
in the above case of the aether, which absolutely excludes the possibility of a large density. As the aether is a gas of excessively small density, it is therefore compressible, as previously inferred, but only by powerful, quick-acting forces.
The study of the aether as a gas, in accordance with the views entertained hy Newton in 17 21, and approved by Maxwell in 1877, thus opens new possibilities, and introduces
criteria of the utmost value to physical science.
2. Geometrical and Physical Outline of the Relationship between Light, Magnetism and the Electrodynamic Action of a Current.
In the 3'^'* edition of the celebrated Treatise on Optics, 17 2 1, Query 28, Sir Isaac Newton treats of Huyghens' theory of double refraction in Iceland spar, on the hypothesis of two several vibrating mediums within that crystal, for refracting the ordinary and extraordinary rays, but says that Huyghens was at a loss to explain them. »For pressions or motions, propagated from a shining body through an uniform medium, must be on all 'sides aliise; whereas by these experiments it appears, that the rays of light have different properties on their different sides.
In proof of this confession of failure, by Huyghens, Newton cites from the Traitd de la Luraiere, 1690, p. qt, the words: »Mais pour dire comment cela se fait, je n'ay
rien trouve jusqu'ici qui me satisfasse.«
Newton then argues effectively against the explanation of Huyghens, and points out the improbability of two aethereal media filling the celestial spaces, which has been emphasized in recent times by Maxwell, who declared it unphilosophical to invent a new aether every time a new phenomenon was to be explained.
In the early days of the modern wave theory of light, the properties of polarized rays were carefully investigated by Fresnel and Arago, and subsequently verified by Sir Joh7i Herschel and Airy, who fully confirmed Newton's conclusion that such rays have sides with dissimilar properties on opposite sides. The account of JFresnel's progress given by Arago in his filoge Historique, July 26, 1830, is -very instructive, since Arago was associated with many of FresneTs discoveries. Besides the able analysis in the celebrated and comprehensive article Light, Encyclopedia Metropolitana, 1849, Sir John HerscheTi, Familiar Lectures on Scientific Subjects, 1867, are valuable, in showing his mature conclusions.
It being thus recognized that a ray of polarized light has sides, with dissimilar properties on opposite sides, it remains for us to forrn.a clear image of such a ray of light,
and to examine the phenomena of magnetism and electricity,
to ascertain if a relationship to light can be established.
The late Professor Paul Drudes comprehensive Lehrbuch der Optik, Leipzig, iqoo, may be consulted for a modern
analysis of purely optical problems ; but, as our object is to
outline relationships not heretofore developed, we shall make
the optical treatment very brief.

Let u denote the displacement of the aether particle

from its vertical position of equilibrium, as on the surface

of still water. Then we have for a flat wave in the plane

= = xy the wellknown equation

z^

asin(27r-//T+-/)

asin(27r-Jc/A-+-/)

(15)

where u represents the displacement at right angles to the
a;-axis, a is the amplitude, X the wave length, and / the
phase angle, from which the revolving vector of radius a is measured. Such a flat wave represents motion like that propagated along the surface of still water, and the movements are given in detail by figure i, Plate 4, which is slightly modified from that used by Airy in his great treatise on
Tides and Waves, 1845.

It will be noticed that each particle of water undergoes
an oscillation about a mean position, shown by the centres of the circles, in this very accurate figure, while the wave form moves on, in a direction corresponding to the axis of X in equation (15). Thus the particles undergo not only a vertical oscillation, as the wave passes, but also a longitudinal oscillation. This is typical of all waves in water.

Now it is usual fo take (15) as the equation of the
motion of the aether in light, and to call u the light vector, and to describe this light vector as revolving, when the wave advances. The motion u in (15), however, is simply a side
displacement normal to the x-axis, which may be produced

by the revolution of the radius a in the circles, as in

our figure modified from Airy's analysis of water wave-
motion. The real motion of the aether particles should be somewhat elliptical, but much like those of the water par-

ticles, about ^ mean position of radius a. Equation (15) then '' will give only the side displacement, normal to the x-axis;

and to get the whole motion of the particles we have to
take the components v and w normal to the jv-axis and z-axis
respectively. Then the three components of the directed

magnitude, which represents the oscillation of the particle

about its mean position, will be

= u acos[2Tf t/r-i-p)

= V

b coh[2TT. tlz-^q)

= w

c 005(271 • t/z-hr)

(16)

= {u/aY+{v/l>Y+(«^/cr ^

(17)

It will be proved hereafter that there is a fundamental
error in the wave-theory of light, as handed down by tradition from the days of Young and Fresnel; and that in a ray of common light the aether particle not only has trans-
verse motion, but also a corresponding longitudinal motion, depending on the small ratio of the amplitude a to the wave length X. After polarization these natural free motions of the aether are restricted, by the resistance impressed upon natural light, in the surface action of reflection, or transmission through transparent bodies, crystals, etc., and by unsymmetrical transparency in different directions, as in tourmaline, which forces half the light into one plane and destroys the other half. Originally the general path of the aetheron was elliptical,
and although now transformed into oscillations near one plane
the vibrations in most cases still are narrow ellipses, because it is proved by the reflection of plane polarized light from

«

241

5079

242

a silver surface that an almost circular polarization results, whereas that reflected from galena has very narrow ellipses. This could not well result unless the polarized light before reflection from these metals described narrow ellipses, which are not exactly straight lines.
Now the elliptical paths established by equations (16),
(17), (18), are similar to those" analysed by Herschel in Section 618 of his great article Light, 1849. Suppose we consider the part of these waves which in a polarized ray have only right-handed rotations. Then if such a selected beam traveling along the ^-axis be looked at flat on, from a point on the 2-axis, the paths of the aetherons would resemble the motions of the particles of water in Airy's figure
given as fig. i, except that the aetherons may have paths more highly elliptical than are shown by At'ry. This is the simplest form of the oscillations in the new wave-theory of light, which will be developed in the fourth paper: and we shall now
see if it is possible to find corresponding oscillations in the field of a magnet and of an electric current.
In the year 1845 Faraday made a celebrated experiment in which he passed a beam of plane polarized light along the lines of force; and discovered that when the light travels in a material medium such as heavy lead glass, carbon-
disulphide, etc., the plane of polarization is twisted by the action of the magnetic field. Not only is the plane of
polarization rotated, but the rotation increases in direct pro-
portion to the length of path traversed; and even when the light is reflected back and forth many times the twisting of the plane of polarization is always in the same direction like the helix of a circular winding stairs, as was long ago noted by Sir John Herschel.
In the article Wave-Theory, Encyclopedia Britannica, <f^ edition. Lord Rayleigh describes this rotation of the plane of polarization by magnetism as follows:
»The possibility of inducing the rotatory property in bodies otherwise free from it was one of the finest of

Faraday'% discoveries. He found that, if heavy glass, bisul-

phide of carbon, etc., are placed in a magnetic field, a ray

of polarized light, propagated along the lines of magnetic

force, suifers rotation. The laws of the phenomenon were carefully studied by Verdet, whose conclusions may be summed

up by saying that in ,a given medium the rotation of the

plane for a ray proceeding in any direction is proportional

to the difference of magnetic potential at the initial and

final points: In bisulphide of carbon, at 18° and for a

difference of potential equal to unit C. G. S., the rotation of

the plane of polarization of a ray of soda light is 0.0402

minute of angle.

»A very important distinction should be noted between

the magnetic rotation and that natural to quartz, syrup, etc.

In the latter the rotation is always right handed or always

left handed with respect to the direction of the ray. Hence

when the ray is reversed the absolute direction of rotation

A is reversed also.

ray which traverses a plate of quartz

in one direction, and then after reflexion traverses the same

thickness again in the opposite direction, recovers its original

plane of polarization. It is quite otherwise with the rotation

under magnetic force. In this case the, rotation is in the

same absolute direction even though the ray be reversed.

Hence, if a ray be reflected backwards and forwards any

number of times along a line of magnetic force, the rotations

due to the several passages are all accumulated. The non-

reversibility of light in a magnetized medium proves the

case to be of a very exceptional character, and (as was

argued by Sir W. Thomson) indicated that the magnetized medium is itself in rotatory motion independently of the

propagation of light through it.«

— Now if I understand this subject aright

and my per-

sonal correspondence with the late Lord Rayleigh shows

— that he concurred in the present writer's views

we must

conceive a line of force, circhng around between the poles

of a rnagnet, to be the axis of rotation in magnetic wave-

motion, as shown by figure 2, repeated
from the first paper on the New Theory

of the Aether.

If this interpretation be admissible,

we see that just as plane polarized light

— has sides,

with dissimilar properties on

— o-''0'O-'O /rVr-t^i^-H^.za-''^'' 0PP°^''^ sides, as remarked by Newton, Fresnel, Arago and Sir John Herschel,

so also there are plane waves receding

from magnets with exactly the same sides,

with dissimilar properties on the opposite

M Wav

Hon , ,t,

The wave-theory of magnetism, which gives a direct and simple explanation of both attraction and repulsion, and harmonizes the known phenomena of magnetism, optics and electrodynamic action.

sides. It is these sides with oppositely directed rotations in the waves of the aether which gives poles to magnets.^)
Magnetic polarity is thus directly connected by similarity of the rotations in the plane waves with plane polarized
light. And just as the amplitude of light
waves decrease inversely as r, the distance from the radiating centre (cf. Drude, Lehrbuch der Optik, 1900, Teil II, Kap. II)

') » Newton came to the conclusion that each of the two rays (qf polarized light) had two sides; and from the analogy of this two-

— sidedness with the two-endedness of a magnet the term polarization arose"

Gage's Principles of Physics, 1897, p. 404.

243

5079

244

A = / so also in magnetism, the wave amplitudes follow the law: kjr, giving the force =^ k'^jr^, as observed in the

actions of magnetism and universal gravitation (cf. Electrod.

Wave-Theory of Phys. Fore, Vol. i, 19 17). Accordingly,

the connection between magnetism and light is obvious, the

moment we do not restrict our conceptions of light to the

side displacement in (15)
u ^^ asm{2n-x/k-hp)

(ig)

but regard light as a disturbance involving a circular or
elliptical displacement of the particles about a mean position, as the vector a representing this displacement in the case of a circle, revolves in a plane, which may be tilted at any

angle relative to the coordinate axes. In his celebrated article Light, 1849, Sir ^eAn Herschel
shows, by carefully considered reasoning, that in the elliptical paths of the aethereal vibrations constituting light, the motion

of the aetheron is about the centre of the ellipses, just as
is the path of a vibrating conical pendulum, which may also
change the path of its motion under the steady application

of small impulses.

Suppose the undisturbed position of an aetheron be

taken as origin, and let two radii vectores, drawn from the

centre of the elliptical path to the disturbed aetheron, be o

and q'\ then we have the wellknown equations

.-vr^+_y^

o'2 == x'2+y2-

= + qq' cos 6

xx'-^yy' zz'

^ cos©

cosa cosct'-Hcos/J cos/S'-Hcos/ cos;''

,

,

+ + = = cos^a cos-/J cos^;'

cos^ct'-Hcos^jS'-i-cos^;''

i.

The angle 6 measures the motion of the light vector

in the plane of the ellipse, while the angles a, /J, y, a', /S', y'

are fixed by the direction cosines of the revolving radius

vector at any time.

It now remains to examine the disturbances taking

place about a wire bearing an electric current flowing from

south to north, as in Oersted's experiment of i8ig. Here

we notice that if the needle be suspended beneath the wire,

the north pole is deflected to the west by the action of the

current. If the needle be suspended above the wire, under

like conditions, the north pole is deflected to the east.

It thus appears that just as magnets have plane waves
— like those of plane polarized light rotating in one direction, — and thus having dissimilar properties on opposite sides

so also an electric current has plane waves with sides, and with dissimilar properties on opposite sides, as shown by

the study of Oersted's experiment of 18 19. This follows
also from the production of magnets from common steel

under the electrodynamic action of a solenoid, as in Amflrcs

experiment of 1822.

The correct theory of an electric current is that it is

made up of plane waves, flat in the plane through the axis

of the wire, as shown in figure 12, section VI, and more fully

in figure 18 (PL 6), section IX, below. In his celebrated address on the relations between

light and electricity, Sept. 20, 1890, Herts tried to illu-

minate the connection previously recognized by Maxwell, and

distinctly referred both light and electricity to the aether.

»I am here«, he says, »to support the assertion that light of

— every kind is itself an electrical phenomenon

the light

of the sun, the light of a candle, the light of a glow-worm. Take away from the world electricity, and light disappears; remove from the world the luminiferous ether, and electric and magnetic actions can no longer traverse space* (cf. Hertz, Miscellaneous papers, p. 313).
Hertz was not able to make out the details of the relationship sought, but the experiments which he devised to show that electric waves are refracted, reflected and interfere, like light waves, marked an epoch in the development of radiotelegraphy, and have long since become classic. Yet when others took up the work, after Hertz's premature death, whilst they verified and used his results, they did not add to the theory of the aether, which Hertz considered essential to scientific progress. Hence the need still remained to tra-
verse the lofty summits not yet explored [Hertz, 1. c, p. 327), and to make out geometrically the nature of the displacements involved in these waves.
Accordingly we have gone into the nature of light and electric waves in such a way as to illuminate this relationship. Hertz remarks that to many persons Maxwell's electromagnetic theory is a book sealed with seven seals. Thus the breaking of the seals, that we may read the details of the illuminated pages, would alone give us a direct view of nature's secrets, and justify any treatment which would throw light on this obscure subject and confirm the doctrine of
continuity in natural philosophy.
3. Elder's Defective Theory of Magnetism has misdirected Thought in Modern Science: Simple
Explanation of Induction, and of the Dynamo on
the Wave-Theory.
(i) Elder's theory of aetherial circulation, and its per-
sistence since 1744.
Nothing could better illustrate the unsatisfactory state of the traditional doctrines of electricity and magnetism, than
the old conception of a magnet, first outlined by Eulcr at Berlin, 1744, and since handed down, with very slight changes, and thus copied, with the original defects of sym,metry, into hundreds of works on physics used by the prin-
cipal nations of the world.
It is authenticated, that in his university career at
Basel, Euler had studied both anatomy and physiology. Asan outcome of this anatomical research he was familiar with the circulation of the blood in the human body. Thus heunderstood the valvular structure in the arteries, which securesthe flow of the blood in one direction only, as the heart beats to expel the blood through the arterial system.
Accordingly when Euler attempted, twenty years later,. to develop a theory of magnetism, which should reconcile all the known facts, including the attraction of unlike and the repulsion of like poles, he assumed a flux of the aether,, along the axis of the magnet, inward at the south pole and outward at the north pole, as shown in figure 3 . Plate 4 ivom Euler' s work (Dissertatio de Magnete, 1744, published
in Euler's Opuscula, vol. Ill, Berlin, 1751, Plate I).
This remarkable figure has been handed down by tradition for 176 years, and its validity apparently seldom or
never questioned, though it probably is less used of late years than formerly. It appears in the physical treatises of

:

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246

all countries, and has vitiated even the mathematical theory of Maxwell (Treatise on Electricity and Magnetism, vol. II.,

p. 28, § 404).
Maxwells reasoning is as follows

»The magnetic force and the magnetic induction are

identical outside the magnet, but within the substance of the

magnet they must be carefully distinguished.*

»In a straight uniformly magnetized bar the magnetic force due to the magnet itself is from the end which points

north, which we call the positive pole, towards the south

end or negative pole, both within the magnet and in the

space without.*

The lack of symmetry and of appropriate physical

basis to this reasoning is so truly remarkable as to occasion

genuine surprise that it should have been used by Maxwell.
He continues:

»The magnetic induction, on the other hand, is from

the positive pole to the negative outside the magnet, and

from the negative pole to the positive within the magnet,

so that the lines and tubes of induction are reentering or

cyclic figures.*

This artificial and unnatural theory is outlined in the

accompanying sketch, see Fig. 4 PL 4. Fig. 5 PL 4 illustrates the usage oi Euler's Circulation Theory of a Magnet

in various modern works. The figure above, on the left is

from Millikan and Gale's First Course in Physics, 1906; that

to the right is from Gazebrook's Electricity and Magnetism,

1903; the sphere below is from CrystaU's article on Magnetism,

Encycl. Brit., g Ed., 1875; while the figure to the right, below,

is from Drude's Physik des Aethers, 1894.

It appears that Maxwell adhered to Eztler'% conceptions

so far as induction is concerned, but added to it to explain

magnetic force.

The anomaly of imagining the magnetic force to oppose

the induction within the body of the magnet, but not with-

out, is striking, and probably due to the habit of referring

all actions to that of a unit north pole.

On the other hand the much simpler conceptions of
the Wave-theory, 19 17, need no emphasis. We there imagine

the stress in the aether to be due to waves from all the

— atoms, so that the lines of force

which are the axes of

— rotation of the receding waves

tend to shorten themselves,

as Faraday had observed, and as we have explained me-

chanically in the second paper on the New Theory of the

Aether.

It is very difficult to account for the defective theory

of 1744 except by remembering that Euler had injured eyesight, which did not enable him to detect the true sym-

metrical nature of magnetism, by experiments with soft iron,

•or with smaller magnetic needles, as shown in the accompanying photograph, see Fig. 6 PL 4, of an experiment made by the present writer, 19 14.
Soft iron paper fasteners freely suspended by threads

are used to indicate the pulling from the equator towards
either pole of the magnet. The lines of force thus visibly

tighten and shorten themselves by the aetherial suction into

either pole; and Euler % defective theory of an inward flow

at the south pole and an outward flow at the north pole is disproved by observations which any^one can make for himself

To be sure that no injustice was done to Euler, I took
a small magnetic needle, suspended by a thread accurately fastened to its centre, and found by actual trial how this small magnet behaved when substituted for the soft iron wire described above.
We find by trial that the suspended needle also is
drawn from the equator of the magnet towards either pole, exactly as in the case of the soft iron wire above used. The deflection of the supporting thread from the vertical direction of gravity, shown by the glass marble suspended in the centre of the field, under actual trial, shows this clearly and
unmistakably. It seems therefore absolutely certain that Euler'% de-
fective theory of magnetism, with fatal lack of essential symmetry, yet copied in all the works on physics for the past 176 years, was an oversight due to the partial blindness of that great mathematician, and thus excusable. But what shall
we say of the careless reasoning of physicists, which has enabled this unsymmetrical and unnatural figure to be handed down unchanged through nearly two centuries, or else mended by strained reasoning like that used by Maxwell above?
It may perhaps be allowed that the above experimental
result definitely establishes the electrod. wave -theory of magnetism, set forth in the Electrod. Wave-Theory of Phys. Fore, vol. I, 1917. Accordingly, since we have attained a natural point of view, based on recognized symmetry, for the theories of electricity and magnetism, we shall see how fully the new theory, is confirmed by definite phenomena which are simple and easily understood.
(ii) Maxwell's, difficulties overcome by the wave-theory.
But, first of all, we call attention to the fact that in his
paper On Physical Lines of Force (Scientific Papers, vol. I,
p. 468) Maxwell searched diligently but in vain for the answer to the question: »what is an electric current?*
»I have found great difficulty,* he says, »in conceiving
of the existence of vortices in a medium side by side, revolving in the same direction about parallel axes. The contiguous portions of consecutive vortices must be moving in opposite directions; and it is difficult to understand how the motion of one part of the medium can coexist with, and even
produce, an opposite motion of a part in contact with it.*
»The only conception which has at all aided me in
conceiving of this kind of motion is that of the vortices being separated by a layer of particles, revolving each on its own axis in the opposite direction to that of the vortices, so that the contiguous surfaces of the particles and of the vortices have the same motion.*
»In mechanism, when two wheels are intended to revolve in the same direction, a wheel is placed ' between them so as to be in gear ^yith both, and this wheel is called an ,idle wheel'. The hypothesis about the vortices which I have
to suggest is that a layer of particles, acting as idle wheels,
is interposed between each vortex and the next, so that each vortex has a tendency to make the neighbouring vortices revolve in the same direction with itself.*
The difficulty here described by Maxwell is immediately solved by the wave-theory, for when a continuous series of
waves are flowing, the rotatory motions of all the particles

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of the medium are in the same direction, as we see from the above Fig. i, PI. 4, from Airy, and no such antagonism as Maxwell mentions can arise. Surely this removal of
Maxwell'?, difficulty, along with the complicated structure of »idle wheels«, which he devised for the stationary aether vortices, in default of wave-motion, must be considered a very remarkable triumph of the wave-theory.
In 1914 I found by careful experiment that a suspended

magnetic metal is at relative rest, but the moment any relative
motion takes place, the wave-field penetrating the non-magnetic metal undergoes change, and this change of the wave-field disturbs the equilibrium of the aether in the non-magnetic metal, and the result is induction, or the generation of electric waves in the metal, which becomes temporarily magnetic.
The metal therefore emits waves with whirls or rotations
opposite to that of the inducing magnet.

magnetic needle is bodily attracted to a wire bearing a current,

Now in our demonstration of the cause of magnetism,

owing to the interactions of the waves from the wire and the 1Q17, it is shown that the reason why opposite poles attract,
needle. But it appears from Maxwell's, address on Action is that the opposite rotations in the waves from such poles

at a Distance, (Scientific Papers, vol. II, p. 317) that he did not look upon an electric current as bodily attracting ^) a

cause an undoing of the stress of the medium, so that it collapses, and this tendency to contract is what we call

suspended magnetic needle.

attraction. In the same way the relative motion of a com-

»We have now arrived at the great discovery by Oersted pass needle over a metal plate induces in it opposite polarity,

of the connection between electricity and magnetism. Oersted with opposite rotations in the waves emitted therefrom; and

found that an electric current acts on a magnetic pole, but then the temporary magnetism induced in the plate by the

that it neither attracts it nor repels it, but causes it to move relative motion of the needle, calls forth attraction between
round the current. He expressed this by saying that ,the the needle and the metal. Accordingly, this induction acts

electric conflict acts in a revolving manner'.*

as a drag on the vibrations of the needle, and brings it to

»The most obvious deduction from this new fact was rest sooner than would be the case if the vibrations were

that the action of the current on the magnet is not a push- over wood, which is almost devoid of inductive effect, because

and-pull force, but a rotatory force, and accordingly many it is non-metallic.

minds were set a-speculating on vortices and streams of aether

(iv) Arago'% rotations and the dynamo explained.

whirling round the current.*

i

Soon after Gambey' % observation in 1824, the subject

And I have not been able to find any clear statement : was investigated by Arago, who found that a copper plate

of the proved attraction of needle to a wire bearing a current, | under the needle was most effective in damping its vibrations.

in

later writers ;

they

all

evade it,

by arguments

as to the On |

rotating

the

copper disc

in

its

own

plane

beneath the

behavior of a unit north pole, when no such single pole needle, he found that the needle M'as dragged around by

exists. In the theory of magnetism it is no more pertinent to discuss the actions of half of a magnet than it would be

an invisible friction ; and when the magnet was rotated near the copper disc, the disc was dragged by the rotating magnet.

in human physiology to treat of one side of our bodies only, This action was spoken of for a time, as a sort of magne-

when the whole body is perfectly symmetrical, and not to be split up into halves, and cannot act as such. One leg, one arm, one side of the brain and spinal column performs no functions alone and all such discussion is unscientific and
a very imperfect makeshift.

tism of rotation, but in 1831, Faraday discovered induction, and showed that Arago'% rotations depend on this cause.
According "to Faraday a magnet moved near a solid mass or plate of metal, induces in it disturbances which result in currents when they are properly directed, as from

(iii) Induction due to motion of a magnet explained a dynamo. If they are not directed through a circuit, they

by the wave-theory.

flow from one point to another, and the energy is frittered

In the year 1824 it was observed by Gambey that a down into heat, but meanwhile the electromagnetic forces-

compass needle oscillating in its box came to rest sooner act as a drag on the rotations taking place.

if the bottom were made of metal than if of wood. What
is the reason of this dragging action of the metal? In the Electrod. Wave-Theory of Phys. Fore, we have explained
induction by wave-action, and shown that when waves having,
say, positive rotation suddenly penetrate a metallic substance, the effect of these positive whirls is to generate negative metallic whirls, in virtue of the disturbances of the aether.
That is to say, no such permanent disturbances will

Fig. 7, PI. 5, illustrates the eddy currents long recognized in such experiments. But from our electrodynaraic wave-theory of magnetism, we recognize these whirls as the elements of rotations in waves receding from the magnet.
If we spin the disc of copper as shown in fig. 7, and lead off the disturbances by a circuit of wire connecting the points a and b we get the current generated by a dynamo,, which was also invented by Faraday.

occur when both the magnet emitting waves and the non-

The above explanation of the generation of a current

') Wkeivell, History of the Inductive Sciences, 3rd ed. 1857, vol. Ill, p. 73, expresses himself in about the same way: »0n attempting

to analyse the electro-magnetic phenomena observed by Oersted and others into their simplest forms, they appeared, at least at first sight, to be

— different from any mechanical actions which had yet been observed. It seemed as if the conducting wire exerted on the pole of the magnet

a force which was not attractive or repulsive, but transverse;

not tending to draw the point acted on nearer, or to push it further off, in

the line which reached from the acting point, but urging it to move at right angles to this line. The forces appeared to be such as Kepler

had dreamt of in the infancy of mechanical conceptions; rather than such as those of which Newton had established the existence in the

solar system, and such as he, and all his successors, had supposed to be the only kinds of force which exist in nature. The north pole of the-

needle move.d as if it were impelled by a vortex revolving round the wire in one direction, while the south pole seemed to be driven by an.,

opposite vortex. The case seemed novel, and almost paradoxical."

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by a dynamo is new. It is so simple that it constitutes, a the subject, which would be altogether beyond the scope of

remarlcable proof of the wave-theory. The old doctrine of these papers.

cutting lines of force, by the revolution of a commutator,

In the secorld paper, section 6, we cited Dolbear'%

between the poles of an electro-magnet, is good enough as experiment with circular discs set loosely but revolving on an

a working rule of thumb, but gives no insight into the axis and thus expelling the air by the centrifugal effects of

mechanism underlying electrodynamics.

the rotation, so as to tend to shorten the resulting vortex,

As set forth in the first paper on the New Theory of as was observed by Faraday for, his lines of force. This

the Aether, Maxwell was greatly occupied with the nature valid dynamical model and its known mechanical effects,

of magnetism; but although he was able to show that certain combined with other phenomena, especially Faraday's experi-

stresses admitting of mathematical formulation will account ment of 1845, o'l the rotation of polarized light by magneitism,

for magnetic phenomena, he was unable to conceive of any enabled us to concur in the conclusions of Lord Kelvin and

natural mechanism from which it could arise. Having out- Maxwell, that around a magnet the elements of the aether

lined the wave-theory very briefly in the first paper, we have are in rapid rotation. And we gave for the angular momen-

here examined the foundations of this new theory somewhat tum (Z), of an element of mass dm, of the aether, in the

— more in detail

without, however, in any way exhausting plane of the equator, taken as that of xy:

= Am a dx dy dz

= Z == ^^ dm [y dxjdt— x djv/d/)

\\\a{ydxldt—x-dyldi)dxdydz

(22)

This expression holds for small regions of space in the equatorial plane of the magnetic field, and the develop-
ment may be made general by proper extension of the action
to any region of the space [x, y, z).

4. Direct Proof of the Un.dulatory Character of an Electric Current deduced from the ratio between the Electromagnetic and Electrostatic Units,
LlT=v.
Notwithstanding the? enormous development of modern

electrical science, it appears that the true physical character of

an electric current has remained a great mystery. It seems

to have successfully challenged the ingenuity of the foremost geometers and natural philosophers. For in his comprehen-

sive Mathematical Theory of Electricity and Magnetism, 3"^ed., 1Q15, Dr. y. H. Jeans acknowledges that no progress has been made:
(a) »We have even obtained formulae for the stresses
and the energy in the ether. But it has not been possible to proceed any further and to explain the existence of these stresses and energy in terms of the ultimate mechanism of

the ether* (p. 485).
(b) »0n the other hand the ultimate mechanism with
which electromagnetic theory is concerned is that of action
in the ether, and we are in utter ignorance of the ultimate
laws which govern action in the ether. We do not know
how the ether behaves, and so can make no progress towards explaining electromagnetic phenomena in terms of the be-

haviour of the ether* (p. 486).
(c) »In nature, there are certain acts which we can perform (analogous to the motion of other ropes), but the

ultimate mechanism by which the cause produces the effect

is unknown. For instance we can close an electric circuit

by pressing a key, and the needle of a distant galvanometer

We may be set into motion.

infer that there must be some

mechanism connecting the two, but the nature of this me-

chanism is almost completely unknown* (p. 486).

I. The only tenable explanation of the mechanism of

an electric current heretofore put forth i) seems to be that

brought to light in the writer's Electrod. Wave-Theory of Phys. Fore, where the undulatory character of the current is shown to be probable in the highest degree. But even a decisive illumination of this difficult subject needs further development, if it be possible to find an element of electric dimensions which is perfectly simple, in the electromagnetic and electrostatic systems, and thus might disclose the true mechanism of a current.
To this end we choose the' element known as resistance,
which in the electromagnetic system has the dimensions
LIT=v, a velocity, and appears in the electrostatic units
in the dimensions TLr^, the diiference v^ being an expression of work done or electric energy transformed by the resistance to the progress of the waves along the wire.
2. It appears by the table given below that in electromagnetic units, resistance is always expressible as a velocity, V == Lj T, and therefore must be a measurable effect, dissipative in character, due to the motion of waves in the aether, traveling along a conductor with very nearly the velocity of light. All electric currents, as is well known, involve some dissipation of energy, in the form of heat and light, and electric circuits usually are arranged so as to ofier small resistance, in order to give minimum loss of electric energy.
When light is to be produced the conversion of energy into
light takes place only in the filaments of the lamps, and the heating of the rest of the electric circuit is kept at a minimum.
3. Now, although the modern theory of electric oscillations has been developed to a vast extent, and the process used in radio-telegraphy, yet it appears that a clear under-
standing of the nature of a steady electric current is not
yet attained by electrical investigators. By means of alternators, in a circuit containing both capacity and inductance, with low Ohmic resistance, these electric oscillations have been made to reach frequencies of from loooo to 15000 per second, and in some cases even 120000. More recently
= the oscillations have been made to exceed 1 0000000 per
second, the minimum wave length being only 0.4 cm 4 mm.

^) Crowther's earlier theory that an electric current consists in the flow of electrons is discussed in Section 12, (ii), below, and shown to be untenable.

«

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252

But we should look into the history of the subject
since the earliest experiments, eighty years ago, in order to get a connected view of the whole ' subject of electric oscillations.

4. In 1842, Professor Joseph Henry was occupied with the study of the discharge of a Leyden jar, and reached the conclusion that what appears to the naked eye as a single spark, »is not correctly represented by the single transfer of an imponderable fluid from one side of the jar to the other. »The phenomena,* he adds, » require us to admit the existence of a principle discharge in one direction and then several reflex actions backward and forward, each more feeble than the -preceeding until equilibrium is obtained. ^Henry'^ conclusions were drawn from observations of the irregular magetizations of steel needles when Leyden jar discharges are directed through a coil, as in Savory's experiments.

5. Henry's conclusions were mathematically confirmed
in 1853 by Lord Kelvin, who reached the formula for the

time of these oscillations:
T— 2nlV[ilKL-Ji'^I^L^)

(23)

K where

is the capacity of the condenser, now usually ex-

L pressed in Farads; the inductance, now usually expressed

H = in Henrys; and

the resistance, in Ohms. If .^

0.01

= R = Microfarad, L

0.0000 1 Henry, and

o, the time of

an oscillation will be found to be i : 503000, or the fre-
quency of the oscillations 503000 per second. They may be

made as rapid as 1 0000000 per second, or even of higher

frequency; yet we cannot make them as rapid as the waves

of light, because our physical apparatus is not of atomic

dimensions.

6. When 'Ji^j ^L^ is so small as to be negligible com-

pared to iJKL, the time of oscillation becomes like that of

undamped simple harmonic motion:

T= 2nVKL.

(24)

But \i H^l /^L"^ is small, yet not wholly insensible, the discharge

is oscillatory, for under the damping due to resistance, the

period is altered, and the time of oscillation becomes of the

form used in radio telegraphy:

T= 2V[n^+l^)-VKL

(25)

where / is the logarithmic decrement.

7. In 1858 Feddersen experimentally confirmed Lord Kelvin's theory of the oscillatory character of the Leyden jar

discharge, by photographing the imiage of the spark in a

rotating mirror, and found that the image of light was drawn

out into a series of images, due to sparks following each
other in rapid succession. The illustration of this oscillatory

discharge in Fig. 8, Plate 5, was obtained in 1904 by Zenneck, who used a Braun tube as an oscillograph.

Now 8.

in the case of a steady electric current, the

conductor connects points having difference of potential:

this difference tends to adjust itself, by the electric contact,

resulting from the conductor, and thus the, aether is set in

oscillation and the waves travel along the wire, just as water

runs down hill from higher to lower gravitational potential,

and in this transfer sorhe dissipation of energy results.

Inductance is present in the wire, and as it has also

capacity, the contact yields electric oscillations, when energy

is. released, as in the discharge of a Leyden jar. If only one of these factors, inductance or capacity, were present, but not both, the disturbance would rise and fallaccording to some exponential function of the time, yet without regular

oscillations.
When both inductance and capacity are present, as in
all metallic systems, the disturbance calls forth both elasticity and inertia, because the electric disturbance is physically impeded and the aether is set into wave motion of the kind

above described.

Q. So long as difference of potential is maintained at the two ends of a circuit this electric wave oscillation is maintained along the wire. As in the case of the Leyden jar, so also for a battery; the oscillatory discharge begins
the moment the circuit is complete, and continues to flow
as a steady current. Since there is finite but small loss of
wave energy through the body of the whire, owing to its physical resistance to the free movements of the aether, the wave disturbance envelopes the wire cylindrically, traveling more rapidly in the free aether outside; but the wave front is continually bent inward towards the metallic cylinder, just as the wireless .wave is bent around the globe, by the greater resistance to the motion of the radio wave in the solid globe
of the earth..
The above explanation of the waves propagated from
a conductor gives a very satisfactory account of the phe-
nomena from a physical standpoint. But it is advisable to look into the matter also from the historical point of view,
in order to perceive the drift of research during the past

sixty years.

10. In the celebrated Treatise on Electricity and Magne-

tism, 1873, § 77 I et seq.. Maxwell first brought out the funda-

mental difference between electromagnetic and electrostatic

T=v, units, and showed that the ratio is always equal to Lj

3.

velocity. Upon this basis Maxwell erected the foundation of

the electromagnetic theory of light, which has come into

general use, though the mystery of the connection between

light and electricity was not fully cleared up. For example.

Lord Kelvin never could see how it helped the wave-theory

of light (Baltimore Lectures, IQ04, p. q).

As already pointed out, it will be seen from the table

given below, that the dimensions of resistance; in electro-

magnetic units, isZr-^, which represents a velocity. This

is a very remarkable fact, having profound physical signifi-
cance, which may well claim our attention. Is it possible

that the resistance felt in all conductors, and obeying Ohm's

law, is an indication of the motion of electromagnetic waves

along the wires, by which the resistance is generated? If

so, the dimensions in electromagnetic units should be v^ times

that in electrostatic units, as actually observed.

11. In his celebrated discussion of the electric medium Maxwell showed how sz;* could be determined experimentally. In fact, Weber and Kohlrausch as early as 1856, 17 years before MaxwelFs treatise appeared, had already carried
= out a numerical determination, and obtained the approximate
value v 310740000 metres per second (PoggendorfTs Ann.,
1856, Aug., pp. 10-25).
This constant has since been determined by many

.

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254

investigators, working along lines indicated "by Maxwell, with very accordant results, the latest and no doubt the best being that by Professor. E. B. Rosa and N. E. Dorsey of Washington,

1Q07, Bulletin of the Bureau of Standards, vol. 3, nos. 3

= and 4, p. 601, namely: V

2.997 1°,10

12. As these publications are universally accessible, we shall not go into the details of these electrical experi-

ments. It suffices to confine our attention to a physical

explanation of the results obtained, but apparently not yet

clearly understood by natural philosophers.

On comparing the dimensions of the electromagnetic

units with those of the electrostatic units, we find that there

LIT=v, = is always a uniform difference depending on the common

factor

or L'^JT^ v^, as shown in the following

tables.

13. Table of the equivalent dimensions in the two theoretical systems of units.

1. Charge of electricity

Electrostatic

Electromagnetic

2. Density 3. Electromotive force 4. Electric intensity 5. Potential

E R {X, Y, Z)
V

6. Electric polarization 7. Capacity 8. Current

P{f,g,h)
C
i

9. Current per unit area 10. Resistance

(u, V, w)
R

11. Specific resistance

T,

12. Strength of magnetic pole m

13- Magnetic force

H («, ^, ;-)

1.4. Magnetic induction

B {a, b, c)

IS- Inductive capacity

K

16. Magnetic permeability

= j^V" ^-V» 7^-1

i/v
^Vs xv= r-^ i/v

M^I'Z-'l' T-'^
M'-l^ Z'l'
M'l'Z'I'T-^

= M'''Z-'I' r-i M'i'Z-'I'-i
L

M"l' L-'l' r-2

= Zr-i-i^2

T

= Z^T-^-i/v''

Z-i T^' j^-^h i)h 7—1
M^'^Z-'f^T-^
ZT-^

M'l' L'l' r-2
I

= M'I'Z-'I'T-'I'-v j/'/s z-'/a 7—1 = M'l'z-^i' r-1 • ijv M'l' z-'i' r-i

:=Z-^T^-v'

Z-^T^

Table of practical units in the two systems.

Quantity

Name of Unit

Charge of electricity Coulomb

Measure in

Measure in

electrostatic units

electromag. units

(J 2/=3-io"CGS)

10,—1

3"i° Q

Electromotive force I

Electric intensity Potential Capacity Capacity Current " Resistance

\ Volt
J
Farad Microfarad
Ampere
Ohm

10
-9 i o'
-15 i o'
10 -1
10'

1/(3
9• 9- lO" 3- I0« 1/(9 •

It will be seen from the element, resistance, no. 10,

in the above table, that to establish equivalence, the electro-
static unit must be divided by {TZ~^Y or by v^, which is

the square of the dimensions in electromagnetic units. This

indicates that electromagnetic waves resisted by a conductor

do work depending on the square of the velocity with which

they travel, which conforms to general experience in all

physical problems where energy is expended.

14. It thus appears that the ratio between the two sets of units is uniformly Z/7'== v, in the first or second power, and thus v undoubtedly represents a velocity, as first clearly set forth by Maxwell, Treatise on Electricity and Magnetism, § 771 et seq. Fortunately it happens that this ratio can also be determined experimentally, from a current of electricity in motion, and from an identical electrostatic charge, at rest: thus v admits of electric measurement, independently of any theory of light. But as the value of z' is the same as the velocity of light. Maxwell naturally concluded
that the electric medium is identical with theluminiferous aether. The following is an outline of the method of measurement.

For simplicity, suppose a condenser is charged with elec-

tricity, and let its quantity, Q, be measured in electrostatic units, by determining for instance the repulsion which a given

proportion of the total charge produces in a torsion balance
of known dimensions.

Let the condenser be again charged to the same extent,

and let it be discharged through a ga:lvanometer. By measuring

the deflection produced, the constants of the instrument being
known, we may determine the quantity of electricity which

deflected the galvanometer. This gives by direct observation

== (2(e.m.)/<2(e.s.)

C-3.o-io"/C= 3.0- iqI"
velocity of light.

16. The process may be numerically illustrated in the

following way. The e. m. f of a Daniell's cell may be measured

by such an instrument as Lord Kelvin's absolute electrometer,

and found to give in electrostatic units of potential say 0.0036.

The same difference of potential measured in electro-

magnetic units will be found to have the value

= = i.o88.- 10®

0.01088 • io"-3/3

0.00.36- (3.0- 10^")

Hence the ratio of the electromagnetic to the electrostatic units is 3.0 - 10^" == velocity of light.

Q The electrostatic quantity

(e. s.) is the quantity of

electricity which attracts or repels another equal quantity at

a distance of i cm, with a force of a dyne. The electro-

Q magnetic quantity

(e. m.) is the quantity of electricity

which traverses the wire of the galvanometer in a second

when the current set up by the discharge has unit intensity.

17.

The

ratio between .

the

units

is

always

of the

dimensions of a velocity, and as it holds under the con-

dition that the centimetre is the unit of length, and the

second the unit of time, we see by experiment that the

.

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ratio is the actual velocity of light, 3.0- lo^", which establishes the identity of the electric medium with that of the lumini-
ferous aether.
This was also shown by Hertz in the celebrated experiments which led to the development of wireless telegraphy, and thus the subject requires no further treatment at present.
We merely call attention to the elgctrodynamic waves about
a wire bearing a current as diagrammed in the author's work of IQ17, Fig. 12, below, and now somewhat better represented
in Fig. 18, Plate 6.

18. This picture shows clearly that an electric current is nothing but a certain type of aether waves propagated away from the wire. Accordingly, when such a current is set up in the aether, through the waves generated and maintained by the e. m. f. of the battery, it is obvious that the electromagnetic measure of this electric action should involve the motion of the waves or velocity; while in the case of the electrostatic action no velocity is involved, but only a stationary difference of potential.
This theory completely accounts for the difference v
in the units, and harmonizes all known electrical phenomena, and is an especially satisfactory termination of a half century
of scientific discussion • of the relation between electromagnetics and electrostatics. It is not by chance that only v and v^ appear in the above table.
If the actions of the medium involved something besides say induction, where v appears, or resistance, where v'' appears,
it should be expected to find v in perhaps the third or fourth powers; but no such powers are established by observation, which confirms the above interpretation.

5. The Geometrical and Physical Significance of Biot and Savarfs Law for the Intensity of a Current on a Straight Wire, and of Ohm's Law for the
Resistance.

1 The law of fiiot and Savart for an electric current on a straight wire has the simple form {^Biot et Savart, Ann.

Chim. Phys., 15 p. 222, 1820):

I=KHlr

(26)

where .AT is a constant, and / the intensity of the electric
action which varies inversely as the distance r from the wire, and directly as the current strength H.

We 2.

shall give a simple geometrical basis for Biot

and Savart's law of the inverse distance. In the Electrod. Wave-Theory of Physic. Fore, we have shown that the action

of an electric current is due to flat waves, with their planes

of rotation containing the axis of the straight wire, the ro-
tation of the wave elements being around the lines of force,

which are circles about that axis. All points of the wire emit waves, but the waves are so conditioned as to expand

in the form of a cylindrical surface, thus spreading as a

circular cylinder around the wire, but not in the direction of

the wire. The element of cylindrical surface becomes:

= d.f dlrdw

(27)

where rdco is an element of the circles of expansion, in-

creasing as the radius r, and d/ is constant, along the length

of the cylinder.

3. Now since the element of length d/ is constant, as

the wave spreads outward, and only rdw varies, the cylin-
drical sector thus increases like the circumference of a circle,
2nr, perpendicular to the axis of the wire. The expansion
of the radius of the circle thus determines the increase in the area of ds, the elementary area of the cylindrical surface, in which the electrical waves must expand.

Now 4.

the area of the circular cylindrical sector varies

as rdco or as the radius, dco being constant in a fixed element
of the sector. And as the waves thus become less crowded,

in the direct ratio of the distance, r, it follows that the in-

tensity of the wave action decreases, varying inversely as r.

This is a direct and simple view of the geometrical basis

of Bwt and Savart's law, heretofore apparently little studied

by natural philosophers.

5. This remarkable law of Bwt and Savart thus has
the simplest of explanations: namely, the elementary cylindrical surface ds increases directly as r, and the resulting
electrical action therefore decreases inversely as r. The law
thus follows at once from the restricted freedom. of the waves propagated from the wire: and as it was confirmed by experiments of Bzot and Savart, 1820, the law in turn establishes the dependence of current action on electrodynamic waves.
No other agency than waves could produce this result, be-
cause waves involve expansion, and the agitation has to follow the geometrical inverse law of the increase of space.

6. By extetiding the above reasoning, we see that if the waves from a body can spread in all directions, they will fill a sphere surface, s ==^ ^n r^, and hence the law of

decrease of the intensity for the action varies inversely as r^,
namely: f=m\r'^, which holds for universal gravitation, magnetism, and other physical forces of nature.

= 7. As the coincidence between the requirements of

waves and the spa'ce expansion is rigorous, from jc

o to

a: =^ 00, the chances against such a mere accidental con-

formity, without physical cause, are infinity to one. Accor-

dingly, Biot and Savart's, law furnishes direct proof of the

utmost rigor that waves underlie electrodynamic action, as

well as gravitation, magnetism, etc.

There has been such a bewildering confusion of thought connected with the whole subject of physical action across space that it is necessary to bear in mind clearly the fun-
damental principles of natural philosophy. To this end we
need obvious proofs of the causes underlying physical action,
under the simplest of nature's laws. T^e simple laws exclude the larger number of complicating circumstances, and enable the cause involved to stand out in such a way that we may
recognize it.

Very different indeed is the confusion of thought carried on in certain scientific circles. At a discussion of the Theory of Relativity, as reported in the Monthly Notices for December, 19 19, Sir Oliver Lodge yjiStlY complains that Professor Eddington thinks he understands it all. »To dispense with a straight line as the shortest distance between two points, and to be satisfied with a crazy geodesic that is the longest distance between two points, is very puzzling. « . . . »The whole relativity trouble arises from giving up the ether as
— the standard of reference ignoring absolute motion through — the ether , rejecting the ether as our standard of reference,

.

:

.

:

:

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and replacing it by the observer. By putting the observer in the forefront and taking him as the standard of reference you get complexity. If you describe a landscape in terms of a man in a train looking out of the window, the description is necessarily complicated. The surprising thing is that this theory has arrived at verifiable results.* . . »The theory is not dynamical. There is no apparent aim at real truth. It is regarded as a convenient mode of expression. Relativists seem just as ready to say you are rising up and hitting the apple as that the apple is falling on you. It. is not common sense, but equations can be worked that way.«

8. It is quite remarkable that heretofore the law of

Biot and Savart should have been so little studied by in-

A vestigators.

law of such simplicity (compare Fig. g, Plate 5)

has enormous advantages over any complex law, especially

when it comes to searching for the causes which produce the

phenomena observed in nature. Thus it is preeminently these

simple laws, which admit of one interpretation and only one,

that should claim the attention of natural philosophers.

9. In the closest analogy with what Biot and Savarfs

law puts before us, for the intensity of an electric current,

on a straight wire, the Newtonian gravitational potential, for

a homogeneous sphere or a heterogeneous sphere made of

concentric layers of uniform density, presents to us the ex-

cessively simple formula

V=Mlr

(28)

-which we have already interpreted in terms of waves freely expanding in tridimensional space.
Any other interpretation than that given for the New-
tonian potential function in these simple cases seems absolutely excluded, by virtue of the simplicity and directness of the most obvious special relations, as when the waves expand outwardly from a spherical mass such as the sun.

10. Any modification which renders these formulae

complicated or non-homogeneous is to be viewed with pro-

found suspicion. Thus the substitution oi Gerber's formula:

= V M/r{i-i/c-dr/dt)^

(29)

for Newton's as cited in equation (28) above, is unjustifiable and indefensible; yet in the perverse search for complexity instead of simplicity, such bewildering confusion goes on.

Dr. P. Gerber first published this unauthorized formula
in the Zeitschrift fiir Mathematische Physik, Band XLIII, 1898, p. 93-104, and the exploitation of it since made by
= — Minstein and his followers ignores the fundamental fact that
by introducing the second power factor, ;'^ (i ilc-drjdtY in the ^ivisor, the dimensions of the equation are changed, which is physically inadmissible and equivalent to violating the essential mathematical condition of homogeneity for the equation for the potential. Such an objection is fatal ^), since it rests upon both geometrical and physical grounds; and thus .we witness the adoption of a mere convenience, in
violation of recognized scientific principles.

1 1 The fact that the Einstein speculations involve this
fatal contradiction seems to have been overlooked by. previous

investigators, who thus exhibit a feeble grasp of the most essential conditions of geometrical and physical research.

Accordingly, since this Gerber formula is invalid, when

applied to a homogeneous sphere, or a spherical mass made

up of concentric layers of uniform density like the sun, its

general admissibility must be wholly denied. In fact it has

neither geometrical nor physical validity; and its use in con-

temporary journals and the transactions of learned societies

is a bizarre performance, in vague and chimerical reasoning,

little to the credit of our time.

1 2 We have now to consider the geometrical and phy-

sical significance ,of the law of electric resistance discovered

by Dr. George Simon Ohm (Ann. d. Phys. VI, 1826, p. 459):

I=HlR

(30)

R H where is the resistance,

the electromotive force, and /

the intensity, as measured at any point by a suitable appa-
ratus, such as a galvanometer. This law of Ohm likewise is

remarkably simple, and quite similar to that oiBiot and Savart

above explained. Accordingly let us see what connection, if

any, exists between Ohm's law and that of Biot and Savart.

a) In Biot and Savarfs law we vary the distance, with fixed electromotive force, and observe the change in the in-
tensity : the observed result confirms the wave-theory.

b) In Ohm's law we also deal with a current in a wire, or wires, and when the electromotive force is fixed, we study
the law of resistance [R], or intensity of action (/), at a
fixed distance, where the needle of the galvanometer may
be located.

c) Thus Biot and Savarfs law, with a fixed steady

current, serves for calculating the varying intensity at any

distance, in accordance with the requirements of the wave-

H , theory. In the same way, Ohm's law, when

is constant,

but with varying resistance, R, serves for calculating the in-

tensity at a fixed distance.

13. Accordingly it appears that these two laws are mutually supplementary. For all the effects, in the field of electrodynamic waves about a wire, should include both those occurring at a fixed distance, as calculated by Chris law, and those occurring at a varying distance, as calculated by
the law of Biot and Savart. The two laws are thus brought into immediate and necessary relationship, and both conform

to the wave-theory.

We may write Biot and Savart's law in the form

I=KHlr

(31)

and Ohm's law in the form

l=HlR.

(32)

Accordingly on combining the two expressions which

we may do by equating the identical intensity at any point,

_ we obtain ^^/^ ^/^ ^^ K^^rJR.

(33)

K Therefore, we find on substituting for

its value, for

H any value

and r,

= = I rHJRr HJR

(34)

V = ^) This may be made a little clearer by noticing what would happen if the exactly analogous formula for the velocity,

LjT,

had a factor Y^ introduced into the divisor T. Such an arbitrary modification of the expression for the potential is purely a change de conTenance, and not permissible on mathematical or physical grounds

s

:

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which again yields Ohm's, law, in the form which holds for any fixed distance.

14. These two laws therefore confirm the wave-theory

of the entire field about a wire bearing a steady current.

— Ohm\ law implies a cylindrical wave field

the resistance

and intensity being the axes of a rectangular hyperbola

— referred to its assymptotes

Biot and Savarfs law also

represents a rectangular hyperbola of the same type, but with

R r varying instead of

(compare Fig. 10, Plate 5).

These two laws give thecomplete theory of the electro-

dynamic wave-action, in the whole field about a wire bearing

a steady or variable current, and thus greatly simplify the

theory of the electromagnetic field.

6. 0^«/fa?'s Experiment, 1819, y^ra^c's Experiment with copper wire, 1820, and the Magnetic whirl shown by iron filings near a conducting wire all confirm the wave-theory, which also agrees with Ampere's, theory of elementary electric currents circulating about the atoms.

In the Electrod. Wave-Theory of Phys. Fore, we have

given a simple and direct explanation of the deflection of

the magnetic needle first observed by Oersted in 18 19, the

adherence of iron filings to copper wire conducting a cur-

We rent, first observed by Arago in 1820.

also explained

the circular whirl assumed by iron filings near a conducting

wire, and finally were enabled to harmonize the wave-theory

with Amplre'% theory of elementary electric currents about

tangential to the lines of force, which are circles normal to
the axis of the wire; If now, without other circumstances being altered, the
direction of the current be changed, the two poles of the needle immediately interchange at all points about the wire The south pole is deflected to the west when beneath the
wire, and to the east when above the wire. And in general,
every point in the orientation is exactly reversed.
What can be the meaning of this phenomenon in which the current act-s as if it has sides, when reacting on the
magnetic needle? We shall see that just as the magnet has
two poles of opposite properties, so also the current has two sides, due to waves which appear to be righthanded rotations
when viewed from the opposite point.
Consider the case first cited above, with the current from the positive copper plate of the battery flowing north and the needle suspended beneath the wire, but with the
north pole deflected to the west when the current flows. This means that the waves descending below the wire have vortices rotating righthanded, as shown in the following figure, from the writer's work of 19 17.

the atoms (comp. Fig. 11, Plate 5).

Such an illumination of the obscure subject of the

magnetic field is too remarkable to rest on mere chance;

and thus we shall describe the argument briefly, as the best

means of unfolding the true order of nature. The electro-^

dynamic waves propagated from the wire bearing the current

lie in planes through the axis of the wire,

= 5

« sin(2 7rjc/A-H^)

= asin(2 7r_)'A-t-/)

and are of the type

,

•,

^^^'

where x and y are interchangeable, owing to the symmetry
of the waves about the z axis, which is taken as the axis of the wire. Owing to cylindrical symmetry the axes of x
and y might be rotated about that of z without any change
in the expressions for the waves receding from the wire
under the action of the current.

But as we have already pointed out the amplitude a

decreases as in Biot and Savart's law, inversely as

= r

1/(^2 +_y 2) _

(i) Oersted's Experiment of 18 19.
In the experiment of 18 19, it was observed by Oersted that if the magnetic needle be below the wire, and the current from the copper positive pole of the battery directed north, the deflection of the north pole would be to. the west.
If the needle be above the wire, but the other circumstances unchanged, the deflection of the north pole was ob-
served to be towards the east. The needle might thus be revolved in a circle about the wire, without any change of
the relative position in relation to the axis of the wire. Accordingly 'it appears that the axis of the needle, sets itself

Fig. 12. New theory of Oersted's aijd Arago'
experiments, 1819-20, and of induction.
It means also that the rotations of the waves receding from the south pole of the needle have the opposite direction of rotation, as shown in the figure.
1. For it is found by experiment that the needle is bodily attracted to the wire, by the action of the current, and hence the waves from the wire must undo the "opposite rotations in the waves from the needle. Accordingly the medium tends to collapse, and by this contraction of the volume of the medium the needle is drawn to the wire.
2. In all the works on electricity and magnetism which I have seen including Maxwell's great treatise, this question is somewhat evaded by the claim that the north pole tends to wrap itself around the wire, in on? direction, while the south pole tends to wrap itself around the wire in the opposite direction; and that this actual bending of the needle would occur if the needle were flexible. I proved by direct experiment in 19 14, that the needle is bodily attracted to the wire in

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every possible position it may take, but I cannot find so simple a statement of this essential fact in any earlier work on electricity and magnetism.

3. The usual discussion about the tendency of the unit

north pole is very unsatisfactory, because while the tendency

thus outlined is fairly accurate, it conveys the impression

tViat all power is centred in the pole, rather than in all the

— particles,

notwithstanding the fact that if we break the

magnet we get as many separate magnets as we have frag-

inents, and since this subdivision may be extended to mole-

cular dimensions, we know that the theory of pole action

is altogether misleading, yet such vague teaching continues

to be handed down from generation to generation, and

eminent scholars have often remarked how difficult it is to

get rid of the most obvious errors, when entrenched in

authority by the lapse of time.

4. Further proof of the above theory of the action of an electric current upon a magnetic needle might be deduced from the fact that in nature physical actions always are mutual. Thus if the needle is attracted to the wire, the conducting wire obviously is equally attracted to the needle
— otherwise action and reaction would not be equal, as
proved by universal experience. Accordingly, no other conclusion can be held than that waves of the kind outlined proceed from the needle and also from the wire, and by their interpenetration develop forces of the kind observed in nature. It is' not enough that waves proceed from one body, but not from the other: there undulations must proceed from both bodies incessantly, and travel with the velocity of light. This is proved by observation, for the wave actions propagated along the wire, and thence inferred also for the waves of a magnet itself, though the velocity of the waves from a natural magnet have never been directly measured.
Yet since magnets are made by the action of a current upon a bar of steel inserted in a solenoid ^) , it follows that the
velocity of the two classes of waves, one from the current and the other, from the magnet, must be the same, and in both cases identical with the velocity of light, i/==3.o- 10^" cms.

(ii) Arago's Experiment of 1820.

5. As to Arago's experiment of 1820, it is obvious that copper wire conducting a current will give a wave field

about it similar to any other wire. If iron filings be near

such a conducting wire, it is obvious that

they should adhere to it, since each filing

will become a temporary magnet, the ends

having opposite. poles, owing to the nature of

the whirl of magnetic waves about the wire.

Accordingly Arago's, experiment is simply a

verification of Oersted's experiment, but ren-

dered more general by the use of a copper

wire, and soft iron filings, which therefore

fall off when the current stops, and the wave
field about the copper wire disappears.

Pig j^.

6. It is worthy of note that since the lines of force

— about a magnet are rentrant vortices,

the filaments within

the axis of the magnet rotating in exactly the opposite direc-

— tion to those in the magnetic equator, for example,

the

waves emitted by the conducting wire in Oersted's and Arago's

experiments, described above, will have their elements rotating

in perfect agreement with the vortices inside the body of the magnetic needle. The waves from the wire thus support

the physical oscillations within the more resisting body of

the needle, and by rendering the sum total of the mutual

actions a minimum, the balanced needle is in equilibrium in

the position observed by Oersted, 18 ig.

7. It is now easy to reconcile Ampire's theory of

elementary electric ' currents about the atoms of a magnet

with the wave-theory. The formula for a plane wave is

= .f

<3;sin(2;r;c/^+/)

(36)

And as we may shift the point of the revolving vector, by altering the phase angle /, we see that by changing p from 0° to 2 7r, we should have a complete oscillation of the wave. This would correspond to the movement of the electric current once about the atom; and abo to the advance of the wave along the ^-axis by one periodic oscillation. The

wave-theory is therefore in perfect accord with Ampere's

theory of elementary electric currents about the atoms of

matter.

8. If it be imagined that the atoms probably have a smaller circumference than a wave length X of the wave emitted from the atom, all we need to do is to point out
that we do not know the mechanism by which waves originate, and it does not follow that the wave length in the aether should correspond to that of the atom. An undetermined multiplier probably is involved here, but at present we cannot
fix it with any accuracy.

(iii) Nature of atomic vibrations con.sidered. For in the case of sound, the dimension of the Helmholtz resonators is not closely related to the length of the corresponding sound waves received and emitted by the
elastic oscillation of the resonator. And even if this could
be found in air, it would not be the same in hydrogen, oxygen, nitrogen, or other gases, but depend on the properties of these media, as well as on the physical properties
of the resonator, its shape, mass, elasticity, rigidity, etc.

Ampere's theory of elementary electric currents about atoms reconciled with the wave-theory.

') As far back as 1820 Ampere showed that if a wire be wound into a solenoid, delicately pivoted' in mercury contacts, and a current passed through it, it behaved as a magnet, with a north and south pole. Hence Ampere was impressed with the solenoidal character of magnets; and imagined that the elementary currents about the atoms mutually destroyed each other within the body, and remained effective only in the -surface layer of the magnet, which was thus viewed as a shell. But Ampere's reasoning is equally useful for proving that there are waves pro-ceeding from the wires bearing the current, and that they arc flat in the plane through the axis of the wire.

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So aiso within the aether, the vibrations of the atoms

are determined by causes which at present are but little

understood ;

and

we

can

only

infer

that

the

atomic dimensions

are not directly related to the wave length, or wave lengths

emitted, though there probably is some correspondence which may be made out in time.

9. It appears from the researches in spectroscopy
heretofore made that the atom of a single element may emit a complicated series of spectral lines, which means a very complicated series of vibrations, some of which are
connected by the formulae of Balmer and other investigators.
Now most of the vibrations of the visible spectrum are below
the resolving power of the microscope, and thus the waves are so short that such vibrations do not penetrate solid or even transparent fluid bodies to any appreciable depth. But we know by the transmission of the sun's rays through such a medium as the terrestrial atmosphere that longer waves
have increased penetrating power. And since Langley extended
the length of the solar spectrum to some 20 times that observed by Newton, without finding any indication of an end, it is natural to hold that the waves upon which gravitation, magnetism, electrodynamic action, etc., depend must be of comparatively great length, otherwise they would not penetrate solid masses as they are observed to do in actual nature.

10. It thus appears that the shorter atomic waves therefore do not produce forces acting across sensible spaces, and in dealing with the long range forces of the universe we must look to waves of considerable length, which have the required penetrating power, and are least delayed in propagation through solid masses. Such waves will explain gravitation, magnetism, electrodynatnic action, and are the only means of making inteUigible the correlation of forces and the conservation of energy, since light and heat certainly are due to waves in the aether. Unless the other energies be due to waves also there would be violation of the doctrine of continuity, which is so fundamental in natural philosophy.

(iv) The wave-theory establishes the attraction of currents flowing in the same direction, and the repulsion of currents flowing in opposite directions, and therefore assigns the true physical cause of these electrodynamic phenomena.
1. From the foregoing discussion it follows that when from the east of the meridian we look at a positive current flowing to the north (from the copper terminal of a battery) we find the elements of the waves propagated away to be rotating
righthanded (clockwise) beneath the wire, but lefthanded (counterclockwise) above the wire (cf. Fig. 18, Plate 6). This follows also from the relative positions taken by the freely pivoted magnetic needle, which presents to us a south pole
when beneath the wire, but a north pole when above the wire.
2. Now suppose we have two such independent currents
flowing north: what will be the mechanical effects of the mutual interactions of their waves? If we imagine one wire above the other, for conformity to the wave picture just outlined in paragraph i, we perceive that between the wires, the wave elements from the two conductors will rotate in opposite directions: which will cause the undoing of the separate wave stresses, and a collapse of the medium, and the result of this contraction will be attraction.

3. On the outside of the two wires, on the other hand,
the rotations of the wave elements will be in the same direction, the stress or agitation of the medium will therefore be increased, so . that it expands: which will tend to press the wires together from the outside. Hence the wires will be made to attract both from the internal and the external wave actions. Accordingly, we have a simple and natural explanation of the mutual attraction of currents flowing
in the same direction. And it is based upon the same con-
ceptions as are involved in the attraction af magnets presenting unlike magnetic poles. In fact by the suspension of magnetic needles close to the two conducting wires, the same conclusions follow: for unlike poles are presented in proximity, which means attraction.

4. Now let the direction of one of the currents be
reversed. It is easy to see that between the wires the ro-

tations of the wave elements will appear to be in the same

direction,

as viewed

from the east of the meridian ;

and thus

the agitation of the medium will be increased, the medium

will expand, and the wires be forced apart, so that the action

leads to repulsion, just as when like poles are presented by

two magnets.

5. On the outside of the two wires, however, the ro-
tations of the waves, flowing in opposite directions, will each
tend to undo the other: in the external region the medium will tend to collapse, which will allow the wires to be forced apart, so that repulsion from the region between the wires will be accentuated by this external tendency of the medium
to collapse. Accordingly mutual repulsion will be observed whenever two currents flow in opposite directions.

6. This is equivalent to the mutual repulsion of two magnets which present like poles : the interpenetration from opposite directions of waves with like rotations caused the
medium to expand between the bodies, and to collapse beyond
them, so that repulsion immediately follows. Accordingly the whole theory of the attraction and repulsion of electric currents flowing in the same and in opposite directions respectively, is analogous to the mutual actions of two magnets,
and the causes are one and the same. And as the outcome
greatly simplifies our theory of electrodynamic action, so also
we are correspondingly assured that the results conform to the true laws of nature. The harmony of so many distinct, phenomena would not be possible unless based upon the true causes involved : for the probability of such an accidental outcome approaches zero.

7. Weber'% Law indicates that Gravitational,
Magnetic, and Electrodynamic Actions are all due to Waves traveling with the Velocity of Light; thus explaining the Semidiurnal Tide in the Earth's Magnetism depending on the Moon, which Newton'?,
Law will not account for.
As we have previously pointed out, Weber's funda-
mental law of electrodynamic action, published in 1846, has the form:
/= {»i»t'lr^){i~{ilc^){^rldtY+[2rlc^)-d^rldt^}. (37)
The first term of the second member is identical with Newton% law of gravitation, 1686, and of course gives the

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principal part of the force which regulates the motions of the heavenly bodies. But there are slight effects resulting
from the second and third terms, which were first numerically
m investigated by Tisserand 1873 (cf Tisserand's Mecanique
Celeste, Tome IV, last chapter), but the theory was rendered
more complete in the present writer's Electrodynamic WaveTheory of Phys. Fore, vol. I, 1917, where tabular data will be found for the planets, satellites, comets and binary stars.

The chief effect of the minor terms of equation (37)

= is to give the perihelion a small progressive motion, which

in the case of the planet Mercury amounts to (3to

-i-i4!'5i

in a Julian century. This reduces the anomaly in the out-

= standing motion of that perihelion to about two-thirds of its

value, namely from dcJ :^ -i-42;'g5 to <3z3

-i-28"44, but

does not obliterate the anomaly, which is more exhaustively

investigated in the second paper on the new theory of the

aether.
A It was in his celebrated paper of 1864, Dynamical
Theory of the Electromagnetic P'ield, that Maxwell reached

the conclusion that the velocity of electrodynamic action is

identical with that of light, as already indicated by Xohlrausch's,

experimental determination off, in 1856. But although such a conclusion followed from Kohlrausch's experiments, and
from MaxweWs theory of the electromagnetic field, it was
necessary to form a more definite conception of the nature

of the action, than was then available, before the use of v could be introduced as a working hypothesis.
MaxiveU's electromagnetic theory of- light was put in such shape that the existence of electric waves was rendered probable, but not directly verified by any tangible experiment, till Herizs discovery of the electric waves (1887-94)" which bear his name, along with a method for investigating their properties, including an experimental demonstration that they

travel with the velocity of light. This practical development of the theory of electric

oscillations, with experimental determination that the velocity of the electric waves is identical with that of light, left no
doubt of the identity of the electric medium with the lumini-
ferous aether. Otherwise it is inconceivable that the two
velocities should be identical. The previous and subsequent
determinations of v have confirmed this conclusion, so that
such a result has now been accepted for about a quarter of a century. It remained, however, to form some demonstrable physical conception of magnetism and of gravitation, which would justify the claim not only that electric waves travel with the speed of light, but also that magnetic and gravi-
tational forces are due to a similar cause, which Tvas the aim of the writer's researches, 1914-1917.

T. First, it was necessary to show that a physical theory
of magnetism may be based on the mutual action of waves-'),
and to disclose the nature of these waves, which must meet certain requirements in electrodynamics, and cosmical magnetism, so as to be adaptable to the more hidden problem of universal gravitation. This requirement was met by the theory of waves from atoms, shown to conform to Ampire's theory of elementary electric currents about these particles.

but of such length- that they may be propagated through
solid masses' without very great loss of energy.
2. The wave is taken to be flat in the etjuator' of the
atom, so that in this plane, the waves are perfectly plane waves, while in the two hemispheres of the atom the rotations give righthanded or lefthanded helices, as actually observed in polarized light when propagated through certain crystals. This specification fulfilled the most necessary optical re^ quirements, and thus presented no difficulty from the point of view of light or electricity.
3. The magnetic requirement, that common steel should
be capable of magnetization by the action of an electric current, was met by the theory of Ampere that before magnetization the planes of the atoms lie haphazard, with their equatorial planes tilted indifferently in all directions. The action of the electric current, with waves flat in the planes through the axis of the conducting wire, will yield electric oscillations in the form of plane waves, oriented at right angles to the axis of a bar of steel under magnetization in a solenoid. Hence these electric oscillations or plane waves due to the current, will force the atoms of the steel bar to tilt around, so as to make their vibrations conform to those due to the current in the solenoid; and when the magnetized steel bar is cooled suddenly, by plunging into water or oil, the result will be a permanent electromagnet of the type first made by Amplre about 1822. Thus the atoms of the magnet are set in planes at right angles to the axis through the poles, and all vibrate in concert.
4. Accordingly, we find a direct relation between magnetism and electrodynamic action, and as dynamic electricity is found by experiment to travel on wires with nearly the velocity of light, it is impossible to doubt that the waves emitted by natural and artificial magnets travel also with the same speed. In fact it follows that before magnetization the steel emitted waves of the same type as after action by the
electric current, yet prior to the action of the current through the solenoid the orientation of the atoms was a haphazard
one. The act of magnetization consists in forcing the equators of the atoms into parallel planes, so that they may vibrate in concert, which explains the great strength of magnetism
in comparison with the feeble force of gravitation.
5. This brings us directly to the problem of cosmical magnetism and of gravitation. In steel magnets of good quality all or nearly all the atoms are forced into parallelism
by the agitations of the current through the solenoid. Now
the heavenly bodies contain some iron, nickel and other magnetic elements, but much of their matter, of a stony or glassy character, exhibits magnetic properties in a very feeble degree. Moreover, the planets are subjected to no very strong solenoidal action other than that due to the sun's magnetic field. It is not remarkable therefore that they are only partially magnetic. Their magnetism may have been acquired or- considerably modified by the secular action of the sun since the formation of the solar system.
6. Accordingly, Faraday's, great discovery that under current action all bodies are more or less magnetic, while

") The fact that waves will explain the attraction and repulsion of magnets, under the observed laws of magnetism, must be regarded as ii very notable triumph. As no other explanation is known, the simple cause thus assigned must be held to be the true cause.

.

267

5079

268

nickel, iron, steel, etc., are the most perfectly adaptable to the process of magnetization, would lead us to expect co3-

magnetic attraction backward and forward in the line from the Red Sea to Hudson's Bay* (Treatise on Magnetism,

mical magnetism to be a very general phenomenon, but 1870, p. 206).

always somewhat feebly developed, in accordance with actual

10. This semidiurnal tide in the earth's magnetism

observation. Herein lies the connection with universal gra-
vitation, which Maxwell found so difficult to conceive. When

the .equators of the atoms are not lined up in parallel planes,

so as to oscillate in concert, they naturally are tilted hap-

— hazard, and do not lead to poles,

as in a magnet, which

— Airy describes as exhibiting a duality of powers,

but to

the central action called gravitation. As the heavenly bodies

depending on the moon's action is shown to be coperiodic with that of gravitation (cf. Electrod. Wave-Theory of Phys. Fore, 1917, pp. 50-53)- And on examining Lloyd's analysis in the Philosophical Magazine for March, 1858, I have shown it to be vitiated by a subtile error, in that he retained the
hour angle 6 instead of the 29 which occurs in the expressions for the tide-generating potential. Apparently he did

are partially magnetic, this means that they have feeble not suspect that there could be such a thing as a magnetic

magnetic poles, in addition to the powerful central gravitational tide, and thus his mode of analysis simply begs the question, action, and thus two independent wave fields are developed and the resulting error is repeating in many later works.

about them, one due to the atoms lined up and acting in For example, in his Mathematical Theory of Electricity and

concert, called magnetism, and the other to gravitation (cf. Magnetism, 1916, p. 402, Jeans asserts that the daily vari-

Fig. 14, Plate 6).

ation of the earth's magnetism is not such as the heavenly

— 7. It is impossible to hold any other view of the bodies could produce thus repeating Lloyds error of 1858.

interlocked magnetic and gravitational fields observed about Of course this is not true, for a careful examination of the

a planet. In the case of the earth Gauss fouad that about problem shows that the larger part of the terrestrial mag-

I : 1380''' part of the matter acts as if it were magnetized netism is constant, as depending on the arrangement of

(AUgemeine Theorie des Erdmagnetismus, 1838, p. 46), while 1/1380"' of the atoms of the globe, whilst the variable effects

the remainder, 1379:1380*^, should give the central action are superposed by the actions of the sun and moon. Thus

of gravitation. By the observations taken at Mt. Wilson all the known periods of the terrestrial magnetism are shown

Solar Observatory the sun's magnetic field appears to be to follow from those of the heavenly bodies.

some 80 times stronger than that of our earth. Whether this

11. Now it is found that Newton's law will explain all

is due to the heat of the sun, and the resulting greater con- gravitational phenomena, but not the phenomena of the

ductivity of wave action through its matter, so that the action on the planets produce a larger secular effect upon their atoms, or to some unknown cause, cannot at present be determined. The strength of the sun's magnetic field has no doubt added to the cosmical magnetism of the planets,

magnetic tide depending on such a body as the moon. For as Airy points out, this implies attraction backward and forward, in the line from the Red Sea to Hudson's Bay, which is along the line of force of the earth's magnetism. The intensity of the earth's magnetism thus varies in semidiurnal

though the changes are excessively slow.

periods, just as the direction of the vertical varies under

8. It is more than probable that the secular changes the gravitational attraction of the moon, and in similar

in the earth's magnetism should be ascribed to the working periods.

of the sun's strong magnetic field, which is not equally power-

12. Accordingly, the attraction to the earth's magnetic

ful at all times, but varies appreciably with the sunspot cycle, pole is subjected to a true tide in the earth's magnetism,

the relative position, and seasonal tilt of the earth's axis, and can only be explained by Weber's law, which takes etc. As the magnetic storms are definitely shown to be account of induction under the changing distance of the

related to the cycles of the sunspots, as is also the aurora,
and the earth currents, these related phenomena deserve a more detailed investigation than they have yet received. The periodic phenomena all appear to depend on the sunspots, with their magnetic fields uncovered, and thus are more active with the maximum of the spot cycle.

partially magnetized matter of the globe, the lines of force towards the magnetic pole being subjected to the same ebb and flow as the central forces called gravitation. This connects magnetism with gravitation, by direct observation: for the earth has feeble polarity, with magnetic lines of force
directed to the magnetic poles, as well as the much more

9. For many years a great difficulty existed in accounting powerful central lines of force producing the phenomenon
for the semidiurnal tide in the magnetism of the earth, of gravitation, Now the phenomenon of local gravitational

depending on the action of the moon. This was first detected change, due to the moon's action, is indicated by the os-

by Kreil at Prague in 1841, but independently discovered cillations of the sea, while that due to the moon's magnetic

^ by John Allan Broun, 1845.

"^^ry accurate analysis of the action is felt only by magnetic instruments which show the

observations at Dublin was published by Dr. Lloyd about variation of the northward component of the earth's magnetism.

1858, which showed that the magnetism of the earth had

13. When the tide-generating potential is developed in

the same semidiurnal period as the tides of our seas. Ac- hour angle h^ (westward), longitude / and latitude I of the

cordingly Airy declared that there is »a true lunar tide of place of observation, declination of the moon (5, the com-

magnetism, occurring twice in the lunar day, and showing ponents of the gravitational attraction are shown to be :

V= — — {^l.,ma^lr^) { ^Acos^A cos^d cos2(/%o -/) sin2Asindcosdcos(/^o ^)-f-V2(V3 sinU)}

= + — Westw. Comp. =dF/acosMl

^/2{m/M){a/r] '{cosAcosMsin2(/%o— ^)

sinAsin2dsin(,^o

0}

= = — — — + ^ Southw. Comp.

-dv/adX

^U{mlM){a/rY sin 2I cos^ (} cos 2 (/^ /) 2cos 2 A sin 2 d cos(/%o /) sin 2 A( i

3 sin^J) }

(38) (39) (40)

269

5079

It will be noticed that the westward component is made up of two periodic terms, one going through its variations twice and the other once a day, while the southward component undergoes like periodic oscillations^ as illustrated by
the following figure, from Sir George Darwin's Tides and Kindred Phenomena of the Solar System, 1899.

16^ 154

270

.

:

,

271

5079

27-

have their equatorial planes tilted at any angles in respect to

the coordinate axes. The plane waves above outlined would

apply to the midplane of a perfect magnet, but it is necessary

to consider the most general case.

Now the equation of a plane passing through the origin

of coordinates is

7^_i_„,„_i_^„

A 1

If the wave be flat in this plane it will travel with the

velocity a and at the end of the time /, will have spread

to a distance at. Accordingly, the argument
= 5 Ix-^my + nz — at

(45)

will represent the motion of the disturbance with velocity a.

But s is the equation of a plane whose normal has

the direction cosines /, 7n, n, and whose distance from the

origin is at-^s. It is inferred that the plane is therefore

traveling in the direction of its normal with the velocity a;

but it is equally logical to say that a wave originating in

= the plane is traveling in all directions with this velocity, and

at the end of time t, the sphere. surface [aiY

x^-\-y'''-\-z^

would be this distance {at-\-s) from the original centre of

disturbance. Thus instead of considering the plane to travel,

= we may consider the wave to travel and carry a plane

s-^at

Ix-^my-^nz, with it parallel to the plane in (45).

The directions cosines of the plane fulfill the law

+ = /2-H;«2 »2

I.

(46)

Now with the value of .f in (45), we may take the

equation

= O g)

(/.t-h.;zj/H-«2-«^)

(47)

and derive the following results by simple differentiation :

= dOl'bx

I O' (s)

= dw/ds

n O' [s]

= dW/dy m O' [s)

= d(D/df

-a(D' [s]

U7a)

^ 8-'a)/8^2 = eaffj/ggS

Q. 1-2 (^)
n^ O"

= d'-at/dy-'

„r O' [s)

d-^QJdf a^W"

17 b)

Therefore, by addition of these terms we find

= d'-(D/dx--^d-^(l)ldy^-hd-^0/dz'-

= = = v'-O)

(/-'-i-ot2+«'-) O' [s)

®" (.r) .

'

(47 c)

And hence by the last of the above second differen-

tials we obtain

820/9^2 =fl2^-'a)

(48)

which is Poisson^ celebrated equation of wave motion. (Sur

I'intdgration de quelques equations lineaires aux differences

partielles, et particuli^rement de I'equation generale du mouve-

ment des fluides elastiques,« Memoires de I'Academie Royale

des Sciences, Tome III, Juillet ig, 18 19.)

If u represents the displacement of the particles above

considered, in the direction of the a;-axis, we may derive a

less general but more obvious form of Poissorii, equation,

which was applied by Euler to the theory of sound.

= Put u

^v!\[nt—kx] n == 2nal). k.^ 2tc\X . (49)

And then we may derive immediately:

= = 8«/8/

nQ.Oi{nt^kx) dujdx

—Acos{nt — kx)

82^/8^2 =_„3^

= d^u/dx^

-hk^i(

whence

= - 8^9/^

{n'/k') d'-u/dx'-

(50) (51) (52)

In the use of Poissoris equation of wave motion

we may multiply both sides of the equation by the element

= of volume d-r djcd^dz, and integrate throughout the volume

bounded by a closed surface S
+ + = JJJ(82<Z)/8^2)dT= «^Jj'J{82(»/9x2 8^®/8y 92®/8^^)d^

= -«^JJ(8(P/8«)d^.

,

(53)

If the surface 5 is a sphere of radius r with its

centre at the point P,

we

may proceed

as

'
follows :

-JJ(8®/8«)d.S=JJ(8(Z)/8r)rMa, =rn9/9^)JJa>rdco (54)

O where <Dr denotes the value of

at points on the surface of

the sphere of radius r, about the centre P.

When we introduce polar coordinates into the first

member of (5,3) we obtain:

= (9V9^')JJJ®dT (92/8/2)JJd(«(ja)rr^dr) . (55)

o

On differentiating the right member relative to r, we

get from the original equation (48) by means of (53):

= /2(82/8/2)JJa),dM

«2(8/8^) (r2(8/8^)JJ®,d«) . (56)

Yet the surface integral

Or dw which appears in

JJ

both members of (56) is ^n times the mean value of the

function Or on the surface of a sphere of radius r. Suppose

this mean value be denoted by Or\ then since jj®rda»
= ^n Or we have

r2(82®,/8/2) == «2(8/8^)(^2.8^^/8r).

(57)

On differentiating and dividing by r, we may put

this in the form:

= 82(r®,)/8/2

^2 82(^0^)/8,-2 .

(58)

We may now introduce two new variables u und v,

as follows:

= u ^= at-hr v at—r.-

(59)

Fig. 16. Illustrating the Wave Theory of Poisson

as in reflected Light.

= Then if, for brevity, we put rOr

ip we have for

the derivatives:
= = 8^/8^- ^^p/^u^ul^t-h^^,/^v^vj^t a [dipjdu = = 8 ip/dr dip/du du/dr -+- drp/dv dvjdr df/du = d'^ip/dt^ «2 [82^/8^2+ 2d^iijjdudv-i-d-iifj/dv']

dxp/dv) (60)^ dip/dv (61)'
(62)

82,///8,-2=82,^/8«2_ 2 d-^ip/dudv-hd'-ip/dv'.

{63)

By equation (58) we have through the addition of the

terms of the right of (62) and 63

d-yj/dudv ;== o .

(64)

,

:

.

:

273

5079

274

This equation yields the general solution:

-ip =/iW+/2W

(6s)

where /i and f^ are perfectly arbitrary functions of their

arguments.

^ If r

o, the left member vanishes:

o =/iHh-/2 («/).

(66)

And as this holds for all values of /, it follows that

the functions /i and/2 are not independent, but one is the

negative of the other, namely

O Suppose, for example, that initially

and do/dt are

both zero, except for a certain region P, whose nearest point

is at a distance i^i from P, while the remotest point lies at

a distance ^2.

O Then so long as 4 <ri/a the mean value of

on

the sphere of radius at, is zero, because the waves from the

nearest point have not yet reached P. After an interval

t.,>r.2/a there will be no more waves and dO/dt will again

be zero at P.

Mat) =- -Mat)

.

by (66), whatever be the value of the argument at.

(67)

Accordingly we now put

/i =/ h=-f

(68)

and then we have

rQir=^ f{at^r)-f{at-r).

When \ye differentiate relative to r, we get:
^ (Dr+rClOr!(lr f{at^r)+f'{at—r) .

And on putting r == o, this leads to

f Or= 2 [at)
= = Op, when r o .

On differentiating (6g) relative to r and t,

successively:

= f (9/ar) [rOr)

[at+A +/' [at-r)

= (8/3^)(r®,) a [f[at+r)-f[at-r)] .

Accordingly, by addition, we obtain

(69)
(70)
(71) (72)
we get
(73) (74)

8(r®.)/8r+(i/fl)-8(r®.)/8/= 2f'{at+r).

= And for / o

= [8(r®.)/8r+(i/«)-8(r®.)/84^^

2f'[r) .

(75) (76)

When we use the original value of ®r =^ ( t-I A^t)

Or doo
\

\

it thus appears that we obtain

2/'{r)=[{d/dr){r/47f^^(Dr<iw}

Fig. 17. Illustrating Poisson'% Tlieory of Waves.

Accordingly disturbances will prevail only in the time

rxla<t<r.ila and the power of disturbance, or velocity po-

tential O, is propagated in all directions with the velocity a.
By using polar coordinates Poisson has obtained a more
O direct solution, because then becomes independent of the

= angular coordinates. Equation (48) becomes:

o'^Ol'df-

«2 (820/9^-2+ 2/^. 90/a^)

or

= d\rO)l'df-

a'- d\rO)\dr''

(gj) (82)

A solution of this equation is

rO=f[at-r)

(83)

which yields:

q) _^(^,_^)/^_

(g^)

-+-(i/«)W47r-JJ(8a)./3/)d«a^^. (77)

= Now suppose that at the initial instant, t

o, the

O values of and its time derivative 8(D/8/ are given in func-

tions of the coordinates of a point in space:

= [(I>l^^ J'(x,y,z)

[dOldt\^^==f[x,y,z).

(78)

Then by (77) we have

= + 2f[r)

(9/8^) {(r/47r)JJi^.d(«} (r/47r«)JJ/,dw. (79)

= = But when r

at, we have by (72) 2f'[ai)

Op at

the centre, and thus finally we obtain:

= Op

(1/471) [(9/8«/) (a/JJiVtdw-t-/JJ/a, d«)]

(80)

which is Poissoii's, general solution of the equation (48), for

wave motion.

O From this solution, it follows that the value of may P be computed for every point if we know the mean value

do of

I'd f at a time earlier by the interval at, for all points

on the surface of a sphere of radius at about P, as well as

O the rate of the variation of the mean value of

as the

radius of the sphere changes. This is the typical condition

specified in wave motion.

— Thus for all points of space, and all times for which
at r has the same particular value we have the same value

O r O, as the particular value of

travels outward with the

velocity a.

O It should be noted that the value of

is inversely

O = proportional to the distance r traversed. And although the

analytical form (84) makes

infinite when r

o, yet in

reality this condition does not occur, because physical limi-

= O tations imposed by the structure of matter excludes the value

r

o, and

is always finite.

Following the method of Poisson, Lord Rayleigh and

other writers on sound are accustomed to take the velocity

potential:

^ = ^

o(,^., t)

Aco^{2nll-[x-at)\

(85)

which fulfills the irrotational condition of hydrodynamics

= '\^AO ^= '\^[uAx+vdy^wAz) o.

(86)

But it is a fact of great importance, which will be discussed at length' in the fourth paper on the new theory of the aether, that Poisson never concurred in the theory 'of transverse vibrations for light. Poisson's, dissent from FrcsneTi, assumptions was based on the mathematical theory of waves

«

«

275

5079

276

in an elastic fluid. Besides the celebrated memoir of 18 19,
already cited, Poisscn treated the matter in another able paper,
presented to the Academy of Sciences, March 24, 1823, Memoire sur la Propagation du Mouvement dans les Fluides filastiques, finally published under the title : Sur le Mouvement de Deux Fluides filastiques Superposes (Memoires de rinstitut. Tome X) in which this celebrated geometer con-
firmed the conclusions previously reached, namely, that

distance, ces ondes sont sensiblement planes dans chaque partie, d'une petite etendue par rapport k leur surface entiere; et alors, la vitesse propre des molecules est, dans tous les cas, sensiblement normale k leur plan tangent. Mais on peut aussi considerer directement la propagation du mouvement par des ondes infinies et planes dans toute leur etendue. Or, on va voir que la vitesse des molecules sera encore perpendiculaire a ces sortes d'ondes en mouvement:

whatever be the direction of the original disturbance, the vibratory motions of the particles finally become normal to the wave front.
When Fresnel and his followers objected to Foisson's

Accordingly, in his most mature memoirs, after researches on the theory of waves extending over 25 years, Poisson confirmed the conclusion that in elastic media, of the type of a gas, the motion of the molecules is always

processes as founded on mathematical abstraction, though like that of sound. This result will be found to have great

deduced from the assumption of contiguous elements, the significance when we come to deal with a fundamental error celebrated geometer returned to the subject in a series of in the wave-theory of light, in the fourth paper on the New

later memoirs, as follows:

Theory of the Aether.

1. Mdmoire sur I'fiquilibre et le Mouvement des Corps filastiques, Avril 14, 1828. Me'moires de I'lnstitut, Tome VIII, PP- 357-627.
2. Memoire sur I'fiquilibre des Fluides, Nov. 24, 1828.
Tome IX, 1-88.
3. Memoire sur la Progagation du, Mouvement dans les Milieux filastiques, Oct. 11, 1830, Tome X, pp. 549-605.
4. Memoire sur I'fiquilibre et le Mouvement des Corps
Crystallises, Tome XVIII, pp. 3-152.
In all of these memoirs the earlier conclusions of 1823 are confirmed and emphasized, that whatever the pri-
mitive disturbance may have been, 'at a great distance the motion of the molecules finally becomes perpendicular to the wave surface. This is deduced in the memoir of 1830, pp. 570—571, by an argument which cannot well be evaded, and announced in these words;
»I1 en resulte done qu'i mesure que Ton s'eloigne du centre de I'ebranlement primitif, la vitesse dupointj/approche de plus en plus d'etre dirigde suivant son rayon vecteur r, et qu'k une tr^s-grande distance, oh I'onde mobile peut ^tre

9. Rejection of Thomsons Corpuscular Theory of an Electric Current, because of the Small Velocity thus attainable: Theory of a Magneton also rejected because of its Inconsistency with Electrodynamic Action: observed High Velocity of Electron under Charge explained by Acceleration due to Aether Waves.
(i) Thomson and other electronists hold that an electric current is due to the motion of electrons.
In his Corpuscular Theory of Matter, 1907, Sir y. J. Thomson put forth the view that an electric current consists in the motion of the electrons. »0n the corpuscular theory of electric conduction through metals the electric current is carried by the drifting of negatively electrified corpuscles against the current.* . . . »The corpuscles we consider are
thus those whose freedom is of long duration. On this view
the drift of the corpuscles which forms the current is brought about by the direct action of the electric field on the free
corpuscles.* (p. 49.)

regardee comme sensiblement plane dans une grande dtendue, on doit, en m^me temps, considerer le mouvement des molecules qui la composent, comme perpendiculaire k sa surface,

»As, however, the mass of a corpuscle is only about 1/1700 of that of an atom of hydrogen, and therefore only about 1/3400 of that of a molecule of hydrogen, the mean

quel qu'ait ete I'dbranlement primitif.

value of the square of the velocity of a corpuscle must be

® = On pages 574-5 of the same memoir of 1830, Poisscn

deduces the formula

i/r-xp{r—a(, k) and passes to

fj,,

the case a(> r-i-s,

W=^ i/r-lHfv,X)

(87)

where we should have
s= j/a'--d(Dldt=o.

(88)

»I1 rdsulte de cette discussion que dans le cas oil la
formule udx -^ vdy -^ wdz ne satisfait pas a la condition d'intdgrabilite, les, lois de la propagation du mouvement, k une grande distance de I'dbranlement, ne different pas essen-

tiellement de celles qui ont lieu, lorsque cette condition est
remplie, ainsi que je I'avais suppose dans mon ancien memoire
sur la theorie du son.«

»Le mouvement imprimd arbitrairement k une portion

limitee d'un fluide homogtoe se propage toujours en ondes

A spheriques autour du lieu de cet dbranlement.

une grande

3400 times that of the same quantity for the molecule of
hydrogen at the same temperature. Thus the average velocity of the corpuscle must be about 58 times that of a molecule of hydrogen at the temperature of the metal in which the molecules are situated^).. At 0° C. the mean velocity of the hydrogen molecule is
about 1.7-10'' cm/sec, hence the average velocity of the corpuscles in a metal at this temperature is about 10^ cm/sec, or approximately 60 miles per sec. Though these corpuscles
are charged, yet since as many are moving in one direction as in the opposite, there will be on the average no flow of
electricity in the metal. Although the change produced in the velocity of the corpuscles by this force is, in general, very small compared with the average velocity of translation of the corpuscles, yet it is in the same direction for all of them, and produces a kind of wind causing the corpuscles to flow in the opposite direction to\he electric force (since

— *) The spacing-out of the concluding sentence is mine

not in the original.

«

«

277

5079

278

the charge on the corpuscle is negative), the velocity of the wind being the velocity imparted to the corpuscles by the
electric force '^).«
Thomson's calculations of the velocity of 60 miles per second are based upon the formulae cited in Section 12, below, which I had made before I found the above statement. Thomson does not dwell on the inadequacy of this velocity of 60 miles per second to explain the transmission of electric signals on wires, which have a velocity only slightly less than that of light.
On page 68, however, he points out that in a Rontgen-
ray-bulb giving out hard rays the velocity of the corpuscles
in air may be about 10^" cm/sec, or 10^ times the velocity
of those in the metals.
It is held in the theory of ionization of gases by X-rays, that the positive and negative parts of the atoms are separated. »The positive ions are attracted to the negative electrode and the negative ions to the positive electrode, and the movement of these electric charges constitutes a current,* says Duff's, Text Book of Physics, (ed. 19 16, p. 4q8). This is used at the University of California, and this discussion was written by Prof. Ji. K. McClung of the University of Manitoba, who is a Doctor of Science of the University of Cambridge, England, and thus speaks with
authority.
Likewise, Crowther says on p. 139 of his Molecular
Physics: »We have now come to connect electricity with
electrons, and hence an electric current is a flow .of electrons
from a place of high to a place of low potential. We may
regard a conductor, then, as a substance containing electrons
which are free to move under the action of an electric field, while in non-conductors the electrons are fixed and unable
to follow the impulse .of the field.

Again, (p. 140) Crowther adds: »These electrons, if no electric force be acting, will be moving in all directions, so that if we take any cross section of the metal the number of electrons qrossing it in one. direction will be the same as the number crossing it in the opposite direction, and so the total transference of electricity across Ithe section will be zero.«
»If, however, we apply an electric field to the body there will be a force on each electron urging it in the direction of the field. Thus in addition to the irregular motion due to the heat energy of the body, there will be a steady
drift of the electrons as a whole in the direction of the elec-
tric force.
This discussion, like that of Thomson, admits that an electric field is necessary so set the electrons in motion, but the nature of the electric field itself is not explained, beyond the general phrase that difference of potential is involved. This is almost as unsatisfactory as the failure of the electronists to account for the high velocity of. electric signals on wires.
(ii) Experimental tests of the velocity of electric waves on wires.
The problem of the velocity of the electric waves along wires has been much discussed, and formulas given in such works as Cohetii, »Calculation of Alternating Current Problems*, whilst the propagation of waves in metals has been treated theoretically by Drude, Lehrbuch der Optik, 2, Chap. IV, and by other authorities.
But when we come to deal with concrete measurements of actual velocities, such measurements do not seem to be plentiful: yet we note a few values in the following
table.

Observed V
463i33Km.
310475 179890
99938 230500I 256600
J
241800

Authority Wheatstone, Phil. Trans., 1834 Kirchhoff, G^aw^^'s Physics § 796 Fizeau and Gounelle
Siemens and Frolich, Poggend. Ann. Bd. CLVII.

Remarks Duration of Electric Spark Method. Theoretical Calculation from the Measurements of Constant Electric Currents. Signals on Copper Wire. Signals on Iron Wire.
Observations on Telegraph Wires of Iron, 23372 Kms. long.
Observations on Telegraph Wires 7352 Kms. long.

These measurements, which are of very unequal value, give a mean of 254618 Kms., which would not seem improbable, in vievif of the fact that the Siemens-Frolich series, apparently by far the best, give a mean 242966 Kms. for electric waves on iron wires. As the electric disturbances should travel with the velocity of light, 300000 Kms., except for the resistance of the wires, it would thus appear that the velocity is reduced about Vs"" or Ve"" of 'he whole. The resistance causes the disturbance to travel slower in the wire and thus the waves around the wire envelope it, and necessarily follow it as a conductor.
A more modern investigation of the velocity of electric
waves on wires was made by Prof. John Trowbridge and

W. Duane, and published in the Philosophical Magazine foi-

1895, '^ol. 40, p. 211. They used a pair of parallel short

wires, 58.6 metres long, but determined the duration of the

electric oscillation in the wire very accurately by photo-

graphy of the sparks in a rapidly rotating mirror. The wave

length was 56.77 m, and the duration of the spark was found

to be 1.8907 10""' second. The mean value of the velocity

V= of the wave on the wire came out

3.003 • 10^" cm/sec.;

which slightly exceeds the adopted velocity of light.

But a much more thorough direct comparison of the velocity of electric waves on wires with light itself was quite recently undertaken by the French physicist C, Gutton,

Journal de Physique, 1912 (5), vol. 2, p. 41. This experiment

^) I quote at length from the chief authorities, in order to feel sure that the views of the electronists are correctly cited. As I consider the electron theory to be greatly overrated, this precaution is deemed necessary, in justice to their researches, which I might find difficulty in accurately condensing into any briefer statements.

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•was arranged with great ingenuity, and the apparatus so

designed as to show a small difference in the two velocities,

if such difference existed. The first observations showed that
the two velocities were nearly identical, yet not rigorously

the same.

Under the delicate and dependable means of adjustment used Gutton discovered that the velocity of the electric wave on the wire was a little less than that of light. And

he found that the difference thus very accurately determined

amounted to' about one-half of one percent. Accordingly for

the velocity of electric waves on wires Guifons values would be:

Electric waves V ^^ 298500 Kms.

Light

V= 300000 Kms.

This retardation of the electric waves by wires is small, but fortunately the experiment of GuHon was so well de.signed that no doubt can attach to the reality of the difference.
We mt,st therefore admit that the electric waves on wires
are slightly retarded by the resistance in the wires. This has been probable on general principles, and indicated by the older experiments, and it now takes its place as an established fact of observation.

The result is similar to that reached in the first paper on the New Theory of the Aether, where we showed that

wireless wawes travel more slowly through the solid mass

of the earth, and the wave front is thus bent around the

— globe,

which explains the observed fact that the wireless

wave travels around the earth. This propagation of the

wireless wave around the globe had proved very mysterious,

and no satisfactory explanation of it had been forthcoming.

As we have now definite proof of the retardation of

electric waves by the resistance encountered within a metallic

wire, we see that the wire is surrounded by an envelope of

waves in the free aether tending to proceed with the velocity

of light, yet held back by the resistance within the wire,

and thus the advancing wave envelopes and is made to follow

•the wire. Is it not probable that we have here the true

explanation of the nature of a conductor?

Of course a conductor must be metal, which has both
— the power of inductance and capacity, otherwise the electric

disturbances would not take the form of waves, thus expen-

ding the energy due to difference of potential. Yet, there

must be another physical cause at work to rnake the distur-

bance follow the wire. It is this, that the wave in the free aether travels more rapidly than within the dense resisting

wire, and owing to this resistance, the waves follow the wire,

being bent towards it on all sides, as shown in the inner

part of the Fig. 18, Plate 6.

The discharge spark of a Leyden jar is due to the

oscillations of the invisible aether, rendering particles of air
luminous by the agitation; and when this spark is photo-

graphed in a rapidly revolving mirror, the oscillations are
We shown as indicated on the axis of the wire to the left.

must therefore assume electric surges from one side of the wire

to the other, just as in a Leyden jar. Moreover, as the aether

is compressible, this compressibility contributes to the develop-

ment of waves.

It is to be noted that the oscillations photographed

in the mirror have their phases spread along in time, and

therefore the disturbances are spread along in space, when we deal with a wire on which the disturbance travels, so that the oscillations diagrammed on the left are repeated
throughout the wire.
The reflection of any element of the aether wave out-
side the wire is given double effect by the surge from the
opposite surface of the wire, as shown in the diagram. And
thus the wave rotations take the reversed directions shown above and below the wire. This is the wave field we investigate in Oersted's experiment, and find to follow Biot and Savarfs law, as already explained in Section 5.
Accordingly the delay in propagation through the wire causes a slight whirling of the aether particles against the wire, then a rebound, with rotations in the opposite direction
— in waves which are propagated away as shown in the
diagram of the wave field. In regard to such reflection from metallic surfaces, Prof Fleming says: »This electrical radiation (waves of length approaching 4 cms.), penetrates easily through dielectric bodies. It is completely reflected from metallic surfaces, and is also more or less reflected from the
surfaces of insulators* (p. 411).
(iii) Rejection of the theory of a magneton as con-
trary to electrodynamics.
We now pass to the discussion of the so - called
magneton. 1. It appears that the existence of the so-called mag-
neton is purely hypothetical. It was at first admitted, with some hesitation, as a possible corpuscle, in magnets, analogousto the electron in the problems of electricity. This idea
seemed logical in terminology, and the name appeared in
certain papers of the Philosophical Transactions of the Royal
Society, and it has since come into more general use.
2. But the above described terminology apparently overlooks the fact that magnets are produced by the action of an electric current. If therefore electrons be active in a current, and the current generates a magnet, it is more natural to explain magnets by the effects of electrons, and to do away with the magneton as superfluous.
3. In the present author's work, however, waves are
made the basis of the generation of a magnet out of steel
by the lining-up action of an electric current. It is thusillogical to introduce fictitious corpuscles imagined to have rotatory properties, when simple waves in the aether sufficefor all practical purposes.
4. In the Principia, Lib. Ill, 1686, Newto7i lays down:
as the first rule of philosophy: »We are to admit no more
causes of natural things than such as are both true and sufficient to explain their appearances.* »To this purpose the philosophers say that nature does nothing in vain, and moreis in vain when less will serve; for nature is pleased with
simplicity, and affects not the pomp of superfluous causes.* 5. Under the circumstances, there is no need for the
hypothesis of a njagneton, and thus we reject it because itsuse in inconsistent with electrodynamic phenomena as explained by the wave-theory.
(iv) Velocity of the electron made to approximate that
of light by the action of electric waves.
In his later researches on the ratio of the charge to-

!

«:

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the mass of cathode ray particle, Thomson devised a method

for exactly balancing the electric and magnetic forces, and

was able to determine the ratio elm, and get V from the

X ratio of the strength of the electric field

to the strength

V= of the magnetic field H, both of which could be measured.

In this way he found

2.8- 10^ cms. per second, or

about one-eleventh of the velocity of light.

This value was found to be not quite constant, but to

vary somewhat with the potential in the. tube, yet the value

elm was found to be 1.7 • 10', and shown to be independent

of the nature of the gas used in the tube. The greatest

value of elm known in electrolysis is for the hydrogen ion,

and comes out 10*, whence it was concluded that the value

for the cathode particle is 1700 times that for the hydrogen

ion. As the charge e carried by the cathode particle was

found to be the same as for the hydrogen ion, it was held

that the mass of the cathode particle is 1/1700 of the

hydrogen ion or atom.

It will be seen that notwithstanding the great ingenuity displayed by Thomson and his pupils, this whole subject is
involved in considerable uncertainty. Perhaps it may fairly be asked whether any of these phenomena are yet interpreted on their final basis. No doubt the experiment as
described s'upporfs the result found, but it is always difficult
to feel sure that some .entirely different view of these matters may not develop hereafter, owing to further experimentation, or improvement in the theory of the aether.

The net result is therefore as follows:

1. Viewing the electron as a corpuscle of a gas, it

would attain a velocity of only about 98 kms. (60 miles)

per second,

or

i

3000'''
:

of

the

velocity

of

light.

This is

very insignificant compared to the velocities observed in light

and electric waves.

2. Under the action of impulses in the tube not yet

fully understood, but generated under considerable electric

tension, the velocity of the charged particle may be augmented

nearly 300 fold, so as to become a little less than a tenth

of the velocity of light and electric waves.

3. The mass of the corpuscle is considered to be due wholly to the charge, but too little is yet known to justify

this claim, and it cannot be admitted. Apparently wave

action alone could produce the velocity of the electron,

2.8- 1 o^ approaching one tenth that of light, because the aetherons move 1.57 times faster yet.
4.- In his work on Molecular Physics, p. 7-8, Crowther
describes how much energy may be given to a small mass by

increasing its speed to about 1/15''' of the velocity of light. »Such particles, however, actually exist, and it is the
discovery of these particles and the measurements made upon

them that have led to the great advances in molecular physics which we are about to describe. Particles having this velocity are shot out in large numbers from radioactive bodies.
To anticipate a little we may say that the o;-particles from
radium consist of atoms of helium shot out with a speed of this order of magnitude, and bearing a positive charge. Thus it is that a single a-particle is able to cause a flash of light when it strikes upon a screen covered with a suitable
material.*
The view that the high velocity attainable by the electron is due to the action of electric waves is suggested by
Crowther's further remarks

»The a-particles consist of helium atoms only. Velo-

cities approaching that of the a-particles can be given to

atoms and molecules of other substances by passing an

electric discharge through them iri the gaseous state at very

low

pressures. The .

phenomena

of

the

discharge

tube

have

indeed afforded the best means of investigating the properties

of moving electrified particles, and we shall proceed to their

consideration immediately.

Accordingly it seems that the electron researches strongly support the wave-theory as the only means of generating the velocity of the electron found by observation^). If helium atoms or a-particles can be given such high velocities by
electric charges, still more may electrons, in view of their
very small size, be given the high velocities approaching i/io* that of light. For as helium gas is monatomic but twice as heavy as hydrogen, the electron is about 6800 times lighter than helium, and under gaseous laws a velocity of over 80 times that of a helium atom might be expected for the electron, if equal energy were concentrated in a single corpuscle. This gives arnpje power to account for the observed velocity of projection of the electron, and the highvelocity therefore is naturally attributed to wave-action.

It is worthy of note that, with Crowther's estimate that

= the electrons attain a velocity of i : is'*" of the speed of

light, the aetherons have . a speed 15-1.57

23-55 times

that of the swiftest corpuscle heretofore recognized. The

New Theory of the Aether thus bids fair to give quite an

impetus to the study of high velocities.

10. The Identity of the Velocity of Electric Waves with that of Light shows that the Aether underlies both Classes of Phenomena: the Formal Public Discussions on doing away with the Aether recently held before the Royal Societies in London striking Evidence of the General Bewilderment.
(i) The physical significance of the identity of the
velocity of electric waves with that of light.

— ') In his History of the Inductive Sciences, Whewell bestows high praise on Roemer,

who lived about a century in advance of

— his contemporaries, so that his discovery of the velocity of light was accepted, by very few, chiefly by Newton and Huyghens,

because this

celebrated discoverer noticed that the eclipses pf Jupiter's satellites were delayed in time in proportion to the distance of the earth from Jupiter.

Thus when Jupiter was near opposition, the eclipses came about 16 minutes earlier than, when the earth was on the opposite side of the sun;

and Whewell remarks on the highly philosophic character of Roeme?'!, argument for the gradual propagation of light across space, which no

one before him had suspected from the earliest ages.
Now in our time the researches of the electronists have occupied great prominence, but without any inquiry, so far as I know, being

instituted by them to account for the known velocity of electric waves on wires and radio waves across free space. This neglect greatly weakens

the position of the electronists, and when they propose to do .away with the aether, without accounting for the propagation of light and elec-

tricity, they add presumption to carelessness; and therefore if Roema^s course was highly philosophic the course adopted by the electronists

— has been just the reverse

unphilosophic and indefensible

,

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The early evidence deduced by Maxwell, in 1864, and

his successors during the next quarter of a century, to the

effect that electrical actions travel sensibly with the velocity

of light, received a remarkable confirmation from the physical
discoveries of Hertz, who devised methods for investigating

electrical wfives of the type since used in radio-telegraphy.
And the progress of radio-telegraphy has been such that the

velocity of these waves between Paris and other parts of

France, and between Paris and Washington, has been measured

as accurately as is humanly possible in the determination of

intervals of time less than a fiftieth of a second.
We cannot say indeed that the measurements between

Paris and Washington give incontrovertible experimental proof

that the electrical waves travel with exactly the velocity of

light. Perhaps the velocity of propagation is involved in say

five percent of uncertainty; yet all the observations are con-
sistent with the speed of light. And in view of the accuracy

of the determinations of V, by such methods as were employed

by the American Bureau of Standards in 1907, we must hold

that the radio-waves between Washington and Paris travel

with the observed laboratory velocity, which appears to be

exactly identical with that of light.

The fact that approximately the same speed is attained

by light and radio-electric waves, reduces us to the necessity

of admitting:

1. Either the two classes of waves travel with precisely

the same velocity.

2. Or we miist assume the existence of two media with

slightly different elastic powers, yet giving waves of practi-

cally the same velocity.

Maxwell long ago protested against the unphilosophic

habit of inventing a new medium every time we have a new

•phenomenon to explain ; and fortunately in this case measure-

ment supports Maxwell's contention, by showing more and

more conclusively that the two velocities are identical. The

difference between the velocity of electric waves in free
aether and light is now so small as to be within the probable

error of the, separate determinations; and it is difficult to

decide which method affords the greater accuracy of measure-

We ment.

must therefore wholly reject any claim for two

media, and acknowledge that light and dynamic electricity
— depend on one and the same medium the aether. And

we have discussed the physical character of that medium,

and fixed the constants with such great accuracy that when the density is calculated by a new method, in the present

paper, it is found to be

= or

1888.15- 10-"

as against the other value, now no longer admissible, as shown above in section I
= a 438-IO-1*

yet found in the first paper by the method invented by Lord Kelvin in 1854 and since improved by Kelvin, Maxwell and the present writer.
The physical significance of the identity of the velocity of light and electricity is therefore unmistakable; namely, electricity in motion consists of waves in the aether, and as they travel with the same velocity as light, we know that electricity and light both depend on the aether, and are

simply waves of different length and type in this all-pervading medium.

(ii) Accordingly, as Sir Oliver Lodge correctly says, Einstein has not done away with the aether, but simply ignored it, and thereby shown a remarkable lack of understanding of the physical ilniverse.

In a public address at San Francisco, April 11, 1920, Sir Oliver Lodge dealt with the physical properties of the aether, as the vehicle of energy, and emphasized the view that although totally invisible, the aether is capable of exerting the most stupendous power throughout space, and thus is the medium or vehicle which transmits the forces which govern the motions of the planets and stars in their orbits.

Not only is the aether necessary for conveying the light of the sun and stars across space, but also for conveying the stresses to generate the planetary forces, which are equivalent to the breaking strength of gigantic cables of steel stretched between the sun and planets. These stupendous gravitative mechanisms are wholly invisible, and yet from the observed operation of centrifugal force, we know that the gravitative forces for balancing them do really exist. Under the circumstances, as Sir Oliver Lodge pointed out,
we cannot hold that appearances correspond to reality. We
know of the aether chiefly from its transmission of wave
action, which in free space travels with the velocity of light.

Accordingly, after tracing the physical properties of

the aether, Sir Oliver Lodge justly exclaimed: »You have

heard of Einstein, and probably know that he has no use

for the aether. He has, however, not done away with the

aether, but simply ignored it.«

This concise statement covers the case exactly; but in

view of the fact that Einstein shuts his eyes to the unseen

operations of the physical universe, which Newton attributed

to impulses in the aethereal medium, it is not remarkable

that the many sagacious investigators of natural phenomena

are obliged to reject the mystical and misleading doctrines

of Einstein.

To turn away from a mechanical explanation of the

world, and attempt to account for phenomena by mere formulae reposing on the supposition of action at a distance,

and to further complicate the reasoning by the assumption

— of the curvature of space, • when such an hypothesis is

— unnecessary and purely fictitious,

is not a sign of pene-

tration, but of lack of experience in natural philosophy.

It is just such unwarranted procedure which Newton denounces as resting on »vain fictions*, in the second sentence
of the discussion following the statement of Third Rule of
Reasoning in Philosophy: »We are certainly not to relinquish
the evidence of experiments for the sake of dreams and vain fictions of our own devising; nor are we to recede from the analogy of nature, which uses to be simple and always consonant to itself* (Principia, Lib. III).
It appears from Newton's discussion that electrical actions conveyed along wires and across space, as in radio-telegraphy, and found by actual experimental measurements to be transmitted with the velocity of light, are the very kind of »evidence of experiments* which that great philosopher says we are not to relinquish for the sake of dreams and vain fictions

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of our own devising; yet Einstein and his followers have thus plainly violated Newton% Third Rule of Philosophy, in proposing to do away with the aether. Without this medium the phenomena here cited are not explainable, so that even a child can see the necessity for the aether. The sun and
stars are the perpetual witnesses to the existence of the aether,
and all who live and behold the light, as Homer says, thereby recognize this superfine medium {^idrjq).

(iii) The formal discussions on the theory of relativity before the Royal Astronomical Society, Dec, iQig, and Royal
Society, Feb. 5, 1920, wholly unprofitable, in default of a kinetic theory of the aether.

In view of the above criticisms it is unnecessary to

emphasize the unprofitable character of the formal discussions

held before the Royal Astronomical Society, Dec, 191Q,

and the Royal Society, Feb. 5, 1920. But the fact that two of the oldest scientific societies in Europe did not refuse

to waste their time and resources of publication on the vague

— and chimerical theory of relativity

thereby still further

confusing the public mind, already bewildered by the mis-

application of mathematics which rests on no .physical basis,

— when the problem is primarily a physical one

may well

deserve our attention.

A report of these meetings will be found in the Monthly

Notices, and in the Proceedings of the Royal Society, and

other journals, such as the Journal of the British Astrono-

mical Association, for Nov., 19 19, and Jan., 1920, which
appear a month or so late. We may conden.se the discussion

as an American physicist summarized a similar discussion

held in Washington about ten years ago:

»When we got through, we did not know any more thari when we started.*

Now we submit that such methods are not those by

which science is advanced. And when the proceedings of

learned societies take the form of unprofitable debates, on

mere subtleties, or on reasoning which rests on false pre-

— mises,

such as a mere mathematical foundation,

— when a physical foundation is required,

it is a sign

of the mysticism which usually accompanies intellectual de-

cadence. There can be no defense for the policy of exploiting

Einsiein'% theory without first considering the kinetic theory

of the aether, which renders such mystical doctrines unnecessary

and wholly inadmissible.

To cite an example of historic interest, the chimerical
character of Kepler'^ early speculations is judiciously pointed out by Laplace (Precis de I'Hist. d'Astron., p. 94):

»I1 est affligeant pour I'esprit humain de voir ce grand
homme, m6me dans ses derni^res ouvrages, se complaire
avec ddlices dans ses chimeriques speculations, et les regarder
comme Time et la vie de I'astronomie.*

Delambre is even more severe, and subscribes to the judgement of Baill'y in regard to Kepler (Astron. du moyen

4ge, 1819, p. 358):

» After this sublime effort (discovering the planetary laws, is xa&araX) . Kepler replunges hirnself into the relations of music to the motions, the distance, and the eccentricities of the planets. In all these harmonic ratios there is not one

true relation; in a crowd of ideas there is not one truth:
he becomes a man after being a spirit of light.*

The results brought out in the first and second papers on the New Theory of the Aether, show the worthless cha-

racter of the whole theory of relativity. We'%re justified in

saying it is a foundation. laid in quicksand, when a foundation of granite was near at hand. And therefore the whole

theory of relativity, as heretofore taught, is now shaken to

its foundations, and thus no longer deserves the serious con-

sideration of natural philosophers.

As throwing some historical light upon the unprofitable

subtleties of the theory of relativity, and the vague and chi-

merical discussions which the Royal Astronomical Society

and the Royal Society have inflicted upon a bewildered and

long suffering public, we recommend an attentive reading of

the latter part of the first volume of WhewelTs History of

the Inductive Sciences. Whewell dedicated this justly celebrated

work to Sir John Herschel, and it ought to be familiar to

every modern investigator.

WheweU's, luminous discussion of the » Indistinctness of

Ideas

in

the Middle Ages* ;

» Collections

of

Opinions* ;

sin-

distinctness of Ideas in Mechanics*; » Indistinctness of Ideas

in Architecture*; » Indistinctness of Ideas in Astronomy*;

»Indistinctness of Ideas shown by Skeptics*, (pp. 253-268) is especially worthy of study.

In opening the treatment of » Indistinctness of Ideas

shown by Skeptics* Whewell remarks:

»The same unsteadiness of ideas which prevents men

from obtaining clear views, and steady and just convictions,

on special subjects, may lead them to despair of or deny

the possibility of acquiring certainty at all, and may thus

make them skeptics with regard to all knowledge. Such skeptics are themselves men of indistinct views, for they

could not otherwise avoid assenting to the demonstrated

truths of science; and, so far as they may be taken as spe-

cimens of their contemporaries, they prove that- indistinct

ideas prevail in the age in which they appear. In the sta-

tionary period, moreover, the indefinite speculations and un-

profitable subtleties of the schools might further impel a man

of bold and acute mind to this universal skepticism, because
they offered nothing which could fix or satisfy him. And thus the skeptical spirit may deserve our notice as indicative

of the defects of a system of doctrine too feeble in demon-

stration to control such resistance.*

Accordingly, from the considerations here advanced,

it follows that the recent formal discussions before the Royal

Society and Royal Astronomical Society of the theory of

relativity, which is both vague and chimerical, have confused

rather than clarified the subject in the public mind; and

thus in the cause of truth I have felt obhged to protest

against the misuse of the powers of these learned societies.

II. Rejection of the Theory of , Electrical
Mass' except for Small Particles of Common Matter
expelled under Electric Charges: the so-called, Electrical Mass' thus not applicable to the Aetherons, or Corpuscles of which the Aether is made up.
(i) Description of the so-called ,electrical mass'.
Of late years a number of physicists occupied with

.

.

28;

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experiments involving the ejection of small charged particles', in an electric field of very considerable intensity, have
laid much stress upon the so-called ,electrical mass', and even gone so far as to entertain the view that all mass is elec-

trical (cf. Cretvther, Molecular Physics, 1914, pp. 67-85). It is true no doubt that under the charges involved in these

experiments there is an ,electrical mass' because the small mechanical mass is thereby thrown out of electric equihbrium

with its surrounding field.
But when we deal with the aether as an all-pervading medium, we have to do with the motions of the aetherons only, afid as common matter is not involved, we have to

reject the ,electrical mass' as applied to the aether, for
the reason that the aetherons make up the field, and nor-

mally are in kinetic equihbrium, so as not to be subjected

to any forces except those due to passing waves in the

aether, involving concerted displacement of neighboring

aetherons.

It is well known that Newton was quite aware of the effect of the resistance of a medium upon the motion of a

sphere or other body projected through it. In the Optics, 1721,1pp. 342—3, Newton discusses the very problem here

treated of in the following manner:

»The resistance of water arises principally and almost

entirely from the vis inertiae of its matter; and by conse-

quence, if the heavens were as dense as water, they would
not have much less resistance than water; if as dense as quick-silver, they would not have much less resistance than

quick -silver; if absolutely dense, or full of matter without

any vacuum, let the matter be ever so subtile and fluid,
A they would have a greater resistance than quick-silver. solid globe in such a medium would lose above
half its motion in moving three times the length of its diameter, and a globe not solid (such as are the planets) would be retarded sooner. And therefore

to make way for the regular and lasting motions of the planets

and comets, it's necessary to empty the heavens of all matter, except perhaps some very thin vapours, steams or effluvia,

arising from the atmospheres of the earth, planets and comets,

and from such an exceedingly rare aethereal medium as we

A described above.

dense fluid can be of no use for ex-

plaining the phenomena of nature, the motions of the planets

and comets being better explain'd without it.«

In this passage we have spaced the sentence especially

applicable to the problem of the ,electrical mass', which
m is explained as follows. Let be the ordinary mechanica;l
mass of the moving particle; then the ordinary kinetic energy

due to its motion becomes

= E ^l^mv\

(89)

But electrical experiments on small particles ejected

under considerable charge, show that there is in addition a

quantity of energy due to that charge. The total energy is

found to be made up of the two parts shown in the right

member of the following equation:

= = + E

^lomv^+^ke^v^la

^kW ^ke^la] v^

(90)

the first term yielding the mechanical energy depending on

m, and the second that depending on the so-called ,elec-

trical mass', ^/ge^/a, where e is the electrical charge .borne

by the particle, and a is the radius of the spherical space occupied by the charge. The .electrical mass' is not quite constant for all velocities, but the above formula holds approximately for moderate speeds.

(ii) The rejection of the theory of the so-called , elec-
trical mass', as an effect of the aether due to the systematic arrangement of the waves, justified by Thomson's views of

the motion of a corpuscle through an electrical field.

In his Elements of Electricity and Magnetism, 4'*^ ed.,
1909, p. 521, Prof. Sir y. y. Thomson indicates that if m
be the mass of an uncharged sphere, the kinetic energy of such a sphere with charge e, magnetic-permeability /*, and

radius of action a, is

= + E ^Im ^l.e-'laW .

(91)

The eff'ect of the charge is to increase the mass of

the sphere by ^j^i^e'la. This is a resistance called the ,electrical mass', and the question arises whether it should be regarded as an increase of mass, as described by Thomson,

or an effect of the field in whigh the sphere moves, as described by Newton in the discussion above cited from the

Optics, 1 7 2 I

Sir y. J. Thomson compares the motion of a corpuscle through an electrical field with that of a sphere through a

liquid, which he says leads to art increase in the effective mass, because the moving sphere drags some of the liquid along with it. Thus when a sphere moves through a liquid it
m behaves as if the mass were increased from to m-^'^j^m',

where m' is the mass of the liquid displaced by the sphere. Again, when a cylinder moves at right angles to its axis through a liquid, its apparent mass is m-^m', where m' is'the hiass of the liquid displaced by the cylinder.

»ln the case of bodies moving through liquids«, says

Thomson, »the increase in mass is due to the motion of the body setting in motion the liquid around it, the site of the increased mass is not the body itself but the space around it where the liquid is moving. In the electrical problem, we
may regard the increased mass as due to the Faraday tubes setting in motion the ether as they move through it» (p. 522).

This reasoning concedes that the so-called .electrical mass' depends not on the sphere itself, but on the field about it; in other words the ,flectrical mass' is an effect due to the surrounding field, and not inherent in the body itself For that reason it is necessary to consider carefully whether the ,electrical mass' in the larger mechanics, ought not to be rejected altogether as fictitious, and due to disturbances in the aether filled with waves and thus polarized, the arrangement of the waves exerting the force called the ,elec-
trical mass'.

(iii) Theory of y. A. Crowther, 19 14.
In his Molecular Physics, 19 14, p. 70, (Philadelphia,
& Blakiston's Son Co.), J. A. Crowther, also of the Cavendish
Physical Laboratory, Cambridge, points out that the extra or ,electrical' mass is due to the fact that the particle carries a charge. Crowther even says^ that if the ,mechanical' mass
m be zero, the .electrical' mas's will still persist. Analytically
this follows from the above formula (91), but physically there is no proof that such an ,electrical' mass can exist

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independently of matter, and thus Crowther's, claim cannot be admitted.

Crowther announces his final conclusions thus (pp. 70 and 71):
»Since this electrical' mass is really that of ,
the magnetic field surrounding the particle, it resides not in the particle itself but in the medium surrounding it, that is, in that mysterious fluid which we call the ether ^). As soon, however, as we
attempt to alter the motion of the particle this energy flows into it from all sides, so that, as far as experiments upon
the particle itself are concerned, the results obtained are precisely the same as if it resided permanently there.*

»To make this somewhat novel idea a little clearer

we may consider a close and very servicable analogy, where

the mechanism of the extra mass is a little clearer than in

the electrical case. If any body is moving through water,

or any viscous fluid, it carries with it a certain amount of

the liquid through which it is moving. In the case of a

sphere, for example, the qiiantity carried along by the motion

•of the- body amounts to half the volume of the sphere itself.
A long cylinder moving at right angles to its own length

will carry with it a quantity of fluid equal to its own volume.
On the other hand, if it moves in the direction of its own

length the fluid entangled is practically nil. Thus, in order

to set the body in motion with a velocity v, ^e have to

•supply to it energy enough to give this velocity, not only

M to the sphere itself, but also to the mass of fluid wbich it

<;arries with it. That is to say, if

is the mass of the

M' sphere itself, and

the mass of the attached fluid, the

work done in starting the body is ^l^i^M-^M'^v^- In other

words, the body will behave as if its mass were increased

by the mass of the fluid entangled by it. Just as in the

electrical case, this extra mass resides in the sur-

Tounding medium.

Accordingly, it clearly appears, from Thomson's and Crowther's arguments, that the ,electrical' mass ^/ge^/a depends wholly on the field in which the charged corpuscle is moving, not upon the body itself, and changes when the motion through the field is altered. All that the arguments can be said to prove therefore is that the aether in a magnetic field, exerts an influence on bodies moving through it. This shows that the aether really exists, is polarized near magnets and electric wires bearing currents, and acts physically according
to definite laws.
This is a-reason therefore why the theory of the aether cannot be rejected, as some superficial writers have held. The other reasons for admitting the aether are as convincing as stupendous cables of steel would be if we could actually see them stretched from the sun to the several planets for holding these huge masses in their orbits. For the centri-
fugal force of the planets has to be balanced and the aether is the medium which sustains the tremendous forces required to curve the paths of the planets at every point, and enable them to describe Keplerian Ellipses about the sun as the focus.

We (iv)

therefore conclude that the ,electrical mass

depends wholly upon the aether.

As the ,electrical' mass admittedly depends on the

aether, and the influence it exerts depends on the wave mo-

tion in this medium, it is better for most purposes to reject

the doctrine of a so-called ,electrical mass' as fictitious, and

consider separately the common Newtonian mass m, and the

m influence exerted by the field in which

is moving.

In case of the , electrical mass'

£=%fie'vya

(92)

where a is the radius of the space occupied by the charge, and jtt the magnetic-permeability of the medium, e the charge, it is ' thus obvious that JS becomes truly a drag exerted on the moving mass wz. It is evident that this effect ought to depend on e'^, and v^, since the induction due to the waves is thus developed like ordinary mechanical work done.
For it must be remembered that there are waves in the field, produced by the bodies and charges of the universe, and also waves, or Faraday tubes of force, produced by the moving corpuscle itself, with charge e. Since the charge e is a: measure of the electrification of the corpuscle, the field about it necessarily will have a corresponding condition, but negative in character, and the interaction of the charged corpuscle on the field will be measured by the product of these charges, and thus by e^.

This explains the nature of the formula (92),- except
the divisor a. And Crowther (pp. 162-3) shows that the
total energy in the field is the integral of the total magnetic energy between two spheres, of radius r arid r-hdr, when

taken from the surface of the electron of radius a to in-

finity, becomes:

-E^ = ^l-ifie^v^Sdrjr^

^/sij,e^v^/a

(93)

From this line of investigation it appears that we are justified in rejecting, and even required to reject, the , electrical mass' for the aetherons, which pervade the universe, and
by their vibrations render the aether the vehicle of energy. Accordingly our conclusions are
1. It appears that Prof. Sir y. j^. Thomson's argument for the , electrical mass' is an extension of that given by Netvton, but is likely to be misapplied, unless the specific condition of non-electric equihbrium underlying the experiments with small particles is clearly borne in mind.
2. The doctrine of the ,electrical mass' has therefore a very limited field of validity. On page 81 of the work above cited Crowther says that most physicists cherish the belief at the bottom of their hearts that all mass is electrical in origin, »but it cannot at present be said to be much more
than a pious hope.«
(v) The nature of the X-rays investigated.
It will be recalled that for a long time great mystery attached to the nature of the X-rays. Soon after these rays were discovered by Rontgen, in the winter of 1895-6, three different theories were formed of their nature: (i) Electrified material particle^ projected with great speed from within the

^) The spacing-out is mine.

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bulb quite through the walls of the glass tube; (2) the Ultraviolet theory, which supposes the energy to be aether-wave motion of the same character as light, but of only about I ; 1 0000"' part of the wave length of visible light; (3) the longitudinal aether-wave theory, at first favored by Rontgen,
Jaumann and others, which ascribed the observed effect to
longitudinal motion in the aether waves.

Probably something could still be said in favor of each of these theories, and it is not yet certain that the nature
of the X-rays is understood. In the usage of men of science
however, the ultra-violet wave-theory has found most favor.

In 19 1 2 the Swiss physicist Dr. Laue first made use

of X-rays to investigate the structure of crystals, and from

this beginning has grown a resourceful method for attacking

the problem of molecular arrangement in crystals, which may

even throw light on the internal structure of the atoms them-
selves. An article on this subject by Prof W. L. Bragg, on

» Crystal Structure*, will be found in Discovery, Feb., 1920; and a review of the subject appears in the Journal of the

British Astronomical Association for March, 1920, pp. 199 till 200.

The following table gives an outline of- the different

types of waves, expressed in Angstrom units, or tenth-metres.

I m 10

Duff'% Physics, p. 640:

Gamma rays

o.

'

X-rays

I

Shortest ultra-violet waves

600

Shortest visible waves (violet), about

3800

Violet, about

4000

Blue

4500

Green

5200

Yellow
Red

5700 6500

Longest visible waves (red)

7500

Longest waves in solar spectrum, more than

53000

Longest waves transmitted by fluorite

95000

Longest waves by selective reflection

from rock salt

500000

from potassium chloride

612000

Longest waves from mercury lamp

3140000

Shortest electric waves

4ooooooo=^4mm.

It is very difficult to understand how such very short waves as X-rays are supposed to be, on the ultra-violet theory, could penetrate so easily through the human body and other semi-solid substances, as they are found to do in practice. The experiments of Laue, Bragg and others in crystal photography show the extreme fineness of the X-rays, and their
great penetrating power.
But it is perhaps possible that what appears to be a passage of X-rays through resisting structures is rather a general agitation of the aether by which the atoms emit waves ^) which can impress the photographic plate, than an

actual passage of such short waves through these resisting masses. If so, the facts of experience would lend a strong
support to the wave-theory since it might be much easier to
evoke vibration of appropriate length than for such short waves
to actually pass. The waves evoked by agitation of the aether would show crystalline structure, and even the diffraction of
X-rays, quite as well as the passage of X-rays waves.
In confirmation of this view that the X-rays observed
are waves evoked by agitation, we quote from Duff's TextBook of Physics, 1916, p. 641:
»Glass is opaque to waves shorter than 3500 Angstrom' units, and longer than about 30000 Angstrom units. Quartzis transparent between the wave-lengths 1800 and 70000, and for some longer waves ; rock salt is transparent between 1800 and 180000, and fluorite, one of the most transparent-
= substances, will transmit ultra-violet waves from about A =^
1000 to 1 95000.
A similar argument has also been adduced by Prof Sir
y. y. Thomson to the effect that X-rays depend on collisionsby negatively charged particles. They are evoked by the somewhat irregular agitation of the wave-field, the disturbance produced being due not so much to regular continuous wave motion, as to isolated wave impulses, which travel throughout the neighboring aether, and set free the corpuscles from the atoms. Such X-rays could not well interfere, and their diffraction, if observed, would be of the type photographed by Laue in crystals, corresponding to short waves, probably produced by the degeneration and breaking up of longer aether impulses of no considerable regularity of movement.
This puts the ultra-violet theory in a new light, in linewith the wave-theory, and at the same time explains the
mechanically injurious effects of X-rays in surgery^) as due to the irregular wave impulses, which regular ultra-violet
waves could hardly produce. And it explains also why cal-r cium tungstate may render the X-rays capable of casting
shadows visible to the eye. For the irregular impulses would come with sufficient rapidity to give an effect which optically
is apparently continuous. When observing the X-ray through
calcium tungstate I have noted an appearance of rapid flickering, as in the case of rapid but irregular electric sparks, or lightning flashes in quick succession but at unequal intervals.
In connection with this subject it is well to bear in mind that magnetism, which in the wave-theory depends on polarized waves of perfect regularity, can penetrate thick plates of glass or any other substance, but the action seems to. take a little time. Probably the polarized character of magnetic waves and their length makes this penetration possible, whereas it is possible for the confused waves of
light only within fixed limits. Thus we hold that the irregular impulses in X-rays correspond to long waves, which under degeneration call forth the very short ones used for the newer investigations in crystals.

^) This idea is suggested by Rdnigen'% original experiment of cutting off all cathode rays with black card board, yet noting that some

A crystals of barium platino-cyanide in the darkened room were rendered luminous by the general agitation in the aether

^)

dispatch from Paris, May 26, quotas M. Daniel Berthdot as reporting, May 25, to the Academy of Sciences a new method for

protecting operators against the injurious effects of X-rays, which are neutralized by a simultaneous application of infra-red rays

'
This use of

— infra-red rays to counteract the X-rays confirms the theory here developed; unless the agitations underlying the X-rays were long, the long

infra-red rays could hardly afford the protection reported.

Note added. May 26, 1920.

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13. The acknowledged Failure of the Electron Theory, which represents a Subordinate Phase of Scientific Progress: The Larger Problems of the Universe can only be attacked through the WaveTheory based on the Kinetic Theory of the Aether.

(i) The acknowledged failure of the electron theory.

In his interesting but unconvincing work on Molecular Physics, Philadelphia, 1Q14, Crowther treats of many molecular phenomena from the point of view of the electron theory. Including the effect of the electrical mass, ^j^e^v^ja,Crowther concludes (p. 81) that the mass of an electron is 8.8 • 10^^* gms., while the value of the charge it carries is 1.57 • io~^" units. Thence he deduces for the radius of the electron 1.87 • io~^^ cms.'-)

Calling attention to the conclusion that the radius of

an atom is of the order of io"~^* cms, he adds a comparison

which I give spaced

«

»We may now say that small as, the atom is,

the electron is so much smaller that the electron

bears to the atom which contains it very much the

same relation as a pea to a cathedral.*

»We have seen that the whole of the mass of the

electron is due to the charge which it carries. The thought

at once suggests itself: Are there indeed two kinds of mass

or

is

all

mass electrical .

in

its origin?

Probably most physi-

cists cherish this belief at the bottom of their hearts, but

it cannot at present be said to be much more than a pious

hope. The mass of a negative electron is about V1700 part of the mass of a hydrogen atom. Neglecting the positive

charge of the atom, of which we know practically nothing,

it would require 1700 electrons to make up the mass of

a single hydrogen atom. This of course is not a priori an

impossible number considering the smallness of the electron;

and speculations along these lines were for a time freely

indulged in. In this case, however, experiment failed to con-

firm the bold conjecture. The number of electrons in the

atom has been determined at any rate approximately, and

affords no support for such a theory.

Crowther then examines at some length the question

of the number of electrons in an atom, and after admitting

the obscurity of positive electrification, finally concludes,

pp. 83-84 as follows: » Unfortunately, we are not yet acquainted with the

nature of positive electricity. Prof.' Sir J. y. Tnomson's experiments on the positive rays, brilliant as they have been,

have not at present thrown much light upon this exceedingly

difficult problem. For the present the term ,positive electri-

fication' remains for the physicist very much what the term

— ,catalytic action' is for the chemist

a not too humiliating

method of confessing ignorance. If we suppose that the

positive electricity is distributed uniformly over a sphere of the

size of the atom (a hypothesis which lends itself very readily

to mathematical treatment), the author's result would indicate

that the number of electrons in an atom is almost exactly

three times its atornic weight. That is to say, the number

of

electrons

in

a

hydrogen

atom

would

be three.

.

^)

If we go the other extreme, and suppose that the positive

electrification is a sort of nucleus at the centre of the atom,

and that the electrons revolve around it somewhat after the

manner of the rings of Saturn, the number of electrons in

a hydrogen atom works out at unity, the number in any

other atom being equal to its atomic weight. The assigning

of unit atomic weight to hydrogen would then have a very

definite physical significance, as it would be the lightest atom

which could possibly exist. In either case the number of

electrons in an atom is only a very small multiple of its

We atomic w'eight.

cannot, therefore, assign any appreciable

fraction of the mass of the atoms to the negative electrons

it contains.

» There still remains, of course, the possibility that the

mass is electrical, but that it resides in the positive portion

of the atom. If the forjnula for the electric mass be exami-

ned, it will be seen that for a given charge the mass is

inversely proportional to the radius of the sphere upon which

it is concentrated. If we suppose the positive charge on

the hydrogen atom to be concentrated upon a sphere of

V1700 of the size of the negative electron, its mass would be 1700 times as great, that is to say, equal to that of the

hydrogen atom. Our perfect ignorance of the nature of

positive electricity renders the suggestion not untenable, though

evidence for it is sadly lacking.

This is a very frank confession of a failure of the

electron theory, for two chief reasons.

1. In size the electron bears to the atom about the

ratio of a pea to a cathedral.

2. The number of such electron peas to the atom

cathedral is very small, either i or 3 for hydrogen, and always a small multiple of the atomic weight. Hence the
important conclusion : »We cannot, therefore, assign any ap-

preciable fraction of the mass of the atoms to the negative

electrons it contains.*

Accordingly it is not surprising that Crowther admits

that »for the present our belief in the electro-magnetic nature

of all mass remains an expression of our faith that all the

varied phenomena with which, we have to deal are mani-

festations of some single principle or essence which under-

lies them all.«

Another important and much more elaborate work,

»The Electron Theory of matter «, by Prof. O. W. Richardson

^) Another proof of the great uncertainty attaching to the theory of the electron is afforded by conflicting deductions as to the absolute dimensions of this little mass.
1. Crowther, pp. 81-165, g'ves for the radius of the electron 1.87' io~'' cm, and for the radius of a hydrogen atom i.ai-io "cm. Thus the hydrogen atom has about 66000 times greater diameter, yet it has only 1700 times the mass of the electron, which makes the electron relatively very heavy for its small diameter. If of equal density with the hydrogen, this mass would make the hydrogen atom have a diameter 11.93 times that of the electron.
= 2. But the diameter of the electron itself must be very uncertain. In Phys. Rev. vol. 114, pp. 247-259, Sept. 1919, A. H. Compton,
who had previously estimated the diameter to be 2-io~"cms, now finds it to be (1.85+0.005)- io~"' cms, or r 0.925 • lo"'" cm. This is about 2000 times larger than Crowthei's value ; so that apparently no confidence whatever can be put in these results.
^) The spacing-out is mine.

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of King's College, London, appeared under the auspices of
We the University Press, at Cambridge, 1Q14, pp. 1-6 12.
cannot attempt to describe the treatment, except to say that it is similar to Crowther^s work, but less experimental, and sets forth the mathematical theory in greater detail.

In spite of the elaborateness of this treatise, Richardson is obliged to admit the short-comings of the electron theory.
On page 592 the author admits that »we cannot be sure
that the mass of the electrons is not appreciably different

in different substances.* Accordingly it would appear that the mass of the electron is definitely fixed only in particular substances which have been experimentally investigated. It is acknowledged that nearly all the atomic problems are

clouded in great obscurity.
Under the head of General Conclusions, p. 600, we read: »A review of the preceding discussion shows that the electron theory is not in a position to make very definite

assertions about the nature of gravitational attraction. It seems likely that the Newtonian law of attraction between

elements of matter is one between elements of mass or con- • fined energy and that it is of a very fundamental character. It is doubtful^) if it can be replaced by a modified
law of electrostatic force between electrons or elements of electric charge, unless the modified law includes the associated mass explicitly. Even

so, the case does not appear very simple.* In closing Richardson concurs in the opinion of Lorentz
that gravitation m^y be an electrodynamic effect propagated

with the velocity of light, like that since developed in greater

detail by the present writer.

(ii) The electrons usually assumed to be more or less ,bound' to atoms, and set free chiefly in metals (conductors), to make up an electric current: but this will not

explain the propagation of electric disturbances with the

velocity of light, and thus the electrons cannot replace the

aether.

It is well known that the electrons usually are taken

to be more or less , bound' to the atoms, with which they

A are associated.

vast amount of discussion has arisen as

to the setting free of the electrons, by heat and electric

disturbances. It will be noted therefore:
1. The electrons are not taken to be entirely free, to pervade all space and all bodies, like the aetherons, which

travel with a velocity. 1.57 times that of light, 471238 kms. 2. The speed of the electrons is not taken to be in
any case greater than one third that of light. As the mass of the electron is considerable, though only about ViJoo of that of a hydrogen atom, this smaller velocity, of say 1 00000 kms. is very intelligible.
The hypothesis of Crowther, and others, (Molecular

Physics, p. 139), that »an electric current is a flow of electrons from a place of high to a place of low potential* cannot be admitted, because the observed velocity of 300000 kms. for light and electricity could not be attained by such heavy

masses as electrons.

Crowther states this electron theory as follows:
»We may regard a conductor, then, as a substance

containing electrons which are free to move under the action

of an electric field, while in non-conductors the electrons are

fixed and unable to follow the impulse of the field.*
»How are these electrons set free? In the first place
it tnay be noticed that the only good conductors of elec-
tricity are metallic, tfiat is to say, electro-positive in character,
substances which we know from other phenomena readily
part with an electron under the slightest provocation. Now in a solid such provocation may well be supplied by the
close propinquity of the neighbouring molecules. It is well
known that a charged body will attract light uncharged substances. The attraction of a well-rubbed stick of sealing wax

for small pieces, of paper is generally our first introduction
to the science of electricity. The attraction is of course mutual, the force on the charged body being equal to that on the uncharged paper. Hence an electron in one atom is attracted by a neighbouring uncharged atom, and under favourable circumstanRs, and especially in the case of an

atom only too ready to part with its electrons, the attraction
may well be sufficient to enable it to make its escape.*

It is obvious without further discussion that this theory

is so very defective that it cannot be seriously entertained

by investigators who are familiar with the propagation of

electric and radio -telegraphic waves and light across free

space. For, in the first place, it claims to account for dis-

turbances along conductors, which cannot be done with

electrons of the recognized mass. And, in the second place,,

the electron theory gives no explanation of light and radio-

telegraphic waves across free space, where the aether alone

is involved.

Accordingly the electron theory cannot explain the phenomena of the aether, and it must be admitted that the

subject of the electron is still involved in great obscurity.
So far as we can judge it can only be cleared up by the

further development of the wave-theory, deduced from the new kinetic theory of the aether.

For although the mass of the aetheron given in the
first paper on the New Theory of the Aether, will have to be
multiplied by about 4.31 to take account of the increased

absolute density of the aether, found by the new method

of section I above, after Lord Kelvin's method was shown

to be invalid: yet the total change in the mass of the
=aetheron is comparatively slight, namely: molecular weight 67.077 10^^^.

Accordingly the general mass and dimensions of the

aetheron are but slightly altered, yet the size of this corpuscle

= is somewhat increased and becomes 1. The radius of the aetheron

V246I.2 of that of a

hydrogen molecule.

2. This radius is equivalent to 5.44- lo""^^ cms., that. of hydrogen being taken as 1.34- io~'' cms.

(iii) The electron theory like that of radio-activity is
a subordinate phase of scientific progress.
The electron theory developed during the last quarter
of a century by a considerable group of experimental physicists led by Prof. Sir J. J. Thomson and others, has now acquired such definite form and shows such defects, that we--

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are safe in considering it a subordinate phase in scientific

progress. If it should prove to be an ultimate development,

apparently this can only be owing to the more fundamental wave-theory, which underlies the electron-theory and gives a physical basis for the phenomena of electrons.
1. The alpha-, beta-, gamma-rays, recently so much

observed, are held to give experimental proof that small

particles, under electric charges of greater or less intensity,

are ejected from certain bodies with velocities which may

be one third that of light.

2. It is very difficult to understand how alpha-, beta-,

gamma-particles can be ejected with this enormous speed

unless commotions incident to wave action underlie the

ejections. For electrodynamic waves travel with the velocity

of light, and material particles caught up by a combination

of such waves might travel more slowly than light, but yet

with so great a speed as to approach that speed or a large

fraction of it.

3. It is inconceivable that velocities approximating one

third that of light could be generated without some asso-

ciation with the release of elastic action in the aether, which

speeds on with the -enormous velocity of 300000 kms per

second. Even in solid bodies the aether waves advance at

a rate which is a large fraction of that in free space.
4. Now molecular and atomic velocities are very small
indeed compared to that of light. Hence it is apparent that

no ordinary molecular collisions or disturbances could eject

particles with these enormous speeds. But if invisible electro-

dynamic waves underlie these ejections their speeds are easily

accounted for. Under oscillating electric charges the par-

ticles might be carried along from the surface or even into the

interior of a solid anode or cathode, or similar terminals.

5. In the author's work of 19 17, p. 20, we have explained the nature of an electric current, and illustrated the

waves about a conducting wire by a figure (cf. fig. 12, p. 260, above) showing the rotations which make up the waves. The

waves act in concert, the elements whirling everywhere in

the same direction. If therefore, there be a particle small

enough to be ejected, yet observable, it might be carried

away with great speed.

6. But in a Geissler-tube, or similar rarified gaseous

medium, we have rarified gas itself for the conductor or

discharge of the electric strain at the terminals. In such a

good conducting partial vacuum, it apparently would be much

easier for a small particle to be ejected with great speed

than from any conductor of metallic constitution.

7. Thus, in all the phenomena of electric discharges through rarified gases, on which Prof. Sir y. y. Thomson has

experimented for so many years, the indications are that the

observed velocities of the ejected particles are attained under

wave influences or releases of electric stresses, by commotions

in the aether traveling with the velocity of light.

— 8. Since the -rarified gas acts as a conductor

Prof.

John Trowbridge of Harvard University having found that

rare air is a more perfect electric conductor than even copper
— wire , we should in fact expect certain solid particles to

be transported along with a large fraction of the velocity of light. Thus the electron phenomena are not remarkable, but

naturally follow from the wave-theory.

9. Accordingly, it hardly seems possible that the alpha-,
beta-, gamma-particles, so much studied in the electron theory,
can be other than a temporary phase in the progress of science. Important as the results attained are, they do not disclose to us any workable theory of the universe. Even the ejections of small charged bodies must rest on the wavetheory: there is no -other possible way in which we can explain the ejection of these corpuscles,, and their enormous velocities, whereas the wave-theory makes their ejection na.tural and requires it to be at high speed.

10. Incidently, the electron theory renders the corpus-
cular theory of the aether more probable than it otherwise would be. It all implies excessively rapid motion for very small bodies. Unless there be waves traveling with the velocity of light, it is impossible to explain the phenomena
of radio-activity.
To show the difficulty of reconciling these results, we
add a few calculations. Let us assume in the first case that the free electrons behave as a gas, and thus follow the law announced by Maxwell, that all molecules have equal kinetic energy, which is verified by experience for many actual gases.
m Then, if and v denote respectively 'Ca,t mass and the ve-'
locity of a molecule of hydrogen, while m! and v' denote corresponding quantities for an electron, we have

^ ^Umv^=^l^m'v'K

(94)

Accordingly if v

i6g6 ms, and m' == Vstoo of a

hydrogen molecule, which contains two atoms, we find

= V = v'

2,^00 -v 58.31-1696 ms ^98.893 kms. (95)

This is a comparatively small velocity, a little over

60 miles per second; and thus we find the electron as a gas

particle could not attain a sensible fraction of the velocity

of light, 300000 kms. Different authorities give different

velocities for charged particles: Crowther (p. 76) considers a particle moving with one tenth of the velocity of light, and

Millikan has asserted the probability of a speed of one-third

that of light. Such high velocities are wholly impossible, on

the kinetic theory of gases; but as expelled under electric

charges they might be possible, if carried along by the

wave action traveling at 300000 kms per second. But the

acceleration of the velocity appropriate to a gas, under the

kinetic theory, would have to be very great.

For the above value 98.893 kms is less than Vsooo'*' that of light; and if we take Millikan' 1, estimate of '/s the
velocity of light for the swiftest charged particles, ejected,

the above kinetic velocity will have to be accelerated a

thousand times its calculated value, or receive energy aug-
mented by the factor (1000)^ =^ loooooofold.

Now in view of our ignorance of molecular physics,

it is difficult to say upon what forces such an acceleration

may depend ; but I know of nothing adequate except waves

traveling with the higher velocity of 300000 kms per second.
A particle having a speed of Ys V, would have only
Yg'*^ of the energy of a particle traveling with the velocity V.
It looks therefore as if waves passing by with much greater

velocity might have given the particle a velocity which is

a considerable fraction of the velocity of light.

On p. 81, Crowther attributes the whole mass of the

We electron to the charge which it carries.

can not admit

299

5079

300

such a supposition, for reasons already given; yet if the charge exerts a drag on the aether in which the waves are traveling, the velocity attained will be reduced to a fraction of that of light, in accordance with observations.
No other hypothesis than that here adopted will explain the
phenomena; and it seems certain that the electron phenomena are explicable by means of the aether, but not without this much finer medium.

(iv) Explanation of inertia, momentum, the laws of .motion and of static electricity.

Ever since the formulation of the Newtonian philosophy
in the Principia, 1686, the problem of inertia, momentum
and the laws of motion have appeared to natural philosophers as phenomena requiring elucidation; yet for a long time no
solid progress could be made in this inquiry, because there was no adequate theory of the aether. Now that a kinetic
•theory of the aether is outlined, and the properties of the
medium somewhat understood, we consider it advisable to
suggest an explanation of the chief mechanical actions which
underlie natural philosophy.

1. Since the aether is filled with waves and presses

— symmetrically upon bodies at rest, or in uniform motion,

— and all bodies carry their wave fields with them,

whatever

their state of rest or motion, we perceive that the high elasti-

city of the aether makes it impossible to move a body at

rest, or alter the velocity of a body in motion, without ex-

pending energy upon it. For in every case the wave-field

about the body must be readjusted, and under the elastic

— power of the aether, this involves work,

just as the aether

waves of solar radiation, for example, do work when arrested

in their motion at the surface of the earth. , The kinetic theory of the aether therefore accounts for inertia, which

represents the energy to be overcome in readjusting the

wave-field about any body.

2. To make this a little clearer we recall a remark
of Tyndall in his work on sound, 3'''* ed., 1896, p. 73: »A certain sharpness of shock, or rapidity of vibration,
is needed for the production of sonorous waves in air. It is still more necessary in hydrogen, because the greater mobility of this gas tends to prevent the formation of condensations and rarefactions.*
In further proof of Tyndall'^ remark as to the increased difficulty of starting waves in hydrogen compared to air, we cite the fact that heretofore Prof F. E. Nipher of St. Louis
is the only experimenter who has been able to generate waves in the aether by mechanical means. To this end Nipher
used dynamite, which generates tremendous forces acting
— with extreme quickness exactly as Tyndall points out should
be the case for a gas having very great mobility of its molecules. This confirms the kinetic theory of the - aether and the cause assigned for inertia by an experimentum crucis.

3. In the case of momentum, the physical cause involved is the same as that assigned for inertia,' for very obvious reasons. For momentum is the product of mass by velocity, mv, and as the mass does not change, the change can only occur in v, the velocity, and thus momentum and
inertia are identical as to physical cause.
We may even go a little further, and say that all

kinetic energy depends on the aether; for the formula for

£ = = the kinetic energy

t/^mv^

^j^mdh/dt^

(96)

involves only mass m, which is constant, and the velocity v, any change in which is resisted by the moving wave-field about the body, exactly as in the case of inertia.
4. As Newtotis laws of motion, Principia, Lib. i, are concerned with motion, which involve chiefly changes of velocity, we perceive that these laws have their recognized form in virtue of the kinetic medium of the aether; and that all changes of motion involve changes in the aether wave-fields about bodies, and are thus proportional to the forces acting, and produce effects in the direction of these

forces, or stresses, in the aether.
5. It only remains to point out that as we ascribe dynamic electricity, or electric currents, to waves of the aether in motion, so also we ascribe static electricity to a non-equilibrium of the wave-field of the aether due to the

escape of certain waves, under friction or other disturbing causes, which facilitates the escape faster than restoration takes place, and thus leads to the development of charges of static electricity. Thus it is easy to throw the universe

out of electric equilibrium, and develop electric stresses. 6. As a charge of static electricity is not permanent,

but accompanied' by a gradual discharge, it is natural to hold

that the insulators on which the electric stress accumulates

do not allow of an adequate flow of aether waves to main-

tain the electric equilibrium in the local field of the universe.
Hence static charges accumulate, and may be discharged by

various causes.
This may involve gradual restoration of the equilibrium,

by wave dissipation through the air or other media, or a sudden restoration, when metallic contact • is made by a con-

ductor connecting the so-called positive and negative charges,

and a motion of aether waves along the wire restores com-

plete equilibrium.

It will be seen that the views set forth in this paper and maintained with vigor are very different from those
previously current among investigators. In the search for truth we do not enter upon such new paths from any mere

love of novelty, but only from the hope of finding a way out

of the general confusion heretofore recogniEed to exist. If it be thought somewhat audacious to depart from
these old ways of thinking, in extenuation thereof I must point to the triumph of the theory of a very small density

for the aether, after a density of 2000 million times that of lead had been held by the electronists, as outlined in the first paper. The small density now appears to be established on an unshakable basis, by the discovery of the new method for determining the absolute density of the aether. And in general when nothing is hazarded in the hope of the discovery of new truth, history shows that important discoveries cannot be made.

Thus I think it infinitely better to venture upon paths which promise progress rather than to hold to lines of mere conservatism, which return to some part of the old dark
labyrinth, without leading out to real light under a clearer and brighter sky. If others are able to add to the development here brought forth I shall heartily welcome their ad-