Philosophy and the new physics; an essay on the relativity theory and the theory of quanta

PHILOSOPHY AND THE
NEW PHYSICS

ROUG1ER

PHILOSOPHY AND THE
NEW PHYSICS

An Essay on the Relativity Theory and
the Theory of Quanta

BY

LOUIS ROUGIER

PROFESSEUR AGREGE DE PHILOSOPHIE, DOCTEUR ES LETTRES

Authorized Translation

From the Author's Corrected Text of

'La Materialisation de I'finergie"

BY
MORTON MASIUS, M.A., PH.D.

PROFESSOR OF PHYSICS IN THE WORCESTER POLYTECHNIC INSTITUTE
TRANSLATOR OF M. PLANCK'S THEORY OF RADIATION

PHILADELPHIA

P. BLAKISTON'S SON & CO.

1012 WALNUT STREET

COPYRIGHT, 1921, BY P. BLAKISTON'S SON & Co.

THE MAPLE PRESS YORK PA

TRANSLATOR'S PREFACE

The recent remarkable developments of physical
theories, especially those concerned with relativity
and quanta of energy, cannot fail to have far-reach-
ing influences on philosophical thought. Physicists,
as a rule, are too much occupied with their special
field to give much attention to matters of more
general philosophical interest, and few philosophers
possess the knowledge of science required for dis-
cussing and criticizing fruitfully the work of the
physicist. Professor Rougier's very wide reading
in mathematical and experimental Physics has en-
abled him to present and interpret the new ad-
vances in Physics in a way which should prove of
great interest to both philosopher and physicist.
This book seems to mark a measurable advance
toward a confluence of the broad streams of philo-
sophical and scientific enquiry.

M. M.

449830

CONTENTS

CHAPTER PAGE

I. THE DUALISM OF MATTER AND ENERGY.

1. Introduction 1

2. The Dualistic Theory 3

3. The Difficulties of the Dualistic Theory and the

Check given to the Monistic Attempts at Reduction 6

4. Ostwald's Energetics 12

5. The Insufficiency of Ostwald's Energetics and the

Experimental Discovery of the Inertia of Energy . 15

II. MASS AND THE RELATIVITY PRINCIPLE.

6. The Idea of Mass; Einstein's Equivalence Principle

and Newton's Principle of Action and Reaction . . 22

7. The Relativity Principle 28

III. ELECTROMAGNETIC DYNAMICS.

8. The Localization of Energy Outside of Matter .... 41

9. Electromagnetic Inertia and the Dynamics of an

Electrified Particle in Motion 47

IV. THE ELECTRONIC THEORY OF MATTER.

10. Lorentz's Synthesis .'.... 57

11. The Dematerialization of Matter 62

V. THE INERTIA OF ENERGY.

12. The Materialization of Energy 73

13. The Evaluation of the Internal Energy of Bodies and

the Variations of Mass 84

VI. THE WEIGHT OF ENERGY.

14. The Weight of Energy; Its Experimental Verifications. 91

15. The Generalized Principle of Relativity and Einstein's

Theory of Gravitation 96

16. Astronomical Verification 106

vii

Vlll CONTENTS

CHAPTER PAGE

VII. THE STRUCTURE OF ENERGY.

17. The Success of the Electronic Theory; the Explanation

of the Relations of Matter and Radiation 1 10

18. Check to the Electronic Theory; Black Radiation and

the Quantum Theory 120

19. The Structure of Radiation 134

20. The Physics of the Discontinuous 143

VIII. CONCLUSION.

21. Conclusion 148

BIBLIOGRAPHY 153

INDEX OF NAMES. 157

INTRODUCTION

It has been customary since the time of Auguste
Comte (1795-1857) to distinguish two entirely
separate categories of problems: those which may
be treated by the methods of science and which
are, because of the perfection these methods have
reached, capable of being solved sooner or later, and
those which, being beyond these methods, lie out-
side of the limits of experience and on that account
are called metaphysical problems. The former
problems, taken together, mark off the field of the
exact science; the latter comprise what Herbert
Spencer and Du Bois-Reymond have called the
unknowable.

We have no criterion by means of which to
decide a priori to which of these two categories a
given problem belongs. In every case in which a
philosophical system has claimed to lay down,
dogmatically, the limits to our experience, later
scientific discoveries have seemed to make a point
of proving it to be wrong. For example, the real
nature of phenomena, according to Auguste Comte,
the founder of positivism, will never be disclosed;
"When a scientific theory," declares Poincare,1

1 H. Poincare, La valeur de la Science, p. 267.

ix

X INTRODUCTION

"claims to tell us what heat, what electricity, or what
life really is, it stands convicted at the outset.7'
This idea led Ostwald to his Energetics, and Duhem
to his Theory of Physics. Who at the present time
would bind himself to this prudent agnosticism, to
the extent of doubting the objective existence of
discontinuous elements, like molecules, atoms, or
electrons? "The atoms are no longer a convenient
fiction; it seems to us that we can, so to speak, see
them, since we know how to count them/'1 as Poin-
care had to admit in the later part of his life when
confronted by the achievements of the atomic
hypotheses.

It occurs much more often that metaphysical
problems, supposedly incapable of solution, vanish,
simply because the progress of ideas shows that
they are fictitious problems or pseudo-problems,
or problems which have been badly conceived. We
have nothing but pity mingled with boredom for
the endless disputes of the Scholastics on the subject
of the unity or the plurality of the substantial
forms in animal species. We know, in fact, that
nothing but individuals really exist, and that, to
the static abstractions of our mind regarding these
genera and species, nothing invariable and essential
corresponds, beyond a mere bond of relationship
and a family resemblance between the individuals
that we range in the same class. The question of
knowing whether a body is at rest or in absolute
motion is, according to Einstein, another example

1 H. PoincarS, Dernieres pensees, p. 196.

INTRODUCTION XI

of a pseudo-problem. There exists no absolute
space which might serve as a privileged reference
system; there exist merely bodies at rest or in
motion relatively to one another.

It is a metaphysical problem of the same kind
that arises from the fundamental dualism between
ponderable matter and imponderable energy, which
classical physics uses for the basis of an explanation
of the world and which gives place to two principles
of invariance, the principle of the conservation of
mass and the principle of the conservation of
energy. There is a radical difference of character
between these two components of all phenomena of
nature, matter and energy; matter alone is endowed
with mass, with weight in proportion thereto, and
with structure; energy has no inertia, no weight, and
no structure. Therefore how is it to be conceived
that an imponderable noncorpuscular agent that has
no distribution in space capable of representation
can be applied to a body with both mass and
inertia, and possessing a definite shape, and act
on it to the point of deforming or moving it?
How, for example, can luminous radiation, if it is
destitute of mass, exert a repulsion in one direction
on the source which emits it and an impulse on the
opaque body absorbing it, as if it represented
momentum ; how, in other words, if it -is deprived of
inertia, can it behave like a material projectile
which exerts a recoil pressure on the fire-arm which
throws it and a ballistic action on the obstacle
which it strikes? And if energy possesses some

Xll INTRODUCTION

inertia how can it accumulate without effect on a
body, like electric energy, without the mass of this
body increasing? This is the metaphysical problem
of the mutual action of energy and matter. If
one assimilates mental labor to a kind of energy
sui generis, the metaphysical problem of the
relations between mind and body presents itself
as a special case of the foregoing.

Vain attempts have been made to reduce one of
the two terms placed in contrast to the other by the
dualistic theory, in order to escape the problem of
their mutual action; these monistic attempts have
merely served to shift the problem by substituting
new difficulties for the one that they attempted to
overcome.

All this became quite different as soon as the
theory of relativity of Einstein and the theory of
quanta of Max Planck led, if not to a complete
rejection of the fundamental dualism of matter
and energy, at any rate to an approach of the two
terms by assigning to them such common properties
as to render their relations intelligible. Thus these
theories confer on energy inertia, weight in propor-
tion thereto, and even a certain kind of structure.
Consequently, radiation represents electromagnetic
momentum and may be properly likened to a ma-
terial projectile. The pressure of radiation ceases
to be incomprehensible and to give rise to the vexa-
tious metaphysical problem of the action of the
imponderable on the ponderable.

Not only does the inertia of energy, which as late

INTRODUCTION Xlll

as 1913 Brillouin1 described as a " paradoxical
fancy/7 relieve us from the drawbacks of such a
problem, but it satisfies our inherent need of uni-
fication by absorbing the principle of the conserva-
tion of mass into the more general one of the
conservation of energy and by extending the law
of Newtonian attraction to radiant energy. More-
over the fundamental formula E = mV2 leads to the
following important result: it permits the evalua-
tion of the internal energy of a gram of matter
at the absolute zero for an observer at rest, an
energy which is no less than that of 3 million kilo-
grams of coal.

The weight of energy, which, according to the
experiments of Eotvos, is proportional to its inertia,
furnishes, as Langevin has shown, a natural inter-
pretation of the discrepancies in Prout's law of
atomic weights. It is the origin of the theory of
gravitation of Einstein based on the generalized
principle of relativity. The practical interest of
this theory is that it leads to a successful calculation
of the secular anomaly of the perihelion of Mercury,
and to the correct interpretation of the shift of
Fraunhofer's lines in the solar spectrum as compared
with those from a terrestrial source, observed by
Fabry and Buisson. But its essential advantage
lies in the fact that it excludes from the domain of
physics those metaphysical entities that are still
encumbering it, such as the absolute space and the

1 Brillouin, Propos sceptiques au sujet du principe de relativite
(Scientia, Janvier 1913, p. 23).

XIV INTRODUCTION

privileged axes of Newton and their successors, the
body alpha of Neumann and the stationary ether
of the opticians. Psycho-physiology teaches us
with respect to this point that our senses perceive
merely relative variations in the external world
without ever detecting an absolute change. Ein-
stein has reconciled natural philosophy with the
requirements of epistemology by showing that it is
possible to put the equations of physics into a form
which is generally invariant with respect to all
changes of coordinate axes. By making use of
the absolute differential calculus he has shown that
it is thus possible to substitute for coordinate equa-
tions intrinsic equations expressed in terms of
tensor equalities in order to have in the terminology
of the physical laws the magnitudes characteristic
of the gravitational field; or, putting it more exactly,
to regard the physical laws as relations between the
quantities characteristic of the gravitational field
and the quantities characteristic of the special
phenomena to be studied.

Lastly, free radiation seems to possess structure.
The law of energy distribution in the spectrum of
the black body and the study of the specific heats
of solids at low temperatures lead to the belief that
the energy exchanges between material systems by
means of radiation take place in sudden jumps,
according to integral multiples of elementary in-
divisible quantities, veritable energy atoms, called
quanta. The discontinuity of emission and ab-
sorption of radiation paves the way for the idea of a

INTRODUCTION XV

discontinuous distribution of radiant energy in the
front of transverse light waves. This follows
necessarily from the interpretation of certain phe-
nomena such as the photo-electric effect and the
production of rays by the impulse of secondary
cathode rays or X-rays. Consequently radiation
appears no longer to be a form of energy propagated
after the manner of continuous1 waves through a
hypothetical stationary medium, Maxwell's dielec-
tric ether, but as expelled into space in the form of
discrete units with a uniform velocity in a constant
gravity field. The ancient dualism of the ponder-
able and the imponderable, of matter and energy,
becomes transformed into one of energy stabilized
in material structures of definite architecture and
free radiation, both of these modes of energy being
endowed equally with inertia, weight in proportion
thereto, and structure. This may then be called
the materialization of energy.

Philosophy and the New Physics

CHAPTER I
THE DUALISM OF MATTER AND ENERGY

1. INTRODUCTION.

It is a general truth that the majority of philo-
sophical problems are insoluble because the prob-
lems do not properly exist. The subjectivism
of our senses, the anthropomorphism of our reason-
ing by analogy, the substantialistic tendency to
realize our ideas and to take purely logical dis-
tinctions as objects lead us to conceive fictitious
problems, or pseudo-problems, that have no more
meaning than the insolubilia on which the eristics
of the ancient sophists or the forensic dialectics of
the theological schools of the middle ages were
exercised. To solve them is always to show that
they were problems which have been badly stated.

One category of these pseudo-problems is derived
from the mental transformation of a simple analogy
into an absolute identity, or of a partial difference
into a perfect contrast. Having obtained certain
dissimilarities between two classes of phenomena,
we deliberately deny to those of one class everything
that is shown to belong to those of the other; and
in this perfect antithesis the mind derives the satis-
faction of symmetry. We hold this radical line of

PHILOSOPHY AND THE NEW PHYSICS

tb l:be the equivalent of reality. If
we begin to reflect on the fact that these diametric-
ally opposed phenomena show mutual interaction,
then the shock of this possibility outrages our
understanding; how can absolutely heterogeneous
agents be combined, and how can they influence
each other? For example, having supposed as a
fact that matter alone has mass, proportional
weight, and shape; and that force or energy pos-
sesses no inertia, no weight, and no structure, then the
following problem inevitably arises : How can an
imponderable agent be applied to and act on a
ponderable one, with mass and inertia, to the point
of deforming it or imparting an impulse to it?
In accordance with the adage of Leibniz, "causam
aequat effectus" our mind refuses to conceive this
and our imagination declares itself incapable of
visualizing it. Of the same nature and issuing from
the same origin is the problem of the relations
between mind and body.

The solutions proposed for such problems ine-
vitably reiterate the following theme. In a dog-
matic period it is declared that one of the two terms
of the antithesis exists only apparently, the other
one alone being reality; one tries to reduce the real
forces either to thrusts of elementary masses or to
fictitious forces of connection and inertia, or, in-
versely, one sacrifices the notion of material mass in
order to avoid contemplating anything but force
centers that attract or repel in a straight line,
according to a certain power of the distance. In

INTRODUCTION 6

supporting such reductions one perceives that in-
surmountable difficulties which merely displace the
original antinomy are encountered. The dogmatic
period is followed by the prudent agnosticism, of a
positive period. It is maintained that science is
merely descriptive, and one is content to express the
laws that govern the relations of the two classes of
agents without seeking to penetrate into their nature
or the hidden mechanism of their interaction; this is,
in the case in which we are interested, the period
of Ostwald's energetics. Finally an experimental
and critical period arrives; in it the claims of the
two terms under discussion to be placed in antithesis
are examined, and it is then discovered that the latter
is not well founded. On the contrary, it is shown to
be true that the two terms, taken to be diametrically
opposite, enjoy such properties in common as
explain their interaction; energy appears to be en-
dowed with inertia, weight, and structure, like
matter. The profound reason for the lack of success
of the preceding attempts at reduction is accounted
for, and the metaphysical problem, thus removed
unexpectedly, vanishes of itself.

2. THE DUALISTIC THEORY.

A superficial view of the external world leads to a
classification of the agents found in it into two quite
distinct categories. In the first place, there are
ponderable bodies, endowed with mass, weight, and
structure, the aggregate of which constitutes matter;
in the second place, there are imponderable forces,

4 PHILOSOPHY AND THE NEW PHYSICS

divested of inertia, weight, and structure, the aggre-
gate of which constitutes energy. Take a piece of
matter and make it undergo all the possible physical
and chemical transformations, such as motions; sub-
divisions and recompositions; expansions and com-
pressions; electrification; magnetization; changes
of state; and chemical combinations. There exists
an invariant with respect to this group of physico-
chemical transformations; that is, a certain coef-
ficient characteristic of the individuality of this
piece of matter which remains invariable and un-
changed: this is its mass. The mass, therefore,
serves for measuring a portion of matter so well
that matter and mass appear to be synonyms.
Lavoisier established the indestructibility of matter
by showing, by means of accurate weighing, the
conservation of mass. A certain amount of energy
is, because of the principle that different forms of
energy are equivalent, measured by the amount of
mechanical work into which it may be converted;
and experiment proves that, in an isolated system,
the amount of energy is constant. This is summar-
ized by a classical passage of Robert Mayer:1
" Nature presents two categories of agents between
which experiment shows an insurmountable barrier
to exist. The first category comprises agents havi ng
the properties of being ponderable and impenetrable :
these are forms of matter; the second comprises
agents lacking these properties: these are forces

1 Robert Mayer, Annalen der Pharmacie und Chemie, von Lie-
big und Wohler, 1842.

DUALISTIC THEORY 5

called imponderables on account of the negative
property which characterizes them. Forces are in-
destructible, variable and imponderable objects."

Matter and energy being equally indestructible
and radically heterogeneous, neither can grow at
the expense of the other or decrease to its gain.
Matter must return the energy to an amount equiva-
lent to what has been given to it in another form.
It serves to store it up like a sponge that has been
saturated with water and is then in turn pressed
dry; but, in contrast with the analogous case, the
presence of energy in matter does not increase its
mass since energy is imponderable. Matter is the
natural receptacle of energy, which does not exist
independently of it. Mass of ponderable bodies
and imponderable energy are conserved, each on its
own account like two distinct worlds, one super-
imposed on the other, which completely penetrate
without knowing each other and without consenting
to reciprocal exchanges. This is what a recent
author expresses as follows:1

"The world where we live is in reality a double
world, or rather it consists of two distinct worlds,
one of which is the world of ^matter, the other the
world of energy. Copper, iron, carbon, that is
the world of matter. Mechanical work, heat, these
are forms of energy. Each of these two worlds is
governed by a law of conservation. Matter can not
be created nor destroyed ; energy can not be created
nor destroyed."

1 Paul Janet, Legons d'Electricite, 2 Edition, pp. 2 and 5.

6 PHILOSOPHY AND THE NEW PHYSICS

" Matter or energy may appear in a large number
of forms, without matter ever changing into energy
or energy into matter."

"We can no more conceive of energy without
matter than of matter without energy."

This dualistic doctrine of the universe rests on
the following principle :

Matter alone is endowed with mass, weight,
and structure; energy has no mass, no weight,
and no structure.

This principle is supposed to be founded on
the following propositions which we shall hereafter
call the postulates of the theory:

1. Energy is never localized outside of matter.

2. The presence of energy in a body does not
increase the inertia of the latter.

3. The presence of kinetic inertia in particular,
that is, the state of motion of a body, does not
increase its mass.

4. Absorption or emission of energy by radiation
neither increases nor diminishes the mass of a body.

5. The mass of bodies being indestructible, the
principle of the conservation of mass is distinct
from the principle of^the conservation of energy.

3. THE DIFFICULTIES OF THE DUALISTIC THEORY AND
THE CHECK GIVEN TO THE MONISTIC ATTEMPTS
AT REDUCTION.

The fundamental dualism of matter and energy
leads to insurmountable difficulties. How can im-
material forces act on inert bodies so as to move

MONISTIC ATTEMPTS

them and verify the ancient formula mens agitat
moleml How can luminous radiation if it is devoid
of mass, exert a repulsion in one direction on the
material source emitting it, and a propulsion on an
opaque body absorbing it, as if it represented an
amount of momentum; how, in other words, can it,
if it is destitute of inertia, behave like a material
projectile, which exerts a recoil pressure on the
fire-arm which throws it and a ballistic action on
the obstacle which it strikes? And if energy pos-
sesses some inertia, how can it accumulate like
electric energy on a body to a considerable amount,
without the mass of the latter being found to have
grown in some manner? In the presence of such an
antinomy our understanding feels outraged and
our imagination declares itself inadequate.

Furthermore there are the attempts at reduction,
by the monists, coming one after another and seek-
ing to resolve this initial contradiction by reducing
one of the two terms of the antithesis to a mere
semblance of the other. But Stallo, Hannequin,
Duhem, and Meyerson1 have shown that in these
attempts the difficulty is simply shifted.

The first attempt, in time, is that of the atomists,
whose fate, from Leucippus and Democritus to Huy-
gens and the Bernouilli brothers, is especially note-
worthy. It consists in reducing the supposedly

1 Stallo, The concepts of modern physics. Hannequin,
Essai critique sur 1'hypothese des atomes dans la science contem-
poraine. — Duhem, L' Evolution de la Mecanique. — Meyerson,
Identite et Realite.

8 PHILOSOPHY AND THE NEW PHYSICS

occult notion of force to the clear and distinct
one of mass; and for this purpose seeks to give
account of all phenomena by the motion of elemen-
tary masses, indivisible and indeformable, impinging
on one another. But if the atoms are rigid, trans-
mission of motion through impact is impossible; if
they are elastic, they are then deformable and com-
posed of parts, which is contrary to the hypothesis
and implies forces of cohesion and elasticity; this
inevitable dilemma leads to shipwreck. Moreover
Hertz,1 in his posthumous mechanics, aims at ex-
plaining everything, not by atoms, but by articulated
systems, by masses subject to firm bonds which
must conform to a single law : every isolated system
traverses with constant speed a trajectory of least
curvature. What we take as real forces are fic-
titious forces of connection, due to the presence
of bodies that we do not perceive, or fictitious
forces of inertia, arising from a motion that we do
not suspect. For example, anyone who, pulling a
body tied to another by an invisible cord, saw the
second move forward, would believe in a mutual at-
traction of the two bodies, while it would be the
case of a force of connection produced by a hidden
mass; and anyone who, not knowing the motion of
rotation of a gyroscope, encountered an active re-
sistance to an attempt to produce a deviation of its
axis, would believe that a real couple tended to

1 Hertz, Die Principien der Mechanik in neuem Zusammenhang
dargestellt (Ges. W. Vol. Ill) Johann Ambrosius Earth, Leipzig
1894.

MONISTIC ATTEMPTS 9

maintain this axis in an invariable direction, while
it would be a case of a force of inertia produced by
a hidden motion.

Thus "what we are accustomed/' says Hertz,
"to denote by the names of force and energy is
nothing more than the action of mass or motion."
As, moreover, nothing limits the motions and the
hidden .masses that may thus be introduced, it seems
as if it were always possible to give an account
of the behaviour of natural phenomena in this man-
ner. But this very elasticity is in itself the cause of
sterility. In spite of all the interest which is at-
tached to attempts of this kind, such as those of
Maxwell on electricity, of Lord Kelvin on the gyro-
static ether, and of Helmholtz on cyclical systems;
the concept of Hertz has not led to a single positive
result. Boltzmann1 has shown that, however great
the number of masses and hidden motions one im-
agines, and, however great, the consequent number
of arbitrary variables to which one resorts, it is im-
possible to represent the simplest phenomenon in a
satisfactory manner. Later, we shall find the
reason for this lack of power to be the incompati-
bility of the form which the relativity principle
imposes on physical laws, with the form of the
equations of classical mechanics which govern
the displacements of the elementary masses of
the atomists and the articulated systems of Hertz.

The inverse reduction, of mass to force, has been

1 Boltzmann, Anfrage die Hertz' sche Mechanik betreffend
(Wiedemann's Annalen, Suppl. 1889).

10 PHILOSOPHY AND THE NEW PHYSICS

the work of Boscovich, following Kant. The atoms
lose all material existence, and all spatial meaning;
they are nothing more than dynamical points, or
force centers. These forces are directed in the
straight line joining them, whence their name of
central forces. They are transformed in the nick
of time from repelling to attracting and their in-
tensity depends on a certain power of the distance.
But if these force centers are mathematical points
in space, how can we imagine that a force can apply
itself to them in order to repel them or attach itself
to them in order to attract them? How can these
entities of thought resist motion, and exhibit iner-
tia? "No arrangement of centers of force," de-
clares Maxwell,1 " however complicated, can account
for this fact; no part of this mass can be due to
the existence of the supposed centers of force." It
seems, moreover, that certain phenomena, such as
crystallization and permanent deformations, can
not be explained if one is limited to purely central
forces.

Lastly Lord Kelvin's2 concept of a gyrostatic
non-dynamical ether, in supressing the rebellious
concepts of force and mass, has not thereby been
more successful. Reviving the ideas of Descartes,
Lord Kelvin contemplates a perfect fluid, homogene-
ous and incompressible, which fills all space. In
this fluid there exist eddy rings, which are eternal

1 Maxwell, Theory of Heat, p. 86.

2 Cf. Tait, Lectures on Some Recent Advances in Physical
Science.

MONISTIC ATTEMPTS 11

and can neither be cut nor penetrated and which
play the part of vortex atoms. Forces are due to
pressure of the medium between these vortices.
But, as Maxwell1 remarks, one gets no sight of the
invariable element which one would agree to con-
sider as the mass of the atom. He contemplates
therefore a pure motion in pure space without
moving object, kinetic energy being half of the
product of the square of a velocity by a zero mass,
which is absurd.

Thus the mechanistic theory of the atomists,
the kinematic theory of Hertz, the dynamical theory
of Boscovich, and the non-dynamical theory of
Lord Kelvin, have conclusively failed in their
attempt to reduce either force to mass or mass to
force. The efforts of this youthful dogmatism are
followed by the prudent attitude of reserve of a
school of physics that takes no interest in a me-
chanism explaining the phenomena, but describes
simply, in its equations, the relations which connect
the simultaneous variations of directly measurable
physical quantities; a kind of physics in which
there are many integral quantities, but no atoms.

Rankine and Ostwald have both remarked that
these directly measurable physical quantities are
always quantities of energy. "To establish such
relations between measurable quantities that, some
of these quantities being given, the others may be
deduced, is the entire task of science. Hereafter
there is no need of troubling ourselves about forces,

1 Maxwell, Art. "Atom" in Encyclopedia Britannica.

12 PHILOSOPHY AND THE NEW PHYSICS .

the existence of which we cannot prove, exerted
between atoms that we know nothing of, but we are
concerned with quantities of energy put into play
by the phenomenon under investigation . . .
All the equations that connect one phenomenon
with one or several of a different kind are neces-
sarily equations between quantities of energy;
there can be no others, for, apart from time and
space, energy is the only quantity common to all
kinds of phenomena."1

4. OSTWALD'S ENERGETICS.

From OstwakTs energetics, the genesis of which
we have just traced, we may accept the following
two propositions:

(1) Of the external reality we know only changes
of energy and all physical phenomena may be
described in terms of energy.

(2) In particular a body is only a 'complex of
indissolubly associated energies, so that the concept
of matter becomes included in the more general
one of energy, and the principle of conservation of
mass is absorbed by the more universal one of
conservation of energy.

The first proposition is easy to justify. In the
first place by psycho-physiology: The apparatus
of our senses is set into action only by energy
changes between it and the external world. The
energy of the physico-chemical agents that im-

1 Ostwald, Zur modernen Energetik, (Scientia, 1907, number
1).

ENERGETICS 13

presses it is transformed into nervous energy,
which itself is transformed, in the cortical centers,
into psychic energy sui generis. "If you receive a
blow with a stick," says Ostwald1 jocularly, "what
do you feel, the stick or its energy?" The physical
phenomena appear, on the other hand, as reducible
to a condition of rest, transfer or transformation
of energies of different forms: kinetic energy;
potential energy of position; radiant energy; electric
energy; magnetic energy; heat energy; and chemical
energy. Every form of energy is the product of
two factors, an intensity factor and a quantity
factor, a variable of equilibrium and a variable of
condition: kinetic energy is half the product of
mass and the square of velocity; gravitational
energy is the product of height and weight ; volume
energy, of pressure and volume; shape energy or
elasticity, of force and displacement; electric energy,
of potential and charge, or of elctromotive force
and quantity; heat energy, of temperature and
entropy; chemical energy of thermodynamic po-
tential and the masses of the constituents.

The idea of a body becomes reduced to that of an
energy complex: volume energy which causes a
body to occupy a definite region of space; energy
of motion which causes it to possess a definite
capacity for kinetic energy or mass; gravitational
energy which causes it to have weight. It is neces-
sary to add to these three fundamental forms of

1 W. Ostwald, Die Ubcrwindung des wissenschaftlichen Mate-
rialismus. Zeitschr. f. phys. Chem,, vol. 18, p. 305, 1895,

14 PHILOSOPHY AND THE NEW PHYSICS

energy another which is essential for solid bodies,
namely, energy of shape or elasticity, by virtue of
which solids resist agents that tend to penetrate or
deform them. Every body possesses, in addition to
these energies, others in varying proportion : chemi-
cal, heat, electric, and magnetic energy. If we ask
why energies of volume, motion, and gravity appear
always associated in material systems, the answer
is found to be in the very conditions of the external
perception. If any one of these three energies were
lacking in a body, the latter would escape our notice.
A body not possessed of volume energy would not
occupy space, it would be imperceptible; in the case
of one not possessed of mass, an infinitely small im-
pulse would give it an infinitely large speed but it
would again be imperceptible; if not possessed of
weight it would leave the earth and escape our ob-
servation. The objects that constitute the world
of our sense experiences must therefore necessarily
possess these three indissolubly associated forms
of" energy, the complex of which expresses all the
positive contents of the idea of matter.

Two general principles govern the states of rest,
transfer, and transformation of energy. They are
the principle of conservation of energy and the
principle of degradation of energy.

The first rests on the discovery of the mechanical
equivalent of heat and its generalization for all
forms of energy. It states that in an isolated
system energy cannot be destroyed or created but
can merely pass from one form into an equivalent

INSUFFICIENCY OF ENERGETICS 15

amount of another form. The second enunciates
that all forms of energy have a tendency to be con-
verted into heat and all temperatures to become
equal, and may be also formulated thus: "In
a closed system the entropy always increases."
Boltzmann, by reducing the entropy to the logar-
ithm of the probability of a certain state, has shown
that this principle is a law of large numbers which
expresses, for very complex systems, the chance of
the most probable states being realized. In the
following we shall have to refer to the principle of
conservation of energy alone.

5. THE INSUFFICIENCY OF OSTWALD'S ENERGETICS
AND THE EXPERIMENTAL DISCOVERY OF THE IN-
ERTIA OF ENERGY.

In proposing his energetics as a method of
exposition, a gnosiological theory, Ostwald is un-
assailable. He is merely applying to physical
questions the positive method, as formulated by
Auguste Comte, who was gratified to see it applied
in the work of Fourier on heat ; that is, he establishes
the equations that connect the simultaneous varia-
tions of measurable physical quantities, without pre-
occupying himself with the question whether they
can be reduced to each other qualitatively, accord-
ing to their real nature. However, by excluding alt
explanatory theories, Ostwald does not solve, but
eludes, the problem of knowing how an imponderable
agent by applying itself to a body with mass and
inertia can impart to it an acceleration or determine

16 PHILOSOPHY AND THE NEW PHYSICS

a deformation in it. He condemns us to an intellec-
tual asceticism, a position which the human mind is
not satisfied to take; and that too at the precise
instant when the success of the hypothesis of elec-
trolytic ions, advanced by Clausius and Svante
Arrhenius, rehabilitated the more concrete theories,
by making it possible, through the efforts of the
latter, van't Hoff, andOstwald himself, to group into
a coherent body of doctrine the aggregate of electro-
lytic, osmotic and chemical properties of aqueous
solutions. Moreover, physicists have come by a
different path to doubt the traditional antithesis
between matter and energy and to establish by
experiment the inertia of the latter.

The experiments of Faraday have demonstrated
the localization of electric and magnetic energy
outside of conductors and magnets, contrary to the
first postulate of the dualistic doctrine. The self-
induction of electric currents in the conductors
has revealed to them the existence of a veritable
electromagnetic inertia. The discovery of con-
vection currents, predicted by Maxwell, realized
by Rowland, has led them to foresee that, on the
inertia proper of a charged particle in motion, there
must be superimposed a supplementary inertia of
electromagnetic origin, contrary to the second
postulate of the dualistic doctrine. This inertia, for
velocities exceeding 30,000 km. per sec., varies with
the velocity. The cathode particles issuing from
Crookes' tubes and the /3 rays from radium, issuing
from the disintegration of the atom, have velocities

INERTIA OF ENERGY 17

of just this order of magnitude. Experimental
study of the variations of the electromagnetic
inertia as a function of the velocity becomes here-
after possible. Undertaken by Kaufmann and
Bucherer, it shows the existence of grains of resinous
(negative) electricity, or electrons, destitute of
material support, the mass of which is solely of
electromagnetic origin and varies as a function of
velocity. Hence we have here a form of energy,
electric energy, that is endowed with mass and struc-
ture, contrary to the fundamental principle of the
dualistic doctrine. The relativity principle, which
results from the failure of all attempts to demonstrate
the absolute movement of a system by experience
within this system, then intervenes to show that
all bodies behave during translation as if their
mass were solely electro-magnetic, that is, as if it
were no more an invariable scalar quantity, but a
tensor quantity, symmetrical and variable, contrary
to the third postulate of the dualistic theory.

Absorption and emission of radiant energy by
bodies and the pressure of radiation resulting there-
from, in accord with the theoretical views of Maxwell
and Bartoli and the experimental results of Lebedew,
lead, on the other hand, to endowing electromagne-
tic radiation with momentum, in order to safeguard
the relativity principle and Newton's principle of
action and reaction or its corollary, that of the
conservation of momentum in an isolated system.
But momentum implies moving mass. Radiant
energy, therefore, has mass; and all other energy,

18 PHILOSOPHY AND THE NEW PHYSICS

no matter what its form, being convertible* into
energy of radiation, possesses a coefficient of inertia.
The mass of a material system changes through
absorption or radiation of energy, since, in the first
case, it is increased by all the inertia of the absorbed
radiation, and, in the second case, diminishes by
the amount appertaining to the radiation emitted.
From the formulae it follows that, if we take the
velocity of light as unity, the inertia of a material
system is the measure of its internal energy. The
mass ceasing to be invariable, the principle of the
conservation of mass becomes merged in the princi-
ple of the conservation of energy, as previously con-
ceived by Ostwald, and contrary to the last postu-
late of the dualistic theory.

Matter and energy are endowed equally with
inertia and, according to the experiments of Eotvos
on the proportionality of inert mass and gravita-
tional mass, with weight in proportion thereto.
There still persists the opposition between matter,
characterized by its structure (the number and na-
ture of the electrons, and possibly also the positive
remainders, of which it is composed) and the pos-
sibility of moving with velocities varying from zero
to that of light, and radiation which moves uni-
formly with the speed of light. This opposition
becomes weaker because of the quantum theory.
This theory shows that radiant energy is not uni-
formly propagated in a hypothetical medium, but is
emitted into space in the form of discrete units.

The metaphysical problem of the action of

INERTIA OF ENERGY 19

an imponderable on a ponderable, of force on mat-
ter, disappears as a pseudo-problem, born of an
artificial antithesis between matter and energy
assumed at the outset. On account of the inertia
of the latter, there is no more difficulty in under-
standing, for example, the pressure on the matter
absorbing it, since, being endowed with momentum,
light behaves strictly like a material projectile
striking an obstacle.

Thus, as already stated, matter was errone-
ously opposed to energy, by denying to the latter
everything that had been found to belong to the
former. This led to a fundamental antinomy which
gave rise to a pseudo-problem. The monistic at-
tempts to reduce one of the terms of the antithesis
to the other have merely served to shift the diffi-
culty without relieving it, and Ostwald's energetics
merely to escape the problem without solving it.
The recent discoveries, however, by opening up a
field of experiment of an extent beyond all expecta-
tion, such as the possibility of having at our dis-
posal velocities approaching that of light, have
led physicists to revise the primitive classification
of natural agents into ponderables and imponder-
ables. It has been discovered that this Classification
was not well founded, that the admitted anti-
thesis between matter and energy was artificial, and
that these two realities, in spite of differences which
forbid their confusion, possess precisely the common
characteristics that permit the explanation of their
mutual action.

20 PHILOSOPHY AND THE NEW PHYSICS

This result, essential for natural philosophy,
is the end of a long line of theoretical reasoning
and experimental verification, which unite conclu-
sively to establish the following proposition: Energy
is endowed with inertia. In order to understand
the inner logic of this wonderful organic de-
velopment, it must be followed without haste, step
by step. The physicists have not found that royal
road leading directly to the goal by which Ptolemy I
asked Euclid to conduct him to the comprehension
of the most transcendent scientific truths. They
have not abandoned the old principles under pres-
sure of the new facts until they had tried all possible
ways of saving them. They have not risked one
step forward without summoning an advocatus
diaboli against themselves. They have been pru-
dent in their innovations. Old mental habits,
stabilized through long ages of scholasticism, and
the narrow evidences offered by a traditional ra-
tionalism are not got rid of in a day; nor does one
easily leave the beaten track of an imagination
which derives satisfaction only from the contempla-
tion of solids. In particular, the consideration of
Maxwell's dielectric ether, which comes under the
category of Hertz's hidden masses and movements,
has for a long time, by misleading physicists into
attempts at mechanical explanations, paralyzed
efforts, of which the relativity principle finally had
to show the futility. Leaving useless details aside,
we shall follow in its essential curves the turnings
of the winding road which has led the physicists of

INERTIA OF ENERGY 21

the new school to a conception of the universe, the
beauty of which is a joy forever. To arrive there
more easily we shall at the outset recall a certain
number of ideas and principles which will be con-
stantly used in the sequel.

CHAPTER II
MASS AND THE RELATIVITY PRINCIPLE

6. THE IDEA OF MASS; EINSTEIN 's EQUIVALENCE
PRINCIPLE AND NEWTON 's PRINCIPLE OF ACTION
AND REACTION.

In order to show how the idea of energy as en-
dowed with mass and weight in proportion thereto
has been arrived at, it is necessary to define these
two ideas and to state two principles which are
closely associated with them.

What constitutes the individuality of a piece of
matter through all motions, divisions, recomposi-
tions, compressions, expansions, changes of state and
chemical combinations that it undergoes, is its mass,
which presents itself as an invariant of the group of
physico-chemical changes.1 It is considered in
classical mechanics as an invariable scalar quantity
that characterizes every piece of matter and may be
defined in three different ways: (1) as a coefficient of
inertia; (2) as capacity for momentum; (3) as capa-
city for kinetic energy. * ^

As coefficient of inertia, mass measures the re-
sistance of a body to any action tending to modify
its state of motion. Newton assumes the propor-

1 Cf. F. Enriques, Les Concepts fondamentaux de la Science,
p. 136-144.

22

IDEA OF MASS 23

tionality of the force acting on a body to the change
in velocity per unit time communicated to it, or the
acceleration; therefore the quotient of force by
acceleration defines the mass of a body. Moreover,
he assumes the principle of the independence of the
effects of a force, which leads to the view that the
mass of a moving body is independent of the veloc-
ity acquired : if a force acts on a body for a second,
starting from rest, and communicates to it the veloc-
ity v, the same force acting through another second
will communicate to it a second increment of veloc-
ity equal to the first, so that its velocity will be-
come 2v} if the same force continues to act through a
third second, the velocity will become 3v and so on.
Theoretically a moving body may be given a veloc-
ity as large as we please by the application of the
same force a sufficiently large number of times.
Lastly the mass of a body is independent of the
sense in which the force acts, whether it be parallel
to the direction of the velocity (tangential accelera-
tion) or at right angles thereto (normal acceleration) .
Mass may also be defined, as was done by Mauper-
tuis, by starting with the idea of an impulse com-
municated to a body by a force during the time
element dt. This quantity is determined in mag-
nitude and direction by the product f-dt; and the
impulse of a body at the instant t is the geometric
sum of the elementary impulses that, starting from
rest, have been successively communicated to it by
the various forces exerted on it. In virtue of the
law of inertia, matter tends to conserve its state of

24 PHILOSOPHY AND THE NEW PHYSICS

motion; the impulse is equal to the momentum of a
body, or the product of its mass by its velocity taken
in the same direction as the latter; hence the vector
relation

g = mv.

Mass may therefore be defined, as capacity for
momentum, by the impulse divided by the velocity
according to the relation

Lastly, the kinetic energy of a body may be de-
fined by the total work which had to be expended
to bring the body from rest into its actual state of
motion without deforming it for observers moving
with it. This leads in rational mechanics to the
relation

w = ^mv2.

Starting from this, mass can be defined, as the
capacity coefficient of kinetic energy, by the quotient
of twice the kinetic energy and the square of the
velocity

2w
™=^

These three definitions are equivalent in classical
mechanics and we shall have to refer to each of
them in succession. But we shall see that in the
new dynamics, the dynamics of the electron and
of relativity, they cease to be identical for velocities
above 30,000 km. per sec. All three lead to variable
values, functions of the velocity, following three

IDEA OF MASS 25

different laws which make them assume an infinitely
large value for the limiting speed of light in a
vacuum. The following leads to a rejection of
Newton's principle of the independence of the
effects of a force. If a force acts for another
second its effect will be less than that produced
during the first; it will be still less during the third
and less in general as the velocity already acquired
by the body becomes greater, since the inertia
increases step by step, until it becomes infinite for
the speed of light. Lastly in the new dynamics the
acceleration communicated to a body by a force
depends on the angle made by the direction of this
force with that of the velocity. We must define a
tangential mass and a transverse mass, identical
with that defined by Maupertuis, which do not
behave symmetrically. Briefly, mass ceases to be
a constant scalar quantity and becomes a tensor
quantity, which is variable and unsymmetrical.1
The idea of mass designates two quite different
things: (1) the coefficient of inertia of a body which
measures its resistance to acceleration, or inert
mass', (2) the coefficient of attraction of a body on
another outside of it, according to Newton's law,
or gravitational mass. How do these two masses
behave with respect to each other? Newton sup-
posed that there was a strict proportionality be-
tween the two coefficients; but that was not proved

1 On the subject of symmetry of physical quantities see L.
Rougier, La symetrie des phcnomenes physiques et le principe de
raison suffisante (Rev. de Met. et Mor. mars 1917, p. 165-198).

26 PHILOSOPHY AND THE NEW PHYSICS

experimentally before Eotvos1 experiment with
a torsion balance. On the surface of our globe all
bodies are immersed in two superimposed fields
of force: the field of gravity, which puts into play
the gravitational mass of bodies, and the field of
the centrifugal force, which puts into play their
inert mass. The resultant of these two actions
combined is the apparent weight of a body. If the
two masses were different, the resultant, that is,
the observed direction of vertical, would not be
exactly the same for all bodies: there would not
be a single vertical at one and the same point.
That this is not so has been established by Eotvos
by the aid of a torsion balance with an exactness
which excludes relative divergencies of the order
10~7? so that the exact coincidence of the two co-
efficients may be taken for granted.

Einstein2 has from this deduced the principle
of the equivalence of acceleration and gravitation; the
effects produced on any system by a gravitational
field are not distinguishable from effects produced
by a suitable state of acceleration of the same system
when removed from the action of the field, or, what
comes to the same thing, from those of a system
referred to axes having an accelerated motion with
respect to it. In order to learn the action of

1 B. Eotvos, Math. u. naturw. Ber. aus Ungarn, Vol. VIII,
1890; Beibl, vol. XV, 1891, p. 688.

2 Einstein, Ann. der Phys., 1911 p. 898 and seq.; 1912, p. 365
and seq.; 1914/p. 341 and seq.; Zeitschr. f. Math. u. Phys., 1913,
p. 6 and seq.; Phys. Zeitschr., 1914, p. 176 and seq.; Archives des
Sciences phys. et nat., 1914, p. 7-12.

ACTION AND REACTION 27

gravity on physical phenomena it will suffice to
study the effects of acceleration on them, that is,
to examine the modifications that the physical phe-
nomena undergo when passing from a reference sys-
tem at rest, or in uniform translatory motion, to one
accelerated with respect to the former. From this
Einstein has made the deduction that if energy is
inert it has weight in proportion. We can no longer
imagine an agent like the ether having a certain
density and yet absolutely imponderable, that is to
say, devoid of weight. Everything that is endowed
with mass must possess a certain coefficient of New-
tonian attraction in proportion thereto.

The idea of mass is intimately connected with
the Newtonian principle of instantaneous equality
of action and reaction. Without attempting to
fathom the meaning of this principle or seeking to
find how it is connected with the definition of equality
of masses,1 we shall restrict ourselves to its enuncia-
tion. If a material point A acts on another B, the
body B reacts on A, and these two actions are
two instantaneously equal and oppositely directed
forces. For example, the attraction exerted by the
earth on the moon is at every instant equal to and
oppositely directed to the attraction exerted by the
moon on the earth. It follows from the principle of
the equality of action and reaction that in the case
of a closed system the momentum g — mv remains
constant. If a body through an internal action calls

1 Cf. Mach, History of Mechanics, p. 210-216. Enriques, 1. c.,
p. 144-149.

28 PHILOSOPHY AND THE NEW PHYSICS

forth the appearance of a certain momentum, count-
ed as positive, by acting on another body, it will
undergo a repulsion on the part of the latter and
consequently take a momentum equal to the first
and directed in the opposite sense so as to com-
pensate it. The center of gravity of the system
will remain at rest. The principle of the conservation
of momentum in a system which is subject to internal
actions only presents itself therefore as a corrollary
of the principle of action and reaction and would
cease to be exact at the same time as the former.

7. THE RELATIVITY PRINCIPLE.

The relativity principle originated from the nega-
tive result of all the attempts to show the ab-
solute motion of a material system by experiments
within that system.

Classical mechanics assumed that all mechan-
ical phenomena in a system in uniform rectilinear
motion are produced exactly as if the system were
at rest. An observer enclosed in Jules Verne's
bomb-shell could detect accelerations or rotations
that this shell undergoes by observing phenomena
taking place inside; he could in no way detect his
uniform translatory motion. This is no longer the
case if he has recourse to optical or electrical experi-
ments. The electromagnetic theory introduces a
medium at rest, the ether, which transmits the
transverse waves of light with a definite speed, just
as air transmits sound waves. In the case of a
source of sound the relative motion of the source -with

RELATIVITY PRINCIPLE 29

respect to the air can be measured without revealing
an absolute motion of the source with respect to the
ether, since air is dragged along by the motion of
bodies. This is not so in the case of the ether. The
latter, if it exists, is incapable of motion, so that
one might hope to show, by electromagnetic or opti-
cal experiments within a system, the motion with
respect to the ether of a source of light connected
with the system.1

The earth possesses in its annual motion a trans-
latory velocity varying constantly by amounts as
high as 60 km. per sec. for the relative velocities cor-
responding to two diametrically opposite positions in
its orbit, in January and July, for example. Let us
consider the optical experiment actually performed
by Michelson in 1881 and repeated by him and
Morley in 1887 the outline of which is as follows.
Let three points O, P, and P' be taken at the vertices
of an isosceles triangle with a right angle at O. OP
corresponds to the direction of the translatory mo-
tion of the earth, OP7 is at right angles thereto; at O
a glass plate is fixed inclined at 45°; at the points P
and P' mirrors are fastened normally to the two
directions OP and OP'. Let us assume that a light
ray comes from a lens on the line OP' produced,
strikes the glass plate O and there is divided into
two rays : one will be reflected towards the mirror P,

1 Cf. H. A. Lorentz, A. Einstein, H. Minkowski, Eine Samm-
limg von Abhandlungen, Teubner 1913. Laue, Das Relativitats-
princip, 1911. P. Langevin, Le temps, 1'espace, et la causalite"
dans la Physique moderne (Bull. Soc. fr. de Philos. vol.. xii, 1912).

30 PHILOSOPHY AND THE NEW PHYSICS

return to O and passing through the glass plate will
fall on the lens L; the other will pass through the
plate O, be reflected from the mirror P' and be
superimposed in the lens on the first ray. If the
apparatus is at rest, the paths OPO and OP'O being
equal by hypothesis, the times t and t' required to
traverse them will also be equal, and the light dis-
turbances brought by the two rays to the focus of
the lens will coincide in such a manner as to give a
maximum of light intensity at this point. The
aspect of the interference fringes will, by reason of
symmetry, remain the same for any rotation what-
ever of the apparatus, the locus of the points P cor-
responding to equal paths OP + PO being a sphere
with its center at O.

If the system has a uniform translatory motion v,
the locus of the points P corresponding to equal
paths traversed by the light, is no longer a sphere
about O but an ellipsoid of revolution flattened in
the direction of motion, the axis of which in a direc-
tion at right angles to the velocity is to that parallel

/ v*
thereto in the proportion 1 : ij 1 — ™ v being the

velocity of the instrument, and V being that of
light. If the apparatus remains undeformed while
passing from rest to motion and if the instrument is
adjusted at the outset by experiment, so that the
paths OPO and OP'O are equal for a given initial
position, the aspect of the interference fringes will
be changed because a rotation through 90° will
interchange the directions OP and OP' and this

RELATIVITY PRINCIPLE 31

change will reveal the absolute motion of the
system.

For example, if the preceding experiment is made
on the earth, in January, and the interchange of the
directions OP and OP' does not bring about any
change in the aspect of the interference fringes, we
might interpret this negative result by saying that
the velocity of the earth relative to the ether is
relatively insignificant. Six months later it will
have increased by 60 km. per sec. and the repetition
of the experiment should bring about an appreciable
change in the aspect of the fringes. Contrary to
this anticipation the Michelson-Morley experiment
gives a negative result, and so too do all optical and
electromagnetic experiments undertaken by Lord
Rayleigh and Brace, Trouton and Noble, Rankine
and Trouton.

To account for this result, Fitz-Gerald and Lor-
entz assumed simultaneously that all linear dimen-
sions of bodies contract in the direction of their

translation in the ratio A| 1 — ™ written more

simply V 1 — |82. This contraction can not be
ascertained by observers O, connected with the
moving bodies, since all measuring instruments con-
tract in the same proportion, but it can be by station-
ary observers O0 who see it pass. Let us call the
configuration of a moving body as measured by
observers connected with it by means of measuring
rods having the same translatory motion, its geo-
metric configuration; and let us call its kinematic

32 PHILOSOPHY AND THE NEW PHYSICS

configuration the configuration of the same body
measured by observers at rest with respect to it,
who observe, at the same instant according to their
clocks, during its passage, different points of its
circumference, and determine the position of these
different points by means of measuring rods grad-
uated at rest; the kinematic configuration will not
be identical with the geometric configuration , it will
differ from it by a contraction in the ratio Vl — /32.
In the reasoning that has just led us to an-
ticipate a change in the aspect of the fringes as
a result of the rotation of Michelson's apparatus,
we have assumed the distances OP and OPf to be in-
variable during this rotation. According to Lor-
entz's hypothesis the distance OP', originally at
right angles to the direction of motion, will, for
observers 00 at rest who see the instrument pass,
contract during the rotation and become
OP = '

while inversely the distance OP, originally parallel
to this direction will expand in the inverse ratio
and become

OP' = 2L-

VI - P2'

so that the equality of the original times of travel
ti and ~t2 will carry with it the equality of the later
times ti and tz.

As a consequence of the Lorentz contraction
spherical bodies become flattened ellipsoids in the
ratio

RELATIVITY PRINCIPLE 33

We shall have to use this result in the dynamics of
the electron.

The negative result of experiments undertaken
to discover the absolute motion of a system with re-
spect to the ether has led physicists to generalize
the relativity principle assumed in rational mechan-
ics for mechanical phenomena:

Given different groups of observers, 00 and 0\, one
of which is in a state of uniform motion with respect
to the other, the laws of nature will be exactly the same
for the different groups of observers. This principle
may also be stated thus: the form of the equations
expressing the laws of phenomena within a system
does not change if they are referred successively to a
reference system at rest and then to a second system
having a uniform translatory motion with respect to
the former.

In order to see the meaning of the relativity
principle thus extended to all natural phenomena in
the case of uniform translatory motion, it will be
best to compare it with the principle of relativity
used in geometry and mechanics.

In Euclidean geometry we assume that the shape
and the dimensions of a figure do not depend on its
absolute position in space: they remain unchanged
for all displacements that it undergoes and this is
what constitutes the relativity of space. We may
express this by saying that if the same figure be
referred successively to different systems of axes
00 and 0i, the equations of transformation that
permit us to pass from the first system to the second,

34 PHILOSOPHY AND THE NEW PHYSICS

form a group,1 called an Euclidean group, in which
the form of the equations that translate the proper-
ties of geometrical figures is an invariant. Geome-
try is nothing but the study of the structure of the
Euclidean group, which is identical with the group
of orthogonal substitutions.

In rational mechanics we assume that the me-
chanical phenomena taking place in an isolated
system do not depend on its state of rest or of uniform
translatory motion: this constitutes the relativity
of motion. We may express this by saying that if
we successively refer the same mechanical system
to a reference system 00 at rest with respect to it,
and then to a system 0\ in uniform translatory
motion with respect to the former, the equations of
transformation that permit us to pass from 00 to 0\
form a group, called a Galilean group, in which the
form of the equations of classical mechanics is an
invariant. In the simplest case we would have for
such a transformation of the space coordinates of
the first system with the axes x,y,z, into those of the
second x', yf, zf

x = x' — vt

V = y'y

z = z',

where v is the velocity of translation of 00 with
respect to 0\.

1 Given an aggregate of transformations we say they form a
group, if the product of any two of these transformations and the
inverse transformation of any transformation still form part of
this aggregate.

RELATIVITY PRINCIPLE 35

We have just seen that in physics all phenomena
whatever taking place within a system are independ-
ent of its state of rest or of uniform translatory
motion, and this constitutes the relativity of all
natural phenomena. This may be expressed by
saying that if we refer successively the same phys-
ical system to a reference system 00 at rest with
respect to it and then to a system Oi in uniform
translatory motion with respect to the first, the
equations of transformation that permit us to pass
from 00 to Oi form a group, called a Lorentz group.
Lorentz's equations of electromagnetism are an
invariant of this group. In the simplest case of a
translatory motion of the reference system 0±
parallel to the rr-axis, the transformation of space
and time coordinates of the first system with the
axes x, y, z, t into the second x', y' ', 2', £', will be
expressed by the four relations

x — vt v

x' =

where 0 = y, and where v represents the relative

velocity of Oi with respect to 00 and V the velocity
of light, which is the same in all directions.

Minkowski has given a very elegant geometric
interpretation of the principles of relativity in a
four-dimensional space. He substitutes in place of
the Galilean reference systems formed by three
axes at right angles in the Euclidean three-dimen-
sional space, much more general systems formed by

36 PHILOSOPHY AND THE NEW PHYSICS

four axes at right angles in four dimensional space,
in which time plays the part of a fourth imaginary
dimension. Because time and the three space co-
ordinates are thus strictly assimilated, Lorentz's
transformation assumes a strictly symmetrical form.
In fact, if the four coordinates are

Xi = x, Xi = y, xz = z, x 4= ict

where i denotes V — 1 and c the velocity of light
in a vacuum, Lorentz's transformation becomes

The axes being at right angles, the coefficients
Apq satisfy the known relations

= 0, when q ^ r;

At = 1.

The Lorentz transformation corresponds, there-
fore, to a displacement of the reference system of
four axes (translation and rotation in the four-di-
mensional space). It occurs spontaneously in na-
ture whenever an electromagnetic system is moved
by a translation as a whole with respect to immov-
able axes. Hence the relativity principle may be
stated as follows : physical laws retain the same form
for all systems of rectangular axes in four-dimensional

RELATIVITY PRINCIPLE 37

space, or again, if we call these systems Lorentz
systems : systems having Lorentz axes are equivalent.

It follows as a result of the structure of the Lorentz
group that the concepts of space and time cease to
be independent concepts; they are absorbed in the
more general concept of the universe. The dura-
tion of phenomena varies according as it is measured
by observers relatively at rest or in motion. For
every portion of matter there exists a local time, or
time proper, which is the interval of time, measured
by observers connected with the system, between .
two successive events in it which for them coincide
in space.

Simultaneity loses all absolute significance and
becomes relative : two events in two different regions
of space which are simultaneous for certain observers
cease to be so for others in motion with respect to
the former. Even the order of succession of two
events, the distance between which in space exceeds
the path traversed by light during their interval,
may be reversed for certain groups of observers.

These new ideas of space and time lead to the
erection of a new kinematics. In it the idea of a
natural Euclidean solid no longer exists, since all
bodies undergo the Lorentz contraction in the direc-
tion of their translatory motion. If we still desire
to talk about solids, it is necessary to substitute
for Euclid's geometry that due to Lobatschewsky :
the natural solids undergoing the Lorentz con-
traction behave therefore like hyperbolic solids in
a space of negative curvature, taking for the

38 PHILOSOPHY AND THE NEW PHYSICS

value of the space constant the velocity of light
V = 3 X 1010 cm. per sec.1

A second consequence consists in the impos-
sibility of observing objects moving with a velocity
exceeding that of light. This follows from the
Lorentz contraction : at this limiting velocity bodies
would become infinitely flattened out and have an
infinite inertia. , This may be derived also from
the constancy of the velocity of propagation of light
in all directions for any observers whatever as
follows from Michelson's experiment. It follows
from this experiment that a luminous ray takes
the same time for the round trip OPO when it is
propagated in the direction of the translatory
motion of the earth, so that its velocity is combined
with the velocity of that motion, and when it is
propagated normally or obliquely to that direction,
a fact that is explained by the existence of local
time. Therefore, Galileo's law for the composition
of velocities ceases to be true: two velocities v and
v' in the same sense and the same direction may not
be added by vector addition according to the class-
ical relation v + vf, but must be added according
to the new formula (v + v') / (1 + w'),* where the
unit^of velocity is taken as the velocity of light:
V = 1. All instantaneous action-at-a-distance be-
comes thereby impossible.

It is just this impossibility of any instantaneous

1 L. Rougier, De 1'utilisation des ge'ome'tries non-euclidiennes
dans la physique de la relativite" (L'Enseignement mathe'matique,
15 Janvier 1914, p. 5-18).

2 This expression is always less than 1. (Tr.)

RELATIVITY PRINCIPLE 39

action-at-a-distance that leads to momentum, and
hence mass, being attributed to radiant energy,
if it is desired to preserve Newton's principle of
the simultaneous equality of action and reaction or
the principle of conservation of the total momentum
in the case of a closed system.

Classical mechanics is in no better accord with
the relativity principle than Galilean kinematics.
There is an incompatibility between the Galileo
group that conserves without change the form of
Lagrange's canonical equations, and the Lorentz
group that conserves the form of Maxwell's equa-
tions of the electromagnetic field. In order to
put them into accord the coefficient of Lorentz

must be introduced in all the equations of dynamics.

It follows from this that all forces of nature
must behave, on passing from one reference system
to another, as if they were of electromagnetic
origin.

In what follows we shall retain the following
consequences of the relativity principle :

1. The existence of absolute motion has no
physical meaning.

2. All bodies contract in the sense of their
translatory motion in the ratio \/l — /32.

3. No velocity exceeding the limiting velocity
of light in a vacuum can be observed; consequently,
there is no instantaneous action-at-a-distance.

4. All forces behave as if they were of electro-
magnetic origin.

40 PHILOSOPHY AND THE NEW PHYSICS

We shall retain one last consequence. The
incompatibility of the Lorentz group and the Galileo
group shows the futility of attempts starting from
the equations of Lagrange and Hamilton to explain
mechanically the phenomena of nature, and in
particular electric and magnetic phenomena.

On the contrary, what must be done is to reduce
Lagrange's equations of mechanics, equations that
are correct as a first approximation for low veloc-
ities, to Maxwell's equations of electromagnetism ;
the problem is to explain mechanical phenomena
on tbe basis of electric phenomena.

CHAPTER III
ELECTROMAGNETIC DYNAMICS

8. THE LOCALIZATION OF ENERGY OUTSIDE OF
MATTER.

The considerations that have led physicists to
the idea of the inertia of 'energy are derived from
Faraday's and Mosotti's views on the localization
of electric energy outside of conductors in the
dielectric space surrounding them.

It is known that the electrification of a body
determines the appearance of attracting and re-
pelling forces in the surrounding space, under the
influence of which oppositely electrified bodies
approach each other and similarly electrified bodies
repel each other in accordance with Coulomb's law.
Before Faraday, the appearance of these forces was
explained by the statement that there exist two
imponderable fluids, vitreous (positive) electricity
and resinous (negative) electricity, to be found in
the interior of electrified conductors, the quanti-
ties of which constitute the charges of these con-
ductors. These fluids have the property of acting
instantaneously on each other at a distance and this
explains the electrostatic actions. The region of
space in which a small electrified body may be
directly influenced by the presence of electric fluid,

41

42 PHILOSOPHY AND THE NEW PHYSICS

distributed inside of a neighboring conductor, is
called the electric field of this conductor. The
field is determined at every point of space by
the magnitude, the direction and the sense1 of the
attracting or repelling force that would be exerted
on an electrified body brought there.

It is possible to draw through each point of an
electric field a curve whose direction coincides
with that of the force capable of thus acting at
that point: an infinite set of lines called lines of
electric force is thus obtained. These lines have a
purely geometric significance : that is, the attracting
and repelling forces, the direction of which they
symbolize, do not exist unless an electrified body
is actually brought to one of the points through
which they pass. In this case only do they acquire
a physical significance and that merely at the
points considered. The intensity of the electric
field of a conductor at a point is defined in magni-
tude, sense and direction, by the magnitude, sense
and direction of the force that acts at this point on
the unit of electric mass conventionally chosen.
If we call / the force exerted on the unit mass of
electricity 77, the intensity of the field is represented
by the relation

1A force acts in a certain line (direction) and in a certain sense
(i.e., either forward or backward) along the line. In works
written in English the word direction usually includes both ideas.
(Tr.)

ENERGY OUTSIDE OF MATTER 43

This idea, which was the current one before Fara-
day, rests on three postulates: (1) there exist im-
ponderable fluids (the positive electric fluid, the
negative electric fluid, the positive magnetic fluid,
the negative magnetic fluid and the caloric fluid)
the presence of which in a body neither increases
nor decreases its mass; (2) these fluids are distrib-
uted in the interior of bodies; (3) instantaneous
action at a distance is possible.

Faraday rejects these postulates. By means of
celebrated experiments he establishes the fact that
the electric field is zero in the interior of conductors,
that is, that their charge does not manifest itself
except at their surface and in the surrounding space.
He rejects the idea of instantaneous action-at-a-
distance and considers the lines of force as having a
real physical significance; they correspond, according
to him, to certain permanent modifications of a
dielectric medium, called the ether, filling all space
and existing between the conductors. The mechan-
ical state of this medium around an electrified body
is what determines the forces to which this body is
subject; and the electric charge carried by a con-
ductor is determined by the number of lines or tubes
of force attached to it. Starting from the concept of
forces propagated by contact from point to point
with the velocity of light, Maxwell has accounted
for the electrostatic actions, in conformity with
Faraday's views and in accord with his experiments.

It is possible to get rid of the consideration of the
ether, the existence of which is hypothetical, and,

44 PHILOSOPHY AND THE NEW PHYSICS

as we shall see, contradictory, and contemplate
nothing but the only positively accessible reality:
electrostatic energy localized outside of the con-
ductors in the form of the field. The mechanical
work of attraction or repulsion, done by the static
forces appearing in an electric field, represents a cer-
tain expenditure of energy, that is, the change of
a certain amount of potential energy into actual
energy of motion. Thus potential energy localized
in empty space around a conductor exists in con-
formity with Faraday's experiments. This elec-
trostatic potential energy comes, by virtue of the
principle of the conservation of energy, from the
work expended in producing the state of electrifica-
tion of the conductor. The energy per unit volume
is proportional to the square of the intensity of the
corresponding field. Let dr be a volume element
taken in this space and let h be the vector defining
in magnitude, sense and direction the intensity of
the field at a point A of this element ; then the density
of the energy localized in the volume dr has the value

where KQ represents the specific inductive capacity
of space, the numerical value of which depends on
the choice of units. To find the energy localized
in a portion of space of finite extent it is sufficient
to calculate the integral

We =

in this space.

ENERGY OUTSIDE OF MATTER 45

Thus, for the empty space surrounding a con-
ductor, Faraday's experiments and the principle of
the conservation of energy lead to the assumption
of the localisation of a certain amount of electric energy
outside of matter.

The same considerations may be applied to a
magnetic field produced by a magnet or a current.
Similarly the energy localized in a region of empty
space is equal to the integral

W. = I ri"- dr,

J ^^

where H denotes the vector defining the intensity of
the field at a point A of the volume element dr and
MO the permeability of empty space.

The same conclusions are reached by consider-
ing radiation freely propagated in empty space with
the velocity of light.

This radiation, if taken at a sufficiently large
distance from its source, may be regarded as formed
by the superposition of an electric and a magnetic
field, one at right angles to the other and both
normal to the direction of propagation.

This electromagnetic field represents a cer-
tain amount of energy outside of any material sub-
stratum, the energy density of which in every unit

Tf h 2 IT 2

volume that it occupies is equal to - - + ^ — ,

O7T O7I

the electric energy being equal to the magnetic en-
ergy in every freely propagated plane wave, so as to
give the relation

46 PHILOSOPHY AND THE NEW PHYSICS

The localisation of electromagnetic energy of free
radiation in empty space follows from the principle
of the conservation of energy, as. may be readily
demonstrated. Let us consider a material source
radiating energy in a definite direction and an
obstacle absorbing it completely. At start there
is a loss of energy of the source and on arrival
a recovery of this energy by the obstacle. The
velocity of propagation of radiation being finite
because equal to that of light, we would not have
conservation of energy at every instant between the
time of emission and that of absorption, unless ra-
diation represented a transfer of energy through
empty space proportional to the energy radiated at
the start and absorbed on arrival.

Thus the principle of the conservation of energy
and Faraday's experiments lead us to assume
the localisation of electric and magnetic energy
in empty space, outside of matter, around charged
conductors and natural or artificial magnets. Nev-
ertheless electrostatic potential energy is, in the
case of a charged conductor, still closely bound
to matter, for the vector representation of the elec-
trostatic field shows the lines or tubes of force to
be attached to the surface of a conductor and to
spread radially roundabout. In the case of an arti-
ficial magnet formed by the magnetic field produced
by a current flowing in a metallic circuit, the mag-
netic lines of force do not abut on the circuit:
they embrace it by returning on themselves; but
they still proclaim its immediate neighborhood.

ELECTROMAGNETIC INERTIA 47

This is no longer so in the case of radiant energy,
which manifests itself to our senses sometimes as
light, sometimes as heat, sometimes in the shape of
Hertzian waves. Radiation represents a localisa-
tion, in empty space, of electromagnetic energy that
is independent of the immediate neighborhood of
any matter, and is capable of being propagated
indefinitely in a given direction without ever meet-
ing bodies which absorb it. Hence the first pos-
tulate of the dualistic theory must be rejected,
namely that energy can not be localized outside of
matter.

9. ELECTROMAGNETIC INERTIA AND THE DYNAMICS
OF AN ELECTRIFIED PARTICLE IN MOTION.

If the first postulate of the dualistic doctrine
has been set at nought as a consequence of Faraday's
experiments, its second postulate has, since 1881,
been shaken as a consequence of the theoretical
researches of J. J. Thomson.1 This young physicist
had the merit of being the first one to understand
that an electrified body possesses, because of the
electrostatic energy of its charge, a supplementary
inertia of electromagnetic origin. This results from
the self-induction of conduction currents; from the
existence of convection currents as a consequence
both of the laws of Maxwell and Hertz of the
electromagnetic field and Rowland's experiments
relating to an electrified body in motion; and lastly

1 J. J. Thomson, Philosophical Magazine, 5 ser. vol. xi, 1887,
p. 219.

48 PHILOSOPHY AND THE NEW PHYSICS

from the identity, as regards magnetic actions, of
conduction and convection currents.

When the intensity of a current changes, a
counter-electromotive force is produced in the cir-
cuit and this, in accordance with Lenz's law, tends
to oppose the change of the current. This is self-
induction which is a veritable electric inertia: it
opposes the change in intensity of a current, just as
inertia of matter opposes a change in velocity of
moving bodies. Just as a certain effort must be
expended to put a body in motion, a certain work
must be expended to establish a current ; and again,
just as a projected body tends to conserve its ve-
locity, so does a current once established tend to
maintain its intensity. If a current increases or
decreases under the action of an external field, a
counter-electromotive force is produced which op-
poses the change of the current, just as the inertia
force of a moving body that is accelerated or re-
tarded opposes the external actions that produce
this change.

The existence of convection currents was fore-
seen theoretically by Maxwell and was verified by
experiment by Rowland and his pupils.1 It
results from the laws established by Maxwell and
Hertz as to the interdependence which, in time and
space, connects the change of the two fields, the
electric and magnetic. They may be summarized
qualitatively as follows: any change in one of the

1 Cre'mieu, Etat actuel de la convection e"lectrique (Bulletin des
stances de la Socie"te" frangaise de Physique, 1902, 3 fasc., p. 155).

ELECTROMAGNETIC INERTIA 49

two fields at a point in space as time goes on, gives
rise to the other field, the field thus created being
distributed in lines of force which encircle the direction
in which the first field changes. A change in the
magnetic field in a given region of space produces
an electric field, the lines of force of which encircle
the direction in which the magnetic field changes:
this is the phenomenon of static induction dis-
covered by Faraday. If the space where this
field is thus created happens to be occupied by a
conductor, currents that encircle the direction in
which the magnetic field changes are induced in it.
Inversely, a change of the electric field in a given
region of space produces a magnetic field, the lines
of force of which encircle the direction in which the
electric field changes; this is the convection current
foreseen by Maxwell and brought to light by
Rowland's celebrated experiment.

Let us consider, according to this law, a point A
taken in the electrostatic field of an electrified
particle that is being displaced carrying its charge
along with it. The intensity at A changes because
the particle approaches this point, passes it, and
moves away. There is a variation of the electric
field in a fixed region of space as time goes on;
therefore a magnetic field is produced on account of
the law of the convection current. Hence an elec-
trified particle in motion behaves like an element
of a voltaic current; to put it more exactly, the
charge e that it carries with a velocity v is equiva-
lent, as regards magnetic actions exerted by it, to an

50 PHILOSOPHY AND THE NEW PHYSICS

element of voltaic current having the intensity i
and the length dl, so that idl = ev. The name
convection current is given to the current thus
produced.

Let us now consider an electrified sphere of
radius a having a surface charge e. At rest it is
surrounded by radial lines of force, distributed
symmetrically all around, which correspond to a
localization of electrostatic energy equal to the
work that had to be expended to produce the state
of electrification of the sphere, and which has the
value

(2) *•-&*

If a rectilinear uniform motion with a velocity
v, small compared with that of light, be communi-
cated to this sphere, it carries along its train of lines
of force, radially and symmetrically distributed
as when at rest. On account of the variation,
as a function of the time, of the electric field at
a point A of space, it produces a magnetic field
distributed in circular lines of force encircling the
direction of motion. The field at the point A in
a direction perpendicular to the plane passing
through A itself, the instantaneous position 0 of the
particle, and the direction of the velocity has the
value

ev sin a
= r2

where a denotes the angle A Ov and r the distance
AO. The field thus produced, which varies inversely

ELECTROMAGNETIC INERTIA 51

as the square of the distance, is determined by the
instantaneous position of the sphere. The latter
carries along in its motion the system of circular
magnetic lines of force superimposed on the radial
electric lines of force. This system of lines of
force constitutes the electromagnetic field of the
moving particle, moving with it like the wave sys-
tem following a ship. It remains invariable so
long as the velocity remains constant. The mag-
netic field thus superimposed on the electric field
represents a localization of energy, equivalent to
the work expended by external forces in communi-
cating the velocity v to the charged sphere. This
energy that continues bound to" it in its motion
would be recovered when it is arrested, in the form of
work done against the retarding actions. An easy
calculation based on the expression for the volume

TJ2

density of energy -|— shows that it is equal to

O7T

(4) *--£*.

which expression may be put into the more sugges-
tive form

(40 *V-

3a

This energy presents all the characteristics
of kinetic energy >^mz>2, including that of being
proportional to the square of the velocity. Every-
thing takes place as if, contrary to the second pos-
tulate of the dualistic doctrine, the sphere possessed,
on account of the potential energy of its charge, a

52 PHILOSOPHY AND THE NEW PHYSICS

supplementary inertia, an additional kinetic mass
of electromagnetic origin, equal to

r*\ 2»*e2

(5) m0 = -p-

This is a necessary consequence of the iden-
tity of conduction and convection currents. The
inertia of a charged particle in motion is due to
the self-induction of the convection current that
it produces; since electric self-induction has the same
properties as the inertia 'of matter, it follows that
this particle, on account of its electrification, has
an increment of its capacity for kinetic and, conse-
quently, electromagnetic energy which becomes
super-imposed on its inertia proper.

Electromagnetic inertia due to the presence
of a charge on a conductor in motion is proportional
to the electrostatic potential energy that this
charge represents and that the sphere carries along
with itself. Any change of this charge or of the
radius of the sphere, causing a change of the poten-
tial energy stored around it, must imply a correlated
change of this inertia. The question might then
be raised, what would happen if the sphere had a
velocity approaching that of light and its motion
remained always quasi-stationary, that is, not sub-
ject to any appreciable acceleration. This is the
theoretical problem that has been conceived by Max
Abraham. l

In order to solve it we must refer to Maxwell's
law on the mutual dependence of the electric and

1 Max Abraham, Annalen der Physik, vol. x, 1903, p. 105-179.

ELECTROMAGNETIC INERTIA 53

the magnetic fields. The magnetic field produced
at a fixed point in space by the moving particle
changes with the time, according as the particle
approaches, passes and recedes, carrying along its
train of lines of force. This change of the mag-
netic field must, in accordance with Maxwell's law,
be accompanied by the production of an induced
electric field which is superimposed on the electric
field given by Coulomb's law and modifies its dis-
tribution. The analysis of the phenomenon shows
that the electric lines of force tend to place them-
selves in a direction transverse to that of the motion,
and reach this state completely when the velocity
reaches that of light. The limiting distribution of
the field thus realized represents an infinite energy
and consequently an infinite inertia; so that
infinite work, requiring an infinite time, would be
necessary to bring an electrified particle to a perma-
nent condition in which it would have the velocity
of light. This velocity appears as a limit that no
electrified body can reach. This is confirmed by
the fact that the velocity of cathode particles
reaches nine-tenths of that of light without succeed-
ing in attaining it; this, moreover, leads to the
kinematic law of the composition of velocities, de-
manded by the relativity principle.

The modification of the electric field in con-
sequence of the induced field superimposed on
it carries with it that of the force of inertia that
the particle opposes to changes of velocity. The
electromagnetic mass ceases to be proportional to

54 PHILOSOPHY AND THE NEW PHYSICS

the velocity with a constant coefficient; it varies
with the velocity according to a certain function,
in such a way as to become infinite for the limiting
velocity of light, and this in a different manner
for the three definitions of mass and according to
the direction of the acceleration with respect to
that of the motion. In the simplest case, that of
an undeformable spherical body, two masses must
be distinguished; the longitudinal mass, the force
divided by the acceleration, if the latter is tan-
gential to the motion; the transverse mass if the
acceleration is normal to the motion. The first
case corresponds to a change in magnitude of the
velocity without a change of direction, the second
to a change in direction without a change in mag-
nitude. We may call the value of m0, which for low
velocities is the same for the different definitions of
mass, initial mass mQ and reserve the name electro-
magnetic mass m for the transverse mass. This
mass m is identical with the Maupertuisian mass; it
is the only one accessible to the measurements on
the electric and magnetic deviations of the cathode
particles in a Crookes' tube.

To find what function connects the change
of mass with that of velocity, the shape of the par-
ticle and the distribution of its charge must be
specified. Max Abraham considers the case of an
undeformable sphere having a surface charge of uni-
form distribution: for the different definitions of
mass he arrives at rather complicated formula?,
all of which assign the velocity of light as the upper

ELECTROMAGNETIC INERTIA 55

limit of the velocity of electrified bodies. Lorentz,1
however, in order to account for the negative
result of the experiments to discover the abso-
lute motion of the earth, was led to assume the
contraction of all bodies in the direction of their

translatory motion in the ratio \/l — 02 f°r ob-
servers who see them pass. A moving sphere be-
comes a flattened ellipsoid. Allowing for this
deformation, which modifies the distribution of the
electric lines of force at the surface of a charged
sphere and, consequently, the intensity of the con-
vection current produced by it and the laws of the
variation of the self-induction of the current as
function of the velocity, Lorentz has obtained a
formula much simpler than that of Abraham for
the Maupertuisian mass or the transverse mass,
which becomes equal to

/ r>\ ^0

(6) ra = .

V1-/32

By starting from this formula the laws of varia-
tion corresponding to the other definitions of mass
are readily obtained.

The fortunate parallelism, which existed at that
time between the progress of theoretical physics
and the discoveries of experimental physics, re-
vealed in the cathode particles of Crookes' tubes,
later in the 0 rays issuing from the atomic dis-
integration of radioactive bodies, electrified bodies

1 H. A. Lorentz, Versuch einer Theorie der elektrischen und
optischen Erscheinungen in bewegten Korpern, Leyden, 1895.

56 PHILOSOPHY AND THE NEW PHYSICS

projected with velocities close to that of light.
It became possible to test whether their inertia
varied with the velocity, according to the theoretical
anticipation of Max Abraham, or according to that
of Lorentz, and to distinguish between the formulae
proposed by these two authors.

The experiments of Kaufmann showed that the
mass actually varies with the velocity according to
the formula of Abraham; but the more recent ex-
periments of Bucherer and of Hupka, of a higher
degree of precision, showed that the change of the
electromagnetic mass of 0 corpuscles is better
represented by the formula of Lorentz. We shall
see that the relativity principle leads to an extension
of this formula to all kinds of moving bodies, whe-
ther electrified or not, so that they behave as if their
inertia was solely of electromagnetic origin. It
follows from this that, contrary to the third postu-
late of the dualistic theory, the mass of bodies is
not an invariable scalar quantity, independent of
their state of motion or of rest. It is a quantity having
the symmetry of a tensor,1 and dissymmetrical and
variable as a function of the velocity.

JIn modern applications of vector analysis, the branch of
mathematics dealing with the algebra and calculus of directed
quantities or vectors, the concept of tensor plays an important
part. A symmetrical tensor is an aggregate of 9 quantities,
which, when combined with the 3 components of a vector by 3
symmetrical relations, give the 3 components of a new vector. A
non-symmetrical tensor is more complicated. Earlier writers
attached a quite different meaning to the word tensor; it was
used by them to denote the mere magnitude of a single vector.
(Tr.)

CHAPTER IV
THE ELECTRONIC THEORY OF MATTER

10. LORENTZ'S SYNTHESIS.

The interest of Kaufmann's and Bucherer's
experiments is, however, not limited to the fore-
going result. By subjecting cathode particles
to the action of an electric field and a magnetic
field the comparison of the two deviations thus pro-
duced permits of finding the velocity of these
particles and the ratio e/m of their charge to their
mass. If their charge is held to be constant and
to be the same, these experiments then reveal the
variation, as a function of the velocity, of the total
apparent mass of these particles, consisting of the
sum of their material mass and their electromagnetic
mass. Comparing, then, the law of the total mass, as
derived from the preceding experiments with the
law of variation of the electromagnetic mass, theo-
retically calculated, the ratio of the material mass
to the total apparent mass may be deduced. The
result obtained is remarkable: the inertia of cathode
particles is solely of electromagnetic origin. These
particles constitute elementary electric charges with-
out material support, atoms of negative electricity
called electrons. Thus we have here, contrary to
the dualistic theory, a form of energy, resinous

57

58 PHILOSOPHY AND THE NEW PHYSICS

(negative) electricity, that appears to be endowed
with inertia and corpuscular structure without any
material substratum.

This result was the starting-point of the electronic
theory of matter.1 It consists in a change of every-
thing for its opposite, a reversal of the relation tra-
ditionally supposed to exist between matter and
electricity. In place of seeking to explain electric
phenomena mechanically, the mechanical pheno-
mena are now to be explained electrically. Instead
of seeking, as Maxwell did, to cast the equations
of the electromagnetic field in the analytical
mould made by Lagrange and Hamilton, which
appears no longer valid except as a first approx-
imation for low velocities and for quasi-stationary
motions, there is substituted for the dynamics of
the material point, conforming to Newton's equa-
tions, the dynamics of the electron, conforming to
Lorentz's equations.2

Matter, the substratum of mechanical phenome-
na, is explained by starting from electricity. The
elementary charges of electrolytic ions, the cath-
ode particles issuing from Crookes' tubes, the
|8 rays issuing from the atomic disintegration of
radioactive bodies, the negative emissions consti-
tuting the Edison and the Hertz phenomena reveal
a universal constituent of matter in the electron.

1 Cf. Les ide"es modernes sur la constitution de la matiere, Con-
ferences faites en 1912 & la Societe" francaise de Physique. Paris,
1913.

2 Cf. W. Wien, Archives ne"erlandaises, 2. ser. vol. V, p. 96.

LORENTZ'S SYNTHESIS 59

The molecular structures constituting ponderable
bodies are nothing but electronic architecture.
Electrons are grains of resinous (negative) elec-
tricity, all identical with one another. They carry
an individual charge of 4.774 X 10~10 electrostatic
C. G. S. units, distributed on a circumference of 2
millionths of a MM (2 X 10~12 millimeter) radius.
They are endowed with an initial electromagnetic
mass equal to 10~17 grams, that is, 1800 times smaller
than that of a hydrogen atom. They play different
parts in the production of phenomena, according to
the position that they occupy in the atomic and
molecular structures and according to the degrees of
freedom that they enjoy because of this position.
Accordingly there are distinguished: perfectly free
electrons moving outside of matter, in the form of
cathode rays and 0 rays; free electrons moving inside
of matter in the intermolecular spaces with a chaotic
motion that gives rise to heat radiation, on which
may be superimposed a translatory motion as a
whole that gives rise to electric current in conduc-
tors; electrons weakly bound to atoms revolving on
their circumference and capable of being detached
easily under the action of shock or an electromagne-
tic action, producing thereafter ionization of solu-
tions and gases; electrons bound to atoms, moving in
closed curves, and determining the spectral rays as
well as the chemical valences, the sources of molecu-
lar union; lastly, the electrons that compose the
central kernel of the atom, inaccessible to external
physical agents, in a chaotic state of agitation,

60 PHILOSOPHY AND THE NEW PHYSICS

which do not become revealed except in the atomic
disintegration of radioactive bodies.

On this view the atoms are formed by negative
electrons, bound more or less to the kernel, and of
positive remainders, the charge of which must be
equivalent to the total charge of the negative elec-
trons in order to maintain in the neutral state the
cohesion of the structure by the mutual attraction
of the electricities of opposite kind. Of the struc-
ture of these positive charges we know next to
nothing. Those that we can capture in the canal
rays of Goldstein and the a rays of radioactive
bodies are atoms of hydrogen or helium, deprived of
one or more negative electrons and having, on that
account, become positive ions. It may be asked
whether there is a vitreous (positive) electricity,
having an independent existence and a corpuscular
structure like the resinous (negative) electricity, so
that there would be positive electrons side by side
with the negative ones, as Jean Becquerel believes
can be inferred from the study of absorption spectra
at low temperatures; or whether positive electrifica-
tion results from the subtraction of one or more
negative electrons from the normal atomic structure
corresponding to the neutral state. In any case
the question of finding whether positive electricity
has a material support, so that there would be nega-
tive electrons but only ions of positive charge, has
lost much of its interest. The relativity prin-
ciple leads, as Lorentz has shown, to the assumption
that the inertia of these positive ions, if they can

LORENTZ'S SYNTHESIS 61

not be decomposed into simpler units, must follow
the same laws of change as a function of the veloc-
ity as that of the negative electrons, that is, that
these ions must behave as if their mass were solely
of electromagnetic origin.

The electronic theory has explained, with in-
creasing success — which has only reached its limit
when confronted by black radiation and the diminu-
tion of the specific heats at low temperatures — the
phenomena of static electricity, of the electr c
current, of induction and magnetism, of the emis-
sion, the propagation in different physical media,
and the absorption of different kinds of radiation;
those of radioactivity, of the ionization of gases and
liquids, of chemical valence, etc. It has led to
the explanation of new phenomena such as the phe-
nomena of Edison and of Hertz, and above all the
Zeeman effect. It has led Lorentz1 to a brilliant
synthesis carrying his name. Presented for the
first time in 1892, this synthesis has been put into
accord with the requirements of the relativity prin-
ciple by its author. According to it there is no
matter, only electrons, positive and negative, in
an ocean of uniform ether; all forces are of elec-
tromagnetic origin or behave like such; and the
measurements effected in a moving system are rela-
tive to the dimensions of the instruments, to the
forces taken as comparison terms, and to local time.

1 Cf. H. A. Lorentz, Sur la theorie des electrons (Les quantity's
elementaires d'61ectricite, ions, electrons, corpuscules, Paris, 1905,
vol. i, p. 430-476).

62 PHILOSOPHY AND THE NEW PHYSICS

In this conception matter, conduction currents and
magnetism become mere modes of manifestation.
The only constitutive principles are the ether and
grains of vitreous (positive) and resinous (negative)
electricity. We shall see how the English physi-
cists have taken hold of this conception and pushed
the reduction in the number of things still further:
according to certain of them not only is the exist-
ence of matter denied but also that of electricity;
and nothing but ether and empty space exists.

11. THE DEMATERIALIZATION OF MATTER.

The conception of the dematerialization of matter
of the English physicists results from the success
of the electronic theory, taken in connection with
the concept of an ether endowed with mechanical
properties, that is, inertia, elasticity and rigidity,
in conformity with the ideas of Faraday and
Maxwell. *

It is the wave theory of light, stated at first
by Leonardo da Vinci and Galileo, made more pre-
cise by Huygens following the discoveries of Grim-
aldi, and established finally by Fresnel following
Foucault's experiment that has given physical
verisimilitude to the idea of an ether. If light and,
in general, any form of radiant energy is a wave
phenomenon that is propagated with a finite
velocity in the interstellar spaces, it is difficult
to avoid the assumption that, because there is wave
vibration and therefore motion, there is something
that moves, a mobile medium that must fill all

DEMATERIALIZATION OF MATTER 63

space. As Lord Salisbury picturesquely said in his
Oxford presidential address to the British Associa-
tion, the first and principal reason for the existence
of the ether is to supply a subject to the verb to
undulate.

The second object of the ether is to account for
the localization of energy in dielectrics, surrounding
conductors or magnets, in accordance with Fara-
day's experiments, and for its accumulation in
the neighborhood of a moving electric charge, in
accordance with the theoretical views of Abraham
and Lorentz and the experimental confirmations of
Kaufmann and Bucherer. This energy, considered
as a mode of manifestation of a substance, requires
a substratum of which it is merely an accident.
Lastly, actions at a distance, such as gravitational
attraction, electric or magnetic attraction and re-
pulsion,rand,without doubt, chemical affinity, be-
tween bodies separated in space are incapable of
mental representation except as pressures or ten-
sions exerted by an intermediate medium in which
the bodies are immersed. To account for the phe-
nomena of gravitation, of optics^ of electricity and
magnetism, physicists have thus been led to con-
sider a series of media, the discrepancies of which
Hannequin1 found pleasure in exposing, but all of
which have in the end become fused together in
Maxwell's dielectric ether.

It was the consideration of the ether that per-

1 Hannequin, Essai critique sur 1'hypothese des atomes dans la
science contemporaine, p. 178-224.

64 PHILOSOPHY AND THE NEW PHYSICS

mitted a marked reduction of the number of pri-
mary principles required for an explanation of
things. At the beginning of the nineteenth cen-
tury the existence of eight energetic imponderable
agents outside of matter was commonly assumed:
the electric fluids, positive, negative, and neutral ;
the magnetic fluids, south, north, and neutral; the
caloric, and the luminous fluid. Gradually these
agents have disappeared: heat has turned out to
be the sensible manifestation of the internal agita-
tion of the molecules of bodies. Inspired by Fres-
nel's ideas Maxwell tried to explain the electric,
magnetic and optical phenomena that ceased to be
attributed to particular fluids by starting from the
mechanical properties of the ether. Electrostatic
phenomena, for example, seemed to him to be
explained by the deformations of the ether. Static
charges of electrified bodies have merely a fictitious
existence : they are the locus of the ends of the lines
or tubes of force corresponding to the deformations
of the ether. These deformations subject the
conductors to pressures and tensions forcing them
to approach each other or to move apart, the electro-
static energy being nothing but the potential
energy of deformation of the ether. The electro-
kinetic phenomena are explained by disturbances
of the ether. The electric current is not a phenome-
non taking place in the conductor but a state
of motion of the adjoining ether, the character,
direction, and intensity of which are determined
by the geometrical and physical properties of the

DEMATERIALIZATION OF MATTER 65

conductor, the energy of the electric current cor-
responding to the kinetic energy of the surrounding
ether. There exist only -two realities, matter and
ether, the former of which acts like a supernumer-
ary; the ether, in which, in the form of static defor-
mations, the electric energy is stored, and in which,
in the form of disturbances, the radiant energy is
propagated, appears more and more as the only
active medium taking part in the production of the
phenomena.

Wherein has the electronic theory strengthened
or weakened this idea, which satisfies our taste for
simplicity? It seems at first that, in addition to
matter and ether, it restores one of the old agents,
the negative electricity, no longer conceived, however,
as a continuous fluid but as a substance endowed
with corpuscular structure, not as an imponderable
but as endowed with inertia. In fact, we have
the phenomena of electrolysis, which show us a
monovalent ion carrying a well defined quantity
of electricity e, which is always the same; a bivalent
ion carrying a quantity of electricity 2e and so on.
Now this elementary charge, which appears to be
indivisible like an atom, is precisely that which is
found again, but without material support, in the
negative electrons, issuing from the cathode dis-
integration in Crookes' tubes, or from the atomic
disintegration in the 0 rays of radium, or the kinetic
agitation in the negative emissions of heated or
illuminated conductors (Edison's and Hertz's phe-
nomena). These charges can no longer play the

66 PHILOSOPHY AND THE NEW PHYSICS

part of pure fictions, by being placed geometrically
at the ends of lines or tubes of force constituted of
deformations of the ether: they have a physical
existence, a structure and inertia of their own. In
these grains of electricity, and not in the mechanical
states of the ether, the initial cause of electric and
magnetic phenomena must be sought. The elec-
tric current, for example, has not its seat in the
ether but in the conductor; it consists of a mass
motion of the free electrons of the metal, superim-
posed on their chaotic kinetic agitation, like the
flow of a gas in a pipe: there is no longer a con-
duction current due to the ether, but merely a
convection current due to electrified particles in
motion.

But at the very time when the discoveries of
contemporary physics seem of necessity to increase
the number of primary principles, by a return to the
old agents, through assuming grains of resinous
(negative) electricity, their offspring, the electronic
theory, works an inverse reduction by destroying
the concept of matter, which from this point of view
has merely a gross semblance of reality. According
to this theory, the molecular and atomic structures
constituting bodies are reduced to electronic archi-
tecture, the electrons being positive and negative,
or simply negative, and their inertia being entirely
of electromagnetic origin and due to the self-in-
duction of the convection currents that they produce
by their displacement. Matter, ceasing to corre-
spond to a distinct reality, is resolved into grains of

DEMATERIALIZATION OF MATTER 67

electricity and these, according to the English
school, become subtilized into mere ether cavities.

Rearming themselves with the ideas of Faraday
and Maxwell, the English physicists, and the most
famous of them, J. J. Thomson, regard the inertia
of the electron as due to the ether surrounding it.
An electron at rest is a surface charge without mate-
rial support, and may be considered as a cavity in
the ether. This cavity is the center from which the
electric lines of force constituting the electro-
static field of the electron diverge. The ether ad-
heres to these lines of force, so that the electron can
not move without displacing it. The inertia of the
electron results from the inertia of the entrained
ether, which alone opposes its motion. Knowing
the volume and the masfe of an electron, the density
of the ether adhering to it may be calculated; it is
found to be equal to about 2000 million times the
density of lead. Matter ceases to exist, since, being
composed of electrons, the sole reason we have to
believe in it, namely its inertia, does not properly
belong to it, but is borrowed from the ether. Elec-
tricity likewise disappears as a substance with an
existence of its own, since the electrons are reduced
to cavities in the ether. Two principles only sur-
vive, ether and empty space, of one of which the
ancients would have said that it is the non-being
and consequently that it does not exist. The
world is merely a bubble of ether in the non-thing.

This theory of the disincarnation of matter,
leading to a complete etherization, should, in spite

68 PHILOSOPHY AND THE NEW PHYSICS

of its alluring aspect, be taken with considerable
caution. It is threatened with downfall on account
of the concept that forms its base, that of an ether
endowed with mechanical properties, the hypo-
thetical existence of which seems, moreover, to be
contradictory.

To fulfill its office the ether must accumulate
the mutually exclusive properties of solids and
fluids. It must behave like an elastic solid, en-
dowed with a rigidity surpassing that of steel in
order to transmit nearly instantaneously the trans-
verse vibrations of light; it must behave like a
fluid with a density much less than that of the
lightest gas, in order not to retard the translatory
motion of the stars and not to rob them of their
atmosphere; but in the neighborhood of the elec-
trons it must have a density far surpassing that
of lead. All this is incomprehensible and no one
can, under the plea of thinking in terms of the
ether, evade thinking according to the law of
contradiction.

If the ether exists, it is incapable of motion,
as is proved by the impossibility . of reconciling
Fizeau's experiment with Hertz's hypothesis of a
complete entrainment of the ether by matter in mo-
tion, and the impossibility of reconciling the prin-
ciple of action and reaction with FresneFs and
Fizeau's hypothesis of a partial entrainment of the
ether. But, if the ether is incapable of motion, our
laboratories and our instruments are continuously
traversed by an ether current, the velocity of which

DEMATERIALIZATION OF MATTER 69

is equal to and opposite to that of the earth and
varies as a function of it. Such a current would
exert a considerable influence on electromagnetic
and optical phenomena. Now the experiments
undertaken to show the absolute motion of the earth
with respect to the ether, with which a privileged set
of reference axes might be connected, show that
there is none. The hypothesis of an immovable
ether is in its turn contradicted by the relativity
principle.

But there is more than that. Neither Max-
well nor any one after him has succeeded in giving
a clear and distinct mechanical representation of
the deformations and disturbances of the ether that
would produce the electric and magnetic phe-
nomena. In attempting it he arrived at a concep-
tion so strange, that of a cellular ether formed of two
substances one of which was impregnated with the
other like a sponge soaked with water, that he did
not make it play a part in his large Treatise on
Electricity and Magnetism. Recently Witte1 has
shown, by a very complete analysis, that the proper-
ties of the electromagnetic field cannot be explained
by the aid of classical mechanics with any supple-
mentary hypothesis, if we assume the hypothesis of
a continuous ether, and he rejects as improbable
that of a discontinuous ether. To-day we see the
underlying reason of this impossibility in the rela-

1 Cf. Witte, Ueber den gegenwartigen Stand der Frage nach
einer mechanischen Erklamng der elektrischen Erscheinungen,
Berlin, 1906.

70 PHILOSOPHY AND THE NEW PHYSICS

tivity principle. The Lorentz group, for transfor-
mations of which the form of the equations of
electromagnetism remains unaltered, excludes the
Galileo group, for the transformations of which the
form of the equations of classical dynamics is
conserved. Mechanical explanations of electric
phenomena are, therefore, definitely condemned.

Lastly, we shall see that there are reasons for
believing that radiation is not propagated by
means of a hypothetical medium, but projected into
empty space in the form of discontinuous elemen-
tary quantities, energy atoms, called quanta. With
this return to an emission theory the most con-
vincing argument in favor of the ether, the
consideration of which becomes superfluous,
disappears. This is expressed by Einstein:1 "The
electric and magnetic fields that constitute light no
longer appear as states of a hypothetical medium,
but as individual realities, which the luminous
sources send into space as in Newton's emission
theory."

If we renounce the mechanical ether of Faraday,
of Maxwell, of Lord Kelvin and of Sir O. Lodge,
and consider nothing but an absolutely empty
space, at every point of which an electric and a
magnetic field may be superimposed, then the
idea of the dematerialization of matter gives place
to that of a materialization of energy. The only
reality that is positively observable and empirically

1 Einstein, Phys. Zeitschr, vol. x, 1909, p. 849. Cf. Campbell,
Phil. Mag. 1910, p. 981.

DEMATERIALIZATION OF MATTER 71

demonstrable is the energy that, at any time, is
localized in a region of space and corresponds to
the two fields, electric and magnetic, which are
at the moment superimposed there, its density
per unit volume being proportional to the
squares of these fields. Nothing prevents us from
considering energy as a substance, endowed in
itself with existence, without the aid of any sub-
stratum whatever. It is therefore convenient,
instead of reducing the inertia of the electron to
the agitation of the ether, to attribute it to the
energy accumulated around it, which forms its
electromagnetic wave system. Moreover we need
not picture the electron as a spherical cell of two
millionths of a w with a surface charge. It is
more natural to suppose either that the density
of this charge gradually diminishes from the center
of the sphere outwards, so that the electron does
not possess a definite surface, or that there is
a uniform distribution of the electric density in
the inside of the volume of the sphere, which implies
a definite contour: in the latter case the same for-
mulae are obtained as in the case of a surface
distribution, with the single difference that all
quantities that play a part in the equations are
multiplied by the factor %.

To sum up, a moving electron appears to us
as a circumscribed region of space, where there is
to be found accumulated electromagnetic energy in
the form of fields,- the intensity and distribution
of which vary as a function of the velocity. The

72 PHILOSOPHY AND THE NEW PHYSICS

mass of an electron can not be attributed to a
material support that does not exist, nor to the sur-
rounding ether, the existence of which is hypothet-
ical, but it is due to its own energy, which consti-
tutes its only substantial reality. But if energy is
inert it is endowed with mass, consequently with
weight in proportion thereto, and, possessing struc-
ture, it becomes a materialized body, while matter
is refined away.

If now, in conformity with Lorentz's theory,
the molecular structures that constitute bodies are
reducible to assemblages of electrons, and if the
electron is inert only because of the energy which
it possesses, material systems are themselves en-
dowed with mass only in proportion to the energy
that they contain. Mass becomes a quantity that
measures their internal energy, and, as foreseen by
Ostwald, the concept of matter is subsumed under
the more general one of energy.

CHAPTER V
THE INERTIA OF ENERGY

12. THE MATERIALIZATION OF ENERGY.

The conclusion stated at the end of the last chapter
appeared as almost an immediate consequence of
a paper by Henri Poincare1 on the longitudinal
contraction of an electron in motion. Taking the
older point of view, that of the partisans of the
mechanical ether, though the point of view thus
taken matters little in this connection, he showed
that this contraction is exactly that demanded for
the maintenance of its equilibrium on the assumption
that the surface charge carried by the moving
electron, the elements of which tend to separate
because of their natural repulsion, is maintained
by a constant pressure of the ether. Assuming
this uniform pressure, the equilibrium configuration
of an electron at rest is that which makes the
potential energy of the actions superimposed on
it — electrostatic repulsions and Poincare pressure —
a minimum. If its shape is that of a sphere of
radius a the total potential energy of an electron
at rest in equilibrium is given by

(7) E • * * *

h°

1 H. Poincare, La theorie de Lorentz et le principe de reaction
(Archives neerlandaises, 1900, p. 252-278).

73

74 PHILOSOPHY AND, THE NEW PHYSICS

• A comparison of this expression with that
of the initial electromagnetic mass m0 (5) leads
at once to the relation

(8) Wo = KQHQ EQ.

According to the relation between the two
coefficients KQ and ^o deduced by Maxwell from the
comparison of the two systems of C. G. S. units,
the electrostatic and electromagnetic, namely,

where V represents the velocity of light, the ex-
pression (8) becomes

Tjl

(9) Wo = Y*

The initial electromagnetic mass of an electron
at rest is equal to its total potential energy divided
by the square of the velocity of light. As the potential
energy represents the only energy that an electron
at rest can have, it is seen immediately that, the
velocity of light being taken as unity, the mass of an
electron at rest is equal to its total energy, of which
it may serve as a measure.

This result may be generalized. If the elec-
tronic theory of matter were confirmed, it would be
applicable to all material systems at rest, since
they could be reduced to assemblages of electrons
without material support. However it may be con-
cerning this last point and postponing the question
of the structure of the positive centers, whether
material or not, Lorentz has shown that the rela-

MATERIALIZATION OF ENERGY 75

tivity principle requires: (1) the longitudinal con-
traction of all bodies in the direction of their

translation in the ratio Vl — 02; (2) that the change

m0
of mass with the velocity, m = ,r-^=^, established

first of all for electromagnetic inertia, applies in
general to all bodies, as if their mass, like the forces
of • elasticity and cohesion, were purely of electro-
magnetic origin. It follows therefrom that the
relation (9) must be applied to all material systems
at rest as if the electronic theory were correct.
This relation may be extended to all bodies
and material systems in motion. The same rela-
tion that exists between the masses m0 and m of
the same body observed by observers 00 at rest
with respect to it and by observers 0i in motion,
must exist, by virtue of the relativity principle,
between the energies E0 and E of the same system
observed simultaneously by 00 and Oi, so that we
have

By virtue of (6)and (10), the relation (9) leads

A

to the generalization already stated, namely,
(11) M = ~

The quantity Vl — j32 being always less than one,
it follows from (10) that the energy of a body set
into motion without deformation is, for observers
connected with it, greater than when it is at rest.

76 PHILOSOPHY AND THE NEW PHYSICS '

The difference represents, by definition, the kinetic

EQ

energy; and the two terms "^ and mQV2, of

which it is the difference, are nothing but two meas-
ures of -the total energy of the same body, made suc-
cessively by observers in motion and at rest.

To sum up, the existence of convection cur-
rents, foreseen theoretically by Maxwell and realized
experimentally by Rowland, led J. J. Thomson,
Max Abraham, and Lorentz to study theoretically
the laws of variation of the inertia of an elec-
trified particle in motion. The discovery of cath-
ode particles permitted Kaufmann and Bucherer
to verify these theoretical anticipations and to
reveal the existence of grains of resinous (negative)
electricity or electrons, the inertia of which is solely
of electromagnetic origin and obeys the preceding
theoretical laws. Starting from this result Pom-
care has shown that the initial mass of an electron
in equilibrium and at rest is equal to its total
potential energy divided by the square of the veloc-
ity of light. The principle of relativity requires,
then, that this result be extended to all systems of
bodies at rest and in motion, so that the formula
M = E/V2, thereafter fundamental, shall hold for
them. Taking the velocity of light as unity, this
formula states that the mass o/ a body is equal to its
total energy, of which it may serve as a measure, and
consequently energy is inert.

The decisive arguments in favor of the inertia of
energy are, however, drawn from considerations

MATERIALIZATION OF ENERGY 77

of another kind. They result from the necessity of
reconciling Maxwell's pressure of radiation with the
principle of relativity and with that of action and
reaction or of the conservation of momentum in a
closed system.1

Maxwell, by starting from the electromagnetic
theory of light, and Bartoli, by starting from the
principles of thermodynamics, foresaw theoretically,
and Lebedew verified experimentally, that all radi-
ation exerts a backward pressure on the source that
emits it in a single direction and a forward pressure
on an obstacle that absorbs it : this is what is called
the pressure of radiation. The inertia of energy is a
consequence of the existence of this pressure, and
brings up the metaphysical problem of the action of
an imponderable on a ponderable in a particularly
acute form.

Let us consider first a material system the motions
of which are due solely to internal actions, such as a
firearm and its projectile. When the shot takes
place the gun undergoes a recoil, that is to say, takes
up a certain momentum which, counted negatively,
represents a loss; the projectile is shot forward and
acquires a momentum which, counted positively, is
equal to that lost by the gun. The conservation of
the total momentum of the system holds at every
instant, and consequently there is no motion of the
center of gravity of the system. The conservation

1 Cf. A. Einstein, Ann. der Phys. vol. xviii, 1905, p. 639. P.
Langevin, L'inertie de Tenergie et ses consequences (Journal de
Physique, juillet 1913, p. 553 et seq).

78 PHILOSOPHY AND THE NEW PHYSICS

of momentum is but a natural consequence of the
instantaneous equality of action and reaction. The
gun recoils because, while it acts on the projectile,
the latter reacts in turn equally on it.

Let us now consider a material source that radi-
ates unsymmetrically in a single direction, such as a
lamp provided with a reflector or a Hertzian exciter
at the center of a parabolic mirror. At the instant
of the emission the source recoils as a consequence
of the pressure of radiation : there is a loss of momen-
tum. If the radiation encounters an obstacle that
absorbs it, it will communicate to it an impulse,
that is, a momentum equal to that lost at departure
by the source. The action experienced by the
obstacle will be equal in magnitude to the reaction
undergone by the source.

Does this mean that the principle of the conserva-
tion, of momentum or of action and reaction is safe-
guarded? Certainly not, for it is not so at every
instant from the start. A certain interval of pro-
pagation elapses between the time when the radia-
tion is emitted and that when it is absorbed, during
which the momentum lost by the source and the
reaction that the latter undergoes remain uncompen-
sated. This compensation would never take place
if the radiation were propagated to infinity without
encountering matter absorbing it. In this case
there would be a definite loss of momentum and the
center of gravity of the system formed by the source
and the radiation would take an absolute motion,
which is contrary to the relativity principle.

MATERIALIZATION OF ENERGY 79

If this principle is to be safeguarded and at the
same time those of the conservation of momentum
and of action and reaction, the system source-
radiation must be assimilated to the material
system of the fire-arm and its proj ectile. The radia-
tion must be treated as a material projectile, that is,
it must be regarded as representing a certain mo-
mentum equal to that lost by the source, so that the
reaction that the source undergoes is the natural
effect of the action exerted on it; only in this case will
the center of gravity of the system remain fixed and
the relativity principle be satisfied. This is what
Henri Poincare has not hesitated to do. He was
the first one to introduce the idea of electro-magne-
tic momentum of radiation to save Newton's
principle of action and reaction, which is sacrificed
in Lorentz 's theory.

But momentum means, by definition, mass in
motion, in virtue of the vectorial relation

g = mv.

The projectile carries away in its motion a part
of the initial mass of the loaded fire-arm, which is
diminished by just so much: that is why we have
instantaneous equality of action and reaction,
conservation of momentum and a stationary center
of gravity of the system. Hence, if radiation is a
vehicle of momentum, it must carry away with it a
part of the initial mass of the radiating material
source. It must be possible to assimilate literally
the sdurce-radiation system to that of the firearm-

80 PHILOSOPHY AND THE NEW PHYSICS

projectile, as also in the case of a radium atom dur-
ing its transmutation when it spontaneously divides
into a helium atom and a niton atom by a sudden
explosion that projects the helium atom and the
niton atom with equal momentum in opposite
directions. After we have discussed the structure
of radiant energy, which tends to make the radiation
assume the characteristics of a corpuscular emission,
the preceding assimilation will appear less bold.
Hence if radiation carries away momentum it must,
just like electric energy, possess electromagnetic
mass apart from any material substratum.

Let us determine quantitatively the momentum
and the Maupertuisian mass that must be thus
attributed to radiant energy, to safeguard the
principle of action and reaction and the relativity
principle.

In the case of a plane wave, the electromagnetic
momentum is in the direction of propagation and
at right angles to the plane of the wave containing
the two fields, the electric and the magnetic. By
taking into account the fact that in this case the
two fields are mutually perpendicular, it may be
shown that the density g, per unit volume, of the
momentum has the value

where V represents the velocity of propagation of
the plane wave, which is equal to that of light.
Since on the other hand, the density, per unit

MATERIALIZATION OF ENERGY 81

volume, of the electromagnetic energy has, by virtue
of (7), the value

# -^ +*£-'- 3*

the result for the density of momentum becomes

(14) g = ~ •

The electromagnetic momentum per unit volume is
equal to the electromagnetic energy divided by the
velocity of light.

To this momentum there corresponds a Mau-
pertuisian mass by virtue of the vectorial relation
g = mv.

The magnitude of this mass is, by definition, the
momentum divided by the velocity, which, in this
case, is that of light,

If we replace g by its value E/V from the relation
(14), we get

(15) M=y-*

Free radiation has a mass equal to its energy
divided by the square of the velocity of light. Since all
forms of energy may be transformed into radiant
energy, the preceding result may be generalized as
follows: every form of energy E possesses a certain
coefficient of inertia determined by the preceding
formula. Contrary to the fundamental principle

82 PHILOSOPHY AND THE NEW PHYSICS

of the dualistic theory energy of any form whatever
is inert.

The identity of the formulae (11) and (15) shows
that the mass of a body and radiant energy are
equivalent quantities, capable of being converted
one into the other, as heat and mechanical work are.
If a body radiates energy, the radiation emitted
carries away a part AE/V2 of its initial mass, and
when an obstacle absorbs this radiation its previous
mass is increased by the entire Maupertuisian mass
AE/V2 of the absorbed radiation, whence:

Any. change AE of the internal energy of a material
system, due to emission or absorption of radia-
tion, is accompanied by a proportional variation
of its mass in accordance with the relation:

(16) AM =

V

If we examine closely this enunciation of the
proposition as to the variation of the mass of bodies
as function of their velocity, it follows, contrary
to the third and fourth postulates of the dualistic
doctrine, that: the mass of a body is not invariable;
it increases or it decreases according as the body ab-
sorbs or radiates energy, and as it is in motion or at
rest with respect to the system to which it is referred.

The last postulate of the dualistic theory is
therefore necessarily unsound. In an isolated sys-
tem, the different parts of which exchange energy,
the individual masses of the bodies present are not
conserved; it is only the total inertia of the system

MATERIALIZATION OF ENERGY 83

(the constant sum of the variable inertia of the
bodies and the variable inertia of the radiation)
that is conserved, provided the system does not per-
mit any exchange with the outside. The principle
of the conservation of mass of material bodies is
no longer valid by itself: it is replaced by the more
general principle, which alone is valid, of the con-
servation of the total inertia of an isolated system.

How are we to evaluate this total inertia? An
inspection of (9) and (10) shows that the total
energy of a body, at rest as well as in motion, is
equal to the product of its mass by V2. If the
velocity of light in a vacuum is taken as the funda-
mental unit, it follows that the mass of a body is equal
to its total energy, a statement that translates the
identity of the nature of mass and energy into a nu-
merical equality; or, better still, the mass of a body
measures its internal energy.

The total inertia of an isolated system, which
neither loses nor receives energy, is, therefore, equal
to its total energy: the internal energy of the bodies
present, the kinetic energy of these bodies, the energy
of free radiation. The principle of the conservation
of the total inertia of a system goes back, therefore,
to the principle of the conservation of energy, into
which the principle of the conservation of mass is
henceforth absorbed. In the new dynamics of
relativity, there exist only two fundamental laws
of invariance : that of the conservation of energy and
that of the conservation of momentum. The first
leads to the assumption of energy localized outside

84 PHILOSOPHY AND THE NEW PHYSICS

of bodies; the second leads to the assumption
of the existence of electromagnetic momentum in
free radiation and consequently of the inertia of
energy. These two laws are not independent. If
we were to adopt Minkowki's terminology of the
" world' ' where the phenomena are referred to four
interchangeable axes, implying four homogeneous
coordinates, three of space and one of time, these
two laws would appear as two different aspects of
one single law, that of the conservation of the world
impulse.

Lastly, as a consequence of the exact proportion-
ality between mass and weight shown by Eotvos,
from the inertia of energy follows its weight in
proportion thereto: a change of internal energy
would at the same time be accompanied by a change
of mass and a change of weight. Since it is easier
to measure the weight than the mass of a body, the
weight of a body might serve to measure its internal
energy.

13. THE EVALUATION OF THE INTERNAL ENERGY
OF BODIES AND THE VARIATIONS OF MASS.

From the inertia of energy the abandonment of
the dualistic theory and numerous special conse-
quences result.

1. Evaluation of the internal energy of bodies.

Whenever a body loses heat or changes its dimen-
sions under the influence of internal actions alone,
it performs thermal or mechanical work that
corresponds to a loss of some of its energy. The

INTERNAL ENERGY 85

internal energy of a body was formerly defined as
the total work it could perform as a consequence
of cooling without limits, or of extension or con-
traction without limits, according as the molecular
forces are attractive or repulsive. There was no
way of evaluating such a quantity of energy;
changes only of internal energy could be measured
by the work performed in starting from an initial
condition.

On the other hand the formula ra0 = E/V2 pro-
vides a very simple method of evaluating this energy
of intermolecular and intra-atomic nature. It is
equal to

for a body at rest for those who observe it. This
relation shows that a gram of matter at rest and
at the temperature of the absolute zero corresponds
to the presence of an internal energy equal to 9 X
1020 ergs, that is, an energy equivalent to the heat
furnished by the combustion of 3 X 109 grams or
3,000,000 kilograms of anthracite.

Let us call the energy of a body thus evaluated
for the temperature T = 0 and the state of rest
latent energy. This enormous energy is nearly
entirely of intra-atomic nature. In fact, at the
absolute zero the degrees of freedom of the mole-
cules are, as it were, anchylosed by the frost. On
the other hand the physical molecular forces and
the chemical atomic forces put in action a quantity
of energy only very small compared with this

86 PHILOSOPHY AND THE NEW PHYSICS

enormous reserve of latent energy, as can easily be
calculated. The changes of mass 'that result from
the presence or absence of heat or kinetic energy or
the presence of radiation within a body are practi-
cally imperceptible, except in the case of radioactive
transformations, where the intra-atomic energy
again comes into play.

2. Change of mass with temperature. — The same
portion of matter, taken at twro different tempera-
tures, may pass from one to the other by emission
or absorption of radiant heat. The change of
mass resulting therefrom may be evaluated by
dividing the heat exchanged with the outside by
V2. To calculate the order of magnitude of the
effect anticipated, water may be taken, the heat
capacity of which is especially large. A mass of
water, having at 0° an inertia equal to 1 g., will have
a larger inertia at 100°. The difference is obtained
by dividing the heat absorbed, 100 gram degree
calories or 4.18 X 109 ergs, by F2, which in the same
system of units is equal to 9 X 1020, which gives
about 5 X 10~12, that is to say a quite imperceptible
change.

Nevertheless this example shows that, from the
theoretical point of view, the idea of mass must not
any longer be confused with that of quantity of
matter, as was done by Newton. Two masses of
water of equal inertia, one taken at 100° and the
other at 0°, do not contain the same quantity of
matter, since they cease to be equal when reduced
to the same temperature; to put it differently, two

CHANGES OF MASS 87

masses of water containing the same number of
molecules do not have the same inertia unless they
are taken at the same temperature, for then their
energies are equal.

3. Change of mass with velocity.- — The mass of a
body depends on its state of rest or of motion with
respect to given observers. In fact, when a body of
initial mass m0 acquires the velocity v, its mass
increases on account of the kinetic energy acquired
according to (6) :

Its total energy E then becomes

or

v4
E =

From this formula it is seen that the quantity
J^WoV2, called ordinarily the kinetic energy of the
moving body, constitutes only a very small part of
the energy corresponding to the passage from the
reference system O0, in which the body is at rest,
to the system Oi, in which it is in motion. The
quantity of latent energy mQV2 remains hidden to
our senses, which perceive only its exceedingly fee-
ble variation. This formula shows, moreover, that
kinetic energy loses its significance as a special
form of energy, which is inevitable, for if one
reduces inertia to energy one may not in turn reduce

88 PHILOSOPHY AND THE NEW PHYSICS

part of energy to inertia. This is why all forms
of energy are functions of the velocity and grow
with it.

4. Change of mass with radiant energy. — If the
space comprised within a material enclosure is
filled with black radiation corresponding to a given
temperature, the mass M of the system will be, by
virtue of the inertia of the radiation, larger than
it would be without the latter: this excess mass is
proportional to the total energy of the radiation.

5. Change of mass in chemical reactions.- — We
have already seen that the principle of the con-
servation of mass, if applied to the individual
masses of the bodies present in a closed system,
is generally erroneous. In particular, there is no
conservation of the mass of the bodies in chemical
reactions or in radioactive transmutations.

Chemical reactions being all exothermic or endo-
thermic, it follows that, by virtue of the relation
deduced from (16),

(17) A#o = Aw0F2

the sum of the masses of the elements combined does
not remain constant.

Take, for example, the formation of water start-
ing from its elements taken in the gaseous state.
The combination of 2 grams of hydrogen with 16
grams of oxygen sets free 69000 gram-degree
calories, equivalent to about 3 X 10 12 ergs. We
would not obtain 18 grams of water, because the
heat liberated in the form of radiation carries with it

CHANGES OF MASS 89

a loss of mass equal to J£ X 10~8 grams, this being a
difference of one-fifth of a billionth (.2 X 1Q-9)
between the mass of the detonating gas and that of
the water that it can form at the same temperature.
6. Change of mass in radioactive transformations. —
The same will hold true of the transformations
of radioactive bodies. The initial mass of one of
these bodies and the total mass of its disintegration
products at the end of a certain time will not be
equivalent, the transformation being accompanied
by radiation. It is known that one gram of metallic
radium sets free 130 calories per hour while it is
transformed into radium D and helium, through the
successive forms of emanation, radium A, B, C.
Taking into account the fact that the mean life of
an atom of radium is about 2600 years, it may be
computed that the complete transformation of one
gram of radium into helium and radium D would
liberate an energy equal to 1.1 X 1017 ergs. The
emission of this energy would correspond to a
difference between the initial mass of the radium
and that of the radium D and the helium, equal, per

gram, to

i i v in17

A • ^> 1 o vx i r\ 4

Am° = -9x16*-

The disintegration of radium into helium and
radium D represents merely one step of the trans-
formations that start from uranium and end with he-
lium and lead. The complete disintegration of a
given quantity of uranium into helium and lead
would represent a loss of mass exceeding one-ten-

90 PHILOSOPHY AND THE NEW PHYSICS

thousandth of the original uranium. The fraction
of the mass thus transformed into radiant energy is of
an order of magnitude much greater than in the case
of chemical reactions. It may be presumed that it
comes from the latent energy of the uranium, that is,
from its intra-atomic energy. If we could succeed
in establishing exactly, to quantities of the order of
magnitude 10~4, the relation of the masses in the
case of radioactive transformations, it would be
possible to verify the identity of mass and energy.
To sum up, energy is inert and the mass of a body
is equal to its internal energy which it serves to
measure. This internal energy represents at the
absolute zero an enormous accumulation of intra-
atomic energy. According as a body acquires or
gives up energy, its mass increases or diminishes.
It is greater when the body is in motion than when
it is at rest, greater when hot than when cold, when
electrified than when discharged, it changes in chem-
ical reactions and in a more perceptible way in ra-
dioactive transformations. The principle of the
conservation of mass formulated by Lavoisier is true
only as a first approximation : it becomes merged in
that of the conservation of energy.

CHAPTER VI
THE WEIGHT OF ENERGY

14. THE WEIGHT OF ENERGY; ITS EXPERIMENTAL
VERIFICATIONS.

The experiments of Eotvos show that if energy
is inert it must have weight in proportion thereto.
If this were not so, a certain quantity of uranium
and its disintegration products, helium and lead,
would have equal weights but different masses,
and consequently, would not be given the same
acceleration under the action of gravity. There
would have to exist at one and the same spot diff-
erences equal to at least one-tenthousandth in the
values corresponding to the acceleration of gravity,
and this seems to be capable of measurement.
Thus energy possesses not only an inert mass, but it
possesses also a ponderable mass /* = E/V2. In
accordance with what is true for inertia, a change in
internal energy is accompanied by a simultaneous
change of mass and weight. A body is heavier when
in motion than when at rest, when hot than when cold,
when in a state of electrification than when neutral,
detonating gas than the water it produces, uranium
than its disintegration products.

Langevin1 sees an experimental proof of the

1 P. Langevin, Journal de Physique, juillet 1913, p. 584.

91

92 PHILOSOPHY AND THE NEW PHYSICS

inertia and of the weight of internal- energy in the
departures from Prout's law. This law states that
the atomic weights are integral multiples of the
same quantity. While it is reasonably exact,
nevertheless the weights do present slight irregulari-
ties with respect to this law. These departures
would be caused by changes of internal energy
through emission or absorption of radiation ac-
companying the formation of atoms from the dis-
integration of primordial elements, as seen in
radioactivity or the inverse process of integration,
not as yet observed, with the formation of heavy
atoms. The sum of the weights of the atoms thus
formed would differ from that of the atoms trans-
formed, by a quantity equal to the change in
energy divided by the square of the velocity of
light. These departures are such that the energy
put into play would be of the same order of magni-
tude as that actually observed in the course of
radioactive transformations. If, for example, the
atom of oxygen resulted from the condensation of
16 atoms of hydrogen or four atoms of helium, it
would be sufficient for an explanation of the atomic
weight 15.87 being less than 16, to assume that this
condensation is accompanied by a loss of energy
only five times greater than that set free during the
transformation of one atom of radium into radium
D. The interest of such an explanation of the
departures from Prout's law is to make the hypothe-
sis of the unity of matter possible, that is, the hypo-
thesis that all atoms are composed of one primordial

WEIGHT OF ENERGY 93

element or several such, and this can not be recon-
ciled with these departures so long as the principle
of the conservation of mass in chemical reactions
is assumed.

Energy possessing a ponderable mass and the
inertia of a body being nothing but the inertia of
its internal energy, Newton's law expresses in
reality the law of attraction of energy by energy.
We shall see what follows from this for free radiation
and consequently for luminous radiation.

Radiation propagated freely in a vacuum repre-
sents, per unit volume, a certain energy density E
and a certain electromagnetic momentum equal
to E/V. It follows therefrom that it possesses
an inert mass, defined as the momentum divided
by the velocity, E/V2. If every inert mass implies
the existence of a ponderable mass in proportion
thereto, a light ray will have weight; it will be
attracted by a mass situated in its neighborhood
by virtue of Newton's law. It will be deviated in a
gravitational field in proportion to the angle be-
tween the direction of the ray and that of the force
of attraction. Einstein1 has calculated the magni-
tude of this deviation and, in 1911, arrived at the
formula

2KM
a =

where a is the deviation of the ray passing by a
spherical mass M (for example the mass of a star),

1 Einstein, Ann. der Phys. vol. xxxv, 1911, p. 898.

94 PHILOSOPHY AND THE NEW PHYSICS

K the constant of gravitation, R the distance from
the center of the sphere to the ray. For a ray
passing in the neighborhood of the surface of the
Sun, a becomes equal to .S3", which constitutes a
quantity that can be measured, by observing, for
example, the position of a star near the edge of the
Sun at the instant of a total eclipse.

By virtue of Einstein's equivalence principle,
luminous radiation in the interior of a system that
undergoes an acceleration must behave like a pro-
jectile; instead of describing a straight line it will
describe a parabola. Observers enclosed in Jules
Verne's cannon ball, which would fall with accelera-
tion, could therefore by the aid of optical experi-
ments detect the state of acceleration of the system,
without otherwise knowing whether they should
attribute it to the presence of a gravitational field
or to the state of acceleration of their cannon ball.

The equivalence between the inert mass and
the ponderable mass carries with it the equiva-
lence of the effects produced on physical phenomena
by a field of gravitation and those due to a suitable
state of acceleration of the reference system to which
they are referred. It must follow therefrom that the
potential of gravitation acts on the passage of time
and the dimensions of bodies in the same manner as
acceleration. Now it follows from the Lorentz
group that a body is the more contracted in the
direction of its translation for observers 00 who see
it pass and that the velocity of the phenomena that
take place in it, measured by these same observers,

WEIGHT OF ENERGY 95

is the more retarded, in proportion as its velocity is
more accelerated relatively to them. In the same
way, a body will be the more contracted and the
march of the phenomena, of which it is the seat, the
more retarded, in proportion as the potential of gravi-
tation of the place where it is found is increased.
Two equal chronometers placed at unequal distances
from the Sun will go at different rates, and the
more distant one will run ahead of the nearer. Now
a chemically defined molecule that, by virtue of its
oscillations, emits a given spectral light constitutes
a chronometer of atomic dimensions. If, therefore
two identical molecules at positions of different
gravitational potential are observed with the aid
of a spectroscope, one on the surface of the Sun
and the other on the surface of the Earth, the os-
cillations of the second being more rapid than those
of the first and consequently the frequency of the
light that it emits being greater, it ought to be
found that the ray emitted by the second is displaced
in the spectrum, with respect to the ray emitted by
the first, in the direction of the violet. Knowing
the difference of the potential of gravitation at the
surface of the Sun and at the surface of the Earth,
it is easy to calculate that the difference in the wave
lengths of the spectral rays ought to reach about
Koo Angstrom unit, that is, one-millionth of a
micron, which is a quantity accessible to experiment.
It is remarkable that displacements of this order
have actually been observed by Fabry and Buisson
by comparing the Fraunhofer rays of the solar

96 PHILOSOPHY AND THE NEW PHYSICS

spectrum with the corresponding rays of a ter-
restrial source.1

15. THE GENERALIZED PRINCIPLE OF RELATIVITY
AND ELNSTEIN'S THEORY OF GRAVITATION.

The relation /* = E/V2 shows that the laws of
the conservation of weight are the same as those
of the conservation of energy. Now the weight of
a body in a gravitational field changes when it is
displaced in the field: it increases when the body
is raised. To this increase in weight there must
be a corresponding increase in energy equivalent,
to the work expended against the weight in raising
the body. This change of energy carries with it,
in virtue of the formula M — E/V2, either a change
of mass or a change ^of the velocity of light in the
gravitational field at the point considered. This
is the starting point of the new theories of gravi-
tation according to the relativistic ideas.

G. Mie2 has developed a theory in which he
, makes the mass but not the velocity of light depend
on the potential of gravitation. He thus safe-
guards the postulate of the constancy of the veloci-
ty of light required by the relativity principle,
but he is obliged to renounce the equivalence be-
tween ponderable mass and inert mass established
by Eotvos. G. Nordstrom3 has sought to maintain

1 Cf. Freundlich, Phys. Zeitschr. vol. xv, 1914, p. 369.

2 G. Mie, Ann. der Phys., vol. xc, 1913, p. 25; Phys. Zeitschr.,
1914, p. 115 and 169.

3G. Nordstrom, Phys. Zeitschr., 1912, p. 1126; 1914, p. 375,
604; Ann. der Phys., 1913, p. 533, 856; 1914, p. 1101.

THEORY OF GRAVITATION 97

the postulate of the constancy of the velocity of
light and the proportionality between ponderable
mass and inert mass over the widest range, but he
is compelled to assume a change in the length of
bodies and in the rate of phenomena, as a function
of the potential of gravitation, which does not agree
with that predicted by the Lorentz group. Einstein
also has resigned himself to abandoning the con-
stancy of the velocity of light in a field with varying
potential and to assuming that it varies with posi-
tion according to the formula

(19) V m 70(l + Y

where <j> represents the magnitude of the Newtonian
potential at the point considered. The Lorentz
group is then applicable only to regions where the
potential of gravitation is constant, or, what in
virtue of the equivalence principle comes to the
same thing, to systems in uniform translatory
motion.

Einstein1 has sought a group of transforma-
tions, having that of Lorentz as a special case,
and such that the equations of the field of gravi-
tation can be reduced to the form that those of a
system without gravitation have, when referred to
a reference system in a state of acceleration. The
discovery of this group, for which he was indebted
to the absolute differential calculus, created by

1 Einstein, Die formalen Grundlagen der allgemeinen Relativi-
tats theorie (Ber. Berl. Ak., vol. XLI, 1914, p. 1030).

7

98 PHILOSOPHY AND THE NEW PHYSICS

Christoffel and developed by Ricci and Levi-Civita,
has enabled him to generalize the relativity prin-
ciple by extending it to any arbitrary motion of
the reference axes whatever, thus bridging the fol-
lowing serious epistemological gap, pointed out by
Mach.

Psycho-physiology teaches us that our senses
make known to us only relative states and changes
of bodies, without ever revealing to us any absolute
state or change. Thus our sight does not reveal
to us the absolute shape and dimensions of a body,
but simply the fact that a figure has such a shape
and such a size relatively to another taken as com-
parison term, this purely relative shape and size
not being altered in any dilatation or any continu-
ous transformation whatever of the universe. In
the same way, we do not perceive Newton's absolute
space, to which we might refer all moving objects,
but merely the relative state of rest or motion of
bodies. Similarly our thermal sensibility does
not teach us anything about the absolute tempera-
ture of bodies, but only about the changes in the
states of affairs as regards heat losses between our
skin and the surrounding medium. If, therefore,
we wish to confine ourselves to the data of sense
perception, we must not in natural philosophy
speak of absolute velocity, acceleration or inertia.

Classical mechanics does not satisfy this require-
ment. It succeeds in preserving the relativity of
velocities,^but it concedes an absolute sense to the
idea of acceleration and to that of inertia, con-

GENERALIZED RELATIVITY 90

sidered as capacity of resistance to acceleration of
a body. According to these principles the motion
of two masses isolated in space and sufficiently
close to be able to exert actions on each other,
would be governed by Newton's law of attraction,
independently of the system of fixed stars to which
it is referred; for: "It would be," says Euler, "a
very strange proposition and contrary to a host of
other dogmas of metaphysics, to say that the
fixed stars influence the inertia of bodies."1 But,
in fact, we perceive merely relative distances of
bodies: hence we can only observe and define the
relative velocities and accelerations of bodies,
that is to say, the first and second derivatives
of their distances. Consequently the inertia of
a body can only be defined as its resistance to the
relative accelerations which it experiences with
respect to other bodies that do not participate in
its state of motion. The inert mass of a body
appears, therefore, as a relative quantity, which
depends on the distribution of the masses about
this body and on their state of rest or motion with
respect to it: it will be greater, the greater the
number of other masses in its neighborhood, which
do not participate in its state of acceleration;
it will disappear in the opposite case. A body
is inert because it is surrounded by other bodies.
Its inertia results from the mean action of all
masses distributed in the universe, so that, con-
trary to Euler's assertion, the fixed stars do deter-

1 Euler, Reflexions sur 1'espace et le temps, p. 328.

100 PHILOSOPHY AND THE NEW PHYSICS

mine in part the inertia and the motion of the
Earth. The principle of inertia thus loses all
absolute sense: it becomes a relative and statistical
principle.

To put our physical conceptions into accord with
the data of our sense perception, and to set natur-
al philosophy free from metaphysical entities that
encumber it, such as the ideas of absolute space
and privileged axes, it is desirable to state the laws
of physics in an intrinsic language, independent
of any reference system, just as Euclid's geometry
as compared with Descartes' is an intrinsic language
free of the consideration of coordinates. For this
purpose it does not suffice to make the form of the
physical laws independent of the state of uniform
translation of the coordinate axes; it must be made
independent of any motion whatever of these axes;
or, in Minkowski's geometrical language, it must
be possible to refer them in four dimensional space
to a system of oblique axes or a system of curvi-
linear coordinates, as well as to a rectangular system
formed by rectangular coordinates.

Einstein's will be the glory of having succeeded
in satisfying this last condition, by giving to the
physical laws a universally invariant form, or, as
we say nowadays, co variant for any change of coordi-
nate axes. To accomplish this generalization of
the relativity principle, Einstein started from the
equivalence principle, deduced by him from Eotvos'
experiments on the strict proportionality of the inert
mass and the gravitational mass of bodies, which

GENERALIZED RELATmiS: 101

states the impossibility of distinguishing the effects
of a field of gravitation from those of a field of mo-
tion. The effects produced by a field of gravitation
can always be interpreted by a state of acceleration
of a body removed from any field of force, and con-
versely. From this it follows that the existence of
a field of gravitation in empty space is purely re-
lative; it depends on the problem, insoluble by ex-
periment, of finding whether the system from which
it is observed is at rest or in accelerated motion;
the real field for a system considered at rest will be
fictitious for other systems in motion which the gen-
eralized relativity principle declares equivalent
to the first. Einstein then shows that the form of
the physical laws may be rendered independent of
any system of privileged axes, provided the quanti-
ties characteristic of the field of gravitation are
made to appear in the physical laws; or, more pre-
cisely, provided these laws be considered as relations
between the quantities characteristic of material
phenomena and the quantities characteristic of the
field of gravitation, these quantities being tensors,
and matter designating everything that is super-
imposed on the field of gravitation. These rela-
tions, being invariant for every transformation of
the reference system, are intrinsic equations, ex-
pressed with the aid of tensor equalities, from which
every coordinate system has disappeared.

This theory involves remarkable consequences.

It appears at first as a universal relativism ex-
pressed with the aid of an absolute calculus. The

102 I'HJLOSOPHi' AND THE NEW PHYSICS

metrical properties of space, the kinematical and
dynamical properties of mechanical systems, the
physical properties of any region whatever of space
vary according to the point of view of the observer.
These properties depend, in fact, on the field of
gravitation and the state of motion of the system
from which they are observed.

The influence of gravitation is exerted on every
physical process, on all matter including the electro-
magnetic and luminous field. Conversely, it has
its origin in every region of the universe where the
material tensor is different from zero. Since the
material tensor corresponds to a reality, gravitation
also involves a real element with which a fictitious
field of gravitation, equivalent to an arbitrary
motion in empty space, may always be 'combined.

Empty space is not the absolute and infinite
void of Newton's followers: it is the pure field of
gravitation on which no matter is superimposed.
From the physical point of view there is no amor-
phous void, endowed with pure receptivity, in
which material points could be imagined, attract-
ing or repelling one another according to certain
laws, like Newton's law, and thus communicating
absolute accelerations to one another. We can not
speak of empty space, except where there is a field
of gravitation, not merely coexistent with this
space, but veritably the creator of space, of its
metrical properties, and, we may say, its extent.
The world must be thought of no more as an as-
semblage of bodies lost in an infinite void, but as

GENERALIZED RELATIVITY 103

systems of bodies and of electromagnetic or lumin-
ous fields, superimposed on gravitational fields of
finite dimensions. The absolute, void, amorphous,
and infinite space of Newton vanishes like other idola
fori; and Kant's antinomies advanced in regard to it
are abolished as referring to a pseudo-problem.

To fathom the meaning of this universal rela-
tivism, it will be well, at this stage, to contrast
the ideas of Einstein and those of Lorentz.

For Einstein there is no infinite void, no motion-
less ether, no uniform course of time, and conse-
quently there are no privileged reference systems
and clocks; there is no region of space enjoying
absolute physical properties. The Lorentz con-
traction is not true in the sense that it corresponds
to an absolute deformation, a body not having any
shape except relatively to another. It is a recipro-
cal semblance of reality, arising from local time,
from the fact that the clocks of observers connected
with one body and those of observers in motion
with respect to it, do not go at the same rate.
The distinction between reality and semblance
vanishes: there are only relative truths, science
being unable to establish anything but comparisons,
by ascertaining coincidences and by comparing
colors (frequencies of radiating sources serving as
clocks). The only absolute reality that it can
attain consists of the laws of physical phenomena,
expressed by intrinsic equations by the aid of tensor
equalities, the form of which is independent of
every system of space and time coordinates. If

104 PHILOSOPHY AND THE NEW PHYSICS

God exists and it should please him to recount the
history of the world in the extrinsic and artificial
language of time and space, it would be merely by
an arbitrary decree of his free will in a complete state
of intellectual indifference that would make him
choose, once for all, a system of space coordinates
and a clock (that is, a radiating source connected
with this system and consequently regarded as at
rest). Having thus fixed arbitrarily the meaning
of simultaneity and order of sequence of events, he
could establish their universal chronology.

The ordinary distinction between semblance
and reality would, on the contrary, exist for an
infinite intelligence, if there be, as Lorentz is in-
clined to believe, an ether which is motionless
but otherwise of a nature unknown to us, but it
would be very different from the mechanical ether
of Faraday, Lord Kelvin, and Sir Oliver Lodge.
There would, therefore, be for an omniscient intelli-
gence a privileged reference system and clock,
whatever the system of axes, provided it be con-
nected with the ether, and whatever the clock at
rest, provided it be free from the influence of
gravitation. This omniscient mind could with
propriety speak of absolute motion, order of succes-
sion, and synchronism. The Lorentz contraction
and the retardation of clocks would appear to him
as physical phenomena, due to the connections
between matter and ether, by which an action is
exerted by the latter on the former. But this
privileged set of three reference axes and this course

GENERALIZED RELATIVITY 105

of absolute time would be concealed from us forever
as a consequence of the same action of the ether on
the bodies, which would be precisely such as to
prevent us from discovering their absolute motion.
The observers 00 would have no better ground for
saying they were at rest and recording true time
than the observers Oi. Any experimenter whatever
could always explain what he observes by supposing
either that he is at rest in the ether or that his
laboratory is traversed by an ether current which
produces the effect of shortening his instruments
and retarding his clocks, or that there is no ether at
all but it is the motion of a rod or a clock in his
laboratory that produces the shortening of the one
and the retardation of the other.

According to the pragmatist theory of truth
the two concepts, that of Einstein and that of Lo-
rentz, are equivalent, since they are equally in
accord with phenomena.

On one hand, Einstein's concept, being in accord
with the data of psycho-physiology, by respecting
the conditions of knowledge imposed by our sense
perceptions, by practising the scholastic adage
non sunt multiplicanda entia sine causa, by reliev-
ing physics of metaphysical entities that encumber
it, by delivering us from a swarm of pseudo-prob-
lems, is strictly positive, more economic than that of
Lorentz, and unassailable in itself; on the other
hand, that of Lorentz, by maintaining the ether,
safeguards our old habits of thought, satisfies our
craving for the absolute, sets our minds at rest,

106 PHILOSOPHY AND THE NEW PHYSICS

establishes a bond of union between the physics of
yesterday and that of today, and falls into the
category of explanatory theories, since the shorten-
ing of bodies, the retardation of clocks, the con-
stancy of the velocity of light in a gravitational field
of constant potential are explained by the connec-
tions of matter and ether. But the existence of
the ether is forever rendered problematic by virtue
of the relativity principle. Its nature is unknown
to us, since the mechanical properties with which
Faraday, Helmholtz, Lord Kelvin, Sir Oliver Lodge
endowed it have already condemned it. It does not
seem to represent necessarily the anticipation of
future observations and experiments, like Pasteur's
theory of microbes or the atomic theory; it is merely
a method of exposition, a figurative hypothesis to
uphold the spirit of abstraction, which, useful for
the minds that Duhem called broad and weak, be-
comes superfluous, cumbersome and tiresome for the
minds that he names narrow but profound.

Whatever the outcome may be, Einstein's re-
sults as to inertia, the weight of energy, and the
relativity of phenomena seem permanent acquisi-
tions. The relativity principle represents one of the
norms of physical research which limits the field of
our investigations and determines, in part, the form
of the equations of physics.

16. ASTRONOMICAL VERIFICATION.

The philosophical importance presented by Ein-
stein's theory of gravitation, based on the general-

ASTRONOMICAL VERIFICATION 107

ized relativity principle, should not lead us to forget
the interest attached to its practical results, the
most sensational of which, independently of those
already indicated, is the calculation of the secular
anomaly of the perihelion of Mercury.1

To account for it, Tisserand,2 as is well known,
proposed to replace Newton's law by a more general
formula, similar to Weber's electrodynamical law.
Of all the theories proposed since, none satisfies the
mind like Einstein's theory of gravitation.

According to this theory, there exists no absolute
invariant appertaining to a material point, that is,
the exact equivalent of inert mass or of gravitational
mass in classical mechanics. We have here to do
with a tensorial theory in which the numbers Gab,
characteristic of the field of gravitation, and the
numbers Tab, characteristic of the field of inertia
(ordinary matter and electromagnetic field), form a
covariant tensor. It is possible to attach to these
tensors two relative scalar invariants, G and T,
which may, if desired, be considered by extension as
measures of a gravitational mass and an inert mass.

Let us now consider what follows from this, tak-
ing account of the inertia of energy, in the case of the
attraction of Mercury by the Sun.

In the study of the motion of a material point
attracted by gravitational masses, a quite natural
simplification consists in treating of this point as "a

1 Einstein, Erklarung der Perihelbewegung des Merkur (Ber.
Berl. Ak., vol. xlvii, 1915, p. 830).

2 Tisserand, Traite de Mecanique celeste, vol. IV, p. 500.

108 PHILOSOPHY AND THE NEW PHYSICS

test body" placed in a field of gravitation due to
other masses and not modifying perceptibly the
field of gravitation of these masses. Given two
bodies, an attracting body and an attracted body,
the inert mass of the attracting body (and the same
holds for the attracted body) is increased in pro-
portion with the increase of the potential of gravi-
tation due to other masses. Now the Sun, con-
sidered as an attracting mass occupying a sphere of
radius a, is surrounded with a field of gravitation, so
that it is immersed in gravitational energy. This
energy, always positive so far as concerns physical
reality, is negative in the sense that in order to
produce an attracting mass by condensation of ele-
ments coming from infinity, negative work must be
expended. It results from this that there is less
energy in the neighborhood of an attracting mass
than in the absence of all mass. If, therefore,
we attribute inertia to the energy of gravitation,
as to all the other forms of energy, it follows that,
for a point situated at a very great distance from the
Sun, the mass of the latter will be

M = Mo - AMo,

AM0 representing the correction term due to the in-
ertia of the total field of gravitation. For a point
situated on the orbit of Mercury the effective solar
mass will be equal to

M + AM,

if we denote by AAf the supplementary mass due to
the inertia of gravitation outside of the orbit of
Mercury. It will thus be larger than the principal
mass M.

ASTRONOMICAL VERIFICATION 109

Taking account of these corrections, it is found
that the elliptical motion is transformed into a
pseudo-elliptic motion with a progressive advance of
the perihelion. Applied to the case of the planet
Mercury, the calculation indicates a secular motion
of the perihelion equal to 43". Since the observa-
tions give 45", this aggreement must be regarded as
the more remarkable, because it is obtained, with-
out any supplementary hypothesis, by the applica-
tion and simplification of the general equations
furnished by the theory.

A hardly less remarkable confirmation of the theory of inertia
of energy and of Einstein's theory of gravitation is obtained from
the deviation of light rays in the neighborhood of the Sun. On
account of both the Newtonian attraction exerted by the Sun on a
light ray propagated in its neighborhood and of the curvature
of space produced by the mass of the Sun according to Einstein's
gravitational equations, the path of the ray should not be recti-
linear but curved towards the center of attraction, with a total
deviation given by the expression

4KM

whic,h is just twice the value given by equation (18), p. 93. In
consequence of this it is possible to predict that a star seen near
the Sun should suffer an outward deviation equal to 1.74" and
varying inversely as the distance from the center of the Sun for
the more distant stars, as compared with the position that it
occupies on the celestial sphere in the absence of the Sun, since
the star is seen in the line of its ray, i.e., in the direction of the
tangent to the path of the ray. This deduction has been success-
fully verified by photographing the same region of the sky in the
absence of the Sun and during a total solar eclipse. The negatives
obtained by the two British expeditions undertaken for this purpose
in the zone of the total solar eclipse of May 29, 1919, have given
a mean deviation of 1.79" + .03". This agrees remarkably well
with the value predicted by Einstein.

CHAPTER VII
' THE STRUCTURE OF ENERGY

17. THE SUCCESS OF THE ELECTRONIC THEORY;
THE EXPLANATION OF THE RELATIONS OF
MATTER AND RADIATION.

We have just seen that a body is inert and has
weight in proportion to the energy it contains,
so that the concept of matter is subsumed under
the more general one of energy, and that the princi-
ple of the conservation of mass becomes merged in
that of the conservation of energy. Energy, as
Ostwald would have it, becomes the only existing
reality, into which are absorbed the ether and the
numerous imponderable agents to which the physics
of the beginning of the nineteenth century was
partial. Nevertheless it appears that energy pre-
sents itself essentially in a double aspect: in the
form of resinous (negative) electricity endowed with
a corpuscular structure and in the form of free
radiation. In its first aspect it is made up of
grains of electricity, capable of moving with veloci-
ties ranging from 0 to 7, its aggregates constituting
atomic and molecular structures, relatively stable
and with astonishing vacant spaces, and appearing
to our senses in the form of continuous bodies. In
its second aspect it appears as made up of transverse

no

ELECTRONIC THEORY HI

waves, infinitely expansible and divisible, sweeping
through all space with the uniform velocity of light.
In the first case it takes the name of matter; in the
second that of radiant energy.

The specific character of a portion of matter must
no longer be sought in its mass and its weight,
since radiant energy is likewise inert and endowed
with weight, and mass is no longer an invariable
scalar quantity, but takes the character of a tensorial
quantity, which is unsymmetric and variable as a
function of the velocity and the internal energy of
bodies. That character must be sought in the
number and nature of the primordial elements
which constitute matter.

These elements, revealed in atomic changes be-
yond the domain of chemistry, are the electrons and
the positive remainders, the latter having a struc-
ture as yet unknown and presented to us in the form
of the positive kernels of helium atoms. These
elements alone remain invariable throughout the
changes that matter undergoes and can serve to
define it.

What are the relations between matter thus
characterized and radiation, and what is the
mechanism of their exchanges of energy? It was
on this point that the metaphysical pseudo-problem
of the action of imponderable on ponderable arose,
and it is to it that the electronic theory of matter
claims to give a satisfactory answer.

Let us, for this purpose, consider again the case
of a charged particle in quasi-stationary motion

112 PHILOSOPHY AND THE NEW PHYSICS

and let us see what happens when it undergoes an
acceleration.

The wave system of the particle in quasi-station-
ary motion is formed by the system of radial
electric lines of force and of circular magnetic
lines of force that it carries with it. It may be,
moreover, considered as the aggregate of the
electromagnetic waves of velocity, emitted at differ-
ent instants in its course, and centered on its former
positions, which envelop one another, so that the
electromagnetic field produced by the displacement
of the particle is determined, not by the instantane-
ous state of the particle, but by all its former states.
The energy of the field thus created is localized
nearly entirely in the immediate neighborhood of
the particle, because the intensity of the field varies
inversely as the square of the distance, and rapidly
approaches zero as the distance from the particle
becomes greater. The waves of velocity which
constitute the wave system of an electron do not
correspond to any energy radiated to a great dis-
tance, since they vanish at infinity. They represent
kinetic energy which accompanies the electron in
its displacement, preserving for a constant velocity
a fixed distribution around it. As space exerts^no
viscous action, no external influence is requiredj to
conserve this energy in motion, and the projected
electron moves indefinitely with the same velocity
in conformity with the principle of inertia, so long
as no external cause modifies its state of motion
and produces acceleration.

ELECTRONIC THEORY 113

Let us examine what happens in the latter case.
In the first place, the magnetic energy of the

e2
wave system, in conformity with the relation ^- v2

ott

which is valid for small velocities, increases or
diminishes by a quantity called energy of change,
which corresponds to a reorganization of the lines
of force of the wave system. In the second place
the change of velocity determines the appearance
of a spherical wave of acceleration, the radius of
which increases with the velocity of light and which
remains centered about the point where the electron
was at the instant of the emission. This wave
corresponds at every point to the passage of an
electric field and of a magnetic field, situated in
the plane tangent to the wave and perpendicular
to each other in this plane. These fields represent
a localization of electric and magnetic energy equal
per unit volume, and this has the effect of giving to
the wave of acceleration all the characteristics of
free radiation.

The fields present in the wave of acceleration
are superimposed on those of the velocity waves.
Since the latter, varying inversely as the square
of the distance, diminish much more rapidly than
the former, which vary simply inversely as the
distance, at a sufficient distance from the electron
only the acceleration wave will exist. The energy
thus radiated to infinity with the velocity of light,
by the radiation which the electron emits during
the time dt, is proportional to the square of the

114 PHILOSOPHY AND THE NEW PHYSICS

charge and the acceleration according to the
relation :

9 /p2-,2

(20) \ *± dt

where, in E. M. U., v denotes the acceleration and
V the velocity of light.

This radiated energy represents the intrinsic
energy of the acceleration wave. It is borrowed
from the external actions which modify the velocity
of the electron. But it represents only a small
part of the energy which the acceleration wave car-
ries at the start when leaving the center. The
latter is the agency by which the electron reorgan-
izes its wave system with the velocity of light,
that is to say, by which the field of the electron
receives the additional magnetic energy necessary
for the increase of the kinetic energy associated
with an increase of velocity, or restores the excess
magnetic energy when its velocity diminishes.
It is through the acceleration wave that the magne-
tic energy of change corresponding to an increase or
a decrease of velocity is distributed to each part
of the wave system or restored in the form of work,
this magnetic energy being in the first case bor-
rowed from external actions and in the second case
restored in the form of work done against the
retarding actions. The energy radiated from the
acceleration wave represents as it were a necessary
shrinkage, a tribute paid to the auxiliary wave for
the service rendered.

ELECTRONIC THEORY 115

The emission of radiation is always connected with
acceleration of electrified particles. It is the difference
in the conditions of electrons present in matter that
enables us to explain the emission of different kinds of
radiation and the phenomena traceable to them such as
mutual induction and self-induction.

Let us consider first these last two phenomena.
Conduction currents are reducible to convection
currents: they correspond to the mass motion
of the free electrons of the metallic or electrolytic
conductors under the influence of a potential dif-
ference, the positive electrons tending to go in
one direction, the negative in the other. If two
wires are placed side by side, such as the two neigh-
boring windings of a transformer, the passage of
the inducing current corresponds to the circulation,
in the first wire, of free electrons of which it is
the conductor. The intensity of the current is
proportional to the ensemble velocity of these
electrons, and any variation of intensity will cor-
respond to an acceleration experienced by the elec-
trons. At the moment when the current varies,
there will be an emission of acceleration waves by the
electrons of the wire. The superposition of these
waves at a point of the neighboring wire will give
rise to. the appearance of an electric field parallel
to the wire and in the opposite direction to the
current if the intensity increases, in the same
direction if it diminishes. In the case when this
point is situated inside of the neighboring wire,
the electric field thus created will determine a

116 PHILOSOPHY AND THE NEW PHYSICS

current, corresponding to the existence of an elec-
tromotive force, the direction of which is given by
Lenz's law.

The phenomena of self-induction are explained
in the same manner. If the intensity of the current
increases, the acceleration waves emitted by the
electrons when their velocity varies will add them-
selves together in the circuit as well as outside, and
produce there an electric field, directed oppositely
to the current, by the agency of which the energy
necessary for the growth of the magnetic field
encircling the circuit is borrowed from the electro-
motive source that produces the current. If the
current diminishes, the accelerations of the positive
particles being opposed to the direction of the cur-
rent, the radiated waves produce in the conductor
an electromotive field in the same direction, by the
agency of which the excess of energy of the magnetic
field, which encircles it, will be returned to the
circuit.

Conduction currents are at basis only con-
vection currents; the explanation of their ' self-
induction must account for the inertia of an elec-
trified particle in motion. This inertia is due to the
production of a magnetic field having its source
in the displacement of the particle, and to the fact
that the energy present in this field must vary with
the velocity by the agency of the acceleration
wave. The force of inertia that the particle
opposes to the change of velocity comes from
the action, on every element of its charge, of the

ELECTRONIC THEORY 117

electric field present in the acceleration waves
emitted by the other elements of this charge.

The character of the free radiation, which mani-
fests itself in the form of Hertzian waves, of light,
of Rontgen rays, and of thermal radiations, depends
on the nature of the electrons that are accelerated
and on the circumstances of their acceleration,
sudden, continuous, or periodic.

A sudden acceleration takes place on the arrest
b^- an obstacle of the cathode particles or the
]8 particles, projected with velocities comprised
between 20.000 km. and 290,000 km. per second.
The radiation consists in a sudden pulsation, a kind
of electromagnetic noise, emitted at the moment of
the arrest of the particle, its thickness being equal
to the product of the velocity of light and the dura-
tion of the shock, that is to say, it is of atomic
dimensions. This extreme thinness explains the
penetrating power as well as the absence of refrac-
tion of X-rays.

The acceleration is periodic in the case of the
electrons that move in closed curves around a posi-
tive center inside the atoms. From it there results
a continual emission of regular waves, the period
of which is equal to the time of revolution of the
electrons. This emission corresponds to light of
a definite wave-length, like that which constitutes
discontinuous spectra.

If the acceleration is due to the chaotic agitation
of the free electrons of incandescent sources, there
result from it radiations of every wave-length,

118 PHILOSOPHY AND THE NEW PHYSICS

which form the continuous spectra of incandescent
bodies.

If the radiation is due to the accelerations which
the free electrons of an opaque metallic enclosure
undergo as a consequence of the thermal agitation
of the molecules that strike them, it constitutes
the heat radiation inside of this enclosure, called
black radiation.

The presence of moving electrons in matter ex-
plains not merely the emission of radiation but also
the laws of its propagation through material media
and those of its absorption.

The absorption of radiation by matter is due
to the fact that the electrons present in the matter
are, under the action of the alternating fields of
the incident electromagnetic waves, set into vibra-
tion in agreement with them. In consequence of
the motions thus" produced, they strike the neigh-
boring material molecules, the kinetic agitation of
which they increase at the expense of their vibra-
tory energy. It is by this mechanism that the
electromagnetic energy of the absorbed radiation
is changed, through the agency of the shocks, into
thermal energy, that is, into kinetic energy of cha-
otic agitation of the molecules of the absorbing
body. It is because of this that a body which ab-
sorbs radiation is heated at the expense of the in-
cident electromagnetic energy, and that its mass
is increased by all the Maupertuisian mass of the
absorbed radiation. In the case of selective ab-
sorption it is not the free electrons but the elec-

ELECTRONIC THEORY 119

trons in a regular periodic motion within the
atoms which absorb, by a resonance phenomenon,
the radiations of a period equal to that of their
motions.

In conclusion, the electronic theory of matter
appears to give an account of the mechanism of the
relations existing between matter and radiation.
By the success of this step, the electronic theory
is correspondingly strengthened. It reinforces
the view that at basis there exists only electro-
magnetic energy, which presents itself in two different
aspects: narrowly circumscribed and concen-
trated in space in the form of elementary charges
in motion, the velocity of which may vary from 0
to V; and in the form of radiation sweeping through
all space with the rapidity of light — in the form of
grains of electricity and in the form of transverse
waves indefinitely expansible and divisible — stabi-
lized in structures of varied and definite architec-
ture, or free to lose itself by radiation to infinity.

The success of the electronic theory and of the
mechanics of relativity reduces finally the prim-
itive pluralism of ponderable matter and imponder-
able agents to the dualism of negative electricity
(possibly also positive), endowed with a corpuscular
structure and of electromagnetic radiation formed of
continuous waves, both of them having inertia and
weight.

120 PHILOSOPHY AND THE NEW PHYSICS

18. CHECK TO THE ELECTRONIC THEORY: BLACK
RADIATION AND THE QUANTUM THEORY.

The electronic theory has nevertheless reached its
limits: it has been revealed as incapable of giving
an account of the law of the distribution of energy
in the spectrum of a black body and of the dimi-
nution of the specific heats of solids at low tempera-
tures, while the classical theory of radiation, due
to Maxwell and Hertz, suffered shipwreck from
certain phenomena of physical optics. To bring
theory and experiment into accord new supple-
mentary hypotheses had to be introduced. Are they
going to modify the previously acquired results, to
give support to a dualism between matter and radi-
ation? Far from it, on the contrary they weaken
it, for they amount to nothing less than endowing
radiant energy with structure, after it has already
been endowed with inertia and weight. In fact they
finally lead to the view that radiation is not a
system of waves infinitely expansible and divisible,
propagated by a hypothetical medium, the ether,
but a projection of matter in empty space with the
velocity of light, in discrete units, emitted and ab-
sorbed by bodies in a discontinuous manner.1

In order to understand the point at issue, we must
begin by defining what black radiation is.

Any body that is not at the absolute zero emits
energy in the form of thermal radiation. When

1 Cf. La thSorie du rayonnement et les quanta (Rapports et dis-
cussions de la reunion de Bruxelles, publics par P. Langevin et M.
de Broglie, Paris, 1912).

BLACK RADIATION 121

unequally hot bodies are placed in an enclosure
observation shows that they finally come to thermal
equilibrium, all bodies in the enclosure reaching
the same temperature. This equilibrium can have
been attained only by exchange of radiation between
the bodies. When it is attained the bodies do not
radiate less, but each of them acquires by absorption
as much as it expends in emission. This result has
led KirchhofT to state the following law on the sub-
ject of thermal radiation: the emissive power of
a body for every kind of radiation and at any tem-
perature is equal to its absorbing power. In the
case of an ideal black body, which completely ab-
sorbs the radiations that strike it, the absorbing
power is equal to unity. We are thus led to seek for
the law of the distribution of radiant energy in
the spectrum emitted by a black body at a given
temperature.

In nature there exists no rigorously black body,
no body that does not reflect or diffuse in part the
radiation that it receives. Kirchhoff has enabled
us^ to get over the difficulty by supplying the
means of realizing a black body artificially. Let
us consider an opaque enclosure and any radiation
whatever that is propagated inside it: it will strike
the wall a first time and will be partly absorbed;
the remaining radiation, reflected or diffused, will
again strike other parts of the wall and be there
absorbed in the same proportion, so that the radia-
tion which escapes absorption will tend rapidly
towards zero. Such an enclosure possesses there-

122 PHILOSOPHY AND THE NEW PHYSICS

fore an absorbing power equal to unity for any
radiation: it realizes the black body.

Let us plunge this enclosure, after having evacu-
ated it, into a bath at constant temperature, so as to
maintain its walls at constant temperature. Ex-
periment proves that the space inside this enclosure
is isothermal, that is, that a thermometer placed at
any point whatever inside of this enclosure, will
finally indicate the same temperature. Any action
on the thermometer placed in 'the vacuum must
be exerted by radiation. In the region where the
thermometer is placed, undulations arriving inces-
santly from different points of the enclosure become
superimposed and form systems of stationary waves
of definite frequency, adapted to the distances ex-
isting between two walls and realizing a permanent
state of extremely rapid changes, the details of
which are beyond our scale of time measurement.
This is what is expressed by saying that the thermal
equilibrium realized in the interior of the enclosure
is a statistical equilibrium. This equilibrium is real-
ized for every kind of radiation separately, and. it
is characterized by the amount of energy that is
contained per unit volume in the space within the
enclosure and by the distribution of this energy
between the different wave lengths of the systems
of stationary waves. It is precisely this energy
density and this distribution of energy in the spec-
trum that has to be determined for black radiation.

This we succeed in doing by the following method.
Experiment proves that the temperature indicated

BLACK RADIATION 123

by the thermometer is independent of the nature,
the shape and the dimensions of the walls of the
enclosure. It follows therefrom that all the direc-
tions are equivalent and that each cubic centimeter
of the enclosure contains the same density of
radiant energy. If we consider in the enclosure
a plane closed contour of one square centimeter
surface, the amount of radiation that passes through
this contour in one second will have a definite value,
proportional to the density of the energy of radi-
ation in equilibrium at this temperature. To study
the composition of the radiation of the isothermal
enclosure, which is identical with that of a black
body and on that account is called black radiation,
it will be sufficient to make a small opening in the
enclosure, so as to collect the radiation that comes
out of it and that we know to be identical with the
radiation which in the isothermal enclosure traver-
ses at every instant a section of equal contour.
By this device we can deduce Stefan's law for the
density of radiated energy: the density of the
total energy radiated per unit time is proportional
to the fourth power of the absolute temperature.
By receiving the radiation in a dispersing apparatus
it has been found, as regards the distribution of
energy in the spectrum, that at a given temperature
the energy radiated shows a maximum for a certain
definite radiation on both sides of which it decreases
rapidly. When the temperature rises the energy
density of each simple radiation always increases,
but the maximum of intensity is displaced towards

124 PHILOSOPHY AND THE NEW PHYSICS

the shorter wave-lengths, that is, for the visible
part of the emitted spectrum, from the infra-red
towards the ultra-violet. The curve of intensities
becomes displaced along the spectrum, mounting
more and more, at first slowly, then with an extreme
rapidity the higher the temperature rises. Wien
has discovered the law of this displacement as a
function of the wave length for a given temperature,
and this determines the distribution curve of the
total energy of the spectrum of a black body: the
wave length corresponding to the intensity maxi-
mum decreases inversely as the absolute temper-
ature, while the intensity of the maximum increases
in proportion to the fifth power of the absolute
temperature.

It remained to express in a single empirical
formula the distribution in the spectrum of the
intensities of the. black radiation for all the tem-
peratures observed: this is what Max Planck has
succeeded in doing, and it is the physical interpreta-
tion of this formula that is the starting point of
the quantum theory.

In the isothermal enclosure thermal equilibrium
exists between the matter of the walls and the
empty space (or ether) in which there is black radi-
ation. The temperature of the walls is due to the
internal agitation of the molecules that constitute
them; the temperature of the empty space is due to
the stationary waves that exist between the walls.
This thermal equilibrium between matter and
radiation is realized by the mechanism previously

BLACK RADIATION 125

described. The molecules of the walls of the
enclosure in their kinetic agitation hit the free
electrons existing in the walls. As a consequence
of these shocks the electrons undergo accelerations
that determine a radiation of all wave lengths,
the electromagnetic energy of which is borrowed
from the thermal energy of the molecular agita-
tion: the temperature of the empty space is increa-
sed at the expense of that of the matter.

Reciprocally, and by a mechanism inversely
symmetrical, the electrons, being subjected to the
action of the radiations, vibrate in resonance with
them. In consequence of the oscillations thus star-
ted they strike the neighboring molecules, the ther-
mal agitation of which increases : the temperature of
the matter is increased at the expense of that of the
empty space. There is thermal equilibrium be-
tween the matter and the radiation, when there is
equality between the exchanges of energy brought
about by means of the electrons.

The aggregate of the material molecules, the
electrons, and the various stationary waves that
exist in the empty space, form a system in statistical
equilibrium to which can be applied the laws of
statistical mechanics, in particular the theorem,
discovered by Maxwell, correctly demonstrated by
Boltzmann, which siims up the properties of such
systems. This is the law of the equipartition of
energy. It states that in a thermal system the
mean kinetic energy is divided equally among all
the degrees of freedom of the system.

126 PHILOSOPHY AND THE NEW PHYSICS

By degrees of freedom of a system are meant the
different motions that it can assume consistently
with the connections to which it is subject. For
example, a material point can move along three
axes, it has three degrees of freedom; a sphere can
undergo a translation parallel to each of these three
axes and a rotation about these axes, it has six de-
grees of freedom. The molecule of a monatomic
gas, like argon, is supposed to have three degrees of
freedom; a molecule of oxygen five; a triatomic mole-
cule six, three degrees of translation and three de-
grees of rotation. If the law of equipartition is
applied to a gas in thermal equilibrium, the vis viva
which, on the average, each molecule" will have, is
proportional to the number of its degrees of freedom :
if, in the statistical equilibrium, a molecule of argon
possesses at a certain temperature the vis viva 3, a
molecule of oxygen must possess the vis viva 5.

This law, which results from the Hamiltonian form
of the equations of dynamics, must be applicable
to the statistical system constituted by the material
walls of the enclosure and the black radiation. It
will be sufficient to count the number of the degrees
of freedom of the system to predict, by this law, the
most probable spectral composition of radiation in
the state of thermal equilibrium, the realization of
which is a necessary physical consequence of Carnot's
principle. We have to consider on one hand the
molecules of the material walls, on the other hand
the various systems of stationary waves possible in
the empty space. Let N be the number of the

BLACK RADIATION 127

material molecules contained in the walls of the
enclosure; the number of their degrees of freedom
being equal to 6, there will be, for the matter, as a
consequence of its discontinuity, only a finite num-
ber of degrees of freedom, namely 67V. Let us con-
sider on the other hand the empty space. It has an
infinite number of degrees of freedom, for there is an
infinite number of systems of possible stationary
waves, the wave-lengths of which lie between oo and
0. Hence, if the law of equipartition among all the
degrees of freedom is applied, the energy will be
found entirely in .the empty space and none would
remain for the matter : equilibrium would cease to be
possible, or rather a single state of equilibrium only
would be possible, that in which the matter is at the
absolute zero. Moreover, the energy received by
the space must be equally apportioned among its
degrees of freedom, infinite in number. Whatever
might be the amount of the total energy, that assign-
ed to each degree of freedom would be zero, at least
if the quantity of energy at our disposal is not in-
finite, which has no physical meaning. This would
be no longer the case if it were assumed that the
length of the luminous oscillations can not descend
below a certain limit X0. This would bring us back
to assuming an ether and endowing it with structure.
In fact, what limits the periodic motions that can be
propagated in a given medium is the necessity that
their wave-lengths be appreciably larger than the
scale of the structure of the medium. The wave-
length of sounds given by a vibrating cord must be

128 PHILOSOPHY AND THE NEW PHYSICS

greater than the mutual distance of the molecules
that constitute the cord or the sounds would not
exist. In the same way the seismic waves that
traverse a continent have reality only for an observer
whose horizon extends beyond the region of local
variations. Similarly, if a structure of the ether ex-
ists, we can no longer speak of infinitely small
wave-lengths in the mathematical sense of the word :
the smallest wave-lengths that it would be possible
to assume are those for which the magnitude X is
near the number that measures the distance between
two ether molecules. The number of degrees of free-
dom of the ether would be limited in number, and
thermal equilibrium between matter and ether then
becomes possible.

This idea has the disadvantage of being based
on the hypothetical existence of the ether, and of an
ether endowed with discontinuous structure, which
is not readily conceived. But, moreover, it is
ineffective, for it leads to predictions at variance
with experiment. In fact, the number of systems
of stationary waves the wave-length of which lies
between the limits X and X + d\ is greater the
smaller X is. The result would be that the degrees
of freedom of the smallest wave-lengths would tend
to appropriate all the disposable energy, which
would be dissipated in extremely short radiations,
and this is contrary to experiment. Thus the
preceding hypothesis leads to a wrong law, formu-
lated first by Lord Rayleigh and Jeans as a conse-
quence of the equipartition of energy, that the

QUANTUM THEORY 129

energy radiated for a given wave-length is propor-
tional to the absolute temperature and varies
inversely as the fourth power of the wave-length.

To escape from these difficulties, Planck has
put forth a radical hypothesis, which has the merit
of being free from the consideration of any hypothe-
tical medium and considers nothing but the only
positively accessible reality, energy. The formula
that he has proposed for representing the distribu-
tion of energy in a black spectrum amounts to sub-
stituting discontinuous series of elements, the sum
of which remains always finite, for an integral which
occurs in the mathematical expression of Lord
Rayleigh's law and which has the disadvantage of
becoming infinite. He interprets this discontinuity,
not by hypotheses on the structure of the medium
in which the radiant energy moves, but by hypo-
theses on the absorption and emission of this energy v
According to him the exchanges of energy between
radiation and matter cannot take place in a con-
tinuous manner in any proportion whatever, for
this introduces an infinite number of degrees of
freedom, but they must take place in a discontinu-
ous manner in definite proportions. The electric
resonators (free electrons) through the agency of
which these exchanges are realized can only absorb
or emit radiant energy in a discontinuous manner,
by sudden jumps, according to integral multiples
of elementary quantities, indivisible energy atoms
called quanta. These quanta, which fix the lower
limit of intake and output of energy, are not the

130 PHILOSOPHY AND THE NEW PHYSICS

same for all the resonators: they are inversely
as the wave-length (or the period of their oscillation)
and connected with the frequency v according to
the relation

(21) q = hv

where h represents a universal constant. As a con-
sequence of this hypothesis the resonators of short
period can absorb and emit energy only in large
mouthfuls, while the resonators of long period can
swallow and give it up in small morsels. It re-
quires a large amount of disposable energy to rouse
a resonator of short period, so that the resonators
of this kind will have a chance to remain at rest,
especially if the temperature is low. By this means
the noxious role of the wave-lengths near zero, the
presence of which made the equilibrium impossible,
is eliminated. Thereby also the fact is explained
that there is relatively little light of short wave-
length in black radiation, which is in accord with
Planck's empirical formula. On the other hand,
the discontinuity in the intake and output of the
energy, which is progressively accentuated and be-
comes enormous for short wave-lengths, tends to
disappear in the region of large wave-lengths, where,
as the result, Lord Rayleigh's law is found again to
hold.

Let us consider our isothermal enclosure and see
what happens when the temperature is progres-
sively raised, starting from the absolute zero. At
first the molecules are motionless and, as it were,

QUANTUM THEORY 131

anchylosed by the frost, the thermal energy is zero,
the resonators are mute. If the temperature is
raised, the resonators whose quantum is the smallest
will, because of the incipient molecular agitation,
begin to vibrate, and the first radiations will appear
in the infra-red which is^far removed from the visi-
ble spectrum. Step by step the other resonators
will begin to be agitated and the spectrum will be
extended towards the luminous radiations, then
towards the ultra-violet, in conformity with
Planck's law and with what experiments reveal to
us. The quantum increasing indefinitely as X tends
towards 0, the radiations corresponding to the limit
will never appear.

Planck's theory seems thus to imply that the
Structure of energy is discontinuous.; Every reso-
nator can emit or absorb only a whole number of
grains of energy. The value of this grain depends
uniquely on the frequency v of this resonator and
is proportional to it. There are atoms of energy,
as there are atoms of electricity and atoms of matter
formed of the first. However, while a hydrogen
atom conserves its mass, whatever be the compound
into which it enters, while the atom of electricity
conserves its individuality through any vicissitude
that it undergoes, it is not the same with the quanta
of energy. If we have, for example, three quanta
of energy on a resonator the wave-length of which
is 3, and if this energy passes to a second reso-
nator the wave-length of which is 5, it represents

132 PHILOSOPHY AND THE NEW PHYSICS

no longer 3 but 5 quanta of energy. This is one
of the numerous difficulties of the theory.

One of the confirmations of the quantum theory
is drawn from the determination of Avogadro's
constant (the number of molecules contained in a
gram-molecule of a gas) which it provides. Two
constants figure in Planck's empirical formula: one
which expresses the discontinuity of the energy of
oscillation of resonators, called the universal constant
h, another which expresses the molecular disconti-
nuity, called Avogadro's constant N. To determine
the numbers h and TV it suffices to use two good
measurements of the emissive power (the quantity
of energy that leaves the opening of the enclosure
per second) for different values of the wave length
X and the temperature T. The value of h is then
found to be

h = 6.2 X 10-27

and this leads to the value of N
N = 64 X 1022

This number agrees quite closely with the mean of
the numbers obtained by the methods considered
most reliable, and this coincidence is the more sur-
prising as the number of molecules is deduced from
measurements made on radiant heat.

A second confirmation, due to Einstein and to
Nernst, is drawn from the study of the specific heats
of solids at low temperature. It is known that
the specific heats of solids decrease rapidly when
the temperature is lowered. Thus, for diamond

QUANTUM THEORY 133

at the temperature of liquid hydrogen, the specific
heat is reduced to about one-seventh of what it is
at ordinary temperatures. Everything takes place
as if the molecules lost degrees of freedom in cool-
ing, as if their joints became anchylosed from the
effect of the frost. This is contrary to the the-
orem of the equipartition of energy, which provides
a method of calculating the atomic heats of solids
and of deducing Dulong and Petit's law, accord-
ing to which the atomic heats are equal for all bodies
and independent of the temperature.

Planck defined the specific heat of a single
resonator as the increase, for one degree centigrade,
of the mean energy, reduced to calories, that a
resonator of given frequency must have at a definite
temperature to be in equilibrium with black radi-
ation. Einstein introduces the following simpli-
fying hypotheses. He considers the solid bodies as
possessing only a single kind of resonators and only
one resonator per molecule; the product of Avoga-
dro's constant by the specific heat of a single
resonator then gives him the specific heat, referred
to a gram-molecule, of the solid considered. Accord-
ing to this formula the specific heat of a solid
hardly varies with the change of temperature
at high temperatures; but at low temperatures it
decreases rapidly and tends towards zero when the
absolute zero is approached. Nernst complicates
Einstein's hypothesis a little by adding to the lat-
ter's unique system of resonators other resonators
tuned to the octave and so succeeds in obtaining

134 PHILOSOPHY AND THE NEW PHYSICS

a surprising coincidence with the numbers obtained
experimental!}' by himself and his pupils, for a very
large number of bodies at temperatures that extend
from the ordinary temperatures down to the low-
est temperatures that Kammerlingh-Onnes has been
able to obtain in his cryogenic laboratory at Ley den.
This theory amounts to the following: if a solid
is regarded as an aggregate of atoms or of molecules
oscillating about an equilibrium position, the en-
ergy of each oscillator thus realized must be, as in
the case of Planck's electric oscillators, an inte-
gral multiple of hv. The diminution of the speci-
fic heat of the solid at low temperatures is then
readily explained. When the temperature de-
creases, the supply of disposable energy offered
to each of the material oscillators falls below the
quantum of a large number of them; instead of
vibrating a little they cease to vibrate at all, so that
the total energy diminishes more rapidly than in
the old theories. On the contrary, at high tem-
peratures, the quantum hv becomes so small that we
again get Dulong and Petit'slaw, obtained by start-
ing from the law of the equipartition of energy.

19. THE STRUCTURE OF RADIATION.

The study of black radiation and of specific
heats at low temperatures has led Planck, and after
him, Einstein to the idea that the exchanges between
radiation and matter do not take place in a continu-
ous manner, but by discrete elements, by quanta of
energy. What becomes of these elements when once

STRUCTURE OF RADIATION 135

set free by matter? For the old theory of free
radiation considered as formed by indefinitely di-
visible and expansible spherical waves propagated
by a continuous hypothetical medium, there is now
substituted the idea of a radiation projected in
space void of matter in the form of distinct ele-
mentary units, which implies a discontinuous dis-
tribution of energy in the front of the luminous
transverse waves. This is an unexpected return
to the emission theory, rendering the consideration
of an ether serving as the "I" to the verb "undulate"
superfluous.

Among the phenomena, the interpretation of
which suggests this point of view, we have Hertz's
phenomenon and the production of rays by shocks
of secondary cathode rays and by X-rays.

Hertz's phenomenon, or the photo-electric effect,
denotes the property that bodies have, in particular
metals, of emitting cathode rays under the action of
light. The electric forces present in the absorbed
luminous waves set the electrons stored in the metal
in motion, and some of them are, because of the
accelerations that they undergo, projected out.
The photo-electric current, which results there-
from, depends on two factors, the number of the
electrons emitted per unit time and the velocity
with which these electrons are emitted. If the
intensity of the light is increased without a change
in its wave-length, the number of the electrons
emitted increases proportionally, but the velocity
of emission remains the same. If, on the other

136 PHILOSOPHY AND THE NEW PHYSICS

hand, at constant luminous intensity a change
is made in the frequency v of the exciting light,
the velocity of emission seems to increase propor-
tionally to the frequency, and consequently in-
versely as the wave length. The velocity with
which the electrons are emitted certainly did not
belong to them before they had undergone the action
of the light, as experiment shows that this velocity
is very much higher than that of the thermal agita-
tion. If the velocity of the electrons is borrowed
from the light, how are we then to understand that
it is the same for a very intense light and a very fee-
ble light? How, above all, explain that it varies
inversely as the wave length?

Stark1 has remarked that these difficulties dis-
appear if the quantum hypothesis is assumed.
The light that meets the metal is not of homo-
geneous structure, it consists of isolated elements
each possessing the energy hv. When one of these
elements strikes the metal the energy that it con-
tains can pass to one of the electrons present in the
metal. On account of this fact the electron acquires
a velocity that can much surpass the velocity of
thermal agitation and leads to its projection from
the metal. As the elements of energy are greater in
proportion as the frequency v is higher, ultra-violet
light will be much more effective than visible light.
Thus not only is light absorbed and emitted solely in
the form of quanta, but, even when it is freely pro-

1 Stark, Phys. Zeitschr., 1909; Principien der Atomdynamik.
Leipzig, 1910.

STRUCTURE OF RADIATION 137

pagated in empty space, it seems to consist of the
projection of discrete units.

J. J. Thomson1 has arrived at similar conclu-
sions by studying the photo-electric effect on gase-
ous bodies. Ultra-violet light of very short wave-
length ionizes gases, that is, it breaks up the gaseous
molecules by setting electrons free. The work
necessary for this rupture can be determined. It
is thus found that if, in conformity with Maxwell's
ideas, ultra-violet light is thought of as formed
by a train of homogeneous waves propagated with-
out inequalities of structure, the energy carried
through a unit section is not sufficient to account for
the work of ionization produced by this pencil. To
do this a discontinuous front must be assumed, so
that there are spots of light and darkness. At
places where the energy is accumulated its density
is sufficient to ionize the molecules. The wave
front possesses a structure, and the wave train, taken
as a whole, is not formed of a regular and uninter-
rupted flow of energy, but of discrete elements of
energy separated by considerable gaps. This is
the old emission theory reappearing in a very modi-
fied form.

Einstein has supplemented Stark's ideas in a way
that has made a new experimental verification of
the quantum theory possible. He assumes that an
electron set free by a luminous ray of frequency
v can bring into action only an amount of energy
equal to Planck's energy element. Consequently

1 J. J. Thomson, Proceed. Camb. Phil. Soc., 1908.

138 PHILOSOPHY AND THE NEW PHYSICS

we have, according to the principle of the conserva-
tion of energy, the equality

%mv2 = hv — V

where ^ denotes the work necessary to separate
the electron from the atom from which it comes.
This formula is capable of direct verification, if we
take into account the fact that the velocity v of the
photo-electric electrons can be determined ex-
perimentally by the measurement of the condenser
potential, V + Fo, capable of reducing the current
to zero, by reducing the velocity v to zero. We
have

e(V + Fo) = Mm*;2

where V denotes the potential difference applied,
and V0 the contact potential difference that always
exists between two different metals, and these two
differences have to be determined separately.
Among the most satisfactory verifications of this
formula, the recent experiments of Millikan1 must
be quoted. Working in a vacuum on freshly
prepared surfaces of sodium, potassium, and lith-
ium, this physicist has employed the entire range
of wave-lengths from the middle of the visible
spectrum to the ultra-violet of the mercury arc.
His results confirm Einstein's theory. In parti-
cular, the linear relations that he obtains between
V and v make possible the determination of a con-
stant angular coefficient practically equal to Planck's
constant.

1 R. A. Millikan, A Direct Photoelectric Determination of
Phanck's "h." Phys. Rev. Ser. 2, vol. 7, p. 355.

STRUCTURE OF RADIATION 139

Lorentz1 has shown, not only that the corpuscular
idea of light results from Hertz's phenomenon, but
that it alone permits the explanation of the absorp-
tion of radiation by fixed quanta, multiples of hv,
in conformity with the views of Planck. When
an incident wave, encountering the molecules of an
isotropic body, sets the electrons in it into vibration,
the absorption of light is the more intense the nearer
its frequency is to the natural frequency of these
electrons. In the case of perfect resonance the
electron borrows from the luminous wave the maxi-
mum amount of energy, and, by taking the case of
the solar light and allowing for the forces of damp-
ing and friction to which the electron is subject,
this maximum energy is found by calculation to be
a little more than twice the atom of energy required
by Planck. A similar amount of light, therefore,
can be absorbed by the electrons. But the ordinary
sources have intensities a million times weaker
than that of the Sun. If the energy that they emit
were uniformly distributed over the surface of a
sphere having the source as center, it could com-
municate to the electron only a very small fraction
of its absorbable quantum. This energy, therefore,
must be unequally concentrated in different direc-
tions, and the sphere must be traversed by the flow
of energy in a certain number of discontinuous
spots, very widely spaced, to provide condensations
of energy compatible with the mechanism of absorp-
tion conceived by Planck.

1 H. A. Lorentz, Phys. Zeitschr., 1910.

140 PHILOSOPHY AND THE NEW PHYSICS

The quantum theory, it is hardly necessary
to say, encounters otherwise many difficulties.
One is the existence of interferences at large differ-
ences of path, which seems to imply that the lum-
inous quanta extend over lengths equal to several
thousand times their wave-length. There are
others which, however, yield to a deeper analysis.
The idea that a point source does not radiate
symmetrically in all directions may seem incom-
patible with experiment. But the physical point
sources contain a number of oscillators sufficiently
great to wipe out any trace of individual discontin-
uity. The physical symmetry, which experiment
leads us to attribute to luminous waves, results
from a mean effect and is not in contradiction to
the possibility of an elementary radiation, endowed
with structure. This has been shown by J. J.
Thomson1 by supposing that the electrified parti-
cles producing the light do not emit lines of force
uniformly in all directions, but only, for example,
in two solid angles opposed at the vertex and of
relatively restricted aperture. Starting from this
hypothesis, he has demonstrated that the principal
properties of the electron would still belong to those
particles, the electromagnetic field of which is
concentrated in privileged directions. They would
have inertia of electromagnetic origin and would
emit radiation on every modification of their state
of motion; but the radiated waves of acceleration,
light, if we are concerned with periodic waves,

1 J. J. Thomson, Phil. Mag., 1910, p. 301.

STRUCTURE OF RADIATION 141

would be concentrated in certain directions and
extraordinarily rarified or absent in others. The
radiation emitted by an oscillator would possess
a particular structure, which would reappear in
part in the emission of real sources and produce the
irregularities of the wave front suggested by
Hertz's phenomenon. Nothing essential would be
changed in the usual laws of electromagnetism,
and they would continue applicable to material
complexes enclosing a large number of particles
distributed according to the law of chance. •
V'The quantum theory is far from having the
dogmatic certainty of the atomic theory or the
electronic theory. The atoms, for example, have
become a physical reality: they are counted, they
are weighed, their radius of action and their mean
velocity are determined, they are seen in the form
of scintillations with the aid of the spinthariscope
of Crookes, and C. T. R. Wilson, by using their
property of becoming the centers of condensation in
supersaturated water vapor, has succeeded in
photographing the atomic trajectory of the a
particles, which are ions of helium, and even the
corpuscular trajectory of the 0 rays, which are
electrons. No device, up to the present, has
enabled us to subject the quanta of radiant energy
to a control capable of transforming them from
theoretical concepts to experimental concepts.
One, however, can be suggested, drawn from the
marvelous properties of selenium.1

1 Cf. Fournier d'Albe, The Future of Selenium (Scientia, 1917,
p. 165-191).

142 PHILOSOPHY AND THE NEW PHYSICS

When one of the conductors in an electric cir-
cuit consists of selenium, a current is produced in
this circuit, as soon as it is subjected to a luminous
flash. The conductivity thus produced from an
instantaneous exposure of the selenium to light is
proportional to the incident energy. This property
makes it possible to detect, electrically, flashes that
are invisible to the naked eye. By applying, for
example, an electromotive force of 1 volt, an easily
perceptible current of 10~12 ampere could be ob-
tained with a cell of selenium of 100 sq. cm., with
a short flash of 10~9 lux, corresponding to a star
of 8th or 9th magnitude, which is quite invisible
to the naked eye. With a selenium cell of the
same surface as the pupil of the eye, a star of
the 6th order, which is the extreme limit of our
vision, could be detected electrically under the
same conditions. But, since we are able to measure
currents of 10~15 ampere, the sensitiveness of
selenium obviously surpasses that of the eye. Now
the quantum theory permits the calculation of the
size and number of the grains of energy absorbed by
a given surface, subject to a radiation of definite
wave-length and intensity. It is found that the
human eye absorbs 360 quanta per second, when
it receives light coming from the visible star of
least luminosity. These quanta are, in the most
favorable case, 20 times too numerous to be per-
ceived as distinct flashes. We can then hope to
count them electrically, aided by the selenium, if
we can succeed in detecting sufficiently feeble cur-

PHYSICS OF THE DISCONTINUOUS 143

rents. The selenium cell would thus render to us
the same service as the zinc sulfide screen of Crookes'
spinthariscope; it would enable us to place the
existence of the quanta on an experimental basis.

20. THE PHYSICS OF THE DISCONTINUOUS.

Modern discoveries lead to the assumption of the
discontinuity of matter, of electricity, of radiant
energy, and of exchanges of energy. Henri Poin-
care has shown the consequences that result there-
from for mathematical physics and natural philo-
sophy. We must give up expressing the laws of the
phenomena in the form of differential equations in
all cases in which the large number of elements
which come into play does not suffice to wipe out
entirely the influence of the individual discontinui-
ties. Contrary to the ancient adage natura non
facit saltus, it becomes apparent that the universe
varies by sudden jumps and not be imperceptible
degrees. A physical system is capable of only a
finite number of distinct states, and this introduces
discontinuity into the distribution even of probabil-
ities. Since between two different and immediately
consecutive states the world remains motionless,
time is suspended so that time itself is discon-
tinuous: there is an atom of time.

The controversy between infinitists and finitists,
idealists and empiricists, cantorians and pragmat-
ists, to follow current terminology, is, on this basis,
settled in favor of the latter. The world does not
glide smoothly down a gentle slope, imperceptibly

144 PHILOSOPHY AND THE NEW PHYSICS

inclined, of the course of events according to Leibniz,
but it descends by steps of events as conceived by
Evellin.1 In the external reality there are no ag-
gregates of elements having the attributes of a
continuum ,but only aggregates that can be counted,
the attributes of which are only intelligible for
the mind, because it can define all their elements.
Nature following mathematics is reduced to arithmetic.
It becomes comprehensible, for if our imagination
does not show us anything except in the form of
spatial intuition, which is that of a physical contin-
uum, our mind, by virtue of the minimum percepti-
ble increment of excitation, can comprehend only
the countable and the discrete. Just as continuity
in mathematics appears more and more as a transi-
tory tool, the utility of which at present is not neg-
ligible, but which must be regarded as a means of
studying the countable aggregates that constitute
the only analytical reality that is accessible, so too
physical continuity, which lends itself well to appli-
cations of the calculus of partial derivatives, will
always appear legitimate, as a first approximation,
for the order of magnitude of ensemble effects of
systems the elements of which are finite in number
but sufficiently numerous to wipe out the individual
discontinuities by virtue of perfect mixing and the
laws of chance. Nevertheless it should not make us
forget that the simple elements of things manifest an
essential discontinuity, which must reappear in the
equations that -translate their individual behavior

*A contemporary French philosopher. (Tr.)

PHYSICS OF THE DISCONTINUOUS 145

and which alone can account, in the hypothesis of
the absolute determinism, for the fluctuations of the
ensemble phenomena to which they give rise.

On mathematical physics there is hereafter
imposed a new task, namely, to establish a bond :—

Between the ensemble phenomena which our
observations reveal, and the elementary phenomena
of which they are a statistical resultant;

Between the physical quantities directly acces-
sible to our measuring instruments, which take
in at once, as the sum or average of the individ-
ual quantities, so many elements that they can be
practically treated as continuous; these quantities
being in themselves, or individually, essentially
discontinuous;

Between the properties of the discrete grains
(molecules, atoms and electrons) and the struc-
tures they form by aggregation.

The differential and integral calculus, used to
translate analytically the idea of continuity, is
appropriate for the study of the systems which
alone are directly perceptible, and which are com-
posed of a very great number of elements. The
calculus of probabilities is appropriate for the study
of the relations between the real world of ele-
ments of discontinuous structure and the apparent
world of continuous phenomena; between the indi-
vidual laws, which govern these elements taken
separately, and the laws of large numbers, which
govern the mixed appearances to which their
incessant mixing gives rise.

10

146 PHILOSOPHY AND THE NEW PHYSICS

By correlation, the concept of explanation be-
comes transformed in natural philosophy. In
former days a physical phenomenon was explained
by reducing it to the principles of classical mechanics,
by giving to its laws the form impressed by Lagrange
on the equations of dynamics. To explain a phen-
omenon today is to give a statistical explanation,
by regarding it as the resultant of a very large
number of underlying phenomena governed by
the laws of chance. Maxwell's attempt in his
Treatise on Electricity and Magnetism is an example
of an explanation of the first type. The statistical
interpretation of Carnot's principle, of the expon-
ential law of the spontaneous destruction of radio-
active substances, and of the law of mass action
are examples of the second type.

Thus not only do the most fundamental catego-
ries of our mind, those of space, of time, and of
causality, pass through an evolution with the pro-
gress of science, but the same holds even for the
concept of intelligibility. To explain a phenomenon
is, for primitive man, to interpret it anthropo-
morphically by a supernatural agent endowed with
psychological life in his own image ; for a scholastic
it is to explain it by ultimate causes; for Bacon to
explain it by efficient causes; for Maxwell it fc to
deduce it from the principles of mechanics; for
Gibbs and Boltzmann it is to account for it by the
calculus of probabilities, by starting from a system
of elements subject to given conditions. Human
reason is not "u'ne et entidre en un chacun" as

PHYSICS OF THE DISCONTINUOUS 147

Descartes taught. It varies with the abstract
or concrete nature of our thought, and in proportion
as, on contact with experimental facts, the adapta-
tion of our mind to nature becomes progressively
realized.

CHAPTER VIII
CONCLUSION

21. CONCLUSION.

The discoveries of modern physics have led
physicists to two quite distinct conceptions of the
universe.

The first can be illustrated by the suggestive
name of the dematerialization of matter. It con-
sists in reducing matter to being only the locus
of singular points of torsion, of condensation, or
even of destruction of a medium endowed with
inertia and mechanical properties, the dielectric
ether of Faraday and Maxwell. From this point
of view an electron is a simple cell in the ether,
behaving like a projectile moving forward in a
perfect fluid having no viscosity. On the sides of
the projectile a cushion of fluid is formed and
behind it a zone of deep eddies: its own inertia is
increased by all the inertia of the wave system thus
created which follows it. At start a part of the
muzzle energy is expended in overcoming the inertia
of the fluid displaced at the same time as the inertia
of the moving body itself; but, when the motion
has been once acquired, it perpetuates itself with-
out resistance, since the body carries its wave
system with it. The electron has no inertia of its
own, but it can not be displaced without entraining

148

CONCLUSION 149

the" surrounding ether coupled to its lines of force,
and its inertia results from that of the ether thus
disturbed which forms its electromagnetic wave
system. Matter resolves itself into cells in the
ether and the ether gains in substantiality and in
reality all that matter loses.

This idea results from Faraday's work, which
has brought to light the importance of the medium
that surrounds conductors and magnets in electric
and magnetic phenomena. The attention of phy-
sicists has been directed to the study of electric
and magnetic fields in which energy is concentrated,
matter serving only as a support of these fields.
But instead of conceiving them as substantial
realities existing in an independent manner, it is
claimed that they are explained by the mechanical
states of this hypothetical medium, the ether, elec-
tric energy being merely the potential energy of its
deformations and magnetic energy merely the
kinetic energy of its displacements. The ether
becomes the active medium in which the transfers
and the transformations of energy are governed
by the equations of the electromagnetic field of
Maxwell and Hertz, and thus matter is gradually
stripped of all its physical contents and they are
referred to the ether, which becomes the only reality
that continues to exist.

Going still further Dr. Gustave Le Bon1 has

1 Dr. G. Le Bon, L' evolution de la matiere. On the relations
and the differences between this theory and that of Einstein see
L. Rougier, L'inertie de 1'energie (Revue scientifique, October
13-20, 1917).

150 PHILOSOPHY AND THE NEW PHYSICS

developed the idea of the evolution of matter.
Let us imagine that the electrons, into which in the
end the molecular structures that constitute bodies
are resolved, are due to vortices in a universal
fluid analogous to Lord Kelvin's gyrostatic ether.
Instead of regarding these vortices as indestructible
in conformity with the hydrodynamic equations of
Cauchy and Helmholtz, let us imagine, quite gratui-
tously, that they vanish at length in the original
fluid, like a waterspout in the ocean, in the form
of liquid waves, owing to the gradual retardation
of their velocity. The rotatory energy of the
electron will be transformed into radiant energy,
which, sweeping through all space, will be lost at
infinity. Thus matter is resolved into electrons,
which themselves vanish in etherized undulations,
so that there is a final loss of matter and an uncom-
pensated dissipation of energy. For the universal
principle of invariance which the Ionic natural
philosophers placed at the basis of natural philoso-
phy and which assured its intelligibility, namely,
" Nothing is created, nothing is lost" one must now
substitute the contrary principle: " Nothing is
created, everything is lost/' The world marches
toward a final bankruptcy, and the ether, of which it
has been asserted in vain that it is the matrix of the
worlds, is revealed as being their final tomb. Thus
Dr. Gustave Le Bon has been, in sumptuous prose,
the Zarathustra announcing, after the death of the
gods, the twilight of their creation.

These ideas encounter insurmountable difficulties.

CONCLUSION 151

The ether is revealed as endowed with contradictory
mechanical properties, and the attempts at an
explanation of electromagnetic phenomena start-
ing from it have all suffered shipwreck. If it
exists it can not be completely entrained by matter,
,as Fizeau's experiment proves; it can not be par-
tially entrained by matter, as the principle of action
and reaction demonstrates; that it can not be
motionless, is implied by the relativity principle.
Less tangible than Proteus, it remains only to
declare it defunct without estate.

To these antinomies the theory of Dr. Gustave
Le Bon adds new difficulties. The hydrodyn mic
equations of Cauchy and Helmholtz show that
vortices, once started in a perfect, homogeneous, and
incompressible fluid, are eternal. The electronic
theory of radiation connects its appearance with the
presence of electrons, which play the part of agents
present in the transformation of different forms
of energy into radiation and permit these trans-
formations, while themselves remaining, like cataliz-
ing agents, unaltered. Their disappearance would
entail therefore that of radiation itself, in which they
are supposed to vanish. Lastly, if the principle
of invariance of the Ionic natural philosophers is
abandoned, the very possibility of science is put
at stake. Science, being the search for the laws
of nature, that is to say, the invariants of all events
in the universe, would remain valid, to a first
approximation, only for systems in which the disin-
tegration of matter and the radiation of energy to

152 PHILOSOPHY AND THE NEW PHYSICS

infinity are practically insignificant; and the meta-
physical problem would arise of understanding how
the universe, if it has not had a beginning, has
not yet finally vanished, milleniums ago, in the
"motionless and sleeping" ether.

Abandoning the ether, we are led to an en-
tirely different theory: that of the materialization
of energy. Energy emerges from the phantom
realm of imponderables to take substance, like the
shades of the Elysian fields evoked by Ulysses on
the Cimmerian river. It appears as endowed with
inertia, with weight and structure and manifests
itself in two forms: one is called, by virtue of long
prescription, matter; the other, radiation.

Matter is characterized by its structure, that
is, by the number and nature of the electrons and
perhaps the positive remainders that constitute
it, and also by its property of moving with veloci-
ties, relatively to a reference system, ranging from
0 to V. We know nothing of it, as stated by Ost-
wald, except its energetic effects: the electric
field of the electron at rest, the magnetic field
of the electron in motion, the gravitational field
of the molecular structures formed, by electronic
architecture, the kinetic effects produced by their
vis viva. The electron is revealed as a grain of resi-
nous (negative) electricity, so that matter is only
a form of energy, enormously accumulated in
a narrowly circumscribed region of space. It does
not, on that account, as in the preceding theory,
lose the reality and the substantial characteristics

CONCLUSION 153

which external perception and common sense have
agreed until now to attribute to it, since energy,
which is its essence, is endowed with mass, weight,
and structure.

Radiation is a form of energy which no longer
appears as propagated in the shape of continuous
waves by a hypothetical medium, but as expelled in
the form of discrete units in space free of matter
with the uniform velocity of light. It also is
endowed with inertia, weight, and structure. Its
possession of fundamental properties in common
with matter permits the explanation of its action on
the latter. Luminous radiation, representing a cer-
tain momentum, can be strictly assimilated to a
material projectile. It is because of this that, by
virtue of the principle of action and reaction, it
exerts a repulsion on the material source that emits
it and a propulsion on a material obstacle that ab-
sorbs it. The ancient metaphysical problem of the
action of the imponderable on the ponderable, of
force on matter, which arose in its most modern and
most urgent form in connection with the pressure of
radiation, disappears henceforth as a pseudo-
problem.

BIBLIOGRAPHY
1. The Relativity Principle

H. A. LORENTZ, A. EINSTEIN, H. MINKOWSKI, Eine Sammlung
Abhandlungen, Teubner, 1913.

LAUE, Das Relativitatsprinzip, Teubner, 1911.

P. LANGEVIN, Le temps, 1'espace et la causalite dans la Physique
moderne (Bulletin de la Societ6 frangaise de Philosophie, t. XII,
1912).

154 PHILOSOPHY AND THE NEW PHYSICS

2. Electromagnetic Dynamics

H. POINCARE, La theorie de Lorentz et le principe de reaction
(Archives neerlandaises des Sciences exactes et naturelles, 2e
se"rie, t. V, 1900).

H. POINCARE, Sur la dynamique de 1' Electron (Rendiconti del
Circolo matematico di Palermo, t. XXI, 1905).

P. LANGEVIN, Les grains d'electricite* et la dynamique electro-
magnetique (Les ide"es modefnes sur la constitution de la matiere,
Paris, 1913).

3. The Electronic Theory of Matter

P. LANGEVIN ET M. DE BROGLIE, Les quantity's e!6mentaires
d'41ectricit4, ions, electrons, corpuscules, 2 vol., Paris, 1905.

Les idees modernes sur la constitution de la matiere (Memoires
de la Societe franc, aise de Physique, Paris, 1913).

N. R. CAMPBELL, Modern Electrical Theory, Cambridge, 1913.

4. The Inertia of Energy

A. EINSTEIN, Annalen der Physik, vol. XVIII, 1905.
P. LANGEVIN, L'inertie de 1'energie et ses consequences (Journal
de Physique, juillet 1913).

5. The Weight of Energy and the Theory of Gravitation

A. EINSTEIN, Annalen der Physik, vol. XXXV, 1911; Ibid.,
vol. XXXVII, 1912; Physikalische Zeitschrift, vol. XIV, 1913.

A. EINSTEIN ET GROSSMANN, Bases physiques d'une theorie
de la gravitation (Archives des Sciences physiques et naturelles,
t. XXXVII, 1914).

A. EINSTEIN, Die formalen Grundlagen der allgemeinen Rela-
tivitatstheorie (Sitzungsberichte der koniglich preussischen Akade-
mie der Wissenschaften, vol. XLI, 1914).

A. EINSTEIN, Erklarung der Perihelbewegung des Merkur
aus der allgemeinen Relativitatstheorie (Sitzungsberichte der
koniglich preussischen Akademie der Wissenschaften, vol. XLII,
1915).

H. A. LORENTZ, La gravitation (Scientia, 1914).

ED. GUILLAUME, Les bases de la Physique moderne (Archives
des Sciences physiques et naturelles, 1916).

L. BLOCK, Relativite et gravitation, d'apres 16s theories recentes
(Revue generate des Sciences pures et applique*es, 15 de"cembre
1917).

BIBLIOGRAPHY 155

L. BLOCH, Sur les theories de la gravitation (Annales de Phy-
sique, janvier-fevrier 1918).

6. The Structure of Energy

P. LANGEVIN ET M. DE BROGLIE, La the"orie du rayonnement
et les quanta, Paris, 1912.

H. POINCARE, Sur la theorie des quanta (Journal de Physique,
Janvier 1912).

H. POINCARE, L'hypothese des quanta (Revue rose, 24 fevrier
1912).

P. LANGEVIN, La physique du discontinu (Les progres de la
physique moleculaire, Paris, 1914).

M. PLANCK, Die physikalische Struktur des Phasenraumes
(Annalen der Physik, vol. L, 1916).

P. S. EPSTEIN, Zur Quantentheorie (Annalen der Physik, vol.
LI, 1916).

A. EINSTEIN, Zur Quantentheorie der Strahlung (Physikalische
Zeitschrift, vol. XVIII, 1917).

Other Works by L. Rougier :

Les Paralogismes de Rationalisme, Paris, 1920. La philos-
ophic ge*ometrique de Henri Poincare, Paris, 1920. En marge
de Curie et d'Einstein, Paris, 1920. Theories formelles et
logique deductive, Paris, 1921.

INDEX OF NAMES

Abraham, 52, 54, 55, 56, 63,
Arrhenius, 16
Avogadro, 132

Bacon, 146
Bartoli, 17, 77
Becquerel, 60
Bernoulli!, 7
Bloch, 154, 155
Boltzmann, 9, 125, 146
Le Bon, 149, 150, 151
Boscovich, 10, 11
Brace, 31
Brillouin, xiii
de Broglie, 120
Bucherer, 17, 56, 57, 63, 76
Buisson, xiii, 95

Campbell, 70, 154
Carnot, 126, 146
Cauchy, 150, 151
Christoffel, 98
Clausius, 16
Comte, ix, 14
Coulomb, 41, 53
Cremieu, 48

Crookes, 16, 54, 55, 58, 65,
. 143

76 Einstein, x, xii, xiii, xiv, 22, 26,
27, 29, 70, 77, 93, 94, 97, 100,
101, 103, 105, 106, 107, 109,
132, 133, 134, 137, 138, 153,
154, 155

Enriques, 22

Eotvos, xiii, 18, 26, 84, 91, 96,
100

Epstein, 155

Euclid, 20, 37, 100

Euler, 99

Evellin, 144

Fabry, xiii, 95

Faraday, 16, 41, 43, 44, 45, 46,

47, 49, 62, 63, 67, 70, 104,

106, 148, 149
Fizeau, 68, 151
Fitz-Gerald, 31
Foucault, 62
Fournier d'Albe, 141
Fourier, 14
Fraunhofer, xiii, 95
Fresnel, 62, 64, 68
Freundlich, 96

Descartes, 10, 100, 147
Democritus, 7
Du Bois-Reymond, ix
Duhem, x, 7, 106
Dulong, 133, 134

Edison, 58, 61, 65

id.1
W* Galileo, 38, 39, 40, 62

Gibbs, 146
Goldstein, 60
Grimaldi, 62
Grossmann, 154
Guillaume, 154

157

Hamilton, 40, 58, 126
Hannequin, 7, 63

158

INDEX OF NAMES

Helmholtz, 9, 106, 150, 151
Hertz, 8, 9, 11, 20, 47, 48, 58,

61, 65, 68, 120, 135, 139, 141,

149

van't Hoff, 16
Hupka, 56
Huygens, 7, 62

Janet, 5
Jeans, 128

Kant, 10, 11, 103
Kaufmann, 17, 56, 57, 63, 76
Kelvin, 9, 10, 70, 104, 106, 150
Kirchhoff, 121

Lagrange, 39, 40, 58, 146
Langevin, xiv, 29, 77, 91, 120,

153

Laue, 29, 153
Lavoisier, 4, 90
Lebedew, 17, 77
Leibniz, 144
Lenz, 48, 116
Leonardo da Vinci, 62
Leukippus, 7
Levi-Civita, 98
Lobatschewsky, 37
Lodge, 70, 104, 106
Lorentz, 29, 31, 32, 35, 36, 37,

38, 39, 40, 55, 56, 57, 58, 60,

61, 63, 72, 73, 74, 76, 79, 103,

104, 105, 139, 153

Mach, 27, 98

Maupertuis, 23, 25

Maxwell, xiv, 9, 10, 11, 16, 17,
20, 39, 40, 43, 47, 48, 49, 52,
53, 58, 62, 63, 64, 67, 69, 70,
74, 76, 77, 120, 125, 137, 146,
148, 149

Mayer, 4

Meyerson, 7

Michelson, 29, 31, 32, 38

Mie, 96

Millikan, 138

Minkowski, 29, 35, 84, 100, 153

Morley, 29, 31

Mosotti, 41

Nernst, 132, 133
Neumann, xiv

Newton, xiv, 17, 22, 25, 39, 58,
70, 79, 86, 93, 98, 99, 102, 107
Noble, 31
Nordstrom, 96

Onnes, 134

Ostwald, x, 3, 11, 12, 13, 14, 16,
18, 19, 72, 110, 152

Pasteur, 106

Petit, 133, 134

Planck, xii, 124, 129, 130, 131,

132, 133, 134, 137, 138, 139,

155
Poincare, ix, x, 73, 76, 79, 154,

155
Prout, xiii, 92

Rankine, xi, 31

Rayleigh, 31, 128, 129, 130

Ricci, 98

Rontgen, 117

Rougier, 25, 38, 149

Rowland, 16, 47, 48, 49, 76

Salisbury, 63
Spencer, 9
Stallo, 7
Stark, 136, 137
Stefan, 123

INDEX OF NAMES 159

Tait, 10 Weber, 107

Tisserand, 107 Wien, 58

Thomson, 47, 67, 76, 137, 140 Wilson, 141

Trouton, 31 Witte, 69

Verne, 28 Zeeman, 61

-°o ON THE

MAR 251933
SEP 161934

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JAN 20 1957

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