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Title: The New Physics and Its Evolution

Author: Lucien Poincaré

Release date: February 28, 2005 [eBook #15207]
Most recently updated: December 14, 2020

Language: English

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The International Scientific Series

THE NEW PHYSICS

AND ITS EVOLUTION
BY

LUCIEN POINCARÉ
Inspéctéur-General de l'Instruction Publique
Being the Authorized Translation of
"LA PHYSIQUE MODERNE, SON ÉVOLUTION"
NEW YORK
D. APPLETON AND COMPANY
1909

Prefatory Note
M. Lucien Poincaré is one of the distinguished family of mathematicians
which has during the last few years given a Minister of Finance to the
Republic and a President to the Académie des Sciences. He is also one of
the nineteen Inspectors-General of Public Instruction who are charged with
the duty of visiting the different universities and lycées in France and of
reporting upon the state of the studies there pursued. Hence he is in an
excellent position to appreciate at its proper value the extraordinary change
which has lately revolutionized physical science, while his official position
has kept him aloof from the controversies aroused by the discovery of
radium and by recent speculations on the constitution of matter.
M. Poincaré's object and method in writing the book are sufficiently
explained in the preface which follows; but it may be remarked that the best
of methods has its defects, and the excessive condensation which has alone
made it possible to include the last decade's discoveries in physical science
within a compass of some 300 pages has, perhaps, made the facts here
noted assimilable with difficulty by the untrained reader. To remedy this as
far as possible, I have prefixed to the present translation a table of contents
so extended as to form a fairly complete digest of the book, while full
indexes of authors and subjects have also been added. The few notes
necessary either for better elucidation of the terms employed, or for giving
account of discoveries made while these pages were passing through the
press, may be distinguished from the author's own by the signature "ED."
THE EDITOR.
ROYAL INSTITUTION OF GREAT BRITAIN, April 1907.

Author's Preface
During the last ten years so many works have accumulated in the domain of
Physics, and so many new theories have been propounded, that those who
follow with interest the progress of science, and even some professed
scholars, absorbed as they are in their own special studies, find themselves
at sea in a confusion more apparent than real.
It has therefore occurred to me that it might be useful to write a book
which, while avoiding too great insistence on purely technical details,
should try to make known the general results at which physicists have lately
arrived, and to indicate the direction and import which should be ascribed to
those speculations on the constitution of matter, and the discussions on the
nature of first principles, to which it has become, so to speak, the fashion of
the present day to devote oneself.
I have endeavoured throughout to rely only on the experiments in which we
can place the most confidence, and, above all, to show how the ideas
prevailing at the present day have been formed, by tracing their evolution,
and rapidly examining the successive transformations which have brought
them to their present condition.
In order to understand the text, the reader will have no need to consult any
treatise on physics, for I have throughout given the necessary definitions
and set forth the fundamental facts. Moreover, while strictly employing
exact expressions, I have avoided the use of mathematical language.
Algebra is an admirable tongue, but there are many occasions where it can
only be used with much discretion.
Nothing would be easier than to point out many great omissions from this
little volume; but some, at all events, are not involuntary.
Certain questions which are still too confused have been put on one side, as
have a few others which form an important collection for a special study to
be possibly made later. Thus, as regards electrical phenomena, the relations
between electricity and optics, as also the theories of ionization, the

electronic hypothesis, etc., have been treated at some length; but it has not
been thought necessary to dilate upon the modes of production and
utilization of the current, upon the phenomena of magnetism, or upon all
the applications which belong to the domain of Electrotechnics.
L. POINCARÉ.

Contents
EDITOR'S PREFATORY NOTE

AUTHOR'S PREFACE

TABLE OF CONTENTS

CHAPTER I
THE EVOLUTION OF PHYSICS
Revolutionary change in modern Physics only apparent: evolution not
revolution the rule in Physical Theory— Revival of metaphysical
speculation and influence of Descartes: all phenomena reduced to matter
and movement— Modern physicists challenge this: physical, unlike
mechanical, phenomena seldom reversible—Two schools, one considering
experimental laws imperative, the other merely studying relations of
magnitudes: both teach something of truth—Third or eclectic school— Is
mechanics a branch of electrical science?

CHAPTER II
MEASUREMENTS
§ 1. Metrology: Lord Kelvin's view of its necessity— Its definition § 2. The
Measure of Length: Necessity for unit— Absolute length—History of
Standard—Description of Standard Metre—Unit of wave-lengths preferable
—The International Metre § 3. The Measure of Mass: Distinction between
mass and weight—Objections to legal kilogramme and its precision—
Possible improvement § 4. The Measure of Time: Unit of time the second—
Alternative units proposed—Improvements in chronometry and invar § 5.
The Measure of Temperature: Fundamental and derived units—Ordinary
unit of temperature purely arbitrary—Absolute unit mass of H at pressure of
1 m. of Hg at 0° C.—Divergence of thermometric and thermodynamic

scales—Helium thermometer for low, thermo-electric couple for high,
temperatures—Lummer and Pringsheim's improvements in thermometry. §
6. Derived Units and Measure of Energy: Importance of erg as unit—
Calorimeter usual means of determination—Photometric units. § 7.
Measure of Physical Constants: Constant of gravitation—Discoveries of
Cavendish, Vernon Boys, Eötvös, Richarz and Krigar-Menzel—Michelson's
improvements on Fizeau and Foucault's experiments— Measure of speed of
light.

CHAPTER III
PRINCIPLES
§ 1. The Principles of Physics: The Principles of Mechanics affected by
recent discoveries—Is mass indestructible?—Landolt and Heydweiller's
experiments —Lavoisier's law only approximately true—Curie's principle
of symmetry. § 2. The Principle of the Conservation of Energy: Its
evolution: Bernoulli, Lavoisier and Laplace, Young, Rumford, Davy, Sadi
Carnot, and Robert Mayer—Mayer's drawbacks—Error of those who would
make mechanics part of energetics—Verdet's predictions—Rankine
inventor of energetics—Usefulness of Work as standard form of energy—
Physicists who think matter form of energy— Objections to this—
Philosophical value of conservation doctrine. § 3. The Principle of Carnot
and Clausius: Originality of Carnot's principle that fall of temperature
necessary for production of work by heat— Clausius' postulate that heat
cannot pass from cold to hot body without accessory phenomena—Entropy
result of this—Definition of entropy—Entropy tends to increase incessantly
—A magnitude which measures evolution of system—Clausius' and
Kelvin's deduction that heat end of all energy in Universe—Objection to
this— Carnot's principle not necessarily referable to mechanics —Brownian
movements—Lippmann's objection to kinetic hypothesis. § 4.
Thermodynamics: Historical work of Massieu, Willard Gibbs, Helmholtz,
and Duhem—Willard Gibbs founder of thermodynamic statics, Van t'Hoff
its reviver—The Phase Law—Raveau explains it without thermodynamics.
§ 5. Atomism: Connection of subject with preceding Hannequin's essay on
the atomic hypothesis—Molecular physics in disfavour—Surface-tension,
etc., vanishes when molecule reached—Size of molecule—Kinetic theory

of gases—Willard Gibbs and Boltzmann introduce into it law of
probabilities—Mean free path of gaseous molecules—Application to optics
—Final division of matter.

CHAPTER IV
THE VARIOUS STATES OF MATTER
§ 1. The Statics of Fluids: Researches of Andrews, Cailletet, and others on
liquid and gaseous states— Amagat's experiments—Van der Waals'
equation—Discovery of corresponding states—Amagat's superposed
diagrams—Exceptions to law—Statics of mixed fluids— Kamerlingh
Onnes' researches—Critical Constants— Characteristic equation of fluid
not yet ascertainable. § 2. The Liquefaction of Gases and Low
Temperatures: Linde's, Siemens', and Claude's methods of liquefying gases
—Apparatus of Claude described—Dewar's experiments—Modification of
electrical properties of matter by extreme cold: of magnetic and chemical—
Vitality of bacteria unaltered—Ramsay's discovery of rare gases of
atmosphere—Their distribution in nature—Liquid hydrogen—Helium. § 3.
Solids and Liquids: Continuity of Solid and Liquid States—Viscosity
common to both—Also Rigidity— Spring's analogies of solids and liquids
—Crystallization —Lehmann's liquid crystals—Their existence doubted —
Tamman's view of discontinuity between crystalline and liquid states. § 4.
The Deformation of Solids: Elasticity— Hoocke's, Bach's, and Bouasse's
researches—Voigt on the elasticity of crystals—Elastic and permanent
deformations—Brillouin's states of unstable equilibria—Duhem and the
thermodynamic postulates— Experimental confirmation—Guillaume's
researches on nickel steel—Alloys.

CHAPTER V
SOLUTIONS AND ELECTROLYTIC DISSOCIATION
§ 1. Solution: Kirchhoff's, Gibb's, Duhem's and Van t'Hoff's researches. § 2.
Osmosis: History of phenomenon—Traube and biologists establish
existence of semi-permeable walls—Villard's experiments with gases—
Pfeffer shows osmotic pressure proportional to concentration—

Disagreement as to cause of phenomenon. § 3. Osmosis applied to Solution:
Van t'Hoff's discoveries—Analogy between dissolved body and perfect gas
—Faults in analogy. § 4. Electrolytic Dissociation: Van t'Hoff's and
Arrhenius' researches—Ionic hypothesis of—Fierce opposition to at first—
Arrhenius' ideas now triumphant —Advantages of Arrhenius' hypothesis
—"The ions which react"—Ostwald's conclusions from this—Nernst's
theory of Electrolysis—Electrolysis of gases makes electronic theory
probable—Faraday's two laws—Valency— Helmholtz's consequences from
Faraday's laws.

CHAPTER VI
THE ETHER
§ 1. The Luminiferous Ether: First idea of Ether due to Descartes—Ether
must be imponderable—Fresnel shows light vibrations to be transverse—
Transverse vibrations cannot exist in fluid—Ether must be discontinuous. §
2. Radiations: Wave-lengths and their measurements—Rubens' and
Lenard's researches— Stationary waves and colour-photography—Fresnel's
hypothesis opposed by Neumann—Wiener's and Cotton's experiments. § 3.
TheElectromagnetic Ether: Ampère's advocacy of mathematical expression
—Faraday first shows influence of medium in electricity—Maxwell's proof
that light-waves electromagnetic—His unintelligibility—Required
confirmation of theory by Hertz. § 4. Electrical Oscillations: Hertz's
experiments— Blondlot proves electromagnetic disturbance propagated
with speed of light—Discovery of ether waves intermediate between
Hertzian and visible ones—Rubens' and Nichols' experiments—Hertzian
and light rays contrasted—Pressure of light. § 5. The X-Rays: Röntgen's
discovery—Properties of X-rays—Not homogeneous—Rutherford and
M'Clung's experiments on energy corresponding to—Barkla's experiments
on polarisation of—Their speed that of light—Are they merely ultra-violet?
—Stokes and Wiechert's theory of independent pulsations generally
preferred—J.J. Thomson's idea of their formation— Sutherland's and Le
Bon's theories—The N-Rays— Blondlot's discovery—Experiments cannot
be repeated outside France—Gutton and Mascart's confirmation— Negative
experiments prove nothing—Supposed wave-length of N-rays. § 6. The
Ether and Gravitation: Descartes' and Newton's ideas on gravitation—Its

speed and other extraordinary characteristics—Lesage's hypothesis—
Crémieux' experiments with drops of liquids—Hypothesis of ether
insufficient.

CHAPTER VII
WIRELESS TELEGRAPHY
§ 1. Histories of wireless telegraphy already written, and difficulties of the
subject. § 2. Two systems: that which uses the material media (earth, air, or
water), and that which employs ether only. § 3. Use of earth as return wire
by Steinheil —Morse's experiments with water of canal—Seine used as
return wire during siege of Paris—Johnson and Melhuish's Indian
experiments—Preece's telegraph over Bristol Channel—He welcomes
Marconi. § 4. Early attempts at transmission of messages through ether—
Experiments of Rathenau and others. § 5. Forerunners of ether telegraphy:
Clerk Maxwell and Hertz—Dolbear, Hughes, and Graham Bell. § 6.
Telegraphy by Hertzian waves first suggested by Threlfall—Crookes',
Tesla's, Lodge's, Rutherford's, and Popoff's contributions—Marconi first
makes it practicable. § 7. The receiver in wireless telegraphy—Varley's,
Calzecchi—Onesti's, and Branly's researches— Explanation of coherer still
obscure. § 8. Wireless telegraphy enters the commercial stage— Defect of
Marconi's system—Braun's, Armstrong's, Lee de Forest's, and Fessenden's
systems make use of earth— Hertz and Marconi entitled to foremost place
among discoverers.

CHAPTER VIII
THE CONDUCTIVITY OF GASES AND THE IONS
§ 1. The Conductivity of Gases: Relations of matter to ether cardinal
problem—Conductivity of gases at first misapprehended—Erman's
forgotten researches—Giese first notices phenomenon—Experiment with
X-rays— J.J. Thomson's interpretation—Ionized gas not obedient to Ohm's
law—Discharge of charged conductors by ionized gas. § 2. The
Condensation of water-vapour by Ions: Vapour will not condense without
nucleus—Wilson's experiments on electrical condensation—Wilson and

Thomson's counting experiment—Twenty million ions per c.cm. of gas—
Estimate of charge borne by ion— Speed of charges—Zeleny's and
Langevin's experiments—Negative ions 1/1000 of size of atoms—Natural
unit of electricity or electrons. § 3. How Ions are Produced: Various causes
of ionization—Moreau's experiments with alkaline salts—Barus and Bloch
on ionization by phosphorus vapours—Ionization always result of shock. §
4. Electrons in Metals: Movement of electrons in metals foreshadowed by
Weber—Giese's, Riecke's, Drude's, and J.J. Thomson's researches—Path of
ions in metals and conduction of heat—Theory of Lorentz—Hesehus'
explanation of electrification by contact—Emission of electrons by charged
body— Thomson's measurement of positive ions.

CHAPTER IX
CATHODE RAYS AND RADIOACTIVE BODIES
§ 1. The Cathode Rays: History of discovery—Crookes' theory—Lenard
rays—Perrin's proof of negative charge—Cathode rays give rise to X-rays
—The canal rays—Villard's researches and magneto-cathode rays—
Ionoplasty—Thomson's measurements of speed of rays —All atoms can be
dissociated. § 2. Radioactive Substances: Uranic rays of Niepce de St
Victor and Becquerel—General radioactivity of matter—Le Bon's and
Rutherford's comparison of uranic with X rays—Pierre and Mme. Curie's
discovery of polonium and radium—Their characteristics—Debierne
discovers actinium. § 3. Radiations and Emanations of Radioactive Bodies:
Giesel's, Becquerel's, and Rutherford's Researches—Alpha, beta, and
gamma rays—Sagnac's secondary rays—Crookes' spinthariscope—The
emanation —Ramsay and Soddy's researches upon it—Transformations of
radioactive bodies—Their order. § 4. Disaggregation of Matter and Atomic
Energy: Actual transformations of matter in radioactive bodies —Helium or
lead final product—Ultimate disappearance of radium from earth—Energy
liberated by radium: its amount and source—Suggested models of
radioactive atoms—Generalization from radioactive phenomena -Le Bon's
theories—Ballistic hypothesis generally admitted—Does energy come from
without—Sagnac's experiments—Elster and Geitel's contra.

CHAPTER X
THE ETHER AND MATTER
§ 1. The Relations between the Ether and Matter: Attempts to reduce all
matter to forms of ether—Emission and absorption phenomena show
reciprocal action— Laws of radiation—Radiation of gases—Production of
spectrum—Differences between light and sound variations show difference
of media—Cauchy's, Briot's, Carvallo's and Boussinesq's researches—
Helmholtz's and Poincaré's electromagnetic theories of dispersion. § 2. The
Theory of Lorentz:—Mechanics fails to explain relations between ether and
matter—Lorentz predicts action of magnet on spectrum—Zeeman's
experiment —Later researches upon Zeeman effect— Multiplicity of
electrons—Lorentz's explanation of thermoelectric phenomena by electrons
—Maxwell's and Lorentz's theories do not agree—Lorentz's probably more
correct—Earth's movement in relation to ether. § 3. The Mass of Electrons:
Thomson's and Max Abraham's view that inertia of charged body due to
charge—Longitudinal and transversal mass—Speed of electrons cannot
exceed that of light—Ratio of charge to mass and its variation—Electron
simple electric charge—Phenomena produced by its acceleration. § 4. New
Views on Ether and Matter: Insufficiency of Larmor's view—Ether
definable by electric and magnetic fields—Is matter all electrons? Atom
probably positive centre surrounded by negative electrons—Ignorance
concerning positive particles—Successive transformations of matter
probable —Gravitation still unaccounted for.

CHAPTER XI
THE FUTURE OF PHYSICS
Persistence of ambition to discover supreme principle in physics—
Supremacy of electron theory at present time—Doubtless destined to
disappear like others— Constant progress of science predicted—Immense
field open before it.
INDEX OF NAMES
INDEX OF SUBJECTS

The New Physics and its Evolution

CHAPTER I

THE EVOLUTION OF PHYSICS
The now numerous public which tries with some success to keep abreast of
the movement in science, from seeing its mental habits every day upset, and
from occasionally witnessing unexpected discoveries that produce a more
lively sensation from their reaction on social life, is led to suppose that we
live in a really exceptional epoch, scored by profound crises and illustrated
by extraordinary discoveries, whose singularity surpasses everything known
in the past. Thus we often hear it said that physics, in particular, has of late
years undergone a veritable revolution; that all its principles have been
made new, that all the edifices constructed by our fathers have been
overthrown, and that on the field thus cleared has sprung up the most
abundant harvest that has ever enriched the domain of science.
It is in fact true that the crop becomes richer and more fruitful, thanks to the
development of our laboratories, and that the quantity of seekers has
considerably increased in all countries, while their quality has not
diminished. We should be sustaining an absolute paradox, and at the same
time committing a crying injustice, were we to contest the high importance
of recent progress, and to seek to diminish the glory of contemporary
physicists. Yet it may be as well not to give way to exaggerations, however
pardonable, and to guard against facile illusions. On closer examination it
will be seen that our predecessors might at several periods in history have
conceived, as legitimately as ourselves, similar sentiments of scientific
pride, and have felt that the world was about to appear to them transformed
and under an aspect until then absolutely unknown.
Let us take an example which is salient enough; for, however arbitrary the
conventional division of time may appear to a physicist's eyes, it is natural,
when instituting a comparison between two epochs, to choose those which
extend over a space of half a score of years, and are separated from each
other by the gap of a century. Let us, then, go back a hundred years and
examine what would have been the state of mind of an erudite amateur who
had read and understood the chief publications on physical research
between 1800 and 1810.

Let us suppose that this intelligent and attentive spectator witnessed in 1800
the discovery of the galvanic battery by Volta. He might from that moment
have felt a presentiment that a prodigious transformation was about to occur
in our mode of regarding electrical phenomena. Brought up in the ideas of
Coulomb and Franklin, he might till then have imagined that electricity had
unveiled nearly all its mysteries, when an entirely original apparatus
suddenly gave birth to applications of the highest interest, and excited the
blossoming of theories of immense philosophical extent.
In the treatises on physics published a little later, we find traces of the
astonishment produced by this sudden revelation of a new world.
"Electricity," wrote the Abbé Haüy, "enriched by the labour of so many
distinguished physicists, seemed to have reached the term when a science
has no further important steps before it, and only leaves to those who
cultivate it the hope of confirming the discoveries of their predecessors, and
of casting a brighter light on the truths revealed. One would have thought
that all researches for diversifying the results of experiment were exhausted,
and that theory itself could only be augmented by the addition of a greater
degree of precision to the applications of principles already known. While
science thus appeared to be making for repose, the phenomena of the
convulsive movements observed by Galvani in the muscles of a frog when
connected by metal were brought to the attention and astonishment of
physicists.... Volta, in that Italy which had been the cradle of the new
knowledge, discovered the principle of its true theory in a fact which
reduces the explanation of all the phenomena in question to the simple
contact of two substances of different nature. This fact became in his hands
the germ of the admirable apparatus to which its manner of being and its
fecundity assign one of the chief places among those with which the genius
of mankind has enriched physics."
Shortly afterwards, our amateur would learn that Carlisle and Nicholson
had decomposed water by the aid of a battery; then, that Davy, in 1803, had
produced, by the help of the same battery, a quite unexpected phenomenon,
and had succeeded in preparing metals endowed with marvellous
properties, beginning with substances of an earthy appearance which had
been known for a long time, but whose real nature had not been discovered.

In another order of ideas, surprises as prodigious would wait for our
amateur. Commencing with 1802, he might have read the admirable series
of memoirs which Young then published, and might thereby have learned
how the study of the phenomena of diffraction led to the belief that the
undulation theory, which, since the works of Newton seemed irretrievably
condemned, was, on the contrary, beginning quite a new life. A little later—
in 1808—he might have witnessed the discovery made by Malus of
polarization by reflexion, and would have been able to note, no doubt with
stupefaction, that under certain conditions a ray of light loses the property
of being reflected.
He might also have heard of one Rumford, who was then promulgating very
singular ideas on the nature of heat, who thought that the then classical
notions might be false, that caloric does not exist as a fluid, and who, in
1804, even demonstrated that heat is created by friction. A few years later
he would learn that Charles had enunciated a capital law on the dilatation of
gases; that Pierre Prevost, in 1809, was making a study, full of original
ideas, on radiant heat. In the meantime he would not have failed to read
volumes iii. and iv. of the Mecanique celeste of Laplace, published in 1804
and 1805, and he might, no doubt, have thought that before long
mathematics would enable physical science to develop with unforeseen
safety.
All these results may doubtless be compared in importance with the present
discoveries. When strange metals like potassium and sodium were isolated
by an entirely new method, the astonishment must have been on a par with
that caused in our time by the magnificent discovery of radium. The
polarization of light is a phenomenon as undoubtedly singular as the
existence of the X rays; and the upheaval produced in natural philosophy by
the theories of the disintegration of matter and the ideas concerning
electrons is probably not more considerable than that produced in the
theories of light and heat by the works of Young and Rumford.
If we now disentangle ourselves from contingencies, it will be understood
that in reality physical science progresses by evolution rather than by
revolution. Its march is continuous. The facts which our theories enable us
to discover, subsist and are linked together long after these theories have

disappeared. Out of the materials of former edifices overthrown, new
dwellings are constantly being reconstructed.
The labour of our forerunners never wholly perishes. The ideas of yesterday
prepare for those of to-morrow; they contain them, so to speak, in potentia.
Science is in some sort a living organism, which gives birth to an indefinite
series of new beings taking the places of the old, and which evolves
according to the nature of its environment, adapting itself to external
conditions, and healing at every step the wounds which contact with reality
may have occasioned.
Sometimes this evolution is rapid, sometimes it is slow enough; but it obeys
the ordinary laws. The wants imposed by its surroundings create certain
organs in science. The problems set to physicists by the engineer who
wishes to facilitate transport or to produce better illumination, or by the
doctor who seeks to know how such and such a remedy acts, or, again, by
the physiologist desirous of understanding the mechanism of the gaseous
and liquid exchanges between the cell and the outer medium, cause new
chapters in physics to appear, and suggest researches adapted to the
necessities of actual life.
The evolution of the different parts of physics does not, however, take place
with equal speed, because the circumstances in which they are placed are
not equally favourable. Sometimes a whole series of questions will appear
forgotten, and will live only with a languishing existence; and then some
accidental circumstance suddenly brings them new life, and they become
the object of manifold labours, engross public attention, and invade nearly
the whole domain of science.
We have in our own day witnessed such a spectacle. The discovery of the X
rays—a discovery which physicists no doubt consider as the logical
outcome of researches long pursued by a few scholars working in silence
and obscurity on an otherwise much neglected subject—seemed to the
public eye to have inaugurated a new era in the history of physics. If, as is
the case, however, the extraordinary scientific movement provoked by
Röntgen's sensational experiments has a very remote origin, it has, at least,
been singularly quickened by the favourable conditions created by the
interest aroused in its astonishing applications to radiography.

A lucky chance has thus hastened an evolution already taking place, and
theories previously outlined have received a singular development. Without
wishing to yield too much to what may be considered a whim of fashion,
we cannot, if we are to note in this book the stage actually reached in the
continuous march of physics, refrain from giving a clearly preponderant
place to the questions suggested by the study of the new radiations. At the
present time it is these questions which move us the most; they have shown
us unknown horizons, and towards the fields recently opened to scientific
activity the daily increasing crowd of searchers rushes in rather disorderly
fashion.
One of the most interesting consequences of the recent discoveries has been
to rehabilitate in the eyes of scholars, speculations relating to the
constitution of matter, and, in a more general way, metaphysical problems.
Philosophy has, of course, never been completely separated from science;
but in times past many physicists dissociated themselves from studies
which they looked upon as unreal word-squabbles, and sometimes not
unreasonably abstained from joining in discussions which seemed to them
idle and of rather puerile subtlety. They had seen the ruin of most of the
systems built up a priori by daring philosophers, and deemed it more
prudent to listen to the advice given by Kirchhoff and "to substitute the
description of facts for a sham explanation of nature."
It should however be remarked that these physicists somewhat deceived
themselves as to the value of their caution, and that the mistrust they
manifested towards philosophical speculations did not preclude their
admitting, unknown to themselves, certain axioms which they did not
discuss, but which are, properly speaking, metaphysical conceptions. They
were unconsciously speaking a language taught them by their predecessors,
of which they made no attempt to discover the origin. It is thus that it was
readily considered evident that physics must necessarily some day re-enter
the domain of mechanics, and thence it was postulated that everything in
nature is due to movement. We, further, accepted the principles of the
classical mechanics without discussing their legitimacy.
This state of mind was, even of late years, that of the most illustrious
physicists. It is manifested, quite sincerely and without the slightest reserve,
in all the classical works devoted to physics. Thus Verdet, an illustrious

professor who has had the greatest and most happy influence on the
intellectual formation of a whole generation of scholars, and whose works
are even at the present day very often consulted, wrote: "The true problem
of the physicist is always to reduce all phenomena to that which seems to us
the simplest and clearest, that is to say, to movement." In his celebrated
course of lectures at l'École Polytechnique, Jamin likewise said: "Physics
will one day form a chapter of general mechanics;" and in the preface to his
excellent course of lectures on physics, M. Violle, in 1884, thus expresses
himself: "The science of nature tends towards mechanics by a necessary
evolution, the physicist being able to establish solid theories only on the
laws of movement." The same idea is again met with in the words of Cornu
in 1896: "The general tendency should be to show how the facts observed
and the phenomena measured, though first brought together by empirical
laws, end, by the impulse of successive progressions, in coming under the
general laws of rational mechanics;" and the same physicist showed clearly
that in his mind this connexion of phenomena with mechanics had a deep
and philosophical reason, when, in the fine discourse pronounced by him at
the opening ceremony of the Congrès de Physique in 1900, he exclaimed:
"The mind of Descartes soars over modern physics, or rather, I should say,
he is their luminary. The further we penetrate into the knowledge of natural
phenomena, the clearer and the more developed becomes the bold Cartesian
conception regarding the mechanism of the universe. There is nothing in the
physical world but matter and movement."
If we adopt this conception, we are led to construct mechanical
representations of the material world, and to imagine movements in the
different parts of bodies capable of reproducing all the manifestations of
nature. The kinematic knowledge of these movements, that is to say, the
determination of the position, speed, and acceleration at a given moment of
all the parts of the system, or, on the other hand, their dynamical study,
enabling us to know what is the action of these parts on each other, would
then be sufficient to enable us to foretell all that can occur in the domain of
nature.
This was the great thought clearly expressed by the Encyclopædists of the
eighteenth century; and if the necessity of interpreting the phenomena of
electricity or light led the physicists of last century to imagine particular
fluids which seemed to obey with some difficulty the ordinary rules of

mechanics, these physicists still continued to retain their hope in the future,
and to treat the idea of Descartes as an ideal to be reached sooner or later.
Certain scholars—particularly those of the English School—outrunning
experiment, and pushing things to extremes, took pleasure in proposing
very curious mechanical models which were often strange images of reality.
The most illustrious of them, Lord Kelvin, may be considered as their
representative type, and he has himself said: "It seems to me that the true
sense of the question, Do we or do we not understand a particular subject in
physics? is—Can we make a mechanical model which corresponds to it? I
am never satisfied so long as I have been unable to make a mechanical
model of the object. If I am able to do so, I understand it. If I cannot make
such a model, I do not understand it." But it must be acknowledged that
some of the models thus devised have become excessively complicated, and
this complication has for a long time discouraged all but very bold minds.
In addition, when it became a question of penetrating into the mechanism of
molecules, and we were no longer satisfied to look at matter as a mass, the
mechanical solutions seemed undetermined and the stability of the edifices
thus constructed was insufficiently demonstrated.
Returning then to our starting-point, many contemporary physicists wish to
subject Descartes' idea to strict criticism. From the philosophical point of
view, they first enquire whether it is really demonstrated that there exists
nothing else in the knowable than matter and movement. They ask
themselves whether it is not habit and tradition in particular which lead us
to ascribe to mechanics the origin of phenomena. Perhaps also a question of
sense here comes in. Our senses, which are, after all, the only windows
open towards external reality, give us a view of one side of the world only;
evidently we only know the universe by the relations which exist between it
and our organisms, and these organisms are peculiarly sensitive to
movement.
Nothing, however, proves that those acquisitions which are the most ancient
in historical order ought, in the development of science, to remain the basis
of our knowledge. Nor does any theory prove that our perceptions are an
exact indication of reality. Many reasons, on the contrary, might be invoked
which tend to compel us to see in nature phenomena which cannot be
reduced to movement.

Mechanics as ordinarily understood is the study of reversible phenomena. If
there be given to the parameter which represents time,[1] and which has
assumed increasing values during the duration of the phenomena,
decreasing values which make it go the opposite way, the whole system will
again pass through exactly the same stages as before, and all the phenomena
will unfold themselves in reversed order. In physics, the contrary rule
appears very general, and reversibility generally does not exist. It is an ideal
and limited case, which may be sometimes approached, but can never,
strictly speaking, be met with in its entirety. No physical phenomenon ever
recommences in an identical manner if its direction be altered. It is true that
certain mathematicians warn us that a mechanics can be devised in which
reversibility would no longer be the rule, but the bold attempts made in this
direction are not wholly satisfactory.
On the other hand, it is established that if a mechanical explanation of a
phenomenon can be given, we can find an infinity of others which likewise
account for all the peculiarities revealed by experiment. But, as a matter of
fact, no one has ever succeeded in giving an indisputable mechanical
representation of the whole physical world. Even were we disposed to
admit the strangest solutions of the problem; to consent, for example, to be
satisfied with the hidden systems devised by Helmholtz, whereby we ought
to divide variable things into two classes, some accessible, and the others
now and for ever unknown, we should never manage to construct an edifice
to contain all the known facts. Even the very comprehensive mechanics of a
Hertz fails where the classical mechanics has not succeeded.
Deeming this check irremediable, many contemporary physicists give up
attempts which they look upon as condemned beforehand, and adopt, to
guide them in their researches, a method which at first sight appears much
more modest, and also much more sure. They make up their minds not to
see at once to the bottom of things; they no longer seek to suddenly strip the
last veils from nature, and to divine her supreme secrets; but they work
prudently and advance but slowly, while on the ground thus conquered foot
by foot they endeavour to establish themselves firmly. They study the
various magnitudes directly accessible to their observation without busying
themselves as to their essence. They measure quantities of heat and of
temperature, differences of potential, currents, and magnetic fields; and
then, varying the conditions, apply the rules of experimental method, and

discover between these magnitudes mutual relations, while they thus
succeed in enunciating laws which translate and sum up their labours.
These empirical laws, however, themselves bring about by induction the
promulgation of more general laws, which are termed principles. These
principles are originally only the results of experiments, and experiment
allows them besides to be checked, and their more or less high degree of
generality to be verified. When they have been thus definitely established,
they may serve as fresh starting-points, and, by deduction, lead to very
varied discoveries.
The principles which govern physical science are few in number, and their
very general form gives them a philosophical appearance, while we cannot
long resist the temptation of regarding them as metaphysical dogmas. It
thus happens that the least bold physicists, those who have wanted to show
themselves the most reserved, are themselves led to forget the experimental
character of the laws they have propounded, and to see in them imperious
beings whose authority, placed above all verification, can no longer be
discussed.
Others, on the contrary, carry prudence to the extent of timidity. They desire
to grievously limit the field of scientific investigation, and they assign to
science a too restricted domain. They content themselves with representing
phenomena by equations, and think that they ought to submit to calculation
magnitudes experimentally determined, without asking themselves whether
these calculations retain a physical meaning. They are thus led to
reconstruct a physics in which there again appears the idea of quality,
understood, of course, not in the scholastic sense, since from this quality we
can argue with some precision by representing it under numerical symbols,
but still constituting an element of differentiation and of heterogeneity.
Notwithstanding the errors they may lead to if carried to excess, both these
doctrines render, as a whole, most important service. It is no bad thing that
these contradictory tendencies should subsist, for this variety in the
conception of phenomena gives to actual science a character of intense life
and of veritable youth, capable of impassioned efforts towards the truth.
Spectators who see such moving and varied pictures passing before them,
experience the feeling that there no longer exist systems fixed in an

immobility which seems that of death. They feel that nothing is
unchangeable; that ceaseless transformations are taking place before their
eyes; and that this continuous evolution and perpetual change are the
necessary conditions of progress.
A great number of seekers, moreover, show themselves on their own
account perfectly eclectic. They adopt, according to their needs, such or
such a manner of looking at nature, and do not hesitate to utilize very
different images when they appear to them useful and convenient. And,
without doubt, they are not wrong, since these images are only symbols
convenient for language. They allow facts to be grouped and associated, but
only present a fairly distant resemblance with the objective reality. Hence it
is not forbidden to multiply and to modify them according to circumstances.
The really essential thing is to have, as a guide through the unknown, a map
which certainly does not claim to represent all the aspects of nature, but
which, having been drawn up according to predetermined rules, allows us to
follow an ascertained road in the eternal journey towards the truth.
Among the provisional theories which are thus willingly constructed by
scholars on their journey, like edifices hastily run up to receive an
unforeseen harvest, some still appear very bold and very singular.
Abandoning the search after mechanical models for all electrical
phenomena, certain physicists reverse, so to speak, the conditions of the
problem, and ask themselves whether, instead of giving a mechanical
interpretation to electricity, they may not, on the contrary, give an electrical
interpretation to the phenomena of matter and motion, and thus merge
mechanics itself in electricity. One thus sees dawning afresh the eternal
hope of co-ordinating all natural phenomena in one grandiose and imposing
synthesis. Whatever may be the fate reserved for such attempts, they
deserve attention in the highest degree; and it is desirable to examine them
carefully if we wish to have an exact idea of the tendencies of modern
physics.

CHAPTER II

MEASUREMENTS
§ 1. METROLOGY
Not so very long ago, the scholar was often content with qualitative
observations. Many phenomena were studied without much trouble being
taken to obtain actual measurements. But it is now becoming more and
more understood that to establish the relations which exist between physical
magnitudes, and to represent the variations of these magnitudes by
functions which allow us to use the power of mathematical analysis, it is
most necessary to express each magnitude by a definite number.
Under these conditions alone can a magnitude be considered as effectively
known. "I often say," Lord Kelvin has said, "that if you can measure that of
which you are speaking and express it by a number you know something of
your subject; but if you cannot measure it nor express it by a number, your
knowledge is of a sorry kind and hardly satisfactory. It may be the
beginning of the acquaintance, but you are hardly, in your thoughts,
advanced towards science, whatever the subject may be."
It has now become possible to measure exactly the elements which enter
into nearly all physical phenomena, and these measurements are taken with
ever increasing precision. Every time a chapter in science progresses,
science shows itself more exacting; it perfects its means of investigation, it
demands more and more exactitude, and one of the most striking features of
modern physics is this constant care for strictness and clearness in
experimentation.
A veritable science of measurement has thus been constituted which
extends over all parts of the domain of physics. This science has its rules
and its methods; it points out the best processes of calculation, and teaches
the method of correctly estimating errors and taking account of them. It has
perfected the processes of experiment, co-ordinated a large number of
results, and made possible the unification of standards. It is thanks to it that
the system of measurements unanimously adopted by physicists has been
formed.

At the present day we designate more peculiarly by the name of metrology
that part of the science of measurements which devotes itself specially to
the determining of the prototypes representing the fundamental units of
dimension and mass, and of the standards of the first order which are
derived from them. If all measurable quantities, as was long thought
possible, could be reduced to the magnitudes of mechanics, metrology
would thus be occupied with the essential elements entering into all
phenomena, and might legitimately claim the highest rank in science. But
even when we suppose that some magnitudes can never be connected with
mass, length, and time, it still holds a preponderating place, and its progress
finds an echo throughout the whole domain of the natural sciences. It is
therefore well, in order to give an account of the general progress of
physics, to examine at the outset the improvements which have been
effected in these fundamental measurements, and to see what precision
these improvements have allowed us to attain.

§ 2. THE MEASURE OF LENGTH
To measure a length is to compare it with another length taken as unity.
Measurement is therefore a relative operation, and can only enable us to
know ratios. Did both the length to be measured and the unit chosen happen
to vary simultaneously and in the same degree, we should perceive no
change. Moreover, the unit being, by definition, the term of comparison,
and not being itself comparable with anything, we have theoretically no
means of ascertaining whether its length varies.
If, however, we were to note that, suddenly and in the same proportions, the
distance between two points on this earth had increased, that all the planets
had moved further from each other, that all objects around us had become
larger, that we ourselves had become taller, and that the distance travelled
by light in the duration of a vibration had become greater, we should not
hesitate to think ourselves the victims of an illusion, that in reality all these
distances had remained fixed, and that all these appearances were due to a
shortening of the rule which we had used as the standard for measuring the
lengths.

From the mathematical point of view, it may be considered that the two
hypotheses are equivalent; all has lengthened around us, or else our
standard has become less. But it is no simple question of convenience and
simplicity which leads us to reject the one supposition and to accept the
other; it is right in this case to listen to the voice of common sense, and
those physicists who have an instinctive trust in the notion of an absolute
length are perhaps not wrong. It is only by choosing our unit from those
which at all times have seemed to all men the most invariable, that we are
able in our experiments to note that the same causes acting under identical
conditions always produce the same effects. The idea of absolute length is
derived from the principle of causality; and our choice is forced upon us by
the necessity of obeying this principle, which we cannot reject without
declaring by that very act all science to be impossible.
Similar remarks might be made with regard to the notions of absolute time
and absolute movement. They have been put in evidence and set forth very
forcibly by a learned and profound mathematician, M. Painlevé.
On the particularly clear example of the measure of length, it is interesting
to follow the evolution of the methods employed, and to run through the
history of the progress in precision from the time that we have possessed
authentic documents relating to this question. This history has been written
in a masterly way by one of the physicists who have in our days done the
most by their personal labours to add to it glorious pages. M. Benoit, the
learned Director of the International Bureau of Weights and Measures, has
furnished in various reports very complete details on the subject, from
which I here borrow the most interesting.
We know that in France the fundamental standard for measures of length
was for a long time the Toise du Châtelet, a kind of callipers formed of a
bar of iron which in 1668 was embedded in the outside wall of the Châtelet,
at the foot of the staircase. This bar had at its extremities two projections
with square faces, and all the toises of commerce had to fit exactly between
them. Such a standard, roughly constructed, and exposed to all the injuries
of weather and time, offered very slight guarantees either as to the
permanence or the correctness of its copies. Nothing, perhaps, can better
convey an idea of the importance of the modifications made in the methods

of experimental physics than the easy comparison between so rudimentary a
process and the actual measurements effected at the present time.
The Toise du Châtelet, notwithstanding its evident faults, was employed for
nearly a hundred years; in 1766 it was replaced by the Toise du Pérou, so
called because it had served for the measurements of the terrestrial arc
effected in Peru from 1735 to 1739 by Bouguer, La Condamine, and Godin.
At that time, according to the comparisons made between this new toise and
the Toise du Nord, which had also been used for the measurement of an arc
of the meridian, an error of the tenth part of a millimetre in measuring
lengths of the order of a metre was considered quite unimportant. At the end
of the eighteenth century, Delambre, in his work Sur la Base du Système
métrique décimal, clearly gives us to understand that magnitudes of the
order of the hundredth of a millimetre appear to him incapable of
observation, even in scientific researches of the highest precision. At the
present date the International Bureau of Weights and Measures guarantees,
in the determination of a standard of length compared with the metre, an
approximation of two or three ten-thousandths of a millimetre, and even a
little more under certain circumstances.
This very remarkable progress is due to the improvements in the method of
comparison on the one hand, and in the manufacture of the standard on the
other. M. Benoit rightly points out that a kind of competition has been set
up between the standard destined to represent the unit with its subdivisions
and multiples and the instrument charged with observing it, comparable, up
to a certain point, with that which in another order of ideas goes on between
the gun and the armour-plate.
The measuring instrument of to-day is an instrument of comparison
constructed with meticulous care, which enables us to do away with causes
of error formerly ignored, to eliminate the action of external phenomena,
and to withdraw the experiment from the influence of even the personality
of the observer. This standard is no longer, as formerly, a flat rule, weak and
fragile, but a rigid bar, incapable of deformation, in which the material is
utilised in the best conditions of resistance. For a standard with ends has
been substituted a standard with marks, which permits much more precise
definition and can be employed in optical processes of observation alone;
that is, in processes which can produce in it no deformation and no

alteration. Moreover, the marks are traced on the plane of the neutral
fibres[2] exposed, and the invariability of their distance apart is thus assured,
even when a change is made in the way the rule is supported.
Thanks to studies thus systematically pursued, we have succeeded in the
course of a hundred years in increasing the precision of measures in the
proportion of a thousand to one, and we may ask ourselves whether such an
increase will continue in the future. No doubt progress will not be stayed;
but if we keep to the definition of length by a material standard, it would
seem that its precision cannot be considerably increased. We have nearly
reached the limit imposed by the necessity of making strokes of such a
thickness as to be observable under the microscope.
It may happen, however, that we shall be brought one of these days to a new
conception of the measure of length, and that very different processes of
determination will be thought of. If we took as unit, for instance, the
distance covered by a given radiation during a vibration, the optical
processes would at once admit of much greater precision.
Thus Fizeau, the first to have this idea, says: "A ray of light, with its series
of undulations of extreme tenuity but perfect regularity, may be considered
as a micrometer of the greatest perfection, and particularly suitable for
determining length." But in the present state of things, since the legal and
customary definition of the unit remains a material standard, it is not
enough to measure length in terms of wave-lengths, and we must also know
the value of these wave-lengths in terms of the standard prototype of the
metre.
This was determined in 1894 by M. Michelson and M. Benoit in an
experiment which will remain classic. The two physicists measured a
standard length of about ten centimetres, first in terms of the wave-lengths
of the red, green, and blue radiations of cadmium, and then in terms of the
standard metre. The great difficulty of the experiment proceeds from the
vast difference which exists between the lengths to be compared, the wave-
lengths barely amounting to half a micron; [3] the process employed
consisted in noting, instead of this length, a length easily made about a
thousand times greater, namely, the distance between the fringes of
interference.

In all measurement, that is to say in every determination of the relation of a
magnitude to the unit, there has to be determined on the one hand the
whole, and on the other the fractional part of this ratio, and naturally the
most delicate determination is generally that of this fractional part. In
optical processes the difficulty is reversed. The fractional part is easily
known, while it is the high figure of the number representing the whole
which becomes a very serious obstacle. It is this obstacle which MM.
Michelson and Benoit overcame with admirable ingenuity. By making use
of a somewhat similar idea, M. Macé de Lépinay and MM. Perot and Fabry,
have lately effected by optical methods, measurements of the greatest
precision, and no doubt further progress may still be made. A day may
perhaps come when a material standard will be given up, and it may
perhaps even be recognised that such a standard in time changes its length
by molecular strain, and by wear and tear: and it will be further noted that,
in accordance with certain theories which will be noticed later on, it is not
invariable when its orientation is changed.
For the moment, however, the need of any change in the definition of the
unit is in no way felt; we must, on the contrary, hope that the use of the unit
adopted by the physicists of the whole world will spread more and more. It
is right to remark that a few errors still occur with regard to this unit, and
that these errors have been facilitated by incoherent legislation. France
herself, though she was the admirable initiator of the metrical system, has
for too long allowed a very regrettable confusion to exist; and it cannot be
noted without a certain sadness that it was not until the 11th July 1903 that a
law was promulgated re-establishing the agreement between the legal and
the scientific definition of the metre.
Perhaps it may not be useless to briefly indicate here the reasons of the
disagreement which had taken place. Two definitions of the metre can be,
and in fact were given. One had for its basis the dimensions of the earth, the
other the length of the material standard. In the minds of the founders of the
metrical system, the first of these was the true definition of the unit of
length, the second merely a simple representation. It was admitted,
however, that this representation had been constructed in a manner perfect
enough for it to be nearly impossible to perceive any difference between the
unit and its representation, and for the practical identity of the two
definitions to be thus assured. The creators of the metrical system were

persuaded that the measurements of the meridian effected in their day could
never be surpassed in precision; and on the other hand, by borrowing from
nature a definite basis, they thought to take from the definition of the unit
some of its arbitrary character, and to ensure the means of again finding the
same unit if by any accident the standard became altered. Their confidence
in the value of the processes they had seen employed was exaggerated, and
their mistrust of the future unjustified. This example shows how imprudent
it is to endeavour to fix limits to progress. It is an error to think the march
of science can be stayed; and in reality it is now known that the ten-
millionth part of the quarter of the terrestrial meridian is longer than the
metre by 0.187 millimetres. But contemporary physicists do not fall into the
same error as their forerunners, and they regard the present result as merely
provisional. They guess, in fact, that new improvements will be effected in
the art of measurement; they know that geodesical processes, though much
improved in our days, have still much to do to attain the precision displayed
in the construction and determination of standards of the first order; and
consequently they do not propose to keep the ancient definition, which
would lead to having for unit a magnitude possessing the grave defect from
a practical point of view of being constantly variable.
We may even consider that, looked at theoretically, its permanence would
not be assured. Nothing, in fact, proves that sensible variations may not in
time be produced in the value of an arc of the meridian, and serious
difficulties may arise regarding the probable inequality of the various
meridians.
For all these reasons, the idea of finding a natural unit has been gradually
abandoned, and we have become resigned to accepting as a fundamental
unit an arbitrary and conventional length having a material representation
recognised by universal consent; and it was this unit which was consecrated
by the following law of the 11th July 1903:—
"The standard prototype of the metrical system is the international metre,
which has been sanctioned by the General Conference on Weights and
Measures."

§ 3. THE MEASURE OF MASS

On the subject of measures of mass, similar remarks to those on measures
of length might be made. The confusion here was perhaps still greater,
because, to the uncertainty relating to the fixing of the unit, was added some
indecision on the very nature of the magnitude defined. In law, as in
ordinary practice, the notions of weight and of mass were not, in fact,
separated with sufficient clearness.
They represent, however, two essentially different things. Mass is the
characteristic of a quantity of matter; it depends neither on the geographical
position one occupies nor on the altitude to which one may rise; it remains
invariable so long as nothing material is added or taken away. Weight is the
action which gravity has upon the body under consideration; this action
does not depend solely on the body, but on the earth as well; and when it is
changed from one spot to another, the weight changes, because gravity
varies with latitude and altitude.
These elementary notions, to-day understood even by young beginners,
appear to have been for a long time indistinctly grasped. The distinction
remained confused in many minds, because, for the most part, masses were
comparatively estimated by the intermediary of weights. The estimations of
weight made with the balance utilize the action of the weight on the beam,
but in such conditions that the influence of the variations of gravity
becomes eliminated. The two weights which are being compared may both
of them change if the weighing is effected in different places, but they are
attracted in the same proportion. If once equal, they remain equal even
when in reality they may both have varied.
The current law defines the kilogramme as the standard of mass, and the
law is certainly in conformity with the rather obscurely expressed intentions
of the founders of the metrical system. Their terminology was vague, but
they certainly had in view the supply of a standard for commercial
transactions, and it is quite evident that in barter what is important to the
buyer as well as to the seller is not the attraction the earth may exercise on
the goods, but the quantity that may be supplied for a given price. Besides,
the fact that the founders abstained from indicating any specified spot in the
definition of the kilogramme, when they were perfectly acquainted with the
considerable variations in the intensity of gravity, leaves no doubt as to their
real desire.

The same objections have been made to the definition of the kilogramme, at
first considered as the mass of a cubic decimetre of water at 4° C., as to the
first definition of the metre. We must admire the incredible precision
attained at the outset by the physicists who made the initial determinations,
but we know at the present day that the kilogramme they constructed is
slightly too heavy (by about 1/25,000). Very remarkable researches have
been carried out with regard to this determination by the International
Bureau, and by MM. Macé de Lépinay and Buisson. The law of the 11th
July 1903 has definitely regularized the custom which physicists had
adopted some years before; and the standard of mass, the legal prototype of
the metrical system, is now the international kilogramme sanctioned by the
Conference of Weights and Measures.
The comparison of a mass with the standard is effected with a precision to
which no other measurement can attain. Metrology vouches for the
hundredth of a milligramme in a kilogramme; that is to say, that it estimates
the hundred-millionth part of the magnitude studied.
We may—as in the case of the lengths—ask ourselves whether this already
admirable precision can be surpassed; and progress would seem likely to be
slow, for difficulties singularly increase when we get to such small
quantities. But it is permitted to hope that the physicists of the future will do
still better than those of to-day; and perhaps we may catch a glimpse of the
time when we shall begin to observe that the standard, which is constructed
from a heavy metal, namely, iridium-platinum, itself obeys an apparently
general law, and little by little loses some particles of its mass by
emanation.

§ 4. THE MEASURE OF TIME
The third fundamental magnitude of mechanics is time. There is, so to
speak, no physical phenomenon in which the notion of time linked to the
sequence of our states of consciousness does not play a considerable part.
Ancestral habits and a very early tradition have led us to preserve, as the
unit of time, a unit connected with the earth's movement; and the unit to-
day adopted is, as we know, the sexagesimal second of mean time. This

magnitude, thus defined by the conditions of a natural motion which may
itself be modified, does not seem to offer all the guarantees desirable from
the point of view of invariability. It is certain that all the friction exercised
on the earth—by the tides, for instance—must slowly lengthen the duration
of the day, and must influence the movement of the earth round the sun.
Such influence is certainly very slight, but it nevertheless gives an
unfortunately arbitrary character to the unit adopted.
We might have taken as the standard of time the duration of another natural
phenomenon, which appears to be always reproduced under identical
conditions; the duration, for instance, of a given luminous vibration. But the
experimental difficulties of evaluation with such a unit of the times which
ordinarily have to be considered, would be so great that such a reform in
practice cannot be hoped for. It should, moreover, be remarked that the
duration of a vibration may itself be influenced by external circumstances,
among which are the variations of the magnetic field in which its source is
placed. It could not, therefore, be strictly considered as independent of the
earth; and the theoretical advantage which might be expected from this
alteration would be somewhat illusory.
Perhaps in the future recourse may be had to very different phenomena.
Thus Curie pointed out that if the air inside a glass tube has been rendered
radioactive by a solution of radium, the tube may be sealed up, and it will
then be noted that the radiation of its walls diminishes with time, in
accordance with an exponential law. The constant of time derived by this
phenomenon remains the same whatever the nature and dimensions of the
walls of the tube or the temperature may be, and time might thus be denned
independently of all the other units.
We might also, as M. Lippmann has suggested in an extremely ingenious
way, decide to obtain measures of time which can be considered as absolute
because they are determined by parameters of another nature than that of
the magnitude to be measured. Such experiments are made possible by the
phenomena of gravitation. We could employ, for instance, the pendulum by
adopting, as the unit of force, the force which renders the constant of
gravitation equal to unity. The unit of time thus defined would be
independent of the unit of length, and would depend only on the substance
which would give us the unit of mass under the unit of volume.

It would be equally possible to utilize electrical phenomena, and one might
devise experiments perfectly easy of execution. Thus, by charging a
condenser by means of a battery, and discharging it a given number of times
in a given interval of time, so that the effect of the current of discharge
should be the same as the effect of the output of the battery through a given
resistance, we could estimate, by the measurement of the electrical
magnitudes, the duration of the interval noted. A system of this kind must
not be looked upon as a simple jeu d'esprit, since this very practicable
experiment would easily permit us to check, with a precision which could
be carried very far, the constancy of an interval of time.
From the practical point of view, chronometry has made in these last few
years very sensible progress. The errors in the movements of chronometers
are corrected in a much more systematic way than formerly, and certain
inventions have enabled important improvements to be effected in the
construction of these instruments. Thus the curious properties which steel
combined with nickel—so admirably studied by M.Ch.Ed. Guillaume—
exhibits in the matter of dilatation are now utilized so as to almost
completely annihilate the influence of variations of temperature.

§ 5. THE MEASURE OF TEMPERATURE
From the three mechanical units we derive secondary units; as, for instance,
the unit of work or mechanical energy. The kinetic theory takes
temperature, as well as heat itself, to be a quantity of energy, and thus
seems to connect this notion with the magnitudes of mechanics. But the
legitimacy of this theory cannot be admitted, and the calorific movement
should also be a phenomenon so strictly confined in space that our most
delicate means of investigation would not enable us to perceive it. It is
better, then, to continue to regard the unit of difference of temperature as a
distinct unit, to be added to the fundamental units.
To define the measure of a certain temperature, we take, in practice, some
arbitrary property of a body. The only necessary condition of this property
is, that it should constantly vary in the same direction when the temperature
rises, and that it should possess, at any temperature, a well-marked value.
We measure this value by melting ice and by the vapour of boiling water

under normal pressure, and the successive hundredths of its variation,
beginning with the melting ice, defines the percentage. Thermodynamics,
however, has made it plain that we can set up a thermometric scale without
relying upon any determined property of a real body. Such a scale has an
absolute value independently of the properties of matter. Now it happens
that if we make use for the estimation of temperatures, of the phenomena of
dilatation under a constant pressure, or of the increase of pressure in a
constant volume of a gaseous body, we obtain a scale very near the
absolute, which almost coincides with it when the gas possesses certain
qualities which make it nearly what is called a perfect gas. This most lucky
coincidence has decided the choice of the convention adopted by physicists.
They define normal temperature by means of the variations of pressure in a
mass of hydrogen beginning with the initial pressure of a metre of mercury
at 0° C.
M.P. Chappuis, in some very precise experiments conducted with much
method, has proved that at ordinary temperatures the indications of such a
thermometer are so close to the degrees of the theoretical scale that it is
almost impossible to ascertain the value of the divergences, or even the
direction that they take. The divergence becomes, however, manifest when
we work with extreme temperatures. It results from the useful researches of
M. Daniel Berthelot that we must subtract +0.18° from the indications of
the hydrogen thermometer towards the temperature -240° C, and add +0.05°
to 1000° to equate them with the thermodynamic scale. Of course, the
difference would also become still more noticeable on getting nearer to the
absolute zero; for as hydrogen gets more and more cooled, it gradually
exhibits in a lesser degree the characteristics of a perfect gas.
To study the lower regions which border on that kind of pole of cold
towards which are straining the efforts of the many physicists who have of
late years succeeded in getting a few degrees further forward, we may turn
to a gas still more difficult to liquefy than hydrogen. Thus, thermometers
have been made of helium; and from the temperature of -260° C. downward
the divergence of such a thermometer from one of hydrogen is very marked.
The measurement of very high temperatures is not open to the same
theoretical objections as that of very low temperatures; but, from a practical
point of view, it is as difficult to effect with an ordinary gas thermometer. It

becomes impossible to guarantee the reservoir remaining sufficiently
impermeable, and all security disappears, notwithstanding the use of
recipients very superior to those of former times, such as those lately
devised by the physicists of the Reichansalt. This difficulty is obviated by
using other methods, such as the employment of thermo-electric couples,
such as the very convenient couple of M. le Chatelier; but the graduation of
these instruments can only be effected at the cost of a rather bold
extrapolation.
M.D. Berthelot has pointed out and experimented with a very interesting
process, founded on the measurement by the phenomena of interference of
the refractive index of a column of air subjected to the temperature it is
desired to measure. It appears admissible that even at the highest
temperatures the variation of the power of refraction is strictly proportional
to that of the density, for this proportion is exactly verified so long as it is
possible to check it precisely. We can thus, by a method which offers the
great advantage of being independent of the power and dimension of the
envelopes employed—since the length of the column of air considered
alone enters into the calculation—obtain results equivalent to those given
by the ordinary air thermometer.
Another method, very old in principle, has also lately acquired great
importance. For a long time we sought to estimate the temperature of a
body by studying its radiation, but we did not know any positive relation
between this radiation and the temperature, and we had no good
experimental method of estimation, but had recourse to purely empirical
formulas and the use of apparatus of little precision. Now, however, many
physicists, continuing the classic researches of Kirchhoff, Boltzmann,
Professors Wien and Planck, and taking their starting-point from the laws of
thermodynamics, have given formulas which establish the radiating power
of a dark body as a function of the temperature and the wave-length, or,
better still, of the total power as a function of the temperature and wave-
length corresponding to the maximum value of the power of radiation. We
see, therefore, the possibility of appealing for the measurement of
temperature to a phenomenon which is no longer the variation of the elastic
force of a gas, and yet is also connected with the principles of
thermodynamics.

This is what Professors Lummer and Pringsheim have shown in a series of
studies which may certainly be reckoned among the greatest experimental
researches of the last few years. They have constructed a radiator closely
resembling the theoretically integral radiator which a closed isothermal
vessel would be, and with only a very small opening, which allows us to
collect from outside the radiations which are in equilibrium with the
interior. This vessel is formed of a hollow carbon cylinder, heated by a
current of high intensity; the radiations are studied by means of a bolometer,
the disposition of which varies with the nature of the experiments.
It is hardly possible to enter into the details of the method, but the result
sufficiently indicates its importance. It is now possible, thanks to their
researches, to estimate a temperature of 2000° C. to within about 5°. Ten
years ago a similar approximation could hardly have been arrived at for a
temperature of 1000° C.

§ 6. DERIVED UNITS AND THE MEASURE OF A QUANTITY OF
ENERGY
It must be understood that it is only by arbitrary convention that a
dependency is established between a derived unit and the fundamental
units. The laws of numbers in physics are often only laws of proportion. We
transform them into laws of equation, because we introduce numerical
coefficients and choose the units on which they depend so as to simplify as
much as possible the formulas most in use. A particular speed, for instance,
is in reality nothing else but a speed, and it is only by the peculiar choice of
unit that we can say that it is the space covered during the unit of time. In
the same way, a quantity of electricity is a quantity of electricity; and there
is nothing to prove that, in its essence, it is really reducible to a function of
mass, of length, and of time.
Persons are still to be met with who seem to have some illusions on this
point, and who see in the doctrine of the dimensions of the units a doctrine
of general physics, while it is, to say truth, only a doctrine of metrology.
The knowledge of dimensions is valuable, since it allows us, for instance, to
easily verify the homogeneity of a formula, but it can in no way give us any
information on the actual nature of the quantity measured.

Magnitudes to which we attribute like dimensions may be qualitatively
irreducible one to the other. Thus the different forms of energy are
measured by the same unit, and yet it seems that some of them, such as
kinetic energy, really depend on time; while for others, such as potential
energy, the dependency established by the system of measurement seems
somewhat fictitious.
The numerical value of a quantity of energy of any nature should, in the
system C.G.S., be expressed in terms of the unit called the erg; but, as a
matter of fact, when we wish to compare and measure different quantities of
energy of varying forms, such as electrical, chemical, and other quantities,
etc., we nearly always employ a method by which all these energies are
finally transformed and used to heat the water of a calorimeter. It is
therefore very important to study well the calorific phenomenon chosen as
the unit of heat, and to determine with precision its mechanical equivalent,
that is to say, the number of ergs necessary to produce this unit. This is a
number which, on the principle of equivalence, depends neither on the
method employed, nor the time, nor any other external circumstance.
As the result of the brilliant researches of Rowland and of Mr Griffiths on
the variations of the specific heat of water, physicists have decided to take
as calorific standard the quantity of heat necessary to raise a gramme of
water from 15° to 16° C., the temperature being measured by the scale of
the hydrogen thermometer of the International Bureau.
On the other hand, new determinations of the mechanical equivalent,
among which it is right to mention that of Mr. Ames, and a full discussion
as to the best results, have led to the adoption of the number 4.187 to
represent the number of ergs capable of producing the unit of heat.
In practice, the measurement of a quantity of heat is very often effected by
means of the ice calorimeter, the use of which is particularly simple and
convenient. There is, therefore, a very special interest in knowing exactly
the melting-point of ice. M. Leduc, who for several years has measured a
great number of physical constants with minute precautions and a
remarkable sense of precision, concludes, after a close discussion of the
various results obtained, that this heat is equal to 79.1 calories. An error of
almost a calorie had been committed by several renowned experimenters,

and it will be seen that in certain points the art of measurement may still be
largely perfected.
To the unit of energy might be immediately attached other units. For
instance, radiation being nothing but a flux of energy, we could, in order to
establish photometric units, divide the normal spectrum into bands of a
given width, and measure the power of each for the unit of radiating
surface.
But, notwithstanding some recent researches on this question, we cannot yet
consider the distribution of energy in the spectrum as perfectly known. If
we adopt the excellent habit which exists in some researches of expressing
radiating energy in ergs, it is still customary to bring the radiations to a
standard giving, by its constitution alone, the unit of one particular
radiation. In particular, the definitions are still adhered to which were
adopted as the result of the researches of M. Violle on the radiation of fused
platinum at the temperature of solidification; and most physicists utilize in
the ordinary methods of photometry the clearly defined notions of M.
Blondel as to the luminous intensity of flux, illumination (éclairement),
light (éclat), and lighting (éclairage), with the corresponding units, decimal
candle, lumen, lux, carcel lamp, candle per square centimetre, and lumen-
hour. [4]

§ 7. MEASURE OF CERTAIN PHYSICAL CONSTANTS
The progress of metrology has led, as a consequence, to corresponding
progress in nearly all physical measurements, and particularly in the
measure of natural constants. Among these, the constant of gravitation
occupies a position quite apart from the importance and simplicity of the
physical law which defines it, as well as by its generality. Two material
particles are mutually attracted to each other by a force directly proportional
to the product of their mass, and inversely proportional to the square of the
distance between them. The coefficient of proportion is determined when
once the units are chosen, and as soon as we know the numerical values of
this force, of the two masses, and of their distance. But when we wish to
make laboratory experiments serious difficulties appear, owing to the
weakness of the attraction between masses of ordinary dimensions.

Microscopic forces, so to speak, have to be observed, and therefore all the
causes of errors have to be avoided which would be unimportant in most
other physical researches. It is known that Cavendish was the first who
succeeded by means of the torsion balance in effecting fairly precise
measurements. This method has been again taken in hand by different
experimenters, and the most recent results are due to Mr Vernon Boys. This
learned physicist is also the author of a most useful practical invention, and
has succeeded in making quartz threads as fine as can be desired and
extremely uniform. He finds that these threads possess valuable properties,
such as perfect elasticity and great tenacity. He has been able, with threads
not more than 1/500 of a millimetre in diameter, to measure with precision
couples of an order formerly considered outside the range of experiment,
and to reduce the dimensions of the apparatus of Cavendish in the
proportion of 150 to 1. The great advantage found in the use of these small
instruments is the better avoidance of the perturbations arising from
draughts of air, and of the very serious influence of the slightest inequality
in temperature.
Other methods have been employed in late years by other experimenters,
such as the method of Baron Eötvös, founded on the use of a torsion lever,
the method of the ordinary balance, used especially by Professors Richarz
and Krigar-Menzel and also by Professor Poynting, and the method of M.
Wilsing, who uses a balance with a vertical beam. The results fairly agree,
and lead to attributing to the earth a density equal to 5.527.
The most familiar manifestation of gravitation is gravity. The action of the
earth on the unit of mass placed in one point, and the intensity of gravity, is
measured, as we know, by the aid of a pendulum. The methods of
measurement, whether by absolute or by relative determinations, so greatly
improved by Borda and Bessel, have been still further improved by various
geodesians, among whom should be mentioned M. von Sterneek and
General Defforges. Numerous observations have been made in all parts of
the world by various explorers, and have led to a fairly complete knowledge
of the distribution of gravity over the surface of the globe. Thus we have
succeeded in making evident anomalies which would not easily find their
place in the formula of Clairaut.

Another constant, the determination of which is of the greatest utility in
astronomy of position, and the value of which enters into electromagnetic
theory, has to-day assumed, with the new ideas on the constitution of
matter, a still more considerable importance. I refer to the speed of light,
which appears to us, as we shall see further on, the maximum value of
speed which can be given to a material body.
After the historical experiments of Fizeau and Foucault, taken up afresh, as
we know, partly by Cornu, and partly by Michelson and Newcomb, it
remained still possible to increase the precision of the measurements.
Professor Michelson has undertaken some new researches by a method
which is a combination of the principle of the toothed wheel of Fizeau with
the revolving mirror of Foucault. The toothed wheel is here replaced,
however, by a grating, in which the lines and the spaces between them take
the place of the teeth and the gaps, the reflected light only being returned
when it strikes on the space between two lines. The illustrious American
physicist estimates that he can thus evaluate to nearly five kilometres the
path traversed by light in one second. This approximation corresponds to a
relative value of a few hundred-thousandths, and it far exceeds those
hitherto attained by the best experimenters. When all the experiments are
completed, they will perhaps solve certain questions still in suspense; for
instance, the question whether the speed of propagation depends on
intensity. If this turns out to be the case, we should be brought to the
important conclusion that the amplitude of the oscillations, which is
certainly very small in relation to the already tiny wave-lengths, cannot be
considered as unimportant in regard to these lengths. Such would seem to
have been the result of the curious experiments of M. Muller and of M.
Ebert, but these results have been recently disputed by M. Doubt.
In the case of sound vibrations, on the other hand, it should be noted that
experiment, consistently with the theory, proves that the speed increases
with the amplitude, or, if you will, with the intensity. M. Violle has
published an important series of experiments on the speed of propagation of
very condensed waves, on the deformations of these waves, and on the
relations of the speed and the pressure, which verify in a remarkable
manner the results foreshadowed by the already old calculations of
Riemann, repeated later by Hugoniot. If, on the contrary, the amplitude is
sufficiently small, there exists a speed limit which is the same in a large

pipe and in free air. By some beautiful experiments, MM. Violle and Vautier
have clearly shown that any disturbance in the air melts somewhat quickly
into a single wave of given form, which is propagated to a distance, while
gradually becoming weaker and showing a constant speed which differs
little in dry air at 0° C. from 331.36 metres per second. In a narrow pipe the
influence of the walls makes itself felt and produces various effects, in
particular a kind of dispersion in space of the harmonics of the sound. This
phenomenon, according to M. Brillouin, is perfectly explicable by a theory
similar to the theory of gratings.

CHAPTER III

PRINCIPLES
§ 1. THE PRINCIPLES OF PHYSICS
Facts conscientiously observed lead by induction to the enunciation of a
certain number of laws or general hypotheses which are the principles
already referred to. These principal hypotheses are, in the eyes of a
physicist, legitimate generalizations, the consequences of which we shall be
able at once to check by the experiments from which they issue.
Among the principles almost universally adopted until lately figure
prominently those of mechanics—such as the principle of relativity, and the
principle of the equality of action and reaction. We will not detail nor
discuss them here, but later on we shall have an opportunity of pointing out
how recent theories on the phenomena of electricity have shaken the
confidence of physicists in them and have led certain scholars to doubt their
absolute value.
The principle of Lavoisier, or principle of the conservation of mass,
presents itself under two different aspects according to whether mass is
looked upon as the coefficient of the inertia of matter or as the factor which
intervenes in the phenomena of universal attraction, and particularly in
gravitation. We shall see when we treat of these theories, how we have been
led to suppose that inertia depended on velocity and even on direction. If
this conception were exact, the principle of the invariability of mass would
naturally be destroyed. Considered as a factor of attraction, is mass really
indestructible?
A few years ago such a question would have seemed singularly audacious.
And yet the law of Lavoisier is so far from self-evident that for centuries it
escaped the notice of physicists and chemists. But its great apparent
simplicity and its high character of generality, when enunciated at the end
of the eighteenth century, rapidly gave it such an authority that no one was
able to any longer dispute it unless he desired the reputation of an oddity
inclined to paradoxical ideas.

It is important, however, to remark that, under fallacious metaphysical
appearances, we are in reality using empty words when we repeat the
aphorism, "Nothing can be lost, nothing can be created," and deduce from it
the indestructibility of matter. This indestructibility, in truth, is an
experimental fact, and the principle depends on experiment. It may even
seem, at first sight, more singular than not that the weight of a bodily
system in a given place, or the quotient of this weight by that of the
standard mass—that is to say, the mass of these bodies—remains invariable,
both when the temperature changes and when chemical reagents cause the
original materials to disappear and to be replaced by new ones. We may
certainly consider that in a chemical phenomenon annihilations and
creations of matter are really produced; but the experimental law teaches us
that there is compensation in certain respects.
The discovery of the radioactive bodies has, in some sort, rendered popular
the speculations of physicists on the phenomena of the disaggregation of
matter. We shall have to seek the exact meaning which ought to be given to
the experiments on the emanation of these bodies, and to discover whether
these experiments really imperil the law of Lavoisier.
For some years different experimenters have also effected many very
precise measurements of the weight of divers bodies both before and after
chemical reactions between these bodies. Two highly experienced and
cautious physicists, Professors Landolt and Heydweiller, have not hesitated
to announce the sensational result that in certain circumstances the weight is
no longer the same after as before the reaction. In particular, the weight of a
solution of salts of copper in water is not the exact sum of the joint weights
of the salt and the water. Such experiments are evidently very delicate; they
have been disputed, and they cannot be considered as sufficient for
conviction. It follows nevertheless that it is no longer forbidden to regard
the law of Lavoisier as only an approximate law; according to Sandford and
Ray, this approximation would be about 1/2,400,000. This is also the result
reached by Professor Poynting in experiments regarding the possible action
of temperature on the weight of a body; and if this be really so, we may
reassure ourselves, and from the point of view of practical application may
continue to look upon matter as indestructible.

The principles of physics, by imposing certain conditions on phenomena,
limit after a fashion the field of the possible. Among these principles is one
which, notwithstanding its importance when compared with that of
universally known principles, is less familiar to some people. This is the
principle of symmetry, more or less conscious applications of which can, no
doubt, be found in various works and even in the conceptions of Copernican
astronomers, but which was generalized and clearly enunciated for the first
time by the late M. Curie. This illustrious physicist pointed out the
advantage of introducing into the study of physical phenomena the
considerations on symmetry familiar to crystallographers; for a
phenomenon to take place, it is necessary that a certain dissymmetry should
previously exist in the medium in which this phenomenon occurs. A body,
for instance, may be animated with a certain linear velocity or a speed of
rotation; it may be compressed, or twisted; it may be placed in an electric or
in a magnetic field; it may be affected by an electric current or by one of
heat; it may be traversed by a ray of light either ordinary or polarized
rectilineally or circularly, etc.:—in each case a certain minimum and
characteristic dissymmetry is necessary at every point of the body in
question.
This consideration enables us to foresee that certain phenomena which
might be imagined a priori cannot exist. Thus, for instance, it is impossible
that an electric field, a magnitude directed and not superposable on its
image in a mirror perpendicular to its direction, could be created at right
angles to the plane of symmetry of the medium; while it would be possible
to create a magnetic field under the same conditions.
This consideration thus leads us to the discovery of new phenomena; but it
must be understood that it cannot of itself give us absolutely precise notions
as to the nature of these phenomena, nor disclose their order of magnitude.

§ 2. THE PRINCIPLE OF THE CONSERVATION OF ENERGY
Dominating not physics alone, but nearly every other science, the principle
of the conservation of energy is justly considered as the grandest conquest
of contemporary thought. It shows us in a powerful light the most diverse
questions; it introduces order into the most varied studies; it leads to a clear

and coherent interpretation of phenomena which, without it, appear to have
no connexion with each other; and it supplies precise and exact numerical
relations between the magnitudes which enter into these phenomena.
The boldest minds have an instinctive confidence in it, and it is the
principle which has most stoutly resisted that assault which the daring of a
few theorists has lately directed to the overthrow of the general principles
of physics. At every new discovery, the first thought of physicists is to find
out how it accords with the principle of the conservation of energy. The
application of the principle, moreover, never fails to give valuable hints on
the new phenomenon, and often even suggests a complementary discovery.
Up till now it seems never to have received a check, even the extraordinary
properties of radium not seriously contradicting it; also the general form in
which it is enunciated gives it such a suppleness that it is no doubt very
difficult to overthrow.
I do not claim to set forth here the complete history of this principle, but I
will endeavour to show with what pains it was born, how it was kept back
in its early days and then obstructed in its development by the unfavourable
conditions of the surroundings in which it appeared. It first of all came, in
fact, to oppose itself to the reigning theories; but, little by little, it acted on
these theories, and they were modified under its pressure; then, in their turn,
these theories reacted on it and changed its primitive form.
It had to be made less wide in order to fit into the classic frame, and was
absorbed by mechanics; and if it thus became less general, it gained in
precision what it lost in extent. When once definitely admitted and classed,
as it were, in the official domain of science, it endeavoured to burst its
bonds and return to a more independent and larger life. The history of this
principle is similar to that of all evolutions.
It is well known that the conservation of energy was, at first, regarded from
the point of view of the reciprocal transformations between heat and work,
and that the principle received its first clear enunciation in the particular
case of the principle of equivalence. It is, therefore, rightly considered that
the scholars who were the first to doubt the material nature of caloric were
the precursors of R. Mayer; their ideas, however, were the same as those of

the celebrated German doctor, for they sought especially to demonstrate that
heat was a mode of motion.
Without going back to early and isolated attempts like those of Daniel
Bernoulli, who, in his hydrodynamics, propounded the basis of the kinetic
theory of gases, or the researches of Boyle on friction, we may recall, to
show how it was propounded in former times, a rather forgotten page of the
Mémoire sur la Chaleur, published in 1780 by Lavoisier and Laplace:
"Other physicists," they wrote, after setting out the theory of caloric, "think
that heat is nothing but the result of the insensible vibrations of matter.... In
the system we are now examining, heat is the vis viva resulting from the
insensible movements of the molecules of a body; it is the sum of the
products of the mass of each molecule by the square of its velocity.... We
shall not decide between the two preceding hypotheses; several phenomena
seem to support the last mentioned—for instance, that of the heat produced
by the friction of two solid bodies. But there are others which are more
simply explained by the first, and perhaps they both operate at once." Most
of the physicists of that period, however, did not share the prudent doubts of
Lavoisier and Laplace. They admitted, without hesitation, the first
hypothesis; and, four years after the appearance of the Mémoire sur la
Chaleur, Sigaud de Lafond, a professor of physics of great reputation,
wrote: "Pure Fire, free from all state of combination, seems to be an
assembly of particles of a simple, homogeneous, and absolutely unalterable
matter, and all the properties of this element indicate that these particles are
infinitely small and free, that they have no sensible cohesion, and that they
are moved in every possible direction by a continual and rapid motion
which is essential to them.... The extreme tenacity and the surprising
mobility of its molecules are manifestly shown by the ease with which it
penetrates into the most compact bodies and by its tendency to put itself in
equilibrium throughout all bodies near to it."
It must be acknowledged, however, that the idea of Lavoisier and Laplace
was rather vague and even inexact on one important point. They admitted it
to be evident that "all variations of heat, whether real or apparent,
undergone by a bodily system when changing its state, are produced in
inverse order when the system passes back to its original state." This phrase
is the very denial of equivalence where these changes of state are
accompanied by external work.

Laplace, moreover, himself became later a very convinced partisan of the
hypothesis of the material nature of caloric, and his immense authority, so
fortunate in other respects for the development of science, was certainly in
this case the cause of the retardation of progress.
The names of Young, Rumford, Davy, are often quoted among those
physicists who, at the commencement of the nineteenth century, caught
sight of the new truths as to the nature of heat. To these names is very
properly added that of Sadi Carnot. A note found among his papers
unquestionably proves that, before 1830, ideas had occurred to him from
which it resulted that in producing work an equivalent amount of heat was
destroyed. But the year 1842 is particularly memorable in the history of
science as the year in which Jules Robert Mayer succeeded, by an entirely
personal effort, in really enunciating the principle of the conservation of
energy. Chemists recall with just pride that the Remarques sur les forces de
la nature animée, contemptuously rejected by all the journals of physics,
were received and published in the Annalen of Liebig. We ought never to
forget this example, which shows with what difficulty a new idea contrary
to the classic theories of the period succeeds in coming to the front; but
extenuating circumstances may be urged on behalf of the physicists.
Robert Mayer had a rather insufficient mathematical education, and his
Memoirs, the Remarques, as well as the ulterior publications, Mémoire sur
le mouvement organique et la nutrition and the Matériaux pour la
dynamique du ciel, contain, side by side with very profound ideas, evident
errors in mechanics. Thus it often happens that discoveries put forward in a
somewhat vague manner by adventurous minds not overburdened by the
heavy baggage of scientific erudition, who audaciously press forward in
advance of their time, fall into quite intelligible oblivion until rediscovered,
clarified, and put into shape by slower but surer seekers. This was the case
with the ideas of Mayer. They were not understood at first sight, not only on
account of their originality, but also because they were couched in incorrect
language.
Mayer was, however, endowed with a singular strength of thought; he
expressed in a rather confused manner a principle which, for him, had a
generality greater than mechanics itself, and so his discovery was in

advance not only of his own time but of half the century. He may justly be
considered the founder of modern energetics.
Freed from the obscurities which prevented its being clearly perceived, his
idea stands out to-day in all its imposing simplicity. Yet it must be
acknowledged that if it was somewhat denaturalised by those who
endeavoured to adapt it to the theories of mechanics, and if it at first lost its
sublime stamp of generality, it thus became firmly fixed and consolidated
on a more stable basis.
The efforts of Helmholtz, Clausius, and Lord Kelvin to introduce the
principle of the conservation of energy into mechanics, were far from
useless. These illustrious physicists succeeded in giving a more precise
form to its numerous applications; and their attempts thus contributed, by
reaction, to give a fresh impulse to mechanics, and allowed it to be linked to
a more general order of facts. If energetics has not been able to be included
in mechanics, it seems indeed that the attempt to include mechanics in
energetics was not in vain.
In the middle of the last century, the explanation of all natural phenomena
seemed more and more referable to the case of central forces. Everywhere it
was thought that reciprocal actions between material points could be
perceived, these points being attracted or repelled by each other with an
intensity depending only on their distance or their mass. If, to a system thus
composed, the laws of the classical mechanics are applied, it is shown that
half the sum of the product of the masses by the square of the velocities, to
which is added the work which might be accomplished by the forces to
which the system would be subject if it returned from its actual to its initial
position, is a sum constant in quantity.
This sum, which is the mechanical energy of the system, is therefore an
invariable quantity in all the states to which it may be brought by the
interaction of its various parts, and the word energy well expresses a capital
property of this quantity. For if two systems are connected in such a way
that any change produced in the one necessarily brings about a change in
the other, there can be no variation in the characteristic quantity of the
second except so far as the characteristic quantity of the first itself varies—
on condition, of course, that the connexions are made in such a manner as

to introduce no new force. It will thus be seen that this quantity well
expresses the capacity possessed by a system for modifying the state of a
neighbouring system to which we may suppose it connected.
Now this theorem of pure mechanics was found wanting every time friction
took place—that is to say, in all really observable cases. The more
perceptible the friction, the more considerable the difference; but, in
addition, a new phenomenon always appeared and heat was produced. By
experiments which are now classic, it became established that the quantity
of heat thus created independently of the nature of the bodies is always
(provided no other phenomena intervene) proportional to the energy which
has disappeared. Reciprocally, also, heat may disappear, and we always find
a constant relation between the quantities of heat and work which mutually
replace each other.
It is quite clear that such experiments do not prove that heat is work. We
might just as well say that work is heat. It is making a gratuitous hypothesis
to admit this reduction of heat to mechanism; but this hypothesis was so
seductive, and so much in conformity with the desire of nearly all physicists
to arrive at some sort of unity in nature, that they made it with eagerness
and became unreservedly convinced that heat was an active internal force.
Their error was not in admitting this hypothesis; it was a legitimate one
since it has proved very fruitful. But some of them committed the fault of
forgetting that it was an hypothesis, and considered it a demonstrated truth.
Moreover, they were thus brought to see in phenomena nothing but these
two particular forms of energy which in their minds were easily identified
with each other.
From the outset, however, it became manifest that the principle is applicable
to cases where heat plays only a parasitical part. There were thus
discovered, by translating the principle of equivalence, numerical relations
between the magnitudes of electricity, for instance, and the magnitudes of
mechanics. Heat was a sort of variable intermediary convenient for
calculation, but introduced in a roundabout way and destined to disappear
in the final result.
Verdet, who, in lectures which have rightly remained celebrated, defined
with remarkable clearness the new theories, said, in 1862: "Electrical

phenomena are always accompanied by calorific manifestations, of which
the study belongs to the mechanical theory of heat. This study, moreover,
will not only have the effect of making known to us interesting facts in
electricity, but will throw some light on the phenomena of electricity
themselves."
The eminent professor was thus expressing the general opinion of his
contemporaries, but he certainly seemed to have felt in advance that the
new theory was about to penetrate more deeply into the inmost nature of
things. Three years previously, Rankine also had put forth some very
remarkable ideas the full meaning of which was not at first well understood.
He it was who comprehended the utility of employing a more inclusive
term, and invented the phrase energetics. He also endeavoured to create a
new doctrine of which rational mechanics should be only a particular case;
and he showed that it was possible to abandon the ideas of atoms and
central forces, and to construct a more general system by substituting for
the ordinary consideration of forces that of the energy which exists in all
bodies, partly in an actual, partly in a potential state.
By giving more precision to the conceptions of Rankine, the physicists of
the end of the nineteenth century were brought to consider that in all
physical phenomena there occur apparitions and disappearances which are
balanced by various energies. It is natural, however, to suppose that these
equivalent apparitions and disappearances correspond to transformations
and not to simultaneous creations and destructions. We thus represent
energy to ourselves as taking different forms—mechanical, electrical,
calorific, and chemical—capable of changing one into the other, but in such
a way that the quantitative value always remains the same. In like manner a
bank draft may be represented by notes, gold, silver, or bullion. The earliest
known form of energy, i.e. work, will serve as the standard as gold serves as
the monetary standard, and energy in all its forms will be estimated by the
corresponding work. In each particular case we can strictly define and
measure, by the correct application of the principle of the conservation of
energy, the quantity of energy evolved under a given form.
We can thus arrange a machine comprising a body capable of evolving this
energy; then we can force all the organs of this machine to complete an
entirely closed cycle, with the exception of the body itself, which, however,

has to return to such a state that all the variables from which this state
depends resume their initial values except the particular variable to which
the evolution of the energy under consideration is linked. The difference
between the work thus accomplished and that which would have been
obtained if this variable also had returned to its original value, is the
measure of the energy evolved.
In the same way that, in the minds of mechanicians, all forces of whatever
origin, which are capable of compounding with each other and of balancing
each other, belong to the same category of beings, so for many physicists
energy is a sort of entity which we find under various aspects. There thus
exists for them a world, which comes in some way to superpose itself upon
the world of matter—that is to say, the world of energy, dominated in its
turn by a fundamental law similar to that of Lavoisier. [5] This conception,
as we have already seen, passes the limit of experience; but others go
further still. Absorbed in the contemplation of this new world, they succeed
in persuading themselves that the old world of matter has no real existence
and that energy is sufficient by itself to give us a complete comprehension
of the Universe and of all the phenomena produced in it. They point out that
all our sensations correspond to changes of energy, and that everything
apparent to our senses is, in truth, energy. The famous experiment of the
blows with a stick by which it was demonstrated to a sceptical philosopher
that an outer world existed, only proves, in reality, the existence of energy,
and not that of matter. The stick in itself is inoffensive, as Professor
Ostwald remarks, and it is its vis viva, its kinetic energy, which is painful to
us; while if we possessed a speed equal to its own, moving in the same
direction, it would no longer exist so far as our sense of touch is concerned.
On this hypothesis, matter would only be the capacity for kinetic energy, its
pretended impenetrability energy of volume, and its weight energy of
position in the particular form which presents itself in universal gravitation;
nay, space itself would only be known to us by the expenditure of energy
necessary to penetrate it. Thus in all physical phenomena we should only
have to regard the quantities of energy brought into play, and all the
equations which link the phenomena to one another would have no meaning
but when they apply to exchanges of energy. For energy alone can be
common to all phenomena.

This extreme manner of regarding things is seductive by its originality, but
appears somewhat insufficient if, after enunciating generalities, we look
more closely into the question. From the philosophical point of view it may,
moreover, seem difficult not to conclude, from the qualities which reveal, if
you will, the varied forms of energy, that there exists a substance possessing
these qualities. This energy, which resides in one region, and which
transports itself from one spot to another, forcibly brings to mind, whatever
view we may take of it, the idea of matter.
Helmholtz endeavoured to construct a mechanics based on the idea of
energy and its conservation, but he had to invoke a second law, the principle
of least action. If he thus succeeded in dispensing with the hypothesis of
atoms, and in showing that the new mechanics gave us to understand the
impossibility of certain movements which, according to the old, ought to
have been but never were experimentally produced, he was only able to do
so because the principle of least action necessary for his theory became
evident in the case of those irreversible phenomena which alone really exist
in Nature. The energetists have thus not succeeded in forming a thoroughly
sound system, but their efforts have at all events been partly successful.
Most physicists are of their opinion, that kinetic energy is only a particular
variety of energy to which we have no right to wish to connect all its other
forms.
If these forms showed themselves to be innumerable throughout the
Universe, the principle of the conservation of energy would, in fact, lose a
great part of its importance. Every time that a certain quantity of energy
seemed to appear or disappear, it would always be permissible to suppose
that an equivalent quantity had appeared or disappeared somewhere else
under a new form; and thus the principle would in a way vanish. But the
known forms of energy are fairly restricted in number, and the necessity of
recognising new ones seldom makes itself felt. We shall see, however, that
to explain, for instance, the paradoxical properties of radium and to re-
establish concord between these properties and the principle of the
conservation of energy, certain physicists have recourse to the hypothesis
that radium borrows an unknown energy from the medium in which it is
plunged. This hypothesis, however, is in no way necessary; and in a few
other rare cases in which similar hypotheses have had to be set up,
experiment has always in the long run enabled us to discover some

phenomenon which had escaped the first observers and which corresponds
exactly to the variation of energy first made evident.
One difficulty, however, arises from the fact that the principle ought only to
be applied to an isolated system. Whether we imagine actions at a distance
or believe in intermediate media, we must always recognise that there exist
no bodies in the world incapable of acting on each other, and we can never
affirm that some modification in the energy of a given place may not have
its echo in some unknown spot afar off. This difficulty may sometimes
render the value of the principle rather illusory.
Similarly, it behoves us not to receive without a certain distrust the
extension by certain philosophers to the whole Universe, of a property
demonstrated for those restricted systems which observation can alone
reach. We know nothing of the Universe as a whole, and every
generalization of this kind outruns in a singular fashion the limit of
experiment.
Even reduced to the most modest proportions, the principle of the
conservation of energy retains, nevertheless, a paramount importance; and it
still preserves, if you will, a high philosophical value. M.J. Perrin justly
points out that it gives us a form under which we are experimentally able to
grasp causality, and that it teaches us that a result has to be purchased at the
cost of a determined effort.
We can, in fact, with M. Perrin and M. Langevin, represent this in a way
which puts this characteristic in evidence by enunciating it as follows: "If at
the cost of a change C we can obtain a change K, there will never be
acquired at the same cost, whatever the mechanism employed, first the
change K and in addition some other change, unless this latter be one that is
otherwise known to cost nothing to produce or to destroy." If, for instance,
the fall of a weight can be accompanied, without anything else being
produced, by another transformation—the melting of a certain mass of ice,
for example—it will be impossible, no matter how you set about it or
whatever the mechanism used, to associate this same transformation with
the melting of another weight of ice.
We can thus, in the transformation in question, obtain an appropriate
number which will sum up that which may be expected from the external

effect, and can give, so to speak, the price at which this transformation is
bought, measure its invariable value by a common measure (for instance,
the melting of the ice), and, without any ambiguity, define the energy lost
during the transformation as proportional to the mass of ice which can be
associated with it. This measure is, moreover, independent of the particular
phenomenon taken as the common measure.

§ 3. THE PRINCIPLE OF CARNOT AND CLAUSIUS
The principle of Carnot, of a nature analogous to the principle of the
conservation of energy, has also a similar origin. It was first enunciated, like
the last named, although prior to it in time, in consequence of
considerations which deal only with heat and mechanical work. Like it, too,
it has evolved, grown, and invaded the entire domain of physics. It may be
interesting to examine rapidly the various phases of this evolution. The
origin of the principle of Carnot is clearly determined, and it is very rare to
be able to go back thus certainly to the source of a discovery. Sadi Carnot
had, truth to say, no precursor. In his time heat engines were not yet very
common, and no one had reflected much on their theory. He was doubtless
the first to propound to himself certain questions, and certainly the first to
solve them.
It is known how, in 1824, in his Réflexions sur la puissance motrice du feu,
he endeavoured to prove that "the motive power of heat is independent of
the agents brought into play for its realization," and that "its quantity is
fixed solely by the temperature of the bodies between which, in the last
resort, the transport of caloric is effected"—at least in all engines in which
"the method of developing the motive power attains the perfection of which
it is capable"; and this is, almost textually, one of the enunciations of the
principle at the present day. Carnot perceived very clearly the great fact
that, to produce work by heat, it is necessary to have at one's disposal a fall
of temperature. On this point he expresses himself with perfect clearness:
"The motive power of a fall of water depends on its height and on the
quantity of liquid; the motive power of heat depends also on the quantity of
caloric employed, and on what might be called—in fact, what we shall call

—the height of fall, that is to say, the difference in temperature of the
bodies between which the exchange of caloric takes place."
Starting with this idea, he endeavours to demonstrate, by associating two
engines capable of working in a reversible cycle, that the principle is
founded on the impossibility of perpetual motion.
His memoir, now celebrated, did not produce any great sensation, and it had
almost fallen into deep oblivion, which, in consequence of the discovery of
the principle of equivalence, might have seemed perfectly justified. Written,
in fact, on the hypothesis of the indestructibility of caloric, it was to be
expected that this memoir should be condemned in the name of the new
doctrine, that is, of the principle recently brought to light.
It was really making a new discovery to establish that Carnot's fundamental
idea survived the destruction of the hypothesis on the nature of heat, on
which he seemed to rely. As he no doubt himself perceived, his idea was
quite independent of this hypothesis, since, as we have seen, he was led to
surmise that heat could disappear; but his demonstrations needed to be
recast and, in some points, modified.
It is to Clausius that was reserved the credit of rediscovering the principle,
and of enunciating it in language conformable to the new doctrines, while
giving it a much greater generality. The postulate arrived at by experimental
induction, and which must be admitted without demonstration, is, according
to Clausius, that in a series of transformations in which the final is identical
with the initial stage, it is impossible for heat to pass from a colder to a
warmer body unless some other accessory phenomenon occurs at the same
time.
Still more correctly, perhaps, an enunciation can be given of the postulate
which, in the main, is analogous, by saying: A heat motor, which after a
series of transformations returns to its initial state, can only furnish work if
there exist at least two sources of heat, and if a certain quantity of heat is
given to one of the sources, which can never be the hotter of the two. By the
expression "source of heat," we mean a body exterior to the system and
capable of furnishing or withdrawing heat from it.

Starting with this principle, we arrive, as does Clausius, at the
demonstration that the output of a reversible machine working between two
given temperatures is greater than that of any non-reversible engine, and
that it is the same for all reversible machines working between these two
temperatures.
This is the very proposition of Carnot; but the proposition thus stated, while
very useful for the theory of engines, does not yet present any very general
interest. Clausius, however, drew from it much more important
consequences. First, he showed that the principle conduces to the definition
of an absolute scale of temperature; and then he was brought face to face
with a new notion which allows a strong light to be thrown on the questions
of physical equilibrium. I refer to entropy.
It is still rather difficult to strip entirely this very important notion of all
analytical adornment. Many physicists hesitate to utilize it, and even look
upon it with some distrust, because they see in it a purely mathematical
function without any definite physical meaning. Perhaps they are here
unduly severe, since they often admit too easily the objective existence of
quantities which they cannot define. Thus, for instance, it is usual almost
every day to speak of the heat possessed by a body. Yet no body in reality
possesses a definite quantity of heat even relatively to any initial state; since
starting from this point of departure, the quantities of heat it may have
gained or lost vary with the road taken and even with the means employed
to follow it. These expressions of heat gained or lost are, moreover,
themselves evidently incorrect, for heat can no longer be considered as a
sort of fluid passing from one body to another.
The real reason which makes entropy somewhat mysterious is that this
magnitude does not fall directly under the ken of any of our senses; but it
possesses the true characteristic of a concrete physical magnitude, since it
is, in principle at least, measurable. Various authors of thermodynamical
researches, amongst whom M. Mouret should be particularly mentioned,
have endeavoured to place this characteristic in evidence.
Consider an isothermal transformation. Instead of leaving the heat
abandoned by the body subjected to the transformation—water condensing
in a state of saturated vapour, for instance—to pass directly into an ice

calorimeter, we can transmit this heat to the calorimeter by the intermediary
of a reversible Carnot engine. The engine having absorbed this quantity of
heat, will only give back to the ice a lesser quantity of heat; and the weight
of the melted ice, inferior to that which might have been directly given
back, will serve as a measure of the isothermal transformation thus effected.
It can be easily shown that this measure is independent of the apparatus
used. It consequently becomes a numerical element characteristic of the
body considered, and is called its entropy. Entropy, thus defined, is a
variable which, like pressure or volume, might serve concurrently with
another variable, such as pressure or volume, to define the state of a body.
It must be perfectly understood that this variable can change in an
independent manner, and that it is, for instance, distinct from the change of
temperature. It is also distinct from the change which consists in losses or
gains of heat. In chemical reactions, for example, the entropy increases
without the substances borrowing any heat. When a perfect gas dilates in a
vacuum its entropy increases, and yet the temperature does not change, and
the gas has neither been able to give nor receive heat. We thus come to
conceive that a physical phenomenon cannot be considered known to us if
the variation of entropy is not given, as are the variations of temperature
and of pressure or the exchanges of heat. The change of entropy is, properly
speaking, the most characteristic fact of a thermal change.
It is important, however, to remark that if we can thus easily define and
measure the difference of entropy between two states of the same body, the
value found depends on the state arbitrarily chosen as the zero point of
entropy; but this is not a very serious difficulty, and is analogous to that
which occurs in the evaluation of other physical magnitudes—temperature,
potential, etc.
A graver difficulty proceeds from its not being possible to define a
difference, or an equality, of entropy between two bodies chemically
different. We are unable, in fact, to pass by any means, reversible or not,
from one to the other, so long as the transmutation of matter is regarded as
impossible; but it is well understood that it is nevertheless possible to
compare the variations of entropy to which these two bodies are both of
them individually subject.

Neither must we conceal from ourselves that the definition supposes, for a
given body, the possibility of passing from one state to another by a
reversible transformation. Reversibility is an ideal and extreme case which
cannot be realized, but which can be approximately attained in many
circumstances. So with gases and with perfectly elastic bodies, we effect
sensibly reversible transformations, and changes of physical state are
practically reversible. The discoveries of Sainte-Claire Deville have brought
many chemical phenomena into a similar category, and reactions such as
solution, which used to be formerly the type of an irreversible phenomenon,
may now often be effected by sensibly reversible means. Be that as it may,
when once the definition is admitted, we arrive, by taking as a basis the
principles set forth at the inception, at the demonstration of the celebrated
theorem of Clausius: The entropy of a thermally isolated system continues
to increase incessantly.
It is very evident that the theorem can only be worth applying in cases
where the entropy can be exactly defined; but, even when thus limited, the
field still remains vast, and the harvest which we can there reap is very
abundant.
Entropy appears, then, as a magnitude measuring in a certain way the
evolution of a system, or, at least, as giving the direction of this evolution.
This very important consequence certainly did not escape Clausius, since
the very name of entropy, which he chose to designate this magnitude, itself
signifies evolution. We have succeeded in defining this entropy by
demonstrating, as has been said, a certain number of propositions which
spring from the postulate of Clausius; it is, therefore, natural to suppose that
this postulate itself contains in potentia the very idea of a necessary
evolution of physical systems. But as it was first enunciated, it contains it in
a deeply hidden way.
No doubt we should make the principle of Carnot appear in an interesting
light by endeavouring to disengage this fundamental idea, and by placing it,
as it were, in large letters. Just as, in elementary geometry, we can replace
the postulate of Euclid by other equivalent propositions, so the postulate of
thermodynamics is not necessarily fixed, and it is instructive to try to give it
the most general and suggestive character.

MM. Perrin and Langevin have made a successful attempt in this direction.
M. Perrin enunciates the following principle: An isolated system never
passes twice through the same state. In this form, the principle affirms that
there exists a necessary order in the succession of two phenomena; that
evolution takes place in a determined direction. If you prefer it, it may be
thus stated: Of two converse transformations unaccompanied by any
external effect, one only is possible. For instance, two gases may diffuse
themselves one in the other in constant volume, but they could not
conversely separate themselves spontaneously.
Starting from the principle thus put forward, we make the logical deduction
that one cannot hope to construct an engine which should work for an
indefinite time by heating a hot source and by cooling a cold one. We thus
come again into the route traced by Clausius, and from this point we may
follow it strictly.
Whatever the point of view adopted, whether we regard the proposition of
M. Perrin as the corollary of another experimental postulate, or whether we
consider it as a truth which we admit a priori and verify through its
consequences, we are led to consider that in its entirety the principle of
Carnot resolves itself into the idea that we cannot go back along the course
of life, and that the evolution of a system must follow its necessary
progress.
Clausius and Lord Kelvin have drawn from these considerations certain
well-known consequences on the evolution of the Universe. Noticing that
entropy is a property added to matter, they admit that there is in the world a
total amount of entropy; and as all real changes which are produced in any
system correspond to an increase of entropy, it may be said that the entropy
of the world is continually increasing. Thus the quantity of energy existing
in the Universe remains constant, but transforms itself little by little into
heat uniformly distributed at a temperature everywhere identical. In the end,
therefore, there will be neither chemical phenomena nor manifestation of
life; the world will still exist, but without motion, and, so to speak, dead.
These consequences must be admitted to be very doubtful; we cannot in any
certain way apply to the Universe, which is not a finite system, a
proposition demonstrated, and that not unreservedly, in the sharply limited

case of a finite system. Herbert Spencer, moreover, in his book on First
Principles, brings out with much force the idea that, even if the Universe
came to an end, nothing would allow us to conclude that, once at rest, it
would remain so indefinitely. We may recognise that the state in which we
are began at the end of a former evolutionary period, and that the end of the
existing era will mark the beginning of a new one.
Like an elastic and mobile object which, thrown into the air, attains by
degrees the summit of its course, then possesses a zero velocity and is for a
moment in equilibrium, and then falls on touching the ground to rebound,
so the world should be subjected to huge oscillations which first bring it to
a maximum of entropy till the moment when there should be produced a
slow evolution in the contrary direction bringing it back to the state from
which it started. Thus, in the infinity of time, the life of the Universe
proceeds without real stop.
This conception is, moreover, in accordance with the view certain physicists
take of the principle of Carnot. We shall see, for example, that in the kinetic
theory we are led to admit that, after waiting sufficiently long, we can
witness the return of the various states through which a mass of gas, for
example, has passed in its series of transformations.
If we keep to the present era, evolution has a fixed direction—that which
leads to an increase of entropy; and it is possible to enquire, in any given
system to what physical manifestations this increase corresponds. We note
that kinetic, potential, electrical, and chemical forms of energy have a great
tendency to transform themselves into calorific energy. A chemical reaction,
for example, gives out energy; but if the reaction is not produced under very
special conditions, this energy immediately passes into the calorific form.
This is so true, that chemists currently speak of the heat given out by
reactions instead of regarding the energy disengaged in general.
In all these transformations the calorific energy obtained has not, from a
practical point of view, the same value at which it started. One cannot, in
fact, according to the principle of Carnot, transform it integrally into
mechanical energy, since the heat possessed by a body can only yield work
on condition that a part of it falls on a body with a lower temperature. Thus
appears the idea that energies which exchange with each other and

correspond to equal quantities have not the same qualitative value. Form
has its importance, and there are persons who prefer a golden louis to four
pieces of five francs. The principle of Carnot would thus lead us to consider
a certain classification of energies, and would show us that, in the
transformations possible, these energies always tend to a sort of diminution
of quality—that is, to a degradation.
It would thus reintroduce an element of differentiation of which it seems
very difficult to give a mechanical explanation. Certain philosophers and
physicists see in this fact a reason which condemns a priori all attempts
made to give a mechanical explanation of the principle of Carnot.
It is right, however, not to exaggerate the importance that should be
attributed to the phrase degraded energy. If the heat is not equivalent to the
work, if heat at 99° is not equivalent to heat at 100°, that means that we
cannot in practice construct an engine which shall transform all this heat
into work, or that, for the same cold source, the output is greater when the
temperature of the hot source is higher; but if it were possible that this cold
source had itself the temperature of absolute zero, the whole heat would
reappear in the form of work. The case here considered is an ideal and
extreme case, and we naturally cannot realize it; but this consideration
suffices to make it plain that the classification of energies is a little arbitrary
and depends more, perhaps, on the conditions in which mankind lives than
on the inmost nature of things.
In fact, the attempts which have often been made to refer the principle of
Carnot to mechanics have not given convincing results. It has nearly always
been necessary to introduce into the attempt some new hypothesis
independent of the fundamental hypotheses of ordinary mechanics, and
equivalent, in reality, to one of the postulates on which the ordinary
exposition of the second law of thermodynamics is founded. Helmholtz, in
a justly celebrated theory, endeavoured to fit the principle of Carnot into the
principle of least action; but the difficulties regarding the mechanical
interpretation of the irreversibility of physical phenomena remain entire.
Looking at the question, however, from the point of view at which the
partisans of the kinetic theories of matter place themselves, the principle is
viewed in a new aspect. Gibbs and afterwards Boltzmann and Professor
Planck have put forward some very interesting ideas on this subject. By

following the route they have traced, we come to consider the principle as
pointing out to us that a given system tends towards the configuration
presented by the maximum probability, and, numerically, the entropy would
even be the logarithm of this probability. Thus two different gaseous
masses, enclosed in two separate receptacles which have just been placed in
communication, diffuse themselves one through the other, and it is highly
improbable that, in their mutual shocks, both kinds of molecules should
take a distribution of velocities which reduce them by a spontaneous
phenomenon to the initial state.
We should have to wait a very long time for so extraordinary a concourse of
circumstances, but, in strictness, it would not be impossible. The principle
would only be a law of probability. Yet this probability is all the greater the
more considerable is the number of molecules itself. In the phenomena
habitually dealt with, this number is such that, practically, the variation of
entropy in a constant sense takes, so to speak, the character of absolute
certainty.
But there may be exceptional cases where the complexity of the system
becomes insufficient for the application of the principle of Carnot;—as in
the case of the curious movements of small particles suspended in a liquid
which are known by the name of Brownian movements and can be
observed under the microscope. The agitation here really seems, as M.
Gouy has remarked, to be produced and continued indefinitely, regardless
of any difference in temperature; and we seem to witness the incessant
motion, in an isothermal medium, of the particles which constitute matter.
Perhaps, however, we find ourselves already in conditions where the too
great simplicity of the distribution of the molecules deprives the principle of
its value.
M. Lippmann has in the same way shown that, on the kinetic hypothesis, it
is possible to construct such mechanisms that we can so take cognizance of
molecular movements that vis viva can be taken from them. The
mechanisms of M. Lippmann are not, like the celebrated apparatus at one
time devised by Maxwell, purely hypothetical. They do not suppose a
partition with a hole impossible to be bored through matter where the
molecular spaces would be larger than the hole itself. They have finite
dimensions. Thus M. Lippmann considers a vase full of oxygen at a

constant temperature. In the interior of this vase is placed a small copper
ring, and the whole is set in a magnetic field. The oxygen molecules are, as
we know, magnetic, and when passing through the interior of the ring they
produce in this ring an induced current. During this time, it is true, other
molecules emerge from the space enclosed by the circuit; but the two
effects do not counterbalance each other, and the resulting current is
maintained. There is elevation of temperature in the circuit in accordance
with Joule's law; and this phenomenon, under such conditions, is
incompatible with the principle of Carnot.
It is possible—and that, I think, is M. Lippmann's idea—to draw from his
very ingenious criticism an objection to the kinetic theory, if we admit the
absolute value of the principle; but we may also suppose that here again we
are in presence of a system where the prescribed conditions diminish the
complexity and render it, consequently, less probable that the evolution is
always effected in the same direction.
In whatever way you look at it, the principle of Carnot furnishes, in the
immense majority of cases, a very sure guide in which physicists continue
to have the most entire confidence.

§ 4. THERMODYNAMICS
To apply the two fundamental principles of thermodynamics, various
methods may be employed, equivalent in the main, but presenting as the
cases vary a greater or less convenience.
In recording, with the aid of the two quantities, energy and entropy, the
relations which translate analytically the two principles, we obtain two
relations between the coefficients which occur in a given phenomenon; but
it may be easier and also more suggestive to employ various functions of
these quantities. In a memoir, of which some extracts appeared as early as
1869, a modest scholar, M. Massieu, indicated in particular a remarkable
function which he termed a characteristic function, and by the employment
of which calculations are simplified in certain cases.
In the same way J.W. Gibbs, in 1875 and 1878, then Helmholtz in 1882,
and, in France, M. Duhem, from the year 1886 onward, have published

works, at first ill understood, of which the renown was, however,
considerable in the sequel, and in which they made use of analogous
functions under the names of available energy, free energy, or internal
thermodynamic potential. The magnitude thus designated, attaching, as a
consequence of the two principles, to all states of the system, is perfectly
determined when the temperature and other normal variables are known. It
allows us, by calculations often very easy, to fix the conditions necessary
and sufficient for the maintenance of the system in equilibrium by foreign
bodies taken at the same temperature as itself.
One may hope to constitute in this way, as M. Duhem in a long and
remarkable series of operations has specially endeavoured to do, a sort of
general mechanics which will enable questions of statics to be treated with
accuracy, and all the conditions of equilibrium of the system, including the
calorific properties, to be determined. Thus, ordinary statics teaches us that
a liquid with its vapour on the top forms a system in equilibrium, if we
apply to the two fluids a pressure depending on temperature alone.
Thermodynamics will furnish us, in addition, with the expression of the
heat of vaporization and of, the specific heats of the two saturated fluids.
This new study has given us also most valuable information on
compressible fluids and on the theory of elastic equilibrium. Added to
certain hypotheses on electric or magnetic phenomena, it gives a coherent
whole from which can be deduced the conditions of electric or magnetic
equilibrium; and it illuminates with a brilliant light the calorific laws of
electrolytic phenomena.
But the most indisputable triumph of this thermodynamic statics is the
discovery of the laws which regulate the changes of physical state or of
chemical constitution. J.W. Gibbs was the author of this immense progress.
His memoir, now celebrated, on "the equilibrium of heterogeneous
substances," concealed in 1876 in a review at that time of limited
circulation, and rather heavy to read, seemed only to contain algebraic
theorems applicable with difficulty to reality. It is known that Helmholtz
independently succeeded, a few years later, in introducing thermodynamics
into the domain of chemistry by his conception of the division of energy
into free and into bound energy: the first, capable of undergoing all
transformations, and particularly of transforming itself into external action;

the second, on the other hand, bound, and only manifesting itself by giving
out heat. When we measure chemical energy, we ordinarily let it fall wholly
into the calorific form; but, in reality, it itself includes both parts, and it is
the variation of the free energy and not that of the total energy measured by
the integral disengagement of heat, the sign of which determines the
direction in which the reactions are effected.
But if the principle thus enunciated by Helmholtz as a consequence of the
laws of thermodynamics is at bottom identical with that discovered by
Gibbs, it is more difficult of application and is presented under a more
mysterious aspect. It was not until M. Van der Waals exhumed the memoir
of Gibbs, when numerous physicists or chemists, most of them Dutch—
Professor Van t'Hoff, Bakhius Roozeboom, and others—utilized the rules
set forth in this memoir for the discussion of the most complicated chemical
reactions, that the extent of the new laws was fully understood.
The chief rule of Gibbs is the one so celebrated at the present day under the
name of the Phase Law. We know that by phases are designated the
homogeneous substances into which a system is divided; thus carbonate of
lime, lime, and carbonic acid gas are the three phases of a system which
comprises Iceland spar partially dissociated into lime and carbonic acid gas.
The number of phases added to the number of independent components—
that is to say, bodies whose mass is left arbitrary by the chemical formulas
of the substances entering into the reaction—fixes the general form of the
law of equilibrium of the system; that is to say, the number of quantities
which, by their variations (temperature and pressure), would be of a nature
to modify its equilibrium by modifying the constitution of the phases.
Several authors, M. Raveau in particular, have indeed given very simple
demonstrations of this law which are not based on thermodynamics; but
thermodynamics, which led to its discovery, continues to give it its true
scope. Moreover, it would not suffice merely to determine quantitatively
those laws of which it makes known the general form. We must, if we wish
to penetrate deeper into details, particularize the hypothesis, and admit, for
instance, with Gibbs that we are dealing with perfect gases; while, thanks to
thermodynamics, we can constitute a complete theory of dissociation which
leads to formulas in complete accord with the numerical results of the
experiment. We can thus follow closely all questions concerning the

displacements of the equilibrium, and find a relation of the first importance
between the masses of the bodies which react in order to constitute a system
in equilibrium.
The statics thus constructed constitutes at the present day an important
edifice to be henceforth classed amongst historical monuments. Some
theorists even wish to go a step beyond. They have attempted to begin by
the same means a more complete study of those systems whose state
changes from one moment to another. This is, moreover, a study which is
necessary to complete satisfactorily the study of equilibrium itself; for
without it grave doubts would exist as to the conditions of stability, and it
alone can give their true meaning to questions relating to displacements of
equilibrium.
The problems with which we are thus confronted are singularly difficult. M.
Duhem has given us many excellent examples of the fecundity of the
method; but if thermodynamic statics may be considered definitely
founded, it cannot be said that the general dynamics of systems, considered
as the study of thermal movements and variations, are yet as solidly
established.

§ 5. ATOMISM
It may appear singularly paradoxical that, in a chapter devoted to general
views on the principles of physics, a few words should be introduced on the
atomic theories of matter.
Very often, in fact, what is called the physics of principles is set in
opposition to the hypotheses on the constitution of matter, particularly to
atomic theories. I have already said that, abandoning the investigation of the
unfathomable mystery of the constitution of the Universe, some physicists
think they may find, in certain general principles, sufficient guides to
conduct them across the physical world. But I have also said, in examining
the history of those principles, that if they are to-day considered
experimental truths, independent of all theories relating to matter, they
have, in fact, nearly all been discovered by scholars who relied on

molecular hypotheses: and the question suggests itself whether this is mere
chance, or whether this chance may not be ordained by higher reasons.
In a very profound work which appeared a few years ago, entitled Essai
critique sur l'hypothese des atomes, M. Hannequin, a philosopher who is
also an erudite scholar, examined the part taken by atomism in the history
of science. He notes that atomism and science were born, in Greece, of the
same problem, and that in modern times the revival of the one was closely
connected with that of the other. He shows, too, by very close analysis, that
the atomic hypothesis is essential to the optics of Fresnel and of Cauchy;
that it penetrates into the study of heat; and that, in its general features, it
presided at the birth of modern chemistry and is linked with all its progress.
He concludes that it is, in a manner, the soul of our knowledge of Nature,
and that contemporary theories are on this point in accord with history: for
these theories consecrate the preponderance of this hypothesis in the
domain of science.
If M. Hannequin had not been prematurely cut off in the full expansion of
his vigorous talent, he might have added another chapter to his excellent
book. He would have witnessed a prodigious budding of atomistic ideas,
accompanied, it is true, by wide modifications in the manner in which the
atom is to be regarded, since the most recent theories make material atoms
into centres constituted of atoms of electricity. On the other hand, he would
have found in the bursting forth of these new doctrines one more proof in
support of his idea that science is indissolubly bound to atomism.
From the philosophical point of view, M. Hannequin, examining the reasons
which may have called these links into being, arrives at the idea that they
necessarily proceed from the constitution of our knowledge, or, perhaps,
from that of Nature itself. Moreover, this origin, double in appearance, is
single at bottom. Our minds could not, in fact, detach and come out of
themselves to grasp reality and the absolute in Nature. According to the idea
of Descartes, it is the destiny of our minds only to take hold of and to
understand that which proceeds from them.
Thus atomism, which is, perhaps, only an appearance containing even some
contradictions, is yet a well-founded appearance, since it conforms to the
laws of our minds; and this hypothesis is, in a way, necessary.

We may dispute the conclusions of M. Hannequin, but no one will refuse to
recognise, as he does, that atomic theories occupy a preponderating part in
the doctrines of physics; and the position which they have thus conquered
gives them, in a way, the right of saying that they rest on a real principle. It
is in order to recognise this right that several physicists—M. Langevin, for
example—ask that atoms be promoted from the rank of hypotheses to that
of principles. By this they mean that the atomistic ideas forced upon us by
an almost obligatory induction based on very exact experiments, enable us
to co-ordinate a considerable amount of facts, to construct a very general
synthesis, and to foresee a great number of phenomena.
It is of moment, moreover, to thoroughly understand that atomism does not
necessarily set up the hypothesis of centres of attraction acting at a distance,
and it must not be confused with molecular physics, which has, on the other
hand, undergone very serious checks. The molecular physics greatly in
favour some fifty years ago leads to such complex representations and to
solutions often so undetermined, that the most courageous are wearied with
upholding it and it has fallen into some discredit. It rested on the
fundamental principles of mechanics applied to molecular actions; and that
was, no doubt, an extension legitimate enough, since mechanics is itself
only an experimental science, and its principles, established for the
movements of matter taken as a whole, should not be applied outside the
domain which belongs to them. Atomism, in fact, tends more and more, in
modern theories, to imitate the principle of the conservation of energy or
that of entropy, to disengage itself from the artificial bonds which attached
it to mechanics, and to put itself forward as an independent principle.
Atomistic ideas also have undergone evolution, and this slow evolution has
been considerably quickened under the influence of modern discoveries.
These reach back to the most remote antiquity, and to follow their
development we should have to write the history of human thought which
they have always accompanied since the time of Leucippus, Democritus,
Epicurus, and Lucretius. The first observers who noticed that the volume of
a body could be diminished by compression or cold, or augmented by heat,
and who saw a soluble solid body mix completely with the water which
dissolved it, must have been compelled to suppose that matter was not
dispersed continuously throughout the space it seemed to occupy. They
were thus brought to consider it discontinuous, and to admit that a

substance having the same composition and the same properties in all its
parts—in a word, perfectly homogeneous—ceases to present this
homogeneity when considered within a sufficiently small volume.
Modern experimenters have succeeded by direct experiments in placing in
evidence this heterogeneous character of matter when taken in small mass.
Thus, for example, the superficial tension, which is constant for the same
liquid at a given temperature, no longer has the same value when the
thickness of the layer of liquid becomes extremely small. Newton noticed
even in his time that a dark zone is seen to form on a soap bubble at the
moment when it becomes so thin that it must burst. Professor Reinold and
Sir Arthur Rücker have shown that this zone is no longer exactly spherical;
and from this we must conclude that the superficial tension, constant for all
thicknesses above a certain limit, commences to vary when the thickness
falls below a critical value, which these authors estimate, on optical
grounds, at about fifty millionths of a millimetre.
From experiments on capillarity, Prof. Quincke has obtained similar results
with regard to layers of solids. But it is not only capillary properties which
allow this characteristic to be revealed. All the properties of a body are
modified when taken in small mass; M. Meslin proves this in a very
ingenious way as regards optical properties, and Mr Vincent in respect of
electric conductivity. M. Houllevigue, who, in a chapter of his excellent
work, Du Laboratoire à l'Usine, has very clearly set forth the most
interesting considerations on atomic hypotheses, has recently demonstrated
that copper and silver cease to combine with iodine as soon as they are
present in a thickness of less than thirty millionths of a millimetre. It is this
same dimension likewise that is possessed, according to M. Wiener, by the
smallest thicknesses it is possible to deposit on glass. These layers are so
thin that they cannot be perceived, but their presence is revealed by a
change in the properties of the light reflected by them.
Thus, below fifty to thirty millionths of a millimetre the properties of matter
depend on its thickness. There are then, no doubt, only a few molecules to
be met with, and it may be concluded, in consequence, that the
discontinuous elements of bodies—that is, the molecules—have linear
dimensions of the order of magnitude of the millionth of a millimetre.
Considerations regarding more complex phenomena, for instance the

phenomena of electricity by contact, and also the kinetic theory of gases,
bring us to the same conclusion.
The idea of the discontinuity of matter forces itself upon us for many other
reasons. All modern chemistry is founded on this principle; and laws like
the law of multiple proportions, introduce an evident discontinuity to which
we find analogies in the law of electrolysis. The elements of bodies we are
thus brought to regard might, as regards solids at all events, be considered
as immobile; but this immobility could not explain the phenomena of heat,
and, as it is entirely inadmissible for gases, it seems very improbable it can
absolutely occur in any state. We are thus led to suppose that these elements
are animated by very complicated movements, each one proceeding in
closed trajectories in which the least variations of temperature or pressure
cause modifications.
The atomistic hypothesis shows itself remarkably fecund in the study of
phenomena produced in gases, and here the mutual independence of the
particles renders the question relatively more simple and, perhaps, allows
the principles of mechanics to be more certainly extended to the movements
of molecules.
The kinetic theory of gases can point to unquestioned successes; and the
idea of Daniel Bernouilli, who, as early as 1738, considered a gaseous mass
to be formed of a considerable number of molecules animated by rapid
movements of translation, has been put into a form precise enough for
mathematical analysis, and we have thus found ourselves in a position to
construct a really solid foundation. It will be at once conceived, on this
hypothesis, that pressure is the resultant of the shocks of the molecules
against the walls of the containing vessel, and we at once come to the
demonstration that the law of Mariotte is a natural consequence of this
origin of pressure; since, if the volume occupied by a certain number of
molecules is doubled, the number of shocks per second on each square
centimetre of the walls becomes half as much. But if we attempt to carry
this further, we find ourselves in presence of a serious difficulty. It is
impossible to mentally follow every one of the many individual molecules
which compose even a very limited mass of gas. The path followed by this
molecule may be every instant modified by the chance of running against
another, or by a shock which may make it rebound in another direction.

The difficulty would be insoluble if chance had not laws of its own. It was
Maxwell who first thought of introducing into the kinetic theory the
calculation of probabilities. Willard Gibbs and Boltzmann later on
developed this idea, and have founded a statistical method which does not,
perhaps, give absolute certainty, but which is certainly most interesting and
curious. Molecules are grouped in such a way that those belonging to the
same group may be considered as having the same state of movement; then
an examination is made of the number of molecules in each group, and
what are the changes in this number from one moment to another. It is thus
often possible to determine the part which the different groups have in the
total properties of the system and in the phenomena which may occur.
Such a method, analogous to the one employed by statisticians for
following the social phenomena in a population, is all the more legitimate
the greater the number of individuals counted in the averages; now, the
number of molecules contained in a limited space—for example, in a
centimetre cube taken in normal conditions—is such that no population
could ever attain so high a figure. All considerations, those we have
indicated as well as others which might be invoked (for example, the recent
researches of M. Spring on the limit of visibility of fluorescence), give this
result:—that there are, in this space, some twenty thousand millions of
molecules. Each of these must receive in the space of a millimetre about ten
thousand shocks, and be ten thousand times thrust out of its course. The free
path of a molecule is then very small, but it can be singularly augmented by
diminishing the number of them. Tait and Dewar have calculated that, in a
good modern vacuum, the length of the free path of the remaining
molecules not taken away by the air-pump easily reaches a few centimetres.
By developing this theory, we come to consider that, for a given
temperature, every molecule (and even every individual particle, atom, or
ion) which takes part in the movement has, on the average, the same kinetic
energy in every body, and that this energy is proportional to the absolute
temperature; so that it is represented by this temperature multiplied by a
constant quantity which is a universal constant.
This result is not an hypothesis but a very great probability. This probability
increases when it is noted that the same value for the constant is met with in
the study of very varied phenomena; for example, in certain theories on

radiation. Knowing the mass and energy of a molecule, it is easy to
calculate its speed; and we find that the average speed is about 400 metres
per second for carbonic anhydride, 500 for nitrogen, and 1850 for hydrogen
at 0° C. and at ordinary pressure. I shall have occasion, later on, to speak of
much more considerable speeds than these as animating other particles.
The kinetic theory has permitted the diffusion of gases to be explained, and
the divers circumstances of the phenomenon to be calculated. It has allowed
us to show, as M. Brillouin has done, that the coefficient of diffusion of two
gases does not depend on the proportion of the gases in the mixture; it gives
a very striking image of the phenomena of viscosity and conductivity; and it
leads us to think that the coefficients of friction and of conductivity are
independent of the density; while all these previsions have been verified by
experiment. It has also invaded optics; and by relying on the principle of
Doppler, Professor Michelson has succeeded in obtaining from it an
explanation of the length presented by the spectral rays of even the most
rarefied gases.
But however interesting are these results, they would not have sufficed to
overcome the repugnance of certain physicists for speculations which, an
imposing mathematical baggage notwithstanding, seemed to them too
hypothetical. The theory, moreover, stopped at the molecule, and appeared
to suggest no idea which could lead to the discovery of the key to the
phenomena where molecules exercise a mutual influence on each other. The
kinetic hypothesis, therefore, remained in some disfavour with a great
number of persons, particularly in France, until the last few years, when all
the recent discoveries of the conductivity of gases and of the new radiations
came to procure for it a new and luxuriant efflorescence. It may be said that
the atomistic synthesis, but yesterday so decried, is to-day triumphant.
The elements which enter into the earlier kinetic theory, and which, to avoid
confusion, should be always designated by the name of molecules, were
not, truth to say, in the eyes of the chemists, the final term of the divisibility
of matter. It is well known that, to them, except in certain particular bodies
like the vapour of mercury and argon, the molecule comprises several
atoms, and that, in compound bodies, the number of these atoms may even
be fairly considerable. But physicists rarely needed to have recourse to the
consideration of these atoms. They spoke of them to explain certain

particularities of the propagation of sound, and to enunciate laws relating to
specific heats; but, in general, they stopped at the consideration of the
molecule.
The present theories carry the division much further. I shall not dwell now
on these theories, since, in order to thoroughly understand them, many other
facts must be examined. But to avoid all confusion, it remains understood
that, contrary, no doubt, to etymology, but in conformity with present
custom, I shall continue in what follows to call atoms those particles of
matter which have till now been spoken of; these atoms being themselves,
according to modern views, singularly complex edifices formed of
elements, of which we shall have occasion to indicate the nature later.

CHAPTER IV

THE VARIOUS STATES OF MATTER
§ 1. THE STATICS OF FLUIDS
The division of bodies into gaseous, liquid, and solid, and the distinction
established for the same substance between the three states, retain a great
importance for the applications and usages of daily life, but have long since
lost their absolute value from the scientific point of view.
So far as concerns the liquid and gaseous states particularly, the already
antiquated researches of Andrews confirmed the ideas of Cagniard de la
Tour and established the continuity of the two states. A group of physical
studies has thus been constituted on what may be called the statics of fluids,
in which we examine the relations existing between the pressure, the
volume, and the temperature of bodies, and in which are comprised, under
the term fluid, gases as well as liquids.
These researches deserve attention by their interest and the generality of the
results to which they have led. They also give a remarkable example of the
happy effects which may be obtained by the combined employment of the
various methods of investigation used in exploring the domain of nature.
Thermodynamics has, in fact, allowed us to obtain numerical relations
between the various coefficients, and atomic hypotheses have led to the
establishment of one capital relation, the characteristic equation of fluids;
while, on the other hand, experiment in which the progress made in the art
of measurement has been utilized, has furnished the most valuable
information on all the laws of compressibility and dilatation.
The classical work of Andrews was not very wide. Andrews did not go
much beyond pressures close to the normal and ordinary temperatures. Of
late years several very interesting and peculiar cases have been examined
by MM. Cailletet, Mathias, Batelli, Leduc, P. Chappuis, and other
physicists. Sir W. Ramsay and Mr S. Young have made known the
isothermal diagrams[6] of a certain number of liquid bodies at the ordinary
temperature. They have thus been able, while keeping to somewhat
restricted limits of temperature and pressure, to touch upon the most

important questions, since they found themselves in the region of the
saturation curve and of the critical point.
But the most complete and systematic body of researches is due to M.
Amagat, who undertook the study of a certain number of bodies, some
liquid and some gaseous, extending the scope of his experiments so as to
embrace the different phases of the phenomena and to compare together,
not only the results relating to the same bodies, but also those concerning
different bodies which happen to be in the same conditions of temperature
and pressure, but in very different conditions as regards their critical points.
From the experimental point of view, M. Amagat has been able, with
extreme skill, to conquer the most serious difficulties. He has managed to
measure with precision pressures amounting to 3000 atmospheres, and also
the very small volumes then occupied by the fluid mass under
consideration. This last measurement, which necessitates numerous
corrections, is the most delicate part of the operation. These researches have
dealt with a certain number of different bodies. Those relating to carbonic
acid and ethylene take in the critical point. Others, on hydrogen and
nitrogen, for instance, are very extended. Others, again, such as the study of
the compressibility of water, have a special interest, on account of the
peculiar properties of this substance. M. Amagat, by a very concise
discussion of the experiments, has also been able to definitely establish the
laws of compressibility and dilatation of fluids under constant pressure, and
to determine the value of the various coefficients as well as their variations.
It ought to be possible to condense all these results into a single formula
representing the volume, the temperature, and the pressure. Rankin and,
subsequently, Recknagel, and then Hirn, formerly proposed formulas of that
kind; but the most famous, the one which first appeared to contain in a
satisfactory manner all the facts which experiments brought to light and led
to the production of many others, was the celebrated equation of Van der
Waals.
Professor Van der Waals arrived at this relation by relying upon
considerations derived from the kinetic theory of gases. If we keep to the
simple idea at the bottom of this theory, we at once demonstrate that the gas
ought to obey the laws of Mariotte and of Gay-Lussac, so that the
characteristic equation would be obtained by the statement that the product

of the number which is the measure of the volume by that which is the
measure of the pressure is equal to a constant coefficient multiplied by the
degree of the absolute temperature. But to get at this result we neglect two
important factors.
We do not take into account, in fact, the attraction which the molecules
must exercise on each other. Now, this attraction, which is never absolutely
non-existent, may become considerable when the molecules are drawn
closer together; that is to say, when the compressed gaseous mass occupies
a more and more restricted volume. On the other hand, we assimilate the
molecules, as a first approximation, to material points without dimensions;
in the evaluation of the path traversed by each molecule no notice is taken
of the fact that, at the moment of the shock, their centres of gravity are still
separated by a distance equal to twice the radius of the molecule.
M. Van der Waals has sought out the modifications which must be
introduced into the simple characteristic equation to bring it nearer to
reality. He extends to the case of gases the considerations by which Laplace,
in his famous theory of capillarity, reduced the effect of the molecular
attraction to a perpendicular pressure exercised on the surface of a liquid.
This leads him to add to the external pressure, that due to the reciprocal
attractions of the gaseous particles. On the other hand, when we attribute
finite dimensions to these particles, we must give a higher value to the
number of shocks produced in a given time, since the effect of these
dimensions is to diminish the mean path they traverse in the time which
elapses between two consecutive shocks.
The calculation thus pursued leads to our adding to the pressure in the
simple equation a term which is designated the internal pressure, and which
is the quotient of a constant by the square of the volume; also to our
deducting from the volume a constant which is the quadruple of the total
and invariable volume which the gaseous molecules would occupy did they
touch one another.
The experiments fit in fairly well with the formula of Van der Waals, but
considerable discrepancies occur when we extend its limits, particularly
when the pressures throughout a rather wider interval are considered; so
that other and rather more complex formulas, on which there is no

advantage in dwelling, have been proposed, and, in certain cases, better
represent the facts.
But the most remarkable result of M. Van der Waals' calculations is the
discovery of corresponding states. For a long time physicists spoke of
bodies taken in a comparable state. Dalton, for example, pointed out that
liquids have vapour-pressures equal to the temperatures equally distant
from their boiling-point; but that if, in this particular property, liquids were
comparable under these conditions of temperature, as regards other
properties the parallelism was no longer to be verified. No general rule was
found until M. Van der Waals first enunciated a primary law, viz., that if the
pressure, the volume, and the temperature are estimated by taking as units
the critical quantities, the constants special to each body disappear in the
characteristic equation, which thus becomes the same for all fluids.
The words corresponding states thus take a perfectly precise signification.
Corresponding states are those for which the numerical values of the
pressure, volume, and temperature, expressed by taking as units the values
corresponding to the critical point, are equal; and, in corresponding states
any two fluids have exactly the same properties.
M. Natanson, and subsequently P. Curie and M. Meslin, have shown by
various considerations that the same result may be arrived at by choosing
units which correspond to any corresponding states; it has also been shown
that the theorem of corresponding states in no way implies the exactitude of
Van der Waals' formula. In reality, this is simply due to the fact that the
characteristic equation only contains three constants.
The philosophical importance and the practical interest of the discovery
nevertheless remain considerable. As was to be expected, numbers of
experimenters have sought whether these consequences are duly verified in
reality. M. Amagat, particularly, has made use for this purpose of a most
original and simple method. He remarks that, in all its generality, the law
may be translated thus: If the isothermal diagrams of two substances be
drawn to the same scale, taking as unit of volume and of pressure the values
of the critical constants, the two diagrams should coincide; that is to say,
their superposition should present the aspect of one diagram appertaining to
a single substance. Further, if we possess the diagrams of two bodies drawn

to any scales and referable to any units whatever, as the changes of units
mean changes in the scale of the axes, we ought to make one of the
diagrams similar to the other by lengthening or shortening it in the direction
of one of the axes. M. Amagat then photographs two isothermal diagrams,
leaving one fixed, but arranging the other so that it may be free to turn
round each axis of the co-ordinates; and by projecting, by means of a magic
lantern, the second on the first, he arrives in certain cases at an almost
complete coincidence.
This mechanical means of proof thus dispenses with laborious calculations,
but its sensibility is unequally distributed over the different regions of the
diagram. M. Raveau has pointed out an equally simple way of verifying the
law, by remarking that if the logarithms of the pressure and volume are
taken as co-ordinates, the co-ordinates of two corresponding points differ
by two constant quantities, and the corresponding curves are identical.
From these comparisons, and from other important researches, among
which should be particularly mentioned those of Mr S. Young and M.
Mathias, it results that the laws of corresponding states have not,
unfortunately, the degree of generality which we at first attributed to them,
but that they are satisfactory when applied to certain groups of bodies.[7]
If in the study of the statics of a simple fluid the experimental results are
already complex, we ought to expect much greater difficulties when we
come to deal with mixtures; still the problem has been approached, and
many points are already cleared up.
Mixed fluids may first of all be regarded as composed of a large number of
invariable particles. In this particularly simple case M. Van der Waals has
established a characteristic equation of the mixtures which is founded on
mechanical considerations. Various verifications of this formula have been
effected, and it has, in particular, been the object of very important remarks
by M. Daniel Berthelot.
It is interesting to note that thermodynamics seems powerless to determine
this equation, for it does not trouble itself about the nature of the bodies
obedient to its laws; but, on the other hand, it intervenes to determine the
properties of coexisting phases. If we examine the conditions of equilibrium
of a mixture which is not subjected to external forces, it will be

demonstrated that the distribution must come back to a juxtaposition of
homogeneous phases; in a given volume, matter ought so to arrange itself
that the total sum of free energy has a minimum value. Thus, in order to
elucidate all questions relating to the number and qualities of the phases
into which the substance divides itself, we are led to regard the geometrical
surface which for a given temperature represents the free energy.
I am unable to enter here into the detail of the questions connected with the
theories of Gibbs, which have been the object of numerous theoretical
studies, and also of a series, ever more and more abundant, of experimental
researches. M. Duhem, in particular, has published, on the subject, memoirs
of the highest importance, and a great number of experimenters, mostly
scholars working in the physical laboratory of Leyden under the guidance
of the Director, Mr Kamerlingh Onnes, have endeavoured to verify the
anticipations of the theory.
We are a little less advanced as regards abnormal substances; that is to say,
those composed of molecules, partly simple and partly complex, and either
dissociated or associated. These cases must naturally be governed by very
complex laws. Recent researches by MM. Van der Waals, Alexeif,
Rothmund, Künen, Lehfeld, etc., throw, however, some light on the
question.
The daily more numerous applications of the laws of corresponding states
have rendered highly important the determination of the critical constants
which permit these states to be defined. In the case of homogeneous bodies
the critical elements have a simple, clear, and precise sense; the critical
temperature is that of the single isothermal line which presents a point of
inflexion at a horizontal tangent; the critical pressure and the critical
volume are the two co-ordinates of this point of inflexion.
The three critical constants may be determined, as Mr S. Young and M.
Amagat have shown, by a direct method based on the consideration of the
saturated states. Results, perhaps more precise, may also be obtained if one
keeps to two constants or even to a single one—temperature, for example—
by employing various special methods. Many others, MM. Cailletet and
Colardeau, M. Young, M.J. Chappuis, etc., have proceeded thus.

The case of mixtures is much more complicated. A binary mixture has a
critical space instead of a critical point. This space is comprised between
two extreme temperatures, the lower corresponding to what is called the
folding point, the higher to that which we call the point of contact of the
mixture. Between these two temperatures an isothermal compression yields
a quantity of liquid which increases, then reaches a maximum, diminishes,
and disappears. This is the phenomenon of retrograde condensation. We
may say that the properties of the critical point of a homogeneous substance
are, in a way, divided, when it is a question of a binary mixture, between the
two points mentioned.
Calculation has enabled M. Van der Waals, by the application of his kinetic
theories, and M. Duhem, by means of thermodynamics, to foresee most of
the results which have since been verified by experiment. All these facts
have been admirably set forth and systematically co-ordinated by M.
Mathias, who, by his own researches, moreover, has made contributions of
the highest value to the study of questions regarding the continuity of the
liquid and gaseous states.
The further knowledge of critical elements has allowed the laws of
corresponding states to be more closely examined in the case of
homogeneous substances. It has shown that, as I have already said, bodies
must be arranged in groups, and this fact clearly proves that the properties
of a given fluid are not determined by its critical constants alone, and that it
is necessary to add to them some other specific parameters; M. Mathias and
M. D. Berthelot have indicated some which seem to play a considerable
part.
It results also from this that the characteristic equation of a fluid cannot yet
be considered perfectly known. Neither the equation of Van der Waals nor
the more complicated formulas which have been proposed by various
authors are in perfect conformity with reality. We may think that researches
of this kind will only be successful if attention is concentrated, not only on
the phenomena of compressibility and dilatation, but also on the
calorimetric properties of bodies. Thermodynamics indeed establishes
relations between those properties and other constants, but does not allow
everything to be foreseen.

Several physicists have effected very interesting calorimetric
measurements, either, like M. Perot, in order to verify Clapeyron's formula
regarding the heat of vaporization, or to ascertain the values of specific
heats and their variations when the temperature or the pressure happens to
change. M. Mathias has even succeeded in completely determining the
specific heats of liquefied gases and of their saturated vapours, as well as
the heat of internal and external vaporization.

§ 2. THE LIQUEFACTION OF GASES, AND THE PROPERTIES OF
BODIES AT A LOW TEMPERATURE
The scientific advantages of all these researches have been great, and, as
nearly always happens, the practical consequences derived from them have
also been most important. It is owing to the more complete knowledge of
the general properties of fluids that immense progress has been made these
last few years in the methods of liquefying gases.
From a theoretical point of view the new processes of liquefaction can be
classed in two categories. Linde's machine and those resembling it utilize,
as is known, expansion without any notable production of external work.
This expansion, nevertheless, causes a fall in the temperature, because the
gas in the experiment is not a perfect gas, and, by an ingenious process, the
refrigerations produced are made cumulative.
Several physicists have proposed to employ a method whereby liquefaction
should be obtained by expansion with recuperable external work. This
method, proposed as long ago as 1860 by Siemens, would offer
considerable advantages. Theoretically, the liquefaction would be more
rapid, and obtained much more economically; but unfortunately in the
experiment serious obstacles are met with, especially from the difficulty of
obtaining a suitable lubricant under intense cold for those parts of the
machine which have to be in movement if the apparatus is to work.
M. Claude has recently made great progress on this point by the use, during
the running of the machine, of the ether of petrol, which is uncongealable,
and a good lubricant for the moving parts. When once the desired region of
cold is reached, air itself is used, which moistens the metals but does not

completely avoid friction; so that the results would have remained only
middling, had not this ingenious physicist devised a new improvement
which has some analogy with superheating of steam in steam engines. He
slightly varies the initial temperature of the compressed air on the verge of
liquefaction so as to avoid a zone of deep perturbations in the properties of
fluids, which would make the work of expansion very feeble and the cold
produced consequently slight. This improvement, simple as it is in
appearance, presents several other advantages which immediately treble the
output.
The special object of M. Claude was to obtain oxygen in a practical manner
by the actual distillation of liquid air. Since nitrogen boils at -194° and
oxygen at -180.5° C., if liquid air be evaporated, the nitrogen escapes,
especially at the commencement of the evaporation, while the oxygen
concentrates in the residual liquid, which finally consists of pure oxygen,
while at the same time the temperature rises to the boiling-point (-180.5°
C.) of oxygen. But liquid air is costly, and if one were content to evaporate
it for the purpose of collecting a part of the oxygen in the residuum, the
process would have a very poor result from the commercial point of view.
As early as 1892, Mr Parkinson thought of improving the output by
recovering the cold produced by liquid air during its evaporation; but an
incorrect idea, which seems to have resulted from certain experiments of
Dewar—the idea that the phenomenon of the liquefaction of air would not
be, owing to certain peculiarities, the exact converse of that of vaporization
—led to the employment of very imperfect apparatus. M. Claude, however,
by making use of a method which he calls the reversal [8] method, obtains a
complete rectification in a remarkably simple manner and under extremely
advantageous economic conditions. Apparatus, of surprisingly reduced
dimensions but of great efficiency, is now in daily work, which easily
enables more than a thousand cubic metres of oxygen to be obtained at the
rate, per horse-power, of more than a cubic metre per hour.
It is in England, thanks to the skill of Sir James Dewar and his pupils—
thanks also, it must be said, to the generosity of the Royal Institution, which
has devoted considerable sums to these costly experiments—that the most
numerous and systematic researches have been effected on the production
of intense cold. I shall here note only the more important results, especially
those relating to the properties of bodies at low temperatures.

Their electrical properties, in particular, undergo some interesting
modifications. The order which metals assume in point of conductivity is no
longer the same as at ordinary temperatures. Thus at -200° C. copper is a
better conductor than silver. The resistance diminishes with the temperature,
and, down to about -200°, this diminution is almost linear, and it would
seem that the resistance tends towards zero when the temperature
approaches the absolute zero. But, after -200°, the pattern of the curves
changes, and it is easy to foresee that at absolute zero the resistivities of all
metals would still have, contrary to what was formerly supposed, a notable
value. Solidified electrolytes which, at temperatures far below their fusion
point, still retain a very appreciable conductivity, become, on the contrary,
perfect insulators at low temperatures. Their dielectric constants assume
relatively high values. MM. Curie and Compan, who have studied this
question from their own point of view, have noted, moreover, that the
specific inductive capacity changes considerably with the temperature.
In the same way, magnetic properties have been studied. A very interesting
result is that found in oxygen: the magnetic susceptibility of this body
increases at the moment of liquefaction. Nevertheless, this increase, which
is enormous (since the susceptibility becomes sixteen hundred times greater
than it was at first), if we take it in connection with equal volumes, is much
less considerable if taken in equal masses. It must be concluded from this
fact that the magnetic properties apparently do not belong to the molecules
themselves, but depend on their state of aggregation.
The mechanical properties of bodies also undergo important modifications.
In general, their cohesion is greatly increased, and the dilatation produced
by slight changes of temperature is considerable. Sir James Dewar has
effected careful measurements of the dilatation of certain bodies at low
temperatures: for example, of ice. Changes in colour occur, and vermilion
and iodide of mercury pass into pale orange. Phosphorescence becomes
more intense, and most bodies of complex structure—milk, eggs, feathers,
cotton, and flowers—become phosphorescent. The same is the case with
certain simple bodies, such as oxygen, which is transformed into ozone and
emits a white light in the process.
Chemical affinity is almost put an end to; phosphorus and potassium remain
inert in liquid oxygen. It should, however, be noted, and this remark has

doubtless some interest for the theories of photographic action, that
photographic substances retain, even at the temperature of liquid hydrogen,
a very considerable part of their sensitiveness to light.
Sir James Dewar has made some important applications of low
temperatures in chemical analysis; he also utilizes them to create a vacuum.
His researches have, in fact, proved that the pressure of air congealed by
liquid hydrogen cannot exceed the millionth of an atmosphere. We have,
then, in this process, an original and rapid means of creating an excellent
vacuum in apparatus of very different kinds—a means which, in certain
cases, may be particularly convenient.[9]
Thanks to these studies, a considerable field has been opened up for
biological research, but in this, which is not our subject, I shall notice one
point only. It has been proved that vital germs—bacteria, for example—
may be kept for seven days at -l90°C. without their vitality being modified.
Phosphorescent organisms cease, it is true, to shine at the temperature of
liquid air, but this fact is simply due to the oxidations and other chemical
reactions which keep up the phosphorescence being then suspended, for
phosphorescent activity reappears so soon as the temperature is again
sufficiently raised. An important conclusion has been drawn from these
experiments which affects cosmogonical theories: since the cold of space
could not kill the germs of life, it is in no way absurd to suppose that, under
proper conditions, a germ may be transmitted from one planet to another.
Among the discoveries made with the new processes, the one which most
strikingly interested public attention is that of new gases in the atmosphere.
We know how Sir William Ramsay and Dr. Travers first observed by means
of the spectroscope the characteristics of the companions of argon in the
least volatile part of the atmosphere. Sir James Dewar on the one hand, and
Sir William Ramsay on the other, subsequently separated in addition to
argon and helium, crypton, xenon, and neon. The process employed consists
essentially in first solidifying the least volatile part of the air and then
causing it to evaporate with extreme slowness. A tube with electrodes
enables the spectrum of the gas in process of distillation to be observed. In
this manner, the spectra of the various gases may be seen following one
another in the inverse order of their volatility. All these gases are
monoatomic, like mercury; that is to say, they are in the most simple state,

they possess no internal molecular energy (unless it is that which heat is
capable of supplying), and they even seem to have no chemical energy.
Everything leads to the belief that they show the existence on the earth of
an earlier state of things now vanished. It may be supposed, for instance,
that helium and neon, of which the molecular mass is very slight, were
formerly more abundant on our planet; but at an epoch when the
temperature of the globe was higher, the very speed of their molecules may
have reached a considerable value, exceeding, for instance, eleven
kilometres per second, which suffices to explain why they should have left
our atmosphere. Crypton and neon, which have a density four times greater
than oxygen, may, on the contrary, have partly disappeared by solution at
the bottom of the sea, where it is not absurd to suppose that considerable
quantities would be found liquefied at great depths. [10]
It is probable, moreover, that the higher regions of the atmosphere are not
composed of the same air as that around us. Sir James Dewar points out that
Dalton's law demands that every gas composing the atmosphere should
have, at all heights and temperatures, the same pressure as if it were alone,
the pressure decreasing the less quickly, all things being equal, as its density
becomes less. It results from this that the temperature becoming gradually
lower as we rise in the atmosphere, at a certain altitude there can no longer
remain any traces of oxygen or nitrogen, which no doubt liquefy, and the
atmosphere must be almost exclusively composed of the most volatile
gases, including hydrogen, which M.A. Gautier has, like Lord Rayleigh and
Sir William Ramsay, proved to exist in the air. The spectrum of the Aurora
borealis, in which are found the lines of those parts of the atmosphere
which cannot be liquefied in liquid hydrogen, together with the lines of
argon, crypton, and xenon, is quite in conformity with this point of view. It
is, however, singular that it should be the spectrum of crypton, that is to say,
of the heaviest gas of the group, which appears most clearly in the upper
regions of the atmosphere.
Among the gases most difficult to liquefy, hydrogen has been the object of
particular research and of really quantitative experiments. Its properties in a
liquid state are now very clearly known. Its boiling-point, measured with a
helium thermometer which has been compared with thermometers of
oxygen and hydrogen, is -252°; its critical temperature is -241° C.; its
critical pressure, 15 atmospheres. It is four times lighter than water, it does

not present any absorption spectrum, and its specific heat is the greatest
known. It is not a conductor of electricity. Solidified at 15° absolute, it is far
from reminding one by its aspect of a metal; it rather resembles a piece of
perfectly pure ice, and Dr Travers attributes to it a crystalline structure. The
last gas which has resisted liquefaction, helium, has recently been obtained
in a liquid state; it appears to have its boiling-point in the neighbourhood of
6° absolute. [11]

§ 3. SOLIDS AND LIQUIDS
The interest of the results to which the researches on the continuity between
the liquid and the gaseous states have led is so great, that numbers of
scholars have naturally been induced to inquire whether something
analogous might not be found in the case of liquids and solids. We might
think that a similar continuity ought to be there met with, that the universal
character of the properties of matter forbade all real discontinuity between
two different states, and that, in truth, the solid was a prolongation of the
liquid state.
To discover whether this supposition is correct, it concerns us to compare
the properties of liquids and solids. If we find that all properties are
common to the two states we have the right to believe, even if they
presented themselves in different degrees, that, by a continuous series of
intermediary bodies, the two classes might yet be connected. If, on the other
hand, we discover that there exists in these two classes some quality of a
different nature, we must necessarily conclude that there is a discontinuity
which nothing can remove.
The distinction established, from the point of view of daily custom, between
solids and liquids, proceeds especially from the difficulty that we meet with
in the one case, and the facility in the other, when we wish to change their
form temporarily or permanently by the action of mechanical force. This
distinction only corresponds, however, in reality, to a difference in the value
of certain coefficients. It is impossible to discover by this means any
absolute characteristic which establishes a separation between the two
classes. Modern researches prove this clearly. It is not without use, in order

to well understand them, to state precisely the meaning of a few terms
generally rather loosely employed.
If a conjunction of forces acting on a homogeneous material mass happens
to deform it without compressing or dilating it, two very distinct kinds of
reactions may appear which oppose themselves to the effort exercised.
During the time of deformation, and during that time only, the first make
their influence felt. They depend essentially on the greater or less rapidity
of the deformation, they cease with the movement, and could not, in any
case, bring the body back to its pristine state of equilibrium. The existence
of these reactions leads us to the idea of viscosity or internal friction.
The second kind of reactions are of a different nature. They continue to act
when the deformation remains stationary, and, if the external forces happen
to disappear, they are capable of causing the body to return to its initial
form, provided a certain limit has not been exceeded. These last constitute
rigidity.
At first sight a solid body appears to have a finite rigidity and an infinite
viscosity; a liquid, on the contrary, presents a certain viscosity, but no
rigidity. But if we examine the matter more closely, beginning either with
the solids or with the liquids, we see this distinction vanish.
Tresca showed long ago that internal friction is not infinite in a solid;
certain bodies can, so to speak, at once flow and be moulded. M.W. Spring
has given many examples of such phenomena. On the other hand, viscosity
in liquids is never non-existent; for were it so for water, for example, in the
celebrated experiment effected by Joule for the determination of the
mechanical equivalent of the caloric, the liquid borne along by the floats
would slide without friction on the surrounding liquid, and the work done
by movement would be the same whether the floats did or did not plunge
into the liquid mass.
In certain cases observed long ago with what are called pasty bodies, this
viscosity attains a value almost comparable to that observed by M. Spring
in some solids. Nor does rigidity allow us to establish a barrier between the
two states. Notwithstanding the extreme mobility of their particles, liquids
contain, in fact, vestiges of the property which we formerly wished to
consider the special characteristic of solids.

Maxwell before succeeded in rendering the existence of this rigidity very
probable by examining the optical properties of a deformed layer of liquid.
But a Russian physicist, M. Schwedoff, has gone further, and has been able
by direct experiments to show that a sheath of liquid set between two solid
cylinders tends, when one of the cylinders is subjected to a slight rotation,
to return to its original position, and gives a measurable torsion to a thread
upholding the cylinder. From the knowledge of this torsion the rigidity can
be deduced. In the case of a solution containing 1/2 per cent. of gelatine, it
is found that this rigidity, enormous compared with that of water, is still,
however, one trillion eight hundred and forty billion times less than that of
steel.
This figure, exact within a few billions, proves that the rigidity is very
slight, but exists; and that suffices for a characteristic distinction to be
founded on this property. In a general way, M. Spring has also established
that we meet in solids, in a degree more or less marked, with the properties
of liquids. When they are placed in suitable conditions of pressure and time,
they flow through orifices, transmit pressure in all directions, diffuse and
dissolve one into the other, and react chemically on each other. They may
be soldered together by compression; by the same means alloys may be
produced; and further, which seems to clearly prove that matter in a solid
state is not deprived of all molecular mobility, it is possible to realise
suitable limited reactions and equilibria between solid salts, and these
equilibria obey the fundamental laws of thermodynamics.
Thus the definition of a solid cannot be drawn from its mechanical
properties. It cannot be said, after what we have just seen, that solid bodies
retain their form, nor that they have a limited elasticity, for M. Spring has
made known a case where the elasticity of solids is without any limit.
It was thought that in the case of a different phenomenon—that of
crystallization—we might arrive at a clear distinction, because here we
should he dealing with a specific quality; and that crystallized bodies would
be the true solids, amorphous bodies being at that time regarded as liquids
viscous in the extreme.
But the studies of a German physicist, Professor 0. Lehmann, seem to prove
that even this means is not infallible. Professor Lehmann has succeeded, in

fact, in obtaining with certain organic compounds—oleate of potassium, for
instance—under certain conditions some peculiar states to which he has
given the name of semi-fluid and liquid crystals. These singular phenomena
can only be observed and studied by means of a microscope, and the
Carlsruhe Professor had to devise an ingenious apparatus which enabled
him to bring the preparation at the required temperature on to the very plate
of the microscope.
It is thus made evident that these bodies act on polarized light in the manner
of a crystal. Those that M. Lehmann terms semi-liquid still present traces of
polyhedric delimitation, but with the peaks and angles rounded by surface-
tension, while the others tend to a strictly spherical form. The optical
examination of the first-named bodies is very difficult, because appearances
may be produced which are due to the phenomena of refraction and imitate
those of polarization. For the other kind, which are often as mobile as water,
the fact that they polarize light is absolutely unquestionable.
Unfortunately, all these liquids are turbid, and it may be objected that they
are not homogeneous. This want of homogeneity may, according to M.
Quincke, be due to the existence of particles suspended in a liquid in
contact with another liquid miscible with it and enveloping it as might a
membrane, and the phenomena of polarization would thus be quite naturally
explained. [12]
M. Tamman is of opinion that it is more a question of an emulsion, and, on
this hypothesis, the action on light would actually be that which has been
observed. Various experimenters have endeavoured of recent years to
elucidate this question. It cannot be considered absolutely settled, but these
very curious experiments, pursued with great patience and remarkable
ingenuity, allow us to think that there really exist certain intermediary forms
between crystals and liquids in which bodies still retain a peculiar structure,
and consequently act on light, but nevertheless possess considerable
plasticity.
Let us note that the question of the continuity of the liquid and solid states
is not quite the same as the question of knowing whether there exist bodies
intermediate in all respects between the solids and liquids. These two
problems are often wrongly confused. The gap between the two classes of

bodies may be filled by certain substances with intermediate properties,
such as pasty bodies and bodies liquid but still crystallized, because they
have not yet completely lost their peculiar structure. Yet the transition is not
necessarily established in a continuous fashion when we are dealing with
the passage of one and the same determinate substance from the liquid to
the solid form. We conceive that this change may take place by insensible
degrees in the case of an amorphous body. But it seems hardly possible to
consider the case of a crystal, in which molecular movements must be
essentially regular, as a natural sequence to the case of the liquid where we
are, on the contrary, in presence of an extremely disordered state of
movement.
M. Taminan has demonstrated that amorphous solids may very well, in fact,
be regarded as superposed liquids endowed with very great viscosity. But it
is no longer the same thing when the solid is once in the crystallized state.
There is then a solution of continuity of the various properties of the
substance, and the two phases may co-exist.
We might presume also, by analogy with what happens with liquids and
gases, that if we followed the curve of transformation of the crystalline into
the liquid phase, we might arrive at a kind of critical point at which the
discontinuity of their properties would vanish.
Professor Poynting, and after him Professor Planck and Professor Ostwald,
supposed this to be the case, but more recently M. Tamman has shown that
such a point does not exist, and that the region of stability of the crystallized
state is limited on all sides. All along the curve of transformation the two
states may exist in equilibrium, but we may assert that it is impossible to
realize a continuous series of intermediaries between these two states. There
will always be a more or less marked discontinuity in some of the
properties.
In the course of his researches M. Tamman has been led to certain very
important observations, and has met with fresh allotropic modifications in
nearly all substances, which singularly complicate the question. In the case
of water, for instance, he finds that ordinary ice transforms itself, under a
given pressure, at the temperature of -80° C. into another crystalline variety
which is denser than water.

The statics of solids under high pressure is as yet, therefore, hardly drafted,
but it seems to promise results which will not be identical with those
obtained for the statics of fluids, though it will present at least an equal
interest.

§ 4. THE DEFORMATIONS OF SOLIDS
If the mechanical properties of the bodies intermediate between solids and
liquids have only lately been the object of systematic studies, admittedly
solid substances have been studied for a long time. Yet, notwithstanding the
abundance of researches published on elasticity by theorists and
experimenters, numerous questions with regard to them still remain in
suspense.
We only propose to briefly indicate here a few problems recently examined,
without going into the details of questions which belong more to the
domain of mechanics than to that of pure physics.
The deformations produced in solid bodies by increasing efforts arrange
themselves in two distinct periods. If the efforts are weak, the deformations
produced are also very weak and disappear when the effort ceases. They are
then termed elastic. If the efforts exceed a certain value, a part only of these
deformations disappear, and a part are permanent.
The purity of the note emitted by a sound has been often invoked as a proof
of the perfect isochronism of the oscillation, and, consequently, as a
demonstration a posteriori of the correctness of the early law of Hoocke
governing elastic deformations. This law has, however, during some years
been frequently disputed. Certain mechanicians or physicists freely admit it
to be incorrect, especially as regards extremely weak deformations.
According to a theory in some favour, especially in Germany, i.e. the theory
of Bach, the law which connects the elastic deformations with the efforts
would be an exponential one. Recent experiments by Professors Kohlrausch
and Gruncisen, executed under varied and precise conditions on brass, cast
iron, slate, and wrought iron, do not appear to confirm Bach's law. Nothing,
in point of fact, authorises the rejection of the law of Hoocke, which
presents itself as the most natural and most simple approximation to reality.

The phenomena of permanent deformation are very complex, and it
certainly seems that they cannot be explained by the older theories which
insisted that the molecules only acted along the straight line which joined
their centres. It becomes necessary, then, to construct more complete
hypotheses, as the MM. Cosserat have done in some excellent memoirs, and
we may then succeed in grouping together the facts resulting from new
experiments. Among the experiments of which every theory must take
account may be mentioned those by which Colonel Hartmann has placed in
evidence the importance of the lines which are produced on the surface of
metals when the limit of elasticity is exceeded.
It is to questions of the same order that the minute and patient researches of
M. Bouasse have been directed. This physicist, as ingenious as he is
profound, has pursued for several years experiments on the most delicate
points relating to the theory of elasticity, and he has succeeded in defining
with a precision not always attained even in the best esteemed works, the
deformations to which a body must be subjected in order to obtain
comparable experiments. With regard to the slight oscillations of torsion
which he has specially studied, M. Bouasse arrives at the conclusion, in an
acute discussion, that we hardly know anything more than was proclaimed a
hundred years ago by Coulomb. We see, by this example, that admirable as
is the progress accomplished in certain regions of physics, there still exist
many over-neglected regions which remain in painful darkness. The skill
shown by M. Bouasse authorises us to hope that, thanks to his researches, a
strong light will some day illumine these unknown corners.
A particularly interesting chapter on elasticity is that relating to the study of
crystals; and in the last few years it has been the object of remarkable
researches on the part of M. Voigt. These researches have permitted a few
controversial questions between theorists and experimenters to be solved: in
particular, M. Voigt has verified the consequences of the calculations,
taking care not to make, like Cauchy and Poisson, the hypothesis of central
forces a mere function of distance, and has recognized a potential which
depends on the relative orientation of the molecules. These considerations
also apply to quasi-isotropic bodies which are, in fact, networks of crystals.
Certain occasional deformations which are produced and disappear slowly
may be considered as intermediate between elastic and permanent

deformations. Of these, the thermal deformation of glass which manifests
itself by the displacement of the zero of a thermometer is an example. So
also the modifications which the phenomena of magnetic hysteresis or the
variations of resistivity have just demonstrated.
Many theorists have taken in hand these difficult questions. M. Brillouin
endeavours to interpret these various phenomena by the molecular
hypothesis. The attempt may seem bold, since these phenomena are, for the
most part, essentially irreversible, and seem, consequently, not adaptable to
mechanics. But M. Brillouin makes a point of showing that, under certain
conditions, irreversible phenomena may be created between two material
points, the actions of which depend solely on their distance; and he
furnishes striking instances which appear to prove that a great number of
irreversible physical and chemical phenomena may be ascribed to the
existence of states of unstable equilibria.
M. Duhem has approached the problem from another side, and endeavours
to bring it within the range of thermodynamics. Yet ordinary
thermodynamics could not account for experimentally realizable states of
equilibrium in the phenomena of viscosity and friction, since this science
declares them to be impossible. M. Duhem, however, arrives at the idea that
the establishment of the equations of thermodynamics presupposes, among
other hypotheses, one which is entirely arbitrary, namely: that when the
state of the system is given, external actions capable of maintaining it in
that state are determined without ambiguity, by equations termed conditions
of equilibrium of the system. If we reject this hypothesis, it will then be
allowable to introduce into thermodynamics laws previously excluded, and
it will be possible to construct, as M. Duhem has done, a much more
comprehensive theory.
The ideas of M. Duhem have been illustrated by remarkable experimental
work. M. Marchis, for example, guided by these ideas, has studied the
permanent modifications produced in glass by an oscillation of temperature.
These modifications, which may be called phenomena of the hysteresis of
dilatation, may be followed in very appreciable fashion by means of a glass
thermometer. The general results are quite in accord with the previsions of
M. Duhem. M. Lenoble in researches on the traction of metallic wires, and
M. Chevalier in experiments on the permanent variations of the electrical

resistance of wires of an alloy of platinum and silver when submitted to
periodical variations of temperature, have likewise afforded verifications of
the theory propounded by M. Duhem.
In this theory, the representative system is considered dependent on the
temperature of one or several other variables, such as, for example, a
chemical variable. A similar idea has been developed in a very fine set of
memoirs on nickel steel, by M. Ch. Ed. Guillaume. The eminent physicist,
who, by his earlier researches, has greatly contributed to the light thrown on
the analogous question of the displacement of the zero in thermometers,
concludes, from fresh researches, that the residual phenomena are due to
chemical variations, and that the return to the primary chemical state causes
the variation to disappear. He applies his ideas not only to the phenomena
presented by irreversible steels, but also to very different facts; for example,
to phosphorescence, certain particularities of which may be interpreted in
an analogous manner.
Nickel steels present the most curious properties, and I have already pointed
out the paramount importance of one of them, hardly capable of perceptible
dilatation, for its application to metrology and chronometry. [13] Others, also
discovered by M. Guillaume in the course of studies conducted with rare
success and remarkable ingenuity, may render great services, because it is
possible to regulate, so to speak, at will their mechanical or magnetic
properties.
The study of alloys in general is, moreover, one of those in which the
introduction of the methods of physics has produced the greatest effects. By
the microscopic examination of a polished surface or of one indented by a
reagent, by the determination of the electromotive force of elements of
which an alloy forms one of the poles, and by the measurement of the
resistivities, the densities, and the differences of potential or contact, the
most valuable indications as to their constitution are obtained. M. Le
Chatelier, M. Charpy, M. Dumas, M. Osmond, in France; Sir W. Roberts
Austen and Mr. Stansfield, in England, have given manifold examples of
the fertility of these methods. The question, moreover, has had a new light
thrown upon it by the application of the principles of thermodynamics and
of the phase rule.

Alloys are generally known in the two states of solid and liquid. Fused
alloys consist of one or several solutions of the component metals and of a
certain number of definite combinations. Their composition may thus be
very complex: but Gibbs' rule gives us at once important information on the
point, since it indicates that there cannot exist, in general, more than two
distinct solutions in an alloy of two metals.
Solid alloys may be classed like liquid ones. Two metals or more dissolve
one into the other, and form a solid solution quite analogous to the liquid
solution. But the study of these solid solutions is rendered singularly
difficult by the fact that the equilibrium so rapidly reached in the case of
liquids in this case takes days and, in certain cases, perhaps even centuries
to become established.

CHAPTER V

SOLUTIONS AND ELECTROLYTIC
DISSOCIATION
§ 1. SOLUTION
Vaporization and fusion are not the only means by which the physical state
of a body may be changed without modifying its chemical constitution.
From the most remote periods solution has also been known and studied,
but only in the last twenty years have we obtained other than empirical
information regarding this phenomenon.
It is natural to employ here also the methods which have allowed us to
penetrate into the knowledge of other transformations. The problem of
solution may be approached by way of thermodynamics and of the
hypotheses of kinetics.
As long ago as 1858, Kirchhoff, by attributing to saline solutions—that is to
say, to mixtures of water and a non-volatile liquid like sulphuric acid—the
properties of internal energy, discovered a relation between the quantity of
heat given out on the addition of a certain quantity of water to a solution
and the variations to which condensation and temperature subject the
vapour-tension of the solution. He calculated for this purpose the variations
of energy which are produced when passing from one state to another by
two different series of transformations; and, by comparing the two
expressions thus obtained, he established a relation between the various
elements of the phenomenon. But, for a long time afterwards, the question
made little progress, because there seemed to be hardly any means of
introducing into this study the second principle of thermodynamics. [14] It
was the memoir of Gibbs which at last opened out this rich domain and
enabled it to be rationally exploited. As early as 1886, M. Duhem showed
that the theory of the thermodynamic potential furnished precise
information on solutions or liquid mixtures. He thus discovered over again
the famous law on the lowering of the congelation temperature of solvents
which had just been established by M. Raoult after a long series of now
classic researches.

In the minds of many persons, however, grave doubts persisted. Solution
appeared to be an essentially irreversible phenomenon. It was therefore, in
all strictness, impossible to calculate the entropy of a solution, and
consequently to be certain of the value of the thermodynamic potential. The
objection would be serious even to-day, and, in calculations, what is called
the paradox of Gibbs would be an obstacle.
We should not hesitate, however, to apply the Phase Law to solutions, and
this law already gives us the key to a certain number of facts. It puts in
evidence, for example, the part played by the eutectic point—that is to say,
the point at which (to keep to the simple case in which we have to do with
two bodies only, the solvent and the solute) the solution is in equilibrium at
once with the two possible solids, the dissolved body and the solvent
solidified. The knowledge of this point explains the properties of
refrigerating mixtures, and it is also one of the most useful for the theory of
alloys. The scruples of physicists ought to have been removed on the
memorable occasion when Professor Van t'Hoff demonstrated that solution
can operate reversibly by reason of the phenomena of osmosis. But the
experiment can only succeed in very rare cases; and, on the other hand,
Professor Van t'Hoff was naturally led to another very bold conception. He
regarded the molecule of the dissolved body as a gaseous one, and
assimilated solution, not as had hitherto been the rule, to fusion, but to a
kind of vaporization. Naturally his ideas were not immediately accepted by
the scholars most closely identified with the classic tradition. It may
perhaps not be without use to examine here the principles of Professor Van
t'Hoff's theory.

§ 2. OSMOSIS
Osmosis, or diffusion through a septum, is a phenomenon which has been
known for some time. The discovery of it is attributed to the Abbé Nollet,
who is supposed to have observed it in 1748, during some "researches on
liquids in ebullition." A classic experiment by Dutrochet, effected about
1830, makes this phenomenon clear. Into pure water is plunged the lower
part of a vertical tube containing pure alcohol, open at the top and closed at
the bottom by a membrane, such as a pig's bladder, without any visible

perforation. In a very short time it will be found, by means of an areometer
for instance, that the water outside contains alcohol, while the alcohol of the
tube, pure at first, is now diluted. Two currents have therefore passed
through the membrane, one of water from the outside to the inside, and one
of alcohol in the converse direction. It is also noted that a difference in the
levels has occurred, and that the liquid in the tube now rises to a
considerable height. It must therefore be admitted that the flow of the water
has been more rapid than that of the alcohol. At the commencement, the
water must have penetrated into the tube much more rapidly than the
alcohol left it. Hence the difference in the levels, and, consequently, a
difference of pressure on the two faces of the membrane. This difference
goes on increasing, reaches a maximum, then diminishes, and vanishes
when the diffusion is complete, final equilibrium being then attained.
The phenomenon is evidently connected with diffusion. If water is very
carefully poured on to alcohol, the two layers, separate at first, mingle by
degrees till a homogeneous substance is obtained. The bladder seems not to
have prevented this diffusion from taking place, but it seems to have shown
itself more permeable to water than to alcohol. May it not therefore be
supposed that there must exist dividing walls in which this difference of
permeability becomes greater and greater, which would be permeable to the
solvent and absolutely impermeable to the solute? If this be so, the
phenomena of these semi-permeable walls, as they are termed, can be
observed in particularly simple conditions.
The answer to this question has been furnished by biologists, at which we
cannot be surprised. The phenomena of osmosis are naturally of the first
importance in the action of organisms, and for a long time have attracted the
attention of naturalists. De Vries imagined that the contractions noticed in
the protoplasm of cells placed in saline solutions were due to a phenomenon
of osmosis, and, upon examining more closely certain peculiarities of cell
life, various scholars have demonstrated that living cells are enclosed in
membranes permeable to certain substances and entirely impermeable to
others. It was interesting to try to reproduce artificially semi-permeable
walls analogous to those thus met with in nature; [15] and Traube and Pfeffer
seem to have succeeded in one particular case. Traube has pointed out that
the very delicate membrane of ferrocyanide of potassium which is obtained
with some difficulty by exposing it to the reaction of sulphate of copper, is

permeable to water, but will not permit the passage of the majority of salts.
Pfeffer, by producing these walls in the interstices of a porous porcelain,
has succeeded in giving them sufficient rigidity to allow measurements to
be made. It must be allowed that, unfortunately, no physicist or chemist has
been as lucky as these two botanists; and the attempts to reproduce semi-
permeable walls completely answering to the definition, have never given
but mediocre results. If, however, the experimental difficulty has not been
overcome in an entirely satisfactory manner, it at least appears very
probable that such walls may nevertheless exist. [16]
Nevertheless, in the case of gases, there exists an excellent example of a
semi-permeable wall, and a partition of platinum brought to a higher than
red heat is, as shown by M. Villard in some ingenious experiments,
completely impermeable to air, and very permeable, on the contrary, to
hydrogen. It can also be experimentally demonstrated that on taking two
recipients separated by such a partition, and both containing nitrogen mixed
with varying proportions of hydrogen, the last-named gas will pass through
the partition in such a way that the concentration—that is to say, the mass of
gas per unit of volume—will become the same on both sides. Only then will
equilibrium be established; and, at that moment, an excess of pressure will
naturally be produced in that recipient which, at the commencement,
contained the gas with the smallest quantity of hydrogen.
This experiment enables us to anticipate what will happen in a liquid
medium with semi-permeable partitions. Between two recipients, one
containing pure water, the other, say, water with sugar in solution, separated
by one of these partitions, there will be produced merely a movement of the
pure towards the sugared water, and following this, an increase of pressure
on the side of the last. But this increase will not be without limits. At a
certain moment the pressure will cease to increase and will remain at a
fixed value which now has a given direction. This is the osmotic pressure.
Pfeffer demonstrated that, for the same substance, the osmotic pressure is
proportional to the concentration, and consequently in inverse ratio to the
volume occupied by a similar mass of the solute. He gave figures from
which it was easy, as Professor Van t'Hoff found, to draw the conclusion
that, in a constant volume, the osmotic pressure is proportional to the
absolute temperature. De Vries, moreover, by his remarks on living cells,

extended the results which Pfeffer had applied to one case only—that is, to
the one that he had been able to examine experimentally.
Such are the essential facts of osmosis. We may seek to interpret them and
to thoroughly examine the mechanism of the phenomenon; but it must be
acknowledged that as regards this point, physicists are not entirely in
accord. In the opinion of Professor Nernst, the permeability of semi-
permeable membranes is simply due to differences of solubility in one of
the substances of the membrane itself. Other physicists think it attributable,
either to the difference in the dimensions of the molecules, of which some
might pass through the pores of the membrane and others be stopped by
their relative size, or to these molecules' greater or less mobility. For others,
again, it is the capillary phenomena which here act a preponderating part.
This last idea is already an old one: Jager, More, and Professor Traube have
all endeavoured to show that the direction and speed of osmosis are
determined by differences in the surface-tensions; and recent experiments,
especially those of Batelli, seem to prove that osmosis establishes itself in
the way which best equalizes the surface-tensions of the liquids on both
sides of the partition. Solutions possessing the same surface-tension, though
not in molecular equilibrium, would thus be always in osmotic equilibrium.
We must not conceal from ourselves that this result would be in
contradiction with the kinetic theory.

§ 3. APPLICATION TO THE THEORY OF SOLUTION
If there really exist partitions permeable to one body and impermeable to
another, it may be imagined that the homogeneous mixture of these two
bodies might be effected in the converse way. It can be easily conceived, in
fact, that by the aid of osmotic pressure it would be possible, for example,
to dilute or concentrate a solution by driving through the partition in one
direction or another a certain quantity of the solvent by means of a pressure
kept equal to the osmotic pressure. This is the important fact which
Professor Van t' Hoff perceived. The existence of such a wall in all possible
cases evidently remains only a very legitimate hypothesis,—a fact which
ought not to be concealed.

Relying solely on this postulate, Professor Van t' Hoff easily established, by
the most correct method, certain properties of the solutions of gases in a
volatile liquid, or of non-volatile bodies in a volatile liquid. To state
precisely the other relations, we must admit, in addition, the experimental
laws discovered by Pfeffer. But without any hypothesis it becomes possible
to demonstrate the laws of Raoult on the lowering of the vapour-tension and
of the freezing point of solutions, and also the ratio which connects the heat
of fusion with this decrease.
These considerable results can evidently be invoked as a posteriori proofs
of the exactitude of the experimental laws of osmosis. They are not,
however, the only ones that Professor Van t' Hoff has obtained by the same
method. This illustrious scholar was thus able to find anew Guldberg and
Waage's law on chemical equilibrium at a constant temperature, and to
show how the position of the equilibrium changes when the temperature
happens to change.
If now we state, in conformity with the laws of Pfeffer, that the product of
the osmotic pressure by the volume of the solution is equal to the absolute
temperature multiplied by a coefficient, and then look for the numerical
figure of this latter in a solution of sugar, for instance, we find that this
value is the same as that of the analogous coefficient of the characteristic
equation of a perfect gas. There is in this a coincidence which has also been
utilized in the preceding thermodynamic calculations. It may be purely
fortuitous, but we can hardly refrain from finding in it a physical meaning.
Professor Van t'Hoff has considered this coincidence a demonstration that
there exists a strong analogy between a body in solution and a gas; as a
matter of fact, it may seem that, in a solution, the distance between the
molecules becomes comparable to the molecular distances met with in
gases, and that the molecule acquires the same degree of liberty and the
same simplicity in both phenomena. In that case it seems probable that
solutions will be subject to laws independent of the chemical nature of the
dissolved molecule and comparable to the laws governing gases, while if
we adopt the kinetic image for the gas, we shall be led to represent to
ourselves in a similar way the phenomena which manifest themselves in a
solution. Osmotic pressure will then appear to be due to the shock of the
dissolved molecules against the membrane. It will come from one side of

this partition to superpose itself on the hydrostatic pressure, which latter
must have the same value on both sides.
The analogy with a perfect gas naturally becomes much greater as the
solution becomes more diluted. It then imitates gas in some other
properties; the internal work of the variation of volume is nil, and the
specific heat is only a function of the temperature. A solution which is
diluted by a reversible method is cooled like a gas which expands
adiabatically. [17]
It must, however, be acknowledged that, in other points, the analogy is
much less perfect. The opinion which sees in solution a phenomenon
resembling fusion, and which has left an indelible trace in everyday
language (we shall always say: to melt sugar in water) is certainly not
without foundation. Certain of the reasons which might be invoked to
uphold this opinion are too evident to be repeated here, though others more
recondite might be quoted. The fact that the internal energy generally
becomes independent of the concentration when the dilution reaches even a
moderately high value is rather in favour of the hypothesis of fusion.
We must not forget, however, the continuity of the liquid and gaseous
states; and we may consider it in an absolute way a question devoid of
sense to ask whether in a solution the solute is in the liquid or the gaseous
state. It is in the fluid state, and perhaps in conditions opposed to those of a
body in the state of a perfect gas. It is known, of course, that in this case the
manometrical pressure must be regarded as very great in relation to the
internal pressure which, in the characteristic equation, is added to the other.
May it not seem possible that in the solution it is, on the contrary, the
internal pressure which is dominant, the manometric pressure becoming of
no account? The coincidence of the formulas would thus be verified, for all
the characteristic equations are symmetrical with regard to these two
pressures. From this point of view the osmotic pressure would be
considered as the result of an attraction between the solvent and the solute;
and it would represent the difference between the internal pressures of the
solution and of the pure solvent. These hypotheses are highly interesting,
and very suggestive; but from the way in which the facts have been set
forth, it will appear, no doubt, that there is no obligation to admit them in

order to believe in the legitimacy of the application of thermodynamics to
the phenomena of solution.

§ 4. ELECTROLYTIC DISSOCIATION
From the outset Professor Van t' Hoff was brought to acknowledge that a
great number of solutions formed very notable exceptions which were very
irregular in appearance. The analogy with gases did not seem to be
maintained, for the osmotic pressure had a very different value from that
indicated by the theory. Everything, however, came right if one multiplied
by a factor, determined according to each case, but greater than unity, the
constant of the characteristic formula. Similar divergences were manifested
in the delays observed in congelation, and disappeared when subjected to an
analogous correction.
Thus the freezing-point of a normal solution, containing a molecule
gramme (that is, the number of grammes equal to the figure representing the
molecular mass) of alcohol or sugar in water, falls 1.85° C. If the laws of
solution were identically the same for a solution of sea-salt, the same
depression should be noticed in a saline solution also containing 1 molecule
per litre. In fact, the fall reaches 3.26°, and the solution behaves as if it
contained, not 1, but 1.75 normal molecules per litre. The consideration of
the osmotic pressures would lead to similar observations, but we know that
the experiment would be more difficult and less precise.
We may wonder whether anything really analogous to this can be met with
in the case of a gas, and we are thus led to consider the phenomena of
dissociation. [18] If we heat a body which, in a gaseous state, is capable of
dissociation—hydriodic acid, for example—at a given temperature, an
equilibrium is established between three gaseous bodies, the acid, the
iodine, and the hydrogen. The total mass will follow with fair closeness
Mariotte's law, but the characteristic constant will no longer be the same as
in the case of a non-dissociated gas. We here no longer have to do with a
single molecule, since each molecule is in part dissociated.
The comparison of the two cases leads to the employment of a new image
for representing the phenomenon which has been produced throughout the

saline solution. We have introduced a single molecule of salt, and
everything occurs as if there were 1.75 molecules. May it not really be said
that the number is 1.75, because the sea-salt is partly dissociated, and a
molecule has become transformed into 0.75 molecule of sodium, 0.75 of
chlorium, and 0.25 of salt?
This is a way of speaking which seems, at first sight, strangely contradicted
by experiment. Professor Van t' Hoff, like other chemists, would certainly
have rejected—in fact, he did so at first—such a conception, if, about the
same time, an illustrious Swedish scholar, M. Arrhenius, had not been
brought to the same idea by another road, and, had not by stating it
precisely and modifying it, presented it in an acceptable form.
A brief examination will easily show that all the substances which are
exceptions to the laws of Van t'Hoff are precisely those which are capable
of conducting electricity when undergoing decomposition—that is to say,
are electrolytes. The coincidence is absolute, and cannot be simply due to
chance.
Now, the phenomena of electrolysis have, for a long time, forced upon us
an almost necessary image. The saline molecule is always decomposed, as
we know, in the primary phenomenon of electrolysis into two elements
which Faraday termed ions. Secondary reactions, no doubt, often come to
complicate the question, but these are chemical reactions belonging to the
general order of things, and have nothing to do with the electric action
working on the solution. The simple phenomenon is always the same—
decomposition into two ions, followed by the appearance of one of these
ions at the positive and of the other at the negative electrode. But as the
very slightest expenditure of energy is sufficient to produce the
commencement of electrolysis, it is necessary to suppose that these two
ions are not united by any force. Thus the two ions are, in a way,
dissociated. Clausius, who was the first to represent the phenomena by this
symbol, supposed, in order not to shock the feelings of chemists too much,
that this dissociation only affected an infinitesimal fraction of the total
number of the molecules of the salt, and thereby escaped all check.
This concession was unfortunate, and the hypothesis thus lost the greater
part of its usefulness. M. Arrhenius was bolder, and frankly recognized that

dissociation occurs at once in the case of a great number of molecules, and
tends to increase more and more as the solution becomes more dilute. It
follows the comparison with a gas which, while partially dissociated in an
enclosed space, becomes wholly so in an infinite one.
M. Arrhenius was led to adopt this hypothesis by the examination of
experimental results relating to the conductivity of electrolytes. In order to
interpret certain facts, it has to be recognized that a part only of the
molecules in a saline solution can be considered as conductors of electricity,
and that by adding water the number of molecular conductors is increased.
This increase, too, though rapid at first, soon becomes slower, and
approaches a certain limit which an infinite dilution would enable it to
attain. If the conducting molecules are the dissociated molecules, then the
dissociation (so long as it is a question of strong acids and salts) tends to
become complete in the case of an unlimited dilution.
The opposition of a large number of chemists and physicists to the ideas of
M. Arrhenius was at first very fierce. It must be noted with regret that, in
France particularly, recourse was had to an arm which scholars often wield
rather clumsily. They joked about these free ions in solution, and they asked
to see this chlorine and this sodium which swam about the water in a state
of liberty. But in science, as elsewhere, irony is not argument, and it soon
had to be acknowledged that the hypothesis of M. Arrhenius showed itself
singularly fertile and had to be regarded, at all events, as a very expressive
image, if not, indeed, entirely in conformity with reality.
It would certainly be contrary to all experience, and even to common sense
itself, to suppose that in dissolved chloride of sodium there is really free
sodium, if we suppose these atoms of sodium to be absolutely identical with
ordinary atoms. But there is a great difference. In the one case the atoms are
electrified, and carry a relatively considerable positive charge, inseparable
from their state as ions, while in the other they are in the neutral state. We
may suppose that the presence of this charge brings about modifications as
extensive as one pleases in the chemical properties of the atom. Thus the
hypothesis will be removed from all discussion of a chemical order, since it
will have been made plastic enough beforehand to adapt itself to all the
known facts; and if we object that sodium cannot subsist in water because it

instantaneously decomposes the latter, the answer is simply that the sodium
ion does not decompose water as does ordinary sodium.
Still, other objections might be raised which could not be so easily refuted.
One, to which chemists not unreasonably attached great importance, was
this:—If a certain quantity of chloride of sodium is dissociated into chlorine
and sodium, it should be possible, by diffusion, for example, which brings
out plainly the phenomena of dissociation in gases, to extract from the
solution a part either of the chlorine or of the sodium, while the
corresponding part of the other compound would remain. This result would
be in flagrant contradiction with the fact that, everywhere and always, a
solution of salt contains strictly the same proportions of its component
elements.
M. Arrhenius answers to this that the electrical forces in ordinary conditions
prevent separation by diffusion or by any other process. Professor Nernst
goes further, and has shown that the concentration currents which are
produced when two electrodes of the same substance are plunged into two
unequally concentrated solutions may be interpreted by the hypothesis that,
in these particular conditions, the diffusion does bring about a separation of
the ions. Thus the argument is turned round, and the proof supposed to be
given of the incorrectness of the theory becomes a further reason in its
favour.
It is possible, no doubt, to adduce a few other experiments which are not
very favourable to M. Arrhenius's point of view, but they are isolated cases;
and, on the whole, his theory has enabled many isolated facts, till then
scattered, to be co-ordinated, and has allowed very varied phenomena to be
linked together. It has also suggested—and, moreover, still daily suggests—
researches of the highest order.
In the first place, the theory of Arrhenius explains electrolysis very simply.
The ions which, so to speak, wander about haphazard, and are uniformly
distributed throughout the liquid, steer a regular course as soon as we dip in
the trough containing the electrolyte the two electrodes connected with the
poles of the dynamo or generator of electricity. Then the charged positive
ions travel in the direction of the electromotive force and the negative ions
in the opposite direction. On reaching the electrodes they yield up to them

the charges they carry, and thus pass from the state of ion into that of
ordinary atom. Moreover, for the solution to remain in equilibrium, the
vanished ions must be immediately replaced by others, and thus the state of
ionisation of the electrolyte remains constant and its conductivity persists.
All the peculiarities of electrolysis are capable of interpretation: the
phenomena of the transport of ions, the fine experiments of M. Bouty, those
of Professor Kohlrausch and of Professor Ostwald on various points in
electrolytic conduction, all support the theory. The verifications of it can
even be quantitative, and we can foresee numerical relations between
conductivity and other phenomena. The measurement of the conductivity
permits the number of molecules dissociated in a given solution to be
calculated, and the number is thus found to be precisely the same as that
arrived at if it is wished to remove the disagreement between reality and the
anticipations which result from the theory of Professor Van t' Hoff. The
laws of cryoscopy, of tonometry, and of osmosis thus again become strict,
and no exception to them remains.
If the dissociation of salts is a reality and is complete in a dilute solution,
any of the properties of a saline solution whatever should be represented
numerically as the sum of three values, of which one concerns the positive
ion, a second the negative ion, and the third the solvent. The properties of
the solutions would then be what are called additive properties. Numerous
verifications may be attempted by very different roads. They generally
succeed very well; and whether we measure the electric conductivity, the
density, the specific heats, the index of refraction, the power of rotatory
polarization, the colour, or the absorption spectrum, the additive property
will everywhere be found in the solution.
The hypothesis, so contested at the outset by the chemists, is, moreover,
assuring its triumph by important conquests in the domain of chemistry
itself. It permits us to give a vivid explanation of chemical reaction, and for
the old motto of the chemists, "Corpora non agunt, nisi soluta," it
substitutes a modern one, "It is especially the ions which react." Thus, for
example, all salts of iron, which contain iron in the state of ions, give
similar reactions; but salts such as ferrocyanide of potassium, in which iron
does not play the part of an ion, never give the characteristic reactions of
iron.

Professor Ostwald and his pupils have drawn from the hypothesis of
Arrhenius manifold consequences which have been the cause of
considerable progress in physical chemistry. Professor Ostwald has shown,
in particular, how this hypothesis permits the quantitative calculation of the
conditions of equilibrium of electrolytes and solutions, and especially of the
phenomena of neutralization. If a dissolved salt is partly dissociated into
ions, this solution must be limited by an equilibrium between the non-
dissociated molecule and the two ions resulting from the dissociation; and,
assimilating the phenomenon to the case of gases, we may take for its study
the laws of Gibbs and of Guldberg and Waage. The results are generally
very satisfactory, and new researches daily furnish new checks.
Professor Nernst, who before gave, as has been said, a remarkable
interpretation of the diffusion of electrolytes, has, in the direction pointed
out by M. Arrhenius, developed a theory of the entire phenomena of
electrolysis, which, in particular, furnishes a striking explanation of the
mechanism of the production of electromotive force in galvanic batteries.
Extending the analogy, already so happily invoked, between the phenomena
met with in solutions and those produced in gases, Professor Nernst
supposes that metals tend, as it were, to vaporize when in presence of a
liquid. A piece of zinc introduced, for example, into pure water gives birth
to a few metallic ions. These ions become positively charged, while the
metal naturally takes an equal charge, but of contrary sign. Thus the
solution and the metal are both electrified; but this sort of vaporization is
hindered by electrostatic attraction, and as the charges borne by the ions are
considerable, an equilibrium will be established, although the number of
ions which enter the solution will be very small.
If the liquid, instead of being a solvent like pure water, contains an
electrolyte, it already contains metallic ions, the osmotic pressure of which
will be opposite to that of the solution. Three cases may then present
themselves—either there will be equilibrium, or the electrostatic attraction
will oppose itself to the pressure of solution and the metal will be
negatively charged, or, finally, the attraction will act in the same direction
as the pressure, and the metal will become positively and the solution
negatively charged. Developing this idea, Professor Nernst calculates, by
means of the action of the osmotic pressures, the variations of energy

brought into play and the value of the differences of potential by the contact
of the electrodes and electrolytes. He deduces this from the electromotive
force of a single battery cell which becomes thus connected with the values
of the osmotic pressures, or, if you will, thanks to the relation discovered by
Van t' Hoff, with the concentrations. Some particularly interesting electrical
phenomena thus become connected with an already very important group,
and a new bridge is built which unites two regions long considered foreign
to each other.
The recent discoveries on the phenomena produced in gases when rendered
conductors of electricity almost force upon us, as we shall see, the idea that
there exist in these gases electrified centres moving through the field, and
this idea gives still greater probability to the analogous theory explaining
the mechanism of the conductivity of liquids. It will also be useful, in order
to avoid confusion, to restate with precision this notion of electrolytic ions,
and to ascertain their magnitude, charge, and velocity.
The two classic laws of Faraday will supply us with important information.
The first indicates that the quantity of electricity passing through the liquid
is proportional to the quantity of matter deposited on the electrodes. This
leads us at once to the consideration that, in any given solution, all the ions
possess individual charges equal in absolute value.
The second law may be stated in these terms: an atom-gramme of metal
carries with it into electrolysis a quantity of electricity proportionate to its
valency. [19]
Numerous experiments have made known the total mass of hydrogen
capable of carrying one coulomb, and it will therefore be possible to
estimate the charge of an ion of hydrogen if the number of atoms of
hydrogen in a given mass be known. This last figure is already furnished by
considerations derived from the kinetic theory, and agrees with the one
which can be deduced from the study of various phenomena. The result is
that an ion of hydrogen having a mass of 1.3 x 10^-20 grammes bears a
charge of 1.3 X 10^-20 electromagnetic units; and the second law will
immediately enable the charge of any other ion to be similarly estimated.
The measurements of conductivity, joined to certain considerations relating
to the differences of concentration which appear round the electrode in

electrolysis, allow the speed of the ions to be calculated. Thus, in a liquid
containing 1/10th of a hydrogen-ion per litre, the absolute speed of an ion
would be 3/10ths of a millimetre per second in a field where the fall of
potential would be 1 volt per centimetre. Sir Oliver Lodge, who has made
direct experiments to measure this speed, has obtained a figure very
approximate to this. This value is very small compared to that which we
shall meet with in gases.
Another consequence of the laws of Faraday, to which, as early as 1881,
Helmholtz drew attention, may be considered as the starting-point of certain
new doctrines we shall come across later.
Helmholtz says: "If we accept the hypothesis that simple bodies are
composed of atoms, we are obliged to admit that, in the same way,
electricity, whether positive or negative, is composed of elementary parts
which behave like atoms of electricity."
The second law seems, in fact, analogous to the law of multiple proportions
in chemistry, and it shows us that the quantities of electricity carried vary
from the simple to the double or treble, according as it is a question of a
uni-, bi-, or trivalent metal; and as the chemical law leads up to the
conception of the material atom, so does the electrolytic law suggest the
idea of an electric atom.

CHAPTER VI

THE ETHER
§ 1. THE LUMINIFEROUS ETHER
It is in the works of Descartes that we find the first idea of attributing those
physical phenomena which the properties of matter fail to explain to some
subtle matter which is the receptacle of the energy of the universe.
In our times this idea has had extraordinary luck. After having been eclipsed
for two hundred years by the success of the immortal synthesis of Newton,
it gained an entirely new splendour with Fresnel and his followers. Thanks
to their admirable discoveries, the first stage seemed accomplished, the
laws of optics were represented by a single hypothesis, marvellously fitted
to allow us to anticipate unknown phenomena, and all these anticipations
were subsequently fully verified by experiment. But the researches of
Faraday, Maxwell, and Hertz authorized still greater ambitions; and it really
seemed that this medium, to which it was agreed to give the ancient name
of ether, and which had already explained light and radiant heat, would also
be sufficient to explain electricity. Thus the hope began to take form that we
might succeed in demonstrating the unity of all physical forces. It was
thought that the knowledge of the laws relating to the inmost movements of
this ether might give us the key to all phenomena, and might make us
acquainted with the method in which energy is stored up, transmitted, and
parcelled out in its external manifestations.
We cannot study here all the problems which are connected with the physics
of the ether. To do this a complete treatise on optics would have to be
written and a very lengthy one on electricity. I shall simply endeavour to
show rapidly how in the last few years the ideas relative to the constitution
of this ether have evolved, and we shall see if it be possible without self-
delusion to imagine that a single medium can really allow us to group all
the known facts in one comprehensive arrangement.
As constructed by Fresnel, the hypothesis of the luminous ether, which had
so great a struggle at the outset to overcome the stubborn resistance of the
partisans of the then classic theory of emission, seemed, on the contrary, to

possess in the sequel an unshakable strength. Lamé, though a prudent
mathematician, wrote: "The existence of the ethereal fluid is incontestably
demonstrated by the propagation of light through the planetary spaces, and
by the explanation, so simple and so complete, of the phenomena of
diffraction in the wave theory of light"; and he adds: "The laws of double
refraction prove with no less certainty that the ether exists in all diaphanous
media." Thus the ether was no longer an hypothesis, but in some sort a
tangible reality. But the ethereal fluid of which the existence was thus
proclaimed has some singular properties.
Were it only a question of explaining rectilinear propagation, reflexion,
refraction, diffraction, and interferences notwithstanding grave difficulties
at the outset and the objections formulated by Laplace and Poisson (some of
which, though treated somewhat lightly at the present day, have not lost all
value), we should be under no obligation to make any hypothesis other than
that of the undulations of an elastic medium, without deciding in advance
anything as to the nature and direction of the vibrations.
This medium would, naturally—since it exists in what we call the void—be
considered as imponderable. It may be compared to a fluid of negligible
mass—since it offers no appreciable resistance to the motion of the planets
—but is endowed with an enormous elasticity, because the velocity of the
propagation of light is considerable. It must be capable of penetrating into
all transparent bodies, and of retaining there, so to speak, a constant
elasticity, but must there become condensed, since the speed of propagation
in these bodies is less than in a vacuum. Such properties belong to no
material gas, even the most rarefied, but they admit of no essential
contradiction, and that is the important point. [20]
It was the study of the phenomena of polarization which led Fresnel to his
bold conception of transverse vibrations, and subsequently induced him to
penetrate further into the constitution of the ether. We know the experiment
of Arago on the noninterference of polarized rays in rectangular planes.
While two systems of waves, proceeding from the same source of natural
light and propagating themselves in nearly parallel directions, increase or
become destroyed according to whether the nature of the superposed waves
are of the same or of contrary signs, the waves of the rays polarized in
perpendicular planes, on the other hand, can never interfere with each other.

Whatever the difference of their course, the intensity of the light is always
the sum of the intensity of the two rays.
Fresnel perceived that this experiment absolutely compels us to reject the
hypothesis of longitudinal vibrations acting along the line of propagation in
the direction of the rays. To explain it, it must of necessity be admitted, on
the contrary, that the vibrations are transverse and perpendicular to the ray.
Verdet could say, in all truth, "It is not possible to deny the transverse
direction of luminous vibrations, without at the same time denying that light
consists of an undulatory movement."
Such vibrations do not and cannot exist in any medium resembling a fluid.
The characteristic of a fluid is that its different parts can displace
themselves with regard to one another without any reaction appearing so
long as a variation of volume is not produced. There certainly may exist, as
we have seen, certain traces of rigidity in a liquid, but we cannot conceive
such a thing in a body infinitely more subtle than rarefied gas. Among
material bodies, a solid alone really possesses the rigidity sufficient for the
production within it of transverse vibrations and for their maintenance
during their propagation.
Since we have to attribute such a property to the ether, we may add that on
this point it resembles a solid, and Lord Kelvin has shown that this solid,
would be much more rigid than steel. This conclusion produces great
surprise in all who hear it for the first time, and it is not rare to hear it
appealed to as an argument against the actual existence of the ether. It does
not seem, however, that such an argument can be decisive. There is no
reason for supposing that the ether ought to be a sort of extension of the
bodies we are accustomed to handle. Its properties may astonish our
ordinary way of thinking, but this rather unscientific astonishment is not a
reason for doubting its existence. Real difficulties would appear only if we
were led to attribute to the ether, not singular properties which are seldom
found united in the same substance, but properties logically contradictory.
In short, however odd such a medium may appear to us, it cannot be said
that there is any absolute incompatibility between its attributes.
It would even be possible, if we wished, to suggest images capable of
representing these contrary appearances. Various authors have done so.

Thus, M. Boussinesq assumes that the ether behaves like a very rarefied gas
in respect of the celestial bodies, because these last move, while bathed in
it, in all directions and relatively slowly, while they permit it to retain, so to
speak, its perfect homogeneity. On the other hand, its own undulations are
so rapid that so far as they are concerned the conditions become very
different, and its fluidity has, one might say, no longer the time to come in.
Hence its rigidity alone appears.
Another consequence, very important in principle, of the fact that vibrations
of light are transverse, has been well put in evidence by Fresnel. He showed
how we have, in order to understand the action which excites without
condensation the sliding of successive layers of the ether during the
propagation of a vibration, to consider the vibrating medium as being
composed of molecules separated by finite distances. Certain authors, it is
true, have proposed theories in which the action at a distance of these
molecules are replaced by actions of contact between parallelepipeds
sliding over one another; but, at bottom, these two points of view both lead
us to conceive the ether as a discontinuous medium, like matter itself. The
ideas gathered from the most recent experiments also bring us to the same
conclusion.

§ 2. RADIATIONS
In the ether thus constituted there are therefore propagated transverse
vibrations, regarding which all experiments in optics furnish very precise
information. The amplitude of these vibrations is exceedingly small, even in
relation to the wave-length, small as these last are. If, in fact, the amplitude
of the vibrations acquired a noticeable value in comparison with the wave-
length, the speed of propagation should increase with the amplitude. Yet, in
spite of some curious experiments which seem to establish that the speed of
light does alter a little with its intensity, we have reason to believe that, as
regards light, the amplitude of the oscillations in relation to the wave-length
is incomparably less than in the case of sound.
It has become the custom to characterise each vibration by the path which
the vibratory movement traverses during the space of a vibration—by the
length of wave, in a word—rather than by the duration of the vibration

itself. To measure wave-lengths, the methods must be employed to which I
have already alluded on the subject of measurements of length. Professor
Michelson, on the one hand, and MM. Perot and Fabry, on the other, have
devised exceedingly ingenious processes, which have led to results of really
unhoped-for precision. The very exact knowledge also of the speed of the
propagation of light allows the duration of a vibration to be calculated when
once the wave-length is known. It is thus found that, in the case of visible
light, the number of the vibrations from the end of the violet to the infra-red
varies from four hundred to two hundred billions per second. This gamut is
not, however, the only one the ether can give. For a long time we have
known ultra-violet radiations still more rapid, and, on the other hand, infra-
red ones more slow, while in the last few years the field of known radiations
has been singularly extended in both directions.
It is to M. Rubens and his fellow-workers that are due the most brilliant
conquests in the matter of great wave-lengths. He had remarked that, in
their study, the difficulty of research proceeds from the fact that the extreme
waves of the infra-red spectrum only contain a small part of the total energy
emitted by an incandescent body; so that if, for the purpose of study, they
are further dispersed by a prism or a grating, the intensity at any one point
becomes so slight as to be no longer observable. His original idea was to
obtain, without prism or grating, a homogeneous pencil of great wave-
length sufficiently intense to be examined. For this purpose the radiant
source used was a strip of platinum covered with fluorine or powdered
quartz, which emits numerous radiations close to two bands of linear
absorption in the absorption spectra of fluorine and quartz, one of which is
situated in the infra-red. The radiations thus emitted are several times
reflected on fluorine or on quartz, as the case may be; and as, in proximity
to the bands, the absorption is of the order of that of metallic bodies for
luminous rays, we no longer meet in the pencil several times reflected or in
the rays remaining after this kind of filtration, with any but radiations of
great wave-length. Thus, for instance, in the case of the quartz, in the
neighbourhood of a radiation corresponding to a wave-length of 8.5
microns, the absorption is thirty times greater in the region of the band than
in the neighbouring region, and consequently, after three reflexions, while
the corresponding radiations will not have been weakened, the

neighbouring waves will be so, on the contrary, in the proportion of 1 to
27,000.

With mirrors of rock salt and of sylvine[21] there have been obtained, by
taking an incandescent gas light (Auer) as source, radiations extending as
far as 70 microns; and these last are the greatest wave-lengths observed in
optical phenomena. These radiations are largely absorbed by the vapour of
water, and it is no doubt owing to this absorption that they are not found in
the solar spectrum. On the other hand, they easily pass through gutta-
percha, india-rubber, and insulating substances in general.
At the opposite end of the spectrum the knowledge of the ultra-violet
regions has been greatly extended by the researches of Lenard. These
extremely rapid radiations have been shown by that eminent physicist to
occur in the light of the electric sparks which flash between two metal
points, and which are produced by a large induction coil with condenser and
a Wehnelt break. Professor Schumann has succeeded in photographing them
by depositing bromide of silver directly on glass plates without fixing it
with gelatine; and he has, by the same process, photographed in the
spectrum of hydrogen a ray with a wave-length of only 0.1 micron.
The spectroscope was formed entirely of fluor-spar, and a vacuum had been
created in it, for these radiations are extremely absorbable by the air.
Notwithstanding the extreme smallness of the luminous wave-lengths, it has
been possible, after numerous fruitless trials, to obtain stationary waves
analogous to those which, in the case of sound, are produced in organ pipes.
The marvellous application M. Lippmann has made of these waves to
completely solve the problem of photography in colours is well known.
This discovery, so important in itself and so instructive, since it shows us
how the most delicate anticipations of theory may be verified in all their
consequences, and lead the physicist to the solution of the problems
occurring in practice, has justly become popular, and there is, therefore, no
need to describe it here in detail.
Professor Wiener obtained stationary waves some little while before M.
Lippmann's discovery, in a layer of a sensitive substance having a grain
sufficiently small in relation to the length of wave. His aim was to solve a
question of great importance to a complete knowledge of the ether. Fresnel

founded his theory of double refraction and reflexion by transparent
surfaces, on the hypothesis that the vibration of a ray of polarized light is
perpendicular to the plane of polarization. But Neumann has proposed, on
the contrary, a theory in which he recognizes that the luminous vibration is
in this very plane. He rather supposes, in opposition to Fresnel's idea, that
the density of the ether remains the same in all media, while its coefficient
of elasticity is variable.
Very remarkable experiments on dispersion by M. Carvallo prove indeed
that the idea of Fresnel was, if not necessary for us to adopt, at least the
more probable of the two; but apart from this indication, and contrary to the
hypothesis of Neumann, the two theories, from the point of view of the
explanation of all known facts, really appear to be equivalent. Are we then
in presence of two mechanical explanations, different indeed, but
nevertheless both adaptable to all the facts, and between which it will
always be impossible to make a choice? Or, on the contrary, shall we
succeed in realising an experimentum crucis, an experiment at the point
where the two theories cross, which will definitely settle the question?
Professor Wiener thought he could draw from his experiment a firm
conclusion on the point in dispute. He produced stationary waves with light
polarized at an angle of 45°,[22] and established that, when light is polarized
in the plane of incidence, the fringes persist; but that, on the other hand,
they disappear when the light is polarized perpendicularly to this plane. If it
be admitted that a photographic impression results from the active force of
the vibratory movement of the ether, the question is, in fact, completely
elucidated, and the discrepancy is abolished in Fresnel's favour.
M.H. Poincaré has pointed out, however, that we know nothing as to the
mechanism of the photographic impression. We cannot consider it evident
that it is the kinetic energy of the ether which produces the decomposition
of the sensitive salt; and if, on the contrary, we suppose it to be due to the
potential energy, all the conclusions are reversed, and Neumann's idea
triumphs.
Recently a very clever physicist, M. Cotton, especially known for his skilful
researches in the domain of optics, has taken up anew the study of
stationary waves. He has made very precise quantitative experiments, and

has demonstrated, in his turn, that it is impossible, even with spherical
waves, to succeed in determining on which of the two vectors which have
to be regarded in all theories of light on the subject of polarization
phenomena the luminous intensity and the chemical action really depend.
This question, therefore, no longer exists for those physicists who admit
that luminous vibrations are electrical oscillations. Whatever, then, the
hypothesis formed, whether it be electric force or, on the contrary, magnetic
force which we place in the plane of polarization, the mode of propagation
foreseen will always be in accord with the facts observed.

§ 3. THE ELECTROMAGNETIC ETHER
The idea of attributing the phenomena of electricity to perturbations
produced in the medium which transmits the light is already of old
standing; and the physicists who witnessed the triumph of Fresnel's theories
could not fail to conceive that this fluid, which fills the whole of space and
penetrates into all bodies, might also play a preponderant part in electrical
actions. Some even formed too hasty hypotheses on this point; for the hour
had not arrived when it was possible to place them on a sufficiently sound
basis, and the known facts were not numerous enough to give the necessary
precision.
The founders of modern electricity also thought it wiser to adopt, with
regard to this science, the attitude taken by Newton in connection with
gravitation: "In the first place to observe facts, to vary the circumstances of
these as much as possible, to accompany this first work by precise
measurements in order to deduce from them general laws founded solely on
experiment, and to deduce from these laws, independently of all hypotheses
on the nature of the forces producing the phenomena, the mathematical
value of these forces—that is to say, the formula representing them. Such
was the system pursued by Newton. It has, in general, been adopted in
France by the scholars to whom physics owe the great progress made of late
years, and it has served as my guide in all my researches on electrodynamic
phenomena.... It is for this reason that I have avoided speaking of the ideas I
may have on the nature of the cause of the force emanating from voltaic
conductors."

Thus did Ampère express himself. The illustrious physicist rightly
considered the results obtained by him through following this wise method
as worthy of comparison with the laws of attraction; but he knew that when
this first halting-place was reached there was still further to go, and that the
evolution of ideas must necessarily continue.
"With whatever physical cause," he adds, "we may wish to connect the
phenomena produced by electro-dynamic action, the formula I have
obtained will always remain the expression of the facts," and he explicitly
indicated that if one could succeed in deducing his formula from the
consideration of the vibrations of a fluid distributed through space, an
enormous step would have been taken in this department of physics. He
added, however, that this research appeared to him premature, and would
change nothing in the results of his work, since, to accord with facts, the
hypothesis adopted would always have to agree with the formula which
exactly represents them.
It is not devoid of interest to observe that Ampère himself, notwithstanding
his caution, really formed some hypotheses, and recognized that electrical
phenomena were governed by the laws of mechanics. Yet the principles of
Newton then appeared to be unshakable.
Faraday was the first to demonstrate, by clear experiment, the influence of
the media in electricity and magnetic phenomena, and he attributed this
influence to certain modifications in the ether which these media enclose.
His fundamental conception was to reject action at a distance, and to
localize in the ether the energy whose evolution is the cause of the actions
manifested, as, for example, in the discharge of a condenser.
Consider the barrel of a pump placed in a vacuum and closed by a piston at
each end, and let us introduce between these a certain mass of air. The two
pistons, through the elastic force of the gas, repel each other with a force
which, according to the law of Mariotte, varies in inverse ratio to the
distance. The method favoured by Ampère would first of all allow this law
of repulsion between the two pistons to be discovered, even if the existence
of a gas enclosed in the barrel of the pump were unsuspected; and it would
then be natural to localize the potential energy of the system on the surface
of the two pistons. But if the phenomenon is more carefully examined, we

shall discover the presence of the air, and we shall understand that every
part of the volume of this air could, if it were drawn off into a recipient of
equal volume, carry away with it a fraction of the energy of the system, and
that consequently this energy belongs really to the air and not to the pistons,
which are there solely for the purpose of enabling this energy to manifest its
existence.
Faraday made, in some sort, an equivalent discovery when he perceived that
the electrical energy belongs, not to the coatings of the condenser, but to the
dielectric which separates them. His audacious views revealed to him a new
world, but to explore this world a surer and more patient method was
needed.
Maxwell succeeded in stating with precision certain points of Faraday's
ideas, and he gave them the mathematical form which, often wrongly,
impresses physicists, but which when it exactly encloses a theory, is a
certain proof that this theory is at least coherent and logical. [23]
The work of Maxwell is over-elaborated, complex, difficult to read, and
often ill-understood, even at the present day. Maxwell is more concerned in
discovering whether it is possible to give an explanation of electrical and
magnetic phenomena which shall be founded on the mechanical properties
of a single medium, than in stating this explanation in precise terms. He is
aware that if we could succeed in constructing such an interpretation, it
would be easy to propose an infinity of others, entirely equivalent from the
point of view of the experimentally verifiable consequences; and his
especial ambition is therefore to extract from the premises a general view,
and to place in evidence something which would remain the common
property of all the theories.
He succeeded in showing that if the electrostatic energy of an
electromagnetic field be considered to represent potential energy, and its
electrodynamic the kinetic energy, it becomes possible to satisfy both the
principle of least action and that of the conservation of energy; from that
moment—if we eliminate a few difficulties which exist regarding the
stability of the solutions—the possibility of finding mechanical
explanations of electromagnetic phenomena must be considered as
demonstrated. He thus succeeded, moreover, in stating precisely the notion

of two electric and magnetic fields which are produced in all points of
space, and which are strictly inter-connected, since the variation of the one
immediately and compulsorily gives birth to the other.
From this hypothesis he deduced that, in the medium where this energy is
localized, an electromagnetic wave is propagated with a velocity equal to
the relation of the units of electric mass in the electromagnetic and
electrostatic systems. Now, experiments made known since his time have
proved that this relation is numerically equal to the speed of light, and the
more precise experiments made in consequence—among which should be
cited the particularly careful ones of M. Max Abraham—have only rendered
the coincidence still more complete.
It is natural henceforth to suppose that this medium is identical with the
luminous ether, and that a luminous wave is an electromagnetic wave—that
is to say, a succession of alternating currents, which exist in the dielectric
and even in the void, and possess an enormous frequency, inasmuch as they
change their direction thousands of billions of times per second, and by
reason of this frequency produce considerable induction effects. Maxwell
did not admit the existence of open currents. To his mind, therefore, an
electrical vibration could not produce condensations of electricity. It was, in
consequence, necessarily transverse, and thus coincided with the vibration
of Fresnel; while the corresponding magnetic vibration was perpendicular
to it, and would coincide with the luminous vibration of Neumann.
Maxwell's theory thus establishes a close correlation between the
phenomena of the luminous and those of the electromagnetic waves, or, we
might even say, the complete identity of the two. But it does not follow
from this that we ought to regard the variation of an electric field produced
at some one point as necessarily consisting of a real displacement of the
ether round that point. The idea of thus bringing electrical phenomena back
to the mechanics of the ether is not, then, forced upon us, and the contrary
idea even seems more probable. It is not the optics of Fresnel which absorbs
the science of electricity, it is rather the optics which is swallowed up by a
more general theory. The attempts of popularizers who endeavour to
represent, in all their details, the mechanism of the electric phenomena, thus
appear vain enough, and even puerile. It is useless to find out to what
material body the ether may be compared, if we content ourselves with

seeing in it a medium of which, at every point, two vectors define the
properties.
For a long time, therefore, we could remark that the theory of Fresnel
simply supposed a medium in which something periodical was propagated,
without its being necessary to admit this something to be a movement; but
we had to wait not only for Maxwell, but also for Hertz, before this idea
assumed a really scientific shape. Hertz insisted on the fact that the six
equations of the electric field permit all the phenomena to be anticipated
without its being necessary to construct one hypothesis or another, and he
put these equations into a very symmetrical form, which brings completely
in evidence the perfect reciprocity between electrical and magnetic actions.
He did yet more, for he brought to the ideas of Maxwell the most striking
confirmation by his memorable researches on electric oscillations.

§ 4. ELECTRICAL OSCILLATIONS
The experiments of Hertz are well known. We know how the Bonn
physicist developed, by means of oscillating electric discharges,
displacement currents and induction effects in the whole of the space round
the spark-gap; and how he excited by induction at some point in a wire a
perturbation which afterwards is propagated along the wire, and how a
resonator enabled him to detect the effect produced.
The most important point made evident by the observation of interference
phenomena and subsequently verified directly by M. Blondlot, is that the
electromagnetic perturbation is propagated with the speed of light, and this
result condemns for ever all the hypotheses which fail to attribute any part
to the intervening media in the propagation of an induction phenomenon.
If the inducing action were, in fact, to operate directly between the inducing
and the induced circuits, the propagation should be instantaneous; for if an
interval were to occur between the moment when the cause acted and the
one when the effect was produced, during this interval there would no
longer be anything anywhere, since the intervening medium does not come
into play, and the phenomenon would then disappear.

Leaving on one side the manifold but purely electrical consequences of this
and the numerous researches relating to the production or to the properties
of the waves—some of which, those of MM. Sarrazin and de la Rive, Righi,
Turpain, Lebedeff, Decombe, Barbillon, Drude, Gutton, Lamotte, Lecher,
etc., are, however, of the highest order—I shall only mention here the
studies more particularly directed to the establishment of the identity of the
electromagnetic and the luminous waves.
The only differences which subsist are necessarily those due to the
considerable discrepancy which exists between the durations of the periods
of these two categories of waves. The length of wave corresponding to the
first spark-gap of Hertz was about 6 metres, and the longest waves
perceptible by the retina are 7/10 of a micron. [24]
These radiations are so far apart that it is not astonishing that their
properties have not a perfect similitude. Thus phenomena like those of
diffraction, which are negligible in the ordinary conditions under which
light is observed, may here assume a preponderating importance. To play
the part, for example, with the Hertzian waves, which a mirror 1 millimetre
square plays with regard to light, would require a colossal mirror which
would attain the size of a myriametre [25] square.
The efforts of physicists have to-day, however, filled up, in great part, this
interval, and from both banks at once they have laboured to build a bridge
between the two domains. We have seen how Rubens showed us calorific
rays 60 metres long; on the other hand, MM. Lecher, Bose, and Lampa have
succeeded, one after the other, in gradually obtaining oscillations with
shorter and shorter periods. There have been produced, and are now being
studied, electromagnetic waves of four millimetres; and the gap subsisting
in the spectrum between the rays left undetected by sylvine and the
radiations of M. Lampa now hardly comprise more than five octaves—that
is to say, an interval perceptibly equal to that which separates the rays
observed by M. Rubens from the last which are evident to the eye.
The analogy then becomes quite close, and in the remaining rays the
properties, so to speak, characteristic of the Hertzian waves, begin to
appear. For these waves, as we have seen, the most transparent bodies are
the most perfect electrical insulators; while bodies still slightly conducting

are entirely opaque. The index of refraction of these substances tends in the
case of great wave-lengths to become, as the theory anticipates, nearly the
square root of the dielectric constant.
MM. Rubens and Nichols have even produced with the waves which
remain phenomena of electric resonance quite similar to those which an
Italian scholar, M. Garbasso, obtained with electric waves. This physicist
showed that, if the electric waves are made to impinge on a flat wooden
stand, on which are a series of resonators parallel to each other and
uniformly arranged, these waves are hardly reflected save in the case where
the resonators have the same period as the spark-gap. If the remaining rays
are allowed to fall on a glass plate silvered and divided by a diamond fixed
on a dividing machine into small rectangles of equal dimensions, there will
be observed variations in the reflecting power according to the orientation
of the rectangles, under conditions entirely comparable with the experiment
of Garbasso.
In order that the phenomenon be produced it is necessary that the remaining
waves should be previously polarized. This is because, in fact, the
mechanism employed to produce the electric oscillations evidently gives
out vibrations which occur on a single plane and are subsequently
polarized.
We cannot therefore entirely assimilate a radiation proceeding from a spark-
gap to a ray of natural light. For the synthesis of light to be realized, still
other conditions must be complied with. During a luminous impression, the
direction and the phase change millions of times in the vibration sensible to
the retina, yet the damping of this vibration is very slow. With the Hertzian
oscillations all these conditions are changed—the damping is very rapid but
the direction remains invariable.
Every time, however, that we deal with general phenomena which are
independent of these special conditions, the parallelism is perfect; and with
the waves, we have put in evidence the reflexion, refraction, total reflexion,
double reflexion, rotatory polarization, dispersion, and the ordinary
interferences produced by rays travelling in the same direction and crossing
each other at a very acute angle, or the interferences analogous to those
which Wiener observed with rays of the contrary direction.

A very important consequence of the electromagnetic theory foreseen by
Maxwell is that the luminous waves which fall on a surface must exercise
on this surface a pressure equal to the radiant energy which exists in the unit
of volume of the surrounding space. M. Lebedeff a few years ago allowed a
sheaf of rays from an arc lamp to fall on a deflection radiometer, [26] and
thus succeeded in revealing the existence of this pressure. Its value is
sufficient, in the case of matter of little density and finely divided, to reduce
and even change into repulsion the attractive action exercised on bodies by
the sun. This is a fact formerly conjectured by Faye, and must certainly play
a great part in the deformation of the heads of comets.
More recently, MM. Nichols and Hull have undertaken experiments on this
point. They have measured not only the pressure, but also the energy of the
radiation by means of a special bolometer. They have thus arrived at
numerical verifications which are entirely in conformity with the
calculations of Maxwell.
The existence of these pressures may be otherwise foreseen even apart from
the electromagnetic theory, by adding to the theory of undulations the
principles of thermodynamics. Bartoli, and more recently Dr Larmor, have
shown, in fact, that if these pressures did not exist, it would be possible,
without any other phenomenon, to pass heat from a cold into a warm body,
and thus transgress the principle of Carnot.

§ 5. THE X RAYS
It appears to-day quite probable that the X rays should be classed among the
phenomena which have their seat in the luminous ether. Doubtless it is not
necessary to recall here how, in December 1895, Röntgen, having wrapped
in black paper a Crookes tube in action, observed that a fluorescent
platinocyanide of barium screen placed in the neighbourhood, had become
visible in the dark, and that a photographic plate had received an impress.
The rays which come from the tube, in conditions now well known, are not
deviated by a magnet, and, as M. Curie and M. Sagnac have conclusively
shown, they carry no electric charge. They are subject to neither reflection
nor refraction, and very precise and very ingenious measurements by M.

Gouy have shown that, in their case, the refraction index of the various
bodies cannot be more than a millionth removed from unity.
We knew from the outset that there existed various X rays differing from
each other as, for instance, the colours of the spectrum, and these are
distinguished from each other by their unequal power of passing through
substances. M. Sagnac, particularly, has shown that there can be obtained a
gradually decreasing scale of more or less absorbable rays, so that the
greater part of their photographic action is stopped by a simple sheet of
black paper. These rays figure among the secondary rays discovered, as is
known, by this ingenious physicist. The X rays falling on matter are thus
subjected to transformations which may be compared to those which the
phenomena of luminescence produce on the ultra-violet rays.
M. Benoist has founded on the transparency of matter to the rays a sure and
practical method of allowing them to be distinguished, and has thus been
enabled to define a specific character analogous to the colour of the rays of
light. It is probable also that the different rays do not transport individually
the same quantity of energy. We have not yet obtained on this point precise
results, but it is roughly known, since the experiments of MM. Rutherford
and M'Clung, what quantity of energy corresponds to a pencil of X rays.
These physicists have found that this quantity would be, on an average, five
hundred times larger than that brought by an analogous pencil of solar light
to the surface of the earth. What is the nature of this energy? The question
does not appear to have been yet solved.
It certainly appears, according to Professors Haga and Wind and to
Professor Sommerfeld, that with the X rays curious experiments of
diffraction may be produced. Dr Barkla has shown also that they can
manifest true polarization. The secondary rays emitted by a metallic surface
when struck by X rays vary, in fact, in intensity when the position of the
plane of incidence round the primary pencil is changed. Various physicists
have endeavoured to measure the speed of propagation, but it seems more
and more probable that it is very nearly that of light.[27]
I must here leave out the description of a crowd of other experiments. Some
very interesting researches by M. Brunhes, M. Broca, M. Colardeau, M.
Villard, in France, and by many others abroad, have permitted the

elucidation of several interesting problems relative to the duration of the
emission or to the best disposition to be adopted for the production of the
rays. The only point which will detain us is the important question as to the
nature of the X rays themselves; the properties which have just been
brought to mind are those which appear essential and which every theory
must reckon with.
The most natural hypothesis would be to consider the rays as ultra-violet
radiations of very short wave-length, or radiations which are in a manner
ultra-ultra-violet. This interpretation can still, at this present moment, be
maintained, and the researches of MM. Buisson, Righi, Lenard, and Merrit
Stewart have even established that rays of very short wave-lengths produce
on metallic conductors, from the point of view of electrical phenomena,
effects quite analogous to those of the X rays. Another resemblance results
also from the experiments by which M. Perreau established that these rays
act on the electric resistance of selenium. New and valuable arguments have
thus added force to those who incline towards a theory which has the merit
of bringing a new phenomenon within the pale of phenomena previously
known.
Nevertheless the shortest ultra-violet radiations, such as those of M.
Schumann, are still capable of refraction by quartz, and this difference
constitutes, in the minds of many physicists, a serious enough reason to
decide them to reject the more simple hypothesis. Moreover, the rays of
Schumann are, as we have seen, extraordinarily absorbable,—so much so
that they have to be observed in a vacuum. The most striking property of
the X rays is, on the contrary, the facility with which they pass through
obstacles, and it is impossible not to attach considerable importance to such
a difference.
Some attribute this marvellous radiation to longitudinal vibrations, which,
as M. Duhem has shown, would be propagated in dielectric media with a
speed equal to that of light. But the most generally accepted idea is the one
formulated from the first by Sir George Stokes and followed up by
Professor Wiechert. According to this theory the X rays should be due to a
succession of independent pulsations of the ether, starting from the points
where the molecules projected by the cathode of the Crookes tube meet the
anticathode. These pulsations are not continuous vibrations like the

radiations of the spectrum; they are isolated and extremely short; they are,
besides, transverse, like the undulations of light, and the theory shows that
they must be propagated with the speed of light. They should present
neither refraction nor reflection, but, under certain conditions, they may be
subject to the phenomena of diffraction. All these characteristics are found
in the Röntgen rays.
Professor J.J. Thomson adopts an analogous idea, and states the precise way
in which the pulsations may be produced at the moment when the
electrified particles forming the cathode rays suddenly strike the
anticathode wall. The electromagnetic induction behaves in such a way that
the magnetic field is not annihilated when the particle stops, and the new
field produced, which is no longer in equilibrium, is propagated in the
dielectric like an electric pulsation. The electric and magnetic pulsations
excited by this mechanism may give birth to effects similar to those of light.
Their slight amplitude, however, is the cause of there here being neither
refraction nor diffraction phenomena, save in very special conditions. If the
cathode particle is not stopped in zero time, the pulsation will take a greater
amplitude, and be, in consequence, more easily absorbable; to this is
probably to be attributed the differences which may exist between different
tubes and different rays.
It is right to add that some authors, notwithstanding the proved
impossibility of deviating them in a magnetic field, have not renounced the
idea of comparing them with the cathode rays. They suppose, for instance,
that the rays are formed by electrons animated with so great a velocity that
their inertia, conformably with theories which I shall examine later, no
longer permit them to be stopped in their course; this is, for instance, the
theory upheld by Mr Sutherland. We know, too, that to M. Gustave Le Bon
they represent the extreme limit of material things, one of the last stages
before the vanishing of matter on its return to the ether.
Everyone has heard of the N rays, whose name recalls the town of Nancy,
where they were discovered. In some of their singular properties they are
akin to the X rays, while in others they are widely divergent from them.
M. Blondlot, one of the masters of contemporary physics, deeply respected
by all who know him, admired by everyone for the penetration of his mind,

and the author of works remarkable for the originality and sureness of his
method, discovered them in radiations emitted from various sources, such
as the sun, an incandescent light, a Nernst lamp, and even bodies previously
exposed to the sun's rays. The essential property which allows them to be
revealed is their action on a small induction spark, of which they increase
the brilliancy; this phenomenon is visible to the eye and is rendered
objective by photography.
Various other physicists and numbers of physiologists, following the path
opened by M. Blondlot, published during 1903 and 1904 manifold but often
rather hasty memoirs, in which they related the results of their researches,
which do not appear to have been always conducted with the accuracy
desirable. These results were most strange; they seemed destined to
revolutionise whole regions not only of the domain of physics, but likewise
of the biological sciences. Unfortunately the method of observation was
always founded on the variations in visibility of the spark or of a
phosphorescent substance, and it soon became manifest that these variations
were not perceptible to all eyes.
No foreign experimenter has succeeded in repeating the experiments, while
in France many physicists have failed; and hence the question has much
agitated public opinion. Are we face to face with a very singular case of
suggestion, or is special training and particular dispositions required to
make the phenomenon apparent? It is not possible, at the present moment,
to declare the problem solved; but very recent experiments by M. Gutton
and a note by M. Mascart have reanimated the confidence of those who
hoped that such a scholar as M. Blondlot could not have been deluded by
appearances. However, these last proofs in favour of the existence of the
rays have themselves been contested, and have not succeeded in bringing
conviction to everyone.
It seems very probable indeed that certain of the most singular conclusions
arrived at by certain authors on the subject will lapse into deserved
oblivion. But negative experiments prove nothing in a case like this, and the
fact that most experimenters have failed where M. Blondlot and his pupils
have succeeded may constitute a presumption, but cannot be regarded as a
demonstrative argument. Hence we must still wait; it is exceedingly
possible that the illustrious physicist of Nancy may succeed in discovering

objective actions of the N rays which shall be indisputable, and may thus
establish on a firm basis a discovery worthy of those others which have
made his name so justly celebrated.
According to M. Blondlot the N rays can be polarised, refracted, and
dispersed, while they have wavelengths comprised within .0030 micron,
and .0760 micron—that is to say, between an eighth and a fifth of that
found for the extreme ultra-violet rays. They might be, perhaps, simply rays
of a very short period. Their existence, stripped of the parasitical and
somewhat singular properties sought to be attributed to them, would thus
appear natural enough. It would, moreover, be extremely important, and
lead, no doubt, to most curious applications; it can be conceived, in fact,
that such rays might serve to reveal what occurs in those portions of matter
whose too minute dimensions escape microscopic examination on account
of the phenomena of diffraction.
From whatever point of view we look at it, and whatever may be the fate of
the discovery, the history of the N rays is particularly instructive, and must
give food for reflection to those interested in questions of scientific
methods.

§ 6. THE ETHER AND GRAVITATION
The striking success of the hypothesis of the ether in optics has, in our own
days, strengthened the hope of being able to explain, by an analogous
representation, the action of gravitation.
For a long time, philosophers who rejected the idea that ponderability is a
primary and essential quality of all bodies have sought to reduce their
weight to pressures exercised in a very subtle fluid. This was the conception
of Descartes, and was perhaps the true idea of Newton himself. Newton
points out, in many passages, that the laws he had discovered were
independent of the hypotheses that could be formed on the way in which
universal attraction was produced, but that with sufficient experiments the
true cause of this attraction might one day be reached. In the preface to the
second edition of the Optics he writes: "To prove that I have not considered
weight as a universal property of bodies, I have added a question as to its

cause, preferring this form of question because my interpretation does not
entirely satisfy me in the absence of experiment"; and he puts the question
in this shape: "Is not this medium (the ether) more rarefied in the interior of
dense bodies like the sun, the planets, the comets, than in the empty spaces
which separate them? Passing from these bodies to great distances, does it
not become continually denser, and in that way does it not produce the
weight of these great bodies with regard to each other and of their parts
with regard to these bodies, each body tending to leave the most dense for
the most rarefied parts?"
Evidently this view is incomplete, but we may endeavour to state it
precisely. If we admit that this medium, the properties of which would
explain the attraction, is the same as the luminous ether, we may first ask
ourselves whether the action of gravitation is itself also due to oscillations.
Some authors have endeavoured to found a theory on this hypothesis, but
we are immediately brought face to face with very serious difficulties.
Gravity appears, in fact, to present quite exceptional characteristics. No
agent, not even those which depend upon the ether, such as light and
electricity, has any influence on its action or its direction. All bodies are, so
to speak, absolutely transparent to universal attraction, and no experiment
has succeeded in demonstrating that its propagation is not instantaneous.
From various astronomical observations, Laplace concluded that its
velocity, in any case, must exceed fifty million times that of light. It is
subject neither to reflection nor to refraction; it is independent of the
structure of bodies; and not only is it inexhaustible, but also (as is pointed
out, according to M. Hannequin, by an English scholar, James Croll) the
distribution of the effects of the attracting force of a mass over the manifold
particles which may successively enter the field of its action in no way
diminishes the attraction it exercises on each of them respectively, a thing
which is seen nowhere else in nature.
Nevertheless it is possible, by means of certain hypotheses, to construct
interpretations whereby the appropriate movements of an elastic medium
should explain the facts clearly enough. But these movements are very
complex, and it seems almost inconceivable that the same medium could
possess simultaneously the state of movement corresponding to the
transmission of a luminous phenomenon and that constantly imposed on it
by the transmission of gravitation.

Another celebrated hypothesis was devised by Lesage, of Geneva. Lesage
supposed space to be overrun in all directions by currents of ultramundane
corpuscles. This hypothesis, contested by Maxwell, is interesting. It might
perhaps be taken up again in our days, and it is not impossible that the
assimilation of these corpuscles to electrons might give a satisfactory
image. [28]
M. Crémieux has recently undertaken experiments directed, as he thinks, to
showing that the divergences between the phenomena of gravitation and all
the other phenomena in nature are more apparent than real. Thus the
evolution in the heart of the ether of a quantity of gravific energy would not
be entirely isolated, and as in the case of all evolutions of all energy of
whatever kind, it should provoke a partial transformation into energy of a
different form. Thus again the liberated energy of gravitation would vary
when passing from one material to another, as from gases into liquids, or
from one liquid to a different one.
On this last point the researches of M. Crémieux have given affirmative
results: if we immerse in a large mass of some liquid several drops of
another not miscible with the first, but of identical density, we form a mass
representing no doubt a discontinuity in the ether, and we may ask
ourselves whether, in conformity with what happens in all other phenomena
of nature, this discontinuity has not a tendency to disappear.
If we abide by the ordinary consequences of the Newtonian theory of
potential, the drops should remain motionless, the hydrostatic impulsion
forming an exact equilibrium to their mutual attraction. Now M. Crémieux
remarks that, as a matter of fact, they slowly approach each other.
Such experiments are very delicate; and with all the precautions taken by
the author, it cannot yet be asserted that he has removed all possibility of
the action of the phenomena of capillarity nor all possible errors proceeding
from extremely slight differences of temperature. But the attempt is
interesting and deserves to be followed up.
Thus, the hypothesis of the ether does not yet explain all the phenomena
which the considerations relating to matter are of themselves powerless to
interpret. If we wished to represent to ourselves, by the mechanical
properties of a medium filling the whole of the universe, all luminous,

electric, and gravitation phenomena, we should be led to attribute to this
medium very strange and almost contradictory characteristics; and yet it
would be still more inconceivable that this medium should be double or
treble, that there should be two or three ethers each occupying space as if it
were alone, and interpenetrating it without exercising any action on one
another. We are thus brought, by a close examination of facts, rather to the
idea that the properties of the ether are not wholly reducible to the rules of
ordinary mechanics.
The physicist has therefore not yet succeeded in answering the question
often put to him by the philosopher: "Has the ether really an objective
existence?" However, it is not necessary to know the answer in order to
utilize the ether. In its ideal properties we find the means of determining the
form of equations which are valid, and to the learned detached from all
metaphysical prepossession this is the essential point.

CHAPTER VII

A CHAPTER IN THE HISTORY OF SCIENCE:
WIRELESS TELEGRAPHY
§1
I have endeavoured in this book to set forth impartially the ideas dominant
at this moment in the domain of physics, and to make known the facts
essential to them. I have had to quote the authors of the principal
discoveries in order to be able to class and, in some sort, to name these
discoveries; but I in no way claim to write even a summary history of the
physics of the day.
I am not unaware that, as has often been said, contemporary history is the
most difficult of all histories to write. A certain step backwards seems
necessary in order to enable us to appreciate correctly the relative
importance of events, and details conceal the full view from eyes which are
too close to them, as the trees prevent us from seeing the forest. The event
which produces a great sensation has often only insignificant consequences;
while another, which seemed at the outset of the least importance and little
worthy of note, has in the long run a widespread and deep influence.
If, however, we deal with the history of a positive discovery,
contemporaries who possess immediate information, and are in a position to
collect authentic evidence at first hand, will make, by bringing to it their
sincere testimony, a work of erudition which may be very useful, but which
we may be tempted to look upon as very easy of execution. Yet such a
labour, even when limited to the study of a very minute question or of a
recent invention, is far from being accomplished without the historian
stumbling over serious obstacles.
An invention is never, in reality, to be attributed to a single author. It is the
result of the work of many collaborators who sometimes have no
acquaintance with one another, and is often the fruit of obscure labours.
Public opinion, however, wilfully simple in face of a sensational discovery,
insists that the historian should also act as judge; and it is the historian's

task to disentangle the truth in the midst of the contest, and to declare
infallibly to whom the acknowledgments of mankind should be paid. He
must, in his capacity as skilled expert, expose piracies, detect the most
carefully hidden plagiarisms, and discuss the delicate question of priority;
while he must not be deluded by those who do not fear to announce, in bold
accents, that they have solved problems of which they find the solution
imminent, and who, the day after its final elucidation by third parties,
proclaim themselves its true discoverers. He must rise above a partiality
which deems itself excusable because it proceeds from national pride; and,
finally, he must seek with patience for what has gone before. While thus
retreating step by step he runs the risk of losing himself in the night of time.
An example of yesterday seems to show the difficulties of such a task.
Among recent discoveries the invention of wireless telegraphy is one of
those which have rapidly become popular, and looks, as it were, an exact
subject clearly marked out. Many attempts have already been made to write
its history. Mr J.J. Fahie published in England as early as 1899 an
interesting work entitled the History of Wireless Telegraphy; and about the
same time M. Broca published in France a very exhaustive work named La
Telegraphie sans fil. Among the reports presented to the Congrès
international de physique (Paris, 1900), Signor Righi, an illustrious Italian
scholar, whose personal efforts have largely contributed to the invention of
the present system of telegraphy, devoted a chapter, short, but sufficiently
complete, of his masterly report on Hertzian waves, to the history of
wireless telegraphy. The same author, in association with Herr Bernhard
Dessau, has likewise written a more important work, Die Telegraphie ohne
Draht; and La Telegraphie sans fil et les ondes Électriques of MM. J.
Boulanger and G. Ferrié may also be consulted with advantage, as may La
Telegraphie sans fil of Signor Dominico Mazotto. Quite recently Mr A.
Story has given us in a little volume called The Story of Wireless
Telegraphy, a condensed but very precise recapitulation of all the attempts
which have been made to establish telegraphic communication without the
intermediary of a conducting wire. Mr Story has examined many
documents, has sometimes brought curious facts to light, and has studied
even the most recently adopted apparatus.
It may be interesting, by utilising the information supplied by these authors
and supplementing them when necessary by others, to trace the sources of

this modern discovery, to follow its developments, and thus to prove once
more how much a matter, most simple in appearance, demands extensive
and complex researches on the part of an author desirous of writing a
definitive work.

§2
The first, and not the least difficulty, is to clearly define the subject. The
words "wireless telegraphy," which at first seem to correspond to a simple
and perfectly clear idea, may in reality apply to two series of questions,
very different in the mind of a physicist, between which it is important to
distinguish. The transmission of signals demands three organs which all
appear indispensable: the transmitter, the receiver, and, between the two, an
intermediary establishing the communication. This intermediary is
generally the most costly part of the installation and the most difficult to set
up, while it is here that the sensible losses of energy at the expense of good
output occur. And yet our present ideas cause us to consider this
intermediary as more than ever impossible to suppress; since, if we are
definitely quit of the conception of action at a distance, it becomes
inconceivable to us that energy can be communicated from one point to
another without being carried by some intervening medium. But,
practically, the line will be suppressed if, instead of constructing it
artificially, we use to replace it one of the natural media which separate two
points on the earth. These natural media are divided into two very distinct
categories, and from this classification arise two series of questions to be
examined.
Between the two points in question there are, first, the material media such
as the air, the earth, and the water. For a long time we have used for
transmissions to a distance the elastic properties of the air, and more
recently the electric conductivity of the soil and of water, particularly that of
the sea.
Modern physics leads us on the other hand, as we have seen, to consider
that there exists throughout the whole of the universe another and more
subtle medium which penetrates everywhere, is endowed with elasticity in
vacuo, and retains its elasticity when it penetrates into a great number of

bodies, such as the air. This medium is the luminous ether which possesses,
as we cannot doubt, the property of being able to transmit energy, since it
itself brings to us by far the larger part of the energy which we possess on
earth and which we find in the movements of the atmosphere, or of
waterfalls, and in the coal mines proceeding from the decomposition of
carbon compounds under the influence of the solar energy. For a long time
also before the existence of the ether was known, the duty of transmitting
signals was entrusted to it. Thus through the ages a double evolution is
unfolded which has to be followed by the historian who is ambitious of
completeness.

§3
If such an historian were to examine from the beginning the first order of
questions, he might, no doubt, speak only briefly of the attempts earlier than
electric telegraphy. Without seeking to be paradoxical, he certainly ought to
mention the invention of the speaking-trumpet and other similar inventions
which for a long time have enabled mankind, by the ingenious use of the
elastic properties of the natural media, to communicate at greater distances
than they could have attained without the aid of art. After this in some sort
prehistoric period had been rapidly run through, he would have to follow
very closely the development of electric telegraphy. Almost from the outset,
and shortly after Ampère had made public the idea of constructing a
telegraph, and the day after Gauss and Weber set up between their houses in
Göttingen the first line really used, it was thought that the conducting
properties of the earth and water might be made of service.
The history of these trials is very long, and is closely mixed up with the
history of ordinary telegraphy; long chapters for some time past have been
devoted to it in telegraphic treatises. It was in 1838, however, that Professor
C.A. Steinheil of Munich expressed, for the first time, the clear idea of
suppressing the return wire and replacing it by a connection of the line wire
to the earth. He thus at one step covered half the way, the easiest, it is true,
which was to lead to the final goal, since he saved the use of one-half of the
line of wire. Steinheil, advised, perhaps, by Gauss, had, moreover, a very
exact conception of the part taken by the earth considered as a conducting

body. He seems to have well understood that, in certain conditions, the
resistance of such a conductor, though supposed to be unlimited, might be
independent of the distance apart of the electrodes which carry the current
and allow it to go forth. He likewise thought of using the railway lines to
transmit telegraphic signals.
Several scholars who from the first had turned their minds to telegraphy,
had analogous ideas. It was thus that S.F.B. Morse, superintendent of the
Government telegraphs in the United States, whose name is universally
known in connection with the very simple apparatus invented by him, made
experiments in the autumn of 1842 before a special commission in New
York and a numerous public audience, to show how surely and how easily
his apparatus worked. In the very midst of his experiments a very happy
idea occurred to him of replacing by the water of a canal, the length of
about a mile of wire which had been suddenly and accidentally destroyed.
This accident, which for a moment compromised the legitimate success the
celebrated engineer expected, thus suggested to him a fruitful idea which he
did not forget. He subsequently repeated attempts to thus utilise the earth
and water, and obtained some very remarkable results.
It is not possible to quote here all the researches undertaken with the same
purpose, to which are more particularly attached the names of S.W. Wilkins,
Wheatstone, and H. Highton, in England; of Bonetti in Italy, Gintl in
Austria, Bouchot and Donat in France; but there are some which cannot be
recalled without emotion.
On the 17th December 1870, a physicist who has left in the University of
Paris a lasting name, M. d'Almeida, at that time Professor at the Lycée
Henri IV. and later Inspector-General of Public Instruction, quitted Paris,
then besieged, in a balloon, and descended in the midst of the German lines.
He succeeded, after a perilous journey, in gaining Havre by way of
Bordeaux and Lyons; and after procuring the necessary apparatus in
England, he descended the Seine as far as Poissy, which he reached on the
14th January 1871. After his departure, two other scholars, MM. Desains
and Bourbouze, relieving each other day and night, waited at Paris, in a
wherry on the Seine, ready to receive the signal which they awaited with
patriotic anxiety. It was a question of working a process devised by the last-
named pair, in which the water of the river acted the part of the line wire.

On the 23rd January the communication at last seemed to be established,
but unfortunately, first the armistice and then the surrender of Paris
rendered useless the valuable result of this noble effort.
Special mention is also due to the experiments made by the Indian
Telegraph Office, under the direction of Mr Johnson and afterwards of Mr
W.F. Melhuish. They led, indeed, in 1889 to such satisfactory results that a
telegraph service, in which the line wire was replaced by the earth, worked
practically and regularly. Other attempts were also made during the latter
half of the nineteenth century to transmit signals through the sea. They
preceded the epoch when, thanks to numerous physicists, among whom
Lord Kelvin undoubtedly occupies a preponderating position, we succeeded
in sinking the first cable; but they were not abandoned, even after that date,
for they gave hopes of a much more economical solution of the problem.
Among the most interesting are remembered those that S.W. Wilkins carried
on for a long time between France and England. Like Cooke and
Wheatstone, he thought of using as a receiver an apparatus which in some
features resembles the present receiver of the submarine telegraph. Later,
George E. Dering, then James Bowman and Lindsay, made on the same
lines trials which are worthy of being remembered.
But it is only in our own days that Sir William H. Preece at last obtained for
the first time really practical results. Sir William himself effected and
caused to be executed by his associates—he is chief consulting engineer to
the General Post Office in England—researches conducted with much
method and based on precise theoretical considerations. He thus succeeded
in establishing very easy, clear, and regular communications between
various places; for example, across the Bristol Channel. The long series of
operations accomplished by so many seekers, with the object of substituting
a material and natural medium for the artificial lines of metal, thus met with
an undoubted success which was soon to be eclipsed by the widely-known
experiments directed into a different line by Marconi.
It is right to add that Sir William Preece had himself utilised induction
phenomena in his experiments, and had begun researches with the aid of
electric waves. Much is due to him for the welcome he gave to Marconi; it
is certainly thanks to the advice and the material support he found in Sir

William that the young scholar succeeded in effecting his sensational
experiments.

§4
The starting-point of the experiments based on the properties of the
luminous ether, and having for their object the transmission of signals, is
very remote; and it would be a very laborious task to hunt up all the work
accomplished in that direction, even if we were to confine ourselves to
those in which electrical reactions play a part. An electric reaction, an
electrostatic influence, or an electromagnetic phenomenon, is transmitted at
a distance through the air by the intermediary of the luminous ether. But
electric influence can hardly be used, as the distances it would allow us to
traverse would be much too restricted, and electrostatic actions are often
very erratic. The phenomena of induction, which are very regular and
insensible to the variations of the atmosphere, have, on the other hand, for a
long time appeared serviceable for telegraphic purposes.
We might find, in a certain number of the attempts just mentioned, a partial
employment of these phenomena. Lindsay, for instance, in his project of
communication across the sea, attributed to them a considerable rôle. These
phenomena even permitted a true telegraphy without intermediary wire
between the transmitter and the receiver, at very restricted distances, it is
true, but in peculiarly interesting conditions. It is, in fact, owing to them
that C. Brown, and later Edison and Gilliland, succeeded in establishing
communications with trains in motion.
Mr Willoughby S. Smith and Mr Charles A. Stevenson also undertook
experiments during the last twenty years, in which they used induction, but
the most remarkable attempts are perhaps those of Professor Emile
Rathenau. With the assistance of Professor Rubens and of Herr W.
Rathenau, this physicist effected, at the request of the German Ministry of
Marine, a series of researches which enabled him, by means of a compound
system of conduction and induction by alternating currents, to obtain clear
and regular communications at a distance of four kilometres. Among the
precursors also should be mentioned Graham Bell; the inventor of the
telephone thought of employing his admirable apparatus as a receiver of

induction phenomena transmitted from a distance; Edison, Herr Sacher of
Vienna, M. Henry Dufour of Lausanne, and Professor Trowbridge of
Boston, also made interesting attempts in the same direction.
In all these experiments occurs the idea of employing an oscillating current.
Moreover, it was known for a long time—since, in 1842, the great
American physicist Henry proved that the discharges from a Leyden jar in
the attic of his house caused sparks in a metallic circuit on the ground floor
—that a flux which varies rapidly and periodically is much more efficacious
than a simple flux, which latter can only produce at a distance a
phenomenon of slight intensity. This idea of the oscillating current was
closely akin to that which was at last to lead to an entirely satisfactory
solution: that is, to a solution which is founded on the properties of electric
waves.

§5
Having thus got to the threshold of the definitive edifice, the historian, who
has conducted his readers over the two parallel routes which have just been
marked out, will be brought to ask himself whether he has been a
sufficiently faithful guide and has not omitted to draw attention to all
essential points in the regions passed through.
Ought we not to place by the side, or perhaps in front, of the authors who
have devised the practical appliances, those scholars who have constructed
the theories and realised the laboratory experiments of which, after all, the
apparatus are only the immediate applications? If we speak of the
propagation of a current in a material medium, can one forget the names of
Fourier and of Ohm, who established by theoretical considerations the laws
which preside over this propagation? When one looks at the phenomena of
induction, would it not be just to remember that Arago foresaw them, and
that Michael Faraday discovered them? It would be a delicate, and also a
rather puerile task, to class men of genius in order of merit. The merit of an
inventor like Edison and that of a theorist like Clerk Maxwell have no
common measure, and mankind is indebted for its great progress to the one
as much as to the other.

Before relating how success attended the efforts to utilise electric waves for
the transmission of signals, we cannot without ingratitude pass over in
silence the theoretical speculations and the work of pure science which led
to the knowledge of these waves. It would therefore be just, without going
further back than Faraday, to say how that illustrious physicist drew
attention to the part taken by insulating media in electrical phenomena, and
to insist also on the admirable memoirs in which for the first time Clerk
Maxwell made a solid bridge between those two great chapters of Physics,
optics and electricity, which till then had been independent of each other.
And no doubt it would be impossible not to evoke the memory of those
who, by establishing, on the other hand, the solid and magnificent structure
of physical optics, and proving by their immortal works the undulatory
nature of light, prepared from the opposite direction the future unity. In the
history of the applications of electrical undulations, the names of Young,
Fresnel, Fizeau, and Foucault must be inscribed; without these scholars, the
assimilation between electrical and luminous phenomena which they
discovered and studied would evidently have been impossible.
Since there is an absolute identity of nature between the electric and the
luminous waves, we should, in all justice, also consider as precursors those
who devised the first luminous telegraphs. Claude Chappe incontestably
effected wireless telegraphy, thanks to the luminous ether, and the learned
men, such as Colonel Mangin, who perfected optical telegraphy, indirectly
suggested certain improvements lately introduced into the present method.
But the physicist whose work should most of all be put in evidence is,
without fear of contradiction, Heinrich Hertz. It was he who demonstrated
irrefutably, by experiments now classic, that an electric discharge produces
an undulatory disturbance in the ether contained in the insulating media in
its neighbourhood; it was he who, as a profound theorist, a clever
mathematician, and an experimenter of prodigious dexterity, made known
the mechanism of the production, and fully elucidated that of the
propagation of these electromagnetic waves.
He must naturally himself have thought that his discoveries might be
applied to the transmission of signals. It would appear, however, that when
interrogated by a Munich engineer named Huber as to the possibility of
utilising the waves for transmissions by telephone, he answered in the

negative, and dwelt on certain considerations relative to the difference
between the periods of sounds and those of electrical vibrations. This
answer does not allow us to judge what might have happened, had not a
cruel death carried off in 1894, at the age of thirty-five, the great and
unfortunate physicist.
We might also find in certain works earlier than the experiments of Hertz
attempts at transmission in which, unconsciously no doubt, phenomena
were already set in operation which would, at this day, be classed as electric
oscillations. It is allowable no doubt, not to speak of an American quack,
Mahlon Loomis, who, according to Mr Story, patented in 1870 a project of
communication in which he utilised the Rocky Mountains on one side and
Mont Blanc on the other, as gigantic antennae to establish communication
across the Atlantic; but we cannot pass over in silence the very remarkable
researches of the American Professor Dolbear, who showed, at the electrical
exhibition of Philadelphia in 1884, a set of apparatus enabling signals to be
transmitted at a distance, which he described as "an exceptional application
of the principles of electrostatic induction." This apparatus comprised
groups of coils and condensers by means of which he obtained, as we
cannot now doubt, effects due to true electric waves.
Place should also be made for a well-known inventor, D.E. Hughes, who
from 1879 to 1886 followed up some very curious experiments in which
also these oscillations certainly played a considerable part. It was this
physicist who invented the microphone, and thus, in another way, drew
attention to the variations of contact resistance, a phenomenon not far from
that produced in the radio-conductors of Branly, which are important organs
in the Marconi system. Unfortunately, fatigued and in ill-health, Hughes
ceased his researches at the moment perhaps when they would have given
him final results.
In an order of ideas different in appearance, but closely linked at bottom
with the one just mentioned, must be recalled the discovery of radiophony
in 1880 by Graham Bell, which was foreshadowed in 1875 by C.A. Brown.
A luminous ray falling on a selenium cell produces a variation of electric
resistance, thanks to which a sound signal can be transmitted by light. That
delicate instrument the radiophone, constructed on this principle, has wide
analogies with the apparatus of to-day.

§6
Starting from the experiments of Hertz, the history of wireless telegraphy
almost merges into that of the researches on electrical waves. All the
progress realised in the manner of producing and receiving these waves
necessarily helped to give rise to the application already indicated. The
experiments of Hertz, after being checked in every laboratory, and having
entered into the strong domain of our most certain knowledge, were about
to yield the expected fruit.
Experimenters like Sir Oliver Lodge in England, Righi in Italy, Sarrazin and
de la Rive in Switzerland, Blondlot in France, Lecher in Germany, Bose in
India, Lebedeff in Russia, and theorists like M.H. Poincaré and Professor
Bjerknes, who devised ingenious arrangements or elucidated certain points
left dark, are among the artisans of the work which followed its natural
evolution.
It was Professor R. Threlfall who seems to have been the first to clearly
propose, in 1890, the application of the Hertzian waves to telegraphy, but it
was certainly Sir W. Crookes who, in a very remarkable article in the
Fortnightly Review of February 1892, pointed out very clearly the road to
be followed. He even showed in what conditions the Morse receiver might
be applied to the new system of telegraphy.
About the same period an American physicist, well known by his celebrated
experiments on high frequency currents—experiments, too, which are not
unconnected with those on electric oscillations,—M. Tesla, demonstrated
that these oscillations could be transmitted to more considerable distances
by making use of two vertical antennae, terminated by large conductors.
A little later, Sir Oliver Lodge succeeded, by the aid of the coherer, in
detecting waves at relatively long distances, and Mr Rutherford obtained
similar results with a magnetic indicator of his own invention.
An important question of meteorology, the study of atmospheric discharges,
at this date led a few scholars, and more particularly the Russian, M.
Popoff, to set up apparatus very analogous to the receiving apparatus of the
present wireless telegraphy. This comprised a long antenna and filings-tube,

and M. Popoff even pointed out that his apparatus might well serve for the
transmission of signals as soon as a generator of waves powerful enough
had been discovered.
Finally, on the 2nd June 1896, a young Italian, born in Bologna on the 25th
April 1874, Guglielmo Marconi, patented a system of wireless telegraphy
destined to become rapidly popular. Brought up in the laboratory of
Professor Righi, one of the physicists who had done most to confirm and
extend the experiments of Hertz, Marconi had long been familiar with the
properties of electric waves, and was well used to their manipulation. He
afterwards had the good fortune to meet Sir William (then Mr) Preece, who
was to him an adviser of the highest authority.
It has sometimes been said that the Marconi system contains nothing
original; that the apparatus for producing the waves was the oscillator of
Righi, that the receiver was that employed for some two or three years by
Professor Lodge and Mr Bose, and was founded on an earlier discovery by
a French scholar, M. Branly; and, finally, that the general arrangement was
that established by M. Popoff.
The persons who thus rather summarily judge the work of M. Marconi
show a severity approaching injustice. It cannot, in truth, be denied that the
young scholar has brought a strictly personal contribution to the solution of
the problem he proposed to himself. Apart from his forerunners, and when
their attempts were almost unknown, he had the very great merit of adroitly
arranging the most favourable combination, and he was the first to succeed
in obtaining practical results, while he showed that the electric waves could
be transmitted and received at distances enormous compared to those
attained before his day. Alluding to a well-known anecdote relating to
Christopher Columbus, Sir W. Preece very justly said: "The forerunners and
rivals of Marconi no doubt knew of the eggs, but he it was who taught them
to make them stand on end." This judgment will, without any doubt, be the
one that history will definitely pronounce on the Italian scholar.

§7

The apparatus which enables the electric waves to be revealed, the detector
or indicator, is the most delicate organ in wireless telegraphy. It is not
necessary to employ as an indicator a filings-tube or radio-conductor. One
can, in principle, for the purpose of constructing a receiver, think of any one
of the multiple effects produced by the Hertzian waves. In many systems in
use, and in the new one of Marconi himself, the use of these tubes has been
abandoned and replaced by magnetic detectors.
Nevertheless, the first and the still most frequent successes are due to radio-
conductors, and public opinion has not erred in attributing to the inventor of
this ingenious apparatus a considerable and almost preponderant part in the
invention of wave telegraphy.
The history of the discovery of radio-conductors is short, but it deserves,
from its importance, a chapter to itself in the history of wireless telegraphy.
From a theoretical point of view, the phenomena produced in those tubes
should be set by the side of those studied by Graham Bell, C.A. Brown, and
Summer Tainter, from the year 1878 onward. The variations to which
luminous waves give rise in the resistance of selenium and other substances
are, doubtless, not unconnected with those which the electric waves
produce in filings. A connection can also be established between this effect
of the waves and the variations of contact resistance which enabled Hughes
to construct the microphone, that admirable instrument which is one of the
essential organs of telephony.
More directly, as an antecedent to the discovery, should be quoted the
remark made by Varley in 1870, that coal-dust changes in conductivity
when the electromotive force of the current which passes through it is made
to vary. But it was in 1884 that an Italian professor, Signor Calzecchi-
Onesti, demonstrated in a series of remarkable experiments that the metallic
filings contained in a tube of insulating material, into which two metallic
electrodes are inserted, acquire a notable conductivity under different
influences such as extra currents, induced currents, sonorous vibrations,
etc., and that this conductivity is easily destroyed; as, for instance, by
turning the tube over and over.
In several memoirs published in 1890 and 1891, M. Ed. Branly
independently pointed out similar phenomena, and made a much more

complete and systematic study of the question. He was the first to note very
clearly that the action described could be obtained by simply making sparks
pass in the neighbourhood of the radio-conductor, and that their great
resistance could be restored to the filings by giving a slight shake to the
tube or to its supports.
The idea of utilising such a very interesting phenomenon as an indicator in
the study of the Hertzian waves seems to have occurred simultaneously to
several physicists, among whom should be especially mentioned M. Ed.
Branly himself, Sir Oliver Lodge, and MM. Le Royer and Van Beschem,
and its use in laboratories rapidly became quite common.
The action of the waves on metallic powders has, however, remained some
what mysterious; for ten years it has been the subject of important
researches by Professor Lodge, M. Branly, and a very great number of the
most distinguished physicists. It is impossible to notice here all these
researches, but from a recent and very interesting work of M. Blanc, it
would seem that the phenomenon is allied to that of ionisation.

§8
The history of wireless telegraphy does not end with the first experiments
of Marconi; but from the moment their success was announced in the public
press, the question left the domain of pure science to enter into that of
commerce. The historian's task here becomes different, but even more
delicate; and he will encounter difficulties which can be only known to one
about to write the history of a commercial invention.
The actual improvements effected in the system are kept secret by the rival
companies, and the most important results are patriotically left in darkness
by the learned officers who operate discreetly in view of the national
defence. Meanwhile, men of business desirous of bringing out a company
proclaim, with great nourish of advertisements, that they are about to
exploit a process superior to all others.
On this slippery ground the impartial historian must nevertheless venture;
and he may not refuse to relate the progress accomplished, which is
considerable. Therefore, after having described the experiments carried out

for nearly ten years by Marconi himself, first across the Bristol Channel,
then at Spezzia, between the coast and the ironclad San Bartolommeo, and
finally by means of gigantic apparatus between America and England, he
must give the names of those who, in the different civilised countries, have
contributed to the improvement of the system of communication by waves;
while he must describe what precious services this system has already
rendered to the art of war, and happily also to peaceful navigation.
From the point of view of the theory of the phenomena, very remarkable
results have been obtained by various physicists, among whom should be
particularly mentioned M. Tissot, whose brilliant studies have thrown a
bright light on different interesting points, such as the rôle of the antennae.
It would be equally impossible to pass over in silence other recent attempts
in a slightly different groove. Marconi's system, however improved it may
be to-day, has one grave defect. The synchronism of the two pieces of
apparatus, the transmitter and the receiver, is not perfect, so that a message
sent off by one station may be captured by some other station. The fact that
the phenomena of resonance are not utilised, further prevents the quantity
of energy received by the receiver from being considerable, and hence the
effects reaped are very weak, so that the system remains somewhat fitful
and the communications are often disturbed by atmospheric phenomena.
Causes which render the air a momentary conductor, such as electrical
discharges, ionisation, etc., moreover naturally prevent the waves from
passing, the ether thus losing its elasticity.
Professor Ferdinand Braun of Strasburg has conceived the idea of
employing a mixed system, in which the earth and the water, which, as we
have seen, have often been utilised to conduct a current for transmitting a
signal, will serve as a sort of guide to the waves themselves. The now well-
known theory of the propagation of waves guided by a conductor enables it
to be foreseen that, according to their periods, these waves will penetrate
more or less deeply into the natural medium, from which fact has been
devised a method of separating them according to their frequency. By
applying this theory, M. Braun has carried out, first in the fortifications of
Strasburg, and then between the island of Heligoland and the mainland,
experiments which have given remarkable results. We might mention also
the researches, in a somewhat analogous order of ideas, by an English

engineer, Mr Armstrong, by Dr Lee de Forest, and also by Professor
Fessenden.
Having thus arrived at the end of this long journey, which has taken him
from the first attempts down to the most recent experiments, the historian
can yet set up no other claim but that of having written the commencement
of a history which others must continue in the future. Progress does not
stop, and it is never permissible to say that an invention has reached its final
form.
Should the historian desire to give a conclusion to his labour and answer the
question the reader would doubtless not fail to put to him, "To whom, in
short, should the invention of wireless telegraphy more particularly be
attributed?" he should certainly first give the name of Hertz, the genius who
discovered the waves, then that of Marconi, who was the first to transmit
signals by the use of Hertzian undulations, and should add those of the
scholars who, like Morse, Popoff, Sir W. Preece, Lodge, and, above all,
Branly, have devised the arrangements necessary for their transmission. But
he might then recall what Voltaire wrote in the Philosophical Dictionary:
"What! We wish to know what was the exact theology of Thot, of Zerdust,
of Sanchuniathon, of the first Brahmins, and we are ignorant of the inventor
of the shuttle! The first weaver, the first mason, the first smith, were no
doubt great geniuses, but they were disregarded. Why? Because none of
them invented a perfected art. The one who hollowed out an oak to cross a
river never made a galley; those who piled up rough stones with girders of
wood did not plan the Pyramids. Everything is made by degrees and the
glory belongs to no one."
To-day, more than ever, the words of Voltaire are true: science becomes
more and more impersonal, and she teaches us that progress is nearly
always due to the united efforts of a crowd of workers, and is thus the best
school of social solidarity.

CHAPTER VIII

THE CONDUCTIVITY OF GASES AND THE
IONS
§ 1. THE CONDUCTIVITY OF GASES
If we were confined to the facts I have set forth above, we might conclude
that two classes of phenomena are to-day being interpreted with increasing
correctness in spite of the few difficulties which have been pointed out. The
hypothesis of the molecular constitution of matter enables us to group
together one of these classes, and the hypothesis of the ether leads us to co-
ordinate the other.
But these two classes of phenomena cannot be considered independent of
each other. Relations evidently exist between matter and the ether, which
manifest themselves in many cases accessible to experiment, and the search
for these relations appears to be the paramount problem the physicist should
set himself. The question has, for a long time, been attacked on various
sides, but the recent discoveries in the conductivity of gases, of the
radioactive substances, and of the cathode and similar rays, have allowed us
of late years to regard it in a new light. Without wishing to set out here in
detail facts which for the most part are well known, we will endeavour to
group the chief of them round a few essential ideas, and will seek to state
precisely the data they afford us for the solution of this grave problem.
It was the study of the conductivity of gases which at the very first
furnished the most important information, and allowed us to penetrate more
deeply than had till then been possible into the inmost constitution of
matter, and thus to, as it were, catch in the act the actions that matter can
exercise on the ether, or, reciprocally, those it may receive from it.
It might, perhaps, have been foreseen that such a study would prove
remarkably fruitful. The examination of the phenomena of electrolysis had,
in fact, led to results of the highest importance on the constitution of
liquids, and the gaseous media which presented themselves as particularly

simple in all their properties ought, it would seem, to have supplied from
the very first a field of investigation easy to work and highly productive.
This, however, was not at all the case. Experimental complications
springing up at every step obscured the problem. One generally found one's
self in the presence of violent disruptive discharges with a train of accessory
phenomena, due, for instance, to the use of metallic electrodes, and made
evident by the complex appearance of aigrettes and effluves; or else one had
to deal with heated gases difficult to handle, which were confined in
receptacles whose walls played a troublesome part and succeeded in veiling
the simplicity of the fundamental facts. Notwithstanding, therefore, the
efforts of a great number of seekers, no general idea disengaged itself out of
a mass of often contradictory information.
Many physicists, in France particularly, discarded the study of questions
which seemed so confused, and it must even be frankly acknowledged that
some among them had a really unfounded distrust of certain results which
should have been considered proved, but which had the misfortune to be in
contradiction with the theories in current use. All the classic ideas relating
to electrical phenomena led to the consideration that there existed a perfect
symmetry between the two electricities, positive and negative. In the
passing of electricity through gases there is manifested, on the contrary, an
evident dissymmetry. The anode and the cathode are immediately
distinguished in a tube of rarefied gas by their peculiar appearance; and the
conductivity does not appear, under certain conditions, to be the same for
the two modes of electrification.
It is not devoid of interest to note that Erman, a German scholar, once very
celebrated and now generally forgotten, drew attention as early as 1815 to
the unipolar conductivity of a flame. His contemporaries, as may be
gathered from the perusal of the treatises on physics of that period, attached
great importance to this discovery; but, as it was somewhat inconvenient
and did not readily fit in with ordinary studies, it was in due course
neglected, then considered as insufficiently established, and finally wholly
forgotten.
All these somewhat obscure facts, and some others—such as the different
action of ultra-violet radiations on positively and negatively charged bodies

—are now, on the contrary, about to be co-ordinated, thanks to the modern
ideas on the mechanism of conduction; while these ideas will also allow us
to interpret the most striking dissymmetry of all, i.e. that revealed by
electrolysis itself, a dissymmetry which certainly can not be denied, but to
which sufficient attention has not been given.
It is to a German physicist, Giese, that we owe the first notions on the
mechanism of the conductivity of gases, as we now conceive it. In two
memoirs published in 1882 and 1889, he plainly arrives at the conception
that conduction in gases is not due to their molecules, but to certain
fragments of them or to ions. Giese was a forerunner, but his ideas could
not triumph so long as there were no means of observing conduction in
simple circumstances. But this means has now been supplied in the
discovery of the X rays. Suppose we pass through some gas at ordinary
pressure, such as hydrogen, a pencil of X rays. The gas, which till then has
behaved as a perfect insulator,[29] suddenly acquires a remarkable
conductivity. If into this hydrogen two metallic electrodes in
communication with the two poles of a battery are introduced, a current is
set up in very special conditions which remind us, when they are checked
by experiments, of the mechanism which allows the passage of electricity in
electrolysis, and which is so well represented to us when we picture to
ourselves this passage as due to the migration towards the electrodes, under
the action of the field, of the two sets of ions produced by the spontaneous
division of the molecule within the solution.
Let us therefore recognise with J.J. Thomson and the many physicists who,
in his wake, have taken up and developed the idea of Giese, that, under the
influence of the X rays, for reasons which will have to be determined later,
certain gaseous molecules have become divided into two portions, the one
positively and the other negatively electrified, which we will call, by
analogy with the kindred phenomenon in electrolysis, by the name of ions.
If the gas be then placed in an electric field, produced, for instance, by two
metallic plates connected with the two poles of a battery respectively, the
positive ions will travel towards the plate connected with the negative pole,
and the negative ions in the contrary direction. There is thus produced a
current due to the transport to the electrodes of the charges which existed on
the ions.

If the gas thus ionised be left to itself, in the absence of any electric field,
the ions, yielding to their mutual attraction, must finally meet, combine, and
reconstitute a neutral molecule, thus returning to their initial condition. The
gas in a short while loses the conductivity which it had acquired; or this is,
at least, the phenomenon at ordinary temperatures. But if the temperature is
raised, the relative speeds of the ions at the moment of impact may be great
enough to render it impossible for the recombination to be produced in its
entirety, and part of the conductivity will remain.
Every element of volume rendered a conductor therefore furnishes, in an
electric field, equal quantities of positive and negative electricity. If we
admit, as mentioned above, that these liberated quantities are borne by ions
each bearing an equal charge, the number of these ions will be proportional
to the quantity of electricity, and instead of speaking of a quantity of
electricity, we could use the equivalent term of number of ions. For the
excitement produced by a given pencil of X rays, the number of ions
liberated will be fixed. Thus, from a given volume of gas there can only be
extracted an equally determinate quantity of electricity.
The conductivity produced is not governed by Ohm's law. The intensity is
not proportional to the electromotive force, and it increases at first as the
electromotive force augments; but it approaches asymptotically to a
maximum value which corresponds to the number of ions liberated, and can
therefore serve as a measure of the power of the excitement. It is this
current which is termed the current of saturation.
M. Righi has ably demonstrated that ionised gas does not obey the law of
Ohm by an experiment very paradoxical in appearance. He found that, the
greater the distance of the two electrode plates from each, the greater may
be, within certain limits, the intensity of the current. The fact is very clearly
interpreted by the theory of ionisation, since the greater the length of the
gaseous column the greater must be the number of ions liberated.
One of the most striking characteristics of ionised gases is that of
discharging electrified conductors. This phenomenon is not produced by the
departure of the charge that these conductors may possess, but by the
advent of opposite charges brought to them by ions which obey the

electrostatic attraction and abandon their own electrification when they
come in contact with these conductors.
This mode of regarding the phenomena is extremely convenient and
eminently suggestive. It may, no doubt, be thought that the image of the
ions is not identical with objective reality, but we are compelled to
acknowledge that it represents with absolute faithfulness all the details of
the phenomena.
Other facts, moreover, will give to this hypothesis a still greater value; we
shall even be able, so to speak, to grasp these ions individually, to count
them, and to measure their charge.

§ 2. THE CONDENSATION OF WATER-VAPOUR BY IONS
If the pressure of a vapour—that of water, for instance—in the atmosphere
reaches the value of the maximum pressure corresponding to the
temperature of the experiment, the elementary theory teaches us that the
slightest decrease in temperature will induce a condensation; that small
drops will form, and the mist will turn into rain.
In reality, matters do not occur in so simple a manner. A more or less
considerable delay may take place, and the vapour will remain
supersaturated. We easily discover that this phenomenon is due to the
intervention of capillary action. On a drop of liquid a surface-tension takes
effect which gives rise to a pressure which becomes greater the smaller the
diameter of the drop.
Pressure facilitates evaporation, and on more closely examining this
reaction we arrive at the conclusion that vapour can never spontaneously
condense itself when liquid drops already formed are not present, unless
forces of another nature intervene to diminish the effect of the capillary
forces. In the most frequent cases, these forces come from the dust which is
always in suspension in the air, or which exists in any recipient. Grains of
dust act by reason of their hygrometrical power, and form germs round
which drops presently form. It is possible to make use, as did M. Coulier as
early as 1875, of this phenomenon to carry off the germs of condensation,
by producing by expansion in a bottle containing a little water a preliminary

mist which purifies the air. In subsequent experiments it will be found
almost impossible to produce further condensation of vapour.
But these forces may also be of electrical origin. Von Helmholtz long since
showed that electricity exercises an influence on the condensation of the
vapour of water, and Mr C.T.R. Wilson, with this view, has made truly
quantitative experiments. It was rapidly discovered after the apparition of
the X rays that gases that have become conductors, that is, ionised gases,
also facilitate the condensation of supersaturated water vapour.
We are thus led by a new road to the belief that electrified centres exist in
gases, and that each centre draws to itself the neighbouring molecules of
water, as an electrified rod of resin does the light bodies around it. There is
produced in this manner round each ion an assemblage of molecules of
water which constitute a germ capable of causing the formation of a drop of
water out of the condensation of excess vapour in the ambient air. As might
be expected, the drops are electrified, and take to themselves the charge of
the centres round which they are formed; moreover, as many drops are
created as there are ions. Thereafter we have only to count these drops to
ascertain the number of ions which existed in the gaseous mass.
To effect this counting, several methods have been used, differing in
principle but leading to similar results. It is possible, as Mr C.T.R. Wilson
and Professor J.J. Thomson have done, to estimate, on the one hand, the
weight of the mist which is produced in determined conditions, and on the
other, the average weight of the drops, according to the formula formerly
given by Sir G. Stokes, by deducting their diameter from the speed with
which this mist falls; or we can, with Professor Lemme, determine the
average radius of the drops by an optical process, viz. by measuring the
diameter of the first diffraction ring produced when looking through the
mist at a point of light.
We thus get to a very high number. There are, for instance, some twenty
million ions per centimetre cube when the rays have produced their
maximum effect, but high as this figure is, it is still very small compared
with the total number of molecules. All conclusions drawn from kinetic
theory lead us to think that in the same space there must exist, by the side of

a molecule divided into two ions, a thousand millions remaining in a neutral
state and intact.
Mr C.T.R. Wilson has remarked that the positive and negative ions do not
produce condensation with the same facility. The ions of a contrary sign
may be almost completely separated by placing the ionised gas in a suitably
disposed field. In the neighbourhood of a negative disk there remain hardly
any but positive ions, and against a positive disk none but negative; and in
effecting a separation of this kind, it will be noticed that condensation by
negative ions is easier than by the positive.
It is, consequently, possible to cause condensation on negative centres only,
and to study separately the phenomena produced by the two kinds of ions. It
can thus be verified that they really bear charges equal in absolute value,
and these charges can even be estimated, since we already know the number
of drops. This estimate can be made, for example, by comparing the speed
of the fall of a mist in fields of different values, or, as did J.J. Thomson, by
measuring the total quantity of electricity liberated throughout the gas.
At the degree of approximation which such experiments imply, we find that
the charge of a drop, and consequently the charge borne by an ion, is
sensibly 3.4 x 10-10 electrostatic or 1.1 x 10-20 electromagnetic units. This
charge is very near that which the study of the phenomena of ordinary
electrolysis leads us to attribute to a univalent atom produced by electrolytic
dissociation.
Such a coincidence is evidently very striking; but it will not be the only one,
for whatever phenomenon be studied it will always appear that the smallest
charge we can conceive as isolated is that mentioned. We are, in fact, in
presence of a natural unit, or, if you will, of an atom of electricity.
We must, however, guard against the belief that the gaseous ion is identical
with the electrolytic ion. Sensible differences between those are
immediately apparent, and still greater ones will be discovered on closer
examination.
As M. Perrin has shown, the ionisation produced by the X-rays in no way
depends on the chemical composition of the gas; and whether we take a
volume of gaseous hydrochloric acid or a mixture of hydrogen and chlorine

in the same condition, all the results will be identical: and chemical
affinities play no part here.
We can also obtain other information regarding ions: we can ascertain, for
instance, their velocities, and also get an idea of their order of magnitude.
By treating the speeds possessed by the liberated charges as components of
the known speed of a gaseous current, Mr Zeleny measures the mobilities,
that is to say, the speeds acquired by the positive and negative charges in a
field equal to the electrostatic unit. He has thus found that these mobilities
are different, and that they vary, for example, between 400 and 200
centimetres per second for the two charges in dry gases, the positive being
less mobile than the negative ions, which suggests the idea that they are of
greater mass.[30]
M. Langevin, who has made himself the eloquent apostle of the new
doctrines in France, and has done much to make them understood and
admitted, has personally undertaken experiments analogous to those of M.
Zeleny, but much more complete. He has studied in a very ingenious
manner, not only the mobilities, but also the law of recombination which
regulates the spontaneous return of the gas to its normal state. He has
determined experimentally the relation of the number of recombinations to
the number of collisions between two ions of contrary sign, by studying the
variation produced by a change in the value of the field, in the quantity of
electricity which can be collected in the gas separating two parallel metallic
plates, after the passage through it for a very short time of the Röntgen rays
emitted during one discharge of a Crookes tube. If the image of the ions is
indeed conformable to reality, this relation must evidently always be
smaller than unity, and must tend towards this value when the mobility of
the ions diminishes, that is to say, when the pressure of the gas increases.
The results obtained are in perfect accord with this anticipation.
On the other hand, M. Langevin has succeeded, by following the
displacement of the ions between the parallel plates after the ionisation
produced by the radiation, in determining the absolute values of the
mobilities with great precision, and has thus clearly placed in evidence the
irregularity of the mobilities of the positive and negative ions respectively.
Their mass can be calculated when we know, through experiments of this

kind, the speed of the ions in a given field, and on the other hand—as we
can now estimate their electric charge—the force which moves them. They
evidently progress more slowly the larger they are; and in the viscous
medium constituted by the gas, the displacement is effected at a speed
sensibly proportional to the motive power.
At the ordinary temperature these masses are relatively considerable, and
are greater for the positive than for the negative ions, that is to say, they are
about the order of some ten molecules. The ions, therefore, seem to be
formed by an agglomeration of neutral molecules maintained round an
electrified centre by electrostatic attraction. If the temperature rises, the
thermal agitation will become great enough to prevent the molecules from
remaining linked to the centre. By measurements effected on the gases of
flames, we arrive at very different values of the masses from those found
for ordinary ions, and above all, very different ones for ions of contrary
sign. The negative ions have much more considerable velocities than the
positive ones. The latter also seem to be of the same size as atoms; and the
first-named must, consequently, be considered as very much smaller, and
probably about a thousand times less.
Thus, for the first time in science, the idea appears that the atom is not the
smallest fraction of matter to be considered. Fragments a thousand times
smaller may exist which possess, however, a negative charge. These are the
electrons, which other considerations will again bring to our notice.

§ 3. HOW IONS ARE PRODUCED
It is very seldom that a gaseous mass does not contain a few ions. They may
have been formed from many causes, for although to give precision to our
studies, and to deal with a well ascertained case, I mentioned only
ionisation by the X rays in the first instance, I ought not to give the
impression that the phenomenon is confined to these rays. It is, on the
contrary, very general, and ionisation is just as well produced by the
cathode rays, by the radiations emitted by radio-active bodies, by the ultra-
violet rays, by heating to a high temperature, by certain chemical actions,
and finally by the impact of the ions already existing in neutral molecules.

Of late years these new questions have been the object of a multitude of
researches, and if it has not always been possible to avoid some confusion,
yet certain general conclusions may be drawn. The ionisation by flames, in
particular, is fairly well known. For it to be produced spontaneously, it
would appear that there must exist simultaneously a rather high temperature
and a chemical action in the gas. According to M. Moreau, the ionisation is
very marked when the flame contains the vapour of the salt of an alkali or
of an alkaline earth, but much less so when it contains that of other salts.
Arrhenius, Mr C.T.R. Wilson, and M. Moreau, have studied all the
circumstances of the phenomenon; and it seems indeed that there is a
somewhat close analogy between what first occurs in the saline vapours and
that which is noted in liquid electrolytes. There should be produced, as soon
as a certain temperature is reached, a dissociation of the saline molecule;
and, as M. Moreau has shown in a series of very well conducted researches,
the ions formed at about 100°C. seem constituted by an electrified centre of
the size of a gas molecule, surrounded by some ten layers of other
molecules. We are thus dealing with rather large ions, but according to Mr
Wilson, this condensation phenomenon does not affect the number of ions
produced by dissociation. In proportion as the temperature rises, the
molecules condensed round the nucleus disappear, and, as in all other
circumstances, the negative ion tends to become an electron, while the
positive ion continues the size of an atom.
In other cases, ions are found still larger than those of saline vapours, as, for
example, those produced by phosphorus. It has long been known that air in
the neighbourhood of phosphorus becomes a conductor, and the fact,
pointed out as far back as 1885 by Matteucci, has been well studied by
various experimenters, by MM. Elster and Geitel in 1890, for instance. On
the other hand, in 1893 Mr Barus established that the approach of a stick of
phosphorus brings about the condensation of water vapour, and we really
have before us, therefore, in this instance, an ionisation. M. Bloch has
succeeded in disentangling the phenomena, which are here very complex,
and in showing that the ions produced are of considerable dimensions; for
their speed in the same conditions is on the average a thousand times less
than that of ions due to the X rays. M. Bloch has established also that the
conductivity of recently-prepared gases, already studied by several authors,
was analogous to that which is produced by phosphorus, and that it is

intimately connected with the presence of the very tenuous solid or liquid
dust which these gases carry with them, while the ions are of the same order
of magnitude. These large ions exist, moreover, in small quantities in the
atmosphere; and M. Langevin lately succeeded in revealing their presence.
It may happen, and this not without singularly complicating matters, that
the ions which were in the midst of material molecules produce, as the
result of collisions, new divisions in these last. Other ions are thus born, and
this production is in part compensated for by recombinations between ions
of opposite signs. The impacts will be more active in the event of the gas
being placed in a field of force and of the pressure being slight, the speed
attained being then greater and allowing the active force to reach a high
value. The energy necessary for the production of an ion is, in fact,
according to Professor Rutherford and Professor Stark, something
considerable, and it much exceeds the analogous force in electrolytic
decomposition.
It is therefore in tubes of rarefied gas that this ionisation by impact will be
particularly felt. This gives us the reason for the aspect presented by
Geissler tubes. Generally, in the case of discharges, new ions produced by
the molecules struck come to add themselves to the electrons produced, as
will be seen, by the cathode. A full discussion has led to the interpretation
of all the known facts, and to our understanding, for instance, why there
exist bright or dark spaces in certain regions of the tube. M. Pellat, in
particular, has given some very fine examples of this concordance between
the theory and the facts he has skilfully observed.
In all the circumstances, then, in which ions appear, their formation has
doubtless been provoked by a mechanism analogous to that of the shock.
The X rays, if they are attributable to sudden variations in the ether—that is
to say, a variation of the two vectors of Hertz—themselves produce within
the atom a kind of electric impulse which breaks it into two electrified
fragments; i.e. the positive centre, the size of the molecule itself, and the
negative centre, constituted by an electron a thousand times smaller. Round
these two centres, at the ordinary temperature, are agglomerated by
attraction other molecules, and in this manner the ions whose properties
have just been studied are formed.

§ 4. ELECTRONS IN METALS
The success of the ionic hypothesis as an interpretation of the conductivity
of electrolytes and gases has suggested the desire to try if a similar
hypothesis can represent the ordinary conductivity of metals. We are thus
led to conceptions which at first sight seem audacious because they are
contrary to our habits of mind. They must not, however, be rejected on that
account. Electrolytic dissociation at first certainly appeared at least as
strange; yet it has ended by forcing itself upon us, and we could, at the
present day, hardly dispense with the image it presents to us.
The idea that the conductivity of metals is not essentially different from that
of electrolytic liquids or gases, in the sense that the passage of the current is
connected with the transport of small electrified particles, is already of old
date. It was enunciated by W. Weber, and afterwards developed by Giese,
but has only obtained its true scope through the effect of recent discoveries.
It was the researches of Riecke, later, of Drude, and, above all, those of J.J.
Thomson, which have allowed it to assume an acceptable form. All these
attempts are connected however with the general theory of Lorentz, which
we will examine later.
It will be admitted that metallic atoms can, like the saline molecule in a
solution, partially dissociate themselves. Electrons, very much smaller than
atoms, can move through the structure, considerable to them, which is
constituted by the atom from which they have just been detached. They may
be compared to the molecules of a gas which is enclosed in a porous body.
In ordinary conditions, notwithstanding the great speed with which they are
animated, they are unable to travel long distances, because they quickly find
their road barred by a material atom. They have to undergo innumerable
impacts, which throw them first in one direction and then in another. The
passage of a current is a sort of flow of these electrons in a determined
direction. This electric flow brings, however, no modification to the
material medium traversed, since every electron which disappears at any
point is replaced by another which appears at once, and in all metals the
electrons are identical.

This hypothesis leads us to anticipate certain facts which experience
confirms. Thus J.J. Thomson shows that if, in certain conditions, a
conductor is placed in a magnetic field, the ions have to describe an
epicycloid, and their journey is thus lengthened, while the electric
resistance must increase. If the field is in the direction of the displacement,
they describe helices round the lines of force and the resistance is again
augmented, but in different proportions. Various experimenters have noted
phenomena of this kind in different substances.
For a long time it has been noticed that a relation exists between the
calorific and the electric conductivity; the relation of these two
conductivities is sensibly the same for all metals. The modern theory tends
to show simply that it must indeed be so. Calorific conductivity is due, in
fact, to an exchange of electrons between the hot and the cold regions, the
heated electrons having the greater velocity, and consequently the more
considerable energy. The calorific exchanges then obey laws similar to
those which govern electric exchanges; and calculation even leads to the
exact values which the measurements have given. [31]
In the same way Professor Hesehus has explained how contact
electrification is produced, by the tendency of bodies to equalise their
superficial properties by means of a transport of electrons, and Mr Jeans has
shown that we should discover the existence of the well-known laws of
distribution over conducting bodies in electrostatic equilibrium. A metal
can, in fact, be electrified, that is to say, may possess an excess of positive
or negative electrons which cannot easily leave it in ordinary conditions. To
cause them to do so would need an appreciable amount of work, on account
of the enormous difference of the specific inductive capacities of the metal
and of the insulating medium in which it is plunged.
Electrons, however, which, on arriving at the surface of the metal,
possessed a kinetic energy superior to this work, might be shot forth and
would be disengaged as a vapour escapes from a liquid. Now, the number of
these rapid electrons, at first very slight, increases, according to the kinetic
theory, when the temperature rises, and therefore we must reckon that a
wire, on being heated, gives out electrons, that is to say, loses negative
electricity and sends into the surrounding media electrified centres capable
of producing the phenomena of ionisation. Edison, in 1884, showed that

from the filament of an incandescent lamp there escaped negative electric
charges. Since then, Richardson and J.J. Thomson have examined
analogous phenomena. This emission is a very general phenomenon which,
no doubt, plays a considerable part in cosmic physics. Professor Arrhenius
explains, for instance, the polar auroras by the action of similar corpuscules
emitted by the sun.
In other phenomena we seem indeed to be confronted by an emission, not
of negative electrons, but of positive ions. Thus, when a wire is heated, not
in vacuo, but in a gas, this wire begins to electrify neighbouring bodies
positively. J.J. Thomson has measured the mass of these positive ions and
finds it considerable, i.e. about 150 times that of an atom of hydrogen.
Some are even larger, and constitute almost a real grain of dust. We here
doubtless meet with the phenomena of disaggregation undergone by metals
at a red heat.

CHAPTER IX

CATHODE RAYS AND RADIOACTIVE
BODIES
§ 1. THE CATHODE RAYS
A wire traversed by an electric current is, as has just been explained, the
seat of a movement of electrons. If we cut this wire, a flood of electrons,
like a current of water which, at the point where a pipe bursts, flows out in
abundance, will appear to spring out between the two ends of the break.
If the energy of the electrons is sufficient, these electrons will in fact rush
forth and be propagated in the air or in the insulating medium interposed;
but the phenomena of the discharge will in general be very complex. We
shall here only examine a particularly simple case, viz., that of the cathode
rays; and without entering into details, we shall only note the results
relating to these rays which furnish valuable arguments in favour of the
electronic hypothesis and supply solid materials for the construction of new
theories of electricity and matter.
For a long time it was noticed that the phenomena in a Geissler tube
changed their aspect considerably, when the gas pressure became very
weak, without, however, a complete vacuum being formed. From the
cathode there is shot forth normally and in a straight line a flood within the
tube, dark but capable of impressing a photographic plate, of developing the
fluorescence of various substances (particularly the glass walls of the tube),
and of producing calorific and mechanical effects. These are the cathode
rays, so named in 1883 by E. Wiedemann, and their name, which was
unknown to a great number of physicists till barely twelve years ago, has
become popular at the present day.
About 1869, Hittorf made an already very complete study of them and put
in evidence their principal properties; but it was the researches of Sir W.
Crookes in especial which drew attention to them. The celebrated physicist
foresaw that the phenomena which were thus produced in rarefied gases

were, in spite of their very great complication, more simple than those
presented by matter under the conditions in which it is generally met with.
He devised a celebrated theory no longer admissible in its entirety, because
it is not in complete accord with the facts, which was, however, very
interesting, and contained, in germ, certain of our present ideas. In the
opinion of Crookes, in a tube in which the gas has been rarefied we are in
presence of a special state of matter. The number of the gas molecules has
become small enough for their independence to be almost absolute, and
they are able in this so-called radiant state to traverse long spaces without
departing from a straight line. The cathode rays are due to a kind of
molecular bombardment of the walls of the tubes, and of the screens which
can be introduced into them; and it is the molecules, electrified by their
contact with the cathode and then forcibly repelled by electrostatic action,
which produce, by their movement and their vis viva, all the phenomena
observed. Moreover, these electrified molecules animated with extremely
rapid velocities correspond, according to the theory verified in the
celebrated experiment of Rowland on convection currents, to a true electric
current, and can be deviated by a magnet.
Notwithstanding the success of Crookes' experiments, many physicists—the
Germans especially—did not abandon an hypothesis entirely different from
that of radiant matter. They continued to regard the cathode radiation as due
to particular radiations of a nature still little known but produced in the
luminous ether. This interpretation seemed, indeed, in 1894, destined to
triumph definitely through the remarkable discovery of Lenard, a discovery
which, in its turn, was to provoke so many others and to bring about
consequences of which the importance seems every day more considerable.
Professor Lenard's fundamental idea was to study the cathode rays under
conditions different from those in which they are produced. These rays are
born in a very rarefied space, under conditions perfectly determined by Sir
W. Crookes; but it was a question whether, when once produced, they
would be capable of propagating themselves in other media, such as a gas at
ordinary pressure, or even in an absolute vacuum. Experiment alone could
answer this question, but there were difficulties in the way of this which
seemed almost insurmountable. The rays are stopped by glass even of slight
thickness, and how then could the almost vacuous space in which they have

to come into existence be separated from the space, absolutely vacuous or
filled with gas, into which it was desired to bring them?
The artifice used was suggested to Professor Lenard by an experiment of
Hertz. The great physicist had, in fact, shortly before his premature death,
taken up this important question of the cathode rays, and his genius left
there, as elsewhere, its powerful impress. He had shown that metallic plates
of very slight thickness were transparent to the cathode rays; and Professor
Lenard succeeded in obtaining plates impermeable to air, but which yet
allowed the pencil of cathode rays to pass through them.
Now if we take a Crookes tube with the extremity hermetically closed by a
metallic plate with a slit across the diameter of 1 mm. in width, and stop
this slit with a sheet of very thin aluminium, it will be immediately noticed
that the rays pass through the aluminium and pass outside the tube. They are
propagated in air at atmospheric pressure, and they can also penetrate into
an absolute vacuum. They therefore can no longer be attributed to radiant
matter, and we are led to think that the energy brought into play in this
phenomenon must have its seat in the light-bearing ether itself.
But it is a very strange light which is thus subject to magnetic action, which
does not obey the principle of equal angles, and for which the most various
gases are already disturbed media. According to Crookes it possesses also
the singular property of carrying with it electric charges.
This convection of negative electricity by the cathode rays seems quite
inexplicable on the hypothesis that the rays are ethereal radiations. Nothing
then remained in order to maintain this hypothesis, except to deny the
convection, which, besides, was only established by indirect experiments.
That the reality of this transport has been placed beyond dispute by means
of an extremely elegant experiment which is all the more convincing that it
is so very simple, is due to M. Perrin. In the interior of a Crookes tube he
collected a pencil of cathode rays in a metal cylinder. According to the
elementary principles of electricity the cylinder must become charged with
the whole charge, if there be one, brought to it by the rays, and naturally
various precautions had to be taken. But the result was very precise, and
doubt could no longer exist—the rays were electrified.

It might have been, and indeed was, maintained, some time after this
experiment was published, that while the phenomena were complex inside
the tube, outside, things might perhaps occur differently. Lenard himself,
however, with that absence of even involuntary prejudice common to all
great minds, undertook to demonstrate that the opinion he at first held could
no longer be accepted, and succeeded in repeating the experiment of M.
Perrin on cathode rays in the air and even in vacuo.
On the wrecks of the two contradictory hypotheses thus destroyed, and out
of the materials from which they had been built, a theory has been
constructed which co-ordinates all the known facts. This theory is
furthermore closely allied to the theory of ionisation, and, like this latter, is
based on the concept of the electron. Cathode rays are electrons in rapid
motion.
The phenomena produced both inside and outside a Crookes tube are,
however, generally complex. In Lenard's first experiments, and in many
others effected later when this region of physics was still very little known,
a few confusions may be noticed even at the present day.
At the spot where the cathode rays strike the walls of the tube the
essentially different X rays appear. These differ from the cathode radiations
by being neither electrified nor deviated by a magnet. In their turn these X
rays may give birth to the secondary rays of M. Sagnac; and often we find
ourselves in presence of effects from these last-named radiations and not
from the true cathode rays.
The electrons, when they are propagated in a gas, can ionise the molecules
of this gas and unite with the neutral atoms to form negative ions, while
positive ions also appear. There are likewise produced, at the expense of the
gas still subsisting after rarefication within the tube, positive ions which,
attracted by the cathode and reaching it, are not all neutralised by the
negative electrons, and can, if the cathode be perforated, pass through it,
and if not, pass round it. We have then what are called the canal rays of
Goldstein, which are deviated by an electric or magnetic field in a contrary
direction to the cathode rays; but, being larger, give weak deviations or may
even remain undeviated through losing their charge when passing through
the cathode.

It may also be the parts of the walls at a distance from the cathode which
send a positive rush to the latter, by a similar mechanism. It may be, again,
that in certain regions of the tube cathode rays are met with diffused by
some solid object, without having thereby changed their nature. All these
complexities have been cleared up by M. Villard, who has published, on
these questions, some remarkably ingenious and particularly careful
experiments.
M. Villard has also studied the phenomena of the coiling of the rays in a
field, as already pointed out by Hittorf and Plücker. When a magnetic field
acts on the cathode particle, the latter follows a trajectory, generally
helicoidal, which is anticipated by the theory. We here have to do with a
question of ballistics, and experiments duly confirm the anticipations of the
calculation. Nevertheless, rather singular phenomena appear in the case of
certain values of the field, and these phenomena, dimly seen by Plücker and
Birkeland, have been the object of experiments by M. Villard. The two
faces of the cathode seem to emit rays which are deviated in a direction
perpendicular to the lines of force by an electric field, and do not seem to be
electrified. M. Villard calls them magneto-cathode rays, and according to
M. Fortin these rays may be ordinary cathode rays, but of very slight
velocity.
In certain cases the cathode itself may be superficially disaggregated, and
extremely tenuous particles detach themselves, which, being carried off at
right angles to its surface, may deposit themselves like a very thin film on
objects placed in their path. Various physicists, among them M.
Houllevigue, have studied this phenomenon, and in the case of pressures
between 1/20 and 1/100 of a millimetre, the last-named scholar has
obtained mirrors of most metals, a phenomenon he designates by the name
of ionoplasty.
But in spite of all these accessory phenomena, which even sometimes
conceal those first observed, the existence of the electron in the cathodic
flux remains the essential characteristic.
The electron can be apprehended in the cathodic ray by the study of its
essential properties; and J.J. Thomson gave great value to the hypothesis by
his measurements. At first he meant to determine the speed of the cathode

rays by direct experiment, and by observing, in a revolving mirror, the
relative displacement of two bands due to the excitement of two fluorescent
screens placed at different distances from the cathode. But he soon
perceived that the effect of the fluorescence was not instantaneous, and that
the lapse of time might form a great source of error, and he then had
recourse to indirect methods. It is possible, by a simple calculation, to
estimate the deviations produced on the rays by a magnetic and an electric
field respectively as a function of the speed of propagation and of the
relation of the charge to the material mass of the electron. The measurement
of these deviations will then permit this speed and this relation to be
ascertained.
Other processes may be used which all give the same two quantities by two
suitably chosen measurements. Such are the radius of the curve taken by the
trajectory of the pencil in a perpendicular magnetic field and the measure of
the fall of potential under which the discharge takes place, or the measure of
the total quantity of electricity carried in one second and the measure of the
calorific energy which may be given, during the same period, to a thermo-
electric junction. The results agree as well as can be expected, having
regard to the difficulty of the experiments; the values of the speed agree
also with those which Professor Wiechert has obtained by direct
measurement.
The speed never depends on the nature of the gas contained in the Crookes
tube, but varies with the value of the fall of potential at the cathode. It is of
the order of one tenth of the speed of light, and it may rise as high as one
third. The cathode particle therefore goes about three thousand times faster
than the earth in its orbit. The relation is also invariable, even when the
substance of which the cathode is formed is changed or one gas is
substituted for another. It is, on the average, a thousand times greater than
the corresponding relation in electrolysis. As experiment has shown, in all
the circumstances where it has been possible to effect measurements, the
equality of the charges carried by all corpuscules, ions, atoms, etc., we
ought to consider that the charge of the electron is here, again, that of a
univalent ion in electrolysis, and therefore that its mass is only a small
fraction of that of the atom of hydrogen, viz., of the order of about a
thousandth part. This is the same result as that to which we were led by the
study of flames.

The thorough examination of the cathode radiation, then, confirms us in the
idea that every material atom can be dissociated and will yield an electron
much smaller than itself—and always identical whatever the matter whence
it comes,—the rest of the atom remaining charged with a positive quantity
equal and contrary to that borne by the electron. In the present case these
positive ions are no doubt those that we again meet with in the canal rays.
Professor Wien has shown that their mass is really, in fact, of the order of
the mass of atoms. Although they are all formed of identical electrons, there
may be various cathode rays, because the velocity is not exactly the same
for all electrons. Thus is explained the fact that we can separate them and
that we can produce a sort of spectrum by the action of the magnet, or,
again, as M. Deslandres has shown in a very interesting experiment, by that
of an electrostatic field. This also probably explains the phenomena studied
by M. Villard, and previously pointed out.

§ 2. RADIOACTIVE SUBSTANCES
Even in ordinary conditions, certain substances called radioactive emit,
quite outside any particular reaction, radiations complex indeed, but which
pass through fairly thin layers of minerals, impress photographic plates,
excite fluorescence, and ionize gases. In these radiations we again find
electrons which thus escape spontaneously from radioactive bodies.
It is not necessary to give here a history of the discovery of radium, for
every one knows the admirable researches of M. and Madame Curie. But
subsequent to these first studies, a great number of facts have accumulated
for the last six years, among which some people find themselves a little lost.
It may, perhaps, not be useless to indicate the essential results actually
obtained.
The researches on radioactive substances have their starting-point in the
discovery of the rays of uranium made by M. Becquerel in 1896. As early
as 1867 Niepce de St Victor proved that salts of uranium impressed
photographic plates in the dark; but at that time the phenomenon could only
pass for a singularity attributable to phosphorescence, and the valuable
remarks of Niepce fell into oblivion. M. Becquerel established, after some
hesitations natural in the face of phenomena which seemed so contrary to

accepted ideas, that the radiating property was absolutely independent of
phosphorescence, that all the salts of uranium, even the uranous salts which
are not phosphorescent, give similar radiant effects, and that these
phenomena correspond to a continuous emission of energy, but do not seem
to be the result of a storage of energy under the influence of some external
radiation. Spontaneous and constant, the radiation is insensible to variations
of temperature and light.

The nature of these radiations was not immediately understood, [32] and
their properties seemed contradictory. This was because we were not
dealing with a single category of rays. But amongst all the effects there is
one which constitutes for the radiations taken as a whole, a veritable
process for the measurement of radioactivity. This is their ionizing action on
gases. A very complete study of the conductivity of air under the influence
of rays of uranium has been made by various physicists, particularly by
Professor Rutherford, and has shown that the laws of the phenomenon are
the same as those of the ionization due to the action of the Röntgen rays.
It was natural to ask one's self if the property discovered in salts of uranium
was peculiar to this body, or if it were not, to a more or less degree, a
general property of matter. Madame Curie and M. Schmidt, independently
of each other, made systematic researches in order to solve the question;
various compounds of nearly all the simple bodies at present known were
thus passed in review, and it was established that radioactivity was
particularly perceptible in the compounds of uranium and thorium, and that
it was an atomic property linked to the matter endowed with it, and
following it in all its combinations. In the course of her researches Madame
Curie observed that certain pitchblendes (oxide of uranium ore, containing
also barium, bismuth, etc.) were four times more active (activity being
measured by the phenomenon of the ionization of the air) than metallic
uranium. Now, no compound containing any other active metal than
uranium or thorium ought to show itself more active than those metals
themselves, since the property belongs to their atoms. It seemed, therefore,
probable that there existed in pitchblendes some substance yet unknown, in
small quantities and more radioactive than uranium.
M. and Madame Curie then commenced those celebrated experiments
which brought them to the discovery of radium. Their method of research

has been justly compared in originality and importance to the process of
spectrum analysis. To isolate a radioactive substance, the first thing is to
measure the activity of a certain compound suspected of containing this
substance, and this compound is chemically separated. We then again take
in hand all the products obtained, and by measuring their activity anew, it is
ascertained whether the substance sought for has remained in one of these
products, or is divided among them, and if so, in what proportion. The
spectroscopic reaction which we may use in the course of this separation is
a thousand times less sensitive than observation of the activity by means of
the electrometer.
Though the principle on which the operation of the concentration of the
radium rests is admirable in its simplicity, its application is nevertheless
very laborious. Tons of uranium residues have to be treated in order to
obtain a few decigrammes of pure salts of radium. Radium is characterised
by a special spectrum, and its atomic weight, as determined by Madame
Curie, is 225; it is consequently the higher homologue of barium in one of
the groups of Mendeléef. Salts of radium have in general the same chemical
properties as the corresponding salts of barium, but are distinguished from
them by the differences of solubility which allow of their separation, and by
their enormous activity, which is about a hundred thousand times greater
than that of uranium.
Radium produces various chemical and some very intense physiological
reactions. Its salts are luminous in the dark, but this luminosity, at first very
bright, gradually diminishes as the salts get older. We have here to do with a
secondary reaction correlative to the production of the emanation, after
which radium undergoes the transformations which will be studied later on.
The method of analysis founded by M. and Madame Curie has enabled
other bodies presenting sensible radioactivity to be discovered. The alkaline
metals appear to possess this property in a slight degree. Recently fallen
snow and mineral waters manifest marked action. The phenomenon may
often be due, however, to a radioactivity induced by radiations already
existing in the atmosphere. But this radioactivity hardly attains the ten-
thousandth part of that presented by uranium, or the ten-millionth of that
appertaining to radium.

Two other bodies, polonium and actinium, the one characterised by the
special nature of the radiations it emits and the other by a particular
spectrum, seem likewise to exist in pitchblende. These chemical properties
have not yet been perfectly defined; thus M. Debierne, who discovered
actinium, has been able to note the active property which seems to belong
to it, sometimes in lanthanum, sometimes in neodynium.[33] It is proved that
all extremely radioactive bodies are the seat of incessant transformations,
and even now we cannot state the conditions under which they present
themselves in a strictly determined form.

§ 3. THE RADIATION OF THE RADIOACTIVE BODIES AND THE
EMANATION
To acquire exact notions as to the nature of the rays emitted by the
radioactive bodies, it was necessary to try to cause magnetic or electric
forces to act on them so as to see whether they behaved in the same way as
light and the X rays, or whether like the cathode rays they were deviated by
a magnetic field. This work was effected by Professor Giesel, then by M.
Becquerel, Professor Rutherford, and by many other experimenters after
them. All the methods which have already been mentioned in principle have
been employed in order to discover whether they were electrified, and, if so,
by electricity of what sign, to measure their speed, and to ascertain their
degree of penetration.
The general result has been to distinguish three sorts of radiations,
designated by the letters alpha, beta, gamma.
The alpha rays are positively charged, and are projected at a speed which
may attain the tenth of that of light; M.H. Becquerel has shown by the aid
of photography that they are deviated by a magnet, and Professor
Rutherford has, on his side, studied this deviation by the electrical method.
The relation of the charge to the mass is, in the case of these rays, of the
same order as in that of the ions of electrolysis. They may therefore be
considered as exactly analogous to the canal rays of Goldstein, and we may
attribute them to a material transport of corpuscles of the magnitude of
atoms. The relatively considerable size of these corpuscles renders them
very absorbable. A flight of a few millimetres in a gas suffices to reduce
their number by one-half. They have great ionizing power.
The beta rays are on all points similar to the cathode rays; they are, as M.
and Madame Curie have shown, negatively charged, and the charge they
carry is always the same. Their size is that of the electrons, and their
velocity is generally greater than that of the cathode rays, while it may
become almost that of light. They have about a hundred times less ionizing
power than the alpha rays.

The gamma rays were discovered by M. Villard.[34] They may be compared
to the X rays; like the latter, they are not deviated by the magnetic field, and
are also extremely penetrating. A strip of aluminium five millimetres thick
will stop the other kinds, but will allow them to pass. On the other hand,
their ionizing power is 10,000 times less than that of the alpha rays.
To these radiations there sometimes are added in the course of experiments
secondary radiations analogous to those of M. Sagnac, and produced when
the alpha, beta, or gamma rays meet various substances. This complication
has often led to some errors of observation.
Phosphorescence and fluorescence seem especially to result from the alpha
and beta rays, particularly from the alpha rays, to which belongs the most
important part of the total energy of the radiation. Sir W. Crookes has
invented a curious little apparatus, the spinthariscope, which enables us to
examine the phosphorescence of the blende excited by these rays. By means
of a magnifying glass, a screen covered with sulphide of zinc is kept under
observation, and in front of it is disposed, at a distance of about half a
millimetre, a fragment of some salt of radium. We then perceive multitudes
of brilliant points on the screen, which appear and at once disappear,
producing a scintillating effect. It seems probable that every particle falling
on the screen produces by its impact a disturbance in the neighbouring
region, and it is this disturbance which the eye perceives as a luminous
point. Thus, says Sir W. Crookes, each drop of rain falling on the surface of
still water is not perceived as a drop of rain, but by reason of the slight
splash which it causes at the moment of impact, and which is manifested by
ridges and waves spreading themselves in circles.
The various radioactive substances do not all give radiations of identical
constitution. Radium and thorium possess in somewhat large proportions
the three kinds of rays, and it is the same with actinium. Polonium contains
especially alpha rays and a few gamma rays. [35] In the case of uranium, the
alpha rays have extremely slight penetrating power, and cannot even
impress photographic plates. But the widest difference between the
substances proceeds from the emanation. Radium, in addition to the three
groups of rays alpha, beta, and gamma, disengages continuously an
extremely subtle emanation, seemingly almost imponderable, but which

may be, for many reasons, looked upon as a vapour of which the elastic
force is extremely feeble.
M. and Madame Curie discovered as early as 1899 that every substance
placed in the neighbourhood of radium, itself acquired a radioactivity which
persisted for several hours after the removal of the radium. This induced
radioactivity seems to be carried to other bodies by the intermediary of a
gas. It goes round obstacles, but there must exist between the radium and
the substance a free and continuous space for the activation to take place; it
cannot, for instance, do so through a wall of glass.
In the case of compounds of thorium Professor Rutherford discovered a
similar phenomenon; since then, various physicists, Professor Soddy, Miss
Brooks, Miss Gates, M. Danne, and others, have studied the properties of
these emanations.
The substance emanated can neither be weighed nor can its elastic force be
ascertained; but its transformations may be followed, as it is luminous, and
it is even more certainly characterised by its essential property, i.e. its
radioactivity. We also see that it can be decanted like a gas, that it will
divide itself between two tubes of different capacity in obedience to the law
of Mariotte, and will condense in a refrigerated tube in accordance with the
principle of Watt, while it even complies with the law of Gay-Lussac.
The activity of the emanation vanishes quickly, and at the end of four days
it has diminished by one-half. If a salt of radium is heated, the emanation
becomes more abundant, and the residue, which, however, does not sensibly
diminish in weight, will have lost all its radioactivity, and will only recover
it by degrees. Professor Rutherford, notwithstanding many different
attempts, has been unable to make this emanation enter into any chemical
reaction. If it be a gaseous body, it must form part of the argon group, and,
like its other members, be perfectly inert.
By studying the spectrum of the gas disengaged by a solution of salt of
radium, Sir William Ramsay and Professor Soddy remarked that when the
gas is radioactive there are first obtained rays of gases belonging to the
argon family, then by degrees, as the activity disappears, the spectrum
slowly changes, and finally presents the characteristic aspect of helium.

We know that the existence of this gas was first discovered by spectrum
analysis in the sun. Later its presence was noted in our atmosphere, and in a
few minerals which happen to be the very ones from which radium has been
obtained. It might therefore have been the case that it pre-existed in the
gases extracted from radium; but a remarkable experiment by M. Curie and
Sir James Dewar seems to show convincingly that this cannot be so. The
spectrum of helium never appears at first in the gas proceeding from pure
bromide of radium; but it shows itself, on the other hand, very distinctly,
after the radioactive transformations undergone by the salt.
All these strange phenomena suggest bold hypotheses, but to construct them
with any solidity they must be supported by the greatest possible number of
facts. Before admitting a definite explanation of the phenomena which have
their seat in the curious substances discovered by them, M. and Madame
Curie considered, with a great deal of reason, that they ought first to enrich
our knowledge with the exact and precise facts relating to these bodies and
to the effects produced by the radiations they emit.
Thus M. Curie particularly set himself to study the manner in which the
radioactivity of the emanation is dissipated, and the radioactivity that this
emanation can induce on all bodies. The radioactivity of the emanation
diminishes in accordance with an exponential law. The constant of time
which characterises this decrease is easily and exactly determined, and has
a fixed value, independent of the conditions of the experiment as well as of
the nature of the gas which is in contact with the radium and becomes
charged with the emanation. The regularity of the phenomenon is so great
that it can be used to measure time: in 3985 seconds [36] the activity is
always reduced one-half.
Radioactivity induced on any body which has been for a long time in
presence of a salt of radium disappears more rapidly. The phenomenon
appears, moreover, more complex, and the formula which expresses the
manner in which the activity diminishes must contain two exponentials. To
find it theoretically we have to imagine that the emanation first deposits on
the body in question a substance which is destroyed in giving birth to a
second, this latter disappearing in its turn by generating a third. The initial
and final substances would be radioactive, but the intermediary one, not. If,
moreover, the bodies acted on are brought to a temperature of over 700°,

they appear to lose by volatilisation certain substances condensed in them,
and at the same time their activity disappears.
The other radioactive bodies behave in a similar way. Bodies which contain
actinium are particularly rich in emanations. Uranium, on the contrary, has
none.[37] This body, nevertheless, is the seat of transformations comparable
to those which the study of emanations reveals in radium; Sir W. Crookes
has separated from uranium a matter which is now called uranium X. This
matter is at first much more active than its parent, but its activity diminishes
rapidly, while the ordinary uranium, which at the time of the separation
loses its activity, regains it by degrees. In the same way, Professors
Rutherford and Soddy have discovered a so-called thorium X to be the
stage through which ordinary thorium has to pass in order to produce its
emanation. [38]
It is not possible to give a complete table which should, as it were, represent
the genealogical tree of the various radioactive substances. Several authors
have endeavoured to do so, but in a premature manner; all the affiliations
are not at the present time yet perfectly known, and it will no doubt be
acknowledged some day that identical states have been described under
different names. [39]

§ 4. THE DISAGGREGATION OF MATTER AND ATOMIC
ENERGY
In spite of uncertainties which are not yet entirely removed, it cannot be
denied that many experiments render it probable that in radioactive bodies
we find ourselves witnessing veritable transformations of matter.
Professor Rutherford, Professor Soddy, and several other physicists, have
come to regard these phenomena in the following way. A radioactive body
is composed of atoms which have little stability, and are able to detach
themselves spontaneously from the parent substance, and at the same time
to divide themselves into two essential component parts, the negative
electron and its residue the positive ion. The first-named constitutes the
beta, and the second the alpha rays.

The emanation is certainly composed of alpha ions with a few molecules
agglomerated round them. Professor Rutherford has, in fact, demonstrated
that the emanation is charged with positive electricity; and this emanation
may, in turn, be destroyed by giving birth to new bodies.
After the loss of the atoms which are carried off by the radiation, the
remainder of the body acquires new properties, but it may still be
radioactive, and again lose atoms. The various stages that we meet with in
the evolution of the radioactive substance or of its emanation, correspond to
the various degrees of atomic disaggregation. Professors Rutherford and
Soddy have described them clearly in the case of uranium and radium. As
regards thorium the results are less satisfactory. The evolution should
continue until a stable atomic condition is finally reached, which, because
of this stability, is no longer radioactive. Thus, for instance, radium would
finally be transformed into helium.[40]
It is possible, by considerations analogous to those set forth above in other
cases, to arrive at an idea of the total number of particles per second
expelled by one gramme of radium; Professor Rutherford in his most recent
evaluation finds that this number approaches 2.5 x 1011.[41] By calculating
from the atomic weight the number of atoms probably contained in this
gramme of radium, and supposing each particle liberated to correspond to
the destruction of one atom, it is found that one half of the radium should
disappear in 1280 years;[42] and from this we may conceive that it has not
yet been possible to discover any sensible loss of weight. Sir W. Ramsay
and Professor Soddy attained a like result by endeavouring to estimate the
mass of the emanation by the quantity of helium produced.
If radium transforms itself in such a way that its activity does not persist
throughout the ages, it loses little by little the provision of energy it had in
the beginning, and its properties furnish no valid argument to oppose to the
principle of the conservation of energy. To put everything right, we have
only to recognise that radium possessed in the potential state at its
formation a finite quantity of energy which is consumed little by little. In
the same manner, a chemical system composed, for instance, of zinc and
sulphuric acid, also contains in the potential state energy which, if we retard
the reaction by any suitable arrangement—such as by amalgamating the

zinc and by constituting with its elements a battery which we cause to act
on a resistance—may be made to exhaust itself as slowly as one may desire.
There can, therefore, be nothing in any way surprising in the fact that a
combination which, like the atomic combination of radium, is not stable—
since it disaggregates itself,—is capable of spontaneously liberating energy,
but what may be a little astonishing, at first sight, is the considerable
amount of this energy.
M. Curie has calculated directly, by the aid of the calorimeter, the quantity
of energy liberated, measuring it entirely in the form of heat. The
disengagement of heat accounted for in a grain of radium is uniform, and
amounts to 100 calories per hour. It must therefore be admitted that an atom
of radium, in disaggregating itself, liberates 30,000 times more energy than
a molecule of hydrogen when the latter combines with an atom of oxygen to
form a molecule of water.
We may ask ourselves how the atomic edifice of the active body can be
constructed, to contain so great a provision of energy. We will remark that
such a question might be asked concerning cases known from the most
remote antiquity, like that of the chemical systems, without any satisfactory
answer ever being given. This failure surprises no one, for we get used to
everything—even to defeat.
When we come to deal with a new problem we have really no right to show
ourselves more exacting; yet there are found persons who refuse to admit
the hypothesis of the atomic disaggregation of radium because they cannot
have set before them a detailed plan of that complex whole known to us as
an atom.
The most natural idea is perhaps the one suggested by comparison with
those astronomical phenomena where our observation most readily allows
us to comprehend the laws of motion. It corresponds likewise to the
tendency ever present in the mind of man, to compare the infinitely small
with the infinitely great. The atom may be regarded as a sort of solar system
in which electrons in considerable numbers gravitate round the sun formed
by the positive ion. It may happen that certain of these electrons are no
longer retained in their orbit by the electric attraction of the rest of the atom,
and may be projected from it like a small planet or comet which escapes

towards the stellar spaces. The phenomena of the emission of light compels
us to think that the corpuscles revolve round the nucleus with extreme
velocities, or at the rate of thousands of billions of evolutions per second. It
is easy to conceive from this that, notwithstanding its lightness, an atom
thus constituted may possess an enormous energy.[43]
Other authors imagine that the energy of the corpuscles is principally due to
the extremely rapid rotations of those elements on their own axes. Lord
Kelvin lately drew up on another model the plan of a radioactive atom
capable of ejecting an electron with a considerable vis viva. He supposes a
spherical atom formed of concentric layers of positive and negative
electricity disposed in such a way that its external action is null, and that,
nevertheless, the force emanated from the centre may be repellent for
certain values when the electron is within it.
The most prudent physicists and those most respectful to established
principles may, without any scruples, admit the explanation of the
radioactivity of radium by a dislocation of its molecular edifice. The matter
of which it is constituted evolves from an admittedly unstable initial state to
another stable one. It is, in a way, a slow allotropic transformation which
takes place by means of a mechanism regarding which, in short, we have no
more information than we have regarding other analogous transformations.
The only astonishment we can legitimately feel is derived from the thought
that we are suddenly and deeply penetrating to the very heart of things.
But those persons who have a little more hardihood do not easily resist the
temptation of forming daring generalisations. Thus it will occur to some
that this property, already discovered in many substances where it exists in
more or less striking degree, is, with differences of intensity, common to all
bodies, and that we are thus confronted by a phenomenon derived from an
essential quality of matter. Quite recently, Professor Rutherford has
demonstrated in a fine series of experiments that the alpha particles of
radium cease to ionize gases when they are made to lose their velocity, but
that they do not on that account cease to exist. It may follow that many
bodies emit similar particles without being easily perceived to do so; since
the electric action, by which this phenomenon of radioactivity is generally
manifested, would, in this case, be but very weak.

If we thus believe radioactivity to be an absolutely general phenomenon, we
find ourselves face to face with a new problem. The transformation of
radioactive bodies can no longer be assimilated to allotropic
transformations, since thus no final form could ever be attained, and the
disaggregation would continue indefinitely up to the complete dislocation
of the atom. [44] The phenomenon might, it is true, have a duration of
perhaps thousands of millions of centuries, but this duration is but a minute
in the infinity of time, and matters little. Our habits of mind, if we adopt
such a conception, will be none the less very deeply disturbed. We shall
have to abandon the idea so instinctively dear to us that matter is the most
stable thing in the universe, and to admit, on the contrary, that all bodies
whatever are a kind of explosive decomposing with extreme slowness.
There is in this, whatever may have been said, nothing contrary to any of
the principles on which the science of energetics rests; but an hypothesis of
this nature carries with it consequences which ought in the highest degree to
interest the philosopher, and we all know with what alluring boldness M.
Gustave Le Bon has developed all these consequences in his work on the
evolution of matter.[45]
There is hardly a physicist who does not at the present day adopt in one
shape or another the ballistic hypothesis. All new facts are co-ordinated so
happily by it, that it more and more satisfies our minds; but it cannot be
asserted that it forces itself on our convictions with irresistible weight.
Another point of view appeared more plausible and simple at the outset,
when there seemed reason to consider the energy radiated by radioactive
bodies as inexhaustible. It was thought that the source of this energy was to
be looked for without the atom, and this idea may perfectly well he
maintained at the present day.
Radium on this hypothesis must be considered as a transformer borrowing
energy from the external medium and returning it in the form of radiation. It
is not impossible, even, to admit that the energy which the atom of radium
withdraws from the surrounding medium may serve to keep up, not only the
heat emitted and its complex radiation, but also the dissociation, supposed
to be endothermic, of this atom. Such seems to be the idea of M. Debierne
and also of M. Sagnac. It does not seem to accord with the experiments that
this borrowed energy can be a part of the heat of the ambient medium; and,
indeed, such a phenomenon would be contrary to the principle of Carnot if

we wished (though we have seen how disputable is this extension) to extend
this principle to the phenomena which are produced in the very bosom of
the atom.
We may also address ourselves to a more noble form of energy, and ask
ourselves whether we are not, for the first time, in presence of a
transformation of gravitational energy. It may be singular, but it is not
absurd, to suppose that the unit of mass of radium is not attached to the
earth with the same intensity as an inert body. M. Sagnac has commenced
some experiments, as yet unpublished, in order to study the laws of the fall
of a fragment of radium. They are necessarily very delicate, and the
energetic and ingenious physicist has not yet succeeded in finishing them.
[46]
Let us suppose that he succeeds in demonstrating that the intensity of
gravity is less for radium than for the platinum or the copper of which the
pendulums used to illustrate the law of Newton are generally made; it
would then be possible still to think that the laws of universal attraction are
perfectly exact as regards the stars, and that ponderability is really a
particular case of universal attraction, while in the case of radioactive
bodies part of the gravitational energy is transformed in the course of its
evolution and appears in the form of active radiation.
But for this explanation to be admitted, it would evidently need to be
supported by very numerous facts. It might, no doubt, appear still more
probable that the energy borrowed from the external medium by radium is
one of those still unknown to us, but of which a vague instinct causes us to
suspect the existence around us. It is indisputable, moreover, that the
atmosphere in all directions is furrowed with active radiations; those of
radium may be secondary radiations reflected by a kind of resonance
phenomenon.
Certain experiments by Professors Elster and Geitel, however, are not
favourable to this point of view. If an active body be surrounded by a
radioactive envelope, a screen should prevent this body from receiving any
impression from outside, and yet there is no diminution apparent in the
activity presented by a certain quantity of radium when it is lowered to a
depth of 800 metres under ground, in a region containing a notable quantity
of pitchblende. These negative results are, on the other hand, so many

successes for the partisans of the explanation of radioactivity by atomic
energy.

CHAPTER X

THE ETHER AND MATTER
§ 1. THE RELATIONS BETWEEN THE ETHER AND MATTER
For some time past it has been the more or less avowed ambition of
physicists to construct with the particles of ether all possible forms of
corporeal existence; but our knowledge of the inmost nature of things has
hitherto seemed too limited for us to attempt such an enterprise with any
chance of success. The electronic hypothesis, however, which has furnished
a satisfactory image of the most curious phenomena produced in the bosom
of matter, has also led to a more complete electromagnetic theory of the
ether than that of Maxwell, and this twofold result has given birth to the
hope of arriving by means of this hypothesis at a complete co-ordination of
the physical world.
The phenomena whose study may bring us to the very threshold of the
problem, are those in which the connections between matter and the ether
appear clearly and in a relatively simple manner. Thus in the phenomena of
emission, ponderable matter is seen to give birth to waves which are
transmitted by the ether, and by the phenomena of absorption it is proved
that these waves disappear and excite modifications in the interior of the
material bodies which receive them. We here catch in operation actual
reciprocal actions and reactions between the ether and matter. If we could
thoroughly comprehend these actions, we should no doubt be in a position
to fill up the gap which separates the two regions separately conquered by
physical science.
In recent years numerous researches have supplied valuable materials which
ought to be utilized by those endeavouring to construct a theory of
radiation. We are, perhaps, still ill informed as to the phenomena of
luminescence in which undulations are produced in a complex manner, as in
the case of a stick of moist phosphorus which is luminescent in the dark, or
in that of a fluorescent screen. But we are very well acquainted with
emission or absorption by incandescence, where the only transformation is
that of calorific into radiating energy, or vice versa. It is in this case alone

that can be correctly applied the celebrated demonstration by which
Kirchhoff established, by considerations borrowed from thermodynamics,
the proportional relations between the power of emission and that of
absorption.
In treating of the measurement of temperature, I have already pointed out
the experiments of Professors Lummer and Pringsheim and the theoretical
researches of Stephan and Professor Wien. We may consider that at the
present day the laws of the radiation of dark bodies are tolerably well
known, and, in particular, the manner in which each elementary radiation
increases with the temperature. A few doubts, however, subsist with respect
to the law of the distribution of energy in the spectrum. In the case of real
and solid bodies the results are naturally less simple than in that of dark
bodies. One side of the question has been specially studied on account of its
great practical interest, that is to say, the fact that the relation of the
luminous energy to the total amount radiated by a body varies with the
nature of this last; and the knowledge of the conditions under which this
relation becomes most considerable led to the discovery of incandescent
lighting by gas in the Auer-Welsbach mantle, and to the substitution for the
carbon thread in the electric light bulb of a filament of osmium or a small
rod of magnesium, as in the Nernst lamp. Careful measurements effected by
M. Fery have furnished, in particular, important information on the
radiation of the white oxides; but the phenomena noticed have not yet found
a satisfactory interpretation. Moreover, the radiation of calorific origin is
here accompanied by a more or less important luminescence, and the
problem becomes very complex.
In the same way that, for the purpose of knowing the constitution of matter,
it first occurred to us to investigate gases, which appear to be molecular
edifices built on a more simple and uniform plan than solids, we ought
naturally to think that an examination of the conditions in which emission
and absorption are produced by gaseous bodies might be eminently
profitable, and might perhaps reveal the mechanism by which the relations
between the molecule of the ether and the molecule of matter might be
established.
Unfortunately, if a gas is not absolutely incapable of emitting some sort of
rays by simple heat, the radiation thus produced, no doubt by reason of the

slightness of the mass in play, always remains of moderate intensity. In
nearly all the experiments, new energies of chemical or electrical origin
come into force. On incandescence, luminescence is superposed; and the
advantage which might have been expected from the simplicity of the
medium vanishes through the complication of the circumstances in which
the phenomenon is produced.
Professor Pringsheim has succeeded, in certain cases, in finding the
dividing line between the phenomena of luminescence and that of
incandescence. Thus the former takes a predominating importance when the
gas is rendered luminous by electrical discharges, and chemical
transformations, especially, play a preponderant rôle in the emission of the
spectrum of flames which contain a saline vapour. In all the ordinary
experiments of spectrum analysis the laws of Kirchhoff cannot therefore be
considered as established, and yet the relation between emission and
absorption is generally tolerably well verified. No doubt we are here in
presence of a kind of resonance phenomenon, the gaseous atoms entering
into vibration when solicited by the ether by a motion identical with the one
they are capable of communicating to it.
If we are not yet very far advanced in the study of the mechanism of the
production of the spectrum,[47] we are, on the other hand, well acquainted
with its constitution. The extreme confusion which the spectra of the lines
of the gases seemed to present is now, in great part at least, cleared up.
Balmer gave some time since, in the case of the hydrogen spectrum, an
empirical formula which enabled the rays discovered later by an eminent
astronomer, M. Deslandres, to be represented; but since then, both in the
cases of line and band spectra, the labours of Professor Rydberg, of M.
Deslandres, of Professors Kayzer and Runge, and of M. Thiele, have
enabled us to comprehend, in their smallest details, the laws of the
distribution of lines and bands.
These laws are simple, but somewhat singular. The radiations emitted by a
gas cannot be compared to the notes to which a sonorous body gives birth,
nor even to the most complicated vibrations of any elastic body. The
number of vibrations of the different rays are not the successive multiples of
one and the same number, and it is not a question of a fundamental radiation
and its harmonics, while—and this is an essential difference—the number

of vibrations of the radiation tend towards a limit when the period
diminishes infinitely instead of constantly increasing, as would be the case
with the vibrations of sound.
Thus the assimilation of the luminous to the elastic vibration is not correct.
Once again we find that the ether does not behave like matter which obeys
the ordinary laws of mechanics, and every theory must take full account of
these curious peculiarities which experiment reveals.
Another difference, likewise very important, between the luminous and the
sonorous vibrations, which also points out how little analogous can be the
constitutions of the media which transmit the vibrations, appears in the
phenomena of dispersion. The speed of propagation, which, as we have
seen when discussing the measurement of the velocity of sound, depends
very little on the musical note, is not at all the same in the case of the
various radiations which can be propagated in the same substance. The
index of refraction varies with the duration of the period, or, if you will,
with the length of wave in vacuo which is proportioned to this duration,
since in vacuo the speed of propagation is entirely the same for all
vibrations.
Cauchy was the first to propose a theory on which other attempts have been
modelled; for example, the very interesting and simple one of Briot. This
last-named supposed that the luminous vibration could not perceptibly drag
with it the molecular material of the medium across which it is propagated,
but that matter, nevertheless, reacts on the ether with an intensity
proportional to the elongation, in such a manner as tends to bring it back to
its position of equilibrium. With this simple hypothesis we can fairly well
interpret the phenomena of the dispersion of light in the case of transparent
substances; but far from well, as M. Carvallo has noted in some extremely
careful experiments, the dispersion of the infra-red spectrum, and not at all
the peculiarities presented by absorbent substances.
M. Boussinesq arrives at almost similar results, by attributing dispersion, on
the other hand, to the partial dragging along of ponderable matter and to its
action on the ether. By combining, in a measure, as was subsequently done
by M. Boussinesq, the two hypotheses, formulas can be established far
better in accord with all the known facts.

These facts are somewhat complex. It was at first thought that the index
always varied in inverse ratio to the wave-length, but numerous substances
have been discovered which present the phenomenon of abnormal
dispersion—that is to say, substances in which certain radiations are
propagated, on the contrary, the more quickly the shorter their period. This
is the case with gases themselves, as demonstrated, for example, by a very
elegant experiment of M. Becquerel on the dispersion of the vapour of
sodium. Moreover, it may happen that yet more complications may be met
with, as no substance is transparent for the whole extent of the spectrum. In
the case of certain radiations the speed of propagation becomes nil, and the
index shows sometimes a maximum and sometimes a minimum. All those
phenomena are in close relation with those of absorption.
It is, perhaps, the formula proposed by Helmholtz which best accounts for
all these peculiarities. Helmholtz came to establish this formula by
supposing that there is a kind of friction between the ether and matter,
which, like that exercised on a pendulum, here produces a double effect,
changing, on the one hand, the duration of this oscillation, and, on the other,
gradually damping it. He further supposed that ponderable matter is acted
on by elastic forces. The theory of Helmholtz has the great advantage of
representing, not only the phenomena of dispersion, but also, as M.
Carvallo has pointed out, the laws of rotatory polarization, its dispersion
and other phenomena, among them the dichroism of the rotatory media
discovered by M. Cotton.
In the establishment of these theories, the language of ordinary optics has
always been employed. The phenomena are looked upon as due to
mechanical deformations or to movements governed by certain forces. The
electromagnetic theory leads, as we have seen, to the employment of other
images. M.H. Poincaré, and, after him, Helmholtz, have both proposed
electromagnetic theories of dispersion. On examining things closely, it will
be found that there are not, in truth, in the two ways of regarding the
problem, two equivalent translations of exterior reality. The electrical
theory gives us to understand, much better than the mechanical one, that in
vacuo the dispersion ought to be strictly null, and this absence of dispersion
appears to be confirmed with extraordinary precision by astronomical
observations. Thus the observation, often repeated, and at different times of
year, proves that in the case of the star Algol, the light of which takes at

least four years to reach us, no sensible difference in coloration
accompanies the changes in brilliancy.

§ 2. THE THEORY OF LORENTZ
Purely mechanical considerations have therefore failed to give an entirely
satisfactory interpretation of the phenomena in which even the simplest
relations between matter and the ether appear. They would, evidently, be
still more insufficient if used to explain certain effects produced on matter
by light, which could not, without grave difficulties, be attributed to
movement; for instance, the phenomena of electrification under the
influence of certain radiations, or, again, chemical reactions such as
photographic impressions.
The problem had to be approached by another road. The electromagnetic
theory was a step in advance, but it comes to a standstill, so to speak, at the
moment when the ether penetrates into matter. If we wish to go deeper into
the inwardness of the phenomena, we must follow, for example, Professor
Lorentz or Dr Larmor, and look with them for a mode of representation
which appears, besides, to be a natural consequence of the fundamental
ideas forming the basis of Hertz's experiments.
The moment we look upon a wave in the ether as an electromagnetic wave,
a molecule which emits light ought to be considered as a kind of excitant.
We are thus led to suppose that in each radiating molecule there are one or
several electrified particles, animated with a to-and-fro movement round
their positions of equilibrium, and these particles are certainly identical with
those electrons the existence of which we have already admitted for so
many other reasons.
In the simplest theory, we will imagine an electron which may be displaced
from its position of equilibrium in all directions, and is, in this
displacement, submitted to attractions which communicate to it a vibration
like a pendulum. These movements are equivalent to tiny currents, and the
mobile electron, when animated with a considerable velocity, must be
sensitive to the action of the magnet which modifies the form of the
trajectory and the value of the period. This almost direct consequence was

perceived by Lorentz, and it led him to the new idea that radiations emitted
by a body ought to be modified by the action of a strong electromagnet.
An experiment enabled this prevision to be verified. It was made, as is well
known, as early as 1896 by Zeeman; and the discovery produced a
legitimate sensation. When a flame is subjected to the action of a magnetic
field, a brilliant line is decomposed in conditions more or less complex
which an attentive study, however, allows us to define. According to
whether the observation is made in a plane normal to the magnetic field or
in the same direction, the line transforms itself into a triplet or doublet, and
the new lines are polarized rectilinearly or circularly.
These are the precise phenomena which the calculation foretells: the
analysis of the modifications undergone by the light supplies, moreover,
valuable information on the electron itself. From the direction of the
circular vibrations of the greatest frequency we can determine the sign of
the electric charge in motion and we find it to be negative. But, further than
this, from the variation of the period we can calculate the relation of the
force acting on the electron to its material mass, and, in addition, the
relation of the charge to the mass. We then find for this relation precisely
that value which we have already met with so many times. Such a
coincidence cannot be fortuitous, and we have the right to believe that the
electron revealed by the luminous wave which emanates from it, is really
the same as the one made known to us by the study of the cathode rays and
of the radioactive substances.
However, the elementary theory does not suffice to interpret the
complications which later experiments have revealed. The physicists most
qualified to effect measurements in these delicate optical questions—M.
Cornu, Mr Preston, M. Cotton, MM. Becquerel and Deslandres, M. Broca,
Professor Michelson, and others—have pointed out some remarkable
peculiarities. Thus in some cases the number of the component rays
dissociated by the magnetic field may be very considerable.
The great modification brought to a radiation by the Zeeman effect may,
besides, combine itself with other phenomena, and alter the light in a still
more complicated manner. A pencil of polarized light, as demonstrated by

Signori Macaluzo and Corbino, undergoes, in a magnetic field,
modifications with regard to absorption and speed of propagation.
Some ingenious researches by M. Becquerel and M. Cotton have perfectly
elucidated all these complications from an experimental point of view. It
would not be impossible to link together all these phenomena without
adopting the electronic hypothesis, by preserving the old optical equations
as modified by the terms relating to the action of the magnetic field. This
has actually been done in some very remarkable work by M. Voigt, but we
may also, like Professor Lorentz, look for more general theories, in which
the essential image of the electrons shall be preserved, and which will allow
all the facts revealed by experiment to be included.
We are thus led to the supposition that there is not in the atom one vibrating
electron only, but that there is to be found in it a dynamical system
comprising several material points which may be subjected to varied
movements. The neutral atom may therefore be considered as composed of
an immovable principal portion positively charged, round which move, like
satellites round a planet, several negative electrons of very inferior mass.
This conclusion leads us to an interpretation in agreement with that which
other phenomena have already suggested.
These electrons, which thus have a variable velocity, generate around
themselves a transverse electromagnetic wave which is propagated with the
velocity of light; for the charged particle becomes, as soon as it experiences
a change of speed, the centre of a radiation. Thus is explained the
phenomenon of the emission of radiations. In the same way, the movement
of electrons may be excited or modified by the electrical forces which exist
in any pencil of light they receive, and this pencil may yield up to them a
part of the energy it is carrying. This is the phenomenon of absorption.
Professor Lorentz has not contented himself with thus explaining all the
mechanism of the phenomena of emission and absorption. He has
endeavoured to rediscover, by starting with the fundamental hypothesis, the
quantitative laws discovered by thermodynamics. He succeeds in showing
that, agreeably to the law of Kirchhoff, the relation between the emitting
and the absorbing power must be independent of the special properties of
the body under observation, and he thus again meets with the laws of

Planck and of Wien: unfortunately the calculation can only be made in the
case of great wave-lengths, and grave difficulties exist. Thus it cannot be
very clearly explained why, by heating a body, the radiation is displaced
towards the side of the short wave-lengths, or, if you will, why a body
becomes luminous from the moment its temperature has reached a
sufficiently high degree. On the other hand, by calculating the energy of the
vibrating particles we are again led to attribute to these particles the same
constitution as that of the electrons.
It is in the same way possible, as Professor Lorentz has shown, to give a
very satisfactory explanation of the thermo-electric phenomena by
supposing that the number of liberated electrons which exist in a given
metal at a given temperature has a determined value varying with each
metal, and is, in the case of each body, a function of the temperature. The
formula obtained, which is based on these hypotheses, agrees completely
with the classic results of Clausius and of Lord Kelvin. Finally, if we
recollect that the phenomena of electric and calorific conductivity are
perfectly interpreted by the hypothesis of electrons, it will no longer be
possible to contest the importance of a theory which allows us to group
together in one synthesis so many facts of such diverse origins.
If we study the conditions under which a wave excited by an electron's
variations in speed can be transmitted, they again bring us face to face, and
generally, with the results pointed out by the ordinary electromagnetic
theory. Certain peculiarities, however, are not absolutely the same. Thus the
theory of Lorentz, as well as that of Maxwell, leads us to foresee that if an
insulating mass be caused to move in a magnetic field normally to its lines
of force, a displacement will be produced in this mass analogous to that of
which Faraday and Maxwell admitted the existence in the dielectric of a
charged condenser. But M.H. Poincaré has pointed out that, according as we
adopt one or other of these authors' points of view, so the value of the
displacement differs. This remark is very important, for it may lead to an
experiment which would enable us to make a definite choice between the
two theories.
To obtain the displacement estimated according to Lorentz, we must
multiply the displacement calculated according to Hertz by a factor
representing the relation between the difference of the specific inductive

capacities of the dielectric and of a vacuum, and the first of these powers. If
therefore we take as dielectric the air of which the specific inductive
capacity is perceptibly the same as that of a vacuum, the displacement,
according to the idea of Lorentz, will be null; while, on the contrary,
according to Hertz, it will have a finite value. M. Blondlot has made the
experiment. He sent a current of air into a condenser placed in a magnetic
field, and was never able to notice the slightest trace of electrification. No
displacement, therefore, is effected in the dielectric. The experiment being a
negative one, is evidently less convincing than one giving a positive result,
but it furnishes a very powerful argument in favour of the theory of Lorentz.
This theory, therefore, appears very seductive, yet it still raises objections
on the part of those who oppose to it the principles of ordinary mechanics.
If we consider, for instance, a radiation emitted by an electron belonging to
one material body, but absorbed by another electron in another body, we
perceive immediately that, the propagation not being instantaneous, there
can be no compensation between the action and the reaction, which are not
simultaneous; and the principle of Newton thus seems to be attacked. In
order to preserve its integrity, it has to be admitted that the movements in
the two material substances are compensated by that of the ether which
separates these substances; but this conception, although in tolerable
agreement with the hypothesis that the ether and matter are not of different
essence, involves, on a closer examination, suppositions hardly satisfactory
as to the nature of movements in the ether.
For a long time physicists have admitted that the ether as a whole must be
considered as being immovable and capable of serving, so to speak, as a
support for the axes of Galileo, in relation to which axes the principle of
inertia is applicable,—or better still, as M. Painlevé has shown, they alone
allow us to render obedience to the principle of causality.
But if it were so, we might apparently hope, by experiments in
electromagnetism, to obtain absolute motion, and to place in evidence the
translation of the earth relatively to the ether. But all the researches
attempted by the most ingenious physicists towards this end have always
failed, and this tends towards the idea held by many geometricians that
these negative results are not due to imperfections in the experiments, but
have a deep and general cause. Now Lorentz has endeavoured to find the

conditions in which the electromagnetic theory proposed by him might
agree with the postulate of the complete impossibility of determining
absolute motion. It is necessary, in order to realise this concord, to imagine
that a mobile system contracts very slightly in the direction of its translation
to a degree proportioned to the square of the ratio of the velocity of
transport to that of light. The electrons themselves do not escape this
contraction, although the observer, since he participates in the same motion,
naturally cannot notice it. Lorentz supposes, besides, that all forces,
whatever their origin, are affected by a translation in the same way as
electromagnetic forces. M. Langevin and M. H. Poincaré have studied this
same question and have noted with precision various delicate consequences
of it. The singularity of the hypotheses which we are thus led to construct in
no way constitutes an argument against the theory of Lorentz; but it has, we
must acknowledge, discouraged some of the more timid partisans of this
theory.[48]

§ 3. THE MASS OF ELECTRONS
Other conceptions, bolder still, are suggested by the results of certain
interesting experiments. The electron affords us the possibility of
considering inertia and mass to be no longer a fundamental notion, but a
consequence of the electromagnetic phenomena.
Professor J.J. Thomson was the first to have the clear idea that a part, at
least, of the inertia of an electrified body is due to its electric charge. This
idea was taken up and precisely stated by Professor Max Abraham, who, for
the first time, was led to regard seriously the seemingly paradoxical notion
of mass as a function of velocity. Consider a small particle bearing a given
electric charge, and let us suppose that this particle moves through the ether.
It is, as we know, equivalent to a current proportional to its velocity, and it
therefore creates a magnetic field the intensity of which is likewise
proportional to its velocity: to set it in motion, therefore, there must be
communicated to it over and above the expenditure corresponding to the
acquisition of its ordinary kinetic energy, a quantity of energy proportional
to the square of its velocity. Everything, therefore, takes place as if, by the
fact of electrification, its capacity for kinetic energy and its material mass

had been increased by a certain constant quantity. To the ordinary mass may
be added, if you will, an electromagnetic mass.
This is the state of things so long as the speed of the translation of the
particle is not very great, but they are no longer quite the same when this
particle is animated with a movement whose rapidity becomes comparable
to that with which light is propagated.
The magnetic field created is then no longer a field in repose, but its energy
depends, in a complicated manner, on the velocity, and the apparent
increase in the mass of the particle itself becomes a function of the velocity.
More than this, this increase may not be the same for the same velocity, but
varies according to whether the acceleration is parallel with or
perpendicular to the direction of this velocity. In other words, there seems
to be a longitudinal; and a transversal mass which need not be the same.
All these results would persist even if the material mass were very small
relatively to the electromagnetic mass; and the electron possesses some
inertia even if its ordinary mass becomes slighter and slighter. The apparent
mass, it can be easily shown, increases indefinitely when the velocity with
which the electrified particle is animated tends towards the velocity of light,
and thus the work necessary to communicate such a velocity to an electron
would be infinite. It is in consequence impossible that the speed of an
electron, in relation to the ether, can ever exceed, or even permanently
attain to, 300,000 kilometres per second.
All the facts thus predicted by the theory are confirmed by experiment.
There is no known process which permits the direct measurement of the
mass of an electron, but it is possible, as we have seen, to measure
simultaneously its velocity and the relation of the electric charge to its
mass. In the case of the cathode rays emitted by radium, these
measurements are particularly interesting, for the reason that the rays which
compose a pencil of cathode rays are animated by very different speeds, as
is shown by the size of the stain produced on a photographic plate by a
pencil of them at first very constricted and subsequently dispersed by the
action of an electric or magnetic field. Professor Kaufmann has effected
some very careful experiments by a method he terms the method of crossed
spectra, which consists in superposing the deviations produced by a

magnetic and an electric field respectively acting in directions at right
angles one to another. He has thus been enabled by working in vacuo to
register the very different velocities which, starting in the case of certain
rays from about seven-tenths of the velocity of light, attain in other cases to
ninety-five hundredths of it.
It is thus noted that the ratio of charge to mass—which for ordinary speeds
is constant and equal to that already found by so many experiments—
diminishes slowly at first, and then very rapidly when the velocity of the
ray increases and approaches that of light. If we represent this variation by a
curve, the shape of this curve inclines us to think that the ratio tends toward
zero when the velocity tends towards that of light.
All the earlier experiments have led us to consider that the electric charge
was the same for all electrons, and it can hardly be conceived that this
charge can vary with the velocity. For in order that the relation, of which
one of the terms remains fixed, should vary, the other term necessarily
cannot remain constant. The experiments of Professor Kaufmann, therefore,
confirm the previsions of Max Abraham's theory: the mass depends on the
velocity, and increases indefinitely in proportion as this velocity approaches
that of light. These experiments, moreover, allow the numerical results of
the calculation to be compared with the values measured. This very
satisfactory comparison shows that the apparent total mass is sensibly equal
to the electromagnetic mass; the material mass of the electron is therefore
nil, and the whole of its mass is electromagnetic.
Thus the electron must be looked upon as a simple electric charge devoid of
matter. Previous examination has led us to attribute to it a mass a thousand
times less that that of the atom of hydrogen, and a more attentive study
shows that this mass was fictitious. The electromagnetic phenomena which
are produced when the electron is set in motion or a change effected in its
velocity, simply have the effect, as it were, of simulating inertia, and it is
the inertia due to the charge which has caused us to be thus deluded.
The electron is therefore simply a small volume determined at a point in the
ether, and possessing special properties; [49] this point is propagated with a
velocity which cannot exceed that of light. When this velocity is constant,
the electron creates around it in its passage an electric and a magnetic field;

round this electrified centre there exists a kind of wake, which follows it
through the ether and does not become modified so long as the velocity
remains invariable. If other electrons follow the first within a wire, their
passage along the wire will be what is called an electric current.
When the electron is subjected to an acceleration, a transverse wave is
produced, and an electromagnetic radiation is generated, of which the
character may naturally change with the manner in which the speed varies.
If the electron has a sufficiently rapid periodical movement, this wave is a
light wave; while if the electron stops suddenly, a kind of pulsation is
transmitted through the ether, and thus we obtain Röntgen rays.

§ 4. NEW VIEWS ON THE CONSTITUTION OF THE ETHER AND
OF MATTER
New and valuable information is thus afforded us regarding the properties
of the ether, but will this enable us to construct a material representation of
this medium which fills the universe, and so to solve a problem which has
baffled, as we have seen, the prolonged efforts of our predecessors?
Certain scholars seem to have cherished this hope. Dr. Larmor in particular,
as we have seen, has proposed a most ingenious image, but one which is
manifestly insufficient. The present tendency of physicists rather tends to
the opposite view; since they consider matter as a very complex object,
regarding which we wrongly imagine ourselves to be well informed
because we are so much accustomed to it, and its singular properties end by
seeming natural to us. But in all probability the ether is, in its objective
reality, much more simple, and has a better right to be considered as
fundamental.
We cannot therefore, without being very illogical, define the ether by
material properties, and it is useless labour, condemned beforehand to
sterility, to endeavour to determine it by other qualities than those of which
experiment gives us direct and exact knowledge.
The ether is defined when we know, in all its points, and in magnitude and
in direction, the two fields, electric and magnetic, which may exist in it.
These two fields may vary; we speak from habit of a movement propagated

in the ether, but the phenomenon within the reach of experiment is the
propagation of these variations.
Since the electrons, considered as a modification of the ether symmetrically
distributed round a point, perfectly counterfeit that inertia which is the
fundamental property of matter, it becomes very tempting to suppose that
matter itself is composed of a more or less complex assemblage of
electrified centres in motion.
This complexity is, in general, very great, as is demonstrated by the
examination of the luminous spectra produced by the atoms, and it is
precisely because of the compensations produced between the different
movements that the essential properties of matter—the law of the
conservation of inertia, for example—are not contrary to the hypothesis.
The forces of cohesion thus would be due to the mutual attractions which
occur in the electric and magnetic fields produced in the interior of bodies;
and it is even conceivable that there may be produced, under the influence
of these actions, a tendency to determine orientation, that is to say, that a
reason can be seen why matter may be crystallised.[50]
All the experiments effected on the conductivity of gases or metals, and on
the radiations of active bodies, have induced us to regard the atom as being
constituted by a positively charged centre having practically the same
magnitude as the atom itself, round which the electrons gravitate; and it
might evidently be supposed that this positive centre itself preserves the
fundamental characteristics of matter, and that it is the electrons alone
which no longer possess any but electromagnetic mass.
We have but little information concerning these positive particles, though
they are met with in an isolated condition, as we have seen, in the canal rays
or in the X rays.[51] It has not hitherto been possible to study them so
successfully as the electrons themselves; but that their magnitude causes
them to produce considerable perturbations in the bodies on which they fall
is manifest by the secondary emissions which complicate and mask the
primitive phenomenon. There are, however, strong reasons for thinking that
these positive centres are not simple. Thus Professor Stark attributes to
them, with experiments in proof of his opinion, the emission of the spectra
of the rays in Geissler tubes, and the complexity of the spectrum discloses

the complexity of the centre. Besides, certain peculiarities in the
conductivity of metals cannot be explained without a supposition of this
kind. So that the atom, deprived of the cathode corpuscle, would be still
liable to decomposition into elements analogous to electrons and positively
charged. Consequently nothing prevents us supposing that this centre
likewise simulates inertia by its electromagnetic properties, and is but a
condition localised in the ether.
However this may be, the edifice thus constructed, being composed of
electrons in periodical motion, necessarily grows old. The electrons become
subject to accelerations which produce a radiation towards the exterior of
the atom; and certain of them may leave the body, while the primitive
stability is, in the end, no longer assured, and a new arrangement tends to be
formed. Matter thus seems to us to undergo those transformations of which
the radio-active bodies have given us such remarkable examples.
We have already had, in fragments, these views on the constitution of
matter; a deeper study of the electron thus enables us to take up a position
from which we obtain a sharp, clear, and comprehensive grasp of the whole
and a glimpse of indefinite horizons.
It would be advantageous, however, in order to strengthen this position, that
a few objections which still menace it should be removed. The instability of
the electron is not yet sufficiently demonstrated. How is it that its charge
does not waste itself away, and what bonds assure the permanence of its
constitution?
On the other hand, the phenomena of gravitation remain a mystery. Lorentz
has endeavoured to build up a theory in which he explains attraction by
supposing that two charges of similar sign repel each other in a slightly less
degree than that in which two charges, equal but of contrary sign, attract
each other, the difference being, however, according to the calculation,
much too small to be directly observed. He has also sought to explain
gravitation by connecting it with the pressures which may be produced on
bodies by the vibratory movements which form very penetrating rays.
Recently M. Sutherland has imagined that attraction is due to the difference
of action in the convection currents produced by the positive and negative
corpuscles which constitute the atoms of the stars, and are carried along by

the astronomical motions. But these hypotheses remain rather vague, and
many authors think, like M. Langevin, that gravitation must result from
some mode of activity of the ether totally different from the electromagnetic
mode.

CHAPTER XI

THE FUTURE OF PHYSICS
It would doubtless be exceedingly rash, and certainly very presumptuous, to
seek to predict the future which may be reserved for physics. The rôle of
prophet is not a scientific one, and the most firmly established previsions of
to-day may be overthrown by the reality of to-morrow.
Nevertheless, the physicist does not shun an extrapolation of some little
scope when it is not too far from the realms of experiment; the knowledge
of the evolution accomplished of late years authorises a few suppositions as
to the direction in which progress may continue.
The reader who has deigned to follow me in the rapid excursion we have
just made through the domain of the science of Nature, will doubtless bring
back with him from his short journey the general impression that the
ancient limits to which the classic treatises still delight in restricting the
divers chapters of physics, are trampled down in all directions.
The fine straight roads traced out by the masters of the last century, and
enlarged and levelled by the labour of such numbers of workmen, are now
joined together by a crowd of small paths which furrow the field of physics.
It is not only because they cover regions as yet little explored where
discoveries are more abundant and more easy, that these cross-cuts are so
frequent, but also because a higher hope guides the seekers who engage in
these new routes.
In spite of the repeated failures which have followed the numerous attempts
of past times, the idea has not been abandoned of one day conquering the
supreme principle which must command the whole of physics.
Some physicists, no doubt, think such a synthesis to be impossible of
realisation, and that Nature is infinitely complex; but, notwithstanding all
the reserves they may make, from the philosophical point of view, as to the
legitimacy of the process, they do not hesitate to construct general
hypotheses which, in default of complete mental satisfaction, at least

furnish them with a highly convenient means of grouping an immense
number of facts till then scattered abroad.
Their error, if error there be, is beneficial, for it is one of those that Kant
would have classed among the fruitful illusions which engender the
indefinite progress of science and lead to great and important co-
ordinations.
It is, naturally, by the study of the relations existing between phenomena
apparently of very different orders that there can be any hope of reaching
the goal; and it is this which justifies the peculiar interest accorded to
researches effected in the debatable land between domains hitherto
considered as separate.
Among all the theories lately proposed, that of the ions has taken a
preponderant place; ill understood at first by some, appearing somewhat
singular, and in any case useless, to others, it met at its inception, in France
at least, with only very moderate favour.
To-day things have greatly changed, and those even who ignored it have
been seduced by the curious way in which it adapts itself to the
interpretation of the most recent experiments on very different subjects. A
very natural reaction has set in; and I might almost say that a question of
fashion has led to some exaggerations.
The electron has conquered physics, and many adore the new idol rather
blindly. Certainly we can only bow before an hypothesis which enables us
to group in the same synthesis all the discoveries on electric discharges and
on radioactive substances, and which leads to a satisfactory theory of optics
and of electricity; while by the intermediary of radiating heat it seems likely
to embrace shortly the principles of thermodynamics also. Certainly one
must admire the power of a creed which penetrates also into the domain of
mechanics and furnishes a simple representation of the essential properties
of matter; but it is right not to lose sight of the fact that an image may be a
well-founded appearance, but may not be capable of being exactly
superposed on the objective reality.
The conception of the atom of electricity, the foundation of the material
atoms, evidently enables us to penetrate further into Nature's secrets than

our predecessors; but we must not be satisfied with words, and the mystery
is not solved when, by a legitimate artifice, the difficulty has simply been
thrust further back. We have transferred to an element ever smaller and
smaller those physical qualities which in antiquity were attributed to the
whole of a substance; and then we shifted them later to those chemical
atoms which, united together, constitute this whole. To-day we pass them on
to the electrons which compose these atoms. The indivisible is thus
rendered, in a way, smaller and smaller, but we are still unacquainted with
what its substance may be. The notion of an electric charge which we
substitute for that of a material mass will permit phenomena to be united
which we thought separate, but it cannot be considered a definite
explanation, or as the term at which science must stop. It is probable,
however, that for a few years still physics will not travel beyond it. The
present hypothesis suffices for grouping known facts, and it will doubtless
enable many more to be foreseen, while new successes will further increase
its possessions.
Then the day will arrive when, like all those which have shone before it,
this seductive hypothesis will lead to more errors than discoveries. It will,
however, have been improved, and it will have become a very vast and very
complete edifice which some will not willingly abandon; for those who
have made to themselves a comfortable dwelling-place on the ruins of
ancient monuments are often too loth to leave it.
In that day the searchers who were in the van of the march after truth will
be caught up and even passed by others who will have followed a longer,
but perhaps surer road. We also have seen at work those prudent physicists
who dreaded too daring creeds, and who sought only to collect all the
documentary evidence possible, or only took for their guide a few
principles which were to them a simple generalisation of facts established
by experiments; and we have been able to prove that they also were
effecting good and highly useful work.
Neither the former nor the latter, however, carry out their work in an
isolated way, and it should be noted that most of the remarkable results of
these last years are due to physicists who have known how to combine their
efforts and to direct their activity towards a common object, while perhaps

it may not be useless to observe also that progress has been in proportion to
the material resources of our laboratories.
It is probable that in the future, as in the past, the greatest discoveries, those
which will suddenly reveal totally unknown regions, and open up entirely
new horizons, will be made by a few scholars of genius who will carry on
their patient labour in solitary meditation, and who, in order to verify their
boldest conceptions, will no doubt content themselves with the most simple
and least costly experimental apparatus. Yet for their discoveries to yield
their full harvest, for the domain to be systematically worked and desirable
results obtained, there will be more and more required the association of
willing minds, the solidarity of intelligent scholars, and it will be also
necessary for these last to have at their disposal the most delicate as well as
the most powerful instruments. These are conditions paramount at the
present day for continuous progress in experimental science.
If, as has already happened, unfortunately, in the history of science, these
conditions are not complied with; if the freedoms of the workers are
trammelled, their unity disturbed, and if material facilities are too
parsimoniously afforded them,—evolution, at present so rapid, may be
retarded, and those retrogressions which, by-the-by, have been known in all
evolutions, may occur, although even then hope in the future would not be
abolished for ever.
There are no limits to progress, and the field of our investigations has no
boundaries. Evolution will continue with invincible force. What we to-day
call the unknowable, will retreat further and further before science, which
will never stay her onward march. Thus physics will give greater and
increasing satisfaction to the mind by furnishing new interpretations of
phenomena; but it will accomplish, for the whole of society, more valuable
work still, by rendering, by the improvements it suggests, life every day
more easy and more agreeable, and by providing mankind with weapons
against the hostile forces of Nature.
FOOTNOTES
[1] I.e., the time-curve.—ED.
[2] The author seems to refer to the fact that in the standard metre, the
measurement is taken from the central one of three marks at each end of the bar.

The transverse section of the bar is an X, and the reading is made by a
microscope.—ED.
[3] I.e. 1/2000 of a millimetre.—ED.
[4] These are the magnitudes and units adopted at the International Congress of
Electricians in 1904. For their definition and explanation, see Demanet, Notes de
Physique Expérimentale (Louvain, 1905), t. iv. p. 8.—ED.
[5] "Nothing is created; nothing is lost"—ED.
[6] By isothermal diagram is meant the pattern or complex formed when the
isothermal lines are arranged in curves of which the pressure is the ordinate and
the volume the abscissa.—ED.
[7] Mr Preston thus puts it: "The law [of corresponding states] seems to be not
quite, but very nearly true for these substances [i.e. the halogen derivatives of
benzene]; but in the case of the other substances examined, the majority of these
generalizations were either only roughly true or altogether departed from"
(Theory of Heat, London, 1904, p. 514.)—ED.
[8] Methode avec retour en arriere.—ED
[9] Professor Soddy, in a paper read before the Royal Society on the 15th
November 1906, warns experimenters against vacua created by charcoal cooled
in liquid air (the method referred-to in the text), unless as much of the air as
possible is first removed with a pump and replaced by some argon-free gas.
According to him, neither helium nor argon is absorbed by charcoal. By the use
of electrically-heated calcium, he claims to have produced an almost perfect
vacuum.—ED.
[10] Another view, viz. that these inert gases are a kind of waste product of
radioactive changes, is also gaining ground. The discovery of the radioactive
mineral malacone, which gives off both helium and argon, goes to support this.
See Messrs Ketchin and Winterson's paper on the subject at the Chemical
Society, 18th October 1906.—ED.
[11] M. Poincaré is here in error. Helium has never been liquefied.—ED.
[12] Professor Quincke's last hypothesis is that all liquids on solidifying pass
through a stage intermediate between solid and liquid, in which they form what
he calls "foam-cells," and assume a viscous structure resembling that of jelly.
See Proc. Roy. Soc. A., 23rd July 1906.—ED.
[13] The metal known as "invar."—ED.
[14] The "second principle" referred to has been thus enunciated: "In every
engine that produces work there is a fall of temperature, and the maximum
output of a perfect engine—i.e. the ratio between the heat consumed in work and
the heat supplied—depends only on the extreme temperatures between which the
fluid is evolved."—Demanet, Notes de Physique Expérimentale, Louvain, 1905,
fasc. 2, p. 147. Clausius put it in a negative form, as thus: No engine can of
itself, without the aid of external agency, transfer heat from a body at low

temperature to a body at a high temperature. Cf. Ganot's Physics, 17th English
edition, § 508.—ED.
[15] See next note.—ED.
[16] M. Stephane Leduc, Professor of Biology of Nantes, has made many
experiments in this connection, and the artificial cells exhibited by him to the
Association française pour l'avancement des Sciences, at their meeting at
Grenoble in 1904 and reproduced in their "Actes," are particularly noteworthy.—
ED.
[17] That is, without receiving or emitting any heat.—ED.
[18] Dissociation must be distinguished from decomposition, which is what
occurs when the whole of a particle (compound, molecule, atom, etc.) breaks up
into its component parts. In dissociation the breaking up is only partial, and the
resultant consists of a mixture of decomposed and undecomposed parts. See
Ganot's Physics, 17th English edition, § 395, for examples.—ED.
[19] The valency or atomicity of an element may be defined as the power it
possesses of entering into compounds in a certain fixed proportion. As hydrogen
is generally taken as the standard, in practice the valency of an atom is the
number of hydrogen atoms it will combine with or replace. Thus chlorine and the
rest of the halogens, the atoms of which combine with one atom of hydrogen, are
called univalent, oxygen a bivalent element, and so on.—ED.
[20] Since this was written, however, men of science have become less
unanimous than they formerly were on this point. The veteran chemist Professor
Mendeléeff has given reasons for thinking that the ether is an inert gas with an
atomic weight a million times less than that of hydrogen, and a velocity of 2250
kilometres per second (Principles of Chemistry, Eng. ed., 1905, vol. ii. p. 526).
On the other hand, the well-known physicist Dr A.H. Bucherer, speaking at the
Naturforscherversammlung, held at Stuttgart in 1906, declared his disbelief in
the existence of the ether, which he thought could not be reconciled at once with
the Maxwellian theory and the known facts.—ED.
[21] A natural chlorate of potassium, generally of volcanic origin.—ED.
[22] That is to say, he reflected the beam of polarized light by a mirror placed at
that angle. See Turpain, Leçons élementaires de Physique, t. ii. p. 311, for details
of the experiment.—ED.
[23] It will no doubt be a shock to those whom Professor Henry Armstrong has
lately called the "mathematically-minded" to find a member of the Poincaré
family speaking disrespectfully of the science they have done so much to
illustrate. One may perhaps compare the expression in the text with M. Henri
Poincaré's remark in his last allocution to the Académie des Sciences, that
"Mathematics are sometimes a nuisance, and even a danger, when they induce us
to affirm more than we know" (Comptes-rendus, 17th December 1906).
[24] See footnote 3.
[25] I.e. 10,000 metres.—ED.

[26] By this M. Poincaré appears to mean a radiometer in which the vanes are
not entirely free to move as in the radiometer of Crookes but are suspended by
one or two threads as in the instrument devised by Professor Poynting.—ED.
[27] See especially the experiments of Professor E. Marx (Vienna), Annalen der
Physik, vol. xx. (No. 9 of 1906), pp. 677 et seq., which seem conclusive on this
point.—ED.
[28] M. Sagnac (Le Radium, Jan. 1906, p. 14), following perhaps Professors
Elster and Geitel, has lately taken up this idea anew.—ED.
[29] At least, so long as it is not introduced between the two coatings of a
condenser having a difference of potential sufficient to overcome what M. Bouty
calls its dielectric cohesion. We leave on one side this phenomenon, regarding
which M. Bouty has arrived at extremely important results by a very remarkable
series of experiments; but this question rightly belongs to a special study of
electrical phenomena which is not yet written.
[30] A full account of these experiments, which were executed at the Cavendish
Laboratory, is to be found in Philosophical Transactions, A., vol. cxcv. (1901),
pp. 193 et seq.—ED.
[31] The whole of this argument is brilliantly set forth by Professor Lorentz in a
lecture delivered to the Electrotechnikerverein at Berlin in December 1904, and
reprinted, with additions, in the Archives Néerlandaises of 1906.—ED.
[32] In his work on L'Évolution de la Matière, M. Gustave Le Bon recalls that in
1897 he published several notes in the Académie des Sciences, in which he
asserted that the properties of uranium were only a particular case of a very
general law, and that the radiations emitted did not polarize, and were akin by
their properties to the X rays.
[33] Polonium has now been shown to be no new element, but one of the
transformation products of radium. Radium itself is also thought to be derived in
some manner, not yet ascertained, from uranium. The same is the case with
actinium, which is said to come in the long run from uranium, but not so directly
as does radium. All this is described in Professor Rutherford's Radioactive
Transformations (London, 1906).—ED.
[34] This is admitted by Professor Rutherford (Radio-Activity, Camb., 1904, p.
141) and Professor Soddy (Radio-Activity, London, 1904, p. 66). Neither Mr
Whetham, in his Recent Development of Physical Science (London, 1904) nor
the Hon. R.J. Strutt in The Becquerel Rays (London, same date), both of whom
deal with the historical side of the subject, seem to have noticed the fact.—ED.
[35] It has now been shown that polonium when freshly separated emits beta
rays also; see Dr Logeman's paper in Proceedings of the Royal Society, A., 6th
September 1906.—ED.
[36] According to Professor Rutherford, in 3.77 days.—ED
[37] Professor Rutherford has lately stated that uranium may possibly produce an
emanation, but that its rate of decay must be too swift for its presence to be
verified (see Radioactive Transformations, p. 161).—ED.

[38] An actinium X was also discovered by Professor Giesel (Jahrbuch d.
Radioaktivitat, i. p. 358, 1904). Since the above was written, another product has
been found to intervene between the X substance and the emanation in the case
of actinium and thorium. They have been named radio-actinium and radio-
thorium respectively.—ED.
[39] Such a table is given on p. 169 of Rutherford's Radioactive
Transformations.—ED.
[40] This opinion, no doubt formed when Sir William Ramsay's discovery of the
formation of helium from the radium emanation was first made known, is now
less tenable. The latest theory is that the alpha particle is in fact an atom of
helium, and that the final transformation product of radium and the other
radioactive substances is lead. Cf. Rutherford, op. cit. passim.—ED.
[41] See Radioactive Transformations (p. 251). Professor Rutherford says that
"each of the alpha ray products present in one gram of radium product (sic)
expels 6.2 x 1010 alpha particles per second." He also remarks on "the
experimental difficulty of accurately determining the number of alpha particles
expelled from radium per second."—ED.
[42] See Rutherford, op. cit. p. 150.—ED.
[43] This view of the case has been made very clear by M. Gustave le Bon in
L'Évolution de la Matière (Paris, 1906). See especially pp. 36-52, where the
amount of the supposed intra-atomic energy is calculated.—ED.
[44] This is the main contention of M. Gustave Le Bon in his work last quoted.
—ED.
[45] See last note.—ED.
[46] In reality M. Sagnac operated in the converse manner. He took two equal
weights of a salt of radium and a salt of barium, which he made oscillate one
after the other in a torsion balance. Had the durations of oscillation been
different, it might be concluded that the mechanical mass is not the same for
radium as for barium.
[47] Many theories as to the cause of the lines and bands of the spectrum have
been put forward since this was written, among which that of Professor Stark
(for which see Physikalische Zeitschrift for 1906, passim) is perhaps the most
advanced. That of M. Jean Becquerel, which would attribute it to the vibration
within the atom of both negative and positive electrons, also deserves notice. A
popular account of this is given in the Athenæum of 20th April 1907.—ED.
[48] An objection not here noticed has lately been formulated with much
frankness by Professor Lorentz himself. It is one of the pillars of his theory that
only the negative electrons move when an electric current passes through a
metal, and that the positive electrons (if any such there be) remain motionless.
Yet in the experiment known as Hall's, the current is deflected by the magnetic
field to one side of the strip in certain metals, and to the opposite side in others.
This seems to show that in certain cases the positive electrons move instead of
the negative, and Professor Lorentz confesses that up to the present he can find

no valid argument against this. See Archives Néerlandaises 1906, parts 1 and 2.
—ED.
[49] This cannot be said to be yet completely proved. Cf. Sir Oliver Lodge,
Electrons, London, 1906, p. 200.—ED.
[50] The reader should, however, be warned that a theory has lately been put
forth which attempts to account for crystallisation on purely mechanical grounds.
See Messrs Barlow and Pope's "Development of the Atomic Theory" in the
Transactions of the Chemical Society, 1906.—ED.
[51] There is much reason for thinking that the canal rays do not contain positive
particles alone, but are accompanied by negative electrons of slow velocity. The
X rays are thought, as has been said above, to contain neither negative nor
positive particles, but to be merely pulses in the ether.—ED.

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