The Project Gutenberg eBook of The New Physics and Its Evolution
    
This ebook is for the use of anyone anywhere in the United States and
most other parts of the world at no cost and with almost no restrictions
whatsoever. You may copy it, give it away or re-use it under the terms
of the Project Gutenberg License included with this ebook or online
at www.gutenberg.org. If you are not located in the United States,
you will have to check the laws of the country where you are located
before using this eBook.

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

Credits: E-text prepared by Jeff Spirko, Juliet Sutherland, Jim Land, and the Project Gutenberg Online Distributed Proofreading Team


*** START OF THE PROJECT GUTENBERG EBOOK THE NEW PHYSICS AND ITS EVOLUTION ***


E-text prepared by Jeff Spirko, Juliet Sutherland, Jim Land, and the
Project Gutenberg Online Distributed Proofreading Team



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. The Electromagnetic 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




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.

[Footnote 1: I.e., the time-curve.--ED.]

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.

[Footnote 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.]

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.

[Footnote 3: I.e. 1/2000 of a millimetre.--ED.]

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]

[Footnote 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.]


§ 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.

[Footnote 5: "Nothing is created; nothing is lost"--ED.]

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.

[Footnote 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.]

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]

[Footnote 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.]

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.

[Footnote 8: Methode avec retour en arriere.--ED]

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]

[Footnote 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.]

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 -190°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]

[Footnote 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.]

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]

[Footnote 11: M. Poincaré is here in error. Helium has never been
liquefied.--ED.]


§ 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 O. 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]

[Footnote 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.]

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. Tamman 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.

[Footnote 13: The metal known as "invar."--ED.]

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.

[Footnote 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.]

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]

[Footnote 15: See next note.--ED.]

[Footnote 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.]

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]

[Footnote 17: That is, without receiving or emitting any heat.--ED.]

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.

[Footnote 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.]

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]

[Footnote 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.]

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]

[Footnote 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.]

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.

[Footnote 21: A natural chlorate of potassium, generally of volcanic
origin.--ED.]

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.

[Footnote 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.]

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]

[Footnote 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).]

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]

[Footnote 24: See footnote 3.]

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.

[Footnote 25: I.e., 10,000 metres.--ED.]

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.

[Footnote 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.]

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]

[Footnote 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.]

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]

[Footnote 28: M. Sagnac (_Le Radium_, Jan. 1906, p. 14), following
perhaps Professors Elster and Geitel, has lately taken up this idea
anew.--ED.]

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.

[Footnote 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.]

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]

[Footnote 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.]

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]

[Footnote 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.]

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.

[Footnote 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.]

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.

[Footnote 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.]


§ 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.

[Footnote 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.]

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.

[Footnote 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.]

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.

[Footnote 36: According to Professor Rutherford, in 3.77 days.--ED]

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]

[Footnote 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.]

[Footnote 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.]

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]

[Footnote 39: Such a table is given on p. 169 of Rutherford's
_Radioactive Transformations_.--ED.]


§ 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]

[Footnote 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.]

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
10^{11}.[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.

[Footnote 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 10^{10} 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.]

[Footnote 42: See Rutherford, op. cit. p. 150.--ED.]

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]

[Footnote 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.]

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]

[Footnote 44: This is the main contention of M. Gustave Le Bon in
his work last quoted.--ED.]

[Footnote 45: See last note.--ED.]

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.

[Footnote 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.]

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.

[Footnote 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.]

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]

[Footnote 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.]


§ 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.

[Footnote 49: This cannot be said to be yet completely proved. _Cf_.
Sir Oliver Lodge, _Electrons_, London, 1906, p. 200.--ED.]

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]

[Footnote 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.]

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.

[Footnote 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.]

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.





*** END OF THE PROJECT GUTENBERG EBOOK THE NEW PHYSICS AND ITS EVOLUTION ***


    

Updated editions will replace the previous one—the old editions will
be renamed.

Creating the works from print editions not protected by U.S. copyright
law means that no one owns a United States copyright in these works,
so the Foundation (and you!) can copy and distribute it in the United
States without permission and without paying copyright
royalties. Special rules, set forth in the General Terms of Use part
of this license, apply to copying and distributing Project
Gutenberg™ electronic works to protect the PROJECT GUTENBERG™
concept and trademark. Project Gutenberg is a registered trademark,
and may not be used if you charge for an eBook, except by following
the terms of the trademark license, including paying royalties for use
of the Project Gutenberg trademark. If you do not charge anything for
copies of this eBook, complying with the trademark license is very
easy. You may use this eBook for nearly any purpose such as creation
of derivative works, reports, performances and research. Project
Gutenberg eBooks may be modified and printed and given away—you may
do practically ANYTHING in the United States with eBooks not protected
by U.S. copyright law. Redistribution is subject to the trademark
license, especially commercial redistribution.


START: FULL LICENSE

THE FULL PROJECT GUTENBERG LICENSE

PLEASE READ THIS BEFORE YOU DISTRIBUTE OR USE THIS WORK

To protect the Project Gutenberg™ mission of promoting the free
distribution of electronic works, by using or distributing this work
(or any other work associated in any way with the phrase “Project
Gutenberg”), you agree to comply with all the terms of the Full
Project Gutenberg™ License available with this file or online at
www.gutenberg.org/license.

Section 1. General Terms of Use and Redistributing Project Gutenberg™
electronic works

1.A. By reading or using any part of this Project Gutenberg™
electronic work, you indicate that you have read, understand, agree to
and accept all the terms of this license and intellectual property
(trademark/copyright) agreement. If you do not agree to abide by all
the terms of this agreement, you must cease using and return or
destroy all copies of Project Gutenberg™ electronic works in your
possession. If you paid a fee for obtaining a copy of or access to a
Project Gutenberg™ electronic work and you do not agree to be bound
by the terms of this agreement, you may obtain a refund from the person
or entity to whom you paid the fee as set forth in paragraph 1.E.8.

1.B. “Project Gutenberg” is a registered trademark. It may only be
used on or associated in any way with an electronic work by people who
agree to be bound by the terms of this agreement. There are a few
things that you can do with most Project Gutenberg™ electronic works
even without complying with the full terms of this agreement. See
paragraph 1.C below. There are a lot of things you can do with Project
Gutenberg™ electronic works if you follow the terms of this
agreement and help preserve free future access to Project Gutenberg™
electronic works. See paragraph 1.E below.

1.C. The Project Gutenberg Literary Archive Foundation (“the
Foundation” or PGLAF), owns a compilation copyright in the collection
of Project Gutenberg™ electronic works. Nearly all the individual
works in the collection are in the public domain in the United
States. If an individual work is unprotected by copyright law in the
United States and you are located in the United States, we do not
claim a right to prevent you from copying, distributing, performing,
displaying or creating derivative works based on the work as long as
all references to Project Gutenberg are removed. Of course, we hope
that you will support the Project Gutenberg™ mission of promoting
free access to electronic works by freely sharing Project Gutenberg™
works in compliance with the terms of this agreement for keeping the
Project Gutenberg™ name associated with the work. You can easily
comply with the terms of this agreement by keeping this work in the
same format with its attached full Project Gutenberg™ License when
you share it without charge with others.

1.D. The copyright laws of the place where you are located also govern
what you can do with this work. Copyright laws in most countries are
in a constant state of change. If you are outside the United States,
check the laws of your country in addition to the terms of this
agreement before downloading, copying, displaying, performing,
distributing or creating derivative works based on this work or any
other Project Gutenberg™ work. The Foundation makes no
representations concerning the copyright status of any work in any
country other than the United States.

1.E. Unless you have removed all references to Project Gutenberg:

1.E.1. The following sentence, with active links to, or other
immediate access to, the full Project Gutenberg™ License must appear
prominently whenever any copy of a Project Gutenberg™ work (any work
on which the phrase “Project Gutenberg” appears, or with which the
phrase “Project Gutenberg” is associated) is accessed, displayed,
performed, viewed, copied or distributed:

    This eBook is for the use of anyone anywhere in the United States and most
    other parts of the world at no cost and with almost no restrictions
    whatsoever. You may copy it, give it away or re-use it under the terms
    of the Project Gutenberg License included with this eBook or online
    at www.gutenberg.org. If you
    are not located in the United States, you will have to check the laws
    of the country where you are located before using this eBook.
  
1.E.2. If an individual Project Gutenberg™ electronic work is
derived from texts not protected by U.S. copyright law (does not
contain a notice indicating that it is posted with permission of the
copyright holder), the work can be copied and distributed to anyone in
the United States without paying any fees or charges. If you are
redistributing or providing access to a work with the phrase “Project
Gutenberg” associated with or appearing on the work, you must comply
either with the requirements of paragraphs 1.E.1 through 1.E.7 or
obtain permission for the use of the work and the Project Gutenberg™
trademark as set forth in paragraphs 1.E.8 or 1.E.9.

1.E.3. If an individual Project Gutenberg™ electronic work is posted
with the permission of the copyright holder, your use and distribution
must comply with both paragraphs 1.E.1 through 1.E.7 and any
additional terms imposed by the copyright holder. Additional terms
will be linked to the Project Gutenberg™ License for all works
posted with the permission of the copyright holder found at the
beginning of this work.

1.E.4. Do not unlink or detach or remove the full Project Gutenberg™
License terms from this work, or any files containing a part of this
work or any other work associated with Project Gutenberg™.

1.E.5. Do not copy, display, perform, distribute or redistribute this
electronic work, or any part of this electronic work, without
prominently displaying the sentence set forth in paragraph 1.E.1 with
active links or immediate access to the full terms of the Project
Gutenberg™ License.

1.E.6. You may convert to and distribute this work in any binary,
compressed, marked up, nonproprietary or proprietary form, including
any word processing or hypertext form. However, if you provide access
to or distribute copies of a Project Gutenberg™ work in a format
other than “Plain Vanilla ASCII” or other format used in the official
version posted on the official Project Gutenberg™ website
(www.gutenberg.org), you must, at no additional cost, fee or expense
to the user, provide a copy, a means of exporting a copy, or a means
of obtaining a copy upon request, of the work in its original “Plain
Vanilla ASCII” or other form. Any alternate format must include the
full Project Gutenberg™ License as specified in paragraph 1.E.1.

1.E.7. Do not charge a fee for access to, viewing, displaying,
performing, copying or distributing any Project Gutenberg™ works
unless you comply with paragraph 1.E.8 or 1.E.9.

1.E.8. You may charge a reasonable fee for copies of or providing
access to or distributing Project Gutenberg™ electronic works
provided that:

    • You pay a royalty fee of 20% of the gross profits you derive from
        the use of Project Gutenberg™ works calculated using the method
        you already use to calculate your applicable taxes. The fee is owed
        to the owner of the Project Gutenberg™ trademark, but he has
        agreed to donate royalties under this paragraph to the Project
        Gutenberg Literary Archive Foundation. Royalty payments must be paid
        within 60 days following each date on which you prepare (or are
        legally required to prepare) your periodic tax returns. Royalty
        payments should be clearly marked as such and sent to the Project
        Gutenberg Literary Archive Foundation at the address specified in
        Section 4, “Information about donations to the Project Gutenberg
        Literary Archive Foundation.”
    
    • You provide a full refund of any money paid by a user who notifies
        you in writing (or by e-mail) within 30 days of receipt that s/he
        does not agree to the terms of the full Project Gutenberg™
        License. You must require such a user to return or destroy all
        copies of the works possessed in a physical medium and discontinue
        all use of and all access to other copies of Project Gutenberg™
        works.
    
    • You provide, in accordance with paragraph 1.F.3, a full refund of
        any money paid for a work or a replacement copy, if a defect in the
        electronic work is discovered and reported to you within 90 days of
        receipt of the work.
    
    • You comply with all other terms of this agreement for free
        distribution of Project Gutenberg™ works.
    

1.E.9. If you wish to charge a fee or distribute a Project
Gutenberg™ electronic work or group of works on different terms than
are set forth in this agreement, you must obtain permission in writing
from the Project Gutenberg Literary Archive Foundation, the manager of
the Project Gutenberg™ trademark. Contact the Foundation as set
forth in Section 3 below.

1.F.

1.F.1. Project Gutenberg volunteers and employees expend considerable
effort to identify, do copyright research on, transcribe and proofread
works not protected by U.S. copyright law in creating the Project
Gutenberg™ collection. Despite these efforts, Project Gutenberg™
electronic works, and the medium on which they may be stored, may
contain “Defects,” such as, but not limited to, incomplete, inaccurate
or corrupt data, transcription errors, a copyright or other
intellectual property infringement, a defective or damaged disk or
other medium, a computer virus, or computer codes that damage or
cannot be read by your equipment.

1.F.2. LIMITED WARRANTY, DISCLAIMER OF DAMAGES - Except for the “Right
of Replacement or Refund” described in paragraph 1.F.3, the Project
Gutenberg Literary Archive Foundation, the owner of the Project
Gutenberg™ trademark, and any other party distributing a Project
Gutenberg™ electronic work under this agreement, disclaim all
liability to you for damages, costs and expenses, including legal
fees. YOU AGREE THAT YOU HAVE NO REMEDIES FOR NEGLIGENCE, STRICT
LIABILITY, BREACH OF WARRANTY OR BREACH OF CONTRACT EXCEPT THOSE
PROVIDED IN PARAGRAPH 1.F.3. YOU AGREE THAT THE FOUNDATION, THE
TRADEMARK OWNER, AND ANY DISTRIBUTOR UNDER THIS AGREEMENT WILL NOT BE
LIABLE TO YOU FOR ACTUAL, DIRECT, INDIRECT, CONSEQUENTIAL, PUNITIVE OR
INCIDENTAL DAMAGES EVEN IF YOU GIVE NOTICE OF THE POSSIBILITY OF SUCH
DAMAGE.

1.F.3. LIMITED RIGHT OF REPLACEMENT OR REFUND - If you discover a
defect in this electronic work within 90 days of receiving it, you can
receive a refund of the money (if any) you paid for it by sending a
written explanation to the person you received the work from. If you
received the work on a physical medium, you must return the medium
with your written explanation. The person or entity that provided you
with the defective work may elect to provide a replacement copy in
lieu of a refund. If you received the work electronically, the person
or entity providing it to you may choose to give you a second
opportunity to receive the work electronically in lieu of a refund. If
the second copy is also defective, you may demand a refund in writing
without further opportunities to fix the problem.

1.F.4. Except for the limited right of replacement or refund set forth
in paragraph 1.F.3, this work is provided to you ‘AS-IS’, WITH NO
OTHER WARRANTIES OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT
LIMITED TO WARRANTIES OF MERCHANTABILITY OR FITNESS FOR ANY PURPOSE.

1.F.5. Some states do not allow disclaimers of certain implied
warranties or the exclusion or limitation of certain types of
damages. If any disclaimer or limitation set forth in this agreement
violates the law of the state applicable to this agreement, the
agreement shall be interpreted to make the maximum disclaimer or
limitation permitted by the applicable state law. The invalidity or
unenforceability of any provision of this agreement shall not void the
remaining provisions.

1.F.6. INDEMNITY - You agree to indemnify and hold the Foundation, the
trademark owner, any agent or employee of the Foundation, anyone
providing copies of Project Gutenberg™ electronic works in
accordance with this agreement, and any volunteers associated with the
production, promotion and distribution of Project Gutenberg™
electronic works, harmless from all liability, costs and expenses,
including legal fees, that arise directly or indirectly from any of
the following which you do or cause to occur: (a) distribution of this
or any Project Gutenberg™ work, (b) alteration, modification, or
additions or deletions to any Project Gutenberg™ work, and (c) any
Defect you cause.

Section 2. Information about the Mission of Project Gutenberg™

Project Gutenberg™ is synonymous with the free distribution of
electronic works in formats readable by the widest variety of
computers including obsolete, old, middle-aged and new computers. It
exists because of the efforts of hundreds of volunteers and donations
from people in all walks of life.

Volunteers and financial support to provide volunteers with the
assistance they need are critical to reaching Project Gutenberg™’s
goals and ensuring that the Project Gutenberg™ collection will
remain freely available for generations to come. In 2001, the Project
Gutenberg Literary Archive Foundation was created to provide a secure
and permanent future for Project Gutenberg™ and future
generations. To learn more about the Project Gutenberg Literary
Archive Foundation and how your efforts and donations can help, see
Sections 3 and 4 and the Foundation information page at www.gutenberg.org.

Section 3. Information about the Project Gutenberg Literary Archive Foundation

The Project Gutenberg Literary Archive Foundation is a non-profit
501(c)(3) educational corporation organized under the laws of the
state of Mississippi and granted tax exempt status by the Internal
Revenue Service. The Foundation’s EIN or federal tax identification
number is 64-6221541. Contributions to the Project Gutenberg Literary
Archive Foundation are tax deductible to the full extent permitted by
U.S. federal laws and your state’s laws.

The Foundation’s business office is located at 809 North 1500 West,
Salt Lake City, UT 84116, (801) 596-1887. Email contact links and up
to date contact information can be found at the Foundation’s website
and official page at www.gutenberg.org/contact

Section 4. Information about Donations to the Project Gutenberg
Literary Archive Foundation

Project Gutenberg™ depends upon and cannot survive without widespread
public support and donations to carry out its mission of
increasing the number of public domain and licensed works that can be
freely distributed in machine-readable form accessible by the widest
array of equipment including outdated equipment. Many small donations
($1 to $5,000) are particularly important to maintaining tax exempt
status with the IRS.

The Foundation is committed to complying with the laws regulating
charities and charitable donations in all 50 states of the United
States. Compliance requirements are not uniform and it takes a
considerable effort, much paperwork and many fees to meet and keep up
with these requirements. We do not solicit donations in locations
where we have not received written confirmation of compliance. To SEND
DONATIONS or determine the status of compliance for any particular state
visit www.gutenberg.org/donate.

While we cannot and do not solicit contributions from states where we
have not met the solicitation requirements, we know of no prohibition
against accepting unsolicited donations from donors in such states who
approach us with offers to donate.

International donations are gratefully accepted, but we cannot make
any statements concerning tax treatment of donations received from
outside the United States. U.S. laws alone swamp our small staff.

Please check the Project Gutenberg web pages for current donation
methods and addresses. Donations are accepted in a number of other
ways including checks, online payments and credit card donations. To
donate, please visit: www.gutenberg.org/donate.

Section 5. General Information About Project Gutenberg™ electronic works

Professor Michael S. Hart was the originator of the Project
Gutenberg™ concept of a library of electronic works that could be
freely shared with anyone. For forty years, he produced and
distributed Project Gutenberg™ eBooks with only a loose network of
volunteer support.

Project Gutenberg™ eBooks are often created from several printed
editions, all of which are confirmed as not protected by copyright in
the U.S. unless a copyright notice is included. Thus, we do not
necessarily keep eBooks in compliance with any particular paper
edition.

Most people start at our website which has the main PG search
facility: www.gutenberg.org.

This website includes information about Project Gutenberg™,
including how to make donations to the Project Gutenberg Literary
Archive Foundation, how to help produce our new eBooks, and how to
subscribe to our email newsletter to hear about new eBooks.