The International Scientific Series

THE NEW PHYSICS AND ITS EVOLUTION

by

LUCIEN POINCARÉInspéctéur-General de l'Instruction Publique

Being the Authorized Translation of _LA PHYSIQUE MODERNE, SON ÉVOLUTION_

New YorkD. Appleton and Company

1909

Prefatory Note

M. Lucien Poincaré is one of the distinguished family ofmathematicians which has during the last few years given aMinister of Finance to the Republic and a President to theAcadémie des Sciences. He is also one of the nineteenInspectors-General of Public Instruction who are charged with theduty of visiting the different universities and _lycées_ inFrance and of reporting upon the state of the studies therepursued. Hence he is in an excellent position to appreciate atits proper value the extraordinary change which has latelyrevolutionized physical science, while his official position haskept him aloof from the controversies aroused by the discovery ofradium and by recent speculations on the constitution of matter. 

M. Poincaré's object and method in writing the book aresufficiently explained in the preface which follows; but it maybe remarked that the best of methods has its defects, and theexcessive condensation which has alone made it possible toinclude the last decade's discoveries in physical science withina compass of some 300 pages has, perhaps, made the facts herenoted assimilable with difficulty by the untrained reader. Toremedy this as far as possible, I have prefixed to the presenttranslation a table of contents so extended as to form a fairlycomplete digest of the book, while full indexes of authors andsubjects have also been added. The few notes necessary either forbetter elucidation of the terms employed, or for giving accountof discoveries made while these pages were passing through thepress, may be distinguished from the author's own by thesignature "ED. "

THE EDITOR. 

ROYAL INSTITUTION OF GREAT BRITAIN, April 1907. 

Author's Preface

During the last ten years so many works have accumulated in thedomain of Physics, and so many new theories have been propounded, that those who follow with interest the progress of science, andeven some professed scholars, absorbed as they are in their ownspecial studies, find themselves at sea in a confusion moreapparent than real. 

It has therefore occurred to me that it might be useful to writea book which, while avoiding too great insistence on purelytechnical details, should try to make known the general resultsat which physicists have lately arrived, and to indicate thedirection and import which should be ascribed to thosespeculations on the constitution of matter, and the discussionson the nature of first principles, to which it has become, so tospeak, the fashion of the present day to devote oneself. 

I have endeavoured throughout to rely only on the experiments inwhich we can place the most confidence, and, above all, to showhow the ideas prevailing at the present day have been formed, bytracing their evolution, and rapidly examining the successivetransformations which have brought them to their presentcondition. 

In order to understand the text, the reader will have no need toconsult any treatise on physics, for I have throughout given thenecessary definitions and set forth the fundamental facts. Moreover, while strictly employing exact expressions, I haveavoided the use of mathematical language. Algebra is an admirabletongue, but there are many occasions where it can only be usedwith much discretion. 

Nothing would be easier than to point out many great omissionsfrom this little volume; but some, at all events, are notinvoluntary. 

Certain questions which are still too confused have been put onone side, as have a few others which form an important collectionfor a special study to be possibly made later. Thus, as regardselectrical phenomena, the relations between electricity andoptics, as also the theories of ionization, the electronichypothesis, etc. , have been treated at some length; but it hasnot been thought necessary to dilate upon the modes of productionand utilization of the current, upon the phenomena of magnetism, or upon all the applications which belong to the domain ofElectrotechnics. 

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 ofDescartes: all phenomena reduced to matter and movement--Modern physicists challenge this: physical, unlikemechanical, phenomena seldom reversible--Two schools, one considering experimental laws imperative, the othermerely studying relations of magnitudes: both teachsomething 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 ofStandard Metre--Unit of wave-lengths preferable--TheInternational Metre

§ 3. The Measure of Mass: Distinction betweenmass and weight--Objections to legal kilogrammeand its precision--Possible improvement

§ 4. The Measure of Time: Unit of time thesecond--Alternative units proposed--Improvements inchronometry and invar

§ 5. The Measure of Temperature: Fundamentaland derived units--Ordinary unit of temperaturepurely arbitrary--Absolute unit mass of H at pressureof 1 m. Of Hg at 0° C. --Divergence of thermometricand thermodynamic scales--Helium thermometer for low, thermo-electric couple for high, temperatures--Lummerand Pringsheim's improvements in thermometry. 

§ 6. Derived Units and Measure of Energy:Importance of erg as unit--Calorimeter usual means ofdetermination--Photometric units. 

§ 7. Measure of Physical Constants: Constant ofgravitation--Discoveries of Cavendish, Vernon Boys, Eötvös, Richarz and Krigar-Menzel--Michelson'simprovements on Fizeau and Foucault's experiments--Measure of speed of light. 

CHAPTER III

PRINCIPLES

§ 1. The Principles of Physics: The Principles ofMechanics affected by recent discoveries--Is massindestructible?--Landolt and Heydweiller's experiments--Lavoisier's law only approximately true--Curie'sprinciple 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'sdrawbacks--Error of those who would make mechanics partof energetics--Verdet's predictions--Rankine inventorof energetics--Usefulness of Work as standard form ofenergy--Physicists who think matter form of energy--Objections to this--Philosophical value of conservationdoctrine. 

§ 3. The Principle of Carnot and Clausius:Originality of Carnot's principle that fall oftemperature necessary for production of work by heat--Clausius' postulate that heat cannot pass from cold tohot body without accessory phenomena--Entropy resultof this--Definition of entropy--Entropy tends to increaseincessantly--A magnitude which measures evolutionof system--Clausius' and Kelvin's deduction thatheat end of all energy in Universe--Objection to this--Carnot's principle not necessarily referable to mechanics--Brownian movements--Lippmann's objection tokinetic hypothesis. 

§ 4. Thermodynamics: Historical work of Massieu, Willard Gibbs, Helmholtz, and Duhem--Willard Gibbsfounder of thermodynamic statics, Van t'Hoff itsreviver--The Phase Law--Raveau explains it withoutthermodynamics. 

§ 5. Atomism: Connection of subject with precedingHannequin's essay on the atomic hypothesis--Molecularphysics in disfavour--Surface-tension, etc. , vanisheswhen molecule reached--Size of molecule--Kinetictheory of gases--Willard Gibbs and Boltzmann introduceinto it law of probabilities--Mean free path of gaseousmolecules--Application to optics--Final division ofmatter. 

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--Discoveryof corresponding states--Amagat's superposeddiagrams--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 liquefyinggases--Apparatus of Claude described--Dewar'sexperiments--Modification of electrical properties ofmatter by extreme cold: of magnetic and chemical--Vitality of bacteria unaltered--Ramsay's discoveryof rare gases of atmosphere--Their distribution innature--Liquid hydrogen--Helium. 

§ 3. Solids and Liquids: Continuity of Solid and LiquidStates--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 crystallineand liquid states. 

§ 4. The Deformation of Solids: Elasticity--Hoocke's, Bach's, and Bouasse's researches--Voigton the elasticity of crystals--Elastic and permanentdeformations--Brillouin's states of unstableequilibria--Duhem and the thermodynamic postulates--Experimental confirmation--Guillaume's researcheson nickel steel--Alloys. 

CHAPTER V

SOLUTIONS AND ELECTROLYTIC DISSOCIATION

§ 1. Solution: Kirchhoff's, Gibb's, Duhem's and Vant'Hoff's researches. 

§ 2. Osmosis: History of phenomenon--Traube andbiologists establish existence of semi-permeablewalls--Villard's experiments with gases--Pfeffershows osmotic pressure proportional to concentration--Disagreement as to cause of phenomenon. 

§ 3. Osmosis applied to Solution: Van t'Hoff'sdiscoveries--Analogy between dissolved body andperfect gas--Faults in analogy. 

§ 4. Electrolytic Dissociation: Van t'Hoff's andArrhenius' researches--Ionic hypothesis of--Fierceopposition to at first--Arrhenius' ideas now triumphant--Advantages of Arrhenius' hypothesis--"The ionswhich react"--Ostwald's conclusions from this--Nernst'stheory of Electrolysis--Electrolysis of gases makeselectronic 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 dueto Descartes--Ether must be imponderable--Fresnel showslight vibrations to be transverse--Transverse vibrationscannot exist in fluid--Ether must be discontinuous. 

§ 2. Radiations: Wave-lengths and theirmeasurements--Rubens' and Lenard's researches--Stationary waves and colour-photography--Fresnel'shypothesis opposed by Neumann--Wiener's and Cotton'sexperiments. 

§ 3. The Electromagnetic Ether: Ampère's advocacyof mathematical expression--Faraday first showsinfluence of medium in electricity--Maxwell's proofthat light-waves electromagnetic--Hisunintelligibility--Required confirmation of theory by Hertz. 

§ 4. Electrical Oscillations: Hertz's experiments--Blondlot proves electromagnetic disturbance propagatedwith speed of light--Discovery of ether wavesintermediate between Hertzian and visible ones--Rubens'and Nichols' experiments--Hertzian and light rayscontrasted--Pressure of light. 

§ 5. The X-Rays: Röntgen's discovery--Propertiesof X-rays--Not homogeneous--Rutherford and M'Clung'sexperiments on energy corresponding to--Barkla'sexperiments on polarisation of--Their speed that oflight--Are they merely ultra-violet?--Stokes andWiechert's theory of independent pulsations generallypreferred--J. J. Thomson's idea of their formation--Sutherland's and Le Bon's theories--The N-Rays--Blondlot's discovery--Experiments cannot be repeatedoutside France--Gutton and Mascart's confirmation--Negative experiments prove nothing--Supposedwave-length of N-rays. 

§ 6. The Ether and Gravitation: Descartes'and Newton's ideas on gravitation--Its speed andother extraordinary characteristics--Lesage'shypothesis--Crémieux' experiments with drops ofliquids--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 asreturn wire during siege of Paris--Johnson and Melhuish'sIndian experiments--Preece's telegraph over BristolChannel--He welcomes Marconi. 

§ 4. Early attempts at transmission of messages throughether--Experiments of Rathenau and others. 

§ 5. Forerunners of ether telegraphy: Clerk Maxwelland Hertz--Dolbear, Hughes, and Graham Bell. 

§ 6. Telegraphy by Hertzian waves first suggestedby Threlfall--Crookes', Tesla's, Lodge's, Rutherford's, and Popoff's contributions--Marconifirst 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 deForest's, and Fessenden's systems make use of earth--Hertz and Marconi entitled to foremost place amongdiscoverers. 

CHAPTER VIII

THE CONDUCTIVITY OF GASES AND THE IONS

§ 1. The Conductivity of Gases: Relations of matter toether cardinal problem--Conductivity of gases at firstmisapprehended--Erman's forgotten researches--Giesefirst notices phenomenon--Experiment with X-rays--J. J. Thomson's interpretation--Ionized gas not obedientto Ohm's law--Discharge of charged conductors byionized gas. 

§ 2. The Condensation of water-vapour by Ions:Vapour will not condense without nucleus--Wilson'sexperiments on electrical condensation--Wilson andThomson's counting experiment--Twenty million ionsper c. Cm. Of gas--Estimate of charge borne by ion--Speed of charges--Zeleny's and Langevin'sexperiments--Negative ions 1/1000 of size ofatoms--Natural unit of electricity or electrons. 

§ 3. How Ions are Produced: Various causesof ionization--Moreau's experiments with alkalinesalts--Barus and Bloch on ionization by phosphorusvapours--Ionization always result of shock. 

§ 4. Electrons in Metals: Movement ofelectrons in metals foreshadowed by Weber--Giese's, Riecke's, Drude's, and J. J. Thomson's researches--Pathof ions in metals and conduction of heat--Theory ofLorentz--Hesehus' explanation of electrification bycontact--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 negativecharge--Cathode rays give rise to X-rays--The canalrays--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 Niepcede St Victor and Becquerel--General radioactivity ofmatter--Le Bon's and Rutherford's comparison of uranicwith X rays--Pierre and Mme. Curie's discovery ofpolonium and radium--Their characteristics--Debiernediscovers actinium. 

§ 3. Radiations and Emanations of RadioactiveBodies: Giesel's, Becquerel's, and Rutherford'sResearches--Alpha, beta, and gamma rays--Sagnac'ssecondary rays--Crookes' spinthariscope--The emanation--Ramsay and Soddy's researches upon it--Transformationsof radioactive bodies--Their order. 

§ 4. Disaggregation of Matter and Atomic Energy:Actual transformations of matter in radioactive bodies--Helium or lead final product--Ultimate disappearanceof radium from earth--Energy liberated by radium:its amount and source--Suggested models of radioactiveatoms--Generalization from radioactive phenomena-Le Bon's theories--Ballistic hypothesis generallyadmitted--Does energy come from without--Sagnac'sexperiments--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--Emissionand absorption phenomena show reciprocal action--Laws of radiation--Radiation of gases--Production ofspectrum--Differences between light and sound variationsshow difference of media--Cauchy's, Briot's, Carvallo'sand Boussinesq's researches--Helmholtz's andPoincaré's electromagnetic theories of dispersion. 

§ 2. The Theory of Lorentz:--Mechanics failsto explain relations between ether and matter--Lorentzpredicts action of magnet on spectrum--Zeeman's experiment--Later researches upon Zeeman effect--Multiplicity of electrons--Lorentz's explanation ofthermoelectric phenomena by electrons--Maxwell's andLorentz's theories do not agree--Lorentz's probably morecorrect--Earth's movement in relation to ether. 

§ 3. The Mass of Electrons: Thomson's andMax Abraham's view that inertia of charged body dueto charge--Longitudinal and transversal mass--Speedof electrons cannot exceed that of light--Ratio ofcharge to mass and its variation--Electron simpleelectric charge--Phenomena produced by its acceleration. 

§ 4. New Views on Ether and Matter:Insufficiency of Larmor's view--Ether definableby electric and magnetic fields--Is matter all electrons?Atom probably positive centre surrounded bynegative electrons--Ignorance concerning positiveparticles--Successive transformations of matter probable--Gravitation still unaccounted for. 

CHAPTER XI

THE FUTURE OF PHYSICS

Persistence of ambition to discover supreme principlein physics--Supremacy of electron theory at presenttime--Doubtless destined to disappear like others--Constant progress of science predicted--Immense fieldopen 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 abreastof the movement in science, from seeing its mental habits every dayupset, and from occasionally witnessing unexpected discoveries thatproduce a more lively sensation from their reaction on social life, isled to suppose that we live in a really exceptional epoch, scored byprofound crises and illustrated by extraordinary discoveries, whosesingularity surpasses everything known in the past. Thus we often hearit said that physics, in particular, has of late years undergone averitable revolution; that all its principles have been made new, thatall the edifices constructed by our fathers have been overthrown, andthat on the field thus cleared has sprung up the most abundant harvestthat 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 quantityof seekers has considerably increased in all countries, while theirquality has not diminished. We should be sustaining an absoluteparadox, and at the same time committing a crying injustice, were weto contest the high importance of recent progress, and to seek todiminish the glory of contemporary physicists. Yet it may be as wellnot to give way to exaggerations, however pardonable, and to guardagainst facile illusions. On closer examination it will be seen thatour 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 transformedand under an aspect until then absolutely unknown. 

Let us take an example which is salient enough; for, however arbitrarythe conventional division of time may appear to a physicist's eyes, itis natural, when instituting a comparison between two epochs, tochoose those which extend over a space of half a score of years, andare 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 ofmind of an erudite amateur who had read and understood the chiefpublications on physical research between 1800 and 1810. 

Let us suppose that this intelligent and attentive spectator witnessedin 1800 the discovery of the galvanic battery by Volta. He might fromthat moment have felt a presentiment that a prodigious transformationwas about to occur in our mode of regarding electrical phenomena. Brought up in the ideas of Coulomb and Franklin, he might till thenhave imagined that electricity had unveiled nearly all its mysteries, when an entirely original apparatus suddenly gave birth toapplications of the highest interest, and excited the blossoming oftheories of immense philosophical extent. 

In the treatises on physics published a little later, we find tracesof the astonishment produced by this sudden revelation of a new world. "Electricity, " wrote the Abbé Haüy, "enriched by the labour of so manydistinguished physicists, seemed to have reached the term when ascience has no further important steps before it, and only leaves tothose who cultivate it the hope of confirming the discoveries of theirpredecessors, and of casting a brighter light on the truths revealed. One would have thought that all researches for diversifying theresults of experiment were exhausted, and that theory itself couldonly be augmented by the addition of a greater degree of precision tothe applications of principles already known. While science thusappeared to be making for repose, the phenomena of the convulsivemovements observed by Galvani in the muscles of a frog when connectedby metal were brought to the attention and astonishment ofphysicists. .. . Volta, in that Italy which had been the cradle of thenew knowledge, discovered the principle of its true theory in a factwhich reduces the explanation of all the phenomena in question to thesimple contact of two substances of different nature. This fact becamein his hands the germ of the admirable apparatus to which its mannerof being and its fecundity assign one of the chief places among thosewith which the genius of mankind has enriched physics. "

Shortly afterwards, our amateur would learn that Carlisle andNicholson had decomposed water by the aid of a battery; then, thatDavy, in 1803, had produced, by the help of the same battery, a quiteunexpected phenomenon, and had succeeded in preparing metals endowedwith marvellous properties, beginning with substances of an earthyappearance which had been known for a long time, but whose real naturehad not been discovered. 

In another order of ideas, surprises as prodigious would wait for ouramateur. Commencing with 1802, he might have read the admirable seriesof memoirs which Young then published, and might thereby have learnedhow the study of the phenomena of diffraction led to the belief thatthe undulation theory, which, since the works of Newton seemedirretrievably condemned, was, on the contrary, beginning quite a newlife. A little later--in 1808--he might have witnessed the discoverymade by Malus of polarization by reflexion, and would have been ableto note, no doubt with stupefaction, that under certain conditions aray of light loses the property of being reflected. 

He might also have heard of one Rumford, who was then promulgatingvery singular ideas on the nature of heat, who thought that the thenclassical notions might be false, that caloric does not exist as afluid, and who, in 1804, even demonstrated that heat is created byfriction. A few years later he would learn that Charles had enunciateda capital law on the dilatation of gases; that Pierre Prevost, in1809, was making a study, full of original ideas, on radiant heat. Inthe meantime he would not have failed to read volumes iii. And iv. Ofthe _Mecanique celeste_ of Laplace, published in 1804 and 1805, and hemight, no doubt, have thought that before long mathematics wouldenable physical science to develop with unforeseen safety. 

All these results may doubtless be compared in importance with thepresent discoveries. When strange metals like potassium and sodiumwere isolated by an entirely new method, the astonishment must havebeen on a par with that caused in our time by the magnificentdiscovery of radium. The polarization of light is a phenomenon asundoubtedly singular as the existence of the X rays; and the upheavalproduced in natural philosophy by the theories of the disintegrationof matter and the ideas concerning electrons is probably not moreconsiderable than that produced in the theories of light and heat bythe works of Young and Rumford. 

If we now disentangle ourselves from contingencies, it will beunderstood that in reality physical science progresses by evolutionrather than by revolution. Its march is continuous. The facts whichour theories enable us to discover, subsist and are linked togetherlong after these theories have disappeared. Out of the materials offormer edifices overthrown, new dwellings are constantly beingreconstructed. 

The labour of our forerunners never wholly perishes. The ideas ofyesterday prepare for those of to-morrow; they contain them, so tospeak, _in potentia_. Science is in some sort a living organism, whichgives birth to an indefinite series of new beings taking the places ofthe old, and which evolves according to the nature of its environment, adapting itself to external conditions, and healing at every step thewounds which contact with reality may have occasioned. 

Sometimes this evolution is rapid, sometimes it is slow enough; but itobeys the ordinary laws. The wants imposed by its surroundings createcertain organs in science. The problems set to physicists by theengineer who wishes to facilitate transport or to produce betterillumination, or by the doctor who seeks to know how such and such aremedy acts, or, again, by the physiologist desirous of understandingthe mechanism of the gaseous and liquid exchanges between the cell andthe outer medium, cause new chapters in physics to appear, and suggestresearches 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 theyare placed are not equally favourable. Sometimes a whole series ofquestions will appear forgotten, and will live only with a languishingexistence; and then some accidental circumstance suddenly brings themnew life, and they become the object of manifold labours, engrosspublic attention, and invade nearly the whole domain of science. 

We have in our own day witnessed such a spectacle. The discovery ofthe X rays--a discovery which physicists no doubt consider as thelogical outcome of researches long pursued by a few scholars workingin silence and obscurity on an otherwise much neglected subject--seemed to the public eye to have inaugurated a new era in the historyof physics. If, as is the case, however, the extraordinary scientificmovement provoked by Röntgen's sensational experiments has a veryremote origin, it has, at least, been singularly quickened by thefavourable conditions created by the interest aroused in itsastonishing 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 offashion, we cannot, if we are to note in this book the stage actuallyreached in the continuous march of physics, refrain from giving aclearly preponderant place to the questions suggested by the study ofthe new radiations. At the present time it is these questions whichmove us the most; they have shown us unknown horizons, and towards thefields recently opened to scientific activity the daily increasingcrowd of searchers rushes in rather disorderly fashion. 

One of the most interesting consequences of the recent discoveries hasbeen to rehabilitate in the eyes of scholars, speculations relating tothe constitution of matter, and, in a more general way, metaphysicalproblems. Philosophy has, of course, never been completely separatedfrom science; but in times past many physicists dissociated themselvesfrom studies which they looked upon as unreal word-squabbles, andsometimes not unreasonably abstained from joining in discussions whichseemed to them idle and of rather puerile subtlety. They had seen theruin of most of the systems built up _a priori_ by daringphilosophers, and deemed it more prudent to listen to the advice givenby Kirchhoff and "to substitute the description of facts for a shamexplanation of nature. "

It should however be remarked that these physicists somewhat deceivedthemselves as to the value of their caution, and that the mistrustthey manifested towards philosophical speculations did not precludetheir admitting, unknown to themselves, certain axioms which they didnot discuss, but which are, properly speaking, metaphysicalconceptions. They were unconsciously speaking a language taught themby their predecessors, of which they made no attempt to discover theorigin. It is thus that it was readily considered evident that physicsmust necessarily some day re-enter the domain of mechanics, and thenceit was postulated that everything in nature is due to movement. We, further, accepted the principles of the classical mechanics withoutdiscussing their legitimacy. 

This state of mind was, even of late years, that of the mostillustrious physicists. It is manifested, quite sincerely and withoutthe slightest reserve, in all the classical works devoted to physics. Thus Verdet, an illustrious professor who has had the greatest andmost happy influence on the intellectual formation of a wholegeneration of scholars, and whose works are even at the present dayvery often consulted, wrote: "The true problem of the physicist isalways to reduce all phenomena to that which seems to us the simplestand clearest, that is to say, to movement. " In his celebrated courseof lectures at l'École Polytechnique, Jamin likewise said: "Physicswill one day form a chapter of general mechanics;" and in the prefaceto his excellent course of lectures on physics, M. Violle, in 1884, thus expresses himself: "The science of nature tends towards mechanicsby a necessary evolution, the physicist being able to establish solidtheories only on the laws of movement. " The same idea is again metwith in the words of Cornu in 1896: "The general tendency should be toshow how the facts observed and the phenomena measured, though firstbrought together by empirical laws, end, by the impulse of successiveprogressions, in coming under the general laws of rational mechanics;"and the same physicist showed clearly that in his mind this connexionof phenomena with mechanics had a deep and philosophical reason, when, in the fine discourse pronounced by him at the opening ceremony of theCongrès de Physique in 1900, he exclaimed: "The mind of Descartessoars over modern physics, or rather, I should say, he is theirluminary. The further we penetrate into the knowledge of naturalphenomena, the clearer and the more developed becomes the boldCartesian conception regarding the mechanism of the universe. There isnothing in the physical world but matter and movement. "

If we adopt this conception, we are led to construct mechanicalrepresentations of the material world, and to imagine movements in thedifferent parts of bodies capable of reproducing all themanifestations of nature. The kinematic knowledge of these movements, that is to say, the determination of the position, speed, andacceleration at a given moment of all the parts of the system, or, onthe other hand, their dynamical study, enabling us to know what is theaction of these parts on each other, would then be sufficient toenable us to foretell all that can occur in the domain of nature. 

This was the great thought clearly expressed by the Encyclopædists ofthe eighteenth century; and if the necessity of interpreting thephenomena of electricity or light led the physicists of last centuryto imagine particular fluids which seemed to obey with some difficultythe ordinary rules of mechanics, these physicists still continued toretain their hope in the future, and to treat the idea of Descartes asan ideal to be reached sooner or later. 

Certain scholars--particularly those of the English School--outrunningexperiment, and pushing things to extremes, took pleasure in proposingvery curious mechanical models which were often strange images ofreality. The most illustrious of them, Lord Kelvin, may be consideredas their representative type, and he has himself said: "It seems to methat the true sense of the question, Do we or do we not understand aparticular subject in physics? is--Can we make a mechanical modelwhich corresponds to it? I am never satisfied so long as I have beenunable to make a mechanical model of the object. If I am able to doso, I understand it. If I cannot make such a model, I do notunderstand it. " But it must be acknowledged that some of the modelsthus devised have become excessively complicated, and thiscomplication has for a long time discouraged all but very bold minds. In addition, when it became a question of penetrating into themechanism of molecules, and we were no longer satisfied to look atmatter as a mass, the mechanical solutions seemed undetermined and thestability of the edifices thus constructed was insufficientlydemonstrated. 

Returning then to our starting-point, many contemporary physicistswish to subject Descartes' idea to strict criticism. From thephilosophical point of view, they first enquire whether it is reallydemonstrated that there exists nothing else in the knowable thanmatter and movement. They ask themselves whether it is not habit andtradition in particular which lead us to ascribe to mechanics theorigin of phenomena. Perhaps also a question of sense here comes in. Our senses, which are, after all, the only windows open towardsexternal reality, give us a view of one side of the world only;evidently we only know the universe by the relations which existbetween it and our organisms, and these organisms are peculiarlysensitive to movement. 

Nothing, however, proves that those acquisitions which are the mostancient in historical order ought, in the development of science, toremain the basis of our knowledge. Nor does any theory prove that ourperceptions are an exact indication of reality. Many reasons, on thecontrary, might be invoked which tend to compel us to see in naturephenomena which cannot be reduced to movement. 

Mechanics as ordinarily understood is the study of reversiblephenomena. If there be given to the parameter which representstime, [1] and which has assumed increasing values during the durationof the phenomena, decreasing values which make it go the opposite way, the whole system will again pass through exactly the same stages asbefore, and all the phenomena will unfold themselves in reversedorder. In physics, the contrary rule appears very general, andreversibility generally does not exist. It is an ideal and limitedcase, which may be sometimes approached, but can never, strictlyspeaking, be met with in its entirety. No physical phenomenon everrecommences in an identical manner if its direction be altered. It istrue that certain mathematicians warn us that a mechanics can bedevised in which reversibility would no longer be the rule, but thebold 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 explanationof a phenomenon can be given, we can find an infinity of others whichlikewise account for all the peculiarities revealed by experiment. But, as a matter of fact, no one has ever succeeded in giving anindisputable 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 systemsdevised by Helmholtz, whereby we ought to divide variable things intotwo classes, some accessible, and the others now and for ever unknown, we should never manage to construct an edifice to contain all theknown facts. Even the very comprehensive mechanics of a Hertz failswhere the classical mechanics has not succeeded. 

Deeming this check irremediable, many contemporary physicists give upattempts which they look upon as condemned beforehand, and adopt, toguide them in their researches, a method which at first sight appearsmuch more modest, and also much more sure. They make up their mindsnot to see at once to the bottom of things; they no longer seek tosuddenly strip the last veils from nature, and to divine her supremesecrets; but they work prudently and advance but slowly, while on theground thus conquered foot by foot they endeavour to establishthemselves firmly. They study the various magnitudes directlyaccessible to their observation without busying themselves as to theiressence. 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, anddiscover between these magnitudes mutual relations, while they thussucceed in enunciating laws which translate and sum up their labours. 

These empirical laws, however, themselves bring about by induction thepromulgation of more general laws, which are termed principles. Theseprinciples are originally only the results of experiments, andexperiment allows them besides to be checked, and their more or lesshigh degree of generality to be verified. When they have been thusdefinitely 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, andtheir very general form gives them a philosophical appearance, whilewe cannot long resist the temptation of regarding them as metaphysicaldogmas. It thus happens that the least bold physicists, those who havewanted to show themselves the most reserved, are themselves led toforget the experimental character of the laws they have propounded, and to see in them imperious beings whose authority, placed above allverification, 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 contentthemselves with representing phenomena by equations, and think thatthey ought to submit to calculation magnitudes experimentallydetermined, without asking themselves whether these calculationsretain a physical meaning. They are thus led to reconstruct a physicsin which there again appears the idea of quality, understood, ofcourse, not in the scholastic sense, since from this quality we canargue with some precision by representing it under numerical symbols, but still constituting an element of differentiation and ofheterogeneity. 

Notwithstanding the errors they may lead to if carried to excess, boththese doctrines render, as a whole, most important service. It is nobad thing that these contradictory tendencies should subsist, for thisvariety in the conception of phenomena gives to actual science acharacter of intense life and of veritable youth, capable ofimpassioned efforts towards the truth. Spectators who see such movingand varied pictures passing before them, experience the feeling thatthere no longer exist systems fixed in an immobility which seems thatof death. They feel that nothing is unchangeable; that ceaselesstransformations are taking place before their eyes; and that thiscontinuous evolution and perpetual change are the necessary conditionsof progress. 

A great number of seekers, moreover, show themselves on their ownaccount perfectly eclectic. They adopt, according to their needs, suchor such a manner of looking at nature, and do not hesitate to utilizevery different images when they appear to them useful and convenient. And, without doubt, they are not wrong, since these images are onlysymbols convenient for language. They allow facts to be grouped andassociated, but only present a fairly distant resemblance with theobjective reality. Hence it is not forbidden to multiply and to modifythem according to circumstances. The really essential thing is tohave, as a guide through the unknown, a map which certainly does notclaim to represent all the aspects of nature, but which, having beendrawn up according to predetermined rules, allows us to follow anascertained road in the eternal journey towards the truth. 

Among the provisional theories which are thus willingly constructed byscholars on their journey, like edifices hastily run up to receive anunforeseen harvest, some still appear very bold and very singular. Abandoning the search after mechanical models for all electricalphenomena, certain physicists reverse, so to speak, the conditions ofthe problem, and ask themselves whether, instead of giving amechanical interpretation to electricity, they may not, on thecontrary, give an electrical interpretation to the phenomena of matterand motion, and thus merge mechanics itself in electricity. One thussees dawning afresh the eternal hope of co-ordinating all naturalphenomena in one grandiose and imposing synthesis. Whatever may be thefate reserved for such attempts, they deserve attention in the highestdegree; and it is desirable to examine them carefully if we wish tohave 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 qualitativeobservations. Many phenomena were studied without much trouble beingtaken to obtain actual measurements. But it is now becoming more andmore understood that to establish the relations which exist betweenphysical magnitudes, and to represent the variations of thesemagnitudes by functions which allow us to use the power ofmathematical analysis, it is most necessary to express each magnitudeby a definite number. 

Under these conditions alone can a magnitude be considered aseffectively known. "I often say, " Lord Kelvin has said, "that if youcan measure that of which you are speaking and express it by a numberyou know something of your subject; but if you cannot measure it norexpress it by a number, your knowledge is of a sorry kind and hardlysatisfactory. It may be the beginning of the acquaintance, but you arehardly, in your thoughts, advanced towards science, whatever thesubject may be. "

It has now become possible to measure exactly the elements which enterinto nearly all physical phenomena, and these measurements are takenwith ever increasing precision. Every time a chapter in scienceprogresses, science shows itself more exacting; it perfects its meansof investigation, it demands more and more exactitude, and one of themost striking features of modern physics is this constant care forstrictness and clearness in experimentation. 

A veritable science of measurement has thus been constituted whichextends over all parts of the domain of physics. This science has itsrules and its methods; it points out the best processes ofcalculation, and teaches the method of correctly estimating errors andtaking account of them. It has perfected the processes of experiment, co-ordinated a large number of results, and made possible theunification of standards. It is thanks to it that the system ofmeasurements unanimously adopted by physicists has been formed. 

At the present day we designate more peculiarly by the name ofmetrology that part of the science of measurements which devotesitself specially to the determining of the prototypes representing thefundamental units of dimension and mass, and of the standards of thefirst order which are derived from them. If all measurable quantities, as was long thought possible, could be reduced to the magnitudes ofmechanics, metrology would thus be occupied with the essentialelements entering into all phenomena, and might legitimately claim thehighest rank in science. But even when we suppose that some magnitudescan never be connected with mass, length, and time, it still holds apreponderating place, and its progress finds an echo throughout thewhole domain of the natural sciences. It is therefore well, in orderto give an account of the general progress of physics, to examine atthe outset the improvements which have been effected in thesefundamental measurements, and to see what precision these improvementshave allowed us to attain. 

§ 2. THE MEASURE OF LENGTH

To measure a length is to compare it with another length taken asunity. Measurement is therefore a relative operation, and can onlyenable us to know ratios. Did both the length to be measured and theunit chosen happen to vary simultaneously and in the same degree, weshould 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 lengthvaries. 

If, however, we were to note that, suddenly and in the sameproportions, the distance between two points on this earth hadincreased, that all the planets had moved further from each other, that all objects around us had become larger, that we ourselves hadbecome taller, and that the distance travelled by light in theduration of a vibration had become greater, we should not hesitate tothink ourselves the victims of an illusion, that in reality all thesedistances had remained fixed, and that all these appearances were dueto a shortening of the rule which we had used as the standard formeasuring the lengths. 

From the mathematical point of view, it may be considered that the twohypotheses are equivalent; all has lengthened around us, or else ourstandard has become less. But it is no simple question of convenienceand simplicity which leads us to reject the one supposition and toaccept the other; it is right in this case to listen to the voice ofcommon sense, and those physicists who have an instinctive trust inthe notion of an absolute length are perhaps not wrong. It is only bychoosing our unit from those which at all times have seemed to all menthe most invariable, that we are able in our experiments to note thatthe same causes acting under identical conditions always produce thesame effects. The idea of absolute length is derived from theprinciple of causality; and our choice is forced upon us by thenecessity of obeying this principle, which we cannot reject withoutdeclaring by that very act all science to be impossible. 

Similar remarks might be made with regard to the notions of absolutetime and absolute movement. They have been put in evidence and setforth very forcibly by a learned and profound mathematician, M. Painlevé. 

On the particularly clear example of the measure of length, it isinteresting to follow the evolution of the methods employed, and torun through the history of the progress in precision from the timethat we have possessed authentic documents relating to this question. This history has been written in a masterly way by one of thephysicists who have in our days done the most by their personallabours to add to it glorious pages. M. Benoit, the learned Directorof the International Bureau of Weights and Measures, has furnished invarious reports very complete details on the subject, from which Ihere borrow the most interesting. 

We know that in France the fundamental standard for measures of lengthwas for a long time the _Toise du Châtelet_, a kind of callipersformed of a bar of iron which in 1668 was embedded in the outside wallof the Châtelet, at the foot of the staircase. This bar had at itsextremities two projections with square faces, and all the _toises_ ofcommerce had to fit exactly between them. Such a standard, roughlyconstructed, and exposed to all the injuries of weather and time, offered very slight guarantees either as to the permanence or thecorrectness of its copies. Nothing, perhaps, can better convey an ideaof the importance of the modifications made in the methods ofexperimental physics than the easy comparison between so rudimentary aprocess and the actual measurements effected at the present time. 

The _Toise du Châtelet_, notwithstanding its evident faults, wasemployed for nearly a hundred years; in 1766 it was replaced by the_Toise du Pérou_, so called because it had served for the measurementsof the terrestrial arc effected in Peru from 1735 to 1739 by Bouguer, La Condamine, and Godin. At that time, according to the comparisonsmade between this new _toise_ and the _Toise du Nord_, which had alsobeen used for the measurement of an arc of the meridian, an error ofthe tenth part of a millimetre in measuring lengths of the order of ametre was considered quite unimportant. At the end of the eighteenthcentury, Delambre, in his work _Sur la Base du Système métriquedécimal_, clearly gives us to understand that magnitudes of the orderof the hundredth of a millimetre appear to him incapable ofobservation, even in scientific researches of the highest precision. At the present date the International Bureau of Weights and Measuresguarantees, in the determination of a standard of length compared withthe metre, an approximation of two or three ten-thousandths of amillimetre, and even a little more under certain circumstances. 

This very remarkable progress is due to the improvements in the methodof comparison on the one hand, and in the manufacture of the standardon the other. M. Benoit rightly points out that a kind of competitionhas been set up between the standard destined to represent the unitwith its subdivisions and multiples and the instrument charged withobserving it, comparable, up to a certain point, with that which inanother order of ideas goes on between the gun and the armour-plate. 

The measuring instrument of to-day is an instrument of comparisonconstructed with meticulous care, which enables us to do away withcauses of error formerly ignored, to eliminate the action of externalphenomena, and to withdraw the experiment from the influence of eventhe personality of the observer. This standard is no longer, asformerly, a flat rule, weak and fragile, but a rigid bar, incapable ofdeformation, in which the material is utilised in the best conditionsof resistance. For a standard with ends has been substituted astandard with marks, which permits much more precise definition andcan be employed in optical processes of observation alone; that is, inprocesses 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 thusassured, 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 thestandard metre, the measurement is taken from the central one of threemarks at each end of the bar. The transverse section of the bar is anX, and the reading is made by a microscope. --ED. ]

Thanks to studies thus systematically pursued, we have succeeded inthe course of a hundred years in increasing the precision of measuresin the proportion of a thousand to one, and we may ask ourselveswhether such an increase will continue in the future. No doubtprogress will not be stayed; but if we keep to the definition oflength by a material standard, it would seem that its precision cannotbe considerably increased. We have nearly reached the limit imposed bythe necessity of making strokes of such a thickness as to beobservable under the microscope. 

It may happen, however, that we shall be brought one of these days toa new conception of the measure of length, and that very differentprocesses of determination will be thought of. If we took as unit, forinstance, the distance covered by a given radiation during avibration, the optical processes would at once admit of much greaterprecision. 

Thus Fizeau, the first to have this idea, says: "A ray of light, withits series of undulations of extreme tenuity but perfect regularity, may be considered as a micrometer of the greatest perfection, andparticularly suitable for determining length. " But in the presentstate of things, since the legal and customary definition of the unitremains a material standard, it is not enough to measure length interms of wave-lengths, and we must also know the value of thesewave-lengths in terms of the standard prototype of the metre. 

This was determined in 1894 by M. Michelson and M. Benoit in anexperiment which will remain classic. The two physicists measured astandard length of about ten centimetres, first in terms of thewave-lengths of the red, green, and blue radiations of cadmium, andthen in terms of the standard metre. The great difficulty of theexperiment proceeds from the vast difference which exists between thelengths to be compared, the wave-lengths barely amounting to half amicron;[3] the process employed consisted in noting, instead of thislength, 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 therelation of a magnitude to the unit, there has to be determined on theone hand the whole, and on the other the fractional part of thisratio, and naturally the most delicate determination is generally thatof this fractional part. In optical processes the difficulty isreversed. The fractional part is easily known, while it is the highfigure of the number representing the whole which becomes a veryserious obstacle. It is this obstacle which MM. Michelson and Benoitovercame with admirable ingenuity. By making use of a somewhat similaridea, M. Macé de Lépinay and MM. Perot and Fabry, have lately effectedby optical methods, measurements of the greatest precision, and nodoubt further progress may still be made. A day may perhaps come whena material standard will be given up, and it may perhaps even berecognised that such a standard in time changes its length bymolecular strain, and by wear and tear: and it will be further notedthat, in accordance with certain theories which will be noticed lateron, it is not invariable when its orientation is changed. 

For the moment, however, the need of any change in the definition ofthe unit is in no way felt; we must, on the contrary, hope that theuse of the unit adopted by the physicists of the whole world willspread more and more. It is right to remark that a few errors stilloccur with regard to this unit, and that these errors have beenfacilitated by incoherent legislation. France herself, though she wasthe admirable initiator of the metrical system, has for too longallowed a very regrettable confusion to exist; and it cannot be notedwithout a certain sadness that it was not until the _11th July 1903_that a law was promulgated re-establishing the agreement between thelegal and the scientific definition of the metre. 

Perhaps it may not be useless to briefly indicate here the reasons ofthe disagreement which had taken place. Two definitions of the metrecan be, and in fact were given. One had for its basis the dimensionsof the earth, the other the length of the material standard. In theminds of the founders of the metrical system, the first of these wasthe true definition of the unit of length, the second merely a simplerepresentation. It was admitted, however, that this representation hadbeen constructed in a manner perfect enough for it to be nearlyimpossible to perceive any difference between the unit and itsrepresentation, and for the practical identity of the two definitionsto be thus assured. The creators of the metrical system were persuadedthat the measurements of the meridian effected in their day couldnever be surpassed in precision; and on the other hand, by borrowingfrom nature a definite basis, they thought to take from the definitionof the unit some of its arbitrary character, and to ensure the meansof again finding the same unit if by any accident the standard becamealtered. Their confidence in the value of the processes they had seenemployed was exaggerated, and their mistrust of the futureunjustified. This example shows how imprudent it is to endeavour tofix limits to progress. It is an error to think the march of sciencecan be stayed; and in reality it is now known that the ten-millionthpart of the quarter of the terrestrial meridian is longer than themetre by 0. 187 millimetres. But contemporary physicists do not fallinto the same error as their forerunners, and they regard the presentresult as merely provisional. They guess, in fact, that newimprovements will be effected in the art of measurement; they knowthat geodesical processes, though much improved in our days, havestill much to do to attain the precision displayed in the constructionand determination of standards of the first order; and consequentlythey do not propose to keep the ancient definition, which would leadto having for unit a magnitude possessing the grave defect from apractical point of view of being constantly variable. 

We may even consider that, looked at theoretically, its permanencewould not be assured. Nothing, in fact, proves that sensiblevariations may not in time be produced in the value of an arc of themeridian, and serious difficulties may arise regarding the probableinequality of the various meridians. 

For all these reasons, the idea of finding a natural unit has beengradually abandoned, and we have become resigned to accepting as afundamental unit an arbitrary and conventional length having amaterial representation recognised by universal consent; and it wasthis unit which was consecrated by the following law of the 11th July1903:--

"The standard prototype of the metrical system is the internationalmetre, which has been sanctioned by the General Conference on Weightsand Measures. "

§ 3. THE MEASURE OF MASS

On the subject of measures of mass, similar remarks to those onmeasures of length might be made. The confusion here was perhaps stillgreater, because, to the uncertainty relating to the fixing of theunit, was added some indecision on the very nature of the magnitudedefined. In law, as in ordinary practice, the notions of weight and ofmass were not, in fact, separated with sufficient clearness. 

They represent, however, two essentially different things. Mass is thecharacteristic of a quantity of matter; it depends neither on thegeographical position one occupies nor on the altitude to which onemay rise; it remains invariable so long as nothing material is addedor taken away. Weight is the action which gravity has upon the bodyunder consideration; this action does not depend solely on the body, but on the earth as well; and when it is changed from one spot toanother, the weight changes, because gravity varies with latitude andaltitude. 

These elementary notions, to-day understood even by young beginners, appear to have been for a long time indistinctly grasped. Thedistinction remained confused in many minds, because, for the mostpart, masses were comparatively estimated by the intermediary ofweights. The estimations of weight made with the balance utilize theaction of the weight on the beam, but in such conditions that theinfluence of the variations of gravity becomes eliminated. The twoweights which are being compared may both of them change if theweighing is effected in different places, but they are attracted inthe same proportion. If once equal, they remain equal even when inreality they may both have varied. 

The current law defines the kilogramme as the standard of mass, andthe law is certainly in conformity with the rather obscurely expressedintentions of the founders of the metrical system. Their terminologywas vague, but they certainly had in view the supply of a standard forcommercial transactions, and it is quite evident that in barter whatis important to the buyer as well as to the seller is not theattraction the earth may exercise on the goods, but the quantity thatmay be supplied for a given price. Besides, the fact that the foundersabstained from indicating any specified spot in the definition of thekilogramme, when they were perfectly acquainted with the considerablevariations in the intensity of gravity, leaves no doubt as to theirreal desire. 

The same objections have been made to the definition of thekilogramme, at first considered as the mass of a cubic decimetre ofwater at 4° C. , as to the first definition of the metre. We mustadmire the incredible precision attained at the outset by thephysicists who made the initial determinations, but we know at thepresent day that the kilogramme they constructed is slightly too heavy(by about 1/25, 000). Very remarkable researches have been carried outwith regard to this determination by the International Bureau, and byMM. Macé de Lépinay and Buisson. The law of the 11th July 1903 hasdefinitely regularized the custom which physicists had adopted someyears before; and the standard of mass, the legal prototype of themetrical system, is now the international kilogramme sanctioned by theConference of Weights and Measures. 

The comparison of a mass with the standard is effected with aprecision to which no other measurement can attain. Metrology vouchesfor 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 thisalready admirable precision can be surpassed; and progress would seemlikely to be slow, for difficulties singularly increase when we get tosuch small quantities. But it is permitted to hope that the physicistsof the future will do still better than those of to-day; and perhapswe may catch a glimpse of the time when we shall begin to observe thatthe standard, which is constructed from a heavy metal, namely, iridium-platinum, itself obeys an apparently general law, and littleby 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 tospeak, no physical phenomenon in which the notion of time linked tothe sequence of our states of consciousness does not play aconsiderable 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; andthe unit to-day adopted is, as we know, the sexagesimal second of meantime. This magnitude, thus defined by the conditions of a naturalmotion which may itself be modified, does not seem to offer all theguarantees desirable from the point of view of invariability. It iscertain that all the friction exercised on the earth--by the tides, for instance--must slowly lengthen the duration of the day, and mustinfluence the movement of the earth round the sun. Such influence iscertainly very slight, but it nevertheless gives an unfortunatelyarbitrary character to the unit adopted. 

We might have taken as the standard of time the duration of anothernatural phenomenon, which appears to be always reproduced underidentical conditions; the duration, for instance, of a given luminousvibration. But the experimental difficulties of evaluation with such aunit of the times which ordinarily have to be considered, would be sogreat that such a reform in practice cannot be hoped for. It should, moreover, be remarked that the duration of a vibration may itself beinfluenced by external circumstances, among which are the variationsof the magnetic field in which its source is placed. It could not, therefore, be strictly considered as independent of the earth; and thetheoretical advantage which might be expected from this alterationwould 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 beenrendered radioactive by a solution of radium, the tube may be sealedup, and it will then be noted that the radiation of its wallsdiminishes with time, in accordance with an exponential law. Theconstant of time derived by this phenomenon remains the same whateverthe nature and dimensions of the walls of the tube or the temperaturemay be, and time might thus be denned independently of all the otherunits. 

We might also, as M. Lippmann has suggested in an extremely ingeniousway, decide to obtain measures of time which can be considered asabsolute because they are determined by parameters of another naturethan that of the magnitude to be measured. Such experiments are madepossible by the phenomena of gravitation. We could employ, forinstance, the pendulum by adopting, as the unit of force, the forcewhich renders the constant of gravitation equal to unity. The unit oftime thus defined would be independent of the unit of length, andwould depend only on the substance which would give us the unit ofmass under the unit of volume. 

It would be equally possible to utilize electrical phenomena, and onemight devise experiments perfectly easy of execution. Thus, bycharging a condenser by means of a battery, and discharging it a givennumber of times in a given interval of time, so that the effect of thecurrent of discharge should be the same as the effect of the output ofthe battery through a given resistance, we could estimate, by themeasurement of the electrical magnitudes, the duration of the intervalnoted. A system of this kind must not be looked upon as a simple _jeud'esprit_, since this very practicable experiment would easily permitus to check, with a precision which could be carried very far, theconstancy of an interval of time. 

From the practical point of view, chronometry has made in these lastfew years very sensible progress. The errors in the movements ofchronometers are corrected in a much more systematic way thanformerly, and certain inventions have enabled important improvementsto be effected in the construction of these instruments. Thus thecurious properties which steel combined with nickel--so admirablystudied by M. Ch. Ed. Guillaume--exhibits in the matter of dilatationare now utilized so as to almost completely annihilate the influenceof variations of temperature. 

§ 5. THE MEASURE OF TEMPERATURE

From the three mechanical units we derive secondary units; as, forinstance, the unit of work or mechanical energy. The kinetic theorytakes temperature, as well as heat itself, to be a quantity of energy, and thus seems to connect this notion with the magnitudes ofmechanics. But the legitimacy of this theory cannot be admitted, andthe calorific movement should also be a phenomenon so strictlyconfined in space that our most delicate means of investigation wouldnot enable us to perceive it. It is better, then, to continue toregard the unit of difference of temperature as a distinct unit, to beadded 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 ofthis property is, that it should constantly vary in the same directionwhen the temperature rises, and that it should possess, at anytemperature, a well-marked value. We measure this value by melting iceand by the vapour of boiling water under normal pressure, and thesuccessive hundredths of its variation, beginning with the meltingice, defines the percentage. Thermodynamics, however, has made itplain that we can set up a thermometric scale without relying upon anydetermined property of a real body. Such a scale has an absolute valueindependently of the properties of matter. Now it happens that if wemake use for the estimation of temperatures, of the phenomena ofdilatation under a constant pressure, or of the increase of pressurein a constant volume of a gaseous body, we obtain a scale very nearthe absolute, which almost coincides with it when the gas possessescertain qualities which make it nearly what is called a perfect gas. This most lucky coincidence has decided the choice of the conventionadopted by physicists. They define normal temperature by means of thevariations of pressure in a mass of hydrogen beginning with theinitial pressure of a metre of mercury at 0° C. 

M. P. Chappuis, in some very precise experiments conducted with muchmethod, has proved that at ordinary temperatures the indications ofsuch a thermometer are so close to the degrees of the theoreticalscale that it is almost impossible to ascertain the value of thedivergences, or even the direction that they take. The divergencebecomes, however, manifest when we work with extreme temperatures. Itresults from the useful researches of M. Daniel Berthelot that we mustsubtract +0. 18° from the indications of the hydrogen thermometertowards the temperature -240° C, and add +0. 05° to 1000° to equatethem with the thermodynamic scale. Of course, the difference wouldalso become still more noticeable on getting nearer to the absolutezero; for as hydrogen gets more and more cooled, it gradually exhibitsin a lesser degree the characteristics of a perfect gas. 

To study the lower regions which border on that kind of pole of coldtowards which are straining the efforts of the many physicists whohave 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 temperatureof -260° C. Downward the divergence of such a thermometer from one ofhydrogen is very marked. 

The measurement of very high temperatures is not open to the sametheoretical objections as that of very low temperatures; but, from apractical point of view, it is as difficult to effect with an ordinarygas thermometer. It becomes impossible to guarantee the reservoirremaining sufficiently impermeable, and all security disappears, notwithstanding the use of recipients very superior to those of formertimes, 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 veryconvenient couple of M. Le Chatelier; but the graduation of theseinstruments can only be effected at the cost of a rather boldextrapolation. 

M. D. Berthelot has pointed out and experimented with a veryinteresting process, founded on the measurement by the phenomena ofinterference of the refractive index of a column of air subjected tothe temperature it is desired to measure. It appears admissible thateven at the highest temperatures the variation of the power ofrefraction is strictly proportional to that of the density, for thisproportion is exactly verified so long as it is possible to check itprecisely. We can thus, by a method which offers the great advantageof being independent of the power and dimension of the envelopesemployed--since the length of the column of air considered aloneenters into the calculation--obtain results equivalent to those givenby the ordinary air thermometer. 

Another method, very old in principle, has also lately acquired greatimportance. For a long time we sought to estimate the temperature of abody by studying its radiation, but we did not know any positiverelation between this radiation and the temperature, and we had nogood experimental method of estimation, but had recourse to purelyempirical formulas and the use of apparatus of little precision. Now, however, many physicists, continuing the classic researches ofKirchhoff, Boltzmann, Professors Wien and Planck, and taking theirstarting-point from the laws of thermodynamics, have given formulaswhich establish the radiating power of a dark body as a function ofthe temperature and the wave-length, or, better still, of the totalpower as a function of the temperature and wave-length correspondingto the maximum value of the power of radiation. We see, therefore, thepossibility of appealing for the measurement of temperature to aphenomenon which is no longer the variation of the elastic force of agas, and yet is also connected with the principles of thermodynamics. 

This is what Professors Lummer and Pringsheim have shown in a seriesof studies which may certainly be reckoned among the greatestexperimental researches of the last few years. They have constructed aradiator closely resembling the theoretically integral radiator whicha closed isothermal vessel would be, and with only a very smallopening, which allows us to collect from outside the radiations whichare in equilibrium with the interior. This vessel is formed of ahollow carbon cylinder, heated by a current of high intensity; theradiations are studied by means of a bolometer, the disposition ofwhich varies with the nature of the experiments. 

It is hardly possible to enter into the details of the method, but theresult sufficiently indicates its importance. It is now possible, thanks to their researches, to estimate a temperature of 2000° C. Towithin about 5°. Ten years ago a similar approximation could hardlyhave 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 adependency is established between a derived unit and the fundamentalunits. The laws of numbers in physics are often only laws ofproportion. We transform them into laws of equation, because weintroduce numerical coefficients and choose the units on which theydepend so as to simplify as much as possible the formulas most in use. A particular speed, for instance, is in reality nothing else but aspeed, and it is only by the peculiar choice of unit that we can saythat 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 isnothing to prove that, in its essence, it is really reducible to afunction of mass, of length, and of time. 

Persons are still to be met with who seem to have some illusions onthis point, and who see in the doctrine of the dimensions of the unitsa doctrine of general physics, while it is, to say truth, only adoctrine of metrology. The knowledge of dimensions is valuable, sinceit allows us, for instance, to easily verify the homogeneity of aformula, but it can in no way give us any information on the actualnature of the quantity measured. 

Magnitudes to which we attribute like dimensions may be qualitativelyirreducible one to the other. Thus the different forms of energy aremeasured by the same unit, and yet it seems that some of them, such askinetic energy, really depend on time; while for others, such aspotential energy, the dependency established by the system ofmeasurement seems somewhat fictitious. 

The numerical value of a quantity of energy of any nature should, inthe 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 measuredifferent quantities of energy of varying forms, such as electrical, chemical, and other quantities, etc. , we nearly always employ a methodby which all these energies are finally transformed and used to heatthe water of a calorimeter. It is therefore very important to studywell the calorific phenomenon chosen as the unit of heat, and todetermine with precision its mechanical equivalent, that is to say, the number of ergs necessary to produce this unit. This is a numberwhich, on the principle of equivalence, depends neither on the methodemployed, nor the time, nor any other external circumstance. 

As the result of the brilliant researches of Rowland and of MrGriffiths on the variations of the specific heat of water, physicistshave decided to take as calorific standard the quantity of heatnecessary to raise a gramme of water from 15° to 16° C. , thetemperature being measured by the scale of the hydrogen thermometer ofthe 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 fulldiscussion as to the best results, have led to the adoption of thenumber 4. 187 to represent the number of ergs capable of producing theunit of heat. 

In practice, the measurement of a quantity of heat is very ofteneffected by means of the ice calorimeter, the use of which isparticularly simple and convenient. There is, therefore, a veryspecial interest in knowing exactly the melting-point of ice. M. Leduc, who for several years has measured a great number of physicalconstants 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 caloriehad been committed by several renowned experimenters, and it will beseen that in certain points the art of measurement may still belargely perfected. 

To the unit of energy might be immediately attached other units. Forinstance, radiation being nothing but a flux of energy, we could, inorder to establish photometric units, divide the normal spectrum intobands of a given width, and measure the power of each for the unit ofradiating surface. 

But, notwithstanding some recent researches on this question, wecannot yet consider the distribution of energy in the spectrum asperfectly known. If we adopt the excellent habit which exists in someresearches of expressing radiating energy in ergs, it is stillcustomary to bring the radiations to a standard giving, by itsconstitution alone, the unit of one particular radiation. Inparticular, the definitions are still adhered to which were adopted asthe result of the researches of M. Violle on the radiation of fusedplatinum at the temperature of solidification; and most physicistsutilize in the ordinary methods of photometry the clearly definednotions 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 theInternational Congress of Electricians in 1904. For their definitionand 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 correspondingprogress in nearly all physical measurements, and particularly in themeasure of natural constants. Among these, the constant of gravitationoccupies a position quite apart from the importance and simplicity ofthe physical law which defines it, as well as by its generality. Twomaterial particles are mutually attracted to each other by a forcedirectly proportional to the product of their mass, and inverselyproportional to the square of the distance between them. Thecoefficient of proportion is determined when once the units arechosen, and as soon as we know the numerical values of this force, ofthe two masses, and of their distance. But when we wish to makelaboratory experiments serious difficulties appear, owing to theweakness of the attraction between masses of ordinary dimensions. Microscopic forces, so to speak, have to be observed, and thereforeall the causes of errors have to be avoided which would be unimportantin most other physical researches. It is known that Cavendish was thefirst who succeeded by means of the torsion balance in effectingfairly precise measurements. This method has been again taken in handby different experimenters, and the most recent results are due to MrVernon Boys. This learned physicist is also the author of a mostuseful practical invention, and has succeeded in making quartz threadsas fine as can be desired and extremely uniform. He finds that thesethreads possess valuable properties, such as perfect elasticity andgreat tenacity. He has been able, with threads not more than 1/500 ofa millimetre in diameter, to measure with precision couples of anorder formerly considered outside the range of experiment, and toreduce the dimensions of the apparatus of Cavendish in the proportionof 150 to 1. The great advantage found in the use of these smallinstruments is the better avoidance of the perturbations arising fromdraughts of air, and of the very serious influence of the slightestinequality 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 torsionlever, the method of the ordinary balance, used especially byProfessors 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 adensity equal to 5. 527. 

The most familiar manifestation of gravitation is gravity. The actionof the earth on the unit of mass placed in one point, and theintensity of gravity, is measured, as we know, by the aid of apendulum. The methods of measurement, whether by absolute or byrelative determinations, so greatly improved by Borda and Bessel, havebeen still further improved by various geodesians, among whom shouldbe mentioned M. Von Sterneek and General Defforges. Numerousobservations have been made in all parts of the world by variousexplorers, and have led to a fairly complete knowledge of thedistribution of gravity over the surface of the globe. Thus we havesucceeded in making evident anomalies which would not easily findtheir place in the formula of Clairaut. 

Another constant, the determination of which is of the greatestutility in astronomy of position, and the value of which enters intoelectromagnetic theory, has to-day assumed, with the new ideas on theconstitution of matter, a still more considerable importance. I referto the speed of light, which appears to us, as we shall see furtheron, the maximum value of speed which can be given to a material body. 

After the historical experiments of Fizeau and Foucault, taken upafresh, as we know, partly by Cornu, and partly by Michelson andNewcomb, it remained still possible to increase the precision of themeasurements. Professor Michelson has undertaken some new researchesby a method which is a combination of the principle of the toothedwheel of Fizeau with the revolving mirror of Foucault. The toothedwheel is here replaced, however, by a grating, in which the lines andthe spaces between them take the place of the teeth and the gaps, thereflected light only being returned when it strikes on the spacebetween two lines. The illustrious American physicist estimates thathe can thus evaluate to nearly five kilometres the path traversed bylight in one second. This approximation corresponds to a relativevalue of a few hundred-thousandths, and it far exceeds those hithertoattained by the best experimenters. When all the experiments arecompleted, they will perhaps solve certain questions still insuspense; for instance, the question whether the speed of propagationdepends on intensity. If this turns out to be the case, we should bebrought to the important conclusion that the amplitude of theoscillations, which is certainly very small in relation to the alreadytiny wave-lengths, cannot be considered as unimportant in regard tothese lengths. Such would seem to have been the result of the curiousexperiments of M. Muller and of M. Ebert, but these results have beenrecently disputed by M. Doubt. 

In the case of sound vibrations, on the other hand, it should be notedthat experiment, consistently with the theory, proves that the speedincreases with the amplitude, or, if you will, with the intensity. M. Violle has published an important series of experiments on the speedof propagation of very condensed waves, on the deformations of thesewaves, and on the relations of the speed and the pressure, whichverify in a remarkable manner the results foreshadowed by the alreadyold calculations of Riemann, repeated later by Hugoniot. If, on thecontrary, the amplitude is sufficiently small, there exists a speedlimit which is the same in a large pipe and in free air. By somebeautiful experiments, MM. Violle and Vautier have clearly shown thatany disturbance in the air melts somewhat quickly into a single waveof given form, which is propagated to a distance, while graduallybecoming weaker and showing a constant speed which differs little indry air at 0° C. From 331. 36 metres per second. In a narrow pipe theinfluence of the walls makes itself felt and produces various effects, in particular a kind of dispersion in space of the harmonics of thesound. This phenomenon, according to M. Brillouin, is perfectlyexplicable 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 ofa certain number of laws or general hypotheses which are theprinciples already referred to. These principal hypotheses are, in theeyes of a physicist, legitimate generalizations, the consequences ofwhich we shall be able at once to check by the experiments from whichthey issue. 

Among the principles almost universally adopted until lately figureprominently those of mechanics--such as the principle of relativity, and the principle of the equality of action and reaction. We will notdetail nor discuss them here, but later on we shall have anopportunity of pointing out how recent theories on the phenomena ofelectricity have shaken the confidence of physicists in them and haveled 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 massis looked upon as the coefficient of the inertia of matter or as thefactor which intervenes in the phenomena of universal attraction, andparticularly in gravitation. We shall see when we treat of thesetheories, how we have been led to suppose that inertia depended onvelocity and even on direction. If this conception were exact, theprinciple 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 singularlyaudacious. And yet the law of Lavoisier is so far from self-evidentthat for centuries it escaped the notice of physicists and chemists. But its great apparent simplicity and its high character ofgenerality, when enunciated at the end of the eighteenth century, rapidly gave it such an authority that no one was able to any longerdispute it unless he desired the reputation of an oddity inclined toparadoxical ideas. 

It is important, however, to remark that, under fallaciousmetaphysical appearances, we are in reality using empty wordswhen we repeat the aphorism, "Nothing can be lost, nothing can becreated, " and deduce from it the indestructibility of matter. Thisindestructibility, in truth, is an experimental fact, and theprinciple depends on experiment. It may even seem, at first sight, more singular than not that the weight of a bodily system in a givenplace, or the quotient of this weight by that of the standardmass--that is to say, the mass of these bodies--remains invariable, both when the temperature changes and when chemical reagents cause theoriginal materials to disappear and to be replaced by new ones. We maycertainly consider that in a chemical phenomenon annihilations andcreations of matter are really produced; but the experimental lawteaches us that there is compensation in certain respects. 

The discovery of the radioactive bodies has, in some sort, renderedpopular the speculations of physicists on the phenomena of thedisaggregation of matter. We shall have to seek the exact meaningwhich ought to be given to the experiments on the emanation of thesebodies, and to discover whether these experiments really imperil thelaw of Lavoisier. 

For some years different experimenters have also effected many veryprecise measurements of the weight of divers bodies both before andafter chemical reactions between these bodies. Two highly experiencedand cautious physicists, Professors Landolt and Heydweiller, have nothesitated to announce the sensational result that in certaincircumstances the weight is no longer the same after as before thereaction. In particular, the weight of a solution of salts of copperin water is not the exact sum of the joint weights of the salt and thewater. Such experiments are evidently very delicate; they have beendisputed, and they cannot be considered as sufficient for conviction. It follows nevertheless that it is no longer forbidden to regard thelaw of Lavoisier as only an approximate law; according to Sandford andRay, this approximation would be about 1/2, 400, 000. This is also theresult reached by Professor Poynting in experiments regarding thepossible action of temperature on the weight of a body; and if this bereally so, we may reassure ourselves, and from the point of view ofpractical application may continue to look upon matter asindestructible. 

The principles of physics, by imposing certain conditions onphenomena, limit after a fashion the field of the possible. Amongthese principles is one which, notwithstanding its importance whencompared with that of universally known principles, is less familiarto some people. This is the principle of symmetry, more or lessconscious applications of which can, no doubt, be found in variousworks and even in the conceptions of Copernican astronomers, but whichwas generalized and clearly enunciated for the first time by the lateM. Curie. This illustrious physicist pointed out the advantage ofintroducing into the study of physical phenomena the considerations onsymmetry familiar to crystallographers; for a phenomenon to takeplace, it is necessary that a certain dissymmetry should previouslyexist in the medium in which this phenomenon occurs. A body, forinstance, may be animated with a certain linear velocity or a speed ofrotation; it may be compressed, or twisted; it may be placed in anelectric or in a magnetic field; it may be affected by an electriccurrent or by one of heat; it may be traversed by a ray of lighteither ordinary or polarized rectilineally or circularly, etc. :--ineach case a certain minimum and characteristic dissymmetry isnecessary at every point of the body in question. 

This consideration enables us to foresee that certain phenomena whichmight be imagined _a priori_ cannot exist. Thus, for instance, it isimpossible that an electric field, a magnitude directed and notsuperposable on its image in a mirror perpendicular to its direction, could be created at right angles to the plane of symmetry of themedium; while it would be possible to create a magnetic field underthe 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 absolutelyprecise notions as to the nature of these phenomena, nor disclosetheir order of magnitude. 

§ 2. THE PRINCIPLE OF THE CONSERVATION OF ENERGY

Dominating not physics alone, but nearly every other science, theprinciple of the conservation of energy is justly considered as thegrandest conquest of contemporary thought. It shows us in a powerfullight the most diverse questions; it introduces order into the mostvaried studies; it leads to a clear and coherent interpretation ofphenomena which, without it, appear to have no connexion with eachother; and it supplies precise and exact numerical relations betweenthe magnitudes which enter into these phenomena. 

The boldest minds have an instinctive confidence in it, and it is theprinciple which has most stoutly resisted that assault which thedaring of a few theorists has lately directed to the overthrow of thegeneral principles of physics. At every new discovery, the firstthought of physicists is to find out how it accords with the principleof 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 itseems never to have received a check, even the extraordinaryproperties of radium not seriously contradicting it; also the generalform in which it is enunciated gives it such a suppleness that it isno doubt very difficult to overthrow. 

I do not claim to set forth here the complete history of thisprinciple, 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 itsdevelopment by the unfavourable conditions of the surroundings inwhich it appeared. It first of all came, in fact, to oppose itself tothe reigning theories; but, little by little, it acted on thesetheories, and they were modified under its pressure; then, in theirturn, 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, itgained in precision what it lost in extent. When once definitelyadmitted and classed, as it were, in the official domain of science, it endeavoured to burst its bonds and return to a more independent andlarger life. The history of this principle is similar to that of allevolutions. 

It is well known that the conservation of energy was, at first, regarded from the point of view of the reciprocal transformationsbetween heat and work, and that the principle received its first clearenunciation in the particular case of the principle of equivalence. Itis, therefore, rightly considered that the scholars who were the firstto doubt the material nature of caloric were the precursors of R. Mayer; their ideas, however, were the same as those of the celebratedGerman doctor, for they sought especially to demonstrate that heat wasa mode of motion. 

Without going back to early and isolated attempts like those of DanielBernoulli, who, in his hydrodynamics, propounded the basis of thekinetic theory of gases, or the researches of Boyle on friction, wemay recall, to show how it was propounded in former times, a ratherforgotten page of the _Mémoire sur la Chaleur_, published in 1780 byLavoisier and Laplace: "Other physicists, " they wrote, after settingout the theory of caloric, "think that heat is nothing but the resultof the insensible vibrations of matter. .. . In the system we are nowexamining, heat is the _vis viva_ resulting from the insensiblemovements of the molecules of a body; it is the sum of the products ofthe mass of each molecule by the square of its velocity. .. . We shallnot decide between the two preceding hypotheses; several phenomenaseem to support the last mentioned--for instance, that of the heatproduced by the friction of two solid bodies. But there are otherswhich are more simply explained by the first, and perhaps they bothoperate at once. " Most of the physicists of that period, however, didnot share the prudent doubts of Lavoisier and Laplace. They admitted, without hesitation, the first hypothesis; and, four years after theappearance of the _Mémoire sur la Chaleur_, Sigaud de Lafond, aprofessor of physics of great reputation, wrote: "Pure Fire, free fromall state of combination, seems to be an assembly of particles of asimple, homogeneous, and absolutely unalterable matter, and all theproperties of this element indicate that these particles areinfinitely small and free, that they have no sensible cohesion, andthat they are moved in every possible direction by a continual andrapid motion which is essential to them. .. . The extreme tenacity andthe surprising mobility of its molecules are manifestly shown by theease with which it penetrates into the most compact bodies and by itstendency to put itself in equilibrium throughout all bodies near toit. "

It must be acknowledged, however, that the idea of Lavoisier andLaplace was rather vague and even inexact on one important point. Theyadmitted it to be evident that "all variations of heat, whether realor apparent, undergone by a bodily system when changing its state, areproduced in inverse order when the system passes back to its originalstate. " This phrase is the very denial of equivalence where thesechanges of state are accompanied by external work. 

Laplace, moreover, himself became later a very convinced partisan ofthe hypothesis of the material nature of caloric, and his immenseauthority, so fortunate in other respects for the development ofscience, was certainly in this case the cause of the retardation ofprogress. 

The names of Young, Rumford, Davy, are often quoted among thosephysicists who, at the commencement of the nineteenth century, caughtsight of the new truths as to the nature of heat. To these names isvery properly added that of Sadi Carnot. A note found among his papersunquestionably proves that, before 1830, ideas had occurred to himfrom which it resulted that in producing work an equivalent amount ofheat was destroyed. But the year 1842 is particularly memorable in thehistory of science as the year in which Jules Robert Mayer succeeded, by an entirely personal effort, in really enunciating the principle ofthe conservation of energy. Chemists recall with just pride that the_Remarques sur les forces de la nature animée_, contemptuouslyrejected by all the journals of physics, were received and publishedin the _Annalen_ of Liebig. We ought never to forget this example, which shows with what difficulty a new idea contrary to the classictheories of the period succeeds in coming to the front; butextenuating circumstances may be urged on behalf of the physicists. 

Robert Mayer had a rather insufficient mathematical education, and hisMemoirs, 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 veryprofound ideas, evident errors in mechanics. Thus it often happensthat discoveries put forward in a somewhat vague manner by adventurousminds not overburdened by the heavy baggage of scientific erudition, who audaciously press forward in advance of their time, fall intoquite intelligible oblivion until rediscovered, clarified, and putinto shape by slower but surer seekers. This was the case with theideas of Mayer. They were not understood at first sight, not only onaccount of their originality, but also because they were couched inincorrect language. 

Mayer was, however, endowed with a singular strength of thought; heexpressed in a rather confused manner a principle which, for him, hada generality greater than mechanics itself, and so his discovery wasin advance not only of his own time but of half the century. He mayjustly be considered the founder of modern energetics. 

Freed from the obscurities which prevented its being clearlyperceived, his idea stands out to-day in all its imposing simplicity. Yet it must be acknowledged that if it was somewhat denaturalised bythose who endeavoured to adapt it to the theories of mechanics, and ifit at first lost its sublime stamp of generality, it thus becamefirmly fixed and consolidated on a more stable basis. 

The efforts of Helmholtz, Clausius, and Lord Kelvin to introduce theprinciple of the conservation of energy into mechanics, were far fromuseless. These illustrious physicists succeeded in giving a moreprecise form to its numerous applications; and their attempts thuscontributed, by reaction, to give a fresh impulse to mechanics, andallowed it to be linked to a more general order of facts. Ifenergetics has not been able to be included in mechanics, it seemsindeed that the attempt to include mechanics in energetics was not invain. 

In the middle of the last century, the explanation of all naturalphenomena seemed more and more referable to the case of centralforces. Everywhere it was thought that reciprocal actions betweenmaterial points could be perceived, these points being attracted orrepelled by each other with an intensity depending only on theirdistance or their mass. If, to a system thus composed, the laws of theclassical mechanics are applied, it is shown that half the sum of theproduct of the masses by the square of the velocities, to which isadded the work which might be accomplished by the forces to which thesystem would be subject if it returned from its actual to its initialposition, is a sum constant in quantity. 

This sum, which is the mechanical energy of the system, is thereforean invariable quantity in all the states to which it may be brought bythe interaction of its various parts, and the word energy wellexpresses a capital property of this quantity. For if two systems areconnected in such a way that any change produced in the onenecessarily brings about a change in the other, there can be novariation in the characteristic quantity of the second except so faras the characteristic quantity of the first itself varies--oncondition, of course, that the connexions are made in such a manner asto introduce no new force. It will thus be seen that this quantitywell expresses the capacity possessed by a system for modifying thestate of a neighbouring system to which we may suppose it connected. 

Now this theorem of pure mechanics was found wanting every timefriction took place--that is to say, in all really observable cases. The more perceptible the friction, the more considerable thedifference; but, in addition, a new phenomenon always appeared andheat was produced. By experiments which are now classic, it becameestablished that the quantity of heat thus created independently ofthe nature of the bodies is always (provided no other phenomenaintervene) proportional to the energy which has disappeared. Reciprocally, also, heat may disappear, and we always find a constantrelation between the quantities of heat and work which mutuallyreplace each other. 

It is quite clear that such experiments do not prove that heat iswork. We might just as well say that work is heat. It is making agratuitous hypothesis to admit this reduction of heat to mechanism;but this hypothesis was so seductive, and so much in conformity withthe desire of nearly all physicists to arrive at some sort of unity innature, that they made it with eagerness and became unreservedlyconvinced that heat was an active internal force. 

Their error was not in admitting this hypothesis; it was a legitimateone since it has proved very fruitful. But some of them committed thefault of forgetting that it was an hypothesis, and considered it ademonstrated truth. Moreover, they were thus brought to see inphenomena nothing but these two particular forms of energy which intheir minds were easily identified with each other. 

From the outset, however, it became manifest that the principle isapplicable to cases where heat plays only a parasitical part. Therewere thus discovered, by translating the principle of equivalence, numerical relations between the magnitudes of electricity, forinstance, and the magnitudes of mechanics. Heat was a sort of variableintermediary convenient for calculation, but introduced in aroundabout 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 calorificmanifestations, of which the study belongs to the mechanical theory ofheat. This study, moreover, will not only have the effect of makingknown to us interesting facts in electricity, but will throw somelight on the phenomena of electricity themselves. "

The eminent professor was thus expressing the general opinion of hiscontemporaries, but he certainly seemed to have felt in advance thatthe new theory was about to penetrate more deeply into the inmostnature of things. Three years previously, Rankine also had put forthsome very remarkable ideas the full meaning of which was not at firstwell understood. He it was who comprehended the utility of employing amore inclusive term, and invented the phrase energetics. He alsoendeavoured to create a new doctrine of which rational mechanicsshould be only a particular case; and he showed that it was possibleto abandon the ideas of atoms and central forces, and to construct amore general system by substituting for the ordinary consideration offorces that of the energy which exists in all bodies, partly in anactual, partly in a potential state. 

By giving more precision to the conceptions of Rankine, the physicistsof the end of the nineteenth century were brought to consider that inall physical phenomena there occur apparitions and disappearanceswhich are balanced by various energies. It is natural, however, tosuppose that these equivalent apparitions and disappearancescorrespond to transformations and not to simultaneous creations anddestructions. We thus represent energy to ourselves as takingdifferent forms--mechanical, electrical, calorific, and chemical--capable of changing one into the other, but in such a way that thequantitative value always remains the same. In like manner a bankdraft may be represented by notes, gold, silver, or bullion. Theearliest known form of energy, _i. E. _ work, will serve as the standardas gold serves as the monetary standard, and energy in all its formswill be estimated by the corresponding work. In each particular casewe can strictly define and measure, by the correct application of theprinciple of the conservation of energy, the quantity of energyevolved under a given form. 

We can thus arrange a machine comprising a body capable of evolvingthis energy; then we can force all the organs of this machine tocomplete an entirely closed cycle, with the exception of the bodyitself, which, however, has to return to such a state that all thevariables from which this state depends resume their initial valuesexcept the particular variable to which the evolution of the energyunder consideration is linked. The difference between the work thusaccomplished and that which would have been obtained if this variablealso had returned to its original value, is the measure of the energyevolved. 

In the same way that, in the minds of mechanicians, all forces ofwhatever origin, which are capable of compounding with each other andof balancing each other, belong to the same category of beings, so formany physicists energy is a sort of entity which we find under variousaspects. There thus exists for them a world, which comes in some wayto superpose itself upon the world of matter--that is to say, theworld of energy, dominated in its turn by a fundamental law similar tothat of Lavoisier. [5] This conception, as we have already seen, passesthe limit of experience; but others go further still. Absorbed in thecontemplation of this new world, they succeed in persuading themselvesthat the old world of matter has no real existence and that energy issufficient by itself to give us a complete comprehension of theUniverse and of all the phenomena produced in it. They point out thatall our sensations correspond to changes of energy, and thateverything apparent to our senses is, in truth, energy. The famousexperiment of the blows with a stick by which it was demonstrated to asceptical philosopher that an outer world existed, only proves, inreality, the existence of energy, and not that of matter. The stick initself is inoffensive, as Professor Ostwald remarks, and it is its_vis viva_, its kinetic energy, which is painful to us; while if wepossessed a speed equal to its own, moving in the same direction, itwould 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 kineticenergy, its pretended impenetrability energy of volume, and its weightenergy of position in the particular form which presents itself inuniversal gravitation; nay, space itself would only be known to us bythe expenditure of energy necessary to penetrate it. Thus in allphysical phenomena we should only have to regard the quantities ofenergy brought into play, and all the equations which link thephenomena to one another would have no meaning but when they apply toexchanges of energy. For energy alone can be common to all phenomena. 

This extreme manner of regarding things is seductive by itsoriginality, but appears somewhat insufficient if, after enunciatinggeneralities, we look more closely into the question. From thephilosophical point of view it may, moreover, seem difficult not toconclude, from the qualities which reveal, if you will, the variedforms of energy, that there exists a substance possessing thesequalities. This energy, which resides in one region, and whichtransports 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 ofenergy and its conservation, but he had to invoke a second law, theprinciple of least action. If he thus succeeded in dispensing with thehypothesis of atoms, and in showing that the new mechanics gave us tounderstand the impossibility of certain movements which, according tothe old, ought to have been but never were experimentally produced, hewas only able to do so because the principle of least action necessaryfor his theory became evident in the case of those irreversiblephenomena which alone really exist in Nature. The energetists havethus not succeeded in forming a thoroughly sound system, but theirefforts have at all events been partly successful. Most physicists areof their opinion, that kinetic energy is only a particular variety ofenergy to which we have no right to wish to connect all its otherforms. 

If these forms showed themselves to be innumerable throughout theUniverse, the principle of the conservation of energy would, in fact, lose a great part of its importance. Every time that a certainquantity of energy seemed to appear or disappear, it would always bepermissible to suppose that an equivalent quantity had appeared ordisappeared somewhere else under a new form; and thus the principlewould in a way vanish. But the known forms of energy are fairlyrestricted in number, and the necessity of recognising new ones seldommakes itself felt. We shall see, however, that to explain, forinstance, the paradoxical properties of radium and to re-establishconcord between these properties and the principle of the conservationof energy, certain physicists have recourse to the hypothesis thatradium borrows an unknown energy from the medium in which it isplunged. This hypothesis, however, is in no way necessary; and in afew other rare cases in which similar hypotheses have had to be setup, experiment has always in the long run enabled us to discover somephenomenon which had escaped the first observers and which correspondsexactly to the variation of energy first made evident. 

One difficulty, however, arises from the fact that the principle oughtonly to be applied to an isolated system. Whether we imagine actionsat a distance or believe in intermediate media, we must alwaysrecognise that there exist no bodies in the world incapable of actingon each other, and we can never affirm that some modification in theenergy of a given place may not have its echo in some unknown spotafar off. This difficulty may sometimes render the value of theprinciple rather illusory. 

Similarly, it behoves us not to receive without a certain distrust theextension by certain philosophers to the whole Universe, of a propertydemonstrated for those restricted systems which observation can alonereach. We know nothing of the Universe as a whole, and everygeneralization of this kind outruns in a singular fashion the limit ofexperiment. 

Even reduced to the most modest proportions, the principle of theconservation 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 areexperimentally able to grasp causality, and that it teaches us that aresult has to be purchased at the cost of a determined effort. 

We can, in fact, with M. Perrin and M. Langevin, represent this in away which puts this characteristic in evidence by enunciating it asfollows: "If at the cost of a change C we can obtain a change K, therewill never be acquired at the same cost, whatever the mechanismemployed, first the change K and in addition some other change, unlessthis latter be one that is otherwise known to cost nothing to produceor to destroy. " If, for instance, the fall of a weight can beaccompanied, without anything else being produced, by anothertransformation--the melting of a certain mass of ice, for example--itwill be impossible, no matter how you set about it or whatever themechanism used, to associate this same transformation with the meltingof another weight of ice. 

We can thus, in the transformation in question, obtain an appropriatenumber which will sum up that which may be expected from the externaleffect, and can give, so to speak, the price at which thistransformation is bought, measure its invariable value by a commonmeasure (for instance, the melting of the ice), and, without anyambiguity, define the energy lost during the transformation asproportional to the mass of ice which can be associated with it. Thismeasure is, moreover, independent of the particular phenomenon takenas the common measure. 

§ 3. THE PRINCIPLE OF CARNOT AND CLAUSIUS

The principle of Carnot, of a nature analogous to the principle of theconservation of energy, has also a similar origin. It was firstenunciated, like the last named, although prior to it in time, inconsequence of considerations which deal only with heat and mechanicalwork. Like it, too, it has evolved, grown, and invaded the entiredomain of physics. It may be interesting to examine rapidly thevarious phases of this evolution. The origin of the principle ofCarnot is clearly determined, and it is very rare to be able to goback thus certainly to the source of a discovery. Sadi Carnot had, truth to say, no precursor. In his time heat engines were not yet verycommon, and no one had reflected much on their theory. He wasdoubtless the first to propound to himself certain questions, andcertainly the first to solve them. 

It is known how, in 1824, in his _Réflexions sur la puissance motricedu feu_, he endeavoured to prove that "the motive power of heat isindependent of the agents brought into play for its realization, " andthat "its quantity is fixed solely by the temperature of the bodiesbetween which, in the last resort, the transport of caloric iseffected"--at least in all engines in which "the method of developingthe motive power attains the perfection of which it is capable"; andthis is, almost textually, one of the enunciations of the principle atthe present day. Carnot perceived very clearly the great fact that, toproduce work by heat, it is necessary to have at one's disposal a fallof temperature. On this point he expresses himself with perfectclearness: "The motive power of a fall of water depends on its heightand on the quantity of liquid; the motive power of heat depends alsoon the quantity of caloric employed, and on what might be called--infact, what we shall call--the height of fall, that is to say, thedifference in temperature of the bodies between which the exchange ofcaloric takes place. "

Starting with this idea, he endeavours to demonstrate, by associatingtwo engines capable of working in a reversible cycle, that theprinciple is founded on the impossibility of perpetual motion. 

His memoir, now celebrated, did not produce any great sensation, andit had almost fallen into deep oblivion, which, in consequence ofthe discovery of the principle of equivalence, might have seemedperfectly justified. Written, in fact, on the hypothesis of theindestructibility of caloric, it was to be expected that this memoirshould be condemned in the name of the new doctrine, that is, of theprinciple recently brought to light. 

It was really making a new discovery to establish that Carnot'sfundamental idea survived the destruction of the hypothesis on thenature of heat, on which he seemed to rely. As he no doubt himselfperceived, his idea was quite independent of this hypothesis, since, as we have seen, he was led to surmise that heat could disappear; buthis demonstrations needed to be recast and, in some points, modified. 

It is to Clausius that was reserved the credit of rediscovering theprinciple, and of enunciating it in language conformable to the newdoctrines, while giving it a much greater generality. The postulatearrived at by experimental induction, and which must be admittedwithout demonstration, is, according to Clausius, that in a series oftransformations in which the final is identical with the initialstage, it is impossible for heat to pass from a colder to a warmerbody unless some other accessory phenomenon occurs at the same time. 

Still more correctly, perhaps, an enunciation can be given of thepostulate 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, andif a certain quantity of heat is given to one of the sources, whichcan never be the hotter of the two. By the expression "source ofheat, " we mean a body exterior to the system and capable of furnishingor withdrawing heat from it. 

Starting with this principle, we arrive, as does Clausius, at thedemonstration that the output of a reversible machine working betweentwo given temperatures is greater than that of any non-reversibleengine, and that it is the same for all reversible machines workingbetween these two temperatures. 

This is the very proposition of Carnot; but the proposition thusstated, while very useful for the theory of engines, does not yetpresent any very general interest. Clausius, however, drew from itmuch more important consequences. First, he showed that the principleconduces to the definition of an absolute scale of temperature; andthen he was brought face to face with a new notion which allows astrong light to be thrown on the questions of physical equilibrium. Irefer to entropy. 

It is still rather difficult to strip entirely this very importantnotion of all analytical adornment. Many physicists hesitate toutilize it, and even look upon it with some distrust, because they seein it a purely mathematical function without any definite physicalmeaning. Perhaps they are here unduly severe, since they often admittoo easily the objective existence of quantities which they cannotdefine. Thus, for instance, it is usual almost every day to speak ofthe heat possessed by a body. Yet no body in reality possesses adefinite quantity of heat even relatively to any initial state; sincestarting from this point of departure, the quantities of heat it mayhave gained or lost vary with the road taken and even with the meansemployed to follow it. These expressions of heat gained or lost are, moreover, themselves evidently incorrect, for heat can no longer beconsidered as a sort of fluid passing from one body to another. 

The real reason which makes entropy somewhat mysterious is that thismagnitude does not fall directly under the ken of any of our senses;but it possesses the true characteristic of a concrete physicalmagnitude, since it is, in principle at least, measurable. Variousauthors of thermodynamical researches, amongst whom M. Mouret shouldbe particularly mentioned, have endeavoured to place thischaracteristic in evidence. 

Consider an isothermal transformation. Instead of leaving the heatabandoned by the body subjected to the transformation--watercondensing in a state of saturated vapour, for instance--to passdirectly into an ice calorimeter, we can transmit this heat to thecalorimeter by the intermediary of a reversible Carnot engine. Theengine having absorbed this quantity of heat, will only give back tothe ice a lesser quantity of heat; and the weight of the melted ice, inferior to that which might have been directly given back, will serveas a measure of the isothermal transformation thus effected. It can beeasily shown that this measure is independent of the apparatus used. It consequently becomes a numerical element characteristic of the bodyconsidered, and is called its entropy. Entropy, thus defined, is avariable which, like pressure or volume, might serve concurrently withanother variable, such as pressure or volume, to define the state of abody. 

It must be perfectly understood that this variable can change in anindependent manner, and that it is, for instance, distinct from thechange of temperature. It is also distinct from the change whichconsists in losses or gains of heat. In chemical reactions, forexample, the entropy increases without the substances borrowing anyheat. When a perfect gas dilates in a vacuum its entropy increases, and yet the temperature does not change, and the gas has neither beenable to give nor receive heat. We thus come to conceive that aphysical phenomenon cannot be considered known to us if the variationof entropy is not given, as are the variations of temperature and ofpressure or the exchanges of heat. The change of entropy is, properlyspeaking, the most characteristic fact of a thermal change. 

It is important, however, to remark that if we can thus easily defineand measure the difference of entropy between two states of the samebody, the value found depends on the state arbitrarily chosen as thezero point of entropy; but this is not a very serious difficulty, andis analogous to that which occurs in the evaluation of other physicalmagnitudes--temperature, potential, etc. 

A graver difficulty proceeds from its not being possible to define adifference, or an equality, of entropy between two bodies chemicallydifferent. We are unable, in fact, to pass by any means, reversible ornot, from one to the other, so long as the transmutation of matter isregarded as impossible; but it is well understood that it isnevertheless possible to compare the variations of entropy to whichthese 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 anotherby a reversible transformation. Reversibility is an ideal and extremecase which cannot be realized, but which can be approximately attainedin many circumstances. So with gases and with perfectly elasticbodies, we effect sensibly reversible transformations, and changesof physical state are practically reversible. The discoveries ofSainte-Claire Deville have brought many chemical phenomena into asimilar category, and reactions such as solution, which used to beformerly the type of an irreversible phenomenon, may now often beeffected by sensibly reversible means. Be that as it may, when once thedefinition is admitted, we arrive, by taking as a basis the principlesset forth at the inception, at the demonstration of the celebratedtheorem of Clausius: _The entropy of a thermally isolated systemcontinues to increase incessantly. _

It is very evident that the theorem can only be worth applying incases where the entropy can be exactly defined; but, even when thuslimited, the field still remains vast, and the harvest which we canthere reap is very abundant. 

Entropy appears, then, as a magnitude measuring in a certain way theevolution of a system, or, at least, as giving the direction of thisevolution. This very important consequence certainly did not escapeClausius, since the very name of entropy, which he chose to designatethis magnitude, itself signifies evolution. We have succeeded indefining this entropy by demonstrating, as has been said, a certainnumber of propositions which spring from the postulate of Clausius; itis, therefore, natural to suppose that this postulate itself contains_in potentia_ the very idea of a necessary evolution of physicalsystems. But as it was first enunciated, it contains it in a deeplyhidden way. 

No doubt we should make the principle of Carnot appear in aninteresting light by endeavouring to disengage this fundamental idea, and by placing it, as it were, in large letters. Just as, inelementary geometry, we can replace the postulate of Euclid by otherequivalent propositions, so the postulate of thermodynamics is notnecessarily fixed, and it is instructive to try to give it the mostgeneral and suggestive character. 

MM. Perrin and Langevin have made a successful attempt in thisdirection. M. Perrin enunciates the following principle: _An isolatedsystem never passes twice through the same state_. In this form, theprinciple affirms that there exists a necessary order in thesuccession of two phenomena; that evolution takes place in adetermined direction. If you prefer it, it may be thus stated: _Of twoconverse transformations unaccompanied by any external effect, oneonly is possible_. For instance, two gases may diffuse themselves onein the other in constant volume, but they could not converselyseparate themselves spontaneously. 

Starting from the principle thus put forward, we make the logicaldeduction that one cannot hope to construct an engine which shouldwork for an indefinite time by heating a hot source and by cooling acold one. We thus come again into the route traced by Clausius, andfrom this point we may follow it strictly. 

Whatever the point of view adopted, whether we regard the propositionof M. Perrin as the corollary of another experimental postulate, orwhether we consider it as a truth which we admit _a priori_ and verifythrough its consequences, we are led to consider that in its entiretythe principle of Carnot resolves itself into the idea that we cannotgo back along the course of life, and that the evolution of a systemmust follow its necessary progress. 

Clausius and Lord Kelvin have drawn from these considerations certainwell-known consequences on the evolution of the Universe. Noticingthat entropy is a property added to matter, they admit that there isin the world a total amount of entropy; and as all real changes whichare produced in any system correspond to an increase of entropy, itmay 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 distributedat a temperature everywhere identical. In the end, therefore, therewill be neither chemical phenomena nor manifestation of life; theworld will still exist, but without motion, and, so to speak, dead. 

These consequences must be admitted to be very doubtful; we cannot inany certain way apply to the Universe, which is not a finite system, aproposition demonstrated, and that not unreservedly, in the sharplylimited case of a finite system. Herbert Spencer, moreover, in hisbook on _First Principles_, brings out with much force the idea that, even if the Universe came to an end, nothing would allow us toconclude that, once at rest, it would remain so indefinitely. We mayrecognise that the state in which we are began at the end of a formerevolutionary period, and that the end of the existing era will markthe beginning of a new one. 

Like an elastic and mobile object which, thrown into the air, attainsby degrees the summit of its course, then possesses a zero velocityand is for a moment in equilibrium, and then falls on touching theground to rebound, so the world should be subjected to hugeoscillations which first bring it to a maximum of entropy till themoment when there should be produced a slow evolution in the contrarydirection bringing it back to the state from which it started. Thus, in the infinity of time, the life of the Universe proceeds withoutreal stop. 

This conception is, moreover, in accordance with the view certainphysicists take of the principle of Carnot. We shall see, for example, that in the kinetic theory we are led to admit that, after waitingsufficiently long, we can witness the return of the various statesthrough which a mass of gas, for example, has passed in its series oftransformations. 

If we keep to the present era, evolution has a fixed direction--thatwhich leads to an increase of entropy; and it is possible to enquire, in any given system to what physical manifestations this increasecorresponds. We note that kinetic, potential, electrical, and chemicalforms of energy have a great tendency to transform themselves intocalorific 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 sotrue, that chemists currently speak of the heat given out by reactionsinstead 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, transformit integrally into mechanical energy, since the heat possessed by abody can only yield work on condition that a part of it falls on abody with a lower temperature. Thus appears the idea that energieswhich exchange with each other and correspond to equal quantities havenot the same qualitative value. Form has its importance, and there arepersons who prefer a golden louis to four pieces of five francs. Theprinciple of Carnot would thus lead us to consider a certainclassification of energies, and would show us that, in thetransformations possible, these energies always tend to a sort ofdiminution of quality--that is, to a _degradation_. 

It would thus reintroduce an element of differentiation of which itseems very difficult to give a mechanical explanation. Certainphilosophers and physicists see in this fact a reason which condemns_a priori_ all attempts made to give a mechanical explanation of theprinciple of Carnot. 

It is right, however, not to exaggerate the importance that should beattributed to the phrase degraded energy. If the heat is notequivalent to the work, if heat at 99° is not equivalent to heat at100°, that means that we cannot in practice construct an engine whichshall transform all this heat into work, or that, for the same coldsource, the output is greater when the temperature of the hot sourceis higher; but if it were possible that this cold source had itselfthe temperature of absolute zero, the whole heat would reappear in theform of work. The case here considered is an ideal and extreme case, and we naturally cannot realize it; but this consideration suffices tomake it plain that the classification of energies is a littlearbitrary and depends more, perhaps, on the conditions in whichmankind lives than on the inmost nature of things. 

In fact, the attempts which have often been made to refer theprinciple of Carnot to mechanics have not given convincing results. Ithas nearly always been necessary to introduce into the attempt somenew hypothesis independent of the fundamental hypotheses of ordinarymechanics, and equivalent, in reality, to one of the postulates onwhich the ordinary exposition of the second law of thermodynamics isfounded. Helmholtz, in a justly celebrated theory, endeavoured to fitthe principle of Carnot into the principle of least action; but thedifficulties regarding the mechanical interpretation of theirreversibility of physical phenomena remain entire. Looking at thequestion, however, from the point of view at which the partisans ofthe kinetic theories of matter place themselves, the principle isviewed in a new aspect. Gibbs and afterwards Boltzmann and ProfessorPlanck have put forward some very interesting ideas on this subject. By following the route they have traced, we come to consider theprinciple as pointing out to us that a given system tends towards theconfiguration presented by the maximum probability, and, numerically, the entropy would even be the logarithm of this probability. Thus twodifferent gaseous masses, enclosed in two separate receptacles whichhave just been placed in communication, diffuse themselves one throughthe other, and it is highly improbable that, in their mutual shocks, both kinds of molecules should take a distribution of velocities whichreduce them by a spontaneous phenomenon to the initial state. 

We should have to wait a very long time for so extraordinary aconcourse of circumstances, but, in strictness, it would not beimpossible. The principle would only be a law of probability. Yet thisprobability is all the greater the more considerable is the number ofmolecules itself. In the phenomena habitually dealt with, this numberis such that, practically, the variation of entropy in a constantsense takes, so to speak, the character of absolute certainty. 

But there may be exceptional cases where the complexity of the systembecomes insufficient for the application of the principle of Carnot;--as in the case of the curious movements of small particles suspendedin a liquid which are known by the name of Brownian movements and canbe observed under the microscope. The agitation here really seems, asM. Gouy has remarked, to be produced and continued indefinitely, regardless of any difference in temperature; and we seem to witnessthe incessant motion, in an isothermal medium, of the particles whichconstitute matter. Perhaps, however, we find ourselves already inconditions where the too great simplicity of the distribution of themolecules 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 takecognizance of molecular movements that _vis viva_ can be taken fromthem. The mechanisms of M. Lippmann are not, like the celebratedapparatus at one time devised by Maxwell, purely hypothetical. They donot suppose a partition with a hole impossible to be bored throughmatter where the molecular spaces would be larger than the holeitself. They have finite dimensions. Thus M. Lippmann considers a vasefull of oxygen at a constant temperature. In the interior of this vaseis placed a small copper ring, and the whole is set in a magneticfield. The oxygen molecules are, as we know, magnetic, and whenpassing through the interior of the ring they produce in this ring aninduced current. During this time, it is true, other molecules emergefrom the space enclosed by the circuit; but the two effects do notcounterbalance each other, and the resulting current is maintained. There is elevation of temperature in the circuit in accordance withJoule's law; and this phenomenon, under such conditions, isincompatible with the principle of Carnot. 

It is possible--and that, I think, is M. Lippmann's idea--to draw fromhis very ingenious criticism an objection to the kinetic theory, if weadmit the absolute value of the principle; but we may also supposethat here again we are in presence of a system where the prescribedconditions diminish the complexity and render it, consequently, lessprobable that the evolution is always effected in the same direction. 

In whatever way you look at it, the principle of Carnot furnishes, inthe immense majority of cases, a very sure guide in which physicistscontinue to have the most entire confidence. 

§ 4. THERMODYNAMICS

To apply the two fundamental principles of thermodynamics, variousmethods may be employed, equivalent in the main, but presenting as thecases 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, weobtain two relations between the coefficients which occur in a givenphenomenon; but it may be easier and also more suggestive to employvarious functions of these quantities. In a memoir, of which someextracts appeared as early as 1869, a modest scholar, M. Massieu, indicated in particular a remarkable function which he termed acharacteristic function, and by the employment of which calculationsare 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 publishedworks, at first ill understood, of which the renown was, however, considerable in the sequel, and in which they made use of analogousfunctions under the names of available energy, free energy, orinternal thermodynamic potential. The magnitude thus designated, attaching, as a consequence of the two principles, to all states ofthe system, is perfectly determined when the temperature and othernormal variables are known. It allows us, by calculations often veryeasy, to fix the conditions necessary and sufficient for themaintenance of the system in equilibrium by foreign bodies taken atthe same temperature as itself. 

One may hope to constitute in this way, as M. Duhem in a long andremarkable series of operations has specially endeavoured to do, asort of general mechanics which will enable questions of statics to betreated with accuracy, and all the conditions of equilibrium of thesystem, including the calorific properties, to be determined. Thus, ordinary statics teaches us that a liquid with its vapour on the topforms a system in equilibrium, if we apply to the two fluids apressure depending on temperature alone. Thermodynamics will furnishus, in addition, with the expression of the heat of vaporization andof, the specific heats of the two saturated fluids. 

This new study has given us also most valuable information oncompressible fluids and on the theory of elastic equilibrium. Added tocertain hypotheses on electric or magnetic phenomena, it gives acoherent whole from which can be deduced the conditions of electric ormagnetic equilibrium; and it illuminates with a brilliant light thecalorific laws of electrolytic phenomena. 

But the most indisputable triumph of this thermodynamic statics is thediscovery of the laws which regulate the changes of physical state orof chemical constitution. J. W. Gibbs was the author of this immenseprogress. His memoir, now celebrated, on "the equilibrium ofheterogeneous substances, " concealed in 1876 in a review at that timeof limited circulation, and rather heavy to read, seemed only tocontain algebraic theorems applicable with difficulty to reality. Itis known that Helmholtz independently succeeded, a few years later, inintroducing thermodynamics into the domain of chemistry by hisconception of the division of energy into free and into bound energy:the first, capable of undergoing all transformations, and particularlyof transforming itself into external action; the second, on the otherhand, bound, and only manifesting itself by giving out heat. When wemeasure chemical energy, we ordinarily let it fall wholly into thecalorific form; but, in reality, it itself includes both parts, and itis the variation of the free energy and not that of the total energymeasured by the integral disengagement of heat, the sign of whichdetermines the direction in which the reactions are effected. 

But if the principle thus enunciated by Helmholtz as a consequence ofthe laws of thermodynamics is at bottom identical with that discoveredby Gibbs, it is more difficult of application and is presented under amore mysterious aspect. It was not until M. Van der Waals exhumed thememoir of Gibbs, when numerous physicists or chemists, most of themDutch--Professor Van t'Hoff, Bakhius Roozeboom, and others--utilizedthe rules set forth in this memoir for the discussion of the mostcomplicated chemical reactions, that the extent of the new laws wasfully understood. 

The chief rule of Gibbs is the one so celebrated at the present dayunder the name of the Phase Law. We know that by phases are designatedthe homogeneous substances into which a system is divided; thuscarbonate of lime, lime, and carbonic acid gas are the three phases ofa system which comprises Iceland spar partially dissociated into limeand carbonic acid gas. The number of phases added to the number ofindependent components--that is to say, bodies whose mass is leftarbitrary by the chemical formulas of the substances entering into thereaction--fixes the general form of the law of equilibrium of thesystem; that is to say, the number of quantities which, by theirvariations (temperature and pressure), would be of a nature to modifyits equilibrium by modifying the constitution of the phases. 

Several authors, M. Raveau in particular, have indeed given verysimple demonstrations of this law which are not based onthermodynamics; but thermodynamics, which led to its discovery, continues to give it its true scope. Moreover, it would not sufficemerely to determine quantitatively those laws of which it makes knownthe general form. We must, if we wish to penetrate deeper intodetails, particularize the hypothesis, and admit, for instance, withGibbs that we are dealing with perfect gases; while, thanks tothermodynamics, we can constitute a complete theory of dissociationwhich leads to formulas in complete accord with the numerical resultsof the experiment. We can thus follow closely all questions concerningthe displacements of the equilibrium, and find a relation of the firstimportance between the masses of the bodies which react in order toconstitute a system in equilibrium. 

The statics thus constructed constitutes at the present day animportant edifice to be henceforth classed amongst historicalmonuments. Some theorists even wish to go a step beyond. They haveattempted to begin by the same means a more complete study of thosesystems whose state changes from one moment to another. This is, moreover, a study which is necessary to complete satisfactorily thestudy of equilibrium itself; for without it grave doubts would existas to the conditions of stability, and it alone can give their truemeaning to questions relating to displacements of equilibrium. 

The problems with which we are thus confronted are singularlydifficult. M. Duhem has given us many excellent examples of thefecundity of the method; but if thermodynamic statics may beconsidered definitely founded, it cannot be said that the generaldynamics of systems, considered as the study of thermal movements andvariations, are yet as solidly established. 

§ 5. ATOMISM

It may appear singularly paradoxical that, in a chapter devoted togeneral views on the principles of physics, a few words should beintroduced on the atomic theories of matter. 

Very often, in fact, what is called the physics of principles is setin opposition to the hypotheses on the constitution of matter, particularly to atomic theories. I have already said that, abandoningthe investigation of the unfathomable mystery of the constitution ofthe Universe, some physicists think they may find, in certain generalprinciples, sufficient guides to conduct them across the physicalworld. But I have also said, in examining the history of thoseprinciples, 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 molecularhypotheses: and the question suggests itself whether this is merechance, 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, aphilosopher who is also an erudite scholar, examined the part taken byatomism in the history of science. He notes that atomism and sciencewere born, in Greece, of the same problem, and that in modern timesthe revival of the one was closely connected with that of the other. He shows, too, by very close analysis, that the atomic hypothesis isessential to the optics of Fresnel and of Cauchy; that it penetratesinto the study of heat; and that, in its general features, it presidedat 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 ofNature, and that contemporary theories are on this point in accordwith history: for these theories consecrate the preponderance of thishypothesis in the domain of science. 

If M. Hannequin had not been prematurely cut off in the full expansionof his vigorous talent, he might have added another chapter to hisexcellent book. He would have witnessed a prodigious budding ofatomistic ideas, accompanied, it is true, by wide modifications in themanner in which the atom is to be regarded, since the most recenttheories make material atoms into centres constituted of atoms ofelectricity. On the other hand, he would have found in the burstingforth of these new doctrines one more proof in support of his ideathat science is indissolubly bound to atomism. 

From the philosophical point of view, M. Hannequin, examining thereasons which may have called these links into being, arrives at theidea that they necessarily proceed from the constitution of ourknowledge, or, perhaps, from that of Nature itself. Moreover, thisorigin, double in appearance, is single at bottom. Our minds couldnot, in fact, detach and come out of themselves to grasp reality andthe absolute in Nature. According to the idea of Descartes, it is thedestiny of our minds only to take hold of and to understand that whichproceeds from them. 

Thus atomism, which is, perhaps, only an appearance containing evensome contradictions, is yet a well-founded appearance, since itconforms 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 refuseto recognise, as he does, that atomic theories occupy a preponderatingpart in the doctrines of physics; and the position which they havethus conquered gives them, in a way, the right of saying that theyrest on a real principle. It is in order to recognise this right thatseveral physicists--M. Langevin, for example--ask that atoms bepromoted from the rank of hypotheses to that of principles. By thisthey mean that the atomistic ideas forced upon us by an almostobligatory induction based on very exact experiments, enable us toco-ordinate a considerable amount of facts, to construct a very generalsynthesis, and to foresee a great number of phenomena. 

It is of moment, moreover, to thoroughly understand that atomism doesnot necessarily set up the hypothesis of centres of attraction actingat a distance, and it must not be confused with molecular physics, which has, on the other hand, undergone very serious checks. Themolecular physics greatly in favour some fifty years ago leads to suchcomplex representations and to solutions often so undetermined, thatthe most courageous are wearied with upholding it and it has falleninto some discredit. It rested on the fundamental principles ofmechanics applied to molecular actions; and that was, no doubt, anextension legitimate enough, since mechanics is itself only anexperimental science, and its principles, established for themovements of matter taken as a whole, should not be applied outsidethe domain which belongs to them. Atomism, in fact, tends more andmore, in modern theories, to imitate the principle of the conservationof energy or that of entropy, to disengage itself from the artificialbonds which attached it to mechanics, and to put itself forward as anindependent principle. 

Atomistic ideas also have undergone evolution, and this slow evolutionhas been considerably quickened under the influence of moderndiscoveries. These reach back to the most remote antiquity, and tofollow their development we should have to write the history of humanthought which they have always accompanied since the time ofLeucippus, Democritus, Epicurus, and Lucretius. The first observerswho noticed that the volume of a body could be diminished bycompression or cold, or augmented by heat, and who saw a soluble solidbody mix completely with the water which dissolved it, must have beencompelled to suppose that matter was not dispersed continuouslythroughout the space it seemed to occupy. They were thus brought toconsider it discontinuous, and to admit that a substance having thesame composition and the same properties in all its parts--in a word, perfectly homogeneous--ceases to present this homogeneity whenconsidered within a sufficiently small volume. 

Modern experimenters have succeeded by direct experiments in placingin evidence this heterogeneous character of matter when taken in smallmass. Thus, for example, the superficial tension, which is constantfor the same liquid at a given temperature, no longer has the samevalue when the thickness of the layer of liquid becomes extremelysmall. Newton noticed even in his time that a dark zone is seen toform on a soap bubble at the moment when it becomes so thin that itmust burst. Professor Reinold and Sir Arthur Rücker have shown thatthis zone is no longer exactly spherical; and from this we mustconclude that the superficial tension, constant for all thicknessesabove a certain limit, commences to vary when the thickness fallsbelow a critical value, which these authors estimate, on opticalgrounds, at about fifty millionths of a millimetre. 

From experiments on capillarity, Prof. Quincke has obtained similarresults with regard to layers of solids. But it is not only capillaryproperties which allow this characteristic to be revealed. All theproperties of a body are modified when taken in small mass; M. Meslinproves this in a very ingenious way as regards optical properties, andMr Vincent in respect of electric conductivity. M. Houllevigue, who, in a chapter of his excellent work, _Du Laboratoire à l'Usine_, hasvery clearly set forth the most interesting considerations on atomichypotheses, has recently demonstrated that copper and silver cease tocombine with iodine as soon as they are present in a thickness of lessthan thirty millionths of a millimetre. It is this same dimensionlikewise that is possessed, according to M. Wiener, by the smallestthicknesses it is possible to deposit on glass. These layers are sothin that they cannot be perceived, but their presence is revealed bya change in the properties of the light reflected by them. 

Thus, below fifty to thirty millionths of a millimetre the propertiesof matter depend on its thickness. There are then, no doubt, only afew 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 amillimetre. Considerations regarding more complex phenomena, forinstance the phenomena of electricity by contact, and also the kinetictheory of gases, bring us to the same conclusion. 

The idea of the discontinuity of matter forces itself upon us for manyother reasons. All modern chemistry is founded on this principle; andlaws like the law of multiple proportions, introduce an evidentdiscontinuity to which we find analogies in the law of electrolysis. The elements of bodies we are thus brought to regard might, as regardssolids at all events, be considered as immobile; but this immobilitycould not explain the phenomena of heat, and, as it is entirelyinadmissible for gases, it seems very improbable it can absolutelyoccur in any state. We are thus led to suppose that these elements areanimated by very complicated movements, each one proceeding in closedtrajectories in which the least variations of temperature or pressurecause modifications. 

The atomistic hypothesis shows itself remarkably fecund in the studyof phenomena produced in gases, and here the mutual independence ofthe particles renders the question relatively more simple and, perhaps, allows the principles of mechanics to be more certainlyextended to the movements of molecules. 

The kinetic theory of gases can point to unquestioned successes; andthe idea of Daniel Bernouilli, who, as early as 1738, considered agaseous mass to be formed of a considerable number of moleculesanimated by rapid movements of translation, has been put into a formprecise enough for mathematical analysis, and we have thus foundourselves in a position to construct a really solid foundation. Itwill be at once conceived, on this hypothesis, that pressure is theresultant of the shocks of the molecules against the walls of thecontaining vessel, and we at once come to the demonstration that thelaw of Mariotte is a natural consequence of this origin of pressure;since, if the volume occupied by a certain number of molecules isdoubled, the number of shocks per second on each square centimetre ofthe walls becomes half as much. But if we attempt to carry thisfurther, we find ourselves in presence of a serious difficulty. It isimpossible to mentally follow every one of the many individualmolecules which compose even a very limited mass of gas. The pathfollowed by this molecule may be every instant modified by the chanceof running against another, or by a shock which may make it rebound inanother direction. 

The difficulty would be insoluble if chance had not laws of its own. It was Maxwell who first thought of introducing into the kinetictheory the calculation of probabilities. Willard Gibbs and Boltzmannlater on developed this idea, and have founded a statistical methodwhich does not, perhaps, give absolute certainty, but which iscertainly most interesting and curious. Molecules are grouped in sucha way that those belonging to the same group may be considered ashaving the same state of movement; then an examination is made of thenumber of molecules in each group, and what are the changes in thisnumber from one moment to another. It is thus often possible todetermine the part which the different groups have in the totalproperties of the system and in the phenomena which may occur. 

Such a method, analogous to the one employed by statisticians forfollowing the social phenomena in a population, is all the morelegitimate the greater the number of individuals counted in theaverages; now, the number of molecules contained in a limited space--for example, in a centimetre cube taken in normal conditions--is suchthat no population could ever attain so high a figure. Allconsiderations, those we have indicated as well as others which mightbe invoked (for example, the recent researches of M. Spring on thelimit of visibility of fluorescence), give this result:--that thereare, in this space, some twenty thousand millions of molecules. Eachof these must receive in the space of a millimetre about ten thousandshocks, and be ten thousand times thrust out of its course. The freepath of a molecule is then very small, but it can be singularlyaugmented by diminishing the number of them. Tait and Dewar havecalculated that, in a good modern vacuum, the length of the free pathof the remaining molecules not taken away by the air-pump easilyreaches a few centimetres. 

By developing this theory, we come to consider that, for a giventemperature, every molecule (and even every individual particle, atom, or ion) which takes part in the movement has, on the average, the samekinetic energy in every body, and that this energy is proportional tothe absolute temperature; so that it is represented by thistemperature multiplied by a constant quantity which is a universalconstant. 

This result is not an hypothesis but a very great probability. Thisprobability increases when it is noted that the same value for theconstant is met with in the study of very varied phenomena; forexample, in certain theories on radiation. Knowing the mass and energyof a molecule, it is easy to calculate its speed; and we find that theaverage speed is about 400 metres per second for carbonic anhydride, 500 for nitrogen, and 1850 for hydrogen at 0° C. And at ordinarypressure. I shall have occasion, later on, to speak of much moreconsiderable speeds than these as animating other particles. 

The kinetic theory has permitted the diffusion of gases to beexplained, and the divers circumstances of the phenomenon to becalculated. It has allowed us to show, as M. Brillouin has done, thatthe coefficient of diffusion of two gases does not depend on theproportion of the gases in the mixture; it gives a very striking imageof the phenomena of viscosity and conductivity; and it leads us tothink that the coefficients of friction and of conductivity areindependent of the density; while all these previsions have beenverified by experiment. It has also invaded optics; and by relying onthe principle of Doppler, Professor Michelson has succeeded inobtaining from it an explanation of the length presented by thespectral rays of even the most rarefied gases. 

But however interesting are these results, they would not havesufficed to overcome the repugnance of certain physicists forspeculations which, an imposing mathematical baggage notwithstanding, seemed to them too hypothetical. The theory, moreover, stopped at themolecule, and appeared to suggest no idea which could lead to thediscovery of the key to the phenomena where molecules exercise amutual 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 recentdiscoveries of the conductivity of gases and of the new radiationscame to procure for it a new and luxuriant efflorescence. It may besaid that the atomistic synthesis, but yesterday so decried, is to-daytriumphant. 

The elements which enter into the earlier kinetic theory, and which, to avoid confusion, should be always designated by the name ofmolecules, were not, truth to say, in the eyes of the chemists, thefinal term of the divisibility of matter. It is well known that, tothem, except in certain particular bodies like the vapour of mercuryand argon, the molecule comprises several atoms, and that, in compoundbodies, the number of these atoms may even be fairly considerable. Butphysicists rarely needed to have recourse to the consideration ofthese atoms. They spoke of them to explain certain particularities ofthe propagation of sound, and to enunciate laws relating to specificheats; but, in general, they stopped at the consideration of themolecule. 

The present theories carry the division much further. I shall notdwell now on these theories, since, in order to thoroughly understandthem, many other facts must be examined. But to avoid all confusion, it remains understood that, contrary, no doubt, to etymology, but inconformity with present custom, I shall continue in what follows tocall atoms those particles of matter which have till now been spokenof; these atoms being themselves, according to modern views, singularly complex edifices formed of elements, of which we shall haveoccasion 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 thedistinction established for the same substance between the threestates, retain a great importance for the applications and usages ofdaily life, but have long since lost their absolute value from thescientific point of view. 

So far as concerns the liquid and gaseous states particularly, thealready antiquated researches of Andrews confirmed the ideas ofCagniard de la Tour and established the continuity of the two states. A group of physical studies has thus been constituted on what may becalled the statics of fluids, in which we examine the relationsexisting between the pressure, the volume, and the temperature ofbodies, and in which are comprised, under the term fluid, gases aswell as liquids. 

These researches deserve attention by their interest and thegenerality of the results to which they have led. They also give aremarkable example of the happy effects which may be obtained by thecombined employment of the various methods of investigation used inexploring the domain of nature. Thermodynamics has, in fact, allowedus to obtain numerical relations between the various coefficients, andatomic hypotheses have led to the establishment of one capitalrelation, the characteristic equation of fluids; while, on the otherhand, experiment in which the progress made in the art of measurementhas been utilized, has furnished the most valuable information on allthe laws of compressibility and dilatation. 

The classical work of Andrews was not very wide. Andrews did not gomuch beyond pressures close to the normal and ordinary temperatures. Of late years several very interesting and peculiar cases have beenexamined by MM. Cailletet, Mathias, Batelli, Leduc, P. Chappuis, andother physicists. Sir W. Ramsay and Mr S. Young have made known theisothermal diagrams[6] of a certain number of liquid bodies at theordinary temperature. They have thus been able, while keeping tosomewhat restricted limits of temperature and pressure, to touch uponthe most important questions, since they found themselves in theregion of the saturation curve and of the critical point. 

[Footnote 6: By isothermal diagram is meant the pattern or complexformed when the isothermal lines are arranged in curves of which thepressure 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, someliquid and some gaseous, extending the scope of his experiments so asto embrace the different phases of the phenomena and to comparetogether, not only the results relating to the same bodies, but alsothose concerning different bodies which happen to be in the sameconditions of temperature and pressure, but in very differentconditions as regards their critical points. 

From the experimental point of view, M. Amagat has been able, withextreme skill, to conquer the most serious difficulties. He hasmanaged to measure with precision pressures amounting to 3000atmospheres, and also the very small volumes then occupied by thefluid mass under consideration. This last measurement, whichnecessitates numerous corrections, is the most delicate part of theoperation. These researches have dealt with a certain number ofdifferent bodies. Those relating to carbonic acid and ethylene take inthe critical point. Others, on hydrogen and nitrogen, for instance, are very extended. Others, again, such as the study of thecompressibility of water, have a special interest, on account of thepeculiar properties of this substance. M. Amagat, by a very concisediscussion of the experiments, has also been able to definitelyestablish the laws of compressibility and dilatation of fluids underconstant pressure, and to determine the value of the variouscoefficients as well as their variations. It ought to be possible tocondense all these results into a single formula representing thevolume, the temperature, and the pressure. Rankin and, subsequently, Recknagel, and then Hirn, formerly proposed formulas of that kind; butthe most famous, the one which first appeared to contain in asatisfactory manner all the facts which experiments brought to lightand led to the production of many others, was the celebrated equationof Van der Waals. 

Professor Van der Waals arrived at this relation by relying uponconsiderations derived from the kinetic theory of gases. If we keep tothe simple idea at the bottom of this theory, we at once demonstratethat the gas ought to obey the laws of Mariotte and of Gay-Lussac, sothat the characteristic equation would be obtained by the statementthat the product of the number which is the measure of the volume bythat which is the measure of the pressure is equal to a constantcoefficient multiplied by the degree of the absolute temperature. Butto get at this result we neglect two important factors. 

We do not take into account, in fact, the attraction which themolecules must exercise on each other. Now, this attraction, which isnever absolutely non-existent, may become considerable when themolecules are drawn closer together; that is to say, when thecompressed gaseous mass occupies a more and more restricted volume. Onthe other hand, we assimilate the molecules, as a first approximation, to material points without dimensions; in the evaluation of the pathtraversed by each molecule no notice is taken of the fact that, at themoment of the shock, their centres of gravity are still separated by adistance equal to twice the radius of the molecule. 

M. Van der Waals has sought out the modifications which must beintroduced into the simple characteristic equation to bring it nearerto reality. He extends to the case of gases the considerations bywhich Laplace, in his famous theory of capillarity, reduced the effectof the molecular attraction to a perpendicular pressure exercised onthe surface of a liquid. This leads him to add to the externalpressure, that due to the reciprocal attractions of the gaseousparticles. On the other hand, when we attribute finite dimensions tothese particles, we must give a higher value to the number of shocksproduced in a given time, since the effect of these dimensions is todiminish the mean path they traverse in the time which elapses betweentwo consecutive shocks. 

The calculation thus pursued leads to our adding to the pressure inthe 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 thequadruple of the total and invariable volume which the gaseousmolecules 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 areconsidered; so that other and rather more complex formulas, on whichthere is no advantage in dwelling, have been proposed, and, in certaincases, better represent the facts. 

But the most remarkable result of M. Van der Waals' calculations isthe discovery of corresponding states. For a long time physicistsspoke of bodies taken in a comparable state. Dalton, for example, pointed out that liquids have vapour-pressures equal to thetemperatures equally distant from their boiling-point; but that if, inthis particular property, liquids were comparable under theseconditions of temperature, as regards other properties the parallelismwas no longer to be verified. No general rule was found until M. Vander Waals first enunciated a primary law, viz. , that if the pressure, the volume, and the temperature are estimated by taking as units thecritical quantities, the constants special to each body disappear inthe characteristic equation, which thus becomes the same for allfluids. 

The words corresponding states thus take a perfectly precisesignification. Corresponding states are those for which the numericalvalues of the pressure, volume, and temperature, expressed by takingas units the values corresponding to the critical point, are equal;and, in corresponding states any two fluids have exactly the sameproperties. 

M. Natanson, and subsequently P. Curie and M. Meslin, have shown byvarious considerations that the same result may be arrived at bychoosing units which correspond to any corresponding states; it hasalso been shown that the theorem of corresponding states in no wayimplies the exactitude of Van der Waals' formula. In reality, this issimply due to the fact that the characteristic equation only containsthree constants. 

The philosophical importance and the practical interest of thediscovery nevertheless remain considerable. As was to be expected, numbers of experimenters have sought whether these consequences areduly verified in reality. M. Amagat, particularly, has made use forthis purpose of a most original and simple method. He remarks that, inall its generality, the law may be translated thus: If the isothermaldiagrams of two substances be drawn to the same scale, taking as unitof volume and of pressure the values of the critical constants, thetwo diagrams should coincide; that is to say, their superpositionshould present the aspect of one diagram appertaining to a singlesubstance. Further, if we possess the diagrams of two bodies drawn toany scales and referable to any units whatever, as the changes ofunits mean changes in the scale of the axes, we ought to make one ofthe diagrams similar to the other by lengthening or shortening it inthe direction of one of the axes. M. Amagat then photographs twoisothermal diagrams, leaving one fixed, but arranging the other sothat it may be free to turn round each axis of the co-ordinates; andby 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 laboriouscalculations, but its sensibility is unequally distributed over thedifferent regions of the diagram. M. Raveau has pointed out an equallysimple way of verifying the law, by remarking that if the logarithmsof the pressure and volume are taken as co-ordinates, the co-ordinatesof two corresponding points differ by two constant quantities, and thecorresponding curves are identical. 

From these comparisons, and from other important researches, amongwhich 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 attributedto them, but that they are satisfactory when applied to certain groupsof bodies. [7]

[Footnote 7: Mr Preston thus puts it: "The law [of correspondingstates] seems to be not quite, but very nearly true for thesesubstances [_i. E. _ the halogen derivatives of benzene]; but in thecase of the other substances examined, the majority of thesegeneralizations were either only roughly true or altogether departedfrom" (_Theory of Heat_, London, 1904, p. 514. )--ED. ]

If in the study of the statics of a simple fluid the experimentalresults are already complex, we ought to expect much greaterdifficulties when we come to deal with mixtures; still the problem hasbeen approached, and many points are already cleared up. 

Mixed fluids may first of all be regarded as composed of a largenumber of invariable particles. In this particularly simple case M. Van der Waals has established a characteristic equation of themixtures which is founded on mechanical considerations. Variousverifications of this formula have been effected, and it has, inparticular, been the object of very important remarks by M. DanielBerthelot. 

It is interesting to note that thermodynamics seems powerless todetermine this equation, for it does not trouble itself about thenature of the bodies obedient to its laws; but, on the other hand, itintervenes to determine the properties of coexisting phases. If weexamine the conditions of equilibrium of a mixture which is notsubjected to external forces, it will be demonstrated that thedistribution must come back to a juxtaposition of homogeneous phases;in a given volume, matter ought so to arrange itself that the totalsum of free energy has a minimum value. Thus, in order to elucidateall questions relating to the number and qualities of the phases intowhich the substance divides itself, we are led to regard thegeometrical surface which for a given temperature represents the freeenergy. 

I am unable to enter here into the detail of the questions connectedwith the theories of Gibbs, which have been the object of numeroustheoretical studies, and also of a series, ever more and moreabundant, of experimental researches. M. Duhem, in particular, haspublished, on the subject, memoirs of the highest importance, and agreat number of experimenters, mostly scholars working in the physicallaboratory of Leyden under the guidance of the Director, Mr KamerlinghOnnes, have endeavoured to verify the anticipations of the theory. 

We are a little less advanced as regards abnormal substances; that isto say, those composed of molecules, partly simple and partly complex, and either dissociated or associated. These cases must naturally begoverned by very complex laws. Recent researches by MM. Van der Waals, Alexeif, Rothmund, Künen, Lehfeld, etc. , throw, however, some light onthe question. 

The daily more numerous applications of the laws of correspondingstates have rendered highly important the determination of thecritical constants which permit these states to be defined. In thecase of homogeneous bodies the critical elements have a simple, clear, and precise sense; the critical temperature is that of the singleisothermal line which presents a point of inflexion at a horizontaltangent; the critical pressure and the critical volume are the twoco-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 ofthe saturated states. Results, perhaps more precise, may also beobtained if one keeps to two constants or even to a single one--temperature, for example--by employing various special methods. Manyothers, 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 acritical space instead of a critical point. This space is comprisedbetween two extreme temperatures, the lower corresponding to what iscalled the folding point, the higher to that which we call the pointof contact of the mixture. Between these two temperatures anisothermal compression yields a quantity of liquid which increases, then reaches a maximum, diminishes, and disappears. This is thephenomenon of retrograde condensation. We may say that the propertiesof the critical point of a homogeneous substance are, in a way, divided, when it is a question of a binary mixture, between the twopoints mentioned. 

Calculation has enabled M. Van der Waals, by the application of hiskinetic theories, and M. Duhem, by means of thermodynamics, to foreseemost of the results which have since been verified by experiment. Allthese facts have been admirably set forth and systematicallyco-ordinated by M. Mathias, who, by his own researches, moreover, hasmade contributions of the highest value to the study of questionsregarding the continuity of the liquid and gaseous states. 

The further knowledge of critical elements has allowed the laws ofcorresponding states to be more closely examined in the case ofhomogeneous substances. It has shown that, as I have already said, bodies must be arranged in groups, and this fact clearly proves thatthe properties of a given fluid are not determined by its criticalconstants alone, and that it is necessary to add to them some otherspecific parameters; M. Mathias and M. D. Berthelot have indicatedsome which seem to play a considerable part. 

It results also from this that the characteristic equation of a fluidcannot yet be considered perfectly known. Neither the equation of Vander Waals nor the more complicated formulas which have been proposedby various authors are in perfect conformity with reality. We maythink that researches of this kind will only be successful ifattention is concentrated, not only on the phenomena ofcompressibility and dilatation, but also on the calorimetricproperties of bodies. Thermodynamics indeed establishes relationsbetween those properties and other constants, but does not alloweverything to be foreseen. 

Several physicists have effected very interesting calorimetricmeasurements, either, like M. Perot, in order to verify Clapeyron'sformula regarding the heat of vaporization, or to ascertain the valuesof specific heats and their variations when the temperature or thepressure happens to change. M. Mathias has even succeeded incompletely determining the specific heats of liquefied gases and oftheir saturated vapours, as well as the heat of internal and externalvaporization. 

§ 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 fromthem have also been most important. It is owing to the more completeknowledge of the general properties of fluids that immense progresshas been made these last few years in the methods of liquefying gases. 

From a theoretical point of view the new processes of liquefaction canbe classed in two categories. Linde's machine and those resembling itutilize, as is known, expansion without any notable production ofexternal work. This expansion, nevertheless, causes a fall in thetemperature, because the gas in the experiment is not a perfect gas, and, by an ingenious process, the refrigerations produced are madecumulative. 

Several physicists have proposed to employ a method wherebyliquefaction should be obtained by expansion with recuperable externalwork. This method, proposed as long ago as 1860 by Siemens, wouldoffer considerable advantages. Theoretically, the liquefaction wouldbe more rapid, and obtained much more economically; but unfortunatelyin the experiment serious obstacles are met with, especially from thedifficulty of obtaining a suitable lubricant under intense cold forthose parts of the machine which have to be in movement if theapparatus 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 isuncongealable, and a good lubricant for the moving parts. When oncethe desired region of cold is reached, air itself is used, whichmoistens the metals but does not completely avoid friction; so thatthe results would have remained only middling, had not this ingeniousphysicist devised a new improvement which has some analogy withsuperheating of steam in steam engines. He slightly varies the initialtemperature of the compressed air on the verge of liquefaction so asto avoid a zone of deep perturbations in the properties of fluids, which would make the work of expansion very feeble and the coldproduced consequently slight. This improvement, simple as it is inappearance, presents several other advantages which immediately treblethe output. 

The special object of M. Claude was to obtain oxygen in a practicalmanner by the actual distillation of liquid air. Since nitrogen boilsat -194° and oxygen at -180. 5° C. , if liquid air be evaporated, thenitrogen escapes, especially at the commencement of the evaporation, while the oxygen concentrates in the residual liquid, which finallyconsists of pure oxygen, while at the same time the temperature risesto 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 collectinga part of the oxygen in the residuum, the process would have a verypoor result from the commercial point of view. As early as 1892, MrParkinson thought of improving the output by recovering the coldproduced by liquid air during its evaporation; but an incorrect idea, which seems to have resulted from certain experiments of Dewar--theidea that the phenomenon of the liquefaction of air would not be, owing to certain peculiarities, the exact converse of that ofvaporization--led to the employment of very imperfect apparatus. M. Claude, however, by making use of a method which he calls thereversal[8] method, obtains a complete rectification in a remarkablysimple 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 cubicmetres of oxygen to be obtained at the rate, per horse-power, of morethan 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 hispupils--thanks also, it must be said, to the generosity of the RoyalInstitution, which has devoted considerable sums to these costlyexperiments--that the most numerous and systematic researches havebeen effected on the production of intense cold. I shall here noteonly the more important results, especially those relating to theproperties of bodies at low temperatures. 

Their electrical properties, in particular, undergo some interestingmodifications. The order which metals assume in point of conductivityis no longer the same as at ordinary temperatures. Thus at -200° C. Copper is a better conductor than silver. The resistance diminisheswith the temperature, and, down to about -200°, this diminution isalmost linear, and it would seem that the resistance tends towardszero when the temperature approaches the absolute zero. But, after-200°, the pattern of the curves changes, and it is easy to foreseethat at absolute zero the resistivities of all metals would stillhave, contrary to what was formerly supposed, a notable value. Solidified electrolytes which, at temperatures far below their fusionpoint, still retain a very appreciable conductivity, become, on thecontrary, perfect insulators at low temperatures. Their dielectricconstants assume relatively high values. MM. Curie and Compan, whohave studied this question from their own point of view, have noted, moreover, that the specific inductive capacity changes considerablywith the temperature. 

In the same way, magnetic properties have been studied. A veryinteresting result is that found in oxygen: the magneticsusceptibility of this body increases at the moment of liquefaction. Nevertheless, this increase, which is enormous (since thesusceptibility becomes sixteen hundred times greater than it was atfirst), if we take it in connection with equal volumes, is much lessconsiderable if taken in equal masses. It must be concluded from thisfact that the magnetic properties apparently do not belong to themolecules themselves, but depend on their state of aggregation. 

The mechanical properties of bodies also undergo importantmodifications. In general, their cohesion is greatly increased, andthe dilatation produced by slight changes of temperature isconsiderable. Sir James Dewar has effected careful measurements of thedilatation of certain bodies at low temperatures: for example, of ice. Changes in colour occur, and vermilion and iodide of mercury pass intopale orange. Phosphorescence becomes more intense, and most bodies ofcomplex structure--milk, eggs, feathers, cotton, and flowers--becomephosphorescent. The same is the case with certain simple bodies, suchas oxygen, which is transformed into ozone and emits a white light inthe process. 

Chemical affinity is almost put an end to; phosphorus and potassiumremain inert in liquid oxygen. It should, however, be noted, and thisremark has doubtless some interest for the theories of photographicaction, that photographic substances retain, even at the temperatureof liquid hydrogen, a very considerable part of their sensitiveness tolight. 

Sir James Dewar has made some important applications of lowtemperatures in chemical analysis; he also utilizes them to create avacuum. His researches have, in fact, proved that the pressure of aircongealed by liquid hydrogen cannot exceed the millionth of anatmosphere. We have, then, in this process, an original and rapidmeans of creating an excellent vacuum in apparatus of very differentkinds--a means which, in certain cases, may be particularlyconvenient. [9]

[Footnote 9: Professor Soddy, in a paper read before the Royal Societyon the 15th November 1906, warns experimenters against vacua createdby 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 andreplaced by some argon-free gas. According to him, neither helium norargon is absorbed by charcoal. By the use of electrically-heatedcalcium, he claims to have produced an almost perfect vacuum. --ED. ]

Thanks to these studies, a considerable field has been opened up forbiological research, but in this, which is not our subject, I shallnotice one point only. It has been proved that vital germs--bacteria, for example--may be kept for seven days at -190°C. Without theirvitality being modified. Phosphorescent organisms cease, it is true, to shine at the temperature of liquid air, but this fact is simply dueto the oxidations and other chemical reactions which keep up thephosphorescence being then suspended, for phosphorescent activityreappears so soon as the temperature is again sufficiently raised. Animportant conclusion has been drawn from these experiments whichaffects cosmogonical theories: since the cold of space could not killthe germs of life, it is in no way absurd to suppose that, underproper conditions, a germ may be transmitted from one planet toanother. 

Among the discoveries made with the new processes, the one which moststrikingly interested public attention is that of new gases in theatmosphere. We know how Sir William Ramsay and Dr. Travers firstobserved 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 firstsolidifying the least volatile part of the air and then causing it toevaporate with extreme slowness. A tube with electrodes enables thespectrum of the gas in process of distillation to be observed. In thismanner, the spectra of the various gases may be seen following oneanother in the inverse order of their volatility. All these gases aremonoatomic, like mercury; that is to say, they are in the most simplestate, they possess no internal molecular energy (unless it is thatwhich heat is capable of supplying), and they even seem to have nochemical energy. Everything leads to the belief that they show theexistence on the earth of an earlier state of things now vanished. Itmay be supposed, for instance, that helium and neon, of which themolecular mass is very slight, were formerly more abundant on ourplanet; but at an epoch when the temperature of the globe was higher, the very speed of their molecules may have reached a considerablevalue, exceeding, for instance, eleven kilometres per second, whichsuffices to explain why they should have left our atmosphere. Cryptonand neon, which have a density four times greater than oxygen, may, onthe contrary, have partly disappeared by solution at the bottom of thesea, where it is not absurd to suppose that considerable quantitieswould be found liquefied at great depths. [10]

[Footnote 10: Another view, viz. That these inert gases are a kind ofwaste product of radioactive changes, is also gaining ground. Thediscovery of the radioactive mineral malacone, which gives off bothhelium and argon, goes to support this. See Messrs Ketchin andWinterson's paper on the subject at the Chemical Society, 18th October1906. --ED. ]

It is probable, moreover, that the higher regions of the atmosphereare not composed of the same air as that around us. Sir James Dewarpoints out that Dalton's law demands that every gas composing theatmosphere should have, at all heights and temperatures, the samepressure as if it were alone, the pressure decreasing the lessquickly, all things being equal, as its density becomes less. Itresults from this that the temperature becoming gradually lower as werise in the atmosphere, at a certain altitude there can no longerremain any traces of oxygen or nitrogen, which no doubt liquefy, andthe atmosphere must be almost exclusively composed of the mostvolatile gases, including hydrogen, which M. A. Gautier has, like LordRayleigh and Sir William Ramsay, proved to exist in the air. Thespectrum of the _Aurora borealis_, in which are found the lines ofthose parts of the atmosphere which cannot be liquefied in liquidhydrogen, together with the lines of argon, crypton, and xenon, isquite in conformity with this point of view. It is, however, singularthat it should be the spectrum of crypton, that is to say, of theheaviest gas of the group, which appears most clearly in the upperregions of the atmosphere. 

Among the gases most difficult to liquefy, hydrogen has been theobject of particular research and of really quantitative experiments. Its properties in a liquid state are now very clearly known. Itsboiling-point, measured with a helium thermometer which has beencompared with thermometers of oxygen and hydrogen, is -252°; itscritical temperature is -241° C. ; its critical pressure, 15atmospheres. It is four times lighter than water, it does not presentany absorption spectrum, and its specific heat is the greatest known. It is not a conductor of electricity. Solidified at 15° absolute, itis far from reminding one by its aspect of a metal; it ratherresembles a piece of perfectly pure ice, and Dr Travers attributes toit a crystalline structure. The last gas which has resistedliquefaction, helium, has recently been obtained in a liquid state; itappears to have its boiling-point in the neighbourhood of 6°absolute. [11]

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

§ 3. SOLIDS AND LIQUIDS

The interest of the results to which the researches on the continuitybetween the liquid and the gaseous states have led is so great, thatnumbers of scholars have naturally been induced to inquire whethersomething analogous might not be found in the case of liquids andsolids. We might think that a similar continuity ought to be there metwith, that the universal character of the properties of matter forbadeall real discontinuity between two different states, and that, intruth, the solid was a prolongation of the liquid state. 

To discover whether this supposition is correct, it concerns us tocompare the properties of liquids and solids. If we find that allproperties are common to the two states we have the right to believe, even if they presented themselves in different degrees, that, by acontinuous series of intermediary bodies, the two classes might yet beconnected. If, on the other hand, we discover that there exists inthese two classes some quality of a different nature, we mustnecessarily conclude that there is a discontinuity which nothing canremove. 

The distinction established, from the point of view of daily custom, between solids and liquids, proceeds especially from the difficultythat we meet with in the one case, and the facility in the other, whenwe wish to change their form temporarily or permanently by the actionof mechanical force. This distinction only corresponds, however, inreality, to a difference in the value of certain coefficients. It isimpossible to discover by this means any absolute characteristic whichestablishes a separation between the two classes. Modern researchesprove this clearly. It is not without use, in order to well understandthem, to state precisely the meaning of a few terms generally ratherloosely employed. 

If a conjunction of forces acting on a homogeneous material masshappens to deform it without compressing or dilating it, two verydistinct kinds of reactions may appear which oppose themselves to theeffort exercised. During the time of deformation, and during that timeonly, the first make their influence felt. They depend essentially onthe greater or less rapidity of the deformation, they cease with themovement, and could not, in any case, bring the body back to itspristine state of equilibrium. The existence of these reactions leadsus to the idea of viscosity or internal friction. 

The second kind of reactions are of a different nature. They continueto act when the deformation remains stationary, and, if the externalforces happen to disappear, they are capable of causing the body toreturn to its initial form, provided a certain limit has not beenexceeded. These last constitute rigidity. 

At first sight a solid body appears to have a finite rigidity and aninfinite viscosity; a liquid, on the contrary, presents a certainviscosity, but no rigidity. But if we examine the matter more closely, beginning either with the solids or with the liquids, we see thisdistinction vanish. 

Tresca showed long ago that internal friction is not infinite in asolid; certain bodies can, so to speak, at once flow and be moulded. M. W. Spring has given many examples of such phenomena. On the otherhand, viscosity in liquids is never non-existent; for were it so forwater, for example, in the celebrated experiment effected by Joule forthe determination of the mechanical equivalent of the caloric, theliquid borne along by the floats would slide without friction on thesurrounding liquid, and the work done by movement would be the samewhether 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 byM. Spring in some solids. Nor does rigidity allow us to establish abarrier between the two states. Notwithstanding the extreme mobilityof their particles, liquids contain, in fact, vestiges of the propertywhich we formerly wished to consider the special characteristic ofsolids. 

Maxwell before succeeded in rendering the existence of this rigidityvery probable by examining the optical properties of a deformed layerof liquid. But a Russian physicist, M. Schwedoff, has gone further, and has been able by direct experiments to show that a sheath ofliquid set between two solid cylinders tends, when one of thecylinders is subjected to a slight rotation, to return to its originalposition, and gives a measurable torsion to a thread upholding thecylinder. From the knowledge of this torsion the rigidity can bededuced. In the case of a solution containing 1/2 per cent. Ofgelatine, it is found that this rigidity, enormous compared with thatof water, is still, however, one trillion eight hundred and fortybillion times less than that of steel. 

This figure, exact within a few billions, proves that the rigidity isvery slight, but exists; and that suffices for a characteristicdistinction to be founded on this property. In a general way, M. Spring has also established that we meet in solids, in a degree moreor less marked, with the properties of liquids. When they are placedin suitable conditions of pressure and time, they flow throughorifices, transmit pressure in all directions, diffuse and dissolveone into the other, and react chemically on each other. They may besoldered together by compression; by the same means alloys may beproduced; and further, which seems to clearly prove that matter in asolid state is not deprived of all molecular mobility, it is possibleto realise suitable limited reactions and equilibria between solidsalts, and these equilibria obey the fundamental laws ofthermodynamics. 

Thus the definition of a solid cannot be drawn from its mechanicalproperties. It cannot be said, after what we have just seen, thatsolid bodies retain their form, nor that they have a limitedelasticity, for M. Spring has made known a case where the elasticityof solids is without any limit. 

It was thought that in the case of a different phenomenon--that ofcrystallization--we might arrive at a clear distinction, because herewe should he dealing with a specific quality; and that crystallizedbodies would be the true solids, amorphous bodies being at that timeregarded as liquids viscous in the extreme. 

But the studies of a German physicist, Professor O. Lehmann, seem toprove that even this means is not infallible. Professor Lehmann hassucceeded, in fact, in obtaining with certain organic compounds--oleate of potassium, for instance--under certain conditions somepeculiar states to which he has given the name of semi-fluid andliquid crystals. These singular phenomena can only be observed andstudied by means of a microscope, and the Carlsruhe Professor had todevise an ingenious apparatus which enabled him to bring thepreparation at the required temperature on to the very plate of themicroscope. 

It is thus made evident that these bodies act on polarized light inthe manner of a crystal. Those that M. Lehmann terms semi-liquid stillpresent traces of polyhedric delimitation, but with the peaks andangles rounded by surface-tension, while the others tend to a strictlyspherical form. The optical examination of the first-named bodies isvery difficult, because appearances may be produced which are due tothe phenomena of refraction and imitate those of polarization. For theother kind, which are often as mobile as water, the fact that theypolarize light is absolutely unquestionable. 

Unfortunately, all these liquids are turbid, and it may be objectedthat they are not homogeneous. This want of homogeneity may, accordingto M. Quincke, be due to the existence of particles suspended in aliquid in contact with another liquid miscible with it and envelopingit as might a membrane, and the phenomena of polarization would thusbe quite naturally explained. [12]

[Footnote 12: Professor Quincke's last hypothesis is that all liquidson solidifying pass through a stage intermediate between solid andliquid, in which they form what he calls "foam-cells, " and assume aviscous 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 thatwhich has been observed. Various experimenters have endeavoured ofrecent years to elucidate this question. It cannot be consideredabsolutely settled, but these very curious experiments, pursued withgreat patience and remarkable ingenuity, allow us to think that therereally exist certain intermediary forms between crystals and liquidsin which bodies still retain a peculiar structure, and consequentlyact on light, but nevertheless possess considerable plasticity. 

Let us note that the question of the continuity of the liquid andsolid states is not quite the same as the question of knowing whetherthere exist bodies intermediate in all respects between the solids andliquids. These two problems are often wrongly confused. The gapbetween the two classes of bodies may be filled by certain substanceswith intermediate properties, such as pasty bodies and bodies liquidbut still crystallized, because they have not yet completely losttheir peculiar structure. Yet the transition is not necessarilyestablished in a continuous fashion when we are dealing with thepassage of one and the same determinate substance from the liquid tothe solid form. We conceive that this change may take place byinsensible degrees in the case of an amorphous body. But it seemshardly possible to consider the case of a crystal, in which molecularmovements must be essentially regular, as a natural sequence to thecase of the liquid where we are, on the contrary, in presence of anextremely disordered state of movement. 

M. Tamman has demonstrated that amorphous solids may very well, infact, be regarded as superposed liquids endowed with very greatviscosity. But it is no longer the same thing when the solid is oncein the crystallized state. There is then a solution of continuity ofthe various properties of the substance, and the two phases mayco-exist. 

We might presume also, by analogy with what happens with liquids andgases, that if we followed the curve of transformation of thecrystalline into the liquid phase, we might arrive at a kind ofcritical point at which the discontinuity of their properties wouldvanish. 

Professor Poynting, and after him Professor Planck and ProfessorOstwald, supposed this to be the case, but more recently M. Tamman hasshown that such a point does not exist, and that the region ofstability of the crystallized state is limited on all sides. All alongthe curve of transformation the two states may exist in equilibrium, but we may assert that it is impossible to realize a continuous seriesof intermediaries between these two states. There will always be amore or less marked discontinuity in some of the properties. 

In the course of his researches M. Tamman has been led to certain veryimportant observations, and has met with fresh allotropicmodifications in nearly all substances, which singularly complicatethe question. In the case of water, for instance, he finds thatordinary ice transforms itself, under a given pressure, at thetemperature of -80° C. Into another crystalline variety which isdenser than water. 

The statics of solids under high pressure is as yet, therefore, hardlydrafted, but it seems to promise results which will not be identicalwith those obtained for the statics of fluids, though it will presentat least an equal interest. 

§ 4. THE DEFORMATIONS OF SOLIDS

If the mechanical properties of the bodies intermediate between solidsand 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 bytheorists and experimenters, numerous questions with regard to themstill remain in suspense. 

We only propose to briefly indicate here a few problems recentlyexamined, without going into the details of questions which belongmore to the domain of mechanics than to that of pure physics. 

The deformations produced in solid bodies by increasing effortsarrange themselves in two distinct periods. If the efforts are weak, the deformations produced are also very weak and disappear when theeffort ceases. They are then termed elastic. If the efforts exceed acertain value, a part only of these deformations disappear, and a partare permanent. 

The purity of the note emitted by a sound has been often invoked as aproof of the perfect isochronism of the oscillation, and, consequently, as a demonstration _a posteriori_ of the correctness ofthe early law of Hoocke governing elastic deformations. This law has, however, during some years been frequently disputed. Certainmechanicians or physicists freely admit it to be incorrect, especiallyas regards extremely weak deformations. According to a theory in somefavour, especially in Germany, i. E. The theory of Bach, the law whichconnects the elastic deformations with the efforts would be anexponential one. Recent experiments by Professors Kohlrausch andGruncisen, executed under varied and precise conditions on brass, castiron, slate, and wrought iron, do not appear to confirm Bach's law. Nothing, in point of fact, authorises the rejection of the law ofHoocke, which presents itself as the most natural and most simpleapproximation to reality. 

The phenomena of permanent deformation are very complex, and itcertainly seems that they cannot be explained by the older theorieswhich insisted that the molecules only acted along the straight linewhich joined their centres. It becomes necessary, then, to constructmore complete hypotheses, as the MM. Cosserat have done in someexcellent memoirs, and we may then succeed in grouping together thefacts resulting from new experiments. Among the experiments of whichevery theory must take account may be mentioned those by which ColonelHartmann has placed in evidence the importance of the lines which areproduced on the surface of metals when the limit of elasticity isexceeded. 

It is to questions of the same order that the minute and patientresearches of M. Bouasse have been directed. This physicist, asingenious as he is profound, has pursued for several years experimentson the most delicate points relating to the theory of elasticity, andhe has succeeded in defining with a precision not always attained evenin the best esteemed works, the deformations to which a body must besubjected in order to obtain comparable experiments. With regard tothe slight oscillations of torsion which he has specially studied, M. Bouasse arrives at the conclusion, in an acute discussion, that wehardly know anything more than was proclaimed a hundred years ago byCoulomb. We see, by this example, that admirable as is the progressaccomplished in certain regions of physics, there still exist manyover-neglected regions which remain in painful darkness. The skillshown by M. Bouasse authorises us to hope that, thanks to hisresearches, a strong light will some day illumine these unknowncorners. 

A particularly interesting chapter on elasticity is that relating tothe study of crystals; and in the last few years it has been theobject of remarkable researches on the part of M. Voigt. Theseresearches have permitted a few controversial questions betweentheorists and experimenters to be solved: in particular, M. Voigt hasverified the consequences of the calculations, taking care not tomake, like Cauchy and Poisson, the hypothesis of central forces a merefunction of distance, and has recognized a potential which depends onthe relative orientation of the molecules. These considerations alsoapply to quasi-isotropic bodies which are, in fact, networks ofcrystals. 

Certain occasional deformations which are produced and disappearslowly may be considered as intermediate between elastic and permanentdeformations. Of these, the thermal deformation of glass whichmanifests itself by the displacement of the zero of a thermometer isan example. So also the modifications which the phenomena of magnetichysteresis 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 themolecular hypothesis. The attempt may seem bold, since these phenomenaare, for the most part, essentially irreversible, and seem, consequently, not adaptable to mechanics. But M. Brillouin makes apoint of showing that, under certain conditions, irreversiblephenomena may be created between two material points, the actions ofwhich depend solely on their distance; and he furnishes strikinginstances which appear to prove that a great number of irreversiblephysical and chemical phenomena may be ascribed to the existence ofstates of unstable equilibria. 

M. Duhem has approached the problem from another side, and endeavoursto bring it within the range of thermodynamics. Yet ordinarythermodynamics could not account for experimentally realizable statesof equilibrium in the phenomena of viscosity and friction, since thisscience declares them to be impossible. M. Duhem, however, arrives atthe idea that the establishment of the equations of thermodynamicspresupposes, among other hypotheses, one which is entirely arbitrary, namely: that when the state of the system is given, external actionscapable of maintaining it in that state are determined withoutambiguity, by equations termed conditions of equilibrium of thesystem. If we reject this hypothesis, it will then be allowable tointroduce into thermodynamics laws previously excluded, and it will bepossible to construct, as M. Duhem has done, a much more comprehensivetheory. 

The ideas of M. Duhem have been illustrated by remarkable experimentalwork. M. Marchis, for example, guided by these ideas, has studied thepermanent modifications produced in glass by an oscillation oftemperature. These modifications, which may be called phenomena of thehysteresis of dilatation, may be followed in very appreciable fashionby means of a glass thermometer. The general results are quite inaccord with the previsions of M. Duhem. M. Lenoble in researches onthe traction of metallic wires, and M. Chevalier in experiments on thepermanent variations of the electrical resistance of wires of an alloyof platinum and silver when submitted to periodical variations oftemperature, have likewise afforded verifications of the theorypropounded by M. Duhem. 

In this theory, the representative system is considered dependent onthe temperature of one or several other variables, such as, forexample, a chemical variable. A similar idea has been developed in avery fine set of memoirs on nickel steel, by M. Ch. Ed. Guillaume. Theeminent physicist, who, by his earlier researches, has greatlycontributed to the light thrown on the analogous question of thedisplacement of the zero in thermometers, concludes, from freshresearches, that the residual phenomena are due to chemicalvariations, and that the return to the primary chemical state causesthe variation to disappear. He applies his ideas not only to thephenomena presented by irreversible steels, but also to very differentfacts; for example, to phosphorescence, certain particularities ofwhich may be interpreted in an analogous manner. 

Nickel steels present the most curious properties, and I have alreadypointed out the paramount importance of one of them, hardly capable ofperceptible dilatation, for its application to metrology andchronometry. [13] Others, also discovered by M. Guillaume in the courseof studies conducted with rare success and remarkable ingenuity, mayrender great services, because it is possible to regulate, so tospeak, 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 theintroduction of the methods of physics has produced the greatesteffects. By the microscopic examination of a polished surface or ofone indented by a reagent, by the determination of the electromotiveforce of elements of which an alloy forms one of the poles, and by themeasurement of the resistivities, the densities, and the differencesof potential or contact, the most valuable indications as to theirconstitution are obtained. M. Le Chatelier, M. Charpy, M. Dumas, M. Osmond, in France; Sir W. Roberts Austen and Mr. Stansfield, inEngland, have given manifold examples of the fertility of thesemethods. The question, moreover, has had a new light thrown upon it bythe application of the principles of thermodynamics and of the phaserule. 

Alloys are generally known in the two states of solid and liquid. Fused alloys consist of one or several solutions of the componentmetals and of a certain number of definite combinations. Theircomposition may thus be very complex: but Gibbs' rule gives us at onceimportant information on the point, since it indicates that therecannot exist, in general, more than two distinct solutions in an alloyof two metals. 

Solid alloys may be classed like liquid ones. Two metals or moredissolve one into the other, and form a solid solution quite analogousto the liquid solution. But the study of these solid solutions isrendered singularly difficult by the fact that the equilibrium sorapidly reached in the case of liquids in this case takes days and, incertain 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 physicalstate of a body may be changed without modifying its chemicalconstitution. From the most remote periods solution has also beenknown and studied, but only in the last twenty years have we obtainedother than empirical information regarding this phenomenon. 

It is natural to employ here also the methods which have allowed us topenetrate into the knowledge of other transformations. The problem ofsolution may be approached by way of thermodynamics and of thehypotheses 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 likesulphuric acid--the properties of internal energy, discovered arelation between the quantity of heat given out on the addition of acertain quantity of water to a solution and the variations to whichcondensation and temperature subject the vapour-tension of thesolution. He calculated for this purpose the variations of energywhich are produced when passing from one state to another by twodifferent series of transformations; and, by comparing the twoexpressions thus obtained, he established a relation between thevarious elements of the phenomenon. But, for a long time afterwards, the question made little progress, because there seemed to be hardlyany means of introducing into this study the second principle ofthermodynamics. [14] It was the memoir of Gibbs which at last openedout this rich domain and enabled it to be rationally exploited. Asearly as 1886, M. Duhem showed that the theory of the thermodynamicpotential furnished precise information on solutions or liquidmixtures. He thus discovered over again the famous law on the loweringof the congelation temperature of solvents which had just beenestablished by M. Raoult after a long series of now classicresearches. 

[Footnote 14: The "second principle" referred to has been thusenunciated: "In every engine that produces work there is a fall oftemperature, and the maximum output of a perfect engine--_i. E. _ theratio between the heat consumed in work and the heat supplied--dependsonly on the extreme temperatures between which the fluid isevolved. "--Demanet, _Notes de Physique Expérimentale_, Louvain, 1905, fasc. 2, p. 147. Clausius put it in a negative form, as thus: Noengine can of itself, without the aid of external agency, transferheat 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 wastherefore, in all strictness, impossible to calculate the entropy of asolution, and consequently to be certain of the value of thethermodynamic potential. The objection would be serious even to-day, and, in calculations, what is called the paradox of Gibbs would be anobstacle. 

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. Itputs 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 inwhich 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 thispoint explains the properties of refrigerating mixtures, and it isalso one of the most useful for the theory of alloys. The scruples ofphysicists ought to have been removed on the memorable occasion whenProfessor Van t'Hoff demonstrated that solution can operate reversiblyby reason of the phenomena of osmosis. But the experiment can onlysucceed in very rare cases; and, on the other hand, Professor Vant'Hoff was naturally led to another very bold conception. He regardedthe molecule of the dissolved body as a gaseous one, and assimilatedsolution, not as had hitherto been the rule, to fusion, but to a kindof vaporization. Naturally his ideas were not immediately accepted bythe scholars most closely identified with the classic tradition. Itmay perhaps not be without use to examine here the principles ofProfessor Van t'Hoff's theory. 

§ 2. OSMOSIS

Osmosis, or diffusion through a septum, is a phenomenon which has beenknown for some time. The discovery of it is attributed to the AbbéNollet, who is supposed to have observed it in 1748, during some"researches on liquids in ebullition. " A classic experiment byDutrochet, effected about 1830, makes this phenomenon clear. Into purewater is plunged the lower part of a vertical tube containing purealcohol, open at the top and closed at the bottom by a membrane, suchas a pig's bladder, without any visible perforation. In a very shorttime it will be found, by means of an areometer for instance, that thewater outside contains alcohol, while the alcohol of the tube, pure atfirst, is now diluted. Two currents have therefore passed through themembrane, one of water from the outside to the inside, and one ofalcohol in the converse direction. It is also noted that a differencein the levels has occurred, and that the liquid in the tube now risesto a considerable height. It must therefore be admitted that the flowof the water has been more rapid than that of the alcohol. At thecommencement, the water must have penetrated into the tube much morerapidly than the alcohol left it. Hence the difference in the levels, and, consequently, a difference of pressure on the two faces of themembrane. This difference goes on increasing, reaches a maximum, thendiminishes, and vanishes when the diffusion is complete, finalequilibrium being then attained. 

The phenomenon is evidently connected with diffusion. If water is verycarefully poured on to alcohol, the two layers, separate at first, mingle by degrees till a homogeneous substance is obtained. Thebladder seems not to have prevented this diffusion from taking place, but it seems to have shown itself more permeable to water than toalcohol. May it not therefore be supposed that there must existdividing walls in which this difference of permeability becomesgreater and greater, which would be permeable to the solvent andabsolutely impermeable to the solute? If this be so, the phenomena ofthese _semi-permeable_ walls, as they are termed, can be observed inparticularly simple conditions. 

The answer to this question has been furnished by biologists, at whichwe cannot be surprised. The phenomena of osmosis are naturally of thefirst importance in the action of organisms, and for a long time haveattracted the attention of naturalists. De Vries imagined that thecontractions noticed in the protoplasm of cells placed in salinesolutions were due to a phenomenon of osmosis, and, upon examiningmore closely certain peculiarities of cell life, various scholars havedemonstrated that living cells are enclosed in membranes permeable tocertain substances and entirely impermeable to others. It wasinteresting to try to reproduce artificially semi-permeable wallsanalogous to those thus met with in nature;[15] and Traube and Pfefferseem to have succeeded in one particular case. Traube has pointed outthat the very delicate membrane of ferrocyanide of potassium which isobtained with some difficulty by exposing it to the reaction ofsulphate of copper, is permeable to water, but will not permit thepassage of the majority of salts. Pfeffer, by producing these walls inthe interstices of a porous porcelain, has succeeded in giving themsufficient rigidity to allow measurements to be made. It must beallowed that, unfortunately, no physicist or chemist has been as luckyas these two botanists; and the attempts to reproduce semi-permeablewalls completely answering to the definition, have never given butmediocre results. If, however, the experimental difficulty has notbeen overcome in an entirely satisfactory manner, it at least appearsvery probable that such walls may nevertheless exist. [16]

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

[Footnote 16: M. Stephane Leduc, Professor of Biology of Nantes, hasmade many experiments in this connection, and the artificial cellsexhibited by him to the Association française pour l'avancement desSciences, 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 exampleof a semi-permeable wall, and a partition of platinum brought to ahigher than red heat is, as shown by M. Villard in some ingeniousexperiments, completely impermeable to air, and very permeable, on thecontrary, to hydrogen. It can also be experimentally demonstrated thaton taking two recipients separated by such a partition, and bothcontaining nitrogen mixed with varying proportions of hydrogen, thelast-named gas will pass through the partition in such a way that theconcentration--that is to say, the mass of gas per unit of volume--will become the same on both sides. Only then will equilibrium beestablished; and, at that moment, an excess of pressure will naturallybe produced in that recipient which, at the commencement, containedthe gas with the smallest quantity of hydrogen. 

This experiment enables us to anticipate what will happen in a liquidmedium with semi-permeable partitions. Between two recipients, onecontaining pure water, the other, say, water with sugar in solution, separated by one of these partitions, there will be produced merely amovement of the pure towards the sugared water, and following this, anincrease of pressure on the side of the last. But this increase willnot be without limits. At a certain moment the pressure will cease toincrease and will remain at a fixed value which now has a givendirection. This is the osmotic pressure. 

Pfeffer demonstrated that, for the same substance, the osmoticpressure is proportional to the concentration, and consequently ininverse 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 osmoticpressure is proportional to the absolute temperature. De Vries, moreover, by his remarks on living cells, extended the results whichPfeffer had applied to one case only--that is, to the one that he hadbeen able to examine experimentally. 

Such are the essential facts of osmosis. We may seek to interpret themand to thoroughly examine the mechanism of the phenomenon; but it mustbe acknowledged that as regards this point, physicists are notentirely in accord. In the opinion of Professor Nernst, thepermeability of semi-permeable membranes is simply due to differencesof solubility in one of the substances of the membrane itself. Otherphysicists think it attributable, either to the difference in thedimensions of the molecules, of which some might pass through thepores of the membrane and others be stopped by their relative size, orto these molecules' greater or less mobility. For others, again, it isthe capillary phenomena which here act a preponderating part. 

This last idea is already an old one: Jager, More, and ProfessorTraube have all endeavoured to show that the direction and speed ofosmosis are determined by differences in the surface-tensions; andrecent experiments, especially those of Batelli, seem to prove thatosmosis establishes itself in the way which best equalizes thesurface-tensions of the liquids on both sides of the partition. Solutions possessing the same surface-tension, though not in molecularequilibrium, would thus be always in osmotic equilibrium. We must notconceal from ourselves that this result would be in contradiction withthe kinetic theory. 

§ 3. APPLICATION TO THE THEORY OF SOLUTION

If there really exist partitions permeable to one body and impermeableto another, it may be imagined that the homogeneous mixture of thesetwo bodies might be effected in the converse way. It can be easilyconceived, in fact, that by the aid of osmotic pressure it would bepossible, for example, to dilute or concentrate a solution by drivingthrough the partition in one direction or another a certain quantityof the solvent by means of a pressure kept equal to the osmoticpressure. This is the important fact which Professor Van t' Hoffperceived. The existence of such a wall in all possible casesevidently remains only a very legitimate hypothesis, --a fact whichought not to be concealed. 

Relying solely on this postulate, Professor Van t' Hoff easilyestablished, by the most correct method, certain properties of thesolutions of gases in a volatile liquid, or of non-volatile bodies ina volatile liquid. To state precisely the other relations, we mustadmit, in addition, the experimental laws discovered by Pfeffer. Butwithout any hypothesis it becomes possible to demonstrate the laws ofRaoult on the lowering of the vapour-tension and of the freezing pointof solutions, and also the ratio which connects the heat of fusionwith this decrease. 

These considerable results can evidently be invoked as _a posteriori_proofs of the exactitude of the experimental laws of osmosis. They arenot, however, the only ones that Professor Van t' Hoff has obtained bythe same method. This illustrious scholar was thus able to find anewGuldberg and Waage's law on chemical equilibrium at a constanttemperature, and to show how the position of the equilibrium changeswhen the temperature happens to change. 

If now we state, in conformity with the laws of Pfeffer, that theproduct of the osmotic pressure by the volume of the solution is equalto the absolute temperature multiplied by a coefficient, and then lookfor the numerical figure of this latter in a solution of sugar, forinstance, we find that this value is the same as that of the analogouscoefficient of the characteristic equation of a perfect gas. There isin this a coincidence which has also been utilized in the precedingthermodynamic calculations. It may be purely fortuitous, but we canhardly refrain from finding in it a physical meaning. 

Professor Van t'Hoff has considered this coincidence a demonstrationthat there exists a strong analogy between a body in solution and agas; as a matter of fact, it may seem that, in a solution, thedistance between the molecules becomes comparable to the moleculardistances met with in gases, and that the molecule acquires the samedegree of liberty and the same simplicity in both phenomena. In thatcase it seems probable that solutions will be subject to lawsindependent of the chemical nature of the dissolved molecule andcomparable to the laws governing gases, while if we adopt the kineticimage for the gas, we shall be led to represent to ourselves in asimilar way the phenomena which manifest themselves in a solution. Osmotic pressure will then appear to be due to the shock of thedissolved molecules against the membrane. It will come from one sideof 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 thesolution becomes more diluted. It then imitates gas in some otherproperties; the internal work of the variation of volume is nil, andthe specific heat is only a function of the temperature. A solutionwhich is diluted by a reversible method is cooled like a gas whichexpands adiabatically. [17]

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

It must, however, be acknowledged that, in other points, the analogyis much less perfect. The opinion which sees in solution a phenomenonresembling fusion, and which has left an indelible trace in everydaylanguage (we shall always say: to melt sugar in water) is certainlynot without foundation. Certain of the reasons which might be invokedto uphold this opinion are too evident to be repeated here, thoughothers more recondite might be quoted. The fact that the internalenergy generally becomes independent of the concentration when thedilution reaches even a moderately high value is rather in favour ofthe hypothesis of fusion. 

We must not forget, however, the continuity of the liquid and gaseousstates; and we may consider it in an absolute way a question devoid ofsense to ask whether in a solution the solute is in the liquid or thegaseous state. It is in the fluid state, and perhaps in conditionsopposed 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 beregarded as very great in relation to the internal pressure which, inthe characteristic equation, is added to the other. May it not seempossible that in the solution it is, on the contrary, the internalpressure which is dominant, the manometric pressure becoming of noaccount? The coincidence of the formulas would thus be verified, forall the characteristic equations are symmetrical with regard to thesetwo pressures. From this point of view the osmotic pressure would beconsidered as the result of an attraction between the solvent and thesolute; and it would represent the difference between the internalpressures of the solution and of the pure solvent. These hypothesesare highly interesting, and very suggestive; but from the way in whichthe facts have been set forth, it will appear, no doubt, that there isno obligation to admit them in order to believe in the legitimacy ofthe application of thermodynamics to the phenomena of solution. 

§ 4. ELECTROLYTIC DISSOCIATION

From the outset Professor Van t' Hoff was brought to acknowledge thata great number of solutions formed very notable exceptions which werevery irregular in appearance. The analogy with gases did not seem tobe maintained, for the osmotic pressure had a very different valuefrom that indicated by the theory. Everything, however, came right ifone multiplied by a factor, determined according to each case, butgreater than unity, the constant of the characteristic formula. Similar divergences were manifested in the delays observed incongelation, and disappeared when subjected to an analogouscorrection. 

Thus the freezing-point of a normal solution, containing a moleculegramme (that is, the number of grammes equal to the figurerepresenting the molecular mass) of alcohol or sugar in water, falls1. 85° C. If the laws of solution were identically the same for asolution of sea-salt, the same depression should be noticed in asaline solution also containing 1 molecule per litre. In fact, thefall reaches 3. 26°, and the solution behaves as if it contained, not1, but 1. 75 normal molecules per litre. The consideration of theosmotic pressures would lead to similar observations, but we know thatthe experiment would be more difficult and less precise. 

We may wonder whether anything really analogous to this can be met within the case of a gas, and we are thus led to consider the phenomena ofdissociation. [18] If we heat a body which, in a gaseous state, iscapable of dissociation--hydriodic acid, for example--at a giventemperature, an equilibrium is established between three gaseous bodies, the acid, the iodine, and the hydrogen. The total mass will follow withfair closeness Mariotte's law, but the characteristic constant will nolonger be the same as in the case of a non-dissociated gas. We here nolonger have to do with a single molecule, since each molecule is in partdissociated. 

[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 thebreaking up is only partial, and the resultant consists of a mixtureof decomposed and undecomposed parts. See Ganot's Physics, 17thEnglish edition, § 395, for examples. --ED. ]

The comparison of the two cases leads to the employment of a new imagefor representing the phenomenon which has been produced throughout thesaline solution. We have introduced a single molecule of salt, andeverything occurs as if there were 1. 75 molecules. May it not reallybe said that the number is 1. 75, because the sea-salt is partlydissociated, and a molecule has become transformed into 0. 75 moleculeof sodium, 0. 75 of chlorium, and 0. 25 of salt?

This is a way of speaking which seems, at first sight, strangelycontradicted by experiment. Professor Van t' Hoff, like otherchemists, would certainly have rejected--in fact, he did so at first--such a conception, if, about the same time, an illustrious Swedishscholar, M. Arrhenius, had not been brought to the same idea byanother 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 areexceptions to the laws of Van t'Hoff are precisely those which arecapable of conducting electricity when undergoing decomposition--thatis to say, are electrolytes. The coincidence is absolute, and cannotbe simply due to chance. 

Now, the phenomena of electrolysis have, for a long time, forced uponus an almost necessary image. The saline molecule is alwaysdecomposed, as we know, in the primary phenomenon of electrolysis intotwo elements which Faraday termed ions. Secondary reactions, no doubt, often come to complicate the question, but these are chemicalreactions belonging to the general order of things, and have nothingto do with the electric action working on the solution. The simplephenomenon is always the same--decomposition into two ions, followedby the appearance of one of these ions at the positive and of theother at the negative electrode. But as the very slightest expenditureof energy is sufficient to produce the commencement of electrolysis, it is necessary to suppose that these two ions are not united by anyforce. Thus the two ions are, in a way, dissociated. Clausius, who wasthe first to represent the phenomena by this symbol, supposed, inorder not to shock the feelings of chemists too much, that thisdissociation only affected an infinitesimal fraction of the totalnumber of the molecules of the salt, and thereby escaped all check. 

This concession was unfortunate, and the hypothesis thus lost thegreater part of its usefulness. M. Arrhenius was bolder, and franklyrecognized that dissociation occurs at once in the case of a greatnumber of molecules, and tends to increase more and more as thesolution becomes more dilute. It follows the comparison with a gaswhich, while partially dissociated in an enclosed space, becomeswholly so in an infinite one. 

M. Arrhenius was led to adopt this hypothesis by the examination ofexperimental results relating to the conductivity of electrolytes. Inorder to interpret certain facts, it has to be recognized that a partonly of the molecules in a saline solution can be considered asconductors of electricity, and that by adding water the number ofmolecular conductors is increased. This increase, too, though rapid atfirst, soon becomes slower, and approaches a certain limit which aninfinite dilution would enable it to attain. If the conductingmolecules are the dissociated molecules, then the dissociation (solong as it is a question of strong acids and salts) tends to becomecomplete in the case of an unlimited dilution. 

The opposition of a large number of chemists and physicists to theideas of M. Arrhenius was at first very fierce. It must be noted withregret that, in France particularly, recourse was had to an arm whichscholars often wield rather clumsily. They joked about these free ionsin solution, and they asked to see this chlorine and this sodium whichswam about the water in a state of liberty. But in science, aselsewhere, irony is not argument, and it soon had to be acknowledgedthat the hypothesis of M. Arrhenius showed itself singularly fertileand had to be regarded, at all events, as a very expressive image, ifnot, indeed, entirely in conformity with reality. 

It would certainly be contrary to all experience, and even to commonsense itself, to suppose that in dissolved chloride of sodium there isreally free sodium, if we suppose these atoms of sodium to beabsolutely identical with ordinary atoms. But there is a greatdifference. In the one case the atoms are electrified, and carry arelatively considerable positive charge, inseparable from their stateas ions, while in the other they are in the neutral state. We maysuppose that the presence of this charge brings about modifications asextensive as one pleases in the chemical properties of the atom. Thusthe hypothesis will be removed from all discussion of a chemicalorder, since it will have been made plastic enough beforehand to adaptitself to all the known facts; and if we object that sodium cannotsubsist in water because it instantaneously decomposes the latter, theanswer is simply that the sodium ion does not decompose water as doesordinary sodium. 

Still, other objections might be raised which could not be so easilyrefuted. One, to which chemists not unreasonably attached greatimportance, was this:--If a certain quantity of chloride of sodium isdissociated into chlorine and sodium, it should be possible, bydiffusion, for example, which brings out plainly the phenomena ofdissociation in gases, to extract from the solution a part either ofthe chlorine or of the sodium, while the corresponding part of theother compound would remain. This result would be in flagrantcontradiction with the fact that, everywhere and always, a solution ofsalt contains strictly the same proportions of its component elements. 

M. Arrhenius answers to this that the electrical forces in ordinaryconditions prevent separation by diffusion or by any other process. Professor Nernst goes further, and has shown that the concentrationcurrents which are produced when two electrodes of the same substanceare plunged into two unequally concentrated solutions may beinterpreted by the hypothesis that, in these particular conditions, the diffusion does bring about a separation of the ions. Thus theargument is turned round, and the proof supposed to be given of theincorrectness of the theory becomes a further reason in its favour. 

It is possible, no doubt, to adduce a few other experiments which arenot very favourable to M. Arrhenius's point of view, but they areisolated cases; and, on the whole, his theory has enabled manyisolated facts, till then scattered, to be co-ordinated, and hasallowed very varied phenomena to be linked together. It has alsosuggested--and, moreover, still daily suggests--researches of thehighest order. 

In the first place, the theory of Arrhenius explains electrolysis verysimply. The ions which, so to speak, wander about haphazard, and areuniformly distributed throughout the liquid, steer a regular course assoon as we dip in the trough containing the electrolyte the twoelectrodes connected with the poles of the dynamo or generator ofelectricity. Then the charged positive ions travel in the direction ofthe electromotive force and the negative ions in the oppositedirection. On reaching the electrodes they yield up to them thecharges they carry, and thus pass from the state of ion into that ofordinary atom. Moreover, for the solution to remain in equilibrium, the vanished ions must be immediately replaced by others, and thus thestate of ionisation of the electrolyte remains constant and itsconductivity 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 onvarious points in electrolytic conduction, all support the theory. Theverifications of it can even be quantitative, and we can foreseenumerical relations between conductivity and other phenomena. Themeasurement of the conductivity permits the number of moleculesdissociated in a given solution to be calculated, and the number isthus found to be precisely the same as that arrived at if it is wishedto remove the disagreement between reality and the anticipations whichresult from the theory of Professor Van t' Hoff. The laws ofcryoscopy, of tonometry, and of osmosis thus again become strict, andno exception to them remains. 

If the dissociation of salts is a reality and is complete in a dilutesolution, any of the properties of a saline solution whatever shouldbe represented numerically as the sum of three values, of which oneconcerns the positive ion, a second the negative ion, and the thirdthe solvent. The properties of the solutions would then be what arecalled additive properties. Numerous verifications may be attempted byvery different roads. They generally succeed very well; and whether wemeasure the electric conductivity, the density, the specific heats, the index of refraction, the power of rotatory polarization, thecolour, or the absorption spectrum, the additive property willeverywhere 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 ofchemistry itself. It permits us to give a vivid explanation ofchemical reaction, and for the old motto of the chemists, "Corpora nonagunt, nisi soluta, " it substitutes a modern one, "It is especiallythe ions which react. " Thus, for example, all salts of iron, whichcontain iron in the state of ions, give similar reactions; but saltssuch as ferrocyanide of potassium, in which iron does not play thepart of an ion, never give the characteristic reactions of iron. 

Professor Ostwald and his pupils have drawn from the hypothesis ofArrhenius manifold consequences which have been the cause ofconsiderable progress in physical chemistry. Professor Ostwald hasshown, in particular, how this hypothesis permits the quantitativecalculation of the conditions of equilibrium of electrolytes andsolutions, and especially of the phenomena of neutralization. If adissolved salt is partly dissociated into ions, this solution must belimited by an equilibrium between the non-dissociated molecule and thetwo ions resulting from the dissociation; and, assimilating thephenomenon to the case of gases, we may take for its study the laws ofGibbs and of Guldberg and Waage. The results are generally verysatisfactory, and new researches daily furnish new checks. 

Professor Nernst, who before gave, as has been said, a remarkableinterpretation of the diffusion of electrolytes, has, in the directionpointed out by M. Arrhenius, developed a theory of the entirephenomena of electrolysis, which, in particular, furnishes a strikingexplanation of the mechanism of the production of electromotive forcein galvanic batteries. 

Extending the analogy, already so happily invoked, between thephenomena met with in solutions and those produced in gases, ProfessorNernst supposes that metals tend, as it were, to vaporize when inpresence of a liquid. A piece of zinc introduced, for example, intopure water gives birth to a few metallic ions. These ions becomepositively charged, while the metal naturally takes an equal charge, but of contrary sign. Thus the solution and the metal are bothelectrified; but this sort of vaporization is hindered byelectrostatic attraction, and as the charges borne by the ions areconsiderable, an equilibrium will be established, although the numberof ions which enter the solution will be very small. 

If the liquid, instead of being a solvent like pure water, contains anelectrolyte, it already contains metallic ions, the osmotic pressureof which will be opposite to that of the solution. Three cases maythen present themselves--either there will be equilibrium, or theelectrostatic attraction will oppose itself to the pressure ofsolution and the metal will be negatively charged, or, finally, theattraction will act in the same direction as the pressure, and themetal will become positively and the solution negatively charged. Developing this idea, Professor Nernst calculates, by means of theaction of the osmotic pressures, the variations of energy brought intoplay and the value of the differences of potential by the contact ofthe electrodes and electrolytes. He deduces this from theelectromotive force of a single battery cell which becomes thusconnected with the values of the osmotic pressures, or, if you will, thanks to the relation discovered by Van t' Hoff, with theconcentrations. Some particularly interesting electrical phenomenathus become connected with an already very important group, and a newbridge is built which unites two regions long considered foreign toeach other. 

The recent discoveries on the phenomena produced in gases whenrendered conductors of electricity almost force upon us, as we shallsee, the idea that there exist in these gases electrified centresmoving through the field, and this idea gives still greaterprobability to the analogous theory explaining the mechanism of theconductivity of liquids. It will also be useful, in order to avoidconfusion, 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 importantinformation. The first indicates that the quantity of electricitypassing through the liquid is proportional to the quantity of matterdeposited on the electrodes. This leads us at once to theconsideration that, in any given solution, all the ions possessindividual charges equal in absolute value. 

The second law may be stated in these terms: an atom-gramme of metalcarries with it into electrolysis a quantity of electricityproportionate to its valency. [19]

[Footnote 19: The valency or atomicity of an element may be defined asthe power it possesses of entering into compounds in a certain fixedproportion. As hydrogen is generally taken as the standard, inpractice the valency of an atom is the number of hydrogen atoms itwill combine with or replace. Thus chlorine and the rest of thehalogens, the atoms of which combine with one atom of hydrogen, arecalled univalent, oxygen a bivalent element, and so on. --ED. ]

Numerous experiments have made known the total mass of hydrogencapable of carrying one coulomb, and it will therefore be possible toestimate the charge of an ion of hydrogen if the number of atoms ofhydrogen in a given mass be known. This last figure is alreadyfurnished by considerations derived from the kinetic theory, andagrees with the one which can be deduced from the study of variousphenomena. The result is that an ion of hydrogen having a mass of 1. 3x 10^{-20} grammes bears a charge of 1. 3 X 10^{-20} electromagneticunits; and the second law will immediately enable the charge of anyother ion to be similarly estimated. 

The measurements of conductivity, joined to certain considerationsrelating to the differences of concentration which appear round theelectrode in electrolysis, allow the speed of the ions to becalculated. Thus, in a liquid containing 1/10th of a hydrogen-ion perlitre, the absolute speed of an ion would be 3/10ths of a millimetreper second in a field where the fall of potential would be 1 volt percentimetre. Sir Oliver Lodge, who has made direct experiments tomeasure this speed, has obtained a figure very approximate to this. This value is very small compared to that which we shall meet with ingases. 

Another consequence of the laws of Faraday, to which, as early as 1881, Helmholtz drew attention, may be considered as the starting-point ofcertain new doctrines we shall come across later. 

Helmholtz says: "If we accept the hypothesis that simple bodies arecomposed of atoms, we are obliged to admit that, in the same way, electricity, whether positive or negative, is composed of elementaryparts which behave like atoms of electricity. "

The second law seems, in fact, analogous to the law of multipleproportions in chemistry, and it shows us that the quantities ofelectricity carried vary from the simple to the double or treble, according as it is a question of a uni-, bi-, or trivalent metal; andas 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 ofattributing those physical phenomena which the properties of matterfail to explain to some subtle matter which is the receptacle of theenergy of the universe. 

In our times this idea has had extraordinary luck. After having beeneclipsed for two hundred years by the success of the immortalsynthesis of Newton, it gained an entirely new splendour with Fresneland his followers. Thanks to their admirable discoveries, the firststage seemed accomplished, the laws of optics were represented by asingle hypothesis, marvellously fitted to allow us to anticipateunknown phenomena, and all these anticipations were subsequently fullyverified by experiment. But the researches of Faraday, Maxwell, andHertz authorized still greater ambitions; and it really seemed thatthis medium, to which it was agreed to give the ancient name of ether, and which had already explained light and radiant heat, would also besufficient to explain electricity. Thus the hope began to take formthat we might succeed in demonstrating the unity of all physicalforces. It was thought that the knowledge of the laws relating to theinmost movements of this ether might give us the key to all phenomena, and might make us acquainted with the method in which energy is storedup, transmitted, and parcelled out in its external manifestations. 

We cannot study here all the problems which are connected with thephysics of the ether. To do this a complete treatise on optics wouldhave to be written and a very lengthy one on electricity. I shallsimply endeavour to show rapidly how in the last few years the ideasrelative to the constitution of this ether have evolved, and we shallsee if it be possible without self-delusion to imagine that a singlemedium can really allow us to group all the known facts in onecomprehensive arrangement. 

As constructed by Fresnel, the hypothesis of the luminous ether, whichhad so great a struggle at the outset to overcome the stubbornresistance of the partisans of the then classic theory of emission, seemed, on the contrary, to possess in the sequel an unshakablestrength. Lamé, though a prudent mathematician, wrote: "_Theexistence_ of the ethereal fluid is _incontestably demonstrated_ bythe propagation of light through the planetary spaces, and by theexplanation, so simple and so complete, of the phenomena ofdiffraction in the wave theory of light"; and he adds: "The laws ofdouble 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 whichthe existence was thus proclaimed has some singular properties. 

Were it only a question of explaining rectilinear propagation, reflexion, refraction, diffraction, and interferences notwithstandinggrave difficulties at the outset and the objections formulated byLaplace and Poisson (some of which, though treated somewhat lightly atthe present day, have not lost all value), we should be under noobligation to make any hypothesis other than that of the undulationsof an elastic medium, without deciding in advance anything as to thenature and direction of the vibrations. 

This medium would, naturally--since it exists in what we call thevoid--be considered as imponderable. It may be compared to a fluid ofnegligible mass--since it offers no appreciable resistance to themotion of the planets--but is endowed with an enormous elasticity, because the velocity of the propagation of light is considerable. Itmust be capable of penetrating into all transparent bodies, and ofretaining there, so to speak, a constant elasticity, but must therebecome condensed, since the speed of propagation in these bodies isless than in a vacuum. Such properties belong to no material gas, eventhe most rarefied, but they admit of no essential contradiction, andthat is the important point. [20]

[Footnote 20: Since this was written, however, men of science havebecome less unanimous than they formerly were on this point. Theveteran chemist Professor Mendeléeff has given reasons for thinkingthat the ether is an inert gas with an atomic weight a million timesless than that of hydrogen, and a velocity of 2250 kilometres persecond (_Principles of Chemistry_, Eng. Ed. , 1905, vol. Ii. P. 526). On the other hand, the well-known physicist Dr A. H. Bucherer, speakingat the Naturforscherversammlung, held at Stuttgart in 1906, declaredhis disbelief in the existence of the ether, which he thought couldnot be reconciled at once with the Maxwellian theory and the knownfacts. --ED. ]

It was the study of the phenomena of polarization which led Fresnel tohis bold conception of transverse vibrations, and subsequently inducedhim to penetrate further into the constitution of the ether. We knowthe experiment of Arago on the noninterference of polarized rays inrectangular planes. While two systems of waves, proceeding from thesame source of natural light and propagating themselves in nearlyparallel directions, increase or become destroyed according to whetherthe nature of the superposed waves are of the same or of contrarysigns, the waves of the rays polarized in perpendicular planes, on theother hand, can never interfere with each other. Whatever thedifference of their course, the intensity of the light is always thesum of the intensity of the two rays. 

Fresnel perceived that this experiment absolutely compels us to rejectthe hypothesis of longitudinal vibrations acting along the line ofpropagation in the direction of the rays. To explain it, it must ofnecessity be admitted, on the contrary, that the vibrations aretransverse and perpendicular to the ray. Verdet could say, in alltruth, "It is not possible to deny the transverse direction ofluminous vibrations, without at the same time denying that lightconsists of an undulatory movement. "

Such vibrations do not and cannot exist in any medium resembling afluid. The characteristic of a fluid is that its different parts candisplace themselves with regard to one another without any reactionappearing so long as a variation of volume is not produced. Therecertainly may exist, as we have seen, certain traces of rigidity in aliquid, but we cannot conceive such a thing in a body infinitely moresubtle than rarefied gas. Among material bodies, a solid alone reallypossesses the rigidity sufficient for the production within it oftransverse vibrations and for their maintenance during theirpropagation. 

Since we have to attribute such a property to the ether, we may addthat on this point it resembles a solid, and Lord Kelvin has shownthat this solid, would be much more rigid than steel. This conclusionproduces great surprise in all who hear it for the first time, and itis not rare to hear it appealed to as an argument against the actualexistence of the ether. It does not seem, however, that such anargument can be decisive. There is no reason for supposing that theether ought to be a sort of extension of the bodies we are accustomedto handle. Its properties may astonish our ordinary way of thinking, but this rather unscientific astonishment is not a reason for doubtingits existence. Real difficulties would appear only if we were led toattribute to the ether, not singular properties which are seldom foundunited in the same substance, but properties logically contradictory. In short, however odd such a medium may appear to us, it cannot besaid that there is any absolute incompatibility between itsattributes. 

It would even be possible, if we wished, to suggest images capable ofrepresenting these contrary appearances. Various authors have done so. Thus, M. Boussinesq assumes that the ether behaves like a veryrarefied gas in respect of the celestial bodies, because these lastmove, 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 asthey are concerned the conditions become very different, and itsfluidity has, one might say, no longer the time to come in. Hence itsrigidity alone appears. 

Another consequence, very important in principle, of the fact thatvibrations of light are transverse, has been well put in evidence byFresnel. He showed how we have, in order to understand the actionwhich excites without condensation the sliding of successive layers ofthe ether during the propagation of a vibration, to consider thevibrating medium as being composed of molecules separated by finitedistances. Certain authors, it is true, have proposed theories inwhich the action at a distance of these molecules are replaced byactions of contact between parallelepipeds sliding over one another;but, at bottom, these two points of view both lead us to conceive theether as a discontinuous medium, like matter itself. The ideasgathered from the most recent experiments also bring us to the sameconclusion. 

§ 2. RADIATIONS

In the ether thus constituted there are therefore propagatedtransverse vibrations, regarding which all experiments in opticsfurnish very precise information. The amplitude of these vibrations isexceedingly small, even in relation to the wave-length, small as theselast are. If, in fact, the amplitude of the vibrations acquired anoticeable value in comparison with the wave-length, the speed ofpropagation should increase with the amplitude. Yet, in spite of somecurious experiments which seem to establish that the speed of lightdoes alter a little with its intensity, we have reason to believethat, as regards light, the amplitude of the oscillations in relationto the wave-length is incomparably less than in the case of sound. 

It has become the custom to characterise each vibration by the pathwhich the vibratory movement traverses during the space of avibration--by the length of wave, in a word--rather than by theduration of the vibration itself. To measure wave-lengths, the methodsmust be employed to which I have already alluded on the subject ofmeasurements of length. Professor Michelson, on the one hand, and MM. Perot and Fabry, on the other, have devised exceedingly ingeniousprocesses, which have led to results of really unhoped-for precision. The very exact knowledge also of the speed of the propagation of lightallows the duration of a vibration to be calculated when once thewave-length is known. It is thus found that, in the case of visiblelight, the number of the vibrations from the end of the violet to theinfra-red varies from four hundred to two hundred billions per second. This gamut is not, however, the only one the ether can give. For along time we have known ultra-violet radiations still more rapid, and, on the other hand, infra-red ones more slow, while in the last fewyears the field of known radiations has been singularly extended inboth directions. 

It is to M. Rubens and his fellow-workers that are due the mostbrilliant conquests in the matter of great wave-lengths. He hadremarked that, in their study, the difficulty of research proceedsfrom the fact that the extreme waves of the infra-red spectrum onlycontain a small part of the total energy emitted by an incandescentbody; so that if, for the purpose of study, they are further dispersedby a prism or a grating, the intensity at any one point becomes soslight as to be no longer observable. His original idea was to obtain, without prism or grating, a homogeneous pencil of great wave-lengthsufficiently intense to be examined. For this purpose the radiantsource used was a strip of platinum covered with fluorine or powderedquartz, which emits numerous radiations close to two bands of linearabsorption in the absorption spectra of fluorine and quartz, one ofwhich is situated in the infra-red. The radiations thus emitted areseveral 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 ofthat of metallic bodies for luminous rays, we no longer meet in thepencil several times reflected or in the rays _remaining_ after thiskind of filtration, with any but radiations of great wave-length. Thus, for instance, in the case of the quartz, in the neighbourhood ofa radiation corresponding to a wave-length of 8. 5 microns, theabsorption is thirty times greater in the region of the band than inthe neighbouring region, and consequently, after three reflexions, while the corresponding radiations will not have been weakened, theneighbouring waves will be so, on the contrary, in the proportion of 1to 27, 000. 

With mirrors of rock salt and of sylvine[21] there have been obtained, by taking an incandescent gas light (Auer) as source, radiationsextending as far as 70 microns; and these last are the greatestwave-lengths observed in optical phenomena. These radiations arelargely absorbed by the vapour of water, and it is no doubt owing tothis absorption that they are not found in the solar spectrum. On theother hand, they easily pass through gutta-percha, india-rubber, andinsulating substances in general. 

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

At the opposite end of the spectrum the knowledge of the ultra-violetregions has been greatly extended by the researches of Lenard. Theseextremely rapid radiations have been shown by that eminent physicistto occur in the light of the electric sparks which flash between twometal points, and which are produced by a large induction coil withcondenser and a Wehnelt break. Professor Schumann has succeeded inphotographing them by depositing bromide of silver directly on glassplates without fixing it with gelatine; and he has, by the sameprocess, photographed in the spectrum of hydrogen a ray with awave-length of only 0. 1 micron. 

The spectroscope was formed entirely of fluor-spar, and a vacuum hadbeen created in it, for these radiations are extremely absorbable bythe air. 

Notwithstanding the extreme smallness of the luminous wave-lengths, ithas been possible, after numerous fruitless trials, to obtainstationary waves analogous to those which, in the case of sound, areproduced in organ pipes. The marvellous application M. Lippmann hasmade of these waves to completely solve the problem of photography incolours is well known. This discovery, so important in itself and soinstructive, since it shows us how the most delicate anticipations oftheory may be verified in all their consequences, and lead thephysicist to the solution of the problems occurring in practice, hasjustly become popular, and there is, therefore, no need to describe ithere in detail. 

Professor Wiener obtained stationary waves some little while before M. Lippmann's discovery, in a layer of a sensitive substance having agrain sufficiently small in relation to the length of wave. His aimwas to solve a question of great importance to a complete knowledge ofthe ether. Fresnel founded his theory of double refraction andreflexion by transparent surfaces, on the hypothesis that thevibration of a ray of polarized light is perpendicular to the plane ofpolarization. But Neumann has proposed, on the contrary, a theory inwhich he recognizes that the luminous vibration is in this very plane. He rather supposes, in opposition to Fresnel's idea, that the densityof the ether remains the same in all media, while its coefficient ofelasticity is variable. 

Very remarkable experiments on dispersion by M. Carvallo prove indeedthat the idea of Fresnel was, if not necessary for us to adopt, atleast the more probable of the two; but apart from this indication, and contrary to the hypothesis of Neumann, the two theories, from thepoint of view of the explanation of all known facts, really appear tobe 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 _experimentumcrucis_, 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 firmconclusion on the point in dispute. He produced stationary waves withlight polarized at an angle of 45°, [22] and established that, whenlight is polarized in the plane of incidence, the fringes persist; butthat, on the other hand, they disappear when the light is polarizedperpendicularly to this plane. If it be admitted that a photographicimpression results from the active force of the vibratory movement ofthe ether, the question is, in fact, completely elucidated, and thediscrepancy is abolished in Fresnel's favour. 

[Footnote 22: That is to say, he reflected the beam of polarized lightby a mirror placed at that angle. See Turpain, _Leçons élementaires dePhysique_, t. Ii. P. 311, for details of the experiment. --ED. ]

M. H. Poincaré has pointed out, however, that we know nothing as to themechanism of the photographic impression. We cannot consider itevident that it is the kinetic energy of the ether which produces thedecomposition of the sensitive salt; and if, on the contrary, wesuppose it to be due to the potential energy, all the conclusions arereversed, and Neumann's idea triumphs. 

Recently a very clever physicist, M. Cotton, especially known for hisskilful researches in the domain of optics, has taken up anew thestudy of stationary waves. He has made very precise quantitativeexperiments, and has demonstrated, in his turn, that it is impossible, even with spherical waves, to succeed in determining on which of thetwo vectors which have to be regarded in all theories of light on thesubject of polarization phenomena the luminous intensity and thechemical action really depend. This question, therefore, no longerexists for those physicists who admit that luminous vibrations areelectrical oscillations. Whatever, then, the hypothesis formed, whether it be electric force or, on the contrary, magnetic force whichwe place in the plane of polarization, the mode of propagationforeseen will always be in accord with the facts observed. 

§ 3. THE ELECTROMAGNETIC ETHER

The idea of attributing the phenomena of electricity to perturbationsproduced in the medium which transmits the light is already of oldstanding; and the physicists who witnessed the triumph of Fresnel'stheories could not fail to conceive that this fluid, which fills thewhole of space and penetrates into all bodies, might also play apreponderant part in electrical actions. Some even formed too hastyhypotheses on this point; for the hour had not arrived when it waspossible to place them on a sufficiently sound basis, and the knownfacts 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 inconnection with gravitation: "In the first place to observe facts, tovary the circumstances of these as much as possible, to accompany thisfirst work by precise measurements in order to deduce from themgeneral laws founded solely on experiment, and to deduce from theselaws, independently of all hypotheses on the nature of the forcesproducing the phenomena, the mathematical value of these forces--thatis to say, the formula representing them. Such was the system pursuedby Newton. It has, in general, been adopted in France by the scholarsto whom physics owe the great progress made of late years, and it hasserved as my guide in all my researches on electrodynamicphenomena. .. . It is for this reason that I have avoided speaking ofthe ideas I may have on the nature of the cause of the force emanatingfrom voltaic conductors. "

Thus did Ampère express himself. The illustrious physicist rightlyconsidered the results obtained by him through following this wisemethod as worthy of comparison with the laws of attraction; but heknew that when this first halting-place was reached there was stillfurther to go, and that the evolution of ideas must necessarilycontinue. 

"With whatever physical cause, " he adds, "we may wish to connect thephenomena produced by electro-dynamic action, the formula I haveobtained will always remain the expression of the facts, " and heexplicitly indicated that if one could succeed in deducing his formulafrom the consideration of the vibrations of a fluid distributedthrough space, an enormous step would have been taken in thisdepartment of physics. He added, however, that this research appearedto him premature, and would change nothing in the results of his work, since, to accord with facts, the hypothesis adopted would always haveto 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, andrecognized that electrical phenomena were governed by the laws ofmechanics. Yet the principles of Newton then appeared to beunshakable. 

Faraday was the first to demonstrate, by clear experiment, theinfluence of the media in electricity and magnetic phenomena, and heattributed this influence to certain modifications in the ether whichthese media enclose. His fundamental conception was to reject actionat a distance, and to localize in the ether the energy whose evolutionis the cause of the actions manifested, as, for example, in thedischarge of a condenser. 

Consider the barrel of a pump placed in a vacuum and closed by apiston at each end, and let us introduce between these a certain massof air. The two pistons, through the elastic force of the gas, repeleach other with a force which, according to the law of Mariotte, varies in inverse ratio to the distance. The method favoured by Ampèrewould first of all allow this law of repulsion between the two pistonsto be discovered, even if the existence of a gas enclosed in thebarrel of the pump were unsuspected; and it would then be natural tolocalize the potential energy of the system on the surface of the twopistons. But if the phenomenon is more carefully examined, we shalldiscover the presence of the air, and we shall understand that everypart of the volume of this air could, if it were drawn off into arecipient of equal volume, carry away with it a fraction of the energyof the system, and that consequently this energy belongs really to theair and not to the pistons, which are there solely for the purpose ofenabling this energy to manifest its existence. 

Faraday made, in some sort, an equivalent discovery when he perceivedthat the electrical energy belongs, not to the coatings of thecondenser, but to the dielectric which separates them. His audaciousviews revealed to him a new world, but to explore this world a surerand more patient method was needed. 

Maxwell succeeded in stating with precision certain points ofFaraday's ideas, and he gave them the mathematical form which, oftenwrongly, impresses physicists, but which when it exactly encloses atheory, is a certain proof that this theory is at least coherent andlogical. [23]

[Footnote 23: It will no doubt be a shock to those whom ProfessorHenry Armstrong has lately called the "mathematically-minded" to finda member of the Poincaré family speaking disrespectfully of thescience they have done so much to illustrate. One may perhaps comparethe expression in the text with M. Henri Poincaré's remark in his lastallocution to the Académie des Sciences, that "Mathematics aresometimes a nuisance, and even a danger, when they induce us to affirmmore 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 moreconcerned in discovering whether it is possible to give an explanationof electrical and magnetic phenomena which shall be founded on themechanical properties of a single medium, than in stating thisexplanation in precise terms. He is aware that if we could succeed inconstructing such an interpretation, it would be easy to propose aninfinity of others, entirely equivalent from the point of view of theexperimentally verifiable consequences; and his especial ambition istherefore to extract from the premises a general view, and to place inevidence something which would remain the common property of all thetheories. 

He succeeded in showing that if the electrostatic energy of anelectromagnetic field be considered to represent potential energy, andits electrodynamic the kinetic energy, it becomes possible to satisfyboth the principle of least action and that of the conservation ofenergy; from that moment--if we eliminate a few difficulties whichexist regarding the stability of the solutions--the possibility offinding mechanical explanations of electromagnetic phenomena must beconsidered as demonstrated. He thus succeeded, moreover, in statingprecisely the notion of two electric and magnetic fields whichare produced in all points of space, and which are strictlyinter-connected, since the variation of the one immediately andcompulsorily gives birth to the other. 

From this hypothesis he deduced that, in the medium where this energyis localized, an electromagnetic wave is propagated with a velocityequal to the relation of the units of electric mass in theelectromagnetic and electrostatic systems. Now, experiments made knownsince his time have proved that this relation is numerically equal tothe speed of light, and the more precise experiments made inconsequence--among which should be cited the particularly careful onesof M. Max Abraham--have only rendered the coincidence still morecomplete. 

It is natural henceforth to suppose that this medium is identical withthe luminous ether, and that a luminous wave is an electromagneticwave--that is to say, a succession of alternating currents, whichexist in the dielectric and even in the void, and possess an enormousfrequency, inasmuch as they change their direction thousands ofbillions of times per second, and by reason of this frequency produceconsiderable induction effects. Maxwell did not admit the existence ofopen currents. To his mind, therefore, an electrical vibration couldnot produce condensations of electricity. It was, in consequence, necessarily transverse, and thus coincided with the vibration ofFresnel; while the corresponding magnetic vibration was perpendicularto it, and would coincide with the luminous vibration of Neumann. 

Maxwell's theory thus establishes a close correlation between thephenomena of the luminous and those of the electromagnetic waves, or, we might even say, the complete identity of the two. But it does notfollow from this that we ought to regard the variation of an electricfield produced at some one point as necessarily consisting of a realdisplacement of the ether round that point. The idea of thus bringingelectrical phenomena back to the mechanics of the ether is not, then, forced upon us, and the contrary idea even seems more probable. It isnot the optics of Fresnel which absorbs the science of electricity, itis rather the optics which is swallowed up by a more general theory. The attempts of popularizers who endeavour to represent, in all theirdetails, the mechanism of the electric phenomena, thus appear vainenough, and even puerile. It is useless to find out to what materialbody the ether may be compared, if we content ourselves with seeing init a medium of which, at every point, two vectors define theproperties. 

For a long time, therefore, we could remark that the theory of Fresnelsimply 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, beforethis idea assumed a really scientific shape. Hertz insisted on thefact that the six equations of the electric field permit all thephenomena to be anticipated without its being necessary to constructone hypothesis or another, and he put these equations into a verysymmetrical form, which brings completely in evidence the perfectreciprocity between electrical and magnetic actions. He did yet more, for he brought to the ideas of Maxwell the most striking confirmationby his memorable researches on electric oscillations. 

§ 4. ELECTRICAL OSCILLATIONS

The experiments of Hertz are well known. We know how the Bonnphysicist developed, by means of oscillating electric discharges, displacement currents and induction effects in the whole of the spaceround the spark-gap; and how he excited by induction at some point ina 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 ofinterference phenomena and subsequently verified directly by M. Blondlot, is that the electromagnetic perturbation is propagated withthe speed of light, and this result condemns for ever all thehypotheses which fail to attribute any part to the intervening mediain the propagation of an induction phenomenon. 

If the inducing action were, in fact, to operate directly between theinducing and the induced circuits, the propagation should beinstantaneous; for if an interval were to occur between the momentwhen the cause acted and the one when the effect was produced, duringthis interval there would no longer be anything anywhere, since theintervening medium does not come into play, and the phenomenon wouldthen disappear. 

Leaving on one side the manifold but purely electrical consequences ofthis and the numerous researches relating to the production or to theproperties of the waves--some of which, those of MM. Sarrazin and dela Rive, Righi, Turpain, Lebedeff, Decombe, Barbillon, Drude, Gutton, Lamotte, Lecher, etc. , are, however, of the highest order--I shallonly mention here the studies more particularly directed to theestablishment of the identity of the electromagnetic and the luminouswaves. 

The only differences which subsist are necessarily those due to theconsiderable discrepancy which exists between the durations of theperiods of these two categories of waves. The length of wavecorresponding to the first spark-gap of Hertz was about 6 metres, andthe 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 thattheir properties have not a perfect similitude. Thus phenomena likethose of diffraction, which are negligible in the ordinary conditionsunder which light is observed, may here assume a preponderatingimportance. To play the part, for example, with the Hertzian waves, which a mirror 1 millimetre square plays with regard to light, wouldrequire a colossal mirror which would attain the size of amyriametre[25] square. 

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

The efforts of physicists have to-day, however, filled up, in greatpart, this interval, and from both banks at once they have laboured tobuild a bridge between the two domains. We have seen how Rubens showedus calorific rays 60 metres long; on the other hand, MM. Lecher, Bose, and Lampa have succeeded, one after the other, in gradually obtainingoscillations with shorter and shorter periods. There have beenproduced, and are now being studied, electromagnetic waves of fourmillimetres; and the gap subsisting in the spectrum between the raysleft undetected by sylvine and the radiations of M. Lampa now hardlycomprise more than five octaves--that is to say, an intervalperceptibly 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 theproperties, so to speak, characteristic of the Hertzian waves, beginto appear. For these waves, as we have seen, the most transparentbodies are the most perfect electrical insulators; while bodies stillslightly conducting are entirely opaque. The index of refraction ofthese substances tends in the case of great wave-lengths to become, asthe theory anticipates, nearly the square root of the dielectricconstant. 

MM. Rubens and Nichols have even produced with the waves which remainphenomena of electric resonance quite similar to those which anItalian scholar, M. Garbasso, obtained with electric waves. Thisphysicist showed that, if the electric waves are made to impinge on aflat wooden stand, on which are a series of resonators parallel toeach other and uniformly arranged, these waves are hardly reflectedsave in the case where the resonators have the same period as thespark-gap. If the remaining rays are allowed to fall on a glass platesilvered and divided by a diamond fixed on a dividing machine intosmall rectangles of equal dimensions, there will be observedvariations in the reflecting power according to the orientation of therectangles, under conditions entirely comparable with the experimentof Garbasso. 

In order that the phenomenon be produced it is necessary that theremaining waves should be previously polarized. This is because, infact, the mechanism employed to produce the electric oscillationsevidently gives out vibrations which occur on a single plane and aresubsequently polarized. 

We cannot therefore entirely assimilate a radiation proceeding from aspark-gap to a ray of natural light. For the synthesis of light to berealized, still other conditions must be complied with. During aluminous impression, the direction and the phase change millions oftimes in the vibration sensible to the retina, yet the damping of thisvibration is very slow. With the Hertzian oscillations all theseconditions are changed--the damping is very rapid but the directionremains invariable. 

Every time, however, that we deal with general phenomena which areindependent 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 samedirection and crossing each other at a very acute angle, or theinterferences analogous to those which Wiener observed with rays ofthe contrary direction. 

A very important consequence of the electromagnetic theory foreseen byMaxwell is that the luminous waves which fall on a surface mustexercise on this surface a pressure equal to the radiant energy whichexists in the unit of volume of the surrounding space. M. Lebedeff afew years ago allowed a sheaf of rays from an arc lamp to fall on adeflection radiometer, [26] and thus succeeded in revealing theexistence of this pressure. Its value is sufficient, in the case ofmatter of little density and finely divided, to reduce and even changeinto repulsion the attractive action exercised on bodies by the sun. This is a fact formerly conjectured by Faye, and must certainly play agreat part in the deformation of the heads of comets. 

[Footnote 26: By this M. Poincaré appears to mean a radiometer inwhich the vanes are not entirely free to move as in the radiometer ofCrookes but are suspended by one or two threads as in the instrumentdevised by Professor Poynting. --ED. ]

More recently, MM. Nichols and Hull have undertaken experiments onthis point. They have measured not only the pressure, but also theenergy of the radiation by means of a special bolometer. They havethus arrived at numerical verifications which are entirely inconformity with the calculations of Maxwell. 

The existence of these pressures may be otherwise foreseen even apartfrom the electromagnetic theory, by adding to the theory ofundulations the principles of thermodynamics. Bartoli, and morerecently Dr Larmor, have shown, in fact, that if these pressures didnot exist, it would be possible, without any other phenomenon, to passheat from a cold into a warm body, and thus transgress the principleof Carnot. 

§ 5. THE X RAYS

It appears to-day quite probable that the X rays should be classedamong 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 inthe neighbourhood, had become visible in the dark, and that aphotographic plate had received an impress. The rays which come fromthe tube, in conditions now well known, are not deviated by a magnet, and, as M. Curie and M. Sagnac have conclusively shown, they carry noelectric charge. They are subject to neither reflection norrefraction, and very precise and very ingenious measurements by M. Gouy have shown that, in their case, the refraction index of thevarious bodies cannot be more than a millionth removed from unity. 

We knew from the outset that there existed various X rays differingfrom each other as, for instance, the colours of the spectrum, andthese are distinguished from each other by their unequal power ofpassing through substances. M. Sagnac, particularly, has shown thatthere can be obtained a gradually decreasing scale of more or lessabsorbable rays, so that the greater part of their photographic actionis stopped by a simple sheet of black paper. These rays figure amongthe secondary rays discovered, as is known, by this ingeniousphysicist. The X rays falling on matter are thus subjected totransformations which may be compared to those which the phenomena ofluminescence produce on the ultra-violet rays. 

M. Benoist has founded on the transparency of matter to the rays asure and practical method of allowing them to be distinguished, andhas thus been enabled to define a specific character analogous to thecolour of the rays of light. It is probable also that the differentrays do not transport individually the same quantity of energy. Wehave not yet obtained on this point precise results, but it is roughlyknown, since the experiments of MM. Rutherford and M'Clung, whatquantity of energy corresponds to a pencil of X rays. These physicistshave found that this quantity would be, on an average, five hundredtimes larger than that brought by an analogous pencil of solar lightto the surface of the earth. What is the nature of this energy? Thequestion does not appear to have been yet solved. 

It certainly appears, according to Professors Haga and Wind and toProfessor Sommerfeld, that with the X rays curious experiments ofdiffraction may be produced. Dr Barkla has shown also that they canmanifest true polarization. The secondary rays emitted by a metallicsurface when struck by X rays vary, in fact, in intensity when theposition of the plane of incidence round the primary pencil ischanged. Various physicists have endeavoured to measure the speed ofpropagation, but it seems more and more probable that it is verynearly 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 _etseq. _, 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, havepermitted the elucidation of several interesting problems relative tothe duration of the emission or to the best disposition to be adoptedfor the production of the rays. The only point which will detain us isthe important question as to the nature of the X rays themselves; theproperties which have just been brought to mind are those which appearessential and which every theory must reckon with. 

The most natural hypothesis would be to consider the rays asultra-violet radiations of very short wave-length, or radiations whichare in a manner ultra-ultra-violet. This interpretation can still, atthis present moment, be maintained, and the researches of MM. Buisson, Righi, Lenard, and Merrit Stewart have even established that rays ofvery short wave-lengths produce on metallic conductors, from the pointof view of electrical phenomena, effects quite analogous to those ofthe X rays. Another resemblance results also from the experiments bywhich M. Perreau established that these rays act on the electricresistance of selenium. New and valuable arguments have thus addedforce to those who incline towards a theory which has the merit ofbringing a new phenomenon within the pale of phenomena previouslyknown. 

Nevertheless the shortest ultra-violet radiations, such as those of M. Schumann, are still capable of refraction by quartz, and thisdifference constitutes, in the minds of many physicists, a seriousenough reason to decide them to reject the more simple hypothesis. Moreover, the rays of Schumann are, as we have seen, extraordinarilyabsorbable, --so much so that they have to be observed in a vacuum. Themost striking property of the X rays is, on the contrary, the facilitywith which they pass through obstacles, and it is impossible not toattach 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 mediawith a speed equal to that of light. But the most generally acceptedidea is the one formulated from the first by Sir George Stokes andfollowed up by Professor Wiechert. According to this theory the X raysshould be due to a succession of independent pulsations of the ether, starting from the points where the molecules projected by the cathodeof the Crookes tube meet the anticathode. These pulsations are notcontinuous vibrations like the radiations of the spectrum; they areisolated and extremely short; they are, besides, transverse, like theundulations of light, and the theory shows that they must bepropagated with the speed of light. They should present neitherrefraction nor reflection, but, under certain conditions, they may besubject to the phenomena of diffraction. All these characteristics arefound in the Röntgen rays. 

Professor J. J. Thomson adopts an analogous idea, and states theprecise way in which the pulsations may be produced at the moment whenthe electrified particles forming the cathode rays suddenly strike theanticathode wall. The electromagnetic induction behaves in such a waythat the magnetic field is not annihilated when the particle stops, and the new field produced, which is no longer in equilibrium, ispropagated in the dielectric like an electric pulsation. The electricand magnetic pulsations excited by this mechanism may give birth toeffects similar to those of light. Their slight amplitude, however, isthe cause of there here being neither refraction nor diffractionphenomena, save in very special conditions. If the cathode particle isnot stopped in zero time, the pulsation will take a greater amplitude, and be, in consequence, more easily absorbable; to this is probably tobe attributed the differences which may exist between different tubesand different rays. 

It is right to add that some authors, notwithstanding the provedimpossibility of deviating them in a magnetic field, have notrenounced the idea of comparing them with the cathode rays. Theysuppose, for instance, that the rays are formed by electrons animatedwith so great a velocity that their inertia, conformably with theorieswhich I shall examine later, no longer permit them to be stopped intheir course; this is, for instance, the theory upheld by MrSutherland. We know, too, that to M. Gustave Le Bon they represent theextreme limit of material things, one of the last stages before thevanishing of matter on its return to the ether. 

Everyone has heard of the N rays, whose name recalls the town ofNancy, where they were discovered. In some of their singularproperties they are akin to the X rays, while in others they arewidely divergent from them. 

M. Blondlot, one of the masters of contemporary physics, deeplyrespected by all who know him, admired by everyone for the penetrationof his mind, and the author of works remarkable for the originalityand sureness of his method, discovered them in radiations emitted fromvarious sources, such as the sun, an incandescent light, a Nernstlamp, and even bodies previously exposed to the sun's rays. Theessential property which allows them to be revealed is their action ona small induction spark, of which they increase the brilliancy; thisphenomenon is visible to the eye and is rendered objective byphotography. 

Various other physicists and numbers of physiologists, following thepath opened by M. Blondlot, published during 1903 and 1904 manifoldbut often rather hasty memoirs, in which they related the results oftheir researches, which do not appear to have been always conductedwith the accuracy desirable. These results were most strange; theyseemed destined to revolutionise whole regions not only of the domainof physics, but likewise of the biological sciences. Unfortunately themethod of observation was always founded on the variations invisibility of the spark or of a phosphorescent substance, and it soonbecame manifest that these variations were not perceptible to alleyes. 

No foreign experimenter has succeeded in repeating the experiments, while in France many physicists have failed; and hence the questionhas much agitated public opinion. Are we face to face with a verysingular case of suggestion, or is special training and particulardispositions required to make the phenomenon apparent? It is notpossible, at the present moment, to declare the problem solved; butvery recent experiments by M. Gutton and a note by M. Mascart havereanimated the confidence of those who hoped that such a scholar as M. Blondlot could not have been deluded by appearances. However, theselast proofs in favour of the existence of the rays have themselvesbeen contested, and have not succeeded in bringing conviction toeveryone. 

It seems very probable indeed that certain of the most singularconclusions arrived at by certain authors on the subject will lapseinto deserved oblivion. But negative experiments prove nothing in acase like this, and the fact that most experimenters have failed whereM. Blondlot and his pupils have succeeded may constitute apresumption, but cannot be regarded as a demonstrative argument. Hencewe must still wait; it is exceedingly possible that the illustriousphysicist of Nancy may succeed in discovering objective actions of theN rays which shall be indisputable, and may thus establish on a firmbasis a discovery worthy of those others which have made his name sojustly celebrated. 

According to M. Blondlot the N rays can be polarised, refracted, anddispersed, while they have wavelengths comprised within . 0030 micron, and . 0760 micron--that is to say, between an eighth and a fifth ofthat found for the extreme ultra-violet rays. They might be, perhaps, simply rays of a very short period. Their existence, stripped of theparasitical and somewhat singular properties sought to be attributedto them, would thus appear natural enough. It would, moreover, beextremely important, and lead, no doubt, to most curious applications;it can be conceived, in fact, that such rays might serve to revealwhat occurs in those portions of matter whose too minute dimensionsescape microscopic examination on account of the phenomena ofdiffraction. 

From whatever point of view we look at it, and whatever may be thefate of the discovery, the history of the N rays is particularlyinstructive, and must give food for reflection to those interested inquestions of scientific methods. 

§ 6. THE ETHER AND GRAVITATION

The striking success of the hypothesis of the ether in optics has, inour own days, strengthened the hope of being able to explain, by ananalogous representation, the action of gravitation. 

For a long time, philosophers who rejected the idea that ponderabilityis a primary and essential quality of all bodies have sought to reducetheir weight to pressures exercised in a very subtle fluid. This wasthe conception of Descartes, and was perhaps the true idea of Newtonhimself. Newton points out, in many passages, that the laws he haddiscovered were independent of the hypotheses that could be formed onthe way in which universal attraction was produced, but that withsufficient experiments the true cause of this attraction might one daybe reached. In the preface to the second edition of the Optics hewrites: "To prove that I have not considered weight as a universalproperty of bodies, I have added a question as to its cause, preferring this form of question because my interpretation does notentirely satisfy me in the absence of experiment"; and he puts thequestion in this shape: "Is not this medium (the ether) more rarefiedin the interior of dense bodies like the sun, the planets, the comets, than in the empty spaces which separate them? Passing from thesebodies to great distances, does it not become continually denser, andin that way does it not produce the weight of these great bodies withregard to each other and of their parts with regard to these bodies, each body tending to leave the most dense for the most rarefiedparts?"

Evidently this view is incomplete, but we may endeavour to state itprecisely. If we admit that this medium, the properties of which wouldexplain the attraction, is the same as the luminous ether, we mayfirst ask ourselves whether the action of gravitation is itself alsodue to oscillations. Some authors have endeavoured to found a theoryon this hypothesis, but we are immediately brought face to face withvery serious difficulties. Gravity appears, in fact, to present quiteexceptional characteristics. No agent, not even those which dependupon the ether, such as light and electricity, has any influence onits action or its direction. All bodies are, so to speak, absolutelytransparent to universal attraction, and no experiment has succeededin demonstrating that its propagation is not instantaneous. Fromvarious astronomical observations, Laplace concluded that itsvelocity, in any case, must exceed fifty million times that of light. It is subject neither to reflection nor to refraction; it isindependent of the structure of bodies; and not only is itinexhaustible, but also (as is pointed out, according to M. Hannequin, by an English scholar, James Croll) the distribution of the effects ofthe attracting force of a mass over the manifold particles which maysuccessively enter the field of its action in no way diminishes theattraction it exercises on each of them respectively, a thing which isseen nowhere else in nature. 

Nevertheless it is possible, by means of certain hypotheses, toconstruct interpretations whereby the appropriate movements of anelastic medium should explain the facts clearly enough. But thesemovements are very complex, and it seems almost inconceivable that thesame medium could possess simultaneously the state of movementcorresponding to the transmission of a luminous phenomenon and thatconstantly imposed on it by the transmission of gravitation. 

Another celebrated hypothesis was devised by Lesage, of Geneva. Lesagesupposed space to be overrun in all directions by currents of_ultramundane_ corpuscles. This hypothesis, contested by Maxwell, isinteresting. It might perhaps be taken up again in our days, and it isnot impossible that the assimilation of these corpuscles to electronsmight give a satisfactory image. [28]

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

M. Crémieux has recently undertaken experiments directed, as hethinks, to showing that the divergences between the phenomena ofgravitation and all the other phenomena in nature are more apparentthan real. Thus the evolution in the heart of the ether of a quantityof gravific energy would not be entirely isolated, and as in the caseof all evolutions of all energy of whatever kind, it should provoke apartial transformation into energy of a different form. Thus again theliberated energy of gravitation would vary when passing from onematerial to another, as from gases into liquids, or from one liquid toa different one. 

On this last point the researches of M. Crémieux have givenaffirmative results: if we immerse in a large mass of some liquidseveral drops of another not miscible with the first, but of identicaldensity, we form a mass representing no doubt a discontinuity in theether, and we may ask ourselves whether, in conformity with whathappens in all other phenomena of nature, this discontinuity has not atendency to disappear. 

If we abide by the ordinary consequences of the Newtonian theory ofpotential, the drops should remain motionless, the hydrostaticimpulsion forming an exact equilibrium to their mutual attraction. NowM. Crémieux remarks that, as a matter of fact, they slowly approacheach other. 

Such experiments are very delicate; and with all the precautions takenby the author, it cannot yet be asserted that he has removed allpossibility of the action of the phenomena of capillarity nor allpossible errors proceeding from extremely slight differences oftemperature. But the attempt is interesting and deserves to befollowed up. 

Thus, the hypothesis of the ether does not yet explain all thephenomena which the considerations relating to matter are ofthemselves powerless to interpret. If we wished to represent toourselves, by the mechanical properties of a medium filling the wholeof the universe, all luminous, electric, and gravitation phenomena, weshould be led to attribute to this medium very strange and almostcontradictory characteristics; and yet it would be still moreinconceivable that this medium should be double or treble, that thereshould be two or three ethers each occupying space as if it werealone, and interpenetrating it without exercising any action on oneanother. We are thus brought, by a close examination of facts, ratherto the idea that the properties of the ether are not wholly reducibleto the rules of ordinary mechanics. 

The physicist has therefore not yet succeeded in answering thequestion often put to him by the philosopher: "Has the ether really anobjective existence?" However, it is not necessary to know the answerin order to utilize the ether. In its ideal properties we find themeans of determining the form of equations which are valid, and to thelearned detached from all metaphysical prepossession this is theessential point. 

CHAPTER VII

A CHAPTER IN THE HISTORY OF SCIENCE: WIRELESS TELEGRAPHY

§ 1

I have endeavoured in this book to set forth impartially the ideasdominant at this moment in the domain of physics, and to make knownthe facts essential to them. I have had to quote the authors of theprincipal 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 asummary history of the physics of the day. 

I am not unaware that, as has often been said, contemporary history isthe most difficult of all histories to write. A certain step backwardsseems necessary in order to enable us to appreciate correctly therelative importance of events, and details conceal the full view fromeyes which are too close to them, as the trees prevent us from seeingthe forest. The event which produces a great sensation has often onlyinsignificant consequences; while another, which seemed at the outsetof the least importance and little worthy of note, has in the long runa widespread and deep influence. 

If, however, we deal with the history of a positive discovery, contemporaries who possess immediate information, and are in aposition to collect authentic evidence at first hand, will make, bybringing to it their sincere testimony, a work of erudition which maybe very useful, but which we may be tempted to look upon as very easyof execution. Yet such a labour, even when limited to the study of avery minute question or of a recent invention, is far from beingaccomplished without the historian stumbling over serious obstacles. 

An invention is never, in reality, to be attributed to a singleauthor. It is the result of the work of many collaborators whosometimes have no acquaintance with one another, and is often thefruit of obscure labours. Public opinion, however, wilfully simple inface of a sensational discovery, insists that the historian shouldalso act as judge; and it is the historian's task to disentangle thetruth in the midst of the contest, and to declare infallibly to whomthe acknowledgments of mankind should be paid. He must, in hiscapacity as skilled expert, expose piracies, detect the most carefullyhidden plagiarisms, and discuss the delicate question of priority;while he must not be deluded by those who do not fear to announce, inbold accents, that they have solved problems of which they find thesolution imminent, and who, the day after its final elucidation bythird parties, proclaim themselves its true discoverers. He must riseabove a partiality which deems itself excusable because it proceedsfrom national pride; and, finally, he must seek with patience for whathas gone before. While thus retreating step by step he runs the riskof 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 oneof those which have rapidly become popular, and looks, as it were, anexact subject clearly marked out. Many attempts have already been madeto write its history. Mr J. J. Fahie published in England as early as1899 an interesting work entitled the _History of WirelessTelegraphy_; and about the same time M. Broca published in France avery exhaustive work named _La Telegraphie sans fil_. Among thereports presented to the Congrès international de physique (Paris, 1900), Signor Righi, an illustrious Italian scholar, whose personalefforts have largely contributed to the invention of the presentsystem of telegraphy, devoted a chapter, short, but sufficientlycomplete, of his masterly report on Hertzian waves, to the history ofwireless telegraphy. The same author, in association with HerrBernhard Dessau, has likewise written a more important work, _DieTelegraphie ohne Draht_; and _La Telegraphie sans fil et les ondesÉlectriques_ of MM. J. Boulanger and G. Ferrié may also be consultedwith advantage, as may _La Telegraphie sans fil_ of Signor DominicoMazotto. Quite recently Mr A. Story has given us in a little volumecalled _The Story of Wireless Telegraphy_, a condensed but veryprecise recapitulation of all the attempts which have been made toestablish telegraphic communication without the intermediary of aconducting wire. Mr Story has examined many documents, has sometimesbrought curious facts to light, and has studied even the most recentlyadopted apparatus. 

It may be interesting, by utilising the information supplied by theseauthors and supplementing them when necessary by others, to trace thesources of this modern discovery, to follow its developments, and thusto prove once more how much a matter, most simple in appearance, demands extensive and complex researches on the part of an authordesirous of writing a definitive work. 

§ 2

The first, and not the least difficulty, is to clearly define thesubject. The words "wireless telegraphy, " which at first seem tocorrespond to a simple and perfectly clear idea, may in reality applyto two series of questions, very different in the mind of a physicist, between which it is important to distinguish. The transmission ofsignals demands three organs which all appear indispensable: thetransmitter, the receiver, and, between the two, an intermediaryestablishing the communication. This intermediary is generally themost 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 ofgood output occur. And yet our present ideas cause us to consider thisintermediary as more than ever impossible to suppress; since, if weare definitely quit of the conception of action at a distance, itbecomes inconceivable to us that energy can be communicated from onepoint to another without being carried by some intervening medium. But, practically, the line will be suppressed if, instead ofconstructing it artificially, we use to replace it one of the naturalmedia which separate two points on the earth. These natural media aredivided into two very distinct categories, and from thisclassification arise two series of questions to be examined. 

Between the two points in question there are, first, the materialmedia such as the air, the earth, and the water. For a long time wehave used for transmissions to a distance the elastic properties ofthe air, and more recently the electric conductivity of the soil andof water, particularly that of the sea. 

Modern physics leads us on the other hand, as we have seen, toconsider that there exists throughout the whole of the universeanother and more subtle medium which penetrates everywhere, is endowedwith elasticity _in vacuo_, and retains its elasticity when itpenetrates into a great number of bodies, such as the air. This mediumis the luminous ether which possesses, as we cannot doubt, theproperty of being able to transmit energy, since it itself brings tous by far the larger part of the energy which we possess on earth andwhich we find in the movements of the atmosphere, or of waterfalls, and in the coal mines proceeding from the decomposition of carboncompounds under the influence of the solar energy. For a long timealso before the existence of the ether was known, the duty oftransmitting signals was entrusted to it. Thus through the ages adouble evolution is unfolded which has to be followed by the historianwho is ambitious of completeness. 

§ 3

If such an historian were to examine from the beginning the firstorder of questions, he might, no doubt, speak only briefly of theattempts earlier than electric telegraphy. Without seeking to beparadoxical, he certainly ought to mention the invention of thespeaking-trumpet and other similar inventions which for a long timehave enabled mankind, by the ingenious use of the elastic propertiesof the natural media, to communicate at greater distances than theycould have attained without the aid of art. After this in some sortprehistoric period had been rapidly run through, he would have tofollow very closely the development of electric telegraphy. Almostfrom the outset, and shortly after Ampère had made public the idea ofconstructing a telegraph, and the day after Gauss and Weber set upbetween their houses in Göttingen the first line really used, it wasthought that the conducting properties of the earth and water might bemade of service. 

The history of these trials is very long, and is closely mixed up withthe history of ordinary telegraphy; long chapters for some time pasthave been devoted to it in telegraphic treatises. It was in 1838, however, that Professor C. A. Steinheil of Munich expressed, for thefirst time, the clear idea of suppressing the return wire andreplacing it by a connection of the line wire to the earth. He thus atone step covered half the way, the easiest, it is true, which was tolead to the final goal, since he saved the use of one-half of the lineof wire. Steinheil, advised, perhaps, by Gauss, had, moreover, a veryexact conception of the part taken by the earth considered as aconducting body. He seems to have well understood that, in certainconditions, the resistance of such a conductor, though supposed to beunlimited, might be independent of the distance apart of theelectrodes which carry the current and allow it to go forth. Helikewise thought of using the railway lines to transmit telegraphicsignals. 

Several scholars who from the first had turned their minds totelegraphy, 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 simpleapparatus invented by him, made experiments in the autumn of 1842before a special commission in New York and a numerous publicaudience, to show how surely and how easily his apparatus worked. Inthe very midst of his experiments a very happy idea occurred to him ofreplacing by the water of a canal, the length of about a mile of wirewhich had been suddenly and accidentally destroyed. This accident, which for a moment compromised the legitimate success the celebratedengineer expected, thus suggested to him a fruitful idea which he didnot forget. He subsequently repeated attempts to thus utilise theearth and water, and obtained some very remarkable results. 

It is not possible to quote here all the researches undertaken withthe same purpose, to which are more particularly attached the names ofS. W. Wilkins, Wheatstone, and H. Highton, in England; of Bonetti inItaly, Gintl in Austria, Bouchot and Donat in France; but there aresome which cannot be recalled without emotion. 

On the 17th December 1870, a physicist who has left in the Universityof Paris a lasting name, M. D'Almeida, at that time Professor at theLycée Henri IV. And later Inspector-General of Public Instruction, quitted Paris, then besieged, in a balloon, and descended in the midstof the German lines. He succeeded, after a perilous journey, ingaining Havre by way of Bordeaux and Lyons; and after procuring thenecessary apparatus in England, he descended the Seine as far asPoissy, which he reached on the 14th January 1871. After hisdeparture, two other scholars, MM. Desains and Bourbouze, relievingeach 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. Onthe 23rd January the communication at last seemed to be established, but unfortunately, first the armistice and then the surrender of Parisrendered useless the valuable result of this noble effort. 

Special mention is also due to the experiments made by the IndianTelegraph Office, under the direction of Mr Johnson and afterwards ofMr W. F. Melhuish. They led, indeed, in 1889 to such satisfactoryresults that a telegraph service, in which the line wire was replacedby the earth, worked practically and regularly. Other attempts werealso made during the latter half of the nineteenth century to transmitsignals through the sea. They preceded the epoch when, thanks tonumerous physicists, among whom Lord Kelvin undoubtedly occupies apreponderating position, we succeeded in sinking the first cable; butthey were not abandoned, even after that date, for they gave hopes ofa much more economical solution of the problem. Among the mostinteresting are remembered those that S. W. Wilkins carried on for along time between France and England. Like Cooke and Wheatstone, hethought of using as a receiver an apparatus which in some featuresresembles the present receiver of the submarine telegraph. Later, George E. Dering, then James Bowman and Lindsay, made on the samelines trials which are worthy of being remembered. 

But it is only in our own days that Sir William H. Preece at lastobtained for the first time really practical results. Sir Williamhimself effected and caused to be executed by his associates--he ischief consulting engineer to the General Post Office in England--researches conducted with much method and based on precise theoreticalconsiderations. He thus succeeded in establishing very easy, clear, and regular communications between various places; for example, acrossthe Bristol Channel. The long series of operations accomplished by somany seekers, with the object of substituting a material and naturalmedium for the artificial lines of metal, thus met with an undoubtedsuccess which was soon to be eclipsed by the widely-known experimentsdirected into a different line by Marconi. 

It is right to add that Sir William Preece had himself utilisedinduction phenomena in his experiments, and had begun researches withthe aid of electric waves. Much is due to him for the welcome he gaveto Marconi; it is certainly thanks to the advice and the materialsupport he found in Sir William that the young scholar succeeded ineffecting his sensational experiments. 

§ 4

The starting-point of the experiments based on the properties of theluminous ether, and having for their object the transmission ofsignals, is very remote; and it would be a very laborious task to huntup all the work accomplished in that direction, even if we were toconfine ourselves to those in which electrical reactions play a part. An electric reaction, an electrostatic influence, or anelectromagnetic phenomenon, is transmitted at a distance through theair by the intermediary of the luminous ether. But electric influencecan hardly be used, as the distances it would allow us to traversewould be much too restricted, and electrostatic actions are often veryerratic. The phenomena of induction, which are very regular andinsensible to the variations of the atmosphere, have, on the otherhand, for a long time appeared serviceable for telegraphic purposes. 

We might find, in a certain number of the attempts just mentioned, apartial employment of these phenomena. Lindsay, for instance, in hisproject of communication across the sea, attributed to them aconsiderable rôle. These phenomena even permitted a true telegraphywithout intermediary wire between the transmitter and the receiver, atvery restricted distances, it is true, but in peculiarly interestingconditions. It is, in fact, owing to them that C. Brown, and laterEdison and Gilliland, succeeded in establishing communications withtrains in motion. 

Mr Willoughby S. Smith and Mr Charles A. Stevenson also undertookexperiments during the last twenty years, in which they usedinduction, but the most remarkable attempts are perhaps those ofProfessor Emile Rathenau. With the assistance of Professor Rubens andof Herr W. Rathenau, this physicist effected, at the request of theGerman Ministry of Marine, a series of researches which enabled him, by means of a compound system of conduction and induction byalternating currents, to obtain clear and regular communications at adistance of four kilometres. Among the precursors also should bementioned Graham Bell; the inventor of the telephone thought ofemploying his admirable apparatus as a receiver of induction phenomenatransmitted from a distance; Edison, Herr Sacher of Vienna, M. HenryDufour of Lausanne, and Professor Trowbridge of Boston, also madeinteresting attempts in the same direction. 

In all these experiments occurs the idea of employing an oscillatingcurrent. Moreover, it was known for a long time--since, in 1842, thegreat American physicist Henry proved that the discharges from aLeyden jar in the attic of his house caused sparks in a metalliccircuit on the ground floor--that a flux which varies rapidly andperiodically is much more efficacious than a simple flux, which lattercan only produce at a distance a phenomenon of slight intensity. Thisidea of the oscillating current was closely akin to that which was atlast to lead to an entirely satisfactory solution: that is, to asolution which is founded on the properties of electric waves. 

§ 5

Having thus got to the threshold of the definitive edifice, thehistorian, who has conducted his readers over the two parallel routeswhich have just been marked out, will be brought to ask himselfwhether he has been a sufficiently faithful guide and has not omittedto draw attention to all essential points in the regions passedthrough. 

Ought we not to place by the side, or perhaps in front, of the authorswho have devised the practical appliances, those scholars who haveconstructed the theories and realised the laboratory experiments ofwhich, after all, the apparatus are only the immediate applications?If we speak of the propagation of a current in a material medium, canone forget the names of Fourier and of Ohm, who established bytheoretical considerations the laws which preside over thispropagation? When one looks at the phenomena of induction, would itnot be just to remember that Arago foresaw them, and that MichaelFaraday discovered them? It would be a delicate, and also a ratherpuerile task, to class men of genius in order of merit. The merit ofan inventor like Edison and that of a theorist like Clerk Maxwell haveno common measure, and mankind is indebted for its great progress tothe one as much as to the other. 

Before relating how success attended the efforts to utilise electricwaves for the transmission of signals, we cannot without ingratitudepass over in silence the theoretical speculations and the work of purescience which led to the knowledge of these waves. It would thereforebe just, without going further back than Faraday, to say how thatillustrious physicist drew attention to the part taken by insulatingmedia in electrical phenomena, and to insist also on the admirablememoirs in which for the first time Clerk Maxwell made a solid bridgebetween those two great chapters of Physics, optics and electricity, which till then had been independent of each other. And no doubt itwould be impossible not to evoke the memory of those who, byestablishing, on the other hand, the solid and magnificent structureof physical optics, and proving by their immortal works the undulatorynature of light, prepared from the opposite direction the futureunity. 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 andluminous phenomena which they discovered and studied would evidentlyhave been impossible. 

Since there is an absolute identity of nature between the electric andthe luminous waves, we should, in all justice, also consider asprecursors those who devised the first luminous telegraphs. ClaudeChappe incontestably effected wireless telegraphy, thanks to theluminous ether, and the learned men, such as Colonel Mangin, whoperfected optical telegraphy, indirectly suggested certainimprovements 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 whodemonstrated irrefutably, by experiments now classic, that an electricdischarge produces an undulatory disturbance in the ether contained inthe insulating media in its neighbourhood; it was he who, as aprofound theorist, a clever mathematician, and an experimenter ofprodigious dexterity, made known the mechanism of the production, andfully elucidated that of the propagation of these electromagneticwaves. 

He must naturally himself have thought that his discoveries might beapplied to the transmission of signals. It would appear, however, thatwhen interrogated by a Munich engineer named Huber as to thepossibility of utilising the waves for transmissions by telephone, heanswered in the negative, and dwelt on certain considerations relativeto the difference between the periods of sounds and those ofelectrical vibrations. This answer does not allow us to judge whatmight have happened, had not a cruel death carried off in 1894, at theage of thirty-five, the great and unfortunate physicist. 

We might also find in certain works earlier than the experiments ofHertz attempts at transmission in which, unconsciously no doubt, phenomena were already set in operation which would, at this day, beclassed as electric oscillations. It is allowable no doubt, not tospeak of an American quack, Mahlon Loomis, who, according to Mr Story, patented in 1870 a project of communication in which he utilised theRocky Mountains on one side and Mont Blanc on the other, as giganticantennae to establish communication across the Atlantic; but we cannotpass over in silence the very remarkable researches of the AmericanProfessor Dolbear, who showed, at the electrical exhibition ofPhiladelphia in 1884, a set of apparatus enabling signals to betransmitted at a distance, which he described as "an exceptionalapplication of the principles of electrostatic induction. " Thisapparatus comprised groups of coils and condensers by means of whichhe obtained, as we cannot now doubt, effects due to true electricwaves. 

Place should also be made for a well-known inventor, D. E. Hughes, whofrom 1879 to 1886 followed up some very curious experiments in whichalso these oscillations certainly played a considerable part. It wasthis physicist who invented the microphone, and thus, in another way, drew attention to the variations of contact resistance, a phenomenonnot far from that produced in the radio-conductors of Branly, whichare important organs in the Marconi system. Unfortunately, fatiguedand in ill-health, Hughes ceased his researches at the moment perhapswhen they would have given him final results. 

In an order of ideas different in appearance, but closely linked atbottom with the one just mentioned, must be recalled the discovery ofradiophony in 1880 by Graham Bell, which was foreshadowed in 1875 byC. A. Brown. A luminous ray falling on a selenium cell produces avariation of electric resistance, thanks to which a sound signal canbe transmitted by light. That delicate instrument the radiophone, constructed on this principle, has wide analogies with the apparatusof to-day. 

§ 6

Starting from the experiments of Hertz, the history of wirelesstelegraphy almost merges into that of the researches on electricalwaves. All the progress realised in the manner of producing andreceiving these waves necessarily helped to give rise to theapplication already indicated. The experiments of Hertz, after beingchecked in every laboratory, and having entered into the strong domainof 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 inGermany, Bose in India, Lebedeff in Russia, and theorists like M. H. Poincaré and Professor Bjerknes, who devised ingenious arrangements orelucidated certain points left dark, are among the artisans of thework which followed its natural evolution. 

It was Professor R. Threlfall who seems to have been the first toclearly propose, in 1890, the application of the Hertzian waves totelegraphy, but it was certainly Sir W. Crookes who, in a veryremarkable article in the _Fortnightly Review_ of February 1892, pointed out very clearly the road to be followed. He even showed inwhat conditions the Morse receiver might be applied to the new systemof telegraphy. 

About the same period an American physicist, well known by hiscelebrated 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 tomore 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 Rutherfordobtained similar results with a magnetic indicator of his owninvention. 

An important question of meteorology, the study of atmosphericdischarges, at this date led a few scholars, and more particularly theRussian, M. Popoff, to set up apparatus very analogous to thereceiving apparatus of the present wireless telegraphy. This compriseda long antenna and filings-tube, and M. Popoff even pointed out thathis apparatus might well serve for the transmission of signals as soonas a generator of waves powerful enough had been discovered. 

Finally, on the 2nd June 1896, a young Italian, born in Bologna on the25th April 1874, Guglielmo Marconi, patented a system of wirelesstelegraphy destined to become rapidly popular. Brought up in thelaboratory of Professor Righi, one of the physicists who had done mostto confirm and extend the experiments of Hertz, Marconi had long beenfamiliar with the properties of electric waves, and was well used totheir manipulation. He afterwards had the good fortune to meet SirWilliam (then Mr) Preece, who was to him an adviser of the highestauthority. 

It has sometimes been said that the Marconi system contains nothingoriginal; that the apparatus for producing the waves was theoscillator of Righi, that the receiver was that employed for some twoor three years by Professor Lodge and Mr Bose, and was founded on anearlier discovery by a French scholar, M. Branly; and, finally, thatthe general arrangement was that established by M. Popoff. 

The persons who thus rather summarily judge the work of M. Marconishow a severity approaching injustice. It cannot, in truth, be deniedthat the young scholar has brought a strictly personal contribution tothe solution of the problem he proposed to himself. Apart from hisforerunners, and when their attempts were almost unknown, he had thevery great merit of adroitly arranging the most favourablecombination, and he was the first to succeed in obtaining practicalresults, while he showed that the electric waves could be transmittedand received at distances enormous compared to those attained beforehis day. Alluding to a well-known anecdote relating to ChristopherColumbus, Sir W. Preece very justly said: "The forerunners and rivalsof Marconi no doubt knew of the eggs, but he it was who taught them tomake them stand on end. " This judgment will, without any doubt, be theone that history will definitely pronounce on the Italian scholar. 

§ 7

The apparatus which enables the electric waves to be revealed, thedetector or indicator, is the most delicate organ in wirelesstelegraphy. It is not necessary to employ as an indicator afilings-tube or radio-conductor. One can, in principle, for the purposeof constructing a receiver, think of any one of the multiple effectsproduced by the Hertzian waves. In many systems in use, and in the newone of Marconi himself, the use of these tubes has been abandoned andreplaced by magnetic detectors. 

Nevertheless, the first and the still most frequent successes are dueto radio-conductors, and public opinion has not erred in attributingto the inventor of this ingenious apparatus a considerable and almostpreponderant part in the invention of wave telegraphy. 

The history of the discovery of radio-conductors is short, but itdeserves, from its importance, a chapter to itself in the history ofwireless telegraphy. From a theoretical point of view, the phenomenaproduced in those tubes should be set by the side of those studied byGraham Bell, C. A. Brown, and Summer Tainter, from the year 1878onward. The variations to which luminous waves give rise in theresistance of selenium and other substances are, doubtless, notunconnected with those which the electric waves produce in filings. Aconnection can also be established between this effect of the wavesand the variations of contact resistance which enabled Hughes toconstruct the microphone, that admirable instrument which is one ofthe essential organs of telephony. 

More directly, as an antecedent to the discovery, should be quoted theremark made by Varley in 1870, that coal-dust changes in conductivitywhen the electromotive force of the current which passes through it ismade to vary. But it was in 1884 that an Italian professor, SignorCalzecchi-Onesti, demonstrated in a series of remarkable experimentsthat the metallic filings contained in a tube of insulating material, into which two metallic electrodes are inserted, acquire a notableconductivity under different influences such as extra currents, induced currents, sonorous vibrations, etc. , and that thisconductivity is easily destroyed; as, for instance, by turning thetube over and over. 

In several memoirs published in 1890 and 1891, M. Ed. Branlyindependently pointed out similar phenomena, and made a much morecomplete and systematic study of the question. He was the first tonote very clearly that the action described could be obtained bysimply making sparks pass in the neighbourhood of the radio-conductor, and that their great resistance could be restored to the filings bygiving a slight shake to the tube or to its supports. 

The idea of utilising such a very interesting phenomenon as anindicator in the study of the Hertzian waves seems to have occurredsimultaneously to several physicists, among whom should be especiallymentioned M. Ed. Branly himself, Sir Oliver Lodge, and MM. Le Royerand Van Beschem, and its use in laboratories rapidly became quitecommon. 

The action of the waves on metallic powders has, however, remainedsome what mysterious; for ten years it has been the subject ofimportant researches by Professor Lodge, M. Branly, and a very greatnumber of the most distinguished physicists. It is impossible tonotice here all these researches, but from a recent and veryinteresting work of M. Blanc, it would seem that the phenomenon isallied to that of ionisation. 

§ 8

The history of wireless telegraphy does not end with the firstexperiments of Marconi; but from the moment their success wasannounced in the public press, the question left the domain of purescience to enter into that of commerce. The historian's task herebecomes different, but even more delicate; and he will encounterdifficulties which can be only known to one about to write the historyof a commercial invention. 

The actual improvements effected in the system are kept secret by therival companies, and the most important results are patriotically leftin darkness by the learned officers who operate discreetly in view ofthe national defence. Meanwhile, men of business desirous of bringingout a company proclaim, with great nourish of advertisements, thatthey are about to exploit a process superior to all others. 

On this slippery ground the impartial historian must neverthelessventure; and he may not refuse to relate the progress accomplished, which is considerable. Therefore, after having described theexperiments carried out for nearly ten years by Marconi himself, firstacross the Bristol Channel, then at Spezzia, between the coast and theironclad _San Bartolommeo_, and finally by means of gigantic apparatusbetween America and England, he must give the names of those who, inthe different civilised countries, have contributed to the improvementof the system of communication by waves; while he must describe whatprecious 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 remarkableresults have been obtained by various physicists, among whom should beparticularly mentioned M. Tissot, whose brilliant studies have throwna bright light on different interesting points, such as the rôle ofthe antennae. It would be equally impossible to pass over in silenceother recent attempts in a slightly different groove. Marconi'ssystem, however improved it may be to-day, has one grave defect. Thesynchronism of the two pieces of apparatus, the transmitter and thereceiver, is not perfect, so that a message sent off by one stationmay be captured by some other station. The fact that the phenomena ofresonance are not utilised, further prevents the quantity of energyreceived by the receiver from being considerable, and hence theeffects reaped are very weak, so that the system remains somewhatfitful and the communications are often disturbed by atmosphericphenomena. Causes which render the air a momentary conductor, such aselectrical discharges, ionisation, etc. , moreover naturally preventthe waves from passing, the ether thus losing its elasticity. 

Professor Ferdinand Braun of Strasburg has conceived the idea ofemploying a mixed system, in which the earth and the water, which, aswe have seen, have often been utilised to conduct a current fortransmitting a signal, will serve as a sort of guide to the wavesthemselves. The now well-known theory of the propagation of wavesguided by a conductor enables it to be foreseen that, according totheir periods, these waves will penetrate more or less deeply into thenatural medium, from which fact has been devised a method ofseparating 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 alsothe researches, in a somewhat analogous order of ideas, by an Englishengineer, Mr Armstrong, by Dr Lee de Forest, and also by ProfessorFessenden. 

Having thus arrived at the end of this long journey, which has takenhim from the first attempts down to the most recent experiments, thehistorian can yet set up no other claim but that of having written thecommencement of a history which others must continue in the future. Progress does not stop, and it is never permissible to say that aninvention has reached its final form. 

Should the historian desire to give a conclusion to his labour andanswer the question the reader would doubtless not fail to put to him, "To whom, in short, should the invention of wireless telegraphy moreparticularly be attributed?" he should certainly first give the nameof Hertz, the genius who discovered the waves, then that of Marconi, who was the first to transmit signals by the use of Hertzianundulations, and should add those of the scholars who, like Morse, Popoff, Sir W. Preece, Lodge, and, above all, Branly, have devised thearrangements necessary for their transmission. But he might thenrecall what Voltaire wrote in the _Philosophical Dictionary_:

"What! We wish to know what was the exact theology of Thot, ofZerdust, of Sanchuniathon, of the first Brahmins, and we are ignorantof the inventor of the shuttle! The first weaver, the first mason, thefirst smith, were no doubt great geniuses, but they were disregarded. Why? Because none of them invented a perfected art. The one whohollowed out an oak to cross a river never made a galley; those whopiled 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: sciencebecomes more and more impersonal, and she teaches us that progress isnearly always due to the united efforts of a crowd of workers, and isthus 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 mightconclude that two classes of phenomena are to-day being interpretedwith increasing correctness in spite of the few difficulties whichhave been pointed out. The hypothesis of the molecular constitution ofmatter enables us to group together one of these classes, and thehypothesis of the ether leads us to co-ordinate the other. 

But these two classes of phenomena cannot be considered independent ofeach other. Relations evidently exist between matter and the ether, which manifest themselves in many cases accessible to experiment, andthe search for these relations appears to be the paramount problem thephysicist should set himself. The question has, for a long time, beenattacked on various sides, but the recent discoveries in theconductivity of gases, of the radioactive substances, and of thecathode and similar rays, have allowed us of late years to regard itin a new light. Without wishing to set out here in detail facts whichfor the most part are well known, we will endeavour to group the chiefof them round a few essential ideas, and will seek to state preciselythe data they afford us for the solution of this grave problem. 

It was the study of the conductivity of gases which at the very firstfurnished the most important information, and allowed us to penetratemore deeply than had till then been possible into the inmostconstitution of matter, and thus to, as it were, catch in the act theactions that matter can exercise on the ether, or, reciprocally, thoseit may receive from it. 

It might, perhaps, have been foreseen that such a study would proveremarkably fruitful. The examination of the phenomena of electrolysishad, in fact, led to results of the highest importance on theconstitution of liquids, and the gaseous media which presentedthemselves as particularly simple in all their properties ought, itwould seem, to have supplied from the very first a field ofinvestigation easy to work and highly productive. 

This, however, was not at all the case. Experimental complicationsspringing up at every step obscured the problem. One generally foundone's self in the presence of violent disruptive discharges with atrain of accessory phenomena, due, for instance, to the use ofmetallic electrodes, and made evident by the complex appearance ofaigrettes and effluves; or else one had to deal with heated gasesdifficult to handle, which were confined in receptacles whose wallsplayed a troublesome part and succeeded in veiling the simplicity ofthe fundamental facts. Notwithstanding, therefore, the efforts of agreat number of seekers, no general idea disengaged itself out of amass of often contradictory information. 

Many physicists, in France particularly, discarded the study ofquestions which seemed so confused, and it must even be franklyacknowledged that some among them had a really unfounded distrust ofcertain results which should have been considered proved, but whichhad the misfortune to be in contradiction with the theories in currentuse. All the classic ideas relating to electrical phenomena led to theconsideration that there existed a perfect symmetry between the twoelectricities, positive and negative. In the passing of electricitythrough gases there is manifested, on the contrary, an evidentdissymmetry. The anode and the cathode are immediately distinguishedin a tube of rarefied gas by their peculiar appearance; and theconductivity does not appear, under certain conditions, to be the samefor 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 asearly as 1815 to the unipolar conductivity of a flame. Hiscontemporaries, as may be gathered from the perusal of the treatiseson physics of that period, attached great importance to thisdiscovery; but, as it was somewhat inconvenient and did not readilyfit in with ordinary studies, it was in due course neglected, thenconsidered as insufficiently established, and finally whollyforgotten. 

All these somewhat obscure facts, and some others--such as thedifferent action of ultra-violet radiations on positively andnegatively charged bodies--are now, on the contrary, about to beco-ordinated, thanks to the modern ideas on the mechanism of conduction;while these ideas will also allow us to interpret the most strikingdissymmetry of all, i. E. That revealed by electrolysis itself, adissymmetry which certainly can not be denied, but to which sufficientattention has not been given. 

It is to a German physicist, Giese, that we owe the first notions onthe mechanism of the conductivity of gases, as we now conceive it. Intwo memoirs published in 1882 and 1889, he plainly arrives at theconception that conduction in gases is not due to their molecules, butto certain fragments of them or to ions. Giese was a forerunner, buthis ideas could not triumph so long as there were no means ofobserving conduction in simple circumstances. But this means has nowbeen supplied in the discovery of the X rays. Suppose we pass throughsome 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 twometallic electrodes in communication with the two poles of a batteryare introduced, a current is set up in very special conditions whichremind us, when they are checked by experiments, of the mechanismwhich allows the passage of electricity in electrolysis, and which isso well represented to us when we picture to ourselves this passage asdue to the migration towards the electrodes, under the action of thefield, of the two sets of ions produced by the spontaneous division ofthe molecule within the solution. 

[Footnote 29: At least, so long as it is not introduced between thetwo coatings of a condenser having a difference of potentialsufficient to overcome what M. Bouty calls its dielectric cohesion. Weleave on one side this phenomenon, regarding which M. Bouty hasarrived at extremely important results by a very remarkable series ofexperiments; but this question rightly belongs to a special study ofelectrical phenomena which is not yet written. ]

Let us therefore recognise with J. J. Thomson and the many physicistswho, 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 bedetermined later, certain gaseous molecules have become divided intotwo portions, the one positively and the other negatively electrified, which we will call, by analogy with the kindred phenomenon inelectrolysis, by the name of ions. If the gas be then placed in anelectric field, produced, for instance, by two metallic platesconnected with the two poles of a battery respectively, the positiveions will travel towards the plate connected with the negative pole, and the negative ions in the contrary direction. There is thusproduced a current due to the transport to the electrodes of thecharges which existed on the ions. 

If the gas thus ionised be left to itself, in the absence of anyelectric field, the ions, yielding to their mutual attraction, mustfinally meet, combine, and reconstitute a neutral molecule, thusreturning to their initial condition. The gas in a short while losesthe conductivity which it had acquired; or this is, at least, thephenomenon at ordinary temperatures. But if the temperature is raised, the relative speeds of the ions at the moment of impact may be greatenough to render it impossible for the recombination to be produced inits entirety, and part of the conductivity will remain. 

Every element of volume rendered a conductor therefore furnishes, inan electric field, equal quantities of positive and negativeelectricity. If we admit, as mentioned above, that these liberatedquantities are borne by ions each bearing an equal charge, the numberof these ions will be proportional to the quantity of electricity, andinstead of speaking of a quantity of electricity, we could use theequivalent term of number of ions. For the excitement produced by agiven pencil of X rays, the number of ions liberated will be fixed. Thus, from a given volume of gas there can only be extracted anequally determinate quantity of electricity. 

The conductivity produced is not governed by Ohm's law. The intensityis not proportional to the electromotive force, and it increases atfirst as the electromotive force augments; but it approachesasymptotically to a maximum value which corresponds to the number ofions liberated, and can therefore serve as a measure of the power ofthe excitement. It is this current which is termed the _current ofsaturation_. 

M. Righi has ably demonstrated that ionised gas does not obey the lawof Ohm by an experiment very paradoxical in appearance. He found that, the greater the distance of the two electrode plates from each, thegreater 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 bethe number of ions liberated. 

One of the most striking characteristics of ionised gases is that ofdischarging electrified conductors. This phenomenon is not produced bythe departure of the charge that these conductors may possess, but bythe advent of opposite charges brought to them by ions which obey theelectrostatic attraction and abandon their own electrification whenthey come in contact with these conductors. 

This mode of regarding the phenomena is extremely convenient andeminently suggestive. It may, no doubt, be thought that the image ofthe ions is not identical with objective reality, but we are compelledto acknowledge that it represents with absolute faithfulness all thedetails of the phenomena. 

Other facts, moreover, will give to this hypothesis a still greatervalue; we shall even be able, so to speak, to grasp these ionsindividually, 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 theatmosphere reaches the value of the maximum pressure corresponding tothe temperature of the experiment, the elementary theory teaches usthat 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 orless considerable delay may take place, and the vapour will remainsupersaturated. We easily discover that this phenomenon is dueto the intervention of capillary action. On a drop of liquid asurface-tension takes effect which gives rise to a pressure whichbecomes greater the smaller the diameter of the drop. 

Pressure facilitates evaporation, and on more closely examining thisreaction we arrive at the conclusion that vapour can neverspontaneously condense itself when liquid drops already formed are notpresent, unless forces of another nature intervene to diminish theeffect of the capillary forces. In the most frequent cases, theseforces come from the dust which is always in suspension in the air, orwhich exists in any recipient. Grains of dust act by reason of theirhygrometrical power, and form germs round which drops presently form. It is possible to make use, as did M. Coulier as early as 1875, ofthis phenomenon to carry off the germs of condensation, by producingby expansion in a bottle containing a little water a preliminary mistwhich purifies the air. In subsequent experiments it will be foundalmost impossible to produce further condensation of vapour. 

But these forces may also be of electrical origin. Von Helmholtz longsince showed that electricity exercises an influence on thecondensation of the vapour of water, and Mr C. T. R. Wilson, with thisview, has made truly quantitative experiments. It was rapidlydiscovered after the apparition of the X rays that gases that havebecome conductors, that is, ionised gases, also facilitate thecondensation of supersaturated water vapour. 

We are thus led by a new road to the belief that electrified centresexist in gases, and that each centre draws to itself the neighbouringmolecules of water, as an electrified rod of resin does the lightbodies around it. There is produced in this manner round each ion anassemblage of molecules of water which constitute a germ capable ofcausing the formation of a drop of water out of the condensation ofexcess vapour in the ambient air. As might be expected, the drops areelectrified, and take to themselves the charge of the centres roundwhich they are formed; moreover, as many drops are created as thereare ions. Thereafter we have only to count these drops to ascertainthe number of ions which existed in the gaseous mass. 

To effect this counting, several methods have been used, differing inprinciple 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 onehand, the weight of the mist which is produced in determinedconditions, and on the other, the average weight of the drops, according to the formula formerly given by Sir G. Stokes, by deductingtheir diameter from the speed with which this mist falls; or we can, with Professor Lemme, determine the average radius of the drops by anoptical process, viz. By measuring the diameter of the firstdiffraction ring produced when looking through the mist at a point oflight. 

We thus get to a very high number. There are, for instance, sometwenty million ions per centimetre cube when the rays have producedtheir maximum effect, but high as this figure is, it is still verysmall compared with the total number of molecules. All conclusionsdrawn from kinetic theory lead us to think that in the same spacethere must exist, by the side of a molecule divided into two ions, athousand millions remaining in a neutral state and intact. 

Mr C. T. R. Wilson has remarked that the positive and negative ions donot produce condensation with the same facility. The ions of acontrary sign may be almost completely separated by placing theionised gas in a suitably disposed field. In the neighbourhood of anegative disk there remain hardly any but positive ions, and against apositive disk none but negative; and in effecting a separation of thiskind, it will be noticed that condensation by negative ions is easierthan by the positive. 

It is, consequently, possible to cause condensation on negativecentres only, and to study separately the phenomena produced by thetwo kinds of ions. It can thus be verified that they really bearcharges equal in absolute value, and these charges can even beestimated, since we already know the number of drops. This estimatecan be made, for example, by comparing the speed of the fall of a mistin fields of different values, or, as did J. J. Thomson, by measuringthe total quantity of electricity liberated throughout the gas. 

At the degree of approximation which such experiments imply, we findthat the charge of a drop, and consequently the charge borne by anion, is sensibly 3. 4 x 10^{-10} electrostatic or 1. 1 x 10^{-20}electromagnetic units. This charge is very near that which the studyof the phenomena of ordinary electrolysis leads us to attribute to aunivalent atom produced by electrolytic dissociation. 

Such a coincidence is evidently very striking; but it will not be theonly one, for whatever phenomenon be studied it will always appearthat the smallest charge we can conceive as isolated is thatmentioned. We are, in fact, in presence of a natural unit, or, if youwill, of an atom of electricity. 

We must, however, guard against the belief that the gaseous ion isidentical with the electrolytic ion. Sensible differences betweenthose are immediately apparent, and still greater ones will bediscovered on closer examination. 

As M. Perrin has shown, the ionisation produced by the X-rays in noway depends on the chemical composition of the gas; and whether wetake a volume of gaseous hydrochloric acid or a mixture of hydrogenand 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 ofmagnitude. 

By treating the speeds possessed by the liberated charges ascomponents of the known speed of a gaseous current, Mr Zeleny measuresthe mobilities, that is to say, the speeds acquired by the positiveand negative charges in a field equal to the electrostatic unit. Hehas thus found that these mobilities are different, and that theyvary, for example, between 400 and 200 centimetres per second for thetwo charges in dry gases, the positive being less mobile than thenegative ions, which suggests the idea that they are of greatermass. [30]

[Footnote 30: A full account of these experiments, which were executedat the Cavendish Laboratory, is to be found in _PhilosophicalTransactions_, A. , vol. Cxcv. (1901), pp. 193 et seq. --ED. ]

M. Langevin, who has made himself the eloquent apostle of the newdoctrines in France, and has done much to make them understood andadmitted, has personally undertaken experiments analogous to those ofM. Zeleny, but much more complete. He has studied in a very ingeniousmanner, not only the mobilities, but also the law of recombinationwhich regulates the spontaneous return of the gas to its normal state. He has determined experimentally the relation of the number ofrecombinations to the number of collisions between two ions ofcontrary sign, by studying the variation produced by a change in thevalue of the field, in the quantity of electricity which can becollected in the gas separating two parallel metallic plates, afterthe passage through it for a very short time of the Röntgen raysemitted during one discharge of a Crookes tube. If the image of theions is indeed conformable to reality, this relation must evidentlyalways be smaller than unity, and must tend towards this value whenthe mobility of the ions diminishes, that is to say, when the pressureof the gas increases. The results obtained are in perfect accord withthis anticipation. 

On the other hand, M. Langevin has succeeded, by following thedisplacement of the ions between the parallel plates after theionisation produced by the radiation, in determining the absolutevalues of the mobilities with great precision, and has thus clearlyplaced in evidence the irregularity of the mobilities of the positiveand negative ions respectively. Their mass can be calculated when weknow, through experiments of this kind, the speed of the ions in agiven field, and on the other hand--as we can now estimate theirelectric charge--the force which moves them. They evidently progressmore slowly the larger they are; and in the viscous medium constitutedby the gas, the displacement is effected at a speed sensiblyproportional 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 isto say, they are about the order of some ten molecules. The ions, therefore, seem to be formed by an agglomeration of neutral moleculesmaintained round an electrified centre by electrostatic attraction. Ifthe temperature rises, the thermal agitation will become great enoughto prevent the molecules from remaining linked to the centre. Bymeasurements effected on the gases of flames, we arrive at verydifferent values of the masses from those found for ordinary ions, andabove all, very different ones for ions of contrary sign. The negativeions have much more considerable velocities than the positive ones. The latter also seem to be of the same size as atoms; and thefirst-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 isnot the smallest fraction of matter to be considered. Fragments athousand times smaller may exist which possess, however, a negativecharge. These are the electrons, which other considerations will againbring 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 giveprecision to our studies, and to deal with a well ascertained case, Imentioned only ionisation by the X rays in the first instance, I oughtnot to give the impression that the phenomenon is confined to theserays. It is, on the contrary, very general, and ionisation is just aswell produced by the cathode rays, by the radiations emitted byradio-active bodies, by the ultra-violet rays, by heating to a hightemperature, by certain chemical actions, and finally by the impact ofthe ions already existing in neutral molecules. 

Of late years these new questions have been the object of a multitudeof researches, and if it has not always been possible to avoid someconfusion, yet certain general conclusions may be drawn. Theionisation by flames, in particular, is fairly well known. For it tobe produced spontaneously, it would appear that there must existsimultaneously a rather high temperature and a chemical action in thegas. According to M. Moreau, the ionisation is very marked when theflame contains the vapour of the salt of an alkali or of an alkalineearth, but much less so when it contains that of other salts. Arrhenius, Mr C. T. R. Wilson, and M. Moreau, have studied all thecircumstances of the phenomenon; and it seems indeed that there is asomewhat close analogy between what first occurs in the saline vapoursand that which is noted in liquid electrolytes. There should beproduced, as soon as a certain temperature is reached, a dissociationof the saline molecule; and, as M. Moreau has shown in a series ofvery well conducted researches, the ions formed at about 100°C. Seemconstituted by an electrified centre of the size of a gas molecule, surrounded by some ten layers of other molecules. We are thus dealingwith rather large ions, but according to Mr Wilson, this condensationphenomenon does not affect the number of ions produced bydissociation. In proportion as the temperature rises, the moleculescondensed round the nucleus disappear, and, as in all othercircumstances, the negative ion tends to become an electron, while thepositive ion continues the size of an atom. 

In other cases, ions are found still larger than those of salinevapours, as, for example, those produced by phosphorus. It has longbeen known that air in the neighbourhood of phosphorus becomes aconductor, and the fact, pointed out as far back as 1885 by Matteucci, has been well studied by various experimenters, by MM. Elster andGeitel in 1890, for instance. On the other hand, in 1893 Mr Barusestablished that the approach of a stick of phosphorus brings aboutthe condensation of water vapour, and we really have before us, therefore, in this instance, an ionisation. M. Bloch has succeeded indisentangling the phenomena, which are here very complex, and inshowing that the ions produced are of considerable dimensions; fortheir speed in the same conditions is on the average a thousand timesless than that of ions due to the X rays. M. Bloch has establishedalso that the conductivity of recently-prepared gases, already studiedby several authors, was analogous to that which is produced byphosphorus, and that it is intimately connected with the presence ofthe very tenuous solid or liquid dust which these gases carry withthem, while the ions are of the same order of magnitude. These largeions 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 ionsare thus born, and this production is in part compensated for byrecombinations between ions of opposite signs. The impacts will bemore active in the event of the gas being placed in a field of forceand of the pressure being slight, the speed attained being thengreater and allowing the active force to reach a high value. Theenergy necessary for the production of an ion is, in fact, accordingto 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 byimpact will be particularly felt. This gives us the reason for theaspect presented by Geissler tubes. Generally, in the case ofdischarges, new ions produced by the molecules struck come to addthemselves to the electrons produced, as will be seen, by the cathode. A full discussion has led to the interpretation of all the knownfacts, and to our understanding, for instance, why there exist brightor dark spaces in certain regions of the tube. M. Pellat, inparticular, has given some very fine examples of this concordancebetween the theory and the facts he has skilfully observed. 

In all the circumstances, then, in which ions appear, their formationhas doubtless been provoked by a mechanism analogous to that of theshock. The X rays, if they are attributable to sudden variations inthe ether--that is to say, a variation of the two vectors of Hertz--themselves produce within the atom a kind of electric impulse whichbreaks it into two electrified fragments; _i. E. _ the positive centre, the size of the molecule itself, and the negative centre, constitutedby an electron a thousand times smaller. Round these two centres, atthe ordinary temperature, are agglomerated by attraction othermolecules, and in this manner the ions whose properties have just beenstudied are formed. 

§ 4. ELECTRONS IN METALS

The success of the ionic hypothesis as an interpretation of theconductivity of electrolytes and gases has suggested the desire to tryif a similar hypothesis can represent the ordinary conductivity ofmetals. We are thus led to conceptions which at first sight seemaudacious because they are contrary to our habits of mind. They mustnot, however, be rejected on that account. Electrolytic dissociationat first certainly appeared at least as strange; yet it has ended byforcing itself upon us, and we could, at the present day, hardlydispense with the image it presents to us. 

The idea that the conductivity of metals is not essentially differentfrom that of electrolytic liquids or gases, in the sense that thepassage of the current is connected with the transport of smallelectrified particles, is already of old date. It was enunciated by W. Weber, and afterwards developed by Giese, but has only obtained itstrue scope through the effect of recent discoveries. It was theresearches of Riecke, later, of Drude, and, above all, those of J. J. Thomson, which have allowed it to assume an acceptable form. All theseattempts 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 moleculein a solution, partially dissociate themselves. Electrons, very muchsmaller than atoms, can move through the structure, considerable tothem, which is constituted by the atom from which they have just beendetached. They may be compared to the molecules of a gas which isenclosed in a porous body. In ordinary conditions, notwithstanding thegreat speed with which they are animated, they are unable to travellong distances, because they quickly find their road barred by amaterial atom. They have to undergo innumerable impacts, which throwthem first in one direction and then in another. The passage of acurrent is a sort of flow of these electrons in a determineddirection. This electric flow brings, however, no modification to thematerial medium traversed, since every electron which disappears atany point is replaced by another which appears at once, and in allmetals the electrons are identical. 

This hypothesis leads us to anticipate certain facts which experienceconfirms. Thus J. J. Thomson shows that if, in certain conditions, aconductor is placed in a magnetic field, the ions have to describe anepicycloid, and their journey is thus lengthened, while the electricresistance must increase. If the field is in the direction of thedisplacement, they describe helices round the lines of force and theresistance is again augmented, but in different proportions. Variousexperimenters have noted phenomena of this kind in differentsubstances. 

For a long time it has been noticed that a relation exists between thecalorific and the electric conductivity; the relation of these twoconductivities is sensibly the same for all metals. The modern theorytends to show simply that it must indeed be so. Calorific conductivityis due, in fact, to an exchange of electrons between the hot and thecold regions, the heated electrons having the greater velocity, andconsequently the more considerable energy. The calorific exchangesthen obey laws similar to those which govern electric exchanges; andcalculation even leads to the exact values which the measurements havegiven. [31]

[Footnote 31: The whole of this argument is brilliantly set forth byProfessor Lorentz in a lecture delivered to the Electrotechnikervereinat Berlin in December 1904, and reprinted, with additions, in the_Archives Néerlandaises_ of 1906. --ED. ]

In the same way Professor Hesehus has explained how contactelectrification is produced, by the tendency of bodies to equalisetheir superficial properties by means of a transport of electrons, andMr Jeans has shown that we should discover the existence of thewell-known laws of distribution over conducting bodies in electrostaticequilibrium. A metal can, in fact, be electrified, that is to say, maypossess an excess of positive or negative electrons which cannoteasily leave it in ordinary conditions. To cause them to do so wouldneed an appreciable amount of work, on account of the enormousdifference of the specific inductive capacities of the metal and ofthe 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 forthand would be disengaged as a vapour escapes from a liquid. Now, thenumber of these rapid electrons, at first very slight, increases, according to the kinetic theory, when the temperature rises, andtherefore we must reckon that a wire, on being heated, gives outelectrons, that is to say, loses negative electricity and sends intothe surrounding media electrified centres capable of producing thephenomena of ionisation. Edison, in 1884, showed that from thefilament of an incandescent lamp there escaped negative electriccharges. Since then, Richardson and J. J. Thomson have examinedanalogous phenomena. This emission is a very general phenomenon which, no doubt, plays a considerable part in cosmic physics. ProfessorArrhenius explains, for instance, the polar auroras by the action ofsimilar corpuscules emitted by the sun. 

In other phenomena we seem indeed to be confronted by an emission, notof negative electrons, but of positive ions. Thus, when a wire isheated, not _in vacuo_, but in a gas, this wire begins to electrifyneighbouring bodies positively. J. J. Thomson has measured the mass ofthese positive ions and finds it considerable, i. E. About 150 timesthat of an atom of hydrogen. Some are even larger, and constitutealmost a real grain of dust. We here doubtless meet with the phenomenaof 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 beenexplained, the seat of a movement of electrons. If we cut this wire, aflood of electrons, like a current of water which, at the point wherea pipe bursts, flows out in abundance, will appear to spring outbetween the two ends of the break. 

If the energy of the electrons is sufficient, these electrons will infact rush forth and be propagated in the air or in the insulatingmedium interposed; but the phenomena of the discharge will in generalbe very complex. We shall here only examine a particularly simplecase, viz. , that of the cathode rays; and without entering intodetails, we shall only note the results relating to these rays whichfurnish valuable arguments in favour of the electronic hypothesis andsupply solid materials for the construction of new theories ofelectricity and matter. 

For a long time it was noticed that the phenomena in a Geissler tubechanged their aspect considerably, when the gas pressure became veryweak, without, however, a complete vacuum being formed. From thecathode there is shot forth normally and in a straight line a floodwithin the tube, dark but capable of impressing a photographic plate, of developing the fluorescence of various substances (particularly theglass walls of the tube), and of producing calorific and mechanicaleffects. These are the cathode rays, so named in 1883 by E. Wiedemann, and their name, which was unknown to a great number of physicists tillbarely twelve years ago, has become popular at the present day. 

About 1869, Hittorf made an already very complete study of them andput in evidence their principal properties; but it was the researchesof Sir W. Crookes in especial which drew attention to them. Thecelebrated physicist foresaw that the phenomena which were thusproduced in rarefied gases were, in spite of their very greatcomplication, more simple than those presented by matter under theconditions 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 ourpresent ideas. In the opinion of Crookes, in a tube in which the gashas been rarefied we are in presence of a special state of matter. Thenumber of the gas molecules has become small enough for theirindependence to be almost absolute, and they are able in thisso-called radiant state to traverse long spaces without departingfrom a straight line. The cathode rays are due to a kind of molecularbombardment of the walls of the tubes, and of the screens which can beintroduced into them; and it is the molecules, electrified by theircontact with the cathode and then forcibly repelled by electrostaticaction, which produce, by their movement and their _vis viva_, all thephenomena observed. Moreover, these electrified molecules animatedwith extremely rapid velocities correspond, according to the theoryverified in the celebrated experiment of Rowland on convectioncurrents, 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 entirelydifferent from that of radiant matter. They continued to regard thecathode radiation as due to particular radiations of a nature stilllittle known but produced in the luminous ether. This interpretationseemed, indeed, in 1894, destined to triumph definitely through theremarkable discovery of Lenard, a discovery which, in its turn, was toprovoke so many others and to bring about consequences of which theimportance seems every day more considerable. 

Professor Lenard's fundamental idea was to study the cathode raysunder conditions different from those in which they are produced. These rays are born in a very rarefied space, under conditionsperfectly determined by Sir W. Crookes; but it was a question whether, when once produced, they would be capable of propagating themselves inother media, such as a gas at ordinary pressure, or even in anabsolute vacuum. Experiment alone could answer this question, butthere were difficulties in the way of this which seemed almostinsurmountable. The rays are stopped by glass even of slightthickness, and how then could the almost vacuous space in which theyhave to come into existence be separated from the space, absolutelyvacuous or filled with gas, into which it was desired to bring them?

The artifice used was suggested to Professor Lenard by an experimentof Hertz. The great physicist had, in fact, shortly before hispremature death, taken up this important question of the cathode rays, and his genius left there, as elsewhere, its powerful impress. He hadshown that metallic plates of very slight thickness were transparentto the cathode rays; and Professor Lenard succeeded in obtainingplates impermeable to air, but which yet allowed the pencil of cathoderays to pass through them. 

Now if we take a Crookes tube with the extremity hermetically closedby 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 beimmediately noticed that the rays pass through the aluminium and passoutside the tube. They are propagated in air at atmospheric pressure, and they can also penetrate into an absolute vacuum. They thereforecan no longer be attributed to radiant matter, and we are led to thinkthat the energy brought into play in this phenomenon must have itsseat in the light-bearing ether itself. 

But it is a very strange light which is thus subject to magneticaction, which does not obey the principle of equal angles, and forwhich the most various gases are already disturbed media. According toCrookes it possesses also the singular property of carrying with itelectric charges. 

This convection of negative electricity by the cathode rays seemsquite inexplicable on the hypothesis that the rays are etherealradiations. Nothing then remained in order to maintain thishypothesis, except to deny the convection, which, besides, was onlyestablished by indirect experiments. That the reality of thistransport has been placed beyond dispute by means of an extremelyelegant experiment which is all the more convincing that it is so verysimple, is due to M. Perrin. In the interior of a Crookes tube hecollected a pencil of cathode rays in a metal cylinder. According tothe elementary principles of electricity the cylinder must becomecharged with the whole charge, if there be one, brought to it by therays, and naturally various precautions had to be taken. But theresult was very precise, and doubt could no longer exist--the rayswere electrified. 

It might have been, and indeed was, maintained, some time after thisexperiment was published, that while the phenomena were complex insidethe tube, outside, things might perhaps occur differently. Lenardhimself, however, with that absence of even involuntary prejudicecommon to all great minds, undertook to demonstrate that the opinionhe at first held could no longer be accepted, and succeeded inrepeating the experiment of M. Perrin on cathode rays in the air andeven _in vacuo_. 

On the wrecks of the two contradictory hypotheses thus destroyed, andout of the materials from which they had been built, a theory has beenconstructed which co-ordinates all the known facts. This theory isfurthermore closely allied to the theory of ionisation, and, like thislatter, is based on the concept of the electron. Cathode rays areelectrons in rapid motion. 

The phenomena produced both inside and outside a Crookes tube are, however, generally complex. In Lenard's first experiments, and in manyothers effected later when this region of physics was still verylittle 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 theessentially different X rays appear. These differ from the cathoderadiations by being neither electrified nor deviated by a magnet. Intheir turn these X rays may give birth to the secondary rays of M. Sagnac; and often we find ourselves in presence of effects from theselast-named radiations and not from the true cathode rays. 

The electrons, when they are propagated in a gas, can ionise themolecules of this gas and unite with the neutral atoms to formnegative ions, while positive ions also appear. There are likewiseproduced, at the expense of the gas still subsisting afterrarefication within the tube, positive ions which, attracted by thecathode and reaching it, are not all neutralised by the negativeelectrons, and can, if the cathode be perforated, pass through it, andif not, pass round it. We have then what are called the canal rays ofGoldstein, which are deviated by an electric or magnetic field in acontrary direction to the cathode rays; but, being larger, give weakdeviations or may even remain undeviated through losing their chargewhen passing through the cathode. 

It may also be the parts of the walls at a distance from the cathodewhich send a positive rush to the latter, by a similar mechanism. Itmay be, again, that in certain regions of the tube cathode rays aremet with diffused by some solid object, without having thereby changedtheir nature. All these complexities have been cleared up by M. Villard, who has published, on these questions, some remarkablyingenious and particularly careful experiments. 

M. Villard has also studied the phenomena of the coiling of the raysin a field, as already pointed out by Hittorf and Plücker. When amagnetic field acts on the cathode particle, the latter follows atrajectory, generally helicoidal, which is anticipated by the theory. We here have to do with a question of ballistics, and experiments dulyconfirm the anticipations of the calculation. Nevertheless, rathersingular phenomena appear in the case of certain values of the field, and these phenomena, dimly seen by Plücker and Birkeland, have beenthe object of experiments by M. Villard. The two faces of the cathodeseem to emit rays which are deviated in a direction perpendicular tothe lines of force by an electric field, and do not seem to beelectrified. M. Villard calls them magneto-cathode rays, and accordingto M. Fortin these rays may be ordinary cathode rays, but of veryslight velocity. 

In certain cases the cathode itself may be superficiallydisaggregated, and extremely tenuous particles detach themselves, which, being carried off at right angles to its surface, may depositthemselves like a very thin film on objects placed in their path. Various physicists, among them M. Houllevigue, have studied thisphenomenon, and in the case of pressures between 1/20 and 1/100 of amillimetre, the last-named scholar has obtained mirrors of mostmetals, a phenomenon he designates by the name of ionoplasty. 

But in spite of all these accessory phenomena, which even sometimesconceal those first observed, the existence of the electron in thecathodic flux remains the essential characteristic. 

The electron can be apprehended in the cathodic ray by the study ofits essential properties; and J. J. Thomson gave great value to thehypothesis by his measurements. At first he meant to determine thespeed of the cathode rays by direct experiment, and by observing, in arevolving mirror, the relative displacement of two bands due to theexcitement of two fluorescent screens placed at different distancesfrom the cathode. But he soon perceived that the effect of thefluorescence was not instantaneous, and that the lapse of time mightform a great source of error, and he then had recourse to indirectmethods. It is possible, by a simple calculation, to estimate thedeviations produced on the rays by a magnetic and an electric fieldrespectively as a function of the speed of propagation and of therelation of the charge to the material mass of the electron. Themeasurement of these deviations will then permit this speed and thisrelation to be ascertained. 

Other processes may be used which all give the same two quantities bytwo suitably chosen measurements. Such are the radius of the curvetaken by the trajectory of the pencil in a perpendicular magneticfield and the measure of the fall of potential under which thedischarge takes place, or the measure of the total quantityof electricity carried in one second and the measure of thecalorific energy which may be given, during the same period, to athermo-electric junction. The results agree as well as can be expected, having regard to the difficulty of the experiments; the values of thespeed agree also with those which Professor Wiechert has obtained bydirect measurement. 

The speed never depends on the nature of the gas contained in theCrookes tube, but varies with the value of the fall of potential atthe 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 thereforegoes about three thousand times faster than the earth in its orbit. The relation is also invariable, even when the substance of which thecathode is formed is changed or one gas is substituted for another. Itis, on the average, a thousand times greater than the correspondingrelation in electrolysis. As experiment has shown, in all thecircumstances where it has been possible to effect measurements, theequality 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 massis only a small fraction of that of the atom of hydrogen, viz. , of theorder of about a thousandth part. This is the same result as that towhich we were led by the study of flames. 

The thorough examination of the cathode radiation, then, confirms usin the idea that every material atom can be dissociated and will yieldan electron much smaller than itself--and always identical whateverthe matter whence it comes, --the rest of the atom remaining chargedwith a positive quantity equal and contrary to that borne by theelectron. In the present case these positive ions are no doubt thosethat we again meet with in the canal rays. Professor Wien has shownthat their mass is really, in fact, of the order of the mass of atoms. Although they are all formed of identical electrons, there may bevarious cathode rays, because the velocity is not exactly the same forall electrons. Thus is explained the fact that we can separate themand that we can produce a sort of spectrum by the action of themagnet, or, again, as M. Deslandres has shown in a very interestingexperiment, by that of an electrostatic field. This also probablyexplains the phenomena studied by M. Villard, and previously pointedout. 

§ 2. RADIOACTIVE SUBSTANCES

Even in ordinary conditions, certain substances called radioactiveemit, quite outside any particular reaction, radiations complexindeed, but which pass through fairly thin layers of minerals, impressphotographic plates, excite fluorescence, and ionize gases. In theseradiations we again find electrons which thus escape spontaneouslyfrom 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 haveaccumulated for the last six years, among which some people findthemselves a little lost. It may, perhaps, not be useless to indicatethe essential results actually obtained. 

The researches on radioactive substances have their starting-point inthe discovery of the rays of uranium made by M. Becquerel in 1896. Asearly as 1867 Niepce de St Victor proved that salts of uraniumimpressed photographic plates in the dark; but at that time thephenomenon could only pass for a singularity attributable tophosphorescence, and the valuable remarks of Niepce fell intooblivion. M. Becquerel established, after some hesitations natural inthe face of phenomena which seemed so contrary to accepted ideas, thatthe radiating property was absolutely independent of phosphorescence, that all the salts of uranium, even the uranous salts which are notphosphorescent, give similar radiant effects, and that these phenomenacorrespond to a continuous emission of energy, but do not seem to bethe result of a storage of energy under the influence of some externalradiation. Spontaneous and constant, the radiation is insensible tovariations of temperature and light. 

The nature of these radiations was not immediately understood, [32] andtheir properties seemed contradictory. This was because we were notdealing with a single category of rays. But amongst all the effectsthere is one which constitutes for the radiations taken as a whole, averitable process for the measurement of radioactivity. This is theirionizing action on gases. A very complete study of the conductivity ofair under the influence of rays of uranium has been made by variousphysicists, particularly by Professor Rutherford, and has shown thatthe laws of the phenomenon are the same as those of the ionization dueto the action of the Röntgen rays. 

[Footnote 32: In his work on _L'Évolution de la Matière_, M. GustaveLe Bon recalls that in 1897 he published several notes in the Académiedes Sciences, in which he asserted that the properties of uranium wereonly a particular case of a very general law, and that the radiationsemitted did not polarize, and were akin by their properties to the Xrays. ]

It was natural to ask one's self if the property discovered in saltsof uranium was peculiar to this body, or if it were not, to a more orless degree, a general property of matter. Madame Curie and M. Schmidt, independently of each other, made systematic researches inorder to solve the question; various compounds of nearly all thesimple bodies at present known were thus passed in review, and it wasestablished that radioactivity was particularly perceptible in thecompounds of uranium and thorium, and that it was an atomic propertylinked to the matter endowed with it, and following it in all itscombinations. In the course of her researches Madame Curie observedthat certain pitchblendes (oxide of uranium ore, containing alsobarium, bismuth, etc. ) were four times more active (activity beingmeasured by the phenomenon of the ionization of the air) than metallicuranium. Now, no compound containing any other active metal thanuranium or thorium ought to show itself more active than those metalsthemselves, since the property belongs to their atoms. It seemed, therefore, probable that there existed in pitchblendes some substanceyet unknown, in small quantities and more radioactive than uranium. 

M. And Madame Curie then commenced those celebrated experiments whichbrought them to the discovery of radium. Their method of research hasbeen justly compared in originality and importance to the process ofspectrum analysis. To isolate a radioactive substance, the first thingis to measure the activity of a certain compound suspected ofcontaining this substance, and this compound is chemically separated. We then again take in hand all the products obtained, and by measuringtheir activity anew, it is ascertained whether the substance soughtfor has remained in one of these products, or is divided among them, and if so, in what proportion. The spectroscopic reaction which we mayuse in the course of this separation is a thousand times lesssensitive than observation of the activity by means of theelectrometer. 

Though the principle on which the operation of the concentration ofthe radium rests is admirable in its simplicity, its application isnevertheless very laborious. Tons of uranium residues have to betreated 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 higherhomologue of barium in one of the groups of Mendeléef. Salts of radiumhave in general the same chemical properties as the correspondingsalts of barium, but are distinguished from them by the differences ofsolubility which allow of their separation, and by their enormousactivity, which is about a hundred thousand times greater than that ofuranium. 

Radium produces various chemical and some very intense physiologicalreactions. Its salts are luminous in the dark, but this luminosity, atfirst very bright, gradually diminishes as the salts get older. Wehave here to do with a secondary reaction correlative to theproduction of the emanation, after which radium undergoes thetransformations which will be studied later on. 

The method of analysis founded by M. And Madame Curie has enabledother bodies presenting sensible radioactivity to be discovered. Thealkaline metals appear to possess this property in a slight degree. Recently fallen snow and mineral waters manifest marked action. Thephenomenon may often be due, however, to a radioactivity induced byradiations already existing in the atmosphere. But this radioactivityhardly 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 thespecial nature of the radiations it emits and the other by aparticular spectrum, seem likewise to exist in pitchblende. Thesechemical properties have not yet been perfectly defined; thus M. Debierne, who discovered actinium, has been able to note the activeproperty which seems to belong to it, sometimes in lanthanum, sometimes in neodynium. [33] It is proved that all extremelyradioactive bodies are the seat of incessant transformations, and evennow we cannot state the conditions under which they present themselvesin a strictly determined form. 

[Footnote 33: Polonium has now been shown to be no new element, butone of the transformation products of radium. Radium itself is alsothought to be derived in some manner, not yet ascertained, fromuranium. The same is the case with actinium, which is said to come inthe long run from uranium, but not so directly as does radium. Allthis is described in Professor Rutherford's _RadioactiveTransformations_ (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 theradioactive bodies, it was necessary to try to cause magnetic orelectric forces to act on them so as to see whether they behaved inthe same way as light and the X rays, or whether like the cathode raysthey were deviated by a magnetic field. This work was effected byProfessor Giesel, then by M. Becquerel, Professor Rutherford, and bymany other experimenters after them. All the methods which havealready been mentioned in principle have been employed in order todiscover whether they were electrified, and, if so, by electricity ofwhat sign, to measure their speed, and to ascertain their degree ofpenetration. 

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 speedwhich may attain the tenth of that of light; M. H. Becquerel has shownby the aid of photography that they are deviated by a magnet, andProfessor Rutherford has, on his side, studied this deviation by theelectrical method. The relation of the charge to the mass is, in thecase of these rays, of the same order as in that of the ions ofelectrolysis. They may therefore be considered as exactly analogous tothe canal rays of Goldstein, and we may attribute them to a materialtransport of corpuscles of the magnitude of atoms. The relativelyconsiderable size of these corpuscles renders them very absorbable. Aflight of a few millimetres in a gas suffices to reduce their numberby 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 chargethey 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 hundredtimes less ionizing power than the alpha rays. 

The gamma rays were discovered by M. Villard. [34] They may be comparedto the X rays; like the latter, they are not deviated by the magneticfield, and are also extremely penetrating. A strip of aluminium fivemillimetres thick will stop the other kinds, but will allow them topass. On the other hand, their ionizing power is 10, 000 times lessthan 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 ofPhysical Science_ (London, 1904) nor the Hon. R. J. Strutt in _TheBecquerel Rays_ (London, same date), both of whom deal with thehistorical side of the subject, seem to have noticed the fact. --ED. ]

To these radiations there sometimes are added in the course ofexperiments secondary radiations analogous to those of M. Sagnac, andproduced 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 thealpha and beta rays, particularly from the alpha rays, to whichbelongs the most important part of the total energy of the radiation. Sir W. Crookes has invented a curious little apparatus, thespinthariscope, which enables us to examine the phosphorescence of theblende excited by these rays. By means of a magnifying glass, a screencovered with sulphide of zinc is kept under observation, and in frontof it is disposed, at a distance of about half a millimetre, afragment of some salt of radium. We then perceive multitudes ofbrilliant points on the screen, which appear and at once disappear, producing a scintillating effect. It seems probable that everyparticle falling on the screen produces by its impact a disturbance inthe neighbouring region, and it is this disturbance which the eyeperceives as a luminous point. Thus, says Sir W. Crookes, each drop ofrain falling on the surface of still water is not perceived as a dropof rain, but by reason of the slight splash which it causes at themoment of impact, and which is manifested by ridges and wavesspreading themselves in circles. 

The various radioactive substances do not all give radiations ofidentical constitution. Radium and thorium possess in somewhat largeproportions the three kinds of rays, and it is the same with actinium. Polonium contains especially alpha rays and a few gamma rays. [35] Inthe case of uranium, the alpha rays have extremely slight penetratingpower, and cannot even impress photographic plates. But the widestdifference 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, seeminglyalmost imponderable, but which may be, for many reasons, looked uponas a vapour of which the elastic force is extremely feeble. 

[Footnote 35: It has now been shown that polonium when freshlyseparated emits beta rays also; see Dr Logeman's paper in _Proceedingsof the Royal Society_, A. , 6th September 1906. --ED. ]

M. And Madame Curie discovered as early as 1899 that every substanceplaced in the neighbourhood of radium, itself acquired a radioactivitywhich persisted for several hours after the removal of the radium. This induced radioactivity seems to be carried to other bodies by theintermediary of a gas. It goes round obstacles, but there must existbetween the radium and the substance a free and continuous space forthe activation to take place; it cannot, for instance, do so through awall of glass. 

In the case of compounds of thorium Professor Rutherford discovered asimilar phenomenon; since then, various physicists, Professor Soddy, Miss Brooks, Miss Gates, M. Danne, and others, have studied theproperties of these emanations. 

The substance emanated can neither be weighed nor can its elasticforce be ascertained; but its transformations may be followed, as itis luminous, and it is even more certainly characterised by itsessential property, i. E. Its radioactivity. We also see that it can bedecanted like a gas, that it will divide itself between two tubes ofdifferent capacity in obedience to the law of Mariotte, and willcondense in a refrigerated tube in accordance with the principle ofWatt, while it even complies with the law of Gay-Lussac. 

The activity of the emanation vanishes quickly, and at the end of fourdays it has diminished by one-half. If a salt of radium is heated, theemanation becomes more abundant, and the residue, which, however, doesnot 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 thisemanation enter into any chemical reaction. If it be a gaseous body, it must form part of the argon group, and, like its other members, beperfectly inert. 

By studying the spectrum of the gas disengaged by a solution of saltof radium, Sir William Ramsay and Professor Soddy remarked that whenthe gas is radioactive there are first obtained rays of gasesbelonging to the argon family, then by degrees, as the activitydisappears, the spectrum slowly changes, and finally presents thecharacteristic aspect of helium. 

We know that the existence of this gas was first discovered byspectrum analysis in the sun. Later its presence was noted in ouratmosphere, and in a few minerals which happen to be the very onesfrom which radium has been obtained. It might therefore have been thecase that it pre-existed in the gases extracted from radium; but aremarkable experiment by M. Curie and Sir James Dewar seems to showconvincingly that this cannot be so. The spectrum of helium neverappears at first in the gas proceeding from pure bromide of radium;but it shows itself, on the other hand, very distinctly, after theradioactive transformations undergone by the salt. 

All these strange phenomena suggest bold hypotheses, but to constructthem with any solidity they must be supported by the greatest possiblenumber of facts. Before admitting a definite explanation of thephenomena which have their seat in the curious substances discoveredby them, M. And Madame Curie considered, with a great deal of reason, that they ought first to enrich our knowledge with the exact andprecise facts relating to these bodies and to the effects produced bythe radiations they emit. 

Thus M. Curie particularly set himself to study the manner in whichthe radioactivity of the emanation is dissipated, and theradioactivity that this emanation can induce on all bodies. Theradioactivity of the emanation diminishes in accordance with anexponential law. The constant of time which characterises thisdecrease is easily and exactly determined, and has a fixed value, independent of the conditions of the experiment as well as of thenature of the gas which is in contact with the radium and becomescharged with the emanation. The regularity of the phenomenon is sogreat that it can be used to measure time: in 3985 seconds[36] theactivity 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 inpresence of a salt of radium disappears more rapidly. The phenomenonappears, moreover, more complex, and the formula which expresses themanner in which the activity diminishes must contain two exponentials. To find it theoretically we have to imagine that the emanation firstdeposits on the body in question a substance which is destroyed ingiving birth to a second, this latter disappearing in its turn bygenerating a third. The initial and final substances would beradioactive, but the intermediary one, not. If, moreover, the bodiesacted on are brought to a temperature of over 700°, they appear tolose by volatilisation certain substances condensed in them, and atthe same time their activity disappears. 

The other radioactive bodies behave in a similar way. Bodies whichcontain actinium are particularly rich in emanations. Uranium, on thecontrary, has none. [37] This body, nevertheless, is the seat oftransformations comparable to those which the study of emanationsreveals in radium; Sir W. Crookes has separated from uranium a matterwhich is now called uranium X. This matter is at first much moreactive than its parent, but its activity diminishes rapidly, while theordinary uranium, which at the time of the separation loses itsactivity, regains it by degrees. In the same way, ProfessorsRutherford and Soddy have discovered a so-called thorium X to be thestage through which ordinary thorium has to pass in order to produceits emanation. [38]

[Footnote 37: Professor Rutherford has lately stated that uranium maypossibly produce an emanation, but that its rate of decay must be tooswift for its presence to be verified (see _RadioactiveTransformations_, p. 161). --ED. ]

[Footnote 38: An actinium X was also discovered by Professor Giesel(_Jahrbuch d. Radioaktivitat_, i. P. 358, 1904). Since the above waswritten, another product has been found to intervene between the Xsubstance and the emanation in the case of actinium and thorium. Theyhave 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 stateshave 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, itcannot be denied that many experiments render it probable that inradioactive bodies we find ourselves witnessing veritabletransformations of matter. 

Professor Rutherford, Professor Soddy, and several other physicists, have come to regard these phenomena in the following way. Aradioactive body is composed of atoms which have little stability, andare able to detach themselves spontaneously from the parent substance, and at the same time to divide themselves into two essential componentparts, the negative electron and its residue the positive ion. Thefirst-named constitutes the beta, and the second the alpha rays. 

The emanation is certainly composed of alpha ions with a few moleculesagglomerated 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 newbodies. 

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 beradioactive, and again lose atoms. The various stages that we meetwith in the evolution of the radioactive substance or of itsemanation, correspond to the various degrees of atomic disaggregation. Professors Rutherford and Soddy have described them clearly in thecase of uranium and radium. As regards thorium the results are lesssatisfactory. The evolution should continue until a stable atomiccondition is finally reached, which, because of this stability, is nolonger radioactive. Thus, for instance, radium would finally betransformed into helium. [40]

[Footnote 40: This opinion, no doubt formed when Sir William Ramsay'sdiscovery of the formation of helium from the radium emanation wasfirst made known, is now less tenable. The latest theory is that thealpha particle is in fact an atom of helium, and that the finaltransformation product of radium and the other radioactive substancesis lead. Cf. Rutherford, op. Cit. Passim. --ED. ]

It is possible, by considerations analogous to those set forth abovein other cases, to arrive at an idea of the total number of particlesper second expelled by one gramme of radium; Professor Rutherford inhis most recent evaluation finds that this number approaches 2. 5 x10^{11}. [41] By calculating from the atomic weight the number of atomsprobably contained in this gramme of radium, and supposing eachparticle liberated to correspond to the destruction of one atom, it isfound 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 todiscover any sensible loss of weight. Sir W. Ramsay and ProfessorSoddy attained a like result by endeavouring to estimate the mass ofthe emanation by the quantity of helium produced. 

[Footnote 41: See _Radioactive Transformations_ (p. 251). ProfessorRutherford says that "each of the alpha ray products present in onegram of radium product (_sic_) expels 6. 2 x 10^{10} alpha particlesper second. " He also remarks on "the experimental difficulty ofaccurately determining the number of alpha particles expelled fromradium per second. "--ED. ]

[Footnote 42: See Rutherford, op. Cit. P. 150. --ED. ]

If radium transforms itself in such a way that its activity does notpersist throughout the ages, it loses little by little the provisionof energy it had in the beginning, and its properties furnish no validargument to oppose to the principle of the conservation of energy. Toput everything right, we have only to recognise that radium possessedin the potential state at its formation a finite quantity of energywhich is consumed little by little. In the same manner, a chemicalsystem composed, for instance, of zinc and sulphuric acid, alsocontains in the potential state energy which, if we retard thereaction by any suitable arrangement--such as by amalgamating the zincand by constituting with its elements a battery which we cause to acton a resistance--may be made to exhaust itself as slowly as one maydesire. 

There can, therefore, be nothing in any way surprising in the factthat a combination which, like the atomic combination of radium, isnot stable--since it disaggregates itself, --is capable ofspontaneously 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, thequantity of energy liberated, measuring it entirely in the form ofheat. The disengagement of heat accounted for in a grain of radium isuniform, and amounts to 100 calories per hour. It must therefore beadmitted that an atom of radium, in disaggregating itself, liberates30, 000 times more energy than a molecule of hydrogen when the lattercombines with an atom of oxygen to form a molecule of water. 

We may ask ourselves how the atomic edifice of the active body can beconstructed, to contain so great a provision of energy. We will remarkthat such a question might be asked concerning cases known from themost remote antiquity, like that of the chemical systems, without anysatisfactory 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 toshow ourselves more exacting; yet there are found persons who refuseto admit the hypothesis of the atomic disaggregation of radium becausethey cannot have set before them a detailed plan of that complex wholeknown to us as an atom. 

The most natural idea is perhaps the one suggested by comparison withthose astronomical phenomena where our observation most readily allowsus to comprehend the laws of motion. It corresponds likewise to thetendency ever present in the mind of man, to compare the infinitelysmall with the infinitely great. The atom may be regarded as a sort ofsolar system in which electrons in considerable numbers gravitateround the sun formed by the positive ion. It may happen that certainof these electrons are no longer retained in their orbit by theelectric attraction of the rest of the atom, and may be projected fromit like a small planet or comet which escapes towards the stellarspaces. The phenomena of the emission of light compels us to thinkthat the corpuscles revolve round the nucleus with extreme velocities, or at the rate of thousands of billions of evolutions per second. Itis easy to conceive from this that, notwithstanding its lightness, anatom 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). Seeespecially pp. 36-52, where the amount of the supposed intra-atomicenergy is calculated. --ED. ]

Other authors imagine that the energy of the corpuscles is principallydue to the extremely rapid rotations of those elements on their ownaxes. Lord Kelvin lately drew up on another model the plan of aradioactive atom capable of ejecting an electron with a considerable_vis viva_. He supposes a spherical atom formed of concentric layersof positive and negative electricity disposed in such a way that itsexternal action is null, and that, nevertheless, the force emanatedfrom the centre may be repellent for certain values when the electronis within it. 

The most prudent physicists and those most respectful to establishedprinciples may, without any scruples, admit the explanation of theradioactivity of radium by a dislocation of its molecular edifice. Thematter of which it is constituted evolves from an admittedly unstableinitial state to another stable one. It is, in a way, a slowallotropic transformation which takes place by means of a mechanismregarding which, in short, we have no more information than we haveregarding other analogous transformations. The only astonishment wecan legitimately feel is derived from the thought that we are suddenlyand deeply penetrating to the very heart of things. 

But those persons who have a little more hardihood do not easilyresist the temptation of forming daring generalisations. Thus it willoccur to some that this property, already discovered in manysubstances where it exists in more or less striking degree, is, withdifferences of intensity, common to all bodies, and that we are thusconfronted by a phenomenon derived from an essential quality ofmatter. Quite recently, Professor Rutherford has demonstrated in afine series of experiments that the alpha particles of radium cease toionize gases when they are made to lose their velocity, but that theydo not on that account cease to exist. It may follow that many bodiesemit similar particles without being easily perceived to do so; sincethe electric action, by which this phenomenon of radioactivity isgenerally manifested, would, in this case, be but very weak. 

If we thus believe radioactivity to be an absolutely generalphenomenon, we find ourselves face to face with a new problem. Thetransformation of radioactive bodies can no longer be assimilated toallotropic transformations, since thus no final form could ever beattained, and the disaggregation would continue indefinitely up to thecomplete dislocation of the atom. [44] The phenomenon might, it istrue, have a duration of perhaps thousands of millions of centuries, but this duration is but a minute in the infinity of time, and matterslittle. Our habits of mind, if we adopt such a conception, will benone the less very deeply disturbed. We shall have to abandon the ideaso instinctively dear to us that matter is the most stable thing inthe universe, and to admit, on the contrary, that all bodies whateverare a kind of explosive decomposing with extreme slowness. There is inthis, whatever may have been said, nothing contrary to any of theprinciples on which the science of energetics rests; but an hypothesisof this nature carries with it consequences which ought in the highestdegree to interest the philosopher, and we all know with what alluringboldness M. Gustave Le Bon has developed all these consequences in hiswork on the evolution of matter. [45]

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

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

There is hardly a physicist who does not at the present day adopt inone shape or another the ballistic hypothesis. All new facts areco-ordinated so happily by it, that it more and more satisfies ourminds; but it cannot be asserted that it forces itself on ourconvictions with irresistible weight. Another point of view appearedmore plausible and simple at the outset, when there seemed reason toconsider the energy radiated by radioactive bodies as inexhaustible. It was thought that the source of this energy was to be looked forwithout the atom, and this idea may perfectly well he maintained atthe present day. 

Radium on this hypothesis must be considered as a transformerborrowing energy from the external medium and returning it in the formof radiation. It is not impossible, even, to admit that the energywhich the atom of radium withdraws from the surrounding medium mayserve 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. Itdoes not seem to accord with the experiments that this borrowed energycan be a part of the heat of the ambient medium; and, indeed, such aphenomenon would be contrary to the principle of Carnot if we wished(though we have seen how disputable is this extension) to extend thisprinciple to the phenomena which are produced in the very bosom of theatom. 

We may also address ourselves to a more noble form of energy, and askourselves whether we are not, for the first time, in presence of atransformation of gravitational energy. It may be singular, but it isnot absurd, to suppose that the unit of mass of radium is not attachedto the earth with the same intensity as an inert body. M. Sagnac hascommenced some experiments, as yet unpublished, in order to study thelaws of the fall of a fragment of radium. They are necessarily verydelicate, and the energetic and ingenious physicist has not yetsucceeded in finishing them. [46] Let us suppose that he succeeds indemonstrating that the intensity of gravity is less for radium thanfor the platinum or the copper of which the pendulums used toillustrate the law of Newton are generally made; it would then bepossible still to think that the laws of universal attraction areperfectly exact as regards the stars, and that ponderability is reallya particular case of universal attraction, while in the case ofradioactive bodies part of the gravitational energy is transformed inthe course of its evolution and appears in the form of activeradiation. 

[Footnote 46: In reality M. Sagnac operated in the converse manner. Hetook 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. Hadthe durations of oscillation been different, it might be concludedthat the mechanical mass is not the same for radium as for barium. ]

But for this explanation to be admitted, it would evidently need to besupported by very numerous facts. It might, no doubt, appear stillmore probable that the energy borrowed from the external medium byradium is one of those still unknown to us, but of which a vagueinstinct causes us to suspect the existence around us. It isindisputable, moreover, that the atmosphere in all directions isfurrowed with active radiations; those of radium may be secondaryradiations reflected by a kind of resonance phenomenon. 

Certain experiments by Professors Elster and Geitel, however, are notfavourable to this point of view. If an active body be surrounded by aradioactive envelope, a screen should prevent this body from receivingany impression from outside, and yet there is no diminution apparentin the activity presented by a certain quantity of radium when it islowered to a depth of 800 metres under ground, in a region containinga notable quantity of pitchblende. These negative results are, on theother hand, so many successes for the partisans of the explanation ofradioactivity 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 ofphysicists to construct with the particles of ether all possible formsof corporeal existence; but our knowledge of the inmost nature ofthings has hitherto seemed too limited for us to attempt such anenterprise with any chance of success. The electronic hypothesis, however, which has furnished a satisfactory image of the most curiousphenomena produced in the bosom of matter, has also led to a morecomplete electromagnetic theory of the ether than that of Maxwell, andthis twofold result has given birth to the hope of arriving by meansof this hypothesis at a complete co-ordination of the physical world. 

The phenomena whose study may bring us to the very threshold of theproblem, are those in which the connections between matter and theether appear clearly and in a relatively simple manner. Thus in thephenomena of emission, ponderable matter is seen to give birth towaves which are transmitted by the ether, and by the phenomena ofabsorption it is proved that these waves disappear and excitemodifications in the interior of the material bodies which receivethem. We here catch in operation actual reciprocal actions andreactions between the ether and matter. If we could thoroughlycomprehend these actions, we should no doubt be in a position to fillup the gap which separates the two regions separately conquered byphysical science. 

In recent years numerous researches have supplied valuable materialswhich ought to be utilized by those endeavouring to construct a theoryof radiation. We are, perhaps, still ill informed as to the phenomenaof luminescence in which undulations are produced in a complex manner, as in the case of a stick of moist phosphorus which is luminescent inthe dark, or in that of a fluorescent screen. But we are very wellacquainted with emission or absorption by incandescence, where theonly transformation is that of calorific into radiating energy, or_vice versa_. It is in this case alone that can be correctly appliedthe celebrated demonstration by which Kirchhoff established, byconsiderations borrowed from thermodynamics, the proportionalrelations between the power of emission and that of absorption. 

In treating of the measurement of temperature, I have already pointedout the experiments of Professors Lummer and Pringsheim and thetheoretical researches of Stephan and Professor Wien. We may considerthat at the present day the laws of the radiation of dark bodies aretolerably well known, and, in particular, the manner in which eachelementary radiation increases with the temperature. A few doubts, however, subsist with respect to the law of the distribution of energyin the spectrum. In the case of real and solid bodies the results arenaturally less simple than in that of dark bodies. One side of thequestion has been specially studied on account of its great practicalinterest, that is to say, the fact that the relation of the luminousenergy to the total amount radiated by a body varies with the natureof this last; and the knowledge of the conditions under which thisrelation becomes most considerable led to the discovery ofincandescent lighting by gas in the Auer-Welsbach mantle, and to thesubstitution for the carbon thread in the electric light bulb of afilament of osmium or a small rod of magnesium, as in the Nernst lamp. Careful measurements effected by M. Fery have furnished, inparticular, important information on the radiation of the whiteoxides; but the phenomena noticed have not yet found a satisfactoryinterpretation. Moreover, the radiation of calorific origin is hereaccompanied by a more or less important luminescence, and the problembecomes very complex. 

In the same way that, for the purpose of knowing the constitution ofmatter, it first occurred to us to investigate gases, which appear tobe molecular edifices built on a more simple and uniform plan thansolids, we ought naturally to think that an examination of theconditions in which emission and absorption are produced by gaseousbodies might be eminently profitable, and might perhaps reveal themechanism by which the relations between the molecule of the ether andthe molecule of matter might be established. 

Unfortunately, if a gas is not absolutely incapable of emitting somesort of rays by simple heat, the radiation thus produced, no doubt byreason of the slightness of the mass in play, always remains ofmoderate intensity. In nearly all the experiments, new energies ofchemical or electrical origin come into force. On incandescence, luminescence is superposed; and the advantage which might have beenexpected from the simplicity of the medium vanishes through thecomplication of the circumstances in which the phenomenon is produced. 

Professor Pringsheim has succeeded, in certain cases, in finding thedividing line between the phenomena of luminescence and that ofincandescence. Thus the former takes a predominating importance whenthe gas is rendered luminous by electrical discharges, and chemicaltransformations, especially, play a preponderant rôle in the emissionof the spectrum of flames which contain a saline vapour. In all theordinary experiments of spectrum analysis the laws of Kirchhoff cannottherefore be considered as established, and yet the relation betweenemission and absorption is generally tolerably well verified. No doubtwe are here in presence of a kind of resonance phenomenon, the gaseousatoms entering into vibration when solicited by the ether by a motionidentical with the one they are capable of communicating to it. 

If we are not yet very far advanced in the study of the mechanism ofthe production of the spectrum, [47] we are, on the other hand, wellacquainted with its constitution. The extreme confusion which thespectra of the lines of the gases seemed to present is now, in greatpart at least, cleared up. Balmer gave some time since, in the case ofthe hydrogen spectrum, an empirical formula which enabled the raysdiscovered later by an eminent astronomer, M. Deslandres, to berepresented; but since then, both in the cases of line and bandspectra, the labours of Professor Rydberg, of M. Deslandres, ofProfessors Kayzer and Runge, and of M. Thiele, have enabled us tocomprehend, in their smallest details, the laws of the distribution oflines and bands. 

[Footnote 47: Many theories as to the cause of the lines and bands ofthe spectrum have been put forward since this was written, among whichthat of Professor Stark (for which see _Physikalische Zeitschrift_ for1906, passim) is perhaps the most advanced. That of M. Jean Becquerel, which would attribute it to the vibration within the atom of bothnegative and positive electrons, also deserves notice. A popularaccount of this is given in the _Athenæum_ of 20th April 1907. --ED. ]

These laws are simple, but somewhat singular. The radiations emittedby a gas cannot be compared to the notes to which a sonorous bodygives birth, nor even to the most complicated vibrations of anyelastic body. The number of vibrations of the different rays are notthe successive multiples of one and the same number, and it is not aquestion of a fundamental radiation and its harmonics, while--and thisis an essential difference--the number of vibrations of the radiationtend towards a limit when the period diminishes infinitely instead ofconstantly increasing, as would be the case with the vibrations ofsound. 

Thus the assimilation of the luminous to the elastic vibration is notcorrect. Once again we find that the ether does not behave like matterwhich obeys the ordinary laws of mechanics, and every theory must takefull account of these curious peculiarities which experiment reveals. 

Another difference, likewise very important, between the luminous andthe sonorous vibrations, which also points out how little analogouscan 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 velocityof sound, depends very little on the musical note, is not at all thesame in the case of the various radiations which can be propagated inthe same substance. The index of refraction varies with the durationof the period, or, if you will, with the length of wave _in vacuo_which is proportioned to this duration, since _in vacuo_ the speed ofpropagation is entirely the same for all vibrations. 

Cauchy was the first to propose a theory on which other attempts havebeen modelled; for example, the very interesting and simple one ofBriot. This last-named supposed that the luminous vibration could notperceptibly drag with it the molecular material of the medium acrosswhich it is propagated, but that matter, nevertheless, reacts on theether with an intensity proportional to the elongation, in such amanner as tends to bring it back to its position of equilibrium. Withthis simple hypothesis we can fairly well interpret the phenomena ofthe dispersion of light in the case of transparent substances; but farfrom well, as M. Carvallo has noted in some extremely carefulexperiments, the dispersion of the infra-red spectrum, and not at allthe peculiarities presented by absorbent substances. 

M. Boussinesq arrives at almost similar results, by attributingdispersion, on the other hand, to the partial dragging along ofponderable matter and to its action on the ether. By combining, in ameasure, as was subsequently done by M. Boussinesq, the twohypotheses, formulas can be established far better in accord with allthe known facts. 

These facts are somewhat complex. It was at first thought that theindex always varied in inverse ratio to the wave-length, but numeroussubstances have been discovered which present the phenomenon ofabnormal dispersion--that is to say, substances in which certainradiations are propagated, on the contrary, the more quickly theshorter their period. This is the case with gases themselves, asdemonstrated, for example, by a very elegant experiment of M. Becquerel on the dispersion of the vapour of sodium. Moreover, it mayhappen that yet more complications may be met with, as no substance istransparent for the whole extent of the spectrum. In the case ofcertain radiations the speed of propagation becomes nil, and the indexshows sometimes a maximum and sometimes a minimum. All those phenomenaare in close relation with those of absorption. 

It is, perhaps, the formula proposed by Helmholtz which best accountsfor all these peculiarities. Helmholtz came to establish this formulaby supposing that there is a kind of friction between the ether andmatter, which, like that exercised on a pendulum, here produces adouble effect, changing, on the one hand, the duration of thisoscillation, and, on the other, gradually damping it. He furthersupposed that ponderable matter is acted on by elastic forces. Thetheory of Helmholtz has the great advantage of representing, not onlythe 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 ordinaryoptics has always been employed. The phenomena are looked upon as dueto mechanical deformations or to movements governed by certain forces. The electromagnetic theory leads, as we have seen, to the employmentof other images. M. H. Poincaré, and, after him, Helmholtz, have bothproposed electromagnetic theories of dispersion. On examining thingsclosely, it will be found that there are not, in truth, in the twoways of regarding the problem, two equivalent translations of exteriorreality. The electrical theory gives us to understand, much betterthan the mechanical one, that _in vacuo_ the dispersion ought to bestrictly null, and this absence of dispersion appears to be confirmedwith extraordinary precision by astronomical observations. Thus theobservation, often repeated, and at different times of year, provesthat in the case of the star Algol, the light of which takes at leastfour years to reach us, no sensible difference in colorationaccompanies the changes in brilliancy. 

§ 2. THE THEORY OF LORENTZ

Purely mechanical considerations have therefore failed to give anentirely satisfactory interpretation of the phenomena in which eventhe simplest relations between matter and the ether appear. Theywould, evidently, be still more insufficient if used to explaincertain effects produced on matter by light, which could not, withoutgrave difficulties, be attributed to movement; for instance, thephenomena of electrification under the influence of certainradiations, or, again, chemical reactions such as photographicimpressions. 

The problem had to be approached by another road. The electromagnetictheory was a step in advance, but it comes to a standstill, so tospeak, at the moment when the ether penetrates into matter. If we wishto go deeper into the inwardness of the phenomena, we must follow, forexample, Professor Lorentz or Dr Larmor, and look with them for a modeof representation which appears, besides, to be a natural consequenceof the fundamental ideas forming the basis of Hertz's experiments. 

The moment we look upon a wave in the ether as an electromagneticwave, a molecule which emits light ought to be considered as a kind ofexcitant. We are thus led to suppose that in each radiating moleculethere are one or several electrified particles, animated with ato-and-fro movement round their positions of equilibrium, and theseparticles are certainly identical with those electrons the existenceof which we have already admitted for so many other reasons. 

In the simplest theory, we will imagine an electron which may bedisplaced from its position of equilibrium in all directions, and is, in this displacement, submitted to attractions which communicate to ita vibration like a pendulum. These movements are equivalent to tinycurrents, and the mobile electron, when animated with a considerablevelocity, must be sensitive to the action of the magnet which modifiesthe form of the trajectory and the value of the period. This almostdirect consequence was perceived by Lorentz, and it led him to the newidea that radiations emitted by a body ought to be modified by theaction of a strong electromagnet. 

An experiment enabled this prevision to be verified. It was made, asis well known, as early as 1896 by Zeeman; and the discovery produceda legitimate sensation. When a flame is subjected to the action of amagnetic field, a brilliant line is decomposed in conditions more orless complex which an attentive study, however, allows us to define. According to whether the observation is made in a plane normal to themagnetic field or in the same direction, the line transforms itselfinto a triplet or doublet, and the new lines are polarizedrectilinearly or circularly. 

These are the precise phenomena which the calculation foretells: theanalysis of the modifications undergone by the light supplies, moreover, valuable information on the electron itself. From thedirection of the circular vibrations of the greatest frequency we candetermine the sign of the electric charge in motion and we find it tobe negative. But, further than this, from the variation of the periodwe can calculate the relation of the force acting on the electron toits material mass, and, in addition, the relation of the charge to themass. We then find for this relation precisely that value which wehave already met with so many times. Such a coincidence cannot befortuitous, and we have the right to believe that the electronrevealed by the luminous wave which emanates from it, is really thesame as the one made known to us by the study of the cathode rays andof the radioactive substances. 

However, the elementary theory does not suffice to interpret thecomplications which later experiments have revealed. The physicistsmost qualified to effect measurements in these delicate opticalquestions--M. Cornu, Mr Preston, M. Cotton, MM. Becquerel andDeslandres, M. Broca, Professor Michelson, and others--have pointedout some remarkable peculiarities. Thus in some cases the number ofthe component rays dissociated by the magnetic field may be veryconsiderable. 

The great modification brought to a radiation by the Zeeman effectmay, besides, combine itself with other phenomena, and alter the lightin a still more complicated manner. A pencil of polarized light, asdemonstrated by Signori Macaluzo and Corbino, undergoes, in a magneticfield, modifications with regard to absorption and speed ofpropagation. 

Some ingenious researches by M. Becquerel and M. Cotton have perfectlyelucidated all these complications from an experimental point of view. It would not be impossible to link together all these phenomenawithout adopting the electronic hypothesis, by preserving the oldoptical equations as modified by the terms relating to the action ofthe magnetic field. This has actually been done in some veryremarkable work by M. Voigt, but we may also, like Professor Lorentz, look for more general theories, in which the essential image of theelectrons shall be preserved, and which will allow all the factsrevealed by experiment to be included. 

We are thus led to the supposition that there is not in the atom onevibrating electron only, but that there is to be found in it adynamical system comprising several material points which may besubjected to varied movements. The neutral atom may therefore beconsidered as composed of an immovable principal portion positivelycharged, round which move, like satellites round a planet, severalnegative electrons of very inferior mass. This conclusion leads us toan interpretation in agreement with that which other phenomena havealready suggested. 

These electrons, which thus have a variable velocity, generate aroundthemselves a transverse electromagnetic wave which is propagated withthe velocity of light; for the charged particle becomes, as soon as itexperiences a change of speed, the centre of a radiation. Thus isexplained the phenomenon of the emission of radiations. In the sameway, the movement of electrons may be excited or modified by theelectrical forces which exist in any pencil of light they receive, andthis 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 allthe mechanism of the phenomena of emission and absorption. He hasendeavoured to rediscover, by starting with the fundamentalhypothesis, the quantitative laws discovered by thermodynamics. Hesucceeds in showing that, agreeably to the law of Kirchhoff, therelation between the emitting and the absorbing power must beindependent 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 greatwave-lengths, and grave difficulties exist. Thus it cannot be veryclearly explained why, by heating a body, the radiation is displacedtowards the side of the short wave-lengths, or, if you will, why abody becomes luminous from the moment its temperature has reached asufficiently high degree. On the other hand, by calculating the energyof the vibrating particles we are again led to attribute to theseparticles the same constitution as that of the electrons. 

It is in the same way possible, as Professor Lorentz has shown, togive a very satisfactory explanation of the thermo-electric phenomenaby supposing that the number of liberated electrons which exist in agiven metal at a given temperature has a determined value varying witheach metal, and is, in the case of each body, a function of thetemperature. The formula obtained, which is based on these hypotheses, agrees completely with the classic results of Clausius and of LordKelvin. Finally, if we recollect that the phenomena of electric andcalorific conductivity are perfectly interpreted by the hypothesis ofelectrons, it will no longer be possible to contest the importance ofa theory which allows us to group together in one synthesis so manyfacts of such diverse origins. 

If we study the conditions under which a wave excited by an electron'svariations in speed can be transmitted, they again bring us face toface, and generally, with the results pointed out by the ordinaryelectromagnetic theory. Certain peculiarities, however, are notabsolutely the same. Thus the theory of Lorentz, as well as that ofMaxwell, leads us to foresee that if an insulating mass be caused tomove in a magnetic field normally to its lines of force, adisplacement will be produced in this mass analogous to that of whichFaraday and Maxwell admitted the existence in the dielectric of acharged condenser. But M. H. Poincaré has pointed out that, accordingas we adopt one or other of these authors' points of view, so thevalue of the displacement differs. This remark is very important, forit may lead to an experiment which would enable us to make a definitechoice between the two theories. 

To obtain the displacement estimated according to Lorentz, we mustmultiply the displacement calculated according to Hertz by a factorrepresenting the relation between the difference of the specificinductive capacities of the dielectric and of a vacuum, and the firstof these powers. If therefore we take as dielectric the air of whichthe specific inductive capacity is perceptibly the same as that of avacuum, the displacement, according to the idea of Lorentz, will benull; while, on the contrary, according to Hertz, it will have afinite value. M. Blondlot has made the experiment. He sent a currentof air into a condenser placed in a magnetic field, and was never ableto notice the slightest trace of electrification. No displacement, therefore, is effected in the dielectric. The experiment being anegative one, is evidently less convincing than one giving a positiveresult, but it furnishes a very powerful argument in favour of thetheory of Lorentz. 

This theory, therefore, appears very seductive, yet it still raisesobjections on the part of those who oppose to it the principles ofordinary mechanics. If we consider, for instance, a radiation emittedby an electron belonging to one material body, but absorbed by anotherelectron in another body, we perceive immediately that, thepropagation not being instantaneous, there can be no compensationbetween the action and the reaction, which are not simultaneous; andthe principle of Newton thus seems to be attacked. In order topreserve its integrity, it has to be admitted that the movements inthe two material substances are compensated by that of the ether whichseparates these substances; but this conception, although in tolerableagreement with the hypothesis that the ether and matter are not ofdifferent essence, involves, on a closer examination, suppositionshardly satisfactory as to the nature of movements in the ether. 

For a long time physicists have admitted that the ether as a wholemust be considered as being immovable and capable of serving, so tospeak, as a support for the axes of Galileo, in relation to which axesthe principle of inertia is applicable, --or better still, as M. Painlevé has shown, they alone allow us to render obedience to theprinciple of causality. 

But if it were so, we might apparently hope, by experiments inelectromagnetism, to obtain absolute motion, and to place in evidencethe translation of the earth relatively to the ether. But all theresearches attempted by the most ingenious physicists towards this endhave always failed, and this tends towards the idea held by manygeometricians that these negative results are not due to imperfectionsin the experiments, but have a deep and general cause. Now Lorentz hasendeavoured to find the conditions in which the electromagnetic theoryproposed by him might agree with the postulate of the completeimpossibility of determining absolute motion. It is necessary, inorder to realise this concord, to imagine that a mobile systemcontracts very slightly in the direction of its translation to adegree proportioned to the square of the ratio of the velocity oftransport to that of light. The electrons themselves do not escapethis contraction, although the observer, since he participates in thesame motion, naturally cannot notice it. Lorentz supposes, besides, that all forces, whatever their origin, are affected by a translationin the same way as electromagnetic forces. M. Langevin and M. H. Poincaré have studied this same question and have noted with precisionvarious delicate consequences of it. The singularity of the hypotheseswhich we are thus led to construct in no way constitutes an argumentagainst 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 formulatedwith much frankness by Professor Lorentz himself. It is one of thepillars of his theory that only the negative electrons move when anelectric current passes through a metal, and that the positiveelectrons (if any such there be) remain motionless. Yet in theexperiment known as Hall's, the current is deflected by the magneticfield to one side of the strip in certain metals, and to the oppositeside in others. This seems to show that in certain cases the positiveelectrons move instead of the negative, and Professor Lorentzconfesses that up to the present he can find no valid argument againstthis. See _Archives Néerlandaises_ 1906, parts 1 and 2. --ED. ]

§ 3. THE MASS OF ELECTRONS

Other conceptions, bolder still, are suggested by the results ofcertain interesting experiments. The electron affords us thepossibility of considering inertia and mass to be no longer afundamental notion, but a consequence of the electromagneticphenomena. 

Professor J. J. Thomson was the first to have the clear idea that apart, at least, of the inertia of an electrified body is due to itselectric charge. This idea was taken up and precisely stated byProfessor Max Abraham, who, for the first time, was led to regardseriously the seemingly paradoxical notion of mass as a function ofvelocity. 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, andit therefore creates a magnetic field the intensity of which islikewise proportional to its velocity: to set it in motion, therefore, there must be communicated to it over and above the expenditurecorresponding to the acquisition of its ordinary kinetic energy, aquantity of energy proportional to the square of its velocity. Everything, therefore, takes place as if, by the fact ofelectrification, its capacity for kinetic energy and its material masshad been increased by a certain constant quantity. To the ordinarymass may be added, if you will, an electromagnetic mass. 

This is the state of things so long as the speed of the translation ofthe particle is not very great, but they are no longer quite the samewhen this particle is animated with a movement whose rapidity becomescomparable to that with which light is propagated. 

The magnetic field created is then no longer a field in repose, butits energy depends, in a complicated manner, on the velocity, and theapparent increase in the mass of the particle itself becomes afunction of the velocity. More than this, this increase may not be thesame for the same velocity, but varies according to whether theacceleration is parallel with or perpendicular to the direction ofthis velocity. In other words, there seems to be a longitudinal; and atransversal mass which need not be the same. 

All these results would persist even if the material mass were verysmall relatively to the electromagnetic mass; and the electronpossesses some inertia even if its ordinary mass becomes slighter andslighter. The apparent mass, it can be easily shown, increasesindefinitely when the velocity with which the electrified particle isanimated tends towards the velocity of light, and thus the worknecessary to communicate such a velocity to an electron would beinfinite. It is in consequence impossible that the speed of anelectron, in relation to the ether, can ever exceed, or evenpermanently attain to, 300, 000 kilometres per second. 

All the facts thus predicted by the theory are confirmed byexperiment. There is no known process which permits the directmeasurement of the mass of an electron, but it is possible, as we haveseen, to measure simultaneously its velocity and the relation of theelectric charge to its mass. In the case of the cathode rays emittedby radium, these measurements are particularly interesting, for thereason that the rays which compose a pencil of cathode rays areanimated by very different speeds, as is shown by the size of thestain produced on a photographic plate by a pencil of them at firstvery constricted and subsequently dispersed by the action of anelectric or magnetic field. Professor Kaufmann has effected some verycareful experiments by a method he terms the method of crossedspectra, which consists in superposing the deviations produced by amagnetic and an electric field respectively acting in directions atright angles one to another. He has thus been enabled by working _invacuo_ to register the very different velocities which, starting inthe case of certain rays from about seven-tenths of the velocity oflight, attain in other cases to ninety-five hundredths of it. 

It is thus noted that the ratio of charge to mass--which for ordinaryspeeds is constant and equal to that already found by so manyexperiments--diminishes slowly at first, and then very rapidly whenthe velocity of the ray increases and approaches that of light. If werepresent this variation by a curve, the shape of this curve inclinesus to think that the ratio tends toward zero when the velocity tendstowards that of light. 

All the earlier experiments have led us to consider that the electriccharge was the same for all electrons, and it can hardly be conceivedthat this charge can vary with the velocity. For in order that therelation, of which one of the terms remains fixed, should vary, theother term necessarily cannot remain constant. The experiments ofProfessor Kaufmann, therefore, confirm the previsions of Max Abraham'stheory: the mass depends on the velocity, and increases indefinitelyin proportion as this velocity approaches that of light. Theseexperiments, moreover, allow the numerical results of the calculationto be compared with the values measured. This very satisfactorycomparison shows that the apparent total mass is sensibly equal to theelectromagnetic mass; the material mass of the electron is thereforenil, and the whole of its mass is electromagnetic. 

Thus the electron must be looked upon as a simple electric chargedevoid of matter. Previous examination has led us to attribute to it amass a thousand times less that that of the atom of hydrogen, and amore attentive study shows that this mass was fictitious. Theelectromagnetic phenomena which are produced when the electron is setin motion or a change effected in its velocity, simply have theeffect, as it were, of simulating inertia, and it is the inertia dueto the charge which has caused us to be thus deluded. 

The electron is therefore simply a small volume determined at a pointin the ether, and possessing special properties;[49] this point ispropagated with a velocity which cannot exceed that of light. Whenthis velocity is constant, the electron creates around it in itspassage an electric and a magnetic field; round this electrifiedcentre there exists a kind of wake, which follows it through the etherand does not become modified so long as the velocity remainsinvariable. If other electrons follow the first within a wire, theirpassage 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 waveis produced, and an electromagnetic radiation is generated, of whichthe character may naturally change with the manner in which the speedvaries. If the electron has a sufficiently rapid periodical movement, this wave is a light wave; while if the electron stops suddenly, akind of pulsation is transmitted through the ether, and thus we obtainRöntgen rays. 

§ 4. NEW VIEWS ON THE CONSTITUTION OF THE ETHER AND OF MATTER

New and valuable information is thus afforded us regarding theproperties of the ether, but will this enable us to construct amaterial representation of this medium which fills the universe, andso to solve a problem which has baffled, as we have seen, theprolonged efforts of our predecessors?

Certain scholars seem to have cherished this hope. Dr. Larmor inparticular, as we have seen, has proposed a most ingenious image, butone which is manifestly insufficient. The present tendency ofphysicists rather tends to the opposite view; since they considermatter as a very complex object, regarding which we wrongly imagineourselves to be well informed because we are so much accustomed to it, and its singular properties end by seeming natural to us. But in allprobability 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 bymaterial properties, and it is useless labour, condemned beforehand tosterility, to endeavour to determine it by other qualities than thoseof which experiment gives us direct and exact knowledge. 

The ether is defined when we know, in all its points, and in magnitudeand in direction, the two fields, electric and magnetic, which mayexist in it. These two fields may vary; we speak from habit of amovement propagated in the ether, but the phenomenon within the reachof experiment is the propagation of these variations. 

Since the electrons, considered as a modification of the ethersymmetrically distributed round a point, perfectly counterfeit thatinertia which is the fundamental property of matter, it becomes verytempting to suppose that matter itself is composed of a more or lesscomplex assemblage of electrified centres in motion. 

This complexity is, in general, very great, as is demonstrated by theexamination of the luminous spectra produced by the atoms, and it isprecisely because of the compensations produced between the differentmovements that the essential properties of matter--the law of theconservation of inertia, for example--are not contrary to thehypothesis. 

The forces of cohesion thus would be due to the mutual attractionswhich occur in the electric and magnetic fields produced in theinterior of bodies; and it is even conceivable that there may beproduced, under the influence of these actions, a tendency todetermine orientation, that is to say, that a reason can be seen whymatter may be crystallised. [50]

[Footnote 50: The reader should, however, be warned that a theory haslately been put forth which attempts to account for crystallisation onpurely mechanical grounds. See Messrs Barlow and Pope's "Developmentof 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 theatom as being constituted by a positively charged centre havingpractically the same magnitude as the atom itself, round which theelectrons gravitate; and it might evidently be supposed that thispositive centre itself preserves the fundamental characteristics ofmatter, and that it is the electrons alone which no longer possess anybut electromagnetic mass. 

We have but little information concerning these positive particles, though they are met with in an isolated condition, as we have seen, inthe canal rays or in the X rays. [51] It has not hitherto been possibleto study them so successfully as the electrons themselves; but thattheir magnitude causes them to produce considerable perturbations inthe bodies on which they fall is manifest by the secondary emissionswhich complicate and mask the primitive phenomenon. There are, however, strong reasons for thinking that these positive centres arenot simple. Thus Professor Stark attributes to them, with experimentsin proof of his opinion, the emission of the spectra of the rays inGeissler tubes, and the complexity of the spectrum discloses thecomplexity of the centre. Besides, certain peculiarities in theconductivity of metals cannot be explained without a supposition ofthis kind. So that the atom, deprived of the cathode corpuscle, wouldbe still liable to decomposition into elements analogous to electronsand positively charged. Consequently nothing prevents us supposingthat this centre likewise simulates inertia by its electromagneticproperties, and is but a condition localised in the ether. 

[Footnote 51: There is much reason for thinking that the canal rays donot contain positive particles alone, but are accompanied by negativeelectrons of slow velocity. The X rays are thought, as has been saidabove, to contain neither negative nor positive particles, but to bemerely pulses in the ether. --ED. ]

However this may be, the edifice thus constructed, being composed ofelectrons in periodical motion, necessarily grows old. The electronsbecome subject to accelerations which produce a radiation towards theexterior of the atom; and certain of them may leave the body, whilethe primitive stability is, in the end, no longer assured, and a newarrangement tends to be formed. Matter thus seems to us to undergothose transformations of which the radio-active bodies have given ussuch remarkable examples. 

We have already had, in fragments, these views on the constitution ofmatter; a deeper study of the electron thus enables us to take up aposition from which we obtain a sharp, clear, and comprehensive graspof the whole and a glimpse of indefinite horizons. 

It would be advantageous, however, in order to strengthen thisposition, that a few objections which still menace it should beremoved. The instability of the electron is not yet sufficientlydemonstrated. 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 explainsattraction by supposing that two charges of similar sign repel eachother in a slightly less degree than that in which two charges, equalbut of contrary sign, attract each other, the difference being, however, according to the calculation, much too small to be directlyobserved. He has also sought to explain gravitation by connecting itwith the pressures which may be produced on bodies by the vibratorymovements which form very penetrating rays. Recently M. Sutherland hasimagined that attraction is due to the difference of action in theconvection currents produced by the positive and negative corpuscleswhich constitute the atoms of the stars, and are carried along by theastronomical motions. But these hypotheses remain rather vague, andmany authors think, like M. Langevin, that gravitation must resultfrom some mode of activity of the ether totally different from theelectromagnetic mode. 

CHAPTER XI

THE FUTURE OF PHYSICS

It would doubtless be exceedingly rash, and certainly verypresumptuous, to seek to predict the future which may be reserved forphysics. The rôle of prophet is not a scientific one, and the mostfirmly established previsions of to-day may be overthrown by thereality of to-morrow. 

Nevertheless, the physicist does not shun an extrapolation of somelittle scope when it is not too far from the realms of experiment; theknowledge of the evolution accomplished of late years authorises a fewsuppositions as to the direction in which progress may continue. 

The reader who has deigned to follow me in the rapid excursion we havejust made through the domain of the science of Nature, will doubtlessbring back with him from his short journey the general impression thatthe ancient limits to which the classic treatises still delight inrestricting the divers chapters of physics, are trampled down in alldirections. 

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 thefield of physics. It is not only because they cover regions as yetlittle explored where discoveries are more abundant and more easy, that these cross-cuts are so frequent, but also because a higher hopeguides the seekers who engage in these new routes. 

In spite of the repeated failures which have followed the numerousattempts of past times, the idea has not been abandoned of one dayconquering the supreme principle which must command the whole ofphysics. 

Some physicists, no doubt, think such a synthesis to be impossible ofrealisation, and that Nature is infinitely complex; but, notwithstanding all the reserves they may make, from the philosophicalpoint of view, as to the legitimacy of the process, they do nothesitate to construct general hypotheses which, in default of completemental satisfaction, at least furnish them with a highly convenientmeans of grouping an immense number of facts till then scatteredabroad. 

Their error, if error there be, is beneficial, for it is one of thosethat Kant would have classed among the fruitful illusions whichengender the indefinite progress of science and lead to great andimportant co-ordinations. 

It is, naturally, by the study of the relations existing betweenphenomena apparently of very different orders that there can be anyhope of reaching the goal; and it is this which justifies the peculiarinterest accorded to researches effected in the debatable land betweendomains hitherto considered as separate. 

Among all the theories lately proposed, that of the ions has taken apreponderant place; ill understood at first by some, appearingsomewhat singular, and in any case useless, to others, it met at itsinception, in France at least, with only very moderate favour. 

To-day things have greatly changed, and those even who ignored it havebeen seduced by the curious way in which it adapts itself to theinterpretation of the most recent experiments on very differentsubjects. A very natural reaction has set in; and I might almost saythat a question of fashion has led to some exaggerations. 

The electron has conquered physics, and many adore the new idol ratherblindly. Certainly we can only bow before an hypothesis which enablesus to group in the same synthesis all the discoveries on electricdischarges and on radioactive substances, and which leads to asatisfactory theory of optics and of electricity; while by theintermediary of radiating heat it seems likely to embrace shortly theprinciples of thermodynamics also. Certainly one must admire the powerof a creed which penetrates also into the domain of mechanics andfurnishes a simple representation of the essential properties ofmatter; but it is right not to lose sight of the fact that an imagemay be a well-founded appearance, but may not be capable of beingexactly superposed on the objective reality. 

The conception of the atom of electricity, the foundation of thematerial atoms, evidently enables us to penetrate further intoNature's secrets than our predecessors; but we must not be satisfiedwith words, and the mystery is not solved when, by a legitimateartifice, the difficulty has simply been thrust further back. We havetransferred to an element ever smaller and smaller those physicalqualities which in antiquity were attributed to the whole of asubstance; and then we shifted them later to those chemical atomswhich, united together, constitute this whole. To-day we pass them onto the electrons which compose these atoms. The indivisible is thusrendered, in a way, smaller and smaller, but we are still unacquaintedwith what its substance may be. The notion of an electric charge whichwe substitute for that of a material mass will permit phenomena to beunited which we thought separate, but it cannot be considered adefinite explanation, or as the term at which science must stop. It isprobable, however, that for a few years still physics will not travelbeyond it. The present hypothesis suffices for grouping known facts, and it will doubtless enable many more to be foreseen, while newsuccesses will further increase its possessions. 

Then the day will arrive when, like all those which have shone beforeit, this seductive hypothesis will lead to more errors thandiscoveries. It will, however, have been improved, and it will havebecome a very vast and very complete edifice which some will notwillingly abandon; for those who have made to themselves a comfortabledwelling-place on the ruins of ancient monuments are often too loth toleave it. 

In that day the searchers who were in the van of the march after truthwill be caught up and even passed by others who will have followed alonger, but perhaps surer road. We also have seen at work thoseprudent physicists who dreaded too daring creeds, and who sought onlyto collect all the documentary evidence possible, or only took fortheir guide a few principles which were to them a simplegeneralisation of facts established by experiments; and we have beenable to prove that they also were effecting good and highly usefulwork. 

Neither the former nor the latter, however, carry out their work in anisolated way, and it should be noted that most of the remarkableresults of these last years are due to physicists who have known howto combine their efforts and to direct their activity towards a commonobject, while perhaps it may not be useless to observe also thatprogress has been in proportion to the material resources of ourlaboratories. 

It is probable that in the future, as in the past, the greatestdiscoveries, those which will suddenly reveal totally unknown regions, and open up entirely new horizons, will be made by a few scholars ofgenius who will carry on their patient labour in solitary meditation, and who, in order to verify their boldest conceptions, will no doubtcontent themselves with the most simple and least costly experimentalapparatus. Yet for their discoveries to yield their full harvest, forthe 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 necessaryfor these last to have at their disposal the most delicate as well asthe most powerful instruments. These are conditions paramount at thepresent 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 workersare trammelled, their unity disturbed, and if material facilities aretoo parsimoniously afforded them, --evolution, at present so rapid, maybe retarded, and those retrogressions which, by-the-by, have beenknown in all evolutions, may occur, although even then hope in thefuture would not be abolished for ever. 

There are no limits to progress, and the field of our investigationshas no boundaries. Evolution will continue with invincible force. Whatwe to-day call the unknowable, will retreat further and further beforescience, which will never stay her onward march. Thus physics willgive greater and increasing satisfaction to the mind by furnishing newinterpretations of phenomena; but it will accomplish, for the whole ofsociety, more valuable work still, by rendering, by the improvementsit suggests, life every day more easy and more agreeable, and byproviding mankind with weapons against the hostile forces of Nature.