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diff --git a/15207-8.txt b/15207-8.txt new file mode 100644 index 0000000..5c54064 --- /dev/null +++ b/15207-8.txt @@ -0,0 +1,8834 @@ +The Project Gutenberg eBook, The New Physics and Its Evolution, by Lucien +Poincare + + +This eBook is for the use of anyone anywhere at no cost and with +almost no restrictions whatsoever. You may copy it, give it away or +re-use it under the terms of the Project Gutenberg License included +with this eBook or online at www.gutenberg.org + + + + + +Title: The New Physics and Its Evolution + +Author: Lucien Poincare + +Release Date: February 28, 2005 [eBook #15207] + +Language: En + +Character set encoding: ISO-8859-1 + + +***START OF THE PROJECT GUTENBERG EBOOK THE NEW PHYSICS AND ITS +EVOLUTION*** + + +E-text prepared by Jeff Spirko, Juliet Sutherland, Jim Land, and the +Project Gutenberg Online Distributed Proofreading Team + + + +The International Scientific Series + +THE NEW PHYSICS AND ITS EVOLUTION + +by + +LUCIEN POINCARÉ +Inspéctéur-General de l'Instruction Publique + +Being the Authorized Translation of _LA PHYSIQUE MODERNE, SON ÉVOLUTION_ + +New York +D. Appleton and Company + +1909 + + + + + + + +Prefatory Note + +M. Lucien Poincaré is one of the distinguished family of +mathematicians which has during the last few years given a +Minister of Finance to the Republic and a President to the +Académie des Sciences. He is also one of the nineteen +Inspectors-General of Public Instruction who are charged with the +duty of visiting the different universities and _lycées_ in +France and of reporting upon the state of the studies there +pursued. Hence he is in an excellent position to appreciate at +its proper value the extraordinary change which has lately +revolutionized physical science, while his official position has +kept him aloof from the controversies aroused by the discovery of +radium and by recent speculations on the constitution of matter. + +M. Poincaré's object and method in writing the book are +sufficiently explained in the preface which follows; but it may +be remarked that the best of methods has its defects, and the +excessive condensation which has alone made it possible to +include the last decade's discoveries in physical science within +a compass of some 300 pages has, perhaps, made the facts here +noted assimilable with difficulty by the untrained reader. To +remedy this as far as possible, I have prefixed to the present +translation a table of contents so extended as to form a fairly +complete digest of the book, while full indexes of authors and +subjects have also been added. The few notes necessary either for +better elucidation of the terms employed, or for giving account +of discoveries made while these pages were passing through the +press, may be distinguished from the author's own by the +signature "ED." + +THE EDITOR. + +ROYAL INSTITUTION OF GREAT BRITAIN, +April 1907. + + + + +Author's Preface + +During the last ten years so many works have accumulated in the +domain of Physics, and so many new theories have been propounded, +that those who follow with interest the progress of science, and +even some professed scholars, absorbed as they are in their own +special studies, find themselves at sea in a confusion more +apparent than real. + +It has therefore occurred to me that it might be useful to write +a book which, while avoiding too great insistence on purely +technical details, should try to make known the general results +at which physicists have lately arrived, and to indicate the +direction and import which should be ascribed to those +speculations on the constitution of matter, and the discussions +on the nature of first principles, to which it has become, so to +speak, the fashion of the present day to devote oneself. + +I have endeavoured throughout to rely only on the experiments in +which we can place the most confidence, and, above all, to show +how the ideas prevailing at the present day have been formed, by +tracing their evolution, and rapidly examining the successive +transformations which have brought them to their present +condition. + +In order to understand the text, the reader will have no need to +consult any treatise on physics, for I have throughout given the +necessary definitions and set forth the fundamental facts. +Moreover, while strictly employing exact expressions, I have +avoided the use of mathematical language. Algebra is an admirable +tongue, but there are many occasions where it can only be used +with much discretion. + +Nothing would be easier than to point out many great omissions +from this little volume; but some, at all events, are not +involuntary. + +Certain questions which are still too confused have been put on +one side, as have a few others which form an important collection +for a special study to be possibly made later. Thus, as regards +electrical phenomena, the relations between electricity and +optics, as also the theories of ionization, the electronic +hypothesis, etc., have been treated at some length; but it has +not been thought necessary to dilate upon the modes of production +and utilization of the current, upon the phenomena of magnetism, +or upon all the applications which belong to the domain of +Electrotechnics. + +L. POINCARÉ. + + + + + +Contents + + +EDITOR'S PREFATORY NOTE + +AUTHOR'S PREFACE + +TABLE OF CONTENTS + + +CHAPTER I + +THE EVOLUTION OF PHYSICS + +Revolutionary change in modern Physics only apparent: +evolution not revolution the rule in Physical Theory-- +Revival of metaphysical speculation and influence of +Descartes: all phenomena reduced to matter and movement-- +Modern physicists challenge this: physical, unlike +mechanical, phenomena seldom reversible--Two schools, +one considering experimental laws imperative, the other +merely studying relations of magnitudes: both teach +something of truth--Third or eclectic school-- +Is mechanics a branch of electrical science? + + +CHAPTER II + +MEASUREMENTS + +§ 1. Metrology: Lord Kelvin's view of its necessity-- +Its definition + +§ 2. The Measure of Length: Necessity for unit-- +Absolute length--History of Standard--Description of +Standard Metre--Unit of wave-lengths preferable--The +International Metre + +§ 3. The Measure of Mass: Distinction between +mass and weight--Objections to legal kilogramme +and its precision--Possible improvement + +§ 4. The Measure of Time: Unit of time the +second--Alternative units proposed--Improvements in +chronometry and invar + +§ 5. The Measure of Temperature: Fundamental +and derived units--Ordinary unit of temperature +purely arbitrary--Absolute unit mass of H at pressure +of 1 m. of Hg at 0° C.--Divergence of thermometric +and thermodynamic scales--Helium thermometer for low, +thermo-electric couple for high, temperatures--Lummer +and Pringsheim's improvements in thermometry. + +§ 6. Derived Units and Measure of Energy: +Importance of erg as unit--Calorimeter usual means of +determination--Photometric units. + +§ 7. Measure of Physical Constants: Constant of +gravitation--Discoveries of Cavendish, Vernon Boys, +Eötvös, Richarz and Krigar-Menzel--Michelson's +improvements on Fizeau and Foucault's experiments-- +Measure of speed of light. + + +CHAPTER III + +PRINCIPLES + +§ 1. The Principles of Physics: The Principles of +Mechanics affected by recent discoveries--Is mass +indestructible?--Landolt and Heydweiller's experiments +--Lavoisier's law only approximately true--Curie's +principle of symmetry. + +§ 2. The Principle of the Conservation of Energy: +Its evolution: Bernoulli, Lavoisier and Laplace, Young, +Rumford, Davy, Sadi Carnot, and Robert Mayer--Mayer's +drawbacks--Error of those who would make mechanics part +of energetics--Verdet's predictions--Rankine inventor +of energetics--Usefulness of Work as standard form of +energy--Physicists who think matter form of energy-- +Objections to this--Philosophical value of conservation +doctrine. + +§ 3. The Principle of Carnot and Clausius: +Originality of Carnot's principle that fall of +temperature necessary for production of work by heat-- +Clausius' postulate that heat cannot pass from cold to +hot body without accessory phenomena--Entropy result +of this--Definition of entropy--Entropy tends to increase +incessantly--A magnitude which measures evolution +of system--Clausius' and Kelvin's deduction that +heat end of all energy in Universe--Objection to this-- +Carnot's principle not necessarily referable to mechanics +--Brownian movements--Lippmann's objection to +kinetic hypothesis. + +§ 4. Thermodynamics: Historical work of Massieu, +Willard Gibbs, Helmholtz, and Duhem--Willard Gibbs +founder of thermodynamic statics, Van t'Hoff its +reviver--The Phase Law--Raveau explains it without +thermodynamics. + +§ 5. Atomism: Connection of subject with preceding +Hannequin's essay on the atomic hypothesis--Molecular +physics in disfavour--Surface-tension, etc., vanishes +when molecule reached--Size of molecule--Kinetic +theory of gases--Willard Gibbs and Boltzmann introduce +into it law of probabilities--Mean free path of gaseous +molecules--Application to optics--Final division of +matter. + + +CHAPTER IV + +THE VARIOUS STATES OF MATTER + +§ 1. The Statics of Fluids: Researches of Andrews, +Cailletet, and others on liquid and gaseous states-- +Amagat's experiments--Van der Waals' equation--Discovery +of corresponding states--Amagat's superposed +diagrams--Exceptions to law--Statics of mixed fluids-- +Kamerlingh Onnes' researches--Critical Constants-- +Characteristic equation of fluid not yet ascertainable. + +§ 2. The Liquefaction of Gases and Low Temperatures: +Linde's, Siemens', and Claude's methods of liquefying +gases--Apparatus of Claude described--Dewar's +experiments--Modification of electrical properties of +matter by extreme cold: of magnetic and chemical-- +Vitality of bacteria unaltered--Ramsay's discovery +of rare gases of atmosphere--Their distribution in +nature--Liquid hydrogen--Helium. + +§ 3. Solids and Liquids: Continuity of Solid and Liquid +States--Viscosity common to both--Also Rigidity-- +Spring's analogies of solids and liquids--Crystallization +--Lehmann's liquid crystals--Their existence doubted +--Tamman's view of discontinuity between crystalline +and liquid states. + +§ 4. The Deformation of Solids: Elasticity-- +Hoocke's, Bach's, and Bouasse's researches--Voigt +on the elasticity of crystals--Elastic and permanent +deformations--Brillouin's states of unstable +equilibria--Duhem and the thermodynamic postulates-- +Experimental confirmation--Guillaume's researches +on nickel steel--Alloys. + + +CHAPTER V + +SOLUTIONS AND ELECTROLYTIC DISSOCIATION + +§ 1. Solution: Kirchhoff's, Gibb's, Duhem's and Van +t'Hoff's researches. + +§ 2. Osmosis: History of phenomenon--Traube and +biologists establish existence of semi-permeable +walls--Villard's experiments with gases--Pfeffer +shows osmotic pressure proportional to concentration-- +Disagreement as to cause of phenomenon. + +§ 3. Osmosis applied to Solution: Van t'Hoff's +discoveries--Analogy between dissolved body and +perfect gas--Faults in analogy. + +§ 4. Electrolytic Dissociation: Van t'Hoff's and +Arrhenius' researches--Ionic hypothesis of--Fierce +opposition to at first--Arrhenius' ideas now triumphant +--Advantages of Arrhenius' hypothesis--"The ions +which react"--Ostwald's conclusions from this--Nernst's +theory of Electrolysis--Electrolysis of gases makes +electronic theory probable--Faraday's two laws--Valency-- +Helmholtz's consequences from Faraday's laws. + + +CHAPTER VI + +THE ETHER + +§ 1. The Luminiferous Ether: First idea of Ether due +to Descartes--Ether must be imponderable--Fresnel shows +light vibrations to be transverse--Transverse vibrations +cannot exist in fluid--Ether must be discontinuous. + +§ 2. Radiations: Wave-lengths and their +measurements--Rubens' and Lenard's researches-- +Stationary waves and colour-photography--Fresnel's +hypothesis opposed by Neumann--Wiener's and Cotton's +experiments. + +§ 3. The Electromagnetic Ether: Ampère's advocacy +of mathematical expression--Faraday first shows +influence of medium in electricity--Maxwell's proof +that light-waves electromagnetic--His +unintelligibility--Required confirmation of theory by Hertz. + +§ 4. Electrical Oscillations: Hertz's experiments-- +Blondlot proves electromagnetic disturbance propagated +with speed of light--Discovery of ether waves +intermediate between Hertzian and visible ones--Rubens' +and Nichols' experiments--Hertzian and light rays +contrasted--Pressure of light. + +§ 5. The X-Rays: Röntgen's discovery--Properties +of X-rays--Not homogeneous--Rutherford and M'Clung's +experiments on energy corresponding to--Barkla's +experiments on polarisation of--Their speed that of +light--Are they merely ultra-violet?--Stokes and +Wiechert's theory of independent pulsations generally +preferred--J.J. Thomson's idea of their formation-- +Sutherland's and Le Bon's theories--The N-Rays-- +Blondlot's discovery--Experiments cannot be repeated +outside France--Gutton and Mascart's confirmation-- +Negative experiments prove nothing--Supposed +wave-length of N-rays. + +§ 6. The Ether and Gravitation: Descartes' +and Newton's ideas on gravitation--Its speed and +other extraordinary characteristics--Lesage's +hypothesis--Crémieux' experiments with drops of +liquids--Hypothesis of ether insufficient. + + +CHAPTER VII + +WIRELESS TELEGRAPHY + +§ 1. Histories of wireless telegraphy already written, +and difficulties of the subject. + +§ 2. Two systems: that which uses the material media (earth, +air, or water), and that which employs ether only. + +§ 3. Use of earth as return wire by Steinheil +--Morse's experiments with water of canal--Seine used as +return wire during siege of Paris--Johnson and Melhuish's +Indian experiments--Preece's telegraph over Bristol +Channel--He welcomes Marconi. + +§ 4. Early attempts at transmission of messages through +ether--Experiments of Rathenau and others. + +§ 5. Forerunners of ether telegraphy: Clerk Maxwell +and Hertz--Dolbear, Hughes, and Graham Bell. + +§ 6. Telegraphy by Hertzian waves first suggested +by Threlfall--Crookes', Tesla's, Lodge's, +Rutherford's, and Popoff's contributions--Marconi +first makes it practicable. + +§ 7. The receiver in wireless telegraphy--Varley's, +Calzecchi--Onesti's, and Branly's researches-- +Explanation of coherer still obscure. + +§ 8. Wireless telegraphy enters the commercial stage-- +Defect of Marconi's system--Braun's, Armstrong's, Lee de +Forest's, and Fessenden's systems make use of earth-- +Hertz and Marconi entitled to foremost place among +discoverers. + + +CHAPTER VIII + +THE CONDUCTIVITY OF GASES AND THE IONS + +§ 1. The Conductivity of Gases: Relations of matter to +ether cardinal problem--Conductivity of gases at first +misapprehended--Erman's forgotten researches--Giese +first notices phenomenon--Experiment with X-rays-- +J.J. Thomson's interpretation--Ionized gas not obedient +to Ohm's law--Discharge of charged conductors by +ionized gas. + +§ 2. The Condensation of water-vapour by Ions: +Vapour will not condense without nucleus--Wilson's +experiments on electrical condensation--Wilson and +Thomson's counting experiment--Twenty million ions +per c.cm. of gas--Estimate of charge borne by ion-- +Speed of charges--Zeleny's and Langevin's +experiments--Negative ions 1/1000 of size of +atoms--Natural unit of electricity or electrons. + +§ 3. How Ions are Produced: Various causes +of ionization--Moreau's experiments with alkaline +salts--Barus and Bloch on ionization by phosphorus +vapours--Ionization always result of shock. + +§ 4. Electrons in Metals: Movement of +electrons in metals foreshadowed by Weber--Giese's, +Riecke's, Drude's, and J.J. Thomson's researches--Path +of ions in metals and conduction of heat--Theory of +Lorentz--Hesehus' explanation of electrification by +contact--Emission of electrons by charged body-- +Thomson's measurement of positive ions. + + +CHAPTER IX + +CATHODE RAYS AND RADIOACTIVE BODIES + +§ 1. The Cathode Rays: History of discovery--Crookes' +theory--Lenard rays--Perrin's proof of negative +charge--Cathode rays give rise to X-rays--The canal +rays--Villard's researches and magneto-cathode rays-- +Ionoplasty--Thomson's measurements of speed of rays-- +All atoms can be dissociated. + +§ 2. Radioactive Substances: Uranic rays of Niepce +de St Victor and Becquerel--General radioactivity of +matter--Le Bon's and Rutherford's comparison of uranic +with X rays--Pierre and Mme. Curie's discovery of +polonium and radium--Their characteristics--Debierne +discovers actinium. + +§ 3. Radiations and Emanations of Radioactive +Bodies: Giesel's, Becquerel's, and Rutherford's +Researches--Alpha, beta, and gamma rays--Sagnac's +secondary rays--Crookes' spinthariscope--The emanation +--Ramsay and Soddy's researches upon it--Transformations +of radioactive bodies--Their order. + +§ 4. Disaggregation of Matter and Atomic Energy: +Actual transformations of matter in radioactive bodies +--Helium or lead final product--Ultimate disappearance +of radium from earth--Energy liberated by radium: +its amount and source--Suggested models of radioactive +atoms--Generalization from radioactive phenomena +-Le Bon's theories--Ballistic hypothesis generally +admitted--Does energy come from without--Sagnac's +experiments--Elster and Geitel's _contra_. + + +CHAPTER X + +THE ETHER AND MATTER + +§ 1. The Relations between the Ether and Matter: +Attempts to reduce all matter to forms of ether--Emission +and absorption phenomena show reciprocal action-- +Laws of radiation--Radiation of gases--Production of +spectrum--Differences between light and sound variations +show difference of media--Cauchy's, Briot's, Carvallo's +and Boussinesq's researches--Helmholtz's and +Poincaré's electromagnetic theories of dispersion. + +§ 2. The Theory of Lorentz:--Mechanics fails +to explain relations between ether and matter--Lorentz +predicts action of magnet on spectrum--Zeeman's experiment +--Later researches upon Zeeman effect-- +Multiplicity of electrons--Lorentz's explanation of +thermoelectric phenomena by electrons--Maxwell's and +Lorentz's theories do not agree--Lorentz's probably more +correct--Earth's movement in relation to ether. + +§ 3. The Mass of Electrons: Thomson's and +Max Abraham's view that inertia of charged body due +to charge--Longitudinal and transversal mass--Speed +of electrons cannot exceed that of light--Ratio of +charge to mass and its variation--Electron simple +electric charge--Phenomena produced by its acceleration. + +§ 4. New Views on Ether and Matter: +Insufficiency of Larmor's view--Ether definable +by electric and magnetic fields--Is matter all electrons? +Atom probably positive centre surrounded by +negative electrons--Ignorance concerning positive +particles--Successive transformations of matter probable +--Gravitation still unaccounted for. + + +CHAPTER XI + +THE FUTURE OF PHYSICS + +Persistence of ambition to discover supreme principle +in physics--Supremacy of electron theory at present +time--Doubtless destined to disappear like others-- +Constant progress of science predicted--Immense field +open before it. + +INDEX OF NAMES + +INDEX OF SUBJECTS + + + + +CHAPTER I + +THE EVOLUTION OF PHYSICS + + +The now numerous public which tries with some success to keep abreast +of the movement in science, from seeing its mental habits every day +upset, and from occasionally witnessing unexpected discoveries that +produce a more lively sensation from their reaction on social life, is +led to suppose that we live in a really exceptional epoch, scored by +profound crises and illustrated by extraordinary discoveries, whose +singularity surpasses everything known in the past. Thus we often hear +it said that physics, in particular, has of late years undergone a +veritable revolution; that all its principles have been made new, that +all the edifices constructed by our fathers have been overthrown, and +that on the field thus cleared has sprung up the most abundant harvest +that has ever enriched the domain of science. + +It is in fact true that the crop becomes richer and more fruitful, +thanks to the development of our laboratories, and that the quantity +of seekers has considerably increased in all countries, while their +quality has not diminished. We should be sustaining an absolute +paradox, and at the same time committing a crying injustice, were we +to contest the high importance of recent progress, and to seek to +diminish the glory of contemporary physicists. Yet it may be as well +not to give way to exaggerations, however pardonable, and to guard +against facile illusions. On closer examination it will be seen that +our predecessors might at several periods in history have conceived, +as legitimately as ourselves, similar sentiments of scientific pride, +and have felt that the world was about to appear to them transformed +and under an aspect until then absolutely unknown. + +Let us take an example which is salient enough; for, however arbitrary +the conventional division of time may appear to a physicist's eyes, it +is natural, when instituting a comparison between two epochs, to +choose those which extend over a space of half a score of years, and +are separated from each other by the gap of a century. Let us, then, +go back a hundred years and examine what would have been the state of +mind of an erudite amateur who had read and understood the chief +publications on physical research between 1800 and 1810. + +Let us suppose that this intelligent and attentive spectator witnessed +in 1800 the discovery of the galvanic battery by Volta. He might from +that moment have felt a presentiment that a prodigious transformation +was about to occur in our mode of regarding electrical phenomena. +Brought up in the ideas of Coulomb and Franklin, he might till then +have imagined that electricity had unveiled nearly all its mysteries, +when an entirely original apparatus suddenly gave birth to +applications of the highest interest, and excited the blossoming of +theories of immense philosophical extent. + +In the treatises on physics published a little later, we find traces +of the astonishment produced by this sudden revelation of a new world. +"Electricity," wrote the Abbé Haüy, "enriched by the labour of so many +distinguished physicists, seemed to have reached the term when a +science has no further important steps before it, and only leaves to +those who cultivate it the hope of confirming the discoveries of their +predecessors, and of casting a brighter light on the truths revealed. +One would have thought that all researches for diversifying the +results of experiment were exhausted, and that theory itself could +only be augmented by the addition of a greater degree of precision to +the applications of principles already known. While science thus +appeared to be making for repose, the phenomena of the convulsive +movements observed by Galvani in the muscles of a frog when connected +by metal were brought to the attention and astonishment of +physicists.... Volta, in that Italy which had been the cradle of the +new knowledge, discovered the principle of its true theory in a fact +which reduces the explanation of all the phenomena in question to the +simple contact of two substances of different nature. This fact became +in his hands the germ of the admirable apparatus to which its manner +of being and its fecundity assign one of the chief places among those +with which the genius of mankind has enriched physics." + +Shortly afterwards, our amateur would learn that Carlisle and +Nicholson had decomposed water by the aid of a battery; then, that +Davy, in 1803, had produced, by the help of the same battery, a quite +unexpected phenomenon, and had succeeded in preparing metals endowed +with marvellous properties, beginning with substances of an earthy +appearance which had been known for a long time, but whose real nature +had not been discovered. + +In another order of ideas, surprises as prodigious would wait for our +amateur. Commencing with 1802, he might have read the admirable series +of memoirs which Young then published, and might thereby have learned +how the study of the phenomena of diffraction led to the belief that +the undulation theory, which, since the works of Newton seemed +irretrievably condemned, was, on the contrary, beginning quite a new +life. A little later--in 1808--he might have witnessed the discovery +made by Malus of polarization by reflexion, and would have been able +to note, no doubt with stupefaction, that under certain conditions a +ray of light loses the property of being reflected. + +He might also have heard of one Rumford, who was then promulgating +very singular ideas on the nature of heat, who thought that the then +classical notions might be false, that caloric does not exist as a +fluid, and who, in 1804, even demonstrated that heat is created by +friction. A few years later he would learn that Charles had enunciated +a capital law on the dilatation of gases; that Pierre Prevost, in +1809, was making a study, full of original ideas, on radiant heat. In +the meantime he would not have failed to read volumes iii. and iv. of +the _Mecanique celeste_ of Laplace, published in 1804 and 1805, and he +might, no doubt, have thought that before long mathematics would +enable physical science to develop with unforeseen safety. + +All these results may doubtless be compared in importance with the +present discoveries. When strange metals like potassium and sodium +were isolated by an entirely new method, the astonishment must have +been on a par with that caused in our time by the magnificent +discovery of radium. The polarization of light is a phenomenon as +undoubtedly singular as the existence of the X rays; and the upheaval +produced in natural philosophy by the theories of the disintegration +of matter and the ideas concerning electrons is probably not more +considerable than that produced in the theories of light and heat by +the works of Young and Rumford. + +If we now disentangle ourselves from contingencies, it will be +understood that in reality physical science progresses by evolution +rather than by revolution. Its march is continuous. The facts which +our theories enable us to discover, subsist and are linked together +long after these theories have disappeared. Out of the materials of +former edifices overthrown, new dwellings are constantly being +reconstructed. + +The labour of our forerunners never wholly perishes. The ideas of +yesterday prepare for those of to-morrow; they contain them, so to +speak, _in potentia_. Science is in some sort a living organism, which +gives birth to an indefinite series of new beings taking the places of +the old, and which evolves according to the nature of its environment, +adapting itself to external conditions, and healing at every step the +wounds which contact with reality may have occasioned. + +Sometimes this evolution is rapid, sometimes it is slow enough; but it +obeys the ordinary laws. The wants imposed by its surroundings create +certain organs in science. The problems set to physicists by the +engineer who wishes to facilitate transport or to produce better +illumination, or by the doctor who seeks to know how such and such a +remedy acts, or, again, by the physiologist desirous of understanding +the mechanism of the gaseous and liquid exchanges between the cell and +the outer medium, cause new chapters in physics to appear, and suggest +researches adapted to the necessities of actual life. + +The evolution of the different parts of physics does not, however, +take place with equal speed, because the circumstances in which they +are placed are not equally favourable. Sometimes a whole series of +questions will appear forgotten, and will live only with a languishing +existence; and then some accidental circumstance suddenly brings them +new life, and they become the object of manifold labours, engross +public attention, and invade nearly the whole domain of science. + +We have in our own day witnessed such a spectacle. The discovery of +the X rays--a discovery which physicists no doubt consider as the +logical outcome of researches long pursued by a few scholars working +in silence and obscurity on an otherwise much neglected subject-- +seemed to the public eye to have inaugurated a new era in the history +of physics. If, as is the case, however, the extraordinary scientific +movement provoked by Röntgen's sensational experiments has a very +remote origin, it has, at least, been singularly quickened by the +favourable conditions created by the interest aroused in its +astonishing applications to radiography. + +A lucky chance has thus hastened an evolution already taking place, +and theories previously outlined have received a singular development. +Without wishing to yield too much to what may be considered a whim of +fashion, we cannot, if we are to note in this book the stage actually +reached in the continuous march of physics, refrain from giving a +clearly preponderant place to the questions suggested by the study of +the new radiations. At the present time it is these questions which +move us the most; they have shown us unknown horizons, and towards the +fields recently opened to scientific activity the daily increasing +crowd of searchers rushes in rather disorderly fashion. + +One of the most interesting consequences of the recent discoveries has +been to rehabilitate in the eyes of scholars, speculations relating to +the constitution of matter, and, in a more general way, metaphysical +problems. Philosophy has, of course, never been completely separated +from science; but in times past many physicists dissociated themselves +from studies which they looked upon as unreal word-squabbles, and +sometimes not unreasonably abstained from joining in discussions which +seemed to them idle and of rather puerile subtlety. They had seen the +ruin of most of the systems built up _a priori_ by daring +philosophers, and deemed it more prudent to listen to the advice given +by Kirchhoff and "to substitute the description of facts for a sham +explanation of nature." + +It should however be remarked that these physicists somewhat deceived +themselves as to the value of their caution, and that the mistrust +they manifested towards philosophical speculations did not preclude +their admitting, unknown to themselves, certain axioms which they did +not discuss, but which are, properly speaking, metaphysical +conceptions. They were unconsciously speaking a language taught them +by their predecessors, of which they made no attempt to discover the +origin. It is thus that it was readily considered evident that physics +must necessarily some day re-enter the domain of mechanics, and thence +it was postulated that everything in nature is due to movement. We, +further, accepted the principles of the classical mechanics without +discussing their legitimacy. + +This state of mind was, even of late years, that of the most +illustrious physicists. It is manifested, quite sincerely and without +the slightest reserve, in all the classical works devoted to physics. +Thus Verdet, an illustrious professor who has had the greatest and +most happy influence on the intellectual formation of a whole +generation of scholars, and whose works are even at the present day +very often consulted, wrote: "The true problem of the physicist is +always to reduce all phenomena to that which seems to us the simplest +and clearest, that is to say, to movement." In his celebrated course +of lectures at l'École Polytechnique, Jamin likewise said: "Physics +will one day form a chapter of general mechanics;" and in the preface +to his excellent course of lectures on physics, M. Violle, in 1884, +thus expresses himself: "The science of nature tends towards mechanics +by a necessary evolution, the physicist being able to establish solid +theories only on the laws of movement." The same idea is again met +with in the words of Cornu in 1896: "The general tendency should be to +show how the facts observed and the phenomena measured, though first +brought together by empirical laws, end, by the impulse of successive +progressions, in coming under the general laws of rational mechanics;" +and the same physicist showed clearly that in his mind this connexion +of phenomena with mechanics had a deep and philosophical reason, when, +in the fine discourse pronounced by him at the opening ceremony of the +Congrès de Physique in 1900, he exclaimed: "The mind of Descartes +soars over modern physics, or rather, I should say, he is their +luminary. The further we penetrate into the knowledge of natural +phenomena, the clearer and the more developed becomes the bold +Cartesian conception regarding the mechanism of the universe. There is +nothing in the physical world but matter and movement." + +If we adopt this conception, we are led to construct mechanical +representations of the material world, and to imagine movements in the +different parts of bodies capable of reproducing all the +manifestations of nature. The kinematic knowledge of these movements, +that is to say, the determination of the position, speed, and +acceleration at a given moment of all the parts of the system, or, on +the other hand, their dynamical study, enabling us to know what is the +action of these parts on each other, would then be sufficient to +enable us to foretell all that can occur in the domain of nature. + +This was the great thought clearly expressed by the Encyclopædists of +the eighteenth century; and if the necessity of interpreting the +phenomena of electricity or light led the physicists of last century +to imagine particular fluids which seemed to obey with some difficulty +the ordinary rules of mechanics, these physicists still continued to +retain their hope in the future, and to treat the idea of Descartes as +an ideal to be reached sooner or later. + +Certain scholars--particularly those of the English School--outrunning +experiment, and pushing things to extremes, took pleasure in proposing +very curious mechanical models which were often strange images of +reality. The most illustrious of them, Lord Kelvin, may be considered +as their representative type, and he has himself said: "It seems to me +that the true sense of the question, Do we or do we not understand a +particular subject in physics? is--Can we make a mechanical model +which corresponds to it? I am never satisfied so long as I have been +unable to make a mechanical model of the object. If I am able to do +so, I understand it. If I cannot make such a model, I do not +understand it." But it must be acknowledged that some of the models +thus devised have become excessively complicated, and this +complication has for a long time discouraged all but very bold minds. +In addition, when it became a question of penetrating into the +mechanism of molecules, and we were no longer satisfied to look at +matter as a mass, the mechanical solutions seemed undetermined and the +stability of the edifices thus constructed was insufficiently +demonstrated. + +Returning then to our starting-point, many contemporary physicists +wish to subject Descartes' idea to strict criticism. From the +philosophical point of view, they first enquire whether it is really +demonstrated that there exists nothing else in the knowable than +matter and movement. They ask themselves whether it is not habit and +tradition in particular which lead us to ascribe to mechanics the +origin of phenomena. Perhaps also a question of sense here comes in. +Our senses, which are, after all, the only windows open towards +external reality, give us a view of one side of the world only; +evidently we only know the universe by the relations which exist +between it and our organisms, and these organisms are peculiarly +sensitive to movement. + +Nothing, however, proves that those acquisitions which are the most +ancient in historical order ought, in the development of science, to +remain the basis of our knowledge. Nor does any theory prove that our +perceptions are an exact indication of reality. Many reasons, on the +contrary, might be invoked which tend to compel us to see in nature +phenomena which cannot be reduced to movement. + +Mechanics as ordinarily understood is the study of reversible +phenomena. If there be given to the parameter which represents +time,[1] and which has assumed increasing values during the duration +of the phenomena, decreasing values which make it go the opposite way, +the whole system will again pass through exactly the same stages as +before, and all the phenomena will unfold themselves in reversed +order. In physics, the contrary rule appears very general, and +reversibility generally does not exist. It is an ideal and limited +case, which may be sometimes approached, but can never, strictly +speaking, be met with in its entirety. No physical phenomenon ever +recommences in an identical manner if its direction be altered. It is +true that certain mathematicians warn us that a mechanics can be +devised in which reversibility would no longer be the rule, but the +bold attempts made in this direction are not wholly satisfactory. + +[Footnote 1: I.e., the time-curve.--ED.] + +On the other hand, it is established that if a mechanical explanation +of a phenomenon can be given, we can find an infinity of others which +likewise account for all the peculiarities revealed by experiment. +But, as a matter of fact, no one has ever succeeded in giving an +indisputable mechanical representation of the whole physical world. +Even were we disposed to admit the strangest solutions of the problem; +to consent, for example, to be satisfied with the hidden systems +devised by Helmholtz, whereby we ought to divide variable things into +two classes, some accessible, and the others now and for ever unknown, +we should never manage to construct an edifice to contain all the +known facts. Even the very comprehensive mechanics of a Hertz fails +where the classical mechanics has not succeeded. + +Deeming this check irremediable, many contemporary physicists give up +attempts which they look upon as condemned beforehand, and adopt, to +guide them in their researches, a method which at first sight appears +much more modest, and also much more sure. They make up their minds +not to see at once to the bottom of things; they no longer seek to +suddenly strip the last veils from nature, and to divine her supreme +secrets; but they work prudently and advance but slowly, while on the +ground thus conquered foot by foot they endeavour to establish +themselves firmly. They study the various magnitudes directly +accessible to their observation without busying themselves as to their +essence. They measure quantities of heat and of temperature, +differences of potential, currents, and magnetic fields; and then, +varying the conditions, apply the rules of experimental method, and +discover between these magnitudes mutual relations, while they thus +succeed in enunciating laws which translate and sum up their labours. + +These empirical laws, however, themselves bring about by induction the +promulgation of more general laws, which are termed principles. These +principles are originally only the results of experiments, and +experiment allows them besides to be checked, and their more or less +high degree of generality to be verified. When they have been thus +definitely established, they may serve as fresh starting-points, and, +by deduction, lead to very varied discoveries. + +The principles which govern physical science are few in number, and +their very general form gives them a philosophical appearance, while +we cannot long resist the temptation of regarding them as metaphysical +dogmas. It thus happens that the least bold physicists, those who have +wanted to show themselves the most reserved, are themselves led to +forget the experimental character of the laws they have propounded, +and to see in them imperious beings whose authority, placed above all +verification, can no longer be discussed. + +Others, on the contrary, carry prudence to the extent of timidity. +They desire to grievously limit the field of scientific investigation, +and they assign to science a too restricted domain. They content +themselves with representing phenomena by equations, and think that +they ought to submit to calculation magnitudes experimentally +determined, without asking themselves whether these calculations +retain a physical meaning. They are thus led to reconstruct a physics +in which there again appears the idea of quality, understood, of +course, not in the scholastic sense, since from this quality we can +argue with some precision by representing it under numerical symbols, +but still constituting an element of differentiation and of +heterogeneity. + +Notwithstanding the errors they may lead to if carried to excess, both +these doctrines render, as a whole, most important service. It is no +bad thing that these contradictory tendencies should subsist, for this +variety in the conception of phenomena gives to actual science a +character of intense life and of veritable youth, capable of +impassioned efforts towards the truth. Spectators who see such moving +and varied pictures passing before them, experience the feeling that +there no longer exist systems fixed in an immobility which seems that +of death. They feel that nothing is unchangeable; that ceaseless +transformations are taking place before their eyes; and that this +continuous evolution and perpetual change are the necessary conditions +of progress. + +A great number of seekers, moreover, show themselves on their own +account perfectly eclectic. They adopt, according to their needs, such +or such a manner of looking at nature, and do not hesitate to utilize +very different images when they appear to them useful and convenient. +And, without doubt, they are not wrong, since these images are only +symbols convenient for language. They allow facts to be grouped and +associated, but only present a fairly distant resemblance with the +objective reality. Hence it is not forbidden to multiply and to modify +them according to circumstances. The really essential thing is to +have, as a guide through the unknown, a map which certainly does not +claim to represent all the aspects of nature, but which, having been +drawn up according to predetermined rules, allows us to follow an +ascertained road in the eternal journey towards the truth. + +Among the provisional theories which are thus willingly constructed by +scholars on their journey, like edifices hastily run up to receive an +unforeseen harvest, some still appear very bold and very singular. +Abandoning the search after mechanical models for all electrical +phenomena, certain physicists reverse, so to speak, the conditions of +the problem, and ask themselves whether, instead of giving a +mechanical interpretation to electricity, they may not, on the +contrary, give an electrical interpretation to the phenomena of matter +and motion, and thus merge mechanics itself in electricity. One thus +sees dawning afresh the eternal hope of co-ordinating all natural +phenomena in one grandiose and imposing synthesis. Whatever may be the +fate reserved for such attempts, they deserve attention in the highest +degree; and it is desirable to examine them carefully if we wish to +have an exact idea of the tendencies of modern physics. + + + + +CHAPTER II + +MEASUREMENTS + + +§ 1. METROLOGY + +Not so very long ago, the scholar was often content with qualitative +observations. Many phenomena were studied without much trouble being +taken to obtain actual measurements. But it is now becoming more and +more understood that to establish the relations which exist between +physical magnitudes, and to represent the variations of these +magnitudes by functions which allow us to use the power of +mathematical analysis, it is most necessary to express each magnitude +by a definite number. + +Under these conditions alone can a magnitude be considered as +effectively known. "I often say," Lord Kelvin has said, "that if you +can measure that of which you are speaking and express it by a number +you know something of your subject; but if you cannot measure it nor +express it by a number, your knowledge is of a sorry kind and hardly +satisfactory. It may be the beginning of the acquaintance, but you are +hardly, in your thoughts, advanced towards science, whatever the +subject may be." + +It has now become possible to measure exactly the elements which enter +into nearly all physical phenomena, and these measurements are taken +with ever increasing precision. Every time a chapter in science +progresses, science shows itself more exacting; it perfects its means +of investigation, it demands more and more exactitude, and one of the +most striking features of modern physics is this constant care for +strictness and clearness in experimentation. + +A veritable science of measurement has thus been constituted which +extends over all parts of the domain of physics. This science has its +rules and its methods; it points out the best processes of +calculation, and teaches the method of correctly estimating errors and +taking account of them. It has perfected the processes of experiment, +co-ordinated a large number of results, and made possible the +unification of standards. It is thanks to it that the system of +measurements unanimously adopted by physicists has been formed. + +At the present day we designate more peculiarly by the name of +metrology that part of the science of measurements which devotes +itself specially to the determining of the prototypes representing the +fundamental units of dimension and mass, and of the standards of the +first order which are derived from them. If all measurable quantities, +as was long thought possible, could be reduced to the magnitudes of +mechanics, metrology would thus be occupied with the essential +elements entering into all phenomena, and might legitimately claim the +highest rank in science. But even when we suppose that some magnitudes +can never be connected with mass, length, and time, it still holds a +preponderating place, and its progress finds an echo throughout the +whole domain of the natural sciences. It is therefore well, in order +to give an account of the general progress of physics, to examine at +the outset the improvements which have been effected in these +fundamental measurements, and to see what precision these improvements +have allowed us to attain. + + +§ 2. THE MEASURE OF LENGTH + +To measure a length is to compare it with another length taken as +unity. Measurement is therefore a relative operation, and can only +enable us to know ratios. Did both the length to be measured and the +unit chosen happen to vary simultaneously and in the same degree, we +should perceive no change. Moreover, the unit being, by definition, +the term of comparison, and not being itself comparable with anything, +we have theoretically no means of ascertaining whether its length +varies. + +If, however, we were to note that, suddenly and in the same +proportions, the distance between two points on this earth had +increased, that all the planets had moved further from each other, +that all objects around us had become larger, that we ourselves had +become taller, and that the distance travelled by light in the +duration of a vibration had become greater, we should not hesitate to +think ourselves the victims of an illusion, that in reality all these +distances had remained fixed, and that all these appearances were due +to a shortening of the rule which we had used as the standard for +measuring the lengths. + +From the mathematical point of view, it may be considered that the two +hypotheses are equivalent; all has lengthened around us, or else our +standard has become less. But it is no simple question of convenience +and simplicity which leads us to reject the one supposition and to +accept the other; it is right in this case to listen to the voice of +common sense, and those physicists who have an instinctive trust in +the notion of an absolute length are perhaps not wrong. It is only by +choosing our unit from those which at all times have seemed to all men +the most invariable, that we are able in our experiments to note that +the same causes acting under identical conditions always produce the +same effects. The idea of absolute length is derived from the +principle of causality; and our choice is forced upon us by the +necessity of obeying this principle, which we cannot reject without +declaring by that very act all science to be impossible. + +Similar remarks might be made with regard to the notions of absolute +time and absolute movement. They have been put in evidence and set +forth very forcibly by a learned and profound mathematician, M. +Painlevé. + +On the particularly clear example of the measure of length, it is +interesting to follow the evolution of the methods employed, and to +run through the history of the progress in precision from the time +that we have possessed authentic documents relating to this question. +This history has been written in a masterly way by one of the +physicists who have in our days done the most by their personal +labours to add to it glorious pages. M. Benoit, the learned Director +of the International Bureau of Weights and Measures, has furnished in +various reports very complete details on the subject, from which I +here borrow the most interesting. + +We know that in France the fundamental standard for measures of length +was for a long time the _Toise du Châtelet_, a kind of callipers +formed of a bar of iron which in 1668 was embedded in the outside wall +of the Châtelet, at the foot of the staircase. This bar had at its +extremities two projections with square faces, and all the _toises_ of +commerce had to fit exactly between them. Such a standard, roughly +constructed, and exposed to all the injuries of weather and time, +offered very slight guarantees either as to the permanence or the +correctness of its copies. Nothing, perhaps, can better convey an idea +of the importance of the modifications made in the methods of +experimental physics than the easy comparison between so rudimentary a +process and the actual measurements effected at the present time. + +The _Toise du Châtelet_, notwithstanding its evident faults, was +employed for nearly a hundred years; in 1766 it was replaced by the +_Toise du Pérou_, so called because it had served for the measurements +of the terrestrial arc effected in Peru from 1735 to 1739 by Bouguer, +La Condamine, and Godin. At that time, according to the comparisons +made between this new _toise_ and the _Toise du Nord_, which had also +been used for the measurement of an arc of the meridian, an error of +the tenth part of a millimetre in measuring lengths of the order of a +metre was considered quite unimportant. At the end of the eighteenth +century, Delambre, in his work _Sur la Base du Système métrique +décimal_, clearly gives us to understand that magnitudes of the order +of the hundredth of a millimetre appear to him incapable of +observation, even in scientific researches of the highest precision. +At the present date the International Bureau of Weights and Measures +guarantees, in the determination of a standard of length compared with +the metre, an approximation of two or three ten-thousandths of a +millimetre, and even a little more under certain circumstances. + +This very remarkable progress is due to the improvements in the method +of comparison on the one hand, and in the manufacture of the standard +on the other. M. Benoit rightly points out that a kind of competition +has been set up between the standard destined to represent the unit +with its subdivisions and multiples and the instrument charged with +observing it, comparable, up to a certain point, with that which in +another order of ideas goes on between the gun and the armour-plate. + +The measuring instrument of to-day is an instrument of comparison +constructed with meticulous care, which enables us to do away with +causes of error formerly ignored, to eliminate the action of external +phenomena, and to withdraw the experiment from the influence of even +the personality of the observer. This standard is no longer, as +formerly, a flat rule, weak and fragile, but a rigid bar, incapable of +deformation, in which the material is utilised in the best conditions +of resistance. For a standard with ends has been substituted a +standard with marks, which permits much more precise definition and +can be employed in optical processes of observation alone; that is, in +processes which can produce in it no deformation and no alteration. +Moreover, the marks are traced on the plane of the neutral fibres[2] +exposed, and the invariability of their distance apart is thus +assured, even when a change is made in the way the rule is supported. + +[Footnote 2: The author seems to refer to the fact that in the +standard metre, the measurement is taken from the central one of three +marks at each end of the bar. The transverse section of the bar is an +X, and the reading is made by a microscope.--ED.] + +Thanks to studies thus systematically pursued, we have succeeded in +the course of a hundred years in increasing the precision of measures +in the proportion of a thousand to one, and we may ask ourselves +whether such an increase will continue in the future. No doubt +progress will not be stayed; but if we keep to the definition of +length by a material standard, it would seem that its precision cannot +be considerably increased. We have nearly reached the limit imposed by +the necessity of making strokes of such a thickness as to be +observable under the microscope. + +It may happen, however, that we shall be brought one of these days to +a new conception of the measure of length, and that very different +processes of determination will be thought of. If we took as unit, for +instance, the distance covered by a given radiation during a +vibration, the optical processes would at once admit of much greater +precision. + +Thus Fizeau, the first to have this idea, says: "A ray of light, with +its series of undulations of extreme tenuity but perfect regularity, +may be considered as a micrometer of the greatest perfection, and +particularly suitable for determining length." But in the present +state of things, since the legal and customary definition of the unit +remains a material standard, it is not enough to measure length in +terms of wave-lengths, and we must also know the value of these +wave-lengths in terms of the standard prototype of the metre. + +This was determined in 1894 by M. Michelson and M. Benoit in an +experiment which will remain classic. The two physicists measured a +standard length of about ten centimetres, first in terms of the +wave-lengths of the red, green, and blue radiations of cadmium, and +then in terms of the standard metre. The great difficulty of the +experiment proceeds from the vast difference which exists between the +lengths to be compared, the wave-lengths barely amounting to half a +micron;[3] the process employed consisted in noting, instead of this +length, a length easily made about a thousand times greater, namely, +the distance between the fringes of interference. + +[Footnote 3: I.e. 1/2000 of a millimetre.--ED.] + +In all measurement, that is to say in every determination of the +relation of a magnitude to the unit, there has to be determined on the +one hand the whole, and on the other the fractional part of this +ratio, and naturally the most delicate determination is generally that +of this fractional part. In optical processes the difficulty is +reversed. The fractional part is easily known, while it is the high +figure of the number representing the whole which becomes a very +serious obstacle. It is this obstacle which MM. Michelson and Benoit +overcame with admirable ingenuity. By making use of a somewhat similar +idea, M. Macé de Lépinay and MM. Perot and Fabry, have lately effected +by optical methods, measurements of the greatest precision, and no +doubt further progress may still be made. A day may perhaps come when +a material standard will be given up, and it may perhaps even be +recognised that such a standard in time changes its length by +molecular strain, and by wear and tear: and it will be further noted +that, in accordance with certain theories which will be noticed later +on, it is not invariable when its orientation is changed. + +For the moment, however, the need of any change in the definition of +the unit is in no way felt; we must, on the contrary, hope that the +use of the unit adopted by the physicists of the whole world will +spread more and more. It is right to remark that a few errors still +occur with regard to this unit, and that these errors have been +facilitated by incoherent legislation. France herself, though she was +the admirable initiator of the metrical system, has for too long +allowed a very regrettable confusion to exist; and it cannot be noted +without a certain sadness that it was not until the _11th July 1903_ +that a law was promulgated re-establishing the agreement between the +legal and the scientific definition of the metre. + +Perhaps it may not be useless to briefly indicate here the reasons of +the disagreement which had taken place. Two definitions of the metre +can be, and in fact were given. One had for its basis the dimensions +of the earth, the other the length of the material standard. In the +minds of the founders of the metrical system, the first of these was +the true definition of the unit of length, the second merely a simple +representation. It was admitted, however, that this representation had +been constructed in a manner perfect enough for it to be nearly +impossible to perceive any difference between the unit and its +representation, and for the practical identity of the two definitions +to be thus assured. The creators of the metrical system were persuaded +that the measurements of the meridian effected in their day could +never be surpassed in precision; and on the other hand, by borrowing +from nature a definite basis, they thought to take from the definition +of the unit some of its arbitrary character, and to ensure the means +of again finding the same unit if by any accident the standard became +altered. Their confidence in the value of the processes they had seen +employed was exaggerated, and their mistrust of the future +unjustified. This example shows how imprudent it is to endeavour to +fix limits to progress. It is an error to think the march of science +can be stayed; and in reality it is now known that the ten-millionth +part of the quarter of the terrestrial meridian is longer than the +metre by 0.187 millimetres. But contemporary physicists do not fall +into the same error as their forerunners, and they regard the present +result as merely provisional. They guess, in fact, that new +improvements will be effected in the art of measurement; they know +that geodesical processes, though much improved in our days, have +still much to do to attain the precision displayed in the construction +and determination of standards of the first order; and consequently +they do not propose to keep the ancient definition, which would lead +to having for unit a magnitude possessing the grave defect from a +practical point of view of being constantly variable. + +We may even consider that, looked at theoretically, its permanence +would not be assured. Nothing, in fact, proves that sensible +variations may not in time be produced in the value of an arc of the +meridian, and serious difficulties may arise regarding the probable +inequality of the various meridians. + +For all these reasons, the idea of finding a natural unit has been +gradually abandoned, and we have become resigned to accepting as a +fundamental unit an arbitrary and conventional length having a +material representation recognised by universal consent; and it was +this unit which was consecrated by the following law of the 11th July +1903:-- + +"The standard prototype of the metrical system is the international +metre, which has been sanctioned by the General Conference on Weights +and Measures." + + +§ 3. THE MEASURE OF MASS + +On the subject of measures of mass, similar remarks to those on +measures of length might be made. The confusion here was perhaps still +greater, because, to the uncertainty relating to the fixing of the +unit, was added some indecision on the very nature of the magnitude +defined. In law, as in ordinary practice, the notions of weight and of +mass were not, in fact, separated with sufficient clearness. + +They represent, however, two essentially different things. Mass is the +characteristic of a quantity of matter; it depends neither on the +geographical position one occupies nor on the altitude to which one +may rise; it remains invariable so long as nothing material is added +or taken away. Weight is the action which gravity has upon the body +under consideration; this action does not depend solely on the body, +but on the earth as well; and when it is changed from one spot to +another, the weight changes, because gravity varies with latitude and +altitude. + +These elementary notions, to-day understood even by young beginners, +appear to have been for a long time indistinctly grasped. The +distinction remained confused in many minds, because, for the most +part, masses were comparatively estimated by the intermediary of +weights. The estimations of weight made with the balance utilize the +action of the weight on the beam, but in such conditions that the +influence of the variations of gravity becomes eliminated. The two +weights which are being compared may both of them change if the +weighing is effected in different places, but they are attracted in +the same proportion. If once equal, they remain equal even when in +reality they may both have varied. + +The current law defines the kilogramme as the standard of mass, and +the law is certainly in conformity with the rather obscurely expressed +intentions of the founders of the metrical system. Their terminology +was vague, but they certainly had in view the supply of a standard for +commercial transactions, and it is quite evident that in barter what +is important to the buyer as well as to the seller is not the +attraction the earth may exercise on the goods, but the quantity that +may be supplied for a given price. Besides, the fact that the founders +abstained from indicating any specified spot in the definition of the +kilogramme, when they were perfectly acquainted with the considerable +variations in the intensity of gravity, leaves no doubt as to their +real desire. + +The same objections have been made to the definition of the +kilogramme, at first considered as the mass of a cubic decimetre of +water at 4° C., as to the first definition of the metre. We must +admire the incredible precision attained at the outset by the +physicists who made the initial determinations, but we know at the +present day that the kilogramme they constructed is slightly too heavy +(by about 1/25,000). Very remarkable researches have been carried out +with regard to this determination by the International Bureau, and by +MM. Macé de Lépinay and Buisson. The law of the 11th July 1903 has +definitely regularized the custom which physicists had adopted some +years before; and the standard of mass, the legal prototype of the +metrical system, is now the international kilogramme sanctioned by the +Conference of Weights and Measures. + +The comparison of a mass with the standard is effected with a +precision to which no other measurement can attain. Metrology vouches +for the hundredth of a milligramme in a kilogramme; that is to say, +that it estimates the hundred-millionth part of the magnitude studied. + +We may--as in the case of the lengths--ask ourselves whether this +already admirable precision can be surpassed; and progress would seem +likely to be slow, for difficulties singularly increase when we get to +such small quantities. But it is permitted to hope that the physicists +of the future will do still better than those of to-day; and perhaps +we may catch a glimpse of the time when we shall begin to observe that +the standard, which is constructed from a heavy metal, namely, +iridium-platinum, itself obeys an apparently general law, and little +by little loses some particles of its mass by emanation. + + +§ 4. THE MEASURE OF TIME + +The third fundamental magnitude of mechanics is time. There is, so to +speak, no physical phenomenon in which the notion of time linked to +the sequence of our states of consciousness does not play a +considerable part. + +Ancestral habits and a very early tradition have led us to preserve, +as the unit of time, a unit connected with the earth's movement; and +the unit to-day adopted is, as we know, the sexagesimal second of mean +time. This magnitude, thus defined by the conditions of a natural +motion which may itself be modified, does not seem to offer all the +guarantees desirable from the point of view of invariability. It is +certain that all the friction exercised on the earth--by the tides, +for instance--must slowly lengthen the duration of the day, and must +influence the movement of the earth round the sun. Such influence is +certainly very slight, but it nevertheless gives an unfortunately +arbitrary character to the unit adopted. + +We might have taken as the standard of time the duration of another +natural phenomenon, which appears to be always reproduced under +identical conditions; the duration, for instance, of a given luminous +vibration. But the experimental difficulties of evaluation with such a +unit of the times which ordinarily have to be considered, would be so +great that such a reform in practice cannot be hoped for. It should, +moreover, be remarked that the duration of a vibration may itself be +influenced by external circumstances, among which are the variations +of the magnetic field in which its source is placed. It could not, +therefore, be strictly considered as independent of the earth; and the +theoretical advantage which might be expected from this alteration +would be somewhat illusory. + +Perhaps in the future recourse may be had to very different phenomena. +Thus Curie pointed out that if the air inside a glass tube has been +rendered radioactive by a solution of radium, the tube may be sealed +up, and it will then be noted that the radiation of its walls +diminishes with time, in accordance with an exponential law. The +constant of time derived by this phenomenon remains the same whatever +the nature and dimensions of the walls of the tube or the temperature +may be, and time might thus be denned independently of all the other +units. + +We might also, as M. Lippmann has suggested in an extremely ingenious +way, decide to obtain measures of time which can be considered as +absolute because they are determined by parameters of another nature +than that of the magnitude to be measured. Such experiments are made +possible by the phenomena of gravitation. We could employ, for +instance, the pendulum by adopting, as the unit of force, the force +which renders the constant of gravitation equal to unity. The unit of +time thus defined would be independent of the unit of length, and +would depend only on the substance which would give us the unit of +mass under the unit of volume. + +It would be equally possible to utilize electrical phenomena, and one +might devise experiments perfectly easy of execution. Thus, by +charging a condenser by means of a battery, and discharging it a given +number of times in a given interval of time, so that the effect of the +current of discharge should be the same as the effect of the output of +the battery through a given resistance, we could estimate, by the +measurement of the electrical magnitudes, the duration of the interval +noted. A system of this kind must not be looked upon as a simple _jeu +d'esprit_, since this very practicable experiment would easily permit +us to check, with a precision which could be carried very far, the +constancy of an interval of time. + +From the practical point of view, chronometry has made in these last +few years very sensible progress. The errors in the movements of +chronometers are corrected in a much more systematic way than +formerly, and certain inventions have enabled important improvements +to be effected in the construction of these instruments. Thus the +curious properties which steel combined with nickel--so admirably +studied by M.Ch.Ed. Guillaume--exhibits in the matter of dilatation +are now utilized so as to almost completely annihilate the influence +of variations of temperature. + + +§ 5. THE MEASURE OF TEMPERATURE + +From the three mechanical units we derive secondary units; as, for +instance, the unit of work or mechanical energy. The kinetic theory +takes temperature, as well as heat itself, to be a quantity of energy, +and thus seems to connect this notion with the magnitudes of +mechanics. But the legitimacy of this theory cannot be admitted, and +the calorific movement should also be a phenomenon so strictly +confined in space that our most delicate means of investigation would +not enable us to perceive it. It is better, then, to continue to +regard the unit of difference of temperature as a distinct unit, to be +added to the fundamental units. + +To define the measure of a certain temperature, we take, in practice, +some arbitrary property of a body. The only necessary condition of +this property is, that it should constantly vary in the same direction +when the temperature rises, and that it should possess, at any +temperature, a well-marked value. We measure this value by melting ice +and by the vapour of boiling water under normal pressure, and the +successive hundredths of its variation, beginning with the melting +ice, defines the percentage. Thermodynamics, however, has made it +plain that we can set up a thermometric scale without relying upon any +determined property of a real body. Such a scale has an absolute value +independently of the properties of matter. Now it happens that if we +make use for the estimation of temperatures, of the phenomena of +dilatation under a constant pressure, or of the increase of pressure +in a constant volume of a gaseous body, we obtain a scale very near +the absolute, which almost coincides with it when the gas possesses +certain qualities which make it nearly what is called a perfect gas. +This most lucky coincidence has decided the choice of the convention +adopted by physicists. They define normal temperature by means of the +variations of pressure in a mass of hydrogen beginning with the +initial pressure of a metre of mercury at 0° C. + +M.P. Chappuis, in some very precise experiments conducted with much +method, has proved that at ordinary temperatures the indications of +such a thermometer are so close to the degrees of the theoretical +scale that it is almost impossible to ascertain the value of the +divergences, or even the direction that they take. The divergence +becomes, however, manifest when we work with extreme temperatures. It +results from the useful researches of M. Daniel Berthelot that we must +subtract +0.18° from the indications of the hydrogen thermometer +towards the temperature -240° C, and add +0.05° to 1000° to equate +them with the thermodynamic scale. Of course, the difference would +also become still more noticeable on getting nearer to the absolute +zero; for as hydrogen gets more and more cooled, it gradually exhibits +in a lesser degree the characteristics of a perfect gas. + +To study the lower regions which border on that kind of pole of cold +towards which are straining the efforts of the many physicists who +have of late years succeeded in getting a few degrees further forward, +we may turn to a gas still more difficult to liquefy than hydrogen. +Thus, thermometers have been made of helium; and from the temperature +of -260° C. downward the divergence of such a thermometer from one of +hydrogen is very marked. + +The measurement of very high temperatures is not open to the same +theoretical objections as that of very low temperatures; but, from a +practical point of view, it is as difficult to effect with an ordinary +gas thermometer. It becomes impossible to guarantee the reservoir +remaining sufficiently impermeable, and all security disappears, +notwithstanding the use of recipients very superior to those of former +times, such as those lately devised by the physicists of the +_Reichansalt_. This difficulty is obviated by using other methods, +such as the employment of thermo-electric couples, such as the very +convenient couple of M. le Chatelier; but the graduation of these +instruments can only be effected at the cost of a rather bold +extrapolation. + +M.D. Berthelot has pointed out and experimented with a very +interesting process, founded on the measurement by the phenomena of +interference of the refractive index of a column of air subjected to +the temperature it is desired to measure. It appears admissible that +even at the highest temperatures the variation of the power of +refraction is strictly proportional to that of the density, for this +proportion is exactly verified so long as it is possible to check it +precisely. We can thus, by a method which offers the great advantage +of being independent of the power and dimension of the envelopes +employed--since the length of the column of air considered alone +enters into the calculation--obtain results equivalent to those given +by the ordinary air thermometer. + +Another method, very old in principle, has also lately acquired great +importance. For a long time we sought to estimate the temperature of a +body by studying its radiation, but we did not know any positive +relation between this radiation and the temperature, and we had no +good experimental method of estimation, but had recourse to purely +empirical formulas and the use of apparatus of little precision. Now, +however, many physicists, continuing the classic researches of +Kirchhoff, Boltzmann, Professors Wien and Planck, and taking their +starting-point from the laws of thermodynamics, have given formulas +which establish the radiating power of a dark body as a function of +the temperature and the wave-length, or, better still, of the total +power as a function of the temperature and wave-length corresponding +to the maximum value of the power of radiation. We see, therefore, the +possibility of appealing for the measurement of temperature to a +phenomenon which is no longer the variation of the elastic force of a +gas, and yet is also connected with the principles of thermodynamics. + +This is what Professors Lummer and Pringsheim have shown in a series +of studies which may certainly be reckoned among the greatest +experimental researches of the last few years. They have constructed a +radiator closely resembling the theoretically integral radiator which +a closed isothermal vessel would be, and with only a very small +opening, which allows us to collect from outside the radiations which +are in equilibrium with the interior. This vessel is formed of a +hollow carbon cylinder, heated by a current of high intensity; the +radiations are studied by means of a bolometer, the disposition of +which varies with the nature of the experiments. + +It is hardly possible to enter into the details of the method, but the +result sufficiently indicates its importance. It is now possible, +thanks to their researches, to estimate a temperature of 2000° C. to +within about 5°. Ten years ago a similar approximation could hardly +have been arrived at for a temperature of 1000° C. + + +§ 6. DERIVED UNITS AND THE MEASURE OF A QUANTITY OF ENERGY + +It must be understood that it is only by arbitrary convention that a +dependency is established between a derived unit and the fundamental +units. The laws of numbers in physics are often only laws of +proportion. We transform them into laws of equation, because we +introduce numerical coefficients and choose the units on which they +depend so as to simplify as much as possible the formulas most in use. +A particular speed, for instance, is in reality nothing else but a +speed, and it is only by the peculiar choice of unit that we can say +that it is the space covered during the unit of time. In the same way, +a quantity of electricity is a quantity of electricity; and there is +nothing to prove that, in its essence, it is really reducible to a +function of mass, of length, and of time. + +Persons are still to be met with who seem to have some illusions on +this point, and who see in the doctrine of the dimensions of the units +a doctrine of general physics, while it is, to say truth, only a +doctrine of metrology. The knowledge of dimensions is valuable, since +it allows us, for instance, to easily verify the homogeneity of a +formula, but it can in no way give us any information on the actual +nature of the quantity measured. + +Magnitudes to which we attribute like dimensions may be qualitatively +irreducible one to the other. Thus the different forms of energy are +measured by the same unit, and yet it seems that some of them, such as +kinetic energy, really depend on time; while for others, such as +potential energy, the dependency established by the system of +measurement seems somewhat fictitious. + +The numerical value of a quantity of energy of any nature should, in +the system C.G.S., be expressed in terms of the unit called the erg; +but, as a matter of fact, when we wish to compare and measure +different quantities of energy of varying forms, such as electrical, +chemical, and other quantities, etc., we nearly always employ a method +by which all these energies are finally transformed and used to heat +the water of a calorimeter. It is therefore very important to study +well the calorific phenomenon chosen as the unit of heat, and to +determine with precision its mechanical equivalent, that is to say, +the number of ergs necessary to produce this unit. This is a number +which, on the principle of equivalence, depends neither on the method +employed, nor the time, nor any other external circumstance. + +As the result of the brilliant researches of Rowland and of Mr +Griffiths on the variations of the specific heat of water, physicists +have decided to take as calorific standard the quantity of heat +necessary to raise a gramme of water from 15° to 16° C., the +temperature being measured by the scale of the hydrogen thermometer of +the International Bureau. + +On the other hand, new determinations of the mechanical equivalent, +among which it is right to mention that of Mr. Ames, and a full +discussion as to the best results, have led to the adoption of the +number 4.187 to represent the number of ergs capable of producing the +unit of heat. + +In practice, the measurement of a quantity of heat is very often +effected by means of the ice calorimeter, the use of which is +particularly simple and convenient. There is, therefore, a very +special interest in knowing exactly the melting-point of ice. M. +Leduc, who for several years has measured a great number of physical +constants with minute precautions and a remarkable sense of precision, +concludes, after a close discussion of the various results obtained, +that this heat is equal to 79.1 calories. An error of almost a calorie +had been committed by several renowned experimenters, and it will be +seen that in certain points the art of measurement may still be +largely perfected. + +To the unit of energy might be immediately attached other units. For +instance, radiation being nothing but a flux of energy, we could, in +order to establish photometric units, divide the normal spectrum into +bands of a given width, and measure the power of each for the unit of +radiating surface. + +But, notwithstanding some recent researches on this question, we +cannot yet consider the distribution of energy in the spectrum as +perfectly known. If we adopt the excellent habit which exists in some +researches of expressing radiating energy in ergs, it is still +customary to bring the radiations to a standard giving, by its +constitution alone, the unit of one particular radiation. In +particular, the definitions are still adhered to which were adopted as +the result of the researches of M. Violle on the radiation of fused +platinum at the temperature of solidification; and most physicists +utilize in the ordinary methods of photometry the clearly defined +notions of M. Blondel as to the luminous intensity of flux, +illumination (_éclairement_), light (_éclat_), and lighting +(_éclairage_), with the corresponding units, decimal candle, _lumen_, +_lux_, carcel lamp, candle per square centimetre, and _lumen_-hour.[4] + +[Footnote 4: These are the magnitudes and units adopted at the +International Congress of Electricians in 1904. For their definition +and explanation, see Demanet, _Notes de Physique Expérimentale_ +(Louvain, 1905), t. iv. p. 8.--ED.] + + +§ 7. MEASURE OF CERTAIN PHYSICAL CONSTANTS + +The progress of metrology has led, as a consequence, to corresponding +progress in nearly all physical measurements, and particularly in the +measure of natural constants. Among these, the constant of gravitation +occupies a position quite apart from the importance and simplicity of +the physical law which defines it, as well as by its generality. Two +material particles are mutually attracted to each other by a force +directly proportional to the product of their mass, and inversely +proportional to the square of the distance between them. The +coefficient of proportion is determined when once the units are +chosen, and as soon as we know the numerical values of this force, of +the two masses, and of their distance. But when we wish to make +laboratory experiments serious difficulties appear, owing to the +weakness of the attraction between masses of ordinary dimensions. +Microscopic forces, so to speak, have to be observed, and therefore +all the causes of errors have to be avoided which would be unimportant +in most other physical researches. It is known that Cavendish was the +first who succeeded by means of the torsion balance in effecting +fairly precise measurements. This method has been again taken in hand +by different experimenters, and the most recent results are due to Mr +Vernon Boys. This learned physicist is also the author of a most +useful practical invention, and has succeeded in making quartz threads +as fine as can be desired and extremely uniform. He finds that these +threads possess valuable properties, such as perfect elasticity and +great tenacity. He has been able, with threads not more than 1/500 of +a millimetre in diameter, to measure with precision couples of an +order formerly considered outside the range of experiment, and to +reduce the dimensions of the apparatus of Cavendish in the proportion +of 150 to 1. The great advantage found in the use of these small +instruments is the better avoidance of the perturbations arising from +draughts of air, and of the very serious influence of the slightest +inequality in temperature. + +Other methods have been employed in late years by other experimenters, +such as the method of Baron Eötvös, founded on the use of a torsion +lever, the method of the ordinary balance, used especially by +Professors Richarz and Krigar-Menzel and also by Professor Poynting, +and the method of M. Wilsing, who uses a balance with a vertical beam. +The results fairly agree, and lead to attributing to the earth a +density equal to 5.527. + +The most familiar manifestation of gravitation is gravity. The action +of the earth on the unit of mass placed in one point, and the +intensity of gravity, is measured, as we know, by the aid of a +pendulum. The methods of measurement, whether by absolute or by +relative determinations, so greatly improved by Borda and Bessel, have +been still further improved by various geodesians, among whom should +be mentioned M. von Sterneek and General Defforges. Numerous +observations have been made in all parts of the world by various +explorers, and have led to a fairly complete knowledge of the +distribution of gravity over the surface of the globe. Thus we have +succeeded in making evident anomalies which would not easily find +their place in the formula of Clairaut. + +Another constant, the determination of which is of the greatest +utility in astronomy of position, and the value of which enters into +electromagnetic theory, has to-day assumed, with the new ideas on the +constitution of matter, a still more considerable importance. I refer +to the speed of light, which appears to us, as we shall see further +on, the maximum value of speed which can be given to a material body. + +After the historical experiments of Fizeau and Foucault, taken up +afresh, as we know, partly by Cornu, and partly by Michelson and +Newcomb, it remained still possible to increase the precision of the +measurements. Professor Michelson has undertaken some new researches +by a method which is a combination of the principle of the toothed +wheel of Fizeau with the revolving mirror of Foucault. The toothed +wheel is here replaced, however, by a grating, in which the lines and +the spaces between them take the place of the teeth and the gaps, the +reflected light only being returned when it strikes on the space +between two lines. The illustrious American physicist estimates that +he can thus evaluate to nearly five kilometres the path traversed by +light in one second. This approximation corresponds to a relative +value of a few hundred-thousandths, and it far exceeds those hitherto +attained by the best experimenters. When all the experiments are +completed, they will perhaps solve certain questions still in +suspense; for instance, the question whether the speed of propagation +depends on intensity. If this turns out to be the case, we should be +brought to the important conclusion that the amplitude of the +oscillations, which is certainly very small in relation to the already +tiny wave-lengths, cannot be considered as unimportant in regard to +these lengths. Such would seem to have been the result of the curious +experiments of M. Muller and of M. Ebert, but these results have been +recently disputed by M. Doubt. + +In the case of sound vibrations, on the other hand, it should be noted +that experiment, consistently with the theory, proves that the speed +increases with the amplitude, or, if you will, with the intensity. M. +Violle has published an important series of experiments on the speed +of propagation of very condensed waves, on the deformations of these +waves, and on the relations of the speed and the pressure, which +verify in a remarkable manner the results foreshadowed by the already +old calculations of Riemann, repeated later by Hugoniot. If, on the +contrary, the amplitude is sufficiently small, there exists a speed +limit which is the same in a large pipe and in free air. By some +beautiful experiments, MM. Violle and Vautier have clearly shown that +any disturbance in the air melts somewhat quickly into a single wave +of given form, which is propagated to a distance, while gradually +becoming weaker and showing a constant speed which differs little in +dry air at 0° C. from 331.36 metres per second. In a narrow pipe the +influence of the walls makes itself felt and produces various effects, +in particular a kind of dispersion in space of the harmonics of the +sound. This phenomenon, according to M. Brillouin, is perfectly +explicable by a theory similar to the theory of gratings. + + + + +CHAPTER III + +PRINCIPLES + + +§ 1. THE PRINCIPLES OF PHYSICS + +Facts conscientiously observed lead by induction to the enunciation of +a certain number of laws or general hypotheses which are the +principles already referred to. These principal hypotheses are, in the +eyes of a physicist, legitimate generalizations, the consequences of +which we shall be able at once to check by the experiments from which +they issue. + +Among the principles almost universally adopted until lately figure +prominently those of mechanics--such as the principle of relativity, +and the principle of the equality of action and reaction. We will not +detail nor discuss them here, but later on we shall have an +opportunity of pointing out how recent theories on the phenomena of +electricity have shaken the confidence of physicists in them and have +led certain scholars to doubt their absolute value. + +The principle of Lavoisier, or principle of the conservation of mass, +presents itself under two different aspects according to whether mass +is looked upon as the coefficient of the inertia of matter or as the +factor which intervenes in the phenomena of universal attraction, and +particularly in gravitation. We shall see when we treat of these +theories, how we have been led to suppose that inertia depended on +velocity and even on direction. If this conception were exact, the +principle of the invariability of mass would naturally be destroyed. +Considered as a factor of attraction, is mass really indestructible? + +A few years ago such a question would have seemed singularly +audacious. And yet the law of Lavoisier is so far from self-evident +that for centuries it escaped the notice of physicists and chemists. +But its great apparent simplicity and its high character of +generality, when enunciated at the end of the eighteenth century, +rapidly gave it such an authority that no one was able to any longer +dispute it unless he desired the reputation of an oddity inclined to +paradoxical ideas. + +It is important, however, to remark that, under fallacious +metaphysical appearances, we are in reality using empty words +when we repeat the aphorism, "Nothing can be lost, nothing can be +created," and deduce from it the indestructibility of matter. This +indestructibility, in truth, is an experimental fact, and the +principle depends on experiment. It may even seem, at first sight, +more singular than not that the weight of a bodily system in a given +place, or the quotient of this weight by that of the standard +mass--that is to say, the mass of these bodies--remains invariable, +both when the temperature changes and when chemical reagents cause the +original materials to disappear and to be replaced by new ones. We may +certainly consider that in a chemical phenomenon annihilations and +creations of matter are really produced; but the experimental law +teaches us that there is compensation in certain respects. + +The discovery of the radioactive bodies has, in some sort, rendered +popular the speculations of physicists on the phenomena of the +disaggregation of matter. We shall have to seek the exact meaning +which ought to be given to the experiments on the emanation of these +bodies, and to discover whether these experiments really imperil the +law of Lavoisier. + +For some years different experimenters have also effected many very +precise measurements of the weight of divers bodies both before and +after chemical reactions between these bodies. Two highly experienced +and cautious physicists, Professors Landolt and Heydweiller, have not +hesitated to announce the sensational result that in certain +circumstances the weight is no longer the same after as before the +reaction. In particular, the weight of a solution of salts of copper +in water is not the exact sum of the joint weights of the salt and the +water. Such experiments are evidently very delicate; they have been +disputed, and they cannot be considered as sufficient for conviction. +It follows nevertheless that it is no longer forbidden to regard the +law of Lavoisier as only an approximate law; according to Sandford and +Ray, this approximation would be about 1/2,400,000. This is also the +result reached by Professor Poynting in experiments regarding the +possible action of temperature on the weight of a body; and if this be +really so, we may reassure ourselves, and from the point of view of +practical application may continue to look upon matter as +indestructible. + +The principles of physics, by imposing certain conditions on +phenomena, limit after a fashion the field of the possible. Among +these principles is one which, notwithstanding its importance when +compared with that of universally known principles, is less familiar +to some people. This is the principle of symmetry, more or less +conscious applications of which can, no doubt, be found in various +works and even in the conceptions of Copernican astronomers, but which +was generalized and clearly enunciated for the first time by the late +M. Curie. This illustrious physicist pointed out the advantage of +introducing into the study of physical phenomena the considerations on +symmetry familiar to crystallographers; for a phenomenon to take +place, it is necessary that a certain dissymmetry should previously +exist in the medium in which this phenomenon occurs. A body, for +instance, may be animated with a certain linear velocity or a speed of +rotation; it may be compressed, or twisted; it may be placed in an +electric or in a magnetic field; it may be affected by an electric +current or by one of heat; it may be traversed by a ray of light +either ordinary or polarized rectilineally or circularly, etc.:--in +each case a certain minimum and characteristic dissymmetry is +necessary at every point of the body in question. + +This consideration enables us to foresee that certain phenomena which +might be imagined _a priori_ cannot exist. Thus, for instance, it is +impossible that an electric field, a magnitude directed and not +superposable on its image in a mirror perpendicular to its direction, +could be created at right angles to the plane of symmetry of the +medium; while it would be possible to create a magnetic field under +the same conditions. + +This consideration thus leads us to the discovery of new phenomena; +but it must be understood that it cannot of itself give us absolutely +precise notions as to the nature of these phenomena, nor disclose +their order of magnitude. + + +§ 2. THE PRINCIPLE OF THE CONSERVATION OF ENERGY + +Dominating not physics alone, but nearly every other science, the +principle of the conservation of energy is justly considered as the +grandest conquest of contemporary thought. It shows us in a powerful +light the most diverse questions; it introduces order into the most +varied studies; it leads to a clear and coherent interpretation of +phenomena which, without it, appear to have no connexion with each +other; and it supplies precise and exact numerical relations between +the magnitudes which enter into these phenomena. + +The boldest minds have an instinctive confidence in it, and it is the +principle which has most stoutly resisted that assault which the +daring of a few theorists has lately directed to the overthrow of the +general principles of physics. At every new discovery, the first +thought of physicists is to find out how it accords with the principle +of the conservation of energy. The application of the principle, +moreover, never fails to give valuable hints on the new phenomenon, +and often even suggests a complementary discovery. Up till now it +seems never to have received a check, even the extraordinary +properties of radium not seriously contradicting it; also the general +form in which it is enunciated gives it such a suppleness that it is +no doubt very difficult to overthrow. + +I do not claim to set forth here the complete history of this +principle, but I will endeavour to show with what pains it was born, +how it was kept back in its early days and then obstructed in its +development by the unfavourable conditions of the surroundings in +which it appeared. It first of all came, in fact, to oppose itself to +the reigning theories; but, little by little, it acted on these +theories, and they were modified under its pressure; then, in their +turn, these theories reacted on it and changed its primitive form. + +It had to be made less wide in order to fit into the classic frame, +and was absorbed by mechanics; and if it thus became less general, it +gained in precision what it lost in extent. When once definitely +admitted and classed, as it were, in the official domain of science, +it endeavoured to burst its bonds and return to a more independent and +larger life. The history of this principle is similar to that of all +evolutions. + +It is well known that the conservation of energy was, at first, +regarded from the point of view of the reciprocal transformations +between heat and work, and that the principle received its first clear +enunciation in the particular case of the principle of equivalence. It +is, therefore, rightly considered that the scholars who were the first +to doubt the material nature of caloric were the precursors of R. +Mayer; their ideas, however, were the same as those of the celebrated +German doctor, for they sought especially to demonstrate that heat was +a mode of motion. + +Without going back to early and isolated attempts like those of Daniel +Bernoulli, who, in his hydrodynamics, propounded the basis of the +kinetic theory of gases, or the researches of Boyle on friction, we +may recall, to show how it was propounded in former times, a rather +forgotten page of the _Mémoire sur la Chaleur_, published in 1780 by +Lavoisier and Laplace: "Other physicists," they wrote, after setting +out the theory of caloric, "think that heat is nothing but the result +of the insensible vibrations of matter.... In the system we are now +examining, heat is the _vis viva_ resulting from the insensible +movements of the molecules of a body; it is the sum of the products of +the mass of each molecule by the square of its velocity.... We shall +not decide between the two preceding hypotheses; several phenomena +seem to support the last mentioned--for instance, that of the heat +produced by the friction of two solid bodies. But there are others +which are more simply explained by the first, and perhaps they both +operate at once." Most of the physicists of that period, however, did +not share the prudent doubts of Lavoisier and Laplace. They admitted, +without hesitation, the first hypothesis; and, four years after the +appearance of the _Mémoire sur la Chaleur_, Sigaud de Lafond, a +professor of physics of great reputation, wrote: "Pure Fire, free from +all state of combination, seems to be an assembly of particles of a +simple, homogeneous, and absolutely unalterable matter, and all the +properties of this element indicate that these particles are +infinitely small and free, that they have no sensible cohesion, and +that they are moved in every possible direction by a continual and +rapid motion which is essential to them.... The extreme tenacity and +the surprising mobility of its molecules are manifestly shown by the +ease with which it penetrates into the most compact bodies and by its +tendency to put itself in equilibrium throughout all bodies near to +it." + +It must be acknowledged, however, that the idea of Lavoisier and +Laplace was rather vague and even inexact on one important point. They +admitted it to be evident that "all variations of heat, whether real +or apparent, undergone by a bodily system when changing its state, are +produced in inverse order when the system passes back to its original +state." This phrase is the very denial of equivalence where these +changes of state are accompanied by external work. + +Laplace, moreover, himself became later a very convinced partisan of +the hypothesis of the material nature of caloric, and his immense +authority, so fortunate in other respects for the development of +science, was certainly in this case the cause of the retardation of +progress. + +The names of Young, Rumford, Davy, are often quoted among those +physicists who, at the commencement of the nineteenth century, caught +sight of the new truths as to the nature of heat. To these names is +very properly added that of Sadi Carnot. A note found among his papers +unquestionably proves that, before 1830, ideas had occurred to him +from which it resulted that in producing work an equivalent amount of +heat was destroyed. But the year 1842 is particularly memorable in the +history of science as the year in which Jules Robert Mayer succeeded, +by an entirely personal effort, in really enunciating the principle of +the conservation of energy. Chemists recall with just pride that the +_Remarques sur les forces de la nature animée_, contemptuously +rejected by all the journals of physics, were received and published +in the _Annalen_ of Liebig. We ought never to forget this example, +which shows with what difficulty a new idea contrary to the classic +theories of the period succeeds in coming to the front; but +extenuating circumstances may be urged on behalf of the physicists. + +Robert Mayer had a rather insufficient mathematical education, and his +Memoirs, the _Remarques_, as well as the ulterior publications, +_Mémoire sur le mouvement organique et la nutrition_ and the +_Matériaux pour la dynamique du ciel_, contain, side by side with very +profound ideas, evident errors in mechanics. Thus it often happens +that discoveries put forward in a somewhat vague manner by adventurous +minds not overburdened by the heavy baggage of scientific erudition, +who audaciously press forward in advance of their time, fall into +quite intelligible oblivion until rediscovered, clarified, and put +into shape by slower but surer seekers. This was the case with the +ideas of Mayer. They were not understood at first sight, not only on +account of their originality, but also because they were couched in +incorrect language. + +Mayer was, however, endowed with a singular strength of thought; he +expressed in a rather confused manner a principle which, for him, had +a generality greater than mechanics itself, and so his discovery was +in advance not only of his own time but of half the century. He may +justly be considered the founder of modern energetics. + +Freed from the obscurities which prevented its being clearly +perceived, his idea stands out to-day in all its imposing simplicity. +Yet it must be acknowledged that if it was somewhat denaturalised by +those who endeavoured to adapt it to the theories of mechanics, and if +it at first lost its sublime stamp of generality, it thus became +firmly fixed and consolidated on a more stable basis. + +The efforts of Helmholtz, Clausius, and Lord Kelvin to introduce the +principle of the conservation of energy into mechanics, were far from +useless. These illustrious physicists succeeded in giving a more +precise form to its numerous applications; and their attempts thus +contributed, by reaction, to give a fresh impulse to mechanics, and +allowed it to be linked to a more general order of facts. If +energetics has not been able to be included in mechanics, it seems +indeed that the attempt to include mechanics in energetics was not in +vain. + +In the middle of the last century, the explanation of all natural +phenomena seemed more and more referable to the case of central +forces. Everywhere it was thought that reciprocal actions between +material points could be perceived, these points being attracted or +repelled by each other with an intensity depending only on their +distance or their mass. If, to a system thus composed, the laws of the +classical mechanics are applied, it is shown that half the sum of the +product of the masses by the square of the velocities, to which is +added the work which might be accomplished by the forces to which the +system would be subject if it returned from its actual to its initial +position, is a sum constant in quantity. + +This sum, which is the mechanical energy of the system, is therefore +an invariable quantity in all the states to which it may be brought by +the interaction of its various parts, and the word energy well +expresses a capital property of this quantity. For if two systems are +connected in such a way that any change produced in the one +necessarily brings about a change in the other, there can be no +variation in the characteristic quantity of the second except so far +as the characteristic quantity of the first itself varies--on +condition, of course, that the connexions are made in such a manner as +to introduce no new force. It will thus be seen that this quantity +well expresses the capacity possessed by a system for modifying the +state of a neighbouring system to which we may suppose it connected. + +Now this theorem of pure mechanics was found wanting every time +friction took place--that is to say, in all really observable cases. +The more perceptible the friction, the more considerable the +difference; but, in addition, a new phenomenon always appeared and +heat was produced. By experiments which are now classic, it became +established that the quantity of heat thus created independently of +the nature of the bodies is always (provided no other phenomena +intervene) proportional to the energy which has disappeared. +Reciprocally, also, heat may disappear, and we always find a constant +relation between the quantities of heat and work which mutually +replace each other. + +It is quite clear that such experiments do not prove that heat is +work. We might just as well say that work is heat. It is making a +gratuitous hypothesis to admit this reduction of heat to mechanism; +but this hypothesis was so seductive, and so much in conformity with +the desire of nearly all physicists to arrive at some sort of unity in +nature, that they made it with eagerness and became unreservedly +convinced that heat was an active internal force. + +Their error was not in admitting this hypothesis; it was a legitimate +one since it has proved very fruitful. But some of them committed the +fault of forgetting that it was an hypothesis, and considered it a +demonstrated truth. Moreover, they were thus brought to see in +phenomena nothing but these two particular forms of energy which in +their minds were easily identified with each other. + +From the outset, however, it became manifest that the principle is +applicable to cases where heat plays only a parasitical part. There +were thus discovered, by translating the principle of equivalence, +numerical relations between the magnitudes of electricity, for +instance, and the magnitudes of mechanics. Heat was a sort of variable +intermediary convenient for calculation, but introduced in a +roundabout way and destined to disappear in the final result. + +Verdet, who, in lectures which have rightly remained celebrated, +defined with remarkable clearness the new theories, said, in 1862: +"Electrical phenomena are always accompanied by calorific +manifestations, of which the study belongs to the mechanical theory of +heat. This study, moreover, will not only have the effect of making +known to us interesting facts in electricity, but will throw some +light on the phenomena of electricity themselves." + +The eminent professor was thus expressing the general opinion of his +contemporaries, but he certainly seemed to have felt in advance that +the new theory was about to penetrate more deeply into the inmost +nature of things. Three years previously, Rankine also had put forth +some very remarkable ideas the full meaning of which was not at first +well understood. He it was who comprehended the utility of employing a +more inclusive term, and invented the phrase energetics. He also +endeavoured to create a new doctrine of which rational mechanics +should be only a particular case; and he showed that it was possible +to abandon the ideas of atoms and central forces, and to construct a +more general system by substituting for the ordinary consideration of +forces that of the energy which exists in all bodies, partly in an +actual, partly in a potential state. + +By giving more precision to the conceptions of Rankine, the physicists +of the end of the nineteenth century were brought to consider that in +all physical phenomena there occur apparitions and disappearances +which are balanced by various energies. It is natural, however, to +suppose that these equivalent apparitions and disappearances +correspond to transformations and not to simultaneous creations and +destructions. We thus represent energy to ourselves as taking +different forms--mechanical, electrical, calorific, and chemical-- +capable of changing one into the other, but in such a way that the +quantitative value always remains the same. In like manner a bank +draft may be represented by notes, gold, silver, or bullion. The +earliest known form of energy, _i.e._ work, will serve as the standard +as gold serves as the monetary standard, and energy in all its forms +will be estimated by the corresponding work. In each particular case +we can strictly define and measure, by the correct application of the +principle of the conservation of energy, the quantity of energy +evolved under a given form. + +We can thus arrange a machine comprising a body capable of evolving +this energy; then we can force all the organs of this machine to +complete an entirely closed cycle, with the exception of the body +itself, which, however, has to return to such a state that all the +variables from which this state depends resume their initial values +except the particular variable to which the evolution of the energy +under consideration is linked. The difference between the work thus +accomplished and that which would have been obtained if this variable +also had returned to its original value, is the measure of the energy +evolved. + +In the same way that, in the minds of mechanicians, all forces of +whatever origin, which are capable of compounding with each other and +of balancing each other, belong to the same category of beings, so for +many physicists energy is a sort of entity which we find under various +aspects. There thus exists for them a world, which comes in some way +to superpose itself upon the world of matter--that is to say, the +world of energy, dominated in its turn by a fundamental law similar to +that of Lavoisier.[5] This conception, as we have already seen, passes +the limit of experience; but others go further still. Absorbed in the +contemplation of this new world, they succeed in persuading themselves +that the old world of matter has no real existence and that energy is +sufficient by itself to give us a complete comprehension of the +Universe and of all the phenomena produced in it. They point out that +all our sensations correspond to changes of energy, and that +everything apparent to our senses is, in truth, energy. The famous +experiment of the blows with a stick by which it was demonstrated to a +sceptical philosopher that an outer world existed, only proves, in +reality, the existence of energy, and not that of matter. The stick in +itself is inoffensive, as Professor Ostwald remarks, and it is its +_vis viva_, its kinetic energy, which is painful to us; while if we +possessed a speed equal to its own, moving in the same direction, it +would no longer exist so far as our sense of touch is concerned. + +[Footnote 5: "Nothing is created; nothing is lost"--ED.] + +On this hypothesis, matter would only be the capacity for kinetic +energy, its pretended impenetrability energy of volume, and its weight +energy of position in the particular form which presents itself in +universal gravitation; nay, space itself would only be known to us by +the expenditure of energy necessary to penetrate it. Thus in all +physical phenomena we should only have to regard the quantities of +energy brought into play, and all the equations which link the +phenomena to one another would have no meaning but when they apply to +exchanges of energy. For energy alone can be common to all phenomena. + +This extreme manner of regarding things is seductive by its +originality, but appears somewhat insufficient if, after enunciating +generalities, we look more closely into the question. From the +philosophical point of view it may, moreover, seem difficult not to +conclude, from the qualities which reveal, if you will, the varied +forms of energy, that there exists a substance possessing these +qualities. This energy, which resides in one region, and which +transports itself from one spot to another, forcibly brings to mind, +whatever view we may take of it, the idea of matter. + +Helmholtz endeavoured to construct a mechanics based on the idea of +energy and its conservation, but he had to invoke a second law, the +principle of least action. If he thus succeeded in dispensing with the +hypothesis of atoms, and in showing that the new mechanics gave us to +understand the impossibility of certain movements which, according to +the old, ought to have been but never were experimentally produced, he +was only able to do so because the principle of least action necessary +for his theory became evident in the case of those irreversible +phenomena which alone really exist in Nature. The energetists have +thus not succeeded in forming a thoroughly sound system, but their +efforts have at all events been partly successful. Most physicists are +of their opinion, that kinetic energy is only a particular variety of +energy to which we have no right to wish to connect all its other +forms. + +If these forms showed themselves to be innumerable throughout the +Universe, the principle of the conservation of energy would, in fact, +lose a great part of its importance. Every time that a certain +quantity of energy seemed to appear or disappear, it would always be +permissible to suppose that an equivalent quantity had appeared or +disappeared somewhere else under a new form; and thus the principle +would in a way vanish. But the known forms of energy are fairly +restricted in number, and the necessity of recognising new ones seldom +makes itself felt. We shall see, however, that to explain, for +instance, the paradoxical properties of radium and to re-establish +concord between these properties and the principle of the conservation +of energy, certain physicists have recourse to the hypothesis that +radium borrows an unknown energy from the medium in which it is +plunged. This hypothesis, however, is in no way necessary; and in a +few other rare cases in which similar hypotheses have had to be set +up, experiment has always in the long run enabled us to discover some +phenomenon which had escaped the first observers and which corresponds +exactly to the variation of energy first made evident. + +One difficulty, however, arises from the fact that the principle ought +only to be applied to an isolated system. Whether we imagine actions +at a distance or believe in intermediate media, we must always +recognise that there exist no bodies in the world incapable of acting +on each other, and we can never affirm that some modification in the +energy of a given place may not have its echo in some unknown spot +afar off. This difficulty may sometimes render the value of the +principle rather illusory. + +Similarly, it behoves us not to receive without a certain distrust the +extension by certain philosophers to the whole Universe, of a property +demonstrated for those restricted systems which observation can alone +reach. We know nothing of the Universe as a whole, and every +generalization of this kind outruns in a singular fashion the limit of +experiment. + +Even reduced to the most modest proportions, the principle of the +conservation of energy retains, nevertheless, a paramount importance; +and it still preserves, if you will, a high philosophical value. M.J. +Perrin justly points out that it gives us a form under which we are +experimentally able to grasp causality, and that it teaches us that a +result has to be purchased at the cost of a determined effort. + +We can, in fact, with M. Perrin and M. Langevin, represent this in a +way which puts this characteristic in evidence by enunciating it as +follows: "If at the cost of a change C we can obtain a change K, there +will never be acquired at the same cost, whatever the mechanism +employed, first the change K and in addition some other change, unless +this latter be one that is otherwise known to cost nothing to produce +or to destroy." If, for instance, the fall of a weight can be +accompanied, without anything else being produced, by another +transformation--the melting of a certain mass of ice, for example--it +will be impossible, no matter how you set about it or whatever the +mechanism used, to associate this same transformation with the melting +of another weight of ice. + +We can thus, in the transformation in question, obtain an appropriate +number which will sum up that which may be expected from the external +effect, and can give, so to speak, the price at which this +transformation is bought, measure its invariable value by a common +measure (for instance, the melting of the ice), and, without any +ambiguity, define the energy lost during the transformation as +proportional to the mass of ice which can be associated with it. This +measure is, moreover, independent of the particular phenomenon taken +as the common measure. + + +§ 3. THE PRINCIPLE OF CARNOT AND CLAUSIUS + +The principle of Carnot, of a nature analogous to the principle of the +conservation of energy, has also a similar origin. It was first +enunciated, like the last named, although prior to it in time, in +consequence of considerations which deal only with heat and mechanical +work. Like it, too, it has evolved, grown, and invaded the entire +domain of physics. It may be interesting to examine rapidly the +various phases of this evolution. The origin of the principle of +Carnot is clearly determined, and it is very rare to be able to go +back thus certainly to the source of a discovery. Sadi Carnot had, +truth to say, no precursor. In his time heat engines were not yet very +common, and no one had reflected much on their theory. He was +doubtless the first to propound to himself certain questions, and +certainly the first to solve them. + +It is known how, in 1824, in his _Réflexions sur la puissance motrice +du feu_, he endeavoured to prove that "the motive power of heat is +independent of the agents brought into play for its realization," and +that "its quantity is fixed solely by the temperature of the bodies +between which, in the last resort, the transport of caloric is +effected"--at least in all engines in which "the method of developing +the motive power attains the perfection of which it is capable"; and +this is, almost textually, one of the enunciations of the principle at +the present day. Carnot perceived very clearly the great fact that, to +produce work by heat, it is necessary to have at one's disposal a fall +of temperature. On this point he expresses himself with perfect +clearness: "The motive power of a fall of water depends on its height +and on the quantity of liquid; the motive power of heat depends also +on the quantity of caloric employed, and on what might be called--in +fact, what we shall call--the height of fall, that is to say, the +difference in temperature of the bodies between which the exchange of +caloric takes place." + +Starting with this idea, he endeavours to demonstrate, by associating +two engines capable of working in a reversible cycle, that the +principle is founded on the impossibility of perpetual motion. + +His memoir, now celebrated, did not produce any great sensation, and +it had almost fallen into deep oblivion, which, in consequence of +the discovery of the principle of equivalence, might have seemed +perfectly justified. Written, in fact, on the hypothesis of the +indestructibility of caloric, it was to be expected that this memoir +should be condemned in the name of the new doctrine, that is, of the +principle recently brought to light. + +It was really making a new discovery to establish that Carnot's +fundamental idea survived the destruction of the hypothesis on the +nature of heat, on which he seemed to rely. As he no doubt himself +perceived, his idea was quite independent of this hypothesis, since, +as we have seen, he was led to surmise that heat could disappear; but +his demonstrations needed to be recast and, in some points, modified. + +It is to Clausius that was reserved the credit of rediscovering the +principle, and of enunciating it in language conformable to the new +doctrines, while giving it a much greater generality. The postulate +arrived at by experimental induction, and which must be admitted +without demonstration, is, according to Clausius, that in a series of +transformations in which the final is identical with the initial +stage, it is impossible for heat to pass from a colder to a warmer +body unless some other accessory phenomenon occurs at the same time. + +Still more correctly, perhaps, an enunciation can be given of the +postulate which, in the main, is analogous, by saying: A heat motor, +which after a series of transformations returns to its initial state, +can only furnish work if there exist at least two sources of heat, and +if a certain quantity of heat is given to one of the sources, which +can never be the hotter of the two. By the expression "source of +heat," we mean a body exterior to the system and capable of furnishing +or withdrawing heat from it. + +Starting with this principle, we arrive, as does Clausius, at the +demonstration that the output of a reversible machine working between +two given temperatures is greater than that of any non-reversible +engine, and that it is the same for all reversible machines working +between these two temperatures. + +This is the very proposition of Carnot; but the proposition thus +stated, while very useful for the theory of engines, does not yet +present any very general interest. Clausius, however, drew from it +much more important consequences. First, he showed that the principle +conduces to the definition of an absolute scale of temperature; and +then he was brought face to face with a new notion which allows a +strong light to be thrown on the questions of physical equilibrium. I +refer to entropy. + +It is still rather difficult to strip entirely this very important +notion of all analytical adornment. Many physicists hesitate to +utilize it, and even look upon it with some distrust, because they see +in it a purely mathematical function without any definite physical +meaning. Perhaps they are here unduly severe, since they often admit +too easily the objective existence of quantities which they cannot +define. Thus, for instance, it is usual almost every day to speak of +the heat possessed by a body. Yet no body in reality possesses a +definite quantity of heat even relatively to any initial state; since +starting from this point of departure, the quantities of heat it may +have gained or lost vary with the road taken and even with the means +employed to follow it. These expressions of heat gained or lost are, +moreover, themselves evidently incorrect, for heat can no longer be +considered as a sort of fluid passing from one body to another. + +The real reason which makes entropy somewhat mysterious is that this +magnitude does not fall directly under the ken of any of our senses; +but it possesses the true characteristic of a concrete physical +magnitude, since it is, in principle at least, measurable. Various +authors of thermodynamical researches, amongst whom M. Mouret should +be particularly mentioned, have endeavoured to place this +characteristic in evidence. + +Consider an isothermal transformation. Instead of leaving the heat +abandoned by the body subjected to the transformation--water +condensing in a state of saturated vapour, for instance--to pass +directly into an ice calorimeter, we can transmit this heat to the +calorimeter by the intermediary of a reversible Carnot engine. The +engine having absorbed this quantity of heat, will only give back to +the ice a lesser quantity of heat; and the weight of the melted ice, +inferior to that which might have been directly given back, will serve +as a measure of the isothermal transformation thus effected. It can be +easily shown that this measure is independent of the apparatus used. +It consequently becomes a numerical element characteristic of the body +considered, and is called its entropy. Entropy, thus defined, is a +variable which, like pressure or volume, might serve concurrently with +another variable, such as pressure or volume, to define the state of a +body. + +It must be perfectly understood that this variable can change in an +independent manner, and that it is, for instance, distinct from the +change of temperature. It is also distinct from the change which +consists in losses or gains of heat. In chemical reactions, for +example, the entropy increases without the substances borrowing any +heat. When a perfect gas dilates in a vacuum its entropy increases, +and yet the temperature does not change, and the gas has neither been +able to give nor receive heat. We thus come to conceive that a +physical phenomenon cannot be considered known to us if the variation +of entropy is not given, as are the variations of temperature and of +pressure or the exchanges of heat. The change of entropy is, properly +speaking, the most characteristic fact of a thermal change. + +It is important, however, to remark that if we can thus easily define +and measure the difference of entropy between two states of the same +body, the value found depends on the state arbitrarily chosen as the +zero point of entropy; but this is not a very serious difficulty, and +is analogous to that which occurs in the evaluation of other physical +magnitudes--temperature, potential, etc. + +A graver difficulty proceeds from its not being possible to define a +difference, or an equality, of entropy between two bodies chemically +different. We are unable, in fact, to pass by any means, reversible or +not, from one to the other, so long as the transmutation of matter is +regarded as impossible; but it is well understood that it is +nevertheless possible to compare the variations of entropy to which +these two bodies are both of them individually subject. + +Neither must we conceal from ourselves that the definition supposes, +for a given body, the possibility of passing from one state to another +by a reversible transformation. Reversibility is an ideal and extreme +case which cannot be realized, but which can be approximately attained +in many circumstances. So with gases and with perfectly elastic +bodies, we effect sensibly reversible transformations, and changes +of physical state are practically reversible. The discoveries of +Sainte-Claire Deville have brought many chemical phenomena into a +similar category, and reactions such as solution, which used to be +formerly the type of an irreversible phenomenon, may now often be +effected by sensibly reversible means. Be that as it may, when once the +definition is admitted, we arrive, by taking as a basis the principles +set forth at the inception, at the demonstration of the celebrated +theorem of Clausius: _The entropy of a thermally isolated system +continues to increase incessantly._ + +It is very evident that the theorem can only be worth applying in +cases where the entropy can be exactly defined; but, even when thus +limited, the field still remains vast, and the harvest which we can +there reap is very abundant. + +Entropy appears, then, as a magnitude measuring in a certain way the +evolution of a system, or, at least, as giving the direction of this +evolution. This very important consequence certainly did not escape +Clausius, since the very name of entropy, which he chose to designate +this magnitude, itself signifies evolution. We have succeeded in +defining this entropy by demonstrating, as has been said, a certain +number of propositions which spring from the postulate of Clausius; it +is, therefore, natural to suppose that this postulate itself contains +_in potentia_ the very idea of a necessary evolution of physical +systems. But as it was first enunciated, it contains it in a deeply +hidden way. + +No doubt we should make the principle of Carnot appear in an +interesting light by endeavouring to disengage this fundamental idea, +and by placing it, as it were, in large letters. Just as, in +elementary geometry, we can replace the postulate of Euclid by other +equivalent propositions, so the postulate of thermodynamics is not +necessarily fixed, and it is instructive to try to give it the most +general and suggestive character. + +MM. Perrin and Langevin have made a successful attempt in this +direction. M. Perrin enunciates the following principle: _An isolated +system never passes twice through the same state_. In this form, the +principle affirms that there exists a necessary order in the +succession of two phenomena; that evolution takes place in a +determined direction. If you prefer it, it may be thus stated: _Of two +converse transformations unaccompanied by any external effect, one +only is possible_. For instance, two gases may diffuse themselves one +in the other in constant volume, but they could not conversely +separate themselves spontaneously. + +Starting from the principle thus put forward, we make the logical +deduction that one cannot hope to construct an engine which should +work for an indefinite time by heating a hot source and by cooling a +cold one. We thus come again into the route traced by Clausius, and +from this point we may follow it strictly. + +Whatever the point of view adopted, whether we regard the proposition +of M. Perrin as the corollary of another experimental postulate, or +whether we consider it as a truth which we admit _a priori_ and verify +through its consequences, we are led to consider that in its entirety +the principle of Carnot resolves itself into the idea that we cannot +go back along the course of life, and that the evolution of a system +must follow its necessary progress. + +Clausius and Lord Kelvin have drawn from these considerations certain +well-known consequences on the evolution of the Universe. Noticing +that entropy is a property added to matter, they admit that there is +in the world a total amount of entropy; and as all real changes which +are produced in any system correspond to an increase of entropy, it +may be said that the entropy of the world is continually increasing. +Thus the quantity of energy existing in the Universe remains constant, +but transforms itself little by little into heat uniformly distributed +at a temperature everywhere identical. In the end, therefore, there +will be neither chemical phenomena nor manifestation of life; the +world will still exist, but without motion, and, so to speak, dead. + +These consequences must be admitted to be very doubtful; we cannot in +any certain way apply to the Universe, which is not a finite system, a +proposition demonstrated, and that not unreservedly, in the sharply +limited case of a finite system. Herbert Spencer, moreover, in his +book on _First Principles_, brings out with much force the idea that, +even if the Universe came to an end, nothing would allow us to +conclude that, once at rest, it would remain so indefinitely. We may +recognise that the state in which we are began at the end of a former +evolutionary period, and that the end of the existing era will mark +the beginning of a new one. + +Like an elastic and mobile object which, thrown into the air, attains +by degrees the summit of its course, then possesses a zero velocity +and is for a moment in equilibrium, and then falls on touching the +ground to rebound, so the world should be subjected to huge +oscillations which first bring it to a maximum of entropy till the +moment when there should be produced a slow evolution in the contrary +direction bringing it back to the state from which it started. Thus, +in the infinity of time, the life of the Universe proceeds without +real stop. + +This conception is, moreover, in accordance with the view certain +physicists take of the principle of Carnot. We shall see, for example, +that in the kinetic theory we are led to admit that, after waiting +sufficiently long, we can witness the return of the various states +through which a mass of gas, for example, has passed in its series of +transformations. + +If we keep to the present era, evolution has a fixed direction--that +which leads to an increase of entropy; and it is possible to enquire, +in any given system to what physical manifestations this increase +corresponds. We note that kinetic, potential, electrical, and chemical +forms of energy have a great tendency to transform themselves into +calorific energy. A chemical reaction, for example, gives out energy; +but if the reaction is not produced under very special conditions, +this energy immediately passes into the calorific form. This is so +true, that chemists currently speak of the heat given out by reactions +instead of regarding the energy disengaged in general. + +In all these transformations the calorific energy obtained has not, +from a practical point of view, the same value at which it started. +One cannot, in fact, according to the principle of Carnot, transform +it integrally into mechanical energy, since the heat possessed by a +body can only yield work on condition that a part of it falls on a +body with a lower temperature. Thus appears the idea that energies +which exchange with each other and correspond to equal quantities have +not the same qualitative value. Form has its importance, and there are +persons who prefer a golden louis to four pieces of five francs. The +principle of Carnot would thus lead us to consider a certain +classification of energies, and would show us that, in the +transformations possible, these energies always tend to a sort of +diminution of quality--that is, to a _degradation_. + +It would thus reintroduce an element of differentiation of which it +seems very difficult to give a mechanical explanation. Certain +philosophers and physicists see in this fact a reason which condemns +_a priori_ all attempts made to give a mechanical explanation of the +principle of Carnot. + +It is right, however, not to exaggerate the importance that should be +attributed to the phrase degraded energy. If the heat is not +equivalent to the work, if heat at 99° is not equivalent to heat at +100°, that means that we cannot in practice construct an engine which +shall transform all this heat into work, or that, for the same cold +source, the output is greater when the temperature of the hot source +is higher; but if it were possible that this cold source had itself +the temperature of absolute zero, the whole heat would reappear in the +form of work. The case here considered is an ideal and extreme case, +and we naturally cannot realize it; but this consideration suffices to +make it plain that the classification of energies is a little +arbitrary and depends more, perhaps, on the conditions in which +mankind lives than on the inmost nature of things. + +In fact, the attempts which have often been made to refer the +principle of Carnot to mechanics have not given convincing results. It +has nearly always been necessary to introduce into the attempt some +new hypothesis independent of the fundamental hypotheses of ordinary +mechanics, and equivalent, in reality, to one of the postulates on +which the ordinary exposition of the second law of thermodynamics is +founded. Helmholtz, in a justly celebrated theory, endeavoured to fit +the principle of Carnot into the principle of least action; but the +difficulties regarding the mechanical interpretation of the +irreversibility of physical phenomena remain entire. Looking at the +question, however, from the point of view at which the partisans of +the kinetic theories of matter place themselves, the principle is +viewed in a new aspect. Gibbs and afterwards Boltzmann and Professor +Planck have put forward some very interesting ideas on this subject. +By following the route they have traced, we come to consider the +principle as pointing out to us that a given system tends towards the +configuration presented by the maximum probability, and, numerically, +the entropy would even be the logarithm of this probability. Thus two +different gaseous masses, enclosed in two separate receptacles which +have just been placed in communication, diffuse themselves one through +the other, and it is highly improbable that, in their mutual shocks, +both kinds of molecules should take a distribution of velocities which +reduce them by a spontaneous phenomenon to the initial state. + +We should have to wait a very long time for so extraordinary a +concourse of circumstances, but, in strictness, it would not be +impossible. The principle would only be a law of probability. Yet this +probability is all the greater the more considerable is the number of +molecules itself. In the phenomena habitually dealt with, this number +is such that, practically, the variation of entropy in a constant +sense takes, so to speak, the character of absolute certainty. + +But there may be exceptional cases where the complexity of the system +becomes insufficient for the application of the principle of Carnot;-- +as in the case of the curious movements of small particles suspended +in a liquid which are known by the name of Brownian movements and can +be observed under the microscope. The agitation here really seems, as +M. Gouy has remarked, to be produced and continued indefinitely, +regardless of any difference in temperature; and we seem to witness +the incessant motion, in an isothermal medium, of the particles which +constitute matter. Perhaps, however, we find ourselves already in +conditions where the too great simplicity of the distribution of the +molecules deprives the principle of its value. + +M. Lippmann has in the same way shown that, on the kinetic hypothesis, +it is possible to construct such mechanisms that we can so take +cognizance of molecular movements that _vis viva_ can be taken from +them. The mechanisms of M. Lippmann are not, like the celebrated +apparatus at one time devised by Maxwell, purely hypothetical. They do +not suppose a partition with a hole impossible to be bored through +matter where the molecular spaces would be larger than the hole +itself. They have finite dimensions. Thus M. Lippmann considers a vase +full of oxygen at a constant temperature. In the interior of this vase +is placed a small copper ring, and the whole is set in a magnetic +field. The oxygen molecules are, as we know, magnetic, and when +passing through the interior of the ring they produce in this ring an +induced current. During this time, it is true, other molecules emerge +from the space enclosed by the circuit; but the two effects do not +counterbalance each other, and the resulting current is maintained. +There is elevation of temperature in the circuit in accordance with +Joule's law; and this phenomenon, under such conditions, is +incompatible with the principle of Carnot. + +It is possible--and that, I think, is M. Lippmann's idea--to draw from +his very ingenious criticism an objection to the kinetic theory, if we +admit the absolute value of the principle; but we may also suppose +that here again we are in presence of a system where the prescribed +conditions diminish the complexity and render it, consequently, less +probable that the evolution is always effected in the same direction. + +In whatever way you look at it, the principle of Carnot furnishes, in +the immense majority of cases, a very sure guide in which physicists +continue to have the most entire confidence. + + +§ 4. THERMODYNAMICS + +To apply the two fundamental principles of thermodynamics, various +methods may be employed, equivalent in the main, but presenting as the +cases vary a greater or less convenience. + +In recording, with the aid of the two quantities, energy and entropy, +the relations which translate analytically the two principles, we +obtain two relations between the coefficients which occur in a given +phenomenon; but it may be easier and also more suggestive to employ +various functions of these quantities. In a memoir, of which some +extracts appeared as early as 1869, a modest scholar, M. Massieu, +indicated in particular a remarkable function which he termed a +characteristic function, and by the employment of which calculations +are simplified in certain cases. + +In the same way J.W. Gibbs, in 1875 and 1878, then Helmholtz in 1882, +and, in France, M. Duhem, from the year 1886 onward, have published +works, at first ill understood, of which the renown was, however, +considerable in the sequel, and in which they made use of analogous +functions under the names of available energy, free energy, or +internal thermodynamic potential. The magnitude thus designated, +attaching, as a consequence of the two principles, to all states of +the system, is perfectly determined when the temperature and other +normal variables are known. It allows us, by calculations often very +easy, to fix the conditions necessary and sufficient for the +maintenance of the system in equilibrium by foreign bodies taken at +the same temperature as itself. + +One may hope to constitute in this way, as M. Duhem in a long and +remarkable series of operations has specially endeavoured to do, a +sort of general mechanics which will enable questions of statics to be +treated with accuracy, and all the conditions of equilibrium of the +system, including the calorific properties, to be determined. Thus, +ordinary statics teaches us that a liquid with its vapour on the top +forms a system in equilibrium, if we apply to the two fluids a +pressure depending on temperature alone. Thermodynamics will furnish +us, in addition, with the expression of the heat of vaporization and +of, the specific heats of the two saturated fluids. + +This new study has given us also most valuable information on +compressible fluids and on the theory of elastic equilibrium. Added to +certain hypotheses on electric or magnetic phenomena, it gives a +coherent whole from which can be deduced the conditions of electric or +magnetic equilibrium; and it illuminates with a brilliant light the +calorific laws of electrolytic phenomena. + +But the most indisputable triumph of this thermodynamic statics is the +discovery of the laws which regulate the changes of physical state or +of chemical constitution. J.W. Gibbs was the author of this immense +progress. His memoir, now celebrated, on "the equilibrium of +heterogeneous substances," concealed in 1876 in a review at that time +of limited circulation, and rather heavy to read, seemed only to +contain algebraic theorems applicable with difficulty to reality. It +is known that Helmholtz independently succeeded, a few years later, in +introducing thermodynamics into the domain of chemistry by his +conception of the division of energy into free and into bound energy: +the first, capable of undergoing all transformations, and particularly +of transforming itself into external action; the second, on the other +hand, bound, and only manifesting itself by giving out heat. When we +measure chemical energy, we ordinarily let it fall wholly into the +calorific form; but, in reality, it itself includes both parts, and it +is the variation of the free energy and not that of the total energy +measured by the integral disengagement of heat, the sign of which +determines the direction in which the reactions are effected. + +But if the principle thus enunciated by Helmholtz as a consequence of +the laws of thermodynamics is at bottom identical with that discovered +by Gibbs, it is more difficult of application and is presented under a +more mysterious aspect. It was not until M. Van der Waals exhumed the +memoir of Gibbs, when numerous physicists or chemists, most of them +Dutch--Professor Van t'Hoff, Bakhius Roozeboom, and others--utilized +the rules set forth in this memoir for the discussion of the most +complicated chemical reactions, that the extent of the new laws was +fully understood. + +The chief rule of Gibbs is the one so celebrated at the present day +under the name of the Phase Law. We know that by phases are designated +the homogeneous substances into which a system is divided; thus +carbonate of lime, lime, and carbonic acid gas are the three phases of +a system which comprises Iceland spar partially dissociated into lime +and carbonic acid gas. The number of phases added to the number of +independent components--that is to say, bodies whose mass is left +arbitrary by the chemical formulas of the substances entering into the +reaction--fixes the general form of the law of equilibrium of the +system; that is to say, the number of quantities which, by their +variations (temperature and pressure), would be of a nature to modify +its equilibrium by modifying the constitution of the phases. + +Several authors, M. Raveau in particular, have indeed given very +simple demonstrations of this law which are not based on +thermodynamics; but thermodynamics, which led to its discovery, +continues to give it its true scope. Moreover, it would not suffice +merely to determine quantitatively those laws of which it makes known +the general form. We must, if we wish to penetrate deeper into +details, particularize the hypothesis, and admit, for instance, with +Gibbs that we are dealing with perfect gases; while, thanks to +thermodynamics, we can constitute a complete theory of dissociation +which leads to formulas in complete accord with the numerical results +of the experiment. We can thus follow closely all questions concerning +the displacements of the equilibrium, and find a relation of the first +importance between the masses of the bodies which react in order to +constitute a system in equilibrium. + +The statics thus constructed constitutes at the present day an +important edifice to be henceforth classed amongst historical +monuments. Some theorists even wish to go a step beyond. They have +attempted to begin by the same means a more complete study of those +systems whose state changes from one moment to another. This is, +moreover, a study which is necessary to complete satisfactorily the +study of equilibrium itself; for without it grave doubts would exist +as to the conditions of stability, and it alone can give their true +meaning to questions relating to displacements of equilibrium. + +The problems with which we are thus confronted are singularly +difficult. M. Duhem has given us many excellent examples of the +fecundity of the method; but if thermodynamic statics may be +considered definitely founded, it cannot be said that the general +dynamics of systems, considered as the study of thermal movements and +variations, are yet as solidly established. + + +§ 5. ATOMISM + +It may appear singularly paradoxical that, in a chapter devoted to +general views on the principles of physics, a few words should be +introduced on the atomic theories of matter. + +Very often, in fact, what is called the physics of principles is set +in opposition to the hypotheses on the constitution of matter, +particularly to atomic theories. I have already said that, abandoning +the investigation of the unfathomable mystery of the constitution of +the Universe, some physicists think they may find, in certain general +principles, sufficient guides to conduct them across the physical +world. But I have also said, in examining the history of those +principles, that if they are to-day considered experimental truths, +independent of all theories relating to matter, they have, in fact, +nearly all been discovered by scholars who relied on molecular +hypotheses: and the question suggests itself whether this is mere +chance, or whether this chance may not be ordained by higher reasons. + +In a very profound work which appeared a few years ago, entitled +_Essai critique sur l'hypothese des atomes_, M. Hannequin, a +philosopher who is also an erudite scholar, examined the part taken by +atomism in the history of science. He notes that atomism and science +were born, in Greece, of the same problem, and that in modern times +the revival of the one was closely connected with that of the other. +He shows, too, by very close analysis, that the atomic hypothesis is +essential to the optics of Fresnel and of Cauchy; that it penetrates +into the study of heat; and that, in its general features, it presided +at the birth of modern chemistry and is linked with all its progress. +He concludes that it is, in a manner, the soul of our knowledge of +Nature, and that contemporary theories are on this point in accord +with history: for these theories consecrate the preponderance of this +hypothesis in the domain of science. + +If M. Hannequin had not been prematurely cut off in the full expansion +of his vigorous talent, he might have added another chapter to his +excellent book. He would have witnessed a prodigious budding of +atomistic ideas, accompanied, it is true, by wide modifications in the +manner in which the atom is to be regarded, since the most recent +theories make material atoms into centres constituted of atoms of +electricity. On the other hand, he would have found in the bursting +forth of these new doctrines one more proof in support of his idea +that science is indissolubly bound to atomism. + +From the philosophical point of view, M. Hannequin, examining the +reasons which may have called these links into being, arrives at the +idea that they necessarily proceed from the constitution of our +knowledge, or, perhaps, from that of Nature itself. Moreover, this +origin, double in appearance, is single at bottom. Our minds could +not, in fact, detach and come out of themselves to grasp reality and +the absolute in Nature. According to the idea of Descartes, it is the +destiny of our minds only to take hold of and to understand that which +proceeds from them. + +Thus atomism, which is, perhaps, only an appearance containing even +some contradictions, is yet a well-founded appearance, since it +conforms to the laws of our minds; and this hypothesis is, in a way, +necessary. + +We may dispute the conclusions of M. Hannequin, but no one will refuse +to recognise, as he does, that atomic theories occupy a preponderating +part in the doctrines of physics; and the position which they have +thus conquered gives them, in a way, the right of saying that they +rest on a real principle. It is in order to recognise this right that +several physicists--M. Langevin, for example--ask that atoms be +promoted from the rank of hypotheses to that of principles. By this +they mean that the atomistic ideas forced upon us by an almost +obligatory induction based on very exact experiments, enable us to +co-ordinate a considerable amount of facts, to construct a very general +synthesis, and to foresee a great number of phenomena. + +It is of moment, moreover, to thoroughly understand that atomism does +not necessarily set up the hypothesis of centres of attraction acting +at a distance, and it must not be confused with molecular physics, +which has, on the other hand, undergone very serious checks. The +molecular physics greatly in favour some fifty years ago leads to such +complex representations and to solutions often so undetermined, that +the most courageous are wearied with upholding it and it has fallen +into some discredit. It rested on the fundamental principles of +mechanics applied to molecular actions; and that was, no doubt, an +extension legitimate enough, since mechanics is itself only an +experimental science, and its principles, established for the +movements of matter taken as a whole, should not be applied outside +the domain which belongs to them. Atomism, in fact, tends more and +more, in modern theories, to imitate the principle of the conservation +of energy or that of entropy, to disengage itself from the artificial +bonds which attached it to mechanics, and to put itself forward as an +independent principle. + +Atomistic ideas also have undergone evolution, and this slow evolution +has been considerably quickened under the influence of modern +discoveries. These reach back to the most remote antiquity, and to +follow their development we should have to write the history of human +thought which they have always accompanied since the time of +Leucippus, Democritus, Epicurus, and Lucretius. The first observers +who noticed that the volume of a body could be diminished by +compression or cold, or augmented by heat, and who saw a soluble solid +body mix completely with the water which dissolved it, must have been +compelled to suppose that matter was not dispersed continuously +throughout the space it seemed to occupy. They were thus brought to +consider it discontinuous, and to admit that a substance having the +same composition and the same properties in all its parts--in a word, +perfectly homogeneous--ceases to present this homogeneity when +considered within a sufficiently small volume. + +Modern experimenters have succeeded by direct experiments in placing +in evidence this heterogeneous character of matter when taken in small +mass. Thus, for example, the superficial tension, which is constant +for the same liquid at a given temperature, no longer has the same +value when the thickness of the layer of liquid becomes extremely +small. Newton noticed even in his time that a dark zone is seen to +form on a soap bubble at the moment when it becomes so thin that it +must burst. Professor Reinold and Sir Arthur Rücker have shown that +this zone is no longer exactly spherical; and from this we must +conclude that the superficial tension, constant for all thicknesses +above a certain limit, commences to vary when the thickness falls +below a critical value, which these authors estimate, on optical +grounds, at about fifty millionths of a millimetre. + +From experiments on capillarity, Prof. Quincke has obtained similar +results with regard to layers of solids. But it is not only capillary +properties which allow this characteristic to be revealed. All the +properties of a body are modified when taken in small mass; M. Meslin +proves this in a very ingenious way as regards optical properties, and +Mr Vincent in respect of electric conductivity. M. Houllevigue, who, +in a chapter of his excellent work, _Du Laboratoire à l'Usine_, has +very clearly set forth the most interesting considerations on atomic +hypotheses, has recently demonstrated that copper and silver cease to +combine with iodine as soon as they are present in a thickness of less +than thirty millionths of a millimetre. It is this same dimension +likewise that is possessed, according to M. Wiener, by the smallest +thicknesses it is possible to deposit on glass. These layers are so +thin that they cannot be perceived, but their presence is revealed by +a change in the properties of the light reflected by them. + +Thus, below fifty to thirty millionths of a millimetre the properties +of matter depend on its thickness. There are then, no doubt, only a +few molecules to be met with, and it may be concluded, in consequence, +that the discontinuous elements of bodies--that is, the molecules-- +have linear dimensions of the order of magnitude of the millionth of a +millimetre. Considerations regarding more complex phenomena, for +instance the phenomena of electricity by contact, and also the kinetic +theory of gases, bring us to the same conclusion. + +The idea of the discontinuity of matter forces itself upon us for many +other reasons. All modern chemistry is founded on this principle; and +laws like the law of multiple proportions, introduce an evident +discontinuity to which we find analogies in the law of electrolysis. +The elements of bodies we are thus brought to regard might, as regards +solids at all events, be considered as immobile; but this immobility +could not explain the phenomena of heat, and, as it is entirely +inadmissible for gases, it seems very improbable it can absolutely +occur in any state. We are thus led to suppose that these elements are +animated by very complicated movements, each one proceeding in closed +trajectories in which the least variations of temperature or pressure +cause modifications. + +The atomistic hypothesis shows itself remarkably fecund in the study +of phenomena produced in gases, and here the mutual independence of +the particles renders the question relatively more simple and, +perhaps, allows the principles of mechanics to be more certainly +extended to the movements of molecules. + +The kinetic theory of gases can point to unquestioned successes; and +the idea of Daniel Bernouilli, who, as early as 1738, considered a +gaseous mass to be formed of a considerable number of molecules +animated by rapid movements of translation, has been put into a form +precise enough for mathematical analysis, and we have thus found +ourselves in a position to construct a really solid foundation. It +will be at once conceived, on this hypothesis, that pressure is the +resultant of the shocks of the molecules against the walls of the +containing vessel, and we at once come to the demonstration that the +law of Mariotte is a natural consequence of this origin of pressure; +since, if the volume occupied by a certain number of molecules is +doubled, the number of shocks per second on each square centimetre of +the walls becomes half as much. But if we attempt to carry this +further, we find ourselves in presence of a serious difficulty. It is +impossible to mentally follow every one of the many individual +molecules which compose even a very limited mass of gas. The path +followed by this molecule may be every instant modified by the chance +of running against another, or by a shock which may make it rebound in +another direction. + +The difficulty would be insoluble if chance had not laws of its own. +It was Maxwell who first thought of introducing into the kinetic +theory the calculation of probabilities. Willard Gibbs and Boltzmann +later on developed this idea, and have founded a statistical method +which does not, perhaps, give absolute certainty, but which is +certainly most interesting and curious. Molecules are grouped in such +a way that those belonging to the same group may be considered as +having the same state of movement; then an examination is made of the +number of molecules in each group, and what are the changes in this +number from one moment to another. It is thus often possible to +determine the part which the different groups have in the total +properties of the system and in the phenomena which may occur. + +Such a method, analogous to the one employed by statisticians for +following the social phenomena in a population, is all the more +legitimate the greater the number of individuals counted in the +averages; now, the number of molecules contained in a limited space-- +for example, in a centimetre cube taken in normal conditions--is such +that no population could ever attain so high a figure. All +considerations, those we have indicated as well as others which might +be invoked (for example, the recent researches of M. Spring on the +limit of visibility of fluorescence), give this result:--that there +are, in this space, some twenty thousand millions of molecules. Each +of these must receive in the space of a millimetre about ten thousand +shocks, and be ten thousand times thrust out of its course. The free +path of a molecule is then very small, but it can be singularly +augmented by diminishing the number of them. Tait and Dewar have +calculated that, in a good modern vacuum, the length of the free path +of the remaining molecules not taken away by the air-pump easily +reaches a few centimetres. + +By developing this theory, we come to consider that, for a given +temperature, every molecule (and even every individual particle, atom, +or ion) which takes part in the movement has, on the average, the same +kinetic energy in every body, and that this energy is proportional to +the absolute temperature; so that it is represented by this +temperature multiplied by a constant quantity which is a universal +constant. + +This result is not an hypothesis but a very great probability. This +probability increases when it is noted that the same value for the +constant is met with in the study of very varied phenomena; for +example, in certain theories on radiation. Knowing the mass and energy +of a molecule, it is easy to calculate its speed; and we find that the +average speed is about 400 metres per second for carbonic anhydride, +500 for nitrogen, and 1850 for hydrogen at 0° C. and at ordinary +pressure. I shall have occasion, later on, to speak of much more +considerable speeds than these as animating other particles. + +The kinetic theory has permitted the diffusion of gases to be +explained, and the divers circumstances of the phenomenon to be +calculated. It has allowed us to show, as M. Brillouin has done, that +the coefficient of diffusion of two gases does not depend on the +proportion of the gases in the mixture; it gives a very striking image +of the phenomena of viscosity and conductivity; and it leads us to +think that the coefficients of friction and of conductivity are +independent of the density; while all these previsions have been +verified by experiment. It has also invaded optics; and by relying on +the principle of Doppler, Professor Michelson has succeeded in +obtaining from it an explanation of the length presented by the +spectral rays of even the most rarefied gases. + +But however interesting are these results, they would not have +sufficed to overcome the repugnance of certain physicists for +speculations which, an imposing mathematical baggage notwithstanding, +seemed to them too hypothetical. The theory, moreover, stopped at the +molecule, and appeared to suggest no idea which could lead to the +discovery of the key to the phenomena where molecules exercise a +mutual influence on each other. The kinetic hypothesis, therefore, +remained in some disfavour with a great number of persons, +particularly in France, until the last few years, when all the recent +discoveries of the conductivity of gases and of the new radiations +came to procure for it a new and luxuriant efflorescence. It may be +said that the atomistic synthesis, but yesterday so decried, is to-day +triumphant. + +The elements which enter into the earlier kinetic theory, and which, +to avoid confusion, should be always designated by the name of +molecules, were not, truth to say, in the eyes of the chemists, the +final term of the divisibility of matter. It is well known that, to +them, except in certain particular bodies like the vapour of mercury +and argon, the molecule comprises several atoms, and that, in compound +bodies, the number of these atoms may even be fairly considerable. But +physicists rarely needed to have recourse to the consideration of +these atoms. They spoke of them to explain certain particularities of +the propagation of sound, and to enunciate laws relating to specific +heats; but, in general, they stopped at the consideration of the +molecule. + +The present theories carry the division much further. I shall not +dwell now on these theories, since, in order to thoroughly understand +them, many other facts must be examined. But to avoid all confusion, +it remains understood that, contrary, no doubt, to etymology, but in +conformity with present custom, I shall continue in what follows to +call atoms those particles of matter which have till now been spoken +of; these atoms being themselves, according to modern views, +singularly complex edifices formed of elements, of which we shall have +occasion to indicate the nature later. + + + + +CHAPTER IV + +THE VARIOUS STATES OF MATTER + + +§ 1. THE STATICS OF FLUIDS + +The division of bodies into gaseous, liquid, and solid, and the +distinction established for the same substance between the three +states, retain a great importance for the applications and usages of +daily life, but have long since lost their absolute value from the +scientific point of view. + +So far as concerns the liquid and gaseous states particularly, the +already antiquated researches of Andrews confirmed the ideas of +Cagniard de la Tour and established the continuity of the two states. +A group of physical studies has thus been constituted on what may be +called the statics of fluids, in which we examine the relations +existing between the pressure, the volume, and the temperature of +bodies, and in which are comprised, under the term fluid, gases as +well as liquids. + +These researches deserve attention by their interest and the +generality of the results to which they have led. They also give a +remarkable example of the happy effects which may be obtained by the +combined employment of the various methods of investigation used in +exploring the domain of nature. Thermodynamics has, in fact, allowed +us to obtain numerical relations between the various coefficients, and +atomic hypotheses have led to the establishment of one capital +relation, the characteristic equation of fluids; while, on the other +hand, experiment in which the progress made in the art of measurement +has been utilized, has furnished the most valuable information on all +the laws of compressibility and dilatation. + +The classical work of Andrews was not very wide. Andrews did not go +much beyond pressures close to the normal and ordinary temperatures. +Of late years several very interesting and peculiar cases have been +examined by MM. Cailletet, Mathias, Batelli, Leduc, P. Chappuis, and +other physicists. Sir W. Ramsay and Mr S. Young have made known the +isothermal diagrams[6] of a certain number of liquid bodies at the +ordinary temperature. They have thus been able, while keeping to +somewhat restricted limits of temperature and pressure, to touch upon +the most important questions, since they found themselves in the +region of the saturation curve and of the critical point. + +[Footnote 6: By isothermal diagram is meant the pattern or complex +formed when the isothermal lines are arranged in curves of which the +pressure is the ordinate and the volume the abscissa.--ED.] + +But the most complete and systematic body of researches is due to M. +Amagat, who undertook the study of a certain number of bodies, some +liquid and some gaseous, extending the scope of his experiments so as +to embrace the different phases of the phenomena and to compare +together, not only the results relating to the same bodies, but also +those concerning different bodies which happen to be in the same +conditions of temperature and pressure, but in very different +conditions as regards their critical points. + +From the experimental point of view, M. Amagat has been able, with +extreme skill, to conquer the most serious difficulties. He has +managed to measure with precision pressures amounting to 3000 +atmospheres, and also the very small volumes then occupied by the +fluid mass under consideration. This last measurement, which +necessitates numerous corrections, is the most delicate part of the +operation. These researches have dealt with a certain number of +different bodies. Those relating to carbonic acid and ethylene take in +the critical point. Others, on hydrogen and nitrogen, for instance, +are very extended. Others, again, such as the study of the +compressibility of water, have a special interest, on account of the +peculiar properties of this substance. M. Amagat, by a very concise +discussion of the experiments, has also been able to definitely +establish the laws of compressibility and dilatation of fluids under +constant pressure, and to determine the value of the various +coefficients as well as their variations. It ought to be possible to +condense all these results into a single formula representing the +volume, the temperature, and the pressure. Rankin and, subsequently, +Recknagel, and then Hirn, formerly proposed formulas of that kind; but +the most famous, the one which first appeared to contain in a +satisfactory manner all the facts which experiments brought to light +and led to the production of many others, was the celebrated equation +of Van der Waals. + +Professor Van der Waals arrived at this relation by relying upon +considerations derived from the kinetic theory of gases. If we keep to +the simple idea at the bottom of this theory, we at once demonstrate +that the gas ought to obey the laws of Mariotte and of Gay-Lussac, so +that the characteristic equation would be obtained by the statement +that the product of the number which is the measure of the volume by +that which is the measure of the pressure is equal to a constant +coefficient multiplied by the degree of the absolute temperature. But +to get at this result we neglect two important factors. + +We do not take into account, in fact, the attraction which the +molecules must exercise on each other. Now, this attraction, which is +never absolutely non-existent, may become considerable when the +molecules are drawn closer together; that is to say, when the +compressed gaseous mass occupies a more and more restricted volume. On +the other hand, we assimilate the molecules, as a first approximation, +to material points without dimensions; in the evaluation of the path +traversed by each molecule no notice is taken of the fact that, at the +moment of the shock, their centres of gravity are still separated by a +distance equal to twice the radius of the molecule. + +M. Van der Waals has sought out the modifications which must be +introduced into the simple characteristic equation to bring it nearer +to reality. He extends to the case of gases the considerations by +which Laplace, in his famous theory of capillarity, reduced the effect +of the molecular attraction to a perpendicular pressure exercised on +the surface of a liquid. This leads him to add to the external +pressure, that due to the reciprocal attractions of the gaseous +particles. On the other hand, when we attribute finite dimensions to +these particles, we must give a higher value to the number of shocks +produced in a given time, since the effect of these dimensions is to +diminish the mean path they traverse in the time which elapses between +two consecutive shocks. + +The calculation thus pursued leads to our adding to the pressure in +the simple equation a term which is designated the internal pressure, +and which is the quotient of a constant by the square of the volume; +also to our deducting from the volume a constant which is the +quadruple of the total and invariable volume which the gaseous +molecules would occupy did they touch one another. + +The experiments fit in fairly well with the formula of Van der Waals, +but considerable discrepancies occur when we extend its limits, +particularly when the pressures throughout a rather wider interval are +considered; so that other and rather more complex formulas, on which +there is no advantage in dwelling, have been proposed, and, in certain +cases, better represent the facts. + +But the most remarkable result of M. Van der Waals' calculations is +the discovery of corresponding states. For a long time physicists +spoke of bodies taken in a comparable state. Dalton, for example, +pointed out that liquids have vapour-pressures equal to the +temperatures equally distant from their boiling-point; but that if, in +this particular property, liquids were comparable under these +conditions of temperature, as regards other properties the parallelism +was no longer to be verified. No general rule was found until M. Van +der Waals first enunciated a primary law, viz., that if the pressure, +the volume, and the temperature are estimated by taking as units the +critical quantities, the constants special to each body disappear in +the characteristic equation, which thus becomes the same for all +fluids. + +The words corresponding states thus take a perfectly precise +signification. Corresponding states are those for which the numerical +values of the pressure, volume, and temperature, expressed by taking +as units the values corresponding to the critical point, are equal; +and, in corresponding states any two fluids have exactly the same +properties. + +M. Natanson, and subsequently P. Curie and M. Meslin, have shown by +various considerations that the same result may be arrived at by +choosing units which correspond to any corresponding states; it has +also been shown that the theorem of corresponding states in no way +implies the exactitude of Van der Waals' formula. In reality, this is +simply due to the fact that the characteristic equation only contains +three constants. + +The philosophical importance and the practical interest of the +discovery nevertheless remain considerable. As was to be expected, +numbers of experimenters have sought whether these consequences are +duly verified in reality. M. Amagat, particularly, has made use for +this purpose of a most original and simple method. He remarks that, in +all its generality, the law may be translated thus: If the isothermal +diagrams of two substances be drawn to the same scale, taking as unit +of volume and of pressure the values of the critical constants, the +two diagrams should coincide; that is to say, their superposition +should present the aspect of one diagram appertaining to a single +substance. Further, if we possess the diagrams of two bodies drawn to +any scales and referable to any units whatever, as the changes of +units mean changes in the scale of the axes, we ought to make one of +the diagrams similar to the other by lengthening or shortening it in +the direction of one of the axes. M. Amagat then photographs two +isothermal diagrams, leaving one fixed, but arranging the other so +that it may be free to turn round each axis of the co-ordinates; and +by projecting, by means of a magic lantern, the second on the first, +he arrives in certain cases at an almost complete coincidence. + +This mechanical means of proof thus dispenses with laborious +calculations, but its sensibility is unequally distributed over the +different regions of the diagram. M. Raveau has pointed out an equally +simple way of verifying the law, by remarking that if the logarithms +of the pressure and volume are taken as co-ordinates, the co-ordinates +of two corresponding points differ by two constant quantities, and the +corresponding curves are identical. + +From these comparisons, and from other important researches, among +which should be particularly mentioned those of Mr S. Young and M. +Mathias, it results that the laws of corresponding states have not, +unfortunately, the degree of generality which we at first attributed +to them, but that they are satisfactory when applied to certain groups +of bodies.[7] + +[Footnote 7: Mr Preston thus puts it: "The law [of corresponding +states] seems to be not quite, but very nearly true for these +substances [_i.e._ the halogen derivatives of benzene]; but in the +case of the other substances examined, the majority of these +generalizations were either only roughly true or altogether departed +from" (_Theory of Heat_, London, 1904, p. 514.)--ED.] + +If in the study of the statics of a simple fluid the experimental +results are already complex, we ought to expect much greater +difficulties when we come to deal with mixtures; still the problem has +been approached, and many points are already cleared up. + +Mixed fluids may first of all be regarded as composed of a large +number of invariable particles. In this particularly simple case M. +Van der Waals has established a characteristic equation of the +mixtures which is founded on mechanical considerations. Various +verifications of this formula have been effected, and it has, in +particular, been the object of very important remarks by M. Daniel +Berthelot. + +It is interesting to note that thermodynamics seems powerless to +determine this equation, for it does not trouble itself about the +nature of the bodies obedient to its laws; but, on the other hand, it +intervenes to determine the properties of coexisting phases. If we +examine the conditions of equilibrium of a mixture which is not +subjected to external forces, it will be demonstrated that the +distribution must come back to a juxtaposition of homogeneous phases; +in a given volume, matter ought so to arrange itself that the total +sum of free energy has a minimum value. Thus, in order to elucidate +all questions relating to the number and qualities of the phases into +which the substance divides itself, we are led to regard the +geometrical surface which for a given temperature represents the free +energy. + +I am unable to enter here into the detail of the questions connected +with the theories of Gibbs, which have been the object of numerous +theoretical studies, and also of a series, ever more and more +abundant, of experimental researches. M. Duhem, in particular, has +published, on the subject, memoirs of the highest importance, and a +great number of experimenters, mostly scholars working in the physical +laboratory of Leyden under the guidance of the Director, Mr Kamerlingh +Onnes, have endeavoured to verify the anticipations of the theory. + +We are a little less advanced as regards abnormal substances; that is +to say, those composed of molecules, partly simple and partly complex, +and either dissociated or associated. These cases must naturally be +governed by very complex laws. Recent researches by MM. Van der Waals, +Alexeif, Rothmund, Künen, Lehfeld, etc., throw, however, some light on +the question. + +The daily more numerous applications of the laws of corresponding +states have rendered highly important the determination of the +critical constants which permit these states to be defined. In the +case of homogeneous bodies the critical elements have a simple, clear, +and precise sense; the critical temperature is that of the single +isothermal line which presents a point of inflexion at a horizontal +tangent; the critical pressure and the critical volume are the two +co-ordinates of this point of inflexion. + +The three critical constants may be determined, as Mr S. Young and M. +Amagat have shown, by a direct method based on the consideration of +the saturated states. Results, perhaps more precise, may also be +obtained if one keeps to two constants or even to a single one-- +temperature, for example--by employing various special methods. Many +others, MM. Cailletet and Colardeau, M. Young, M.J. Chappuis, etc., +have proceeded thus. + +The case of mixtures is much more complicated. A binary mixture has a +critical space instead of a critical point. This space is comprised +between two extreme temperatures, the lower corresponding to what is +called the folding point, the higher to that which we call the point +of contact of the mixture. Between these two temperatures an +isothermal compression yields a quantity of liquid which increases, +then reaches a maximum, diminishes, and disappears. This is the +phenomenon of retrograde condensation. We may say that the properties +of the critical point of a homogeneous substance are, in a way, +divided, when it is a question of a binary mixture, between the two +points mentioned. + +Calculation has enabled M. Van der Waals, by the application of his +kinetic theories, and M. Duhem, by means of thermodynamics, to foresee +most of the results which have since been verified by experiment. All +these facts have been admirably set forth and systematically +co-ordinated by M. Mathias, who, by his own researches, moreover, has +made contributions of the highest value to the study of questions +regarding the continuity of the liquid and gaseous states. + +The further knowledge of critical elements has allowed the laws of +corresponding states to be more closely examined in the case of +homogeneous substances. It has shown that, as I have already said, +bodies must be arranged in groups, and this fact clearly proves that +the properties of a given fluid are not determined by its critical +constants alone, and that it is necessary to add to them some other +specific parameters; M. Mathias and M. D. Berthelot have indicated +some which seem to play a considerable part. + +It results also from this that the characteristic equation of a fluid +cannot yet be considered perfectly known. Neither the equation of Van +der Waals nor the more complicated formulas which have been proposed +by various authors are in perfect conformity with reality. We may +think that researches of this kind will only be successful if +attention is concentrated, not only on the phenomena of +compressibility and dilatation, but also on the calorimetric +properties of bodies. Thermodynamics indeed establishes relations +between those properties and other constants, but does not allow +everything to be foreseen. + +Several physicists have effected very interesting calorimetric +measurements, either, like M. Perot, in order to verify Clapeyron's +formula regarding the heat of vaporization, or to ascertain the values +of specific heats and their variations when the temperature or the +pressure happens to change. M. Mathias has even succeeded in +completely determining the specific heats of liquefied gases and of +their saturated vapours, as well as the heat of internal and external +vaporization. + + +§ 2. THE LIQUEFACTION OF GASES, AND THE PROPERTIES OF BODIES AT A + LOW TEMPERATURE + +The scientific advantages of all these researches have been great, +and, as nearly always happens, the practical consequences derived from +them have also been most important. It is owing to the more complete +knowledge of the general properties of fluids that immense progress +has been made these last few years in the methods of liquefying gases. + +From a theoretical point of view the new processes of liquefaction can +be classed in two categories. Linde's machine and those resembling it +utilize, as is known, expansion without any notable production of +external work. This expansion, nevertheless, causes a fall in the +temperature, because the gas in the experiment is not a perfect gas, +and, by an ingenious process, the refrigerations produced are made +cumulative. + +Several physicists have proposed to employ a method whereby +liquefaction should be obtained by expansion with recuperable external +work. This method, proposed as long ago as 1860 by Siemens, would +offer considerable advantages. Theoretically, the liquefaction would +be more rapid, and obtained much more economically; but unfortunately +in the experiment serious obstacles are met with, especially from the +difficulty of obtaining a suitable lubricant under intense cold for +those parts of the machine which have to be in movement if the +apparatus is to work. + +M. Claude has recently made great progress on this point by the use, +during the running of the machine, of the ether of petrol, which is +uncongealable, and a good lubricant for the moving parts. When once +the desired region of cold is reached, air itself is used, which +moistens the metals but does not completely avoid friction; so that +the results would have remained only middling, had not this ingenious +physicist devised a new improvement which has some analogy with +superheating of steam in steam engines. He slightly varies the initial +temperature of the compressed air on the verge of liquefaction so as +to avoid a zone of deep perturbations in the properties of fluids, +which would make the work of expansion very feeble and the cold +produced consequently slight. This improvement, simple as it is in +appearance, presents several other advantages which immediately treble +the output. + +The special object of M. Claude was to obtain oxygen in a practical +manner by the actual distillation of liquid air. Since nitrogen boils +at -194° and oxygen at -180.5° C., if liquid air be evaporated, the +nitrogen escapes, especially at the commencement of the evaporation, +while the oxygen concentrates in the residual liquid, which finally +consists of pure oxygen, while at the same time the temperature rises +to the boiling-point (-180.5° C.) of oxygen. But liquid air is costly, +and if one were content to evaporate it for the purpose of collecting +a part of the oxygen in the residuum, the process would have a very +poor result from the commercial point of view. As early as 1892, Mr +Parkinson thought of improving the output by recovering the cold +produced by liquid air during its evaporation; but an incorrect idea, +which seems to have resulted from certain experiments of Dewar--the +idea that the phenomenon of the liquefaction of air would not be, +owing to certain peculiarities, the exact converse of that of +vaporization--led to the employment of very imperfect apparatus. M. +Claude, however, by making use of a method which he calls the +reversal[8] method, obtains a complete rectification in a remarkably +simple manner and under extremely advantageous economic conditions. +Apparatus, of surprisingly reduced dimensions but of great efficiency, +is now in daily work, which easily enables more than a thousand cubic +metres of oxygen to be obtained at the rate, per horse-power, of more +than a cubic metre per hour. + +[Footnote 8: Methode avec retour en arriere.--ED] + +It is in England, thanks to the skill of Sir James Dewar and his +pupils--thanks also, it must be said, to the generosity of the Royal +Institution, which has devoted considerable sums to these costly +experiments--that the most numerous and systematic researches have +been effected on the production of intense cold. I shall here note +only the more important results, especially those relating to the +properties of bodies at low temperatures. + +Their electrical properties, in particular, undergo some interesting +modifications. The order which metals assume in point of conductivity +is no longer the same as at ordinary temperatures. Thus at -200° C. +copper is a better conductor than silver. The resistance diminishes +with the temperature, and, down to about -200°, this diminution is +almost linear, and it would seem that the resistance tends towards +zero when the temperature approaches the absolute zero. But, after +-200°, the pattern of the curves changes, and it is easy to foresee +that at absolute zero the resistivities of all metals would still +have, contrary to what was formerly supposed, a notable value. +Solidified electrolytes which, at temperatures far below their fusion +point, still retain a very appreciable conductivity, become, on the +contrary, perfect insulators at low temperatures. Their dielectric +constants assume relatively high values. MM. Curie and Compan, who +have studied this question from their own point of view, have noted, +moreover, that the specific inductive capacity changes considerably +with the temperature. + +In the same way, magnetic properties have been studied. A very +interesting result is that found in oxygen: the magnetic +susceptibility of this body increases at the moment of liquefaction. +Nevertheless, this increase, which is enormous (since the +susceptibility becomes sixteen hundred times greater than it was at +first), if we take it in connection with equal volumes, is much less +considerable if taken in equal masses. It must be concluded from this +fact that the magnetic properties apparently do not belong to the +molecules themselves, but depend on their state of aggregation. + +The mechanical properties of bodies also undergo important +modifications. In general, their cohesion is greatly increased, and +the dilatation produced by slight changes of temperature is +considerable. Sir James Dewar has effected careful measurements of the +dilatation of certain bodies at low temperatures: for example, of ice. +Changes in colour occur, and vermilion and iodide of mercury pass into +pale orange. Phosphorescence becomes more intense, and most bodies of +complex structure--milk, eggs, feathers, cotton, and flowers--become +phosphorescent. The same is the case with certain simple bodies, such +as oxygen, which is transformed into ozone and emits a white light in +the process. + +Chemical affinity is almost put an end to; phosphorus and potassium +remain inert in liquid oxygen. It should, however, be noted, and this +remark has doubtless some interest for the theories of photographic +action, that photographic substances retain, even at the temperature +of liquid hydrogen, a very considerable part of their sensitiveness to +light. + +Sir James Dewar has made some important applications of low +temperatures in chemical analysis; he also utilizes them to create a +vacuum. His researches have, in fact, proved that the pressure of air +congealed by liquid hydrogen cannot exceed the millionth of an +atmosphere. We have, then, in this process, an original and rapid +means of creating an excellent vacuum in apparatus of very different +kinds--a means which, in certain cases, may be particularly +convenient.[9] + +[Footnote 9: Professor Soddy, in a paper read before the Royal Society +on the 15th November 1906, warns experimenters against vacua created +by charcoal cooled in liquid air (the method referred-to in the text), +unless as much of the air as possible is first removed with a pump and +replaced by some argon-free gas. According to him, neither helium nor +argon is absorbed by charcoal. By the use of electrically-heated +calcium, he claims to have produced an almost perfect vacuum.--ED.] + +Thanks to these studies, a considerable field has been opened up for +biological research, but in this, which is not our subject, I shall +notice one point only. It has been proved that vital germs--bacteria, +for example--may be kept for seven days at -190°C. without their +vitality being modified. Phosphorescent organisms cease, it is true, +to shine at the temperature of liquid air, but this fact is simply due +to the oxidations and other chemical reactions which keep up the +phosphorescence being then suspended, for phosphorescent activity +reappears so soon as the temperature is again sufficiently raised. An +important conclusion has been drawn from these experiments which +affects cosmogonical theories: since the cold of space could not kill +the germs of life, it is in no way absurd to suppose that, under +proper conditions, a germ may be transmitted from one planet to +another. + +Among the discoveries made with the new processes, the one which most +strikingly interested public attention is that of new gases in the +atmosphere. We know how Sir William Ramsay and Dr. Travers first +observed by means of the spectroscope the characteristics of the +_companions_ of argon in the least volatile part of the atmosphere. +Sir James Dewar on the one hand, and Sir William Ramsay on the other, +subsequently separated in addition to argon and helium, crypton, +xenon, and neon. The process employed consists essentially in first +solidifying the least volatile part of the air and then causing it to +evaporate with extreme slowness. A tube with electrodes enables the +spectrum of the gas in process of distillation to be observed. In this +manner, the spectra of the various gases may be seen following one +another in the inverse order of their volatility. All these gases are +monoatomic, like mercury; that is to say, they are in the most simple +state, they possess no internal molecular energy (unless it is that +which heat is capable of supplying), and they even seem to have no +chemical energy. Everything leads to the belief that they show the +existence on the earth of an earlier state of things now vanished. It +may be supposed, for instance, that helium and neon, of which the +molecular mass is very slight, were formerly more abundant on our +planet; but at an epoch when the temperature of the globe was higher, +the very speed of their molecules may have reached a considerable +value, exceeding, for instance, eleven kilometres per second, which +suffices to explain why they should have left our atmosphere. Crypton +and neon, which have a density four times greater than oxygen, may, on +the contrary, have partly disappeared by solution at the bottom of the +sea, where it is not absurd to suppose that considerable quantities +would be found liquefied at great depths.[10] + +[Footnote 10: Another view, viz. that these inert gases are a kind of +waste product of radioactive changes, is also gaining ground. The +discovery of the radioactive mineral malacone, which gives off both +helium and argon, goes to support this. See Messrs Ketchin and +Winterson's paper on the subject at the Chemical Society, 18th October +1906.--ED.] + +It is probable, moreover, that the higher regions of the atmosphere +are not composed of the same air as that around us. Sir James Dewar +points out that Dalton's law demands that every gas composing the +atmosphere should have, at all heights and temperatures, the same +pressure as if it were alone, the pressure decreasing the less +quickly, all things being equal, as its density becomes less. It +results from this that the temperature becoming gradually lower as we +rise in the atmosphere, at a certain altitude there can no longer +remain any traces of oxygen or nitrogen, which no doubt liquefy, and +the atmosphere must be almost exclusively composed of the most +volatile gases, including hydrogen, which M.A. Gautier has, like Lord +Rayleigh and Sir William Ramsay, proved to exist in the air. The +spectrum of the _Aurora borealis_, in which are found the lines of +those parts of the atmosphere which cannot be liquefied in liquid +hydrogen, together with the lines of argon, crypton, and xenon, is +quite in conformity with this point of view. It is, however, singular +that it should be the spectrum of crypton, that is to say, of the +heaviest gas of the group, which appears most clearly in the upper +regions of the atmosphere. + +Among the gases most difficult to liquefy, hydrogen has been the +object of particular research and of really quantitative experiments. +Its properties in a liquid state are now very clearly known. Its +boiling-point, measured with a helium thermometer which has been +compared with thermometers of oxygen and hydrogen, is -252°; its +critical temperature is -241° C.; its critical pressure, 15 +atmospheres. It is four times lighter than water, it does not present +any absorption spectrum, and its specific heat is the greatest known. +It is not a conductor of electricity. Solidified at 15° absolute, it +is far from reminding one by its aspect of a metal; it rather +resembles a piece of perfectly pure ice, and Dr Travers attributes to +it a crystalline structure. The last gas which has resisted +liquefaction, helium, has recently been obtained in a liquid state; it +appears to have its boiling-point in the neighbourhood of 6° +absolute.[11] + +[Footnote 11: M. Poincaré is here in error. Helium has never been +liquefied.--ED.] + + +§ 3. SOLIDS AND LIQUIDS + +The interest of the results to which the researches on the continuity +between the liquid and the gaseous states have led is so great, that +numbers of scholars have naturally been induced to inquire whether +something analogous might not be found in the case of liquids and +solids. We might think that a similar continuity ought to be there met +with, that the universal character of the properties of matter forbade +all real discontinuity between two different states, and that, in +truth, the solid was a prolongation of the liquid state. + +To discover whether this supposition is correct, it concerns us to +compare the properties of liquids and solids. If we find that all +properties are common to the two states we have the right to believe, +even if they presented themselves in different degrees, that, by a +continuous series of intermediary bodies, the two classes might yet be +connected. If, on the other hand, we discover that there exists in +these two classes some quality of a different nature, we must +necessarily conclude that there is a discontinuity which nothing can +remove. + +The distinction established, from the point of view of daily custom, +between solids and liquids, proceeds especially from the difficulty +that we meet with in the one case, and the facility in the other, when +we wish to change their form temporarily or permanently by the action +of mechanical force. This distinction only corresponds, however, in +reality, to a difference in the value of certain coefficients. It is +impossible to discover by this means any absolute characteristic which +establishes a separation between the two classes. Modern researches +prove this clearly. It is not without use, in order to well understand +them, to state precisely the meaning of a few terms generally rather +loosely employed. + +If a conjunction of forces acting on a homogeneous material mass +happens to deform it without compressing or dilating it, two very +distinct kinds of reactions may appear which oppose themselves to the +effort exercised. During the time of deformation, and during that time +only, the first make their influence felt. They depend essentially on +the greater or less rapidity of the deformation, they cease with the +movement, and could not, in any case, bring the body back to its +pristine state of equilibrium. The existence of these reactions leads +us to the idea of viscosity or internal friction. + +The second kind of reactions are of a different nature. They continue +to act when the deformation remains stationary, and, if the external +forces happen to disappear, they are capable of causing the body to +return to its initial form, provided a certain limit has not been +exceeded. These last constitute rigidity. + +At first sight a solid body appears to have a finite rigidity and an +infinite viscosity; a liquid, on the contrary, presents a certain +viscosity, but no rigidity. But if we examine the matter more closely, +beginning either with the solids or with the liquids, we see this +distinction vanish. + +Tresca showed long ago that internal friction is not infinite in a +solid; certain bodies can, so to speak, at once flow and be moulded. +M.W. Spring has given many examples of such phenomena. On the other +hand, viscosity in liquids is never non-existent; for were it so for +water, for example, in the celebrated experiment effected by Joule for +the determination of the mechanical equivalent of the caloric, the +liquid borne along by the floats would slide without friction on the +surrounding liquid, and the work done by movement would be the same +whether the floats did or did not plunge into the liquid mass. + +In certain cases observed long ago with what are called pasty bodies, +this viscosity attains a value almost comparable to that observed by +M. Spring in some solids. Nor does rigidity allow us to establish a +barrier between the two states. Notwithstanding the extreme mobility +of their particles, liquids contain, in fact, vestiges of the property +which we formerly wished to consider the special characteristic of +solids. + +Maxwell before succeeded in rendering the existence of this rigidity +very probable by examining the optical properties of a deformed layer +of liquid. But a Russian physicist, M. Schwedoff, has gone further, +and has been able by direct experiments to show that a sheath of +liquid set between two solid cylinders tends, when one of the +cylinders is subjected to a slight rotation, to return to its original +position, and gives a measurable torsion to a thread upholding the +cylinder. From the knowledge of this torsion the rigidity can be +deduced. In the case of a solution containing 1/2 per cent. of +gelatine, it is found that this rigidity, enormous compared with that +of water, is still, however, one trillion eight hundred and forty +billion times less than that of steel. + +This figure, exact within a few billions, proves that the rigidity is +very slight, but exists; and that suffices for a characteristic +distinction to be founded on this property. In a general way, M. +Spring has also established that we meet in solids, in a degree more +or less marked, with the properties of liquids. When they are placed +in suitable conditions of pressure and time, they flow through +orifices, transmit pressure in all directions, diffuse and dissolve +one into the other, and react chemically on each other. They may be +soldered together by compression; by the same means alloys may be +produced; and further, which seems to clearly prove that matter in a +solid state is not deprived of all molecular mobility, it is possible +to realise suitable limited reactions and equilibria between solid +salts, and these equilibria obey the fundamental laws of +thermodynamics. + +Thus the definition of a solid cannot be drawn from its mechanical +properties. It cannot be said, after what we have just seen, that +solid bodies retain their form, nor that they have a limited +elasticity, for M. Spring has made known a case where the elasticity +of solids is without any limit. + +It was thought that in the case of a different phenomenon--that of +crystallization--we might arrive at a clear distinction, because here +we should he dealing with a specific quality; and that crystallized +bodies would be the true solids, amorphous bodies being at that time +regarded as liquids viscous in the extreme. + +But the studies of a German physicist, Professor O. Lehmann, seem to +prove that even this means is not infallible. Professor Lehmann has +succeeded, in fact, in obtaining with certain organic compounds-- +oleate of potassium, for instance--under certain conditions some +peculiar states to which he has given the name of semi-fluid and +liquid crystals. These singular phenomena can only be observed and +studied by means of a microscope, and the Carlsruhe Professor had to +devise an ingenious apparatus which enabled him to bring the +preparation at the required temperature on to the very plate of the +microscope. + +It is thus made evident that these bodies act on polarized light in +the manner of a crystal. Those that M. Lehmann terms semi-liquid still +present traces of polyhedric delimitation, but with the peaks and +angles rounded by surface-tension, while the others tend to a strictly +spherical form. The optical examination of the first-named bodies is +very difficult, because appearances may be produced which are due to +the phenomena of refraction and imitate those of polarization. For the +other kind, which are often as mobile as water, the fact that they +polarize light is absolutely unquestionable. + +Unfortunately, all these liquids are turbid, and it may be objected +that they are not homogeneous. This want of homogeneity may, according +to M. Quincke, be due to the existence of particles suspended in a +liquid in contact with another liquid miscible with it and enveloping +it as might a membrane, and the phenomena of polarization would thus +be quite naturally explained.[12] + +[Footnote 12: Professor Quincke's last hypothesis is that all liquids +on solidifying pass through a stage intermediate between solid and +liquid, in which they form what he calls "foam-cells," and assume a +viscous structure resembling that of jelly. See _Proc. Roy. Soc. A._, +23rd July 1906.--ED.] + +M. Tamman is of opinion that it is more a question of an emulsion, +and, on this hypothesis, the action on light would actually be that +which has been observed. Various experimenters have endeavoured of +recent years to elucidate this question. It cannot be considered +absolutely settled, but these very curious experiments, pursued with +great patience and remarkable ingenuity, allow us to think that there +really exist certain intermediary forms between crystals and liquids +in which bodies still retain a peculiar structure, and consequently +act on light, but nevertheless possess considerable plasticity. + +Let us note that the question of the continuity of the liquid and +solid states is not quite the same as the question of knowing whether +there exist bodies intermediate in all respects between the solids and +liquids. These two problems are often wrongly confused. The gap +between the two classes of bodies may be filled by certain substances +with intermediate properties, such as pasty bodies and bodies liquid +but still crystallized, because they have not yet completely lost +their peculiar structure. Yet the transition is not necessarily +established in a continuous fashion when we are dealing with the +passage of one and the same determinate substance from the liquid to +the solid form. We conceive that this change may take place by +insensible degrees in the case of an amorphous body. But it seems +hardly possible to consider the case of a crystal, in which molecular +movements must be essentially regular, as a natural sequence to the +case of the liquid where we are, on the contrary, in presence of an +extremely disordered state of movement. + +M. Tamman has demonstrated that amorphous solids may very well, in +fact, be regarded as superposed liquids endowed with very great +viscosity. But it is no longer the same thing when the solid is once +in the crystallized state. There is then a solution of continuity of +the various properties of the substance, and the two phases may +co-exist. + +We might presume also, by analogy with what happens with liquids and +gases, that if we followed the curve of transformation of the +crystalline into the liquid phase, we might arrive at a kind of +critical point at which the discontinuity of their properties would +vanish. + +Professor Poynting, and after him Professor Planck and Professor +Ostwald, supposed this to be the case, but more recently M. Tamman has +shown that such a point does not exist, and that the region of +stability of the crystallized state is limited on all sides. All along +the curve of transformation the two states may exist in equilibrium, +but we may assert that it is impossible to realize a continuous series +of intermediaries between these two states. There will always be a +more or less marked discontinuity in some of the properties. + +In the course of his researches M. Tamman has been led to certain very +important observations, and has met with fresh allotropic +modifications in nearly all substances, which singularly complicate +the question. In the case of water, for instance, he finds that +ordinary ice transforms itself, under a given pressure, at the +temperature of -80° C. into another crystalline variety which is +denser than water. + +The statics of solids under high pressure is as yet, therefore, hardly +drafted, but it seems to promise results which will not be identical +with those obtained for the statics of fluids, though it will present +at least an equal interest. + + +§ 4. THE DEFORMATIONS OF SOLIDS + +If the mechanical properties of the bodies intermediate between solids +and liquids have only lately been the object of systematic studies, +admittedly solid substances have been studied for a long time. Yet, +notwithstanding the abundance of researches published on elasticity by +theorists and experimenters, numerous questions with regard to them +still remain in suspense. + +We only propose to briefly indicate here a few problems recently +examined, without going into the details of questions which belong +more to the domain of mechanics than to that of pure physics. + +The deformations produced in solid bodies by increasing efforts +arrange themselves in two distinct periods. If the efforts are weak, +the deformations produced are also very weak and disappear when the +effort ceases. They are then termed elastic. If the efforts exceed a +certain value, a part only of these deformations disappear, and a part +are permanent. + +The purity of the note emitted by a sound has been often invoked as a +proof of the perfect isochronism of the oscillation, and, +consequently, as a demonstration _a posteriori_ of the correctness of +the early law of Hoocke governing elastic deformations. This law has, +however, during some years been frequently disputed. Certain +mechanicians or physicists freely admit it to be incorrect, especially +as regards extremely weak deformations. According to a theory in some +favour, especially in Germany, i.e. the theory of Bach, the law which +connects the elastic deformations with the efforts would be an +exponential one. Recent experiments by Professors Kohlrausch and +Gruncisen, executed under varied and precise conditions on brass, cast +iron, slate, and wrought iron, do not appear to confirm Bach's law. +Nothing, in point of fact, authorises the rejection of the law of +Hoocke, which presents itself as the most natural and most simple +approximation to reality. + +The phenomena of permanent deformation are very complex, and it +certainly seems that they cannot be explained by the older theories +which insisted that the molecules only acted along the straight line +which joined their centres. It becomes necessary, then, to construct +more complete hypotheses, as the MM. Cosserat have done in some +excellent memoirs, and we may then succeed in grouping together the +facts resulting from new experiments. Among the experiments of which +every theory must take account may be mentioned those by which Colonel +Hartmann has placed in evidence the importance of the lines which are +produced on the surface of metals when the limit of elasticity is +exceeded. + +It is to questions of the same order that the minute and patient +researches of M. Bouasse have been directed. This physicist, as +ingenious as he is profound, has pursued for several years experiments +on the most delicate points relating to the theory of elasticity, and +he has succeeded in defining with a precision not always attained even +in the best esteemed works, the deformations to which a body must be +subjected in order to obtain comparable experiments. With regard to +the slight oscillations of torsion which he has specially studied, M. +Bouasse arrives at the conclusion, in an acute discussion, that we +hardly know anything more than was proclaimed a hundred years ago by +Coulomb. We see, by this example, that admirable as is the progress +accomplished in certain regions of physics, there still exist many +over-neglected regions which remain in painful darkness. The skill +shown by M. Bouasse authorises us to hope that, thanks to his +researches, a strong light will some day illumine these unknown +corners. + +A particularly interesting chapter on elasticity is that relating to +the study of crystals; and in the last few years it has been the +object of remarkable researches on the part of M. Voigt. These +researches have permitted a few controversial questions between +theorists and experimenters to be solved: in particular, M. Voigt has +verified the consequences of the calculations, taking care not to +make, like Cauchy and Poisson, the hypothesis of central forces a mere +function of distance, and has recognized a potential which depends on +the relative orientation of the molecules. These considerations also +apply to quasi-isotropic bodies which are, in fact, networks of +crystals. + +Certain occasional deformations which are produced and disappear +slowly may be considered as intermediate between elastic and permanent +deformations. Of these, the thermal deformation of glass which +manifests itself by the displacement of the zero of a thermometer is +an example. So also the modifications which the phenomena of magnetic +hysteresis or the variations of resistivity have just demonstrated. + +Many theorists have taken in hand these difficult questions. M. +Brillouin endeavours to interpret these various phenomena by the +molecular hypothesis. The attempt may seem bold, since these phenomena +are, for the most part, essentially irreversible, and seem, +consequently, not adaptable to mechanics. But M. Brillouin makes a +point of showing that, under certain conditions, irreversible +phenomena may be created between two material points, the actions of +which depend solely on their distance; and he furnishes striking +instances which appear to prove that a great number of irreversible +physical and chemical phenomena may be ascribed to the existence of +states of unstable equilibria. + +M. Duhem has approached the problem from another side, and endeavours +to bring it within the range of thermodynamics. Yet ordinary +thermodynamics could not account for experimentally realizable states +of equilibrium in the phenomena of viscosity and friction, since this +science declares them to be impossible. M. Duhem, however, arrives at +the idea that the establishment of the equations of thermodynamics +presupposes, among other hypotheses, one which is entirely arbitrary, +namely: that when the state of the system is given, external actions +capable of maintaining it in that state are determined without +ambiguity, by equations termed conditions of equilibrium of the +system. If we reject this hypothesis, it will then be allowable to +introduce into thermodynamics laws previously excluded, and it will be +possible to construct, as M. Duhem has done, a much more comprehensive +theory. + +The ideas of M. Duhem have been illustrated by remarkable experimental +work. M. Marchis, for example, guided by these ideas, has studied the +permanent modifications produced in glass by an oscillation of +temperature. These modifications, which may be called phenomena of the +hysteresis of dilatation, may be followed in very appreciable fashion +by means of a glass thermometer. The general results are quite in +accord with the previsions of M. Duhem. M. Lenoble in researches on +the traction of metallic wires, and M. Chevalier in experiments on the +permanent variations of the electrical resistance of wires of an alloy +of platinum and silver when submitted to periodical variations of +temperature, have likewise afforded verifications of the theory +propounded by M. Duhem. + +In this theory, the representative system is considered dependent on +the temperature of one or several other variables, such as, for +example, a chemical variable. A similar idea has been developed in a +very fine set of memoirs on nickel steel, by M. Ch. Ed. Guillaume. The +eminent physicist, who, by his earlier researches, has greatly +contributed to the light thrown on the analogous question of the +displacement of the zero in thermometers, concludes, from fresh +researches, that the residual phenomena are due to chemical +variations, and that the return to the primary chemical state causes +the variation to disappear. He applies his ideas not only to the +phenomena presented by irreversible steels, but also to very different +facts; for example, to phosphorescence, certain particularities of +which may be interpreted in an analogous manner. + +Nickel steels present the most curious properties, and I have already +pointed out the paramount importance of one of them, hardly capable of +perceptible dilatation, for its application to metrology and +chronometry.[13] Others, also discovered by M. Guillaume in the course +of studies conducted with rare success and remarkable ingenuity, may +render great services, because it is possible to regulate, so to +speak, at will their mechanical or magnetic properties. + +[Footnote 13: The metal known as "invar."--ED.] + +The study of alloys in general is, moreover, one of those in which the +introduction of the methods of physics has produced the greatest +effects. By the microscopic examination of a polished surface or of +one indented by a reagent, by the determination of the electromotive +force of elements of which an alloy forms one of the poles, and by the +measurement of the resistivities, the densities, and the differences +of potential or contact, the most valuable indications as to their +constitution are obtained. M. Le Chatelier, M. Charpy, M. Dumas, M. +Osmond, in France; Sir W. Roberts Austen and Mr. Stansfield, in +England, have given manifold examples of the fertility of these +methods. The question, moreover, has had a new light thrown upon it by +the application of the principles of thermodynamics and of the phase +rule. + +Alloys are generally known in the two states of solid and liquid. +Fused alloys consist of one or several solutions of the component +metals and of a certain number of definite combinations. Their +composition may thus be very complex: but Gibbs' rule gives us at once +important information on the point, since it indicates that there +cannot exist, in general, more than two distinct solutions in an alloy +of two metals. + +Solid alloys may be classed like liquid ones. Two metals or more +dissolve one into the other, and form a solid solution quite analogous +to the liquid solution. But the study of these solid solutions is +rendered singularly difficult by the fact that the equilibrium so +rapidly reached in the case of liquids in this case takes days and, in +certain cases, perhaps even centuries to become established. + + + + +CHAPTER V + +SOLUTIONS AND ELECTROLYTIC DISSOCIATION + + +§ 1. SOLUTION + +Vaporization and fusion are not the only means by which the physical +state of a body may be changed without modifying its chemical +constitution. From the most remote periods solution has also been +known and studied, but only in the last twenty years have we obtained +other than empirical information regarding this phenomenon. + +It is natural to employ here also the methods which have allowed us to +penetrate into the knowledge of other transformations. The problem of +solution may be approached by way of thermodynamics and of the +hypotheses of kinetics. + +As long ago as 1858, Kirchhoff, by attributing to saline solutions-- +that is to say, to mixtures of water and a non-volatile liquid like +sulphuric acid--the properties of internal energy, discovered a +relation between the quantity of heat given out on the addition of a +certain quantity of water to a solution and the variations to which +condensation and temperature subject the vapour-tension of the +solution. He calculated for this purpose the variations of energy +which are produced when passing from one state to another by two +different series of transformations; and, by comparing the two +expressions thus obtained, he established a relation between the +various elements of the phenomenon. But, for a long time afterwards, +the question made little progress, because there seemed to be hardly +any means of introducing into this study the second principle of +thermodynamics.[14] It was the memoir of Gibbs which at last opened +out this rich domain and enabled it to be rationally exploited. As +early as 1886, M. Duhem showed that the theory of the thermodynamic +potential furnished precise information on solutions or liquid +mixtures. He thus discovered over again the famous law on the lowering +of the congelation temperature of solvents which had just been +established by M. Raoult after a long series of now classic +researches. + +[Footnote 14: The "second principle" referred to has been thus +enunciated: "In every engine that produces work there is a fall of +temperature, and the maximum output of a perfect engine--_i.e._ the +ratio between the heat consumed in work and the heat supplied--depends +only on the extreme temperatures between which the fluid is +evolved."--Demanet, _Notes de Physique Expérimentale_, Louvain, 1905, +fasc. 2, p. 147. Clausius put it in a negative form, as thus: No +engine can of itself, without the aid of external agency, transfer +heat from a body at low temperature to a body at a high temperature. +Cf. Ganot's _Physics_, 17th English edition, § 508.--ED.] + +In the minds of many persons, however, grave doubts persisted. +Solution appeared to be an essentially irreversible phenomenon. It was +therefore, in all strictness, impossible to calculate the entropy of a +solution, and consequently to be certain of the value of the +thermodynamic potential. The objection would be serious even to-day, +and, in calculations, what is called the paradox of Gibbs would be an +obstacle. + +We should not hesitate, however, to apply the Phase Law to solutions, +and this law already gives us the key to a certain number of facts. It +puts in evidence, for example, the part played by the eutectic point-- +that is to say, the point at which (to keep to the simple case in +which we have to do with two bodies only, the solvent and the solute) +the solution is in equilibrium at once with the two possible solids, +the dissolved body and the solvent solidified. The knowledge of this +point explains the properties of refrigerating mixtures, and it is +also one of the most useful for the theory of alloys. The scruples of +physicists ought to have been removed on the memorable occasion when +Professor Van t'Hoff demonstrated that solution can operate reversibly +by reason of the phenomena of osmosis. But the experiment can only +succeed in very rare cases; and, on the other hand, Professor Van +t'Hoff was naturally led to another very bold conception. He regarded +the molecule of the dissolved body as a gaseous one, and assimilated +solution, not as had hitherto been the rule, to fusion, but to a kind +of vaporization. Naturally his ideas were not immediately accepted by +the scholars most closely identified with the classic tradition. It +may perhaps not be without use to examine here the principles of +Professor Van t'Hoff's theory. + + +§ 2. OSMOSIS + +Osmosis, or diffusion through a septum, is a phenomenon which has been +known for some time. The discovery of it is attributed to the Abbé +Nollet, who is supposed to have observed it in 1748, during some +"researches on liquids in ebullition." A classic experiment by +Dutrochet, effected about 1830, makes this phenomenon clear. Into pure +water is plunged the lower part of a vertical tube containing pure +alcohol, open at the top and closed at the bottom by a membrane, such +as a pig's bladder, without any visible perforation. In a very short +time it will be found, by means of an areometer for instance, that the +water outside contains alcohol, while the alcohol of the tube, pure at +first, is now diluted. Two currents have therefore passed through the +membrane, one of water from the outside to the inside, and one of +alcohol in the converse direction. It is also noted that a difference +in the levels has occurred, and that the liquid in the tube now rises +to a considerable height. It must therefore be admitted that the flow +of the water has been more rapid than that of the alcohol. At the +commencement, the water must have penetrated into the tube much more +rapidly than the alcohol left it. Hence the difference in the levels, +and, consequently, a difference of pressure on the two faces of the +membrane. This difference goes on increasing, reaches a maximum, then +diminishes, and vanishes when the diffusion is complete, final +equilibrium being then attained. + +The phenomenon is evidently connected with diffusion. If water is very +carefully poured on to alcohol, the two layers, separate at first, +mingle by degrees till a homogeneous substance is obtained. The +bladder seems not to have prevented this diffusion from taking place, +but it seems to have shown itself more permeable to water than to +alcohol. May it not therefore be supposed that there must exist +dividing walls in which this difference of permeability becomes +greater and greater, which would be permeable to the solvent and +absolutely impermeable to the solute? If this be so, the phenomena of +these _semi-permeable_ walls, as they are termed, can be observed in +particularly simple conditions. + +The answer to this question has been furnished by biologists, at which +we cannot be surprised. The phenomena of osmosis are naturally of the +first importance in the action of organisms, and for a long time have +attracted the attention of naturalists. De Vries imagined that the +contractions noticed in the protoplasm of cells placed in saline +solutions were due to a phenomenon of osmosis, and, upon examining +more closely certain peculiarities of cell life, various scholars have +demonstrated that living cells are enclosed in membranes permeable to +certain substances and entirely impermeable to others. It was +interesting to try to reproduce artificially semi-permeable walls +analogous to those thus met with in nature;[15] and Traube and Pfeffer +seem to have succeeded in one particular case. Traube has pointed out +that the very delicate membrane of ferrocyanide of potassium which is +obtained with some difficulty by exposing it to the reaction of +sulphate of copper, is permeable to water, but will not permit the +passage of the majority of salts. Pfeffer, by producing these walls in +the interstices of a porous porcelain, has succeeded in giving them +sufficient rigidity to allow measurements to be made. It must be +allowed that, unfortunately, no physicist or chemist has been as lucky +as these two botanists; and the attempts to reproduce semi-permeable +walls completely answering to the definition, have never given but +mediocre results. If, however, the experimental difficulty has not +been overcome in an entirely satisfactory manner, it at least appears +very probable that such walls may nevertheless exist.[16] + +[Footnote 15: See next note.--ED.] + +[Footnote 16: M. Stephane Leduc, Professor of Biology of Nantes, has +made many experiments in this connection, and the artificial cells +exhibited by him to the Association française pour l'avancement des +Sciences, at their meeting at Grenoble in 1904 and reproduced in their +"Actes," are particularly noteworthy.--ED.] + +Nevertheless, in the case of gases, there exists an excellent example +of a semi-permeable wall, and a partition of platinum brought to a +higher than red heat is, as shown by M. Villard in some ingenious +experiments, completely impermeable to air, and very permeable, on the +contrary, to hydrogen. It can also be experimentally demonstrated that +on taking two recipients separated by such a partition, and both +containing nitrogen mixed with varying proportions of hydrogen, the +last-named gas will pass through the partition in such a way that the +concentration--that is to say, the mass of gas per unit of volume-- +will become the same on both sides. Only then will equilibrium be +established; and, at that moment, an excess of pressure will naturally +be produced in that recipient which, at the commencement, contained +the gas with the smallest quantity of hydrogen. + +This experiment enables us to anticipate what will happen in a liquid +medium with semi-permeable partitions. Between two recipients, one +containing pure water, the other, say, water with sugar in solution, +separated by one of these partitions, there will be produced merely a +movement of the pure towards the sugared water, and following this, an +increase of pressure on the side of the last. But this increase will +not be without limits. At a certain moment the pressure will cease to +increase and will remain at a fixed value which now has a given +direction. This is the osmotic pressure. + +Pfeffer demonstrated that, for the same substance, the osmotic +pressure is proportional to the concentration, and consequently in +inverse ratio to the volume occupied by a similar mass of the solute. +He gave figures from which it was easy, as Professor Van t'Hoff found, +to draw the conclusion that, in a constant volume, the osmotic +pressure is proportional to the absolute temperature. De Vries, +moreover, by his remarks on living cells, extended the results which +Pfeffer had applied to one case only--that is, to the one that he had +been able to examine experimentally. + +Such are the essential facts of osmosis. We may seek to interpret them +and to thoroughly examine the mechanism of the phenomenon; but it must +be acknowledged that as regards this point, physicists are not +entirely in accord. In the opinion of Professor Nernst, the +permeability of semi-permeable membranes is simply due to differences +of solubility in one of the substances of the membrane itself. Other +physicists think it attributable, either to the difference in the +dimensions of the molecules, of which some might pass through the +pores of the membrane and others be stopped by their relative size, or +to these molecules' greater or less mobility. For others, again, it is +the capillary phenomena which here act a preponderating part. + +This last idea is already an old one: Jager, More, and Professor +Traube have all endeavoured to show that the direction and speed of +osmosis are determined by differences in the surface-tensions; and +recent experiments, especially those of Batelli, seem to prove that +osmosis establishes itself in the way which best equalizes the +surface-tensions of the liquids on both sides of the partition. +Solutions possessing the same surface-tension, though not in molecular +equilibrium, would thus be always in osmotic equilibrium. We must not +conceal from ourselves that this result would be in contradiction with +the kinetic theory. + + +§ 3. APPLICATION TO THE THEORY OF SOLUTION + +If there really exist partitions permeable to one body and impermeable +to another, it may be imagined that the homogeneous mixture of these +two bodies might be effected in the converse way. It can be easily +conceived, in fact, that by the aid of osmotic pressure it would be +possible, for example, to dilute or concentrate a solution by driving +through the partition in one direction or another a certain quantity +of the solvent by means of a pressure kept equal to the osmotic +pressure. This is the important fact which Professor Van t' Hoff +perceived. The existence of such a wall in all possible cases +evidently remains only a very legitimate hypothesis,--a fact which +ought not to be concealed. + +Relying solely on this postulate, Professor Van t' Hoff easily +established, by the most correct method, certain properties of the +solutions of gases in a volatile liquid, or of non-volatile bodies in +a volatile liquid. To state precisely the other relations, we must +admit, in addition, the experimental laws discovered by Pfeffer. But +without any hypothesis it becomes possible to demonstrate the laws of +Raoult on the lowering of the vapour-tension and of the freezing point +of solutions, and also the ratio which connects the heat of fusion +with this decrease. + +These considerable results can evidently be invoked as _a posteriori_ +proofs of the exactitude of the experimental laws of osmosis. They are +not, however, the only ones that Professor Van t' Hoff has obtained by +the same method. This illustrious scholar was thus able to find anew +Guldberg and Waage's law on chemical equilibrium at a constant +temperature, and to show how the position of the equilibrium changes +when the temperature happens to change. + +If now we state, in conformity with the laws of Pfeffer, that the +product of the osmotic pressure by the volume of the solution is equal +to the absolute temperature multiplied by a coefficient, and then look +for the numerical figure of this latter in a solution of sugar, for +instance, we find that this value is the same as that of the analogous +coefficient of the characteristic equation of a perfect gas. There is +in this a coincidence which has also been utilized in the preceding +thermodynamic calculations. It may be purely fortuitous, but we can +hardly refrain from finding in it a physical meaning. + +Professor Van t'Hoff has considered this coincidence a demonstration +that there exists a strong analogy between a body in solution and a +gas; as a matter of fact, it may seem that, in a solution, the +distance between the molecules becomes comparable to the molecular +distances met with in gases, and that the molecule acquires the same +degree of liberty and the same simplicity in both phenomena. In that +case it seems probable that solutions will be subject to laws +independent of the chemical nature of the dissolved molecule and +comparable to the laws governing gases, while if we adopt the kinetic +image for the gas, we shall be led to represent to ourselves in a +similar way the phenomena which manifest themselves in a solution. +Osmotic pressure will then appear to be due to the shock of the +dissolved molecules against the membrane. It will come from one side +of this partition to superpose itself on the hydrostatic pressure, +which latter must have the same value on both sides. + +The analogy with a perfect gas naturally becomes much greater as the +solution becomes more diluted. It then imitates gas in some other +properties; the internal work of the variation of volume is nil, and +the specific heat is only a function of the temperature. A solution +which is diluted by a reversible method is cooled like a gas which +expands adiabatically.[17] + +[Footnote 17: That is, without receiving or emitting any heat.--ED.] + +It must, however, be acknowledged that, in other points, the analogy +is much less perfect. The opinion which sees in solution a phenomenon +resembling fusion, and which has left an indelible trace in everyday +language (we shall always say: to melt sugar in water) is certainly +not without foundation. Certain of the reasons which might be invoked +to uphold this opinion are too evident to be repeated here, though +others more recondite might be quoted. The fact that the internal +energy generally becomes independent of the concentration when the +dilution reaches even a moderately high value is rather in favour of +the hypothesis of fusion. + +We must not forget, however, the continuity of the liquid and gaseous +states; and we may consider it in an absolute way a question devoid of +sense to ask whether in a solution the solute is in the liquid or the +gaseous state. It is in the fluid state, and perhaps in conditions +opposed to those of a body in the state of a perfect gas. It is known, +of course, that in this case the manometrical pressure must be +regarded as very great in relation to the internal pressure which, in +the characteristic equation, is added to the other. May it not seem +possible that in the solution it is, on the contrary, the internal +pressure which is dominant, the manometric pressure becoming of no +account? The coincidence of the formulas would thus be verified, for +all the characteristic equations are symmetrical with regard to these +two pressures. From this point of view the osmotic pressure would be +considered as the result of an attraction between the solvent and the +solute; and it would represent the difference between the internal +pressures of the solution and of the pure solvent. These hypotheses +are highly interesting, and very suggestive; but from the way in which +the facts have been set forth, it will appear, no doubt, that there is +no obligation to admit them in order to believe in the legitimacy of +the application of thermodynamics to the phenomena of solution. + + +§ 4. ELECTROLYTIC DISSOCIATION + +From the outset Professor Van t' Hoff was brought to acknowledge that +a great number of solutions formed very notable exceptions which were +very irregular in appearance. The analogy with gases did not seem to +be maintained, for the osmotic pressure had a very different value +from that indicated by the theory. Everything, however, came right if +one multiplied by a factor, determined according to each case, but +greater than unity, the constant of the characteristic formula. +Similar divergences were manifested in the delays observed in +congelation, and disappeared when subjected to an analogous +correction. + +Thus the freezing-point of a normal solution, containing a molecule +gramme (that is, the number of grammes equal to the figure +representing the molecular mass) of alcohol or sugar in water, falls +1.85° C. If the laws of solution were identically the same for a +solution of sea-salt, the same depression should be noticed in a +saline solution also containing 1 molecule per litre. In fact, the +fall reaches 3.26°, and the solution behaves as if it contained, not +1, but 1.75 normal molecules per litre. The consideration of the +osmotic pressures would lead to similar observations, but we know that +the experiment would be more difficult and less precise. + +We may wonder whether anything really analogous to this can be met with +in the case of a gas, and we are thus led to consider the phenomena of +dissociation.[18] If we heat a body which, in a gaseous state, is +capable of dissociation--hydriodic acid, for example--at a given +temperature, an equilibrium is established between three gaseous bodies, +the acid, the iodine, and the hydrogen. The total mass will follow with +fair closeness Mariotte's law, but the characteristic constant will no +longer be the same as in the case of a non-dissociated gas. We here no +longer have to do with a single molecule, since each molecule is in part +dissociated. + +[Footnote 18: Dissociation must be distinguished from decomposition, +which is what occurs when the whole of a particle (compound, molecule, +atom, etc.) breaks up into its component parts. In dissociation the +breaking up is only partial, and the resultant consists of a mixture +of decomposed and undecomposed parts. See Ganot's Physics, 17th +English edition, § 395, for examples.--ED.] + +The comparison of the two cases leads to the employment of a new image +for representing the phenomenon which has been produced throughout the +saline solution. We have introduced a single molecule of salt, and +everything occurs as if there were 1.75 molecules. May it not really +be said that the number is 1.75, because the sea-salt is partly +dissociated, and a molecule has become transformed into 0.75 molecule +of sodium, 0.75 of chlorium, and 0.25 of salt? + +This is a way of speaking which seems, at first sight, strangely +contradicted by experiment. Professor Van t' Hoff, like other +chemists, would certainly have rejected--in fact, he did so at first-- +such a conception, if, about the same time, an illustrious Swedish +scholar, M. Arrhenius, had not been brought to the same idea by +another road, and, had not by stating it precisely and modifying it, +presented it in an acceptable form. + +A brief examination will easily show that all the substances which are +exceptions to the laws of Van t'Hoff are precisely those which are +capable of conducting electricity when undergoing decomposition--that +is to say, are electrolytes. The coincidence is absolute, and cannot +be simply due to chance. + +Now, the phenomena of electrolysis have, for a long time, forced upon +us an almost necessary image. The saline molecule is always +decomposed, as we know, in the primary phenomenon of electrolysis into +two elements which Faraday termed ions. Secondary reactions, no doubt, +often come to complicate the question, but these are chemical +reactions belonging to the general order of things, and have nothing +to do with the electric action working on the solution. The simple +phenomenon is always the same--decomposition into two ions, followed +by the appearance of one of these ions at the positive and of the +other at the negative electrode. But as the very slightest expenditure +of energy is sufficient to produce the commencement of electrolysis, +it is necessary to suppose that these two ions are not united by any +force. Thus the two ions are, in a way, dissociated. Clausius, who was +the first to represent the phenomena by this symbol, supposed, in +order not to shock the feelings of chemists too much, that this +dissociation only affected an infinitesimal fraction of the total +number of the molecules of the salt, and thereby escaped all check. + +This concession was unfortunate, and the hypothesis thus lost the +greater part of its usefulness. M. Arrhenius was bolder, and frankly +recognized that dissociation occurs at once in the case of a great +number of molecules, and tends to increase more and more as the +solution becomes more dilute. It follows the comparison with a gas +which, while partially dissociated in an enclosed space, becomes +wholly so in an infinite one. + +M. Arrhenius was led to adopt this hypothesis by the examination of +experimental results relating to the conductivity of electrolytes. In +order to interpret certain facts, it has to be recognized that a part +only of the molecules in a saline solution can be considered as +conductors of electricity, and that by adding water the number of +molecular conductors is increased. This increase, too, though rapid at +first, soon becomes slower, and approaches a certain limit which an +infinite dilution would enable it to attain. If the conducting +molecules are the dissociated molecules, then the dissociation (so +long as it is a question of strong acids and salts) tends to become +complete in the case of an unlimited dilution. + +The opposition of a large number of chemists and physicists to the +ideas of M. Arrhenius was at first very fierce. It must be noted with +regret that, in France particularly, recourse was had to an arm which +scholars often wield rather clumsily. They joked about these free ions +in solution, and they asked to see this chlorine and this sodium which +swam about the water in a state of liberty. But in science, as +elsewhere, irony is not argument, and it soon had to be acknowledged +that the hypothesis of M. Arrhenius showed itself singularly fertile +and had to be regarded, at all events, as a very expressive image, if +not, indeed, entirely in conformity with reality. + +It would certainly be contrary to all experience, and even to common +sense itself, to suppose that in dissolved chloride of sodium there is +really free sodium, if we suppose these atoms of sodium to be +absolutely identical with ordinary atoms. But there is a great +difference. In the one case the atoms are electrified, and carry a +relatively considerable positive charge, inseparable from their state +as ions, while in the other they are in the neutral state. We may +suppose that the presence of this charge brings about modifications as +extensive as one pleases in the chemical properties of the atom. Thus +the hypothesis will be removed from all discussion of a chemical +order, since it will have been made plastic enough beforehand to adapt +itself to all the known facts; and if we object that sodium cannot +subsist in water because it instantaneously decomposes the latter, the +answer is simply that the sodium ion does not decompose water as does +ordinary sodium. + +Still, other objections might be raised which could not be so easily +refuted. One, to which chemists not unreasonably attached great +importance, was this:--If a certain quantity of chloride of sodium is +dissociated into chlorine and sodium, it should be possible, by +diffusion, for example, which brings out plainly the phenomena of +dissociation in gases, to extract from the solution a part either of +the chlorine or of the sodium, while the corresponding part of the +other compound would remain. This result would be in flagrant +contradiction with the fact that, everywhere and always, a solution of +salt contains strictly the same proportions of its component elements. + +M. Arrhenius answers to this that the electrical forces in ordinary +conditions prevent separation by diffusion or by any other process. +Professor Nernst goes further, and has shown that the concentration +currents which are produced when two electrodes of the same substance +are plunged into two unequally concentrated solutions may be +interpreted by the hypothesis that, in these particular conditions, +the diffusion does bring about a separation of the ions. Thus the +argument is turned round, and the proof supposed to be given of the +incorrectness of the theory becomes a further reason in its favour. + +It is possible, no doubt, to adduce a few other experiments which are +not very favourable to M. Arrhenius's point of view, but they are +isolated cases; and, on the whole, his theory has enabled many +isolated facts, till then scattered, to be co-ordinated, and has +allowed very varied phenomena to be linked together. It has also +suggested--and, moreover, still daily suggests--researches of the +highest order. + +In the first place, the theory of Arrhenius explains electrolysis very +simply. The ions which, so to speak, wander about haphazard, and are +uniformly distributed throughout the liquid, steer a regular course as +soon as we dip in the trough containing the electrolyte the two +electrodes connected with the poles of the dynamo or generator of +electricity. Then the charged positive ions travel in the direction of +the electromotive force and the negative ions in the opposite +direction. On reaching the electrodes they yield up to them the +charges they carry, and thus pass from the state of ion into that of +ordinary atom. Moreover, for the solution to remain in equilibrium, +the vanished ions must be immediately replaced by others, and thus the +state of ionisation of the electrolyte remains constant and its +conductivity persists. + +All the peculiarities of electrolysis are capable of interpretation: +the phenomena of the transport of ions, the fine experiments of M. +Bouty, those of Professor Kohlrausch and of Professor Ostwald on +various points in electrolytic conduction, all support the theory. The +verifications of it can even be quantitative, and we can foresee +numerical relations between conductivity and other phenomena. The +measurement of the conductivity permits the number of molecules +dissociated in a given solution to be calculated, and the number is +thus found to be precisely the same as that arrived at if it is wished +to remove the disagreement between reality and the anticipations which +result from the theory of Professor Van t' Hoff. The laws of +cryoscopy, of tonometry, and of osmosis thus again become strict, and +no exception to them remains. + +If the dissociation of salts is a reality and is complete in a dilute +solution, any of the properties of a saline solution whatever should +be represented numerically as the sum of three values, of which one +concerns the positive ion, a second the negative ion, and the third +the solvent. The properties of the solutions would then be what are +called additive properties. Numerous verifications may be attempted by +very different roads. They generally succeed very well; and whether we +measure the electric conductivity, the density, the specific heats, +the index of refraction, the power of rotatory polarization, the +colour, or the absorption spectrum, the additive property will +everywhere be found in the solution. + +The hypothesis, so contested at the outset by the chemists, is, +moreover, assuring its triumph by important conquests in the domain of +chemistry itself. It permits us to give a vivid explanation of +chemical reaction, and for the old motto of the chemists, "Corpora non +agunt, nisi soluta," it substitutes a modern one, "It is especially +the ions which react." Thus, for example, all salts of iron, which +contain iron in the state of ions, give similar reactions; but salts +such as ferrocyanide of potassium, in which iron does not play the +part of an ion, never give the characteristic reactions of iron. + +Professor Ostwald and his pupils have drawn from the hypothesis of +Arrhenius manifold consequences which have been the cause of +considerable progress in physical chemistry. Professor Ostwald has +shown, in particular, how this hypothesis permits the quantitative +calculation of the conditions of equilibrium of electrolytes and +solutions, and especially of the phenomena of neutralization. If a +dissolved salt is partly dissociated into ions, this solution must be +limited by an equilibrium between the non-dissociated molecule and the +two ions resulting from the dissociation; and, assimilating the +phenomenon to the case of gases, we may take for its study the laws of +Gibbs and of Guldberg and Waage. The results are generally very +satisfactory, and new researches daily furnish new checks. + +Professor Nernst, who before gave, as has been said, a remarkable +interpretation of the diffusion of electrolytes, has, in the direction +pointed out by M. Arrhenius, developed a theory of the entire +phenomena of electrolysis, which, in particular, furnishes a striking +explanation of the mechanism of the production of electromotive force +in galvanic batteries. + +Extending the analogy, already so happily invoked, between the +phenomena met with in solutions and those produced in gases, Professor +Nernst supposes that metals tend, as it were, to vaporize when in +presence of a liquid. A piece of zinc introduced, for example, into +pure water gives birth to a few metallic ions. These ions become +positively charged, while the metal naturally takes an equal charge, +but of contrary sign. Thus the solution and the metal are both +electrified; but this sort of vaporization is hindered by +electrostatic attraction, and as the charges borne by the ions are +considerable, an equilibrium will be established, although the number +of ions which enter the solution will be very small. + +If the liquid, instead of being a solvent like pure water, contains an +electrolyte, it already contains metallic ions, the osmotic pressure +of which will be opposite to that of the solution. Three cases may +then present themselves--either there will be equilibrium, or the +electrostatic attraction will oppose itself to the pressure of +solution and the metal will be negatively charged, or, finally, the +attraction will act in the same direction as the pressure, and the +metal will become positively and the solution negatively charged. +Developing this idea, Professor Nernst calculates, by means of the +action of the osmotic pressures, the variations of energy brought into +play and the value of the differences of potential by the contact of +the electrodes and electrolytes. He deduces this from the +electromotive force of a single battery cell which becomes thus +connected with the values of the osmotic pressures, or, if you will, +thanks to the relation discovered by Van t' Hoff, with the +concentrations. Some particularly interesting electrical phenomena +thus become connected with an already very important group, and a new +bridge is built which unites two regions long considered foreign to +each other. + +The recent discoveries on the phenomena produced in gases when +rendered conductors of electricity almost force upon us, as we shall +see, the idea that there exist in these gases electrified centres +moving through the field, and this idea gives still greater +probability to the analogous theory explaining the mechanism of the +conductivity of liquids. It will also be useful, in order to avoid +confusion, to restate with precision this notion of electrolytic ions, +and to ascertain their magnitude, charge, and velocity. + +The two classic laws of Faraday will supply us with important +information. The first indicates that the quantity of electricity +passing through the liquid is proportional to the quantity of matter +deposited on the electrodes. This leads us at once to the +consideration that, in any given solution, all the ions possess +individual charges equal in absolute value. + +The second law may be stated in these terms: an atom-gramme of metal +carries with it into electrolysis a quantity of electricity +proportionate to its valency.[19] + +[Footnote 19: The valency or atomicity of an element may be defined as +the power it possesses of entering into compounds in a certain fixed +proportion. As hydrogen is generally taken as the standard, in +practice the valency of an atom is the number of hydrogen atoms it +will combine with or replace. Thus chlorine and the rest of the +halogens, the atoms of which combine with one atom of hydrogen, are +called univalent, oxygen a bivalent element, and so on.--ED.] + +Numerous experiments have made known the total mass of hydrogen +capable of carrying one coulomb, and it will therefore be possible to +estimate the charge of an ion of hydrogen if the number of atoms of +hydrogen in a given mass be known. This last figure is already +furnished by considerations derived from the kinetic theory, and +agrees with the one which can be deduced from the study of various +phenomena. The result is that an ion of hydrogen having a mass of 1.3 +x 10^{-20} grammes bears a charge of 1.3 X 10^{-20} electromagnetic +units; and the second law will immediately enable the charge of any +other ion to be similarly estimated. + +The measurements of conductivity, joined to certain considerations +relating to the differences of concentration which appear round the +electrode in electrolysis, allow the speed of the ions to be +calculated. Thus, in a liquid containing 1/10th of a hydrogen-ion per +litre, the absolute speed of an ion would be 3/10ths of a millimetre +per second in a field where the fall of potential would be 1 volt per +centimetre. Sir Oliver Lodge, who has made direct experiments to +measure this speed, has obtained a figure very approximate to this. +This value is very small compared to that which we shall meet with in +gases. + +Another consequence of the laws of Faraday, to which, as early as 1881, +Helmholtz drew attention, may be considered as the starting-point of +certain new doctrines we shall come across later. + +Helmholtz says: "If we accept the hypothesis that simple bodies are +composed of atoms, we are obliged to admit that, in the same way, +electricity, whether positive or negative, is composed of elementary +parts which behave like atoms of electricity." + +The second law seems, in fact, analogous to the law of multiple +proportions in chemistry, and it shows us that the quantities of +electricity carried vary from the simple to the double or treble, +according as it is a question of a uni-, bi-, or trivalent metal; and +as the chemical law leads up to the conception of the material atom, +so does the electrolytic law suggest the idea of an electric atom. + + + + +CHAPTER VI + +THE ETHER + + +§ 1. THE LUMINIFEROUS ETHER + +It is in the works of Descartes that we find the first idea of +attributing those physical phenomena which the properties of matter +fail to explain to some subtle matter which is the receptacle of the +energy of the universe. + +In our times this idea has had extraordinary luck. After having been +eclipsed for two hundred years by the success of the immortal +synthesis of Newton, it gained an entirely new splendour with Fresnel +and his followers. Thanks to their admirable discoveries, the first +stage seemed accomplished, the laws of optics were represented by a +single hypothesis, marvellously fitted to allow us to anticipate +unknown phenomena, and all these anticipations were subsequently fully +verified by experiment. But the researches of Faraday, Maxwell, and +Hertz authorized still greater ambitions; and it really seemed that +this medium, to which it was agreed to give the ancient name of ether, +and which had already explained light and radiant heat, would also be +sufficient to explain electricity. Thus the hope began to take form +that we might succeed in demonstrating the unity of all physical +forces. It was thought that the knowledge of the laws relating to the +inmost movements of this ether might give us the key to all phenomena, +and might make us acquainted with the method in which energy is stored +up, transmitted, and parcelled out in its external manifestations. + +We cannot study here all the problems which are connected with the +physics of the ether. To do this a complete treatise on optics would +have to be written and a very lengthy one on electricity. I shall +simply endeavour to show rapidly how in the last few years the ideas +relative to the constitution of this ether have evolved, and we shall +see if it be possible without self-delusion to imagine that a single +medium can really allow us to group all the known facts in one +comprehensive arrangement. + +As constructed by Fresnel, the hypothesis of the luminous ether, which +had so great a struggle at the outset to overcome the stubborn +resistance of the partisans of the then classic theory of emission, +seemed, on the contrary, to possess in the sequel an unshakable +strength. Lamé, though a prudent mathematician, wrote: "_The +existence_ of the ethereal fluid is _incontestably demonstrated_ by +the propagation of light through the planetary spaces, and by the +explanation, so simple and so complete, of the phenomena of +diffraction in the wave theory of light"; and he adds: "The laws of +double refraction prove with no less certainty that the _ether exists_ +in all diaphanous media." Thus the ether was no longer an hypothesis, +but in some sort a tangible reality. But the ethereal fluid of which +the existence was thus proclaimed has some singular properties. + +Were it only a question of explaining rectilinear propagation, +reflexion, refraction, diffraction, and interferences notwithstanding +grave difficulties at the outset and the objections formulated by +Laplace and Poisson (some of which, though treated somewhat lightly at +the present day, have not lost all value), we should be under no +obligation to make any hypothesis other than that of the undulations +of an elastic medium, without deciding in advance anything as to the +nature and direction of the vibrations. + +This medium would, naturally--since it exists in what we call the +void--be considered as imponderable. It may be compared to a fluid of +negligible mass--since it offers no appreciable resistance to the +motion of the planets--but is endowed with an enormous elasticity, +because the velocity of the propagation of light is considerable. It +must be capable of penetrating into all transparent bodies, and of +retaining there, so to speak, a constant elasticity, but must there +become condensed, since the speed of propagation in these bodies is +less than in a vacuum. Such properties belong to no material gas, even +the most rarefied, but they admit of no essential contradiction, and +that is the important point.[20] + +[Footnote 20: Since this was written, however, men of science have +become less unanimous than they formerly were on this point. The +veteran chemist Professor Mendeléeff has given reasons for thinking +that the ether is an inert gas with an atomic weight a million times +less than that of hydrogen, and a velocity of 2250 kilometres per +second (_Principles of Chemistry_, Eng. ed., 1905, vol. ii. p. 526). +On the other hand, the well-known physicist Dr A.H. Bucherer, speaking +at the Naturforscherversammlung, held at Stuttgart in 1906, declared +his disbelief in the existence of the ether, which he thought could +not be reconciled at once with the Maxwellian theory and the known +facts.--ED.] + +It was the study of the phenomena of polarization which led Fresnel to +his bold conception of transverse vibrations, and subsequently induced +him to penetrate further into the constitution of the ether. We know +the experiment of Arago on the noninterference of polarized rays in +rectangular planes. While two systems of waves, proceeding from the +same source of natural light and propagating themselves in nearly +parallel directions, increase or become destroyed according to whether +the nature of the superposed waves are of the same or of contrary +signs, the waves of the rays polarized in perpendicular planes, on the +other hand, can never interfere with each other. Whatever the +difference of their course, the intensity of the light is always the +sum of the intensity of the two rays. + +Fresnel perceived that this experiment absolutely compels us to reject +the hypothesis of longitudinal vibrations acting along the line of +propagation in the direction of the rays. To explain it, it must of +necessity be admitted, on the contrary, that the vibrations are +transverse and perpendicular to the ray. Verdet could say, in all +truth, "It is not possible to deny the transverse direction of +luminous vibrations, without at the same time denying that light +consists of an undulatory movement." + +Such vibrations do not and cannot exist in any medium resembling a +fluid. The characteristic of a fluid is that its different parts can +displace themselves with regard to one another without any reaction +appearing so long as a variation of volume is not produced. There +certainly may exist, as we have seen, certain traces of rigidity in a +liquid, but we cannot conceive such a thing in a body infinitely more +subtle than rarefied gas. Among material bodies, a solid alone really +possesses the rigidity sufficient for the production within it of +transverse vibrations and for their maintenance during their +propagation. + +Since we have to attribute such a property to the ether, we may add +that on this point it resembles a solid, and Lord Kelvin has shown +that this solid, would be much more rigid than steel. This conclusion +produces great surprise in all who hear it for the first time, and it +is not rare to hear it appealed to as an argument against the actual +existence of the ether. It does not seem, however, that such an +argument can be decisive. There is no reason for supposing that the +ether ought to be a sort of extension of the bodies we are accustomed +to handle. Its properties may astonish our ordinary way of thinking, +but this rather unscientific astonishment is not a reason for doubting +its existence. Real difficulties would appear only if we were led to +attribute to the ether, not singular properties which are seldom found +united in the same substance, but properties logically contradictory. +In short, however odd such a medium may appear to us, it cannot be +said that there is any absolute incompatibility between its +attributes. + +It would even be possible, if we wished, to suggest images capable of +representing these contrary appearances. Various authors have done so. +Thus, M. Boussinesq assumes that the ether behaves like a very +rarefied gas in respect of the celestial bodies, because these last +move, while bathed in it, in all directions and relatively slowly, +while they permit it to retain, so to speak, its perfect homogeneity. +On the other hand, its own undulations are so rapid that so far as +they are concerned the conditions become very different, and its +fluidity has, one might say, no longer the time to come in. Hence its +rigidity alone appears. + +Another consequence, very important in principle, of the fact that +vibrations of light are transverse, has been well put in evidence by +Fresnel. He showed how we have, in order to understand the action +which excites without condensation the sliding of successive layers of +the ether during the propagation of a vibration, to consider the +vibrating medium as being composed of molecules separated by finite +distances. Certain authors, it is true, have proposed theories in +which the action at a distance of these molecules are replaced by +actions of contact between parallelepipeds sliding over one another; +but, at bottom, these two points of view both lead us to conceive the +ether as a discontinuous medium, like matter itself. The ideas +gathered from the most recent experiments also bring us to the same +conclusion. + + +§ 2. RADIATIONS + +In the ether thus constituted there are therefore propagated +transverse vibrations, regarding which all experiments in optics +furnish very precise information. The amplitude of these vibrations is +exceedingly small, even in relation to the wave-length, small as these +last are. If, in fact, the amplitude of the vibrations acquired a +noticeable value in comparison with the wave-length, the speed of +propagation should increase with the amplitude. Yet, in spite of some +curious experiments which seem to establish that the speed of light +does alter a little with its intensity, we have reason to believe +that, as regards light, the amplitude of the oscillations in relation +to the wave-length is incomparably less than in the case of sound. + +It has become the custom to characterise each vibration by the path +which the vibratory movement traverses during the space of a +vibration--by the length of wave, in a word--rather than by the +duration of the vibration itself. To measure wave-lengths, the methods +must be employed to which I have already alluded on the subject of +measurements of length. Professor Michelson, on the one hand, and MM. +Perot and Fabry, on the other, have devised exceedingly ingenious +processes, which have led to results of really unhoped-for precision. +The very exact knowledge also of the speed of the propagation of light +allows the duration of a vibration to be calculated when once the +wave-length is known. It is thus found that, in the case of visible +light, the number of the vibrations from the end of the violet to the +infra-red varies from four hundred to two hundred billions per second. +This gamut is not, however, the only one the ether can give. For a +long time we have known ultra-violet radiations still more rapid, and, +on the other hand, infra-red ones more slow, while in the last few +years the field of known radiations has been singularly extended in +both directions. + +It is to M. Rubens and his fellow-workers that are due the most +brilliant conquests in the matter of great wave-lengths. He had +remarked that, in their study, the difficulty of research proceeds +from the fact that the extreme waves of the infra-red spectrum only +contain a small part of the total energy emitted by an incandescent +body; so that if, for the purpose of study, they are further dispersed +by a prism or a grating, the intensity at any one point becomes so +slight as to be no longer observable. His original idea was to obtain, +without prism or grating, a homogeneous pencil of great wave-length +sufficiently intense to be examined. For this purpose the radiant +source used was a strip of platinum covered with fluorine or powdered +quartz, which emits numerous radiations close to two bands of linear +absorption in the absorption spectra of fluorine and quartz, one of +which is situated in the infra-red. The radiations thus emitted are +several times reflected on fluorine or on quartz, as the case may be; +and as, in proximity to the bands, the absorption is of the order of +that of metallic bodies for luminous rays, we no longer meet in the +pencil several times reflected or in the rays _remaining_ after this +kind of filtration, with any but radiations of great wave-length. +Thus, for instance, in the case of the quartz, in the neighbourhood of +a radiation corresponding to a wave-length of 8.5 microns, the +absorption is thirty times greater in the region of the band than in +the neighbouring region, and consequently, after three reflexions, +while the corresponding radiations will not have been weakened, the +neighbouring waves will be so, on the contrary, in the proportion of 1 +to 27,000. + +With mirrors of rock salt and of sylvine[21] there have been obtained, +by taking an incandescent gas light (Auer) as source, radiations +extending as far as 70 microns; and these last are the greatest +wave-lengths observed in optical phenomena. These radiations are +largely absorbed by the vapour of water, and it is no doubt owing to +this absorption that they are not found in the solar spectrum. On the +other hand, they easily pass through gutta-percha, india-rubber, and +insulating substances in general. + +[Footnote 21: A natural chlorate of potassium, generally of volcanic +origin.--ED.] + +At the opposite end of the spectrum the knowledge of the ultra-violet +regions has been greatly extended by the researches of Lenard. These +extremely rapid radiations have been shown by that eminent physicist +to occur in the light of the electric sparks which flash between two +metal points, and which are produced by a large induction coil with +condenser and a Wehnelt break. Professor Schumann has succeeded in +photographing them by depositing bromide of silver directly on glass +plates without fixing it with gelatine; and he has, by the same +process, photographed in the spectrum of hydrogen a ray with a +wave-length of only 0.1 micron. + +The spectroscope was formed entirely of fluor-spar, and a vacuum had +been created in it, for these radiations are extremely absorbable by +the air. + +Notwithstanding the extreme smallness of the luminous wave-lengths, it +has been possible, after numerous fruitless trials, to obtain +stationary waves analogous to those which, in the case of sound, are +produced in organ pipes. The marvellous application M. Lippmann has +made of these waves to completely solve the problem of photography in +colours is well known. This discovery, so important in itself and so +instructive, since it shows us how the most delicate anticipations of +theory may be verified in all their consequences, and lead the +physicist to the solution of the problems occurring in practice, has +justly become popular, and there is, therefore, no need to describe it +here in detail. + +Professor Wiener obtained stationary waves some little while before M. +Lippmann's discovery, in a layer of a sensitive substance having a +grain sufficiently small in relation to the length of wave. His aim +was to solve a question of great importance to a complete knowledge of +the ether. Fresnel founded his theory of double refraction and +reflexion by transparent surfaces, on the hypothesis that the +vibration of a ray of polarized light is perpendicular to the plane of +polarization. But Neumann has proposed, on the contrary, a theory in +which he recognizes that the luminous vibration is in this very plane. +He rather supposes, in opposition to Fresnel's idea, that the density +of the ether remains the same in all media, while its coefficient of +elasticity is variable. + +Very remarkable experiments on dispersion by M. Carvallo prove indeed +that the idea of Fresnel was, if not necessary for us to adopt, at +least the more probable of the two; but apart from this indication, +and contrary to the hypothesis of Neumann, the two theories, from the +point of view of the explanation of all known facts, really appear to +be equivalent. Are we then in presence of two mechanical explanations, +different indeed, but nevertheless both adaptable to all the facts, +and between which it will always be impossible to make a choice? Or, +on the contrary, shall we succeed in realising an _experimentum +crucis_, an experiment at the point where the two theories cross, +which will definitely settle the question? + +Professor Wiener thought he could draw from his experiment a firm +conclusion on the point in dispute. He produced stationary waves with +light polarized at an angle of 45°,[22] and established that, when +light is polarized in the plane of incidence, the fringes persist; but +that, on the other hand, they disappear when the light is polarized +perpendicularly to this plane. If it be admitted that a photographic +impression results from the active force of the vibratory movement of +the ether, the question is, in fact, completely elucidated, and the +discrepancy is abolished in Fresnel's favour. + +[Footnote 22: That is to say, he reflected the beam of polarized light +by a mirror placed at that angle. See Turpain, _Leçons élementaires de +Physique_, t. ii. p. 311, for details of the experiment.--ED.] + +M.H. Poincaré has pointed out, however, that we know nothing as to the +mechanism of the photographic impression. We cannot consider it +evident that it is the kinetic energy of the ether which produces the +decomposition of the sensitive salt; and if, on the contrary, we +suppose it to be due to the potential energy, all the conclusions are +reversed, and Neumann's idea triumphs. + +Recently a very clever physicist, M. Cotton, especially known for his +skilful researches in the domain of optics, has taken up anew the +study of stationary waves. He has made very precise quantitative +experiments, and has demonstrated, in his turn, that it is impossible, +even with spherical waves, to succeed in determining on which of the +two vectors which have to be regarded in all theories of light on the +subject of polarization phenomena the luminous intensity and the +chemical action really depend. This question, therefore, no longer +exists for those physicists who admit that luminous vibrations are +electrical oscillations. Whatever, then, the hypothesis formed, +whether it be electric force or, on the contrary, magnetic force which +we place in the plane of polarization, the mode of propagation +foreseen will always be in accord with the facts observed. + + +§ 3. THE ELECTROMAGNETIC ETHER + +The idea of attributing the phenomena of electricity to perturbations +produced in the medium which transmits the light is already of old +standing; and the physicists who witnessed the triumph of Fresnel's +theories could not fail to conceive that this fluid, which fills the +whole of space and penetrates into all bodies, might also play a +preponderant part in electrical actions. Some even formed too hasty +hypotheses on this point; for the hour had not arrived when it was +possible to place them on a sufficiently sound basis, and the known +facts were not numerous enough to give the necessary precision. + +The founders of modern electricity also thought it wiser to adopt, +with regard to this science, the attitude taken by Newton in +connection with gravitation: "In the first place to observe facts, to +vary the circumstances of these as much as possible, to accompany this +first work by precise measurements in order to deduce from them +general laws founded solely on experiment, and to deduce from these +laws, independently of all hypotheses on the nature of the forces +producing the phenomena, the mathematical value of these forces--that +is to say, the formula representing them. Such was the system pursued +by Newton. It has, in general, been adopted in France by the scholars +to whom physics owe the great progress made of late years, and it has +served as my guide in all my researches on electrodynamic +phenomena.... It is for this reason that I have avoided speaking of +the ideas I may have on the nature of the cause of the force emanating +from voltaic conductors." + +Thus did Ampère express himself. The illustrious physicist rightly +considered the results obtained by him through following this wise +method as worthy of comparison with the laws of attraction; but he +knew that when this first halting-place was reached there was still +further to go, and that the evolution of ideas must necessarily +continue. + +"With whatever physical cause," he adds, "we may wish to connect the +phenomena produced by electro-dynamic action, the formula I have +obtained will always remain the expression of the facts," and he +explicitly indicated that if one could succeed in deducing his formula +from the consideration of the vibrations of a fluid distributed +through space, an enormous step would have been taken in this +department of physics. He added, however, that this research appeared +to him premature, and would change nothing in the results of his work, +since, to accord with facts, the hypothesis adopted would always have +to agree with the formula which exactly represents them. + +It is not devoid of interest to observe that Ampère himself, +notwithstanding his caution, really formed some hypotheses, and +recognized that electrical phenomena were governed by the laws of +mechanics. Yet the principles of Newton then appeared to be +unshakable. + +Faraday was the first to demonstrate, by clear experiment, the +influence of the media in electricity and magnetic phenomena, and he +attributed this influence to certain modifications in the ether which +these media enclose. His fundamental conception was to reject action +at a distance, and to localize in the ether the energy whose evolution +is the cause of the actions manifested, as, for example, in the +discharge of a condenser. + +Consider the barrel of a pump placed in a vacuum and closed by a +piston at each end, and let us introduce between these a certain mass +of air. The two pistons, through the elastic force of the gas, repel +each other with a force which, according to the law of Mariotte, +varies in inverse ratio to the distance. The method favoured by Ampère +would first of all allow this law of repulsion between the two pistons +to be discovered, even if the existence of a gas enclosed in the +barrel of the pump were unsuspected; and it would then be natural to +localize the potential energy of the system on the surface of the two +pistons. But if the phenomenon is more carefully examined, we shall +discover the presence of the air, and we shall understand that every +part of the volume of this air could, if it were drawn off into a +recipient of equal volume, carry away with it a fraction of the energy +of the system, and that consequently this energy belongs really to the +air and not to the pistons, which are there solely for the purpose of +enabling this energy to manifest its existence. + +Faraday made, in some sort, an equivalent discovery when he perceived +that the electrical energy belongs, not to the coatings of the +condenser, but to the dielectric which separates them. His audacious +views revealed to him a new world, but to explore this world a surer +and more patient method was needed. + +Maxwell succeeded in stating with precision certain points of +Faraday's ideas, and he gave them the mathematical form which, often +wrongly, impresses physicists, but which when it exactly encloses a +theory, is a certain proof that this theory is at least coherent and +logical.[23] + +[Footnote 23: It will no doubt be a shock to those whom Professor +Henry Armstrong has lately called the "mathematically-minded" to find +a member of the Poincaré family speaking disrespectfully of the +science they have done so much to illustrate. One may perhaps compare +the expression in the text with M. Henri Poincaré's remark in his last +allocution to the Académie des Sciences, that "Mathematics are +sometimes a nuisance, and even a danger, when they induce us to affirm +more than we know" (_Comptes-rendus_, 17th December 1906).] + +The work of Maxwell is over-elaborated, complex, difficult to read, +and often ill-understood, even at the present day. Maxwell is more +concerned in discovering whether it is possible to give an explanation +of electrical and magnetic phenomena which shall be founded on the +mechanical properties of a single medium, than in stating this +explanation in precise terms. He is aware that if we could succeed in +constructing such an interpretation, it would be easy to propose an +infinity of others, entirely equivalent from the point of view of the +experimentally verifiable consequences; and his especial ambition is +therefore to extract from the premises a general view, and to place in +evidence something which would remain the common property of all the +theories. + +He succeeded in showing that if the electrostatic energy of an +electromagnetic field be considered to represent potential energy, and +its electrodynamic the kinetic energy, it becomes possible to satisfy +both the principle of least action and that of the conservation of +energy; from that moment--if we eliminate a few difficulties which +exist regarding the stability of the solutions--the possibility of +finding mechanical explanations of electromagnetic phenomena must be +considered as demonstrated. He thus succeeded, moreover, in stating +precisely the notion of two electric and magnetic fields which +are produced in all points of space, and which are strictly +inter-connected, since the variation of the one immediately and +compulsorily gives birth to the other. + +From this hypothesis he deduced that, in the medium where this energy +is localized, an electromagnetic wave is propagated with a velocity +equal to the relation of the units of electric mass in the +electromagnetic and electrostatic systems. Now, experiments made known +since his time have proved that this relation is numerically equal to +the speed of light, and the more precise experiments made in +consequence--among which should be cited the particularly careful ones +of M. Max Abraham--have only rendered the coincidence still more +complete. + +It is natural henceforth to suppose that this medium is identical with +the luminous ether, and that a luminous wave is an electromagnetic +wave--that is to say, a succession of alternating currents, which +exist in the dielectric and even in the void, and possess an enormous +frequency, inasmuch as they change their direction thousands of +billions of times per second, and by reason of this frequency produce +considerable induction effects. Maxwell did not admit the existence of +open currents. To his mind, therefore, an electrical vibration could +not produce condensations of electricity. It was, in consequence, +necessarily transverse, and thus coincided with the vibration of +Fresnel; while the corresponding magnetic vibration was perpendicular +to it, and would coincide with the luminous vibration of Neumann. + +Maxwell's theory thus establishes a close correlation between the +phenomena of the luminous and those of the electromagnetic waves, or, +we might even say, the complete identity of the two. But it does not +follow from this that we ought to regard the variation of an electric +field produced at some one point as necessarily consisting of a real +displacement of the ether round that point. The idea of thus bringing +electrical phenomena back to the mechanics of the ether is not, then, +forced upon us, and the contrary idea even seems more probable. It is +not the optics of Fresnel which absorbs the science of electricity, it +is rather the optics which is swallowed up by a more general theory. +The attempts of popularizers who endeavour to represent, in all their +details, the mechanism of the electric phenomena, thus appear vain +enough, and even puerile. It is useless to find out to what material +body the ether may be compared, if we content ourselves with seeing in +it a medium of which, at every point, two vectors define the +properties. + +For a long time, therefore, we could remark that the theory of Fresnel +simply supposed a medium in which something periodical was propagated, +without its being necessary to admit this something to be a movement; +but we had to wait not only for Maxwell, but also for Hertz, before +this idea assumed a really scientific shape. Hertz insisted on the +fact that the six equations of the electric field permit all the +phenomena to be anticipated without its being necessary to construct +one hypothesis or another, and he put these equations into a very +symmetrical form, which brings completely in evidence the perfect +reciprocity between electrical and magnetic actions. He did yet more, +for he brought to the ideas of Maxwell the most striking confirmation +by his memorable researches on electric oscillations. + + +§ 4. ELECTRICAL OSCILLATIONS + +The experiments of Hertz are well known. We know how the Bonn +physicist developed, by means of oscillating electric discharges, +displacement currents and induction effects in the whole of the space +round the spark-gap; and how he excited by induction at some point in +a wire a perturbation which afterwards is propagated along the wire, +and how a resonator enabled him to detect the effect produced. + +The most important point made evident by the observation of +interference phenomena and subsequently verified directly by M. +Blondlot, is that the electromagnetic perturbation is propagated with +the speed of light, and this result condemns for ever all the +hypotheses which fail to attribute any part to the intervening media +in the propagation of an induction phenomenon. + +If the inducing action were, in fact, to operate directly between the +inducing and the induced circuits, the propagation should be +instantaneous; for if an interval were to occur between the moment +when the cause acted and the one when the effect was produced, during +this interval there would no longer be anything anywhere, since the +intervening medium does not come into play, and the phenomenon would +then disappear. + +Leaving on one side the manifold but purely electrical consequences of +this and the numerous researches relating to the production or to the +properties of the waves--some of which, those of MM. Sarrazin and de +la Rive, Righi, Turpain, Lebedeff, Decombe, Barbillon, Drude, Gutton, +Lamotte, Lecher, etc., are, however, of the highest order--I shall +only mention here the studies more particularly directed to the +establishment of the identity of the electromagnetic and the luminous +waves. + +The only differences which subsist are necessarily those due to the +considerable discrepancy which exists between the durations of the +periods of these two categories of waves. The length of wave +corresponding to the first spark-gap of Hertz was about 6 metres, and +the longest waves perceptible by the retina are 7/10 of a micron.[24] + +[Footnote 24: See footnote 3.] + +These radiations are so far apart that it is not astonishing that +their properties have not a perfect similitude. Thus phenomena like +those of diffraction, which are negligible in the ordinary conditions +under which light is observed, may here assume a preponderating +importance. To play the part, for example, with the Hertzian waves, +which a mirror 1 millimetre square plays with regard to light, would +require a colossal mirror which would attain the size of a +myriametre[25] square. + +[Footnote 25: I.e., 10,000 metres.--ED.] + +The efforts of physicists have to-day, however, filled up, in great +part, this interval, and from both banks at once they have laboured to +build a bridge between the two domains. We have seen how Rubens showed +us calorific rays 60 metres long; on the other hand, MM. Lecher, Bose, +and Lampa have succeeded, one after the other, in gradually obtaining +oscillations with shorter and shorter periods. There have been +produced, and are now being studied, electromagnetic waves of four +millimetres; and the gap subsisting in the spectrum between the rays +left undetected by sylvine and the radiations of M. Lampa now hardly +comprise more than five octaves--that is to say, an interval +perceptibly equal to that which separates the rays observed by M. +Rubens from the last which are evident to the eye. + +The analogy then becomes quite close, and in the remaining rays the +properties, so to speak, characteristic of the Hertzian waves, begin +to appear. For these waves, as we have seen, the most transparent +bodies are the most perfect electrical insulators; while bodies still +slightly conducting are entirely opaque. The index of refraction of +these substances tends in the case of great wave-lengths to become, as +the theory anticipates, nearly the square root of the dielectric +constant. + +MM. Rubens and Nichols have even produced with the waves which remain +phenomena of electric resonance quite similar to those which an +Italian scholar, M. Garbasso, obtained with electric waves. This +physicist showed that, if the electric waves are made to impinge on a +flat wooden stand, on which are a series of resonators parallel to +each other and uniformly arranged, these waves are hardly reflected +save in the case where the resonators have the same period as the +spark-gap. If the remaining rays are allowed to fall on a glass plate +silvered and divided by a diamond fixed on a dividing machine into +small rectangles of equal dimensions, there will be observed +variations in the reflecting power according to the orientation of the +rectangles, under conditions entirely comparable with the experiment +of Garbasso. + +In order that the phenomenon be produced it is necessary that the +remaining waves should be previously polarized. This is because, in +fact, the mechanism employed to produce the electric oscillations +evidently gives out vibrations which occur on a single plane and are +subsequently polarized. + +We cannot therefore entirely assimilate a radiation proceeding from a +spark-gap to a ray of natural light. For the synthesis of light to be +realized, still other conditions must be complied with. During a +luminous impression, the direction and the phase change millions of +times in the vibration sensible to the retina, yet the damping of this +vibration is very slow. With the Hertzian oscillations all these +conditions are changed--the damping is very rapid but the direction +remains invariable. + +Every time, however, that we deal with general phenomena which are +independent of these special conditions, the parallelism is perfect; +and with the waves, we have put in evidence the reflexion, refraction, +total reflexion, double reflexion, rotatory polarization, dispersion, +and the ordinary interferences produced by rays travelling in the same +direction and crossing each other at a very acute angle, or the +interferences analogous to those which Wiener observed with rays of +the contrary direction. + +A very important consequence of the electromagnetic theory foreseen by +Maxwell is that the luminous waves which fall on a surface must +exercise on this surface a pressure equal to the radiant energy which +exists in the unit of volume of the surrounding space. M. Lebedeff a +few years ago allowed a sheaf of rays from an arc lamp to fall on a +deflection radiometer,[26] and thus succeeded in revealing the +existence of this pressure. Its value is sufficient, in the case of +matter of little density and finely divided, to reduce and even change +into repulsion the attractive action exercised on bodies by the sun. +This is a fact formerly conjectured by Faye, and must certainly play a +great part in the deformation of the heads of comets. + +[Footnote 26: By this M. Poincaré appears to mean a radiometer in +which the vanes are not entirely free to move as in the radiometer of +Crookes but are suspended by one or two threads as in the instrument +devised by Professor Poynting.--ED.] + +More recently, MM. Nichols and Hull have undertaken experiments on +this point. They have measured not only the pressure, but also the +energy of the radiation by means of a special bolometer. They have +thus arrived at numerical verifications which are entirely in +conformity with the calculations of Maxwell. + +The existence of these pressures may be otherwise foreseen even apart +from the electromagnetic theory, by adding to the theory of +undulations the principles of thermodynamics. Bartoli, and more +recently Dr Larmor, have shown, in fact, that if these pressures did +not exist, it would be possible, without any other phenomenon, to pass +heat from a cold into a warm body, and thus transgress the principle +of Carnot. + + +§ 5. THE X RAYS + +It appears to-day quite probable that the X rays should be classed +among the phenomena which have their seat in the luminous ether. +Doubtless it is not necessary to recall here how, in December 1895, +Röntgen, having wrapped in black paper a Crookes tube in action, +observed that a fluorescent platinocyanide of barium screen placed in +the neighbourhood, had become visible in the dark, and that a +photographic plate had received an impress. The rays which come from +the tube, in conditions now well known, are not deviated by a magnet, +and, as M. Curie and M. Sagnac have conclusively shown, they carry no +electric charge. They are subject to neither reflection nor +refraction, and very precise and very ingenious measurements by M. +Gouy have shown that, in their case, the refraction index of the +various bodies cannot be more than a millionth removed from unity. + +We knew from the outset that there existed various X rays differing +from each other as, for instance, the colours of the spectrum, and +these are distinguished from each other by their unequal power of +passing through substances. M. Sagnac, particularly, has shown that +there can be obtained a gradually decreasing scale of more or less +absorbable rays, so that the greater part of their photographic action +is stopped by a simple sheet of black paper. These rays figure among +the secondary rays discovered, as is known, by this ingenious +physicist. The X rays falling on matter are thus subjected to +transformations which may be compared to those which the phenomena of +luminescence produce on the ultra-violet rays. + +M. Benoist has founded on the transparency of matter to the rays a +sure and practical method of allowing them to be distinguished, and +has thus been enabled to define a specific character analogous to the +colour of the rays of light. It is probable also that the different +rays do not transport individually the same quantity of energy. We +have not yet obtained on this point precise results, but it is roughly +known, since the experiments of MM. Rutherford and M'Clung, what +quantity of energy corresponds to a pencil of X rays. These physicists +have found that this quantity would be, on an average, five hundred +times larger than that brought by an analogous pencil of solar light +to the surface of the earth. What is the nature of this energy? The +question does not appear to have been yet solved. + +It certainly appears, according to Professors Haga and Wind and to +Professor Sommerfeld, that with the X rays curious experiments of +diffraction may be produced. Dr Barkla has shown also that they can +manifest true polarization. The secondary rays emitted by a metallic +surface when struck by X rays vary, in fact, in intensity when the +position of the plane of incidence round the primary pencil is +changed. Various physicists have endeavoured to measure the speed of +propagation, but it seems more and more probable that it is very +nearly that of light.[27] + +[Footnote 27: See especially the experiments of Professor E. Marx +(Vienna), _Annalen der Physik_, vol. xx. (No. 9 of 1906), pp. 677 _et +seq._, which seem conclusive on this point.--ED.] + +I must here leave out the description of a crowd of other experiments. +Some very interesting researches by M. Brunhes, M. Broca, M. +Colardeau, M. Villard, in France, and by many others abroad, have +permitted the elucidation of several interesting problems relative to +the duration of the emission or to the best disposition to be adopted +for the production of the rays. The only point which will detain us is +the important question as to the nature of the X rays themselves; the +properties which have just been brought to mind are those which appear +essential and which every theory must reckon with. + +The most natural hypothesis would be to consider the rays as +ultra-violet radiations of very short wave-length, or radiations which +are in a manner ultra-ultra-violet. This interpretation can still, at +this present moment, be maintained, and the researches of MM. Buisson, +Righi, Lenard, and Merrit Stewart have even established that rays of +very short wave-lengths produce on metallic conductors, from the point +of view of electrical phenomena, effects quite analogous to those of +the X rays. Another resemblance results also from the experiments by +which M. Perreau established that these rays act on the electric +resistance of selenium. New and valuable arguments have thus added +force to those who incline towards a theory which has the merit of +bringing a new phenomenon within the pale of phenomena previously +known. + +Nevertheless the shortest ultra-violet radiations, such as those of M. +Schumann, are still capable of refraction by quartz, and this +difference constitutes, in the minds of many physicists, a serious +enough reason to decide them to reject the more simple hypothesis. +Moreover, the rays of Schumann are, as we have seen, extraordinarily +absorbable,--so much so that they have to be observed in a vacuum. The +most striking property of the X rays is, on the contrary, the facility +with which they pass through obstacles, and it is impossible not to +attach considerable importance to such a difference. + +Some attribute this marvellous radiation to longitudinal vibrations, +which, as M. Duhem has shown, would be propagated in dielectric media +with a speed equal to that of light. But the most generally accepted +idea is the one formulated from the first by Sir George Stokes and +followed up by Professor Wiechert. According to this theory the X rays +should be due to a succession of independent pulsations of the ether, +starting from the points where the molecules projected by the cathode +of the Crookes tube meet the anticathode. These pulsations are not +continuous vibrations like the radiations of the spectrum; they are +isolated and extremely short; they are, besides, transverse, like the +undulations of light, and the theory shows that they must be +propagated with the speed of light. They should present neither +refraction nor reflection, but, under certain conditions, they may be +subject to the phenomena of diffraction. All these characteristics are +found in the Röntgen rays. + +Professor J.J. Thomson adopts an analogous idea, and states the +precise way in which the pulsations may be produced at the moment when +the electrified particles forming the cathode rays suddenly strike the +anticathode wall. The electromagnetic induction behaves in such a way +that the magnetic field is not annihilated when the particle stops, +and the new field produced, which is no longer in equilibrium, is +propagated in the dielectric like an electric pulsation. The electric +and magnetic pulsations excited by this mechanism may give birth to +effects similar to those of light. Their slight amplitude, however, is +the cause of there here being neither refraction nor diffraction +phenomena, save in very special conditions. If the cathode particle is +not stopped in zero time, the pulsation will take a greater amplitude, +and be, in consequence, more easily absorbable; to this is probably to +be attributed the differences which may exist between different tubes +and different rays. + +It is right to add that some authors, notwithstanding the proved +impossibility of deviating them in a magnetic field, have not +renounced the idea of comparing them with the cathode rays. They +suppose, for instance, that the rays are formed by electrons animated +with so great a velocity that their inertia, conformably with theories +which I shall examine later, no longer permit them to be stopped in +their course; this is, for instance, the theory upheld by Mr +Sutherland. We know, too, that to M. Gustave Le Bon they represent the +extreme limit of material things, one of the last stages before the +vanishing of matter on its return to the ether. + +Everyone has heard of the N rays, whose name recalls the town of +Nancy, where they were discovered. In some of their singular +properties they are akin to the X rays, while in others they are +widely divergent from them. + +M. Blondlot, one of the masters of contemporary physics, deeply +respected by all who know him, admired by everyone for the penetration +of his mind, and the author of works remarkable for the originality +and sureness of his method, discovered them in radiations emitted from +various sources, such as the sun, an incandescent light, a Nernst +lamp, and even bodies previously exposed to the sun's rays. The +essential property which allows them to be revealed is their action on +a small induction spark, of which they increase the brilliancy; this +phenomenon is visible to the eye and is rendered objective by +photography. + +Various other physicists and numbers of physiologists, following the +path opened by M. Blondlot, published during 1903 and 1904 manifold +but often rather hasty memoirs, in which they related the results of +their researches, which do not appear to have been always conducted +with the accuracy desirable. These results were most strange; they +seemed destined to revolutionise whole regions not only of the domain +of physics, but likewise of the biological sciences. Unfortunately the +method of observation was always founded on the variations in +visibility of the spark or of a phosphorescent substance, and it soon +became manifest that these variations were not perceptible to all +eyes. + +No foreign experimenter has succeeded in repeating the experiments, +while in France many physicists have failed; and hence the question +has much agitated public opinion. Are we face to face with a very +singular case of suggestion, or is special training and particular +dispositions required to make the phenomenon apparent? It is not +possible, at the present moment, to declare the problem solved; but +very recent experiments by M. Gutton and a note by M. Mascart have +reanimated the confidence of those who hoped that such a scholar as M. +Blondlot could not have been deluded by appearances. However, these +last proofs in favour of the existence of the rays have themselves +been contested, and have not succeeded in bringing conviction to +everyone. + +It seems very probable indeed that certain of the most singular +conclusions arrived at by certain authors on the subject will lapse +into deserved oblivion. But negative experiments prove nothing in a +case like this, and the fact that most experimenters have failed where +M. Blondlot and his pupils have succeeded may constitute a +presumption, but cannot be regarded as a demonstrative argument. Hence +we must still wait; it is exceedingly possible that the illustrious +physicist of Nancy may succeed in discovering objective actions of the +N rays which shall be indisputable, and may thus establish on a firm +basis a discovery worthy of those others which have made his name so +justly celebrated. + +According to M. Blondlot the N rays can be polarised, refracted, and +dispersed, while they have wavelengths comprised within .0030 micron, +and .0760 micron--that is to say, between an eighth and a fifth of +that found for the extreme ultra-violet rays. They might be, perhaps, +simply rays of a very short period. Their existence, stripped of the +parasitical and somewhat singular properties sought to be attributed +to them, would thus appear natural enough. It would, moreover, be +extremely important, and lead, no doubt, to most curious applications; +it can be conceived, in fact, that such rays might serve to reveal +what occurs in those portions of matter whose too minute dimensions +escape microscopic examination on account of the phenomena of +diffraction. + +From whatever point of view we look at it, and whatever may be the +fate of the discovery, the history of the N rays is particularly +instructive, and must give food for reflection to those interested in +questions of scientific methods. + + +§ 6. THE ETHER AND GRAVITATION + +The striking success of the hypothesis of the ether in optics has, in +our own days, strengthened the hope of being able to explain, by an +analogous representation, the action of gravitation. + +For a long time, philosophers who rejected the idea that ponderability +is a primary and essential quality of all bodies have sought to reduce +their weight to pressures exercised in a very subtle fluid. This was +the conception of Descartes, and was perhaps the true idea of Newton +himself. Newton points out, in many passages, that the laws he had +discovered were independent of the hypotheses that could be formed on +the way in which universal attraction was produced, but that with +sufficient experiments the true cause of this attraction might one day +be reached. In the preface to the second edition of the Optics he +writes: "To prove that I have not considered weight as a universal +property of bodies, I have added a question as to its cause, +preferring this form of question because my interpretation does not +entirely satisfy me in the absence of experiment"; and he puts the +question in this shape: "Is not this medium (the ether) more rarefied +in the interior of dense bodies like the sun, the planets, the comets, +than in the empty spaces which separate them? Passing from these +bodies to great distances, does it not become continually denser, and +in that way does it not produce the weight of these great bodies with +regard to each other and of their parts with regard to these bodies, +each body tending to leave the most dense for the most rarefied +parts?" + +Evidently this view is incomplete, but we may endeavour to state it +precisely. If we admit that this medium, the properties of which would +explain the attraction, is the same as the luminous ether, we may +first ask ourselves whether the action of gravitation is itself also +due to oscillations. Some authors have endeavoured to found a theory +on this hypothesis, but we are immediately brought face to face with +very serious difficulties. Gravity appears, in fact, to present quite +exceptional characteristics. No agent, not even those which depend +upon the ether, such as light and electricity, has any influence on +its action or its direction. All bodies are, so to speak, absolutely +transparent to universal attraction, and no experiment has succeeded +in demonstrating that its propagation is not instantaneous. From +various astronomical observations, Laplace concluded that its +velocity, in any case, must exceed fifty million times that of light. +It is subject neither to reflection nor to refraction; it is +independent of the structure of bodies; and not only is it +inexhaustible, but also (as is pointed out, according to M. Hannequin, +by an English scholar, James Croll) the distribution of the effects of +the attracting force of a mass over the manifold particles which may +successively enter the field of its action in no way diminishes the +attraction it exercises on each of them respectively, a thing which is +seen nowhere else in nature. + +Nevertheless it is possible, by means of certain hypotheses, to +construct interpretations whereby the appropriate movements of an +elastic medium should explain the facts clearly enough. But these +movements are very complex, and it seems almost inconceivable that the +same medium could possess simultaneously the state of movement +corresponding to the transmission of a luminous phenomenon and that +constantly imposed on it by the transmission of gravitation. + +Another celebrated hypothesis was devised by Lesage, of Geneva. Lesage +supposed space to be overrun in all directions by currents of +_ultramundane_ corpuscles. This hypothesis, contested by Maxwell, is +interesting. It might perhaps be taken up again in our days, and it is +not impossible that the assimilation of these corpuscles to electrons +might give a satisfactory image.[28] + +[Footnote 28: M. Sagnac (_Le Radium_, Jan. 1906, p. 14), following +perhaps Professors Elster and Geitel, has lately taken up this idea +anew.--ED.] + +M. Crémieux has recently undertaken experiments directed, as he +thinks, to showing that the divergences between the phenomena of +gravitation and all the other phenomena in nature are more apparent +than real. Thus the evolution in the heart of the ether of a quantity +of gravific energy would not be entirely isolated, and as in the case +of all evolutions of all energy of whatever kind, it should provoke a +partial transformation into energy of a different form. Thus again the +liberated energy of gravitation would vary when passing from one +material to another, as from gases into liquids, or from one liquid to +a different one. + +On this last point the researches of M. Crémieux have given +affirmative results: if we immerse in a large mass of some liquid +several drops of another not miscible with the first, but of identical +density, we form a mass representing no doubt a discontinuity in the +ether, and we may ask ourselves whether, in conformity with what +happens in all other phenomena of nature, this discontinuity has not a +tendency to disappear. + +If we abide by the ordinary consequences of the Newtonian theory of +potential, the drops should remain motionless, the hydrostatic +impulsion forming an exact equilibrium to their mutual attraction. Now +M. Crémieux remarks that, as a matter of fact, they slowly approach +each other. + +Such experiments are very delicate; and with all the precautions taken +by the author, it cannot yet be asserted that he has removed all +possibility of the action of the phenomena of capillarity nor all +possible errors proceeding from extremely slight differences of +temperature. But the attempt is interesting and deserves to be +followed up. + +Thus, the hypothesis of the ether does not yet explain all the +phenomena which the considerations relating to matter are of +themselves powerless to interpret. If we wished to represent to +ourselves, by the mechanical properties of a medium filling the whole +of the universe, all luminous, electric, and gravitation phenomena, we +should be led to attribute to this medium very strange and almost +contradictory characteristics; and yet it would be still more +inconceivable that this medium should be double or treble, that there +should be two or three ethers each occupying space as if it were +alone, and interpenetrating it without exercising any action on one +another. We are thus brought, by a close examination of facts, rather +to the idea that the properties of the ether are not wholly reducible +to the rules of ordinary mechanics. + +The physicist has therefore not yet succeeded in answering the +question often put to him by the philosopher: "Has the ether really an +objective existence?" However, it is not necessary to know the answer +in order to utilize the ether. In its ideal properties we find the +means of determining the form of equations which are valid, and to the +learned detached from all metaphysical prepossession this is the +essential point. + + + + +CHAPTER VII + +A CHAPTER IN THE HISTORY OF SCIENCE: WIRELESS TELEGRAPHY + + +§ 1 + +I have endeavoured in this book to set forth impartially the ideas +dominant at this moment in the domain of physics, and to make known +the facts essential to them. I have had to quote the authors of the +principal discoveries in order to be able to class and, in some sort, +to name these discoveries; but I in no way claim to write even a +summary history of the physics of the day. + +I am not unaware that, as has often been said, contemporary history is +the most difficult of all histories to write. A certain step backwards +seems necessary in order to enable us to appreciate correctly the +relative importance of events, and details conceal the full view from +eyes which are too close to them, as the trees prevent us from seeing +the forest. The event which produces a great sensation has often only +insignificant consequences; while another, which seemed at the outset +of the least importance and little worthy of note, has in the long run +a widespread and deep influence. + +If, however, we deal with the history of a positive discovery, +contemporaries who possess immediate information, and are in a +position to collect authentic evidence at first hand, will make, by +bringing to it their sincere testimony, a work of erudition which may +be very useful, but which we may be tempted to look upon as very easy +of execution. Yet such a labour, even when limited to the study of a +very minute question or of a recent invention, is far from being +accomplished without the historian stumbling over serious obstacles. + +An invention is never, in reality, to be attributed to a single +author. It is the result of the work of many collaborators who +sometimes have no acquaintance with one another, and is often the +fruit of obscure labours. Public opinion, however, wilfully simple in +face of a sensational discovery, insists that the historian should +also act as judge; and it is the historian's task to disentangle the +truth in the midst of the contest, and to declare infallibly to whom +the acknowledgments of mankind should be paid. He must, in his +capacity as skilled expert, expose piracies, detect the most carefully +hidden plagiarisms, and discuss the delicate question of priority; +while he must not be deluded by those who do not fear to announce, in +bold accents, that they have solved problems of which they find the +solution imminent, and who, the day after its final elucidation by +third parties, proclaim themselves its true discoverers. He must rise +above a partiality which deems itself excusable because it proceeds +from national pride; and, finally, he must seek with patience for what +has gone before. While thus retreating step by step he runs the risk +of losing himself in the night of time. + +An example of yesterday seems to show the difficulties of such a task. +Among recent discoveries the invention of wireless telegraphy is one +of those which have rapidly become popular, and looks, as it were, an +exact subject clearly marked out. Many attempts have already been made +to write its history. Mr J.J. Fahie published in England as early as +1899 an interesting work entitled the _History of Wireless +Telegraphy_; and about the same time M. Broca published in France a +very exhaustive work named _La Telegraphie sans fil_. Among the +reports presented to the Congrès international de physique (Paris, +1900), Signor Righi, an illustrious Italian scholar, whose personal +efforts have largely contributed to the invention of the present +system of telegraphy, devoted a chapter, short, but sufficiently +complete, of his masterly report on Hertzian waves, to the history of +wireless telegraphy. The same author, in association with Herr +Bernhard Dessau, has likewise written a more important work, _Die +Telegraphie ohne Draht_; and _La Telegraphie sans fil et les ondes +Électriques_ of MM. J. Boulanger and G. Ferrié may also be consulted +with advantage, as may _La Telegraphie sans fil_ of Signor Dominico +Mazotto. Quite recently Mr A. Story has given us in a little volume +called _The Story of Wireless Telegraphy_, a condensed but very +precise recapitulation of all the attempts which have been made to +establish telegraphic communication without the intermediary of a +conducting wire. Mr Story has examined many documents, has sometimes +brought curious facts to light, and has studied even the most recently +adopted apparatus. + +It may be interesting, by utilising the information supplied by these +authors and supplementing them when necessary by others, to trace the +sources of this modern discovery, to follow its developments, and thus +to prove once more how much a matter, most simple in appearance, +demands extensive and complex researches on the part of an author +desirous of writing a definitive work. + + +§ 2 + +The first, and not the least difficulty, is to clearly define the +subject. The words "wireless telegraphy," which at first seem to +correspond to a simple and perfectly clear idea, may in reality apply +to two series of questions, very different in the mind of a physicist, +between which it is important to distinguish. The transmission of +signals demands three organs which all appear indispensable: the +transmitter, the receiver, and, between the two, an intermediary +establishing the communication. This intermediary is generally the +most costly part of the installation and the most difficult to set up, +while it is here that the sensible losses of energy at the expense of +good output occur. And yet our present ideas cause us to consider this +intermediary as more than ever impossible to suppress; since, if we +are definitely quit of the conception of action at a distance, it +becomes inconceivable to us that energy can be communicated from one +point to another without being carried by some intervening medium. +But, practically, the line will be suppressed if, instead of +constructing it artificially, we use to replace it one of the natural +media which separate two points on the earth. These natural media are +divided into two very distinct categories, and from this +classification arise two series of questions to be examined. + +Between the two points in question there are, first, the material +media such as the air, the earth, and the water. For a long time we +have used for transmissions to a distance the elastic properties of +the air, and more recently the electric conductivity of the soil and +of water, particularly that of the sea. + +Modern physics leads us on the other hand, as we have seen, to +consider that there exists throughout the whole of the universe +another and more subtle medium which penetrates everywhere, is endowed +with elasticity _in vacuo_, and retains its elasticity when it +penetrates into a great number of bodies, such as the air. This medium +is the luminous ether which possesses, as we cannot doubt, the +property of being able to transmit energy, since it itself brings to +us by far the larger part of the energy which we possess on earth and +which we find in the movements of the atmosphere, or of waterfalls, +and in the coal mines proceeding from the decomposition of carbon +compounds under the influence of the solar energy. For a long time +also before the existence of the ether was known, the duty of +transmitting signals was entrusted to it. Thus through the ages a +double evolution is unfolded which has to be followed by the historian +who is ambitious of completeness. + + +§ 3 + +If such an historian were to examine from the beginning the first +order of questions, he might, no doubt, speak only briefly of the +attempts earlier than electric telegraphy. Without seeking to be +paradoxical, he certainly ought to mention the invention of the +speaking-trumpet and other similar inventions which for a long time +have enabled mankind, by the ingenious use of the elastic properties +of the natural media, to communicate at greater distances than they +could have attained without the aid of art. After this in some sort +prehistoric period had been rapidly run through, he would have to +follow very closely the development of electric telegraphy. Almost +from the outset, and shortly after Ampère had made public the idea of +constructing a telegraph, and the day after Gauss and Weber set up +between their houses in Göttingen the first line really used, it was +thought that the conducting properties of the earth and water might be +made of service. + +The history of these trials is very long, and is closely mixed up with +the history of ordinary telegraphy; long chapters for some time past +have been devoted to it in telegraphic treatises. It was in 1838, +however, that Professor C.A. Steinheil of Munich expressed, for the +first time, the clear idea of suppressing the return wire and +replacing it by a connection of the line wire to the earth. He thus at +one step covered half the way, the easiest, it is true, which was to +lead to the final goal, since he saved the use of one-half of the line +of wire. Steinheil, advised, perhaps, by Gauss, had, moreover, a very +exact conception of the part taken by the earth considered as a +conducting body. He seems to have well understood that, in certain +conditions, the resistance of such a conductor, though supposed to be +unlimited, might be independent of the distance apart of the +electrodes which carry the current and allow it to go forth. He +likewise thought of using the railway lines to transmit telegraphic +signals. + +Several scholars who from the first had turned their minds to +telegraphy, had analogous ideas. It was thus that S.F.B. Morse, +superintendent of the Government telegraphs in the United States, +whose name is universally known in connection with the very simple +apparatus invented by him, made experiments in the autumn of 1842 +before a special commission in New York and a numerous public +audience, to show how surely and how easily his apparatus worked. In +the very midst of his experiments a very happy idea occurred to him of +replacing by the water of a canal, the length of about a mile of wire +which had been suddenly and accidentally destroyed. This accident, +which for a moment compromised the legitimate success the celebrated +engineer expected, thus suggested to him a fruitful idea which he did +not forget. He subsequently repeated attempts to thus utilise the +earth and water, and obtained some very remarkable results. + +It is not possible to quote here all the researches undertaken with +the same purpose, to which are more particularly attached the names of +S.W. Wilkins, Wheatstone, and H. Highton, in England; of Bonetti in +Italy, Gintl in Austria, Bouchot and Donat in France; but there are +some which cannot be recalled without emotion. + +On the 17th December 1870, a physicist who has left in the University +of Paris a lasting name, M. d'Almeida, at that time Professor at the +Lycée Henri IV. and later Inspector-General of Public Instruction, +quitted Paris, then besieged, in a balloon, and descended in the midst +of the German lines. He succeeded, after a perilous journey, in +gaining Havre by way of Bordeaux and Lyons; and after procuring the +necessary apparatus in England, he descended the Seine as far as +Poissy, which he reached on the 14th January 1871. After his +departure, two other scholars, MM. Desains and Bourbouze, relieving +each other day and night, waited at Paris, in a wherry on the Seine, +ready to receive the signal which they awaited with patriotic anxiety. +It was a question of working a process devised by the last-named pair, +in which the water of the river acted the part of the line wire. On +the 23rd January the communication at last seemed to be established, +but unfortunately, first the armistice and then the surrender of Paris +rendered useless the valuable result of this noble effort. + +Special mention is also due to the experiments made by the Indian +Telegraph Office, under the direction of Mr Johnson and afterwards of +Mr W.F. Melhuish. They led, indeed, in 1889 to such satisfactory +results that a telegraph service, in which the line wire was replaced +by the earth, worked practically and regularly. Other attempts were +also made during the latter half of the nineteenth century to transmit +signals through the sea. They preceded the epoch when, thanks to +numerous physicists, among whom Lord Kelvin undoubtedly occupies a +preponderating position, we succeeded in sinking the first cable; but +they were not abandoned, even after that date, for they gave hopes of +a much more economical solution of the problem. Among the most +interesting are remembered those that S.W. Wilkins carried on for a +long time between France and England. Like Cooke and Wheatstone, he +thought of using as a receiver an apparatus which in some features +resembles the present receiver of the submarine telegraph. Later, +George E. Dering, then James Bowman and Lindsay, made on the same +lines trials which are worthy of being remembered. + +But it is only in our own days that Sir William H. Preece at last +obtained for the first time really practical results. Sir William +himself effected and caused to be executed by his associates--he is +chief consulting engineer to the General Post Office in England-- +researches conducted with much method and based on precise theoretical +considerations. He thus succeeded in establishing very easy, clear, +and regular communications between various places; for example, across +the Bristol Channel. The long series of operations accomplished by so +many seekers, with the object of substituting a material and natural +medium for the artificial lines of metal, thus met with an undoubted +success which was soon to be eclipsed by the widely-known experiments +directed into a different line by Marconi. + +It is right to add that Sir William Preece had himself utilised +induction phenomena in his experiments, and had begun researches with +the aid of electric waves. Much is due to him for the welcome he gave +to Marconi; it is certainly thanks to the advice and the material +support he found in Sir William that the young scholar succeeded in +effecting his sensational experiments. + + +§ 4 + +The starting-point of the experiments based on the properties of the +luminous ether, and having for their object the transmission of +signals, is very remote; and it would be a very laborious task to hunt +up all the work accomplished in that direction, even if we were to +confine ourselves to those in which electrical reactions play a part. +An electric reaction, an electrostatic influence, or an +electromagnetic phenomenon, is transmitted at a distance through the +air by the intermediary of the luminous ether. But electric influence +can hardly be used, as the distances it would allow us to traverse +would be much too restricted, and electrostatic actions are often very +erratic. The phenomena of induction, which are very regular and +insensible to the variations of the atmosphere, have, on the other +hand, for a long time appeared serviceable for telegraphic purposes. + +We might find, in a certain number of the attempts just mentioned, a +partial employment of these phenomena. Lindsay, for instance, in his +project of communication across the sea, attributed to them a +considerable rôle. These phenomena even permitted a true telegraphy +without intermediary wire between the transmitter and the receiver, at +very restricted distances, it is true, but in peculiarly interesting +conditions. It is, in fact, owing to them that C. Brown, and later +Edison and Gilliland, succeeded in establishing communications with +trains in motion. + +Mr Willoughby S. Smith and Mr Charles A. Stevenson also undertook +experiments during the last twenty years, in which they used +induction, but the most remarkable attempts are perhaps those of +Professor Emile Rathenau. With the assistance of Professor Rubens and +of Herr W. Rathenau, this physicist effected, at the request of the +German Ministry of Marine, a series of researches which enabled him, +by means of a compound system of conduction and induction by +alternating currents, to obtain clear and regular communications at a +distance of four kilometres. Among the precursors also should be +mentioned Graham Bell; the inventor of the telephone thought of +employing his admirable apparatus as a receiver of induction phenomena +transmitted from a distance; Edison, Herr Sacher of Vienna, M. Henry +Dufour of Lausanne, and Professor Trowbridge of Boston, also made +interesting attempts in the same direction. + +In all these experiments occurs the idea of employing an oscillating +current. Moreover, it was known for a long time--since, in 1842, the +great American physicist Henry proved that the discharges from a +Leyden jar in the attic of his house caused sparks in a metallic +circuit on the ground floor--that a flux which varies rapidly and +periodically is much more efficacious than a simple flux, which latter +can only produce at a distance a phenomenon of slight intensity. This +idea of the oscillating current was closely akin to that which was at +last to lead to an entirely satisfactory solution: that is, to a +solution which is founded on the properties of electric waves. + + +§ 5 + +Having thus got to the threshold of the definitive edifice, the +historian, who has conducted his readers over the two parallel routes +which have just been marked out, will be brought to ask himself +whether he has been a sufficiently faithful guide and has not omitted +to draw attention to all essential points in the regions passed +through. + +Ought we not to place by the side, or perhaps in front, of the authors +who have devised the practical appliances, those scholars who have +constructed the theories and realised the laboratory experiments of +which, after all, the apparatus are only the immediate applications? +If we speak of the propagation of a current in a material medium, can +one forget the names of Fourier and of Ohm, who established by +theoretical considerations the laws which preside over this +propagation? When one looks at the phenomena of induction, would it +not be just to remember that Arago foresaw them, and that Michael +Faraday discovered them? It would be a delicate, and also a rather +puerile task, to class men of genius in order of merit. The merit of +an inventor like Edison and that of a theorist like Clerk Maxwell have +no common measure, and mankind is indebted for its great progress to +the one as much as to the other. + +Before relating how success attended the efforts to utilise electric +waves for the transmission of signals, we cannot without ingratitude +pass over in silence the theoretical speculations and the work of pure +science which led to the knowledge of these waves. It would therefore +be just, without going further back than Faraday, to say how that +illustrious physicist drew attention to the part taken by insulating +media in electrical phenomena, and to insist also on the admirable +memoirs in which for the first time Clerk Maxwell made a solid bridge +between those two great chapters of Physics, optics and electricity, +which till then had been independent of each other. And no doubt it +would be impossible not to evoke the memory of those who, by +establishing, on the other hand, the solid and magnificent structure +of physical optics, and proving by their immortal works the undulatory +nature of light, prepared from the opposite direction the future +unity. In the history of the applications of electrical undulations, +the names of Young, Fresnel, Fizeau, and Foucault must be inscribed; +without these scholars, the assimilation between electrical and +luminous phenomena which they discovered and studied would evidently +have been impossible. + +Since there is an absolute identity of nature between the electric and +the luminous waves, we should, in all justice, also consider as +precursors those who devised the first luminous telegraphs. Claude +Chappe incontestably effected wireless telegraphy, thanks to the +luminous ether, and the learned men, such as Colonel Mangin, who +perfected optical telegraphy, indirectly suggested certain +improvements lately introduced into the present method. + +But the physicist whose work should most of all be put in evidence is, +without fear of contradiction, Heinrich Hertz. It was he who +demonstrated irrefutably, by experiments now classic, that an electric +discharge produces an undulatory disturbance in the ether contained in +the insulating media in its neighbourhood; it was he who, as a +profound theorist, a clever mathematician, and an experimenter of +prodigious dexterity, made known the mechanism of the production, and +fully elucidated that of the propagation of these electromagnetic +waves. + +He must naturally himself have thought that his discoveries might be +applied to the transmission of signals. It would appear, however, that +when interrogated by a Munich engineer named Huber as to the +possibility of utilising the waves for transmissions by telephone, he +answered in the negative, and dwelt on certain considerations relative +to the difference between the periods of sounds and those of +electrical vibrations. This answer does not allow us to judge what +might have happened, had not a cruel death carried off in 1894, at the +age of thirty-five, the great and unfortunate physicist. + +We might also find in certain works earlier than the experiments of +Hertz attempts at transmission in which, unconsciously no doubt, +phenomena were already set in operation which would, at this day, be +classed as electric oscillations. It is allowable no doubt, not to +speak of an American quack, Mahlon Loomis, who, according to Mr Story, +patented in 1870 a project of communication in which he utilised the +Rocky Mountains on one side and Mont Blanc on the other, as gigantic +antennae to establish communication across the Atlantic; but we cannot +pass over in silence the very remarkable researches of the American +Professor Dolbear, who showed, at the electrical exhibition of +Philadelphia in 1884, a set of apparatus enabling signals to be +transmitted at a distance, which he described as "an exceptional +application of the principles of electrostatic induction." This +apparatus comprised groups of coils and condensers by means of which +he obtained, as we cannot now doubt, effects due to true electric +waves. + +Place should also be made for a well-known inventor, D.E. Hughes, who +from 1879 to 1886 followed up some very curious experiments in which +also these oscillations certainly played a considerable part. It was +this physicist who invented the microphone, and thus, in another way, +drew attention to the variations of contact resistance, a phenomenon +not far from that produced in the radio-conductors of Branly, which +are important organs in the Marconi system. Unfortunately, fatigued +and in ill-health, Hughes ceased his researches at the moment perhaps +when they would have given him final results. + +In an order of ideas different in appearance, but closely linked at +bottom with the one just mentioned, must be recalled the discovery of +radiophony in 1880 by Graham Bell, which was foreshadowed in 1875 by +C.A. Brown. A luminous ray falling on a selenium cell produces a +variation of electric resistance, thanks to which a sound signal can +be transmitted by light. That delicate instrument the radiophone, +constructed on this principle, has wide analogies with the apparatus +of to-day. + + +§ 6 + +Starting from the experiments of Hertz, the history of wireless +telegraphy almost merges into that of the researches on electrical +waves. All the progress realised in the manner of producing and +receiving these waves necessarily helped to give rise to the +application already indicated. The experiments of Hertz, after being +checked in every laboratory, and having entered into the strong domain +of our most certain knowledge, were about to yield the expected fruit. + +Experimenters like Sir Oliver Lodge in England, Righi in Italy, +Sarrazin and de la Rive in Switzerland, Blondlot in France, Lecher in +Germany, Bose in India, Lebedeff in Russia, and theorists like M.H. +Poincaré and Professor Bjerknes, who devised ingenious arrangements or +elucidated certain points left dark, are among the artisans of the +work which followed its natural evolution. + +It was Professor R. Threlfall who seems to have been the first to +clearly propose, in 1890, the application of the Hertzian waves to +telegraphy, but it was certainly Sir W. Crookes who, in a very +remarkable article in the _Fortnightly Review_ of February 1892, +pointed out very clearly the road to be followed. He even showed in +what conditions the Morse receiver might be applied to the new system +of telegraphy. + +About the same period an American physicist, well known by his +celebrated experiments on high frequency currents--experiments, too, +which are not unconnected with those on electric oscillations,--M. +Tesla, demonstrated that these oscillations could be transmitted to +more considerable distances by making use of two vertical antennae, +terminated by large conductors. + +A little later, Sir Oliver Lodge succeeded, by the aid of the coherer, +in detecting waves at relatively long distances, and Mr Rutherford +obtained similar results with a magnetic indicator of his own +invention. + +An important question of meteorology, the study of atmospheric +discharges, at this date led a few scholars, and more particularly the +Russian, M. Popoff, to set up apparatus very analogous to the +receiving apparatus of the present wireless telegraphy. This comprised +a long antenna and filings-tube, and M. Popoff even pointed out that +his apparatus might well serve for the transmission of signals as soon +as a generator of waves powerful enough had been discovered. + +Finally, on the 2nd June 1896, a young Italian, born in Bologna on the +25th April 1874, Guglielmo Marconi, patented a system of wireless +telegraphy destined to become rapidly popular. Brought up in the +laboratory of Professor Righi, one of the physicists who had done most +to confirm and extend the experiments of Hertz, Marconi had long been +familiar with the properties of electric waves, and was well used to +their manipulation. He afterwards had the good fortune to meet Sir +William (then Mr) Preece, who was to him an adviser of the highest +authority. + +It has sometimes been said that the Marconi system contains nothing +original; that the apparatus for producing the waves was the +oscillator of Righi, that the receiver was that employed for some two +or three years by Professor Lodge and Mr Bose, and was founded on an +earlier discovery by a French scholar, M. Branly; and, finally, that +the general arrangement was that established by M. Popoff. + +The persons who thus rather summarily judge the work of M. Marconi +show a severity approaching injustice. It cannot, in truth, be denied +that the young scholar has brought a strictly personal contribution to +the solution of the problem he proposed to himself. Apart from his +forerunners, and when their attempts were almost unknown, he had the +very great merit of adroitly arranging the most favourable +combination, and he was the first to succeed in obtaining practical +results, while he showed that the electric waves could be transmitted +and received at distances enormous compared to those attained before +his day. Alluding to a well-known anecdote relating to Christopher +Columbus, Sir W. Preece very justly said: "The forerunners and rivals +of Marconi no doubt knew of the eggs, but he it was who taught them to +make them stand on end." This judgment will, without any doubt, be the +one that history will definitely pronounce on the Italian scholar. + + +§ 7 + +The apparatus which enables the electric waves to be revealed, the +detector or indicator, is the most delicate organ in wireless +telegraphy. It is not necessary to employ as an indicator a +filings-tube or radio-conductor. One can, in principle, for the purpose +of constructing a receiver, think of any one of the multiple effects +produced by the Hertzian waves. In many systems in use, and in the new +one of Marconi himself, the use of these tubes has been abandoned and +replaced by magnetic detectors. + +Nevertheless, the first and the still most frequent successes are due +to radio-conductors, and public opinion has not erred in attributing +to the inventor of this ingenious apparatus a considerable and almost +preponderant part in the invention of wave telegraphy. + +The history of the discovery of radio-conductors is short, but it +deserves, from its importance, a chapter to itself in the history of +wireless telegraphy. From a theoretical point of view, the phenomena +produced in those tubes should be set by the side of those studied by +Graham Bell, C.A. Brown, and Summer Tainter, from the year 1878 +onward. The variations to which luminous waves give rise in the +resistance of selenium and other substances are, doubtless, not +unconnected with those which the electric waves produce in filings. A +connection can also be established between this effect of the waves +and the variations of contact resistance which enabled Hughes to +construct the microphone, that admirable instrument which is one of +the essential organs of telephony. + +More directly, as an antecedent to the discovery, should be quoted the +remark made by Varley in 1870, that coal-dust changes in conductivity +when the electromotive force of the current which passes through it is +made to vary. But it was in 1884 that an Italian professor, Signor +Calzecchi-Onesti, demonstrated in a series of remarkable experiments +that the metallic filings contained in a tube of insulating material, +into which two metallic electrodes are inserted, acquire a notable +conductivity under different influences such as extra currents, +induced currents, sonorous vibrations, etc., and that this +conductivity is easily destroyed; as, for instance, by turning the +tube over and over. + +In several memoirs published in 1890 and 1891, M. Ed. Branly +independently pointed out similar phenomena, and made a much more +complete and systematic study of the question. He was the first to +note very clearly that the action described could be obtained by +simply making sparks pass in the neighbourhood of the radio-conductor, +and that their great resistance could be restored to the filings by +giving a slight shake to the tube or to its supports. + +The idea of utilising such a very interesting phenomenon as an +indicator in the study of the Hertzian waves seems to have occurred +simultaneously to several physicists, among whom should be especially +mentioned M. Ed. Branly himself, Sir Oliver Lodge, and MM. Le Royer +and Van Beschem, and its use in laboratories rapidly became quite +common. + +The action of the waves on metallic powders has, however, remained +some what mysterious; for ten years it has been the subject of +important researches by Professor Lodge, M. Branly, and a very great +number of the most distinguished physicists. It is impossible to +notice here all these researches, but from a recent and very +interesting work of M. Blanc, it would seem that the phenomenon is +allied to that of ionisation. + + +§ 8 + +The history of wireless telegraphy does not end with the first +experiments of Marconi; but from the moment their success was +announced in the public press, the question left the domain of pure +science to enter into that of commerce. The historian's task here +becomes different, but even more delicate; and he will encounter +difficulties which can be only known to one about to write the history +of a commercial invention. + +The actual improvements effected in the system are kept secret by the +rival companies, and the most important results are patriotically left +in darkness by the learned officers who operate discreetly in view of +the national defence. Meanwhile, men of business desirous of bringing +out a company proclaim, with great nourish of advertisements, that +they are about to exploit a process superior to all others. + +On this slippery ground the impartial historian must nevertheless +venture; and he may not refuse to relate the progress accomplished, +which is considerable. Therefore, after having described the +experiments carried out for nearly ten years by Marconi himself, first +across the Bristol Channel, then at Spezzia, between the coast and the +ironclad _San Bartolommeo_, and finally by means of gigantic apparatus +between America and England, he must give the names of those who, in +the different civilised countries, have contributed to the improvement +of the system of communication by waves; while he must describe what +precious services this system has already rendered to the art of war, +and happily also to peaceful navigation. + +From the point of view of the theory of the phenomena, very remarkable +results have been obtained by various physicists, among whom should be +particularly mentioned M. Tissot, whose brilliant studies have thrown +a bright light on different interesting points, such as the rôle of +the antennae. It would be equally impossible to pass over in silence +other recent attempts in a slightly different groove. Marconi's +system, however improved it may be to-day, has one grave defect. The +synchronism of the two pieces of apparatus, the transmitter and the +receiver, is not perfect, so that a message sent off by one station +may be captured by some other station. The fact that the phenomena of +resonance are not utilised, further prevents the quantity of energy +received by the receiver from being considerable, and hence the +effects reaped are very weak, so that the system remains somewhat +fitful and the communications are often disturbed by atmospheric +phenomena. Causes which render the air a momentary conductor, such as +electrical discharges, ionisation, etc., moreover naturally prevent +the waves from passing, the ether thus losing its elasticity. + +Professor Ferdinand Braun of Strasburg has conceived the idea of +employing a mixed system, in which the earth and the water, which, as +we have seen, have often been utilised to conduct a current for +transmitting a signal, will serve as a sort of guide to the waves +themselves. The now well-known theory of the propagation of waves +guided by a conductor enables it to be foreseen that, according to +their periods, these waves will penetrate more or less deeply into the +natural medium, from which fact has been devised a method of +separating them according to their frequency. By applying this theory, +M. Braun has carried out, first in the fortifications of Strasburg, +and then between the island of Heligoland and the mainland, +experiments which have given remarkable results. We might mention also +the researches, in a somewhat analogous order of ideas, by an English +engineer, Mr Armstrong, by Dr Lee de Forest, and also by Professor +Fessenden. + +Having thus arrived at the end of this long journey, which has taken +him from the first attempts down to the most recent experiments, the +historian can yet set up no other claim but that of having written the +commencement of a history which others must continue in the future. +Progress does not stop, and it is never permissible to say that an +invention has reached its final form. + +Should the historian desire to give a conclusion to his labour and +answer the question the reader would doubtless not fail to put to him, +"To whom, in short, should the invention of wireless telegraphy more +particularly be attributed?" he should certainly first give the name +of Hertz, the genius who discovered the waves, then that of Marconi, +who was the first to transmit signals by the use of Hertzian +undulations, and should add those of the scholars who, like Morse, +Popoff, Sir W. Preece, Lodge, and, above all, Branly, have devised the +arrangements necessary for their transmission. But he might then +recall what Voltaire wrote in the _Philosophical Dictionary_: + +"What! We wish to know what was the exact theology of Thot, of +Zerdust, of Sanchuniathon, of the first Brahmins, and we are ignorant +of the inventor of the shuttle! The first weaver, the first mason, the +first smith, were no doubt great geniuses, but they were disregarded. +Why? Because none of them invented a perfected art. The one who +hollowed out an oak to cross a river never made a galley; those who +piled up rough stones with girders of wood did not plan the Pyramids. +Everything is made by degrees and the glory belongs to no one." + +To-day, more than ever, the words of Voltaire are true: science +becomes more and more impersonal, and she teaches us that progress is +nearly always due to the united efforts of a crowd of workers, and is +thus the best school of social solidarity. + + + + +CHAPTER VIII + +THE CONDUCTIVITY OF GASES AND THE IONS + + +§ 1. THE CONDUCTIVITY OF GASES + +If we were confined to the facts I have set forth above, we might +conclude that two classes of phenomena are to-day being interpreted +with increasing correctness in spite of the few difficulties which +have been pointed out. The hypothesis of the molecular constitution of +matter enables us to group together one of these classes, and the +hypothesis of the ether leads us to co-ordinate the other. + +But these two classes of phenomena cannot be considered independent of +each other. Relations evidently exist between matter and the ether, +which manifest themselves in many cases accessible to experiment, and +the search for these relations appears to be the paramount problem the +physicist should set himself. The question has, for a long time, been +attacked on various sides, but the recent discoveries in the +conductivity of gases, of the radioactive substances, and of the +cathode and similar rays, have allowed us of late years to regard it +in a new light. Without wishing to set out here in detail facts which +for the most part are well known, we will endeavour to group the chief +of them round a few essential ideas, and will seek to state precisely +the data they afford us for the solution of this grave problem. + +It was the study of the conductivity of gases which at the very first +furnished the most important information, and allowed us to penetrate +more deeply than had till then been possible into the inmost +constitution of matter, and thus to, as it were, catch in the act the +actions that matter can exercise on the ether, or, reciprocally, those +it may receive from it. + +It might, perhaps, have been foreseen that such a study would prove +remarkably fruitful. The examination of the phenomena of electrolysis +had, in fact, led to results of the highest importance on the +constitution of liquids, and the gaseous media which presented +themselves as particularly simple in all their properties ought, it +would seem, to have supplied from the very first a field of +investigation easy to work and highly productive. + +This, however, was not at all the case. Experimental complications +springing up at every step obscured the problem. One generally found +one's self in the presence of violent disruptive discharges with a +train of accessory phenomena, due, for instance, to the use of +metallic electrodes, and made evident by the complex appearance of +aigrettes and effluves; or else one had to deal with heated gases +difficult to handle, which were confined in receptacles whose walls +played a troublesome part and succeeded in veiling the simplicity of +the fundamental facts. Notwithstanding, therefore, the efforts of a +great number of seekers, no general idea disengaged itself out of a +mass of often contradictory information. + +Many physicists, in France particularly, discarded the study of +questions which seemed so confused, and it must even be frankly +acknowledged that some among them had a really unfounded distrust of +certain results which should have been considered proved, but which +had the misfortune to be in contradiction with the theories in current +use. All the classic ideas relating to electrical phenomena led to the +consideration that there existed a perfect symmetry between the two +electricities, positive and negative. In the passing of electricity +through gases there is manifested, on the contrary, an evident +dissymmetry. The anode and the cathode are immediately distinguished +in a tube of rarefied gas by their peculiar appearance; and the +conductivity does not appear, under certain conditions, to be the same +for the two modes of electrification. + +It is not devoid of interest to note that Erman, a German scholar, +once very celebrated and now generally forgotten, drew attention as +early as 1815 to the unipolar conductivity of a flame. His +contemporaries, as may be gathered from the perusal of the treatises +on physics of that period, attached great importance to this +discovery; but, as it was somewhat inconvenient and did not readily +fit in with ordinary studies, it was in due course neglected, then +considered as insufficiently established, and finally wholly +forgotten. + +All these somewhat obscure facts, and some others--such as the +different action of ultra-violet radiations on positively and +negatively charged bodies--are now, on the contrary, about to be +co-ordinated, thanks to the modern ideas on the mechanism of conduction; +while these ideas will also allow us to interpret the most striking +dissymmetry of all, i.e. that revealed by electrolysis itself, a +dissymmetry which certainly can not be denied, but to which sufficient +attention has not been given. + +It is to a German physicist, Giese, that we owe the first notions on +the mechanism of the conductivity of gases, as we now conceive it. In +two memoirs published in 1882 and 1889, he plainly arrives at the +conception that conduction in gases is not due to their molecules, but +to certain fragments of them or to ions. Giese was a forerunner, but +his ideas could not triumph so long as there were no means of +observing conduction in simple circumstances. But this means has now +been supplied in the discovery of the X rays. Suppose we pass through +some gas at ordinary pressure, such as hydrogen, a pencil of X rays. +The gas, which till then has behaved as a perfect insulator,[29] +suddenly acquires a remarkable conductivity. If into this hydrogen two +metallic electrodes in communication with the two poles of a battery +are introduced, a current is set up in very special conditions which +remind us, when they are checked by experiments, of the mechanism +which allows the passage of electricity in electrolysis, and which is +so well represented to us when we picture to ourselves this passage as +due to the migration towards the electrodes, under the action of the +field, of the two sets of ions produced by the spontaneous division of +the molecule within the solution. + +[Footnote 29: At least, so long as it is not introduced between the +two coatings of a condenser having a difference of potential +sufficient to overcome what M. Bouty calls its dielectric cohesion. We +leave on one side this phenomenon, regarding which M. Bouty has +arrived at extremely important results by a very remarkable series of +experiments; but this question rightly belongs to a special study of +electrical phenomena which is not yet written.] + +Let us therefore recognise with J.J. Thomson and the many physicists +who, in his wake, have taken up and developed the idea of Giese, that, +under the influence of the X rays, for reasons which will have to be +determined later, certain gaseous molecules have become divided into +two portions, the one positively and the other negatively electrified, +which we will call, by analogy with the kindred phenomenon in +electrolysis, by the name of ions. If the gas be then placed in an +electric field, produced, for instance, by two metallic plates +connected with the two poles of a battery respectively, the positive +ions will travel towards the plate connected with the negative pole, +and the negative ions in the contrary direction. There is thus +produced a current due to the transport to the electrodes of the +charges which existed on the ions. + +If the gas thus ionised be left to itself, in the absence of any +electric field, the ions, yielding to their mutual attraction, must +finally meet, combine, and reconstitute a neutral molecule, thus +returning to their initial condition. The gas in a short while loses +the conductivity which it had acquired; or this is, at least, the +phenomenon at ordinary temperatures. But if the temperature is raised, +the relative speeds of the ions at the moment of impact may be great +enough to render it impossible for the recombination to be produced in +its entirety, and part of the conductivity will remain. + +Every element of volume rendered a conductor therefore furnishes, in +an electric field, equal quantities of positive and negative +electricity. If we admit, as mentioned above, that these liberated +quantities are borne by ions each bearing an equal charge, the number +of these ions will be proportional to the quantity of electricity, and +instead of speaking of a quantity of electricity, we could use the +equivalent term of number of ions. For the excitement produced by a +given pencil of X rays, the number of ions liberated will be fixed. +Thus, from a given volume of gas there can only be extracted an +equally determinate quantity of electricity. + +The conductivity produced is not governed by Ohm's law. The intensity +is not proportional to the electromotive force, and it increases at +first as the electromotive force augments; but it approaches +asymptotically to a maximum value which corresponds to the number of +ions liberated, and can therefore serve as a measure of the power of +the excitement. It is this current which is termed the _current of +saturation_. + +M. Righi has ably demonstrated that ionised gas does not obey the law +of Ohm by an experiment very paradoxical in appearance. He found that, +the greater the distance of the two electrode plates from each, the +greater may be, within certain limits, the intensity of the current. +The fact is very clearly interpreted by the theory of ionisation, +since the greater the length of the gaseous column the greater must be +the number of ions liberated. + +One of the most striking characteristics of ionised gases is that of +discharging electrified conductors. This phenomenon is not produced by +the departure of the charge that these conductors may possess, but by +the advent of opposite charges brought to them by ions which obey the +electrostatic attraction and abandon their own electrification when +they come in contact with these conductors. + +This mode of regarding the phenomena is extremely convenient and +eminently suggestive. It may, no doubt, be thought that the image of +the ions is not identical with objective reality, but we are compelled +to acknowledge that it represents with absolute faithfulness all the +details of the phenomena. + +Other facts, moreover, will give to this hypothesis a still greater +value; we shall even be able, so to speak, to grasp these ions +individually, to count them, and to measure their charge. + + +§ 2. THE CONDENSATION OF WATER-VAPOUR BY IONS + +If the pressure of a vapour--that of water, for instance--in the +atmosphere reaches the value of the maximum pressure corresponding to +the temperature of the experiment, the elementary theory teaches us +that the slightest decrease in temperature will induce a condensation; +that small drops will form, and the mist will turn into rain. + +In reality, matters do not occur in so simple a manner. A more or +less considerable delay may take place, and the vapour will remain +supersaturated. We easily discover that this phenomenon is due +to the intervention of capillary action. On a drop of liquid a +surface-tension takes effect which gives rise to a pressure which +becomes greater the smaller the diameter of the drop. + +Pressure facilitates evaporation, and on more closely examining this +reaction we arrive at the conclusion that vapour can never +spontaneously condense itself when liquid drops already formed are not +present, unless forces of another nature intervene to diminish the +effect of the capillary forces. In the most frequent cases, these +forces come from the dust which is always in suspension in the air, or +which exists in any recipient. Grains of dust act by reason of their +hygrometrical power, and form germs round which drops presently form. +It is possible to make use, as did M. Coulier as early as 1875, of +this phenomenon to carry off the germs of condensation, by producing +by expansion in a bottle containing a little water a preliminary mist +which purifies the air. In subsequent experiments it will be found +almost impossible to produce further condensation of vapour. + +But these forces may also be of electrical origin. Von Helmholtz long +since showed that electricity exercises an influence on the +condensation of the vapour of water, and Mr C.T.R. Wilson, with this +view, has made truly quantitative experiments. It was rapidly +discovered after the apparition of the X rays that gases that have +become conductors, that is, ionised gases, also facilitate the +condensation of supersaturated water vapour. + +We are thus led by a new road to the belief that electrified centres +exist in gases, and that each centre draws to itself the neighbouring +molecules of water, as an electrified rod of resin does the light +bodies around it. There is produced in this manner round each ion an +assemblage of molecules of water which constitute a germ capable of +causing the formation of a drop of water out of the condensation of +excess vapour in the ambient air. As might be expected, the drops are +electrified, and take to themselves the charge of the centres round +which they are formed; moreover, as many drops are created as there +are ions. Thereafter we have only to count these drops to ascertain +the number of ions which existed in the gaseous mass. + +To effect this counting, several methods have been used, differing in +principle but leading to similar results. It is possible, as Mr C.T.R. +Wilson and Professor J.J. Thomson have done, to estimate, on the one +hand, the weight of the mist which is produced in determined +conditions, and on the other, the average weight of the drops, +according to the formula formerly given by Sir G. Stokes, by deducting +their diameter from the speed with which this mist falls; or we can, +with Professor Lemme, determine the average radius of the drops by an +optical process, viz. by measuring the diameter of the first +diffraction ring produced when looking through the mist at a point of +light. + +We thus get to a very high number. There are, for instance, some +twenty million ions per centimetre cube when the rays have produced +their maximum effect, but high as this figure is, it is still very +small compared with the total number of molecules. All conclusions +drawn from kinetic theory lead us to think that in the same space +there must exist, by the side of a molecule divided into two ions, a +thousand millions remaining in a neutral state and intact. + +Mr C.T.R. Wilson has remarked that the positive and negative ions do +not produce condensation with the same facility. The ions of a +contrary sign may be almost completely separated by placing the +ionised gas in a suitably disposed field. In the neighbourhood of a +negative disk there remain hardly any but positive ions, and against a +positive disk none but negative; and in effecting a separation of this +kind, it will be noticed that condensation by negative ions is easier +than by the positive. + +It is, consequently, possible to cause condensation on negative +centres only, and to study separately the phenomena produced by the +two kinds of ions. It can thus be verified that they really bear +charges equal in absolute value, and these charges can even be +estimated, since we already know the number of drops. This estimate +can be made, for example, by comparing the speed of the fall of a mist +in fields of different values, or, as did J.J. Thomson, by measuring +the total quantity of electricity liberated throughout the gas. + +At the degree of approximation which such experiments imply, we find +that the charge of a drop, and consequently the charge borne by an +ion, is sensibly 3.4 x 10^{-10} electrostatic or 1.1 x 10^{-20} +electromagnetic units. This charge is very near that which the study +of the phenomena of ordinary electrolysis leads us to attribute to a +univalent atom produced by electrolytic dissociation. + +Such a coincidence is evidently very striking; but it will not be the +only one, for whatever phenomenon be studied it will always appear +that the smallest charge we can conceive as isolated is that +mentioned. We are, in fact, in presence of a natural unit, or, if you +will, of an atom of electricity. + +We must, however, guard against the belief that the gaseous ion is +identical with the electrolytic ion. Sensible differences between +those are immediately apparent, and still greater ones will be +discovered on closer examination. + +As M. Perrin has shown, the ionisation produced by the X-rays in no +way depends on the chemical composition of the gas; and whether we +take a volume of gaseous hydrochloric acid or a mixture of hydrogen +and chlorine in the same condition, all the results will be identical: +and chemical affinities play no part here. + +We can also obtain other information regarding ions: we can ascertain, +for instance, their velocities, and also get an idea of their order of +magnitude. + +By treating the speeds possessed by the liberated charges as +components of the known speed of a gaseous current, Mr Zeleny measures +the mobilities, that is to say, the speeds acquired by the positive +and negative charges in a field equal to the electrostatic unit. He +has thus found that these mobilities are different, and that they +vary, for example, between 400 and 200 centimetres per second for the +two charges in dry gases, the positive being less mobile than the +negative ions, which suggests the idea that they are of greater +mass.[30] + +[Footnote 30: A full account of these experiments, which were executed +at the Cavendish Laboratory, is to be found in _Philosophical +Transactions_, A., vol. cxcv. (1901), pp. 193 et seq.--ED.] + +M. Langevin, who has made himself the eloquent apostle of the new +doctrines in France, and has done much to make them understood and +admitted, has personally undertaken experiments analogous to those of +M. Zeleny, but much more complete. He has studied in a very ingenious +manner, not only the mobilities, but also the law of recombination +which regulates the spontaneous return of the gas to its normal state. +He has determined experimentally the relation of the number of +recombinations to the number of collisions between two ions of +contrary sign, by studying the variation produced by a change in the +value of the field, in the quantity of electricity which can be +collected in the gas separating two parallel metallic plates, after +the passage through it for a very short time of the Röntgen rays +emitted during one discharge of a Crookes tube. If the image of the +ions is indeed conformable to reality, this relation must evidently +always be smaller than unity, and must tend towards this value when +the mobility of the ions diminishes, that is to say, when the pressure +of the gas increases. The results obtained are in perfect accord with +this anticipation. + +On the other hand, M. Langevin has succeeded, by following the +displacement of the ions between the parallel plates after the +ionisation produced by the radiation, in determining the absolute +values of the mobilities with great precision, and has thus clearly +placed in evidence the irregularity of the mobilities of the positive +and negative ions respectively. Their mass can be calculated when we +know, through experiments of this kind, the speed of the ions in a +given field, and on the other hand--as we can now estimate their +electric charge--the force which moves them. They evidently progress +more slowly the larger they are; and in the viscous medium constituted +by the gas, the displacement is effected at a speed sensibly +proportional to the motive power. + +At the ordinary temperature these masses are relatively considerable, +and are greater for the positive than for the negative ions, that is +to say, they are about the order of some ten molecules. The ions, +therefore, seem to be formed by an agglomeration of neutral molecules +maintained round an electrified centre by electrostatic attraction. If +the temperature rises, the thermal agitation will become great enough +to prevent the molecules from remaining linked to the centre. By +measurements effected on the gases of flames, we arrive at very +different values of the masses from those found for ordinary ions, and +above all, very different ones for ions of contrary sign. The negative +ions have much more considerable velocities than the positive ones. +The latter also seem to be of the same size as atoms; and the +first-named must, consequently, be considered as very much smaller, +and probably about a thousand times less. + +Thus, for the first time in science, the idea appears that the atom is +not the smallest fraction of matter to be considered. Fragments a +thousand times smaller may exist which possess, however, a negative +charge. These are the electrons, which other considerations will again +bring to our notice. + + +§ 3. HOW IONS ARE PRODUCED + +It is very seldom that a gaseous mass does not contain a few ions. +They may have been formed from many causes, for although to give +precision to our studies, and to deal with a well ascertained case, I +mentioned only ionisation by the X rays in the first instance, I ought +not to give the impression that the phenomenon is confined to these +rays. It is, on the contrary, very general, and ionisation is just as +well produced by the cathode rays, by the radiations emitted by +radio-active bodies, by the ultra-violet rays, by heating to a high +temperature, by certain chemical actions, and finally by the impact of +the ions already existing in neutral molecules. + +Of late years these new questions have been the object of a multitude +of researches, and if it has not always been possible to avoid some +confusion, yet certain general conclusions may be drawn. The +ionisation by flames, in particular, is fairly well known. For it to +be produced spontaneously, it would appear that there must exist +simultaneously a rather high temperature and a chemical action in the +gas. According to M. Moreau, the ionisation is very marked when the +flame contains the vapour of the salt of an alkali or of an alkaline +earth, but much less so when it contains that of other salts. +Arrhenius, Mr C.T.R. Wilson, and M. Moreau, have studied all the +circumstances of the phenomenon; and it seems indeed that there is a +somewhat close analogy between what first occurs in the saline vapours +and that which is noted in liquid electrolytes. There should be +produced, as soon as a certain temperature is reached, a dissociation +of the saline molecule; and, as M. Moreau has shown in a series of +very well conducted researches, the ions formed at about 100°C. seem +constituted by an electrified centre of the size of a gas molecule, +surrounded by some ten layers of other molecules. We are thus dealing +with rather large ions, but according to Mr Wilson, this condensation +phenomenon does not affect the number of ions produced by +dissociation. In proportion as the temperature rises, the molecules +condensed round the nucleus disappear, and, as in all other +circumstances, the negative ion tends to become an electron, while the +positive ion continues the size of an atom. + +In other cases, ions are found still larger than those of saline +vapours, as, for example, those produced by phosphorus. It has long +been known that air in the neighbourhood of phosphorus becomes a +conductor, and the fact, pointed out as far back as 1885 by Matteucci, +has been well studied by various experimenters, by MM. Elster and +Geitel in 1890, for instance. On the other hand, in 1893 Mr Barus +established that the approach of a stick of phosphorus brings about +the condensation of water vapour, and we really have before us, +therefore, in this instance, an ionisation. M. Bloch has succeeded in +disentangling the phenomena, which are here very complex, and in +showing that the ions produced are of considerable dimensions; for +their speed in the same conditions is on the average a thousand times +less than that of ions due to the X rays. M. Bloch has established +also that the conductivity of recently-prepared gases, already studied +by several authors, was analogous to that which is produced by +phosphorus, and that it is intimately connected with the presence of +the very tenuous solid or liquid dust which these gases carry with +them, while the ions are of the same order of magnitude. These large +ions exist, moreover, in small quantities in the atmosphere; and M. +Langevin lately succeeded in revealing their presence. + +It may happen, and this not without singularly complicating matters, +that the ions which were in the midst of material molecules produce, +as the result of collisions, new divisions in these last. Other ions +are thus born, and this production is in part compensated for by +recombinations between ions of opposite signs. The impacts will be +more active in the event of the gas being placed in a field of force +and of the pressure being slight, the speed attained being then +greater and allowing the active force to reach a high value. The +energy necessary for the production of an ion is, in fact, according +to Professor Rutherford and Professor Stark, something considerable, +and it much exceeds the analogous force in electrolytic decomposition. + +It is therefore in tubes of rarefied gas that this ionisation by +impact will be particularly felt. This gives us the reason for the +aspect presented by Geissler tubes. Generally, in the case of +discharges, new ions produced by the molecules struck come to add +themselves to the electrons produced, as will be seen, by the cathode. +A full discussion has led to the interpretation of all the known +facts, and to our understanding, for instance, why there exist bright +or dark spaces in certain regions of the tube. M. Pellat, in +particular, has given some very fine examples of this concordance +between the theory and the facts he has skilfully observed. + +In all the circumstances, then, in which ions appear, their formation +has doubtless been provoked by a mechanism analogous to that of the +shock. The X rays, if they are attributable to sudden variations in +the ether--that is to say, a variation of the two vectors of Hertz-- +themselves produce within the atom a kind of electric impulse which +breaks it into two electrified fragments; _i.e._ the positive centre, +the size of the molecule itself, and the negative centre, constituted +by an electron a thousand times smaller. Round these two centres, at +the ordinary temperature, are agglomerated by attraction other +molecules, and in this manner the ions whose properties have just been +studied are formed. + + +§ 4. ELECTRONS IN METALS + +The success of the ionic hypothesis as an interpretation of the +conductivity of electrolytes and gases has suggested the desire to try +if a similar hypothesis can represent the ordinary conductivity of +metals. We are thus led to conceptions which at first sight seem +audacious because they are contrary to our habits of mind. They must +not, however, be rejected on that account. Electrolytic dissociation +at first certainly appeared at least as strange; yet it has ended by +forcing itself upon us, and we could, at the present day, hardly +dispense with the image it presents to us. + +The idea that the conductivity of metals is not essentially different +from that of electrolytic liquids or gases, in the sense that the +passage of the current is connected with the transport of small +electrified particles, is already of old date. It was enunciated by W. +Weber, and afterwards developed by Giese, but has only obtained its +true scope through the effect of recent discoveries. It was the +researches of Riecke, later, of Drude, and, above all, those of J.J. +Thomson, which have allowed it to assume an acceptable form. All these +attempts are connected however with the general theory of Lorentz, +which we will examine later. + +It will be admitted that metallic atoms can, like the saline molecule +in a solution, partially dissociate themselves. Electrons, very much +smaller than atoms, can move through the structure, considerable to +them, which is constituted by the atom from which they have just been +detached. They may be compared to the molecules of a gas which is +enclosed in a porous body. In ordinary conditions, notwithstanding the +great speed with which they are animated, they are unable to travel +long distances, because they quickly find their road barred by a +material atom. They have to undergo innumerable impacts, which throw +them first in one direction and then in another. The passage of a +current is a sort of flow of these electrons in a determined +direction. This electric flow brings, however, no modification to the +material medium traversed, since every electron which disappears at +any point is replaced by another which appears at once, and in all +metals the electrons are identical. + +This hypothesis leads us to anticipate certain facts which experience +confirms. Thus J.J. Thomson shows that if, in certain conditions, a +conductor is placed in a magnetic field, the ions have to describe an +epicycloid, and their journey is thus lengthened, while the electric +resistance must increase. If the field is in the direction of the +displacement, they describe helices round the lines of force and the +resistance is again augmented, but in different proportions. Various +experimenters have noted phenomena of this kind in different +substances. + +For a long time it has been noticed that a relation exists between the +calorific and the electric conductivity; the relation of these two +conductivities is sensibly the same for all metals. The modern theory +tends to show simply that it must indeed be so. Calorific conductivity +is due, in fact, to an exchange of electrons between the hot and the +cold regions, the heated electrons having the greater velocity, and +consequently the more considerable energy. The calorific exchanges +then obey laws similar to those which govern electric exchanges; and +calculation even leads to the exact values which the measurements have +given.[31] + +[Footnote 31: The whole of this argument is brilliantly set forth by +Professor Lorentz in a lecture delivered to the Electrotechnikerverein +at Berlin in December 1904, and reprinted, with additions, in the +_Archives Néerlandaises_ of 1906.--ED.] + +In the same way Professor Hesehus has explained how contact +electrification is produced, by the tendency of bodies to equalise +their superficial properties by means of a transport of electrons, and +Mr Jeans has shown that we should discover the existence of the +well-known laws of distribution over conducting bodies in electrostatic +equilibrium. A metal can, in fact, be electrified, that is to say, may +possess an excess of positive or negative electrons which cannot +easily leave it in ordinary conditions. To cause them to do so would +need an appreciable amount of work, on account of the enormous +difference of the specific inductive capacities of the metal and of +the insulating medium in which it is plunged. + +Electrons, however, which, on arriving at the surface of the metal, +possessed a kinetic energy superior to this work, might be shot forth +and would be disengaged as a vapour escapes from a liquid. Now, the +number of these rapid electrons, at first very slight, increases, +according to the kinetic theory, when the temperature rises, and +therefore we must reckon that a wire, on being heated, gives out +electrons, that is to say, loses negative electricity and sends into +the surrounding media electrified centres capable of producing the +phenomena of ionisation. Edison, in 1884, showed that from the +filament of an incandescent lamp there escaped negative electric +charges. Since then, Richardson and J.J. Thomson have examined +analogous phenomena. This emission is a very general phenomenon which, +no doubt, plays a considerable part in cosmic physics. Professor +Arrhenius explains, for instance, the polar auroras by the action of +similar corpuscules emitted by the sun. + +In other phenomena we seem indeed to be confronted by an emission, not +of negative electrons, but of positive ions. Thus, when a wire is +heated, not _in vacuo_, but in a gas, this wire begins to electrify +neighbouring bodies positively. J.J. Thomson has measured the mass of +these positive ions and finds it considerable, i.e. about 150 times +that of an atom of hydrogen. Some are even larger, and constitute +almost a real grain of dust. We here doubtless meet with the phenomena +of disaggregation undergone by metals at a red heat. + + + + +CHAPTER IX + +CATHODE RAYS AND RADIOACTIVE BODIES + + +§ 1. THE CATHODE RAYS + +A wire traversed by an electric current is, as has just been +explained, the seat of a movement of electrons. If we cut this wire, a +flood of electrons, like a current of water which, at the point where +a pipe bursts, flows out in abundance, will appear to spring out +between the two ends of the break. + +If the energy of the electrons is sufficient, these electrons will in +fact rush forth and be propagated in the air or in the insulating +medium interposed; but the phenomena of the discharge will in general +be very complex. We shall here only examine a particularly simple +case, viz., that of the cathode rays; and without entering into +details, we shall only note the results relating to these rays which +furnish valuable arguments in favour of the electronic hypothesis and +supply solid materials for the construction of new theories of +electricity and matter. + +For a long time it was noticed that the phenomena in a Geissler tube +changed their aspect considerably, when the gas pressure became very +weak, without, however, a complete vacuum being formed. From the +cathode there is shot forth normally and in a straight line a flood +within the tube, dark but capable of impressing a photographic plate, +of developing the fluorescence of various substances (particularly the +glass walls of the tube), and of producing calorific and mechanical +effects. These are the cathode rays, so named in 1883 by E. Wiedemann, +and their name, which was unknown to a great number of physicists till +barely twelve years ago, has become popular at the present day. + +About 1869, Hittorf made an already very complete study of them and +put in evidence their principal properties; but it was the researches +of Sir W. Crookes in especial which drew attention to them. The +celebrated physicist foresaw that the phenomena which were thus +produced in rarefied gases were, in spite of their very great +complication, more simple than those presented by matter under the +conditions in which it is generally met with. + +He devised a celebrated theory no longer admissible in its entirety, +because it is not in complete accord with the facts, which was, +however, very interesting, and contained, in germ, certain of our +present ideas. In the opinion of Crookes, in a tube in which the gas +has been rarefied we are in presence of a special state of matter. The +number of the gas molecules has become small enough for their +independence to be almost absolute, and they are able in this +so-called radiant state to traverse long spaces without departing +from a straight line. The cathode rays are due to a kind of molecular +bombardment of the walls of the tubes, and of the screens which can be +introduced into them; and it is the molecules, electrified by their +contact with the cathode and then forcibly repelled by electrostatic +action, which produce, by their movement and their _vis viva_, all the +phenomena observed. Moreover, these electrified molecules animated +with extremely rapid velocities correspond, according to the theory +verified in the celebrated experiment of Rowland on convection +currents, to a true electric current, and can be deviated by a magnet. + +Notwithstanding the success of Crookes' experiments, many physicists-- +the Germans especially--did not abandon an hypothesis entirely +different from that of radiant matter. They continued to regard the +cathode radiation as due to particular radiations of a nature still +little known but produced in the luminous ether. This interpretation +seemed, indeed, in 1894, destined to triumph definitely through the +remarkable discovery of Lenard, a discovery which, in its turn, was to +provoke so many others and to bring about consequences of which the +importance seems every day more considerable. + +Professor Lenard's fundamental idea was to study the cathode rays +under conditions different from those in which they are produced. +These rays are born in a very rarefied space, under conditions +perfectly determined by Sir W. Crookes; but it was a question whether, +when once produced, they would be capable of propagating themselves in +other media, such as a gas at ordinary pressure, or even in an +absolute vacuum. Experiment alone could answer this question, but +there were difficulties in the way of this which seemed almost +insurmountable. The rays are stopped by glass even of slight +thickness, and how then could the almost vacuous space in which they +have to come into existence be separated from the space, absolutely +vacuous or filled with gas, into which it was desired to bring them? + +The artifice used was suggested to Professor Lenard by an experiment +of Hertz. The great physicist had, in fact, shortly before his +premature death, taken up this important question of the cathode rays, +and his genius left there, as elsewhere, its powerful impress. He had +shown that metallic plates of very slight thickness were transparent +to the cathode rays; and Professor Lenard succeeded in obtaining +plates impermeable to air, but which yet allowed the pencil of cathode +rays to pass through them. + +Now if we take a Crookes tube with the extremity hermetically closed +by a metallic plate with a slit across the diameter of 1 mm. in width, +and stop this slit with a sheet of very thin aluminium, it will be +immediately noticed that the rays pass through the aluminium and pass +outside the tube. They are propagated in air at atmospheric pressure, +and they can also penetrate into an absolute vacuum. They therefore +can no longer be attributed to radiant matter, and we are led to think +that the energy brought into play in this phenomenon must have its +seat in the light-bearing ether itself. + +But it is a very strange light which is thus subject to magnetic +action, which does not obey the principle of equal angles, and for +which the most various gases are already disturbed media. According to +Crookes it possesses also the singular property of carrying with it +electric charges. + +This convection of negative electricity by the cathode rays seems +quite inexplicable on the hypothesis that the rays are ethereal +radiations. Nothing then remained in order to maintain this +hypothesis, except to deny the convection, which, besides, was only +established by indirect experiments. That the reality of this +transport has been placed beyond dispute by means of an extremely +elegant experiment which is all the more convincing that it is so very +simple, is due to M. Perrin. In the interior of a Crookes tube he +collected a pencil of cathode rays in a metal cylinder. According to +the elementary principles of electricity the cylinder must become +charged with the whole charge, if there be one, brought to it by the +rays, and naturally various precautions had to be taken. But the +result was very precise, and doubt could no longer exist--the rays +were electrified. + +It might have been, and indeed was, maintained, some time after this +experiment was published, that while the phenomena were complex inside +the tube, outside, things might perhaps occur differently. Lenard +himself, however, with that absence of even involuntary prejudice +common to all great minds, undertook to demonstrate that the opinion +he at first held could no longer be accepted, and succeeded in +repeating the experiment of M. Perrin on cathode rays in the air and +even _in vacuo_. + +On the wrecks of the two contradictory hypotheses thus destroyed, and +out of the materials from which they had been built, a theory has been +constructed which co-ordinates all the known facts. This theory is +furthermore closely allied to the theory of ionisation, and, like this +latter, is based on the concept of the electron. Cathode rays are +electrons in rapid motion. + +The phenomena produced both inside and outside a Crookes tube are, +however, generally complex. In Lenard's first experiments, and in many +others effected later when this region of physics was still very +little known, a few confusions may be noticed even at the present day. + +At the spot where the cathode rays strike the walls of the tube the +essentially different X rays appear. These differ from the cathode +radiations by being neither electrified nor deviated by a magnet. In +their turn these X rays may give birth to the secondary rays of M. +Sagnac; and often we find ourselves in presence of effects from these +last-named radiations and not from the true cathode rays. + +The electrons, when they are propagated in a gas, can ionise the +molecules of this gas and unite with the neutral atoms to form +negative ions, while positive ions also appear. There are likewise +produced, at the expense of the gas still subsisting after +rarefication within the tube, positive ions which, attracted by the +cathode and reaching it, are not all neutralised by the negative +electrons, and can, if the cathode be perforated, pass through it, and +if not, pass round it. We have then what are called the canal rays of +Goldstein, which are deviated by an electric or magnetic field in a +contrary direction to the cathode rays; but, being larger, give weak +deviations or may even remain undeviated through losing their charge +when passing through the cathode. + +It may also be the parts of the walls at a distance from the cathode +which send a positive rush to the latter, by a similar mechanism. It +may be, again, that in certain regions of the tube cathode rays are +met with diffused by some solid object, without having thereby changed +their nature. All these complexities have been cleared up by M. +Villard, who has published, on these questions, some remarkably +ingenious and particularly careful experiments. + +M. Villard has also studied the phenomena of the coiling of the rays +in a field, as already pointed out by Hittorf and Plücker. When a +magnetic field acts on the cathode particle, the latter follows a +trajectory, generally helicoidal, which is anticipated by the theory. +We here have to do with a question of ballistics, and experiments duly +confirm the anticipations of the calculation. Nevertheless, rather +singular phenomena appear in the case of certain values of the field, +and these phenomena, dimly seen by Plücker and Birkeland, have been +the object of experiments by M. Villard. The two faces of the cathode +seem to emit rays which are deviated in a direction perpendicular to +the lines of force by an electric field, and do not seem to be +electrified. M. Villard calls them magneto-cathode rays, and according +to M. Fortin these rays may be ordinary cathode rays, but of very +slight velocity. + +In certain cases the cathode itself may be superficially +disaggregated, and extremely tenuous particles detach themselves, +which, being carried off at right angles to its surface, may deposit +themselves like a very thin film on objects placed in their path. +Various physicists, among them M. Houllevigue, have studied this +phenomenon, and in the case of pressures between 1/20 and 1/100 of a +millimetre, the last-named scholar has obtained mirrors of most +metals, a phenomenon he designates by the name of ionoplasty. + +But in spite of all these accessory phenomena, which even sometimes +conceal those first observed, the existence of the electron in the +cathodic flux remains the essential characteristic. + +The electron can be apprehended in the cathodic ray by the study of +its essential properties; and J.J. Thomson gave great value to the +hypothesis by his measurements. At first he meant to determine the +speed of the cathode rays by direct experiment, and by observing, in a +revolving mirror, the relative displacement of two bands due to the +excitement of two fluorescent screens placed at different distances +from the cathode. But he soon perceived that the effect of the +fluorescence was not instantaneous, and that the lapse of time might +form a great source of error, and he then had recourse to indirect +methods. It is possible, by a simple calculation, to estimate the +deviations produced on the rays by a magnetic and an electric field +respectively as a function of the speed of propagation and of the +relation of the charge to the material mass of the electron. The +measurement of these deviations will then permit this speed and this +relation to be ascertained. + +Other processes may be used which all give the same two quantities by +two suitably chosen measurements. Such are the radius of the curve +taken by the trajectory of the pencil in a perpendicular magnetic +field and the measure of the fall of potential under which the +discharge takes place, or the measure of the total quantity +of electricity carried in one second and the measure of the +calorific energy which may be given, during the same period, to a +thermo-electric junction. The results agree as well as can be expected, +having regard to the difficulty of the experiments; the values of the +speed agree also with those which Professor Wiechert has obtained by +direct measurement. + +The speed never depends on the nature of the gas contained in the +Crookes tube, but varies with the value of the fall of potential at +the cathode. It is of the order of one tenth of the speed of light, +and it may rise as high as one third. The cathode particle therefore +goes about three thousand times faster than the earth in its orbit. +The relation is also invariable, even when the substance of which the +cathode is formed is changed or one gas is substituted for another. It +is, on the average, a thousand times greater than the corresponding +relation in electrolysis. As experiment has shown, in all the +circumstances where it has been possible to effect measurements, the +equality of the charges carried by all corpuscules, ions, atoms, etc., +we ought to consider that the charge of the electron is here, again, +that of a univalent ion in electrolysis, and therefore that its mass +is only a small fraction of that of the atom of hydrogen, viz., of the +order of about a thousandth part. This is the same result as that to +which we were led by the study of flames. + +The thorough examination of the cathode radiation, then, confirms us +in the idea that every material atom can be dissociated and will yield +an electron much smaller than itself--and always identical whatever +the matter whence it comes,--the rest of the atom remaining charged +with a positive quantity equal and contrary to that borne by the +electron. In the present case these positive ions are no doubt those +that we again meet with in the canal rays. Professor Wien has shown +that their mass is really, in fact, of the order of the mass of atoms. +Although they are all formed of identical electrons, there may be +various cathode rays, because the velocity is not exactly the same for +all electrons. Thus is explained the fact that we can separate them +and that we can produce a sort of spectrum by the action of the +magnet, or, again, as M. Deslandres has shown in a very interesting +experiment, by that of an electrostatic field. This also probably +explains the phenomena studied by M. Villard, and previously pointed +out. + + +§ 2. RADIOACTIVE SUBSTANCES + +Even in ordinary conditions, certain substances called radioactive +emit, quite outside any particular reaction, radiations complex +indeed, but which pass through fairly thin layers of minerals, impress +photographic plates, excite fluorescence, and ionize gases. In these +radiations we again find electrons which thus escape spontaneously +from radioactive bodies. + +It is not necessary to give here a history of the discovery of radium, +for every one knows the admirable researches of M. and Madame Curie. +But subsequent to these first studies, a great number of facts have +accumulated for the last six years, among which some people find +themselves a little lost. It may, perhaps, not be useless to indicate +the essential results actually obtained. + +The researches on radioactive substances have their starting-point in +the discovery of the rays of uranium made by M. Becquerel in 1896. As +early as 1867 Niepce de St Victor proved that salts of uranium +impressed photographic plates in the dark; but at that time the +phenomenon could only pass for a singularity attributable to +phosphorescence, and the valuable remarks of Niepce fell into +oblivion. M. Becquerel established, after some hesitations natural in +the face of phenomena which seemed so contrary to accepted ideas, that +the radiating property was absolutely independent of phosphorescence, +that all the salts of uranium, even the uranous salts which are not +phosphorescent, give similar radiant effects, and that these phenomena +correspond to a continuous emission of energy, but do not seem to be +the result of a storage of energy under the influence of some external +radiation. Spontaneous and constant, the radiation is insensible to +variations of temperature and light. + +The nature of these radiations was not immediately understood,[32] and +their properties seemed contradictory. This was because we were not +dealing with a single category of rays. But amongst all the effects +there is one which constitutes for the radiations taken as a whole, a +veritable process for the measurement of radioactivity. This is their +ionizing action on gases. A very complete study of the conductivity of +air under the influence of rays of uranium has been made by various +physicists, particularly by Professor Rutherford, and has shown that +the laws of the phenomenon are the same as those of the ionization due +to the action of the Röntgen rays. + +[Footnote 32: In his work on _L'Évolution de la Matière_, M. Gustave +Le Bon recalls that in 1897 he published several notes in the Académie +des Sciences, in which he asserted that the properties of uranium were +only a particular case of a very general law, and that the radiations +emitted did not polarize, and were akin by their properties to the X +rays.] + +It was natural to ask one's self if the property discovered in salts +of uranium was peculiar to this body, or if it were not, to a more or +less degree, a general property of matter. Madame Curie and M. +Schmidt, independently of each other, made systematic researches in +order to solve the question; various compounds of nearly all the +simple bodies at present known were thus passed in review, and it was +established that radioactivity was particularly perceptible in the +compounds of uranium and thorium, and that it was an atomic property +linked to the matter endowed with it, and following it in all its +combinations. In the course of her researches Madame Curie observed +that certain pitchblendes (oxide of uranium ore, containing also +barium, bismuth, etc.) were four times more active (activity being +measured by the phenomenon of the ionization of the air) than metallic +uranium. Now, no compound containing any other active metal than +uranium or thorium ought to show itself more active than those metals +themselves, since the property belongs to their atoms. It seemed, +therefore, probable that there existed in pitchblendes some substance +yet unknown, in small quantities and more radioactive than uranium. + +M. and Madame Curie then commenced those celebrated experiments which +brought them to the discovery of radium. Their method of research has +been justly compared in originality and importance to the process of +spectrum analysis. To isolate a radioactive substance, the first thing +is to measure the activity of a certain compound suspected of +containing this substance, and this compound is chemically separated. +We then again take in hand all the products obtained, and by measuring +their activity anew, it is ascertained whether the substance sought +for has remained in one of these products, or is divided among them, +and if so, in what proportion. The spectroscopic reaction which we may +use in the course of this separation is a thousand times less +sensitive than observation of the activity by means of the +electrometer. + +Though the principle on which the operation of the concentration of +the radium rests is admirable in its simplicity, its application is +nevertheless very laborious. Tons of uranium residues have to be +treated in order to obtain a few decigrammes of pure salts of radium. +Radium is characterised by a special spectrum, and its atomic weight, +as determined by Madame Curie, is 225; it is consequently the higher +homologue of barium in one of the groups of Mendeléef. Salts of radium +have in general the same chemical properties as the corresponding +salts of barium, but are distinguished from them by the differences of +solubility which allow of their separation, and by their enormous +activity, which is about a hundred thousand times greater than that of +uranium. + +Radium produces various chemical and some very intense physiological +reactions. Its salts are luminous in the dark, but this luminosity, at +first very bright, gradually diminishes as the salts get older. We +have here to do with a secondary reaction correlative to the +production of the emanation, after which radium undergoes the +transformations which will be studied later on. + +The method of analysis founded by M. and Madame Curie has enabled +other bodies presenting sensible radioactivity to be discovered. The +alkaline metals appear to possess this property in a slight degree. +Recently fallen snow and mineral waters manifest marked action. The +phenomenon may often be due, however, to a radioactivity induced by +radiations already existing in the atmosphere. But this radioactivity +hardly attains the ten-thousandth part of that presented by uranium, +or the ten-millionth of that appertaining to radium. + +Two other bodies, polonium and actinium, the one characterised by the +special nature of the radiations it emits and the other by a +particular spectrum, seem likewise to exist in pitchblende. These +chemical properties have not yet been perfectly defined; thus M. +Debierne, who discovered actinium, has been able to note the active +property which seems to belong to it, sometimes in lanthanum, +sometimes in neodynium.[33] It is proved that all extremely +radioactive bodies are the seat of incessant transformations, and even +now we cannot state the conditions under which they present themselves +in a strictly determined form. + +[Footnote 33: Polonium has now been shown to be no new element, but +one of the transformation products of radium. Radium itself is also +thought to be derived in some manner, not yet ascertained, from +uranium. The same is the case with actinium, which is said to come in +the long run from uranium, but not so directly as does radium. All +this is described in Professor Rutherford's _Radioactive +Transformations_ (London, 1906).--ED.] + + +§ 3. THE RADIATION OF THE RADIOACTIVE BODIES AND THE EMANATION + +To acquire exact notions as to the nature of the rays emitted by the +radioactive bodies, it was necessary to try to cause magnetic or +electric forces to act on them so as to see whether they behaved in +the same way as light and the X rays, or whether like the cathode rays +they were deviated by a magnetic field. This work was effected by +Professor Giesel, then by M. Becquerel, Professor Rutherford, and by +many other experimenters after them. All the methods which have +already been mentioned in principle have been employed in order to +discover whether they were electrified, and, if so, by electricity of +what sign, to measure their speed, and to ascertain their degree of +penetration. + +The general result has been to distinguish three sorts of radiations, +designated by the letters alpha, beta, gamma. + +The alpha rays are positively charged, and are projected at a speed +which may attain the tenth of that of light; M.H. Becquerel has shown +by the aid of photography that they are deviated by a magnet, and +Professor Rutherford has, on his side, studied this deviation by the +electrical method. The relation of the charge to the mass is, in the +case of these rays, of the same order as in that of the ions of +electrolysis. They may therefore be considered as exactly analogous to +the canal rays of Goldstein, and we may attribute them to a material +transport of corpuscles of the magnitude of atoms. The relatively +considerable size of these corpuscles renders them very absorbable. A +flight of a few millimetres in a gas suffices to reduce their number +by one-half. They have great ionizing power. + +The beta rays are on all points similar to the cathode rays; they are, +as M. and Madame Curie have shown, negatively charged, and the charge +they carry is always the same. Their size is that of the electrons, +and their velocity is generally greater than that of the cathode rays, +while it may become almost that of light. They have about a hundred +times less ionizing power than the alpha rays. + +The gamma rays were discovered by M. Villard.[34] They may be compared +to the X rays; like the latter, they are not deviated by the magnetic +field, and are also extremely penetrating. A strip of aluminium five +millimetres thick will stop the other kinds, but will allow them to +pass. On the other hand, their ionizing power is 10,000 times less +than that of the alpha rays. + +[Footnote 34: This is admitted by Professor Rutherford (_Radio-Activity_, +Camb., 1904, p. 141) and Professor Soddy (_Radio-Activity_, London, +1904, p. 66). Neither Mr Whetham, in his Recent _Development of +Physical Science_ (London, 1904) nor the Hon. R.J. Strutt in _The +Becquerel Rays_ (London, same date), both of whom deal with the +historical side of the subject, seem to have noticed the fact.--ED.] + +To these radiations there sometimes are added in the course of +experiments secondary radiations analogous to those of M. Sagnac, and +produced when the alpha, beta, or gamma rays meet various substances. +This complication has often led to some errors of observation. + +Phosphorescence and fluorescence seem especially to result from the +alpha and beta rays, particularly from the alpha rays, to which +belongs the most important part of the total energy of the radiation. +Sir W. Crookes has invented a curious little apparatus, the +spinthariscope, which enables us to examine the phosphorescence of the +blende excited by these rays. By means of a magnifying glass, a screen +covered with sulphide of zinc is kept under observation, and in front +of it is disposed, at a distance of about half a millimetre, a +fragment of some salt of radium. We then perceive multitudes of +brilliant points on the screen, which appear and at once disappear, +producing a scintillating effect. It seems probable that every +particle falling on the screen produces by its impact a disturbance in +the neighbouring region, and it is this disturbance which the eye +perceives as a luminous point. Thus, says Sir W. Crookes, each drop of +rain falling on the surface of still water is not perceived as a drop +of rain, but by reason of the slight splash which it causes at the +moment of impact, and which is manifested by ridges and waves +spreading themselves in circles. + +The various radioactive substances do not all give radiations of +identical constitution. Radium and thorium possess in somewhat large +proportions the three kinds of rays, and it is the same with actinium. +Polonium contains especially alpha rays and a few gamma rays.[35] In +the case of uranium, the alpha rays have extremely slight penetrating +power, and cannot even impress photographic plates. But the widest +difference between the substances proceeds from the emanation. Radium, +in addition to the three groups of rays alpha, beta, and gamma, +disengages continuously an extremely subtle emanation, seemingly +almost imponderable, but which may be, for many reasons, looked upon +as a vapour of which the elastic force is extremely feeble. + +[Footnote 35: It has now been shown that polonium when freshly +separated emits beta rays also; see Dr Logeman's paper in _Proceedings +of the Royal Society_, A., 6th September 1906.--ED.] + +M. and Madame Curie discovered as early as 1899 that every substance +placed in the neighbourhood of radium, itself acquired a radioactivity +which persisted for several hours after the removal of the radium. +This induced radioactivity seems to be carried to other bodies by the +intermediary of a gas. It goes round obstacles, but there must exist +between the radium and the substance a free and continuous space for +the activation to take place; it cannot, for instance, do so through a +wall of glass. + +In the case of compounds of thorium Professor Rutherford discovered a +similar phenomenon; since then, various physicists, Professor Soddy, +Miss Brooks, Miss Gates, M. Danne, and others, have studied the +properties of these emanations. + +The substance emanated can neither be weighed nor can its elastic +force be ascertained; but its transformations may be followed, as it +is luminous, and it is even more certainly characterised by its +essential property, i.e. its radioactivity. We also see that it can be +decanted like a gas, that it will divide itself between two tubes of +different capacity in obedience to the law of Mariotte, and will +condense in a refrigerated tube in accordance with the principle of +Watt, while it even complies with the law of Gay-Lussac. + +The activity of the emanation vanishes quickly, and at the end of four +days it has diminished by one-half. If a salt of radium is heated, the +emanation becomes more abundant, and the residue, which, however, does +not sensibly diminish in weight, will have lost all its radioactivity, +and will only recover it by degrees. Professor Rutherford, +notwithstanding many different attempts, has been unable to make this +emanation enter into any chemical reaction. If it be a gaseous body, +it must form part of the argon group, and, like its other members, be +perfectly inert. + +By studying the spectrum of the gas disengaged by a solution of salt +of radium, Sir William Ramsay and Professor Soddy remarked that when +the gas is radioactive there are first obtained rays of gases +belonging to the argon family, then by degrees, as the activity +disappears, the spectrum slowly changes, and finally presents the +characteristic aspect of helium. + +We know that the existence of this gas was first discovered by +spectrum analysis in the sun. Later its presence was noted in our +atmosphere, and in a few minerals which happen to be the very ones +from which radium has been obtained. It might therefore have been the +case that it pre-existed in the gases extracted from radium; but a +remarkable experiment by M. Curie and Sir James Dewar seems to show +convincingly that this cannot be so. The spectrum of helium never +appears at first in the gas proceeding from pure bromide of radium; +but it shows itself, on the other hand, very distinctly, after the +radioactive transformations undergone by the salt. + +All these strange phenomena suggest bold hypotheses, but to construct +them with any solidity they must be supported by the greatest possible +number of facts. Before admitting a definite explanation of the +phenomena which have their seat in the curious substances discovered +by them, M. and Madame Curie considered, with a great deal of reason, +that they ought first to enrich our knowledge with the exact and +precise facts relating to these bodies and to the effects produced by +the radiations they emit. + +Thus M. Curie particularly set himself to study the manner in which +the radioactivity of the emanation is dissipated, and the +radioactivity that this emanation can induce on all bodies. The +radioactivity of the emanation diminishes in accordance with an +exponential law. The constant of time which characterises this +decrease is easily and exactly determined, and has a fixed value, +independent of the conditions of the experiment as well as of the +nature of the gas which is in contact with the radium and becomes +charged with the emanation. The regularity of the phenomenon is so +great that it can be used to measure time: in 3985 seconds[36] the +activity is always reduced one-half. + +[Footnote 36: According to Professor Rutherford, in 3.77 days.--ED] + +Radioactivity induced on any body which has been for a long time in +presence of a salt of radium disappears more rapidly. The phenomenon +appears, moreover, more complex, and the formula which expresses the +manner in which the activity diminishes must contain two exponentials. +To find it theoretically we have to imagine that the emanation first +deposits on the body in question a substance which is destroyed in +giving birth to a second, this latter disappearing in its turn by +generating a third. The initial and final substances would be +radioactive, but the intermediary one, not. If, moreover, the bodies +acted on are brought to a temperature of over 700°, they appear to +lose by volatilisation certain substances condensed in them, and at +the same time their activity disappears. + +The other radioactive bodies behave in a similar way. Bodies which +contain actinium are particularly rich in emanations. Uranium, on the +contrary, has none.[37] This body, nevertheless, is the seat of +transformations comparable to those which the study of emanations +reveals in radium; Sir W. Crookes has separated from uranium a matter +which is now called uranium X. This matter is at first much more +active than its parent, but its activity diminishes rapidly, while the +ordinary uranium, which at the time of the separation loses its +activity, regains it by degrees. In the same way, Professors +Rutherford and Soddy have discovered a so-called thorium X to be the +stage through which ordinary thorium has to pass in order to produce +its emanation.[38] + +[Footnote 37: Professor Rutherford has lately stated that uranium may +possibly produce an emanation, but that its rate of decay must be too +swift for its presence to be verified (see _Radioactive +Transformations_, p. 161).--ED.] + +[Footnote 38: An actinium X was also discovered by Professor Giesel +(_Jahrbuch d. Radioaktivitat_, i. p. 358, 1904). Since the above was +written, another product has been found to intervene between the X +substance and the emanation in the case of actinium and thorium. They +have been named radio-actinium and radio-thorium respectively.--ED.] + +It is not possible to give a complete table which should, as it were, +represent the genealogical tree of the various radioactive substances. +Several authors have endeavoured to do so, but in a premature manner; +all the affiliations are not at the present time yet perfectly known, +and it will no doubt be acknowledged some day that identical states +have been described under different names.[39] + +[Footnote 39: Such a table is given on p. 169 of Rutherford's +_Radioactive Transformations_.--ED.] + + +§ 4. THE DISAGGREGATION OF MATTER AND ATOMIC ENERGY + +In spite of uncertainties which are not yet entirely removed, it +cannot be denied that many experiments render it probable that in +radioactive bodies we find ourselves witnessing veritable +transformations of matter. + +Professor Rutherford, Professor Soddy, and several other physicists, +have come to regard these phenomena in the following way. A +radioactive body is composed of atoms which have little stability, and +are able to detach themselves spontaneously from the parent substance, +and at the same time to divide themselves into two essential component +parts, the negative electron and its residue the positive ion. The +first-named constitutes the beta, and the second the alpha rays. + +The emanation is certainly composed of alpha ions with a few molecules +agglomerated round them. Professor Rutherford has, in fact, +demonstrated that the emanation is charged with positive electricity; +and this emanation may, in turn, be destroyed by giving birth to new +bodies. + +After the loss of the atoms which are carried off by the radiation, +the remainder of the body acquires new properties, but it may still be +radioactive, and again lose atoms. The various stages that we meet +with in the evolution of the radioactive substance or of its +emanation, correspond to the various degrees of atomic disaggregation. +Professors Rutherford and Soddy have described them clearly in the +case of uranium and radium. As regards thorium the results are less +satisfactory. The evolution should continue until a stable atomic +condition is finally reached, which, because of this stability, is no +longer radioactive. Thus, for instance, radium would finally be +transformed into helium.[40] + +[Footnote 40: This opinion, no doubt formed when Sir William Ramsay's +discovery of the formation of helium from the radium emanation was +first made known, is now less tenable. The latest theory is that the +alpha particle is in fact an atom of helium, and that the final +transformation product of radium and the other radioactive substances +is lead. Cf. Rutherford, op. cit. passim.--ED.] + +It is possible, by considerations analogous to those set forth above +in other cases, to arrive at an idea of the total number of particles +per second expelled by one gramme of radium; Professor Rutherford in +his most recent evaluation finds that this number approaches 2.5 x +10^{11}.[41] By calculating from the atomic weight the number of atoms +probably contained in this gramme of radium, and supposing each +particle liberated to correspond to the destruction of one atom, it is +found that one half of the radium should disappear in 1280 years;[42] +and from this we may conceive that it has not yet been possible to +discover any sensible loss of weight. Sir W. Ramsay and Professor +Soddy attained a like result by endeavouring to estimate the mass of +the emanation by the quantity of helium produced. + +[Footnote 41: See _Radioactive Transformations_ (p. 251). Professor +Rutherford says that "each of the alpha ray products present in one +gram of radium product (_sic_) expels 6.2 x 10^{10} alpha particles +per second." He also remarks on "the experimental difficulty of +accurately determining the number of alpha particles expelled from +radium per second."--ED.] + +[Footnote 42: See Rutherford, op. cit. p. 150.--ED.] + +If radium transforms itself in such a way that its activity does not +persist throughout the ages, it loses little by little the provision +of energy it had in the beginning, and its properties furnish no valid +argument to oppose to the principle of the conservation of energy. To +put everything right, we have only to recognise that radium possessed +in the potential state at its formation a finite quantity of energy +which is consumed little by little. In the same manner, a chemical +system composed, for instance, of zinc and sulphuric acid, also +contains in the potential state energy which, if we retard the +reaction by any suitable arrangement--such as by amalgamating the zinc +and by constituting with its elements a battery which we cause to act +on a resistance--may be made to exhaust itself as slowly as one may +desire. + +There can, therefore, be nothing in any way surprising in the fact +that a combination which, like the atomic combination of radium, is +not stable--since it disaggregates itself,--is capable of +spontaneously liberating energy, but what may be a little astonishing, +at first sight, is the considerable amount of this energy. + +M. Curie has calculated directly, by the aid of the calorimeter, the +quantity of energy liberated, measuring it entirely in the form of +heat. The disengagement of heat accounted for in a grain of radium is +uniform, and amounts to 100 calories per hour. It must therefore be +admitted that an atom of radium, in disaggregating itself, liberates +30,000 times more energy than a molecule of hydrogen when the latter +combines with an atom of oxygen to form a molecule of water. + +We may ask ourselves how the atomic edifice of the active body can be +constructed, to contain so great a provision of energy. We will remark +that such a question might be asked concerning cases known from the +most remote antiquity, like that of the chemical systems, without any +satisfactory answer ever being given. This failure surprises no one, +for we get used to everything--even to defeat. + +When we come to deal with a new problem we have really no right to +show ourselves more exacting; yet there are found persons who refuse +to admit the hypothesis of the atomic disaggregation of radium because +they cannot have set before them a detailed plan of that complex whole +known to us as an atom. + +The most natural idea is perhaps the one suggested by comparison with +those astronomical phenomena where our observation most readily allows +us to comprehend the laws of motion. It corresponds likewise to the +tendency ever present in the mind of man, to compare the infinitely +small with the infinitely great. The atom may be regarded as a sort of +solar system in which electrons in considerable numbers gravitate +round the sun formed by the positive ion. It may happen that certain +of these electrons are no longer retained in their orbit by the +electric attraction of the rest of the atom, and may be projected from +it like a small planet or comet which escapes towards the stellar +spaces. The phenomena of the emission of light compels us to think +that the corpuscles revolve round the nucleus with extreme velocities, +or at the rate of thousands of billions of evolutions per second. It +is easy to conceive from this that, notwithstanding its lightness, an +atom thus constituted may possess an enormous energy.[43] + +[Footnote 43: This view of the case has been made very clear by M. +Gustave le Bon in _L'Évolution de la Matière_ (Paris, 1906). See +especially pp. 36-52, where the amount of the supposed intra-atomic +energy is calculated.--ED.] + +Other authors imagine that the energy of the corpuscles is principally +due to the extremely rapid rotations of those elements on their own +axes. Lord Kelvin lately drew up on another model the plan of a +radioactive atom capable of ejecting an electron with a considerable +_vis viva_. He supposes a spherical atom formed of concentric layers +of positive and negative electricity disposed in such a way that its +external action is null, and that, nevertheless, the force emanated +from the centre may be repellent for certain values when the electron +is within it. + +The most prudent physicists and those most respectful to established +principles may, without any scruples, admit the explanation of the +radioactivity of radium by a dislocation of its molecular edifice. The +matter of which it is constituted evolves from an admittedly unstable +initial state to another stable one. It is, in a way, a slow +allotropic transformation which takes place by means of a mechanism +regarding which, in short, we have no more information than we have +regarding other analogous transformations. The only astonishment we +can legitimately feel is derived from the thought that we are suddenly +and deeply penetrating to the very heart of things. + +But those persons who have a little more hardihood do not easily +resist the temptation of forming daring generalisations. Thus it will +occur to some that this property, already discovered in many +substances where it exists in more or less striking degree, is, with +differences of intensity, common to all bodies, and that we are thus +confronted by a phenomenon derived from an essential quality of +matter. Quite recently, Professor Rutherford has demonstrated in a +fine series of experiments that the alpha particles of radium cease to +ionize gases when they are made to lose their velocity, but that they +do not on that account cease to exist. It may follow that many bodies +emit similar particles without being easily perceived to do so; since +the electric action, by which this phenomenon of radioactivity is +generally manifested, would, in this case, be but very weak. + +If we thus believe radioactivity to be an absolutely general +phenomenon, we find ourselves face to face with a new problem. The +transformation of radioactive bodies can no longer be assimilated to +allotropic transformations, since thus no final form could ever be +attained, and the disaggregation would continue indefinitely up to the +complete dislocation of the atom.[44] The phenomenon might, it is +true, have a duration of perhaps thousands of millions of centuries, +but this duration is but a minute in the infinity of time, and matters +little. Our habits of mind, if we adopt such a conception, will be +none the less very deeply disturbed. We shall have to abandon the idea +so instinctively dear to us that matter is the most stable thing in +the universe, and to admit, on the contrary, that all bodies whatever +are a kind of explosive decomposing with extreme slowness. There is in +this, whatever may have been said, nothing contrary to any of the +principles on which the science of energetics rests; but an hypothesis +of this nature carries with it consequences which ought in the highest +degree to interest the philosopher, and we all know with what alluring +boldness M. Gustave Le Bon has developed all these consequences in his +work on the evolution of matter.[45] + +[Footnote 44: This is the main contention of M. Gustave Le Bon in +his work last quoted.--ED.] + +[Footnote 45: See last note.--ED.] + +There is hardly a physicist who does not at the present day adopt in +one shape or another the ballistic hypothesis. All new facts are +co-ordinated so happily by it, that it more and more satisfies our +minds; but it cannot be asserted that it forces itself on our +convictions with irresistible weight. Another point of view appeared +more plausible and simple at the outset, when there seemed reason to +consider the energy radiated by radioactive bodies as inexhaustible. +It was thought that the source of this energy was to be looked for +without the atom, and this idea may perfectly well he maintained at +the present day. + +Radium on this hypothesis must be considered as a transformer +borrowing energy from the external medium and returning it in the form +of radiation. It is not impossible, even, to admit that the energy +which the atom of radium withdraws from the surrounding medium may +serve to keep up, not only the heat emitted and its complex radiation, +but also the dissociation, supposed to be endothermic, of this atom. +Such seems to be the idea of M. Debierne and also of M. Sagnac. It +does not seem to accord with the experiments that this borrowed energy +can be a part of the heat of the ambient medium; and, indeed, such a +phenomenon would be contrary to the principle of Carnot if we wished +(though we have seen how disputable is this extension) to extend this +principle to the phenomena which are produced in the very bosom of the +atom. + +We may also address ourselves to a more noble form of energy, and ask +ourselves whether we are not, for the first time, in presence of a +transformation of gravitational energy. It may be singular, but it is +not absurd, to suppose that the unit of mass of radium is not attached +to the earth with the same intensity as an inert body. M. Sagnac has +commenced some experiments, as yet unpublished, in order to study the +laws of the fall of a fragment of radium. They are necessarily very +delicate, and the energetic and ingenious physicist has not yet +succeeded in finishing them.[46] Let us suppose that he succeeds in +demonstrating that the intensity of gravity is less for radium than +for the platinum or the copper of which the pendulums used to +illustrate the law of Newton are generally made; it would then be +possible still to think that the laws of universal attraction are +perfectly exact as regards the stars, and that ponderability is really +a particular case of universal attraction, while in the case of +radioactive bodies part of the gravitational energy is transformed in +the course of its evolution and appears in the form of active +radiation. + +[Footnote 46: In reality M. Sagnac operated in the converse manner. He +took two equal _weights_ of a salt of radium and a salt of barium, +which he made oscillate one after the other in a torsion balance. Had +the durations of oscillation been different, it might be concluded +that the mechanical mass is not the same for radium as for barium.] + +But for this explanation to be admitted, it would evidently need to be +supported by very numerous facts. It might, no doubt, appear still +more probable that the energy borrowed from the external medium by +radium is one of those still unknown to us, but of which a vague +instinct causes us to suspect the existence around us. It is +indisputable, moreover, that the atmosphere in all directions is +furrowed with active radiations; those of radium may be secondary +radiations reflected by a kind of resonance phenomenon. + +Certain experiments by Professors Elster and Geitel, however, are not +favourable to this point of view. If an active body be surrounded by a +radioactive envelope, a screen should prevent this body from receiving +any impression from outside, and yet there is no diminution apparent +in the activity presented by a certain quantity of radium when it is +lowered to a depth of 800 metres under ground, in a region containing +a notable quantity of pitchblende. These negative results are, on the +other hand, so many successes for the partisans of the explanation of +radioactivity by atomic energy. + + + + +CHAPTER X + +THE ETHER AND MATTER + + +§ 1. THE RELATIONS BETWEEN THE ETHER AND MATTER + +For some time past it has been the more or less avowed ambition of +physicists to construct with the particles of ether all possible forms +of corporeal existence; but our knowledge of the inmost nature of +things has hitherto seemed too limited for us to attempt such an +enterprise with any chance of success. The electronic hypothesis, +however, which has furnished a satisfactory image of the most curious +phenomena produced in the bosom of matter, has also led to a more +complete electromagnetic theory of the ether than that of Maxwell, and +this twofold result has given birth to the hope of arriving by means +of this hypothesis at a complete co-ordination of the physical world. + +The phenomena whose study may bring us to the very threshold of the +problem, are those in which the connections between matter and the +ether appear clearly and in a relatively simple manner. Thus in the +phenomena of emission, ponderable matter is seen to give birth to +waves which are transmitted by the ether, and by the phenomena of +absorption it is proved that these waves disappear and excite +modifications in the interior of the material bodies which receive +them. We here catch in operation actual reciprocal actions and +reactions between the ether and matter. If we could thoroughly +comprehend these actions, we should no doubt be in a position to fill +up the gap which separates the two regions separately conquered by +physical science. + +In recent years numerous researches have supplied valuable materials +which ought to be utilized by those endeavouring to construct a theory +of radiation. We are, perhaps, still ill informed as to the phenomena +of luminescence in which undulations are produced in a complex manner, +as in the case of a stick of moist phosphorus which is luminescent in +the dark, or in that of a fluorescent screen. But we are very well +acquainted with emission or absorption by incandescence, where the +only transformation is that of calorific into radiating energy, or +_vice versa_. It is in this case alone that can be correctly applied +the celebrated demonstration by which Kirchhoff established, by +considerations borrowed from thermodynamics, the proportional +relations between the power of emission and that of absorption. + +In treating of the measurement of temperature, I have already pointed +out the experiments of Professors Lummer and Pringsheim and the +theoretical researches of Stephan and Professor Wien. We may consider +that at the present day the laws of the radiation of dark bodies are +tolerably well known, and, in particular, the manner in which each +elementary radiation increases with the temperature. A few doubts, +however, subsist with respect to the law of the distribution of energy +in the spectrum. In the case of real and solid bodies the results are +naturally less simple than in that of dark bodies. One side of the +question has been specially studied on account of its great practical +interest, that is to say, the fact that the relation of the luminous +energy to the total amount radiated by a body varies with the nature +of this last; and the knowledge of the conditions under which this +relation becomes most considerable led to the discovery of +incandescent lighting by gas in the Auer-Welsbach mantle, and to the +substitution for the carbon thread in the electric light bulb of a +filament of osmium or a small rod of magnesium, as in the Nernst lamp. +Careful measurements effected by M. Fery have furnished, in +particular, important information on the radiation of the white +oxides; but the phenomena noticed have not yet found a satisfactory +interpretation. Moreover, the radiation of calorific origin is here +accompanied by a more or less important luminescence, and the problem +becomes very complex. + +In the same way that, for the purpose of knowing the constitution of +matter, it first occurred to us to investigate gases, which appear to +be molecular edifices built on a more simple and uniform plan than +solids, we ought naturally to think that an examination of the +conditions in which emission and absorption are produced by gaseous +bodies might be eminently profitable, and might perhaps reveal the +mechanism by which the relations between the molecule of the ether and +the molecule of matter might be established. + +Unfortunately, if a gas is not absolutely incapable of emitting some +sort of rays by simple heat, the radiation thus produced, no doubt by +reason of the slightness of the mass in play, always remains of +moderate intensity. In nearly all the experiments, new energies of +chemical or electrical origin come into force. On incandescence, +luminescence is superposed; and the advantage which might have been +expected from the simplicity of the medium vanishes through the +complication of the circumstances in which the phenomenon is produced. + +Professor Pringsheim has succeeded, in certain cases, in finding the +dividing line between the phenomena of luminescence and that of +incandescence. Thus the former takes a predominating importance when +the gas is rendered luminous by electrical discharges, and chemical +transformations, especially, play a preponderant rôle in the emission +of the spectrum of flames which contain a saline vapour. In all the +ordinary experiments of spectrum analysis the laws of Kirchhoff cannot +therefore be considered as established, and yet the relation between +emission and absorption is generally tolerably well verified. No doubt +we are here in presence of a kind of resonance phenomenon, the gaseous +atoms entering into vibration when solicited by the ether by a motion +identical with the one they are capable of communicating to it. + +If we are not yet very far advanced in the study of the mechanism of +the production of the spectrum,[47] we are, on the other hand, well +acquainted with its constitution. The extreme confusion which the +spectra of the lines of the gases seemed to present is now, in great +part at least, cleared up. Balmer gave some time since, in the case of +the hydrogen spectrum, an empirical formula which enabled the rays +discovered later by an eminent astronomer, M. Deslandres, to be +represented; but since then, both in the cases of line and band +spectra, the labours of Professor Rydberg, of M. Deslandres, of +Professors Kayzer and Runge, and of M. Thiele, have enabled us to +comprehend, in their smallest details, the laws of the distribution of +lines and bands. + +[Footnote 47: Many theories as to the cause of the lines and bands of +the spectrum have been put forward since this was written, among which +that of Professor Stark (for which see _Physikalische Zeitschrift_ for +1906, passim) is perhaps the most advanced. That of M. Jean Becquerel, +which would attribute it to the vibration within the atom of both +negative and positive electrons, also deserves notice. A popular +account of this is given in the _Athenæum_ of 20th April 1907.--ED.] + +These laws are simple, but somewhat singular. The radiations emitted +by a gas cannot be compared to the notes to which a sonorous body +gives birth, nor even to the most complicated vibrations of any +elastic body. The number of vibrations of the different rays are not +the successive multiples of one and the same number, and it is not a +question of a fundamental radiation and its harmonics, while--and this +is an essential difference--the number of vibrations of the radiation +tend towards a limit when the period diminishes infinitely instead of +constantly increasing, as would be the case with the vibrations of +sound. + +Thus the assimilation of the luminous to the elastic vibration is not +correct. Once again we find that the ether does not behave like matter +which obeys the ordinary laws of mechanics, and every theory must take +full account of these curious peculiarities which experiment reveals. + +Another difference, likewise very important, between the luminous and +the sonorous vibrations, which also points out how little analogous +can be the constitutions of the media which transmit the vibrations, +appears in the phenomena of dispersion. The speed of propagation, +which, as we have seen when discussing the measurement of the velocity +of sound, depends very little on the musical note, is not at all the +same in the case of the various radiations which can be propagated in +the same substance. The index of refraction varies with the duration +of the period, or, if you will, with the length of wave _in vacuo_ +which is proportioned to this duration, since _in vacuo_ the speed of +propagation is entirely the same for all vibrations. + +Cauchy was the first to propose a theory on which other attempts have +been modelled; for example, the very interesting and simple one of +Briot. This last-named supposed that the luminous vibration could not +perceptibly drag with it the molecular material of the medium across +which it is propagated, but that matter, nevertheless, reacts on the +ether with an intensity proportional to the elongation, in such a +manner as tends to bring it back to its position of equilibrium. With +this simple hypothesis we can fairly well interpret the phenomena of +the dispersion of light in the case of transparent substances; but far +from well, as M. Carvallo has noted in some extremely careful +experiments, the dispersion of the infra-red spectrum, and not at all +the peculiarities presented by absorbent substances. + +M. Boussinesq arrives at almost similar results, by attributing +dispersion, on the other hand, to the partial dragging along of +ponderable matter and to its action on the ether. By combining, in a +measure, as was subsequently done by M. Boussinesq, the two +hypotheses, formulas can be established far better in accord with all +the known facts. + +These facts are somewhat complex. It was at first thought that the +index always varied in inverse ratio to the wave-length, but numerous +substances have been discovered which present the phenomenon of +abnormal dispersion--that is to say, substances in which certain +radiations are propagated, on the contrary, the more quickly the +shorter their period. This is the case with gases themselves, as +demonstrated, for example, by a very elegant experiment of M. +Becquerel on the dispersion of the vapour of sodium. Moreover, it may +happen that yet more complications may be met with, as no substance is +transparent for the whole extent of the spectrum. In the case of +certain radiations the speed of propagation becomes nil, and the index +shows sometimes a maximum and sometimes a minimum. All those phenomena +are in close relation with those of absorption. + +It is, perhaps, the formula proposed by Helmholtz which best accounts +for all these peculiarities. Helmholtz came to establish this formula +by supposing that there is a kind of friction between the ether and +matter, which, like that exercised on a pendulum, here produces a +double effect, changing, on the one hand, the duration of this +oscillation, and, on the other, gradually damping it. He further +supposed that ponderable matter is acted on by elastic forces. The +theory of Helmholtz has the great advantage of representing, not only +the phenomena of dispersion, but also, as M. Carvallo has pointed out, +the laws of rotatory polarization, its dispersion and other phenomena, +among them the dichroism of the rotatory media discovered by M. +Cotton. + +In the establishment of these theories, the language of ordinary +optics has always been employed. The phenomena are looked upon as due +to mechanical deformations or to movements governed by certain forces. +The electromagnetic theory leads, as we have seen, to the employment +of other images. M.H. Poincaré, and, after him, Helmholtz, have both +proposed electromagnetic theories of dispersion. On examining things +closely, it will be found that there are not, in truth, in the two +ways of regarding the problem, two equivalent translations of exterior +reality. The electrical theory gives us to understand, much better +than the mechanical one, that _in vacuo_ the dispersion ought to be +strictly null, and this absence of dispersion appears to be confirmed +with extraordinary precision by astronomical observations. Thus the +observation, often repeated, and at different times of year, proves +that in the case of the star Algol, the light of which takes at least +four years to reach us, no sensible difference in coloration +accompanies the changes in brilliancy. + + +§ 2. THE THEORY OF LORENTZ + +Purely mechanical considerations have therefore failed to give an +entirely satisfactory interpretation of the phenomena in which even +the simplest relations between matter and the ether appear. They +would, evidently, be still more insufficient if used to explain +certain effects produced on matter by light, which could not, without +grave difficulties, be attributed to movement; for instance, the +phenomena of electrification under the influence of certain +radiations, or, again, chemical reactions such as photographic +impressions. + +The problem had to be approached by another road. The electromagnetic +theory was a step in advance, but it comes to a standstill, so to +speak, at the moment when the ether penetrates into matter. If we wish +to go deeper into the inwardness of the phenomena, we must follow, for +example, Professor Lorentz or Dr Larmor, and look with them for a mode +of representation which appears, besides, to be a natural consequence +of the fundamental ideas forming the basis of Hertz's experiments. + +The moment we look upon a wave in the ether as an electromagnetic +wave, a molecule which emits light ought to be considered as a kind of +excitant. We are thus led to suppose that in each radiating molecule +there are one or several electrified particles, animated with a +to-and-fro movement round their positions of equilibrium, and these +particles are certainly identical with those electrons the existence +of which we have already admitted for so many other reasons. + +In the simplest theory, we will imagine an electron which may be +displaced from its position of equilibrium in all directions, and is, +in this displacement, submitted to attractions which communicate to it +a vibration like a pendulum. These movements are equivalent to tiny +currents, and the mobile electron, when animated with a considerable +velocity, must be sensitive to the action of the magnet which modifies +the form of the trajectory and the value of the period. This almost +direct consequence was perceived by Lorentz, and it led him to the new +idea that radiations emitted by a body ought to be modified by the +action of a strong electromagnet. + +An experiment enabled this prevision to be verified. It was made, as +is well known, as early as 1896 by Zeeman; and the discovery produced +a legitimate sensation. When a flame is subjected to the action of a +magnetic field, a brilliant line is decomposed in conditions more or +less complex which an attentive study, however, allows us to define. +According to whether the observation is made in a plane normal to the +magnetic field or in the same direction, the line transforms itself +into a triplet or doublet, and the new lines are polarized +rectilinearly or circularly. + +These are the precise phenomena which the calculation foretells: the +analysis of the modifications undergone by the light supplies, +moreover, valuable information on the electron itself. From the +direction of the circular vibrations of the greatest frequency we can +determine the sign of the electric charge in motion and we find it to +be negative. But, further than this, from the variation of the period +we can calculate the relation of the force acting on the electron to +its material mass, and, in addition, the relation of the charge to the +mass. We then find for this relation precisely that value which we +have already met with so many times. Such a coincidence cannot be +fortuitous, and we have the right to believe that the electron +revealed by the luminous wave which emanates from it, is really the +same as the one made known to us by the study of the cathode rays and +of the radioactive substances. + +However, the elementary theory does not suffice to interpret the +complications which later experiments have revealed. The physicists +most qualified to effect measurements in these delicate optical +questions--M. Cornu, Mr Preston, M. Cotton, MM. Becquerel and +Deslandres, M. Broca, Professor Michelson, and others--have pointed +out some remarkable peculiarities. Thus in some cases the number of +the component rays dissociated by the magnetic field may be very +considerable. + +The great modification brought to a radiation by the Zeeman effect +may, besides, combine itself with other phenomena, and alter the light +in a still more complicated manner. A pencil of polarized light, as +demonstrated by Signori Macaluzo and Corbino, undergoes, in a magnetic +field, modifications with regard to absorption and speed of +propagation. + +Some ingenious researches by M. Becquerel and M. Cotton have perfectly +elucidated all these complications from an experimental point of view. +It would not be impossible to link together all these phenomena +without adopting the electronic hypothesis, by preserving the old +optical equations as modified by the terms relating to the action of +the magnetic field. This has actually been done in some very +remarkable work by M. Voigt, but we may also, like Professor Lorentz, +look for more general theories, in which the essential image of the +electrons shall be preserved, and which will allow all the facts +revealed by experiment to be included. + +We are thus led to the supposition that there is not in the atom one +vibrating electron only, but that there is to be found in it a +dynamical system comprising several material points which may be +subjected to varied movements. The neutral atom may therefore be +considered as composed of an immovable principal portion positively +charged, round which move, like satellites round a planet, several +negative electrons of very inferior mass. This conclusion leads us to +an interpretation in agreement with that which other phenomena have +already suggested. + +These electrons, which thus have a variable velocity, generate around +themselves a transverse electromagnetic wave which is propagated with +the velocity of light; for the charged particle becomes, as soon as it +experiences a change of speed, the centre of a radiation. Thus is +explained the phenomenon of the emission of radiations. In the same +way, the movement of electrons may be excited or modified by the +electrical forces which exist in any pencil of light they receive, and +this pencil may yield up to them a part of the energy it is carrying. +This is the phenomenon of absorption. + +Professor Lorentz has not contented himself with thus explaining all +the mechanism of the phenomena of emission and absorption. He has +endeavoured to rediscover, by starting with the fundamental +hypothesis, the quantitative laws discovered by thermodynamics. He +succeeds in showing that, agreeably to the law of Kirchhoff, the +relation between the emitting and the absorbing power must be +independent of the special properties of the body under observation, +and he thus again meets with the laws of Planck and of Wien: +unfortunately the calculation can only be made in the case of great +wave-lengths, and grave difficulties exist. Thus it cannot be very +clearly explained why, by heating a body, the radiation is displaced +towards the side of the short wave-lengths, or, if you will, why a +body becomes luminous from the moment its temperature has reached a +sufficiently high degree. On the other hand, by calculating the energy +of the vibrating particles we are again led to attribute to these +particles the same constitution as that of the electrons. + +It is in the same way possible, as Professor Lorentz has shown, to +give a very satisfactory explanation of the thermo-electric phenomena +by supposing that the number of liberated electrons which exist in a +given metal at a given temperature has a determined value varying with +each metal, and is, in the case of each body, a function of the +temperature. The formula obtained, which is based on these hypotheses, +agrees completely with the classic results of Clausius and of Lord +Kelvin. Finally, if we recollect that the phenomena of electric and +calorific conductivity are perfectly interpreted by the hypothesis of +electrons, it will no longer be possible to contest the importance of +a theory which allows us to group together in one synthesis so many +facts of such diverse origins. + +If we study the conditions under which a wave excited by an electron's +variations in speed can be transmitted, they again bring us face to +face, and generally, with the results pointed out by the ordinary +electromagnetic theory. Certain peculiarities, however, are not +absolutely the same. Thus the theory of Lorentz, as well as that of +Maxwell, leads us to foresee that if an insulating mass be caused to +move in a magnetic field normally to its lines of force, a +displacement will be produced in this mass analogous to that of which +Faraday and Maxwell admitted the existence in the dielectric of a +charged condenser. But M.H. Poincaré has pointed out that, according +as we adopt one or other of these authors' points of view, so the +value of the displacement differs. This remark is very important, for +it may lead to an experiment which would enable us to make a definite +choice between the two theories. + +To obtain the displacement estimated according to Lorentz, we must +multiply the displacement calculated according to Hertz by a factor +representing the relation between the difference of the specific +inductive capacities of the dielectric and of a vacuum, and the first +of these powers. If therefore we take as dielectric the air of which +the specific inductive capacity is perceptibly the same as that of a +vacuum, the displacement, according to the idea of Lorentz, will be +null; while, on the contrary, according to Hertz, it will have a +finite value. M. Blondlot has made the experiment. He sent a current +of air into a condenser placed in a magnetic field, and was never able +to notice the slightest trace of electrification. No displacement, +therefore, is effected in the dielectric. The experiment being a +negative one, is evidently less convincing than one giving a positive +result, but it furnishes a very powerful argument in favour of the +theory of Lorentz. + +This theory, therefore, appears very seductive, yet it still raises +objections on the part of those who oppose to it the principles of +ordinary mechanics. If we consider, for instance, a radiation emitted +by an electron belonging to one material body, but absorbed by another +electron in another body, we perceive immediately that, the +propagation not being instantaneous, there can be no compensation +between the action and the reaction, which are not simultaneous; and +the principle of Newton thus seems to be attacked. In order to +preserve its integrity, it has to be admitted that the movements in +the two material substances are compensated by that of the ether which +separates these substances; but this conception, although in tolerable +agreement with the hypothesis that the ether and matter are not of +different essence, involves, on a closer examination, suppositions +hardly satisfactory as to the nature of movements in the ether. + +For a long time physicists have admitted that the ether as a whole +must be considered as being immovable and capable of serving, so to +speak, as a support for the axes of Galileo, in relation to which axes +the principle of inertia is applicable,--or better still, as M. +Painlevé has shown, they alone allow us to render obedience to the +principle of causality. + +But if it were so, we might apparently hope, by experiments in +electromagnetism, to obtain absolute motion, and to place in evidence +the translation of the earth relatively to the ether. But all the +researches attempted by the most ingenious physicists towards this end +have always failed, and this tends towards the idea held by many +geometricians that these negative results are not due to imperfections +in the experiments, but have a deep and general cause. Now Lorentz has +endeavoured to find the conditions in which the electromagnetic theory +proposed by him might agree with the postulate of the complete +impossibility of determining absolute motion. It is necessary, in +order to realise this concord, to imagine that a mobile system +contracts very slightly in the direction of its translation to a +degree proportioned to the square of the ratio of the velocity of +transport to that of light. The electrons themselves do not escape +this contraction, although the observer, since he participates in the +same motion, naturally cannot notice it. Lorentz supposes, besides, +that all forces, whatever their origin, are affected by a translation +in the same way as electromagnetic forces. M. Langevin and M. H. +Poincaré have studied this same question and have noted with precision +various delicate consequences of it. The singularity of the hypotheses +which we are thus led to construct in no way constitutes an argument +against the theory of Lorentz; but it has, we must acknowledge, +discouraged some of the more timid partisans of this theory.[48] + +[Footnote 48: An objection not here noticed has lately been formulated +with much frankness by Professor Lorentz himself. It is one of the +pillars of his theory that only the negative electrons move when an +electric current passes through a metal, and that the positive +electrons (if any such there be) remain motionless. Yet in the +experiment known as Hall's, the current is deflected by the magnetic +field to one side of the strip in certain metals, and to the opposite +side in others. This seems to show that in certain cases the positive +electrons move instead of the negative, and Professor Lorentz +confesses that up to the present he can find no valid argument against +this. See _Archives Néerlandaises_ 1906, parts 1 and 2.--ED.] + + +§ 3. THE MASS OF ELECTRONS + +Other conceptions, bolder still, are suggested by the results of +certain interesting experiments. The electron affords us the +possibility of considering inertia and mass to be no longer a +fundamental notion, but a consequence of the electromagnetic +phenomena. + +Professor J.J. Thomson was the first to have the clear idea that a +part, at least, of the inertia of an electrified body is due to its +electric charge. This idea was taken up and precisely stated by +Professor Max Abraham, who, for the first time, was led to regard +seriously the seemingly paradoxical notion of mass as a function of +velocity. Consider a small particle bearing a given electric charge, +and let us suppose that this particle moves through the ether. It is, +as we know, equivalent to a current proportional to its velocity, and +it therefore creates a magnetic field the intensity of which is +likewise proportional to its velocity: to set it in motion, therefore, +there must be communicated to it over and above the expenditure +corresponding to the acquisition of its ordinary kinetic energy, a +quantity of energy proportional to the square of its velocity. +Everything, therefore, takes place as if, by the fact of +electrification, its capacity for kinetic energy and its material mass +had been increased by a certain constant quantity. To the ordinary +mass may be added, if you will, an electromagnetic mass. + +This is the state of things so long as the speed of the translation of +the particle is not very great, but they are no longer quite the same +when this particle is animated with a movement whose rapidity becomes +comparable to that with which light is propagated. + +The magnetic field created is then no longer a field in repose, but +its energy depends, in a complicated manner, on the velocity, and the +apparent increase in the mass of the particle itself becomes a +function of the velocity. More than this, this increase may not be the +same for the same velocity, but varies according to whether the +acceleration is parallel with or perpendicular to the direction of +this velocity. In other words, there seems to be a longitudinal; and a +transversal mass which need not be the same. + +All these results would persist even if the material mass were very +small relatively to the electromagnetic mass; and the electron +possesses some inertia even if its ordinary mass becomes slighter and +slighter. The apparent mass, it can be easily shown, increases +indefinitely when the velocity with which the electrified particle is +animated tends towards the velocity of light, and thus the work +necessary to communicate such a velocity to an electron would be +infinite. It is in consequence impossible that the speed of an +electron, in relation to the ether, can ever exceed, or even +permanently attain to, 300,000 kilometres per second. + +All the facts thus predicted by the theory are confirmed by +experiment. There is no known process which permits the direct +measurement of the mass of an electron, but it is possible, as we have +seen, to measure simultaneously its velocity and the relation of the +electric charge to its mass. In the case of the cathode rays emitted +by radium, these measurements are particularly interesting, for the +reason that the rays which compose a pencil of cathode rays are +animated by very different speeds, as is shown by the size of the +stain produced on a photographic plate by a pencil of them at first +very constricted and subsequently dispersed by the action of an +electric or magnetic field. Professor Kaufmann has effected some very +careful experiments by a method he terms the method of crossed +spectra, which consists in superposing the deviations produced by a +magnetic and an electric field respectively acting in directions at +right angles one to another. He has thus been enabled by working _in +vacuo_ to register the very different velocities which, starting in +the case of certain rays from about seven-tenths of the velocity of +light, attain in other cases to ninety-five hundredths of it. + +It is thus noted that the ratio of charge to mass--which for ordinary +speeds is constant and equal to that already found by so many +experiments--diminishes slowly at first, and then very rapidly when +the velocity of the ray increases and approaches that of light. If we +represent this variation by a curve, the shape of this curve inclines +us to think that the ratio tends toward zero when the velocity tends +towards that of light. + +All the earlier experiments have led us to consider that the electric +charge was the same for all electrons, and it can hardly be conceived +that this charge can vary with the velocity. For in order that the +relation, of which one of the terms remains fixed, should vary, the +other term necessarily cannot remain constant. The experiments of +Professor Kaufmann, therefore, confirm the previsions of Max Abraham's +theory: the mass depends on the velocity, and increases indefinitely +in proportion as this velocity approaches that of light. These +experiments, moreover, allow the numerical results of the calculation +to be compared with the values measured. This very satisfactory +comparison shows that the apparent total mass is sensibly equal to the +electromagnetic mass; the material mass of the electron is therefore +nil, and the whole of its mass is electromagnetic. + +Thus the electron must be looked upon as a simple electric charge +devoid of matter. Previous examination has led us to attribute to it a +mass a thousand times less that that of the atom of hydrogen, and a +more attentive study shows that this mass was fictitious. The +electromagnetic phenomena which are produced when the electron is set +in motion or a change effected in its velocity, simply have the +effect, as it were, of simulating inertia, and it is the inertia due +to the charge which has caused us to be thus deluded. + +The electron is therefore simply a small volume determined at a point +in the ether, and possessing special properties;[49] this point is +propagated with a velocity which cannot exceed that of light. When +this velocity is constant, the electron creates around it in its +passage an electric and a magnetic field; round this electrified +centre there exists a kind of wake, which follows it through the ether +and does not become modified so long as the velocity remains +invariable. If other electrons follow the first within a wire, their +passage along the wire will be what is called an electric current. + +[Footnote 49: This cannot be said to be yet completely proved. _Cf_. +Sir Oliver Lodge, _Electrons_, London, 1906, p. 200.--ED.] + +When the electron is subjected to an acceleration, a transverse wave +is produced, and an electromagnetic radiation is generated, of which +the character may naturally change with the manner in which the speed +varies. If the electron has a sufficiently rapid periodical movement, +this wave is a light wave; while if the electron stops suddenly, a +kind of pulsation is transmitted through the ether, and thus we obtain +Röntgen rays. + + +§ 4. NEW VIEWS ON THE CONSTITUTION OF THE ETHER AND OF MATTER + +New and valuable information is thus afforded us regarding the +properties of the ether, but will this enable us to construct a +material representation of this medium which fills the universe, and +so to solve a problem which has baffled, as we have seen, the +prolonged efforts of our predecessors? + +Certain scholars seem to have cherished this hope. Dr. Larmor in +particular, as we have seen, has proposed a most ingenious image, but +one which is manifestly insufficient. The present tendency of +physicists rather tends to the opposite view; since they consider +matter as a very complex object, regarding which we wrongly imagine +ourselves to be well informed because we are so much accustomed to it, +and its singular properties end by seeming natural to us. But in all +probability the ether is, in its objective reality, much more simple, +and has a better right to be considered as fundamental. + +We cannot therefore, without being very illogical, define the ether by +material properties, and it is useless labour, condemned beforehand to +sterility, to endeavour to determine it by other qualities than those +of which experiment gives us direct and exact knowledge. + +The ether is defined when we know, in all its points, and in magnitude +and in direction, the two fields, electric and magnetic, which may +exist in it. These two fields may vary; we speak from habit of a +movement propagated in the ether, but the phenomenon within the reach +of experiment is the propagation of these variations. + +Since the electrons, considered as a modification of the ether +symmetrically distributed round a point, perfectly counterfeit that +inertia which is the fundamental property of matter, it becomes very +tempting to suppose that matter itself is composed of a more or less +complex assemblage of electrified centres in motion. + +This complexity is, in general, very great, as is demonstrated by the +examination of the luminous spectra produced by the atoms, and it is +precisely because of the compensations produced between the different +movements that the essential properties of matter--the law of the +conservation of inertia, for example--are not contrary to the +hypothesis. + +The forces of cohesion thus would be due to the mutual attractions +which occur in the electric and magnetic fields produced in the +interior of bodies; and it is even conceivable that there may be +produced, under the influence of these actions, a tendency to +determine orientation, that is to say, that a reason can be seen why +matter may be crystallised.[50] + +[Footnote 50: The reader should, however, be warned that a theory has +lately been put forth which attempts to account for crystallisation on +purely mechanical grounds. See Messrs Barlow and Pope's "Development +of the Atomic Theory" in the _Transactions of the Chemical Society_, +1906.--ED.] + +All the experiments effected on the conductivity of gases or metals, +and on the radiations of active bodies, have induced us to regard the +atom as being constituted by a positively charged centre having +practically the same magnitude as the atom itself, round which the +electrons gravitate; and it might evidently be supposed that this +positive centre itself preserves the fundamental characteristics of +matter, and that it is the electrons alone which no longer possess any +but electromagnetic mass. + +We have but little information concerning these positive particles, +though they are met with in an isolated condition, as we have seen, in +the canal rays or in the X rays.[51] It has not hitherto been possible +to study them so successfully as the electrons themselves; but that +their magnitude causes them to produce considerable perturbations in +the bodies on which they fall is manifest by the secondary emissions +which complicate and mask the primitive phenomenon. There are, +however, strong reasons for thinking that these positive centres are +not simple. Thus Professor Stark attributes to them, with experiments +in proof of his opinion, the emission of the spectra of the rays in +Geissler tubes, and the complexity of the spectrum discloses the +complexity of the centre. Besides, certain peculiarities in the +conductivity of metals cannot be explained without a supposition of +this kind. So that the atom, deprived of the cathode corpuscle, would +be still liable to decomposition into elements analogous to electrons +and positively charged. Consequently nothing prevents us supposing +that this centre likewise simulates inertia by its electromagnetic +properties, and is but a condition localised in the ether. + +[Footnote 51: There is much reason for thinking that the canal rays do +not contain positive particles alone, but are accompanied by negative +electrons of slow velocity. The X rays are thought, as has been said +above, to contain neither negative nor positive particles, but to be +merely pulses in the ether.--ED.] + +However this may be, the edifice thus constructed, being composed of +electrons in periodical motion, necessarily grows old. The electrons +become subject to accelerations which produce a radiation towards the +exterior of the atom; and certain of them may leave the body, while +the primitive stability is, in the end, no longer assured, and a new +arrangement tends to be formed. Matter thus seems to us to undergo +those transformations of which the radio-active bodies have given us +such remarkable examples. + +We have already had, in fragments, these views on the constitution of +matter; a deeper study of the electron thus enables us to take up a +position from which we obtain a sharp, clear, and comprehensive grasp +of the whole and a glimpse of indefinite horizons. + +It would be advantageous, however, in order to strengthen this +position, that a few objections which still menace it should be +removed. The instability of the electron is not yet sufficiently +demonstrated. How is it that its charge does not waste itself away, +and what bonds assure the permanence of its constitution? + +On the other hand, the phenomena of gravitation remain a mystery. +Lorentz has endeavoured to build up a theory in which he explains +attraction by supposing that two charges of similar sign repel each +other in a slightly less degree than that in which two charges, equal +but of contrary sign, attract each other, the difference being, +however, according to the calculation, much too small to be directly +observed. He has also sought to explain gravitation by connecting it +with the pressures which may be produced on bodies by the vibratory +movements which form very penetrating rays. Recently M. Sutherland has +imagined that attraction is due to the difference of action in the +convection currents produced by the positive and negative corpuscles +which constitute the atoms of the stars, and are carried along by the +astronomical motions. But these hypotheses remain rather vague, and +many authors think, like M. Langevin, that gravitation must result +from some mode of activity of the ether totally different from the +electromagnetic mode. + + + + +CHAPTER XI + +THE FUTURE OF PHYSICS + + +It would doubtless be exceedingly rash, and certainly very +presumptuous, to seek to predict the future which may be reserved for +physics. The rôle of prophet is not a scientific one, and the most +firmly established previsions of to-day may be overthrown by the +reality of to-morrow. + +Nevertheless, the physicist does not shun an extrapolation of some +little scope when it is not too far from the realms of experiment; the +knowledge of the evolution accomplished of late years authorises a few +suppositions as to the direction in which progress may continue. + +The reader who has deigned to follow me in the rapid excursion we have +just made through the domain of the science of Nature, will doubtless +bring back with him from his short journey the general impression that +the ancient limits to which the classic treatises still delight in +restricting the divers chapters of physics, are trampled down in all +directions. + +The fine straight roads traced out by the masters of the last century, +and enlarged and levelled by the labour of such numbers of workmen, +are now joined together by a crowd of small paths which furrow the +field of physics. It is not only because they cover regions as yet +little explored where discoveries are more abundant and more easy, +that these cross-cuts are so frequent, but also because a higher hope +guides the seekers who engage in these new routes. + +In spite of the repeated failures which have followed the numerous +attempts of past times, the idea has not been abandoned of one day +conquering the supreme principle which must command the whole of +physics. + +Some physicists, no doubt, think such a synthesis to be impossible of +realisation, and that Nature is infinitely complex; but, +notwithstanding all the reserves they may make, from the philosophical +point of view, as to the legitimacy of the process, they do not +hesitate to construct general hypotheses which, in default of complete +mental satisfaction, at least furnish them with a highly convenient +means of grouping an immense number of facts till then scattered +abroad. + +Their error, if error there be, is beneficial, for it is one of those +that Kant would have classed among the fruitful illusions which +engender the indefinite progress of science and lead to great and +important co-ordinations. + +It is, naturally, by the study of the relations existing between +phenomena apparently of very different orders that there can be any +hope of reaching the goal; and it is this which justifies the peculiar +interest accorded to researches effected in the debatable land between +domains hitherto considered as separate. + +Among all the theories lately proposed, that of the ions has taken a +preponderant place; ill understood at first by some, appearing +somewhat singular, and in any case useless, to others, it met at its +inception, in France at least, with only very moderate favour. + +To-day things have greatly changed, and those even who ignored it have +been seduced by the curious way in which it adapts itself to the +interpretation of the most recent experiments on very different +subjects. A very natural reaction has set in; and I might almost say +that a question of fashion has led to some exaggerations. + +The electron has conquered physics, and many adore the new idol rather +blindly. Certainly we can only bow before an hypothesis which enables +us to group in the same synthesis all the discoveries on electric +discharges and on radioactive substances, and which leads to a +satisfactory theory of optics and of electricity; while by the +intermediary of radiating heat it seems likely to embrace shortly the +principles of thermodynamics also. Certainly one must admire the power +of a creed which penetrates also into the domain of mechanics and +furnishes a simple representation of the essential properties of +matter; but it is right not to lose sight of the fact that an image +may be a well-founded appearance, but may not be capable of being +exactly superposed on the objective reality. + +The conception of the atom of electricity, the foundation of the +material atoms, evidently enables us to penetrate further into +Nature's secrets than our predecessors; but we must not be satisfied +with words, and the mystery is not solved when, by a legitimate +artifice, the difficulty has simply been thrust further back. We have +transferred to an element ever smaller and smaller those physical +qualities which in antiquity were attributed to the whole of a +substance; and then we shifted them later to those chemical atoms +which, united together, constitute this whole. To-day we pass them on +to the electrons which compose these atoms. The indivisible is thus +rendered, in a way, smaller and smaller, but we are still unacquainted +with what its substance may be. The notion of an electric charge which +we substitute for that of a material mass will permit phenomena to be +united which we thought separate, but it cannot be considered a +definite explanation, or as the term at which science must stop. It is +probable, however, that for a few years still physics will not travel +beyond it. The present hypothesis suffices for grouping known facts, +and it will doubtless enable many more to be foreseen, while new +successes will further increase its possessions. + +Then the day will arrive when, like all those which have shone before +it, this seductive hypothesis will lead to more errors than +discoveries. It will, however, have been improved, and it will have +become a very vast and very complete edifice which some will not +willingly abandon; for those who have made to themselves a comfortable +dwelling-place on the ruins of ancient monuments are often too loth to +leave it. + +In that day the searchers who were in the van of the march after truth +will be caught up and even passed by others who will have followed a +longer, but perhaps surer road. We also have seen at work those +prudent physicists who dreaded too daring creeds, and who sought only +to collect all the documentary evidence possible, or only took for +their guide a few principles which were to them a simple +generalisation of facts established by experiments; and we have been +able to prove that they also were effecting good and highly useful +work. + +Neither the former nor the latter, however, carry out their work in an +isolated way, and it should be noted that most of the remarkable +results of these last years are due to physicists who have known how +to combine their efforts and to direct their activity towards a common +object, while perhaps it may not be useless to observe also that +progress has been in proportion to the material resources of our +laboratories. + +It is probable that in the future, as in the past, the greatest +discoveries, those which will suddenly reveal totally unknown regions, +and open up entirely new horizons, will be made by a few scholars of +genius who will carry on their patient labour in solitary meditation, +and who, in order to verify their boldest conceptions, will no doubt +content themselves with the most simple and least costly experimental +apparatus. Yet for their discoveries to yield their full harvest, for +the domain to be systematically worked and desirable results obtained, +there will be more and more required the association of willing minds, +the solidarity of intelligent scholars, and it will be also necessary +for these last to have at their disposal the most delicate as well as +the most powerful instruments. These are conditions paramount at the +present day for continuous progress in experimental science. + +If, as has already happened, unfortunately, in the history of science, +these conditions are not complied with; if the freedoms of the workers +are trammelled, their unity disturbed, and if material facilities are +too parsimoniously afforded them,--evolution, at present so rapid, may +be retarded, and those retrogressions which, by-the-by, have been +known in all evolutions, may occur, although even then hope in the +future would not be abolished for ever. + +There are no limits to progress, and the field of our investigations +has no boundaries. Evolution will continue with invincible force. What +we to-day call the unknowable, will retreat further and further before +science, which will never stay her onward march. Thus physics will +give greater and increasing satisfaction to the mind by furnishing new +interpretations of phenomena; but it will accomplish, for the whole of +society, more valuable work still, by rendering, by the improvements +it suggests, life every day more easy and more agreeable, and by +providing mankind with weapons against the hostile forces of Nature. + + + +***END OF THE PROJECT GUTENBERG EBOOK THE NEW PHYSICS AND ITS EVOLUTION*** + + +******* This file should be named 15207-8.txt or 15207-8.zip ******* + + +This and all associated files of various formats will be found in: +https://www.gutenberg.org/dirs/1/5/2/0/15207 + + + +Updated editions will replace the previous one--the old editions +will be renamed. + +Creating the works from public domain print editions means that no +one owns a United States copyright in these works, so the Foundation +(and you!) can copy and distribute it in the United States without +permission and without paying copyright royalties. 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