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. TheElectromagnetic Ether: Ampère's advocacy of mathematical expression—Faraday first shows influence of medium in electricity—Maxwell's proof that light-waves electromagnetic—His unintelligibility—Required confirmation of theory by Hertz. § 4. Electrical Oscillations: Hertz's experiments— Blondlot proves electromagnetic disturbance propagated with speed of light— Discovery of ether waves intermediate between Hertzian and visible ones—Rubens' and Nichols' experiments— Hertzian and light rays contrasted—Pressure of light. § 5. The X-Rays: Röntgen's discovery—Properties of X-rays— Not homogeneous—Rutherford and M'Clung's experiments on energy corresponding to—Barkla's experiments on polarisation of—Their speed that of light—Are they merely ultra-violet?—Stokes and Wiechert's theory of independent pulsations generally preferred—J.J. Thomson's idea of their formation— Sutherland's and Le Bon's theories—The N- Rays— Blondlot's discovery—Experiments cannot be repeated outside France—Gutton and Mascart's confirmation— Negative experiments prove nothing—Supposed wave-length of N-rays. § 6. The Ether and Gravitation: Descartes' and Newton's ideas on gravitation—Its speed and other extraordinary characteristics—Lesage's hypothesis— Crémieux' experiments with drops of liquids—Hypothesis of ether insufficient. CHAPTER VII WIRELESS TELEGRAPHY § 1. Histories of wireless telegraphy already written, and difficulties of the subject. § 2. Two systems: that which uses the material media (earth, air, or water), and that which employs ether only. § 3. Use of earth as return wire by Steinheil —Morse's experiments with water of canal—Seine used as return wire during siege of Paris—Johnson and Melhuish's Indian experiments—Preece's telegraph over Bristol Channel—He welcomes Marconi. § 4. Early attempts at transmission of messages through ether—Experiments of Rathenau and others. § 5. Forerunners of ether telegraphy: Clerk Maxwell and Hertz—Dolbear, Hughes, and Graham Bell. § 6. Telegraphy by Hertzian waves first suggested by Threlfall—Crookes', Tesla's, Lodge's, Rutherford's, and Popoff's contributions—Marconi first makes it practicable. § 7. The receiver in wireless telegraphy—Varley's, Calzecchi—Onesti's, and Branly's researches— Explanation of coherer still obscure. § 8. Wireless telegraphy enters the commercial stage— Defect of Marconi's system—Braun's, Armstrong's, Lee de Forest's, and Fessenden's systems make use of earth— Hertz and Marconi entitled to foremost place among discoverers. CHAPTER VIII THE CONDUCTIVITY OF GASES AND THE IONS § 1. The Conductivity of Gases: Relations of matter to ether cardinal problem—Conductivity of gases at first misapprehended—Erman's forgotten researches—Giese first notices phenomenon—Experiment with X-rays— J.J. Thomson's interpretation—Ionized gas not obedient to Ohm's law—Discharge of charged conductors by ionized gas. § 2. The Condensation of water-vapour by Ions: Vapour will not condense without nucleus—Wilson's experiments on electrical condensation—Wilson and Thomson's counting experiment—Twenty million ions per c.cm. of gas—Estimate of charge borne by ion— Speed of charges—Zeleny's and Langevin's experiments—Negative ions 1/1000 of size of atoms—Natural unit of electricity or electrons. § 3. How Ions are Produced: Various causes of ionization—Moreau's experiments with alkaline salts—Barus and Bloch on ionization by phosphorus vapours—Ionization always result of shock. § 4. Electrons in Metals: Movement of electrons in metals foreshadowed by Weber—Giese's, Riecke's, Drude's, and J.J. Thomson's researches—Path of ions in metals and conduction of heat—Theory of Lorentz—Hesehus' explanation of electrification by contact—Emission of electrons by charged body— Thomson's measurement of positive ions. CHAPTER IX CATHODE RAYS AND RADIOACTIVE BODIES § 1. The Cathode Rays: History of discovery—Crookes' theory—Lenard rays—Perrin's proof of negative charge— Cathode rays give rise to X-rays—The canal rays—Villard's researches and magneto-cathode rays— Ionoplasty— Thomson's measurements of speed of rays —All atoms can be dissociated. § 2. Radioactive Substances: Uranic rays of Niepce de St Victor and Becquerel—General radioactivity of matter—Le Bon's and Rutherford's comparison of uranic with X rays—Pierre and Mme. Curie's discovery of polonium and radium—Their characteristics—Debierne discovers actinium. § 3. Radiations and Emanations of Radioactive Bodies: Giesel's, Becquerel's, and Rutherford's Researches—Alpha, beta, and gamma rays—Sagnac's secondary rays—Crookes' spinthariscope—The emanation — Ramsay and Soddy's researches upon it—Transformations of radioactive bodies—Their order. § 4. Disaggregation of Matter and Atomic Energy: Actual transformations of matter in radioactive bodies —Helium or lead final product —Ultimate disappearance of radium from earth—Energy liberated by radium: its amount and source—Suggested models of radioactive atoms—Generalization from radioactive phenomena -Le Bon's theories—Ballistic hypothesis generally admitted—Does energy come from without—Sagnac's experiments—Elster and Geitel's contra. CHAPTER X THE ETHER AND MATTER § 1. The Relations between the Ether and Matter: Attempts to reduce all matter to forms of ether—Emission and absorption phenomena show reciprocal action— Laws of radiation—Radiation of gases—Production of spectrum— Differences between light and sound variations show difference of media—Cauchy's, Briot's, Carvallo's and Boussinesq's researches—Helmholtz's and Poincaré's electromagnetic theories of dispersion. § 2. The Theory of Lorentz:—Mechanics fails to explain relations between ether and matter—Lorentz predicts action of magnet on spectrum—Zeeman's experiment —Later researches upon Zeeman effect— Multiplicity of electrons—Lorentz's explanation of thermoelectric phenomena by electrons—Maxwell's and Lorentz's theories do not agree—Lorentz's probably more correct—Earth's movement in relation to ether. § 3. The Mass of Electrons: Thomson's and Max Abraham's view that inertia of charged body due to charge—Longitudinal and transversal mass—Speed of electrons cannot exceed that of light—Ratio of charge to mass and its variation—Electron simple electric charge—Phenomena produced by its acceleration. § 4. New Views on Ether and Matter: Insufficiency of Larmor's view—Ether definable by electric and magnetic fields—Is matter all electrons? Atom probably positive centre surrounded by negative electrons—Ignorance concerning positive particles—Successive transformations of matter probable —Gravitation still unaccounted for. CHAPTER XI THE FUTURE OF PHYSICS Persistence of ambition to discover supreme principle in physics—Supremacy of electron theory at present time— Doubtless destined to disappear like others— Constant progress of science predicted—Immense field open before it. INDEX OF NAMES INDEX OF SUBJECTS The New Physics and its Evolution CHAPTER I THE EVOLUTION OF PHYSICS The now numerous public which tries with some success to keep abreast of the movement in science, from seeing its mental habits every day upset, and from occasionally witnessing unexpected discoveries that produce a more lively sensation from their reaction on social life, is led to suppose that we live in a really exceptional epoch, scored by profound crises and illustrated by extraordinary discoveries, whose singularity surpasses everything known in the past. Thus we often hear it said that physics, in particular, has of late years undergone a veritable revolution; that all its principles have been made new, that all the edifices constructed by our fathers have been overthrown, and that on the field thus cleared has sprung up the most abundant harvest that has ever enriched the domain of science. It is in fact true that the crop becomes richer and more fruitful, thanks to the development of our laboratories, and that the quantity of seekers has considerably increased in all countries, while their quality has not diminished. We should be sustaining an absolute paradox, and at the same time committing a crying injustice, were we to contest the high importance of recent progress, and to seek to diminish the glory of contemporary physicists. Yet it may be as well not to give way to exaggerations, however pardonable, and to guard against facile illusions. On closer examination it will be seen that our predecessors might at several periods in history have conceived, as legitimately as ourselves, similar sentiments of scientific pride, and have felt that the world was about to appear to them transformed and under an aspect until then absolutely unknown. Let us take an example which is salient enough; for, however arbitrary the conventional division of time may appear to a physicist's eyes, it is natural, when instituting a comparison between two epochs, to choose those which extend over a space of half a score of years, and are separated from each other by the gap of a century. Let us, then, go back a hundred years and examine what would have been the state of mind of an erudite amateur who had read and understood the chief publications on physical research between 1800 and 1810. Let us suppose that this intelligent and attentive spectator witnessed in 1800 the discovery of the galvanic battery by Volta. He might from that moment have felt a presentiment that a prodigious transformation was about to occur in our mode of regarding electrical phenomena. Brought up in the ideas of Coulomb and Franklin, he might till then have imagined that electricity had unveiled nearly all its mysteries, when an entirely original apparatus suddenly gave birth to applications of the highest interest, and excited the blossoming of theories of immense philosophical extent. In the treatises on physics published a little later, we find traces of the astonishment produced by this sudden revelation of a new world. "Electricity," wrote the Abbé Haüy, "enriched by the labour of so many distinguished physicists, seemed to have reached the term when a science has no further important steps before it, and only leaves to those who cultivate it the hope of confirming the discoveries of their predecessors, and of casting a brighter light on the truths revealed. One would have thought that all researches for diversifying the results of experiment were exhausted, and that theory itself could only be augmented by the addition of a greater degree of precision to the applications of principles already known. While science thus appeared to be making for repose, the phenomena of the convulsive movements observed by Galvani in the muscles of a frog when connected by metal were brought to the attention and astonishment of physicists.... Volta, in that Italy which had been the cradle of the new knowledge, discovered the principle of its true theory in a fact which reduces the explanation of all the phenomena in question to the simple contact of two substances of different nature. This fact became in his hands the germ of the admirable apparatus to which its manner of being and its fecundity assign one of the chief places among those with which the genius of mankind has enriched physics." Shortly afterwards, our amateur would learn that Carlisle and Nicholson had decomposed water by the aid of a battery; then, that Davy, in 1803, had produced, by the help of the same battery, a quite unexpected phenomenon, and had succeeded in preparing metals endowed with marvellous properties, beginning with substances of an earthy appearance which had been known for a long time, but whose real nature had not been discovered. In another order of ideas, surprises as prodigious would wait for our amateur. Commencing with 1802, he might have read the admirable series of memoirs which Young then published, and might thereby have learned how the study of the phenomena of diffraction led to the belief that the undulation theory, which, since the works of Newton seemed irretrievably condemned, was, on the contrary, beginning quite a new life. A little later—in 1808—he might have witnessed the discovery made by Malus of polarization by reflexion, and would have been able to note, no doubt with stupefaction, that under certain conditions a ray of light loses the property of being reflected. He might also have heard of one Rumford, who was then promulgating very singular ideas on the nature of heat, who thought that the then classical notions might be false, that caloric does not exist as a fluid, and who, in 1804, even demonstrated that heat is created by friction. A few years later he would learn that Charles had enunciated a capital law on the dilatation of gases; that Pierre Prevost, in 1809, was making a study, full of original ideas, on radiant heat. In the meantime he would not have failed to read volumes iii. and iv. of the Mecanique celeste of Laplace, published in 1804 and 1805, and he might, no doubt, have thought that before long mathematics would enable physical science to develop with unforeseen safety. All these results may doubtless be compared in importance with the present discoveries. When strange metals like potassium and sodium were isolated by an entirely new method, the astonishment must have been on a par with that caused in our time by the magnificent discovery of radium. The polarization of light is a phenomenon as undoubtedly singular as the existence of the X rays; and the upheaval produced in natural philosophy by the theories of the disintegration of matter and the ideas concerning electrons is probably not more considerable than that produced in the theories of light and heat by the works of Young and Rumford. If we now disentangle ourselves from contingencies, it will be understood that in reality physical science progresses by evolution rather than by revolution. Its march is continuous. The facts which our theories enable us to discover, subsist and are linked together long after these theories have disappeared. Out of the materials of former edifices overthrown, new dwellings are constantly being reconstructed. The labour of our forerunners never wholly perishes. The ideas of yesterday prepare for those of to-morrow; they contain them, so to speak, in potentia. Science is in some sort a living organism, which gives birth to an indefinite series of new beings taking the places of the old, and which evolves according to the nature of its environment, adapting itself to external conditions, and healing at every step the wounds which contact with reality may have occasioned. Sometimes this evolution is rapid, sometimes it is slow enough; but it obeys the ordinary laws. The wants imposed by its surroundings create certain organs in science. The problems set to physicists by the engineer who wishes to facilitate transport or to produce better illumination, or by the doctor who seeks to know how such and such a remedy acts, or, again, by the physiologist desirous of understanding the mechanism of the gaseous and liquid exchanges between the cell and the outer medium, cause new chapters in physics to appear, and suggest researches adapted to the necessities of actual life. The evolution of the different parts of physics does not, however, take place with equal speed, because the circumstances in which they are placed are not equally favourable. Sometimes a whole series of questions will appear forgotten, and will live only with a languishing existence; and then some accidental circumstance suddenly brings them new life, and they become the object of manifold labours, engross public attention, and invade nearly the whole domain of science. We have in our own day witnessed such a spectacle. The discovery of the X rays—a discovery which physicists no doubt consider as the logical outcome of researches long pursued by a few scholars working in silence and obscurity on an otherwise much neglected subject—seemed to the public eye to have inaugurated a new era in the history of physics. If, as is the case, however, the extraordinary scientific movement provoked by Röntgen's sensational experiments has a very remote origin, it has, at least, been singularly quickened by the favourable conditions created by the interest aroused in its astonishing applications to radiography. A lucky chance has thus hastened an evolution already taking place, and theories previously outlined have received a singular development. Without wishing to yield too much to what may be considered a whim of fashion, we cannot, if we are to note in this book the stage actually reached in the continuous march of physics, refrain from giving a clearly preponderant place to the questions suggested by the study of the new radiations. At the present time it is these questions which move us the most; they have shown us unknown horizons, and towards the fields recently opened to scientific activity the daily increasing crowd of searchers rushes in rather disorderly fashion. One of the most interesting consequences of the recent discoveries has been to rehabilitate in the eyes of scholars, speculations relating to the constitution of matter, and, in a more general way, metaphysical problems. Philosophy has, of course, never been completely separated from science; but in times past many physicists dissociated themselves from studies which they looked upon as unreal word-squabbles, and sometimes not unreasonably abstained from joining in discussions which seemed to them idle and of rather puerile subtlety. They had seen the ruin of most of the systems built up a priori by daring philosophers, and deemed it more prudent to listen to the advice given by Kirchhoff and "to substitute the description of facts for a sham explanation of nature." It should however be remarked that these physicists somewhat deceived themselves as to the value of their caution, and that the mistrust they manifested towards philosophical speculations did not preclude their admitting, unknown to themselves, certain axioms which they did not discuss, but which are, properly speaking, metaphysical conceptions. They were unconsciously speaking a language taught them by their predecessors, of which they made no attempt to discover the origin. It is thus that it was readily considered evident that physics must necessarily some day re-enter the domain of mechanics, and thence it was postulated that everything in nature is due to movement. We, further, accepted the principles of the classical mechanics without discussing their legitimacy. This state of mind was, even of late years, that of the most illustrious physicists. It is manifested, quite sincerely and without the slightest reserve, in all the classical works devoted to physics. Thus Verdet, an illustrious professor who has had the greatest and most happy influence on the intellectual formation of a whole generation of scholars, and whose works are even at the present day very often consulted, wrote: "The true problem of the physicist is always to reduce all phenomena to that which seems to us the simplest and clearest, that is to say, to movement." In his celebrated course of lectures at l'École Polytechnique, Jamin likewise said: "Physics will one day form a chapter of general mechanics;" and in the preface to his excellent course of lectures on physics, M. Violle, in 1884, thus expresses himself: "The science of nature tends towards mechanics by a necessary evolution, the physicist being able to establish solid theories only on the laws of movement." The same idea is again met with in the words of Cornu in 1896: "The general tendency should be to show how the facts observed and the phenomena measured, though first brought together by empirical laws, end, by the impulse of successive progressions, in coming under the general laws of rational mechanics;" and the same physicist showed clearly that in his mind this connexion of phenomena with mechanics had a deep and philosophical reason, when, in the fine discourse pronounced by him at the opening ceremony of the Congrès de Physique in 1900, he exclaimed: "The mind of Descartes soars over modern physics, or rather, I should say, he is their luminary. The further we penetrate into the knowledge of natural phenomena, the clearer and the more developed becomes the bold Cartesian conception regarding the mechanism of the universe. There is nothing in the physical world but matter and movement." If we adopt this conception, we are led to construct mechanical representations of the material world, and to imagine movements in the different parts of bodies capable of reproducing all the manifestations of nature. The kinematic knowledge of these movements, that is to say, the determination of the position, speed, and acceleration at a given moment of all the parts of the system, or, on the other hand, their dynamical study, enabling us to know what is the action of these parts on each other, would then be sufficient to enable us to foretell all that can occur in the domain of nature. This was the great thought clearly expressed by the Encyclopædists of the eighteenth century; and if the necessity of interpreting the phenomena of electricity or light led the physicists of last century to imagine particular fluids which seemed to obey with some difficulty the ordinary rules of mechanics, these physicists still continued to retain their hope in the future, and to treat the idea of Descartes as an ideal to be reached sooner or later. Certain scholars—particularly those of the English School—outrunning experiment, and pushing things to extremes, took pleasure in proposing very curious mechanical models which were often strange images of reality. The most illustrious of them, Lord Kelvin, may be considered as their representative type, and he has himself said: "It seems to me that the true sense of the question, Do we or do we not understand a particular subject in physics? is—Can we make a mechanical model which corresponds to it? I am never satisfied so long as I have been unable to make a mechanical model of the object. If I am able to do so, I understand it. If I cannot make such a model, I do not understand it." But it must be acknowledged that some of the models thus devised have become excessively complicated, and this complication has for a long time discouraged all but very bold minds. In addition, when it became a question of penetrating into the mechanism of molecules, and we were no longer satisfied to look at matter as a mass, the mechanical solutions seemed undetermined and the stability of the edifices thus constructed was insufficiently demonstrated. Returning then to our starting-point, many contemporary physicists wish to subject Descartes' idea to strict criticism. From the philosophical point of view, they first enquire whether it is really demonstrated that there exists nothing else in the knowable than matter and movement. They ask themselves whether it is not habit and tradition in particular which lead us to ascribe to mechanics the origin of phenomena. Perhaps also a question of sense here comes in. Our senses, which are, after all, the only windows open towards external reality, give us a view of one side of the world only; evidently we only know the universe by the relations which exist between it and our organisms, and these organisms are peculiarly sensitive to movement. Nothing, however, proves that those acquisitions which are the most ancient in historical order ought, in the development of science, to remain the basis of our knowledge. Nor does any theory prove that our perceptions are an exact indication of reality. Many reasons, on the contrary, might be invoked which tend to compel us to see in nature phenomena which cannot be reduced to movement. Mechanics as ordinarily understood is the study of reversible phenomena. If there be given to the parameter which represents time,[1] and which has assumed increasing values during the duration of the phenomena, decreasing values which make it go the opposite way, the whole system will again pass through exactly the same stages as before, and all the phenomena will unfold themselves in reversed order. In physics, the contrary rule appears very general, and reversibility generally does not exist. It is an ideal and limited case, which may be sometimes approached, but can never, strictly speaking, be met with in its entirety. No physical phenomenon ever recommences in an identical manner if its direction be altered. It is true that certain mathematicians warn us that a mechanics can be devised in which reversibility would no longer be the rule, but the bold attempts made in this direction are not wholly satisfactory. On the other hand, it is established that if a mechanical explanation of a phenomenon can be given, we can find an infinity of others which likewise account for all the peculiarities revealed by experiment. But, as a matter of fact, no one has ever succeeded in giving an indisputable mechanical representation of the whole physical world. Even were we disposed to admit the strangest solutions of the problem; to consent, for example, to be satisfied with the hidden systems devised by Helmholtz, whereby we ought to divide variable things into two classes, some accessible, and the others now and for ever unknown, we should never manage to construct an edifice to contain all the known facts. Even the very comprehensive mechanics of a Hertz fails where the classical mechanics has not succeeded. Deeming this check irremediable, many contemporary physicists give up attempts which they look upon as condemned beforehand, and adopt, to guide them in their researches, a method which at first sight appears much more modest, and also much more sure. They make up their minds not to see at once to the bottom of things; they no longer seek to suddenly strip the last veils from nature, and to divine her supreme secrets; but they work prudently and advance but slowly, while on the ground thus conquered foot by foot they endeavour to establish themselves firmly. They study the various magnitudes directly accessible to their observation without busying themselves as to their essence. They measure quantities of heat and of temperature, differences of potential, currents, and magnetic fields; and then, varying the conditions, apply the rules of experimental method, and discover between these magnitudes mutual relations, while they thus succeed in enunciating laws which translate and sum up their labours. These empirical laws, however, themselves bring about by induction the promulgation of more general laws, which are termed principles. These principles are originally only the results of experiments, and experiment allows them besides to be checked, and their more or less high degree of generality to be verified. When they have been thus definitely established, they may serve as fresh starting-points, and, by deduction, lead to very varied discoveries. The principles which govern physical science are few in number, and their very general form gives them a philosophical appearance, while we cannot long resist the temptation of regarding them as metaphysical dogmas. It thus happens that the least bold physicists, those who have wanted to show themselves the most reserved, are themselves led to forget the experimental character of the laws they have propounded, and to see in them imperious beings whose authority, placed above all verification, can no longer be discussed. Others, on the contrary, carry prudence to the extent of timidity. They desire to grievously limit the field of scientific investigation, and they assign to science a too restricted domain. They content themselves with representing phenomena by equations, and think that they ought to submit to calculation magnitudes experimentally determined, without asking themselves whether these calculations retain a physical meaning. They are thus led to reconstruct a physics in which there again appears the idea of quality, understood, of course, not in the scholastic sense, since from this quality we can argue with some precision by representing it under numerical symbols, but still constituting an element of differentiation and of heterogeneity. Notwithstanding the errors they may lead to if carried to excess, both these doctrines render, as a whole, most important service. It is no bad thing that these contradictory tendencies should subsist, for this variety in the conception of phenomena gives to actual science a character of intense life and of veritable youth, capable of impassioned efforts towards the truth. Spectators who see such moving and varied pictures passing before them, experience the feeling that there no longer exist systems fixed in an immobility which seems that of death. They feel that nothing is unchangeable; that ceaseless transformations are taking place before their eyes; and that this continuous evolution and perpetual change are the necessary conditions of progress. A great number of seekers, moreover, show themselves on their own account perfectly eclectic. They adopt, according to their needs, such or such a manner of looking at nature, and do not hesitate to utilize very different images when they appear to them useful and convenient. And, without doubt, they are not wrong, since these images are only symbols convenient for language. They allow facts to be grouped and associated, but only present a fairly distant resemblance with the objective reality. Hence it is not forbidden to multiply and to modify them according to circumstances. The really essential thing is to have, as a guide through the unknown, a map which certainly does not claim to represent all the aspects of nature, but which, having been drawn up according to predetermined rules, allows us to follow an ascertained road in the eternal journey towards the truth. Among the provisional theories which are thus willingly constructed by scholars on their journey, like edifices hastily run up to receive an unforeseen harvest, some still appear very bold and very singular. Abandoning the search after mechanical models for all electrical phenomena, certain physicists reverse, so to speak, the conditions of the problem, and ask themselves whether, instead of giving a mechanical interpretation to electricity, they may not, on the contrary, give an electrical interpretation to the phenomena of matter and motion, and thus merge mechanics itself in electricity. One thus sees dawning afresh the eternal hope of co-ordinating all natural phenomena in one grandiose and imposing synthesis. Whatever may be the fate reserved for such attempts, they deserve attention in the highest degree; and it is desirable to examine them carefully if we wish to have an exact idea of the tendencies of modern physics. CHAPTER II MEASUREMENTS § 1. METROLOGY Not so very long ago, the scholar was often content with qualitative observations. Many phenomena were studied without much trouble being taken to obtain actual measurements. But it is now becoming more and more understood that to establish the relations which exist between physical magnitudes, and to represent the variations of these magnitudes by functions which allow us to use the power of mathematical analysis, it is most necessary to express each magnitude by a definite number. Under these conditions alone can a magnitude be considered as effectively known. "I often say," Lord Kelvin has said, "that if you can measure that of which you are speaking and express it by a number you know something of your subject; but if you cannot measure it nor express it by a number, your knowledge is of a sorry kind and hardly satisfactory. It may be the beginning of the acquaintance, but you are hardly, in your thoughts, advanced towards science, whatever the subject may be." It has now become possible to measure exactly the elements which enter into nearly all physical phenomena, and these measurements are taken with ever increasing precision. Every time a chapter in science progresses, science shows itself more exacting; it perfects its means of investigation, it demands more and more exactitude, and one of the most striking features of modern physics is this constant care for strictness and clearness in experimentation. A veritable science of measurement has thus been constituted which extends over all parts of the domain of physics. This science has its rules and its methods; it points out the best processes of calculation, and teaches the method of correctly estimating errors and taking account of them. It has perfected the processes of experiment, co-ordinated a large number of results, and made possible the unification of standards. It is thanks to it that the system of measurements unanimously adopted by physicists has been formed. At the present day we designate more peculiarly by the name of metrology that part of the science of measurements which devotes itself specially to the determining of the prototypes representing the fundamental units of dimension and mass, and of the standards of the first order which are derived from them. If all measurable quantities, as was long thought possible, could be reduced to the magnitudes of mechanics, metrology would thus be occupied with the essential elements entering into all phenomena, and might legitimately claim the highest rank in science. But even when we suppose that some magnitudes can never be connected with mass, length, and time, it still holds a preponderating place, and its progress finds an echo throughout the whole domain of the natural sciences. It is therefore well, in order to give an account of the general progress of physics, to examine at the outset the improvements which have been effected in these fundamental measurements, and to see what precision these improvements have allowed us to attain. § 2. THE MEASURE OF LENGTH To measure a length is to compare it with another length taken as unity. Measurement is therefore a relative operation, and can only enable us to know ratios. Did both the length to be measured and the unit chosen happen to vary simultaneously and in the same degree, we should perceive no change. Moreover, the unit being, by definition, the term of comparison, and not being itself comparable with anything, we have theoretically no means of ascertaining whether its length varies. If, however, we were to note that, suddenly and in the same proportions, the distance between two points on this earth had increased, that all the planets had moved further from each other, that all objects around us had become larger, that we ourselves had become taller, and that the distance travelled by light in the duration of a vibration had become greater, we should not hesitate to think ourselves the victims of an illusion, that in reality all these distances had remained fixed, and that all these appearances were due to a shortening of the rule which we had used as the standard for measuring the lengths. From the mathematical point of view, it may be considered that the two hypotheses are equivalent; all has lengthened around us, or else our standard has become less. But it is no simple question of convenience and simplicity which leads us to reject the one supposition and to accept the other; it is right in this case to listen to the voice of common sense, and those physicists who have an instinctive trust in the notion of an absolute length are perhaps not wrong. It is only by choosing our unit from those which at all times have seemed to all men the most invariable, that we are able in our experiments to note that the same causes acting under identical conditions always produce the same effects. The idea of absolute length is derived from the principle of causality; and our choice is forced upon us by the necessity of obeying this principle, which we cannot reject without declaring by that very act all science to be impossible. Similar remarks might be made with regard to the notions of absolute time and absolute movement. They have been put in evidence and set forth very forcibly by a learned and profound mathematician, M. Painlevé. On the particularly clear example of the measure of length, it is interesting to follow the evolution of the methods employed, and to run through the history of the progress in precision from the time that we have possessed authentic documents relating to this question. This history has been written in a masterly way by one of the physicists who have in our days done the most by their personal labours to add to it glorious pages. M. Benoit, the learned Director of the International Bureau of Weights and Measures, has furnished in various reports very complete details on the subject, from which I here borrow the most interesting. We know that in France the fundamental standard for measures of length was for a long time the Toise du Châtelet, a kind of callipers formed of a bar of iron which in 1668 was embedded in the outside wall of the Châtelet, at the foot of the staircase. This bar had at its extremities two projections with square faces, and all the toises of commerce had to fit exactly between them. Such a standard, roughly constructed, and exposed to all the injuries of weather and time, offered very slight guarantees either as to the permanence or the correctness of its copies. Nothing, perhaps, can better convey an idea of the importance of the modifications made in the methods of experimental physics than the easy comparison between so rudimentary a process and the actual measurements effected at the present time. The Toise du Châtelet, notwithstanding its evident faults, was employed for nearly a hundred years; in 1766 it was replaced by the Toise du Pérou, so called because it had served for the measurements of the terrestrial arc effected in Peru from 1735 to 1739 by Bouguer, La Condamine, and Godin. At that time, according to the comparisons made between this new toise and the Toise du Nord, which had also been used for the measurement of an arc of the meridian, an error of the tenth part of a millimetre in measuring lengths of the order of a metre was considered quite unimportant. At the end of the eighteenth century, Delambre, in his work Sur la Base du Système métrique décimal, clearly gives us to understand that magnitudes of the order of the hundredth of a millimetre appear to him incapable of observation, even in scientific researches of the highest precision. At the present date the International Bureau of Weights and Measures guarantee...