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?
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.
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.
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.
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.
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.
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.
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.
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.
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.
THE FUTURE OF PHYSICS
Persistence of ambition to discover supreme principle in physics—Supremacy of electron theory at present time—Doubtless destined to disappear like others— Constant progress of science predicted—Immense field open before it.
INDEX OF NAMES
INDEX OF SUBJECTS
The New Physics and its Evolution
CHAPTER I
THE EVOLUTION OF PHYSICS
The now numerous public which tries with some success to keep abreast of the movement in science, from seeing its mental habits every day upset, and from occasionally witnessing unexpected discoveries that produce a more lively sensation from their reaction on social life, is led to suppose that we live in a really exceptional epoch, scored by profound crises and illustrated by extraordinary discoveries, whose singularity surpasses everything known in the past. Thus we often hear it said that physics, in particular, has of late years undergone a veritable revolution; that all its principles have been made new, that all the edifices constructed by our fathers have been overthrown, and that on the field thus cleared has sprung up the most abundant harvest that has ever enriched the domain of science.
It is in fact true that the crop becomes richer and more fruitful, thanks to the development of our laboratories, and that the quantity of seekers has considerably increased in all countries, while their quality has not diminished. We should be sustaining an absolute paradox, and at the same time committing a crying injustice, were we to contest the high importance of recent progress, and to seek to diminish the glory of contemporary physicists. Yet it may be as well not to give way to exaggerations, however pardonable, and to guard against facile illusions. On closer examination it will be seen that our predecessors might at several periods in history have conceived, as legitimately as ourselves, similar sentiments of scientific pride, and have felt that the world was about to appear to them transformed and under an aspect until then absolutely unknown.
Let us take an example which is salient enough; for, however arbitrary the conventional division of time may appear to a physicist's eyes, it is natural, when instituting a comparison between two epochs, to choose those which extend over a space of half a score of years, and are separated from each other by the gap of a century. Let us, then, go back a hundred years and examine what would have been the state of mind of an erudite amateur who had read and understood the chief publications on physical research between 1800 and 1810.
Let us suppose that this intelligent and attentive spectator witnessed in 1800 the discovery of the galvanic battery by Volta. He might from that moment have felt a presentiment that a prodigious transformation was about to occur in our mode of regarding electrical phenomena. Brought up in the ideas of Coulomb and Franklin, he might till then have imagined that electricity had unveiled nearly all its mysteries, when an entirely original apparatus suddenly gave birth to applications of the highest interest, and excited the blossoming of theories of immense philosophical extent.
In the treatises on physics published a little later, we find traces of the astonishment produced by this sudden revelation of a new world. "Electricity," wrote the Abbé Haüy, "enriched by the labour of so many distinguished physicists, seemed to have reached the term when a science has no further important steps before it, and only leaves to those who cultivate it the hope of confirming the discoveries of their predecessors, and of casting a brighter light on the truths revealed. One would have thought that all researches for diversifying the results of experiment were exhausted, and that theory itself could only be augmented by the addition of a greater degree of precision to the applications of principles already known. While science thus appeared to be making for repose, the phenomena of the convulsive movements observed by Galvani in the muscles of a frog when connected by metal were brought to the attention and astonishment of physicists.... Volta, in that Italy which had been the cradle of the new knowledge, discovered the principle of its true theory in a fact which reduces the explanation of all the phenomena in question to the simple contact of two substances of different nature. This fact became in his hands the germ of the admirable apparatus to which its manner of being and its fecundity assign one of the chief places among those with which the genius of mankind has enriched physics."
Shortly afterwards, our amateur would learn that Carlisle and Nicholson had decomposed water by the aid of a battery; then, that Davy, in 1803, had produced, by the help of the same battery, a quite unexpected phenomenon, and had succeeded in preparing metals endowed with marvellous properties, beginning with substances of an earthy appearance which had been known for a long time, but whose real nature had not been discovered.
In another order of ideas, surprises as prodigious would wait for our amateur. Commencing with 1802, he might have read the admirable series of memoirs which Young then published, and might thereby have learned how the study of the phenomena of diffraction led to the belief that the undulation theory, which, since the works of Newton seemed irretrievably condemned, was, on the contrary, beginning quite a new life. A little later—in 1808—he might have witnessed the discovery made by Malus of polarization by reflexion, and would have been able to note, no doubt with stupefaction, that under certain conditions a ray of light loses the property of being reflected.
He might also have heard of one Rumford, who was then promulgating very singular ideas on the nature of heat, who thought that the then classical notions might be false, that caloric does not exist as a fluid, and who, in 1804, even demonstrated that heat is created by friction. A few years later he would learn that Charles had enunciated a capital law on the dilatation of gases; that Pierre Prevost, in 1809, was making a study, full of original ideas, on radiant heat. In the meantime he would not have failed to read volumes iii. and iv. of the Mecanique celeste of Laplace, published in 1804 and 1805, and he might, no doubt, have thought that before long mathematics would enable physical science to develop with unforeseen safety.
All these results may doubtless be compared in importance with the present discoveries. When strange metals like potassium and sodium were isolated by an entirely new method, the astonishment must have been on a par with that caused in our time by the magnificent discovery of radium. The polarization of light is a phenomenon as undoubtedly singular as the existence of the X rays; and the upheaval produced in natural philosophy by the theories of the disintegration of matter and the ideas concerning electrons is probably not more considerable than that produced in the theories of light and heat by the works of Young and Rumford.
If we now disentangle ourselves from contingencies, it will be understood that in reality physical science progresses by evolution rather than by revolution. Its march is continuous. The facts which our theories enable us to discover, subsist and are linked together long after these theories have disappeared. Out of the materials of former edifices overthrown, new dwellings are constantly being reconstructed.
The labour of our forerunners never wholly perishes. The ideas of yesterday prepare for those of to-morrow; they contain them, so to speak, in potentia. Science is in some sort a living organism, which gives birth to an indefinite series of new beings taking the places of the old, and which evolves according to the nature of its environment, adapting itself to external conditions, and healing at every step the wounds which contact with reality may have occasioned.
Sometimes this evolution is rapid, sometimes it is slow enough; but it obeys the ordinary laws. The wants imposed by its surroundings create certain organs in science. The problems set to physicists by the engineer who wishes to facilitate transport or to produce better illumination, or by the doctor who seeks to know how such and such a remedy acts, or, again, by the physiologist desirous of understanding the mechanism of the gaseous and liquid exchanges between the cell and the outer medium, cause new chapters in physics to appear, and suggest researches adapted to the necessities of actual life.
The evolution of the different parts of physics does not, however, take place with equal speed, because the circumstances in which they are placed are not equally favourable. Sometimes a whole series of questions will appear forgotten, and will live only with a languishing existence; and then some accidental circumstance suddenly brings them new life, and they become the object of manifold labours, engross public attention, and invade nearly the whole domain of science.
We have in our own day witnessed such a spectacle. The discovery of the X rays—a discovery which physicists no doubt consider as the logical outcome of researches long pursued by a few scholars working in silence and obscurity on an otherwise much neglected subject—seemed to the public eye to have inaugurated a new era in the history of physics. If, as is the case, however, the extraordinary scientific movement provoked by Röntgen's sensational experiments has a very remote origin, it has, at least, been singularly quickened by the favourable conditions created by the interest aroused in its astonishing applications to radiography.
A lucky chance has thus hastened an evolution already taking place, and theories previously outlined have received a singular development. Without wishing to yield too much to what may be considered a whim of fashion, we cannot, if we are to note in this book the stage actually reached in the continuous march of physics, refrain from giving a clearly preponderant place to the questions suggested by the study of the new radiations. At the present time it is these questions which move us the most; they have shown us unknown horizons, and towards the fields recently opened to scientific activity the daily increasing crowd of searchers rushes in rather disorderly fashion.
One of the most interesting consequences of the recent discoveries has been to rehabilitate in the eyes of scholars, speculations relating to the constitution of matter, and, in a more general way, metaphysical problems. Philosophy has, of course, never been completely separated from science; but in times past many physicists dissociated themselves from studies which they looked upon as unreal word-squabbles, and sometimes not unreasonably abstained from joining in discussions which seemed to them idle and of rather puerile subtlety. They had seen the ruin of most of the systems built up a priori by daring philosophers, and deemed it more prudent to listen to the advice given by Kirchhoff and "to substitute the description of facts for a sham explanation of nature."
It should however be remarked that these physicists somewhat deceived themselves as to the value of their caution, and that the mistrust they manifested towards philosophical speculations did not preclude their admitting, unknown to themselves, certain axioms which they did not discuss, but which are, properly speaking, metaphysical conceptions. They were unconsciously speaking a language taught them by their predecessors, of which they made no attempt to discover the origin. It is thus that it was readily considered evident that physics must necessarily some day re-enter the domain of mechanics, and thence it was postulated that everything in nature is due to movement. We, further, accepted the principles of the classical mechanics without discussing their legitimacy.
This state of mind was, even of late years, that of the most illustrious physicists. It is manifested, quite sincerely and without the slightest reserve, in all the classical works devoted to physics. Thus Verdet, an illustrious professor who has had the greatest and most happy influence on the intellectual formation of a whole generation of scholars, and whose works are even at the present day very often consulted, wrote: "The true problem of the physicist is always to reduce all phenomena to that which seems to us the simplest and clearest, that is to say, to movement." In his celebrated course of lectures at l'École Polytechnique, Jamin likewise said: "Physics will one day form a chapter of general mechanics;" and in the preface to his excellent course of lectures on physics, M. Violle, in 1884, thus expresses himself: "The science of nature tends towards mechanics by a necessary evolution, the physicist being able to establish solid theories only on the laws of movement." The same idea is again met with in the words of Cornu in 1896: "The general tendency should be to show how the facts observed and the phenomena measured, though first brought together by empirical laws, end, by the impulse of successive progressions, in coming under the general laws of rational mechanics;" and the same physicist showed clearly that in his mind this connexion of phenomena with mechanics had a deep and philosophical reason, when, in the fine discourse pronounced by him at the opening ceremony of the Congrès de Physique in 1900, he exclaimed: "The mind of Descartes soars over modern physics, or rather, I should say, he is their luminary. The further we penetrate into the knowledge of natural phenomena, the clearer and the more developed becomes the bold Cartesian conception regarding the mechanism of the universe. There is nothing in the physical world but matter and movement."
If we adopt this conception, we are led to construct mechanical representations of the material world, and to imagine movements in the different parts of bodies capable of reproducing all the manifestations of nature. The kinematic knowledge of these movements, that is to say, the determination of the position, speed, and acceleration at a given moment of all the parts of the system, or, on the other hand, their dynamical study, enabling us to know what is the action of these parts on each other, would then be sufficient to enable us to foretell all that can occur in the domain of nature.
This was the great thought clearly expressed by the Encyclopædists of the eighteenth century; and if the necessity of interpreting the phenomena of electricity or light led the physicists of last century to imagine particular fluids which seemed to obey with some difficulty the ordinary rules of mechanics, these physicists still continued to retain their hope in the future, and to treat the idea of Descartes as an ideal to be reached sooner or later.
Certain scholars—particularly those of the English School—outrunning experiment, and pushing things to extremes, took pleasure in proposing very curious mechanical models which were often strange images of reality. The most illustrious of them, Lord Kelvin, may be considered as their representative type, and he has himself said: "It seems to me that the true sense of the question, Do we or do we not understand a particular subject in physics? is—Can we make a mechanical model which corresponds to it? I am never satisfied so long as I have been unable to make a mechanical model of the object. If I am able to do so, I understand it. If I cannot make such a model, I do not understand it." But it must be acknowledged that some of the models thus devised have become excessively complicated, and this complication has for a long time discouraged all but very bold minds. In addition, when it became a question of penetrating into the mechanism of molecules, and we were no longer satisfied to look at matter as a mass, the mechanical solutions seemed undetermined and the stability of the edifices thus constructed was insufficiently demonstrated.
Returning then to our starting-point, many contemporary physicists wish to subject Descartes' idea to strict criticism. From the philosophical point of view, they first enquire whether it is really demonstrated that there exists nothing else in the knowable than matter and movement. They ask themselves whether it is not habit and tradition in particular which lead us to ascribe to mechanics the origin of phenomena. Perhaps also a question of sense here comes in. Our senses, which are, after all, the only windows open towards external reality, give us a view of one side of the world only; evidently we only know the universe by the relations which exist between it and our organisms, and these organisms are peculiarly sensitive to movement.
Nothing, however, proves that those acquisitions which are the most ancient in historical order ought, in the development of science, to remain the basis of our knowledge. Nor does any theory prove that our perceptions are an exact indication of reality. Many reasons, on the contrary, might be invoked which tend to compel us to see in nature phenomena which cannot be reduced to movement.
Mechanics as ordinarily understood is the study of reversible phenomena. If there be given to the parameter which represents time,[1] and which has assumed increasing values during the duration of the phenomena, decreasing values which make it go the opposite way, the whole system will again pass through exactly the same stages as before, and all the phenomena will unfold themselves in reversed order. In physics, the contrary rule appears very general, and reversibility generally does not exist. It is an ideal and limited case, which may be sometimes approached, but can never, strictly speaking, be met with in its entirety. No physical phenomenon ever recommences in an identical manner if its direction be altered. It is true that certain mathematicians warn us that a mechanics can be devised in which reversibility would no longer be the rule, but the bold attempts made in this direction are not wholly satisfactory.
On the other hand, it is established that if a mechanical explanation of a phenomenon can be given, we can find an infinity of others which likewise account for all the peculiarities revealed by experiment. But, as a matter of fact, no one has ever succeeded in giving an indisputable mechanical representation of the whole physical world. Even were we disposed to admit the strangest solutions of the problem; to consent, for example, to be satisfied with the hidden systems devised by Helmholtz, whereby we ought to divide variable things into two classes, some accessible, and the others now and for ever unknown, we should never manage to construct an edifice to contain all the known facts. Even the very comprehensive mechanics of a Hertz fails where the classical mechanics has not succeeded.
Deeming this check irremediable, many contemporary physicists give up attempts which they look upon as condemned beforehand, and adopt, to guide them in their researches, a method which at first sight appears much more modest, and also much more sure. They make up their minds not to see at once to the bottom of things; they no longer seek to suddenly strip the last veils from nature, and to divine her supreme secrets; but they work prudently and advance but slowly, while on the ground thus conquered foot by foot they endeavour to establish themselves firmly. They study the various magnitudes directly accessible to their observation without busying themselves as to their essence. They measure quantities of heat and of temperature, differences of potential, currents, and magnetic fields; and then, varying the conditions, apply the rules of experimental method, and discover between these magnitudes mutual relations, while they thus succeed in enunciating laws which translate and sum up their labours.
These empirical laws, however, themselves bring about by induction the promulgation of more general laws, which are termed principles. These principles are originally only the results of experiments, and experiment allows them besides to be checked, and their more or less high degree of generality to be verified. When they have been thus definitely established, they may serve as fresh starting-points, and, by deduction, lead to very varied discoveries.
The principles which govern physical science are few in number, and their very general form gives them a philosophical appearance, while we cannot long resist the temptation of regarding them as metaphysical dogmas. It thus happens that the least bold physicists, those who have wanted to show themselves the most reserved, are themselves led to forget the experimental character of the laws they have propounded, and to see in them imperious beings whose authority, placed above all verification, can no longer be discussed.
Others, on the contrary, carry prudence to the extent of timidity. They desire to grievously limit the field of scientific investigation, and they assign to science a too restricted domain. They content themselves with representing phenomena by equations, and think that they ought to submit to calculation magnitudes experimentally determined, without asking themselves whether these calculations retain a physical meaning. They are thus led to reconstruct a physics in which there again appears the idea of quality, understood, of course, not in the scholastic sense, since from this quality we can argue with some precision by representing it under numerical symbols, but still constituting an element of differentiation and of heterogeneity.
Notwithstanding the errors they may lead to if carried to excess, both these doctrines render, as a whole, most important service. It is no bad thing that these contradictory tendencies should subsist, for this variety in the conception of phenomena gives to actual science a character of intense life and of veritable youth, capable of impassioned efforts towards the truth. Spectators who see such moving and varied pictures passing before them, experience the feeling that there no longer exist systems fixed in an immobility which seems that of death. They feel that nothing is unchangeable; that ceaseless transformations are taking place before their eyes; and that this continuous evolution and perpetual change are the necessary conditions of progress.
A great number of seekers, moreover, show themselves on their own account perfectly eclectic. They adopt, according to their needs, such or such a manner of looking at nature, and do not hesitate to utilize very different images when they appear to them useful and convenient. And, without doubt, they are not wrong, since these images are only symbols convenient for language. They allow facts to be grouped and associated, but only present a fairly distant resemblance with the objective reality. Hence it is not forbidden to multiply and to modify them according to circumstances. The really essential thing is to have, as a guide through the unknown, a map which certainly does not claim to represent all the aspects of nature, but which, having been drawn up according to predetermined rules, allows us to follow an ascertained road in the eternal journey towards the truth.
Among the provisional theories which are thus willingly constructed by scholars on their journey, like edifices hastily run up to receive an unforeseen harvest, some still appear very bold and very singular. Abandoning the search after mechanical models for all electrical phenomena, certain physicists reverse, so to speak, the conditions of the problem, and ask themselves whether, instead of giving a mechanical interpretation to electricity, they may not, on the contrary, give an electrical interpretation to the phenomena of matter and motion, and thus merge mechanics itself in electricity. One thus sees dawning afresh the eternal hope of co-ordinating all natural phenomena in one grandiose and imposing synthesis. Whatever may be the fate reserved for such attempts, they deserve attention in the highest degree; and it is desirable to examine them carefully if we wish to have an exact idea of the tendencies of modern physics.
CHAPTER II
MEASUREMENTS
§ 1. METROLOGY
Not so very long ago, the scholar was often content with qualitative observations. Many phenomena were studied without much trouble being taken to obtain actual measurements. But it is now becoming more and more understood that to establish the relations which exist between physical magnitudes, and to represent the variations of these magnitudes by functions which allow us to use the power of mathematical analysis, it is most necessary to express each magnitude by a definite number.
Under these conditions alone can a magnitude be considered as effectively known. "I often say," Lord Kelvin has said, "that if you can measure that of which you are speaking and express it by a number you know something of your subject; but if you cannot measure it nor express it by a number, your knowledge is of a sorry kind and hardly satisfactory. It may be the beginning of the acquaintance, but you are hardly, in your thoughts, advanced towards science, whatever the subject may be."
It has now become possible to measure exactly the elements which enter into nearly all physical phenomena, and these measurements are taken with ever increasing precision. Every time a chapter in science progresses, science shows itself more exacting; it perfects its means of investigation, it demands more and more exactitude, and one of the most striking features of modern physics is this constant care for strictness and clearness in experimentation.
A veritable science of measurement has thus been constituted which extends over all parts of the domain of physics. This science has its rules and its methods; it points out the best processes of calculation, and teaches the method of correctly estimating errors and taking account of them. It has perfected the processes of experiment, co-ordinated a large number of results, and made possible the unification of standards. It is thanks to it that the system of measurements unanimously adopted by physicists has been formed.
At the present day we designate more peculiarly by the name of metrology that part of the science of measurements which devotes itself specially to the determining of the prototypes representing the fundamental units of dimension and mass, and of the standards of the first order which are derived from them. If all measurable quantities, as was long thought possible, could be reduced to the magnitudes of mechanics, metrology would thus be occupied with the essential elements entering into all phenomena, and might legitimately claim the highest rank in science. But even when we suppose that some magnitudes can never be connected with mass, length, and time, it still holds a preponderating place, and its progress finds an echo throughout the whole domain of the natural sciences. It is therefore well, in order to give an account of the general progress of physics, to examine at the outset the improvements which have been effected in these fundamental measurements, and to see what precision these improvements have allowed us to attain.
§ 2. THE MEASURE OF LENGTH
To measure a length is to compare it with another length taken as unity. Measurement is therefore a relative operation, and can only enable us to know ratios. Did both the length to be measured and the unit chosen happen to vary simultaneously and in the same degree, we should perceive no change. Moreover, the unit being, by definition, the term of comparison, and not being itself comparable with anything, we have theoretically no means of ascertaining whether its length varies.
If, however, we were to note that, suddenly and in the same proportions, the distance between two points on this earth had increased, that all the planets had moved further from each other, that all objects around us had become larger, that we ourselves had become taller, and that the distance travelled by light in the duration of a vibration had become greater, we should not hesitate to think ourselves the victims of an illusion, that in reality all these distances had remained fixed, and that all these appearances were due to a shortening of the rule which we had used as the standard for measuring the lengths.
From the mathematical point of view, it may be considered that the two hypotheses are equivalent; all has lengthened around us, or else our standard has become less. But it is no simple question of convenience and simplicity which leads us to reject the one supposition and to accept the other; it is right in this case to listen to the voice of common sense, and those physicists who have an instinctive trust in the notion of an absolute length are perhaps not wrong. It is only by choosing our unit from those which at all times have seemed to all men the most invariable, that we are able in our experiments to note that the same causes acting under identical conditions always produce the same effects. The idea of absolute length is derived from the principle of causality; and our choice is forced upon us by the necessity of obeying this principle, which we cannot reject without declaring by that very act all science to be impossible.
Similar remarks might be made with regard to the notions of absolute time and absolute movement. They have been put in evidence and set forth very forcibly by a learned and profound mathematician, M. Painlevé.
On the particularly clear example of the measure of length, it is interesting to follow the evolution of the methods employed, and to run through the history of the progress in precision from the time that we have possessed authentic documents relating to this question. This history has been written in a masterly way by one of the physicists who have in our days done the most by their personal labours to add to it glorious pages. M. Benoit, the learned Director of the International Bureau of Weights and Measures, has furnished in various reports very complete details on the subject, from which I here borrow the most interesting.
We know that in France the fundamental standard for measures of length was for a long time the Toise du Châtelet, a kind of callipers formed of a bar of iron which in 1668 was embedded in the outside wall of the Châtelet, at the foot of the staircase. This bar had at its extremities two projections with square faces, and all the toises of commerce had to fit exactly between them. Such a standard, roughly constructed, and exposed to all the injuries of weather and time, offered very slight guarantees either as to the permanence or the correctness of its copies. Nothing, perhaps, can better convey an idea of the importance of the modifications made in the methods of experimental physics than the easy comparison between so rudimentary a process and the actual measurements effected at the present time.
The Toise du Châtelet, notwithstanding its evident faults, was employed for nearly a hundred years; in 1766 it was replaced by the Toise du Pérou, so called because it had served for the measurements of the terrestrial arc effected in Peru from 1735 to 1739 by Bouguer, La Condamine, and Godin. At that time, according to the comparisons made between this new toise and the Toise du Nord, which had also been used for the measurement of an arc of the meridian, an error of the tenth part of a millimetre in measuring lengths of the order of a metre was considered quite unimportant. At the end of the eighteenth century, Delambre, in his work Sur la Base du Système métrique décimal, clearly gives us to understand that magnitudes of the order of the hundredth of a millimetre appear to him incapable of observation, even in scientific researches of the highest precision. At the present date the International Bureau of Weights and Measures guarantees, in the determination of a standard of length compared with the metre, an approximation of two or three ten-thousandths of a millimetre, and even a little more under certain circumstances.
This very remarkable progress is due to the improvements in the method of comparison on the one hand, and in the manufacture of the standard on the other. M. Benoit rightly points out that a kind of competition has been set up between the standard destined to represent the unit with its subdivisions and multiples and the instrument charged with observing it, comparable, up to a certain point, with that which in another order of ideas goes on between the gun and the armour-plate.
The measuring instrument of to-day is an instrument of comparison constructed with meticulous care, which enables us to do away with causes of error formerly ignored, to eliminate the action of external phenomena, and to withdraw the experiment from the influence of even the personality of the observer. This standard is no longer, as formerly, a flat rule, weak and fragile, but a rigid bar, incapable of deformation, in which the material is utilised in the best conditions of resistance. For a standard with ends has been substituted a standard with marks, which permits much more precise definition and can be employed in optical processes of observation alone; that is, in processes which can produce in it no deformation and no alteration. Moreover, the marks are traced on the plane of the neutral fibres[2] exposed, and the invariability of their distance apart is thus assured, even when a change is made in the way the rule is supported.
Thanks to studies thus systematically pursued, we have succeeded in the course of a hundred years in increasing the precision of measures in the proportion of a thousand to one, and we may ask ourselves whether such an increase will continue in the future. No doubt progress will not be stayed; but if we keep to the definition of length by a material standard, it would seem that its precision cannot be considerably increased. We have nearly reached the limit imposed by the necessity of making strokes of such a thickness as to be observable under the microscope.
It may happen, however, that we shall be brought one of these days to a new conception of the measure of length, and that very different processes of determination will be thought of. If we took as unit, for instance, the distance covered by a given radiation during a vibration, the optical processes would at once admit of much greater precision.
Thus Fizeau, the first to have this idea, says: "A ray of light, with its series of undulations of extreme tenuity but perfect regularity, may be considered as a micrometer of the greatest perfection, and particularly suitable for determining length." But in the present state of things, since the legal and customary definition of the unit remains a material standard, it is not enough to measure length in terms of wave-lengths, and we must also know the value of these wave-lengths in terms of the standard prototype of the metre.
This was determined in 1894 by M. Michelson and M. Benoit in an experiment which will remain classic. The two physicists measured a standard length of about ten centimetres, first in terms of the wave-lengths of the red, green, and blue radiations of cadmium, and then in terms of the standard metre. The great difficulty of the experiment proceeds from the vast difference which exists between the lengths to be compared, the wave-lengths barely amounting to half a micron; [3] the process employed consisted in noting, instead of this length, a length easily made about a thousand times greater, namely, the distance between the fringes of interference.
In all measurement, that is to say in every determination of the relation of a magnitude to the unit, there has to be determined on the one hand the whole, and on the other the fractional part of this ratio, and naturally the most delicate determination is generally that of this fractional part. In optical processes the difficulty is reversed. The fractional part is easily known, while it is the high figure of the number representing the whole which becomes a very serious obstacle. It is this obstacle which MM. Michelson and Benoit overcame with admirable ingenuity. By making use of a somewhat similar idea, M. Macé de Lépinay and MM. Perot and Fabry, have lately effected by optical methods, measurements of the greatest precision, and no doubt further progress may still be made. A day may perhaps come when a material standard will be given up, and it may perhaps even be recognised that such a standard in time changes its length by molecular strain, and by wear and tear: and it will be further noted that, in accordance with certain theories which will be noticed later on, it is not invariable when its orientation is changed.
For the moment, however, the need of any change in the definition of the unit is in no way felt; we must, on the contrary, hope that the use of the unit adopted by the physicists of the whole world will spread more and more. It is right to remark that a few errors still occur with regard to this unit, and that these errors have been facilitated by incoherent legislation. France herself, though she was the admirable initiator of the metrical system, has for too long allowed a very regrettable confusion to exist; and it cannot be noted without a certain sadness that it was not until the 11th July 1903 that a law was promulgated re-establishing the agreement between the legal and the scientific definition of the metre.
Perhaps it may not be useless to briefly indicate here the reasons of the disagreement which had taken place. Two definitions of the metre can be, and in fact were given. One had for its basis the dimensions of the earth, the other the length of the material standard. In the minds of the founders of the metrical system, the first of these was the true definition of the unit of length, the second merely a simple representation. It was admitted, however, that this representation had been constructed in a manner perfect enough for it to be nearly impossible to perceive any difference between the unit and its representation, and for the practical identity of the two definitions to be thus assured. The creators of the metrical system were persuaded that the measurements of the meridian effected in their day could never be surpassed in precision; and on the other hand, by borrowing from nature a definite basis, they thought to take from the definition of the unit some of its arbitrary character, and to ensure the means of again finding the same unit if by any accident the standard became altered. Their confidence in the value of the processes they had seen employed was exaggerated, and their mistrust of the future unjustified. This example shows how imprudent it is to endeavour to fix limits to progress. It is an error to think the march of science can be stayed; and in reality it is now known that the ten-millionth part of the quarter of the terrestrial meridian is longer than the metre by 0.187 millimetres. But contemporary physicists do not fall into the same error as their forerunners, and they regard the present result as merely provisional. They guess, in fact, that new improvements will be effected in the art of measurement; they know that geodesical processes, though much improved in our days, have still much to do to attain the precision displayed in the construction and determination of standards of the first order; and consequently they do not propose to keep the ancient definition, which would lead to having for unit a magnitude possessing the grave defect from a practical point of view of being constantly variable.
We may even consider that, looked at theoretically, its permanence would not be assured. Nothing, in fact, proves that sensible variations may not in time be produced in the value of an arc of the meridian, and serious difficulties may arise regarding the probable inequality of the various meridians.
For all these reasons, the idea of finding a natural unit has been gradually abandoned, and we have become resigned to accepting as a fundamental unit an arbitrary and conventional length having a material representation recognised by universal consent; and it was this unit which was consecrated by the following law of the 11th July 1903:—
"The standard prototype of the metrical system is the international metre, which has been sanctioned by the General Conference on Weights and Measures."
§ 3. THE MEASURE OF MASS
On the subject of measures of mass, similar remarks to those on measures of length might be made. The confusion here was perhaps still greater, because, to the uncertainty relating to the fixing of the unit, was added some indecision on the very nature of the magnitude defined. In law, as in ordinary practice, the notions of weight and of mass were not, in fact, separated with sufficient clearness.
They represent, however, two essentially different things. Mass is the characteristic of a quantity of matter; it depends neither on the geographical position one occupies nor on the altitude to which one may rise; it remains invariable so long as nothing material is added or taken away. Weight is the action which gravity has upon the body under consideration; this action does not depend solely on the body, but on the earth as well; and when it is changed from one spot to another, the weight changes, because gravity varies with latitude and altitude.
These elementary notions, to-day understood even by young beginners, appear to have been for a long time indistinctly grasped. The distinction remained confused in many minds, because, for the most part, masses were comparatively estimated by the intermediary of weights. The estimations of weight made with the balance utilize the action of the weight on the beam, but in such conditions that the influence of the variations of gravity becomes eliminated. The two weights which are being compared may both of them change if the weighing is effected in different places, but they are attracted in the same proportion. If once equal, they remain equal even when in reality they may both have varied.
The current law defines the kilogramme as the standard of mass, and the law is certainly in conformity with the rather obscurely expressed intentions of the founders of the metrical system. Their terminology was vague, but they certainly had in view the supply of a standard for commercial transactions, and it is quite evident that in barter what is important to the buyer as well as to the seller is not the attraction the earth may exercise on the goods, but the quantity that may be supplied for a given price. Besides, the fact that the founders abstained from indicating any specified spot in the definition of the kilogramme, when they were perfectly acquainted with the considerable variations in the intensity of gravity, leaves no doubt as to their real desire.
The same objections have been made to the definition of the kilogramme, at first considered as the mass of a cubic decimetre of water at 4° C., as to the first definition of the metre. We must admire the incredible precision attained at the outset by the physicists who made the initial determinations, but we know at the present day that the kilogramme they constructed is slightly too heavy (by about 1/25,000). Very remarkable researches have been carried out with regard to this determination by the International Bureau, and by MM. Macé de Lépinay and Buisson. The law of the 11th July 1903 has definitely regularized the custom which physicists had adopted some years before; and the standard of mass, the legal prototype of the metrical system, is now the international kilogramme sanctioned by the Conference of Weights and Measures.
The comparison of a mass with the standard is effected with a precision to which no other measurement can attain. Metrology vouches for the hundredth of a milligramme in a kilogramme; that is to say, that it estimates the hundred-millionth part of the magnitude studied.
We may—as in the case of the lengths—ask ourselves whether this already admirable precision can be surpassed; and progress would seem likely to be slow, for difficulties singularly increase when we get to such small quantities. But it is permitted to hope that the physicists of the future will do still better than those of to-day; and perhaps we may catch a glimpse of the time when we shall begin to observe that the standard, which is constructed from a heavy metal, namely, iridium-platinum, itself obeys an apparently general law, and little by little loses some particles of its mass by emanation.
§ 4. THE MEASURE OF TIME
The third fundamental magnitude of mechanics is time. There is, so to speak, no physical phenomenon in which the notion of time linked to the sequence of our states of consciousness does not play a considerable part.
Ancestral habits and a very early tradition have led us to preserve, as the unit of time, a unit connected with the earth's movement; and the unit to-day adopted is, as we know, the sexagesimal second of mean time. This magnitude, thus defined by the conditions of a natural motion which may itself be modified, does not seem to offer all the guarantees desirable from the point of view of invariability. It is certain that all the friction exercised on the earth—by the tides, for instance—must slowly lengthen the duration of the day, and must influence the movement of the earth round the sun. Such influence is certainly very slight, but it nevertheless gives an unfortunately arbitrary character to the unit adopted.
We might have taken as the standard of time the duration of another natural phenomenon, which appears to be always reproduced under identical conditions; the duration, for instance, of a given luminous vibration. But the experimental difficulties of evaluation with such a unit of the times which ordinarily have to be considered, would be so great that such a reform in practice cannot be hoped for. It should, moreover, be remarked that the duration of a vibration may itself be influenced by external circumstances, among which are the variations of the magnetic field in which its source is placed. It could not, therefore, be strictly considered as independent of the earth; and the theoretical advantage which might be expected from this alteration would be somewhat illusory.
Perhaps in the future recourse may be had to very different phenomena. Thus Curie pointed out that if the air inside a glass tube has been rendered radioactive by a solution of radium, the tube may be sealed up, and it will then be noted that the radiation of its walls diminishes with time, in accordance with an exponential law. The constant of time derived by this phenomenon remains the same whatever the nature and dimensions of the walls of the tube or the temperature may be, and time might thus be denned independently of all the other units.
We might also, as M. Lippmann has suggested in an extremely ingenious way, decide to obtain measures of time which can be considered as absolute because they are determined by parameters of another nature than that of the magnitude to be measured. Such experiments are made possible by the phenomena of gravitation. We could employ, for instance, the pendulum by adopting, as the unit of force, the force which renders the constant of gravitation equal to unity. The unit of time thus defined would be independent of the unit of length, and would depend only on the substance which would give us the unit of mass under the unit of volume.
It would be equally possible to utilize electrical phenomena, and one might devise experiments perfectly easy of execution. Thus, by charging a condenser by means of a battery, and discharging it a given number of times in a given interval of time, so that the effect of the current of discharge should be the same as the effect of the output of the battery through a given resistance, we could estimate, by the measurement of the electrical magnitudes, the duration of the interval noted. A system of this kind must not be looked upon as a simple jeu d'esprit, since this very practicable experiment would easily permit us to check, with a precision which could be carried very far, the constancy of an interval of time.
From the practical point of view, chronometry has made in these last few years very sensible progress. The errors in the movements of chronometers are corrected in a much more systematic way than formerly, and certain inventions have enabled important improvements to be effected in the construction of these instruments. Thus the curious properties which steel combined with nickel—so admirably studied by M.Ch.Ed. Guillaume—exhibits in the matter of dilatation are now utilized so as to almost completely annihilate the influence of variations of temperature.
§ 5. THE MEASURE OF TEMPERATURE
From the three mechanical units we derive secondary units; as, for instance, the unit of work or mechanical energy. The kinetic theory takes temperature, as well as heat itself, to be a quantity of energy, and thus seems to connect this notion with the magnitudes of mechanics. But the legitimacy of this theory cannot be admitted, and the calorific movement should also be a phenomenon so strictly confined in space that our most delicate means of investigation would not enable us to perceive it. It is better, then, to continue to regard the unit of difference of temperature as a distinct unit, to be added to the fundamental units.
To define the measure of a certain temperature, we take, in practice, some arbitrary property of a body. The only necessary condition of this property is, that it should constantly vary in the same direction when the temperature rises, and that it should possess, at any temperature, a well-marked value. We measure this value by melting ice and by the vapour of boiling water under normal pressure, and the successive hundredths of its variation, beginning with the melting ice, defines the percentage. Thermodynamics, however, has made it plain that we can set up a thermometric scale without relying upon any determined property of a real body. Such a scale has an absolute value independently of the properties of matter. Now it happens that if we make use for the estimation of temperatures, of the phenomena of dilatation under a constant pressure, or of the increase of pressure in a constant volume of a gaseous body, we obtain a scale very near the absolute, which almost coincides with it when the gas possesses certain qualities which make it nearly what is called a perfect gas. This most lucky coincidence has decided the choice of the convention adopted by physicists. They define normal temperature by means of the variations of pressure in a mass of hydrogen beginning with the initial pressure of a metre of mercury at 0° C.
M.P. Chappuis, in some very precise experiments conducted with much method, has proved that at ordinary temperatures the indications of such a thermometer are so close to the degrees of the theoretical scale that it is almost impossible to ascertain the value of the divergences, or even the direction that they take. The divergence becomes, however, manifest when we work with extreme temperatures. It results from the useful researches of M. Daniel Berthelot that we must subtract +0.18° from the indications of the hydrogen thermometer towards the temperature -240° C, and add +0.05° to 1000° to equate them with the thermodynamic scale. Of course, the difference would also become still more noticeable on getting nearer to the absolute zero; for as hydrogen gets more and more cooled, it gradually exhibits in a lesser degree the characteristics of a perfect gas.
To study the lower regions which border on that kind of pole of cold towards which are straining the efforts of the many physicists who have of late years succeeded in getting a few degrees further forward, we may turn to a gas still more difficult to liquefy than hydrogen. Thus, thermometers have been made of helium; and from the temperature of -260° C. downward the divergence of such a thermometer from one of hydrogen is very marked.
The measurement of very high temperatures is not open to the same theoretical objections as that of very low temperatures; but, from a practical point of view, it is as difficult to effect with an ordinary gas thermometer. It becomes impossible to guarantee the reservoir remaining sufficiently impermeable, and all security disappears, notwithstanding the use of recipients very superior to those of former times, such as those lately devised by the physicists of the Reichansalt. This difficulty is obviated by using other methods, such as the employment of thermo-electric couples, such as the very convenient couple of M. le Chatelier; but the graduation of these instruments can only be effected at the cost of a rather bold extrapolation.
M.D. Berthelot has pointed out and experimented with a very interesting process, founded on the measurement by the phenomena of interference of the refractive index of a column of air subjected to the temperature it is desired to measure. It appears admissible that even at the highest temperatures the variation of the power of refraction is strictly proportional to that of the density, for this proportion is exactly verified so long as it is possible to check it precisely. We can thus, by a method which offers the great advantage of being independent of the power and dimension of the envelopes employed—since the length of the column of air considered alone enters into the calculation—obtain results equivalent to those given by the ordinary air thermometer.
Another method, very old in principle, has also lately acquired great importance. For a long time we sought to estimate the temperature of a body by studying its radiation, but we did not know any positive relation between this radiation and the temperature, and we had no good experimental method of estimation, but had recourse to purely empirical formulas and the use of apparatus of little precision. Now, however, many physicists, continuing the classic researches of Kirchhoff, Boltzmann, Professors Wien and Planck, and taking their starting-point from the laws of thermodynamics, have given formulas which establish the radiating power of a dark body as a function of the temperature and the wave-length, or, better still, of the total power as a function of the temperature and wave-length corresponding to the maximum value of the power of radiation. We see, therefore, the possibility of appealing for the measurement of temperature to a phenomenon which is no longer the variation of the elastic force of a gas, and yet is also connected with the principles of thermodynamics.
This is what Professors Lummer and Pringsheim have shown in a series of studies which may certainly be reckoned among the greatest experimental researches of the last few years. They have constructed a radiator closely resembling the theoretically integral radiator which a closed isothermal vessel would be, and with only a very small opening, which allows us to collect from outside the radiations which are in equilibrium with the interior. This vessel is formed of a hollow carbon cylinder, heated by a current of high intensity; the radiations are studied by means of a bolometer, the disposition of which varies with the nature of the experiments.
It is hardly possible to enter into the details of the method, but the result sufficiently indicates its importance. It is now possible, thanks to their researches, to estimate a temperature of 2000° C. to within about 5°. Ten years ago a similar approximation could hardly have been arrived at for a temperature of 1000° C.
§ 6. DERIVED UNITS AND THE MEASURE OF A QUANTITY OF ENERGY
It must be understood that it is only by arbitrary convention that a dependency is established between a derived unit and the fundamental units. The laws of numbers in physics are often only laws of proportion. We transform them into laws of equation, because we introduce numerical coefficients and choose the units on which they depend so as to simplify as much as possible the formulas most in use. A particular speed, for instance, is in reality nothing else but a speed, and it is only by the peculiar choice of unit that we can say that it is the space covered during the unit of time. In the same way, a quantity of electricity is a quantity of electricity; and there is nothing to prove that, in its essence, it is really reducible to a function of mass, of length, and of time.
Persons are still to be met with who seem to have some illusions on this point, and who see in the doctrine of the dimensions of the units a doctrine of general physics, while it is, to say truth, only a doctrine of metrology. The knowledge of dimensions is valuable, since it allows us, for instance, to easily verify the homogeneity of a formula, but it can in no way give us any information on the actual nature of the quantity measured.
Magnitudes to which we attribute like dimensions may be qualitatively irreducible one to the other. Thus the different forms of energy are measured by the same unit, and yet it seems that some of them, such as kinetic energy, really depend on time; while for others, such as potential energy, the dependency established by the system of measurement seems somewhat fictitious.
The numerical value of a quantity of energy of any nature should, in the system C.G.S., be expressed in terms of the unit called the erg; but, as a matter of fact, when we wish to compare and measure different quantities of energy of varying forms, such as electrical, chemical, and other quantities, etc., we nearly always employ a method by which all these energies are finally transformed and used to heat the water of a calorimeter. It is therefore very important to study well the calorific phenomenon chosen as the unit of heat, and to determine with precision its mechanical equivalent, that is to say, the number of ergs necessary to produce this unit. This is a number which, on the principle of equivalence, depends neither on the method employed, nor the time, nor any other external circumstance.
As the result of the brilliant researches of Rowland and of Mr Griffiths on the variations of the specific heat of water, physicists have decided to take as calorific standard the quantity of heat necessary to raise a gramme of water from 15° to 16° C., the temperature being measured by the scale of the hydrogen thermometer of the International Bureau.
On the other hand, new determinations of the mechanical equivalent, among which it is right to mention that of Mr. Ames, and a full discussion as to the best results, have led to the adoption of the number 4.187 to represent the number of ergs capable of producing the unit of heat.
In practice, the measurement of a quantity of heat is very often effected by means of the ice calorimeter, the use of which is particularly simple and convenient. There is, therefore, a very special interest in knowing exactly the melting-point of ice. M. Leduc, who for several years has measured a great number of physical constants with minute precautions and a remarkable sense of precision, concludes, after a close discussion of the various results obtained, that this heat is equal to 79.1 calories. An error of almost a calorie had been committed by several renowned experimenters, and it will be seen that in certain points the art of measurement may still be largely perfected.
To the unit of energy might be immediately attached other units. For instance, radiation being nothing but a flux of energy, we could, in order to establish photometric units, divide the normal spectrum into bands of a given width, and measure the power of each for the unit of radiating surface.
But, notwithstanding some recent researches on this question, we cannot yet consider the distribution of energy in the spectrum as perfectly known. If we adopt the excellent habit which exists in some researches of expressing radiating energy in ergs, it is still customary to bring the radiations to a standard giving, by its constitution alone, the unit of one particular radiation. In particular, the definitions are still adhered to which were adopted as the result of the researches of M. Violle on the radiation of fused platinum at the temperature of solidification; and most physicists utilize in the ordinary methods of photometry the clearly defined notions of M. Blondel as to the luminous intensity of flux, illumination (éclairement), light (éclat), and lighting (éclairage), with the corresponding units, decimal candle, lumen, lux, carcel lamp, candle per square centimetre, and lumen-hour. [4]
§ 7. MEASURE OF CERTAIN PHYSICAL CONSTANTS
The progress of metrology has led, as a consequence, to corresponding progress in nearly all physical measurements, and particularly in the measure of natural constants. Among these, the constant of gravitation occupies a position quite apart from the importance and simplicity of the physical law which defines it, as well as by its generality. Two material particles are mutually attracted to each other by a force directly proportional to the product of their mass, and inversely proportional to the square of the distance between them. The coefficient of proportion is determined when once the units are chosen, and as soon as we know the numerical values of this force, of the two masses, and of their distance. But when we wish to make laboratory experiments serious difficulties appear, owing to the weakness of the attraction between masses of ordinary dimensions. Microscopic forces, so to speak, have to be observed, and therefore all the causes of errors have to be avoided which would be unimportant in most other physical researches. It is known that Cavendish was the first who succeeded by means of the torsion balance in effecting fairly precise measurements. This method has been again taken in hand by different experimenters, and the most recent results are due to Mr Vernon Boys. This learned physicist is also the author of a most useful practical invention, and has succeeded in making quartz threads as fine as can be desired and extremely uniform. He finds that these threads possess valuable properties, such as perfect elasticity and great tenacity. He has been able, with threads not more than 1/500 of a millimetre in diameter, to measure with precision couples of an order formerly considered outside the range of experiment, and to reduce the dimensions of the apparatus of Cavendish in the proportion of 150 to 1. The great advantage found in the use of these small instruments is the better avoidance of the perturbations arising from draughts of air, and of the very serious influence of the slightest inequality in temperature.
Other methods have been employed in late years by other experimenters, such as the method of Baron Eötvös, founded on the use of a torsion lever, the method of the ordinary balance, used especially by Professors Richarz and Krigar-Menzel and also by Professor Poynting, and the method of M. Wilsing, who uses a balance with a vertical beam. The results fairly agree, and lead to attributing to the earth a density equal to 5.527.
The most familiar manifestation of gravitation is gravity. The action of the earth on the unit of mass placed in one point, and the intensity of gravity, is measured, as we know, by the aid of a pendulum. The methods of measurement, whether by absolute or by relative determinations, so greatly improved by Borda and Bessel, have been still further improved by various geodesians, among whom should be mentioned M. von Sterneek and General Defforges. Numerous observations have been made in all parts of the world by various explorers, and have led to a fairly complete knowledge of the distribution of gravity over the surface of the globe. Thus we have succeeded in making evident anomalies which would not easily find their place in the formula of Clairaut.
Another constant, the determination of which is of the greatest utility in astronomy of position, and the value of which enters into electromagnetic theory, has to-day assumed, with the new ideas on the constitution of matter, a still more considerable importance. I refer to the speed of light, which appears to us, as we shall see further on, the maximum value of speed which can be given to a material body.
After the historical experiments of Fizeau and Foucault, taken up afresh, as we know, partly by Cornu, and partly by Michelson and Newcomb, it remained still possible to increase the precision of the measurements. Professor Michelson has undertaken some new researches by a method which is a combination of the principle of the toothed wheel of Fizeau with the revolving mirror of Foucault. The toothed wheel is here replaced, however, by a grating, in which the lines and the spaces between them take the place of the teeth and the gaps, the reflected light only being returned when it strikes on the space between two lines. The illustrious American physicist estimates that he can thus evaluate to nearly five kilometres the path traversed by light in one second. This approximation corresponds to a relative value of a few hundred-thousandths, and it far exceeds those hitherto attained by the best experimenters. When all the experiments are completed, they will perhaps solve certain questions still in suspense; for instance, the question whether the speed of propagation depends on intensity. If this turns out to be the case, we should be brought to the important conclusion that the amplitude of the oscillations, which is certainly very small in relation to the already tiny wave-lengths, cannot be considered as unimportant in regard to these lengths. Such would seem to have been the result of the curious experiments of M. Muller and of M. Ebert, but these results have been recently disputed by M. Doubt.
In the case of sound vibrations, on the other hand, it should be noted that experiment, consistently with the theory, proves that the speed increases with the amplitude, or, if you will, with the intensity. M. Violle has published an important series of experiments on the speed of propagation of very condensed waves, on the deformations of these waves, and on the relations of the speed and the pressure, which verify in a remarkable manner the results foreshadowed by the already old calculations of Riemann, repeated later by Hugoniot. If, on the contrary, the amplitude is sufficiently small, there exists a speed limit which is the same in a large pipe and in free air. By some beautiful experiments, MM. Violle and Vautier have clearly shown that any disturbance in the air melts somewhat quickly into a single wave of given form, which is propagated to a distance, while gradually becoming weaker and showing a constant speed which differs little in dry air at 0° C. from 331.36 metres per second. In a narrow pipe the influence of the walls makes itself felt and produces various effects, in particular a kind of dispersion in space of the harmonics of the sound. This phenomenon, according to M. Brillouin, is perfectly explicable by a theory similar to the theory of gratings.
CHAPTER III
PRINCIPLES
§ 1. THE PRINCIPLES OF PHYSICS
Facts conscientiously observed lead by induction to the enunciation of a certain number of laws or general hypotheses which are the principles already referred to. These principal hypotheses are, in the eyes of a physicist, legitimate generalizations, the consequences of which we shall be able at once to check by the experiments from which they issue.
Among the principles almost universally adopted until lately figure prominently those of mechanics—such as the principle of relativity, and the principle of the equality of action and reaction. We will not detail nor discuss them here, but later on we shall have an opportunity of pointing out how recent theories on the phenomena of electricity have shaken the confidence of physicists in them and have led certain scholars to doubt their absolute value.
The principle of Lavoisier, or principle of the conservation of mass, presents itself under two different aspects according to whether mass is looked upon as the coefficient of the inertia of matter or as the factor which intervenes in the phenomena of universal attraction, and particularly in gravitation. We shall see when we treat of these theories, how we have been led to suppose that inertia depended on velocity and even on direction. If this conception were exact, the principle of the invariability of mass would naturally be destroyed. Considered as a factor of attraction, is mass really indestructible?
A few years ago such a question would have seemed singularly audacious. And yet the law of Lavoisier is so far from self-evident that for centuries it escaped the notice of physicists and chemists. But its great apparent simplicity and its high character of generality, when enunciated at the end of the eighteenth century, rapidly gave it such an authority that no one was able to any longer dispute it unless he desired the reputation of an oddity inclined to paradoxical ideas.
It is important, however, to remark that, under fallacious metaphysical appearances, we are in reality using empty words when we repeat the aphorism, "Nothing can be lost, nothing can be created," and deduce from it the indestructibility of matter. This indestructibility, in truth, is an experimental fact, and the principle depends on experiment. It may even seem, at first sight, more singular than not that the weight of a bodily system in a given place, or the quotient of this weight by that of the standard mass—that is to say, the mass of these bodies—remains invariable, both when the temperature changes and when chemical reagents cause the original materials to disappear and to be replaced by new ones. We may certainly consider that in a chemical phenomenon annihilations and creations of matter are really produced; but the experimental law teaches us that there is compensation in certain respects.
The discovery of the radioactive bodies has, in some sort, rendered popular the speculations of physicists on the phenomena of the disaggregation of matter. We shall have to seek the exact meaning which ought to be given to the experiments on the emanation of these bodies, and to discover whether these experiments really imperil the law of Lavoisier.
For some years different experimenters have also effected many very precise measurements of the weight of divers bodies both before and after chemical reactions between these bodies. Two highly experienced and cautious physicists, Professors Landolt and Heydweiller, have not hesitated to announce the sensational result that in certain circumstances the weight is no longer the same after as before the reaction. In particular, the weight of a solution of salts of copper in water is not the exact sum of the joint weights of the salt and the water. Such experiments are evidently very delicate; they have been disputed, and they cannot be considered as sufficient for conviction. It follows nevertheless that it is no longer forbidden to regard the law of Lavoisier as only an approximate law; according to Sandford and Ray, this approximation would be about 1/2,400,000. This is also the result reached by Professor Poynting in experiments regarding the possible action of temperature on the weight of a body; and if this be really so, we may reassure ourselves, and from the point of view of practical application may continue to look upon matter as indestructible.
The principles of physics, by imposing certain conditions on phenomena, limit after a fashion the field of the possible. Among these principles is one which, notwithstanding its importance when compared with that of universally known principles, is less familiar to some people. This is the principle of symmetry, more or less conscious applications of which can, no doubt, be found in various works and even in the conceptions of Copernican astronomers, but which was generalized and clearly enunciated for the first time by the late M. Curie. This illustrious physicist pointed out the advantage of introducing into the study of physical phenomena the considerations on symmetry familiar to crystallographers; for a phenomenon to take place, it is necessary that a certain dissymmetry should previously exist in the medium in which this phenomenon occurs. A body, for instance, may be animated with a certain linear velocity or a speed of rotation; it may be compressed, or twisted; it may be placed in an electric or in a magnetic field; it may be affected by an electric current or by one of heat; it may be traversed by a ray of light either ordinary or polarized rectilineally or circularly, etc.:—in each case a certain minimum and characteristic dissymmetry is necessary at every point of the body in question.
This consideration enables us to foresee that certain phenomena which might be imagined a priori cannot exist. Thus, for instance, it is impossible that an electric field, a magnitude directed and not superposable on its image in a mirror perpendicular to its direction, could be created at right angles to the plane of symmetry of the medium; while it would be possible to create a magnetic field under the same conditions.
This consideration thus leads us to the discovery of new phenomena; but it must be understood that it cannot of itself give us absolutely precise notions as to the nature of these phenomena, nor disclose their order of magnitude.
§ 2. THE PRINCIPLE OF THE CONSERVATION OF ENERGY
Dominating not physics alone, but nearly every other science, the principle of the conservation of energy is justly considered as the grandest conquest of contemporary thought. It shows us in a powerful light the most diverse questions; it introduces order into the most varied studies; it leads to a clear and coherent interpretation of phenomena which, without it, appear to have no connexion with each other; and it supplies precise and exact numerical relations between the magnitudes which enter into these phenomena.
The boldest minds have an instinctive confidence in it, and it is the principle which has most stoutly resisted that assault which the daring of a few theorists has lately directed to the overthrow of the general principles of physics. At every new discovery, the first thought of physicists is to find out how it accords with the principle of the conservation of energy. The application of the principle, moreover, never fails to give valuable hints on the new phenomenon, and often even suggests a complementary discovery. Up till now it seems never to have received a check, even the extraordinary properties of radium not seriously contradicting it; also the general form in which it is enunciated gives it such a suppleness that it is no doubt very difficult to overthrow.
I do not claim to set forth here the complete history of this principle, but I will endeavour to show with what pains it was born, how it was kept back in its early days and then obstructed in its development by the unfavourable conditions of the surroundings in which it appeared. It first of all came, in fact, to oppose itself to the reigning theories; but, little by little, it acted on these theories, and they were modified under its pressure; then, in their turn, these theories reacted on it and changed its primitive form.
It had to be made less wide in order to fit into the classic frame, and was absorbed by mechanics; and if it thus became less general, it gained in precision what it lost in extent. When once definitely admitted and classed, as it were, in the official domain of science, it endeavoured to burst its bonds and return to a more independent and larger life. The history of this principle is similar to that of all evolutions.
It is well known that the conservation of energy was, at first, regarded from the point of view of the reciprocal transformations between heat and work, and that the principle received its first clear enunciation in the particular case of the principle of equivalence. It is, therefore, rightly considered that the scholars who were the first to doubt the material nature of caloric were the precursors of R. Mayer; their ideas, however, were the same as those of the celebrated German doctor, for they sought especially to demonstrate that heat was a mode of motion.
Without going back to early and isolated attempts like those of Daniel Bernoulli, who, in his hydrodynamics, propounded the basis of the kinetic theory of gases, or the researches of Boyle on friction, we may recall, to show how it was propounded in former times, a rather forgotten page of the Mémoire sur la Chaleur, published in 1780 by Lavoisier and Laplace: "Other physicists," they wrote, after setting out the theory of caloric, "think that heat is nothing but the result of the insensible vibrations of matter.... In the system we are now examining, heat is the vis viva resulting from the insensible movements of the molecules of a body; it is the sum of the products of the mass of each molecule by the square of its velocity.... We shall not decide between the two preceding hypotheses; several phenomena seem to support the last mentioned—for instance, that of the heat produced by the friction of two solid bodies. But there are others which are more simply explained by the first, and perhaps they both operate at once." Most of the physicists of that period, however, did not share the prudent doubts of Lavoisier and Laplace. They admitted, without hesitation, the first hypothesis; and, four years after the appearance of the Mémoire sur la Chaleur, Sigaud de Lafond, a professor of physics of great reputation, wrote: "Pure Fire, free from all state of combination, seems to be an assembly of particles of a simple, homogeneous, and absolutely unalterable matter, and all the properties of this element indicate that these particles are infinitely small and free, that they have no sensible cohesion, and that they are moved in every possible direction by a continual and rapid motion which is essential to them.... The extreme tenacity and the surprising mobility of its molecules are manifestly shown by the ease with which it penetrates into the most compact bodies and by its tendency to put itself in equilibrium throughout all bodies near to it."
It must be acknowledged, however, that the idea of Lavoisier and Laplace was rather vague and even inexact on one important point. They admitted it to be evident that "all variations of heat, whether real or apparent, undergone by a bodily system when changing its state, are produced in inverse order when the system passes back to its original state." This phrase is the very denial of equivalence where these changes of state are accompanied by external work.
Laplace, moreover, himself became later a very convinced partisan of the hypothesis of the material nature of caloric, and his immense authority, so fortunate in other respects for the development of science, was certainly in this case the cause of the retardation of progress.
The names of Young, Rumford, Davy, are often quoted among those physicists who, at the commencement of the nineteenth century, caught sight of the new truths as to the nature of heat. To these names is very properly added that of Sadi Carnot. A note found among his papers unquestionably proves that, before 1830, ideas had occurred to him from which it resulted that in producing work an equivalent amount of heat was destroyed. But the year 1842 is particularly memorable in the history of science as the year in which Jules Robert Mayer succeeded, by an entirely personal effort, in really enunciating the principle of the conservation of energy. Chemists recall with just pride that the Remarques sur les forces de la nature animée, contemptuously rejected by all the journals of physics, were received and published in the Annalen of Liebig. We ought never to forget this example, which shows with what difficulty a new idea contrary to the classic theories of the period succeeds in coming to the front; but extenuating circumstances may be urged on behalf of the physicists.
Robert Mayer had a rather insufficient mathematical education, and his Memoirs, the Remarques, as well as the ulterior publications, Mémoire sur le mouvement organique et la nutrition and the Matériaux pour la dynamique du ciel, contain, side by side with very profound ideas, evident errors in mechanics. Thus it often happens that discoveries put forward in a somewhat vague manner by adventurous minds not overburdened by the heavy baggage of scientific erudition, who audaciously press forward in advance of their time, fall into quite intelligible oblivion until rediscovered, clarified, and put into shape by slower but surer seekers. This was the case with the ideas of Mayer. They were not understood at first sight, not only on account of their originality, but also because they were couched in incorrect language.
Mayer was, however, endowed with a singular strength of thought; he expressed in a rather confused manner a principle which, for him, had a generality greater than mechanics itself, and so his discovery was in advance not only of his own time but of half the century. He may justly be considered the founder of modern energetics.
Freed from the obscurities which prevented its being clearly perceived, his idea stands out to-day in all its imposing simplicity. Yet it must be acknowledged that if it was somewhat denaturalised by those who endeavoured to adapt it to the theories of mechanics, and if it at first lost its sublime stamp of generality, it thus became firmly fixed and consolidated on a more stable basis.
The efforts of Helmholtz, Clausius, and Lord Kelvin to introduce the principle of the conservation of energy into mechanics, were far from useless. These illustrious physicists succeeded in giving a more precise form to its numerous applications; and their attempts thus contributed, by reaction, to give a fresh impulse to mechanics, and allowed it to be linked to a more general order of facts. If energetics has not been able to be included in mechanics, it seems indeed that the attempt to include mechanics in energetics was not in vain.
In the middle of the last century, the explanation of all natural phenomena seemed more and more referable to the case of central forces. Everywhere it was thought that reciprocal actions between material points could be perceived, these points being attracted or repelled by each other with an intensity depending only on their distance or their mass. If, to a system thus composed, the laws of the classical mechanics are applied, it is shown that half the sum of the product of the masses by the square of the velocities, to which is added the work which might be accomplished by the forces to which the system would be subject if it returned from its actual to its initial position, is a sum constant in quantity.
This sum, which is the mechanical energy of the system, is therefore an invariable quantity in all the states to which it may be brought by the interaction of its various parts, and the word energy well expresses a capital property of this quantity. For if two systems are connected in such a way that any change produced in the one necessarily brings about a change in the other, there can be no variation in the characteristic quantity of the second except so far as the characteristic quantity of the first itself varies—on condition, of course, that the connexions are made in such a manner as to introduce no new force. It will thus be seen that this quantity well expresses the capacity possessed by a system for modifying the state of a neighbouring system to which we may suppose it connected.
Now this theorem of pure mechanics was found wanting every time friction took place—that is to say, in all really observable cases. The more perceptible the friction, the more considerable the difference; but, in addition, a new phenomenon always appeared and heat was produced. By experiments which are now classic, it became established that the quantity of heat thus created independently of the nature of the bodies is always (provided no other phenomena intervene) proportional to the energy which has disappeared. Reciprocally, also, heat may disappear, and we always find a constant relation between the quantities of heat and work which mutually replace each other.
It is quite clear that such experiments do not prove that heat is work. We might just as well say that work is heat. It is making a gratuitous hypothesis to admit this reduction of heat to mechanism; but this hypothesis was so seductive, and so much in conformity with the desire of nearly all physicists to arrive at some sort of unity in nature, that they made it with eagerness and became unreservedly convinced that heat was an active internal force.
Their error was not in admitting this hypothesis; it was a legitimate one since it has proved very fruitful. But some of them committed the fault of forgetting that it was an hypothesis, and considered it a demonstrated truth. Moreover, they were thus brought to see in phenomena nothing but these two particular forms of energy which in their minds were easily identified with each other.
From the outset, however, it became manifest that the principle is applicable to cases where heat plays only a parasitical part. There were thus discovered, by translating the principle of equivalence, numerical relations between the magnitudes of electricity, for instance, and the magnitudes of mechanics. Heat was a sort of variable intermediary convenient for calculation, but introduced in a roundabout way and destined to disappear in the final result.
Verdet, who, in lectures which have rightly remained celebrated, defined with remarkable clearness the new theories, said, in 1862: "Electrical phenomena are always accompanied by calorific manifestations, of which the study belongs to the mechanical theory of heat. This study, moreover, will not only have the effect of making known to us interesting facts in electricity, but will throw some light on the phenomena of electricity themselves."
The eminent professor was thus expressing the general opinion of his contemporaries, but he certainly seemed to have felt in advance that the new theory was about to penetrate more deeply into the inmost nature of things. Three years previously, Rankine also had put forth some very remarkable ideas the full meaning of which was not at first well understood. He it was who comprehended the utility of employing a more inclusive term, and invented the phrase energetics. He also endeavoured to create a new doctrine of which rational mechanics should be only a particular case; and he showed that it was possible to abandon the ideas of atoms and central forces, and to construct a more general system by substituting for the ordinary consideration of forces that of the energy which exists in all bodies, partly in an actual, partly in a potential state.
By giving more precision to the conceptions of Rankine, the physicists of the end of the nineteenth century were brought to consider that in all physical phenomena there occur apparitions and disappearances which are balanced by various energies. It is natural, however, to suppose that these equivalent apparitions and disappearances correspond to transformations and not to simultaneous creations and destructions. We thus represent energy to ourselves as taking different forms—mechanical, electrical, calorific, and chemical—capable of changing one into the other, but in such a way that the quantitative value always remains the same. In like manner a bank draft may be represented by notes, gold, silver, or bullion. The earliest known form of energy, i.e. work, will serve as the standard as gold serves as the monetary standard, and energy in all its forms will be estimated by the corresponding work. In each particular case we can strictly define and measure, by the correct application of the principle of the conservation of energy, the quantity of energy evolved under a given form.
We can thus arrange a machine comprising a body capable of evolving this energy; then we can force all the organs of this machine to complete an entirely closed cycle, with the exception of the body itself, which, however, has to return to such a state that all the variables from which this state depends resume their initial values except the particular variable to which the evolution of the energy under consideration is linked. The difference between the work thus accomplished and that which would have been obtained if this variable also had returned to its original value, is the measure of the energy evolved.
In the same way that, in the minds of mechanicians, all forces of whatever origin, which are capable of compounding with each other and of balancing each other, belong to the same category of beings, so for many physicists energy is a sort of entity which we find under various aspects. There thus exists for them a world, which comes in some way to superpose itself upon the world of matter—that is to say, the world of energy, dominated in its turn by a fundamental law similar to that of Lavoisier. [5] This conception, as we have already seen, passes the limit of experience; but others go further still. Absorbed in the contemplation of this new world, they succeed in persuading themselves that the old world of matter has no real existence and that energy is sufficient by itself to give us a complete comprehension of the Universe and of all the phenomena produced in it. They point out that all our sensations correspond to changes of energy, and that everything apparent to our senses is, in truth, energy. The famous experiment of the blows with a stick by which it was demonstrated to a sceptical philosopher that an outer world existed, only proves, in reality, the existence of energy, and not that of matter. The stick in itself is inoffensive, as Professor Ostwald remarks, and it is its vis viva, its kinetic energy, which is painful to us; while if we possessed a speed equal to its own, moving in the same direction, it would no longer exist so far as our sense of touch is concerned.
On this hypothesis, matter would only be the capacity for kinetic energy, its pretended impenetrability energy of volume, and its weight energy of position in the particular form which presents itself in universal gravitation; nay, space itself would only be known to us by the expenditure of energy necessary to penetrate it. Thus in all physical phenomena we should only have to regard the quantities of energy brought into play, and all the equations which link the phenomena to one another would have no meaning but when they apply to exchanges of energy. For energy alone can be common to all phenomena.
This extreme manner of regarding things is seductive by its originality, but appears somewhat insufficient if, after enunciating generalities, we look more closely into the question. From the philosophical point of view it may, moreover, seem difficult not to conclude, from the qualities which reveal, if you will, the varied forms of energy, that there exists a substance possessing these qualities. This energy, which resides in one region, and which transports itself from one spot to another, forcibly brings to mind, whatever view we may take of it, the idea of matter.
Helmholtz endeavoured to construct a mechanics based on the idea of energy and its conservation, but he had to invoke a second law, the principle of least action. If he thus succeeded in dispensing with the hypothesis of atoms, and in showing that the new mechanics gave us to understand the impossibility of certain movements which, according to the old, ought to have been but never were experimentally produced, he was only able to do so because the principle of least action necessary for his theory became evident in the case of those irreversible phenomena which alone really exist in Nature. The energetists have thus not succeeded in forming a thoroughly sound system, but their efforts have at all events been partly successful. Most physicists are of their opinion, that kinetic energy is only a particular variety of energy to which we have no right to wish to connect all its other forms.
If these forms showed themselves to be innumerable throughout the Universe, the principle of the conservation of energy would, in fact, lose a great part of its importance. Every time that a certain quantity of energy seemed to appear or disappear, it would always be permissible to suppose that an equivalent quantity had appeared or disappeared somewhere else under a new form; and thus the principle would in a way vanish. But the known forms of energy are fairly restricted in number, and the necessity of recognising new ones seldom makes itself felt. We shall see, however, that to explain, for instance, the paradoxical properties of radium and to re-establish concord between these properties and the principle of the conservation of energy, certain physicists have recourse to the hypothesis that radium borrows an unknown energy from the medium in which it is plunged. This hypothesis, however, is in no way necessary; and in a few other rare cases in which similar hypotheses have had to be set up, experiment has always in the long run enabled us to discover some phenomenon which had escaped the first observers and which corresponds exactly to the variation of energy first made evident.
One difficulty, however, arises from the fact that the principle ought only to be applied to an isolated system. Whether we imagine actions at a distance or believe in intermediate media, we must always recognise that there exist no bodies in the world incapable of acting on each other, and we can never affirm that some modification in the energy of a given place may not have its echo in some unknown spot afar off. This difficulty may sometimes render the value of the principle rather illusory.
Similarly, it behoves us not to receive without a certain distrust the extension by certain philosophers to the whole Universe, of a property demonstrated for those restricted systems which observation can alone reach. We know nothing of the Universe as a whole, and every generalization of this kind outruns in a singular fashion the limit of experiment.
Even reduced to the most modest proportions, the principle of the conservation of energy retains, nevertheless, a paramount importance; and it still preserves, if you will, a high philosophical value. M.J. Perrin justly points out that it gives us a form under which we are experimentally able to grasp causality, and that it teaches us that a result has to be purchased at the cost of a determined effort.
We can, in fact, with M. Perrin and M. Langevin, represent this in a way which puts this characteristic in evidence by enunciating it as follows: "If at the cost of a change C we can obtain a change K, there will never be acquired at the same cost, whatever the mechanism employed, first the change K and in addition some other change, unless this latter be one that is otherwise known to cost nothing to produce or to destroy." If, for instance, the fall of a weight can be accompanied, without anything else being produced, by another transformation—the melting of a certain mass of ice, for example—it will be impossible, no matter how you set about it or whatever the mechanism used, to associate this same transformation with the melting of another weight of ice.
We can thus, in the transformation in question, obtain an appropriate number which will sum up that which may be expected from the external effect, and can give, so to speak, the price at which this transformation is bought, measure its invariable value by a common measure (for instance, the melting of the ice), and, without any ambiguity, define the energy lost during the transformation as proportional to the mass of ice which can be associated with it. This measure is, moreover, independent of the particular phenomenon taken as the common measure.
§ 3. THE PRINCIPLE OF CARNOT AND CLAUSIUS
The principle of Carnot, of a nature analogous to the principle of the conservation of energy, has also a similar origin. It was first enunciated, like the last named, although prior to it in time, in consequence of considerations which deal only with heat and mechanical work. Like it, too, it has evolved, grown, and invaded the entire domain of physics. It may be interesting to examine rapidly the various phases of this evolution. The origin of the principle of Carnot is clearly determined, and it is very rare to be able to go back thus certainly to the source of a discovery. Sadi Carnot had, truth to say, no precursor. In his time heat engines were not yet very common, and no one had reflected much on their theory. He was doubtless the first to propound to himself certain questions, and certainly the first to solve them.
It is known how, in 1824, in his Réflexions sur la puissance motrice du feu, he endeavoured to prove that "the motive power of heat is independent of the agents brought into play for its realization," and that "its quantity is fixed solely by the temperature of the bodies between which, in the last resort, the transport of caloric is effected"—at least in all engines in which "the method of developing the motive power attains the perfection of which it is capable"; and this is, almost textually, one of the enunciations of the principle at the present day. Carnot perceived very clearly the great fact that, to produce work by heat, it is necessary to have at one's disposal a fall of temperature. On this point he expresses himself with perfect clearness: "The motive power of a fall of water depends on its height and on the quantity of liquid; the motive power of heat depends also on the quantity of caloric employed, and on what might be called—in fact, what we shall call—the height of fall, that is to say, the difference in temperature of the bodies between which the exchange of caloric takes place."
Starting with this idea, he endeavours to demonstrate, by associating two engines capable of working in a reversible cycle, that the principle is founded on the impossibility of perpetual motion.
His memoir, now celebrated, did not produce any great sensation, and it had almost fallen into deep oblivion, which, in consequence of the discovery of the principle of equivalence, might have seemed perfectly justified. Written, in fact, on the hypothesis of the indestructibility of caloric, it was to be expected that this memoir should be condemned in the name of the new doctrine, that is, of the principle recently brought to light.
It was really making a new discovery to establish that Carnot's fundamental idea survived the destruction of the hypothesis on the nature of heat, on which he seemed to rely. As he no doubt himself perceived, his idea was quite independent of this hypothesis, since, as we have seen, he was led to surmise that heat could disappear; but his demonstrations needed to be recast and, in some points, modified.
It is to Clausius that was reserved the credit of rediscovering the principle, and of enunciating it in language conformable to the new doctrines, while giving it a much greater generality. The postulate arrived at by experimental induction, and which must be admitted without demonstration, is, according to Clausius, that in a series of transformations in which the final is identical with the initial stage, it is impossible for heat to pass from a colder to a warmer body unless some other accessory phenomenon occurs at the same time.
Still more correctly, perhaps, an enunciation can be given of the postulate which, in the main, is analogous, by saying: A heat motor, which after a series of transformations returns to its initial state, can only furnish work if there exist at least two sources of heat, and if a certain quantity of heat is given to one of the sources, which can never be the hotter of the two. By the expression "source of heat," we mean a body exterior to the system and capable of furnishing or withdrawing heat from it.
Starting with this principle, we arrive, as does Clausius, at the demonstration that the output of a reversible machine working between two given temperatures is greater than that of any non-reversible engine, and that it is the same for all reversible machines working between these two temperatures.
This is the very proposition of Carnot; but the proposition thus stated, while very useful for the theory of engines, does not yet present any very general interest. Clausius, however, drew from it much more important consequences. First, he showed that the principle conduces to the definition of an absolute scale of temperature; and then he was brought face to face with a new notion which allows a strong light to be thrown on the questions of physical equilibrium. I refer to entropy.
It is still rather difficult to strip entirely this very important notion of all analytical adornment. Many physicists hesitate to utilize it, and even look upon it with some distrust, because they see in it a purely mathematical function without any definite physical meaning. Perhaps they are here unduly severe, since they often admit too easily the objective existence of quantities which they cannot define. Thus, for instance, it is usual almost every day to speak of the heat possessed by a body. Yet no body in reality possesses a definite quantity of heat even relatively to any initial state; since starting from this point of departure, the quantities of heat it may have gained or lost vary with the road taken and even with the means employed to follow it. These expressions of heat gained or lost are, moreover, themselves evidently incorrect, for heat can no longer be considered as a sort of fluid passing from one body to another.
The real reason which makes entropy somewhat mysterious is that this magnitude does not fall directly under the ken of any of our senses; but it possesses the true characteristic of a concrete physical magnitude, since it is, in principle at least, measurable. Various authors of thermodynamical researches, amongst whom M. Mouret should be particularly mentioned, have endeavoured to place this characteristic in evidence.
Consider an isothermal transformation. Instead of leaving the heat abandoned by the body subjected to the transformation—water condensing in a state of saturated vapour, for instance—to pass directly into an ice calorimeter, we can transmit this heat to the calorimeter by the intermediary of a reversible Carnot engine. The engine having absorbed this quantity of heat, will only give back to the ice a lesser quantity of heat; and the weight of the melted ice, inferior to that which might have been directly given back, will serve as a measure of the isothermal transformation thus effected. It can be easily shown that this measure is independent of the apparatus used. It consequently becomes a numerical element characteristic of the body considered, and is called its entropy. Entropy, thus defined, is a variable which, like pressure or volume, might serve concurrently with another variable, such as pressure or volume, to define the state of a body.
It must be perfectly understood that this variable can change in an independent manner, and that it is, for instance, distinct from the change of temperature. It is also distinct from the change which consists in losses or gains of heat. In chemical reactions, for example, the entropy increases without the substances borrowing any heat. When a perfect gas dilates in a vacuum its entropy increases, and yet the temperature does not change, and the gas has neither been able to give nor receive heat. We thus come to conceive that a physical phenomenon cannot be considered known to us if the variation of entropy is not given, as are the variations of temperature and of pressure or the exchanges of heat. The change of entropy is, properly speaking, the most characteristic fact of a thermal change.
It is important, however, to remark that if we can thus easily define and measure the difference of entropy between two states of the same body, the value found depends on the state arbitrarily chosen as the zero point of entropy; but this is not a very serious difficulty, and is analogous to that which occurs in the evaluation of other physical magnitudes—temperature, potential, etc.
A graver difficulty proceeds from its not being possible to define a difference, or an equality, of entropy between two bodies chemically different. We are unable, in fact, to pass by any means, reversible or not, from one to the other, so long as the transmutation of matter is regarded as impossible; but it is well understood that it is nevertheless possible to compare the variations of entropy to which these two bodies are both of them individually subject.
Neither must we conceal from ourselves that the definition supposes, for a given body, the possibility of passing from one state to another by a reversible transformation. Reversibility is an ideal and extreme case which cannot be realized, but which can be approximately attained in many circumstances. So with gases and with perfectly elastic bodies, we effect sensibly reversible transformations, and changes of physical state are practically reversible. The discoveries of Sainte-Claire Deville have brought many chemical phenomena into a similar category, and reactions such as solution, which used to be formerly the type of an irreversible phenomenon, may now often be effected by sensibly reversible means. Be that as it may, when once the definition is admitted, we arrive, by taking as a basis the principles set forth at the inception, at the demonstration of the celebrated theorem of Clausius: The entropy of a thermally isolated system continues to increase incessantly.
It is very evident that the theorem can only be worth applying in cases where the entropy can be exactly defined; but, even when thus limited, the field still remains vast, and the harvest which we can there reap is very abundant.
Entropy appears, then, as a magnitude measuring in a certain way the evolution of a system, or, at least, as giving the direction of this evolution. This very important consequence certainly did not escape Clausius, since the very name of entropy, which he chose to designate this magnitude, itself signifies evolution. We have succeeded in defining this entropy by demonstrating, as has been said, a certain number of propositions which spring from the postulate of Clausius; it is, therefore, natural to suppose that this postulate itself contains in potentia the very idea of a necessary evolution of physical systems. But as it was first enunciated, it contains it in a deeply hidden way.
No doubt we should make the principle of Carnot appear in an interesting light by endeavouring to disengage this fundamental idea, and by placing it, as it were, in large letters. Just as, in elementary geometry, we can replace the postulate of Euclid by other equivalent propositions, so the postulate of thermodynamics is not necessarily fixed, and it is instructive to try to give it the most general and suggestive character.
MM. Perrin and Langevin have made a successful attempt in this direction. M. Perrin enunciates the following principle: An isolated system never passes twice through the same state. In this form, the principle affirms that there exists a necessary order in the succession of two phenomena; that evolution takes place in a determined direction. If you prefer it, it may be thus stated: Of two converse transformations unaccompanied by any external effect, one only is possible. For instance, two gases may diffuse themselves one in the other in constant volume, but they could not conversely separate themselves spontaneously.
Starting from the principle thus put forward, we make the logical deduction that one cannot hope to construct an engine which should work for an indefinite time by heating a hot source and by cooling a cold one. We thus come again into the route traced by Clausius, and from this point we may follow it strictly.
Whatever the point of view adopted, whether we regard the proposition of M. Perrin as the corollary of another experimental postulate, or whether we consider it as a truth which we admit a priori and verify through its consequences, we are led to consider that in its entirety the principle of Carnot resolves itself into the idea that we cannot go back along the course of life, and that the evolution of a system must follow its necessary progress.
Clausius and Lord Kelvin have drawn from these considerations certain well-known consequences on the evolution of the Universe. Noticing that entropy is a property added to matter, they admit that there is in the world a total amount of entropy; and as all real changes which are produced in any system correspond to an increase of entropy, it may be said that the entropy of the world is continually increasing. Thus the quantity of energy existing in the Universe remains constant, but transforms itself little by little into heat uniformly distributed at a temperature everywhere identical. In the end, therefore, there will be neither chemical phenomena nor manifestation of life; the world will still exist, but without motion, and, so to speak, dead.
These consequences must be admitted to be very doubtful; we cannot in any certain way apply to the Universe, which is not a finite system, a proposition demonstrated, and that not unreservedly, in the sharply limited case of a finite system. Herbert Spencer, moreover, in his book on First Principles, brings out with much force the idea that, even if the Universe came to an end, nothing would allow us to conclude that, once at rest, it would remain so indefinitely. We may recognise that the state in which we are began at the end of a former evolutionary period, and that the end of the existing era will mark the beginning of a new one.
Like an elastic and mobile object which, thrown into the air, attains by degrees the summit of its course, then possesses a zero velocity and is for a moment in equilibrium, and then falls on touching the ground to rebound, so the world should be subjected to huge oscillations which first bring it to a maximum of entropy till the moment when there should be produced a slow evolution in the contrary direction bringing it back to the state from which it started. Thus, in the infinity of time, the life of the Universe proceeds without real stop.
This conception is, moreover, in accordance with the view certain physicists take of the principle of Carnot. We shall see, for example, that in the kinetic theory we are led to admit that, after waiting sufficiently long, we can witness the return of the various states through which a mass of gas, for example, has passed in its series of transformations.
If we keep to the present era, evolution has a fixed direction—that which leads to an increase of entropy; and it is possible to enquire, in any given system to what physical manifestations this increase corresponds. We note that kinetic, potential, electrical, and chemical forms of energy have a great tendency to transform themselves into calorific energy. A chemical reaction, for example, gives out energy; but if the reaction is not produced under very special conditions, this energy immediately passes into the calorific form. This is so true, that chemists currently speak of the heat given out by reactions instead of regarding the energy disengaged in general.
In all these transformations the calorific energy obtained has not, from a practical point of view, the same value at which it started. One cannot, in fact, according to the principle of Carnot, transform it integrally into mechanical energy, since the heat possessed by a body can only yield work on condition that a part of it falls on a body with a lower temperature. Thus appears the idea that energies which exchange with each other and correspond to equal quantities have not the same qualitative value. Form has its importance, and there are persons who prefer a golden louis to four pieces of five francs. The principle of Carnot would thus lead us to consider a certain classification of energies, and would show us that, in the transformations possible, these energies always tend to a sort of diminution of quality—that is, to a degradation.
It would thus reintroduce an element of differentiation of which it seems very difficult to give a mechanical explanation. Certain philosophers and physicists see in this fact a reason which condemns a priori all attempts made to give a mechanical explanation of the principle of Carnot.
It is right, however, not to exaggerate the importance that should be attributed to the phrase degraded energy. If the heat is not equivalent to the work, if heat at 99° is not equivalent to heat at 100°, that means that we cannot in practice construct an engine which shall transform all this heat into work, or that, for the same cold source, the output is greater when the temperature of the hot source is higher; but if it were possible that this cold source had itself the temperature of absolute zero, the whole heat would reappear in the form of work. The case here considered is an ideal and extreme case, and we naturally cannot realize it; but this consideration suffices to make it plain that the classification of energies is a little arbitrary and depends more, perhaps, on the conditions in which mankind lives than on the inmost nature of things.
In fact, the attempts which have often been made to refer the principle of Carnot to mechanics have not given convincing results. It has nearly always been necessary to introduce into the attempt some new hypothesis independent of the fundamental hypotheses of ordinary mechanics, and equivalent, in reality, to one of the postulates on which the ordinary exposition of the second law of thermodynamics is founded. Helmholtz, in a justly celebrated theory, endeavoured to fit the principle of Carnot into the principle of least action; but the difficulties regarding the mechanical interpretation of the irreversibility of physical phenomena remain entire. Looking at the question, however, from the point of view at which the partisans of the kinetic theories of matter place themselves, the principle is viewed in a new aspect. Gibbs and afterwards Boltzmann and Professor Planck have put forward some very interesting ideas on this subject. By following the route they have traced, we come to consider the principle as pointing out to us that a given system tends towards the configuration presented by the maximum probability, and, numerically, the entropy would even be the logarithm of this probability. Thus two different gaseous masses, enclosed in two separate receptacles which have just been placed in communication, diffuse themselves one through the other, and it is highly improbable that, in their mutual shocks, both kinds of molecules should take a distribution of velocities which reduce them by a spontaneous phenomenon to the initial state.
We should have to wait a very long time for so extraordinary a concourse of circumstances, but, in strictness, it would not be impossible. The principle would only be a law of probability. Yet this probability is all the greater the more considerable is the number of molecules itself. In the phenomena habitually dealt with, this number is such that, practically, the variation of entropy in a constant sense takes, so to speak, the character of absolute certainty.
But there may be exceptional cases where the complexity of the system becomes insufficient for the application of the principle of Carnot;—as in the case of the curious movements of small particles suspended in a liquid which are known by the name of Brownian movements and can be observed under the microscope. The agitation here really seems, as M. Gouy has remarked, to be produced and continued indefinitely, regardless of any difference in temperature; and we seem to witness the incessant motion, in an isothermal medium, of the particles which constitute matter. Perhaps, however, we find ourselves already in conditions where the too great simplicity of the distribution of the molecules deprives the principle of its value.
M. Lippmann has in the same way shown that, on the kinetic hypothesis, it is possible to construct such mechanisms that we can so take cognizance of molecular movements that vis viva can be taken from them. The mechanisms of M. Lippmann are not, like the celebrated apparatus at one time devised by Maxwell, purely hypothetical. They do not suppose a partition with a hole impossible to be bored through matter where the molecular spaces would be larger than the hole itself. They have finite dimensions. Thus M. Lippmann considers a vase full of oxygen at a constant temperature. In the interior of this vase is placed a small copper ring, and the whole is set in a magnetic field. The oxygen molecules are, as we know, magnetic, and when passing through the interior of the ring they produce in this ring an induced current. During this time, it is true, other molecules emerge from the space enclosed by the circuit; but the two effects do not counterbalance each other, and the resulting current is maintained. There is elevation of temperature in the circuit in accordance with Joule's law; and this phenomenon, under such conditions, is incompatible with the principle of Carnot.
It is possible—and that, I think, is M. Lippmann's idea—to draw from his very ingenious criticism an objection to the kinetic theory, if we admit the absolute value of the principle; but we may also suppose that here again we are in presence of a system where the prescribed conditions diminish the complexity and render it, consequently, less probable that the evolution is always effected in the same direction.
In whatever way you look at it, the principle of Carnot furnishes, in the immense majority of cases, a very sure guide in which physicists continue to have the most entire confidence.
§ 4. THERMODYNAMICS
To apply the two fundamental principles of thermodynamics, various methods may be employed, equivalent in the main, but presenting as the cases vary a greater or less convenience.
In recording, with the aid of the two quantities, energy and entropy, the relations which translate analytically the two principles, we obtain two relations between the coefficients which occur in a given phenomenon; but it may be easier and also more suggestive to employ various functions of these quantities. In a memoir, of which some extracts appeared as early as 1869, a modest scholar, M. Massieu, indicated in particular a remarkable function which he termed a characteristic function, and by the employment of which calculations are simplified in certain cases.
In the same way J.W. Gibbs, in 1875 and 1878, then Helmholtz in 1882, and, in France, M. Duhem, from the year 1886 onward, have published works, at first ill understood, of which the renown was, however, considerable in the sequel, and in which they made use of analogous functions under the names of available energy, free energy, or internal thermodynamic potential. The magnitude thus designated, attaching, as a consequence of the two principles, to all states of the system, is perfectly determined when the temperature and other normal variables are known. It allows us, by calculations often very easy, to fix the conditions necessary and sufficient for the maintenance of the system in equilibrium by foreign bodies taken at the same temperature as itself.
One may hope to constitute in this way, as M. Duhem in a long and remarkable series of operations has specially endeavoured to do, a sort of general mechanics which will enable questions of statics to be treated with accuracy, and all the conditions of equilibrium of the system, including the calorific properties, to be determined. Thus, ordinary statics teaches us that a liquid with its vapour on the top forms a system in equilibrium, if we apply to the two fluids a pressure depending on temperature alone. Thermodynamics will furnish us, in addition, with the expression of the heat of vaporization and of, the specific heats of the two saturated fluids.
This new study has given us also most valuable information on compressible fluids and on the theory of elastic equilibrium. Added to certain hypotheses on electric or magnetic phenomena, it gives a coherent whole from which can be deduced the conditions of electric or magnetic equilibrium; and it illuminates with a brilliant light the calorific laws of electrolytic phenomena.
But the most indisputable triumph of this thermodynamic statics is the discovery of the laws which regulate the changes of physical state or of chemical constitution. J.W. Gibbs was the author of this immense progress. His memoir, now celebrated, on "the equilibrium of heterogeneous substances," concealed in 1876 in a review at that time of limited circulation, and rather heavy to read, seemed only to contain algebraic theorems applicable with difficulty to reality. It is known that Helmholtz independently succeeded, a few years later, in introducing thermodynamics into the domain of chemistry by his conception of the division of energy into free and into bound energy: the first, capable of undergoing all transformations, and particularly of transforming itself into external action; the second, on the other hand, bound, and only manifesting itself by giving out heat. When we measure chemical energy, we ordinarily let it fall wholly into the calorific form; but, in reality, it itself includes both parts, and it is the variation of the free energy and not that of the total energy measured by the integral disengagement of heat, the sign of which determines the direction in which the reactions are effected.
But if the principle thus enunciated by Helmholtz as a consequence of the laws of thermodynamics is at bottom identical with that discovered by Gibbs, it is more difficult of application and is presented under a more mysterious aspect. It was not until M. Van der Waals exhumed the memoir of Gibbs, when numerous physicists or chemists, most of them Dutch—Professor Van t'Hoff, Bakhius Roozeboom, and others—utilized the rules set forth in this memoir for the discussion of the most complicated chemical reactions, that the extent of the new laws was fully understood.
The chief rule of Gibbs is the one so celebrated at the present day under the name of the Phase Law. We know that by phases are designated the homogeneous substances into which a system is divided; thus carbonate of lime, lime, and carbonic acid gas are the three phases of a system which comprises Iceland spar partially dissociated into lime and carbonic acid gas. The number of phases added to the number of independent components—that is to say, bodies whose mass is left arbitrary by the chemical formulas of the substances entering into the reaction—fixes the general form of the law of equilibrium of the system; that is to say, the number of quantities which, by their variations (temperature and pressure), would be of a nature to modify its equilibrium by modifying the constitution of the phases.
Several authors, M. Raveau in particular, have indeed given very simple demonstrations of this law which are not based on thermodynamics; but thermodynamics, which led to its discovery, continues to give it its true scope. Moreover, it would not suffice merely to determine quantitatively those laws of which it makes known the general form. We must, if we wish to penetrate deeper into details, particularize the hypothesis, and admit, for instance, with Gibbs that we are dealing with perfect gases; while, thanks to thermodynamics, we can constitute a complete theory of dissociation which leads to formulas in complete accord with the numerical results of the experiment. We can thus follow closely all questions concerning the displacements of the equilibrium, and find a relation of the first importance between the masses of the bodies which react in order to constitute a system in equilibrium.
The statics thus constructed constitutes at the present day an important edifice to be henceforth classed amongst historical monuments. Some theorists even wish to go a step beyond. They have attempted to begin by the same means a more complete study of those systems whose state changes from one moment to another. This is, moreover, a study which is necessary to complete satisfactorily the study of equilibrium itself; for without it grave doubts would exist as to the conditions of stability, and it alone can give their true meaning to questions relating to displacements of equilibrium.
The problems with which we are thus confronted are singularly difficult. M. Duhem has given us many excellent examples of the fecundity of the method; but if thermodynamic statics may be considered definitely founded, it cannot be said that the general dynamics of systems, considered as the study of thermal movements and variations, are yet as solidly established.
§ 5. ATOMISM
It may appear singularly paradoxical that, in a chapter devoted to general views on the principles of physics, a few words should be introduced on the atomic theories of matter.
Very often, in fact, what is called the physics of principles is set in opposition to the hypotheses on the constitution of matter, particularly to atomic theories. I have already said that, abandoning the investigation of the unfathomable mystery of the constitution of the Universe, some physicists think they may find, in certain general principles, sufficient guides to conduct them across the physical world. But I have also said, in examining the history of those principles, that if they are to-day considered experimental truths, independent of all theories relating to matter, they have, in fact, nearly all been discovered by scholars who relied on molecular hypotheses: and the question suggests itself whether this is mere chance, or whether this chance may not be ordained by higher reasons.
In a very profound work which appeared a few years ago, entitled Essai critique sur l'hypothese des atomes, M. Hannequin, a philosopher who is also an erudite scholar, examined the part taken by atomism in the history of science. He notes that atomism and science were born, in Greece, of the same problem, and that in modern times the revival of the one was closely connected with that of the other. He shows, too, by very close analysis, that the atomic hypothesis is essential to the optics of Fresnel and of Cauchy; that it penetrates into the study of heat; and that, in its general features, it presided at the birth of modern chemistry and is linked with all its progress. He concludes that it is, in a manner, the soul of our knowledge of Nature, and that contemporary theories are on this point in accord with history: for these theories consecrate the preponderance of this hypothesis in the domain of science.
If M. Hannequin had not been prematurely cut off in the full expansion of his vigorous talent, he might have added another chapter to his excellent book. He would have witnessed a prodigious budding of atomistic ideas, accompanied, it is true, by wide modifications in the manner in which the atom is to be regarded, since the most recent theories make material atoms into centres constituted of atoms of electricity. On the other hand, he would have found in the bursting forth of these new doctrines one more proof in support of his idea that science is indissolubly bound to atomism.
From the philosophical point of view, M. Hannequin, examining the reasons which may have called these links into being, arrives at the idea that they necessarily proceed from the constitution of our knowledge, or, perhaps, from that of Nature itself. Moreover, this origin, double in appearance, is single at bottom. Our minds could not, in fact, detach and come out of themselves to grasp reality and the absolute in Nature. According to the idea of Descartes, it is the destiny of our minds only to take hold of and to understand that which proceeds from them.
Thus atomism, which is, perhaps, only an appearance containing even some contradictions, is yet a well-founded appearance, since it conforms to the laws of our minds; and this hypothesis is, in a way, necessary.
We may dispute the conclusions of M. Hannequin, but no one will refuse to recognise, as he does, that atomic theories occupy a preponderating part in the doctrines of physics; and the position which they have thus conquered gives them, in a way, the right of saying that they rest on a real principle. It is in order to recognise this right that several physicists—M. Langevin, for example—ask that atoms be promoted from the rank of hypotheses to that of principles. By this they mean that the atomistic ideas forced upon us by an almost obligatory induction based on very exact experiments, enable us to co-ordinate a considerable amount of facts, to construct a very general synthesis, and to foresee a great number of phenomena.
It is of moment, moreover, to thoroughly understand that atomism does not necessarily set up the hypothesis of centres of attraction acting at a distance, and it must not be confused with molecular physics, which has, on the other hand, undergone very serious checks. The molecular physics greatly in favour some fifty years ago leads to such complex representations and to solutions often so undetermined, that the most courageous are wearied with upholding it and it has fallen into some discredit. It rested on the fundamental principles of mechanics applied to molecular actions; and that was, no doubt, an extension legitimate enough, since mechanics is itself only an experimental science, and its principles, established for the movements of matter taken as a whole, should not be applied outside the domain which belongs to them. Atomism, in fact, tends more and more, in modern theories, to imitate the principle of the conservation of energy or that of entropy, to disengage itself from the artificial bonds which attached it to mechanics, and to put itself forward as an independent principle.
Atomistic ideas also have undergone evolution, and this slow evolution has been considerably quickened under the influence of modern discoveries. These reach back to the most remote antiquity, and to follow their development we should have to write the history of human thought which they have always accompanied since the time of Leucippus, Democritus, Epicurus, and Lucretius. The first observers who noticed that the volume of a body could be diminished by compression or cold, or augmented by heat, and who saw a soluble solid body mix completely with the water which dissolved it, must have been compelled to suppose that matter was not dispersed continuously throughout the space it seemed to occupy. They were thus brought to consider it discontinuous, and to admit that a substance having the same composition and the same properties in all its parts—in a word, perfectly homogeneous—ceases to present this homogeneity when considered within a sufficiently small volume.
Modern experimenters have succeeded by direct experiments in placing in evidence this heterogeneous character of matter when taken in small mass. Thus, for example, the superficial tension, which is constant for the same liquid at a given temperature, no longer has the same value when the thickness of the layer of liquid becomes extremely small. Newton noticed even in his time that a dark zone is seen to form on a soap bubble at the moment when it becomes so thin that it must burst. Professor Reinold and Sir Arthur Rücker have shown that this zone is no longer exactly spherical; and from this we must conclude that the superficial tension, constant for all thicknesses above a certain limit, commences to vary when the thickness falls below a critical value, which these authors estimate, on optical grounds, at about fifty millionths of a millimetre.
From experiments on capillarity, Prof. Quincke has obtained similar results with regard to layers of solids. But it is not only capillary properties which allow this characteristic to be revealed. All the properties of a body are modified when taken in small mass; M. Meslin proves this in a very ingenious way as regards optical properties, and Mr Vincent in respect of electric conductivity. M. Houllevigue, who, in a chapter of his excellent work, Du Laboratoire à l'Usine, has very clearly set forth the most interesting considerations on atomic hypotheses, has recently demonstrated that copper and silver cease to combine with iodine as soon as they are present in a thickness of less than thirty millionths of a millimetre. It is this same dimension likewise that is possessed, according to M. Wiener, by the smallest thicknesses it is possible to deposit on glass. These layers are so thin that they cannot be perceived, but their presence is revealed by a change in the properties of the light reflected by them.
Thus, below fifty to thirty millionths of a millimetre the properties of matter depend on its thickness. There are then, no doubt, only a few molecules to be met with, and it may be concluded, in consequence, that the discontinuous elements of bodies—that is, the molecules—have linear dimensions of the order of magnitude of the millionth of a millimetre. Considerations regarding more complex phenomena, for instance the phenomena of electricity by contact, and also the kinetic theory of gases, bring us to the same conclusion.
The idea of the discontinuity of matter forces itself upon us for many other reasons. All modern chemistry is founded on this principle; and laws like the law of multiple proportions, introduce an evident discontinuity to which we find analogies in the law of electrolysis. The elements of bodies we are thus brought to regard might, as regards solids at all events, be considered as immobile; but this immobility could not explain the phenomena of heat, and, as it is entirely inadmissible for gases, it seems very improbable it can absolutely occur in any state. We are thus led to suppose that these elements are animated by very complicated movements, each one proceeding in closed trajectories in which the least variations of temperature or pressure cause modifications.
The atomistic hypothesis shows itself remarkably fecund in the study of phenomena produced in gases, and here the mutual independence of the particles renders the question relatively more simple and, perhaps, allows the principles of mechanics to be more certainly extended to the movements of molecules.
The kinetic theory of gases can point to unquestioned successes; and the idea of Daniel Bernouilli, who, as early as 1738, considered a gaseous mass to be formed of a considerable number of molecules animated by rapid movements of translation, has been put into a form precise enough for mathematical analysis, and we have thus found ourselves in a position to construct a really solid foundation. It will be at once conceived, on this hypothesis, that pressure is the resultant of the shocks of the molecules against the walls of the containing vessel, and we at once come to the demonstration that the law of Mariotte is a natural consequence of this origin of pressure; since, if the volume occupied by a certain number of molecules is doubled, the number of shocks per second on each square centimetre of the walls becomes half as much. But if we attempt to carry this further, we find ourselves in presence of a serious difficulty. It is impossible to mentally follow every one of the many individual molecules which compose even a very limited mass of gas. The path followed by this molecule may be every instant modified by the chance of running against another, or by a shock which may make it rebound in another direction.
The difficulty would be insoluble if chance had not laws of its own. It was Maxwell who first thought of introducing into the kinetic theory the calculation of probabilities. Willard Gibbs and Boltzmann later on developed this idea, and have founded a statistical method which does not, perhaps, give absolute certainty, but which is certainly most interesting and curious. Molecules are grouped in such a way that those belonging to the same group may be considered as having the same state of movement; then an examination is made of the number of molecules in each group, and what are the changes in this number from one moment to another. It is thus often possible to determine the part which the different groups have in the total properties of the system and in the phenomena which may occur.
Such a method, analogous to the one employed by statisticians for following the social phenomena in a population, is all the more legitimate the greater the number of individuals counted in the averages; now, the number of molecules contained in a limited space—for example, in a centimetre cube taken in normal conditions—is such that no population could ever attain so high a figure. All considerations, those we have indicated as well as others which might be invoked (for example, the recent researches of M. Spring on the limit of visibility of fluorescence), give this result:—that there are, in this space, some twenty thousand millions of molecules. Each of these must receive in the space of a millimetre about ten thousand shocks, and be ten thousand times thrust out of its course. The free path of a molecule is then very small, but it can be singularly augmented by diminishing the number of them. Tait and Dewar have calculated that, in a good modern vacuum, the length of the free path of the remaining molecules not taken away by the air-pump easily reaches a few centimetres.
By developing this theory, we come to consider that, for a given temperature, every molecule (and even every individual particle, atom, or ion) which takes part in the movement has, on the average, the same kinetic energy in every body, and that this energy is proportional to the absolute temperature; so that it is represented by this temperature multiplied by a constant quantity which is a universal constant.
This result is not an hypothesis but a very great probability. This probability increases when it is noted that the same value for the constant is met with in the study of very varied phenomena; for example, in certain theories on radiation. Knowing the mass and energy of a molecule, it is easy to calculate its speed; and we find that the average speed is about 400 metres per second for carbonic anhydride, 500 for nitrogen, and 1850 for hydrogen at 0° C. and at ordinary pressure. I shall have occasion, later on, to speak of much more considerable speeds than these as animating other particles.
The kinetic theory has permitted the diffusion of gases to be explained, and the divers circumstances of the phenomenon to be calculated. It has allowed us to show, as M. Brillouin has done, that the coefficient of diffusion of two gases does not depend on the proportion of the gases in the mixture; it gives a very striking image of the phenomena of viscosity and conductivity; and it leads us to think that the coefficients of friction and of conductivity are independent of the density; while all these previsions have been verified by experiment. It has also invaded optics; and by relying on the principle of Doppler, Professor Michelson has succeeded in obtaining from it an explanation of the length presented by the spectral rays of even the most rarefied gases.
But however interesting are these results, they would not have sufficed to overcome the repugnance of certain physicists for speculations which, an imposing mathematical baggage notwithstanding, seemed to them too hypothetical. The theory, moreover, stopped at the molecule, and appeared to suggest no idea which could lead to the discovery of the key to the phenomena where molecules exercise a mutual influence on each other. The kinetic hypothesis, therefore, remained in some disfavour with a great number of persons, particularly in France, until the last few years, when all the recent discoveries of the conductivity of gases and of the new radiations came to procure for it a new and luxuriant efflorescence. It may be said that the atomistic synthesis, but yesterday so decried, is to-day triumphant.
The elements which enter into the earlier kinetic theory, and which, to avoid confusion, should be always designated by the name of molecules, were not, truth to say, in the eyes of the chemists, the final term of the divisibility of matter. It is well known that, to them, except in certain particular bodies like the vapour of mercury and argon, the molecule comprises several atoms, and that, in compound bodies, the number of these atoms may even be fairly considerable. But physicists rarely needed to have recourse to the consideration of these atoms. They spoke of them to explain certain particularities of the propagation of sound, and to enunciate laws relating to specific heats; but, in general, they stopped at the consideration of the molecule.
The present theories carry the division much further. I shall not dwell now on these theories, since, in order to thoroughly understand them, many other facts must be examined. But to avoid all confusion, it remains understood that, contrary, no doubt, to etymology, but in conformity with present custom, I shall continue in what follows to call atoms those particles of matter which have till now been spoken of; these atoms being themselves, according to modern views, singularly complex edifices formed of elements, of which we shall have occasion to indicate the nature later.
CHAPTER IV
THE VARIOUS STATES OF MATTER
§ 1. THE STATICS OF FLUIDS
The division of bodies into gaseous, liquid, and solid, and the distinction established for the same substance between the three states, retain a great importance for the applications and usages of daily life, but have long since lost their absolute value from the scientific point of view.
So far as concerns the liquid and gaseous states particularly, the already antiquated researches of Andrews confirmed the ideas of Cagniard de la Tour and established the continuity of the two states. A group of physical studies has thus been constituted on what may be called the statics of fluids, in which we examine the relations existing between the pressure, the volume, and the temperature of bodies, and in which are comprised, under the term fluid, gases as well as liquids.
These researches deserve attention by their interest and the generality of the results to which they have led. They also give a remarkable example of the happy effects which may be obtained by the combined employment of the various methods of investigation used in exploring the domain of nature. Thermodynamics has, in fact, allowed us to obtain numerical relations between the various coefficients, and atomic hypotheses have led to the establishment of one capital relation, the characteristic equation of fluids; while, on the other hand, experiment in which the progress made in the art of measurement has been utilized, has furnished the most valuable information on all the laws of compressibility and dilatation.
The classical work of Andrews was not very wide. Andrews did not go much beyond pressures close to the normal and ordinary temperatures. Of late years several very interesting and peculiar cases have been examined by MM. Cailletet, Mathias, Batelli, Leduc, P. Chappuis, and other physicists. Sir W. Ramsay and Mr S. Young have made known the isothermal diagrams[6] of a certain number of liquid bodies at the ordinary temperature. They have thus been able, while keeping to somewhat restricted limits of temperature and pressure, to touch upon the most important questions, since they found themselves in the region of the saturation curve and of the critical point.